Machinery's Handbook

Machinery's Handbook 27th Edition A REFERENCE BOOK FOR THE MECHANICAL ENGINEER, DESIGNER, MANUFACTURING ENGINEER, DRA...

Author: Franklin D Jones | Henry H Ryffel | Erik Oberg | Christopher J McCauley | Ricardo M Heald

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Machinery's Handbook 27th Edition

A REFERENCE BOOK FOR THE MECHANICAL ENGINEER, DESIGNER,

MANUFACTURING ENGINEER, DRAFTSMAN, TOOLMAKER, AND MACHINIST

27th Edition

Machinery’s Handbook BY ERIK OBERG, FRANKLIN D. JONES, HOLBROOK L. HORTON, AND HENRY H. RYFFEL

CHRISTOPHER J. MCCAULEY, EDITOR RICCARDO M. HEALD, ASSOCIATE EDITOR MUHAMMED IQBAL HUSSAIN, ASSOCIATE EDITOR

2004 INDUSTRIAL PRESS INC. NEW YORK

Copyright 2004, Industrial Press, Inc., New York, NY

Machinery's Handbook 27th Edition COPYRIGHT COPYRIGHT 1914, 1924, 1928, 1930, 1931, 1934, 1936, 1937, 1939, 1940, 1941, 1942, 1943, 1944, 1945, 1946, 1948, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1957,© 1959, © 1962, © 1964, © 1966, © 1968, © 1971, © 1974, © 1975, © 1977, © 1979, © 1984, © 1988, © 1992, © 1996, © 1997, © 1998, © 2000, © 2004 by Industrial Press Inc., New York, NY. Library of Congress Cataloging-in-Publication Data Oberg, Erik, 1881—1951 Machinery's Handbook. 2640 p. Includes index. I. Mechanical engineering—Handbook, manuals, etc. I. Jones, Franklin Day, 1879-1967 II. Horton, Holbrook Lynedon, 1907-2001 III. Ryffel, Henry H. I920- IV. Title. TJ151.0245 2000 621.8'0212 72-622276 ISBN 0-8311-2700-7 (Toolbox Thumb Indexed 11.7 x 17.8 cm) ISBN 0-8311-2711-2 (Large Print Thumb Indexed 17.8 x 25.4 cm) ISBN 0-8311-2777-5 (CD-ROM) ISBN 0-8311-2727-9 (Toolbox Thumb Indexed / CD-ROM Combo 11.7 x 17.8 cm) ISBN 0-8311-2737-6 (Large Print Thumb Indexed / CD-ROM Combo 17.8 x 25.4 cm) LC card number 72-622276

INDUSTRIAL PRESS, INC. 200 Madison Avenue New York, New York 10016-4078 MACHINERY'S HANDBOOK 27th Edition First Printing

Printed and bound in the United States of America by National Publishing Company, Philadelphia, Pa. All rights reserved. This book or parts thereof may not be reproduced, stored in a retrieval system, or transmitted in any form without permission of the publishers.


Machinery's Handbook 27th Edition PREFACE Machinery's Handbook has served as the principal reference work in metalworking, design and manufacturing facilities, and in technical schools and colleges throughout the world, for more than 90 years of continuous publication. Throughout this period, the intention of the Handbook editors has always been to create a comprehensive and practical tool, combining the most basic and essential aspects of sophisticated manufacturing practice. A tool to be used in much the same way that other tools are used, to make and repair products of high quality, at the lowest cost, and in the shortest time possible. The essential basics, material that is of proven and everlasting worth, must always be included if the Handbook is to continue to provide for the needs of the manufacturing community. But, it remains a difficult task to select suitable material from the almost unlimited supply of data pertaining to the manufacturing and mechanical engineering fields, and to provide for the needs of design and production departments in all sizes of manufacturing plants and workshops, as well as those of job shops, the hobbyist, and students of trade and technical schools. The editors rely to a great extent on conversations and written communications with users of the Handbook for guidance on topics to be introduced, revised, lengthened, shortened, or omitted. In response to such suggestions, in recent years material on logarithms, trigonometry, and sine-bar constants have been restored after numerous requests for these topics. Also at the request of users, in 1997 the first ever large-print or “desktop” edition of the Handbook was published, followed in 1998 by the publication of Machinery's Handbook CD-ROM including hundreds of additional pages of material restored from earlier editions. The large-print and CD-ROM editions have since become permanent additions to the growing family of Machinery's Handbook products. Regular users of the Handbook will quickly discover some of the many changes embodied in the present edition. One is the combined Mechanics and Strength of Materials section, arising out of the two former sections of similar name; another is the Index of Standards, intended to assist in locating standards information. “Old style” numerals, in continuous use in the first through twenty-fifth editions, are now used only in the index for page references, and in cross reference throughout the text. The entire text of this edition, including all the tables and equations, has been reset, and a great many of the numerous figures have been redrawn. This edition contains more information than ever before, and sixty-four additional pages brings the total length of the book to 2704 pages, the longest Handbook ever. The 27th edition of the Handbook contains significant format changes and major revisions of existing content, as well as new material on a variety of topics. The detailed tables of contents located at the beginning of each section have been expanded and fine tuned to simplify locating your topic; numerous major sections have been extensively reworked and renovated throughout, including Mathematics, Mechanics and Strength of Materials, Properties of Materials, Fasteners, Threads and Threading, and Unit Conversions. New material includes fundamentals of basic math operations, engineering economic analysis, matrix operations, disc springs, constants for metric sine-bars, additional screw thread data and information on obscure and historical threads, aerodynamic lubrication, high speed machining, grinding feeds and speeds, machining econometrics, metalworking fluids, ISO surface texture, pipe welding, geometric dimensioning and tolerancing, gearing, and EDM. Other subjects in the Handbook that are new or have been revised, expanded, or updated are: analytical geometry, formulas for circular segments, construction of four-arc ellipse, geometry of rollers on a shaft, mechanisms, additional constants for measuring weight of piles, Ohm’s law, binary multiples, force on inclined planes, and measurement over pins. The large-print edition is identical to the traditional toolbox edition, but the size is increased by a comfortable 140% for easier reading, making it ideal as a desktop reference. Other than size, there are no differences between the toolbox and large-print editions.

v


Machinery's Handbook 27th Edition PREFACE The Machinery's Handbook 27 CD-ROM contains the complete contents of the printed edition, presented in Adobe Acrobat PDF format. This popular and well known format enables viewing and printing of pages, identical to those of the printed book, rapid searching, and the ability to magnify the view of any page. Navigation aids in the form of thousands of clickable bookmarks, page cross references, and index entries take you instantly to any page referenced. The CD contains additional material that is not included in the toolbox or large print editions, including an extensive index of materials referenced in the Handbook, numerous useful mathematical tables, sine-bar constants for sine-bars of various lengths, material on cement and concrete, adhesives and sealants, recipes for coloring and etching metals, forge shop equipment, silent chain, worm gearing and other material on gears, and other topics. Also new on the CD are numerous interactive math problems. Solutions are accessed from the CD by clicking an icon, located in the page margin adjacent to a covered problem, (see figure shown here). An internet connection is required to use these problems. The list of interactive math solutions currently available can be found in the Index of Interactive Equations, starting on page 2689. Additional interactive solutions will be added from time to time as the need becomes clear. Those users involved in aspects of machining and grinding will be interested in the topics Machining Econometrics and Grinding Feeds and Speeds, presented in the Machining section. The core of all manufacturing methods start with the cutting edge and the metal removal process. Improving the control of the machining process is a major component necessary to achieve a Lean chain of manufacturing events. These sections describe the means that are necessary to get metal cutting processes under control and how to properly evaluate the decision making. A major goal of the editors is to make the Handbook easier to use. The 27th edition of the Handbook continues to incorporate the timesaving thumb tabs, much requested by users in the past. The table of contents pages beginning each major section, first introduced for the 25th edition, have proven very useful to readers. Consequently, the number of contents pages has been increased to several pages each for many of the larger sections, to more thoroughly reflect the contents of these sections. In the present edition, the Plastics section, formerly a separate thumb tab, has been incorporated into the Properties of Materials section. A major task in assembling this edition has been the expansion and reorganization of the index. For the first time, most of the many Standards referenced in the Handbook are now included in a separate Index Of Standards starting on page 2677. The editors are greatly indebted to readers who call attention to possible errors and defects in the Handbook, who offer suggestions concerning the omission of some matter that is considered to be of general value, or who have technical questions concerning the solution of difficult or troublesome Handbook problems. Such dialog is often invaluable and helps to identify topics that require additional clarification or are the source of reader confusion. Queries involving Handbook material usually entail an in depth review of the topic in question, and may result in the addition of new material to the Handbook intended to resolve or clarify the issue. The new material on the mass moment of inertia of hollow circular rings, page 248, and on the effect of temperature on the radius of thin circular rings, page 405, are good examples. Our goal is to increase the usefulness of the Handbook to the greatest extent possible. All criticisms and suggestions about revisions, omissions, or inclusion of new material, and requests for assistance with manufacturing problems encountered in the shop are always welcome. Christopher J. McCauley, Senior Editor

vi


Machinery's Handbook 27th Edition ACKNOWLEDGMENTS The editors would like to acknowledge all those who contributed ideas, suggestions, and criticisms concerning the Handbook. Most importantly, we thank the readers who have contacted us with suggestions for new topics to present in this edition of the Handbook. We are grateful for your continuing constructive suggestions and criticisms with regard to Handbook topics and presentation. Your comments for this edition, as well as past and future ones are invaluable, and well appreciated. Special thanks are also extended to current and former members of our staff, the talented engineers, recent-graduates, who performed much of the fact checking, calculations, artwork, and standards verification involved in preparing the printed and CD-ROM editions of the Handbook. Many thanks to Janet Romano for her great Handbook cover designs. Her printing, packaging, and production expertise are irreplacable, continuing the long tradition of Handbook quality and ruggedness. Many of the American National Standards Institute (ANSI) Standards that deal with mechanical engineering, extracts from which are included in the Handbook, are published by the American Society of Mechanical Engineers (ASME), and we are grateful for their permission to quote extracts and to update the information contained in the standards, based on the revisions regularly carried out by the ASME. ANSI Standards are copyrighted by the publisher. Information regarding current editions of any of these Standards can be obtained from ASME International, Three Park Avenue, New York, NY 10016, or by contacting the American National Standards Institute, West 42nd Street, New York, NY 10017, from whom current copies may be purchased. Additional information concerning Standards nomenclature and other Standards bodies that may be of interest is located on page 2079. Several individuals in particular, contributed substantial amounts of time and information to this edition. Mr. David Belforte, for his thorough contribution on lasers. Manfred K. Brueckner, for his excellent presentation of formulas for circular segments, and for the material on construction of the four-arc oval. Dr. Bertil Colding, provided extensive material on grinding speeds, feeds, depths of cut, and tool life for a wide range of materials. He also provided practical information on machining econometrics, including tool wear and tool life and machining cost relationships. Mr. Edward Craig contributed information on welding. Dr. Edmund Isakov, contributed material on coned disc springs as well as numerous other suggestions related to hardness scales, material properties, and other topics. Mr. Sidney Kravitz, a frequent contributor, provided additional data on weight of piles, excellent proof reading assistance, and many useful comments and suggestions concerning many topics throughout the book. Mr. Richard Kuzmack, for his contributions on the subject of dividing heads, and additions to the tables of dividing head indexing movements. Mr. Robert E. Green, as editor emeritus, contributed much useful, well organized material to this edition. He also provided invaluable practical guidance to the editorial staff during the Handbook’s compilation. Finally, Industrial Press is extremely fortunate that Mr. Henry H. Ryffel, author and editor of Machinery’s Handbook, continues to be deeply involved with the Handbook. Henry’s ideas, suggestions, and vision are deeply appreciated by everyone who worked on this book.

ix


Machinery's Handbook 27th Edition TABLE OF CONTENTS

COPYRIGHT

iv

PREFACE

v

ACKNOWLEDGMENTS

ix

MATHEMATICS

1

• NUMBERS, FRACTIONS, AND DECIMALS • ALGEBRA AND EQUATIONS • GEOMETRY • SOLUTION OF TRIANGLES • LOGARITHMS • MATRICES • ENGINEERING ECONOMICS

MECHANICS AND STRENGTH OF MATERIALS

138

• MECHANICS • VELOCITY, ACCELERATION, WORK, AND ENERGY • FLYWHEELS • STRENGTH OF MATERIALS • PROPERTIES OF BODIES • BEAMS • COLUMNS • PLATES, SHELLS, AND CYLINDERS • SHAFTS • SPRINGS • DISC SPRINGS • WIRE ROPE, CHAIN, ROPE, AND HOOKS

PROPERTIES, TREATMENT, AND TESTING OF MATERIALS

396

• THE ELEMENTS, HEAT, MASS, AND WEIGHT • PROPERTIES OF WOOD, CERAMICS, PLASTICS, METALS, WATER, AND AIR • STANDARD STEELS • TOOL STEELS • HARDENING, TEMPERING, AND ANNEALING • NONFERROUS ALLOYS • PLASTICS

DIMENSIONING, GAGING, AND MEASURING

629

• DRAFTING PRACTICES • ALLOWANCES AND TOLERANCES FOR FITS • MEASURING INSTRUMENTS AND INSPECTION METHODS • SURFACE TEXTURE

TOOLING AND TOOLMAKING

746

• CUTTING TOOLS • CEMENTED CARBIDES • FORMING TOOLS • MILLING CUTTERS • REAMERS • TWIST DRILLS AND COUNTERBORES • TAPS AND THREADING DIES • STANDARD TAPERS • ARBORS, CHUCKS, AND SPINDLES • BROACHES AND BROACHING • FILES AND BURS • TOOL WEAR AND SHARPENING • JIGS AND FIXTURES

MACHINING OPERATIONS

1005

• CUTTING SPEEDS AND FEEDS • SPEED AND FEED TABLES • ESTIMATING SPEEDS AND MACHINING POWER • MACHINING ECONOMETRICS • SCREW MACHINE FEEDS AND SPEEDS • CUTTING FLUIDS • MACHINING NONFERROUS METALS AND NONMETALLIC MATERIALS • GRINDING FEEDS AND SPEEDS • GRINDING AND OTHER ABRASIVE PROCESSES • KNURLS AND KNURLING • MACHINE TOOL ACCURACY • NUMERICAL CONTROL • NUMERICAL CONTROL PROGRAMMING • CAD/CAM

MANUFACTURING PROCESSES

1326

• PUNCHES, DIES, AND PRESS WORK • ELECTRICAL DISCHARGE MACHINING • IRON AND STEEL CASTINGS • SOLDERING AND BRAZING • WELDING • LASERS • FINISHING OPERATIONS

Each section has a detailed Table of Contents or Index located on the page indicated

vii

TABLE OF CONTENTS

FASTENERS

1473

• NAILS, SPIKES, AND WOOD SCREWS • RIVETS AND RIVETED JOINTS • TORQUE AND TENSION IN FASTENERS • INCH THREADED FASTENERS • METRIC THREADED FASTENERS • BRITISH FASTENERS • MACHINE SCREWS AND NUTS • CAP AND SET SCREWS • SELF-THREADING SCREWS • T-SLOTS, BOLTS, AND NUTS • PINS AND STUDS • RETAINING RINGS • WING NUTS, WING SCREWS, AND THUMB SCREWS

THREADS AND THREADING

1721

• SCREW THREAD SYSTEMS • UNIFIED SCREW THREADS • METRIC SCREW THREADS • ACME SCREW THREADS • BUTTRESS THREADS • WHITWORTH THREADS • PIPE AND HOSE THREADS • OTHER THREADS • MEASURING SCREW THREADS • TAPPING AND THREAD CUTTING • THREAD ROLLING • THREAD GRINDING • THREAD MILLING • SIMPLE, COMPOUND, DIFFERENTIAL, AND BLOCK INDEXING

GEARS, SPLINES, AND CAMS

2026

• GEARS AND GEARING • HYPOID AND BEVEL GEARING • WORM GEARING • HELICAL GEARING • OTHER GEAR TYPES • CHECKING GEAR SIZES • GEAR MATERIALS • SPLINES AND SERRATIONS • CAMS AND CAM DESIGN

MACHINE ELEMENTS

2214

• PLAIN BEARINGS • BALL, ROLLER, AND NEEDLE BEARINGS • STANDARD METAL BALLS • LUBRICANTS AND LUBRICATION • COUPLINGS AND CLUTCHES • FRICTION BRAKES • KEYS AND KEYSEATS • FLEXIBLE BELTS AND SHEAVES • TRANSMISSION CHAINS • STANDARDS FOR ELECTRIC MOTORS • ADHESIVES AND SEALANTS • MOTION CONTROL • O-RINGS • ROLLED STEEL SECTIONS, WIRE, AND SHEET-METAL GAGES • PIPE AND PIPE FITTINGS

MEASURING UNITS

2539

• SYMBOLS AND ABBREVIATIONS • MEASURING UNITS • U.S. SYSTEM AND METRIC SYSTEM CONVERSIONS

INDEX

2588

INDEX OF STANDARDS

2677

INDEX OF INTERACTIVE EQUATIONS

2689

INDEX OF MATERIALS

2694

ADDITIONAL INFORMATION FROM THE CD

2741

• MATHEMATICS • CEMENT, CONCRETE, LUTES, ADHESIVES, AND SEALANTS • SURFACE TREATMENTS FOR METALS • MANUFACTURING • SYMBOLS FOR DRAFTING • FORGE SHOP EQUIPMENT • SILENT OR INVERTED TOOTH CHAIN • GEARS AND GEARING • MISCELLANEOUS TOPICS

Each section has a detailed Table of Contents or Index located on the page indicated

viii

Machinery's Handbook 27th Edition TABLE OF CONTENTS MATHEMATICS NUMBERS, FRACTIONS, AND DECIMALS

GEOMETRY 36 Arithmetical & Geometrical Progression 39 Analytical Geometry 39 Straight Line 42 Coordinate Systems 45 Circle 45 Parabola 46 Ellipse 47 Four-arc Approximate Ellipse 47 Hyperbola 59 Areas and Volumes 59 The Prismoidal Formula 59 Pappus or Guldinus Rules 60 Area of Revolution Surface 60 Area of Irregular Plane Surface 61 Areas Enclosed by Cycloidal Curves 61 Contents of Cylindrical Tanks 63 Areas and Dimensions of Figures 69 Formulas for Regular Polygons 70 Circular Segments 73 Circles and Squares of Equal Area 74 Diagonals of Squares and Hexagons 75 Volumes of Solids 81 Circles in Circles and Rectangles 86 Circles within Rectangles 87 Rollers on a Shaft

3 Fractional Inch, Decimal, Millimeter Conversion 4 Numbers 4 Positive and Negative Numbers 5 Sequence of Arithmetic Operations 5 Ratio and Proportion 7 Percentage 8 Fractions 8 Common Fractions 8 Reciprocals 9 Addition, Subtraction, Multiplication, Division 10 Decimal Fractions 11 Continued Fractions 12 Conjugate Fractions 13 Using Continued Fraction Convergents as Conjugates 14 Powers and Roots 14 Powers of Ten Notation 15 Converting to Power of Ten 15 Multiplication 16 Division 16 Constants Frequently Used in Mathematical Expressions 17 Imaginary and Complex Numbers 18 Factorial 18 Permutations 18 Combinations 19 Prime Numbers and Factors

SOLUTION OF TRIANGLES 88 Functions of Angles 89 Laws of Sines and Cosines 89 Trigonometric Identities 91 Solution of Right-angled Triangles 94 Solution of Obtuse-angled Triangles 96 Degree-radian Conversion 98 Functions of Angles, Graphic Illustration 99 Trig Function Tables 103 Versed Sine and Versed Cosine 103 Sevolute and Involute Functions 104 Involute Functions Tables 108 Compound Angles 110 Interpolation

ALGEBRA AND EQUATIONS 29 Rearrangement of Formulas 30 Principle Algebraic Expressions 31 Solving First Degree Equations 31 Solving Quadratic Equations 32 Factoring a Quadratic Expression 33 Cubic Equations 33 Solving Numerical Equations 34 Series 34 Derivatives and Integrals

1


Machinery's Handbook 27th Edition TABLE OF CONTENTS MATHEMATICS LOGARITHMS 111 112 113 113 114 115

ENGINEERING ECONOMICS

Common Logarithms Inverse Logarithm Natural Logarithms Powers of Number by Logarithms Roots of Number by Logarithms Tables of Logarithms

125 Interest 125 Simple and Compound Interest 126 Nominal vs. Effective Interest Rates 127 Cash Flow and Equivalence 128 Cash Flow Diagrams 130 Depreciation 130 Straight Line Depreciation 130 Sum of the Years Digits 130 Double Declining Balance Method 130 Statutory Depreciation System 131 Evaluating Alternatives 131 Net Present Value 132 Capitalized Cost 133 Equivalent Uniform Annual Cost 134 Rate of Return 134 Benefit-cost Ratio 134 Payback Period 134 Break-even Analysis 137 Overhead Expenses

MATRICES 119 Matrix Operations 119 Matrix Addition and Subtraction 119 Matrix Multiplication 120 Transpose of a Matrix 120 Determinant of a Square Matrix 121 Minors and Cofactors 121 Adjoint of a Matrix 122 Singularity and Rank of a Matrix 122 Inverse of a Matrix 122 Simultaneous Equations

2


Machinery's Handbook 27th Edition FRACTION, INCH, MILLIMETER CONVERSION

3

NUMBERS, FRACTIONS, AND DECIMALS Table 1. Fractional and Decimal Inch to Millimeter, Exacta Values Fractional Inch

Decimal Inch

Millimeters

1/64 1/32

0.015625 0.03125 0.039370079 0.046875 0.0625 0.078125 0.078740157 0.0833b 0.09375 0.109375 0.118110236 0.125 0.140625 0.15625 0.157480315 0.166 0.171875 0.1875 0.196850394 0.203125 0.21875 0.234375 0.236220472 0.25 0.265625 0.275590551 0.28125 0.296875 0.3125 0.31496063 0.328125 0.33 0.34375 0.354330709 0.359375 0.375 0.390625 0.393700787 0.40625 0.4166 0.421875 0.433070866 0.4375 0.453125 0.46875 0.472440945 0.484375 0.5

0.396875 0.79375 1 1.190625 1.5875 1.984375 2 2.1166 2.38125 2.778125 3 3.175 3.571875 3.96875 4 4.233 4.365625 4.7625 5 5.159375 5.55625 5.953125 6 6.35 6.746875 7 7.14375 7.540625 7.9375 8 8.334375 8.466 8.73125 9 9.128125 9.525 9.921875 10 10.31875 10.5833 10.715625 11 11.1125 11.509375 11.90625 12 12.303125 12.7

3/64 1/16 5/64 1/12 3/32 7/64 1/8 9/64 5/32 1/6 11/64 3/16 13/64 7/32 15/64 1/4 17/64 9/32 19/64 5/16 21/64 1/3 11/32 23/64 3/8 25/64 13/32 5/12 27/64 7/16 29/64 15/32 31/64 1/2

Fractional Inch 33/64 17/32 35/64 9/16 37/64 7/12 19/32 39/64 5/8 41/64 21/32 2/3 43/64 11/16 45/64 23/32 47/64 3/4 49/64 25/32 51/64 13/16 53/64 27/32 55/64 7/8 57/64 29/32 11/12 59/64 15/16 61/64 31/32 63/64

Decimal Inch

Millimeters

0.511811024 0.515625 0.53125 0.546875 0.551181102 0.5625 0.578125 0.5833 0.590551181 0.59375 0.609375 0.625 0.62992126 0.640625 0.65625 0.66 0.669291339 0.671875 0.6875 0.703125 0.708661417 0.71875 0.734375 0.748031496 0.75 0.765625 0.78125 0.787401575 0.796875 0.8125 0.826771654 0.828125 0.84375 0.859375 0.866141732 0.875 0.890625 0.905511811 0.90625 0.9166 0.921875 0.9375 0.94488189 0.953125 0.96875 0.984251969 0.984375

13 13.096875 13.49375 13.890625 14 14.2875 14.684375 14.8166 15 15.08125 15.478125 15.875 16 16.271875 16.66875 16.933 17 17.065625 17.4625 17.859375 18 18.25625 18.653125 19 19.05 19.446875 19.84375 20 20.240625 20.6375 21 21.034375 21.43125 21.828125 22 22.225 22.621875 23 23.01875 23.2833 23.415625 23.8125 24 24.209375 24.60625 25 25.003125

a Table data are based on 1 inch = 25.4 mm, exactly. Inch to millimeter conversion values are exact. Whole number millimeter to inch conversions are rounded to 9 decimal places. b Numbers with an overbar, repeat indefinately after the last figure, for example 0.0833 = 0.08333...


Machinery's Handbook 27th Edition 4

POSITIVE AND NEGATIVE NUMBERS Numbers

Numbers are the basic instrumentation of computation. Calculations are made by operations of numbers. The whole numbers greater than zero are called natural numbers. The first ten numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 are called numerals. Numbers follow certain fomulas. The following properties hold true: Associative law: x + (y + z) = (x + y) + z, x(yz) = (xy)z Distributive law: x(y + z) = xy + xz Commutative law: x + y = y + x Identity law: 0 + x = x, 1x = x Inverse law: x − x = 0, x/x = 1 Positive and Negative Numbers.—The degrees on a thermometer scale extending upward from the zero point may be called positive and may be preceded by a plus sign; thus +5 degrees means 5 degrees above zero. The degrees below zero may be called negative and may be preceded by a minus sign; thus, − 5 degrees means 5 degrees below zero. In the same way, the ordinary numbers 1, 2, 3, etc., which are larger than 0, are called positive numbers; but numbers can be conceived of as extending in the other direction from 0, numbers that, in fact, are less than 0, and these are called negative. As these numbers must be expressed by the same figures as the positive numbers they are designated by a minus sign placed before them, thus: (−3). A negative number should always be enclosed within parentheses whenever it is written in line with other numbers; for example: 17 + (−13) − 3 × (−0.76). Negative numbers are most commonly met with in the use of logarithms and natural trigonometric functions. The following rules govern calculations with negative numbers. A negative number can be added to a positive number by subtracting its numerical value from the positive number. Example:4 + (−3) = 4 − 3 = 1 A negative number can be subtracted from a positive number by adding its numerical value to the positive number. Example:4 − (−3) = 4 + 3 = 7 A negative number can be added to a negative number by adding the numerical values and making the sum negative. Example:(−4) + (−3) = −7 A negative number can be subtracted from a larger negative number by subtracting the numerical values and making the difference negative. Example:(−4) − (−3) = −1 A negative number can be subtracted from a smaller negative number by subtracting the numerical values and making the difference positive. Example:(−3) − (−4) = 1 If in a subtraction the number to be subtracted is larger than the number from which it is to be subtracted, the calculation can be carried out by subtracting the smaller number from the larger, and indicating that the remainder is negative. Example:3 − 5 = − (5 − 3) = −2 When a positive number is to be multiplied or divided by a negative numbers, multiply or divide the numerical values as usual; the product or quotient, respectively, is negative. The same rule is true if a negative number is multiplied or divided by a positive number. Examples: 4 × ( – 3 ) = – 12 ( – 4 ) × 3 = – 12 15 ÷ ( – 3 ) = – 5 ( – 15 ) ÷ 3 = – 5 When two negative numbers are to be multiplied by each other, the product is positive. When a negative number is divided by a negative number, the quotient is positive.


Machinery's Handbook 27th Edition RATIO AND PROPORTION

5

Examples:(−4) × (−3) = 12; (−4) ÷ (−3) = 1.333 The two last rules are often expressed for memorizing as follows: “Equal signs make plus, unequal signs make minus.” Sequence of Performing Arithmetic Operations.—When several numbers or quantities in a formula are connected by signs indicating that additions, subtractions, multiplications, and divisions are to be made, the multiplications and divisions should be carried out first, in the sequence in which they appear, before the additions or subtractions are performed. Example: 10 + 26 × 7 – 2 = 10 + 182 – 2 = 190 18 ÷ 6 + 15 × 3 = 3 + 45 = 48 12 + 14 ÷ 2 – 4 = 12 + 7 – 4 = 15 When it is required that certain additions and subtractions should precede multiplications and divisions, use is made of parentheses ( ) and brackets [ ]. These signs indicate that the calculation inside the parentheses or brackets should be carried out completely by itself before the remaining calculations are commenced. If one bracket is placed inside another, the one inside is first calculated. Example: ( 6 – 2 ) × 5 + 8 = 4 × 5 + 8 = 20 + 8 = 28 6 × ( 4 + 7 ) ÷ 22 = 6 × 11 ÷ 22 = 66 ÷ 22 = 3 2 + [ 10 × 6 ( 8 + 2 ) – 4 ] × 2 = 2 + [ 10 × 6 × 10 – 4 ] × 2 = 2 + [ 600 – 4 ] × 2 = 2 + 596 × 2 = 2 + 1192 = 1194 The parentheses are considered as a sign of multiplication; for example: 6(8 + 2) = 6 × (8 + 2). The line or bar between the numerator and denominator in a fractional expression is to be considered as a division sign. For example, 12 + 16 + 22 ------------------------------ = ( 12 + 16 + 22 ) ÷ 10 = 50 ÷ 10 = 5 10 In formulas, the multiplication sign (×) is often left out between symbols or letters, the values of which are to be multiplied. Thus, AB = A × B

and

ABC ------------ = ( A × B × C ) ÷ D D

Ratio and Proportion.—The ratio between two quantities is the quotient obtained by dividing the first quantity by the second. For example, the ratio between 3 and 12 is 1⁄4, and the ratio between 12 and 3 is 4. Ratio is generally indicated by the sign (:); thus, 12 : 3 indicates the ratio of 12 to 3. A reciprocal, or inverse ratio, is the opposite of the original ratio. Thus, the inverse ratio of 5 : 7 is 7 : 5. In a compound ratio, each term is the product of the corresponding terms in two or more simple ratios. Thus, when 8:2 = 4 then the compound ratio is

9:3 = 3

10:5 = 2

8 × 9 × 10:2 × 3 × 5 = 4 × 3 × 2 720:30 = 24 Proportion is the equality of ratios. Thus, 6:3 = 10:5

or

6:3::10:5



RATIO AND PROPORTION

The first and last terms in a proportion are called the extremes; the second and third, the means. The product of the extremes is equal to the product of the means. Thus, 25:2 = 100:8 and 25 × 8 = 2 × 100 If three terms in a proportion are known, the remaining term may be found by the following rules: The first term is equal to the product of the second and third terms, divided by the fourth. The second term is equal to the product of the first and fourth terms, divided by the third. The third term is equal to the product of the first and fourth terms, divided by the second. The fourth term is equal to the product of the second and third terms, divided by the first. Example:Let x be the term to be found, then, x : 12 = 3.5 : 21 1⁄ 4

: x = 14 : 42

5 : 9 = x : 63 1⁄ 4

: 7⁄8 = 4 : x

12 × 3.5 42 x = ------------------- = ------ = 2 21 21 1⁄ × 42 4 x = --------------- = 1--- × 3 = 3--14 4 4

× 63- = 315 x = 5---------------------- = 35 9 9 7⁄ × 4 1⁄ 3-----8 2- = 14 x = -----------= 1⁄ 1⁄ 4 4

If the second and third terms are the same, that number is the mean proportional between the other two. Thus, 8 : 4 = 4 : 2, and 4 is the mean proportional between 8 and 2. The mean proportional between two numbers may be found by multiplying the numbers together and extracting the square root of the product. Thus, the mean proportional between 3 and 12 is found as follows: 3 × 12 = 36 and 36 = 6 which is the mean proportional. Practical Examples Involving Simple Proportion: If it takes 18 days to assemble 4 lathes, how long would it take to assemble 14 lathes? Let the number of days to be found be x. Then write out the proportion as follows: 4:18 = 14:x ( lathes : days = lathes : days ) Now find the fourth term by the rule given: 18 × 14 x = ------------------ = 63 days 4 Thirty-four linear feet of bar stock are required for the blanks for 100 clamping bolts. How many feet of stock would be required for 912 bolts? Let x = total length of stock required for 912 bolts. 34:100 = x:912 ( feet : bolts = feet : bolts ) Then, the third term x = (34 × 912)/100 = 310 feet, approximately. Inverse Proportion: In an inverse proportion, as one of the items involved increases, the corresponding item in the proportion decreases, or vice versa. For example, a factory employing 270 men completes a given number of typewriters weekly, the number of working hours being 44 per week. How many men would be required for the same production if the working hours were reduced to 40 per week?


Machinery's Handbook 27th Edition PERCENTAGE

7

The time per week is in an inverse proportion to the number of men employed; the shorter the time, the more men. The inverse proportion is written: 270 : x = 40 : 44 (men, 44-hour basis: men, 40-hour basis = time, 40-hour basis: time, 44-hour basis) Thus 270 × 44- = 297 men --------- = 40 -----and x = 270 -------------------x 44 40 Problems Involving Both Simple and Inverse Proportions: If two groups of data are related both by direct (simple) and inverse proportions among the various quantities, then a simple mathematical relation that may be used in solving problems is as follows: Product of all directly proportional items in first group -------------------------------------------------------------------------------------------------------------------------------------Product of all inversely proportional items in first group Product of all directly proportional items in second group= -------------------------------------------------------------------------------------------------------------------------------------------Product of all inversely proportional items in second group Example:If a man capable of turning 65 studs in a day of 10 hours is paid $6.50 per hour, how much per hour ought a man be paid who turns 72 studs in a 9-hour day, if compensated in the same proportion? The first group of data in this problem consists of the number of hours worked by the first man, his hourly wage, and the number of studs which he produces per day; the second group contains similar data for the second man except for his unknown hourly wage, which may be indicated by x. The labor cost per stud, as may be seen, is directly proportional to the number of hours worked and the hourly wage. These quantities, therefore, are used in the numerators of the fractions in the formula. The labor cost per stud is inversely proportional to the number of studs produced per day. (The greater the number of studs produced in a given time the less the cost per stud.) The numbers of studs per day, therefore, are placed in the denominators of the fractions in the formula. Thus, 10 × 6.50 = 9----------×x ---------------------65 72 × 6.50 × 72- = $8.00 per hour x = 10 ---------------------------------65 × 9 Percentage.—If out of 100 pieces made, 12 do not pass inspection, it is said that 12 per cent (12 of the hundred) are rejected. If a quantity of steel is bought for $100 and sold for $140, the profit is 28.6 per cent of the selling price. The per cent of gain or loss is found by dividing the amount of gain or loss by the original number of which the percentage is wanted, and multiplying the quotient by 100. Example:Out of a total output of 280 castings a day, 30 castings are, on an average, rejected. What is the percentage of bad castings? 30- × 100 = 10.7 per cent -------280 If by a new process 100 pieces can be made in the same time as 60 could formerly be made, what is the gain in output of the new process over the old, expressed in per cent? Original number, 60; gain 100 − 60 = 40. Hence, 40 ------ × 100 = 66.7 per cent 60 Care should be taken always to use the original number, or the number of which the percentage is wanted, as the divisor in all percentage calculations. In the example just given, it



FRACTIONS

is the percentage of gain over the old output 60 that is wanted and not the percentage with relation to the new output too. Mistakes are often made by overlooking this important point. Fractions Common Fractions.— Common fractions consist of two basic parts, a denominator, or bottom number, and a numerator, or top number. The denominator shows how many parts the whole unit has been divided into. The numerator indicates the number of parts of the whole that are being considered. A fraction having a value of 5⁄32, means the whole unit has been divided into 32 equal parts and 5 of these parts are considered in the value of the fraction. The following are the basic facts, rules, and definitions concerning common fractions. A common fraction having the same numerator and denominator is equal to 1. For example, 2⁄2, 4⁄4, 8⁄8, 16⁄16, 32⁄32, and 64⁄64 all equal 1. Proper Fraction: A proper fraction is a common fraction having a numerator smaller than its denominator, such as 1⁄4, 1⁄2, and 47⁄64. Improper Fraction: An improper fraction is a common fraction having a numerator larger than its denominator. For example, 3⁄2, 5⁄4, and 10⁄8. To convert a whole number to an improper fractions place the whole number over 1, as in 4 = 4⁄1 and 3 = 3⁄1 Reducible Fraction: A reducible fraction is a common fraction that can be reduced to lower terms. For example, 2⁄4 can be reduced to 1⁄2, and 28⁄32 can be reduced to 7⁄8. To reduce a common fraction to lower terms, divide both the numerator and the denominator by the same number. For example, 24⁄32 ÷ 8⁄8 = 3⁄8 and 6⁄8 ÷ 2⁄2 = 3⁄4. Least Common Denominator: A least common denominator is the smallest denominator value that is evenly divisible by the other denominator values in the problem. For example, given the following numbers, 1⁄2 , 1⁄4 , and 3⁄8, the least common denominator is 8. Mixed Number: A mixed number is a combination of a whole number and a common fraction, such as 21⁄2, 17⁄8, 315⁄16 and 19⁄32. To convert mixed numbers to improper fractions, multiply the whole number by the denominator and add the numerator to obtain the new numerator. The denominator remains the same. For example, 2×2+1 5 1- = -------------------2 -- = --2 2 2 7- = 3----------------------× 16 + 7- = 55 3 ---------16 16 16 To convert an improper fraction to a mixed number, divide the numerator by the denominator and reduce the remaining fraction to its lowest terms. For example, 17⁄ = 17 ÷ 8 = 21⁄ and 26⁄ = 26 ÷ 16 = 110⁄ = 15⁄ 8 8 16 16 8 A fraction may be converted to higher terms by multiplying the numerator and denominator by the same number. For example, 1⁄4 in 16ths = 1⁄4 × 4⁄4 = 4⁄16 and 3⁄8 in 32nds = 3⁄8 × 4⁄4 = 12⁄ . 32 To change a whole number to a common fraction with a specific denominator value, convert the whole number to a fraction and multiply the numerator and denominator by the desired denominator value. Example: 4 in 16ths = 4⁄1 × 16⁄16 = 64⁄16 and 3 in 32nds = 3⁄1 × 32⁄32 = 96⁄32 Reciprocals.—The reciprocal R of a number N is obtained by dividing 1 by the number; R = 1/N. Reciprocals are useful in some calculations because they avoid the use of negative characteristics as in calculations with logarithms and in trigonometry. In trigonometry, the


Machinery's Handbook 27th Edition FRACTIONS

9

values cosecant, secant, and cotangent are often used for convenience and are the reciprocals of the sine, cosine, and tangent, respectively (see page 88). The reciprocal of a fraction, for instance 3⁄4, is the fraction inverted, since 1 ÷ 3⁄4 = 1 × 4⁄3 = 4⁄3. Adding Fractions and Mixed Numbers To Add Common Fractions: 1) Find and convert to the least common denominator; 2 ) Add the numerators; 3) Convert the answer to a mixed number, if necessary; a n d 4) Reduce the fraction to its lowest terms. To Add Mixed Numbers: 1) Find and convert to the least common denominator; 2) Add the numerators; 3) Add the whole numbers; and 4) Reduce the answer to its lowest terms. Example, Addition of Common Fractions:

Example, Addition of Mixed Numbers:

1--- + ----3- + 7--- = 4 16 8

2 1--- + 4 1--- + 1 15 ------ = 2 4 32

1 ⎛ 4⎞ + ----3- + 7 ⎛ 2⎞ = --- ⎝ ---⎠ --- --16 8 ⎝ 2⎠ 4 4

1 8 15 2 1--- ⎛ 16 ------⎞ + 4 --- ⎛⎝ ---⎞⎠ + 1 ------ = 2 ⎝ 16⎠ 4 8 32

4- + ----3- + 14 ---------- = 21 -----16 16 16 16

8- + 1 15 72 16 ------ + 4 ---------- = 7 39 ------ = 8 ----32 32 32 32 32

Subtracting Fractions and Mixed Numbers To Subtract Common Fractions: 1) Convert to the least common denominator; 2) Subtract the numerators; and 3) Reduce the answer to its lowest terms. To Subtract Mixed Numbers: 1) Convert to the least common denominator; 2) Subtract the numerators; 3) Subtract the whole numbers; and 4) Reduce the answer to its lowest terms. Example, Subtraction of Common Fractions:

Example, Subtraction of Mixed Numbers:

15 7- = ------ – ----16 32

1- = 2 3--- – 1 ----8 16

15 ⎛ 2⎞ – ----7- = ------ ⎝ ---⎠ 16 2 32

1 = 2 3--- ⎛ 2---⎞ – 1 ----8 ⎝ 2⎠ 16

30 7- = 23 ------ – ---------32 32 32

6- – 1 ----1- = 1 ----52 ----16 16 16

Multiplying Fractions and Mixed Numbers To Multiply Common Fractions: 1) Multiply the numerators; 2) Multiply the denominators; and 3) Convert improper fractions to mixed numbers, if necessary. To Multiply Mixed Numbers: 1) Convert the mixed numbers to improper fractions; 2 ) Multiply the numerators; 3) Multiply the denominators; and 4) Convert improper fractions to mixed numbers, if necessary. Example, Multiplication of Common Fractions:

Example, Multiplication of Mixed Numbers:

3×7 21 3--- × ----7- = -------------- = -----4 16 4 × 16 64

9×7 63 2 1--- × 3 1--- = ------------ = ------ = 7 7--4 2 4×2 8 8

Dividing Fractions and Mixed Numbers To Divide Common Fractions: 1) Write the fractions to be divided; 2) Invert (switch) the numerator and denominator in the dividing fraction; 3) Multiply the numerators and denominators; and 4) Convert improper fractions to mixed numbers, if necessary.



FRACTIONS

To Divide Mixed Numbers: 1) Convert the mixed numbers to improper fractions; 2) Write the improper fraction to be divided; 3) Invert (switch) the numerator and denominator in the dividing fraction; 4) Multiplying numerators and denominators; a n d 5) Convert improper fractions to mixed numbers, if necessary. Example, Division of Common Fractions:

Example, Division of Mixed Numbers:

×2 6 3--- ÷ 1--- = 3----------- = --- = 1 1--4×1 4 4 2 2

5×8 40 2 1--- ÷ 1 7--- = --------------- = ------ = 1 1--2 × 15 30 2 8 3

Decimal Fractions.—Decimal fractions are fractional parts of a whole unit, which have implied denominators that are multiples of 10. A decimal fraction of 0.1 has a value of 1/10th, 0.01 has a value of 1/100th, and 0.001 has a value of 1/1000th. As the number of decimal place values increases, the value of the decimal number changes by a multiple of 10. A single number placed to the right of a decimal point has a value expressed in tenths; two numbers to the right of a decimal point have a value expressed in hundredths; three numbers to the right have a value expressed in thousandths; and four numbers are expressed in ten-thousandths. Since the denominator is implied, the number of decimal places in the numerator indicates the value of the decimal fraction. So a decimal fraction expressed as a 0.125 means the whole unit has been divided into 1000 parts and 125 of these parts are considered in the value of the decimal fraction. In industry, most decimal fractions are expressed in terms of thousandths rather than tenths or hundredths. So a decimal fraction of 0.2 is expressed as 200 thousandths, not 2 tenths, and a value of 0.75 is expressed as 750 thousandths, rather than 75 hundredths. In the case of four place decimals, the values are expressed in terms of ten-thousandths. So a value of 0.1875 is expressed as 1 thousand 8 hundred and 75 ten-thousandths. When whole numbers and decimal fractions are used together, whole units are shown to the left of a decimal point, while fractional parts of a whole unit are shown to the right. Example: 10.125 Whole Fraction Units Units Adding Decimal Fractions: 1) Write the problem with all decimal points aligned vertically; 2) Add the numbers as whole number values; and 3) Insert the decimal point in the same vertical column in the answer. Subtracting Decimal Fractions: 1) Write the problem with all decimal points aligned vertically; 2) Subtract the numbers as whole number values; and 3) Insert the decimal point in the same vertical column in the answer. Multiplying Decimal Fractions: 1) Write the problem with the decimal points aligned; 2) Multiply the values as whole numbers; 3) Count the number of decimal places in both multiplied values; and 4) Counting from right to left in the answer, insert the decimal point so the number of decimal places in the answer equals the total number of decimal places in the numbers multiplied. Example, Adding Decimal Fractions:

0.125 1.0625 2.50 0.1875 3.8750

or

1.750 0.875 0.125 2.0005

Example, Subtracting Decimal Fractions:

1.750 – 0.250

or

2.625 – 1.125

1.500

4.7505


1.500

Machinery's Handbook 27th Edition CONTINUED FRACTIONS

11

Example, Multiplying Decimal Fractions:

0.75 0.25 375 150

1.625 0.033 (four decimal places)

0.1875

4875 4875

(six decimal places)

0.053625

Continued Fractions.—In dealing with a cumbersome fraction, or one which does not have satisfactory factors, it may be possible to substitute some other, approximately equal, fraction which is simpler or which can be factored satisfactorily. Continued fractions provide a means of computing a series of fractions each of which is a closer approximation to the original fraction than the one preceding it in the series. A continued fraction is a proper fraction (one whose numerator is smaller than its denominator) expressed in the form shown at the left below; or, it may be convenient to write the left expression as shown at the right below. N 1 ---- = ---------------------------------------------D 1 D 1 + ------------------------------1 D 2 + -----------------D3 + …

N- = -----1 -----1 -----1 -----1 … --D D1 + D2 + D3 + D4 +

The continued fraction is produced from a proper fraction N/D by dividing the numerator N both into itself and into the denominator D. Dividing the numerator into itself gives a result of 1; dividing the numerator into the denominator gives a whole number D1 plus a remainder fraction R1. The process is then repeated on the remainder fraction R1 to obtain D2 and R2; then D3, R3, etc., until a remainder of zero results. As an example, using N/D = 2153⁄9277, 2153 2153 ÷ 2153 1 1 ------------ = ------------------------------ = --------------------- = ------------------9277 9277 ÷ 2153 665 D1 + R1 4 + -----------2153 665 1 1 R 1 = ------------ = ------------------ = ------------------- etc. 2153 158D2 + R2 3 + -------665 from which it may be seen that D1 = 4, R1 = 665⁄2153; D2 = 3, R2 = 158⁄665; and, continuing as was explained previously, it would be found that: D3 = 4, R3 = 33⁄158; …; D9 = 2, R9 = 0. The complete set of continued fraction elements representing 2153⁄9277 may then be written as 2153 1 1 1 1 1 1 1 1 1 ------------ = --- + --- + --- + --- + --- + --- + --- + --- + --9277 4 3 4 4 1 3 1 2 2 D 1 ...........D 5 .............D 9 By following a simple procedure, together with a table organized similar to the one below for the fraction 2153⁄9277, the denominators D1, D2, … of the elements of a continued fraction may be used to calculate a series of fractions, each of which is a successively closer approximation, called a convergent, to the original fraction N/D. 1) The first row of the table contains column numbers numbered from 1 through 2 plus the number of elements, 2 + 9 = 11 in this example.



CONJUGATE FRACTIONS

2) The second row contains the denominators of the continued fraction elements in sequence but beginning in column 3 instead of column 1 because columns 1 and 2 must be blank in this procedure. 3) The third row contains the convergents to the original fraction as they are calculated and entered. Note that the fractions 1⁄0 and 0⁄1 have been inserted into columns 1 and 2. These are two arbitrary convergents, the first equal to infinity, the second to zero, which are used to facilitate the calculations. 4) The convergent in column 3 is now calculated. To find the numerator, multiply the denominator in column 3 by the numerator of the convergent in column 2 and add the numerator of the convergent in column 1. Thus, 4 × 0 + 1 = 1. 5) The denominator of the convergent in column 3 is found by multiplying the denominator in column 3 by the denominator of the convergent in column 2 and adding the denominator of the convergent in column 1. Thus, 4 × 1 + 0 = 4, and the convergent in column 3 is then 1⁄4 as shown in the table. 6) Finding the remaining successive convergents can be reduced to using the simple equation ( D n ) ( NUM n – 1 ) + NUM n – 2 CONVERGENT n = --------------------------------------------------------------------( D n ) ( DEN n – 1 ) + DEN n – 2

in which n = column number in the table; Dn = denominator in column n; NUMn−1 and NUMn−2 are numerators and DENn−1 and DENn−2 are denominators of the convergents in the columns indicated by their subscripts; and CONVERGENTn is the convergent in column n. Convergents of the Continued Fraction for 2153⁄9277 Column Number, n Denominator, Dn

1 —

2 —

3 4

4 3

5 4

6 4

7 1

8 3

9 1

10 2

11 2

Convergentn

1--0

0--1

1 --4

3----13

13 -----56

55-------237

68-------293

259----------1116

327----------1409

913----------3934

2153 -----------9277

Notes: The decimal values of the successive convergents in the table are alternately larger and smaller than the value of the original fraction 2153⁄9277. If the last convergent in the table has the same value as the original fraction 2153⁄9277, then all of the other calculated convergents are correct.

Conjugate Fractions.—In addition to finding approximate ratios by the use of continued fractions and logarithms of ratios, conjugate fractions may be used for the same purpose, independently, or in combination with the other methods. Two fractions a⁄b and c⁄d are said to be conjugate if ad − bc = ± 1. Examples of such pairs are: 0⁄1 and 1⁄1; 1⁄2 and 1⁄1; and 9⁄10 and 8⁄9. Also, every successive pair of the convergents of a continued fraction are conjugate. Conjugate fractions have certain properties that are useful for solving ratio problems: 1) No fraction between two conjugate fractions a⁄b and c⁄d can have a denominator smaller than either b or d. 2) A new fraction, e⁄f, conjugate to both fractions of a given pair of conjugate fractions, a⁄b and c⁄d, and lying between them, may be created by adding respective numerators, a + c, and denominators, b + d, so that e⁄f = (a + c)⁄(b + d). 3) The denominator f = b + d of the new fraction e⁄f is the smallest of any possible fraction lying between a⁄b and c⁄d. Thus, 17⁄19 is conjugate to both 8⁄9 and 9⁄10 and no fraction with denominator smaller than 19 lies between them. This property is important if it is desired to minimize the size of the factors of the ratio to be found. The following example shows the steps to approximate a ratio for a set of gears to any desired degree of accuracy within the limits established for the allowable size of the factors in the ratio.


Machinery's Handbook 27th Edition CONJUGATE FRACTIONS

13

Example:Find a set of four change gears, ab⁄cd, to approximate the ratio 2.105399 accurate to within ± 0.0001; no gear is to have more than 120 teeth. Step 1. Convert the given ratio R to a number r between 0 and 1 by taking its reciprocal: 1⁄R = 1⁄2.105399 = 0.4749693 = r. Step 2. Select a pair of conjugate fractions a⁄b and c⁄d that bracket r. The pair a⁄b = 0⁄1 and c⁄d = 1⁄1, for example, will bracket 0.4749693. Step 3. Add the respective numerators and denominators of the conjugates 0⁄1 and 1⁄1 to create a new conjugate e⁄f between 0 and 1: e⁄f = (a + c)⁄(b + d) = (0 +1)⁄(1 + 1) = 1⁄2. Step 4. Since 0.4749693 lies between 0⁄1 and 1⁄2, e⁄f must also be between 0⁄1 and 1⁄2: e⁄f = (0 + 1)⁄(1 + 2) = 1⁄3. Step 5. Since 0.4749693 now lies between 1⁄3 and 1⁄2, e⁄f must also be between 1⁄3 and 1⁄2: e⁄f = (1 + 1)⁄(3 + 2) = 2⁄5. Step 6. Continuing as above to obtain successively closer approximations of e ⁄f to 0.4749693, and using a handheld calculator and a scratch pad to facilitate the process, the fractions below, each of which has factors less than 120, were determined: Fraction 19⁄40 28⁄59 47⁄99 104⁄219 123⁄259 142⁄299 161⁄339 218⁄459 256⁄539 370⁄779 759⁄1598

Numerator Factors 19 2×2×7 47 2 × 2 × 2 × 13 3 × 41 2 × 71 7 × 23 2 × 109 2 × 2 × 2 × 2 × 2 × 2 ×2 ×2 2 × 5 × 37 3 × 11 × 23

Denominator Factors 2×2×2×5 59 3 × 3 × 11 3 × 73 7 × 37 13 × 23 3 × 113 3 × 3 × 3 × 17 7 × 7 × 11 19 × 41 2 × 17 × 47

Error + .000031 − .00039 − .00022 −.000083 − .000066 − .000053 − .000043 − .000024 − .000016 − .0000014 − .00000059

Factors for the numerators and denominators of the fractions shown above were found with the aid of the Prime Numbers and Factors tables beginning on page 20. Since in Step 1 the desired ratio of 2.105399 was converted to its reciprocal 0.4749693, all of the above fractions should be inverted. Note also that the last fraction, 759⁄1598, when inverted to become 1598⁄759, is in error from the desired value by approximately one-half the amount obtained by trial and error using earlier methods. Using Continued Fraction Convergents as Conjugates.—Since successive convergents of a continued fraction are also conjugate, they may be used to find a series of additional fractions in between themselves. As an example, the successive convergents 55⁄237 and 68⁄293 from the table of convergents for 2153⁄9277 on page 12 will be used to demonstrate the process for finding the first few in-between ratios. Desired Fraction N⁄D = 2153⁄9277 = 0.2320793 (1) (2) (3) (4) (5) (6)

a/b 55⁄ 237 = .2320675 123⁄ 530 = .2320755 191⁄ 823 = .2320778 259⁄ 1116 = .2320789 259⁄ 1116 = .2320789 586⁄ 2525 = .2320792

e/f = .2320755 error = −.0000039 191⁄ 823 = .2320778 error = −.0000016 a259⁄ 1116 = .2320789 error = −.0000005 327⁄ 1409 = .2320795 error = + .0000002 586⁄ 2525 = .2320792 error = − .0000001 913⁄ 3934 = .2320793 error = − .0000000 a123⁄ 530

c/d 68⁄ 293 = .2320819 68⁄ 293 = .2320819 68⁄ 293 = .2320819 68⁄ 293 = .2320819 327⁄1409 = .2320795 327⁄1409 = .2320795

a Only these ratios had suitable factors below 120.

Step 1. Check the convergents for conjugateness: 55 × 293 − 237 × 68 = 16115 − 16116 = −1 proving the pair to be conjugate.



POWERS AND ROOTS

Step 2. Set up a table as shown above. The leftmost column of line (1) contains the convergent of lowest value, a⁄b; the rightmost the higher value, c⁄d; and the center column the derived value e⁄f found by adding the respective numerators and denominators of a⁄b and c⁄d. The error or difference between e⁄f and the desired value N⁄D, error = N⁄D − e⁄f, is also shown. Step 3. On line (2), the process used on line (1) is repeated with the e⁄f value from line (1) becoming the new value of a⁄b while the c⁄d value remains unchanged. Had the error in e⁄f been + instead of −, then e ⁄ f would have been the new c ⁄ d value and a ⁄ b would be unchanged. Step 4. The process is continued until, as seen on line (4), the error changes sign to + from the previous −. When this occurs, the e⁄f value becomes the c⁄d value on the next line instead of a⁄b as previously and the a⁄b value remains unchanged. Powers and Roots The square of a number (or quantity) is the product of that number multiplied by itself. Thus, the square of 9 is 9 × 9 = 81. The square of a number is indicated by the exponent (2), thus: 92 = 9 × 9 = 81. The cube or third power of a number is the product obtained by using that number as a factor three times. Thus, the cube of 4 is 4 × 4 × 4 = 64, and is written 43. If a number is used as a factor four or five times, respectively, the product is the fourth or fifth power. Thus, 34 = 3 × 3 × 3 × 3 = 81, and 25 = 2 × 2 × 2 × 2 × 2 = 32. A number can be raised to any power by using it as a factor the required number of times. The square root of a given number is that number which, when multiplied by itself, will give a product equal to the given number. The square root of 16 (written 16 ) equals 4, because 4 × 4 = 16. The cube root of a given number is that number which, when used as a factor three times, will give a product equal to the given number. Thus, the cube root of 64 (written 3 64 ) equals 4, because 4 × 4 × 4 = 64. The fourth, fifth, etc., roots of a given number are those numbers which when used as factors four, five, etc., times, will give as a product the given number. Thus, 4 16 = 2 , because 2 × 2 × 2 × 2 = 16. In some formulas, there may be such expressions as (a2)3 and a3⁄2. The first of these, (a2)3, means that the number a is first to be squared, a2, and the result then cubed to give a6. Thus, (a2)3 is equivalent to a6 which is obtained by multiplying the exponents 2 and 3. Similarly, a3⁄2 may be interpreted as the cube of the square root of a, ( a ) 3 , or (a1⁄2)3, so that, for example, 16 3 ⁄ 2 = ( 16 ) 3 = 64 . The multiplications required for raising numbers to powers and the extracting of roots are greatly facilitated by the use of logarithms. Extracting the square root and cube root by the regular arithmetical methods is a slow and cumbersome operation, and any roots can be more rapidly found by using logarithms. When the power to which a number is to be raised is not an integer, say 1.62, the use of either logarithms or a scientific calculator becomes the only practical means of solution. Powers of Ten Notation.—Powers of ten notation is used to simplify calculations and ensure accuracy, particularly with respect to the position of decimal points, and also simplifies the expression of numbers which are so large or so small as to be unwieldy. For example, the metric (SI) pressure unit pascal is equivalent to 0.00000986923 atmosphere or 0.0001450377 pound/inch2. In powers of ten notation, these figures are 9.86923 × 10−6


Machinery's Handbook 27th Edition POWERS OF TEN NOTATION

15

atmosphere and 1.450377 × 10−4 pound/inch2. The notation also facilitates adaptation of numbers for electronic data processing and computer readout. Expressing Numbers in Powers of Ten Notation.—In this system of notation, every number is expressed by two factors, one of which is some integer from 1 to 9 followed by a decimal and the other is some power of 10. Thus, 10,000 is expressed as 1.0000 × 104 and 10,463 as 1.0463 × 104. The number 43 is expressed as 4.3 × 10 and 568 is expressed. as 5.68 × 102. In the case of decimals, the number 0.0001, which as a fraction is 1⁄10,000 and is expressed as 1 × 10−4 and 0.0001463 is expressed as 1.463 × 10−4. The decimal 0.498 is expressed as 4.98 × 10−1 and 0.03146 is expressed as 3.146 × 10−2. Rules for Converting Any Number to Powers of Ten Notation.—Any number can be converted to the powers of ten notation by means of one of two rules. Rule 1: If the number is a whole number or a whole number and a decimal so that it has digits to the left of the decimal point, the decimal point is moved a sufficient number of places to the left to bring it to the immediate right of the first digit. With the decimal point shifted to this position, the number so written comprises the first factor when written in powers of ten notation. The number of places that the decimal point is moved to the left to bring it immediately to the right of the first digit is the positive index or power of 10 that comprises the second factor when written in powers of ten notation. Thus, to write 4639 in this notation, the decimal point is moved three places to the left giving the two factors: 4.639 × 103. Similarly, 431.412 = 4.31412 × 10 2

986388 = 9.86388 × 10 5

Rule 2: If the number is a decimal, i.e., it has digits entirely to the right of the decimal point, then the decimal point is moved a sufficient number of places to the right to bring it immediately to the right of the first digit. With the decimal point shifted to this position, the number so written comprises the first factor when written in powers of ten notation. The number of places that the decimal point is moved to the right to bring it immediately to the right of the first digit is the negative index or power of 10 that follows the number when written in powers of ten notation. Thus, to bring the decimal point in 0.005721 to the immediate right of the first digit, which is 5, it must be moved three places to the right, giving the two factors: 5.721 × 10−3. Similarly, 0.469 = 4.69 × 10 – 1

0.0000516 = 5.16 × 10 – 5

Multiplying Numbers Written in Powers of Ten Notation.—When multiplying two numbers written in the powers of ten notation together, the procedure is as follows: 1) Multiply the first factor of one number by the first factor of the other to obtain the first factor of the product. 2) Add the index of the second factor (which is some power of 10) of one number to the index of the second factor of the other number to obtain the index of the second factor (which is some power of 10) in the product. Thus: ( 4.31 × 10 – 2 ) × ( 9.0125 × 10 ) = ( 4.31 × 9.0125 ) × 10 – 2 + 1 = 38.844 × 10 – 1 ( 5.986 × 10 4 ) × ( 4.375 × 10 3 ) = ( 5.986 × 4.375 ) × 10 4 + 3 = 26.189 × 10 7 In the preceding calculations, neither of the results shown are in the conventional powers of ten form since the first factor in each has two digits. In the conventional powers of ten notation, the results would be 38.844 × 10−1 = 3.884 × 100 = 3.884, since 100 =1, and 26.189 × 107 = 2.619 × 108 in each case rounding off the first factor to three decimal places.



POWERS OF TEN NOTATION

When multiplying several numbers written in this notation together, the procedure is the same. All of the first factors are multiplied together to get the first factor of the product and all of the indices of the respective powers of ten are added together, taking into account their respective signs, to get the index of the second factor of the product. Thus, (4.02 × 10−3) × (3.987 × 10) × (4.863 × 105) = (4.02 × 3.987 × 4.863) × 10(−3+1+5) = 77.94 × 103 = 7.79 × 104 rounding off the first factor to two decimal places. Dividing Numbers Written in Powers of Ten Notation.—When dividing one number by another when both are written in this notation, the procedure is as follows: 1) Divide the first factor of the dividend by the first factor of the divisor to get the first factor of the quotient. 2) Subtract the index of the second factor of the divisor from the index of the second factor of the dividend, taking into account their respective signs, to get the index of the second factor of the quotient. Thus: ( 4.31 × 10 – 2 ) ÷ ( 9.0125 × 10 ) = ( 4.31 ÷ 9.0125 ) × ( 10 – 2 – 1 ) = 0.4782 × 10 – 3 = 4.782 × 10 – 4 It can be seen that this system of notation is helpful where several numbers of different magnitudes are to be multiplied and divided. 250 × 4698 × 0.00039 Example:Find the quotient of -------------------------------------------------------43678 × 0.002 × 0.0147 Solution: Changing all these numbers to powers of ten notation and performing the operations indicated: ( 2.5 × 10 2 ) × ( 4.698 × 10 3 ) × ( 3.9 × 10 – 4 ) ---------------------------------------------------------------------------------------------------------- = ( 4.3678 × 10 4 ) × ( 2 × 10 – 3 ) × ( 1.47 × 10 – 2 ) ( 2.5 × 4.698 × 3.9 ) ( 10 2 + 3 – 4 ) 45.8055 × 10 = --------------------------------------------------------------------------- = -----------------------------------( 4.3678 × 2 × 1.47 ) ( 10 4 – 3 – 2 ) 12.8413 × 10 – 1 = 3.5670 × 10 1 – ( –1 ) = 3.5670 × 10 2 = 356.70 Constants Frequently Used in Mathematical Expressions π0.00872665 = -------360

0.8660254 = ------32

2π2.0943951 = ----3

3π4.712389 = ----2

π0.01745329 = -------180

1.0471975 = π --3

3π2.3561945 = ----4

5π5.2359878 = ----3

π0.26179939 = ----12

1.1547005 = 2---------33

2.5980762 = 3---------32

5.4977871 = 7π -----4

0.39269908 = π --8

1.2247449 =

2.6179939 = 5π -----6

5.7595865 = 11π --------6

0.52359878 = π --6

3-2

1.4142136 =

2

0.57735027 = ------33

1.5707963 = π --2

0.62035049 =

3

0.78539816 = π --4

3----4π

3.1415927 = π

6.2831853 = 2π

3.6651914 = 7π -----6

9.8696044 = π 2

3

3.9269908 = 5π -----4

12.566371 = 4π

π2 2.4674011 = ----4

4.1887902 = 4π -----3

1.7320508 =

9.424778 = 3π

18057.29578 = -------π 114.59156 = 360 --------π


Machinery's Handbook 27th Edition COMPLEX NUMBERS

17

Imaginary and Complex Numbers Complex or Imaginary Numbers.—Complex or imaginary numbers represent a class of mathematical objects that are used to simplify certain problems, such as the solution of polynomial equations. The basis of the complex number system is the unit imaginary number i that satisfies the following relations: 2

2

i = ( –i ) = –1 i = –1 –i = – –1 In electrical engineering and other fields, the unit imaginary number is often represented by j rather than i. However, the meaning of the two terms is identical. Rectangular or Trigonometric Form: Every complex number, Z, can be written as the sum of a real number and an imaginary number. When expressed as a sum, Z = a + bi, the complex number is said to be in rectangular or trigonometric form. The real part of the number is a, and the imaginary portion is bi because it has the imaginary unit assigned to it. Polar Form: A complex number Z = a + bi can also be expressed in polar form, also known as phasor form. In polar form, the complex number Z is represented by a magnitude r and an angle θ as follows: Z = r ∠θ ∠θ = a direction, the angle whose tangent is b ÷ a, thus θ = atan b--- and a r = a 2 + b 2 is the magnitude A complex number can be plotted on a real-imaginary coordinate system known as the complex plane. The figure below illustrates the relationship between the rectangular coordinates a and b, and the polar coordinates r and θ.

a + bi

b imaginary axis

r

a

real axis

Complex Number in the Complex Plane

The rectangular form can be determined from r and θ as follows: a = r cos θ b = r sin θ a + bi = r cos θ + ir sin θ = r ( cos θ + i sin θ ) The rectangular form can also be written using Euler’s Formula: e

± iθ

= cos θ ± i sin θ

iθ

– iθ

e –e sin θ = ---------------------2i

iθ

– iθ

e +e cos θ = ---------------------2

Complex Conjugate: Complex numbers commonly arise in finding the solution of polynomials. A polynomial of nth degree has n solutions, an even number of which are complex and the rest are real. The complex solutions always appear as complex conjugate pairs in the form a + bi and a − bi. The product of these two conjugates, (a + bi) × (a − bi) = a2 + b2, is the square of the magnitude r illustrated in the previous figure. Operations on Complex Numbers Example 1, Addition:When adding two complex numbers, the real parts and imaginary parts are added separately, the real parts added to real parts and the imaginary to imaginary parts. Thus,



FACTORIAL ( a 1 + ib 1 ) + ( a 2 + ib 2 ) = ( a 1 + a 2 ) + i ( b 1 + b 2 ) ( a 1 + ib 1 ) – ( a 2 + ib 2 ) = ( a 1 – a 2 ) + i ( b 1 – b 2 ) ( 3 + 4i ) + ( 2 + i ) = ( 3 + 2 ) + ( 4 + 1 )i = 5 + 5i

Example 2, Multiplication:Multiplication of two complex numbers requires the use of the imaginary unit, i2 = −1 and the algebraic distributive law. 2

( a 1 + ib 1 ) ( a 2 + ib 2 ) = a 1 a 2 + ia 1 b 2 + ia 2 b 1 + i b 1 b 2 = a 1 a 2 + ia 1 b 2 + ia 2 b 1 – b 1 b 2 ( 7 + 2i ) × ( 5 – 3i ) = ( 7 ) ( 5 ) – ( 7 ) ( 3i ) + ( 2i ) ( 5 ) – ( 2i ) ( 3i ) 2

= 35 – 21i + 10i – 6i = 35 – 21i + 10i – ( 6 ) ( – 1 ) = 41 – 11i Multiplication of two complex numbers, Z1 = r1(cosθ1 + isinθ1) and Z2 = r2(cosθ2 + isinθ2), results in the following: Z1 × Z2 = r1(cosθ1 + isinθ1) × r2(cosθ2 + isinθ2) = r1r2[cos(θ1 + θ2) + isin(θ1 + θ2)] Example 3, Division:Divide the following two complex numbers, 2 + 3i and 4 − 5i. Dividing complex numbers makes use of the complex conjugate. 2

2 + 3i ( 2 + 3i ) ( 4 + 5i ) 8 + 12i + 10i + 15i – 7 + 22i –7 22 -------------- = --------------------------------------- = --------------------------------------------------- = ---------------------- = ⎛ ------⎞ + i ⎛ ------⎞ ⎝ 41⎠ ⎝ 41⎠ 2 4 – 5i ( 4 – 5i ) ( 4 + 5i ) 16 + 25 16 + 20i – 20i – 25i Example 4:Convert the complex number 8+6i into phasor form. First find the magnitude of the phasor vector and then the direction. 2 2 6 magnitude = 8 + 6 = 10 direction = atan --- = 36.87° 8 phasor = 10 ∠36.87° Factorial.—A factorial is a mathematical shortcut denoted by the symbol ! following a number (for example, 3! is three factorial). A factorial is found by multiplying together all the integers greater than zero and less than or equal to the factorial number wanted, except for zero factorial (0!), which is defined as 1. For example: 3! = 1 × 2 × 3 = 6; 4! = 1 × 2 × 3 × 4 = 24; 7! = 1 × 2 × 3 × 4 × 5 × 6 × 7 = 5040; etc. Example:How many ways can the letters X, Y, and Z be arranged? Solution: The numbers of possible arrangements for the three letters are 3! = 3 × 2 × 1 = 6. Permutations.—The number of ways r objects may be arranged from a set of n elements n n! is given by Pr = -----------------( n – r )! Example:There are 10 people are participating in the final run. In how many different ways can these people come in first, second and third. Solution: Here r is 3 and n is 10. So the possible numbers of winning number will be 10 10! P3 = --------------------= 10! -------- = 10 × 9 × 8 = 720 ( 10 – 3 )! 7! Combinations.—The number of ways r distinct objects may be chosen from a set of n elen n! ments is given by Cr = ---------------------( n – r )!r! Example:How many possible sets of 6 winning numbers can be picked from 52 numbers.


Machinery's Handbook 27th Edition FACTORS AND PRIME NUMBERS

19

Solution: Here r is 6 and n is 52. So the possible number of winning combinations will be 52! 52! 52 × 51 × 50 × 49 × 48 × 47 C6 = --------------------------- = ------------- = ------------------------------------------------------------------- = 20358520 ( 52 – 6 )!6! 46!6! 1×2×3×4×5×6

52

Prime Numbers and Factors of Numbers The factors of a given number are those numbers which when multiplied together give a product equal to that number; thus, 2 and 3 are factors of 6; and 5 and 7 are factors of 35. A prime number is one which has no factors except itself and 1. Thus, 2, 3, 5, 7, 11, etc., are prime numbers. A factor which is a prime number is called a prime factor. The accompanying “Prime Number and Factor Tables,” starting on page 20, give the smallest prime factor of all odd numbers from 1 to 9600, and can be used for finding all the factors for numbers up to this limit. For example, find the factors of 931. In the column headed “900” and in the line indicated by “31” in the left-hand column, the smallest prime factor is found to be 7. As this leaves another factor 133 (since 931 ÷ 7 = 133), find the smallest prime factor of this number. In the column headed “100” and in the line “33”, this is found to be 7, leaving a factor 19. This latter is a prime number; hence, the factors of 931 are 7 × 7 × 19. Where no factor is given for a number in the factor table, it indicates that the number is a prime number. The last page of the tables lists all prime numbers from 9551 through 18691; and can be used to identify quickly all unfactorable numbers in that range. For factoring, the following general rules will be found useful: 2 is a factor of any number the right-hand figure of which is an even number or 0. Thus, 28 = 2 × 14, and 210 = 2 × 105. 3 is a factor of any number the sum of the figures of which is evenly divisible by 3. Thus, 3 is a factor of 1869, because 1 + 8 + 6 + 9 = 24 ÷ 3 = 8. 4 is a factor of any number the two right-hand figures of which, considered as one number, are evenly divisible by 4. Thus, 1844 has a factor 4, because 44 ÷ 4 = 11. 5 is a factor of any number the right-hand figure of which is 0 or 5. Thus, 85 = 5 × 17; 70 = 5 × 14. Tables of prime numbers and factors of numbers are particularly useful for calculations involving change-gear ratios for compound gearing, dividing heads, gear-generating machines, and mechanical designs having gear trains. Example 1:A set of four gears is required in a mechanical design to provide an overall gear ratio of 4104 ÷ 1200. Furthermore, no gear in the set is to have more than 120 teeth or less than 24 teeth. Determine the tooth numbers. First, as explained previously, the factors of 4104 are determined to be: 2 × 2 × 2 × 3 × 3 × 57 = 4104. Next, the factors of 1200 are determined: 2 × 2 × 2 × 2 × 5 × 5 × 3 = 1200. 4104 2 × 2 × 2 × 3 × 3 × 57 72 × 57 Therefore ------------ = ---------------------------------------------------------- = ------------------ . If the factors had been com1200 2×2×2×2×5×5×3 24 × 50 72 × 57 bined differently, say, to give ------------------ , then the 16-tooth gear in the denominator would 16 × 75 not satisfy the requirement of no less than 24 teeth. Example 2:Factor the number 25078 into two numbers neither of which is larger than 200. The first factor of 25078 is obviously 2, leaving 25078 ÷ 2 = 12539 to be factored further. However, from the last table, Prime Numbers from 9551 to 18691, it is seen that 12539 is a prime number; therefore, no solution exists.



FACTORS AND PRIME NUMBERS Prime Number and Factor Table for 1 to 1199

From To

0 100

100 200

200 300

300 400

400 500

500 600

600 700

700 800

800 900

900 1000

1000 1100

1100 1200

1 2 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

P P P P P 3 P P 3 P P 3 P 5 3 P P 3 5 P 3 P P 3 P 7 3 P 5 3 P P 3 5 P 3 P P 3 7 P 3 P 5 3 P 7 3 5 P 3

P 2 P 3 P P 3 P 5 3 7 11 3 5 P 3 P 7 3 P P 3 11 5 3 P P 3 5 P 3 7 P 3 P 13 3 P 5 3 P P 3 5 11 3 P P 3 P P

3 2 7 5 3 11 P 3 5 7 3 13 P 3 P P 3 P 5 3 P P 3 5 13 3 P 11 3 P 7 3 P 5 3 P P 3 5 P 3 P P 3 7 17 3 P 5 3 13

7 2 3 5 P 3 P P 3 P 11 3 17 5 3 7 P 3 5 P 3 11 7 3 P P 3 P 5 3 P 19 3 5 P 3 7 P 3 13 P 3 P 5 3 P 17 3 5 P 3

P 2 13 3 11 P 3 7 5 3 P P 3 5 7 3 P P 3 19 P 3 P 5 3 P 11 3 5 P 3 P P 3 P 7 3 11 5 3 P 13 3 5 P 3 P 17 3 7 P

3 2 P 5 3 P 7 3 5 11 3 P P 3 17 23 3 13 5 3 7 P 3 5 P 3 19 7 3 P 13 3 P 5 3 P P 3 5 P 3 7 11 3 P 19 3 P 5 3 P

P 2 3 5 P 3 13 P 3 P P 3 7 5 3 17 P 3 5 7 3 P P 3 P 11 3 P 5 3 P P 3 5 23 3 11 P 3 P 7 3 P 5 3 13 P 3 5 17 3

P 2 19 3 7 P 3 23 5 3 P 7 3 5 P 3 17 P 3 11 P 3 P 5 3 7 P 3 5 P 3 P 7 3 13 P 3 P 5 3 19 11 3 5 P 3 7 13 3 P 17

3 2 11 5 3 P P 3 5 19 3 P P 3 P P 3 7 5 3 P 29 3 5 7 3 23 P 3 P P 3 P 5 3 11 13 3 5 P 3 P P 3 P 7 3 19 5 3 29

17 2 3 5 P 3 P 11 3 7 P 3 13 5 3 P 7 3 5 P 3 P 23 3 P 13 3 P 5 3 7 31 3 5 P 3 P 7 3 P 11 3 P 5 3 23 P 3 5 P 3

7 2 17 3 19 P 3 P 5 3 P P 3 5 13 3 P P 3 17 P 3 7 5 3 P P 3 5 7 3 P P 3 11 P 3 29 5 3 13 23 3 5 P 3 P P 3 P 7

3 2 P 5 3 P 11 3 5 P 3 19 P 3 7 P 3 11 5 3 17 7 3 5 31 3 P P 3 13 19 3 P 5 3 7 P 3 5 11 3 P 7 3 P 29 3 P 5 3 11



21

Prime Number and Factor Table for 1201 to 2399 From To

1200 1300

1300 1400

1400 1500

1500 1600

1600 1700

1700 1800

1800 1900

1900 2000

2000 2100

2100 2200

2200 2300

2300 2400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

P 3 5 17 3 7 P 3 P 23 3 P 5 3 P P 3 5 P 3 17 11 3 29 P 3 7 5 3 P 13 3 5 7 3 31 19 3 P P 3 P 5 3 P P 3 5 P 3

P P 3 P 7 3 13 5 3 P P 3 5 P 3 11 31 3 7 13 3 17 5 3 19 7 3 5 23 3 P 29 3 P 37 3 P 5 3 7 P 3 5 19 3 13 7 3 11 P

3 23 5 3 P 17 3 5 13 3 7 P 3 P P 3 P 5 3 P 11 3 5 P 3 P P 3 31 P 3 7 5 3 13 P 3 5 7 3 P P 3 P P 3 P 5 3 P

19 3 5 11 3 P 17 3 37 7 3 P 5 3 11 P 3 5 29 3 23 P 3 7 P 3 P 5 3 P 7 3 5 P 3 P 11 3 19 P 3 P 5 3 7 37 3 5 P 3

P 7 3 P P 3 P 5 3 P P 3 5 P 3 7 23 3 P 11 3 31 5 3 17 13 3 5 P 3 11 P 3 P P 3 7 5 3 23 41 3 5 7 3 19 P 3 P P

3 13 5 3 P 29 3 5 17 3 P P 3 11 7 3 P 5 3 37 P 3 5 P 3 17 P 3 7 P 3 41 5 3 29 7 3 5 P 3 13 P 3 P P 3 11 5 3 7

P 3 5 13 3 P 7 3 23 17 3 P 5 3 31 P 3 5 11 3 7 19 3 P 43 3 17 5 3 11 P 3 5 P 3 P P 3 P P 3 7 5 3 P 31 3 5 7 3

P 11 3 P 23 3 P 5 3 19 17 3 5 41 3 P P 3 13 7 3 29 5 3 P P 3 5 19 3 37 13 3 7 11 3 P 5 3 P 7 3 5 P 3 11 P 3 P P

3 P 5 3 7 P 3 5 P 3 43 7 3 P P 3 19 5 3 P 13 3 5 23 3 7 P 3 11 29 3 P 5 3 P 19 3 5 31 3 P P 3 P P 3 7 5 3 P

11 3 5 7 3 P P 3 29 13 3 11 5 3 P P 3 5 P 3 P P 3 19 7 3 P 5 3 17 P 3 5 11 3 13 41 3 7 P 3 37 5 3 11 7 3 5 13 3

31 P 3 P 47 3 P 5 3 7 P 3 5 17 3 23 7 3 P P 3 P 5 3 13 P 3 5 37 3 7 31 3 P P 3 P 5 3 43 P 3 5 P 3 29 P 3 P 11

3 7 5 3 P P 3 5 7 3 11 23 3 13 17 3 P 5 3 P P 3 5 P 3 P 13 3 P 7 3 17 5 3 23 P 3 5 P 3 P P 3 7 P 3 P 5 3 P




From To

2400 2500

2500 2600

2600 2700

2700 2800

2800 2900

2900 3000

3000 3100

3100 3200

3200 3300

3300 3400

3400 3500

3500 3600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

7 3 5 29 3 P 19 3 P 41 3 P 5 3 7 11 3 5 P 3 P 7 3 P 31 3 11 5 3 P 23 3 5 P 3 7 P 3 P 37 3 13 5 3 19 47 3 5 11 3

41 P 3 23 13 3 7 5 3 11 P 3 5 7 3 P 17 3 43 P 3 P 5 3 P P 3 5 P 3 13 11 3 17 7 3 31 5 3 P 29 3 5 13 3 P P 3 7 23

3 19 5 3 P 7 3 5 P 3 P 43 3 37 11 3 P 5 3 7 19 3 5 P 3 11 7 3 P P 3 P 5 3 17 P 3 5 P 3 7 P 3 P P 3 P 5 3 P

37 3 5 P 3 P P 3 11 P 3 7 5 3 P P 3 5 7 3 P 13 3 41 P 3 P 5 3 31 11 3 5 P 3 17 47 3 P 7 3 11 5 3 P P 3 5 P 3

P P 3 7 53 3 29 5 3 P 7 3 5 11 3 19 P 3 P 17 3 P 5 3 7 P 3 5 P 3 P 7 3 47 19 3 13 5 3 P 43 3 5 P 3 7 11 3 P 13

3 P 5 3 P 41 3 5 P 3 23 37 3 P 29 3 7 5 3 P 17 3 5 7 3 13 P 3 P 11 3 P 5 3 P P 3 5 13 3 11 19 3 29 7 3 41 5 3 P

P 3 5 31 3 P 23 3 7 P 3 P 5 3 13 7 3 5 P 3 P 17 3 11 P 3 43 5 3 7 P 3 5 P 3 37 7 3 17 P 3 P 5 3 P 11 3 5 19 3

7 29 3 13 P 3 11 5 3 P P 3 5 53 3 31 13 3 P 43 3 7 5 3 47 23 3 5 7 3 29 P 3 P P 3 19 5 3 11 P 3 5 P 3 P 31 3 23 7

3 P 5 3 P 13 3 5 P 3 P 11 3 7 P 3 53 5 3 41 7 3 5 17 3 P P 3 P P 3 13 5 3 7 P 3 5 29 3 17 7 3 19 11 3 37 5 3 P

P 3 5 P 3 7 P 3 31 P 3 P 5 3 P P 3 5 47 3 13 P 3 P 17 3 7 5 3 P P 3 5 7 3 P P 3 11 31 3 17 5 3 P P 3 5 43 3

19 41 3 P 7 3 P 5 3 13 11 3 5 23 3 47 P 3 7 19 3 11 5 3 P 7 3 5 P 3 P P 3 P P 3 23 5 3 7 59 3 5 11 3 P 7 3 13 P

3 31 5 3 11 P 3 5 P 3 7 13 3 P P 3 P 5 3 P P 3 5 P 3 53 11 3 P P 3 7 5 3 43 P 3 5 7 3 P P 3 17 37 3 P 5 3 59



23


3600 3700

3700 3800

3800 3900

3900 4000

4000 4100

4100 4200

4200 4300

4300 4400

4400 4500

4500 4600

4600 4700

4700 4800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

13 3 5 P 3 23 P 3 P 7 3 P 5 3 19 P 3 5 P 3 11 P 3 7 41 3 13 5 3 P 7 3 5 19 3 P P 3 P 13 3 29 5 3 7 P 3 5 P 3

P 7 3 11 P 3 47 5 3 P 61 3 5 P 3 7 P 3 37 P 3 19 5 3 23 11 3 5 13 3 P 53 3 P P 3 7 5 3 P 19 3 5 7 3 17 P 3 P 29

3 P 5 3 13 37 3 5 11 3 P P 3 43 7 3 P 5 3 11 23 3 5 P 3 P P 3 7 17 3 P 5 3 53 7 3 5 P 3 P 11 3 13 P 3 17 5 3 7

47 3 5 P 3 P 7 3 P P 3 P 5 3 P P 3 5 31 3 7 P 3 P 11 3 59 5 3 37 17 3 5 P 3 11 29 3 41 23 3 7 5 3 P 13 3 5 7 3

P P 3 P 19 3 P 5 3 P P 3 5 P 3 29 37 3 11 7 3 13 5 3 P P 3 5 P 3 31 17 3 7 13 3 P 5 3 P 7 3 5 61 3 P P 3 17 P

3 11 5 3 7 P 3 5 23 3 13 7 3 P P 3 P 5 3 P 41 3 5 11 3 7 P 3 P P 3 23 5 3 11 43 3 5 P 3 37 47 3 53 59 3 7 5 3 13

P 3 5 7 3 P 11 3 P P 3 41 5 3 P P 3 5 19 3 P P 3 31 7 3 P 5 3 P P 3 5 17 3 P P 3 7 11 3 P 5 3 P 7 3 5 P 3

11 13 3 59 31 3 19 5 3 7 29 3 5 P 3 61 7 3 P P 3 43 5 3 P 19 3 5 P 3 7 P 3 11 17 3 P 5 3 29 13 3 5 41 3 P 23 3 P 53

3 7 5 3 P 11 3 5 7 3 P P 3 19 43 3 11 5 3 23 P 3 5 P 3 P 61 3 P 7 3 P 5 3 41 17 3 5 11 3 P P 3 7 67 3 P 5 3 11

7 3 5 P 3 13 P 3 P P 3 P 5 3 7 23 3 5 13 3 19 7 3 P P 3 29 5 3 47 P 3 5 P 3 7 17 3 23 19 3 P 5 3 13 P 3 5 P 3

43 P 3 17 11 3 7 5 3 31 P 3 5 7 3 11 41 3 P P 3 P 5 3 P P 3 5 P 3 59 P 3 13 7 3 P 5 3 P 31 3 5 43 3 P 13 3 7 37

3 P 5 3 17 7 3 5 53 3 P P 3 29 P 3 P 5 3 7 11 3 5 47 3 P 7 3 67 P 3 11 5 3 19 13 3 5 17 3 7 P 3 P P 3 P 5 3 P




From To

4800 4900

4900 5000

5000 5100

5100 5200

5200 5300

5300 5400

5400 5500

5500 5600

5600 5700

5700 5800

5800 5900

5900 6000

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

P 3 5 11 3 17 P 3 P 61 3 7 5 3 11 P 3 5 7 3 47 29 3 37 13 3 23 5 3 43 P 3 5 31 3 P 11 3 P 7 3 19 5 3 P 67 3 5 59 3

13 P 3 7 P 3 17 5 3 P 7 3 5 13 3 P P 3 P 11 3 P 5 3 7 P 3 5 P 3 11 7 3 P P 3 P 5 3 13 17 3 5 P 3 7 P 3 19 P

3 P 5 3 P P 3 5 29 3 P P 3 11 47 3 7 5 3 P 71 3 5 7 3 P 31 3 13 P 3 61 5 3 37 11 3 5 P 3 P 13 3 P 7 3 11 5 3 P

P 3 5 P 3 19 P 3 7 P 3 47 5 3 23 7 3 5 11 3 53 37 3 P 19 3 P 5 3 7 13 3 5 P 3 P 7 3 31 P 3 71 5 3 P 29 3 5 P 3

7 11 3 41 P 3 13 5 3 17 23 3 5 P 3 P P 3 P 13 3 7 5 3 29 59 3 5 7 3 P 19 3 23 11 3 P 5 3 P P 3 5 17 3 11 67 3 P 7

3 P 5 3 P 47 3 5 13 3 17 P 3 7 73 3 P 5 3 19 7 3 5 P 3 P 53 3 11 23 3 31 5 3 7 41 3 5 19 3 P 7 3 P 17 3 P 5 3 P

11 3 5 P 3 7 P 3 P P 3 11 5 3 61 P 3 5 P 3 P P 3 13 P 3 7 5 3 53 43 3 5 7 3 P 13 3 P P 3 P 5 3 11 17 3 5 23 3

P P 3 P 7 3 37 5 3 P P 3 5 P 3 P 11 3 7 29 3 23 5 3 31 7 3 5 P 3 67 P 3 19 P 3 P 5 3 7 P 3 5 37 3 P 7 3 29 11

3 13 5 3 71 31 3 5 41 3 7 P 3 17 13 3 43 5 3 P P 3 5 P 3 P P 3 P P 3 7 5 3 P 53 3 5 7 3 13 P 3 11 P 3 P 5 3 41

P 3 5 13 3 P 29 3 P 7 3 59 5 3 17 11 3 5 P 3 P P 3 7 P 3 11 5 3 13 7 3 5 73 3 29 23 3 53 P 3 P 5 3 7 P 3 5 11 3

P 7 3 P 37 3 P 5 3 11 P 3 5 P 3 7 19 3 13 P 3 P 5 3 P P 3 5 P 3 P 11 3 P P 3 7 5 3 P P 3 5 7 3 43 71 3 P 17

3 P 5 3 19 23 3 5 61 3 31 P 3 P 7 3 17 5 3 P 13 3 5 19 3 11 P 3 7 59 3 67 5 3 47 7 3 5 43 3 P 31 3 P 53 3 13 5 3 7



25


6000 6100

6100 6200

6200 6300

6300 6400

6400 6500

6500 6600

6600 6700

6700 6800

6800 6900

6900 7000

7000 7100

7100 7200

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

17 3 5 P 3 P 7 3 11 13 3 19 5 3 P 37 3 5 P 3 7 P 3 P 23 3 P 5 3 73 11 3 5 P 3 13 P 3 59 P 3 7 5 3 P P 3 5 7 3

P 17 3 31 41 3 P 5 3 29 P 3 5 11 3 P P 3 17 7 3 P 5 3 11 P 3 5 47 3 61 P 3 7 31 3 P 5 3 37 7 3 5 23 3 41 11 3 P P

3 P 5 3 7 P 3 5 P 3 P 7 3 13 P 3 23 5 3 17 79 3 5 P 3 7 13 3 P 11 3 P 5 3 P P 3 5 P 3 11 61 3 P 19 3 7 5 3 P

P 3 5 7 3 P 59 3 P 71 3 P 5 3 P 13 3 5 P 3 17 P 3 11 7 3 P 5 3 P P 3 5 P 3 23 P 3 7 P 3 13 5 3 P 7 3 5 P 3

37 19 3 43 13 3 11 5 3 7 P 3 5 P 3 59 7 3 41 47 3 17 5 3 P P 3 5 11 3 7 23 3 29 P 3 P 5 3 11 P 3 5 13 3 P 43 3 73 67

3 7 5 3 23 17 3 5 7 3 P 11 3 61 P 3 47 5 3 13 31 3 5 P 3 P P 3 79 7 3 P 5 3 P P 3 5 P 3 P 29 3 7 11 3 19 5 3 P

7 3 5 P 3 11 17 3 13 P 3 37 5 3 7 19 3 5 P 3 29 7 3 17 61 3 P 5 3 P P 3 5 59 3 7 P 3 11 P 3 41 5 3 P P 3 5 37 3

P P 3 19 P 3 7 5 3 P 11 3 5 7 3 53 P 3 P 23 3 11 5 3 17 43 3 5 29 3 P P 3 67 7 3 13 5 3 P P 3 5 11 3 P P 3 7 13

3 P 5 3 11 7 3 5 17 3 19 P 3 P P 3 P 5 3 7 P 3 5 41 3 13 7 3 P 19 3 P 5 3 P P 3 5 13 3 7 P 3 71 83 3 61 5 3 P

67 3 5 P 3 P 31 3 P 11 3 7 5 3 13 29 3 5 7 3 11 53 3 P P 3 17 5 3 P P 3 5 P 3 P 19 3 P 7 3 P 5 3 29 P 3 5 P 3

P 47 3 7 43 3 P 5 3 P 7 3 5 P 3 79 13 3 31 P 3 P 5 3 7 11 3 5 P 3 23 7 3 37 P 3 11 5 3 P 73 3 5 19 3 7 41 3 47 31

3 P 5 3 P 13 3 5 11 3 P 17 3 P P 3 7 5 3 11 37 3 5 7 3 P 23 3 17 P 3 13 5 3 67 71 3 5 P 3 43 11 3 P 7 3 P 5 3 23




From To

7200 7300

7300 7400

7400 7500

7500 7600

7600 7700

7700 7800

7800 7900

7900 8000

8000 8100

8100 8200

8200 8300

8300 8400

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

19 3 5 P 3 P P 3 7 P 3 31 5 3 P 7 3 5 P 3 13 P 3 P 11 3 P 5 3 7 53 3 5 13 3 11 7 3 19 29 3 P 5 3 37 23 3 5 P 3

7 67 3 P P 3 71 5 3 13 P 3 5 17 3 P P 3 11 41 3 7 5 3 P P 3 5 7 3 17 37 3 53 P 3 73 5 3 47 11 3 5 83 3 19 P 3 13 7

3 11 5 3 31 P 3 5 P 3 41 13 3 7 17 3 P 5 3 43 7 3 5 11 3 P 29 3 P P 3 17 5 3 7 31 3 5 P 3 P 7 3 P P 3 59 5 3 P

13 3 5 P 3 7 11 3 P 73 3 P 5 3 P 17 3 5 P 3 P 19 3 P P 3 7 5 3 P P 3 5 7 3 67 P 3 P 11 3 P 5 3 P P 3 5 71 3

11 P 3 P 7 3 23 5 3 19 P 3 5 29 3 13 17 3 7 P 3 P 5 3 P 7 3 5 13 3 47 79 3 11 P 3 P 5 3 7 P 3 5 P 3 P 7 3 43 P

3 P 5 3 13 11 3 5 P 3 7 P 3 P 59 3 11 5 3 71 P 3 5 61 3 23 P 3 P P 3 7 5 3 17 19 3 5 7 3 31 43 3 13 P 3 P 5 3 11

29 3 5 37 3 73 13 3 P 7 3 P 5 3 P 41 3 5 17 3 P 11 3 7 47 3 P 5 3 29 7 3 5 P 3 17 P 3 P P 3 P 5 3 7 13 3 5 53 3

P 7 3 P 11 3 41 5 3 P 89 3 5 P 3 7 P 3 P 17 3 13 5 3 P P 3 5 73 3 19 P 3 31 13 3 7 5 3 79 23 3 5 7 3 61 P 3 11 19

3 53 5 3 P P 3 5 P 3 13 71 3 23 7 3 29 5 3 P 11 3 5 13 3 83 P 3 7 P 3 11 5 3 P 7 3 5 41 3 P 59 3 P P 3 P 5 3 7

P 3 5 11 3 P 7 3 P 23 3 P 5 3 11 47 3 5 79 3 7 17 3 P 29 3 31 5 3 41 P 3 5 P 3 P 11 3 13 P 3 7 5 3 19 P 3 5 7 3

59 13 3 29 P 3 43 5 3 P P 3 5 19 3 P P 3 P 7 3 P 5 3 73 37 3 5 23 3 11 P 3 7 P 3 P 5 3 17 7 3 5 P 3 P P 3 P 43

3 19 5 3 7 P 3 5 P 3 53 7 3 11 P 3 13 5 3 31 19 3 5 17 3 7 P 3 61 13 3 P 5 3 P 11 3 5 P 3 17 83 3 P P 3 7 5 3 37



27


8400 8500

8500 8600

8600 8700

8700 8800

8800 8900

8900 9000

9000 9100

9100 9200

9200 9300

9300 9400

9400 9500

9500 9600

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95 97 99

31 3 5 7 3 13 47 3 19 P 3 P 5 3 P P 3 5 11 3 23 P 3 P 7 3 79 5 3 11 P 3 5 P 3 43 37 3 7 61 3 17 5 3 13 7 3 5 29 3

P 11 3 47 67 3 P 5 3 7 P 3 5 P 3 19 7 3 P P 3 P 5 3 83 17 3 5 43 3 7 P 3 13 11 3 P 5 3 23 P 3 5 31 3 11 13 3 P P

3 7 5 3 P 79 3 5 7 3 37 P 3 P P 3 89 5 3 53 P 3 5 P 3 41 17 3 11 7 3 P 5 3 P 13 3 5 P 3 P 19 3 7 P 3 P 5 3 P

7 3 5 P 3 31 P 3 23 P 3 11 5 3 7 P 3 5 P 3 P 7 3 P 13 3 P 5 3 19 P 3 5 11 3 7 31 3 67 P 3 P 5 3 11 59 3 5 19 3

13 P 3 P 23 3 7 5 3 P P 3 5 7 3 P 11 3 P P 3 37 5 3 P 53 3 5 17 3 P P 3 P 7 3 19 5 3 13 83 3 5 P 3 17 P 3 7 11

3 29 5 3 59 7 3 5 37 3 11 P 3 79 P 3 P 5 3 7 P 3 5 23 3 P 7 3 13 17 3 P 5 3 P P 3 5 47 3 7 13 3 11 89 3 17 5 3 P

P 3 5 P 3 P P 3 71 29 3 7 5 3 P 11 3 5 7 3 P P 3 83 P 3 11 5 3 P 13 3 5 P 3 47 43 3 29 7 3 31 5 3 61 P 3 5 11 3

19 P 3 7 P 3 13 5 3 11 7 3 5 P 3 23 P 3 P 13 3 41 5 3 7 P 3 5 P 3 P 7 3 89 53 3 P 5 3 67 P 3 5 P 3 7 29 3 17 P

3 P 5 3 P 61 3 5 13 3 P 23 3 P 11 3 7 5 3 P P 3 5 7 3 11 19 3 P 47 3 59 5 3 13 73 3 5 P 3 P P 3 37 7 3 P 5 3 17

71 3 5 41 3 P 67 3 7 P 3 P 5 3 19 7 3 5 P 3 P P 3 13 P 3 47 5 3 7 11 3 5 17 3 P 7 3 P 83 3 11 5 3 41 P 3 5 P 3

7 P 3 23 97 3 P 5 3 P P 3 5 11 3 P P 3 P P 3 7 5 3 11 13 3 5 7 3 P P 3 P 17 3 P 5 3 P 19 3 5 53 3 P 11 3 P 7

3 13 5 3 37 P 3 5 31 3 P 89 3 7 13 3 P 5 3 P 7 3 5 P 3 P 41 3 19 11 3 73 5 3 7 17 3 5 61 3 11 7 3 P 43 3 53 5 3 29



PRIME NUMBERS Prime Numbers from 9551 to 18691

9551 9587 9601 9613 9619 9623 9629 9631 9643 9649 9661 9677 9679 9689 9697 9719 9721 9733 9739 9743 9749 9767 9769 9781 9787 9791 9803 9811 9817 9829 9833 9839 9851 9857 9859 9871 9883 9887 9901 9907 9923 9929 9931 9941 9949 9967 9973 10007 10009 10037 10039 10061 10067 10069 10079 10091 10093 10099 10103 10111 10133 10139 10141 10151 10159 10163 10169 10177

10181 10193 10211 10223 10243 10247 10253 10259 10267 10271 10273 10289 10301 10303 10313 10321 10331 10333 10337 10343 10357 10369 10391 10399 10427 10429 10433 10453 10457 10459 10463 10477 10487 10499 10501 10513 10529 10531 10559 10567 10589 10597 10601 10607 10613 10627 10631 10639 10651 10657 10663 10667 10687 10691 10709 10711 10723 10729 10733 10739 10753 10771 10781 10789 10799 10831 10837 10847

10853 10859 10861 10867 10883 10889 10891 10903 10909 10937 10939 10949 10957 10973 10979 10987 10993 11003 11027 11047 11057 11059 11069 11071 11083 11087 11093 11113 11117 11119 11131 11149 11159 11161 11171 11173 11177 11197 11213 11239 11243 11251 11257 11261 11273 11279 11287 11299 11311 11317 11321 11329 11351 11353 11369 11383 11393 11399 11411 11423 11437 11443 11447 11467 11471 11483 11489 11491

11497 11503 11519 11527 11549 11551 11579 11587 11593 11597 11617 11621 11633 11657 11677 11681 11689 11699 11701 11717 11719 11731 11743 11777 11779 11783 11789 11801 11807 11813 11821 11827 11831 11833 11839 11863 11867 11887 11897 11903 11909 11923 11927 11933 11939 11941 11953 11959 11969 11971 11981 11987 12007 12011 12037 12041 12043 12049 12071 12073 12097 12101 12107 12109 12113 12119 12143 12149

12157 12161 12163 12197 12203 12211 12227 12239 12241 12251 12253 12263 12269 12277 12281 12289 12301 12323 12329 12343 12347 12373 12377 12379 12391 12401 12409 12413 12421 12433 12437 12451 12457 12473 12479 12487 12491 12497 12503 12511 12517 12527 12539 12541 12547 12553 12569 12577 12583 12589 12601 12611 12613 12619 12637 12641 12647 12653 12659 12671 12689 12697 12703 12713 12721 12739 12743 12757

12763 12781 12791 12799 12809 12821 12823 12829 12841 12853 12889 12893 12899 12907 12911 12917 12919 12923 12941 12953 12959 12967 12973 12979 12983 13001 13003 13007 13009 13033 13037 13043 13049 13063 13093 13099 13103 13109 13121 13127 13147 13151 13159 13163 13171 13177 13183 13187 13217 13219 13229 13241 13249 13259 13267 13291 13297 13309 13313 13327 13331 13337 13339 13367 13381 13397 13399 13411

13417 13421 13441 13451 13457 13463 13469 13477 13487 13499 13513 13523 13537 13553 13567 13577 13591 13597 13613 13619 13627 13633 13649 13669 13679 13681 13687 13691 13693 13697 13709 13711 13721 13723 13729 13751 13757 13759 13763 13781 13789 13799 13807 13829 13831 13841 13859 13873 13877 13879 13883 13901 13903 13907 13913 13921 13931 13933 13963 13967 13997 13999 14009 14011 14029 14033 14051 14057

14071 14081 14083 14087 14107 14143 14149 14153 14159 14173 14177 14197 14207 14221 14243 14249 14251 14281 14293 14303 14321 14323 14327 14341 14347 14369 14387 14389 14401 14407 14411 14419 14423 14431 14437 14447 14449 14461 14479 14489 14503 14519 14533 14537 14543 14549 14551 14557 14561 14563 14591 14593 14621 14627 14629 14633 14639 14653 14657 14669 14683 14699 14713 14717 14723 14731 14737 14741

14747 14753 14759 14767 14771 14779 14783 14797 14813 14821 14827 14831 14843 14851 14867 14869 14879 14887 14891 14897 14923 14929 14939 14947 14951 14957 14969 14983 15013 15017 15031 15053 15061 15073 15077 15083 15091 15101 15107 15121 15131 15137 15139 15149 15161 15173 15187 15193 15199 15217 15227 15233 15241 15259 15263 15269 15271 15277 15287 15289 15299 15307 15313 15319 15329 15331 15349 15359

15361 15373 15377 15383 15391 15401 15413 15427 15439 15443 15451 15461 15467 15473 15493 15497 15511 15527 15541 15551 15559 15569 15581 15583 15601 15607 15619 15629 15641 15643 15647 15649 15661 15667 15671 15679 15683 15727 15731 15733 15737 15739 15749 15761 15767 15773 15787 15791 15797 15803 15809 15817 15823 15859 15877 15881 15887 15889 15901 15907 15913 15919 15923 15937 15959 15971 15973 15991

16001 16007 16033 16057 16061 16063 16067 16069 16073 16087 16091 16097 16103 16111 16127 16139 16141 16183 16187 16189 16193 16217 16223 16229 16231 16249 16253 16267 16273 16301 16319 16333 16339 16349 16361 16363 16369 16381 16411 16417 16421 16427 16433 16447 16451 16453 16477 16481 16487 16493 16519 16529 16547 16553 16561 16567 16573 16603 16607 16619 16631 16633 16649 16651 16657 16661 16673 16691

16693 16699 16703 16729 16741 16747 16759 16763 16787 16811 16823 16829 16831 16843 16871 16879 16883 16889 16901 16903 16921 16927 16931 16937 16943 16963 16979 16981 16987 16993 17011 17021 17027 17029 17033 17041 17047 17053 17077 17093 17099 17107 17117 17123 17137 17159 17167 17183 17189 17191 17203 17207 17209 17231 17239 17257 17291 17293 17299 17317 17321 17327 17333 17341 17351 17359 17377 17383


17387 17389 17393 17401 17417 17419 17431 17443 17449 17467 17471 17477 17483 17489 17491 17497 17509 17519 17539 17551 17569 17573 17579 17581 17597 17599 17609 17623 17627 17657 17659 17669 17681 17683 17707 17713 17729 17737 17747 17749 17761 17783 17789 17791 17807 17827 17837 17839 17851 17863 17881 17891 17903 17909 17911 17921 17923 17929 17939 17957 17959 17971 17977 17981 17987 17989 18013 18041

18043 18047 18049 18059 18061 18077 18089 18097 18119 18121 18127 18131 18133 18143 18149 18169 18181 18191 18199 18211 18217 18223 18229 18233 18251 18253 18257 18269 18287 18289 18301 18307 18311 18313 18329 18341 18353 18367 18371 18379 18397 18401 18413 18427 18433 18439 18443 18451 18457 18461 18481 18493 18503 18517 18521 18523 18539 18541 18553 18583 18587 18593 18617 18637 18661 18671 18679 18691

Machinery's Handbook 27th Edition ALGEBRA AND EQUATIONS

29

ALGEBRA AND EQUATIONS An unknown number can be represented by a symbol or a letter which can be manipulated like an ordinary numeral within an arithmatic expression. The rules of arithmetic are also applicable in algebra. Rearrangement and Transposition of Terms in Formulas A formula is a rule for a calculation expressed by using letters and signs instead of writing out the rule in words; by this means, it is possible to condense, in a very small space, the essentials of long and cumbersome rules. The letters used in formulas simply stand in place of the figures that are to be substituted when solving a specific problem. As an example, the formula for the horsepower transmitted by belting may be written SVW P = ---------------33 ,000 where P = horsepower transmitted; S = working stress of belt per inch of width in pounds; V = velocity of belt in feet per minute; and, W = width of belt in inches. If the working stress S, the velocity V, and the width W are known, the horsepower can be found directly from this formula by inserting the given values. Assume S = 33; V = 600; and W = 5. Then 33 × 600 × 5 P = ------------------------------ = 3 33 ,000 Assume that the horsepower P, the stress S, and the velocity V are known, and that the width of belt, W, is to be found. The formula must then be rearranged so that the symbol W will be on one side of the equals sign and all the known quantities on the other. The rearranged formula is as follows: P × 33 ,000 = W -------------------------SV The quantities (S and V) that were in the numerator on the right side of the equals sign are moved to the denominator on the left side, and “33,000,” which was in the denominator on the right side of the equals sign, is moved to the numerator on the other side. Symbols that are not part of a fraction, like “P” in the formula first given, are to be considered as being numerators (having the denominator 1). Thus, any formula of the form A = B/C can be rearranged as follows: A×C = B and C = B --A B×C D

Suppose a formula to be of the form A = -------------

B×C A×D A×D D = -------------------------- = B -------------- = C A C B The method given is only directly applicable when all the quantities in the numerator or denominator are standing independently or are factors of a product. If connected by + or − signs, the entire numerator or denominator must be moved as a unit, thus, Then

Given: To solve for F, rearrange in two steps as follows:

B+C D+E -------------- = -------------A F F D+E A(D + E) --- = -------------- and F = ----------------------A B+C B+C



ALGEBRA AND EQUATIONS

A quantity preceded by a + or − sign can be transposed to the opposite side of the equals sign by changing its sign; if the sign is +, change it to − on the other side; if it is −, change it to +. This process is called transposition of terms. Example: B+C = A–D then A = B+C+D B = A–D–C C = A–D–B Principal Algebraic Expressions and Formulas a × a = aa = a 2

a----3- = ⎛ a---⎞ 3 ⎝ b⎠ b3

a × a × a = aaa = a 3 a × b = ab a 2 b 2 = ( ab ) 2

3 1 ----- = ⎛ 1---⎞ = a – 3 ⎝ a⎠ a3

a2 a3 = a2 + 3 = a5

( a2 )3 = a2 × 3 = ( a3 )2 = a6

a4 ÷ a3 = a4 – 3 = a

a 3 + b 3 = ( a + b ) ( a 2 – ab + b 2 )

a0 = 1

a 3 – b 3 = ( a – b ) ( a 2 + ab + b 2 )

a2 – b2 = ( a + b ) ( a – b )

( a + b ) = a + 3a b + 3ab + b

( a + b ) 2 = a 2 + 2ab + b 2

a×

a×

2

3

2

3

3

3

3

3

a – b = ( a – b ) + 3ab ( a – b )

a× a = a 3

2

2

a 3 + b 3 = ( a + b ) – 3ab ( a + b )

– b-⎞ 2 + b-⎞ 2 – ⎛ a----------ab = ⎛ a----------⎝ 2 ⎠ ⎝ 2 ⎠

3

3

3

( a – b ) = a – 3a b + 3ab – b

( a – b ) 2 = a 2 – 2ab + b 2

3

3

3

3

a = a

3

a =

4×3

a =

3 4

a×3 b

3

a a --- = ------b 3 b

3

1--- = -----1 - = a – 1⁄3 a 3 a

2

a2 = ( 3 a ) = a2 / 3

4 3

3

3

(3 a) = a 3

ab =

a

a+ b =

a + b + 2 ab

When

a×b = x a÷b = x

then then

log a + log b = log x log a – log b = log x

a3 = x

then

3 log a = log x

then

log a- = log x ---------3

3

a = x


Machinery's Handbook 27th Edition QUADRATIC EQUATIONS

31

Equation Solving An equation is a statement of equality between two expressions, as 5x = 105. The unknown quantity in an equation is frequently designated by the letter such as x. If there is more than one unknown quantity, the others are designated by letters also usually selected from the end of the alphabet, as y, z, u, t, etc. An equation of the first degree is one which contains the unknown quantity only in the first power, as in 3x = 9. A quadratic equation is one which contains the unknown quantity in the second, but no higher, power, as in x2 + 3x = 10. Solving Equations of the First Degree with One Unknown.—Transpose all the terms containing the unknown x to one side of the equals sign, and all the other terms to the other side. Combine and simplify the expressions as far as possible, and divide both sides by the coefficient of the unknown x. (See the rules given for transposition of formulas.) Example:

22x – 11 22x – 15x 7x x

= = = =

15x + 10 10 + 11 21 3

Solution of Equations of the First Degree with Two Unknowns.—The form of the simplified equations is a1x + b1y = c1 a2x + b2y = c2 Then, c1 b2 – c2 b1 a1 c2 – a2 c1 x = ----------------------------y = ---------------------------a1 b2 – a2 b1 a1 b2 – a2 b1 Example:

3x + 4y = 17 5x – 2y = 11 17 × ( – 2 ) – 11 × 4- = –--------------------34 – 44- = -------– 78- = 3 x = ------------------------------------------3 × ( –2 ) – 5 × 4 – 6 – 20 – 26

The value of y can now be most easily found by inserting the value of x in one of the equations: 5 × 3 – 2y = 11

2y = 15 – 11 = 4

y = 2

Solution of Quadratic Equations with One Unknown.—If the form of the equation is ax2 + bx + c = 0, then b ± b 2 – 4acx = –-------------------------------------2a Example:Given the equation, 1x2 + 6x + 5 = 0, then a = 1, b = 6, and c = 5. – 6 ± 62 – 4 × 1 × 5 ( –6 ) + 4 x = --------------------------------------------------- = -------------------- = – 1 2×1 2

or

(------------------– 6 ) – 4- = – 5 2

If the form of the equation is ax2 + bx = c, then – b ± b 2 + 4ac x = --------------------------------------2a Example:A right-angle triangle has a hypotenuse 5 inches long and one side which is one inch longer than the other; find the lengths of the two sides.



FACTORING QUADRATIC EQUATIONS

Let x = one side and x + 1 = other side; then x2 + (x + 1)2 = 52 or x2 + x2 + 2x + 1 = 25; or 2x2 + 2x = 24; or x2 + x = 12. Now referring to the basic formula, ax2 + bx = c, we find that a = 1, b = 1, and c = 12; hence, – 1 ± 1 + 4 × 1 × 12 ( –1 ) + 7 x = ---------------------------------------------------- = -------------------- = 3 2×1 2

( –1 ) – 7 or x = -------------------- = – 4 2

Since the positive value (3) would apply in this case, the lengths of the two sides are x = 3 inches and x + 1 = 4 inches. Factoring a Quadratic Expression.—The method described below is useful in determining factors of the quadratic equation in the form ax2 + bx + c = 0. First, obtain the product ac from the coefficients a and c, and then determine two numbers, f1 and f2, such that f1 × f2 = |ac|, and f1 + f2 = b if ac is positive, or f1 − f2 = b if ac is negative. The numbers f1 and f2 are used to modify or rearrange the bx term to simplify factoring the quadratic expression. The roots of the quadratic equation can be easily obtained from the factors. Example:Factor 8x2 + 22x + 5 = 0 and find the values of x that satisfy the equation. Solution: In this example, a = 8, b = 22, and c=5. Therefore, ac = 8 × 5 = 40, and ac is positive, so we are looking for two factors of ac, f1 and f2, such that f1 × f2 = 40, and f1 + f2 = 22. The ac term can be written as 2 × 2 × 2 × 5 = 40, and the possible combination of numbers for f1 and f2 are (20 and 2), (8 and 5), (4 and 10) and (40 and 1). The requirements for f1 and f2 are satisfied by f1=20 and f2 = 2, i.e., 20 × 2 = 40 and 20 + 2 = 22. Using f1 and f2, the original quadratic expression is rewritten and factored as follows: 2

8x + 22x + 5 = 0 2

8x + 20x + 2x + 5 = 0 4x ( 2x + 5 ) + 1 ( 2x + 5 ) = 0 ( 2x + 5 ) ( 4x + 1 ) = 0 If the product of the two factors equals zero, then each of the factors equals zero, thus, 2x + 5 = 0 and 4x +1 = 0. Rearranging and solving, x = −5⁄2 and x = −1⁄4. Example:Factor 8x2 + 3x − 5 = 0 and find the solutions for x. Solution: Here a = 8, b = 3, c = −5, and ac = 8 × (−5) = −40. Because ac is negative, the required numbers, f1 and f2, must satisfy f1 × f2 = |ac| = 40 and f1 − f2 = 3. As in the previous example, the possible combinations for f1 and f2 are (20 and 2), (8 and 5), (4 and 10) and (40 and 1). The numbers f1 = 8 and f2 = 5 satisy the requirements because 8 × 5 = 40 and 8 − 5 = 3. In the second line below, 5x is both added to and subtrtacted from the original equation, making it possible to rearrange and simplify the expression. 2

8x + 3x – 5 = 0 2

8x + 8x – 5x – 5 = 0 8x ( x + 1 ) – 5 ( x + 1 ) = 0 ( x + 1 ) ( 8x – 5 ) = 0 Solving, for x + 1 = 0, x = −1; and, for 8x − 5 = 0, x = 5⁄8.


Machinery's Handbook 27th Edition SOLUTION OF EQUATIONS

33

Cubic Equations.—If the given equation has the form: x3 + ax + b = 0 then a 3 b 2⎞ x = ⎛ – b--- + ----- + ----⎝ 2 27 4 ⎠

1/3

a 3 b 2⎞ + ⎛ – b--- – ----- + ----⎝ 2 27 4 ⎠

1/3

The equation x3 + px2 + qx + r = 0, may be reduced to the form x13 + ax1 + b = 0 by substituting x 1 – p--- for x in the given equation. 3 Solving Numerical Equations Having One Unknown.—The Newton-Raphson method is a procedure for solving various kinds of numerical algebraic and transcendental equations in one unknown. The steps in the procedure are simple and can be used with either a handheld calculator or as a subroutine in a computer program. Examples of types of equations that can be solved to any desired degree of accuracy by this method are f ( x ) = x 2 – 101 = 0 , f ( x ) = x 3 – 2x 2 – 5 = 0 and f ( x ) = 2.9x – cos x – 1 = 0 The procedure begins with an estimate, r1, of the root satisfying the given equation. This estimate is obtained by judgment, inspection, or plotting a rough graph of the equation and observing the value r1 where the curve crosses the x axis. This value is then used to calculate values r2, r3, … , rn progressively closer to the exact value. Before continuing, it is necessary to calculate the first derivative. f ′(x), of the function. In the above examples, f ′(x) is, respectively, 2x, 3x2 − 4x, and 2.9 + sin x. These values were found by the methods described in Derivatives and Integrals of Functions on page 34. In the steps that follow, r1 is the first estimate of the value of the root of f(x) = 0; f(r1) is the value of f(x) for x = r1; f ′(x) is the first derivative of f(x); f ′(r1) is the value of f ′(x) for x = r1. The second approximation of the root of f(x) = 0, r2, is calculated from r 2 = r 1 – [ f ( r 1 ) ⁄ f ′( r 1 ) ] and, to continue further approximations, r n = r n – 1 – [ f ( r n – 1 ) ⁄ f ′( r n – 1 ) ] Example:Find the square root of 101 using the Newton-Raphson method. This problem can be restated as an equation to be solved, i.e., f ( x ) = x 2 – 101 = 0 Step 1. By inspection, it is evident that r1 = 10 may be taken as the first approximation of the root of this equation. Then, f ( r 1 ) = f ( 10 ) = 10 2 – 101 = – 1 Step 2. The first derivative, f ′(x), of x2 − 101 is 2x as stated previously, so that f ′(10) = 2(10) = 20. Then, r2 = r1 − f(r1)/f ′(r1) = 10 − (−1)/20 = 10 + 0.05 = 10.05 Check: 10.052 = 101.0025; error = 0.0025 Step 3. The next, better approximation is r 3 = r 2 – [ f ( r 2 ) ⁄ f ′( r 2 ) ] = 10.05 – [ f ( 10.05 ) ⁄ f ′( 10.05 ) ] = 10.05 – [ ( 10.05 2 – 101 ) ⁄ 2 ( 10.05 ) ] = 10.049875 Check:10.049875 2 = 100.9999875 ; error = 0.0000125



SERIES

Series.—Some hand calculations, as well as computer programs of certain types of mathematical problems, may be facilitated by the use of an appropriate series. For example, in some gear problems, the angle corresponding to a given or calculated involute function is found by using a series together with an iterative procedure such as the Newton-Raphson method described on page 33. The following are those series most commonly used for such purposes. In the series for trigonometric functions, the angles x are in radians (1 radian = 180/π degrees). The expression exp(−x2) means that the base e of the natural logarithm system is raised to the −x2 power; e = 2.7182818. (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16)

sin x = x − x3/3! + x5/5! − x7/7! + ··· cos x = 1 − x2/2! + x4 /4! − x6/6! + ··· tan x = x + x3/3 + 2x5/15 + 17x7/315 + 62x9/2835 + ··· arcsin x = x + x3/6 + 1 · 3 · x5/(2 · 4 · 5) + 1 · 3 · 5 · x7/(2 · 4 · 6 · 7) + ··· arccos x = π/2 − arcsin x arctan x = x − x3/3 + x5/5 − x7/7 + ··· π/4 =1 − 1/3 + 1/5 − 1/7 + 1/9 ··· ±1/(2x − 1)⫿ ··· e =1 + 1/1! + 2/2! + 1/3! + ··· ex =1 + x + x2/2! + x3/3! + ··· exp(− x2) = 1 − x2 + x4/2! − x6/3! + ··· ax = 1 + x loge a + (x loge a)2/2! + (x loge a)3/3! + ···

for all values of x. for all values of x. for |x| < π/2. for |x| ≤ 1. for |x| ≤ 1. for all values of x. for all values of x. for all values of x. for all values of x. for all values of x.

1/(1 + x) = 1 − x + x2 − x3 + x4 −··· 1/(1 − x) = 1 + x + x2 + x3 + x4 + ··· 1/(1 + x)2 = 1 − 2x + 3x2 − 4x3 + 5x4 − ··· 1/(1 − x)2 = 1 + 2x + 3x2 + 4x3 + 5x5 + ···

for |x| < 1. for |x| < 1. for |x| < 1. for |x| < 1. for |x| < 1.

( 1 + x ) = 1 + x/2 − x2/(2 · 4) + 1 · 3 · x3/(2 · 4 · 6)

− 1 · 3 · 5 · x4/(2 · 4 · 6 · 8) −··· 1 ⁄ ( 1 + x ) = 1 − x/2 + 1 · 3 · x2/(2 · 4) − 1 · 3 · 5 · x3/(2 · 4 · 6) + ···

for |x| < 1.

(18) (a + x)n = an + nan−1 x + n(n − 1)an−2 x2/2! + n(n − 1)(n − 2)an−3 x3/3! + ···

for x2 < a2.

(17)

Derivatives and Integrals of Functions.—The following are formulas for obtaining the derivatives and integrals of basic mathematical functions. In these formulas, the letters a and c denotes constants; the letter x denotes a variable; and the letters u and v denote functions of the variable x. The expression d/dx means the derivative with respect to x, and as such applies to whatever expression in parentheses follows it. Thus, d/dx (ax) means the derivative with respect to x of the product (ax) of the constant a and the variable x. Formulas for Differential and Integral Calculus Derivative

Value

Integral

Value

d (c) dx

0

∫ c dx

cx

d (x) dx

1

∫ 1 dx

d ( xn ) dx

nx

n–1

∫x

x n+1

n dx

x ----------n+1

d (g(u)) dx

d du g(u) du dx

∫ -------------ax + b

dx

1 --- log ax + b a

d (u(x) + v(x)) dx

d u(x) + d v(x) dx dx

∫ ( u ( x ) ± v ( x ) ) dx

∫ u ( x ) dx ± ∫ v ( x ) dx

d (u(x) × v(x)) dx

u(x) d v (x) + v(x) d u(x) dx dx

∫ u ( x )v ( x ) dx

u ( x )v ( x ) – ∫ v ( x ) du ( x )


Machinery's Handbook 27th Edition DERIVATIVES AND INTEGRALS

35

Formulas for Differential and Integral Calculus (Continued) Derivative

Value

Integral

Value

d ⎛ u---------( x )⎞ d x ⎝ v ( x )⎠

v(x) d u(x) – u(x) d v(x) dx dx -------------------------------------------------------------2 v(x)

dx ∫ ------x

2 x

d ( sin x ) dx

cos x

∫ cos x dx

sin x

d ( cos x ) dx

– sin x

∫ sin x dx

– cos x

d ( tan x ) dx

sec x

∫ tan x dx

– log cos x

d ( cot x ) dx

2

2

∫ cot x dx

– cosec x

log sin x ⎛ – 1---⎞ sin ( 2x ) + 1--- x ⎝ 4⎠ 2

d ( sec x ) dx

sec x tan x

∫ sin

d ( csc x ) dx

– csc x cot x

∫ cos

d ( ex ) dx

e

x

∫ e dx

d ( log x ) dx

1--x

∫ --x- dx

log x

d ( ax ) dx

a log a

x

a ---------log a

d ( asin x ) dx

1 ----------------2 1–x

∫ -------------------2 2

asin --xb

d ( acos x ) dx

–1 ----------------2 1–x

∫ -------------------2 2

dx

acosh --x- = log ( x + x – b ) b

d ( atan x ) dx

1 -------------2 1+x

∫ ---------------2 2 b +x

dx

1--- atan --xb b

d ( acot x ) dx

–1 ------------2 1+x

∫ b--------------2 2 –x

dx

– 1- log ------------------(x–b) --1- atanh --x- = ----b b 2b ( x + b )

d ( asec x ) dx

1 --------------------x x2 – 1

∫ --------------2 2 x –b

dx

1- log ------------------(x–b) – 1--- acoth --x- = ----b b 2b ( x + b )

d ( acsc x ) dx

–1 -------------------x x2 – 1

∫ ----------------------------ax 2 + bx + c

d ( log sin x ) dx

cot x

d ( log cos x ) dx

– tan x

d ( log tan x ) dx

2 ------------sin 2x

- dx ∫ --------sin x

1

log tan --x2

d ( log cot x ) dx

–2 -------------sin 2x

- dx ∫ ---------cos x

1

log tan ⎛⎝ π --- + --x-⎞⎠ 4 2

d ( x) dx

1--------2 x

- dx ∫ -------------------1 + cos x

1

x tan --2

d ( log x ) 10 dx

log 10 e --------------x

∫ log x dx

x log x – x

2

x dx

2

x dx

1--- sin ( 2x ) + 1--- x 4 2

x

1

∫a

x

dx

x –b

dx

∫e

2

2

2 ( 2ax + b ) ------------------------- atan ------------------------2 2 4ac – b 4ac – b

sin bx dx

(--------------------------------------------asin bx – b cos bx )- e ax 2 2 a +b

cos ( bx ) dx

( acos ( bx ) + b sin ( bx ) ) ax -------------------------------------------------------- e 2 2 a +b

ax

ax

x

x

dx

b –x

∫e

e



ARITHMATICAL PROGRESSION

GEOMETRY Arithmetical Progression An arithmetical progression is a series of numbers in which each consecutive term differs from the preceding one by a fixed amount called the common difference, d. Thus, 1, 3, 5, 7, etc., is an arithmetical progression where the difference d is 2. The difference here is added to the preceding term, and the progression is called increasing. In the series 13, 10, 7, 4, etc., the difference is ( −3), and the progression is called decreasing. In any arithmetical progression (or part of progression), let a =first term considered l =last term considered n =number of terms d =common difference S =sum of n terms Then the general formulas are l = a + ( n – 1 )d

and

+ -l × n S = a---------2

In these formulas, d is positive in an increasing and negative in a decreasing progression. When any three of the preceding live quantities are given, the other two can be found by the formulas in the accompanying table of arithmetical progression. Example:In an arithmetical progression, the first term equals 5, and the last term 40. The difference is 7. Find the sum of the progression. + -l l d + 40- ( 40 + 7 – 5 ) = 135 S = a---------( + – a ) = 5-------------2d 2×7 Geometrical Progression A geometrical progression or a geometrical series is a series in which each term is derived by multiplying the preceding term by a constant multiplier called the ratio. When the ratio is greater than 1, the progression is increasing; when less than 1, it is decreasing. Thus, 2, 6, 18, 54, etc., is an increasing geometrical progression with a ratio of 3, and 24, 12, 6, etc., is a decreasing progression with a ratio of 1⁄2. In any geometrical progression (or part of progression), let a =first term l =last (or nth) term n =number of terms r =ratio of the progression S =sum of n terms Then the general formulas are l = ar n – 1

and

– aS = rl -----------r–1

When any three of the preceding five quantities are given, the other two can be found by the formulas in the accompanying table. For instance, geometrical progressions are used for finding the successive speeds in machine tool drives, and in interest calculations. Example:The lowest speed of a lathe is 20 rpm. The highest speed is 225 rpm. There are 18 speeds. Find the ratio between successive speeds. n–1

Ratio r =

l --- = a

17

225 --------- = 20

17

11.25 = 1.153


Machinery's Handbook 27th Edition ARITHMATICAL PROGRESSION Formulas for Arithmetical Progression Given Use Equation

To Find

a = l – ( n – 1 )d

d

l

n

d

n

S

d

l

S

l

n

S

2S a = ------ – l n

a

l

n

l – ad = ----------n–1

a

n

S

– 2and = 2S --------------------n(n – 1)

a

l

S

l

n

S

a

d

n

a

d

S

l = – d--- ± 1--- 8dS + ( 2a – d ) 2 2 2

a

n

S

l = 2S ------ – a n

d

n

S

a

d

l

a

d

S

– 2a ± 1 8dS + ( 2a – d ) 2 n = d-------------- -----2d 2d

a

l

S

2S n = ---------a+l

d

l

S

+ d- ----1 n = 2l ------------± - ( 2l + d ) 2 – 8dS 2d 2d

a

d

n

S = n--- [ 2a + ( n – 1 )d ] 2

a

d

l

a

l

n

d

l

n

a

d

l

n

S

– 1- × d a = S--- – n----------n 2 a = d--- ± 1--- ( 2l + d ) 2 – 8dS 2 2

l2 – a2 d = ----------------------2S – l – a – 2Sd = 2nl -------------------n(n – 1) l = a + ( n – 1 )d

–1×d l = S--- + n----------n 2 l–a n = 1 + ---------d

a + l l2 – a2 + -l ( l + d – a ) S = ----------- + --------------- = a---------2 2d 2d S = n--- ( a + l ) 2 S = n--- [ 2l – ( n – 1 )d ] 2


37


ARITHMATICAL PROGRESSION

To Find l n a

Formulas for Geometrical Progression Given Use Equation l a = ----------n r rn – 1 r – 1 )Sa = (-----------------r S rn – 1

l

r

S

a = lr – ( r – 1 )S

l

n

S

a ( S – a )n – 1 = l ( S – l )n – 1

a

n

r

l = ar n – 1

a

r

S

l = 1--- [ a + ( r – 1 )S ] r

a

n

S

l ( S – l )n – 1 = a ( S – a )n – 1

n

r

S

a

l

r

a

r

S

a

l

S

l

r

S

a

l

n

a

n

S

a

l

S

l

n

S

a

n

r

a

l

r

a

l

n

n–1 n n–1 n l – aS = -------------------------------------n–1 l–n–1 a

l

n

r

l ( rn – 1 ) S = --------------------------( r – 1 )r n – 1

l

n

( r – 1 )r n – 1l = S------------------------------rn – 1 log l – log a- + 1 n = -------------------------log r log [ a + ( r – 1 )S ] – log an = ---------------------------------------------------------log r log l – log a n = ------------------------------------------------------ + 1 log ( S – a ) – log ( S – l ) log l – log [ lr – ( r – 1 )S -] + 1 n = ---------------------------------------------------------log r n–1

r

S

r =

--la

Sr a – S r n = ----- + -----------a a S–a r = -----------S–l n–1 l --------------- – --------r n = Sr S–l S–l

( r n – 1 )S = a--------------------r–1 lr – a S = ------------r–1


Machinery's Handbook 27th Edition STRAIGHT LINES

39

Analytical Geometry Straight Line.—A straight line is a line between two points with the minimum distance. Coordinate System: It is possible to locate any point on a plane by a pair of numbers called the coordinates of the point. If P is a point on a plane, and perpendiculars are drawn from P to the coordinate axes, one perpendicular meets the X–axis at the x– coordinate of P and the other meets the Y–axis at the y–coordinate of P. The pair of numbers (x1, y1), in that order, is called the coordinates or coordinate pair for P. 4

Y

3

P(x1,y1)

2 1

X −4

−3

−2 −1 −1

1

2

3

4

−2 −3 −4

Fig. 1. Coordinate Plan

Distance Between Two Points: The distance d between two points P1(x1,y1) and P2(x2,y2) is given by the formula: d ( P 1 ,P 2 ) =

2

( x2 – x1 ) + ( y2 – y1 )

2

Example 1:What is the distance AB between points A(4,5) and B(7,8)? Solution: The length of line AB is d =

2

2

(7 – 4) + (8 – 5) =

2

2

3 +3 =

18 = 3 2

Intermediate Point: An intermediate point, P(x, y) on a line between two points, P1(x1,y1) and P2(x2,y2), Fig. 2, can be obtained by linear interpolation as follows, r1 x1 + r2 x2 x = -------------------------r1 + r2

and

r1 y1 + r2 y2 y = -------------------------r1 + r2

where r1 is the ratio of the distance of P1 to P to the distance of P1 to P2, and r2 is the ratio of the distance of P2 to P to the distance of P1 to P2. If the desired point is the midpoint of line P1P2, then r1 = r2 = 1, and the coordinates of P are: x1 + x2 x = ---------------2

and

y1 + y2 y = ---------------2

Example 2:What is the coordinate of point P(x,y), if P divides the line defined by points A(0,0) and B(8,6) at the ratio of 5:3. 5×0+3×8 24 5×0+3×6 18 Solution: x = ------------------------------- = ------ = 3 y = ------------------------------- = ------ = 2.25 5+3 8 5+3 8



STRAIGHT LINES

External Point: A point, Q(x, y) on the line P1P2, and beyond the two points, P1(x1,y1) and P2(x2,y2), can be obtained by external interpolation as follows, r1 x1 – r2 x2 x = -------------------------r1 – r2

and

r1 y1 – r2 y2 y = -------------------------r1 – r2

where r1 is the ratio of the distance of P1 to Q to the distance of P1 to P2, and r2 is the ratio of the distance of P2 to Q to the distance of P1 to P2. Y Q (x, y) m2 m1

P2 (x2, y2 )

P(x, y)

P1 (x1,y 1) X

O

Fig. 2. Finding Intermediate and External Points on a Line

Equation of a line P1P2: The general equation of a line passing through points P1(x1,y1) x – x1 y – y1 and P2(x2,y2) is --------------- = ---------------. y1 – y2 x1 – x2 y1 – y2 The previous equation is frequently written in the form y – y 1 = --------------- ( x – x1 ) x1 – x2 y1 – y2 where --------------- is the slope of the line, m, and thus becomes y – y 1 = m ( x – x 1 ) where y1 x1 – x2 is the coordinate of the y-intercept (0, y1) and x1 is the coordinate of the x-intercept (x1, 0). If the line passes through point (0,0), then x1 = y1 = 0 and the equation becomes y = mx. The y-intercept is the y-coordinate of the point at which a line intersects the Y-axis at x = 0. The x-intercept is the x-coordinate of the point at which a line intersects the X-axis at y = 0. If a line AB intersects the X–axis at point A(a,0) and the Y–axis at point B(0,b) then the equation of line AB is --x- + --y- = 1 a b Slope: The equation of a line in a Cartesian coordinate system is y = mx + b, where x and y are coordinates of a point on a line, m is the slope of the line, and b is the y-intercept. The slope is the rate at which the x coordinates are increasing or decreasing relative to the y coordinates. Another form of the equation of a line is the point-slope form (y − y1) = m(x − x1). The slope, m, is defined as a ratio of the change in the y coordinates, y2 − y1, to the change in the x coordinates, x2 − x1, y2 – y1 m = ∆y ------ = --------------∆x x2 – x1


Machinery's Handbook 27th Edition STRAIGHT LINES

41

Example 3:What is the equation of a line AB between points A(4,5) and B(7,8)? Solution: x – x1 y – y1 --------------- = --------------y1 – y2 x1 – x2 y–5 x–4 ------------ = -----------5–8 4–7 y–5 = x–4 y–x = 1 Example 4:Find the general equation of a line passing through the points (3, 2) and (5, 6), and its intersection point with the y-axis. First, find the slope using the equation above ∆y 6–2 4 m = ------ = ------------ = --- = 2 ∆x 5–3 2 The line has a general form of y = 2x + b, and the value of the constant b can be determined by substituting the coordinates of a point on the line into the general form. Using point (3,2), 2 = 2 × 3 + b and rearranging, b = 2 − 6 = −4. As a check, using another point on the line, (5,6), yields equivalent results, y = 6 = 2 × 5 + b and b = 6 − 10 = −4. The equation of the line, therefore, is y = 2x − 4, indicating that line y = 2x − 4 intersects the y-axis at point (0,−4), the y-intercept. Example 5:Use the point-slope form to find the equation of the line passing through the point (3,2) and having a slope of 2. (y – 2) = 2(x – 3) y = 2x – 6 + 2 y = 2x – 4 The slope of this line is positive and crosses the y-axis at the y-intercept, point (0,−4). Parallel Lines: The two lines, P1P2 and Q1Q2, are parallel if both lines have the same slope, that is, if m1= m2. Y

Y

Q ( x ,y4 ) 2

Q ( x ,y4 ) 2 4

4

m2 m1

m1

Q1( x 3, y3 ) P1( x 1, y1 ) O Fig. 3. Parallel Lines

P2( x 2, y2 )

m2

P2( x 2, y2 )

P1( x 1, y1 ) X

Q1( x 3, y3 ) X

O Fig. 4. Perpendicular Lines

Perpendicular Lines: The two lines P1P2 and Q1Q2 are perpendicular if the product of their slopes equal −1, that is, m1m2 = −1. Example 6:Find an equation of a line that passes through the point (3,4) and is (a) parallel to and (b) perpendicular to the line 2x − 3y = 16? Solution (a): Line 2x − 3y = 16 in standard form is y = 2⁄3 x − 16⁄3, and the equation of a line passing through (3,4) is y – 4 = m ( x – 3 ) .



COORDINATE SYSTEMS

If the lines are parallel, their slopes are equal. Thus, y – 4 = 2--- ( x – 3 ) is parallel to line 3 2x − 3y = −6 and passes through point (3,4). Solution (b): As illustrated in part (a), line 2x − 3y = −6 has a slope of 2⁄3. The product of the slopes of perpendicular lines = −1, thus the slope m of a line passing through point (4,3) and perpendicular to 2x − 3y = −6 must satisfy the following: – 1 = –-----1- = – 3--m = -----2 2 m1 --3 The equation of a line passing through point (4,3) and perpendicular to the line 2x − 3y = 16 is y − 4 = −3⁄2(x − 3), which rewritten is 3x + 2y = 17. Angle Between Two Lines: For two non-perpendicular lines with slopes m1 and m2, the angle between the two lines is given by m1 – m2 tan θ = ---------------------1 + m1 m2 Note: The straight brackets surrounding a symbol or number, as in |x|, stands for absolute value and means use the positive value of the bracketed quantity, irrespective of its sign. Example 7:Find the angle between the following two lines: 2x − y = 4 and 3x + 4y =12 Solution: The slopes are 2 and −3⁄4, respectively. The angle between two lines is given by 3 8----------+ 32 – ⎛ – ---⎞ 2 + 3--⎝ 4⎠ m1 – m2 4 4 - = ----11- = 11 tan θ = ---------------------= = = -------------------------------------------------2 6 4 – 6 – 2 1 + m1 m2 3 1 – -------------1 + 2 ⎛ – ---⎞ ⎝ 4⎠ 4 4 θ = atan 11 ------ = 79.70° 2 Distance Between a Point and a Line: The distance between a point (x1,y1) and a line given by A x + B y + C = 0 is Ax 1 + By 1 + C d = ------------------------------------2 2 A +B Example 8:Find the distance between the point (4,6) and the line 2x + 3y − 9 = 0. Solution: The distance between a point and the line is Ax 1 + By 1 + C 2×4+3×6–9 8 + 18 – 9 17 d = ------------------------------------- = ------------------------------------------ = --------------------------- = ---------2 2 2 2 4 + 9 13 A +B 2 +3 Coordinate Systems.—Rectangular, Cartesian Coordinates: In a Cartesian coordinate system the coordinate axes are perpendicular to one another, and the same unit of length is chosen on the two axes. This rectangular coordinate system is used in the majority of cases. Polar Coordinates: Another coordinate system is determined by a fixed point O, the origin or pole, and a zero direction or axis through it, on which positive lengths can be laid off and measured, as a number line. A point P can be fixed to the zero direction line at a distance r away and then rotated in a positive sense at an angle θ. The angle, θ, in polar coordinates can take on values from 0° to 360°. A point in polar coordinates takes the form of (r, θ).


Machinery's Handbook 27th Edition COORDINATE SYSTEMS

43

Changing Coordinate Systems: For simplicity it may be assumed that the origin on a Cartesian coordinate system coincides with the pole on a polar coordinate system, and it’s axis with the x-axis. Then, if point P has polar coordinates of (r,θ) and Cartesian coordinates of (x, y), by trigonometry x = r × cos(θ) and y = r × sin(θ). By the Pythagorean theorem and trigonometry r =

2

x +y

y θ = atan -x

2

Example 1:Convert the Cartesian coordinate (3, 2) into polar coordinates. 2

r =

2

3 +2 =

9+4 =

θ = atan 2--- = 33.69° 3

13 = 3.6

Therefore the point (3.6, 33.69) is the polar form of the Cartesian point (3, 2). Graphically, the polar and Cartesian coordinates are related in the following figure (3, 2) 2

5

1

33.78 0 0

1

2

3

Example 2:Convert the polar form (5, 608) to Cartesian coordinates. By trigonometry, x = r × cos(θ) and y = r × sin(θ). Then x = 5 cos(608) = −1.873 and y = 5 sin(608) = −4.636. Therefore, the Cartesian point equivalent is (−1.873, −4.636). Spherical Coordinates: It is convenient in certain problems, for example, those concerned with spherical surfaces, to introduce non-parallel coordinates. An arbitrary point P in space can be expressed in terms of the distance r between point P and the origin O, the angle φ that OP′makes with the x–y plane, and the angle λ that the projection OP′ (of the segment OP onto the x–y plane) makes with the positive x-axis.

m

z

an idi er

z

pole

P

P

r

r

O ␭ P⬘

λ

eq u ator x

O

φ

y

x

y

The rectangular coordinates of a point in space can therefore be calculated by the formulas in the following table.



COORDINATE SYSTEMS Relationship Between Spherical and Rectangular Coordinates Spherical to Rectangular

Rectangular to Spherical

r =

x = r cos φ cos λ y = r cos φ sin λ z = r sin φ

2

2

x +y +z

2

z φ = atan -------------------2 2 x +y

(for x2 + y2 ≠ 0)

λ = atan y-x

(for x > 0, y > 0)

y λ = π + atan -x

(for x < 0)

λ = 2π + atan y-x

(for x > 0, y < 0)

Example 3:What are the spherical coordinates of the point P(3, −4, −12)? r =

2

2

2

3 + ( – 4 ) + ( – 12 ) = 13

– 12 - = atan – 12 φ = atan --------------------------------- = – 67.38° 5 2 2 3 + ( –4 ) 4 λ = 360° + atan – --- = 360° – 53.13° = 306.87° 3 The spherical coordinates of P are therefore r = 13, φ = − 67.38°, and λ = 306.87°. Cylindrical Coordinates: For problems on the surface of a cylinder it is convenient to use cylindrical coordinates. The cylindrical coordinates r, θ, z, of P coincide with the polar coordinates of the point P′ in the x-y plane and the rectangular z-coordinate of P. This gives the conversion formula. Those for θ hold only if x2 + y2 ≠ 0; θ is undetermined if x = y = 0. Cylindrical to Rectangular Rectangular to Cylindrical z

x = r cos θ y = r sin θ z = z

1 r = -------------------2 2 x +y x cos θ = -------------------2 2 x +y y sin θ = --------------------2 2 x +y z = z

P

O θ

r

x

P⬘

y

Example 4:Given the cylindrical coordinates of a point P, r = 3, θ = −30°, z = 51, find the rectangular coordinates. Using the above formulas x = 3cos (−30°) = 3cos (30°) = 2.598; y = 3sin (−30°) = −3 sin(30°) = −1.5; and z = 51. Therefore, the rectangular coordinates of point P are x = 2.598, y = −1.5, and z = 51.


Machinery's Handbook 27th Edition CIRCLE

45

Circle.—The general form for the equation of a circle is x2 + y2 + 2gx + 2fy + c = 0, where 2

−g and −f are the coordinates of the center and the radius is r = The center radius form of the circle equation is 2

2

Y

2

(x – h) + (y – k) = r where r = radius and point (h, k) is the center. When the center of circle is at point (0,0), the equation of 2

2

or

Center (h, k) r

2

circle reduces to x + y = r

2

g +f –c.

x2 + y2

r =

Example:Point (4,6) lies on a circle whose center is at (− 2,3). Find the circle equation? Solution: The radius is the distance between the center (− 2,3) and point (4,6), found using the method of Example 1 on page 39. 2

2

r = [ 4 – ( –2 ) ] + ( 6 – 3 ) = The equation of the circle is

2

2

6 +3 = 2

45 2

(x – h) + (y – k) = r 2

2

2

X

2

2

( x + 2 ) + ( y – 3 ) = x + 4x + 4 + y – 6y + 9 = 45 2

2

x + y + 4x – 6y – 32 = 0 Parabola.—A parabola is the set of all points P in the plane that are equidistant from focus F and a line called the directrix. A parabola is symmetric with respect to its parabolic axis. The line perpendicular to the parabolic axis which passing through the focus is known as latus rectum. 2

The general equation of a parabola is given by ( y – k ) = 4p ( x – h ) , where the vertex is located at point (h, k), the focus F is located at point (h + p, k), the directrix is located at x = h − p, and the latus rectum is located at x = h + p. Example:Determine the focus, directrix, axis, vertex, and latus rectum of the parabola 2

4y – 8x – 12y + 1 = 0 Solution: Format the equation into the general form of a parabolic equation Y

2

Directrix x = h − p

4y – 8x – 12y + 1 = 0 2

(y − k) = 4p(x − h)

2

4y – 12y = 8x – 1 2 1 y – 3y = 2x – --4 2 y – 2y 3--- + ⎛ 3---⎞ = 2x – 1--- + 9--2 ⎝ 2⎠ 4 4 2

⎛ y – 3---⎞ ⎝ 2⎠

2

= 2(x + 1)

Vertex (h, k) Focus (h + p, k)

V F

Parabolic axis

x=h X

Lectus rectum x = h + p

Parabola

Thus, k = 3⁄2, h = −1 and p = 1⁄2. Focus F is located at point (h + p, k) = ( 1⁄2, 3⁄2); the directrix is located at x = h − p = −1 − 1⁄2 = − 3⁄2; the parabolic axis is the horizontal line y = 3⁄2; the vertex V(h,k) is located at point (−1, 3⁄2); and the latus rectum is located at x = h + p = −1⁄2.



ELLIPSE

Ellipse.—The ellipse with eccentricity e, focus F and a directrix L is the set of all points P such that the distance PF is e times the distance from P to the line L. The general equation of an ellipse is 2

2

Ax + Cy + Dx + Ey + F = 0

AC > 0 and A ≠ C

The ellipse has two foci separated along the major axis by a distance 2c. The line passing through the focus perpendicular to the major axis is called the latus rectum. The line passing through the center, perpendicular to the major axis, is called the minor axis. The distances 2a and 2b are the major distance, and the minor distance.The ellipse is the locus of points such that the sum of the distances from the two foci to a point on the ellipse is 2a, thus, PF1 + PF2 = 2a Y

Minor axis

P b

V1

(h, k)

F1

V2 Major axis

F2

2

c 2= a 2 − b e=c/a

c a Latus rectum

Latus rectum

X

Ellipse 2

2

(x – h) y – k) - = 1 If (h,k) are the center, the general equation of an ellipse is ------------------ + (----------------2 2 a b 2

2

a –b The eccentricity of the ellipse, e = --------------------- , is always less than 1. a 2

2

The distance between the two foci is 2c = 2 a – b . The aspect ratio of the ellipse is a/b. 2

2

x y - = 1 , and the The equation of an ellipse centered at (0, 0) with foci at (±c, 0) is ---- + ---2 2 a b ellipse is symmetric about both coordinate axes. Its x-intercepts are (±a, 0) and y-intercepts are (0, ±b). The line joining (0, b) and (0, −b) is called the minor axis.The vertices of the ellipse are (±a, 0), and the line joining vertices is the major axis of the ellipse. Example:Determine the values of h, k, a, b, c, and e of the ellipse 2

2

3x + 5y – 12x + 30y + 42 = 0

Solution: Rearrange the ellipse equation into the general form as follows: 2

2

2

2

3x + 5y – 12x + 30y + 42 = 3x – 12x + 5y + 30y + 42 = 0 2

2

2

2

3 ( x – 4x + 2 ) + 5 ( y + 6y + 3 ) = 15 2

2

2

2

3(x – 2) y + 3)- = 1 ( y + 3 ) = (-----------------x – 2 ) - + (--------------------------------------- + 5---------------------2 2 15 15 ( 5) ( 3)


Machinery's Handbook 27th Edition HYPERBOLA

47 2

2

3

c =

x – h ) - + (----------------y – k ) - = 1 , and solving for c Comparing the result with the general form, (-----------------2 2 a b and e gives h = 2

k = –3

a =

5

b =

2

e =

2--5

Four-Arc Oval that Approximates an Ellipse*.—The method of constructing an approximate ellipse by circular arcs, described on page 57, fails when the ratio of the major to minor diameter equals four or greater. Additionally, it is reported that the method always draws a somewhat larger minor axes than intended. The method described below presents an alternative. An oval that approximates an ellipse, illustrated in Fig. 1, can be constructed from the following equations: B 2 ⎛ A⎞ 0.38 r = ------ --2A ⎝ B⎠

(1)

where A and B are dimensions of the major and minor axis, respectively, and r is the radius of the curve at the long ends. The radius R and its location are found from Equations (2) and (3): 2 2 A ------ – Ar + Br – B -----4 4 X = -------------------------------------------B – 2r

B R = -----------2+X

(2)

(3)

A

r

B R X

Fig. 1.

To make an oval thinner or fatter than that given, select a smaller or larger radius r than calculated by Equation (1) and then find X and R using Equations (2) and (3). Hyperbola.—The hyperbola with eccentricity e, focus F and a directrix L is the set of all points P such that the distance PF is e times the distance from P to the line L.The general equation of an hyperbola is 2

2

Ax + Cy + Dx + Ey + F = 0

AC < 0 and AC ≠ 0

The hyperbola has two foci separated along the transverse axis by a distance 2c. Lines perpendicular to the transverse axis passing through the foci are the conjugate axis. The distance between two vertices is 2a. The distance along a conjugate axis between two * Four-Arc Oval material contributed by Manfred K. Brueckner



HYPERBOLA

points on the hyperbola is 2b.The hyperbola is the locus of points such that the difference of the distances from the two foci is 2a, thus, PF2− PF1 = 2a 2

2

(x – h) (y – k) If point (h,k) is the center, the general equation of an ellipse is ------------------ – ------------------ = 1 2 2 a b Conjugate axis

Y

Asymptote

y − k = (b / a)(x − h)

V1 (h − a, k)

c 2 = a2 + b2 e = c /a V2 (h + a, k)

2b

Transverse axis

F1 (h − c, k)

F2 (h + c, k)

(h, k) 2a 2c

Asymptote y − k = − (b / a)(x − h)

X

Hyperbola 2

2

a +b The eccentricity of hyperbola, e = --------------------- is always less than 1. a 2

2

The distance between the two foci is 2c = 2 a + b . 2

2

x y The equation of a hyperbola with center at (0, 0) and focus at (±c, 0) is ----- – ----- = 1 . 2 2 a b Example:Determine the values of h, k, a, b, c, and e of the hyperbola 2

2

9x – 4y – 36x + 8y – 4 = 0 Solution: Convert the hyperbola equation into the general form 2

2

2

2

9x – 4y – 36x + 8y – 4 = ( 9x – 36x ) – ( 4y – 8y ) – 4 = 0 2

2

9 ( x – 4x + 4 ) – 4 ( y – 2y + 1 ) = 36 2

2

2

2

4(y – 1) (x – 2) (y – 1) x – 2 ) - – --------------------9 (------------------ = ------------------- – ------------------- = 1 2 2 36 36 2 3 2

2

(x – h) (y – k) Comparing the results above with the general form ------------------- – ------------------ = 1 and calcu2 2 a b 2

2

a +b lating the eccentricity from e = --------------------- and c from c = a h = 2

k = 1

a = 2

b = 3

c =

2

2

a + b gives 13

13 e = ---------2


Machinery's Handbook 27th Edition GEOMETRICAL PROPOSITIONS

49

Geometrical Propositions The sum of the three angles in a triangle always equals 180 degrees. Hence, if two angles are known, the third angle can always be found.

A

A + B + C = 180° B = 180° – ( A + C )

C

B

If one side and two angles in one triangle are equal to one side and similarly located angles in another triangle, then the remaining two sides and angle also are equal.

A A1 B

B1

a

a1

If a = a1, A = A1, and B = B1, then the two other sides and the remaining angle also are equal. If two sides and the angle between them in one triangle are equal to two sides and a similarly located angle in another triangle, then the remaining side and angles also are equal.

b1

b

A = 180° – ( B + C ) C = 180° – ( A + B )

A1

A a

If a = a1, b = b1, and A = A1, then the remaining side and angles also are equal.

a1

b

b1

If the three sides in one triangle are equal to the three sides of another triangle, then the angles in the two triangles also are equal. a

c

A

b

a1

c1

e

c

F E

B

C

D

If a = a1, b = b1, and c = c1, then the angles between the respective sides also are equal.

f

If the three sides of one triangle are proportional to corresponding sides in another triangle, then the triangles are called similar, and the angles in the one are equal to the angles in the other. If a : b : c = d : e : f, then A = D, B = E, and C = F.

d

a

f D

c A B b C a

e

F

E d

If the angles in one triangle are equal to the angles in another triangle, then the triangles are similar and their corresponding sides are proportional. If A = D, B = E, and C = F, then a : b : c = d : e : f.

If the three sides in a triangle are equal—that is, if the triangle is equilateral—then the three angles also are equal.

60 a

a 60

60 a

Each of the three equal angles in an equilateral triangle is 60 degrees. If the three angles in a triangle are equal, then the three sides also are equal.



GEOMETRICAL PROPOSITIONS Geometrical Propositions A

A line in an equilateral triangle that bisects or divides any of the angles into two equal parts also bisects the side opposite the angle and is at right angles to it. 30

30

90 C

1/ 2 a

B

1/ 2 a

a

b

D

If line AB divides angle CAD into two equal parts, it also divides line CD into two equal parts and is at right angles to it.

If two sides in a triangle are equal—that is, if the triangle is an isosceles triangle—then the angles opposite these sides also are equal. If side a equals side b, then angle A equals angle B.

B

A

b

a

If two angles in a triangle are equal, the sides opposite these angles also are equal. If angles A and B are equal, then side a equals side b.

B

A

a

b

1/ 2 B

90

B 1/ 2 b

1/ 2 b

In an isosceles triangle, if a straight line is drawn from the point where the two equal sides meet, so that it bisects the third side or base of the triangle, then it also bisects the angle between the equal sides and is perpendicular to the base.

b

a

b

B

A

a

a

If a is longer than b, then angle A is greater than B. If angle A is greater than B, then side a is longer than b.

In every triangle, the sum of the lengths of two sides is always greater than the length of the third.

c b

c

In every triangle, that angle is greater that is opposite a longer side. In every triangle, that side is greater which is opposite a greater angle.

Side a + side b is always greater than side c.

In a right-angle triangle, the square of the hypotenuse or the side opposite the right angle is equal to the sum of the squares on the two sides that form the right angle. a2 = b2 + c2

b



51

Geometrical Propositions If one side of a triangle is produced, then the exterior angle is equal to the sum of the two interior opposite angles.

A

Angle D = angle A + angle B

D

B

D

If two lines intersect, then the opposite angles formed by the intersecting lines are equal.

B

A

Angle A = angle B AngleC = angle D

C B

A

a A B

If a line intersects two parallel lines, then the corresponding angles formed by the intersecting line and the parallel lines are equal.

d

Lines ab and cd are parallel. Then all the angles designated A are equal, and all those designated B are equal.

B

A

c A

b

B

;; ;; ;; C

A B

D

A + B + C + D = 360 degrees

D

The sides that are opposite each other in a parallelogram are equal; the angles that are opposite each other are equal; the diagonal divides it into two equal parts. If two diagonals are drawn, they bisect each other.

1 /2

A

b

1 /2

B

In any figure having four sides, the sum of the interior angles equals 360 degrees.

d

a

A

A1

h

a

h1

a1

h

A

A1

Area A = area A 1

The areas of triangles having equal base and equal height are equal. If a = a1 and h = h1, then Area A = area A 1

If a diameter of a circle is at right angles to a chord, then it bisects or divides the chord into two equal parts.

1/ 2

c

90

h1

If a = a1 and h = h1, then

c

a1

1/ 2

a

The areas of two parallelograms that have equal base and equal height are equal.



GEOMETRICAL PROPOSITIONS Geometrical Propositions

If a line is tangent to a circle, then it is also at right angles to a line drawn from the center of the circle to the point of tangency— that is, to a radial line through the point of tangency.

90

Point of Tangency If two circles are tangent to each other, then the straight line that passes through the centers of the two circles must also pass through the point of tangency.

a A A

If from a point outside a circle, tangents are drawn to a circle, the two tangents are equal and make equal angles with the chord joining the points of tangency.

a

d The angle between a tangent and a chord drawn from the point of tangency equals one-half the angle at the center subtended by the chord.

A

B

Angle B = 1⁄2 angle A

d The angle between a tangent and a chord drawn from the point of tangency equals the angle at the periphery subtended by the chord.

A

B

b

Angle B, between tangent ab and chord cd, equals angle A subtended at the periphery by chord cd.

c

a

B

All angles having their vertex at the periphery of a circle and subtended by the same chord are equal.

C

A

d

c

A B

Angles A, B, and C, all subtended by chord cd, are equal.

If an angle at the circumference of a circle, between two chords, is subtended by the same arc as the angle at the center, between two radii, then the angle at the circumference is equal to one-half of the angle at the center. Angle A = 1⁄2 angle B



53

Geometrical Propositions A = Less than 90

B = More than 90

A

B

An angle subtended by a chord in a circular segment larger than one-half the circle is an acute angle—an angle less than 90 degrees. An angle subtended by a chord in a circular segment less than onehalf the circle is an obtuse angle—an angle greater than 90 degrees.

If two chords intersect each other in a circle, then the rectangle of the segments of the one equals the rectangle of the segments of the other.

c d

a

a×b = c×d

b

If from a point outside a circle two lines are drawn, one of which intersects the circle and the other is tangent to it, then the rectangle contained by the total length of the intersecting line, and that part of it that is between the outside point and the periphery, equals the square of the tangent.

a c b

a2 = b × c

If a triangle is inscribed in a semicircle, the angle opposite the diameter is a right (90-degree) angle. All angles at the periphery of a circle, subtended by the diameter, are right (90-degree) angles.

90

b a The lengths of circular arcs of the same circle are proportional to the corresponding angles at the center.

B A

A:B = a:b

b

a A r

B

The lengths of circular arcs having the same center angle are proportional to the lengths of the radii.

R If A = B, then a : b = r : R.

Circumf. = c Area = a

r

Circumf. = C Area = A

R

The circumferences of two circles are proportional to their radii. The areas of two circles are proportional to the squares of their radii. c:C = r:R a : A = r2 : R

2



GEOMETRICAL CONSTRUCTIONS Geometrical Constructions C

To divide a line AB into two equal parts:

A

With the ends A and B as centers and a radius greater than onehalf the line, draw circular arcs. Through the intersections C and D, draw line CD. This line divides AB into two equal parts and is also perpendicular to AB.

B

D

To draw a perpendicular to a straight line from a point A on that line:

D

B

With A as a center and with any radius, draw circular arcs intersecting the given line at B and C. Then, with B and C as centers and a radius longer than AB, draw circular arcs intersecting at D. Line DA is perpendicular to BC at A.

C

A

To draw a perpendicular line from a point A at the end of a line AB:

C D

A

With any point D, outside of the line AB, as a center, and with AD as a radius, draw a circular arc intersecting AB at E. Draw a line through E and D intersecting the arc at C; then join AC. This line is the required perpendicular.

E B

To draw a perpendicular to a line AB from a point C at a distance from it:

C A

E

F

B

D

5

To divide a straight line AB into a number of equal parts:

C

4 3 2 1 A

With C as a center, draw a circular arc intersecting the given line at E and F. With E and F as centers, draw circular arcs with a radius longer than one-half the distance between E and F. These arcs intersect at D. Line CD is the required perpendicular.

B

Let it be required to divide AB into five equal parts. Draw line AC at an angle with AB. Set off on AC five equal parts of any convenient length. Draw B–5 and then draw lines parallel with B–5 through the other division points on AC. The points where these lines intersect AB are the required division points.


Machinery's Handbook 27th Edition GEOMETRICAL CONSTRUCTIONS

55

Geometrical Constructions

E

To draw a straight line parallel to a given line AB, at a given distance from it:

F

A C

With any points C and D on AB as centers, draw circular arcs with the given distance as radius. Line EF, drawn to touch the circular arcs, is the required parallel line.

D B

D

B To bisect or divide an angle BAC into two equal parts: With A as a center and any radius, draw arc DE. With D and E as centers and a radius greater than one-half DE, draw circular arcs intersecting at F. Line AF divides the angle into two equal parts.

A F C

E

C

H

E

A

To draw an angle upon a line AB, equal to a given angle FGH:

L

B

D

G

K

F

To lay out a 60-degree angle:

E

C

With point G as a center and with any radius, draw arc KL. With A as a center and with the same radius, draw arc DE. Make arc DE equal to KL and draw AC through E. Angle BAC then equals angle FGH.

With A as a center and any radius, draw an arc BC. With point B as a center and AB as a radius, draw an arc intersecting at E the arc just drawn. EAB is a 60-degree angle.

A

G

A 30-degree angle may be obtained either by dividing a 60degree angle into two equal parts or by drawing a line EG perpendicular to AB. Angle AEG is then 30 degrees.

B

D E

To draw a 45-degree angle: From point A on line AB, set off a distance AC. Draw the perpendicular DC and set off a distance CE equal to AC. Draw AE. Angle EAC is a 45-degree angle.

A

C

B

C To draw an equilateral triangle, the length of the sides of which equals AB: With A and B as centers and AB as radius, draw circular arcs intersecting at C. Draw AC and BC. Then ABC is an equilateral triangle.

A

B



GEOMETRICAL CONSTRUCTIONS Geometrical Constructions C To draw a circular arc with a given radius through two given points A and B:

A

With A and B as centers, and the given radius as radius, draw circular arcs intersecting at C. With C as a center, and the same radius, draw a circular arc through A and B.

B

To find the center of a circle or of an arc of a circle:

R C D G A

B

E

E

F

C

To draw a tangent to a circle from a given point on the circumference:

A

F

B

C A

Select three points on the periphery of the circle, as A, B, and C. With each of these points as a center and the same radius, describe arcs intersecting each other. Through the points of intersection, draw lines DE and FG. Point H, where these lines intersect, is the center of the circle.

Through the point of tangency A, draw a radial line BC. At point A, draw a line EF at right angles to BC. This line is the required tangent.

To divide a circular arc AB into two equal parts:

B

E

With A and B as centers, and a radius larger than half the distance between A and B, draw circular arcs intersecting at C and D. Line CD divides arc AB into two equal parts at E.

D

C F A

To describe a circle about a triangle:

G B

E

Divide the sides AB and AC into two equal parts, and from the division points E and F, draw lines at right angles to the sides. These lines intersect at G. With G as a center and GA as a radius, draw circle ABC.

B To inscribe a circle in a triangle:

E

F D

A

Bisect two of the angles, A and B, by lines intersecting at D. From D, draw a line DE perpendicular to one of the sides, and with DE as a radius, draw circle EFG.

G


Machinery's Handbook 27th Edition GEOMETRICAL CONSTRUCTIONS

57

Geometrical Constructions A

B

To describe a circle about a square and to inscribe a circle in a square: The centers of both the circumscribed and inscribed circles are located at the point E, where the two diagonals of the square intersect. The radius of the circumscribed circle is AE, and of the inscribed circle, EF.

F E D

C

D

E To inscribe a hexagon in a circle:

A

B

C

F

Draw a diameter AB. With A and B as centers and with the radius of the circle as radius, describe circular arcs intersecting the given circle at D, E, F, and G. Draw lines AD, DE, etc., forming the required hexagon.

G

To describe a hexagon about a circle:

F

A

C

E

Draw a diameter AB, and with A as a center and the radius of the circle as radius, cut the circumference of the given circle at D. Join AD and bisect it with radius CE. Through E, draw FG parallel to AD and intersecting line AB at F. With C as a center and CF as radius, draw a circle. Within this circle, inscribe the hexagon as in the preceding problem.

B

D G

E

To describe an ellipse with the given axes AB and CD:

F

D e

G f g

A

B

O

C

D

Describe circles with O as a center and AB and CD as diameters. From a number of points, E, F, G, etc., on the outer circle, draw radii intersecting the inner circle at e, f, and g. From E, F, and G, draw lines perpendicular to AB, and from e, f, and g, draw lines parallel to AB. The intersections of these perpendicular and parallel lines are points on the curve of the ellipse.

To construct an approximate ellipse by circular arcs:

B K A M

F

E L

G O N

C H

P

Let AC be the major axis and BN the minor. Draw half circle ADC with O as a center. Divide BD into three equal parts and set off BE equal to one of these parts. With A and C as centers and OE as radius, describe circular arcs KLM and FGH; with G and L as centers, and the same radius, describe arcs FCH and KAM. Through F and G, drawn line FP, and with P as a center, draw the arc FBK. Arc HNM is drawn in the same manner.



GEOMETRICAL CONSTRUCTIONS Geometrical Constructions

6 5 4 3 2 1

B 1 2 3 4 5 6 C

To construct a parabola: Divide line AB into a number of equal parts and divide BC into the same number of parts. From the division points on AB, draw horizontal lines. From the division points on BC, draw lines to point A. The points of intersection between lines drawn from points numbered alike are points on the parabola.

A

To construct a hyperbola:

C

From focus F, lay off a distance FD equal to the transverse axis, or the distance AB between the two branches of the curve. With F as a center and any distance FE greater than FB as a radius, describe a circular arc. Then with F1 as a center and DE as a radius, describe arcs intersecting at C and G the arc just described. C and G are points on the hyperbola. Any number of points can be found in a similar manner.

A B F

F1 E

D

To construct an involute:

F 2

E

Divide the circumference of the base circle ABC into a number of equal parts. Through the division points 1, 2, 3, etc., draw tangents to the circle and make the lengths D–1, E–2, F–3, etc., of these tangents equal to the actual length of the arcs A–1, A–2, A–3, etc.

3

1 D A

C

1/ 2

Lead

6 5 4 3 2 1 0

2

3

4

5

1 0

6

To construct a helix: Divide half the circumference of the cylinder, on the surface of which the helix is to be described, into a number of equal parts. Divide half the lead of the helix into the same number of equal parts. From the division points on the circle representing the cylinder, draw vertical lines, and from the division points on the lead, draw horizontal lines as shown. The intersections between lines numbered alike are points on the helix.


Machinery's Handbook 27th Edition AREAS AND VOLUMES

59

Areas and Volumes The Prismoidal Formula.—The prismoidal formula is a general formula by which the volume of any prism, pyramid, or frustum of a pyramid may be found. A1 =area at one end of the body A2 =area at the other end Am =area of middle section between the two end surfaces h =height of body Then, volume V of the body is V = h--- ( A 1 + 4A m + A 2 ) 6 Pappus or Guldinus Rules.—By means of these rules the area of any surface of revolution and the volume of any solid of revolution may be found. The area of the surface swept out by the revolution of a line ABC (see illustration) about the axis DE equals the length of the line multiplied by the length of the path of its center of gravity, P. If the line is of such a shape that it is difficult to determine its center of gravity, then the line may be divided into a number of short sections, each of which may be considered as a straight line, and the areas swept out by these different sections, as computed by the rule given, may be added to find the total area. The line must lie wholly on one side of the axis of revolution and must be in the same plane.

The volume of a solid body formed by the revolution of a surface FGHJ about axis KL equals the area of the surface multiplied by the length of the path of its center of gravity. The surface must lie wholly on one side of the axis of revolution and in the same plane.

Example:By means of these rules, the area and volume of a cylindrical ring or torus may be found. The torus is formed by a circle AB being rotated about axis CD. The center of gravity of the circle is at its center. Hence, with the dimensions given in the illustration, the length of the path of the center of gravity of the circle is 3.1416 × 10 = 31.416 inches. Multiplying by the length of the circumference of the circle, which is 3.1416 × 3 = 9.4248 inches, gives 31.416 × 9.4248 = 296.089 square inches which is the area of the torus. The volume equals the area of the circle, which is 0.7854 × 9 = 7.0686 square inches, multiplied by the path of the center of gravity, which is 31.416, as before; hence, Volume = 7.0686 × 31.416 = 222.067 cubic inches



AREAS AND VOLUMES

Approximate Method for Finding the Area of a Surface of Revolution.—The accompanying illustration is shown in order to give an example of the approximate method based on Guldinus' rule, that can be used for finding the area of a symmetrical body. In the illustration, the dimensions in common fractions are the known dimensions; those in decimals are found by actual measurements on a figure drawn to scale. The method for finding the area is as follows: First, separate such areas as are cylindrical, conical, or spherical, as these can be found by exact formulas. In the illustration ABCD is a cylinder, the area of the surface of which can be easily found. The top area EF is simply a circular area, and can thus be computed separately. The remainder of the surface generated by rotating line AF about the axis GH is found by the approximate method explained in the previous section. From point A, set off equal distances on line AF. In the illustration, each division indicated is 1⁄8 inch long. From the central or middle point of each of these parts draw a line at right angles to the axis of rotation GH, measure the length of these lines or diameters (the length of each is given in decimals), add all these lengths together and multiply the sum by the length of one division set off on line AF (in this case, 1⁄8 inch), and multiply this product by π to find the approximate area of the surface of revolution. In setting off divisions 1⁄8 inch long along line AF, the last division does not reach exactly to point F, but only to a point 0.03 inch below it. The part 0.03 inch high at the top of the cup can be considered as a cylinder of 1⁄2 inch diameter and 0.03 inch height, the area of the cylindrical surface of which is easily computed. By adding the various surfaces together, the total surface of the cup is found as follows: Cylinder, 1 5⁄8 inch diameter, 0.41 inch high

2.093 square inches

Circle, 1⁄2 inch diameter

0.196 square inch

Cylinder, 1⁄2 inch diameter, 0.03 inch high

0.047 square inch

Irregular surface

3.868 square inches

Total

6.204 square inches

Area of Plane Surfaces of Irregular Outline.—One of the most useful and accurate methods for determining the approximate area of a plane figure or irregular outline is known as Simpson's Rule. In applying Simpson's Rule to find an area the work is done in four steps: 1) Divide the area into an even number, N, of parallel strips of equal width W; for example, in the accompanying diagram, the area has been divided into 8 strips of equal width. 2) Label the sides of the strips V0, V1, V2, etc., up to VN. 3) Measure the heights V0, V1, V2, … , VN of the sides of the strips. 4) Substitute the heights V0, V1, etc., in the following formula to find the area A of the figure:



61

A = W ----- [ ( V 0 + V N ) + 4 ( V 1 + V 3 + … + V N – 1 ) + 2 ( V 2 + V 4 + … + V N – 3 Example:The area of the accompanying figure was divided into 8 strips on a full-size drawing and the following data obtained. Calculate the area using Simpson's Rule. W = 1⁄2″ V0 =0″ V1 = 3⁄4″ V2 =11⁄4″ V3 =11⁄2″ V4 =15⁄8″ V5 =21⁄4″ V6 =21⁄2″ V7 =13⁄4″ V8 = 1⁄2″

Substituting the given data in the Simpson formula, 1 A = ---⁄2- [ ( 0 + 1⁄2 ) + 4 ( 3⁄4 + 1 1⁄2 + 2 1⁄4 + 1 3⁄4 ) + 2 ( 1 1⁄4 + 1 5⁄8 + 2 1⁄2 ) ] 3 = 1⁄6 [ ( 1⁄2 ) + 4 ( 6 1⁄4 ) + 2 ( 5 3⁄8 ) ] = 1⁄6 [ 36 1⁄4 ] = 6.04 square inches In applying Simpson's Rule, it should be noted that the larger the number of strips into which the area is divided the more accurate the results obtained. Areas Enclosed by Cycloidal Curves.—The area between a cycloid and the straight line upon which the generating circle rolls, equals three times the area of the generating circle (see diagram, page 66). The areas between epicycloidal and hypocycloidal curves and the “fixed circle” upon which the generating circle is rolled, may be determined by the following formulas, in which a = radius of the fixed circle upon which the generating circle rolls; b = radius of the generating circle; A = the area for the epicycloidal curve; and A1 = the area for the hypocycloidal curve.

2 ( 3a + 2b ) A = 3.1416b ---------------------------------------------a

3.1416b 2 ( 3a – 2b ) A 1 = ---------------------------------------------a

Find the Contents of Cylindrical Tanks at Different Levels.—In conjunction with the table Segments of Circles for Radius = 1 starting on page 71, the following relations can give a close approximation of the liquid contents, at any level, in a cylindrical tank.

A long measuring rule calibrated in length units or simply a plain stick can be used for measuring contents at a particular level. In turn, the rule or stick can be graduated to serve as a volume gauge for the tank in question. The only requirements are that the cross-section of the tank is circular; the tank's dimensions are known; the gauge rod is inserted vertically through the top center of the tank so that it rests on the exact bottom of the tank; and that consistent English or metric units are used throughout the calculations.



AREAS AND VOLUMES K =Cr2L = Tank Constant (remains the same for any given tank) VT =πK, for a tank that is completely full Vs =KA V =Vs when tank is less than half full V =VT − Vs = VT − KA, when tank is more than half full

(1) (2) (3) (4) (5)

where C =liquid volume conversion factor, the exact value of which depends on the length and liquid volume units being used during measurement: 0.00433 U.S. gal/in3; 7.48 U.S. gal/ft3; 0.00360 U.K. gal/in3; 6.23 U.K. gal/ft3; 0.001 liter/cm3; or 1000 liters/m3 VT =total volume of liquid tank can hold Vs =volume formed by segment of circle having depth = x in given tank (see diagram) V =volume of liquid at particular level in tank d =diameter of tank; L = length of tank; r = radius of tank ( = 1⁄2 diameter) A =segment area of a corresponding unit circle taken from the table starting on page 71 y =actual depth of contents in tank as shown on a gauge rod or stick x =depth of the segment of a circle to be considered in given tank. As can be seen in above diagram, x is the actual depth of contents (y) when the tank is less than half full, and is the depth of the void (d − y) above the contents when the tank is more than half full. From pages 71 and 74 it can also be seen that h, the height of a segment of a corresponding unit circle, is x/r Example:A tank is 20 feet long and 6 feet in diameter. Convert a long inch-stick into a gauge that is graduated at 1000 and 3000 U.S. gallons. L = 20 × 12 = 240in.

r = 6⁄2 × 12 = 36in.

From Formula (1): K = 0.00433(36)2(240) = 1346.80 From Formula (2): VT = 3.1416 × 1347 = 4231.1 US gal. The 72-inch mark from the bottom on the inch-stick can be graduated for the rounded full volume “4230”; and the halfway point 36″ for 4230⁄2 or “2115.” It can be seen that the 1000-gal mark would be below the halfway mark. From Formulas (3) and (4): 1000 A 1000 = ------------ = 0.7424 from the table starting on page 71, h can be interpolated as 1347 0.5724; and x = y = 36 × 0.5724 = 20.61. If the desired level of accuracy permits, interpolation can be omitted by choosing h directly from the table on page 71 for the value of A nearest that calculated above. Therefore, the 1000-gal mark is graduated 205⁄8″ from bottom of rod. It can be seen that the 3000 mark would be above the halfway mark. Therefore, the circular segment considered is the cross-section of the void space at the top of the tank. From Formulas (3) and (5): – 3000- = 0.9131 ; h= 0.6648 ; x = 36 × 0.6648 = 23.93″ A 3000 = 4230 ----------------------------1347 Therefore, the 3000-gal mark is 72.00 − 23.93 = 48.07, or at the 48 1⁄16″ mark from the bottom.



63

Areas and Dimensions of Plane Figures In the following tables are given formulas for the areas of plane figures, together with other formulas relating to their dimensions and properties; the surfaces of solids; and the volumes of solids. The notation used in the formulas is, as far as possible, given in the illustration accompanying them; where this has not been possible, it is given at the beginning of each set of formulas. Examples are given with each entry, some in English and some in metric units, showing the use of the preceding formula. Square: Area = A = s 2 = 1⁄2 d 2 s = 0.7071d =

A

d = 1.414s = 1.414 A

Example: Assume that the side s of a square is 15 inches. Find the area and the length of the diagonal. Area = A = s 2 = 15 2 = 225 square inches Diagonal = d = 1.414s = 1.414 × 15 = 21.21 inches

Example: The area of a square is 625 square inches. Find the length of the side s and the diagonal d. s =

A =

625 = 25 inches

d = 1.414 A = 1.414 × 25 = 35.35 inches

Rectangle: 2

2

2

Area = A = ab = a d – a = b d – b d =

a2

a =

d2 – b2 = A ÷ b

a =

d2 – a2 = A ÷ a

+

2

b2

Example: The side a of a rectangle is 12 centimeters, and the area 70.5 square centimeters. Find the length of the side b, and the diagonal d. b = A ÷ a = 70.5 ÷ 12 = 5.875 centimeters d =

a2 + b2 =

12 2 + 5.875 2 =

178.516 = 13.361 centimeters

Example: The sides of a rectangle are 30.5 and 11 centimeters long. Find the area. Area = A = a × b = 30.5 × 11 = 335.5 square centimeters

Parallelogram: Area = A = ab a = A÷b b = A÷a

Note: The dimension a is measured at right angles to line b. Example: The base b of a parallelogram is 16 feet. The height a is 5.5 feet. Find the area. Area = A = a × b = 5.5 × 16 = 88 square feet

Example: The area of a parallelogram is 12 square inches. The height is 1.5 inches. Find the length of the base b. b = A ÷ a = 12 ÷ 1.5 = 8 inches



AREAS AND VOLUMES

Right-Angled Triangle: bcArea = A = ----2 a =

b2 + c2

b =

a2 – c2

c =

a2 – b2

Example: The sides b and c in a right-angled triangle are 6 and 8 inches. Find side a and the area a = b 2 + c 2 = 6 2 + 8 2 = 36 + 64 = 100 = 10 inches × c = 6----------× 8- = 48 A = b---------------- = 24 square inches 2 2 2

Example: If a = 10 and b = 6 had been known, but not c, the latter would have been found as follows: c =

a2 – b2 =

10 2 – 6 2 =

100 – 36 =

64 = 8 inches

Acute-Angled Triangle: 2 + b2 – c2 2 2 Area = A = bh ------ = b--- a – ⎛ a---------------------------⎞ ⎝ ⎠ 2 2 2b

If S = 1⁄2 ( a + b + c ), then A =

S(S – a)(S – b)(S – c)

Example: If a = 10, b = 9, and c = 8 centimeters, what is the area of the triangle? b- a 2 – ⎛ --------------------------a 2 + b 2 – c 2-⎞ 2 = --9- 10 2 – ⎛ ------------------------------10 2 + 9 2 – 8 2-⎞ 2 = 4.5 100 – ⎛ -------117-⎞ 2 A = -⎝ ⎠ ⎝ ⎠ ⎝ 18 ⎠ 2 2b 2 2×9 = 4.5 100 – 42.25 = 4.5 57.75 = 4.5 × 7.60 = 34.20 square centimeters

Obtuse-Angled Triangle: 2 – a2 – b2 2 Area = A = bh ------ = b--- a 2 – ⎛ c---------------------------⎞ ⎝ ⎠ 2 2 2b

If S = 1⁄2 ( a + b + c ), then A =

S(S – a)(S – b)(S – c)

Example: The side a = 5, side b = 4, and side c = 8 inches. Find the area. S = 1⁄2 ( a + b + c ) = 1⁄2 ( 5 + 4 + 8 ) = 1⁄2 × 17 = 8.5 A = =

S(S – a)(S – b)(S – c) = 8.5 × 3.5 × 4.5 × 0.5 =

8.5 ( 8.5 – 5 ) ( 8.5 – 4 ) ( 8.5 – 8 )

66.937 = 8.18 square inches

Trapezoid: ( a + b )hArea = A = ------------------2

Note: In Britain, this figure is called a trapezium and the one below it is known as a trapezoid, the terms being reversed. Example: Side a = 23 meters, side b = 32 meters, and height h = 12 meters. Find the area. a + b )h- = (---------------------------23 + 32 )12- = 55 × 12- = 330 square meters A = (----------------------------------2 2 2



65

Trapezium: ( H + h )a + bh + cHArea = A = ----------------------------------------------2

A trapezium can also be divided into two triangles as indicated by the dashed line. The area of each of these triangles is computed, and the results added to find the area of the trapezium. Example: Let a = 10, b = 2, c = 3, h = 8, and H = 12 inches. Find the area. H + h )a + bh + cHA = (----------------------------------------------2 × 10 + 16 + 36- = = 20 -----------------------------------------2

( 12 + 8 )10 + 2 × 8 + 3 × 12= -----------------------------------------------------------------2 252 --------- = 126 square inches 2

Regular Hexagon: A =2.598s2 = 2.598R2 = 3.464r2 R = s = radius of circumscribed circle = 1.155r r =radius of inscribed circle = 0.866s = 0.866R s =R = 1.155r Example: The side s of a regular hexagon is 40 millimeters. Find the area and the radius r of the inscribed circle. A = 2.598s 2 = 2.598 × 40 2 = 2.598 × 1600 = 4156.8 square millimeters r = 0.866s = 0.866 × 40 = 34.64 millimeters

Example: What is the length of the side of a hexagon that is drawn around a circle of 50 millimeters radius? — Here r = 50. Hence, s = 1.155r = 1.155 × 50 = 57.75 millimeters

Regular Octagon: A =area = 4.828s2 = 2.828R2 = 3.3 14r2 R =radius of circumscribed circle = 1.307s = 1.082r r =radius of inscribed circle = 1.207s = 0.924R s =0.765R = 0.828r Example: Find the area and the length of the side of an octagon that is inscribed in a circle of 12 inches diameter. Diameter of circumscribed circle = 12 inches; hence, R = 6 inches. A = 2.828R 2 = 2.828 × 6 2 = 2.828 × 36 = 101.81 square inches s = 0.765R = 0.765 × 6 = 4.590 inches

Regular Polygon: A = area α = 360° ÷ n

n = number of sides β = 180° – α

s2 A = nsr -------- = ns ----- R 2 – ---2 2 4 R =

2

s r 2 + ---4

r =

2

R 2 – s---4

s = 2 R2 – r2

Example: Find the area of a polygon having 12 sides, inscribed in a circle of 8 centimeters radius. The length of the side s is 4.141 centimeters. 2 2 × 4.141 8 2 – 4.141 A = ns ----- R 2 – s---- = 12 ---------------------------------------- = 24.846 59.713 2 4 2 4 = 24.846 × 7.727 = 191.98 square centimeters



AREAS AND VOLUMES

Circle: Area = A = πr 2 = 3.1416r 2 = 0.7854d 2 Circumference = C = 2πr = 6.2832r = 3.1416d r = C ÷ 6.2832 =

A ÷ 3.1416 = 0.564 A

d = C ÷ 3.1416 =

A ÷ 0.7854 = 1.128 A

Length of arc for center angle of 1° = 0.008727d Length of arc for center angle of n° = 0.008727nd Example: Find the area A and circumference C of a circle with a diameter of 23⁄4 inches. A = 0.7854d 2 = 0.7854 × 2.75 2 = 0.7854 × 2.75 × 2.75 = 5.9396 square inches C = 3.1416d = 3.1416 × 2.75 = 8.6394 inches

Example: The area of a circle is 16.8 square inches. Find its diameter. d = 1.128 A = 1.128 16.8 = 1.128 × 4.099 = 4.624 inches

Circular Sector: × α × 3.1416- = 0.01745rα = 2A Length of arc = l = r---------------------------------------180 r Area = A = 1⁄2 rl = 0.008727αr 2 Angle, in degrees = α = 57.296 --------------------l r = 2A ------- = 57.296 --------------------l r l α

Example: The radius of a circle is 35 millimeters, and angle α of a sector of the circle is 60 degrees. Find the area of the sector and the length of arc l. A = 0.008727αr 2 = 0.008727 × 60 × 35 2 = 641.41mm 2 = 6.41cm 2 l = 0.01745rα = 0.01745 × 35 × 60 = 36.645 millimeters

Circular Segment: A = area

l = length of arc

c = 2 h ( 2r – h ) c 2 + 4h 2r = ------------------8h

α = angle, in degrees

A = 1⁄2 [ rl – c ( r – h ) ] l = 0.01745rα

h = r – 1⁄2 4r 2 – c 2 = r [ 1 – cos ( α ⁄ 2 ) ]

57.296 -l α = ------------------r

See also, Circular Segments starting on page 70. Example: The radius r is 60 inches and the height h is 8 inches. Find the length of the chord c. c = 2 h ( 2r – h ) = 2 8 × ( 2 × 60 – 8 ) = 2 896 = 2 × 29.93 = 59.86 inches

Example: If c = 16, and h = 6 inches, what is the radius of the circle of which the segment is a part? 2 + 4 × 62 c 2 + 4h 2- = 16 256 + 144- = -------400- = 8 1⁄ inches r = ---------------------------------------------- = ----------------------3 8h 8×6 48 48

Cycloid: Area = A = 3πr 2 = 9.4248r 2 = 2.3562d 2 = 3 × area of generating circle Length of cycloid = l = 8r = 4d

See also, Areas Enclosed by Cycloidal Curves on page 61. Example: The diameter of the generating circle of a cycloid is 6 inches. Find the length l of the cycloidal curve, and the area enclosed between the curve and the base line. l = 4d = 4 × 6 = 24 inches

A = 2.3562d 2 = 2.3562 × 6 2 = 84.82 square inches



67

Circular Ring: Area = A = π ( R 2 – r 2 ) = 3.1416 ( R 2 – r 2 ) = 3.1416 ( R + r ) ( R – r ) = 0.7854 ( D 2 – d 2 ) = 0.7854 ( D + d ) ( D – d )

Example: Let the outside diameter D = 12 centimeters and the inside diameter d = 8 centimeters. Find the area of the ring. A = 0.7854 ( D 2 – d 2 ) = 0.7854 ( 12 2 – 8 2 ) = 0.7854 ( 144 – 64 ) = 0.7854 × 80 = 62.83 square centimeters

By the alternative formula: A = 0.7854 ( D + d ) ( D – d ) = 0.7854 ( 12 + 8 ) ( 12 – 8 ) = 0.7854 × 20 × 4 = 62.83 square centimeters

Circular Ring Sector: A = area α = angle, in degrees απ- ( R 2 – r 2 ) = 0.00873α ( R 2 – r 2 ) A = -------360 απ - ( D 2 – d 2 ) = 0.00218α ( D 2 – d 2 ) = ----------------4 × 360

Example: Find the area, if the outside radius R = 5 inches, the inside radius r = 2 inches, and α = 72 degrees. A = 0.00873α ( R 2 – r 2 ) = 0.00873 × 72 ( 5 2 – 2 2 ) = 0.6286 ( 25 – 4 ) = 0.6286 × 21 = 13.2 square inches

Spandrel or Fillet:

2 Area = A = r 2 – πr -------- = 0.215r 2 = 0.1075c 2 4

Example: Find the area of a spandrel, the radius of which is 0.7 inch. A = 0.215r 2 = 0.215 × 0.7 2 = 0.105 square inch

Example: If chord c were given as 2.2 inches, what would be the area? A = 0.1075c 2 = 0.1075 × 2.2 2 = 0.520 square inch

Parabola: Area = A = 2⁄3 xy

(The area is equal to two-thirds of a rectangle which has x for its base and y for its height.) Example: Let x in the illustration be 15 centimeters, and y, 9 centimeters. Find the area of the shaded portion of the parabola. A = 2⁄3 × xy = 2⁄3 × 15 × 9 = 10 × 9 = 90 square centimeters



AREAS AND VOLUMES

Parabola: l = length of arc = p--2

2x 2x- + 1 + 2x ------ ⎛⎝ 1 + 2x ------⎞⎠ + ln ⎛⎝ ----------⎞⎠ p p p p

When x is small in proportion to y, the following is a close approximation: 2 4 l = y 1 + 2--- ⎛ x--⎞ – 2--- ⎛ x--⎞ or , l= 3 ⎝ y⎠ 5 ⎝ y⎠

y 2 + 4--- x 2 3

Example: If x = 2 and y = 24 feet, what is the approximate length l of the parabolic curve? 2 4 2-⎞ 2 – 2--- ⎛ ----2-⎞ 4 l = y 1 + 2--- ⎛⎝ x--⎞⎠ – 2--- ⎛⎝ x--⎞⎠ = 24 1 + 2--- ⎛⎝ ----3 y 5 y 3 24⎠ 5 ⎝ 24⎠

2- × -------1 - – --2- × ---------------1 = 24 1 + -= 24 × 1.0046 = 24.11 feet 3 144 5 20,736

Segment of Parabola: Area BFC = A = 2⁄3 area of parallelogram BCDE

If FG is the height of the segment, measured at right angles to BC, then: Area of segment BFC = 2⁄3 BC × FG

Example: The length of the chord BC = 19.5 inches. The distance between lines BC and DE, measured at right angles to BC, is 2.25 inches. This is the height of the segment. Find the area. Area = A = 2⁄3 BC × FG = 2⁄3 × 19.5 × 2.25 = 29.25 square inches

Hyperbola: x y xy ab Area BCD = A = ----- – ------ ln ⎛⎝ --- + ---⎞⎠ 2 2 a b

Example: The half-axes a and b are 3 and 2 inches, respectively. Find the area shown shaded in the illustration for x = 8 and y = 5. Inserting the known values in the formula: × 5- – 3----------× 2- × ln ⎛ 8--- + 5---⎞ = 20 – 3 × ln 5.167 A = 8----------⎝ 3 2⎠ 2 2 = 20 – 3 × 1.6423 = 20 – 4.927 = 15.073 square inches

Ellipse: Area = A = πab = 3.1416ab

An approximate formula for the perimeter is Perimeter = P = 3.1416 2 ( a 2 + b 2 )

A closer approximation is a – b ) 2P = 3.1416 2 ( a 2 + b 2 ) – (-----------------2.2

Example: The larger or major axis is 200 millimeters. The smaller or minor axis is 150 millimeters. Find the area and the approximate circumference. Here, then, a = 100, and b = 75. A = 3.1416ab = 3.1416 × 100 × 75 = 23,562 square millimeters = 235.62 square centimeters P = 3.1416 2 ( a 2 + b 2 ) = 3.1416 2 ( 100 2 + 75 2 ) = 3.1416 2 × 15,625 = 3.1416 31,250 = 3.1416 × 176.78 = 555.37 millimeters = ( 55.537 centimeters )


Machinery's Handbook 27th Edition REGULAR POLYGONS

69

Formulas and Table for Regular Polygons.—The following formulas and table can be used to calculate the area, length of side, and radii of the inscribed and circumscribed circles of regular polygons (equal sided). A = NS 2 cot α ÷ 4 = NR 2 sin α cos α = Nr 2 tan α r = R cos α = ( S cot α ) ÷ 2 =

( A × cot α ) ÷ N

R = S ÷ ( 2 sin α ) = r ÷ cos α =

A ÷ ( N sin α cos α )

S = 2R sin α = 2r tan α = 2 ( A × tan α ) ÷ N where N = number of sides; S = length of side; R = radius of circumscribed circle; r = radius of inscribed circle; A = area of polygon; and, α = 180° ÷ N = one-half center angle of one side. See also Regular Polygon on page 65. Area, Length of Side, and Inscribed and Circumscribed Radii of Regular Polygons No. A ----of S2 Sides 3 0.4330 4 1.0000 5 1.7205 6 2.5981 7 3.6339 8 4.8284 9 6.1818 10 7.6942 12 11.196 16 20.109 20 31.569 24 45.575 32 81.225 48 183.08 64 325.69

A -----R2

A ---r2

R --S

R --r

S --R

S --r

r --R

r --S

1.2990 2.0000 2.3776 2.5981 2.7364 2.8284 2.8925 2.9389 3.0000 3.0615 3.0902 3.1058 3.1214 3.1326 3.1365

5.1962 4.0000 3.6327 3.4641 3.3710 3.3137 3.2757 3.2492 3.2154 3.1826 3.1677 3.1597 3.1517 3.1461 3.1441

0.5774 0.7071 0.8507 1.0000 1.1524 1.3066 1.4619 1.6180 1.9319 2.5629 3.1962 3.8306 5.1011 7.6449 10.190

2.0000 1.4142 1.2361 1.1547 1.1099 1.0824 1.0642 1.0515 1.0353 1.0196 1.0125 1.0086 1.0048 1.0021 1.0012

1.7321 1.4142 1.1756 1.0000 0.8678 0.7654 0.6840 0.6180 0.5176 0.3902 0.3129 0.2611 0.1960 0.1308 0.0981

3.4641 2.0000 1.4531 1.1547 0.9631 0.8284 0.7279 0.6498 0.5359 0.3978 0.3168 0.2633 0.1970 0.1311 0.0983

0.5000 0.7071 0.8090 0.8660 0.9010 0.9239 0.9397 0.9511 0.9659 0.9808 0.9877 0.9914 0.9952 0.9979 0.9988

0.2887 0.5000 0.6882 0.8660 1.0383 1.2071 1.3737 1.5388 1.8660 2.5137 3.1569 3.7979 5.0766 7.6285 10.178

Example 1:A regular hexagon is inscribed in a circle of 6 inches diameter. Find the area and the radius of an inscribed circle. Here R = 3. From the table, area A = 2.5981R2 = 2.5981 × 9 = 23.3829 square inches. Radius of inscribed circle, r = 0.866R = 0.866 × 3 = 2.598 inches. Example 2:An octagon is inscribed in a circle of 100 millimeters diameter. Thus R = 50. Find the area and radius of an inscribed circle. A = 2.8284R2 = 2.8284 × 2500 = 7071 mm2 = 70.7 cm2. Radius of inscribed circle, r = 0.9239R = 09239 × 50 = 46.195 mm. Example 3:Thirty-two bolts are to be equally spaced on the periphery of a bolt-circle, 16 inches in diameter. Find the chordal distance between the bolts. Chordal distance equals the side S of a polygon with 32 sides. R = 8. Hence, S = 0.196R = 0.196 × 8 = 1.568 inch. Example 4:Sixteen bolts are to be equally spaced on the periphery of a bolt-circle, 250 millimeters diameter. Find the chordal distance between the bolts. Chordal distance equals the side S of a polygon with 16 sides. R = 125. Thus, S = 0.3902R = 0.3902 × 125 = 48.775 millimeters.



REGULAR POLYGONS

Circular Segments.—The table that follows gives the principle formulas for dimensions of circular segments. The dimensions are illustrated in the figures on pages 66 and 71. When two of the dimensions found together in the first column are known, the other dimensions are found by using the formulas in the corresponding row. For example, if radius r and chord c are known, solve for angle α using Equation (13), then use Equations (14) and (15) to solve for h and l, respectively. In these formulas, the value of α is in degrees between 0 and 180°. Formulas for Circular Segments Given

Formulas

α, r

c = 2r sin α --2

α, c

c r = -------------2 sin α

α, h

h r = --------------------α 1 – cos --2

α, l

r = 180 --------- --lπ α

(10)

α 360l sin --c = ----------------------2πα

r, c

⎛ 1 – c 2⎞ α = acos ⎜ --------------⎟ ⎝ 2R 2 ⎠

(13)

4r – c h = r – ---------------------2

r, h

α = 2 acos ⎛ 1 – h---⎞ (16) ⎝ r⎠

r, l

α = 180 --------- -l π r

c, h

α = 4 atan 2h -----c

Given

c, l

(1)

h = r ⎛ 1 – cos α ---⎞ ⎝ 2⎠

(2)

l = πrα ---------180

(4)

h = – --c- tan α 2

(5)

πcα l = -------------------α 360 sin --2

(7)

2h c = ----------α tan --4

(8)

(11)

πHα l = -----------------------------------α 180 ⎛ 1 – cos ---⎞ ⎝ ⎠ 2

(3)

(6)

(9)

α 180l ⎛ 1 – cos ---⎞ ⎝ 2⎠ h = --------------------------------------- (12) πα π- r asin ⎛ ----c⎞ l = ----⎝ 2r⎠ 90

(15)

c = 2 h ( 2r – h ) (17)

π r acos ⎛ 1 – h---⎞ l = ----⎝ r⎠ 90

(18)

(19)

90l c = 2r sin -------πR

(20)

90l h = r ⎛ 1 – cos --------⎞ ⎝ πr ⎠

(21)

(22)

+ 4h r = c------------------8H

(23)

2h c 2 + 4h 2 l = π ⎛⎝ --------------------⎞⎠ atan -----360h c

(24)

2

2

Formula To Find

360 α--------- -l- = ----------π c sin α --2

2

(14)

2

Given (25)

Solve Equation (25) for α by iterationa, then r =Equation (10) h =Equation (5)

h, l

Formula To Find

180 α --------- --l- = --------------------π h 1 – cos α --2

(26)

Solve Equation (26) for α by iterationa, then r =Equation (10) c =Equation (11)

a Equations (25) and (26) can not be easily solved by ordinary means. To solve these equations, test various values of α until the left side of the equation equals the right side. For example, if given c = 4 and l = 5, the left side of Equation (25) equals 143.24, and by testing various values of α it will be found that the right side equals 143.24 when α = 129.62°.

Angle α is in degrees, 0 < α < 180 Formulas for Circular Segments contributed by Manfred Brueckner


Machinery's Handbook 27th Edition SEGMENTS OF CIRCLES

71

Segments of Circles for Radius = 1.—Formulas for segments of circles are given on pages 66 and 70. When the central angle α and radius r are known, the tables on this and the following page can be used to find the length of arc l, height of segment h, chord length c, and segment area A. When angle α and radius r are not known, but segment l height h and chord length c are known or can be meah sured, the ratio h/c can be used to enter the table and find α, l, and A by linear interpolation. Radius r is found by c the formula on page 66 or 70. The value of l is then mul␣ tiplied by the radius r and the area A by r2, the square of r the radius. Angle α can be found thus with an accuracy of about 0.001 degree; arc length l with an error of about 0.02 per cent; and area A with an error ranging from about 0.02 per cent for the highest entry value of h/c to about 1 per cent for values of h/c of about 0.050. For lower values of h/c, and where greater accuracy is required, area A should be found by the formula on page 66. Segments of Circles for Radius = 1 (English or metric units) θ, Deg.

l

h

c

Area A

h/c

θ, Deg.

l

h

c

Area A

h/c

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

0.01745 0.03491 0.05236 0.06981 0.08727 0.10472 0.12217 0.13963 0.15708 0.17453 0.19199 0.20944 0.22689 0.24435 0.26180 0.27925 0.29671 0.31416 0.33161 0.34907 0.36652 0.38397 0.40143 0.41888 0.43633 0.45379 0.47124 0.48869 0.50615 0.52360 0.54105 0.55851 0.57596 0.59341 0.61087 0.62832 0.64577 0.66323 0.68068 0.69813

0.00004 0.00015 0.00034 0.00061 0.00095 0.00137 0.00187 0.00244 0.00308 0.00381 0.00460 0.00548 0.00643 0.00745 0.00856 0.00973 0.01098 0.01231 0.01371 0.01519 0.01675 0.01837 0.02008 0.02185 0.02370 0.02563 0.02763 0.02970 0.03185 0.03407 0.03637 0.03874 0.04118 0.04370 0.04628 0.04894 0.05168 0.05448 0.05736 0.06031

0.01745 0.03490 0.05235 0.06980 0.08724 0.10467 0.12210 0.13951 0.15692 0.17431 0.19169 0.20906 0.22641 0.24374 0.26105 0.27835 0.29562 0.31287 0.33010 0.34730 0.36447 0.38162 0.39874 0.41582 0.43288 0.44990 0.46689 0.48384 0.50076 0.51764 0.53448 0.55127 0.56803 0.58474 0.60141 0.61803 0.63461 0.65114 0.66761 0.68404

0.0000 0.0000 0.0000 0.0000 0.0001 0.0001 0.0002 0.0002 0.0003 0.0004 0.0006 0.0008 0.0010 0.0012 0.0015 0.0018 0.0022 0.0026 0.0030 0.0035 0.0041 0.0047 0.0053 0.0061 0.0069 0.0077 0.0086 0.0096 0.0107 0.0118 0.0130 0.0143 0.0157 0.0171 0.0186 0.0203 0.0220 0.0238 0.0257 0.0277

0.00218 0.00436 0.00655 0.00873 0.01091 0.01309 0.01528 0.01746 0.01965 0.02183 0.02402 0.02620 0.02839 0.03058 0.03277 0.03496 0.03716 0.03935 0.04155 0.04374 0.04594 0.04814 0.05035 0.05255 0.05476 0.05697 0.05918 0.06139 0.06361 0.06583 0.06805 0.07027 0.07250 0.07473 0.07696 0.07919 0.08143 0.08367 0.08592 0.08816

41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

0.71558 0.73304 0.75049 0.76794 0.78540 0.80285 0.82030 0.83776 0.85521 0.87266 0.89012 0.90757 0.92502 0.94248 0.95993 0.97738 0.99484 1.01229 1.02974 1.04720 1.06465 1.08210 1.09956 1.11701 1.13446 1.15192 1.16937 1.18682 1.20428 1.22173 1.23918 1.25664 1.27409 1.29154 1.30900 1.32645 1.34390 1.36136 1.37881 1.39626

0.06333 0.06642 0.06958 0.07282 0.07612 0.07950 0.08294 0.08645 0.09004 0.09369 0.09741 0.10121 0.10507 0.10899 0.11299 0.11705 0.12118 0.12538 0.12964 0.13397 0.13837 0.14283 0.14736 0.15195 0.15661 0.16133 0.16611 0.17096 0.17587 0.18085 0.18588 0.19098 0.19614 0.20136 0.20665 0.21199 0.21739 0.22285 0.22838 0.23396

0.70041 0.71674 0.73300 0.74921 0.76537 0.78146 0.79750 0.81347 0.82939 0.84524 0.86102 0.87674 0.89240 0.90798 0.92350 0.93894 0.95432 0.96962 0.98485 1.00000 1.01508 1.03008 1.04500 1.05984 1.07460 1.08928 1.10387 1.11839 1.13281 1.14715 1.16141 1.17557 1.18965 1.20363 1.21752 1.23132 1.24503 1.25864 1.27216 1.28558

0.0298 0.0320 0.0342 0.0366 0.0391 0.0418 0.0445 0.0473 0.0503 0.0533 0.0565 0.0598 0.0632 0.0667 0.0704 0.0742 0.0781 0.0821 0.0863 0.0906 0.0950 0.0996 0.1043 0.1091 0.1141 0.1192 0.1244 0.1298 0.1353 0.1410 0.1468 0.1528 0.1589 0.1651 0.1715 0.1781 0.1848 0.1916 0.1986 0.2057

0.09041 0.09267 0.09493 0.09719 0.09946 0.10173 0.10400 0.10628 0.10856 0.11085 0.11314 0.11543 0.11773 0.12004 0.12235 0.12466 0.12698 0.12931 0.13164 0.13397 0.13632 0.13866 0.14101 0.14337 0.14574 0.14811 0.15048 0.15287 0.15525 0.15765 0.16005 0.16246 0.16488 0.16730 0.16973 0.17216 0.17461 0.17706 0.17952 0.18199



SEGMENTS OF CIRCLES Segments of Circles for Radius = 1 (English or metric units) (Continued)

θ, Deg. 81

l 1.41372

h 0.23959

c 1.29890

Area A 0.2130

h/c 0.18446

θ, Deg. 131

l 2.28638

h 0.58531

c 1.81992

Area A 0.7658

h/c 0.32161

82

1.43117

0.24529

1.31212

0.2205

0.18694

132

2.30383

0.59326

1.82709

0.7803

0.32470

83

1.44862

0.25104

1.32524

0.2280

0.18943

133

2.32129

0.60125

1.83412

0.7950

0.32781

84

1.46608

0.25686

1.33826

0.2358

0.19193

134

2.33874

0.60927

1.84101

0.8097

0.33094

85

1.48353

0.26272

1.35118

0.2437

0.19444

135

2.35619

0.61732

1.84776

0.8245

0.33409

86

1.50098

0.26865

1.36400

0.2517

0.19696

136

2.37365

0.62539

1.85437

0.8395

0.33725

87

1.51844

0.27463

1.37671

0.2599

0.19948

137

2.39110

0.63350

1.86084

0.8546

0.34044

88

1.53589

0.28066

1.38932

0.2682

0.20201

138

2.40855

0.64163

1.86716

0.8697

0.34364

89

1.55334

0.28675

1.40182

0.2767

0.20456

139

2.42601

0.64979

1.87334

0.8850

0.34686

90

1.57080

0.29289

1.41421

0.2854

0.20711

140

2.44346

0.65798

1.87939

0.9003

0.35010

91

1.58825

0.29909

1.42650

0.2942

0.20967

141

2.46091

0.66619

1.88528

0.9158

0.35337

92

1.60570

0.30534

1.43868

0.3032

0.21224

142

2.47837

0.67443

1.89104

0.9314

0.35665

93

1.62316

0.31165

1.45075

0.3123

0.21482

143

2.49582

0.68270

1.89665

0.9470

0.35995

94

1.64061

0.31800

1.46271

0.3215

0.21741

144

2.51327

0.69098

1.90211

0.9627

0.36327

95

1.65806

0.32441

1.47455

0.3309

0.22001

145

2.53073

0.69929

1.90743

0.9786

0.36662

96

1.67552

0.33087

1.48629

0.3405

0.22261

146

2.54818

0.70763

1.91261

0.9945

0.36998

97

1.69297

0.33738

1.49791

0.3502

0.22523

147

2.56563

0.71598

1.91764

1.0105

0.37337

98

1.71042

0.34394

1.50942

0.3601

0.22786

148

2.58309

0.72436

1.92252

1.0266

0.37678

99

1.72788

0.35055

1.52081

0.3701

0.23050

149

2.60054

0.73276

1.92726

1.0428

0.38021

100

1.74533

0.35721

1.53209

0.3803

0.23315

150

2.61799

0.74118

1.93185

1.0590

0.38366

101

1.76278

0.36392

1.54325

0.3906

0.23582

151

2.63545

0.74962

1.93630

1.0753

0.38714

102

1.78024

0.37068

1.55429

0.4010

0.23849

152

2.65290

0.75808

1.94059

1.0917

0.39064

103

1.79769

0.37749

1.56522

0.4117

0.24117

153

2.67035

0.76655

1.94474

1.1082

0.39417

104

1.81514

0.38434

1.57602

0.4224

0.24387

154

2.68781

0.77505

1.94874

1.1247

0.39772

105

1.83260

0.39124

1.58671

0.4333

0.24657

155

2.70526

0.78356

1.95259

1.1413

0.40129

106

1.85005

0.39818

1.59727

0.4444

0.24929

156

2.72271

0.79209

1.95630

1.1580

0.40489

107

1.86750

0.40518

1.60771

0.4556

0.25202

157

2.74017

0.80063

1.95985

1.1747

0.40852

108

1.88496

0.41221

1.61803

0.4669

0.25476

158

2.75762

0.80919

1.96325

1.1915

0.41217

109

1.90241

0.41930

1.62823

0.4784

0.25752

159

2.77507

0.81776

1.96651

1.2084

0.41585

110

1.91986

0.42642

1.63830

0.4901

0.26028

160

2.79253

0.82635

1.96962

1.2253

0.41955

111

1.93732

0.43359

1.64825

0.5019

0.26306

161

2.80998

0.83495

1.97257

1.2422

0.42328

112

1.95477

0.44081

1.65808

0.5138

0.26585

162

2.82743

0.84357

1.97538

1.2592

0.42704

113

1.97222

0.44806

1.66777

0.5259

0.26866

163

2.84489

0.85219

1.97803

1.2763

0.43083

114

1.98968

0.45536

1.67734

0.5381

0.27148

164

2.86234

0.86083

1.98054

1.2934

0.43464

115

2.00713

0.46270

1.68678

0.5504

0.27431

165

2.87979

0.86947

1.98289

1.3105

0.43849

116

2.02458

0.47008

1.69610

0.5629

0.27715

166

2.89725

0.87813

1.98509

1.3277

0.44236

117

2.04204

0.47750

1.70528

0.5755

0.28001

167

2.91470

0.88680

1.98714

1.3449

0.44627

118

2.05949

0.48496

1.71433

0.5883

0.28289

168

2.93215

0.89547

1.98904

1.3621

0.45020

119

2.07694

0.49246

1.72326

0.6012

0.28577

169

2.94961

0.90415

1.99079

1.3794

0.45417

120

2.09440

0.50000

1.73205

0.6142

0.28868

170

2.96706

0.91284

1.99239

1.3967

0.45817

121

2.11185

0.50758

1.74071

0.6273

0.29159

171

2.98451

0.92154

1.99383

1.4140

0.46220

122

2.12930

0.51519

1.74924

0.6406

0.29452

172

3.00197

0.93024

1.99513

1.4314

0.46626

123

2.14675

0.52284

1.75763

0.6540

0.29747

173

3.01942

0.93895

1.99627

1.4488

0.47035

124

2.16421

0.53053

1.76590

0.6676

0.30043

174

3.03687

0.94766

1.99726

1.4662

0.47448

125

2.18166

0.53825

1.77402

0.6813

0.30341

175

3.05433

0.95638

1.99810

1.4836

0.47865

126

2.19911

0.54601

1.78201

0.6950

0.30640

176

3.07178

0.96510

1.99878

1.5010

0.48284

127

2.21657

0.55380

1.78987

0.7090

0.30941

177

3.08923

0.97382

1.99931

1.5184

0.48708

128

2.23402

0.56163

1.79759

0.7230

0.31243

178

3.10669

0.98255

1.99970

1.5359

0.49135

129

2.25147

0.56949

1.80517

0.7372

0.31548

179

3.12414

0.99127

1.99992

1.5533

0.49566

130

2.26893

0.57738

1.81262

0.7514

0.31854

180

3.14159

1.00000

2.00000

1.5708

0.50000


Machinery's Handbook 27th Edition CIRCLES AND SQUARES

73

Diameters of Circles and Sides of Squares of Equal Area The table below will be found useful for determining the diameter of a circle of an area equal to that of a square, the side of which is known, or for determining the side of a square which has an area equal to that of a circle, the area or diameter of which is known. For example, if the diameter of a circle is 171⁄2 inches, it is found from the table that the side of a square of the same area is 15.51 inches.

Diam. of Circle, D

Side of Square, S

Area of Circle or Square

Diam. of Circle, D

Side of Square, S


Diam. of Circle, D

Side of Square, S

1⁄ 2

0.44

0.196

201⁄2

18.17

330.06

401⁄2

35.89

1288.25

0.89

0.785

21

18.61

346.36

41

36.34

1320.25

1


11⁄2

1.33

1.767

211⁄2

19.05

363.05

411⁄2

36.78

1352.65

2

1.77

3.142

22

19.50

380.13

42

37.22

1385.44

19.94

397.61

421⁄2

37.66

1418.63

20.38

415.48

43

38.11

1452.20

21⁄2

2.22

4.909

221⁄2

3

2.66

7.069

23

31⁄2

3.10

9.621

231⁄2

20.83

433.74

431⁄2

38.55

1486.17

4

3.54

12.566

24

21.27

452.39

44

38.99

1520.53

41⁄2

3.99

15.904

241⁄2

21.71

471.44

441⁄2

39.44

1555.28

5

4.43

19.635

25

22.16

490.87

45

39.88

1590.43

51⁄2

4.87

23.758

251⁄2

22.60

510.71

451⁄2

40.32

1625.97

6

5.32

28.274

26

23.04

530.93

46

40.77

1661.90

61⁄2

5.76

33.183

261⁄2

23.49

551.55

461⁄2

41.21

1698.23

7

6.20

38.485

27

23.93

572.56

47

41.65

1734.94

71⁄2

6.65

44.179

271⁄2

24.37

593.96

471⁄2

42.10

1772.05

8

7.09

50.265

28

24.81

615.75

48

42.54

1809.56

25.26

637.94

481⁄2

42.98

1847.45

25.70

660.52

49

43.43

1885.74

81⁄2

7.53

56.745

281⁄2

9

7.98

63.617

29

91⁄2

8.42

70.882

291⁄2

26.14

683.49

491⁄2

43.87

1924.42

10

8.86

78.540

30

26.59

706.86

50

44.31

1963.50

101⁄2

9.31

86.590

301⁄2

27.03

730.62

501⁄2

44.75

2002.96

11

9.75

95.033

31

27.47

754.77

51

45.20

2042.82

111⁄2

10.19

103.87

311⁄2

27.92

779.31

511⁄2

45.64

2083.07

12

10.63

113.10

32

28.36

804.25

52

46.08

2123.72

121⁄2

11.08

122.72

321⁄2

28.80

829.58

521⁄2

46.53

2164.75

13

11.52

132.73

33

29.25

855.30

53

46.97

2206.18

131⁄2

11.96

143.14

331⁄2

29.69

881.41

531⁄2

47.41

2248.01

14

12.41

153.94

34

30.13

907.92

54

47.86

2290.22

141⁄2

12.85

165.13

341⁄2

30.57

934.82

541⁄2

48.30

2332.83

15

13.29

176.71

35

31.02

962.11

55

48.74

2375.83

151⁄2

13.74

188.69

351⁄2

31.46

989.80

551⁄2

49.19

2419.22

16

14.18

201.06

36

31.90

1017.88

56

49.63

2463.01

161⁄2

14.62

213.82

361⁄2

32.35

1046.35

561⁄2

50.07

2507.19

17

15.07

226.98

37

32.79

1075.21

57

50.51

2551.76

171⁄2

15.51

240.53

371⁄2

33.23

1104.47

571⁄2

50.96

2596.72

18

15.95

254.47

38

33.68

1134.11

58

51.40

2642.08

181⁄2

16.40

268.80

381⁄2

34.12

1164.16

581⁄2

51.84

2687.83

19

16.84

283.53

39

34.56

1194.59

59

52.29

2733.97

191⁄2

17.28

298.65

391⁄2

35.01

1225.42

591⁄2

52.73

2780.51

20

17.72

314.16

40

35.45

1256.64

60

53.17

2827.43



SQUARES AND HEXAGONS

Distance Across Corners of Squares and Hexagons.—The table below gives values of dimensions D and E described in the figures and equations that follow.

D

d

2 3-d = 1.154701d D = --------3

E

E = d 2 = 1.414214 d

A desired value not given directly in the table can be obtained directly from the equations above, or by the simple addition of two or more values taken directly from the table. Further values can be obtained by shifting the decimal point. Example 1: Find D when d = 2 5⁄16 inches. From the table, 2 = 2.3094, and 5⁄16 = 0.3608. Therefore, D = 2.3094 + 0.3608 = 2.6702 inches. Example 2: Find E when d = 20.25 millimeters. From the table, 20 = 28.2843; 0.2 = 0.2828; and 0.05 = 0.0707 (obtained by shifting the decimal point one place to the left at d = 0.5). Thus, E = 28.2843 + 0.2828 + 0.0707 = 28.6378 millimeters. Distance Across Corners of Squares and Hexagons (English and metric units) d

D

E

d

D

E

d

d

D

E

0.0361

0.0442

0.9

1.0392

1.2728

32

D 36.9504

E

1⁄ 32

45.2548

67

77.3650

94.7523

1⁄ 16

0.0722

0.0884

29⁄ 32

1.0464

1.2816

33

38.1051

46.6691

68

78.5197

96.1666

3⁄ 32

0.1083

0.1326

15⁄ 16

1.0825

1.3258

34

39.2598

48.0833

69

79.6744

97.5808

0.1

0.1155

0.1414

31⁄ 32

1.1186

1.3700

35

40.4145

49.4975

70

80.8291

98.9950

1⁄ 8

0.1443

0.1768

1.0

1.1547

1.4142

36

41.5692

50.9117

71

81.9838

100.409

5⁄ 32

0.1804

0.2210

2.0

2.3094

2.8284

37

42.7239

52.3259

72

83.1385

101.823

3⁄ 16

0.2165

0.2652

3.0

3.4641

4.2426

38

43.8786

53.7401

73

84.2932

103.238

0.2 7⁄ 32

0.2309 0.2526

0.2828 0.3094

4.0 5.0

4.6188 5.7735

5.6569 7.0711

39 40

45.0333 46.1880

55.1543 56.5686

74 75

85.4479 86.6026

104.652 106.066 107.480

1⁄ 4

0.2887

0.3536

6.0

6.9282

8.4853

41

47.3427

57.9828

76

87.7573

9⁄ 32

0.3248

0.3977

7.0

8.0829

9.8995

42

48.4974

59.3970

77

88.9120

108.894

0.3 5⁄ 16

0.3464 0.3608

0.4243 0.4419

8.0 9.0

9.2376 10.3923

11.3137 12.7279

43 44

49.6521 50.8068

60.8112 62.2254

78 79

90.0667 91.2214

110.309 111.723

11⁄ 32

0.3969

0.4861

10

11.5470

14.1421

45

51.9615

63.6396

80

92.3761

113.137

3⁄ 8

0.4330

0.5303

11

12.7017

15.5564

46

53.1162

65.0538

81

93.5308

114.551

0.4 13⁄ 32

0.4619 0.4691

0.5657 0.5745

12 13

13.8564 15.0111

16.9706 18.3848

47 48

54.2709 55.4256

66.4681 67.8823

82 83

94.6855 95.8402

115.966 117.380 118.794

7⁄ 16

0.5052

0.6187

14

16.1658

19.7990

49

56.5803

69.2965

84

96.9949

15⁄ 32

0.5413

0.6629

15

17.3205

21.2132

50

57.7351

70.7107

85

98.1496

120.208

0.5 17⁄ 32

0.5774 0.6134

0.7071 0.7513

16 17

18.4752 19.6299

22.6274 24.0416

51 52

58.8898 60.0445

72.1249 73.5391

86 87

99.3043 100.459

121.622 123.037 124.451

9⁄ 16

0.6495

0.7955

18

20.7846

25.4559

53

61.1992

74.9533

88

101.614

19⁄ 32

0.6856

0.8397

19

21.9393

26.8701

54

62.3539

76.3676

89

102.768

125.865

0.6 5⁄ 8

0.6928 0.7217

0.8485 0.8839

20 21

23.0940 24.2487

28.2843 29.6985

55 56

63.5086 64.6633

77.7818 79.1960

90 91

103.923 105.078

127.279 128.693

21⁄ 32

0.7578

0.9281

22

25.4034

31.1127

57

65.8180

80.6102

92

106.232

130.108

11⁄ 16

0.7939

0.9723

23

26.5581

32.5269

58

66.9727

82.0244

93

107.387

131.522

0.7 23⁄ 32

0.8083 0.8299

0.9899 1.0165

24 25

27.7128 28.8675

33.9411 35.3554

59 60

68.1274 69.2821

83.4386 84.8528

94 95

108.542 109.697

132.936 134.350 135.765

3⁄ 4

0.8660

1.0607

26

30.0222

36.7696

61

70.4368

86.2671

96

110.851

25⁄ 32

0.9021

1.1049

27

31.1769

38.1838

62

71.5915

87.6813

97

112.006

137.179

0.8 13⁄ 16

0.9238 0.9382

1.1314 1.1490

28 29

32.3316 33.4863

39.5980 41.0122

63 64

72.7462 73.9009

89.0955 90.5097

98 99

113.161 114.315

138.593 140.007

27⁄ 32

0.9743

1.1932

30

34.6410

42.4264

65

75.0556

91.9239

100

115.470

141.421

7⁄ 8

1.0104

1.2374

31

35.7957

43.8406

66

76.2103

93.3381

…

…

…


Machinery's Handbook 27th Edition VOLUMES OF SOLIDS

75

Volumes of Solids Cube: Diagonal of cube face = d = s 2 Diagonal of cube = D =

3d 2 --------- = s 3 = 1.732s 2

Volume = V = s 3 s =

3

V

Example: The side of a cube equals 9.5 centimeters. Find its volume. Volume = V = s 3 = 9.5 3 = 9.5 × 9.5 × 9.5 = 857.375 cubic centimeters

Example: The volume of a cube is 231 cubic centimeters. What is the length of the side? s =

3

V =

3

231 = 6.136 centimeters

Square Prism:

Va = ----bc

Volume = V = abc VVb = ----c = ----ac ab

Example: In a square prism, a = 6, b = 5, c = 4. Find the volume. V = a × b × c = 6 × 5 × 4 = 120 cubic inches

Example: How high should a box be made to contain 25 cubic feet, if it is 4 feet long and 21⁄2 feet wide? Here, a = 4, c = 2.5, and V = 25. Then, V25 b = depth = ----= ---------------- = 25 ------ = 2.5 feet ac 4 × 2.5 10

Prism: V =volume A =area of end surface V =h × A The area A of the end surface is found by the formulas for areas of plane figures on the preceding pages. Height h must be measured perpendicular to the end surface. Example: A prism, having for its base a regular hexagon with a side s of 7.5 centimeters, is 25 centimeters high. Find the volume. Area of hexagon = A = 2.598s 2 = 2.598 × 56.25 = 146.14 square centimeters Volume of prism = h × A = 25 × 146.14 = 3653.5 cubic centimeters

Pyramid: Volume = V = 1⁄3 h × area of base

If the base is a regular polygon with n sides, and s = length of side, r = radius of inscribed circle, and R = radius of circumscribed circle, then: nsrhnsh s2 V = ----------= --------- R 2 – ---6 6 4

Example: A pyramid, having a height of 9 feet, has a base formed by a rectangle, the sides of which are 2 and 3 feet, respectively. Find the volume. Area of base = 2 × 3 = 6 square feet; h = 9 feet Volume = V = 1⁄3 h × area of base = 1⁄3 × 9 × 6 = 18 cubic feet



VOLUMES OF SOLIDS

Frustum of Pyramid:

Volume = V = h--- ( A 1 + A 2 + A 1 × A 2 ) 3

Example: The pyramid in the previous example is cut off 41⁄2 feet from the base, the upper part being removed. The sides of the rectangle forming the top surface of the frustum are, then, 1 and 11⁄2 feet long, respectively. Find the volume of the frustum. Area of top = A 1 = 1 × 1 1⁄2 = 1 1⁄2 sq. ft.

Area of base = A 2 = 2 × 3 = 6 sq. ft.

⋅ 5- ( 1.5 + 6 + 1.5 × 6 ) = 1.5 ( 7.5 + 9 ) = 1.5 × 10.5 = 15.75 cubic feet V = 4--------3

Wedge: ( 2a + c )bhVolume = V = -------------------------6

Example: Let a = 4 inches, b = 3 inches, and c = 5 inches. The height h = 4.5 inches. Find the volume. 2a + c )bh- = (-----------------------------------------------2 × 4 + 5 ) × 3 × 4.5- = (--------------------------------8 + 5 ) × 13.5V = (-------------------------6 6 6 = 175.5 ------------- = 29.25 cubic inches 6

Cylinder: Volume = V = 3.1416r 2 h = 0.7854d 2 h Area of cylindrical surface = S = 6.2832rh = 3.1416dh

Total area A of cylindrical surface and end surfaces: A = 6.2832r ( r + h ) = 3.1416d ( 1⁄2 d + h )

Example: The diameter of a cylinder is 2.5 inches. The length or height is 20 inches. Find the volume and the area of the cylindrical surface S. V = 0.7854d 2 h = 0.7854 × 2.5 2 × 20 = 0.7854 × 6.25 × 20 = 98.17 cubic inches S = 3.1416dh = 3.1416 × 2.5 × 20 = 157.08 square inches

Portion of Cylinder: Volume = V = 1.5708r 2 ( h 1 + h 2 ) = 0.3927d 2 ( h 1 + h 2 ) Cylindrical surface area = S = 3.1416r ( h 1 + h 2 ) = 1.5708d ( h 1 + h 2 )

Example: A cylinder 125 millimeters in diameter is cut off at an angle, as shown in the illustration. Dimension h1 = 150, and h2 = 100 mm. Find the volume and the area S of the cylindrical surface. V = 0.3927d 2 ( h 1 + h 2 ) = 0.3927 × 125 2 × ( 150 + 100 ) = 0.3927 × 15 ,625 × 250 = 1 ,533 ,984 cubic millimeters = 1534 cm 3 S = 1.5708d ( h 1 + h 2 ) = 1.5708 × 125 × 250 = 49 ,087.5 square millimeters = 490.9 square centimeters



77

Portion of Cylinder: hVolume = V = ( 2⁄3 a 3 ± b × area ABC ) ---------r±b h Cylindrical surface area = S = ( ad ± b × length of arc ABC ) ----------r±b

Use + when base area is larger, and − when base area is less than one-half the base circle. Example: Find the volume of a cylinder so cut off that line AC passes through the center of the base circle — that is, the base area is a half-circle. The diameter of the cylinder = 5 inches, and the height h = 2 inches. In this case, a = 2.5; b = 0; area ABC = 0.5 × 0.7854 × 52 = 9.82; r = 2.5. 2 V = ⎛ 2--- × 2.5 3 + 0 × 9.82⎞ ---------------= 2--- × 15.625 × 0.8 = 8.33 cubic inches ⎝3 ⎠ 2.5 + 0 3

Hollow Cylinder: Volume = V = = = =

3.1416h ( R 2 – r 2 ) = 0.7854h ( D 2 – d 2 ) 3.1416ht ( 2R – t ) = 3.1416ht ( D – t ) 3.1416ht ( 2r + t ) = 3.1416ht ( d + t ) 3.1416ht ( R + r ) = 1.5708ht ( D + d )

Example: A cylindrical shell, 28 centimeters high, is 36 centimeters in outside diameter, and 4 centimeters thick. Find its volume. V = 3.1416ht ( D – t ) = 3.1416 × 28 × 4 ( 36 – 4 ) = 3.1416 × 28 × 4 × 32 = 11 ,259.5 cubic centimeters

Cone: 2 Volume = V = 3.1416r ------------------------h- = 1.0472r 2 h = 0.2618d 2 h 3

Conical surface area = A = 3.1416r r 2 + h 2 = 3.1416rs = 1.5708ds s =

d----2- + h 2 4

r2 + h2 =

Example: Find the volume and area of the conical surface of a cone, the base of which is a circle of 6 inches diameter, and the height of which is 4 inches. V = 0.2618d 2 h = 0.2618 × 6 2 × 4 = 0.2618 × 36 × 4 = 37.7 cubic inches A = 3.1416r r 2 + h 2 = 3.1416 × 3 × 3 2 + 4 2 = 9.4248 × 25 = 47.124 square inches

Frustum of Cone: V = volume

A = area of conical surface

V = 1.0472h ( R 2 + Rr + r 2 ) = 0.2618h ( D 2 + Dd + d 2 ) A = 3.1416s ( R + r ) = 1.5708s ( D + d ) a = R–r

s =

a2 + h2 =

( R – r )2 + h2

Example: Find the volume of a frustum of a cone of the following dimensions: D = 8 centimeters; d = 4 centimeters; h = 5 centimeters. V = 0.2618 × 5 ( 8 2 + 8 × 4 + 4 2 ) = 0.2618 × 5 ( 64 + 32 + 16 ) = 0.2618 × 5 × 112 = 146.61 cubic centimeters



VOLUMES OF SOLIDS

Sphere: 3 4πr 3- = πd --------- = 4.1888r 3 = 0.5236d 3 Volume = V = ----------3 6

Surface area = A = 4πr 2 = πd 2 = 12.5664r 2 = 3.1416d 2 r =

3

3V ------- = 0.6024 3 V 4π

Example: Find the volume and the surface of a sphere 6.5 centimeters diameter. V = 0.5236d 3 = 0.5236 × 6.5 3 = 0.5236 × 6.5 × 6.5 × 6.5 = 143.79 cm 3 A = 3.1416d 2 = 3.1416 × 6.5 2 = 3.1416 × 6.5 × 6.5 = 132.73 cm 2

Example: The volume of a sphere is 64 cubic centimeters. Find its radius. r = 0.6204 3 64 = 0.6204 × 4 = 2.4816 centimeters

Spherical Sector: 2πr 2 h- = 2.0944r 2 h = Volume V = -------------3 A = 3.1416r ( 2h + 1⁄2 c ) = total area of conical and spherical surface c = 2 h ( 2r – h )

Example: Find the volume of a sector of a sphere 6 inches in diameter, the height h of the sector being 1.5 inch. Also find the length of chord c. Here r = 3 and h = 1.5. V = 2.0944r 2 h = 2.0944 × 3 2 × 1.5 = 2.0944 × 9 × 1.5 = 28.27 cubic inches c = 2 h ( 2r – h ) = 2 1.5 ( 2 × 3 – 1.5 ) = 2 6.75 = 2 × 2.598 = 5.196 inches

Spherical Segment: V = volume V =

A = area of spherical surface 2 2 – h---⎞ = 3.1416h ⎛ c----- + h-----⎞ ⎝ 3⎠ ⎝8 6⎠

3.1416h 2 ⎛ r

c 2- + h 2⎞ A = 2πrh = 6.2832rh = 3.1416 ⎛⎝ ---⎠ 4 c = 2 h ( 2r – h ) ;

2 + 4h 2 r = c------------------8h

Example: A segment of a sphere has the following dimensions: h = 50 millimeters; c = 125 millimeters. Find the volume V and the radius of the sphere of which the segment is a part. 2

2

125 50 -⎞ = 157.08 × ⎛ ---------------15 ,625 + ----------2500-⎞ = 372 ,247 mm 3 = 372 cm 3 V = 3.1416 × 50 × ⎛ ---------- + ------⎝ 8 ⎝ 8 6 ⎠ 6 ⎠ 2 + 4 × 50 2 ,625 + 10 ,000- = 25 ,625 = 64 millimeters r = 125 ----------------------------------= 15 -----------------------------------------------------8 × 50 400 400

Ellipsoid: Volume = V = 4π ------abc = 4.1888abc 3

In an ellipsoid of revolution, or spheroid, where c = b: V = 4.1888ab 2

Example: Find the volume of a spheroid in which a = 5, and b = c = 1.5 inches. V = 4.1888 × 5 × 1.5 2 = 47.124 cubic inches



79

Spherical Zone: 3c 2 3c 2 Volume = V = 0.5236h ⎛ --------1 + --------2 + h 2⎞ ⎝ 4 ⎠ 4 A = 2πrh = 6.2832rh = area of spherical surface r =

c 22 ⎛ c 22 – c 12 – 4h 2⎞ 2 ----- + ------------------------------⎠ 8h 4 ⎝

Example: In a spherical zone, let c1 = 3; c2 = 4; and h = 1.5 inch. Find the volume. × 3 2 + -------------3 × 4 2 + 1.5 2⎞ = 0.5236 × 1.5 × ⎛ 27 V = 0.5236 × 1.5 × ⎛ 3------------------- + 48 ------ + 2.25⎞ = 16.493 in 3 ⎝ 4 ⎠ ⎝4 ⎠ 4 4

Spherical Wedge: V = volume A = area of spherical surface α = center angle in degrees 3 α - × 4πr V = ------------------- = 0.0116αr 3 360 3

α - × 4πr 2 = 0.0349αr 2 A = -------360

Example: Find the area of the spherical surface and the volume of a wedge of a sphere. The diameter of the sphere is 100 millimeters, and the center angle α is 45 degrees. V = 0.0116 × 45 × 50 3 = 0.0116 × 45 × 125 ,000 = 65 ,250 mm 3 = 65.25 cm 3 A = 0.0349 × 45 × 50 2 = 3926.25 square millimeters = 39.26 cm 2

Hollow Sphere: V = volume of material used to make a hollow sphere 4π- ( R 3 – r 3 ) = 4.1888 ( R 3 – r 3 ) V = ----3 = --π- ( D 3 – d 3 ) = 0.5236 ( D 3 – d 3 ) 6

Example: Find the volume of a hollow sphere, 8 inches in outside diameter, with a thickness of material of 1.5 inch. Here R = 4; r = 4 − 1.5 = 2.5. V = 4.1888 ( 4 3 – 2.5 3 ) = 4.1888 ( 64 – 15.625 ) = 4.1888 × 48.375 = 202.63 cubic inches

Paraboloid: Volume = V = 1⁄2 πr 2 h = 0.3927d 2 h Area = A = 2π -----3p

3

⎛ d----2- + p 2⎞ – p 3 ⎝4 ⎠ d 2in which p = ----8h

Example: Find the volume of a paraboloid in which h = 300 millimeters and d = 125 millimeters. V = 0.3927d 2 h = 0.3927 × 125 2 × 300 = 1 ,840 ,781 mm 3 = 1 ,840.8 cm 3



VOLUMES OF SOLIDS

Paraboloidal Segment: Volume = V = --π- h ( R 2 + r 2 ) = 1.5708h ( R 2 + r 2 ) 2 = π --- h ( D 2 + d 2 ) = 0.3927h ( D 2 + d 2 ) 8

Example: Find the volume of a segment of a paraboloid in which D = 5 inches, d = 3 inches, and h = 6 inches. V = 0.3927h ( D 2 + d 2 ) = 0.3927 × 6 × ( 5 2 + 3 2 ) = 0.3927 × 6 × 34 = 80.11 cubic inches

Torus: Volume = V = 2π 2 Rr 2 = 19.739Rr 2 2 = π -----Dd 2 = 2.4674Dd 2 4

Area of surface = A = 4π 2 Rr = 39.478Rr = π 2 Dd = 9.8696Dd

Example: Find the volume and area of surface of a torus in which d = 1.5 and D = 5 inches. V = 2.4674 × 5 × 1.5 2 = 2.4674 × 5 × 2.25 = 27.76 cubic inches A = 9.8696 × 5 × 1.5 = 74.022 square inches

Barrel: V = approximate volume. If the sides are bent to the arc of a circle: 1- πh ( 2D 2 + d 2 ) = 0.262h ( 2D 2 + d 2 ) V = ----12

If the sides are bent to the arc of a parabola: V = 0.209h ( 2D 2 + Dd + 3⁄4 d 2 )

Example: Find the approximate contents of a barrel, the inside dimensions of which are D = 60 centimeters, d = 50 centimeters; h = 120 centimeters. V = 0.262h ( 2D 2 + d 2 ) = 0.262 × 120 × ( 2 × 60 2 + 50 2 ) = 0.262 × 120 × ( 7200 + 2500 ) = 0.262 × 120 × 9700 = 304 ,968 cubic centimeters = 0.305 cubic meter

Ratio of Volumes:

If d = base diameter and height of a cone, a paraboloid and a cylinder, and the diameter of a sphere, then the volumes of these bodies are to each other as follows: Cone:paraboloid:sphere:cylinder = 1⁄3 : 1⁄2 : 2⁄3 : 1

Example: Assume, as an example, that the diameter of the base of a cone, paraboloid, and cylinder is 2 inches, that the height is 2 inches, and that the diameter of a sphere is 2 inches. Then the volumes, written in formula form, are as follows: Cone

Paraboloid

Sphere

Cylinder

3.1416 × 2 2 × 2-: ---------------------------------------------: 3.1416 × ( 2p ) 2 × 2 3.1416 × 2 3- : 3.1416 × 2 2 × 2- = 1⁄ : 1⁄ : 2⁄ : 1 ------------------------------------------------------------------------------------------------3 2 3 12 8 6 4


Machinery's Handbook 27th Edition CIRCLES IN A CIRCLE

81

Packing Circles in Circles and Rectangles Diameter of Circle Enclosing a Given Number of Smaller Circles.—F o u r o f m a n y possible compact arrangements of circles within a circle are shown at A, B, C, and D in Fig. 1. To determine the diameter of the smallest enclosing circle for a particular number of enclosed circles all of the same size, three factors that influence the size of the enclosing circle should be considered. These are discussed in the paragraphs that follow, which are based on the article “How Many Wires Can Be Packed into a Circular Conduit,” by Jacques Dutka, Machinery, October 1956. 1) Arrangement of Center or Core Circles: The four most common arrangements of center or core circles are shown cross-sectioned in Fig. 1. It may seem, offhand, that the “A” pattern would require the smallest enclosing circle for a given number of enclosed circles but this is not always the case since the most compact arrangement will, in part, depend on the number of circles to be enclosed.

Fig. 1. Arrangements of Circles within a Circle

2) Diameter of Enclosing Circle When Outer Layer of Circles Is Complete: Successive, complete “layers” of circles may be placed around each of the central cores, Fig. 1, of 1, 2, 3, or 4 circles as the case may be. The number of circles contained in arrangements of complete “layers” around a central core of circles, as well as the diameter of the enclosing circle, may be obtained using the data in Table 1. Thus, for example, the “A” pattern in Fig. 1 shows, by actual count, a total of 19 circles arranged in two complete “layers” around a central core consisting of one circle; this agrees with the data shown in the left half of Table 1 for n = 2. To determine the diameter of the enclosing circle, the data in the right half of Table 1 is used. Thus, for n = 2 and an “A” pattern, the diameter D is 5 times the diameter d of the enclosed circles. 3) Diameter of Enclosing Circle When Outer Layer of Circles Is Not Complete: In most cases, it is possible to reduce the size of the enclosing circle from that required if the outer layer were complete. Thus, for example, the “B” pattern in Fig. 1 shows that the central core consisting of 2 circles is surrounded by 1 complete layer of 8 circles and 1 partial, outer layer of 4 circles, so that the total number of circles enclosed is 14. If the outer layer were complete, then (from Table 1) the total number of enclosed circles would be 24 and the diameter of the enclosing circle would be 6d; however, since the outer layer is composed of only 4 circles out of a possible 14 for a complete second layer, a smaller diameter of enclosing circle may be used. Table 2 shows that for a total of 14 enclosed circles arranged in a “B” pattern with the outer layer of circles incomplete, the diameter for the enclosing circle is 4.606d. Table 2 can be used to determine the smallest enclosing circle for a given number of circles to be enclosed by direct comparison of the “A,” “B,” and “C” columns. For data outside the range of Table 2, use the formulas in Dr. Dutka's article.



CIRCLES IN A CIRCLE Table 1. Number of Circles Contained in Complete Layers of Circles and Diameter of Enclosing Circle (English or metric units) 1

No. Complete Layers Over Core, n 0 1 2 3 4 5 n

2

“A”

“B”

Number of Circles in Center Pattern 3 4 1 2 3 Arrangement of Circles in Center Pattern (see Fig. 1) “C” “D” “A” “B” “C”

4 “D”

Diameter, D, of Enclosing Circlea

Number of Circles, N, Enclosed 1 7 19 37 61 91

2 10 24 44 70 102

3 12 27 48 75 108

4 14 30 52 80 114

d 3d 5d 7d 9d 11d

2d 4d 6d 8d 10d 12d

b

b

b

b

b

b

2.155d 4.055d 6.033d 8.024d 10.018d 12.015d b

2.414d 4.386d 6.379d 8.375d 10.373d 12.372d b

a Diameter D is given in terms of d, the diameter of the enclosed circles. b For n complete layers over core, the number of enclosed circles N for the “A” center pattern is 3n2 + 3n + 1; for “B,” 3n2 + 5n + 2; for “C,” 3n2 + 6n + 3; for “D,” 3n2 + 7n + 4. The diameter D of the

enclosing circle for “A” center pattern is (2n + 1)d; for “B,” (2n + 2)d; for “C,” ( 1 + 2 n 2 + n + 1⁄3 )d and for “D,” ( 1 + 4n 2 + 5.644n + 2 )d .

Table 2. Factors for Determining Diameter, D, of Smallest Enclosing Circle for Various Numbers, N, of Enclosed Circles (English or metric units) No. N 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33

Center Circle Pattern “A” “B” “C” Diameter Factor K

No. N

3 3 3 3 3 3 4.465 4.465 4.465 4.465 4.465 4.465 5 5 5 5 5 5 6.292 6.292 6.292 6.292 6.292 6.292 6.292 6.292 6.292 6.292 6.292 6.292 7.001 7.001

34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65

2 2.733 2.733 3.646 3.646 3.646 3.646 4 4 4.606 4.606 4.606 4.606 5.359 5.359 5.359 5.359 5.583 5.583 5.583 5.583 6.001 6.001 6.197 6.197 6.568 6.568 6.568 6.568 7.083 7.083 7.083

... 2.155 3.310 3.310 3.310 4.056 4.056 4.056 4.056 4.056 4.056 5.164 5.164 5.164 5.164 5.164 5.164 5.619 5.619 5.619 6.034 6.034 6.034 6.034 6.034 6.034 6.774 6.774 6.774 7.111 7.111 7.111

Center Circle Pattern “A” “B” “C” Diameter Factor K 7.001 7.001 7.001 7.001 7.929 7.929 7.929 7.929 7.929 7.929 8.212 8.212 8.212 8.212 8.212 8.212 8.212 8.212 8.212 8.212 8.212 8.212 9.001 9.001 9.001 9.001 9.001 9.001 9.718 9.718 9.718 9.718

7.083 7.245 7.245 7.245 7.245 7.558 7.558 7.558 7.558 8.001 8.001 8.001 8.001 8.001 8.001 8.550 8.550 8.550 8.550 8.811 8.811 8.811 8.811 8.938 8.938 8.938 8.938 9.186 9.186 9.186 9.186 9.545

7.111 7.111 7.111 7.430 7.430 7.430 7.430 7.430 7.430 8.024 8.024 8.024 8.024 8.024 8.024 8.572 8.572 8.572 8.572 8.572 8.572 9.083 9.083 9.083 9.083 9.083 9.083 9.083 9.083 9.083 9.327 9.327

No. N 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97

Center Circle Pattern “A” “B” “C” Diameter Factor K 9.718 9.718 9.718 9.718 9.718 9.718 9.718 9.718 10.166 10.166 10.166 10.166 10.166 10.166 10.166 10.166 10.166 10.166 10.166 10.166 11 11 11 11 11 11 11.393 11.393 11.393 11.393 11.393 11.393

9.545 9.545 9.545 9.661 9.661 9.889 9.889 9.889 9.889 10 10 10.540 10.540 10.540 10.540 10.540 10.540 10.540 10.540 10.644 10.644 10.644 10.644 10.849 10.849 10.849 10.849 11.149 11.149 11.149 11.149 11.441


9.327 9.327 9.327 9.327 10.019 10.019 10.019 10.019 10.019 10.019 10.238 10.238 10.238 10.452 10.452 10.452 10.452 10.452 10.452 10.866 10.866 10.866 10.866 10.866 10.866 11.067 11.067 11.067 11.067 11.067 11.067 11.264


83

Table 2. (Continued) Factors for Determining Diameter, D, of Smallest Enclosing Circle for Various Numbers, N, of Enclosed Circles (English or metric units) No. N 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152

Center Circle Pattern “A” “B” “C” Diameter Factor K 11.584 11.584 11.584 11.584 11.584 11.584 11.584 11.584 11.584 11.584 11.584 11.584 12.136 12.136 12.136 12.136 12.136 12.136 12.136 12.136 12.136 12.136 12.136 12.136 13 13 13 13 13 13 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.166 13.490 13.490 13.490 13.490 13.490 13.490 13.490 13.490 13.490 13.490 13.490 13.490 14.115

11.441 11.441 11.441 11.536 11.536 11.536 11.536 11.817 11.817 11.817 11.817 12 12 12.270 12.270 12.270 12.270 12.358 12.358 12.358 12.358 12.533 12.533 12.533 12.533 12.533 12.533 12.533 12.533 12.790 12.790 12.790 12.790 13.125 13.125 13.125 13.125 13.125 13.125 13.289 13.289 13.289 13.289 13.530 13.530 13.530 13.530 13.768 13.768 13.768 13.768 14 14 14 14

11.264 11.264 11.264 11.264 11.264 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.016 12.373 12.373 12.373 12.373 12.373 12.373 12.548 12.548 12.548 12.719 12.719 12.719 12.719 12.719 12.719 13.056 13.056 13.056 13.056 13.056 13.056 13.221 13.221 13.221 13.221 13.221 13.221 13.702 13.702 13.702 13.859 13.859 13.859 13.859 13.859 13.859 14.013 14.013

No. N 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207

Center Circle Pattern “A” “B” “C” Diameter Factor K 14.115 14.115 14.115 14.115 14.115 14.115 14.115 14.115 14.115 14.115 14.115 14.857 14.857 14.857 14.857 14.857 14.857 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15 15.423 15.423 15.423 15.423 15.423 15.423 15.423 15.423 15.423 15.423 15.423 15.423 16.100 16.100 16.100 16.100 16.100 16.100 16.100 16.100

14 14 14.077 14.077 14.077 14.077 14.229 14.229 14.229 14.229 14.454 14.454 14.454 14.454 14.528 14.528 14.528 14.528 14.748 14.748 14.748 14.748 14.893 14.893 14.893 14.893 15.107 15.107 15.107 15.107 15.178 15.178 15.178 15.178 15.526 15.526 15.526 15.526 15.731 15.731 15.731 15.731 15.731 15.731 15.731 15.731 15.799 15.799 15.799 15.799 15.934 15.934 15.934 15.934 16

14.013 14.013 14.013 14.013 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.317 14.614 14.614 14.614 14.614 14.614 14.614 15.048 15.048 15.048 15.048 15.048 15.048 15.190 15.190 15.190 15.190 15.190 15.190 15.469 15.469 15.469 15.469 15.469 15.469 15.743 15.743 15.743 15.743 15.743 15.743 16.012 16.012 16.012 16.012 16.012 16.012 16.012 16.012 16.012

No. N 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262

Center Circle Pattern “A” “B” “C” Diameter Factor K 16.100 16.100 16.100 16.100 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.621 16.875 16.875 16.875 16.875 16.875 16.875 16.875 16.875 16.875 16.875 16.875 16.875 17 17 17 17 17 17 17.371 17.371 17.371 17.371 17.371 17.371 17.371 17.371 17.371 17.371 17.371 17.371 18.089 18.089 18.089 18.089 18.089 18.089 18.089 18.089 18.089

16 16.133 16.133 16.133 16.133 16.395 16.395 16.395 16.395 16.525 16.525 16.525 16.525 16.589 16.589 16.716 16.716 16.716 16.716 16.716 16.716 16.716 16.716 17.094 17.094 17.094 17.094 17.094 17.094 17.094 17.094 17.463 17.463 17.463 17.463 17.523 17.523 17.523 17.523 17.523 17.523 17.523 17.523 17.644 17.644 17.644 17.644 17.704 17.704 17.704 17.704 17.823 17.823 17.823 17.823


16.144 16.144 16.144 16.144 16.144 16.144 16.276 16.276 16.276 16.276 16.276 16.276 16.535 16.535 16.535 16.535 16.535 16.535 17.042 17.042 17.042 17.042 17.042 17.042 17.166 17.166 17.166 17.166 17.166 17.166 17.166 17.166 17.166 17.290 17.290 17.290 17.290 17.290 17.290 17.654 17.654 17.654 17.654 17.654 17.654 17.773 17.773 17.773 17.773 17.773 17.773 18.010 18.010 18.010 18.010


CIRCLES IN A CIRCLE

The diameter D of the enclosing circle is equal to the diameter factor, K, multiplied by d, the diameter of the enclosed circles, or D = K × d. For example, if the number of circles to be enclosed, N, is 12, and the center circle arrangement is “C,” then for d = 11⁄2 inches, D = 4.056 × 11⁄2 = 6.084 inches. If d = 50 millimeters, then D = 4.056 × 50 = 202.9 millimeters.

Approximate Formula When Number of Enclosed Circles Is Large: When a large number of circles are to be enclosed, the arrangement of the center circles has little effect on the diameter of the enclosing circle. For numbers of circles greater than 10,000, the diameter of the enclosing circle may be calculated within 2 per cent from the formula D = d ( 1 + N ÷ 0.907 ) . In this formula, D = diameter of the enclosing circle; d = diameter of the enclosed circles; and N is the number of enclosed circles. An alternative approach relates the area of each of the same-sized circles to be enclosed to the area of the enclosing circle (or container), as shown in Figs. 1 through 27. The table shows efficient ways for packing various numbers of circles N, from 2 up to 97. In the table, D = the diameter of each circle to be enclosed, d = the diameter of the enclosing circle or container, and Φ = Nd2/D2 = ratio of the area of the N circles to the area of the enclosing circle or container, which is the packing efficiency. Cross-hatching in the diagrams indicates loose circles that may need packing constraints. Data for Numbers of Circles in Circles N 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

D/d 2.0000 2.1547 2.4142 2.7013 3.0000 3.0000 3.3048 3.6131 3.8130 3.9238 4.0296 4.2361 4.3284 4.5214 4.6154

Φ 0.500 0.646 0.686 0.685 0.667 0.778 0.733 0.689 0.688 0.714 0.739 0.724 0.747 0.734 0.751

Fig. 1 2 3 4 5 5 6 7 8 9 10 11 12 13 14

N 17 18 19 20 21 22 23 24 25 31 37 55 61 97 ...

D/d 4.7920 4.8637 4.8637 5.1223 5.2523 5.4397 5.5452 5.6517 5.7608 6.2915 6.7588 8.2111 8.6613 11.1587 ...

Φ 0.740 0.761 0.803 0.762 0.761 0.743 9.748 0.751 0.753 0.783 0.810 0.816 0.813 0.779 ...

Fig. 15 16 16 17 18 19 20 21 22 23 24 25 26 27 ...

Packing of large numbers of circles, such as the 97 in Fig. 27, may be approached by drawing a triangular pattern of circles, as shown in Fig. 28, which represents three circles near the center of the array. The point of a compass is then placed at A, B, or C, or anywhere within triangle ABC, and the radius of the compass is gradually enlarged until it encompasses the number of circles to be enclosed. As a first approximation of the diameter, D = 1.14d N may be tried.

Fig. 1. N = 2

Fig. 2. N = 3

Fig. 3. N = 4

Fig. 4. N = 5



85

;; ;; ;; ;; Fig. 5. N = 7

Fig. 6. N = 8

Fig. 7. N = 9

Fig. 8. N = 10

Fig. 9. N = 11

Fig. 10. N = 12

Fig. 11. N = 13

Fig. 12. N = 14

;;

;; ;; ;; ;; ;; ;; ;; ;;; ;; ;; Fig. 13. N = 15

Fig. 14. N = 16

Fig. 15. N = 17

Fig. 16. N = 19

Fig. 17. N = 20

Fig. 18. N = 21

Fig. 19. N = 22

Fig. 20. N = 23

Fig. 21. N = 24

Fig. 22. N = 25

Fig. 23. N = 31

Fig. 24. N = 37

Fig. 25. N = 55

Fig. 26. N = 61

C A Fig. 27. N = 97


B Fig. 28.


CIRCLES IN A RECTANGLE

Circles within Rectangles.—For small numbers N of circles, packing (for instance, of cans) is less vital than for larger numbers and the number will usually govern the decision whether to use a rectangular or a triangular pattern, examples of which are seen in Figs. 29 and 30.

Fig. 30. Triangular Pattern (r = 3, c = 7) Fig. 29. Rectangular Pattern (r = 4, c = 5)

If D is the can diameter and H its height, the arrangement in Fig. 29 will hold 20 circles or cans in a volume of 5D × 4D × H = 20D2 H. The arrangement in Fig. 30 will pack the same 20 cans into a volume of 7D × 2.732D × H = 19.124D2 H, a reduction of 4.4 per cent. When the ratio of H/D is less than 1.196:1, the rectangular pattern requires less surface area (therefore less material) for the six sides of the box, but for greater ratios, the triangular pattern is better. Some numbers, such as 19, can be accommodated only in a triangular pattern. The following table shows possible patterns for 3 to 25 cans, where N = number of circles, P = pattern (R rectangular or T triangular), and r and c = numbers of rows and columns, respectively. The final table column shows the most economical application, where V = best volume, S = best surface area (sometimes followed by a condition on H/D). For the rectangular pattern, the area of the container is rD × cD, and for the triangular pattern, the area is cD × [ 1 + ( r – 1 ) 3 ⁄ 2 ] D , or cD2[1 + 0.866(r − 1)]. Numbers of Circles in Rectangular Arrangements N

P

r

c

Application

N

P

r

c

Application

R

3

5

(S, H/D > 0.038) V, (S, H/D < 0.038)

3

T

2

2

V, S

15

T

2

8

4

R

2

2

V, S

16

R

4

4

V, S

5

T

3

2

V, S

17

T

3

6

V, S

6

R

2

3

V, S

18

T

5

4

V, S

7

T

2

4

V, S

19

T

2

10

V, S

R

4

5

(S, H/D > 1.196)

T

3

7

V, (S, H/D < 1.196) (S, 0.165 < H/D < 0.479)

8 9 10

R

4

2

V, (S, H/D < 0.732)

T

3

3

(S, H/D > 0.732)

R

3

3

V, S

R

5

2

V, (S, H/D > 1.976)

T

4

3

(S, H/D > 1.976)

11 T

3

4

V, S

12 R

3

4

V, S

T

5

3

(S, H/D > 0.236)

T

2

7

V, (S, H/D < 0.236)

T

4

4

(S, H/D > 5.464)

14 T

3

5

V, (S, H/D < 5.464)

13

20

21 22 23 24 25

R

3

7

T

6

4

(S, H/D > 0.479)

T

2

11

V, (S, H/D < 0.165)

T

4

6

V, S

T

5

5

(S, H/D > 0.366) V, (S, H/D < 0.366)

T

3

8

R

4

6

V, S

R

5

5

(S, H/D > 1.10)

T

7

4

(S, 0.113 < H/D < 1.10)

T

2

13

V, (S, H/D < 0.133)


Machinery's Handbook 27th Edition CIRCLES IN A RECTANGLE

87

Rollers on a Shaft*.—The following formulas illustrate the geometry of rollers on a shaft. In Fig. 31, D is the diameter of the center line of the roller circle, d is the diameter of a roller, DS = D − d is the shaft diameter, and C is the clearance along the center line of the roller circle. In the equations that follow, N is the number of rollers, and N > 3. Equation (1a) applies when the clearance C = 0 d D = --------------------⎛ sin 180 -⎞ ⎝ -------N ⎠

(1a)

Equation (1b) applies when clearance C > 0 then d-⎞ ⎞ – d C = D sin ⎛ 180° – ( N – 1 ) asin ⎛ --⎝ ⎝ D⎠ ⎠

(1b)

d

DS

C

D

Fig. 31.

Example:Forty bearings are to be placed around a 3-inch diameter shaft with no clearance. What diameter bearings are needed? Solution: Rearrange Equation (1a), and substitute in the value of N. Use the result to eliminate d, using DS = D − d . Finally, solve for D and d. d = D sin ⎛ 180 ---------⎞ = D sin ⎛ 180 ---------⎞ = 0.078459D ⎝ N ⎠ ⎝ 40 ⎠ D = D S + d = 3 + 0.078459D 3 - = 3.2554 D = -----------------0.92154 d = D – D S = 0.2554 * Rollers on a Shaft contributed by Manfred K. Brueckner.



SOLUTION OF TRIANGLES

SOLUTION OF TRIANGLES Any figure bounded by three straight lines is called a triangle. Any one of the three lines may be called the base, and the line drawn from the angle opposite the base at right angles to it is called the height or altitude of the triangle. If all three sides of a triangle are of equal length, the triangle is called equilateral. Each of the three angles in an equilateral triangle equals 60 degrees. If two sides are of equal length, the triangle is an isosceles triangle. If one angle is a right or 90-degree angle, the triangle is a right or right-angled triangle. The side opposite the right angle is called the hypotenuse. If all the angles are less than 90 degrees, the triangle is called an acute or acute-angled triangle. If one of the angles is larger than 90 degrees, the triangle is called an obtuseangled triangle. Both acute and obtuse-angled triangles are known under the common name of oblique-angled triangles. The sum of the three angles in every triangle is 180 degrees. The sides and angles of any triangle that are not known can be found when: 1 ) a l l t h e three sides; 2) two sides and one angle; and 3) one side and two angles are given. In other words, if a triangle is considered as consisting of six parts, three angles and three sides, the unknown parts can be determined when any three parts are given, provided at least one of the given parts is a side. Functions of Angles For every right triangle, a set of six ratios is defined; each is the length of one side of the triangle divided by the length of another side. The six ratios are the trigonometric (trig) functions sine, cosine, tangent, cosecant, secant, and cotangent (abbreviated sin, cos, tan, csc, sec, and cot). Trig functions are usually expressed in terms of an angle in degree or radian measure, as in cos 60° = 0.5. “Arc” in front of a trig function name, as in arcsin or arccos, means find the angle whose function value is given. For example, arcsin 0.5 = 30° means that 30° is the angle whose sin is equal to 0.5. Electronic calculators frequently use sin−1, cos−1, and tan−1 to represent the arc functions. Example:tan 53.1° = 1.332; arctan 1.332 = tan−1 1.332 = 53.1° = 53° 6′ The sine of an angle equals the opposite side divided by the hypotenuse. Hence, sin B = b ÷ c, and sin A = a ÷ c. The cosine of an angle equals the adjacent side divided by the hypotenuse. Hence, cos B = a ÷ c, and c B cos A = b ÷ c. a The tangent of an angle equals the opposite side C = 90˚ A divided by the adjacent side. Hence, tan B = b ÷ a, and tan A = a ÷ b. b The cotangent of an angle equals the adjacent side divided by the opposite side. Hence, cot B = a ÷ b, and cot A = b ÷ a. The secant of an angle equals the hypotenuse divided by the adjacent side. Hence, sec B = c ÷ a, and sec A = c ÷ b. The cosecant of an angle equals the hypotenuse divided by the opposite side. Hence, csc B = c ÷ b, and csc A = c ÷ a. It should be noted that the functions of the angles can be found in this manner only when the triangle is right-angled. If in a right-angled triangle (see preceding illustration), the lengths of the three sides are represented by a, b, and c, and the angles opposite each of these sides by A, B, and C, then the side c opposite the right angle is the hypotenuse; side b is called the side adjacent to angle A and is also the side opposite to angle B; side a is the side adjacent to angle B and the


Machinery's Handbook 27th Edition TRIGONOMETRIC IDENTITIES

89

side opposite to angle A. The meanings of the various functions of angles can be explained with the aid of a right-angled triangle. Note that the cosecant, secant, and cotangent are the reciprocals of, respectively, the sine, cosine, and tangent. The following relation exists between the angular functions of the two acute angles in a right-angled triangle: The sine of angle B equals the cosine of angle A; the tangent of angle B equals the cotangent of angle A, and vice versa. The sum of the two acute angles in a right-angled triangle always equals 90 degrees; hence, when one angle is known, the other can easily be found. When any two angles together make 90 degrees, one is called the complement of the other, and the sine of the one angle equals the cosine of the other, and the tangent of the one equals the cotangent of the other. The Law of Sines.—In any triangle, any side is to the sine of the angle opposite that side as any other side is to the sine of the angle opposite that side. If a, b, and c are the sides, and A, B, and C their opposite angles, respectively, then: a b- = c , ---------- = --------------------sin A sin B sin C b sin A a = --------------sin B a sin B b = --------------sin A a sin C c = --------------sin A

or or or

so that: c sin A a = -------------sin C c sin B b = -------------sin C b sin C c = --------------sin B

The Law of Cosines.—In any triangle, the square of any side is equal to the sum of the squares of the other two sides minus twice their product times the cosine of the included angle; or if a, b and c are the sides and A, B, and C are the opposite angles, respectively, then: a 2 = b 2 + c 2 – 2bc cos A b 2 = a 2 + c 2 – 2ac cos B c 2 = a 2 + b 2 – 2ab cos C These two laws, together with the proposition that the sum of the three angles equals 180 degrees, are the basis of all formulas relating to the solution of triangles. Formulas for the solution of right-angled and oblique-angled triangles, arranged in tabular form, are given on the following pages. Signs of Trigonometric Functions.—The diagram, Fig. 1 on page 98, shows the proper sign (+ or −) for the trigonometric functions of angles in each of the four quadrants, 0 to 90, 90 to 180, 180 to 270, and 270 to 360 degrees. Thus, the cosine of an angle between 90 and 180 degrees is negative; the sine of the same angle is positive. Trigonometric Identities.—Trigonometric identities are formulas that show the relationship between different trigonometric functions. They may be used to change the form of some trigonometric expressions to simplify calculations. For example, if a formula has a term, 2sinAcosA, the equivalent but simpler term sin2A may be substituted. The identities that follow may themselves be combined or rearranged in various ways to form new identities.



TRIGONOMETRIC IDENTITIES

Basic sin A- = ----------1 tan A = ----------cos A cot A

1 sec A = ----------cos A

1csc A = ---------sin A

Negative Angle sin ( – A ) = – sin A

cos ( – A ) = cos A

tan ( – A ) = – tan A

Pythagorean sin2 A + cos2 A = 1

1 + tan2 A = sec2 A

1 + cot2 A = csc2 A

Sum and Difference of Angles tan A + tan Btan ( A + B ) = -------------------------------1 – tan A tan B

tan A – tan Btan ( A – B ) = --------------------------------1 + tan A tan B

cot A cot B – 1cot ( A + B ) = -------------------------------cot B + cot A

cot A cot B + 1cot ( A – B ) = --------------------------------cot B – cot A

sin ( A + B ) = sin A cos B + cos A sin B

sin ( A – B ) = sin A cos B – cos A sin B

cos ( A + B ) = cos A cos B – sin A sin B

cos ( A – B ) = cos A cos B + sin A sin B

Double-Angle cos 2A = cos2 A – sin2 A = 2 cos2 A – 1 = 1 – 2 sin2 A 2 tan A - = ----------------------------2 tan 2A = ---------------------sin 2A = 2 sin A cos A cot A – tan A 1 – tan2 A Half-Angle sin 1⁄2 A =

1⁄ ( 1 2

– cos A )

tan 1⁄2 A =

sin A 1 – cos A 1 – cos A ---------------------- = --------------------- = ---------------------1 + cos A sin A 1 + cos A

cos 1⁄2 A =

1⁄ ( 1 2

+ cos A )

Product-to-Sum sin A cos B = 1⁄2 [ sin ( A + B ) + sin ( A – B ) ] cos A cos B = 1⁄2 [ cos ( A + B ) + cos ( A – B ) ] sin A sin B = 1⁄2 [ cos ( A – B ) – cos ( A + B ) ] tan A + tan Btan A tan B = ----------------------------cot A + cot B Sum and Difference of Functions sin A + sin B = 2 [ sin 1⁄2 ( A + B ) cos 1⁄2 ( A – B ) ] sin A – sin B = 2 [ sin 1⁄2 ( A – B ) cos 1⁄2 ( A + B ) ] cos A + cos B = 2 [ cos 1⁄2 ( A + B ) cos 1⁄2 ( A – B ) ] cos A – cos B = – 2 [ sin 1⁄2 ( A + B ) sin 1⁄2 ( A – B ) ] sin ( A + B ) tan A + tan B = -------------------------cos A cos B

sin ( A – B ) tan A – tan B = -------------------------cos A cos B

sin ( B + A ) cot A + cot B = -------------------------sin A sin B

sin ( B – A ) cot A – cot B = -------------------------sin A sin B


Machinery's Handbook 27th Edition RIGHT-ANGLE TRIANGLES

91

Solution of Right-Angled Triangles As shown in the illustration, the sides of the rightangled triangle are designated a and b and the hypotenuse, c. The angles opposite each of these sides are designated A and B, respectively. Angle C, opposite the hypotenuse c is the right angle, and is therefore always one of the known quantities. Sides and Angles Known

Formulas for Sides and Angles to be Found

Side a; side b

c =

a2 + b2

tan A = a--b

B = 90° − A

Side a; hypotenuse c

b =

c2 – a2

sin A = a--c

B = 90° − A

Side b; hypotenuse c

a =

c2 – b2

b sin B = --c

A = 90° − B

Hypotenuse c; angle B

b = c × sin B

a = c × cos B

A = 90° − B

Hypotenuse c; angle A

b = c × cos A

a = c × sin A

B = 90° − A

Side b; angle B

bc = ---------sin B

a = b × cot B

A = 90° − B

Side b; angle A

b c = ----------cos A

a = b × tan A

B = 90° − A

Side a; angle B

a c = ----------cos B

b = a × tan B

A = 90° − B

Side a; angle A

ac = ---------sin A

b = a × cot A

B = 90° − A

Trig Functions Values for Common Angles sin 0° = 0 πsin 30° = sin -6 πsin 45° = sin -4 πsin 60° = sin -3 sin 90° = sin π --2

cos 0° = 1 = 0.5 = 0.70710678 = 0.8660254 = 1

cos 30° = cos --π6 cos 45° = cos --π4 cos 60° = cos --π3 ° cos 90 = cos π --2

tan 0° = 0 = 0.8660254 = 0.70710678 = 0.5 = 0

πtan 30° = tan -6 πtan 45° = tan -4 πtan 60° = tan -3 tan 90° = tan π --2


= 0.57735027 = 1 = 1.7320508 = ∞


RIGHT-ANGLE TRIANGLES Examples of the Solution of Right-Angled Triangles (English and metric units) c = 22 inches; B = 41° 36′. a = c × cos B = 22 × cos 41 ° 36′ = 22 × 0.74780 = 16.4516 inches b = c × sin B = 22 × sin 41 ° 36′ = 22 × 0.66393 = 14.6065 inches A = 90 ° – B = 90 ° – 41 ° 36′ = 48 ° 24′

Hypotenuse and One Angle Known

c = 25 centimeters; a = 20 centimeters. b =

c2 – a2 = =

25 2 – 20 2 =

625 – 400

225 = 15 centimeters

sin A = a--- = 20 ------ = 0.8 c 25 Hypotenuse and One Side Known

Hence,

A = 53°8′ B = 90° – A = 90° – 53°8′ = 36°52′

a = 36 inches; b = 15 inches. c =

a2 + b2 = =

36 2 + 15 2 =

1296 + 225

1521 = 39 inches

tan A = a--- = 36 ------ = 2.4 b 15 Hence,

A = 67 ° 23′ B = 90 ° – A = 90 ° – 67 ° 23′ = 22 ° 37′

Two Sides Known

a = 12 meters; A = 65°. a12 12 - = 13.2405 meters c = ---------= ---------------- = -----------------sin A 0.90631 sin 65 ° b = a × cot A = 12 × cot 65 ° = 12 × 0.46631 = 5.5957 meters B = 90 ° – A = 90 ° – 65 ° = 25 °

One Side and One Angle Known


Machinery's Handbook 27th Edition RIGHT- AND OBLIQUE-ANGLE TRIANGLES Chart For The Rapid Solution of Right-Angle and Oblique-Angle Triangles


93


OBLIQUE-ANGLE TRIANGLES Solution of Oblique-Angled Triangles

One Side and Two Angles Known (Law of Sines): Call the known side a, the angle opposite it A, and the other known angle B. Then, C = 180° − (A + B). If angles B and C are given, but not A, then A = 180° − (B + C). C = 180 ° – ( A + B ) a × sin B b = --------------------sin A

One Side and Two Angles Known

Side and Angles Known

a × sin C c = --------------------sin A

× b × sin CArea = a----------------------------2 a = 5 centimeters; A = 80°; B = 62° C = 180° – ( 80° + 62° ) = 180° – 142° = 38° × sin B- = 5------------------------× sin 62 °- = 5---------------------------× 0.88295 b = a-------------------sin A sin 80 ° 0.98481 = 4.483 centimeters × sin C- = 5------------------------× sin 38 °- = 5---------------------------× 0.61566 c = a-------------------sin A sin 80 ° 0.98481 = 3.126 centimeters

Two Sides and the Angle Between Them Known: Call the known sides a and b, and the known angle between them C. Then, a × sin C tan A = ----------------------------------b – ( a × cos C ) × sin Cc = a-------------------sin A Side c may also be found directly as below: B = 180 ° – ( A + C )

c = Two Sides and the Angle Between Them Known

Sides and Angle Known

a 2 + b 2 – ( 2ab × cos C )

a × b × sin C Area = -----------------------------2 a = 9 inches; b = 8 inches; C = 35°. a × sin C - = ---------------------------------------9 × sin 35 ° tan A = ----------------------------------b – ( a × cos C ) 8 – ( 9 × cos 35 ° ) 9 × 0.57358 5.16222 = ------------------------------------------ = ------------------- = 8.22468 8 – ( 9 × 0.81915 ) 0.62765 Hence, A = 83°4′ B = 180° – ( A + C ) = 180° – 118°4′ = 61°56′ × sin C- = 9---------------------------× 0.57358 = 5.2 inches c = a-------------------sin A 0.99269


Machinery's Handbook 27th Edition OBLIQUE-ANGLE TRIANGLES

95

Two Sides and the Angle Opposite One of the Sides Known: Call the known angle A, the side opposite it a, and the other known side b. Then, b × sin A sin B = --------------------C = 180° – ( A + B ) a a × sin C a × b × sin C c = --------------------Area = -----------------------------sin A 2 If, in the above, angle B > angle A but ± ------------5.83Z

If a < 0.5858l, maximum deflection is

located between load and support, at

nx = --m

b v = l ------------2l + b If a = 0.5858l, maximum deflec-

tion is at load and is

0.5858l, the second is the maximum stress. Stress is zero at

2 Wa b - and -------------b- ------------6EI 2l + b

Wl 3 -------------------101.9EI

If a > 0.5858l, maximum deflection is

Wbn 3 - and located -------------------3EIm 2 l 3

between load and point of fixture, at


x = 2n -----m

BEAM STRESS AND DEFLECTION TABLES

W ( 3l – 11x ) s = --------16Z

Deflections at Critical Pointsa


Table 1. (Continued) Stresses and Deflections in Beams Type of Beam

Stresses Deflections General Formula for Stress at any Point Stresses at Critical Points General Formula for Deflection at any Pointa Case 15. — Fixed at One End, Supported at the Other, Uniform Load

( l – x )- ( 1⁄ l – x ) s = W ------------------4 2Zl

Maximum stress at point

Wl-----8Z

Wx 2 ( l – x -) ( 3l – 2x ) y = ------------------------48EIl

Stress is zero at x = 1⁄4l. Greatest negative stress is

Maximum deflection is at x = 0.5785l, and is

Wl 3 -------------185EI

Deflection at center,

9 Wl at x = 5⁄8l and is – --------- ------128 Z

Wl 3 -------------192EI

Deflection at point of greatest negative stress, at x = 5⁄8l is

Wl 3 -------------187EI Case 16. — Fixed at One End, Free but Guided at the Other, Uniform Load 2⎫ ⎧ s = Wl ------- ⎨ 1⁄3 – x-- + 1⁄2 ⎛ x--⎞ ⎬ ⎝ l⎠ Z ⎩ l ⎭

Maximum stress, at support,

Wl-----3Z

Wx 2- ( 2l – x ) 2 y = ------------24EIl

Maximum deflection, at free end,

Wl 3----------24EI

Stress is zero at x = 0.4227l Greatest negative stress, at free end,

– Wl ------6Z

Case 17. — Fixed at One End, Free but Guided at the Other, with Load

W s = ----- ( 1⁄2 l – x ) Z

Stress at support,

Wl ------2Z

Stress at free end

Wl – ------2Z

Wx 2- ( 3l – 2x ) y = ----------12EI


Wl 3----------12EI

267

These are the maximum stresses and are equal and opposite. Stress is zero at center.

Maximum deflection, at free end,


of fixture,



Type of Beam

Stresses Deflections General Formula for Stress at any Point Stresses at Critical Points General Formula for Deflection at any Pointa Case 18. — Fixed at Both Ends, Load at Center Between each end and load,

Wl ------8Z

Stress at load

Wl– -----8Z

Deflections at Critical Pointsa Maximum deflection, at load,

Wl 3 -------------192EI

These are the maximum stresses and are equal and opposite. Stress is zero at x = 1⁄4l Case 19. — Fixed at Both Ends, Load at any Point For segment of length a,

Wb 2 s = ----------- [ al – x ( l + 2a ) ] Zl 3 For segment of length b, 2

s = Wa ---------- [ bl – v ( l + 2b ) ] 3 Zl

Stress at end next to segment of length a,

Wab 2 -------------Zl 2

Stress at end next to

Wa 2 b segment of length b, -------------Zl 2

For segment of length a,

Wx 2 b 2 y = ---------------- [ 2a ( l – x ) + l ( a – x ) ] 6EIl 3 For segment of length b,

Wv 2 a 2

y = ---------------- [ 2b ( l – v ) + l ( b – v ) ] 6EIl 3

Maximum stress is at end next to shorter segment. Stress is zero at

al x = ------------l + 2a and

bl v = ------------l + 2b Greatest negative stress, at 2 2

load,

2Wa b – ------------------Zl 3


Deflection at load,

Wa 3 b 3---------------3EIl 3

Let b be the length of the longer segment and a of the shorter one. The maximum deflection is in the longer segment, at

2bl v = ------------and is l + 2b 2 3

2Wa b ------------------------------2 3EI ( l + 2b )


Wx 2- ( 3l – 4x ) y = ----------48EI

Stress at ends

W ( 1⁄ l – x ) s = -----2Z 4

268

Table 1. (Continued) Stresses and Deflections in Beams


Table 1. (Continued) Stresses and Deflections in Beams Type of Beam

Stresses Deflections General Formula for Stress at any Point Stresses at Critical Points General Formula for Deflection at any Pointa Case 20. — Fixed at Both Ends, Uniform Load Maximum stress, at ends,

Wl --------12Z

Wx 2- ( l – x ) 2 y = ------------24EIl

Maximum deflection, at center,

Wl 3 -------------384EI

Stress is zero at x = 0.7887l and at x = 0.2113l Greatest negative stress, at center,

Wl– -------24Z

Case 21. — Continuous Beam, with Two Unequal Spans, Unequal, Uniform Loads Between R1 and R,

l 1 – x ⎧ ( l 1 – x )W 1 ⎫ s = -----------⎨ ------------------------- – R 1 ⎬ Z ⎩ 2l 1 ⎭ Between R2 and R,

l 2 – u ⎧ ( l 2 – u )W 2 ⎫ s = ------------ ⎨ ------------------------- – R 2 ⎬ 2l 2 Z ⎩ ⎭

Stress at support R,

W 1 l 12 + W 2 l 22 ------------------------------8Z ( l 1 + l 2 ) Greatest stress in the first span is at

l1 x = ------ ( W – R1 ) W1 1 2

R1 l1 and is – -------------2ZW 1

Between R1 and R,

x ( l1 – x ) ⎧ y = ------------------- ⎨ ( 2l – x ) ( 4R 1 – W 1 ) 24EI ⎩ 1 W1 ( l1 – x )2 ⎫ – ---------------------------⎬ l1 ⎭ Between R2 and R,

u ( l2 – u ) ⎧ y = -------------------- ⎨ ( 2l – u ) ( 4R 2 – W 2 ) 24EI ⎩ 2

Greatest stress in the second span is at

l2 u = ------ ( W – R2 ) W2 2 and is,

W2 ( l2 – u ) 2 ⎫ – ---------------------------⎬ l2 ⎭

This case is so complicated that convenient general expressions for the critical deflections cannot be obtained.


2⎫ ⎧ s = Wl ------- ⎨ 1⁄6 – x-- + ⎛⎝ x--⎞⎠ ⎬ 2Z ⎩ l l ⎭


R 22 l 2 – ------------2ZW 2

269



Type of Beam

Stresses Deflections General Formula for Stress at any Point Stresses at Critical Points General Formula for Deflection at any Pointa Case 22. — Continuous Beam, with Two Equal Spans, Uniform Load

( l – x )- ( 1⁄ l – x ) s = W ------------------4 2Zl

Maximum stress at

Wl-----8Z

Wx 2 ( l – x -) ( 3l – 2x ) y = ------------------------48EIl

Stress is zero at x = 1⁄4l Greatest negative stress is at x = 5⁄8l and is,

Deflections at Critical Pointsa Maximum deflection is at x = 0.5785l, and is

Wl 3 -------------185EI

Deflection at center of span,

Wl 3 --------------192EI

9 - Wl – -------------128 Z

Deflection at point of greatest negative stress, at x = 5⁄8l is

Wl 3 -------------187EI

Case 23. — Continuous Beam, with Two Equal Spans, Equal Loads at Center of Each Between point A and load,

W ( 3l – 11x ) s = --------16Z Between point B and load,

5- Wv s = – -----------16 Z

Maximum stress at point A,

3- Wl ----------16 Z

Stress is zero at

3- l x = ----11

Between point A and load,

Wx 2- ( 9l – 11x ) y = ----------96EI

Maximum deflection is at v = 0.4472l, and is

Wl 3 ---------------------107.33EI

Between point B and load,

Wv - 3l 2 y = ----------( – 5v 2 ) 96EI

Greatest negative stress at center of span,

5- -----Wl– ----32 Z


Deflection at load,

7 - -------Wl 3-------768 EI


point A,

270

Table 1. (Continued) Stresses and Deflections in Beams


Table 1. (Continued) Stresses and Deflections in Beams Stresses Deflections General Formula for Stress at any Point Stresses at Critical Points General Formula for Deflection at any Pointa Case 24. — Continuous Beam, with Two Unequal Spans, Unequal Loads at any Point of Each

Type of Beam

Between R1 and W1,

Between R and W1, s =

1 m= 2(l1 + l 2)

W1a1b1 Wab (l1 + a1) + 2 2 2 (l2 + a2) l1 l2 W1

R1 w a1

W2

R u b1

x b2

a2

v

R2

Between R and W2, s =

1 ------- [ m ( l 2 – x ) – W 2 a 2 x ] l2 Z Between R2 and W2,

l2

l1

1 ------- [ m ( l 1 – u ) – W 1 a 1 u ] l1 Z

W1b1 – m W1a1 + m W2a2 + m W2b2 – m + l1 l1 l2 l2

vr s = – -------2 Z

Stress at load W1,

a1 r1 – --------Z Stress at support R,

m ---Z Stress at load W2,

a2 r2 – --------Z

Between R1 and W1,

W 1 b 13 ⎫ w -⎧ l y = -------⎨ ( – w ) ( l 1 + w )r 1 – ------------- ⎬ 6EI ⎩ 1 l1 ⎭ Between R and W1,

u - [W a b (l + a ) y = ------------1 6EIl 1 1 1 1 1 – W 1 a 1 u 2 – m ( 2l 1 – u ) ( l 1 – u ) ] Between R and W2

The greatest of these is the maximum stress.

x - [W a b (l + a ) y = ------------2 6EIl 2 2 2 2 2 – W 2 a 2 x 2 – m ( 2l 2 – x ) ( l 2 – x ) ]

Deflection at load W1,

a1 b1 ------------- [ 2a 1 b 1 W 1 6EIl 1 – m ( l1 + a1 ) ] Deflection at load W2,

a2 b2 ------------- [ 2a 2 b 2 W 2 6EIl 2 – m ( l2 + a2 ) ] This case is so complicated that convenient general expressions for the maximum deflections cannot be obtained.

Between R2 and W2,

= r1

=r

= r2

3 v - ⎧ ( l – v ) ( l + v )r – W 2 b2 ⎫ y = -------⎨ 2 2 ------------- ⎬ 6EI ⎩ 2 l2 ⎭

a The deflections apply only to cases where the cross section of the beam is constant for its entire length.

In the diagrammatical illustrations of the beams and their loading, the values indicated near, but below, the supports are the “reactions” or upward forces at the supports. For Cases 1 to 12, inclusive, the reactions, as well as the formulas for the stresses, are the same whether the beam is of constant or variable cross-section. For the other cases, the reactions and the stresses given are for constant cross-section beams only.


271

The bending moment at any point in inch-pounds is s × Z and can be found by omitting the divisor Z in the formula for the stress given in the tables. A positive value of the bending moment denotes tension in the upper fibers and compression in the lower ones. A negative value denotes the reverse, The value of W corresponding to a given stress is found by transposition of the formula. For example, in Case 1, the stress at the critical point is s = − Wl ÷ 8Z. From this formula we find W = − 8Zs ÷ l. Of course, the negative sign of W may be ignored.


wr s = – --------1Z



RECTANGULAR AND ROUND SOLID BEAMS

In Table 1, if there are several kinds of loads, as, for instance, a uniform load and a load at any point, or separate loads at different points, the total stress and the total deflection at any point is found by adding together the various stresses or deflections at the point considered due to each load acting by itself. If the stress or deflection due to any one of the loads is negative, it must be subtracted instead of added. Tables 2a and 2b give expressions for determining dimensions of rectangular and round beams in terms of beam stresses and load. Table 2a. Rectangular Solid Beams Style of Loading and Support

Breadth of Beam, b inch (mm)

6lW ---------- = b fh 2

Stress in Extreme Fibers, f Beam Height, h Beam Length, l inch (mm) lb/in2 (N/mm2) inch (mm) Beam fixed at one end, loaded at the other

6lW ---------- = h bf

6lW ---------- = f bh 2

Total Load, W lb (N)

bfh 2 ----------- = l 6W

2 bfh ----------- = W 6l

Beam fixed at one end, uniformly loaded

3lW ---------- = b fh 2

3lW ---------- = h bf

3lW ---------- = f bh 2

bfh 2- = l ---------3W

2 bfh ----------- = W 3l

Beam supported at both ends, single load in middle

3lW- = b ---------2fh 2

3lW ---------- = h 2bf

3lW- = f ----------2bh 2

2bfh 2- = l ------------3W

2 2bfh -------------- = W 3l

Beam supported at both ends, uniformly loaded

3lW- = b ---------4fh 2

3lW ---------- = h 4bf

3lW- = f ----------4bh 2

4bfh 2 -------------- = l 3W

4bfh 2 -------------- = W 3l

Beam supported at both ends, single unsymmetrical load

6Wac- = b -------------fh 2 l

6Wac --------------- = h bfl

6Wac --------------- = f bh 2 l

a+c=l

bh 2 fl ------------ = W 6ac

Beam supported at both ends, two symmetrical loads l, any length

3Wa ----------- = b fh 2

3Wa ----------- = h bf

3Wa ----------- = f bh 2

2 bh -----------f = a 3W

2 bh -----------f = W 3a

Deflection of Beam Uniformly Loaded for Part of Its Length.—In the following formulas, lengths are in inches, weights in pounds. W = total load; L = total length between supports; E = modulus of elasticity; I = moment of inertia of beam section; a = fraction of length of beam at each end, that is not loaded = b ÷ L; and f = deflection. WL 3 f = ------------------------------------ ( 5 – 24a 2 + 16a 4 ) 384EI ( 1 – 2a ) The expression for maximum bending moment is: Mmax = 1⁄8WL (1 + 2a).


Machinery's Handbook 27th Edition UNIFORMLY LOADED BEAMS

273

Table 2b. Round Solid Beams Style of Loading and Support

Diameter of Beam, d inch (mm)

3

10.18lW --------------------- = d f

Stress in Extreme Fibers, f Beam Length, l inch (mm) lb/in2 (N/mm2) Beam fixed at one end, loaded at the other

10.18lW --------------------- = f d3

Total Load, W lb (N)

d3 f = l -----------------10.18W

d3 f - = W -------------10.18l

Beam fixed at one end, uniformly loaded

3

5.092Wl --------------------- = d f

5.092Wl- = f -------------------d3

d3 f = l -----------------5.092W

d3 f - = W -------------5.092l

Beam supported at both ends, single load in middle

3

2.546Wl --------------------- = d f

2.546Wl --------------------- = f d3

d3 f = l -----------------2.546W

d3 f - = W -------------2.546l

Beam supported at both ends, uniformly loaded

3

1.273Wl --------------------- = d f

1.273Wl --------------------- = f d3

d3 f = l -----------------1.273W

d3 f - = W -------------1.273l

Beam supported at both ends, single unsymmetrical load

3

10.18Wac ------------------------- = d fl

10.18Wac ------------------------- = f d3 l

a+c=l

d 3 fl ------------------- = W 10.18ac

Beam supported at both ends, two symmetrical loads l, any length 3

5.092Wa ---------------------- = d f

5.092Wa ---------------------- = f d3

d3 f = a -----------------5.092W

d3 f = W ---------------5.092a

These formulas apply to simple beams resting on supports at the ends.

If the formulas are used with metric SI units, W = total load in newtons; L = total length between supports in millimeters; E = modulus of elasticity in newtons per millimeter2; I = moment of inertia of beam section in millimeters4; a = fraction of length of beam at each end, that is not loaded = b ÷ L; and f = deflection in millimeters. The bending moment Mmax is in newton-millimeters (N · mm). Note: A load due to the weight of a mass of M kilograms is Mg newtons, where g = approximately 9.81 meters per second 2.



BEAMS OF UNIFORM STRENGTH

Bending Stress Due to an Oblique Transverse Force.—The following illustration shows a beam and a channel being subjected to a transverse force acting at an angle φ to the center of gravity. To find the bending stress, the moments of inertia I around axes 3-3 and 4-4 are computed from the following equations: I3 = Ixsin2φ + Iycos2φ, and I4 = Ixcos2φ + Iysin2φ. y- sin φ + --x- cos φ⎞ where M The computed bending stress fb is then found from f b = M ⎛ --⎝I ⎠ I x

y

is the bending moment due to force F.

Beams of Uniform Strength Throughout Their Length.—The bending moment in a beam is generally not uniform throughout its length, but varies. Therefore, a beam of uniform cross-section which is made strong enough at its most strained section, will have an excess of material at every other section. Sometimes it may be desirable to have the crosssection uniform, but at other times the metal can be more advantageously distributed if the beam is so designed that its cross-section varies from point to point, so that it is at every point just great enough to take care of the bending stresses at that point. Tables 3a and 3b are given showing beams in which the load is applied in different ways and which are supported by different methods, and the shape of the beam required for uniform strength is indicated. It should be noted that the shape given is the theoretical shape required to resist bending only. It is apparent that sufficient cross-section of beam must also be added either at the points of support (in beams supported at both ends), or at the point of application of the load (in beams loaded at one end), to take care of the vertical shear. It should be noted that the theoretical shapes of the beams given in the two tables that follow are based on the stated assumptions of uniformity of width or depth of cross-section, and unless these are observed in the design, the theoretical outlines do not apply without modifications. For example, in a cantilever with the load at one end, the outline is a parabola only when the width of the beam is uniform. It is not correct to use a strictly parabolic shape when the thickness is not uniform, as, for instance, when the beam is made of an I- or T-section. In such cases, some modification may be necessary; but it is evident that whatever the shape adopted, the correct depth of the section can be obtained by an investigation of the bending moment and the shearing load at a number of points, and then a line can be drawn through the points thus ascertained, which will provide for a beam of practically uniform strength whether the cross-section be of uniform width or not.


Machinery's Handbook 27th Edition BEAMS OF UNIFORM STRENGTH

275

Table 3a. Beams of Uniform Strength Throughout Their Length Type of Beam

Formulaa

Description

Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end. Outline of beam-shape, parabola with vertex at loaded end.

2 P = Sbh -----------6l

Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end. Outline of beam, one-half of a parabola with vertex at loaded end. Beam may be reversed so that upper edge is parabolic.

Sbh 2 P = -----------6l

Load at one end. Depth of beam uniform. Width of beam decreasing towards loaded end. Outline of beam triangular, with apex at loaded end.

Sbh 2 P = -----------6l

Beam of approximately uniform strength. Load at one end. Width of beam uniform. Depth of beam decreasing towards loaded end, but not tapering to a sharp point.

2 P = Sbh -----------6l

Uniformly distributed load. Width of beam uniform. Depth of beam decreasing towards outer end. Outline of beam, right-angled triangle.

Sbh 2 P = -----------3l

Uniformly distributed load. Depth of beam uniform. Width of beam gradually decreasing towards outer end. Outline of beam is formed by two parabolas which tangent each other at their vertexes at the outer end of the beam.

Sbh 2 P = -----------3l

a In the formulas, P = load in pounds; S = safe stress in pounds per square inch; and a, b, c, h, and l are in inches. If metric SI units are used, P is in newtons; S = safe stress in N/mm2; and a, b, c, h, and l are in millimeters.



BEAMS OF UNIFORM STRENGTH Table 3b. Beams of Uniform Strength Throughout Their Length Type of Beam

Description

Formulaa

Beam supported at both ends. Load concentrated at any point. Depth of beam uniform. Width of beam maximum at point of loading. Outline of beam, two triangles with apexes at points of support.

Sbh 2 l P = ------------6ac

Beam supported at both ends. Load concentrated at any point. Width of beam uniform. Depth of beam maximum at point of loading. Outline of beam is formed by two parabolas with their vertexes at points of support.

Sbh 2-l P = ------------6ac

Beam supported at both ends. Load concentrated in the middle. Depth of beam uniform. Width of beam maximum at point of loading. Outline of beam, two triangles with apexes at points of support.

2 P = 2Sbh ---------------3l

Beam supported at both ends. Load concentrated at center. Width of beam uniform. Depth of beam maximum at point of loading. Outline of beam, two parabolas with vertices at points of support.

2Sbh 2 P = ---------------3l

Beam supported at both ends. Load uniformly distributed. Depth of beam uniform. Width of beam maximum at center. Outline of beam, two parabolas with vertexes at middle of beam.

4Sbh 2 P = ---------------3l

Beam supported at both ends. Load uniformly distributed. Width of beam uniform. Depth of beam maximum at center. Outline of beam onehalf of an ellipse.

2 P = 4Sbh ---------------3l

a For details of English and metric SI units used in the formulas, see footnote on page


275.

Machinery's Handbook 27th Edition DEFLECTION IN BEAM DESIGN

277

Deflection as a Limiting Factor in Beam Design.—For some applications, a beam must be stronger than required by the maximum load it is to support, in order to prevent excessive deflection. Maximum allowable deflections vary widely for different classes of service, so a general formula for determining them cannot be given. When exceptionally stiff girders are required, one rule is to limit the deflection to 1 inch per 100 feet of span; hence, if l = length of span in inches, deflection = l ÷ 1200. According to another formula, deflection limit = l ÷ 360 where beams are adjacent to materials like plaster which would be broken by excessive beam deflection. Some machine parts of the beam type must be very rigid to maintain alignment under load. For example, the deflection of a punch press column may be limited to 0.010 inch or less. These examples merely illustrate variations in practice. It is impracticable to give general formulas for determining the allowable deflection in any specific application, because the allowable amount depends on the conditions governing each class of work. Procedure in Designing for Deflection: Assume that a deflection equal to l ÷ 1200 is to be the limiting factor in selecting a wide-flange (W-shape) beam having a span length of 144 inches. Supports are at both ends and load at center is 15,000 pounds. Deflection y is to be limited to 144 ÷ 1200 = 0.12 inch. According to the formula on page 261 (Case 2), in which W = load on beam in pounds, l = length of span in inches, E = modulus of elasticity of material, I = moment of inertia of cross section: Wl 3- hence, I = -----------Wl 3- = -------------------------------------------------------15 ,000 × 144 3 Deflection y = ----------- = 268.1 48EI 48yE 48 × 0.12 × 29 ,000 ,000 A structural wide-flange beam, see Steel Wide-Flange Sections on page 2511, having a depth of 12 inches and weighing 35 pounds per foot has a moment of inertia I of 285 and a section modulus (Z or S) of 45.6. Checking now for maximum stress s (Case 2, page 261): Wl 15 ,000 × 144 s = ------- = -------------------------------- = 11 ,842 lbs/in2 4Z 4 × 46.0 Although deflection is the limiting factor in this case, the maximum stress is checked to make sure that it is within the allowable limit. As the limiting deflection is decreased, for a given load and length of span, the beam strength and rigidity must be increased, and, consequently, the maximum stress is decreased. Thus, in the preceding example, if the maximum deflection is 0.08 inch instead of 0.12 inch, then the calculated value for the moment of inertia I will be 402; hence a W 12 × 53 beam having an I value of 426 could be used (nearest value above 402). The maximum stress then would be reduced to 7640 pounds per square inch and the calculated deflection is 0.076 inch. A similar example using metric SI units is as follows. Assume that a deflection equal to l ÷ 1000 millimeters is to be the limiting factor in selecting a W-beam having a span length of 5 meters. Supports are at both ends and the load at the center is 30 kilonewtons. Deflection y is to be limited to 5000 ÷ 1000 = 5 millimeters. The formula on page 261 (Case 2) is applied, and W = load on beam in newtons; l = length of span in mm; E = modulus of elasticity (assume 200,000 N/mm2 in this example); and I = moment of inertia of cross-section in millimeters4. Thus, Wl 3 Deflection y = ------------48EI hence

Wl 3 30 ,000 × 5000 3 I = ------------- = ----------------------------------------- = 78 ,125 ,000 mm 4 48yE 48 × 5 × 200 ,000 Although deflection is the limiting factor in this case, the maximum stress is checked to make sure that it is within the allowable limit, using the formula from page 261 (Case 2):



CURVED BEAMS Wl s = ------4Z

The units of s are newtons per square millimeter; W is the load in newtons; l is the length in mm; and Z = section modulus of the cross-section of the beam = I ÷ distance in mm from neutral axis to extreme fiber. Curved Beams.—The formula S = Mc/I used to compute stresses due to bending of beams is based on the assumption that the beams are straight before any loads are applied. In beams having initial curvature, however, the stresses may be considerably higher than predicted by the ordinary straight-beam formula because the effect of initial curvature is to shift the neutral axis of a curved member in from the gravity axis toward the center of curvature (the concave side of the beam). This shift in the position of the neutral axis causes an increase in the stress on the concave side of the beam and decreases the stress at the outside fibers. Hooks, press frames, and other machine members which as a rule have a rather pronounced initial curvature may have a maximum stress at the inside fibers of up to about 31⁄2 times that predicted by the ordinary straight-beam formula. Stress Correction Factors for Curved Beams: A simple method for determining the maximum fiber stress due to bending of curved members consists of 1) calculating the maximum stress using the straight-beam formula S = Mc/I; and; and 2) multiplying the calculated stress by a stress correction factor. Table 4 on page 279 gives stress correction factors for some of the common cross-sections and proportions used in the design of curved members. An example in the application of the method using English units of measurement is given at the bottom of the table. A similar example using metric SI units is as follows: The fiber stresses of a curved rectangular beam are calculated as 40 newtons per millimeter2, using the straight beam formula, S = Mc/I. If the beam is 150 mm deep and its radius of curvature is 300 mm, what are the true stresses? R/c = 300⁄75 = 4. From Table 4 on page 279, the K factors corresponding to R/c = 4 are 1.20 and 0.85. Thus, the inside fiber stress is 40 × 1.20 = 48 N/mm2 = 48 megapascals; and the outside fiber stress is 40 × 0.85 = 34 N/mm2 = 34 megapascals. Approximate Formula for Stress Correction Factor: The stress correction factors given in Table 4 on page 279 were determined by Wilson and Quereau and published in the University of Illinois Engineering Experiment Station Circular No. 16, “A Simple Method of Determining Stress in Curved Flexural Members.” In this same publication the authors indicate that the following empirical formula may be used to calculate the value of the stress correction factor for the inside fibers of sections not covered by the tabular data to within 5 per cent accuracy except in triangular sections where up to 10 per cent deviation may be expected. However, for most engineering calculations, this formula should prove satisfactory for general use in determining the factor for the inside fibers. 1 - --1I - ----------+ K = 1.00 + 0.5 ------bc 2 R – c R (Use 1.05 instead of 0.5 in this formula for circular and elliptical sections.) I =Moment of inertia of section about centroidal axis b =maximum width of section c =distance from centroidal axis to inside fiber, i.e., to the extreme fiber nearest the center of curvature R =radius of curvature of centroidal axis of beam


Machinery's Handbook 27th Edition CURVED BEAMS

279

Table 4. Values of Stress Correction Factor K for Various Curved Beam Sections Section

R⁄ c

1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0

Factor K Inside Outside Fiber Fiber 3.41 .54 2.40 .60 1.96 .65 1.75 .68 1.62 .71 1.33 .79 1.23 .84 1.14 .89 1.10 .91 1.08 .93 2.89 .57 2.13 .63 1.79 .67 1.63 .70 1.52 .73 1.30 .81 1.20 .85 1.12 .90 1.09 .92 1.07 .94 3.01 .54 2.18 .60 1.87 .65 1.69 .68 1.58 .71 1.33 .80 1.23 .84 1.13 .88 1.10 .91 1.08 .93 3.09 .56 2.25 .62 1.91 .66 1.73 .70 1.61 .73 1.37 .81 1.26 .86 1.17 .91 1.13 .94 1.11 .95 3.14 .52 2.29 .54 1.93 .62 1.74 .65 1.61 .68 1.34 .76 1.24 .82 1.15 .87 1.12 .91 1.10 .93 3.26 .44 2.39 .50 1.99 .54 1.78 .57 1.66 .60 1.37 .70 1.27 .75 1.16 .82 1.12 .86 1.09 .88

a

y0

.224R .151R .108R .084R .069R .030R .016R .0070R .0039R .0025R .305R .204R .149R .112R .090R .041R .021R .0093R .0052R .0033R .336R .229R .168R .128R .102R .046R .024R .011R .0060R .0039R .336R .229R .168R .128R .102R .046R .024R .011R .0060R .0039R .352R .243R .179R .138R .110R .050R .028R .012R .0060R .0039R .361R .251R .186R .144R .116R .052R .029R .013R .0060R .0039R

Section

R⁄ c

1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0 1.2 1.4 1.6 1.8 2.0 3.0 4.0 6.0 8.0 10.0

Factor K Inside Outside Fiber Fiber 3.63 .58 2.54 .63 2.14 .67 1.89 .70 1.73 .72 1.41 .79 1.29 .83 1.18 .88 1.13 .91 1.10 .92 3.55 .67 2.48 .72 2.07 .76 1.83 .78 1.69 .80 1.38 .86 1.26 .89 1.15 .92 1.10 .94 1.08 .95 2.52 .67 1.90 .71 1.63 .75 1.50 .77 1.41 .79 1.23 .86 1.16 .89 1.10 .92 1.07 .94 1.05 .95 3.28 .58 2.31 .64 1.89 .68 1.70 .71 1.57 .73 1.31 .81 1.21 .85 1.13 .90 1.10 .92 1.07 .93 2.63 .68 1.97 .73 1.66 .76 1.51 .78 1.43 .80 1.23 .86 1.15 .89 1.09 .92 1.07 .94 1.06 .95

y0a .418R .299R .229R .183R .149R .069R .040R .018R .010R .0065R .409R .292R .224R .178R .144R .067R .038R .018R .010R .0065R .408R .285R .208R .160R .127R .058R .030R .013R .0076R .0048R .269R .182R .134R .104R .083R .038R .020R .0087R .0049R .0031R .399R .280R .205R .159R .127R .058R .031R .014R .0076R .0048R

Example: The fiber stresses of a curved rectangular beam are calculated as 5000 psi using the straight beam formula, S = Mc/I. If the beam is 8 inches deep and its radius of curvature is 12 inches, what are the true stresses? R/c = 12⁄4 = 3. The factors in the table corresponding to R/c = 3 are 0.81 and 1.30. Outside fiber stress = 5000 × 0.81 = 4050 psi; inside fiber stress = 5000 × 1.30 = 6500 psi.

a y is the distance from the centroidal axis to the neutral axis of curved beams subjected to pure 0 bending and is measured from the centroidal axis toward the center of curvature.



CURVED BEAMS

Example:The accompanying diagram shows the dimensions of a clamp frame of rectangular cross-section. Determine the maximum stress at points A and B due to a clamping force of 1000 pounds.

The cross-sectional area = 2 × 4 = 8 square inches; the bending moment at section AB is 1000 (24 + 6 + 2) = 32,000 inch pounds; the distance from the center of gravity of the section at AB to point B is c = 2 inches; and using the formula on page 239, the moment of inertia of the section is 2 × (4)3 ÷ 12 = 10.667 inches4. Using the straight-beam formula, page 278, the stress at points A and B due to the bending moment is: ,000 × 2- = 6000 psi S = Mc -------- = 32 ------------------------I 10.667 The stress at A is a compressive stress of 6000 psi and that at B is a tensile stress of 6000 psi. These values must be corrected to account for the curvature effect. In Table 4 on page 279 for R/c = (6 + 2)/(2) = 4, the value of K is found to be 1.20 and 0.85 for points B and A respectively. Thus, the actual stress due to bending at point B is 1.20 × 6000 = 7200 psi in tension and the stress at point A is 0.85 × 6000 = 5100 psi in compression. To these stresses at A and B must be added, algebraically, the direct stress at section AB due to the 1000-pound clamping force. The direct stress on section AB will be a tensile stress equal to the clamping force divided by the section area. Thus 1000 ÷ 8 = 125 psi in tension. The maximum unit stress at A is, therefore, 5100 − 125 = 4975 psi in compression and the maximum unit stress at B is 7200 + 125 = 7325 psi in tension. The following is a similar calculation using metric SI units, assuming that it is required to determine the maximum stress at points A and B due to clamping force of 4 kilonewtons acting on the frame. The frame cross-section is 50 by 100 millimeters, the radius R = 200 mm, and the length of the straight portions is 600 mm. Thus, the cross-sectional area = 50 × 100 = 5000 mm2; the bending moment at AB is 4000(600 + 200) = 3,200,000 newton-millimeters; the distance from the center of gravity of the section at AB to point B is c = 50 mm; and the moment of inertia of the section is, using the formula on page 239, 50 × (100)3 = 4,170,000 mm4. Using the straight-beam formula, page 278, the stress at points A and B due to the bending moment is: Mc 3 ,200 ,000 × 50 s = -------- = ------------------------------------I 4 ,170 ,000 = 38.4 newtons per millimeter 2 = 38.4 megapascals The stress at A is a compressive stress of 38.4 N/mm2, while that at B is a tensile stress of 38.4 N/mm2. These values must be corrected to account for the curvature


Machinery's Handbook 27th Edition SIZE OF RAIL TO CARRY LOAD

281

effect. From the table on page 279, the K factors are 1.20 and 0.85 for points A and B respectively, derived from R/c = 200⁄50 = 4. Thus, the actual stress due to bending at point B is 1.20 × 38.4 = 46.1 N/mm2 (46.1 megapascals) in tension; and the stress at point A is 0.85 × 38.4 = 32.6 N/mm2 (32.6 megapascals) in compression. To these stresses at A and B must be added, algebraically, the direct stress at section AB due to the 4 kN clamping force. The direct stress on section AB will be a tensile stress equal to the clamping force divided by the section area. Thus, 4000⁄5000 = 0.8 N/mm 2. The maximum unit stress at A is, therefore, 32.61 − 0.8 = 31.8 N/mm 2 (31.8 megapascals) in compression, and the maximum unit stress at B is 46.1 + 0.8 = 46.9 N/mm 2 (46.9 megapascals) in tension. Size of Rail Necessary to Carry a Given Load.—The following formulas may be employed for determining the size of rail and wheel suitable for carrying a given load. Let, A = the width of the head of the rail in inches; B = width of the tread of the rail in inches; C = the wheel-load in pounds; D = the diameter of the wheel in inches.

Then the width of the tread of the rail in inches is found from the formula: C B = ---------------1250D

(1)

The width A of the head equals B + 5⁄8 inch. The diameter D of the smallest track wheel that will safely carry the load is found from the formula: C D = ------------(2) A×K in which K = 600 to 800 for steel castings; K = 300 to 400 for cast iron. As an example, assume that the wheel-load is 10,000 pounds; the diameter of the wheel is 20 inches; and the material is cast steel. Determine the size of rail necessary to carry this load. From Formula (1): 10,000 B = ------------------------ = 0.4 inch 1250 × 20 The width of the rail required equals 0.4 + 5⁄8 inch = 1.025 inch. Determine also whether a wheel 20 inches in diameter is large enough to safely carry the load. From Formula (2): 10,000 D = ---------------------------= 16 1⁄4 inches 1.025 × 600 This is the smallest diameter of track wheel that will safely carry the load; hence a 20inch wheel is ample. American Railway Engineering Association Formulas.—The American Railway Engineering Association recommends for safe operation of steel cylinders rolling on steel plates that the allowable load p in pounds per inch of length of the cylinder should not exceed the value calculated from the formula



STRESSES PRODUCED BY SHOCKS y.s. – 13,000 p = ------------------------------- 600d for diameterd less than 25 inches 20,000

This formula is based on steel having a yield strength, y.s., of 32,000 pounds per square inch. For roller or wheel diameters of up to 25 inches, the Hertz stress (contact stress) resulting from the calculated load p will be approximately 76,000 pounds per square inch. For a 10-inch diameter roller the safe load per inch of roller length is 32,000 – 13,000 p = ------------------------------------------ 600 × 10 = 5700 lbs per inch of length 20,000 Therefore, to support a 10,000 pound load the roller or wheel would need to be 10,000⁄5700 = 1.75 inches wide. Stresses Produced by Shocks Stresses in Beams Produced by Shocks.—Any elastic structure subjected to a shock will deflect until the product of the average resistance, developed by the deflection, and the distance through which it has been overcome, has reached a value equal to the energy of the shock. It follows that for a given shock, the average resisting stresses are inversely proportional to the deflection. If the structure were perfectly rigid, the deflection would be zero, and the stress infinite. The effect of a shock is, therefore, to a great extent dependent upon the elastic property (the springiness) of the structure subjected to the impact. The energy of a body in motion, such as a falling body, may be spent in each of four ways: 1) In deforming the body struck as a whole. 2) In deforming the falling body as a whole. 3) In partial deformation of both bodies on the surface of contact (most of this energy will be transformed into heat). 4) Part of the energy will be taken up by the supports, if these are not perfectly rigid and inelastic. How much energy is spent in the last three ways it is usually difficult to determine, and for this reason it is safest to figure as if the whole amount were spent as in Case 1. If a reliable judgment is possible as to what percentage of the energy is spent in other ways than the first, a corresponding fraction of the total energy can be assumed as developing stresses in the body subjected to shocks. One investigation into the stresses produced by shocks led to the following conclusions: 1) A suddenly applied load will produce the same deflection, and, therefore, the same stress as a static load twice as great; and 2) The unit stress p (see formulas in Table 1, "Stresses Produced in Beams by Shocks") for a given load producing a shock, varies directly as the square root of the modulus of elasticity E, and inversely as the square root of the length L of the beam and the area of the section. Thus, for instance, if the sectional area of a beam is increased by four times, the unit stress will diminish only by half. This result is entirely different from those produced by static loads where the stress would vary inversely with the area, and within certain limits be practically independent of the modulus of elasticity. In Table 1, the expression for the approximate value of p, which is applicable whenever the deflection of the beam is small as compared with the total height h through which the body producing the shock is dropped, is always the same for beams supported at both ends and subjected to shock at any point between the supports. In the formulas all dimensions are in inches and weights in pounds.


Machinery's Handbook 27th Edition STRESSES PRODUCED BY SHOCKS

283

Table 1. Stresses Produced in Beams by Shocks Method of Support and Point Struck by Falling Body

Fiber (Unit) Stress p produced by Weight Q Dropped Through a Distance h

Approximate Value of p

Supported at both ends; struck in center.

96hEI p = QaL ----------- ⎛ 1 + 1 + ----------------⎞ 4I ⎝ QL 3 ⎠

p = a 6QhE --------------LI

Fixed at one end; struck at the other.

p = QaL ----------- ⎛ 1 + 1 + 6hEI -------------⎞ I ⎝ QL 3 ⎠

p = a 6QhE --------------LI

Fixed at both ends; struck in center.

p = QaL ----------- ⎛ 1 + 1 + 384hEI -------------------⎞ 8I ⎝ QL 3 ⎠

p = a 6QhE --------------LI

I = moment of inertia of section; a = distance of extreme fiber from neutral axis; L = length of beam; E = modulus of elasticity.

If metric SI units are used, p is in newtons per square millimeter; Q is in newtons; E = modulus of elasticity in N/mm2; I = moment of inertia of section in millimeters4; and h, a, and L in millimeters. Note: If Q is given in kilograms, the value referred to is mass. The weight Q of a mass M kilograms is Mg newtons, where g = approximately 9.81 meters per second2. Examples of How Formulas for Stresses Produced by Shocks are Derived: The general formula from which specific formulas for shock stresses in beams, springs, and other machine and structural members are derived is: p = p s ⎛ 1 + 1 + 2h ------⎞ ⎝ y⎠

(1)

In this formula, p = stress in pounds per square inch due to shock caused by impact of a moving load; ps = stress in pounds per square inch resulting when moving load is applied statically; h = distance in inches that load falls before striking beam, spring, or other member; y = deflection, in inches, resulting from static load. As an example of how Formula (1) may be used to obtain a formula for a specific application, suppose that the load W shown applied to the beam in Case 2 on page 261 were dropped on the beam from a height of h inches instead of being gradually applied (static loading). The maximum stress ps due to load W for Case 2 is given as Wl ÷ 4 Z and the maximum deflection y is given as Wl3 ÷ 48 EI. Substituting these values in Formula (1), 96hEI 2h Wl p = Wl ------- ⎛ 1 + 1 + ----------------------------⎞ = ------- ⎛ 1 + 1 + ----------------⎞ 4Z ⎝ 4Z ⎝ Wl 3 ⎠ Wl 3 ÷ 48EI⎠

(2)

If in Formula (2) the letter Q is used in place of W and if Z, the section modulus, is replaced by its equivalent, I ÷ distance a from neutral axis to extreme fiber of beam, then Formula (2) becomes the first formula given in the accompanying Table 1, Stresses Produced in Beams by Shocks Stresses in Helical Springs Produced by Shocks.—A load suddenly applied on a spring will produce the same deflection, and, therefore, also the same unit stress, as a static load twice as great. When the load drops from a height h, the stresses are as given in the accompanying Table 2. The approximate values are applicable when the deflection is small as compared with the height h. The formulas show that the fiber stress for a given shock will be greater in a spring made from a square bar than in one made from a round bar, if the diameter of coil be the same and the side of the square bar equals the diameter of the round



STRESSES PRODUCED BY SHOCKS

bar. It is, therefore, more economical to use round stock for springs which must withstand shocks, due to the fact that the deflection for the same fiber stress for a square bar spring is smaller than that for a round bar spring, the ratio being as 4 to 5. The round bar spring is therefore capable of storing more energy than a square bar spring for the same stress. Table 2. Stresses Produced in Springs by Shocks Form of Bar from Which Spring is Made

Fiber (Unit) Stress f Produced by Weight Q Dropped a Height h on a Helical Spring

Approximate Value of f

Round

Ghd 4 8QD f = ------------ ⎛ 1 + 1 + ------------------⎞ πd 3 ⎝ 4QD 3 n⎠

QhG f = 1.27 ------------Dd 2 n

Square

Ghd 4 f = 9QD ------------ ⎛ 1 + 1 + --------------------------⎞ 0.9πQD 3 n⎠ 4d 3 ⎝

QhG f = 1.34 ------------Dd 2 n

G = modulus of elasticity for torsion; d = diameter or side of bar; D = mean diameter of spring; n = number of coils in spring.

Shocks from Bodies in Motion.—The formulas given can be applied, in general, to shocks from bodies in motion. A body of weight W moving horizontally with the velocity of v feet per second, has a stored-up energy: 2 E K = 1--- × Wv ---------- foot-pounds 2 g

or

2 6Wv -------------- inch-pounds g

This expression may be substituted for Qh in the tables in the equations for unit stresses containing this quantity, and the stresses produced by the energy of the moving body thereby determined. The formulas in the tables give the maximum value of the stresses, providing the designer with some definitive guidance even where there may be justification for assuming that only a part of the energy of the shock is taken up by the member under stress. The formulas can also be applied using metric SI units. The stored-up energy of a body of mass M kilograms moving horizontally with the velocity of v meters per second is: E K = 1⁄2 Mv 2 newton-meters This expression may be substituted for Qh in the appropriate equations in the tables. For calculation in millimeters, Qh = 1000 EK newton-millimeters. Fatigue Stresses.—So-called "fatigue ruptures" occur in parts that are subjected to continually repeated shocks or stresses of small magnitude. Machine parts that are subjected to continual stresses in varying directions, or to repeated shocks, even if of comparatively small magnitude, may fail ultimately if designed, from a mere knowledge of the behavior of the material under a steady stress, such as is imposed upon it by ordinary tensile stress testing machines. Examinations of numerous cases of machine parts, broken under actual working conditions, indicate that at least 80 per cent of these ruptures are caused by fatigue stresses. Most fatigue ruptures are caused by bending stresses, and frequently by a revolving bending stress. Hence, to test materials for this class of stress, the tests should be made to stress the material in a manner similar to that in which it will be stressed under actual working conditions. See Fatigue Properties on page 205 for more on this topic.


Machinery's Handbook 27th Edition STRENGTH OF COLUMNS

285

COLUMNS Strength of Columns or Struts Structural members which are subject to compression may be so long in proportion to the diameter or lateral dimensions that failure may be the result 1) of both compression and bending; and 2) of bending or buckling to such a degree that compression stress may be ignored. In such cases, the slenderness ratio is important. This ratio equals the length l of the column in inches divided by the least radius of gyration r of the cross-section. Various formulas have been used for designing columns which are too slender to be designed for compression only. Rankine or Gordon Formula.—This formula is generally applied when slenderness ratios range between 20 and 100, and sometimes for ratios up to 120. The notation, in English and metric SI units of measurement, is given on page 287. S p = ------------------------ = ultimate load, lbs. per sq. in. 2 1 + K ⎛ -l ⎞ ⎝ r⎠ Factor K may be established by tests with a given material and end condition, and for the probable range of l/r. If determined by calculation, K = S/Cπ2E. Factor C equals 1 for either rounded or pivoted column ends, 4 for fixed ends, and 1 to 4 for square flat ends. The factors 25,000, 12,500, etc., in the Rankine formulas, arranged as on page 287, equal 1/K, and have been used extensively. Straight-line Formula.—This general type of formula is often used in designing compression members for buildings, bridges, or similar structural work. It is convenient especially in designing a number of columns that are made of the same material but vary in size, assuming that factor B is known. This factor is determined by tests. l p = S y – B ⎛ - ⎞ = ultimate load, lbs. per sq. in. ⎝ r⎠ Sy equals yield point, lbs. per square inch, and factor B ranges from 50 to 100. Safe unit stress = p ÷ factor of safety. Formulas of American Railway Engineering Association.—The formulas that follow apply to structural steel having an ultimate strength of 60,000 to 72,000 pounds per square inch. For building columns having l/r ratios not greater than 120, allowable unit stress = 17,000 − 0.485 l2/r2. For columns having l/r ratios greater than 120, allowable unit stress 18 ,000 allowable unit stress = --------------------------------------1 + l 2 ⁄ 18 ,000r 2 For bridge compression members centrally loaded and with values of l/r not greater than 140: 1 l2 Allowable unit stress, riveted ends = 15 ,000 – --- ---4 r2 1 l2 Allowable unit stress, pin ends = 15 ,000 – --- ---3 r2



STRENGTH OF COLUMNS

Euler Formula.—This formula is for columns that are so slender that bending or buckling action predominates and compressive stresses are not taken into account. 2 IE P = Cπ ---------------= total ultimate load, in pounds l2 The notation, in English and metric SI units of measurement, is given in the table Rankine' s and Euler' s Formulas for Columns on page 287. Factors C for different end conditions are included in the Euler formulas at the bottom of the table. According to a series of experiments, Euler formulas should be used if the values of l/r exceed the following ratios: Structural steel and flat ends, 195; hinged ends, 155; round ends, 120; cast iron with flat ends, 120; hinged ends, 100; round ends, 75; oak with flat ends, 130. The critical slenderness ratio, which marks the dividing line between the shorter columns and those slender enough to warrant using the Euler formula, depends upon the column material and its end conditions. If the Euler formula is applied when the slenderness ratio is too small, the calculated ultimate strength will exceed the yield point of the material and, obviously, will be incorrect. Eccentrically Loaded Columns.—In the application of the column formulas previously referred to, it is assumed that the action of the load coincides with the axis of the column. If the load is offset relative to the column axis, the column is said to be eccentrically loaded, and its strength is then calculated by using a modification of the Rankine formula, the quantity cz/r2 being added to the denominator, as shown in the table on the next page. This modified formula is applicable to columns having a slenderness ratio varying from 20 or 30 to about 100. Machine Elements Subjected to Compressive Loads.—As in structural compression members, an unbraced machine member that is relatively slender (i.e., its length is more than, say, six times the least dimension perpendicular to its longitudinal axis) is usually designed as a column, because failure due to overloading (assuming a compressive load centrally applied in an axial direction) may occur by buckling or a combination of buckling and compression rather than by direct compression alone. In the design of unbraced steel machine “columns” which are to carry compressive loads applied along their longitudinal axes, two formulas are in general use:

(Euler)

S y Ar 2 P cr = -------------Q

(1)

Sy l 2 Q = ------------ (3) nπ 2 E In these formulas, Pcr = critical load in pounds that would result in failure of the column; A = cross-sectional area, square inches; Sy = yield point of material, pounds per square inch; r = least radius of gyration of cross-section, inches; E = modulus of elasticity, pounds per square inch; l = column length, inches; and n = coefficient for end conditions. For both ends fixed, n = 4; for one end fixed, one end free, n = 0.25; for one end fixed and the other end free but guided, n = 2; for round or pinned ends, free but guided, n = 1; and for flat ends, n = 1 to 4. It should be noted that these values of n represent ideal conditions that are seldom attained in practice; for example, for both ends fixed, a value of n = 3 to 3.5 may be more realistic than n = 4. If metric SI units are used in these formulas, Pcr = critical load in newtons that would result in failure of the column; A = cross-sectional area, square millimeters; Sy = yield point of the material, newtons per square mm; r = least radius of gyration of cross-section, mm; E = modulus of elasticity, newtons per square mm; l = column length, mm; and n = a coefficient for end conditions. The coefficients given are valid for calculations in metric units. (J. B. Johnson)

Q P cr = AS y ⎛ 1 – --------⎞ ⎝ 4r 2⎠

(2)

where


Machinery's Handbook 27th Edition RANKINE AND EULER FORMULAS

287

Rankine's and Euler's Formulas for Columns Symbol p P S l r I r2 E c z

Quantity Ultimate unit load Total ultimate load Ultimate compressive strength of material Length of column or strut Least radius of gyration Least moment of inertia Moment of inertia/area of section Modulus of elasticity of material Distance from neutral axis of cross-section to side under compression Distance from axis of load to axis coinciding with center of gravity of cross-section

English Unit Lbs./sq. in. Pounds Lbs./sq. in. Inches Inches Inches4 Inches2 Lbs./sq. in.

Metric SI Units Newtons/sq. mm. Newtons Newtons/sq. mm. Millimeters Millimeters Millimeters4 Millimeters2 Newtons/sq. mm.

Inches

Millimeters

Inches

Millimeters

Rankine's Formulas Both Ends of One End Fixed and Column Fixed One End Rounded

Material

Both Ends Rounded

Steel

S p = -------------------------------l2 1 + ---------------------25 ,000r 2

S p = -------------------------------l2 1 + ---------------------12 ,500r 2

S p = --------------------------l2 1 + ----------------6250r 2

Cast Iron

S p = -------------------------l2 1 + ----------------5000r 2

S p = -------------------------l2 1 + ----------------2500r 2

S p = -------------------------l2 1 + ----------------1250r 2

Wrought Iron

S p = ------------------------------l2 1 + --------------------35 ,000r 2

S p = ------------------------------l2 1 + --------------------17 ,500r 2

S p = -------------------------l2 1 + ---------------8750r 2

Timber

S p = --------------------------l2 1 + ----------------3000r 2

S p = --------------------------l2 1 + ----------------1500r 2

S p = -----------------------l2 1 + -------------750r 2

Formulas Modified for Eccentrically Loaded Columns Material

Steel

Both Ends of Column Fixed

One End Fixed and One End Rounded

Both Ends Rounded

S p = ------------------------------------------l2 cz 1 + ---------------------- + ----25 ,000r 2 r 2

S p = ------------------------------------------l2 cz 1 + ---------------------- + ----12 ,500r 2 r 2

S p = -------------------------------------2 l cz 1 + ----------------- + ----6250r 2 r 2

For materials other than steel, such as cast iron, use the Rankine formulas given in the upper table and add to the denominator the quantity cz ⁄ r 2 Both Ends of Column Fixed 2 IE P = 4π --------------l2

Euler's Formulas for Slender Columns One End Fixed and Both Ends One End Rounded Rounded 2 IE P = 2π --------------l2

2 IE P = π ----------l2

One End Fixed and One End Free 2 IE P = π ----------4l 2

Allowable Working Loads for Columns: To find the total allowable working load for a given section, divide the total ultimate load P (or p × area), as found by the appropriate formula above, by a suitable factor of safety.



COLUMNS

Factor of Safety for Machine Columns: When the conditions of loading and the physical qualities of the material used are accurately known, a factor of safety as low as 1.25 is sometimes used when minimum weight is important. Usually, however, a factor of safety of 2 to 2.5 is applied for steady loads. The factor of safety represents the ratio of the critical load Pcr to the working load. Application of Euler and Johnson Formulas: To determine whether the Euler or Johnson formula is applicable in any particular case, it is necessary to determine the value of the quantity Q ÷ r2. If Q ÷ r2 is greater than 2, then the Euler Formula (1) should be used; if Q ÷ r2 is less than 2, then the J. B. Johnson formula is applicable. Most compression members in machine design are in the range of proportions covered by the Johnson formula. For this reason a good procedure is to design machine elements on the basis of the Johnson formula and then as a check calculate Q ÷ r2 to determine whether the Johnson formula applies or the Euler formula should have been used. Example 1, Compression Member Design:A rectangular machine member 24 inches long and 1⁄2 × 1 inch in cross-section is to carry a compressive load of 4000 pounds along its axis. What is the factor of safety for this load if the material is machinery steel having a yield point of 40,000 pounds per square inch, the load is steady, and each end of the rod has a ball connection so that n = 1? From Formula (3) 40 ,000 × 24 × 24 Q = ---------------------------------------------------------------------------------- = 0.0778 1 × 3.1416 × 3.1416 × 30 ,000 ,000 (The values 40,000 and 30,000,000 were obtained from the table Strength Data for Iron and Steel on page 474.) The radius of gyration r for a rectangular section (page 239) is 0.289 × the dimension in the direction of bending. In columns, bending is most apt to occur in the direction in which the section is the weakest, the 1⁄2-inch dimension in this example. Hence, least radius of gyration r = 0.289 × 1⁄2 = 0.145 inch. Q 0.0778 = 3.70 ---- = -------------------r2 ( 0.145 ) 2 which is more than 2 so that the Euler formula will be used. s y Ar 2 40 ,000 × 1⁄2 × 1 P cr = ------------- = ----------------------------------3.70 Q = 5400 pounds so that the factor of safety is 5400 ÷ 4000 = 1.35 Example 2, Compression Member Design:In the preceding example, the column formulas were used to check the adequacy of a column of known dimensions. The more usual problem involves determining what the dimensions should be to resist a specified load. For example,: A 24-inch long bar of rectangular cross-section with width w twice its depth d is to carry a load of 4000 pounds. What must the width and depth be if a factor of safety of 1.35 is to be used? First determine the critical load Pcr: P cr = working load × factor of safety = 4000 × 1.35 = 5400 pounds


Machinery's Handbook 27th Edition COLUMNS

289

Next determine Q which, as in Example 1, will be 0.0778. Assume Formula (2) applies: Q-⎞ P cr = As y ⎛ 1 – ------⎝ 4r 2⎠ 0.0778 5400 = w × d × 40 ,000 ⎛ 1 – ----------------⎞ ⎝ 4r 2 ⎠ 0.01945 = 2d 2 × 40 ,000 ⎛⎝ 1 – -------------------⎞⎠ r2 5400 0.01945 -------------------------- = d 2 ⎛ 1 – -------------------⎞ ⎝ 40 ,000 × 2 r2 ⎠ As mentioned in Example 1 the least radius of gyration r of a rectangle is equal to 0.289 times the least dimension, d, in this case. Therefore, substituting for d the value r ÷ 0.289, 5400 r -⎞ 2 ⎛ 1 – 0.01945 -------------------------------------------⎞ = ⎛ -----------⎝ 0.289⎠ ⎝ 40 ,000 × 2 r2 ⎠ 5400 × 0.289 × 0.289-------------------------------------------------= r 2 – 0.01945 40 ,000 × 2 0.005638 = r 2 – 0.01945 r 2 = 0.0251 Checking to determine if Q ÷ r2 is greater or less than 2, Q = 0.0778 ------------------- = 3.1 0.0251 r2 therefore Formula (1) should have been used to determine r and dimensions w and d. Using Formula (1), 2

r -⎞ r 2 40 ,000 × 2 × ⎛ -----------⎝ 0.289⎠ × - = ----------------------------------------------------------,000 × -----------------------------------------5400 = 40 Q 0.0778 2d 2

r2

× 0.0778 × 0.289 × 0.289- = 0.0004386 r 4 = 5400 ------------------------------------------------------------------------40 ,000 × 2 0.145 d = ------------- = 0.50 inch 0.289 and w = 2d = 1 inch as in the previous example. American Institute of Steel Construction.—For main or secondary compression members with l/r ratios up to 120, safe unit stress = 17,000 − 0.485l2/r2. For columns and bracing or other secondary members with l/r ratios above 120, 18 ,000 Safe unit stress, psi = --------------------------------------- for bracing and secondary members. For main 1 + l 2 ⁄ 18 ,000r 2 18 ,000 l ⁄ r-⎞ members, safe unit stress, psi = --------------------------------------- × ⎛ 1.6 – -------200⎠ 1 + l 2 ⁄ 18 ,000r 2 ⎝ Pipe Columns: Allowable concentric loads for steel pipe columns based on the above formulas are given in the table on page 290.



ALLOWABLE LOADS FOR STEEL PIPE COLUMNS Allowable Concentric Loads for Steel Pipe Columns STANDARD STEEL PIPE 12

10

8

6

5

4

31⁄2

3

Wall Thickness, Inch

0.375

0.365

0.322

0.280

0.258

0.237

0.226

0.216

Weight per Foot, Pounds

49.56

40.48

28.55

18.97

14.62

10.79

9.11

7.58

Nominal Diameter, Inches

Effective Length (KL), Feeta 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 24 25 26

Allowable Concentric Loads in Thousands of Pounds 303 301 299 296 293 291 288 285 282 278 275 272 268 265 261 254 246 242 238

246 243 241 238 235 232 229 226 223 220 216 213 209 205 201 193 185 180 176

171 168 166 163 161 158 155 152 149 145 142 138 135 131 127 119 111 106 102

110 108 106 103 101 98 95 92 89 86 82 79 75 71 67 59 51 47 43

83 81 78 76 73 71 68 65 61 58 55 51 47 43 39 32 27 25 23

59 57 54 52 49 46 43 40 36 33 29 26 23 21 19 15 13 12

48 46 44 41 38 35 32 29 25 22 19 17 15 14 12 10

38 36 34 31 28 25 22 19 16 14 12 11 10 9

EXTRA STRONG STEEL PIPE Nominal Diameter, Inches Wall Thickness, Inch Weight per Foot, Pounds Effective Length (KL), Feeta 6 7 8 9 10 11 12 13 14 15 16 18 19 20 21 22 24 26 28

12 0.500 65.42 400 397 394 390 387 383 379 375 371 367 363 353 349 344 337 334 323 312 301

31⁄2 10 8 6 5 4 0.500 0.500 0.432 0.375 0.337 0.318 54.74 43.39 28.57 20.78 14.98 12.50 Allowable Concentric Loads in Thousands of Pounds 332 259 166 118 81 66 328 255 162 114 78 63 325 251 159 111 75 59 321 247 155 107 71 55 318 243 151 103 67 51 314 239 146 99 63 47 309 234 142 95 59 43 305 229 137 91 54 38 301 224 132 86 49 33 296 219 127 81 44 29 291 214 122 76 39 25 281 203 111 65 31 20 276 197 105 59 28 18 271 191 99 54 25 16 265 185 92 48 22 14 260 179 86 44 21 248 166 73 37 17 236 152 62 32 224 137 54 27

3 0.300 10.25 52 48 45 41 37 33 28 24 21 18 16 12 11

a With respect to radius of gyration. The effective length (KL) is the actual unbraced length, L, in feet, multiplied by the effective length factor (K) which is dependent upon the restraint at the ends of the unbraced length and the means available to resist lateral movements. K may be determined by referring to the last portion of this table.


Machinery's Handbook 27th Edition ALLOWABLE LOADS FOR STEEL PIPE COLUMNS

291

Allowable Concentric Loads for Steel Pipe Columns (Continued) DOUBLE-EXTRA STRONG STEEL PIPE Nominal Diameter, Inches

8

6

5

4

3

Wall Thickness, Inch

0.875

0.864

0.750

0.674

0.600

Weight per Foot, Pounds

72.42

53.16

38.55

27.54

18.58

Effective Length (KL), Feeta

Allowable Concentric Loads in Thousands of Pounds

6

431

306

216

147

91

7

424

299

209

140

84

8

417

292

202

133

77

9

410

284

195

126

69

10

403

275

187

118

60

11

395

266

178

109

51

12

387

257

170

100

43

13

378

247

160

91

37

14

369

237

151

81

32

15

360

227

141

70

28

16

351

216

130

62

24

17

341

205

119

55

22

18

331

193

108

49

19

321

181

97

44

20

310

168

87

40

22

288

142

72

33

24

264

119

61

26

240

102

52

28

213

88

44

EFFECTIVE LENGTH FACTORS (K) FOR VARIOUS COLUMN CONFIGURATIONS (a)

(b)

(c)

(d)

(e)

(f)

Buckled shape of column is shown by dashed line

Theoretical K value

0.5

0.7

1.0

1.0

2.0

2.0

Recommended design value when ideal conditions are approximated

0.65

0.80

1.2

1.0

2.10

2.0

Rotation fixed and translation fixed Rotation free and translation fixed End condition code Rotation fixed and translation free Rotation free and translation free

Load tables are given for 36 ksi yield stress steel. No load values are given below the heavy horizontal lines, because the Kl/r ratios (where l is the actual unbraced length in inches and r is the governing radius of gyration in inches) would exceed 200. Data from “Manual of Steel Construction,” 8th ed., 1980, with permission of the American Institute of Steel Construction.



PLATES, SHELLS, AND CYLINDERS

PLATES, SHELLS, AND CYLINDERS Flat Stayed Surfaces.—Large flat areas are often held against pressure by stays distributed at regular intervals over the surface. In boiler work, these stays are usually screwed into the plate and the projecting end riveted over to insure steam tightness. The U.S. Board of Supervising Inspectors and the American Boiler Makers Association rules give the following formula for flat stayed surfaces: C × t 2P = ------------S2 in which P =pressure in pounds per square inch C =a constant, which equals 112 for plates 7⁄16 inch and under 120, for plates over 7⁄16 inch thick 140, for plates with stays having a nut and bolt on the inside and outside 160, for plates with stays having washers of at least one-half the thickness of the plate, and with a diameter at least one-half of the greatest pitch t =thickness of plate in 16ths of an inch (thickness = 7⁄16, t = 7) S =greatest pitch of stays in inches Strength and Deflection of Flat Plates.—Generally, the formulas used to determine stresses and deflections in flat plates are based on certain assumptions that can be closely approximated in practice. These assumptions are: 1) the thickness of the plate is not greater than one-quarter the least width of the plate; 2) the greatest deflection when the plate is loaded is less than one-half the plate thickness; 3) the maximum tensile stress resulting from the load does not exceed the elastic limit of the material; and 4) all loads are perpendicular to the plane of the plate. Plates of ductile materials fail when the maximum stress resulting from deflection under load exceeds the yield strength; for brittle materials, failure occurs when the maximum stress reaches the ultimate tensile strength of the material involved. Square and Rectangular Flat Plates.—The formulas that follow give the maximum stress and deflection of flat steel plates supported in various ways and subjected to the loading indicated. These formulas are based upon a modulus of elasticity for steel of 30,000,000 pounds per square inch and a value of Poisson's ratio of 0.3. If the formulas for maximum stress, S, are applied without modification to other materials such as cast iron, aluminum, and brass for which the range of Poisson's ratio is about 0.26 to 0.34, the maximum stress calculations will be in error by not more than about 3 per cent. The deflection formulas may also be applied to materials other than steel by substituting in these formulas the appropriate value for E, the modulus of elasticity of the material (see pages 474 and 554). The deflections thus obtained will not be in error by more than about 3 per cent. In the stress and deflection formulas that follow, p =uniformly distributed load acting on plate, pounds per square inch W =total load on plate, pounds; W = p × area of plate L =distance between supports (length of plate), inches. For rectangular plates, L = long side, l = short side t =thickness of plate, inches S =maximum tensile stress in plate, pounds per square inch d =maximum deflection of plate, inches E =modulus of elasticity in tension. E = 30,000,000 pounds per square inch for steel


Machinery's Handbook 27th Edition PLATES, SHELLS, AND CYLINDERS

293

If metric SI units are used in the formulas, then, W =total load on plate, newtons L =distance between supports (length of plate), millimeters. For rectangular plates, L = long side, l = short side t =thickness of plate, millimeters S =maximum tensile stress in plate, newtons per mm squared d =maximum deflection of plate, mm E =modulus of elasticity, newtons per mm squared a) Square flat plate supported at top and bottom of all four edges and a uniformly distributed load over the surface of the plate. 0.0443WL 2S = 0.29W --------------(1) (2) d = --------------------------t2 Et 3 b) Square flat plate supported at the bottom only of all four edges and a uniformly distributed load over the surface of the plate. 0.0443WL 2 (3) S = 0.28W --------------(4) d = --------------------------t2 Et 3 c) Square flat plate with all edges firmly fixed and a uniformly distributed load over the surface of the plate. 0.0138WL 2 (5) S = 0.31W --------------(6) d = --------------------------t2 Et 3 d) Square flat plate with all edges firmly fixed and a uniform load over small circular area at the center. In Equations (7) and (9), r0 = radius of area to which load is applied. If r0 < 1.7t, use rs where r s =

1.6r 0 2 + t 2 – 0.675t .

L -⎞ S = 0.62W --------------- log ⎛ ------e⎝ 2r ⎠ t2 0

0.0568WL 2(8) d = --------------------------Et 3 e) Square flat plate with all edges supported above and below, or below only, and a concentrated load at the center. (See Case 4, above, for definition of r0). (7)

L -⎞ + 0.577 S = 0.62W --------------- log ⎛ ------e⎝ 2r ⎠ t2 0

2 (10) d = 0.1266WL ---------------------------Et 3 f) Rectangular plate with all edges supported at top and bottom and a uniformly distributed load over the surface of the plate.

(9)

0.75W 0.1422W (11) (12) S = -----------------------------------d = ----------------------------------L 2.21 l2 ⎞ Et 3 ⎛⎝ ---- + ----------⎞⎠ t2 ⎛ L --- + 1.61 ----3 2 ⎝l ⎠ 2 l L L g) Rectangular plate with all edges fixed and a uniformly distributed load over the surface of the plate. 0.5W S = -------------------------------------5 t2 ⎛ L --- + 0.623l ------------------⎞ ⎝l L5 ⎠

(13)

0.0284W d = ------------------------------------------L- + ----------------1.056l 2-⎞ Et 3 ⎛ --⎝ l3 L4 ⎠


(14)



Circular Flat Plates.—In the following formulas, R = radius of plate to supporting edge in inches; W = total load in pounds; and other symbols are the same as used for square and rectangular plates. If metric SI units are used, R = radius of plate to supporting edge in millimeters, and the values of other symbols are the same as those used for square and rectangular plates. a) Edge supported around the circumference and a uniformly distributed load over the surface of the plate. 0.221WR 2S = 0.39W --------------(15) (16) d = -----------------------t2 Et 3 b) Edge fixed around circumference and a uniformly distributed load over the surface of the plate. 0.0543WR 2 (17) S = 0.24W --------------(18) d = --------------------------t2 Et 3 c) Edge supported around the circumference and a concentrated load at the center. 0.55WR 2 R - – 0.0185 ----t 2d = ---------------------(19) --------------- 1 + 1.3 loge -------------S = 0.48W 0.325t Et 3 R2 t2 d) Edge fixed around circumference and a concentrated load at the center. R t 2S = 0.62W --------------- loge --------------- + 0.0264 ----0.325t t2 R2

(21)

0.22WR 2 d = ---------------------Et 3

(20)

(22)

Strength of Cylinders Subjected to Internal Pressure.—In designing a cylinder to withstand internal pressure, the choice of formula to be used depends on 1) the kind of material of which the cylinder is made (whether brittle or ductile); 2) the construction of the cylinder ends (whether open or closed); and 3) whether the cylinder is classed as a thin- or a thick-walled cylinder. A cylinder is considered to be thin-walled when the ratio of wall thickness to inside diameter is 0.1 or less and thick-walled when this ratio is greater than 0.1. Materials such as cast iron, hard steel, cast aluminum are considered to be brittle materials; low-carbon steel, brass, bronze, etc. are considered to be ductile. In the formulas that follow, p = internal pressure, pounds per square inch; D = inside diameter of cylinder, inches; t = wall thickness of cylinder, inches; µ = Poisson's ratio, = 0.3 for steel, 0.26 for cast iron, 0.34 for aluminum and brass; and S = allowable tensile stress, pounds per square inch. Metric SI units can be used in Formulas (23), (25), (26), and (27), where p = internal pressure in newtons per square millimeter; D = inside diameter of cylinder, millimeters; t = wall thickness, mm; µ = Poisson's ratio, = 0.3 for steel, 0.26 for cast iron, and 0.34 for aluminum and brass; and S = allowable tensile stress, N/mm2. For the use of metric SI units in Formula (24), see below. Dp Thin-walled Cylinders: (23) t = ------2S For low-pressure cylinders of cast iron such as are used for certain engine and press applications, a formula in common use is Dp t = ------------ + 0.3 2500


(24)


295

This formula is based on allowable stress of 1250 pounds per square inch and will give a wall thickness 0.3 inch greater than Formula (23) to allow for variations in metal thickness that may result from the casting process. If metric SI units are used in Formula (24), t = cylinder wall thickness in millimeters; D = inside diameter of cylinder, mm; and the allowable stress is in newtons per square millimeter. The value of 0.3 inches additional wall thickness is 7.62 mm, and the next highest number in preferred metric basic sizes is 8 mm. Thick-walled Cylinders of Brittle Material, Ends Open or Closed: Lamé's equation is used when cylinders of this type are subjected to internal pressure. + p- – 1⎞ t = D ---- ⎛ S----------⎠ 2⎝ S–p

(25)

The table Ratio of Outside Radius to Inside Radius, Thick Cylinders on page 296 is for convenience in calculating the dimensions of cylinders under high internal pressure without the use of Formula (25). Example, Use of the Table:Assume that a cylinder of 10 inches inside diameter is to withstand a pressure of 2500 pounds per square inch; the material is cast iron and the allowable stress is 6000 pounds per square inch. To solve the problem, locate the allowable stress per square inch in the left-hand column of the table and the working pressure at the top of the columns. Then find the ratio between the outside and inside radii in the body of the table. In this example, the ratio is 1.558, and hence the outside diameter of the cylinder should be 10 × 1.558, or about 155⁄8 inches. The thickness of the cylinder wall will therefore be (15.558 − 10)/2 = 2.779 inches. Unless very high-grade material is used and sound castings assured, cast iron should not be used for pressures exceeding 2000 pounds per square inch. It is well to leave more metal in the bottom of a hydraulic cylinder than is indicated by the results of calculations, because a hole of some size must be cored in the bottom to permit the entrance of a boring bar when finishing the cylinder, and when this hole is subsequently tapped and plugged it often gives trouble if there is too little thickness. For steady or gradually applied stresses, the maximum allowable fiber stress S may be assumed to be from 3500 to 4000 pounds per square inch for cast iron; from 6000 to 7000 pounds per square inch for brass; and 12,000 pounds per square inch for steel castings. For intermittent stresses, such as in cylinders for steam and hydraulic work, 3000 pounds per square inch for cast iron; 5000 pounds per square inch for brass; and 10,000 pounds per square inch for steel castings, is ordinarily used. These values give ample factors of safety. Note: In metric SI units, 1000 pounds per square inch equals 6.895 newtons per square millimeter. Thick-walled Cylinders of Ductile Material, Closed Ends: Clavarino's equation is used: D t = ---2

S + ( 1 – 2µ )p --------------------------------- – 1 S – ( 1 + µ )p

(26)

Thick-walled Cylinders of Ductile Material, Open Ends: Birnie's equation is used: t = D ---2

S----------------------------+ ( 1 – µ )p- – 1 S – ( 1 + µ )p

Spherical Shells Subjected to Internal Pressure.—Let: D =internal diameter of shell in inches p =internal pressure in pounds per square inch S =safe tensile stress per square inch t =thickness of metal in the shell, in inches.


(27)


PLATES, SHELLS, AND CYLINDERS Ratio of Outside Radius to Inside Radius, Thick Cylinders

Allowable Stress in Metal per Sq. In. of Section

Working Pressure in Cylinder, Pounds per Square Inch

2,000 2,500 3,000 3,500 4,000 4,500 5000 5,500 6,000 6,500 7,000 7,500 8,000 8,500 9,000 9,500 10,000 10,500 11,000 11,500 12,000 12,500 13,000 13,500 14,000 14,500 15,000 16,000

1000

2000

3000

4000

5000

6000

7000

1.732 1.527 1.414 1.341 1.291 1.253 1.224 1.201 1.183 … … … … … … … … … … … … … … … … … … …

… … 2.236 1.915 1.732 1.612 1.527 1.464 1.414 1.374 1.341 1.314 1.291 1.271 1.253 1.235 1.224 1.212 1.201 1.193 1.183 … … … … … … …

… … … … 2.645 2.236 2.000 1.844 1.732 1.647 1.581 1.527 1.483 1.446 1.414 1.386 1.362 1.341 1.322 1.306 1.291 1.277 1.264 1.253 1.243 1.233 1.224 1.209

… … … … … … 3.000 2.516 2.236 2.049 1.914 1.813 1.732 1.666 1.612 1.566 1.527 1.493 1.464 1.437 1.414 1.393 1.374 1.357 1.341 1.327 1.314 1.291

… … … … … … … … 3.316 2.768 2.449 2.236 2.081 1.963 1.871 1.795 1.732 1.678 1.633 1.593 1.558 1.527 1.500 1.475 1.453 1.432 1.414 1.381

… … … … … … … … … … 3.605 3.000 2.645 2.408 2.236 2.104 2.000 1.915 1.844 1.784 1.732 1.687 1.647 1.612 1.581 1.553 1.527 1.483

… … … … … … … … … … … … 3.872 3.214 2.828 2.569 2.380 2.236 2.121 2.027 1.949 1.878 1.825 1.775 1.732 1.693 1.658 1.599

pD Then, t = ------4S This formula also applies to hemi-spherical shells, such as the hemi-spherical head of a cylindrical container subjected to internal pressure, etc. If metric SI units are used, then: D =internal diameter of shell in millimeters p =internal pressure in newtons per square millimeter S =safe tensile stress in newtons per square millimeter t =thickness of metal in the shell in millimeters Meters can be used in the formula in place of millimeters, providing the treatment is consistent throughout.



297

Example:Find the thickness of metal required in the hemi-spherical end of a cylindrical vessel, 2 feet in diameter, subjected to an internal pressure of 500 pounds per square inch. The material is mild steel and a tensile stress of 10,000 pounds per square inch is allowable. × 2 × 12- = 0.3 inch t = 500 ----------------------------4 × 10 ,000 A similar example using metric SI units is as follows: find the thickness of metal required in the hemi-spherical end of a cylindrical vessel, 750 mm in diameter, subjected to an internal pressure of 3 newtons/mm2. The material is mild steel and a tensile stress of 70 newtons/mm2 is allowable. 3 × 750 t = ------------------ = 8.04 mm 4 × 70 If the radius of curvature of the domed head of a boiler or container subjected to internal pressure is made equal to the diameter of the boiler, the thickness of the cylindrical shell and of the spherical head should be made the same. For example, if a boiler is 3 feet in diameter, the radius of curvature of its head should also be 3 feet, if material of the same thickness is to be used and the stresses are to be equal in both the head and cylindrical portion. Collapsing Pressure of Cylinders and Tubes Subjected to External Pressures.—The following formulas may be used for finding the collapsing pressures of lap-welded Bessemer steel tubes: (28) P = 86 ,670 ---t- – 1386 D 3 P = 50 ,210 ,000 ⎛ ---t-⎞ ⎝ D⎠

(29)

in which P = collapsing pressure in pounds per square inch; D = outside diameter of tube or cylinder in inches; t = thickness of wall in inches. Formula (28) is for values of P greater than 580 pounds per square inch, and Formula (29) is for values of P less than 580 pounds per square inch. These formulas are substantially correct for all lengths of pipe greater than six diameters between transverse joints that tend to hold the pipe to a circular form. The pressure P found is the actual collapsing pressure, and a suitable factor of safety must be used. Ordinarily, a factor of safety of 5 is sufficient. In cases where there are repeated fluctuations of the pressure, vibration, shocks and other stresses, a factor of safety of from 6 to 12 should be used. If metric SI units are used the formulas are: (30) P = 597.6 ---t- – 9.556 D 3 P = 346 ,200 ⎛ ---t-⎞ ⎝ D⎠

(31)

where P = collapsing pressure in newtons per square millimeter; D = outside diameter of tube or cylinder in millimeters; and t = thickness of wall in millimeters. Formula (30) is for values of P greater than 4 N/mm2, and Formula (31) is for values of P less than 4 N/mm2. The table Tubes Subjected to External Pressure is based upon the requirements of the Steam Boat Inspection Service of the Department of Commerce and Labor and gives the permissible working pressures and corresponding minimum wall thickness for long, plain, lap-welded and seamless steel flues subjected to external pressure only. The table thicknesses have been calculated from the formula:




( F × p ) + 1386 ]D t = [--------------------------------------------86 ,670 in which D = outside diameter of flue or tube in inches; t = thickness of wall in inches; p = working pressure in pounds per square inch; F = factor of safety. The formula is applicable to working pressures greater than 100 pounds per square inch, to outside diameters from 7 to 18 inches, and to temperatures less than 650°F. The preceding Formulas (28) and (29) were determined by Prof. R. T. Stewart, Dean of the Mechanical Engineering Department of the University of Pittsburgh, in a series of experiments carried out at the plant of the National Tube Co., McKeesport, Pa. The apparent fiber stress under which the different tubes failed varied from about 7000 pounds per square inch for the relatively thinnest to 35,000 pounds per square inch for the relatively thickest walls. The average yield point of the material tested was 37,000 pounds and the tensile strength 58,000 pounds per square inch, so it is evident that the strength of a tube subjected to external fluid collapsing pressure is not dependent alone upon the elastic limit or ultimate strength of the material from which it is made. Tubes Subjected to External Pressure Outside Diameter of Tube, Inches

100

Working Pressure in Pounds per Square Inch

7 8 9 10 11 12 13 14 15 16 16 18

0.152 0.174 0.196 0.218 0.239 0.261 0.283 0.301 0.323 0.344 0.366 0.387

120

140

160

180

200

220

Thickness of Tube in Inches. Safety Factor, 5 0.160 0.183 0.206 0.229 0.252 0.275 0.298 0.320 0.343 0.366 0.389 0.412

0.168 0.193 0.217 0.241 0.265 0.289 0.313 0.337 0.361 0.385 0.409 0.433

0.177 0.202 0.227 0.252 0.277 0.303 0.328 0.353 0.378 0.404 0.429 0.454

0.185 0.211 0.237 0.264 0.290 0.317 0.343 0.369 0.396 0.422 0.448 0.475

0.193 0.220 0.248 0.275 0.303 0.330 0.358 0.385 0.413 0.440 0.468 0.496

0.201 0.229 0.258 0.287 0.316 0.344 0.373 0.402 0.430 0.459 0.488 0.516

Dimensions and Maximum Allowable Pressure of Tubes Subjected to External Pressure

Outside Dia., Inches

ThickMax. ness Pressure of Allowed, Material, psi Inches





2

0.095

427

3

0.109

327

4

0.134

21⁄4

0.095

380

31⁄4

0.120

332

41⁄2

0.134

238

21⁄2

0.109

392

31⁄2

0.120

308

5

0.148

235

23⁄4

0.109

356

33⁄4

0.120

282

6

0.165

199


303

Machinery's Handbook 27th Edition SHAFTS

299

SHAFTS Shaft Calculations Torsional Strength of Shafting.—In the formulas that follow, α =angular deflection of shaft in degrees c =distance from center of gravity to extreme fiber D =diameter of shaft in inches G =torsional modulus of elasticity = 11,500,000 pounds per square inch for steel J =polar moment of inertia of shaft cross-section (see table) l =length of shaft in inches N =angular velocity of shaft in revolutions per minute P =power transmitted in horsepower Ss =allowable torsional shearing stress in pounds per square inch T =torsional or twisting moment in inch-pounds Zp =polar section modulus (see table page 249) The allowable twisting moment for a shaft of any cross-section such as circular, square, etc., is: T = Ss × Zp

(1)

For a shaft delivering P horsepower at N revolutions per minute the twisting moment T being transmitted is: ,000PT = 63 -------------------N

(2)

The twisting moment T as determined by this formula should be less than the value determined by using Formula (7) if the maximum allowable stress Ss is not to be exceeded. The diameter of a solid circular shaft required to transmit a given torque T is: D =

3

5.1T ----------Ss

(3a)

or

D =

3

321 ,000 P----------------------NS s

(3b)

The allowable stresses that are generally used in practice are: 4000 pounds per square inch for main power-transmitting shafts; 6000 pounds per square inch for lineshafts carrying pulleys; and 8500 pounds per square inch for small, short shafts, countershafts, etc. Using these allowable stresses, the horsepower P transmitted by a shaft of diameter D, or the diameter D of a shaft to transmit a given horsepower P may be determined from the following formulas: For main power-transmitting shafts: 3

D NP = ---------80

(4a)

or

D =

3

80P ---------N

(4b)

53.5P -------------N

(5b)

For lineshafts carrying pulleys: 3

D N P = ----------53.5

(5a)

or

D =

3



SHAFTS

For small, short shafts: 3 38PD ND = 3 --------(6b) or P = ---------(6a) N 38 Shafts that are subjected to shocks, such as sudden starting and stopping, should be given a greater factor of safety resulting in the use of lower allowable stresses than those just mentioned. Example:What should be the diameter of a lineshaft to transmit 10 horsepower if the shaft is to make 150 revolutions per minute? Using Formula (5b),

D =

3

53.5 × 10 = 1.53 or, say, 1 9⁄ inches ---------------------16 150

Example:What horsepower would be transmitted by a short shaft, 2 inches in diameter, carrying two pulleys close to the bearings, if the shaft makes 300 revolutions per minute? Using Formula (6a), 3

2 × 300 = 63 horsepower P = -------------------38 Torsional Strength of Shafting, Calculations in Metric SI Units.—T h e a l l o w a b l e twisting moment for a shaft of any cross-section such as circular, square, etc., can be calculated from: T = Ss × Zp (7) where T = torsional or twisting moment in newton-millimeters; Ss = allowable torsional shearing stress in newtons per square millimeter; and Zp = polar section modulus in millimeters3. For a shaft delivering power of P kilowatts at N revolutions per minute, the twisting moment T being transmitted is: 6

6

10 P 9.55 × 10 P or T = -----------T = ----------------------------(8a) (8) N ω where T is in newton-millimeters, and ω = angular velocity in radians per second. The diameter D of a solid circular shaft required to transmit a given torque T is: D =

3

5.1T ----------Ss

(9a)

6

or

D =

3

48.7 × 10 P ----------------------------NS s

or

D =

3

5.1 × 10 P -------------------------ωS s

(9b)

6

(9c)

where D is in millimeters; T is in newton-millimeters; P is power in kilowatts; N = revolutions per minute; Ss = allowable torsional shearing stress in newtons per square millimeter, and ω = angular velocity in radians per second. If 28 newtons/mm2 and 59 newtons/mm2 are taken as the generally allowed stresses for main power-transmitting shafts and small short shafts, respectively, then using these allowable stresses, the power P transmitted by a shaft of diameter D, or the diameter D of a shaft to transmit a given power P may be determined from the following formulas:



301

For main power-transmitting shafts: 3

6

D N P = ------------------------(10a) 6 1.77 × 10 For small, short shafts:

or

D =

3

1.77 × 10 P ----------------------------N

(10b)

3

6 D N × 10 P P = ------------------------(11a) or D = 3 0.83 (11b) ----------------------------6 N 0.83 × 10 where P is in kilowatts, D is in millimeters, and N = revolutions per minute. Example:What should be the diameter of a power-transmitting shaft to transmit 150 kW at 500 rpm? 6

D =

3

1.77 × 10 × 150 ---------------------------------------- = 81 millimeters 500

Example:What power would a short shaft, 50 millimeters in diameter, transmit at 400 rpm? 3

50 × 400 P = ------------------------- = 60 kilowatts 6 0.83 × 10 Torsional Deflection of Circular Shafts.—Shafting must often be proportioned not only to provide the strength required to transmit a given torque, but also to prevent torsional deflection (twisting) through a greater angle than has been found satisfactory for a given type of service. For a solid circular shaft the torsional deflection in degrees is given by: α = 584Tl -------------(12) 4 D G Example:Find the torsional deflection for a solid steel shaft 4 inches in diameter and 48 inches long, subjected to a twisting moment of 24,000 inch-pounds. By Formula (12), 584 × 24 ,000 × 48 α = -------------------------------------------- = 0.23 degree 4 4 × 11 ,500 ,000 Formula (12) can be used with metric SI units, where α = angular deflection of shaft in degrees; T = torsional moment in newton-millimeters; l = length of shaft in millimeters; D = diameter of shaft in millimeters; and G = torsional modulus of elasticity in newtons per square millimeter. Example:Find the torsional deflection of a solid steel shaft, 100 mm in diameter and 1300 mm long, subjected to a twisting moment of 3 × 10 6 newton-millimeters. The torsional modulus of elasticity is 80,000 newtons/mm 2. By Formula (12) 6

584 × 3 × 10 × 1300 α = --------------------------------------------------- = 0.285 degree 4 100 × 80 ,000 The diameter of a shaft that is to have a maximum torsional deflection α is given by: TlD = 4.9 × 4 ------(13) Gα Formula (13) can be used with metric SI units, where D = diameter of shaft in millimeters; T = torsional moment in newton-millimeters; l = length of shaft in millime-



SHAFTS

ters; G = torsional modulus of elasticity in newtons per square millimeter; and α = angular deflection of shaft in degrees. According to some authorities, the allowable twist in steel transmission shafting should not exceed 0.08 degree per foot length of the shaft. The diameter D of a shaft that will permit a maximum angular deflection of 0.08 degree per foot of length for a given torque T or for a given horsepower P can be determined from the formulas: D = 0.29 4 T

P(14b) D = 4.6 × 4 --N Using metric SI units and assuming an allowable twist in steel transmission shafting of 0.26 degree per meter length, Formulas (14a) and (14b) become: (14a)

D = 2.26 4 T

or

P D = 125.7 × 4 --N where D = diameter of shaft in millimeters; T = torsional moment in newton-millimeters; P = power in kilowatts; and N = revolutions per minute. Another rule that has been generally used in mill practice limits the deflection to 1 degree in a length equal to 20 times the shaft diameter. For a given torque or horsepower, the diameter of a shaft having this maximum deflection is given by: D = 0.1 3 T

or

P(15b) D = 4.0 × 3 --N Example:Find the diameter of a steel lineshaft to transmit 10 horsepower at 150 revolutions per minute with a torsional deflection not exceeding 0.08 degree per foot of length. By Formula (14b), (15a)

or

10- = 2.35 inches D = 4.6 × 4 -------150 This diameter is larger than that obtained for the same horsepower and rpm in the example given for Formula (5b) in which the diameter was calculated for strength considerations only. The usual procedure in the design of shafting which is to have a specified maximum angular deflection is to compute the diameter first by means of Formulas (13), (14a), (14b), (15a), or (15b) and then by means of Formulas (3a), (3b), (4b), (5b), or (6b), using the larger of the two diameters thus found. Linear Deflection of Shafting.—For steel line shafting, it is considered good practice to limit the linear deflection to a maximum of 0.010 inch per foot of length. The maximum distance in feet between bearings, for average conditions, in order to avoid excessive linear deflection, is determined by the formulas: 2

L = 8.95 3 D for shafting subject to no bending action except it’s own weight 3

2

L = 5.2 D for shafting subject to bending action of pulleys, etc. in which D = diameter of shaft in inches and L = maximum distance between bearings in feet. Pulleys should be placed as close to the bearings as possible. In general, shafting up to three inches in diameter is almost always made from cold-rolled steel. This shafting is true and straight and needs no turning, but if keyways are cut in the shaft, it must usually be straightened afterwards, as the cutting of the keyways relieves the tension on the surface of the shaft produced by the cold-rolling process. Sizes of shafting from three to five inches in diameter may be either cold-rolled or turned, more frequently the latter, and all larger sizes of shafting must be turned because cold-rolled shafting is not available in diameters larger than 5 in.



303

Diameters of Finished Shafting (former American Standard ASA B17.1) Diameters, Inches TransmisMachinery sion Shafting Shafting 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

15⁄ 16

1

13⁄16

17⁄16

111⁄16

11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4

Minus Tolerances, Inchesa 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003 0.003

Diameters, Inches TransmisMachinery sion Shafting Shafting

1 15⁄16

23⁄16

27⁄16

215⁄16

37⁄16

113⁄16 17⁄8 115⁄16 2 21⁄16 21⁄8 23⁄16 21⁄4 25⁄16 23⁄8 27⁄16 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2 35⁄8

Minus Tolerances Inchesa 0.003 0.003 0.003 0.003 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004 0.004

Diameters, Inches TransmisMachinery sion Shafting Shafting

3 15⁄16 47⁄16 415⁄16 57⁄16 515⁄16 61⁄2 7 71⁄2 8 … …

33⁄4 37⁄8 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2 63⁄4 7 71⁄4 71⁄2 73⁄4 8 … …

Minus Tolerances, Inchesa 0.004 0.004 0.004 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.005 0.006 0.006 0.006 0.006 0.006 0.006 0.006 0.006 … …

a Note:—These tolerances are negative or minus and represent the maximum allowable variation below the exact nominal size. For instance the maximum diameter of the 115⁄16 inch shaft is 1.938 inch and its minimum allowable diameter is 1.935 inch. Stock lengths of finished transmission shafting shall be: 16, 20 and 24 feet.

Design of Transmission Shafting.—The following guidelines for the design of shafting for transmitting a given amount of power under various conditions of loading are based upon formulas given in the former American Standard ASA B17c Code for the Design of Transmission Shafting. These formulas are based on the maximum-shear theory of failure which assumes that the elastic limit of a ductile ferrous material in shear is practically onehalf its elastic limit in tension. This theory agrees, very nearly, with the results of tests on ductile materials and has gained wide acceptance in practice. The formulas given apply in all shaft designs including shafts for special machinery. The limitation of these formulas is that they provide only for the strength of shafting and are not concerned with the torsional or lineal deformations which may, in shafts used in machine design, be the controlling factor (see Torsional Deflection of Circular Shafts on page 301 and Linear Deflection of Shafting on page 302 for deflection considerations). In the formulas that follow, 4

B = 3 1 ÷ ( 1 – K ) (see Table 3) D =outside diameter of shaft in inches D1 =inside diameter of a hollow shaft in inches Km =shock and fatigue factor to be applied in every case to the computed bending moment (see Table 1) Kt =combined shock and fatigue factor to be applied in every case to the computed torsional moment (see Table 1) M =maximum bending moment in inch-pounds N =revolutions per minute P =maximum power to be transmitted by the shaft in horsepower



SHAFTS

pt =maximum allowable shearing stress under combined loading conditions in pounds per square inch (see Table 2) S =maximum allowable flexural (bending) stress, in either tension or compression in pounds per square inch (see Table 2) Ss =maximum allowable torsional shearing stress in pounds per square inch (see Table 2) T =maximum torsional moment in inch-pounds V =maximum transverse shearing load in pounds For shafts subjected to pure torsional loads only, 5.1K t T D = B 3 ---------------Ss

(16a)

or

321 ,000K t P D = B 3 ----------------------------Ss N

(16b)

For stationary shafts subjected to bending only, 10.2K m M D = B 3 ----------------------S For shafts subjected to combined torsion and bending,

or

(17)

5.1- ( K M ) 2 + ( K T ) 2 D = B 3 -----m t pt

(18a)

,000K t P⎞ 2 5.1- ( K M ) 2 + ⎛ 63 -------------------------D = B 3 -----m ⎝ ⎠ N pt

(18b)

Formulas (16a) to (18b) may be used for solid shafts or for hollow shafts. For solid shafts the factor B is equal to 1, whereas for hollow shafts the value of B depends on the value of K which, in turn, depends on the ratio of the inside diameter of the shaft to the outside diameter (D1 ÷ D = K). Table 3 gives values of B corresponding to various values of K. For short solid shafts subjected only to heavy transverse shear, the diameter of shaft required is: D =

1.7V---------Ss

(19)

Formulas (16a), (17), (18a) and (19), can be used unchanged with metric SI units. Formula (16b) becomes: 48.7K t P D = B 3 ------------------- and Formula (18b) becomes: Ss N 5.1 ( M ) 2 + ⎛ 9.55K t P⎞ 2 D = B 3 ------ Km ⎝ ------------------pt N ⎠ Throughout the formulas, D = outside diameter of shaft in millimeters; T = maximum torsional moment in newton-millimeters; Ss = maximum allowable torsional shearing stress in newtons per millimeter squared (see Table 2); P = maximum power to be transmitted in milliwatts; N = revolutions per minute; M = maximum bending moment in newton-millimeters; S = maximum allowable flexural (bending) stress, either in tension or compression in newtons per millimeter squared (see Table 2); pt = maximum allowable shearing stress under combined loading conditions in newtons



305

per millimeter squared; and V = maximum transverse shearing load in kilograms. The factors Km, Kt, and B are unchanged, and D1 = the inside diameter of a hollow shaft in millimeters. Table 1. Recommended Values of the Combined Shock and Fatigue Factors for Various Types of Load Stationary Shafts Kt Km

Type of Load Gradually applied and steady Suddenly applied, minor shocks only Suddenly applied, heavy shocks

1.0 1.5–2.0 …

Rotating Shafts Km Kt

1.0 1.5–2.0 …

1.5 1.5–2.0 2.0–3.0

1.0 1.0–1.5 1.5–3.0

Table 2. Recommended Maximum Allowable Working Stresses for Shafts Under Various Types of Load Type of Load Material “Commercial Steel” shafting without keyways “Commercial Steel” shafting with keyways Steel purchased under definite physical specs.

Simple Bending S = 16,000 S = 12,000 (See note a)

Pure Torsion Ss = 8000 Ss = 6000 (See note b)

Combined Stress pt = 8000 pt = 6000 (See note b)

a S = 60 per cent of the elastic limit in tension but not more than 36 per cent of the ultimate tensile strength. b S and p = 30 per cent of the elastic limit in tension but not more than 18 per cent of the ultimate s t tensile strength.

If the values in the Table are converted to metric SI units, note that 1000 pounds per square inch = 6.895 newtons per square millimeter.

Table 3. Values of the Factor B Corresponding to Various Values of K for Hollow Shafts D K = ------1 = D B =

3

4

1 ÷ (1 – K )

0.95

0.90

0.85

0.80

0.75

0.70

0.65

0.60

0.55

0.50

1.75

1.43

1.28

1.19

1.14

1.10

1.07

1.05

1.03

1.02

For solid shafts, B = 1 because K = 0, as follows: B =

3

4

1 ÷ (1 – K ) =

3

1 ÷ (1 – 0) = 1

Effect of Keyways on Shaft Strength.—Keyways cut into a shaft reduce its load carrying ability, particularly when impact loads or stress reversals are involved. To ensure an adequate factor of safety in the design of a shaft with standard keyway (width, one-quarter, and depth, one-eighth of shaft diameter), the former Code for Transmission Shafting tentatively recommended that shafts with keyways be designed on the basis of a solid circular shaft using not more than 75 per cent of the working stress recommended for the solid shaft. See also page 2363. Formula for Shafts of Brittle Materials.—The preceding formulas are applicable to ductile materials and are based on the maximum-shear theory of failure which assumes that the elastic limit of a ductile material in shear is one-half its elastic limit in tension. Brittle materials are generally stronger in shear than in tension; therefore, the maximumshear theory is not applicable. The maximum-normal-stress theory of failure is now generally accepted for the design of shafts made from brittle materials. A material may be considered to be brittle if its elongation in a 2-inch gage length is less than 5 per cent. Materials such as cast iron, hardened tool steel, hard bronze, etc., conform to this rule. The diameter of a shaft made of a brittle material may be determined from the following formula which is based on the maximum-normal-stress theory of failure:



SHAFTS 2 2 D = B 3 5.1 ------- ( K m M ) + ( K m M ) + ( K t T ) St

where St is the maximum allowable tensile stress in pounds per square inch and the other quantities are as previously defined. The formula can be used unchanged with metric SI units, where D = outside diameter of shaft in millimeters; St = the maximum allowable tensile stress in newtons per millimeter squared; M = maximum bending moment in newton-millimeters; and T = maximum torsional moment in newton-millimeters. The factors Km, Kt, and B are unchanged. Critical Speed of Rotating Shafts.—At certain speeds, a rotating shaft will become dynamically unstable and the resulting vibrations and deflections can result in damage not only to the shaft but to the machine of which it is a part. The speeds at which such dynamic instability occurs are called the critical speeds of the shaft. On page 196 are given formulas for the critical speeds of shafts subject to various conditions of loading and support. A shaft may be safely operated either above or below its critical speed, good practice indicating that the operating speed be at least 20 per cent above or below the critical. The formulas commonly used to determine critical speeds are sufficiently accurate for general purposes. However, the torque applied to a shaft has an important effect on its critical speed. Investigations have shown that the critical speeds of a uniform shaft are decreased as the applied torque is increased, and that there exist critical torques which will reduce the corresponding critical speed of the shaft to zero. A detailed analysis of the effects of applied torques on critical speeds may be found in a paper. “Critical Speeds of Uniform Shafts under Axial Torque,” by Golomb and Rosenberg presented at the First U.S. National Congress of Applied Mechanics in 1951. Shaft Couplings.—A shaft coupling is a device for fastening together the ends of two shafts, so that the rotary motion of one causes rotary motion of the other. One of the most simple and common forms of coupling is the flange coupling Figs. 1a and 1b. It consists of two flanged sleeves or hubs, each of which is keyed to the end of one of the two shafts to be connected. The sleeves are held together and prevented from rotating relative to each other by bolts through the flanges as indicated. Flange Coupling

Fig. 1a.

Fig. 1b.

Flexible Couplings: Flexible couplings are the most common mechanical means of compensating for unavoidable errors in alignment of shafts and shafting. When correctly applied, they are highly efficient for joining lengths of shafting without causing loss of power from bearing friction due to misalignment, and for use in direct motor drives for all kinds of machinery. Flexible couplings are not intended to be used for connecting a driven shaft and a driving shaft that are purposely placed in different planes or at an angle but are intended simply to overcome slight unavoidable errors in alignment that develop in service. There is a wide variety of flexible coupling designs; most of them consist essentially



307

of two flanged members or hubs, fastened to the shafts and connected by some yielding arrangement. Balance is an important factor in coupling selection or design; it is not sufficient that the coupling be perfectly balanced when installed, but it must remain in balance after wear has taken place. Comparison of Hollow and Solid Shafting with Same Outside Diameter.—T a b l e 4 that follows gives the per cent decrease in strength and weight of a hollow shaft relative to the strength and weight of a solid shaft of the same diameter. The upper figures in each line give the per cent decrease in strength and the lower figures give the per cent decrease in weight. Example:A 4-inch shaft, with a 2-inch hole through it, has a weight 25 per cent less than a solid 4-inch shaft, but its strength is decreased only 6.25 per cent. Table 4. Comparative Torsional Strengths and Weights of Hollow and Solid Shafting with Same Outside Diameter Dia. of Solid and Hollow Shaft, Inches 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4 4 41⁄4 41⁄2 43⁄4 5 51⁄2 6 61⁄2 7 71⁄2 8

Diameter of Axial Hole in Hollow Shaft, Inches 1

11⁄4

11⁄2

13⁄4

2

21⁄2

3

31⁄2

4

41⁄2

19.76 44.44 10.67 32.66 6.25 25.00 3.91 19.75 2.56 16.00 1.75 13.22 1.24 11.11 0.87 9.46 0.67 8.16 0.51 7.11 0.40 6.25 0.31 5.54 0.25 4.94 0.20 4.43 0.16 4.00 0.11 3.30 0.09 2.77 0.06 2.36 0.05 2.04 0.04 1.77 0.03 1.56

48.23 69.44 26.04 51.02 15.26 39.07 9.53 30.87 6.25 25.00 4.28 20.66 3.01 17.36 2.19 14.80 1.63 12.76 1.24 11.11 0.96 9.77 0.74 8.65 0.70 7.72 0.50 6.93 0.40 6.25 0.27 5.17 0.19 4.34 0.14 3.70 0.11 3.19 0.08 2.77 0.06 2.44

… … 53.98 73.49 31.65 56.25 19.76 44.44 12.96 36.00 8.86 29.74 6.25 25.00 4.54 21.30 3.38 18.36 2.56 16.00 1.98 14.06 1.56 12.45 1.24 11.11 1.00 9.97 0.81 8.10 0.55 7.43 0.40 6.25 0.29 5.32 0.22 4.59 0.16 4.00 0.13 3.51

… … … … 58.62 76.54 36.60 60.49 24.01 49.00 16.40 40.48 11.58 34.01 8.41 29.00 6.25 25.00 4.75 21.77 3.68 19.14 2.89 16.95 2.29 15.12 1.85 13.57 1.51 12.25 1.03 10.12 0.73 8.50 0.59 7.24 0.40 6.25 0.30 5.44 0.23 4.78

… … … … … … 62.43 79.00 40.96 64.00 27.98 52.89 19.76 44.44 14.35 37.87 10.67 32.66 8.09 28.45 6.25 25.00 4.91 22.15 3.91 19.75 3.15 17.73 2.56 16.00 1.75 13.22 1.24 11.11 0.90 9.47 0.67 8.16 0.51 7.11 0.40 6.25

… … … … … … … … … … 68.30 82.63 48.23 69.44 35.02 59.17 26.04 51.02 19.76 44.44 15.26 39.07 11.99 34.61 9.53 30.87 7.68 27.70 6.25 25.00 4.27 20.66 3.02 17.36 2.19 14.79 1.63 12.76 1.24 11.11 0.96 9.77

… … … … … … … … … … … … … … 72.61 85.22 53.98 73.49 40.96 64.00 31.65 56.25 24.83 49.85 19.76 44.44 15.92 39.90 12.96 36.00 8.86 29.76 6.25 25.00 4.54 21.30 3.38 18.36 2.56 16.00 1.98 14.06

… … … … … … … … … … … … … … … … … … 75.89 87.10 58.62 76.56 46.00 67.83 36.60 60.49 29.48 54.29 24.01 49.00 16.40 40.48 11.58 34.02 8.41 28.99 6.25 25.00 4.75 21.77 3.68 19.14

… … … … … … … … … … … … … … … … … … … … … … 78.47 88.59 62.43 79.00 50.29 70.91 40.96 64.00 27.98 52.89 19.76 44.44 14.35 37.87 10.67 32.66 8.09 28.45 6.25 25.00

… … … … … … … … … … … … … … … … … … … … … … … … … … 80.56 89.75 65.61 81.00 44.82 66.94 31.65 56.25 23.98 47.93 17.08 41.33 12.96 36.00 10.02 31.64

The upper figures in each line give number of per cent decrease in strength; the lower figures give per cent decrease in weight.



SPRINGS

SPRINGS Introduction to Spring Design Many advances have been made in the spring industry in recent years. For example: developments in materials permit longer fatigue life at higher stresses; simplified design procedures reduce the complexities of design, and improved methods of manufacture help to speed up some of the complicated fabricating procedures and increase production. New types of testing instruments and revised tolerances also permit higher standards of accuracy. Designers should also consider the possibility of using standard springs now available from stock. They can be obtained from spring manufacturing companies located in different areas, and small shipments usually can be made quickly. Designers of springs require information in the following order of precedence to simplify design procedures. 1) Spring materials and their applications 2) Allowable spring stresses 3) Spring design data with tables of spring characteristics, tables of formulas, and tolerances. Only the more commonly used types of springs are covered in detail here. Special types and designs rarely used such as torsion bars, volute springs, Belleville washers, constant force, ring and spiral springs and those made from rectangular wire are only described briefly. Belleville and disc springs are discussed in the section DISC SPRINGS starting on page 354 Notation.—The following symbols are used in spring equations: AC = Active coils b =Widest width of rectangular wire, inches CL = Compressed length, inches D =Mean coil diameter, inches = OD − d d =Diameter of wire or side of square, inches E =Modulus of elasticity in tension, pounds per square inch F =Deflection, for N coils, inches F° =Deflection, for N coils, rotary, degrees f =Deflection, for one active coil FL = Free length, unloaded spring, inches G =Modulus of elasticity in torsion, pounds per square inch IT = Initial tension, pounds K =Curvature stress correction factor L =Active length subject to deflection, inches N =Number of active coils, total P =Load, pounds p =pitch, inches R =Distance from load to central axis, inches S or St = Stress, torsional, pounds per square inch Sb =Stress, bending, pounds per square inch SH = Solid height Sit = Stress, torsional, due to initial tension, pounds per square inch T =Torque = P × R, pound-inches TC = Total coils t =Thickness, inches U =Number of revolutions = F °/360°


Machinery's Handbook 27th Edition SPRING MATERIALS

309

Spring Materials The spring materials most commonly used include high-carbon spring steels, alloy spring steels, stainless spring steels, copper-base spring alloys, and nickel-base spring alloys. High-Carbon Spring Steels in Wire Form.—These spring steels are the most commonly used of all spring materials because they are the least expensive, are easily worked, and are readily available. However, they are not satisfactory for springs operating at high or low temperatures or for shock or impact loading. The following wire forms are available: Music Wire, ASTM A228 (0.80–0.95 per cent carbon): This is the most widely used of all spring materials for small springs operating at temperatures up to about 250 degrees F. It is tough, has a high tensile strength, and can withstand high stresses under repeated loading. The material is readily available in round form in diameters ranging from 0.005 to 0.125 inch and in some larger sizes up to 3⁄16 inch. It is not available with high tensile strengths in square or rectangular sections. Music wire can be plated easily and is obtainable pretinned or preplated with cadmium, but plating after spring manufacture is usually preferred for maximum corrosion resistance. Oil-Tempered MB Grade, ASTM A229 (0.60–0.70 per cent carbon): This general-purpose spring steel is commonly used for many types of coil springs where the cost of music wire is prohibitive and in sizes larger than are available in music wire. It is readily available in diameters ranging from 0.125 to 0.500 inch, but both smaller and larger sizes may be obtained. The material should not be used under shock and impact loading conditions, at temperatures above 350 degrees F., or at temperatures in the sub-zero range. Square and rectangular sections of wire are obtainable in fractional sizes. Annealed stock also can be obtained for hardening and tempering after coiling. This material has a heat-treating scale that must be removed before plating. Oil-Tempered HB Grade, SAE 1080 (0.75–0.85 per cent carbon): This material is similar to the MB Grade except that it has a higher carbon content and a higher tensile strength. It is obtainable in the same sizes and is used for more accurate requirements than the MB Grade, but is not so readily available. In lieu of using this material it may be better to use an alloy spring steel, particularly if a long fatigue life or high endurance properties are needed. Round and square sections are obtainable in the oil-tempered or annealed conditions. Hard-Drawn MB Grade, ASTM A227 (0.60–0.70 per cent carbon): This grade is used for general-purpose springs where cost is the most important factor. Although increased use in recent years has resulted in improved quality, it is best not to use it where long life and accuracy of loads and deflections are important. It is available in diameters ranging from 0.031 to 0.500 inch and in some smaller and larger sizes also. The material is available in square sections but at reduced tensile strengths. It is readily plated. Applications should be limited to those in the temperature range of 0 to 250 degrees F. High-Carbon Spring Steels in Flat Strip Form.—Two types of thin, flat, high-carbon spring steel strip are most widely used although several other types are obtainable for specific applications in watches, clocks, and certain instruments. These two compositions are used for over 95 per cent of all such applications. Thin sections of these materials under 0.015 inch having a carbon content of over 0.85 per cent and a hardness of over 47 on the Rockwell C scale are susceptible to hydrogen-embrittlement even though special plating and heating operations are employed. The two types are described as follows: Cold-Rolled Spring Steel, Blue-Tempered or Annealed, SAE 1074, also 1064, and 1070 (0.60 to 0.80 per cent carbon): This very popular spring steel is available in thicknesses ranging from 0.005 to 0.062 inch and in some thinner and thicker sections. The material is available in the annealed condition for forming in 4-slide machines and in presses, and can



SPRING MATERIALS

readily be hardened and tempered after forming. It is also available in the heat-treated or blue-tempered condition. The steel is obtainable in several finishes such as straw color, blue color, black, or plain. Hardnesses ranging from 42 to 46 Rockwell C are recommended for spring applications. Uses include spring clips, flat springs, clock springs, and motor, power, and spiral springs. Cold-Rolled Spring Steel, Blue-Tempered Clock Steel, SAE 1095 (0.90 to 1.05 per cent carbon): This popular type should be used principally in the blue-tempered condition. Although obtainable in the annealed condition, it does not always harden properly during heat-treatment as it is a “shallow” hardening type. It is used principally in clocks and motor springs. End sections of springs made from this steel are annealed for bending or piercing operations. Hardnesses usually range from 47 to 51 Rockwell C. Other materials available in strip form and used for flat springs are brass, phosphorbronze, beryllium-copper, stainless steels, and nickel alloys. Alloy Spring Steels.—These spring steels are used for conditions of high stress, and shock or impact loadings. They can withstand both higher and lower temperatures than the high-carbon steels and are obtainable in either the annealed or pretempered conditions. Chromium Vanadium, ASTM A231: This very popular spring steel is used under conditions involving higher stresses than those for which the high-carbon spring steels are recommended and is also used where good fatigue strength and endurance are needed. It behaves well under shock and impact loading. The material is available in diameters ranging from 0.031 to 0.500 inch and in some larger sizes also. In square sections it is available in fractional sizes. Both the annealed and pretempered types are available in round, square, and rectangular sections. It is used extensively in aircraft-engine valve springs and for springs operating at temperatures up to 425 degrees F. Silicon Manganese: This alloy steel is quite popular in Great Britain. It is less expensive than chromium-vanadium steel and is available in round, square, and rectangular sections in both annealed and pretempered conditions in sizes ranging from 0.031 to 0.500 inch. It was formerly used for knee-action springs in automobiles. It is used in flat leaf springs for trucks and as a substitute for more expensive spring steels. Chromium Silicon, ASTM A401: This alloy is used for highly stressed springs that require long life and are subjected to shock loading. It can be heat-treated to higher hardnesses than other spring steels so that high tensile strengths are obtainable. The most popular sizes range from 0.031 to 0.500 inch in diameter. Very rarely are square, flat, or rectangular sections used. Hardnesses ranging from 50 to 53 Rockwell C are quite common and the alloy may be used at temperatures up to 475 degrees F. This material is usually ordered specially for each job. Stainless Spring Steels.—The use of stainless spring steels has increased and several compositions are available all of which may be used for temperatures up to 550 degrees F. They are all corrosion resistant. Only the stainless 18-8 compositions should be used at sub-zero temperatures. Stainless Type 302, ASTM A313 (18 per cent chromium, 8 per cent nickel): This stainless spring steel is very popular because it has the highest tensile strength and quite uniform properties. It is cold-drawn to obtain its mechanical properties and cannot be hardened by heat treatment. This material is nonmagnetic only when fully annealed and becomes slightly magnetic due to the cold-working performed to produce spring properties. It is suitable for use at temperatures up to 550 degrees F. and for sub-zero temperatures. It is very corrosion resistant. The material best exhibits its desirable mechanical properties in diameters ranging from 0.005 to 0.1875 inch although some larger diameters are available. It is also available as hard-rolled flat strip. Square and rectangular sections are available but are infrequently used.


Machinery's Handbook 27th Edition SPRING MATERIALS

311

Stainless Type 304, ASTM A313 (18 per cent chromium, 8 per cent nickel): This material is quite similar to Type 302, but has better bending properties and about 5 per cent lower tensile strength. It is a little easier to draw, due to the slightly lower carbon content. Stainless Type 316, ASTM A313 (18 per cent chromium, 12 per cent nickel, 2 per cent molybdenum): This material is quite similar to Type 302 but is slightly more corrosion resistant because of its higher nickel content. Its tensile strength is 10 to 15 per cent lower than Type 302. It is used for aircraft springs. Stainless Type 17-7 PH ASTM A313 (17 per cent chromium, 7 per cent nickel): T h i s alloy, which also contains small amounts of aluminum and titanium, is formed in a moderately hard state and then precipitation hardened at relatively low temperatures for several hours to produce tensile strengths nearly comparable to music wire. This material is not readily available in all sizes, and has limited applications due to its high manufacturing cost. Stainless Type 414, SAE 51414 (12 per cent chromium, 2 per cent nickel): This alloy has tensile strengths about 15 per cent lower than Type 302 and can be hardened by heat-treatment. For best corrosion resistance it should be highly polished or kept clean. It can be obtained hard drawn in diameters up to 0.1875 inch and is commonly used in flat coldrolled strip for stampings. The material is not satisfactory for use at low temperatures. Stainless Type 420, SAE 51420 (13 per cent chromium): This is the best stainless steel for use in large diameters above 0.1875 inch and is frequently used in smaller sizes. It is formed in the annealed condition and then hardened and tempered. It does not exhibit its stainless properties until after it is hardened. Clean bright surfaces provide the best corrosion resistance, therefore the heat-treating scale must be removed. Bright hardening methods are preferred. Stainless Type 431, SAE 51431 (16 per cent chromium, 2 per cent nickel): This spring alloy acquires high tensile properties (nearly the same as music wire) by a combination of heat-treatment to harden the wire plus cold-drawing after heat-treatment. Its corrosion resistance is not equal to Type 302. Copper-Base Spring Alloys.—Copper-base alloys are important spring materials because of their good electrical properties combined with their good resistance to corrosion. Although these materials are more expensive than the high-carbon and the alloy steels, they nevertheless are frequently used in electrical components and in sub-zero temperatures. Spring Brass, ASTM B 134 (70 per cent copper, 30 per cent zinc): This material is the least expensive and has the highest electrical conductivity of the copper-base alloys. It has a low tensile strength and poor spring qualities, but is extensively used in flat stampings and where sharp bends are needed. It cannot be hardened by heat-treatment and should not be used at temperatures above 150 degrees F., but is especially good at sub-zero temperatures. Available in round sections and flat strips, this hard-drawn material is usually used in the “spring hard” temper. Phosphor Bronze, ASTM B 159 (95 per cent copper, 5 per cent tin): This alloy is the most popular of this group because it combines the best qualities of tensile strength, hardness, electrical conductivity, and corrosion resistance with the least cost. It is more expensive than brass, but can withstand stresses 50 per cent higher.The material cannot be hardened by heat-treatment. It can be used at temperatures up to 212 degrees F. and at subzero temperatures. It is available in round sections and flat strip, usually in the “extra-hard” or “spring hard” tempers. It is frequently used for contact fingers in switches because of its low arcing properties. An 8 per cent tin composition is used for flat springs and a superfine grain composition called “Duraflex,” has good endurance properties. Beryllium Copper, ASTM B 197 (98 per cent copper, 2 per cent beryllium): T h i s a l l o y can be formed in the annealed condition and then precipitation hardened after forming at



SPRING MATERIALS

temperatures around 600 degrees F, for 2 to 3 hours. This treatment produces a high hardness combined with a high tensile strength. After hardening, the material becomes quite brittle and can withstand very little or no forming. It is the most expensive alloy in the group and heat-treating is expensive due to the need for holding the parts in fixtures to prevent distortion. The principal use of this alloy is for carrying electric current in switches and in electrical components. Flat strip is frequently used for contact fingers. Nickel-Base Spring Alloys.—Nickel-base alloys are corrosion resistant, withstand both elevated and sub-zero temperatures, and their non-magnetic characteristic makes them useful for such applications as gyroscopes, chronoscopes, and indicating instruments. These materials have a high electrical resistance and therefore should not be used for conductors of electrical current. Monel* (67 per cent nickel, 30 per cent copper): This material is the least expensive of the nickel-base alloys. It also has the lowest tensile strength but is useful due to its resistance to the corrosive effects of sea water and because it is nearly non-magnetic. The alloy can be subjected to stresses slightly higher than phosphor bronze and nearly as high as beryllium copper. Its high tensile strength and hardness are obtained as a result of colddrawing and cold-rolling only, since it can not be hardened by heat-treatment. It can be used at temperatures ranging from −100 to +425 degrees F. at normal operating stresses and is available in round wires up to 3⁄16 inch in diameter with quite high tensile strengths. Larger diameters and flat strip are available with lower tensile strengths. “K” Monel * (66 per cent nickel, 29 per cent copper, 3 per cent aluminum): This material is quite similar to Monel except that the addition of the aluminum makes it a precipitation-hardening alloy. It may be formed in the soft or fairly hard condition and then hardened by a long-time age-hardening heat-treatment to obtain a tensile strength and hardness above Monel and nearly as high as stainless steel. It is used in sizes larger than those usually used with Monel, is non-magnetic and can be used in temperatures ranging from − 100 to + 450 degrees F. at normal working stresses under 45,000 pounds per square inch. Inconel*(78 per cent nickel, 14 per cent chromium, 7 per cent iron): This is one of the most popular of the non-magnetic nickel-base alloys because of its corrosion resistance and because it can be used at temperatures up to 700 degrees F. It is more expensive than stainless steel but less expensive than beryllium copper. Its hardness and tensile strength is higher than that of “K” Monel and is obtained as a result of cold-drawing and cold-rolling only. It cannot be hardened by heat treatment. Wire diameters up to 1⁄4 inch have the best tensile properties. It is often used in steam valves, regulating valves, and for springs in boilers, compressors, turbines, and jet engines. Inconel “X”*(70 per cent nickel, 16 per cent chromium, 7 per cent iron): This material is quite similar to Inconel but the small amounts of titanium, columbium and aluminum in its composition make it a precipitation-hardening alloy. It can be formed in the soft or partially hard condition and then hardened by holding it at 1200 degrees F. for 4 hours. It is non-magnetic and is used in larger sections than Inconel. This alloy is used at temperatures up to 850 degrees F. and at stresses up to 55,000 pounds per square inch. Duranickel* (“Z” Nickel) (98 per cent nickel): This alloy is non-magnetic, corrosion resistant, has a high tensile strength and is hardenable by precipitation hardening at 900 degrees F. for 6 hours. It may be used at the same stresses as Inconel but should not be used at temperatures above 500 degrees F. Nickel-Base Spring Alloys with Constant Moduli of Elasticity.—Some special nickel alloys have a constant modulus of elasticity over a wide temperature range. These materials are especially useful where springs undergo temperature changes and must exhibit uniform spring characteristics. These materials have a low or zero thermo-elastic coefficient * Trade name of the International Nickel Company.


Machinery's Handbook 27th Edition STRESSES IN SPRINGS

313

and therefore do not undergo variations in spring stiffness because of modulus changes due to temperature differentials. They also have low hysteresis and creep values which makes them preferred for use in food-weighing scales, precision instruments, gyroscopes, measuring devices, recording instruments and computing scales where the temperature ranges from − 50 to + 150 degrees F. These materials are expensive, none being regularly stocked in a wide variety of sizes. They should not be specified without prior discussion with spring manufacturers because some suppliers may not fabricate springs from these alloys due to the special manufacturing processes required. All of these alloys are used in small wire diameters and in thin strip only and are covered by U.S. patents. They are more specifically described as follows: Elinvar* (nickel, iron, chromium): This alloy, the first constant-modulus alloy used for hairsprings in watches, is an austenitic alloy hardened only by cold-drawing and cold-rolling. Additions of titanium, tungsten, molybdenum and other alloying elements have brought about improved characteristics and precipitation-hardening abilities. These improved alloys are known by the following trade names: Elinvar Extra, Durinval, Modulvar and Nivarox. Ni-Span C* (nickel, iron, chromium, titanium): This very popular constant-modulus alloy is usually formed in the 50 per cent cold-worked condition and precipitation-hardened at 900 degrees F. for 8 hours, although heating up to 1250 degrees F. for 3 hours produces hardnesses of 40 to 44 Rockwell C, permitting safe torsional stresses of 60,000 to 80,000 pounds per square inch. This material is ferromagnetic up to 400 degrees F; above that temperature it becomes non-magnetic. Iso-Elastic† (nickel, iron, chromium, molybdenum): This popular alloy is relatively easy to fabricate and is used at safe torsional stresses of 40,000 to 60,000 pounds per square inch and hardnesses of 30 to 36 Rockwell C. It is used principally in dynamometers, instruments, and food-weighing scales. Elgiloy‡ (nickel, iron, chromium, cobalt): This alloy, also known by the trade names 8J Alloy, Durapower, and Cobenium, is a non-magnetic alloy suitable for sub-zero temperatures and temperatures up to about 1000 degrees F., provided that torsional stresses are kept under 75,000 pounds per square inch. It is precipitation-hardened at 900 degrees F. for 8 hours to produce hardnesses of 48 to 50 Rockwell C. The alloy is used in watch and instrument springs. Dynavar** (nickel, iron, chromium, cobalt): This alloy is a non-magnetic, corrosionresistant material suitable for sub-zero temperatures and temperatures up to about 750 degrees F., provided that torsional stresses are kept below 75,000 pounds per square inch. It is precipitation-hardened to produce hardnesses of 48 to 50 Rockwell C and is used in watch and instrument springs. Spring Stresses Allowable Working Stresses for Springs.—The safe working stress for any particular spring depends to a large extent on the following items: 1) Type of spring — whether compression, extension, torsion, etc. 2) Size of spring — small or large, long or short 3) Spring material 4) Size of spring material 5) Type of service — light, average, or severe 6) Stress range — low, average, or high * Trade name of Soc. Anon. de Commentry Fourchambault et Decazeville, Paris, France. † Trade name of John Chatillon & Sons. ‡ Trade name of Elgin National Watch Company. ** Trade name of Hamilton Watch Company.



STRESSES IN SPRINGS

7) Loading — static, dynamic, or shock 8) Operating temperature 9) Design of spring — spring index, sharp bends, hooks. Consideration should also be given to other factors that affect spring life: corrosion, buckling, friction, and hydrogen embrittlement decrease spring life; manufacturing operations such as high-heat stress-equalizing, presetting, and shot-peening increase spring life. Item 5, the type of service to which a spring is subjected, is a major factor in determining a safe working stress once consideration has been given to type of spring, kind and size of material, temperature, type of loading, and so on. The types of service are: Light Service: This includes springs subjected to static loads or small deflections and seldom-used springs such as those in bomb fuses, projectiles, and safety devices. This service is for 1,000 to 10,000 deflections. Average Service: This includes springs in general use in machine tools, mechanical products, and electrical components. Normal frequency of deflections not exceeding 18,000 per hour permit such springs to withstand 100,000 to 1,000,000 deflections. Severe Service: This includes springs subjected to rapid deflections over long periods of time and to shock loading such as in pneumatic hammers, hydraulic controls and valves. This service is for 1,000,000 deflections, and above. Lowering the values 10 per cent permits 10,000,000 deflections. Figs. 1 through 6 show curves that relate the three types of service conditions to allowable working stresses and wire sizes for compression and extension springs, and safe values are provided. Figs. 7 through 10 provide similar information for helical torsion springs. In each chart, the values obtained from the curves may be increased by 20 per cent (but not beyond the top curves on the charts if permanent set is to be avoided) for springs that are baked, and shot-peened, and compression springs that are pressed. Springs stressed slightly above the Light Service curves will take a permanent set. A curvature correction factor is included in all curves, and is used in spring design calculations (see examples beginning page 321). The curves may be used for materials other than those designated in Figs. 1 through 10, by applying multiplication factors as given in Table 1. LIVE GRAPH Click here to view

160

Torsional Stress (corrected) Pounds per Square Inch (thousands)

150

Hard Drawn Steel Wire QQ-W-428, Type II; ASTM A227, Class II

140 130 120

Light Service

Average Service

110

Severe Service 100 90 80

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500

70

Wire Diameter (inch)

Fig. 1. Allowable Working Stresses for Compression Springs — Hard Drawn Steel Wirea



315

LIVE GRAPH 220 210 200 190 180 170 160 150 140 130 120 110 100 90 80

MUSIC WIRE QQ-Q-470, ASTM A228

Light Service Average Service Severe Service

0 .010 .020 .030 .040 .050 .060 .070 .080 .090 .100 .110 .120 .130 .140 .150 .160 .170 .180 .190 .200 .210 .220 .230 .240 .250

Torsional Stress (Corrected) Pounds per Square Inch (thousands)

Click here to view


Fig. 2. Allowable Working Stresses for Compression Springs — Music Wirea LIVE GRAPH Click here to view

160


150

Oil-tempered Steel Wire QQ-W-428, Type I; ASTM A229, Class II

140

Light Service

130

Average Service

120

Severe Service

110 100 90 80

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500

70


Fig. 3. Allowable Working Stresses for Compression Springs — Oil-Tempereda LIVE GRAPH


190 180 170

Click here to view

Chrome-silicon Alloy Steel Wire QQ-W-412, comp 2, Type II; ASTM A401 Light Service Average Service Severe Service

160 150 140 130 120

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500

110


Fig. 4. Allowable Working Stresses for Compression Springs — Chrome-Silicon Alloy Steel Wirea



STRESSES IN SPRINGS LIVE GRAPH Click here to view

160

Corrosion-resisting Steel Wire QQ-W-423, ASTM A313


150 140

Light service Average service

130 120

Severe service 110 100 90

70

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500

80


Fig. 5. Allowable Working Stresses for Compression Springs — Corrosion-Resisting Steel Wirea LIVE GRAPH Chrome-vanadium Alloy Steel Wire, ASTM A231 Light service Average service

Severe service

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500


Click here to view

190 180 170 160 150 140 130 120 110 100 90 80


Fig. 6. Allowable Working Stresses for Compression Springs — Chrome-Vanadium Alloy Steel Wirea Click here to view

Music Wire, ASTM A228

Light service Average service Severe service

0 .010 .020 .030 .040 .050 .060 .070 .080 .090 .100 .110 .120 .130 .140 .150 .160 .170 .180 .190 .200 .210 .220 .230 .240 .250

Stress, Pounds per Square Inch (thousands)

LIVE GRAPH

270 260 250 240 230 220 210 200 190 180 170 160 150 140 130 120


Fig. 7. Recommended Design Stresses in Bending for Helical Torsion Springs — Round Music Wire



317

260 250 240 230 220 210 200 190 180 170 160 150 140 130 120 110

Click here to view

Oil-tempered MB Grade, ASTM A229 Type I

Light service Average service Severe service

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500


LIVE GRAPH


Fig. 8. Recommended Design Stresses in Bending for Helical Torsion Springs — Oil-Tempered MB Round Wire Click here to view

Stainless Steel, “18-8,” Types 302 & 304 ASTM A313 Light Service Average Service Severe Service

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500


LIVE GRAPH

220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70


Fig. 9. Recommended Design Stresses in Bending for Helical Torsion Springs — Stainless Steel Round Wire Click here to view

Chrome-silicon, ASTM A401 Light service Average service Severe service

0 .020 .040 .060 .080 .100 .120 .140 .160 .180 .200 .220 .240 .260 .280 .300 .320 .340 .360 .380 .400 .420 .440 .460 .480 .500


LIVE GRAPH

290 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140


Fig. 10. Recommended Design Stresses in Bending for Helical Torsion Springs — Chrome-Silicon Round Wire a Although Figs. 1 through 6 are for compression springs, they may also be used for extension springs; for extension springs, reduce the values obtained from the curves by 10 to 15 per cent.



STRESSES IN SPRINGS Table 1. Correction Factors for Other Materials Compression and Tension Springs Material

Factor

Material

Factor

Silicon-manganese

Multiply the values in the chromium-vanadium curves (Fig. 6) by 0.90

Stainless Steel, 316

Valve-spring quality wire

Use the values in the chromiumvanadium curves (Fig. 6)

Multiply the values in the corrosion-resisting steel curves (Fig. 5) by 0.90

Stainless Steel, 304 and 420

Multiply the values in the corrosion-resisting steel curves (Fig. 5) by 0.95

Stainless Steel, 431 and 17-7PH

Multiply the values in the music wire curves (Fig. 2) by 0.90

Helical Torsion Springs Material

Factora

Material

Hard Drawn MB

0.70


Up to 1⁄32 inch diameter

0.75

Over 1⁄32 to 1⁄16 inch

0.85


0.70


0.95


0.65

Over 1⁄8 inch

1.00

Over 1⁄4 inch

0.50

Chromium-Vanadium Up to 1⁄16 inch diameter

1.05

1.00

Over 1⁄16 inch

1.10


1.07

Phosphor Bronze

Over 3⁄16 inch

1.12



Stainless Steel, 17-7 PH Up to 1⁄8 inch diameter


Factora 0.80


0.45

Over 1⁄8 inch

0.55


0.70

Beryllium Copperb


0.75



0.80


0.60


0.90


0.70

Over 3⁄16 inch

1.00

Over 1⁄8 inch

0.80

0.55

a Multiply the values in the curves for oil-tempered MB grade ASTM A229 Type 1 steel (Fig. 8) by

these factors to obtain required values. b Hard drawn and heat treated after coiling. For use with design stress curves shown in Figs. 2, 5, 6, and 8.

Endurance Limit for Spring Materials.—When a spring is deflected continually it will become “tired” and fail at a stress far below its elastic limit. This type of failure is called fatigue failure and usually occurs without warning. Endurance limit is the highest stress, or range of stress, in pounds per square inch that can be repeated indefinitely without failure of the spring. Usually ten million cycles of deflection is called “infinite life” and is satisfactory for determining this limit. For severely worked springs of long life, such as those used in automobile or aircraft engines and in similar applications, it is best to determine the allowable working stresses by referring to the endurance limit curves seen in Fig. 11. These curves are based principally upon the range or difference between the stress caused by the first or initial load and the stress caused by the final load. Experience with springs designed to stresses within the limits of these curves indicates that they should have infinite or unlimited fatigue life. All values include Wahl curvature correction factor. The stress ranges shown may be increased 20 to 30 per cent for springs that have been properly heated, pressed to remove set, and then shot peened, provided that the increased values are lower than the torsional elastic limit by at least 10 per cent.



319

120

Final Stress, Including Curvature Correction, 1000 psi

110 ′′ .030 der 0 5′′ e un 0.12 o Wir t ic ′′ s .031 Mu ire 0 m W ic adiu Mus Van %C 0.80 ome e teel Chr S g grad in B r p M el OT S g Ste 0.08%c in r p el e OT S ring Ste grad Sp l mb Stee *HD g in Spr e 302 *HD 8 typ l 18e e t sS H.T. inles ard *Sta ull h per f p o ard mC ng h ylliu spri % *Ber 5 e ronz ur B osph s *Ph s Bra ring *Sp and st L Fir o t ue ss D

100 90 80 70 60 50 40 30 20 10 0 0

tial

Ini

e

Str

5 10 15 20 25 30 35 40 45 50 55 Initial Stress, Due to First Load, Corrected for Curvature, 1000 psi

60

Fig. 11. Endurance Limit Curves for Compression Springs Notes: For commercial spring materials with wire diameters up to 1⁄4 inch except as noted. Stress ranges may be increased by approximately 30 per cent for properly heated, preset, shot-peened springs. Materials preceeded by * are not ordinarily recommended for long continued service under severe operating conditions.

Working Stresses at Elevated Temperatures.—Since modulus of elasticity decreases with increase in temperature, springs used at high temperatures exert less load and have larger deflections under load than at room temperature. The torsional modulus of elasticity for steel may be 11,200,000 pounds per square inch at room temperature, but it will drop to 10,600,000 pounds per square inch at 400°F. and will be only 10,000,000 pounds per square inch at 600°F. Also, the elastic limit is reduced, thereby lowering the permissible working stress. Design stresses should be as low as possible for all springs used at elevated temperatures. In addition, corrosive conditions that usually exist at high temperatures, especially with steam, may require the use of corrosion-resistant material. Table 2 shows the permissible elevated temperatures at which various spring materials may be operated, together with the maximum recommended working stresses at these temperatures. The loss in load at the temperatures shown is less than 5 per cent in 48 hours; however, if the temperatures listed are increased by 20 to 40 degrees, the loss of load may be nearer 10 per cent. Maximum stresses shown in the table are for compression and extension springs and may be increased



SPRING DESIGN

by 75 per cent for torsion and flat springs. In using the data in Table 2 it should be noted that the values given are for materials in the heat-treated or spring temper condition. Table 2. Recommended Maximum Working Temperatures and Corresponding Maximum Working Stresses for Springs Spring Material

Max. Working Temp., °F

Max. Working Stress, psi

Brass Spring Wire

150

30,000

Phosphor Bronze Music Wire Beryllium-Copper Hard Drawn Steel Wire Carbon Spring Steels

225 250 300 325 375

35,000 75,000 40,000 50,000 55,000

Alloy Spring Steels

400

65,000

Monel K-Monel

425 450

40,000 45,000

Spring Material Permanickela Stainless Steel 18-8 Stainless Chromium 431 Inconel High Speed Steel Inconel X Chromium-MolybdenumVanadium Cobenium, Elgiloy

Max. Working Temp, °F

Max. Working Stress, psi

500

50,000

550 600 700 775 850

55,000 50,000 50,000 70,000 55,000

900

55,000

1000

75,000

a Formerly called Z-Nickel, Type B.

Loss of load at temperatures shown is less than 5 per cent in 48 hours.

Spring Design Data Spring Characteristics.—This section provides tables of spring characteristics, tables of principal formulas, and other information of a practical nature for designing the more commonly used types of springs. Standard wire gages for springs: Information on wire gages is given in the section beginning on page 2519, and gages in decimals of an inch are given in the table on page 2520. It should be noted that the range in this table extends from Number 7⁄0 through Number 80. However, in spring design, the range most commonly used extends only from Gage Number 4⁄0 through Number 40. When selecting wire use Steel Wire Gage or Washburn and Moen gage for all carbon steels and alloy steels except music wire; use Brown & Sharpe gage for brass and phosphor bronze wire; use Birmingham gage for flat spring steels, and cold rolled strip; and use piano or music wire gage for music wire. Spring index: The spring index is the ratio of the mean coil diameter of a spring to the wire diameter (D/d). This ratio is one of the most important considerations in spring design because the deflection, stress, number of coils, and selection of either annealed or tempered material depend to a considerable extent on this ratio. The best proportioned springs have an index of 7 through 9. Indexes of 4 through 7, and 9 through 16 are often used. Springs with values larger than 16 require tolerances wider than standard for manufacturing; those with values less than 5 are difficult to coil on automatic coiling machines. Direction of helix: Unless functional requirements call for a definite hand, the helix of compression and extension springs should be specified as optional. When springs are designed to operate, one inside the other, the helices should be opposite hand to prevent intermeshing. For the same reason, a spring that is to operate freely over a threaded member should have a helix of opposite hand to that of the thread. When a spring is to engage with a screw or bolt, it should, of course, have the same helix as that of the thread. Helical Compression Spring Design.—After selecting a suitable material and a safe stress value for a given spring, designers should next determine the type of end coil formation best suited for the particular application. Springs with unground ends are less expensive but they do not stand perfectly upright; if this requirement has to be met, closed ground ends are used. Helical compression springs with different types of ends are shown in Fig. 12.


Machinery's Handbook 27th Edition SPRING DESIGN

321

Fig. 12. Types of Helical Compression Spring Ends

Spring design formulas: Table 3 gives formulas for compression spring dimensional characteristics, and Table 4 gives design formulas for compression and extension springs. Curvature correction: In addition to the stress obtained from the formulas for load or deflection, there is a direct shearing stress and an increased stress on the inside of the section due to curvature. Therefore, the stress obtained by the usual formulas should be multiplied by a factor K taken from the curve in Fig. 13. The corrected stress thus obtained is used only for comparison with the allowable working stress (fatigue strength) curves to determine if it is a safe stress and should not be used in formulas for deflection. The curvature correction factor K is for compression and extension springs made from round wire. For square wire reduce the K value by approximately 4 per cent. Design procedure: The limiting dimensions of a spring are often determined by the available space in the product or assembly in which it is to be used. The loads and deflections on a spring may also be known or can be estimated, but the wire size and number of coils are usually unknown. Design can be carried out with the aid of the tabular data that appears later in this section (see Table 5, which is a simple method, or by calculation alone using the formulas in Tables 3 and 4. Example:A compression spring with closed and ground ends is to be made from ASTM A229 high carbon steel wire, as shown in Fig. 14. Determine the wire size and number of coils. Method 1, using table: Referring to Table 5, starting on page 325, locate the spring outside diameter (13⁄16 inches, from Fig. 14) in the left-hand column. Note from the drawing that the spring load is 36 pounds. Move to the right in the table to the figure nearest this value, which is 41.7 pounds. This is somewhat above the required value but safe. Immediately above the load value, the deflection f is given, which in this instance is 0.1594 inch. This is the deflection of one coil under a load of 41.7 pounds with an uncorrected torsional stress S of 100,000 pounds per square inch for ASTM A229 oil-tempered MB steel. For other spring materials, see the footnotes to Table 5 on page 325. Moving vertically in Table 5 from the load entry, the wire diameter is found to be 0.0915 inch. The remaining spring design calculations are completed as follows: Step 1: The stress with a load of 36 pounds is obtained by proportion, as follows: The 36 pound load is 86.3 per cent of the 41.7 pound load; therefore, the stress S at 36 pounds = 0.863 × 100,000 = 86,300 pounds per square inch.



SPRING DESIGN Table 3. Formulas for Compression Springs Type of End Open or Plain (not ground)

Open or Plain (with ends ground)

Pitch (p)

FL – d--------------N

FL ------TC

FL – 3d ------------------N

FL – 2d ------------------N

Solid Height (SH)

(TC + 1)d

TC × d

(TC + I)d

TC × d

Number of Active Coils (N)

N = TC FL – d = --------------p

N = TC – 1 = FL ------- – 1 p

N = TC – 2 – 3d = FL ------------------p

N = TC – 2 – 2d = FL ------------------p

Total Coils (TC)

FL – d--------------p

FL ------p

FL – 3d + 2 ------------------p

FL – 2d + 2 ------------------p

Free Length (FL)

(p × TC) + d

p × TC

(p × N) + 3d

(p × N) + 2d

Squared or Closed (not ground)

Closed and Ground

Formulaa

Feature

a The symbol notation is given on page

308.

Table 4. Formulas for Compression and Extension Springs Formulaa, b Feature

Springs made from round wire

Springs made from square wire

0.393Sd 3 = -------------Gd 4 F P = ---------------------D 8ND 3

0.416Sd 3 = --------------------Gd 4 F P = ---------------------D 5.58ND 3

GdF PD S = --------------- = ------------------0.393d 3 πND 2

GdF D S = ---------------------- = P ------------------2.32ND 2 0.416d 3

3 πSND 2F = 8PND ------------------ = ----------------Gd Gd 4

3 2 F = 5.58PND -------------------------------------------------- = 2.32SND Gd Gd 4

Gd 4 F GdFN = ------------- = ------------8PD 3 πSD 2

Gd 4 F = -------------------GdF N = --------------------5.58PD 3 2.32SD 2

Wire Diameter, d Inch

2 d = πSND ------------------ = GF

2 d = 2.32SND ------------------------- = GF

Stress due to Initial Tension, Sit

S it = --S- × IT P

Load, P Pounds Stress, Torsional, S Pounds per square inch Deflection, F Inch Number of Active Coils, N

3

2.55PD ------------------S

3

PD ---------------0.416S

S it = --S- × IT P

308. b Two formulas are given for each feature, and designers can use the one found to be appropriate for a given design. The end result from either of any two formulas is the same. a The symbol notation is given on page

Step 2: The 86.3 per cent figure is also used to determine the deflection per coil f at 36 pounds load: 0.863 × 0.1594 = 0.1375 inch. 1.25 - = 9.1 Step 3: The number of active coils AC = F --- = --------------f 0.1375



323

LIVE GRAPH Click here to view

2.1 2.0 1.9

Correction Factor, K

1.8 1.7 1.6 1.5 1.4 1.3 1.2 1.1 1.0

1

2

3

4

5 6 7 Spring Index

8

9

10

11

12

Fig. 13. Compression and Extension Spring-Stress Correction for Curvaturea a For springs made from round wire. For springs made from square wire, reduce the K factor

values by approximately 4 per cent.

Fig. 14. Compression Spring Design Example

Step 4: Total Coils TC = AC + 2 (Table 3) = 9 + 2 = 11 Therefore, a quick answer is: 11 coils of 0.0915 inch diameter wire. However, the design procedure should be completed by carrying out these remaining steps: Step 5: From Table 3, Solid Height = SH = TC × d = 11 × 0.0915 ≅ 1 inch Therefore, Total Deflection = FL − SH = 1.5 inches



SPRING DESIGN

,300 × 1.5 = 103 ,500 pounds per square inch Step 6: Stress Solid = 86 ---------------1.25 Step 7: Spring Index = O.D. ------------- – 1 = 0.8125 ---------------- – 1 = 7.9 d 0.0915 Step 8: From Fig. 13, the curvature correction factor K = 1.185 Step 9: Total Stress at 36 pounds load = S × K = 86,300 × 1.185 = 102,300 pounds per square inch. This stress is below the 117,000 pounds per square inch permitted for 0.0915 inch wire shown on the middle curve in Fig. 3, so it is a safe working stress. Step 10: Total Stress at Solid = 103,500 × 1.185 = 122,800 pounds per square inch. This stress is also safe, as it is below the 131,000 pounds per square inch shown on the top curve Fig. 3, and therefore the spring will not set. Method 2, using formulas: The procedure for design using formulas is as follows (the design example is the same as in Method 1, and the spring is shown in Fig. 14): Step 1: Select a safe stress S below the middle fatigue strength curve Fig. 8 for ASTM A229 steel wire, say 90,000 pounds per square inch. Assume a mean diameter D slightly below the 13⁄16-inch O.D., say 0.7 inch. Note that the value of G is 11,200,000 pounds per square inch (Table 20). Step 2: A trial wire diameter d and other values are found by formulas from Table 4 as follows: 2.55 × 36 × 0.7----------------------------------90 ,000

d =

3

2.55PD ------------------- = S

=

3

0.000714 = 0.0894 inch

3

Note: Table 21 can be used to avoid solving the cube root. Step 3: From the table on page 2520, select the nearest wire gauge size, which is 0.0915 inch diameter. Using this value, the mean diameter D = 13⁄16 inch − 0.0915 = 0.721 inch. PD - = -------------------------------------36 × 0.721 Step 4: The stress S = -----------------= 86 ,300 lb/in 2 0.393d 3 0.393 × 0.0915 3 Step 5: The number of active coils is GdF- = 11 ,200 ,000 × 0.0915 × 1.25- = 9.1 (say 9) N = -----------------------------------------------------------------------------πSD 2 3.1416 × 86 ,300 × 0.721 2 The answer is the same as before, which is to use 11 total coils of 0.0915-inch diameter wire. The total coils, solid height, etc., are determined in the same manner as in Method 1. Table of Spring Characteristics.—Table 5 gives characteristics for compression and extension springs made from ASTM A229 oil-tempered MB spring steel having a torsional modulus of elasticity G of 11,200,000 pounds per square inch, and an uncorrected torsional stress S of 100,000 pounds per square inch. The deflection f for one coil under a load P is shown in the body of the table. The method of using these data is explained in the problems for compression and extension spring design. The table may be used for other materials by applying factors to f. The factors are given in a footnote to the table.



Table 5. Compression and Extension Spring Deflections a Spring Outside Dia. Nom.

Dec.

7⁄ 64

.1094

1⁄ 8

.125

9⁄ 64

.1406 .1563 .1719

3⁄ 16

.1875

13⁄ 64

.2031

7⁄ 32

.2188

15⁄ 64

.2344

1⁄ 4

.250

9⁄ 32

.2813

5⁄ 16

.3125

11⁄ 32

.3438

3⁄ 8

.375

.012

.014

.016

.018

.020

.022

.024

.026

.028

.030

.032

.034

.036

.038

19 .041

18 .0475

17 .054

16 .0625

… … .00683 16.95 .00937 14.47 .01234 12.62 .01569 11.19 .01944 10.05 .0236 9.13 .0282 8.35 .0331 7.70 .0385 7.14 .0505 6.24 .0640 5.54 .0792 4.98 .0960 4.53

… … .00617 20.6 .00852 17.51 .01128 15.23 .01439 13.48 .01788 12.09 .0218 10.96 .0260 10.02 .0307 9.23 .0357 8.56 .0469 7.47 .0596 6.63 .0733 5.95 .0895 5.40

… … … … .00777 21.0 .01033 18.22 .01324 16.09 .01650 14.41 .0201 13.05 .0241 11.92 .0285 10.97 .0332 10.17 .0437 8.86 .0556 7.85 .0690 7.05 .0839 6.40

… … … … … … .00909 23.5 .01172 21.8 .01468 18.47 .01798 16.69 .0216 15.22 .0256 13.99 .0299 12.95 .0395 11.26 .0504 9.97 .0627 8.94 .0764 8.10

… … … … … … … … .00914 33.8 .01157 30.07 .01430 27.1 .01733 24.6 .0206 22.5 .0242 20.8 .0323 18.01 .0415 15.89 .0518 14.21 .0634 12.85

… … … … … … … … … … .00926 46.3 .01155 41.5 .01411 37.5 .01690 34.3 .01996 31.6 .0268 27.2 .0347 23.9 .0436 21.3 .0535 19.27

… … … … … … … … … … … … … … .01096 61.3 .01326 55.8 .01578 51.1 .0215 43.8 .0281 38.3 .0355 34.1 .0438 30.7

Deflection f (inch) per coil, at Load P (pounds) c .0277 .395 .0371 .342 .0478 .301 .0600 .268 .0735 .243 .0884 .221 .1046 .203 … … … … … … … … … … … … … …

.0222 .697 .0299 .600 .0387 .528 .0487 .470 .0598 .424 .0720 .387 .0854 .355 .1000 .328 .1156 .305 … … … … … … … … … …

.01824 1.130 .0247 .971 .0321 .852 .0406 .758 .0500 .683 .0603 .621 .0717 .570 .0841 .526 .0974 .489 .1116 .457 .1432 .403 … … … … … …

.01529 1.722 .0208 1.475 .0272 1.291 .0345 1.146 .0426 1.031 .0516 .938 .0614 .859 .0721 .793 .0836 .736 .0960 .687 .1234 .606 .1541 .542 … … … …

.01302 2.51 .01784 2.14 .0234 1.868 .0298 1.656 .0369 1.488 .0448 1.351 .0534 1.237 .0628 1.140 .0730 1.058 .0839 .987 .1080 .870 .1351 .778 .1633 .703 … …

.01121 3.52 .01548 2.99 .0204 2.61 .0261 2.31 .0324 2.07 .0394 1.876 .0470 1.716 .0555 1.580 .0645 1.465 .0742 1.366 .0958 1.202 .1200 1.074 .1470 .970 .1768 .885

.00974 4.79 .01353 4.06 .01794 3.53 .0230 3.11 .0287 2.79 .0349 2.53 .0418 2.31 .0494 2.13 .0575 1.969 .0663 1.834 .0857 1.613 .1076 1.440 .1321 1.300 .1589 1.185

.00853 6.36 .01192 5.37 .01590 4.65 .0205 4.10 .0256 3.67 .0313 3.32 .0375 3.03 .0444 2.79 .0518 2.58 .0597 2.40 .0774 2.11 .0973 1.881 .1196 1.697 .1440 1.546

.00751 8.28 .01058 6.97 .01417 6.02 .01832 5.30 .0230 4.73 .0281 4.27 .0338 3.90 .0401 3.58 .0469 3.21 .0541 3.08 .0703 2.70 .0886 2.41 .1090 2.17 .1314 1.978

.00664 10.59 .00943 8.89 .01271 7.66 0.1649 6.72 .0208 5.99 .0255 5.40 .0307 4.92 .0365 4.52 .0427 4.18 .0494 3.88 .0643 3.40 .0811 3.03 .0999 2.73 .1206 2.48

.00589 13.35 .00844 11.16 .01144 9.58 .01491 8.39 .01883 7.47 .0232 6.73 .0280 6.12 .0333 5.61 .0391 5.19 .0453 4.82 .0591 4.22 .0746 3.75 .0921 3.38 .1113 3.07

… … .00758 13.83 .01034 11.84 .01354 10.35 .01716 9.19 .0212 8.27 .0257 7.52 .0306 6.88 .0359 6.35 .0417 5.90 .0545 5.16 .0690 4.58 .0852 4.12 .1031 3.75

SPRING DESIGN

5⁄ 32 11⁄ 64

Wire Size or Washburn and Moen Gauge, and Decimal Equivalent b .010

a This


325

table is for ASTM A229 oil tempered spring steel with a torsional modulus G of 11,200,000 psi, and an uncorrected torsional stress of 100,000 psi. For other materials use the following factors: stainless steel, multiply f by 1.067; spring brass, multiply f by 2.24; phosphor bronze, multiply f by 1.867; Monel metal, multiply f by 1.244; beryllium copper, multiply f by 1.725; Inconel (non-magnetic), multiply f by 1.045. b Round wire. For square wire, multiply f by 0.707, and p, by 1.2 c The upper figure is the deflection and the lower figure the load as read against each spring size. Note: Intermediate values can be obtained within reasonable accuracy by interpolation.


326

Table 5. (Continued) Compression and Extension Spring Deflections a Wire Size or Washburn and Moen Gauge, and Decimal Equivalent Spring Outside Dia. Nom.

Dec.

13⁄ 32

.4063

7⁄ 16

.4375

15⁄ 32

.4688 .500

17⁄ 32

.5313

9⁄ 16

.5625

19⁄ 32

.5938

5⁄ 8

.625

21⁄ 32

.6563

11⁄ 16

.6875

23⁄ 32

.7188

3⁄ 4

.750

25⁄ 32

.7813

13⁄ 16

.8125

.028

.030

.032

.034

.036

.038

.1560 1.815 .1827 1.678 .212 1.559 .243 1.456 .276 1.366 … … … … … … … … … … … … … … … … … …

.1434 2.28 .1680 2.11 .1947 1.956 .223 1.826 .254 1.713 .286 1.613 … … … … … … … … … … … … … … … …

.1324 2.82 .1553 2.60 .1800 2.42 .207 2.26 .235 2.12 .265 1.991 .297 1.880 .331 1.782 … … … … … … … … … … … …

.1228 3.44 .1441 3.17 .1673 2.94 .1920 2.75 .219 2.58 .247 2.42 .277 2.29 .308 2.17 .342 2.06 … … … … … … … … … …

.1143 4.15 .1343 3.82 .1560 3.55 .1792 3.31 .204 3.10 .230 2.92 .259 2.76 .288 2.61 .320 2.48 .352 2.36 … … … … … … … …

.1068 4.95 .1256 4.56 .1459 4.23 .1678 3.95 .1911 3.70 .216 3.48 .242 3.28 .270 3.11 .300 2.95 .331 2.81 .363 2.68 … … … … … …

.1001 5.85 .1178 5.39 .1370 5.00 .1575 4.67 .1796 4.37 .203 4.11 .228 3.88 .254 3.67 .282 3.49 .311 3.32 .342 3.17 .374 3.03 … … … …

19

18

17

16

15

14

13

3⁄ 32

12

11

1⁄ 8

.041

.0475

.054

.0625

.072

.080

.0915

.0938

.1055

.1205

.125

.0436 43.9 .0521 40.1 .0614 37.0 .0714 34.3 .0822 31.9 .0937 29.9 .1061 28.1 .1191 26.5 .1330 25.1 .1476 23.8 .1630 22.7 .1791 21.6 .1960 20.7 .214 19.80

.0373 61.6 .0448 56.3 .0530 51.7 .0619 47.9 .0714 44.6 .0816 41.7 .0926 39.1 .1041 36.9 .1164 34.9 .1294 33.1 .1431 31.5 .1574 30.0 .1724 28.7 .1881 27.5

.0304 95.6 .0367 86.9 .0437 79.7 .0512 73.6 .0593 68.4 .0680 63.9 .0774 60.0 .0873 56.4 .0978 53.3 .1089 50.5 .1206 48.0 .1329 45.7 .1459 43.6 .1594 41.7

.0292 103.7 .0353 94.3 .0420 86.4 .0494 80.0 .0572 74.1 .0657 69.1 .0748 64.8 .0844 61.0 .0946 57.6 .1054 54.6 .1168 51.9 .1288 49.4 .1413 47.1 .1545 45.1

.0241 153.3 .0293 138.9 .0351 126.9 .0414 116.9 .0482 108.3 .0555 100.9 .0634 94.4 .0718 88.7 .0807 83.7 .0901 79.2 .1000 75.2 .1105 71.5 .1214 68.2 .1329 65.2

… … .0234 217. .0282 197.3 .0335 181.1 .0393 167.3 .0455 155.5 .0522 145.2 .0593 136.2 .0668 128.3 .0748 121.2 .0833 114.9 .0923 109.2 .1017 104.0 .1115 99.3

… … .0219 245. .0265 223. .0316 205. .0371 188.8 .0430 175.3 .0493 163.6 .0561 153.4 .0634 144.3 .0710 136.3 .0791 129.2 .0877 122.7 .0967 116.9 .1061 111.5

Deflection f (inch) per coil, at Load P (pounds) .0913 7.41 .1075 6.82 .1252 6.33 .1441 5.90 .1645 5.52 .1861 5.19 .209 4.90 .233 4.63 .259 4.40 .286 4.19 .314 3.99 .344 3.82 .375 3.66 .407 3.51

.0760 11.73 .0898 10.79 .1048 9.99 .1209 9.30 .1382 8.70 .1566 8.18 .1762 7.71 .1969 7.29 .219 6.92 .242 6.58 .266 6.27 .291 5.99 .318 5.74 .346 5.50

.0645 17.56 .0764 16.13 .0894 14.91 .1033 13.87 .1183 12.96 .1343 12.16 .1514 11.46 .1693 10.83 .1884 10.27 .208 9.76 .230 9.31 .252 8.89 .275 8.50 .299 8.15

.0531 27.9 .0631 25.6 .0741 23.6 .0859 21.9 .0987 20.5 .1122 19.17 .1267 18.04 .1420 17.04 .1582 16.14 .1753 15.34 .1933 14.61 .212 13.94 .232 13.34 .253 12.78

a This

table is for ASTM A229 oil tempered spring steel with a torsional modulus G of 11,200,000 psi, and an uncorrected torsional stress of 100,000 psi. For other materials, and other important footnotes, see page 325.


SPRING DESIGN

1⁄ 2

.026


Table 5. (Continued) Compression and Extension Spring Deflections a Wire Size or Washburn and Moen Gauge, and Decimal Equivalent Spring Outside Dia. Nom. 7⁄ 8

14

13

3⁄ 32

12

11

1⁄ 8

10

9

5⁄ 32

8

7

3⁄ 16

6

5

7⁄ 32

4

.072

.080

.0915

.0938

.1055

.1205

.125

.135

.1483

.1563

.162

.177

.1875

.192

.207

.2188

.2253

.251 18.26 .271 17.57 .292 16.94 .313 16.35 .336 15.80 .359 15.28 .382 14.80 .407 14.34 .432 13.92 .485 13.14 .541 12.44 .600 11.81 .662 11.25 .727 10.73

.222 25.3 .239 24.3 .258 23.5 .277 22.6 .297 21.9 .317 21.1 .338 20.5 .360 19.83 .383 19.24 .431 18.15 .480 17.19 .533 16.31 .588 15.53 .647 14.81

.1882 39.4 .204 36.9 .219 35.6 .236 34.3 .253 33.1 .271 32.0 .289 31.0 .308 30.0 .328 29.1 .368 27.5 .412 26.0 .457 24.6 .506 23.4 .556 22.3

.1825 41.5 .1974 39.9 .213 38.4 .229 37.0 .246 35.8 .263 34.6 .281 33.5 .299 32.4 .318 31.4 .358 29.6 .400 28.0 .444 26.6 .491 25.3 .540 24.1

.1574 59.9 .1705 57.6 .1841 55.4 .1982 53.4 .213 51.5 .228 49.8 .244 48.2 .260 46.7 .277 45.2 .311 42.6 .349 40.3 .387 38.2 .429 36.3 .472 34.6

.1325 91.1 .1438 87.5 .1554 84.1 .1675 81.0 .1801 78.1 .1931 75.5 .207 73.0 .221 70.6 .235 68.4 .265 64.4 .297 60.8 .331 57.7 .367 54.8 .404 52.2

.1262 102.3 .1370 98.2 .1479 94.4 .1598 90.9 .1718 87.6 .1843 84.6 .1972 81.8 .211 79.2 .224 76.7 .254 72.1 .284 68.2 .317 64.6 .351 61.4 .387 58.4

.0772 312. .0843 299. .0917 286. .0994 275. .1074 264. .1157 255. .1243 246. .1332 238. .1424 230. .1620 215. .1824 203. .205 191.6 .227 181.7 .252 172.6

.0707 377. .0772 360. .0842 345. .0913 332. .0986 319. .1065 307. .1145 296. .1229 286. .1315 276. .1496 259. .1690 244. .1894 230. .211 218. .234 207.

.0682 407. .0746 389. .0812 373. .0882 358. .0954 344. .1029 331. .1107 319. .1188 308. .1272 298. .1448 279. .1635 263. .1836 248. .204 235. .227 223.

.0605 521. .0663 498. .0723 477. .0786 457. .0852 439. .0921 423. .0993 407. .1066 393. .1142 379. .1303 355. .1474 334. .1657 315. .1848 298. .205 283.

.0552 626. .0606 598. .0662 572. .0721 548. .0783 526. .0845 506. .0913 487. .0982 470. .1053 454. .1203 424. .1363 399. .1535 376. .1713 356. .1905 337.

.0526 691. .0577 660. .0632 631. .0688 604. .0747 580. .0809 557. .0873 537. .0939 517. .1008 499. .1153 467. .1308 438. .1472 413. .1650 391 .1829 371.

Dec. .875

29⁄ 32

.9063

15⁄ 16

.9375

31⁄ 32

15

.9688 1.000

11⁄32

1.031

11⁄16

1.063

11⁄32

1.094

11⁄8

1.125

13⁄16

1.188

11⁄4

1.250

15⁄16

1.313

13⁄8

1.375

17⁄16

1.438

.1138 130.5 .1236 125.2 .1338 120.4 .1445 115.9 .1555 111.7 .1669 107.8 .1788 104.2 .1910 100.8 .204 97.6 .231 91.7 .258 86.6 .288 82.0 .320 77.9 .353 74.1

.0999 176.3 .1087 169.0 .1178 162.3 .1273 156.1 .1372 150.4 .1474 145.1 .1580 140.1 .1691 135.5 .1804 131.2 .204 123.3 .230 116.2 .256 110.1 .285 104.4 .314 99.4

.0928 209. .1010 199.9 .1096 191.9 .1183 184.5 .1278 177.6 .1374 171.3 .1474 165.4 .1578 159.9 .1685 154.7 .1908 145.4 .215 137.0 .240 129.7 .267 123.0 .295 117.0

.0880 234. .0959 224. .1041 215. .1127 207. .1216 198.8 .1308 191.6 .1404 185.0 .1503 178.8 .1604 173.0 .1812 162.4 .205 153.1 .229 144.7 .255 137.3 .282 130.6

SPRING DESIGN

1

Deflection f (inch) per coil, at Load P (pounds)

a This


327



328

Table 5. (Continued) Compression and Extension Spring Deflections a Wire Size or Washburn and Moen Gauge, and Decimal Equivalent Spring Outside Dia. Dec.

11⁄2

1.500

15⁄8

1.625

13⁄4

1.750

17⁄8

1.875

115⁄16

1.938

2

2.000

21⁄16

2.063

21⁄8

2.125

23⁄16

2.188

21⁄4

2.250

25⁄16

2.313

23⁄8

2.375

27⁄16

2.438

21⁄2

2.500

1⁄ 8

10

9

5⁄ 32

8

7

3⁄ 16

6

5

7⁄ 32

4

3

1⁄ 4

2

9⁄ 32

0

5⁄ 16

.1205

.125

.135

.1483

.1563

.162

.177

.1875

.192

.207

.2188

.2253

.2437

.250

.2625

.2813

.3065

.3125

.443 49.8 .527 45.7 .619 42.2 .717 39.2 .769 37.8 .823 36.6 .878 35.4 .936 34.3 .995 33.3 1.056 32.3 1.119 31.4 1.184 30.5 … … … …

.424 55.8 .505 51.1 .593 47.2 .687 43.8 .738 42.3 .789 40.9 .843 39.6 .898 38.3 .955 37.2 1.013 36.1 1.074 35.1 1.136 34.1 1.201 33.2 1.266 32.3

.387 70.8 .461 64.8 .542 59.8 .629 55.5 .676 53.6 .723 51.8 .768 50.1 .823 48.5 .876 47.1 .930 45.7 .986 44.4 1.043 43.1 1.102 42.0 1.162 40.9

.350 94.8 .413 86.7 .485 80.0 .564 74.2 .605 71.6 .649 69.2 .693 66.9 .739 64.8 .786 62.8 .835 60.9 .886 59.2 .938 57.5 .991 56.0 1.046 54.5

.324 111.5 .387 102.0 .456 94.0 .530 87.2 .569 84.2 .610 81.3 .652 78.7 .696 76.1 .740 73.8 .787 71.6 .834 69.5 .884 67.6 .934 65.7 .986 64.0

.310 124.5 .370 113.9 .437 104.9 .508 97.3 .546 93.8 .585 90.6 .626 87.6 .667 84.9 .711 82.2 .755 79.8 .801 77.5 .848 75.3 .897 73.2 .946 71.3

.277 164.6 .332 150.3 .392 138.5 .457 128.2 .492 123.6 .527 119.4 .564 115.4 .602 111.8 .641 108.3 .681 105.7 .723 101.9 .763 99.1 .810 96.3 .855 93.7

.202 352. .244 321. .290 295. .339 272. .365 262. .392 253. .421 245. .449 236. .479 229. .511 222. .542 215. .576 209. .609 203. .644 197.5

.1815 452. .220 411. .261 377. .306 348. .331 335. .355 324. .381 312. .407 302. .435 292. .463 283. .493 275. .523 267. .554 259. .586 252.

.1754 499. .212 446. .253 409. .296 378. .320 364. .344 351. .369 339. .395 327. .421 317. .449 307. .478 298. .507 289. .537 281. .568 273.

.1612 574. .1986 521. .237 477. .278 440. .300 425. .323 409. .346 395. .371 381. .396 369. .423 357. .449 347. .477 336. .506 327. .536 317.

.1482 717. .1801 650. .215 595. .253 548. .273 528. .295 509. .316 491. .339 474. .362 459. .387 444. .411 430. .437 417. .464 405. .491 394.

.1305 947. .1592 858. .1908 783. .225 721. .243 693. .263 668. .282 644. .303 622. .324 601. .346 582. .368 564. .392 547. .416 531. .441 516.

.1267 1008. .1547 912. .1856 833. .219 767. .237 737. .256 710. .275 685. .295 661. .316 639. .337 618. .359 599. .382 581. .405 564. .430 548.

Deflection f (inch) per coil, at Load P (pounds) .258 197.1 .309 180.0 .366 165.6 .426 153.4 .458 147.9 .492 142.8 .526 138.1 .562 133.6 .598 129.5 .637 125.5 .676 121.8 .716 118.3 .757 115.1 .800 111.6

.250 213. .300 193.9 .355 178.4 .414 165.1 .446 159.2 .478 153.7 .512 148.5 .546 143.8 .582 139.2 .619 135.0 .657 131.0 .696 127.3 .737 123.7 .778 120.4

.227 269. .273 246. .323 226. .377 209. .405 201. .436 194.3 .467 187.7 .499 181.6 .532 175.8 .566 170.5 .601 165.4 .637 160.7 .674 156.1 .713 151.9

.210 321. .254 292. .301 269. .351 248. .379 239. .407 231. .436 223. .466 216. .497 209. .529 202. .562 196.3 .596 190.7 .631 185.3 .667 180.2

a This



SPRING DESIGN

Nom.

11


329

Extension Springs.—About 10 per cent of all springs made by many companies are of this type, and they frequently cause trouble because insufficient consideration is given to stress due to initial tension, stress and deflection of hooks, special manufacturing methods, secondary operations and overstretching at assembly. Fig. 15 shows types of ends used on these springs.

Machine loop and machine hook shown in line

Machine loop and machine hook shown at right angles

Hand loop and hook at right angles

Full loop on side and small eye from center

Double twisted full loop over center

Single full loop centered

Full loop at side

Small off-set hook at side

Machine half-hook over center

Small eye at side

Small eye over center

Reduced loop to center

Hand half-loop over center

Plain squarecut ends

All the Above Ends are Standard Types for Which No Special Tools are Required

Long round-end hook over center

Long square-end hook over center

Extended eye from either center or side

V-hook over center

Straight end annealed to allow forming

Coned end with short swivel eye

Coned end to hold long swivel eye

Coned end with swivel bolt

Coned end with swivel hook

This Group of Special Ends Requires Special Tools Fig. 15. Types of Helical Extension Spring Ends

Initial tension: In the spring industry, the term “Initial tension” is used to define a force or load, measurable in pounds or ounces, which presses the coils of a close wound extension spring against one another. This force must be overcome before the coils of a spring begin to open up. Initial tension is wound into extension springs by bending each coil as it is wound away from its normal plane, thereby producing a slight twist in the wire which causes the coil to spring back tightly against the adjacent coil. Initial tension can be wound into cold-coiled



SPRING DESIGN LIVE GRAPH Click here to view

44 42

The values in the curves in the chart are for springs made from spring steel. They should be reduced 15 per cent for stainless steel. 20 per cent for copper-nickel alloys and 50 per cent for phosphor bronze.

40 Torsional Stress, Pounds per Square Inch (thousands)

38 36 34 32 30 28

Initial tension in this area is readily obtainable. Use whenever possible.

26 24 22

Maximum initial tension

20 18 Pe

rm

16

iss

ibl

14 12 10

et

ors

ion

al

str

ess

8 Inital tension in this area is difficult to maintain with accurate and uniform results.

6 4

3

4

5

6

7

8 9 10 11 12 13 14 15 16 Spring Index

Fig. 16. Permissible Torsional Stress Caused by Initial Tension in Coiled Extension Springs for Different Spring Indexes

extension springs only. Hot-wound springs and springs made from annealed steel are hardened and tempered after coiling, and therefore initial tension cannot be produced. It is possible to make a spring having initial tension only when a high tensile strength, obtained by cold drawing or by heat-treatment, is possessed by the material as it is being wound into springs. Materials that possess the required characteristics for the manufacture of such springs include hard-drawn wire, music wire, pre-tempered wire, 18-8 stainless steel, phosphor-bronze, and many of the hard-drawn copper-nickel, and nonferrous alloys. Permissible torsional stresses resulting from initial tension for different spring indexes are shown in Fig. 16. Hook failure: The great majority of breakages in extension springs occurs in the hooks. Hooks are subjected to both bending and torsional stresses and have higher stresses than the coils in the spring. Stresses in regular hooks: The calculations for the stresses in hooks are quite complicated and lengthy. Also, the radii of the bends are difficult to determine and frequently vary between specifications and actual production samples. However, regular hooks are more



331

highly stressed than the coils in the body and are subjected to a bending stress at section B (see Table 6.) The bending stress Sb at section B should be compared with allowable stresses for torsion springs and with the elastic limit of the material in tension (See Figs. 7 through 10.) Stresses in cross over hooks: Results of tests on springs having a normal average index show that the cross over hooks last longer than regular hooks. These results may not occur on springs of small index or if the cross over bend is made too sharply. In as much as both types of hooks have the same bending stress, it would appear that the fatigue life would be the same. However, the large bend radius of the regular hooks causes some torsional stresses to coincide with the bending stresses, thus explaining the earlier breakages. If sharper bends were made on the regular hooks, the life should then be the same as for cross over hooks. Table 6. Formula for Bending Stress at Section B Type of Hook

Stress in Bending

5PD 2 S b = --------------I.D.d 3 Regular Hook

Cross-over Hook

Stresses in half hooks: The formulas for regular hooks can also be used for half hooks, because the smaller bend radius allows for the increase in stress. It will therefore be observed that half hooks have the same stress in bending as regular hooks. Frequently overlooked facts by many designers are that one full hook deflects an amount equal to one half a coil and each half hook deflects an amount equal to one tenth of a coil. Allowances for these deflections should be made when designing springs. Thus, an extension spring, with regular full hooks and having 10 coils, will have a deflection equal to 11 coils, or 10 per cent more than the calculated deflection. Extension Spring Design.—The available space in a product or assembly usually determines the limiting dimensions of a spring, but the wire size, number of coils, and initial tension are often unknown. Example:An extension spring is to be made from spring steel ASTM A229, with regular hooks as shown in Fig. 17. Calculate the wire size, number of coils and initial tension. Note: Allow about 20 to 25 per cent of the 9 pound load for initial tension, say 2 pounds, and then design for a 7 pound load (not 9 pounds) at 5⁄8 inch deflection. Also use lower stresses than for a compression spring to allow for overstretching during assembly and to obtain a safe stress on the hooks. Proceed as for compression springs, but locate a load in the tables somewhat higher than the 9 pound load. Method 1, using table: From Table 5 locate 3⁄4 inch outside diameter in the left column and move to the right to locate a load P of 13.94 pounds. A deflection f of 0.212 inch appears above this figure. Moving vertically from this position to the top of the column a suitable wire diameter of 0.0625 inch is found. The remaining design calculations are completed as follows: Step 1: The stress with a load of 7 pounds is obtained as follows: The 7 pound load is 50.2 per cent of the 13.94 pound load. Therefore, the stress S at 7 pounds = 0.502 per cent × 100,000 = 50,200 pounds per square inch.



SPRING DESIGN

Fig. 17. Extension Spring Design Example

Step 2: The 50.2 per cent figure is also used to determine the deflection per coil f: 0.502 per cent × 0.212 = 0.1062 inch. Step 3: The number of active coils. (say 6) 0.625- = 5.86 AC = F --- = --------------f 0.1062 This result should be reduced by 1 to allow for deflection of 2 hooks (see notes 1 and 2 that follow these calculations.) Therefore, a quick answer is: 5 coils of 0.0625 inch diameter wire. However, the design procedure should be completed by carrying out the following steps: Step 4: The body length = (TC + 1) × d = (5 + 1) × 0.0625 = 3⁄8 inch. Step 5: The length from the body to inside hook – Body- = 1.4375 – 0.375- = 0.531 inch = FL ----------------------------------------------------------2 2 Percentage of I.D. = 0.531 ------------- = 0.531 ------------- = 85 per cent I.D. 0.625 This length is satisfactory, see Note 3 following this proceedure. Step 6: 0.75 - – 1 = 11 The spring index = O.D. ----------- – 1 = --------------d 0.0625 Step 7: The initial tension stress is S × IT 50 ,200 × 2 S it = --------------- = -------------------------- = 14 ,340 pounds per square inch P 7 This stress is satisfactory, as checked against curve in Fig. 16. Step 8: The curvature correction factor K = 1.12 (Fig. 13). Step 9: The total stress = (50,200 + 14,340) × 1.12 = 72.285 pounds per square inch This result is less than 106,250 pounds per square inch permitted by the middle curve for 0.0625 inch wire in Fig. 3 and therefore is a safe working stress that permits some additional deflection that is usually necessary for assembly purposes.



333

Step 10: The large majority of hook breakage is due to high stress in bending and should be checked as follows: From Table 6, stress on hook in bending is: 5 × 9 × 0.6875 2 = 139 ,200 pounds per square inch 5PD 2- = -------------------------------------S b = -------------I.D.d 3 0.625 × 0.0625 3 This result is less than the top curve value, Fig. 8, for 0.0625 inch diameter wire, and is therefore safe. Also see Note 5 that follows. Notes: The following points should be noted when designing extension springs: 1) All coils are active and thus AC = TC. 2) Each full hook deflection is approximately equal to 1⁄2 coil. Therefore for 2 hooks, reduce the total coils by 1. (Each half hook deflection is nearly equal to 1⁄10 of a coil.) 3) The distance from the body to the inside of a regular full hook equals 75 to 85 per cent (90 per cent maximum) of the I.D. For a cross over center hook, this distance equals the I.D. 4) Some initial tension should usually be used to hold the spring together. Try not to exceed the maximum curve shown on Fig. 16. Without initial tension, a long spring with many coils will have a different length in the horizontal position than it will when hung vertically. 5) The hooks are stressed in bending, therefore their stress should be less than the maximum bending stress as used for torsion springs — use top fatigue strength curves Figs. 7 through 10. Method 2, using formulas: The sequence of steps for designing extension springs by formulas is similar to that for compression springs. The formulas for this method are given in Table 3. Tolerances for Compression and Extension Springs.—Tolerances for coil diameter, free length, squareness, load, and the angle between loop planes for compression and extension springs are given in Tables 7 through 12. To meet the requirements of load, rate, free length, and solid height, it is necessary to vary the number of coils for compression springs by ± 5 per cent. For extension springs, the tolerances on the numbers of coils are: for 3 to 5 coils, ± 20 per cent; for 6 to 8 coils, ± 30 per cent; for 9 to 12 coils, ± 40 per cent. For each additional coil, a further 11⁄2 per cent tolerance is added to the extension spring values. Closer tolerances on the number of coils for either type of spring lead to the need for trimming after coiling, and manufacturing time and cost are increased. Fig. 18 shows deviations allowed on the ends of extension springs, and variations in end alignments. Table 7. Compression and Extension Spring Coil Diameter Tolerances Spring Index Wire Diameter, Inch 0.015 0.023 0.035 0.051 0.076 0.114 0.171 0.250 0.375 0.500

4

6

8

10

12

14

16

0.005 0.007 0.009 0.012 0.016 0.021 0.028 0.035 0.046 0.080

0.006 0.008 0.011 0.015 0.019 0.025 0.033 0.042 0.054 0.100

0.007 0.010 0.013 0.017 0.022 0.029 0.038 0.049 0.064 0.125

Tolerance, ± inch 0.002 0.002 0.002 0.003 0.004 0.006 0.008 0.011 0.016 0.021

0.002 0.003 0.004 0.005 0.007 0.009 0.012 0.015 0.020 0.030

0.003 0.004 0.006 0.007 0.010 0.013 0.017 0.021 0.026 0.040

0.004 0.006 0.007 0.010 0.013 0.018 0.023 0.028 0.037 0.062

Courtesy of the Spring Manufacturers Institute



SPRING DESIGN .05 inch × Outside diameter

± .05 inch × Outside diameter

5 degrees

.05 inch × Outside diameter

d 2

or

1 64

inch.

Whichever is greater

45 degrees

Maximum Opening for Closed Loop

Maximum Overlap for Closed Loop

Fig. 18. Maximum Deviations Allowed on Ends and Variation in Alignment of Ends (Loops) for Extension Springs

Table 8. Compression Spring Normal Free-Length Tolerances, Squared and Ground Ends Spring Index

Number of Active Coils per Inch

4

0.5 1 2 4 8 12 16 20

0.010 0.011 0.013 0.016 0.019 0.021 0.022 0.023

6

8

10

12

14

16

0.016 0.018 0.022 0.026 0.030 0.034 0.036 0.038

0.016 0.019 0.023 0.027 0.032 0.036 0.038 0.040

Tolerance, ± Inch per Inch of Free Lengtha 0.011 0.013 0.015 0.018 0.022 0.024 0.026 0.027

0.012 0.015 0.017 0.021 0.024 0.027 0.029 0.031

0.013 0.016 0.019 0.023 0.026 0.030 0.032 0.034

0.015 0.017 0.020 0.024 0.028 0.032 0.034 0.036

a For springs less than 0.5 inch long, use the tolerances for 0.5 inch long springs. For springs with unground closed ends, multiply the tolerances by 1.7. Courtesy of the Spring Manufacturers Institute

Table 9. Extension Spring Normal Free-Length and End Tolerances Free-Length Tolerances Spring Free Length (inch) Up to 0.5 Over 0.5 to 1.0 Over 1.0 to 2.0 Over 2.0 to 4.0

End Tolerances

Tolerance (inch)

Total Number of Coils

Angle Between Loop Planes

±0.020 ±0.030 ±0.040 ±0.060

3 to 6 7 to 9 10 to 12

±25° ±35° ±45°

Free-Length Tolerances Spring Free Length (inch)

Tolerance (inch)

Over 4.0 to 8.0 Over 8.0 to 16.0 Over 16.0 to 24.0

±0.093 ±0.156 ±0.218

End Tolerances Total Number of Coils

Angle Between Loop Planes

13 to 16 Over 16

±60° Random

Courtesy of the Spring Manufacturers Institute



335

Table 10. Compression Spring Squareness Tolerances Slenderness Ratio FL/Da 0.5 1.0 1.5 2.0 3.0 4.0 6.0 8.0 10.0 12.0

4

6

3.0 2.5 2.5 2.5 2.0 2.0 2.0 2.0 2.0 2.0

3.0 3.0 2.5 2.5 2.5 2.0 2.0 2.0 2.0 2.0

Spring Index 8 10 12 Squareness Tolerances (± degrees) 3.5 3.5 3.5 3.0 3.0 3.0 2.5 3.0 3.0 2.5 2.5 3.0 2.5 2.5 2.5 2.5 2.5 2.5 2.0 2.5 2.5 2.0 2.0 2.5 2.0 2.0 2.0 2.0 2.0 2.0

14

16

3.5 3.5 3.0 3.0 2.5 2.5 2.5 2.5 2.5 2.0

4.0 3.5 3.0 3.0 3.0 2.5 2.5 2.5 2.5 2.5

a Slenderness Ratio = FL÷D

Springs with closed and ground ends, in the free position. Squareness tolerances closer than those shown require special process techniques which increase cost. Springs made from fine wire sizes, and with high spring indices, irregular shapes or long free lengths, require special attention in determining appropriate tolerance and feasibility of grinding ends.

Table 11. Compression Spring Normal Load Tolerances Deflection (inch)a

Length Tolerance, ± inch

0.05

0.005 0.010 0.020 0.030 0.040 0.050 0.060 0.070 0.080 0.090 0.100 0.200 0.300 0.400 0.500

12 … … … … … … … … … … … … … …

0.10

0.15

0.20

0.25

0.30

0.40

0.50

0.75

1.00

1.50

2.00

3.00

4.00

6.00

… … … … 5 5.5 6 6.5 7.5 8 8.5 15.5 22 … …

… … … … … … 5 5.5 6 6 7 12 17 21 25

… … … … … … … … 5 5 5.5 8.5 12 15 18.5

… … … … … … … … … … … 7 9.5 12 14.5

… … … … … … … … … … … 5.5 7 8.5 10.5

Tolerance, ± Per Cent of Load 7 12 22 … … … … … … … … … … … …

6 8.5 15.5 22 … … … … … … … … … … …

5 7 12 17 22 … … … … … … … … … …

… 6.5 10 14 18 22 25 … … … … … … … …

… 5.5 8.5 12 15.5 19 22 25 … … … … … … …

… 5 7 9.5 12 14.5 17 19.5 22 25 … … … … …

… … 6 8 10 12 14 16 18 20 22 … … … …

… … 5 6 7.5 9 10 11 12.5 14 15.5 … … … …

… … … 5 6 7 8 9 10 11 12 22 … … …

a From free length to loaded position.

Torsion Spring Design.—Fig. 19 shows the types of ends most commonly used on torsion springs. To produce them requires only limited tooling. The straight torsion end is the least expensive and should be used whenever possible. After determining the spring load or torque required and selecting the end formations, the designer usually estimates suitable space or size limitations. However, the space should be considered approximate until the wire size and number of coils have been determined. The wire size is dependent principally upon the torque. Design data can be devoloped with the aid of the tabular data, which is a simple method, or by calculation alone, as shown in the following sections. Many other factors affecting the design and operation of torsion springs are also covered in the section, Torsion Spring Design Recommendations on page 341. Design formulas are shown in Table 13. Curvature correction: In addition to the stress obtained from the formulas for load or deflection, there is a direct shearing stress on the inside of the section due to curvature. Therefore, the stress obtained by the usual formulas should be multiplied by the factor K



SPRING DESIGN Table 12. Extension Spring Normal Load Tolerances Wire Diameter (inch)

Spring Index

4

6

8

10

12

14

16

FL ------F

0.015

12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5 12 8 6 4.5 2.5 1.5 0.5

20.0 18.5 16.8 15.0 13.1 10.2 6.2 17.0 16.2 15.2 13.7 11.9 9.9 6.3 15.8 15.0 14.2 12.8 11.2 9.5 6.3 14.8 14.2 13.4 12.3 10.8 9.2 6.4 14.0 13.2 12.6 11.7 10.5 8.9 6.5 13.1 12.4 11.8 11.1 10.1 8.6 6.6 12.3 11.7 11.0 10.5 9.7 8.3 6.7

0.022

0.032

0.044

0.062

0.092

0.125

0.187

0.250

0.375

0.437

14.3 13.2 11.8 10.3 8.5 6.5 3.8 12.0 11.0 10.0 9.0 7.9 6.4 4.0 10.8 10.1 9.3 8.3 7.4 6.2 4.1 9.9 9.2 8.6 7.8 7.0 6.0 4.2 9.0 8.4 7.9 7.2 6.6 5.7 4.3 8.1 7.6 7.2 6.7 6.2 5.5 4.4 7.2 6.8 6.5 6.2 5.7 5.3 4.6

13.8 12.5 11.2 9.7 8.0 6.1 3.6 11.5 10.5 9.4 8.3 7.2 6.0 3.7 10.2 9.4 8.6 7.8 6.9 5.8 3.9 9.3 8.6 8.0 7.3 6.5 5.6 4.0 8.5 7.9 7.4 6.8 6.1 5.4 4.2 7.6 7.2 6.8 6.3 5.7 5.2 4.3 6.8 6.5 6.2 5.8 5.4 5.1 4.5

13.0 11.5 9.9 8.4 6.8 5.3 3.3 11.2 10.0 8.8 7.6 6.2 4.9 3.5 10.0 9.0 8.1 7.2 6.1 4.9 3.6 9.2 8.3 7.6 6.8 5.9 5.0 3.8 8.2 7.5 6.9 6.3 5.6 4.8 4.0 7.2 6.8 6.3 5.8 5.2 4.7 4.2 6.3 6.0 5.7 5.3 4.9 4.6 4.3

12.6 11.0 9.4 7.9 6.2 4.8 3.2 10.7 9.5 8.3 7.1 6.0 4.7 3.4 9.5 8.6 7.6 6.6 5.6 4.5 3.5 8.8 8.0 7.2 6.4 5.5 4.6 3.7 7.9 7.2 6.4 5.8 5.2 4.5 3.3 7.0 6.4 5.9 5.4 5.0 4.5 4.0 6.1 5.7 5.4 5.1 4.7 4.4 4.1

Tolerance, ± Per Cent of Load 18.5 17.5 16.1 14.7 12.4 9.9 5.4 15.5 14.7 14.0 12.4 10.8 9.0 5.5 14.3 13.7 13.0 11.7 10.2 8.6 5.6 13.3 12.8 12.1 10.8 9.6 8.3 5.7 12.3 11.8 11.2 10.2 9.2 8.0 5.8 11.3 10.9 10.4 9.7 8.8 7.7 5.9 10.3 10.0 9.6 9.1 8.4 7.4 5.9

17.6 16.7 15.5 14.1 12.1 9.3 4.8 14.6 13.9 12.9 11.5 10.2 8.3 4.9 13.1 12.5 11.7 10.7 9.5 7.8 5.0 12.0 11.6 10.8 10.0 9.0 7.5 5.1 11.1 10.7 10.2 9.4 8.5 7.2 5.3 10.2 9.8 9.3 8.7 8.1 7.0 5.4 9.2 8.9 8.5 8.1 7.6 6.6 5.5

16.9 15.8 14.7 13.5 11.8 8.9 4.6 14.1 13.4 12.3 11.0 9.8 7.7 4.7 13.0 12.1 11.2 10.1 8.8 7.1 4.8 11.9 11.2 10.5 9.5 8.4 6.9 4.9 10.8 10.2 9.7 9.0 8.0 6.8 5.1 9.7 9.2 8.8 8.2 7.6 6.7 5.2 8.6 8.3 8.0 7.5 7.0 6.2 5.3

16.2 15.0 13.8 12.6 10.6 8.0 4.3 13.5 12.6 11.6 10.5 9.4 7.3 4.5 12.1 11.4 10.6 9.7 8.3 6.9 4.5 11.1 10.5 9.8 9.0 8.0 6.7 4.7 10.1 9.6 9.0 8.4 7.8 6.5 4.9 9.1 8.7 8.3 7.8 7.1 6.3 5.0 8.1 7.8 7.5 7.2 6.7 6.0 5.1

15.5 14.5 13.2 12.0 10.0 7.5 4.1 13.1 12.2 10.9 10.0 9.0 7.0 4.3 12.0 11.0 10.0 9.0 7.9 6.7 4.4 10.9 10.2 9.3 8.5 7.7 6.5 4.5 9.8 9.3 8.5 8.0 7.4 6.3 4.7 8.8 8.3 7.7 7.2 6.7 6.0 4.8 7.7 7.4 7.1 6.8 6.3 5.8 5.0

15.0 14.0 12.7 11.5 9.1 7.0 4.0 12.7 11.7 10.7 9.6 8.5 6.7 4.1 11.5 10.6 9.7 8.7 7.7 6.5 4.2 10.5 9.7 8.9 8.1 7.3 6.3 4.3 9.5 8.9 8.2 7.6 7.0 6.1 4.5 8.4 8.0 7.5 7.0 6.5 5.8 4.6 7.4 7.2 6.9 6.5 6.1 5.6 4.8

FL ⁄ F = the ratio of the spring free length FL to the deflection F.



337

Fig. 19. The Most Commonly Used Types of Ends for Torsion Springs


Correction Factor, K

1.3

1.2

Round Wire Square Wire and Rectangular Wire K × S = Total Stress

1.1

1.0 3

4

5

6

7

8 9 10 Spring Index

11

12

13

14

15

16

Fig. 20. Torsion Spring Stress Correction for Curvature

obtained from the curve in Fig. 20. The corrected stress thus obtained is used only for comparison with the allowable working stress (fatigue strength) curves to determine if it is a safe value, and should not be used in the formulas for deflection. Torque: Torque is a force applied to a moment arm and tends to produce rotation. Torsion springs exert torque in a circular arc and the arms are rotated about the central axis. It should be noted that the stress produced is in bending, not in torsion. In the spring industry it is customary to specify torque in conjunction with the deflection or with the arms of a spring at a definite position. Formulas for torque are expressed in pound-inches. If ounceinches are specified, it is necessary to divide this value by 16 in order to use the formulas. When a load is specified at a distance from a centerline, the torque is, of course, equal to the load multiplied by the distance. The load can be in pounds or ounces with the distances in inches or the load can be in grams or kilograms with the distance in centimeters or millimeters, but to use the design formulas, all values must be converted to pounds and inches. Design formulas for torque are based on the tangent to the arc of rotation and presume that a rod is used to support the spring. The stress in bending caused by the moment P × R is identical in magnitude to the torque T, provided a rod is used. Theoretically, it makes no difference how or where the load is applied to the arms of torsion springs. Thus, in Fig. 21, the loads shown multiplied by their respective distances pro-



SPRING DESIGN Table 13. Formulas for Torsion Springs Springs made from round wire Feature

d= Wire diameter, Inches

Sb = Stress, bending pounds per square inch

N= Active Coils

F° = Deflection

T= Torque Inch lbs. (Also = P × R) I D1 = Inside Diameter After Deflection, Inches

Springs made from square wire Formula a,b

3

10.18T ----------------Sb

3

6T -----Sb

4

4000TND ------------------------EF °

4

2375TND ------------------------EF °

10.18T ----------------d3

6T -----d3

EdF ° -----------------392ND

EdF ° -----------------392ND

EdF ° ------------------392S b D

EdF ° ------------------392S b D

Ed 4 F ° ------------------4000TD

Ed 4 F ° ------------------2375TD

392S b ND ----------------------Ed

392S b ND -----------------------Ed

4000TND ------------------------Ed 4

2375TND ------------------------Ed 4

0.0982S b d 3

0.1666S b d 3

Ed 4 F ° -------------------4000ND

Ed 4 F ° -------------------2375ND

N ( ID free ) --------------------------F °N + -------360

N ( ID free ) --------------------------F °N + -------360

a Where two formulas are given for one feature, the designer should use the one found to be appropriate for the given design. The end result from either of any two formulas is the same. b The symbol notation is given on page 308.

duce the same torque; i.e., 20 × 0.5 = 10 pound-inches; 10 × 1 = 10 pound-inches; and 5 × 2 = 10 pound-inches. To further simplify the understanding of torsion spring torque, observe in both Fig. 22 and Fig. 23 that although the turning force is in a circular arc the torque is not equal to P times the radius. The torque in both designs equals P × R because the spring rests against the support rod at point a. Design Procedure: Torsion spring designs require more effort than other kinds because consideration has to be given to more details such as the proper size of a supporting rod, reduction of the inside diameter, increase in length, deflection of arms, allowance for friction, and method of testing.



Fig. 21. Right-Hand Torsion Spring

Fig. 22. Left-Hand Torsion Spring The Torque is T = P × R, Not P × Radius, because the Spring is Resting Against the Support Rod at Point a

Fig. 23. Left-Hand Torsion Spring As with the Spring in Fig. 22, the Torque is T = P × R, Not P × Radius, Because the Support Point Is at a


339


SPRING DESIGN

Example: What music wire diameter and how many coils are required for the torsion spring shown in Fig. 24, which is to withstand at least 1000 cycles? Determine the corrected stress and the reduced inside diameter after deflection.

Fig. 24. Torsion Spring Design Example. The Spring Is to be Assembled on a 7⁄16-Inch Support Rod

Method 1, using table: From Table 14, page 343, locate the 1⁄2 inch inside diameter for the spring in the left-hand column. Move to the right and then vertically to locate a torque value nearest to the required 10 pound-inches, which is 10.07 pound-inches. At the top of the same column, the music wire diameter is found, which is Number 31 gauge (0.085 inch). At the bottom of the same column the deflection for one coil is found, which is 15.81 degrees. As a 90-degree deflection is required, the number of coils needed is 90⁄15.81 = 5.69 (say 53⁄4 coils). D 0.500 + 0.085 The spring index ---- = --------------------------------- = 6.88 and thus the curvature correction factor d 0.085 K from Fig. 20 = 1.13. Therefore the corrected stress equals 167,000 × 1.13 = 188,700 pounds per square inch which is below the Light Service curve (Fig. 7) and therefore should provide a fatigue life of over 1,000 cycles. The reduced inside diameter due to deflection is found from the formula in Table 13: N ( ID free ) 5.75 × 0.500 ID 1 = --------------------------- = ------------------------------ = 0.479 in. F 90N + --------5.75 + -------360 360 This reduced diameter easily clears a suggested 7⁄16 inch diameter supporting rod: 0.479 − 0.4375 = 0.041 inch clearance, and it also allows for the standard tolerance. The overall length of the spring equals the total number of coils plus one, times the wire diameter. Thus, 63⁄4 × 0.085 = 0.574 inch. If a small space of about 1⁄64 in. is allowed between the coils to eliminate coil friction, an overall length of 21⁄32 inch results. Although this completes the design calculations, other tolerances should be applied in accordance with the Torsion Spring Tolerance Tables 16 through 17 shown at the end of this section.



341

Longer fatigue life: If a longer fatigue life is desired, use a slightly larger wire diameter. Usually the next larger gage size is satisfactory. The larger wire will reduce the stress and still exert the same torque, but will require more coils and a longer overall length. Percentage method for calculating longer life: The spring design can be easily adjusted for longer life as follows: 1) Select the next larger gage size, which is Number 32 (0.090 inch) from Table 14. The torque is 11.88 pound-inches, the design stress is 166,000 pounds per square inch, and the deflection is 14.9 degrees per coil. As a percentage the torque is 10⁄11.88 × 100 = 84 per cent. 2) The new stress is 0.84 × 166,000 = 139,440 pounds per square inch. This value is under the bottom or Severe Service curve, Fig. 7, and thus assures longer life. 3) The new deflection per coil is 0.84 × 14.97 = 12.57 degrees. Therefore, the total number of coils required = 90⁄12.57 = 7.16 (say 7 1⁄8). The new overall length = 8 1⁄8 × 0.090 = 0.73 inch (say 3⁄4 inch). A slight increase in the overall length and new arm location are thus necessary. Method 2, using formulas: When using this method, it is often necessary to solve the formulas several times because assumptions must be made initially either for the stress or for a wire size. The procedure for design using formulas is as follows (the design example is the same as in Method 1, and the spring is shown in Fig. 24): Step 1: Note from Table 13, page 338 that the wire diameter formula is: d =

3

10.18T ----------------Sb

Step 2: Referring to Fig. 7, select a trial stress, say 150,000 pounds per square inch. Step 3: Apply the trial stress, and the 10 pound-inches torque value in the wire diameter formula: d =

3

10.18T ----------------- = Sb

3

10.18 × 10 = ------------------------150 ,000

3

0.000679 = 0.0879 inch

The nearest gauge sizes are 0.085 and 0.090 inch diameter. Note: Table 21, page 351, can be used to avoid solving the cube root. Step 4: Select 0.085 inch wire diameter and solve the equation for the actual stress: 10.18T 10.18 × 10 S b = ----------------- = ------------------------- = 165 ,764 pounds per square inch d3 0.085 3 Step 5: Calculate the number of coils from the equation, Table 13: 28 ,500 ,000 × 0.085 × 90EdF ° = ----------------------------------------------------------= 5.73 (say 5 3⁄4 ) N = ------------------392S b D 392 × 165 ,764 × 0.585 Step 6: Calculate the total stress. The spring index is 6.88, and the correction factor K is 1.13, therefore total stress = 165,764 × 1.13 = 187,313 pounds per square inch. Note: The corrected stress should not be used in any of the formulas as it does not determine the torque or the deflection. Torsion Spring Design Recommendations.—The following recommendations should be taken into account when designing torsion springs: Hand: The hand or direction of coiling should be specified and the spring designed so deflection causes the spring to wind up and to have more coils. This increase in coils and overall length should be allowed for during design. Deflecting the spring in an unwinding direction produces higher stresses and may cause early failure. When a spring is sighted down the longitudinal axis, it is “right hand” when the direction of the wire into the spring takes a clockwise direction or if the angle of the coils follows an angle similar to the threads



SPRING DESIGN

of a standard bolt or screw, otherwise it is “left hand.” A spring must be coiled right-handed to engage the threads of a standard machine screw. Rods: Torsion springs should be supported by a rod running through the center whenever possible. If unsupported, or if held by clamps or lugs, the spring will buckle and the torque will be reduced or unusual stresses may occur. Diameter Reduction: The inside diameter reduces during deflection. This reduction should be computed and proper clearance provided over the supporting rod. Also, allowances should be considered for normal spring diameter tolerances. Winding: The coils of a spring may be closely or loosely wound, but they seldom should be wound with the coils pressed tightly together. Tightly wound springs with initial tension on the coils do not deflect uniformly and are difficult to test accurately. A small space between the coils of about 20 to 25 per cent of the wire thickness is desirable. Square and rectangular wire sections should be avoided whenever possible as they are difficult to wind, expensive, and are not always readily available. Arm Length: All the wire in a torsion spring is active between the points where the loads are applied. Deflection of long extended arms can be calculated by allowing one third of the arm length, from the point of load contact to the body of the spring, to be converted into coils. However, if the length of arm is equal to or less than one-half the length of one coil, it can be safely neglected in most applications. Total Coils: Torsion springs having less than three coils frequently buckle and are difficult to test accurately. When thirty or more coils are used, light loads will not deflect all the coils simultaneously due to friction with the supporting rod. To facilitate manufacturing it is usually preferable to specify the total number of coils to the nearest fraction in eighths or quarters such as 5 1⁄8, 5 1⁄4, 5 1⁄2, etc. Double Torsion: This design consists of one left-hand-wound series of coils and one series of right-hand-wound coils connected at the center. These springs are difficult to manufacture and are expensive, so it often is better to use two separate springs. For torque and stress calculations, each series is calculated separately as individual springs; then the torque values are added together, but the deflections are not added. Bends: Arms should be kept as straight as possible. Bends are difficult to produce and often are made by secondary operations, so they are therefore expensive. Sharp bends raise stresses that cause early failure. Bend radii should be as large as practicable. Hooks tend to open during deflection; their stresses can be calculated by the same procedure as that for tension springs. Spring Index: The spring index must be used with caution. In design formulas it is D/d. For shop measurement it is O.D./d. For arbor design it is I.D./d. Conversions are easily performed by either adding or subtracting 1 from D/d. Proportions: A spring index between 4 and 14 provides the best proportions. Larger ratios may require more than average tolerances. Ratios of 3 or less, often cannot be coiled on automatic spring coiling machines because of arbor breakage. Also, springs with smaller or larger spring indexes often do not give the same results as are obtained using the design formulas. Table of Torsion Spring Characteristics.—Table 14 shows design characteristics for the most commonly used torsion springs made from wire of standard gauge sizes. The deflection for one coil at a specified torque and stress is shown in the body of the table. The figures are based on music wire (ASTM A228) and oil-tempered MB grade (ASTM A229), and can be used for several other materials which have similar values for the modulus of elasticity E. However, the design stress may be too high or too low, and the design stress, torque, and deflection per coil should each be multiplied by the appropriate correction factor in Table 15 when using any of the materials given in that table.



Table 14. Torsion Spring Deflections AMW Wire Gauge Decimal Equivalenta

1 .010

2 .011

3 .012

4 .013

5 .014

6 .016

7 .018

8 .020

9 .022

10 .024

11 .026

12 .029

13 .031

14 .033

15 .035

16 .037

Design Stress, kpsi

232

229

226

224

221

217

214

210

207

205

202

199

197

196

194

192

Torque, pound-inch

.0228

.0299

.0383

.0483

.0596

.0873

.1226

.1650

.2164

.2783

.3486

.4766

.5763

.6917

.8168

.9550 …

Inside Diameter, inch

Deflection, degrees per coil

0.0625

22.35

20.33

18.64

17.29

16.05

14.15

18.72

11.51

10.56

9.818

9.137

8.343

7.896

…

…

5⁄ 64

0.078125

27.17

24.66

22.55

20.86

19.32

16.96

15.19

13.69

12.52

11.59

10.75

9.768

9.215

…

…

…

3⁄ 32

0.09375

31.98

28.98

26.47

24.44

22.60

19.78

17.65

15.87

14.47

13.36

12.36

11.19

10.53

10.18

9.646

9.171

7⁄ 64

0.109375

36.80

33.30

30.38

28.02

25.88

22.60

20.12

18.05

16.43

15.14

13.98

12.62

11.85

11.43

10.82

10.27

1⁄ 8

0.125

41.62

37.62

34.29

31.60

29.16

25.41

22.59

20.23

18.38

16.91

15.59

14.04

13.17

12.68

11.99

11.36

9⁄ 64

0.140625

46.44

41.94

38.20

35.17

32.43

28.23

25.06

22.41

20.33

18.69

17.20

15.47

14.49

13.94

13.16

12.46

5⁄ 32

0.15625

51.25

46.27

42.11

38.75

35.71

31.04

27.53

24.59

22.29

20.46

18.82

16.89

15.81

15.19

14.33

13.56

3⁄ 16

0.1875

60.89

54.91

49.93

45.91

42.27

36.67

32.47

28.95

26.19

24.01

22.04

19.74

18.45

17.70

16.67

15.75

7⁄ 32

0.21875

70.52

63.56

57.75

53.06

48.82

42.31

37.40

33.31

30.10

27.55

25.27

22.59

21.09

20.21

19.01

17.94

1⁄ 4

0.250

80.15

72.20

65.57

60.22

55.38

47.94

42.34

37.67

34.01

31.10

28.49

25.44

23.73

22.72

21.35

20.13

AMW Wire Gauge Decimal Equivalenta

17 .039

18 .041

19 .043

20 .045

21 .047

22 .049

23 .051

24 .055

25 .059

26 .063

27 .067

28 .071

29 .075

30 .080

31 .085

Design Stress, kpsi

190

188

187

185

184

183

182

180

178

176

174

173

171

169

167

Torque, pound-inch

1.107

1.272

1.460

1.655

1.876

2.114

2.371

2.941

3.590

4.322

5.139

6.080

7.084

8.497

10.07


SPRING DESIGN

1⁄ 16


1⁄ 8

0.125

10.80

10.29

9.876

9.447

9.102

8.784

…

…

…

…

…

…

…

…

…

9⁄ 64

0.140625

11.83

11.26

10.79

10.32

9.929

9.572

9.244

8.654

8.141

…

…

…

…

…

…

5⁄ 32

0.15625

12.86

12.23

11.71

11.18

10.76

10.36

9.997

9.345

8.778

8.279

7.975

…

…

…

…

3⁄ 16

0.1875

14.92

14.16

13.55

12.92

12.41

11.94

11.50

10.73

10.05

9.459

9.091

8.663

8.232

7.772

7.364

7⁄ 32

0.21875

16.97

16.10

15.39

14.66

14.06

13.52

13.01

12.11

11.33

10.64

10.21

9.711

9.212

8.680

8.208

1⁄ 4

0.250

19.03

18.04

17.22

16.39

15.72

15.09

14.52

13.49

12.60

11.82

11.32

10.76

10.19

9.588

9.053

with a modulus of 28,500,000 psi.


343

a For sizes up to 13 gauge, the table values are for music wire with a modulus E of 29,000,000 psi; and for sizes from 27 to 31 guage, the values are for oil-tempered MB


8 .020

9 .022

10 .024

11 .026

12 .029

13 .031

14 .033

15 .035

16 .037

17 .039

344

Table 14. (Continued) Torsion Spring Deflections AMW Wire Gauge Decimal Equivalenta

18 .041

19 .043

20 .045

21 .047

22 .049

23 .051

Design Stress, kpsi

210

207

205

202

199

197

196

194

192

190

188

187

185

184

183

182

Torque, pound-inch

.1650

.2164

.2783

.3486

.4766

.5763

.6917

.8168

.9550

1.107

1.272

1.460

1.655

1.876

2.114

2.371



0.28125

42.03

37.92

34.65

31.72

28.29

26.37

25.23

23.69

22.32

21.09

19.97

19.06

18.13

17.37

16.67

16.03

5⁄ 16

0.3125

46.39

41.82

38.19

34.95

31.14

29.01

27.74

26.04

24.51

23.15

21.91

20.90

19.87

19.02

18.25

17.53

11⁄ 32

0.34375

50.75

45.73

41.74

38.17

33.99

31.65

30.25

28.38

26.71

25.21

23.85

22.73

21.60

20.68

19.83

19.04

0.375

55.11

49.64

45.29

41.40

36.84

34.28

32.76

30.72

28.90

27.26

25.78

24.57

23.34

22.33

21.40

20.55

13⁄ 32

0.40625

59.47

53.54

48.85

44.63

39.69

36.92

35.26

33.06

31.09

29.32

27.72

26.41

25.08

23.99

22.98

22.06

7⁄ 16

0.4375

63.83

57.45

52.38

47.85

42.54

39.56

37.77

35.40

33.28

31.38

29.66

28.25

26.81

25.64

24.56

23.56

15⁄ 32

0.46875

68.19

61.36

55.93

51.00

45.39

42.20

40.28

37.74

35.47

33.44

31.59

30.08

28.55

27.29

26.14

25.07

0.500

72.55

65.27

59.48

54.30

48.24

44.84

42.79

40.08

37.67

35.49

33.53

31.92

30.29

28.95

27.71

26.58

3⁄ 8

1⁄ 2

AMW Wire Gauge Decimal Equivalenta

24 .055

25 .059

26 .063

27 .067

28 .071

29 .075

30 .080

31 .085

32 .090

33 .095

34 .100

35 .106

36 .112

37 .118

1⁄ 8 125

Design Stress, kpsi

180

178

176

174

173

171

169

167

166

164

163

161

160

158

156

Torque, pound-inch

2.941

3.590

4.322

5.139

6.080

7.084

8.497

10.07

11.88

13.81

16.00

18.83

22.07

25.49

29.92



9⁄ 32

0.28125

14.88

13.88

13.00

12.44

11.81

11.17

10.50

9.897

9.418

8.934

8.547

8.090

7.727

7.353

6.973

5⁄ 16

0.3125

16.26

15.15

14.18

13.56

12.85

12.15

11.40

10.74

10.21

9.676

9.248

8.743

8.341

7.929

7.510

11⁄ 32

0.34375

17.64

16.42

15.36

14.67

13.90

13.13

12.31

11.59

11.00

10.42

9.948

9.396

8.955

8.504

8.046

0.375

19.02

17.70

16.54

15.79

14.95

14.11

13.22

12.43

11.80

11.16

10.65

10.05

9.569

9.080

8.583

13⁄ 32

0.40625

20.40

18.97

17.72

16.90

15.99

15.09

14.13

13.28

12.59

11.90

11.35

10.70

10.18

9.655

9.119

7⁄ 16

0.4375

21.79

20.25

18.90

18.02

17.04

16.07

15.04

14.12

13.38

12.64

12.05

11.35

10.80

10.23

9.655

15⁄ 32

0.46875

23.17

21.52

20.08

19.14

18.09

17.05

15.94

14.96

14.17

13.39

12.75

12.01

11.41

10.81

10.19

0.500

24.55

22.80

21.26

20.25

19.14

18.03

16.85

15.81

14.97

14.13

13.45

12.66

12.03

11.38

10.73

3⁄ 8

1⁄ 2

a For sizes up to 13 gauge, the table values are for music wire with a modulus E of 29,000,000 psi; and for sizes from 27 to 31 guage, the values are for oil-tempered MB

with a modulus of 28,500,000 psi.


SPRING DESIGN

9⁄ 32



16 .037

17 .039

18 .041

19 .043

20 .045

21 .047

22 .049

23 .051

24 .055

25 .059

26 .063

27 .067

28 .071

29 .075

Design Stress, kpsi

192

190

188

187

185

184

183

182

180

178

176

174

173

171

169

Torque, pound-inch

.9550

1.107

1.272

1.460

1.655

1.876

2.114

2.371

2.941

3.590

4.322

5.139

6.080

7.084

8.497


30 .080


0.53125

39.86

37.55

35.47

33.76

32.02

30.60

29.29

28.09

25.93

24.07

22.44

21.37

20.18

19.01

17.76

9⁄ 16

0.5625

42.05

39.61

37.40

35.59

33.76

32.25

30.87

29.59

27.32

25.35

23.62

22.49

21.23

19.99

18.67

19⁄ 32

0.59375

44.24

41.67

39.34

37.43

35.50

33.91

32.45

31.10

28.70

26.62

24.80

23.60

22.28

20.97

19.58

0.625

46.43

43.73

41.28

39.27

37.23

35.56

34.02

32.61

30.08

27.89

25.98

24.72

23.33

21.95

20.48

21⁄ 32

0.65625

48.63

45.78

43.22

41.10

38.97

37.22

35.60

34.12

31.46

29.17

27.16

25.83

24.37

22.93

21.39

11⁄ 16

0.6875

50.82

47.84

45.15

42.94

40.71

38.87

37.18

35.62

32.85

30.44

28.34

26.95

25.42

23.91

22.30

23⁄ 32

0.71875

53.01

49.90

47.09

44.78

42.44

40.52

38.76

37.13

34.23

31.72

29.52

28.07

26.47

24.89

23.21

0.750

55.20

51.96

49.03

46.62

44.18

42.18

40.33

38.64

35.61

32.99

30.70

29.18

27.52

25.87

24.12 5 .207

5⁄ 8

3⁄ 4

Gaugeab

1⁄ 8

5⁄ 32

3⁄ 16

or Wire Size and Decimal Equivalent

31 .085

32 .090

33 .095

34 .100

35 .106

36 .112

37 .118

.125

10 .135

9 .1483

.1563

8 .162

7 .177

.1875

6 .192

Design Stress, kpsi

167

166

164

163

161

160

158

156

161

158

156

154

150

149

146

143

Torque, pound-inch

10.07

11.88

13.81

16.00

18.83

22.07

25.49

29.92

38.90

50.60

58.44

64.30

81.68

96.45

101.5

124.6



17⁄ 32

0.53125

16.65

15.76

14.87

14.15

13.31

12.64

11.96

11.26

10.93

9.958

9.441

9.064

8.256

7.856

7.565

7.015

9⁄ 16

0.5625

17.50

16.55

15.61

14.85

13.97

13.25

12.53

11.80

11.44

10.42

9.870

9.473

8.620

8.198

7.891

7.312

19⁄ 32

0.59375

18.34

17.35

16.35

15.55

14.62

13.87

13.11

12.34

11.95

10.87

10.30

9.882

8.984

8.539

8.218

7.609

0.625

19.19

18.14

17.10

16.25

15.27

14.48

13.68

12.87

12.47

11.33

10.73

10.29

9.348

8.881

8.545

7.906

21⁄ 32

0.65625

20.03

18.93

17.84

16.95

15.92

15.10

14.26

13.41

12.98

11.79

11.16

10.70

9.713

9.222

8.872

8.202

11⁄ 16

0.6875

20.88

19.72

18.58

17.65

16.58

15.71

14.83

13.95

13.49

12.25

11.59

11.11

10.08

9.564

9.199

8.499

23⁄ 32

0.71875

21.72

20.52

19.32

18.36

17.23

16.32

15.41

14.48

14.00

12.71

12.02

11.52

10.44

9.905

9.526

8.796

0.750

22.56

21.31

20.06

19.06

17.88

16.94

15.99

15.02

14.52

13.16

12.44

11.92

10.81

10.25

9.852

9.093

5⁄ 8

3⁄ 4

sizes up to 26 gauge, the table values are for music wire with a modulus E of 29,500,000 psi; for sizes from 27 to 1⁄8 inch diameter the table values are for music wire with a modulus of 28,500,000 psi; for sizes from 10 gauge to 1⁄8 inch diameter, the values are for oil-tempered MB with a modulus of 28,500,000 psi. b Gauges 31 through 37 are AMW gauges. Gauges 10 through 5 are Washburn and Moen.

SPRING DESIGN

17⁄ 32

a For

345



24 .055

25 .059

26 .063

27 .067

28 .071

29 .075

30 .080

31 .085

32 .090

33 .095

34 .100

35 .106

36 .112

37 .118

1⁄ 8 .125

Design Stress, kpsi

180

178

176

174

173

171

169

167

166

164

163

161

160

158

156

Torque, pound-inch

2.941

3.590

4.322

5.139

6.080

7.084

8.497

10.07

11.88

13.81

16.00

18.83

22.07

25.49

29.92

0.8125

38.38

35.54

33.06

31.42

29.61

27.83

25.93

24.25

22.90

21.55

20.46

19.19

18.17

17.14

16.09

0.875

41.14

38.09

35.42

33.65

31.70

29.79

27.75

25.94

24.58

23.03

21.86

20.49

19.39

18.29

17.17

0.9375

43.91

40.64

37.78

35.88

33.80

31.75

29.56

27.63

26.07

24.52

23.26

21.80

20.62

19.44

18.24

1

1.000

46.67

43.19

40.14

38.11

35.89

33.71

31.38

29.32

27.65

26.00

24.66

23.11

21.85

20.59

19.31

11⁄16

1.0625

49.44

45.74

42.50

40.35

37.99

35.67

33.20

31.01

29.24

27.48

26.06

24.41

23.08

21.74

20.38

11⁄8

1.125

52.20

48.28

44.86

42.58

40.08

37.63

35.01

32.70

30.82

28.97

27.46

25.72

24.31

22.89

21.46

13⁄16

1.1875

54.97

50.83

47.22

44.81

42.18

39.59

36.83

34.39

32.41

30.45

28.86

27.02

25.53

24.04

22.53

11⁄4

1.250

57.73

53.38

49.58

47.04

44.27

41.55

38.64

36.08

33.99

31.94

30.27

28.33

26.76

25.19

23.60 3⁄ 8 .375

Inside Diameter, inch 13⁄ 16 7⁄ 8 15⁄ 16


10 .135

9 .1483

5⁄ 32

.1563

8 .162

7 .177

3⁄ 16

.1875

6 .192

5 .207

7⁄ 32

.2188

4 .2253

3 .2437

1⁄ 4

9⁄ 32

5⁄ 16

11⁄ 32

.250

.2813

.3125

.3438

Design Stress, kpsi

161

158

156

154

150

149

146

143

142

141

140

139

138

137

136

135

Torque, pound-inch

38.90

50.60

58.44

64.30

81.68

96.45

101.5

124.6

146.0

158.3

199.0

213.3

301.5

410.6

542.5

700.0

0.8125

15.54

14.08

13.30

12.74

11.53

10.93

10.51

9.687

9.208

8.933

8.346

8.125

7.382

6.784

6.292

5.880

0.875

16.57

15.00

14.16

13.56

12.26

11.61

11.16

10.28

9.766

9.471

8.840

8.603

7.803

7.161

6.632

6.189

15⁄ 16

0.9375

17.59

15.91

15.02

14.38

12.99

12.30

11.81

10.87

10.32

10.01

9.333

9.081

8.225

7.537

6.972

6.499

1 11⁄16

1.000 1.0625

18.62 19.64

16.83 17.74

15.88 16.74

15.19 16.01

13.72 14.45

12.98 13.66

12.47 13.12

11.47 12.06

10.88 11.44

10.55 11.09

9.827 10.32

9.559 10.04

8.647 9.069

7.914 8.291

7.312 7.652

6.808 7.118

Inside Diameter, inch 13⁄ 16 7⁄ 8


11⁄8

1.125

20.67

18.66

17.59

16.83

15.18

14.35

13.77

12.66

12.00

11.62

10.81

10.52

9.491

8.668

7.993

7.427

13⁄16

1.1875

21.69

19.57

18.45

17.64

15.90

15.03

14.43

13.25

12.56

12.16

11.31

10.99

9.912

9.045

8.333

7.737

11⁄4

1.250

22.72

20.49

19.31

18.46

16.63

15.71

15.08

13.84

13.11

12.70

11.80

11.47

10.33

9.422

8.673

8.046

sizes up to 26 gauge, the table values are for music wire with a modulus E of 29,500,000 psi; for sizes from 27 to 1⁄8 inch diameter the table values are for music wire with a modulus of 28,500,000 psi; for sizes from 10 gauge to 1⁄8 inch diameter, the values are for oil-tempered MB with a modulus of 28,500,000 psi. For an example in the use of the table, see the example starting on page 340. Note: Intermediate values may be interpolated within reasonable accuracy. a For


SPRING DESIGN

Washburn and Moen Gauge or Size and Decimal Equivalent a

346



347

Table 15. Correction Factors for Other Materials Materiala

Material a

Factor

Hard Drawn MB Chrome-vanadium

0.75 1.10

Chrome-silicon

1.20

Stainless 302 and 304 Up to 1⁄8 inch diameter

0.85

Over 1⁄8 to 1⁄4 inch diameter

Factor

Stainless 316 Up to 1⁄8 inch diameter

0.75


0.65

Over 1⁄4 inch diameter

0.65

Stainless 17–7 PH

0.75


1.00

0.65


1.07

Stainless 431

0.80

Over 3⁄16 inch diameter

Stainless 420

0.85

Over

1⁄ inch 4

diameter

1.12

…

…

a For use with values in Table 14. Note: The figures in Table 14 are for music wire (ASTM A228) and oil-tempered MB grade (ASTM A229) and can be used for several other materials that have a similar modulus of elasticity E. However, the design stress may be too high or too low, and therefore the design stress, torque, and deflection per coil should each be multiplied by the appropriate correction factor when using any of the materials given in this table (Table 15).

Torsion Spring Tolerances.—Torsion springs are coiled in a different manner from other types of coiled springs and therefore different tolerances apply. The commercial tolerance on loads is ± 10 per cent and is specified with reference to the angular deflection. For example: 100 pound-inches ± 10 per cent at 45 degrees deflection. One load specified usually suffices. If two loads and two deflections are specified, the manufacturing and testing times are increased. Tolerances smaller than ± 10 per cent require each spring to be individually tested and adjusted, which adds considerably to manufacturing time and cost. Tables 16, 17, and 18 give, respectively, free angle tolerances, tolerances on the number of coils, and coil diameter tolerances. Table 16. Torsion Spring Tolerances for Angular Relationship of Ends Spring Index Number of Coils (N) 1 2 3 4 5 6 8 10 15 20 25 30 50

4

6

8

10

12

14

16

18

5.5 9 12 16 20 21 27 31.5 38 47 56 65 90

5.5 9.5 13 16.5 20.5 22.5 28 32.5 40 49 60 68 95

20

Free Angle Tolerance, ± degrees 2 4 5.5 7 8 9.5 12 14 20 25 29 32 45

3 5 7 9 10 12 15 19 25 30 35 38 55

3.5 6 8 10 12 14.5 18 21 28 34 40 44 63

4 7 9.5 12 14 16 20.5 24 31 37 44 50 70

4.5 8 10.5 14 16 19 23 27 34 41 48 55 77

5 8.5 11 15 18 20.5 25 29 36 44 52 60 84

6 10 14 17 21 24 29 34 42 51 63 70 100

Table 17. Torsion Spring Tolerance on Number of Coils Number of Coils

Tolerance

Number of Coils

Tolerance

up to 5

±5°

over 10 to 20

±15°

over 5 to 10

±10°

over 20 to 40

±30°



SPRING DESIGN Table 18. Torsion Spring Coil Diameter Tolerances Spring Index Wire Diameter, Inch

4

0.015 0.023 0.035 0.051 0.076 0.114 0.172 0.250

0.002 0.002 0.002 0.002 0.003 0.004 0.006 0.008

6

8

10

12

14

16

0.003 0.005 0.007 0.010 0.015 0.022 0.034 0.050

0.004 0.006 0.009 0.012 0.018 0.028 0.042 0.060

Coil Diameter Tolerance, ± inch 0.002 0.002 0.002 0.003 0.005 0.007 0.010 0.014

0.002 0.002 0.003 0.005 0.007 0.010 0.013 0.022

0.002 0.003 0.004 0.007 0.009 0.013 0.020 0.030

0.003 0.004 0.006 0.008 0.012 0.018 0.027 0.040

Miscellaneous Springs.—This section provides information on various springs, some in common use, some less commonly used. Conical compression: These springs taper from top to bottom and are useful where an increasing (instead of a constant) load rate is needed, where solid height must be small, and where vibration must be damped. Conical springs with a uniform pitch are easiest to coil. Load and deflection formulas for compression springs can be used – using the average mean coil diameter, and providing the deflection does not cause the largest active coil to lie against the bottom coil. When this happens, each coil must be calculated separately, using the standard formulas for compression springs. Constant force springs: Those springs are made from flat spring steel and are finding more applications each year. Complicated design procedures can be eliminated by selecting a standard design from thousands now available from several spring manufacturers. Spiral, clock, and motor springs: Although often used in wind-up type motors for toys and other products, these springs are difficult to design and results cannot be calculated with precise accuracy. However, many useful designs have been developed and are available from spring manufacturing companies. Flat springs: These springs are often used to overcome operating space limitations in various products such as electric switches and relays. Table 19 lists formulas for designing flat springs. The formulas are based on standard beam formulas where the deflection is small. Table 19. Formulas for Flat Springs

Feature

Deflect., f Inches

Load, P Pounds

PL 3 f = -------------4Ebt 3 Sb L2 = ----------6Et 2S b bt 2 P = ---------------3L 3F = 4Ebt -----------------L3

3 f = 4PL ------------Ebt 3

2S b L 2 = -------------3Et S b bt 2 P = -----------6L 3F = Ebt --------------4L 3

3 f = 6PL ------------Ebt 3

Sb L2 = ----------Et S b bt 2 P = -----------6L 3F = Ebt --------------6L 3

3 f = 5.22PL -------------------Ebt 3

0.87S b L 2 = ---------------------Et S b bt 2 P = -----------6L Ebt 3 F = ---------------5.22L 3



349

Table 19. (Continued) Formulas for Flat Springs

Feature

Stress, Sb Bending psi

Thickness, t Inches

3PL S b = ----------2bt 2

6PL S b = ---------bt 2

= 6EtF ------------L2 Sb L2 t = ----------6EF =

3

PL 3 -------------4EbF

6PL S b = ---------bt 2

= 3EtF ------------2L 2 2S b L 2 t = -------------3EF =

3

4PL 3 ------------EbF

6PL S b = ---------bt 2

= EtF --------L2 Sb L2 t = ----------EF =

3

6PL 3 ------------EbF

EtF = ---------------0.87L 2 0.87S b L 2 t = ---------------------EF =

3

5.22PL 3 -------------------EbF

Based on standard beam formulas where the deflection is small. See page 308 for notation. Note: Where two formulas are given for one feature, the designer should use the one found to be appropriate for the given design. The result from either of any two formulas is the same.

Belleville washers or disc springs: These washer type springs can sustain relatively large loads with small deflections, and the loads and deflections can be increased by stacking the springs. Information on springs of this type is given in the section DISC SPRINGS starting on page 354. Volute springs: These springs are often used on army tanks and heavy field artillery, and seldom find additional uses because of their high cost, long production time, difficulties in manufacture, and unavailability of a wide range of materials and sizes. Small volute springs are often replaced with standard compression springs. Torsion bars: Although the more simple types are often used on motor cars, the more complicated types with specially forged ends are finding fewer applications as time goes. Moduli of Elasticity of Spring Materials.—The modulus of elasticity in tension, denoted by the letter E, and the modulus of elasticity in torsion, denoted by the letter G, are used in formulas relating to spring design. Values of these moduli for various ferrous and nonferrous spring materials are given in Table 20. General Heat Treating Information for Springs.—The following is general information on the heat treatment of springs, and is applicable to pre-tempered or hard-drawn spring materials only. Compression springs are baked after coiling (before setting) to relieve residual stresses and thus permit larger deflections before taking a permanent set. Extension springs also are baked, but heat removes some of the initial tension. Allowance should be made for this loss. Baking at 500 degrees F for 30 minutes removes approximately 50 per cent of the initial tension. The shrinkage in diameter however, will slightly increase the load and rate. Outside diameters shrink when springs of music wire, pretempered MB, and other carbon or alloy steels are baked. Baking also slightly increases the free length and these changes produce a little stronger load and increase the rate. Outside diameters expand when springs of stainless steel (18-8) are baked. The free length is also reduced slightly and these changes result in a little lighter load and a decrease the spring rate. Inconel, Monel, and nickel alloys do not change much when baked.



SPRING DESIGN

Beryllium-copper shrinks and deforms when heated. Such springs usually are baked in fixtures or supported on arbors or rods during heating. Brass and phosphor bronze springs should be given a light heat only. Baking above 450 degrees F will soften the material. Do not heat in salt pots. Torsion springs do not require baking because coiling causes residual stresses in a direction that is helpful, but such springs frequently are baked so that jarring or handling will not cause them to lose the position of their ends. Table 20. Moduli of Elasticity in Torsion and Tension of Spring Materials Ferrous Materials Material (Commercial Name) Hard Drawn MB Up to 0.032 inch 0.033 to 0.063 inch 0.064 to 0.125 inch 0.126 to 0.625 inch Music Wire Up to 0.032 inch 0.033 to 0.063 inch 0.064 to 0.125 inch 0.126 to 0.250 inch Oil-Tempered MB Chrome-Vanadium Chrome-Silicon Silicon-Manganese Stainless Steel Types 302, 304, 316 Type 17–7 PH Type 420 Type 431

Nonferrous Materials

Modulus of Elasticity a, psi In Torsion, G

In Tension, E

11,700,000 11,600,000 11,500,000 11,400,000

28,800,000 28,700,000 28,600,000 28,500,000

12,000,000 11,850,000 11,750,000 11,600,000 11,200,000 11,200,000 11,200,000 10,750,000

29,500,000 29,000,000 28,500,000 28,000,000 28,500,000 28,500,000 29,500,000 29,000,000

10,000,000 10,500,000 11,000,000 11,400,000

28,000,000c 29,500,000 29,000,000 29,500,000

Material (Commercial Name) Spring Brass Type 70–30 Phosphor Bronze 5 per cent tin Beryllium-Copper Cold Drawn 4 Nos. Pretempered, fully hard Inconelb 600 Inconelb X 750 Monelb 400 Monelb K 500 Duranickelb 300 Permanickelb Ni Spanb C 902 Elgiloyd Iso-Elastice

Modulus of Elasticity a, psi In Torsion, G

In Tension, E

5,000,000

15,000,000

6,000,000

15,000,000

7,000,000 7,250,000 10,500,000 10,500,000 9,500,000 9,500,000 11,000,000 11,000,000 10,000,000 12,000,000 9,200,000

17,000,000 19,000,000 31,000,000c 31,000,000c 26,000,000 26,000,000 30,000,000 30,000,000 27,500,000 29,500,000 26,000,000

a Note: Modulus G (shear modulus) is used for compression and extension springs; modulus E (Young's modulus) is used for torsion, flat, and spiral springs. b Trade name of International Nickel Company. c May be 2,000,000 pounds per square inch less if material is not fully hard. d Trade name of Hamilton Watch Company. e Trade name of John Chatillon & Sons.

Spring brass and phosphor bronze springs that are not very highly stressed and are not subject to severe operating use may be stress relieved after coiling by immersing them in boiling water for a period of 1 hour. Positions of loops will change with heat. Parallel hooks may change as much as 45 degrees during baking. Torsion spring arms will alter position considerably. These changes should be allowed for during looping or forming. Quick heating after coiling either in a high-temperature salt pot or by passing a spring through a gas flame is not good practice. Samples heated in this way will not conform with production runs that are properly baked. A small, controlled-temperature oven should be used for samples and for small lot orders. Plated springs should always be baked before plating to relieve coiling stresses and again after plating to relieve hydrogen embrittlement. Hardness values fall with high heat—but music wire, hard drawn, and stainless steel will increase 2 to 4 points Rockwell C.



351

Table 21. Squares, Cubes, and Fourth Powers of Wire Diameters Steel Wire Gage (U.S.)

Music or Piano Wire Gage

7-0 6-0 5-0 4-0 3-0 2-0 1-0 1 2 3 4 5 6 … 7 … 8 … 9 … … 10 … … 11 … … … 12 … … 13 … … 14 … 15 … … … 16 … … 17 … … 18 … … … 19 … … … 20 … 21 … … 22 … 23 … 24 …

… … … … … … … … … … … … … 45 … 44 43 42 … 41 40 … 39 38 … 37 36 35 … 34 33 … 32 31 30 29 … 28 27 26 … 25 24 … 23 22 … 21 20 19 18 17 16 15 … 14 … 13 12 … 11 … 10 … 9

Diameter Inch 0.4900 0.4615 0.4305 0.3938 0.3625 0.331 0.3065 0.283 0.2625 0.2437 0.2253 0.207 0.192 0.180 0.177 0.170 0.162 0.154 0.1483 0.146 0.138 0.135 0.130 0.124 0.1205 0.118 0.112 0.106 0.1055 0.100 0.095 0.0915 0.090 0.085 0.080 0.075 0.072 0.071 0.067 0.063 0.0625 0.059 0.055 0.054 0.051 0.049 0.0475 0.047 0.045 0.043 0.041 0.039 0.037 0.035 0.0348 0.033 0.0317 0.031 0.029 0.0286 0.026 0.0258 0.024 0.023 0.022

Section Area

Square

0.1886 0.1673 0.1456 0.1218 0.1032 0.0860 0.0738 0.0629 0.0541 0.0466 0.0399 0.0337 0.0290 0.0254 0.0246 0.0227 0.0206 0.0186 0.0173 0.0167 0.0150 0.0143 0.0133 0.0121 0.0114 0.0109 0.0099 0.0088 0.0087 0.0078 0.0071 0.0066 0.0064 0.0057 0.0050 0.0044 0.0041 0.0040 0.0035 0.0031 0.0031 0.0027 0.0024 0.0023 0.0020 0.00189 0.00177 0.00173 0.00159 0.00145 0.00132 0.00119 0.00108 0.00096 0.00095 0.00086 0.00079 0.00075 0.00066 0.00064 0.00053 0.00052 0.00045 0.00042 0.00038

0.24010 0.21298 0.18533 0.15508 0.13141 0.10956 0.09394 0.08009 0.06891 0.05939 0.05076 0.04285 0.03686 0.03240 0.03133 0.02890 0.02624 0.02372 0.02199 0.02132 0.01904 0.01822 0.01690 0.01538 0.01452 0.01392 0.01254 0.01124 0.01113 0.0100 0.00902 0.00837 0.00810 0.00722 0.0064 0.00562 0.00518 0.00504 0.00449 0.00397 0.00391 0.00348 0.00302 0.00292 0.00260 0.00240 0.00226 0.00221 0.00202 0.00185 0.00168 0.00152 0.00137 0.00122 0.00121 0.00109 0.00100 0.00096 0.00084 0.00082 0.00068 0.00067 0.00058 0.00053 0.00048

Cube 0.11765 0.09829 0.07978 0.06107 0.04763 0.03626 0.02879 0.02267 0.01809 0.01447 0.01144 0.00887 0.00708 0.00583 0.00555 0.00491 0.00425 0.00365 0.00326 0.00311 0.00263 0.00246 0.00220 0.00191 0.00175 0.00164 0.00140 0.00119 0.001174 0.001000 0.000857 0.000766 0.000729 0.000614 0.000512 0.000422 0.000373 0.000358 0.000301 0.000250 0.000244 0.000205 0.000166 0.000157 0.000133 0.000118 0.000107 0.000104 0.000091 0.0000795 0.0000689 0.0000593 0.0000507 0.0000429 0.0000421 0.0000359 0.0000319 0.0000298 0.0000244 0.0000234 0.0000176 0.0000172 0.0000138 0.0000122 0.0000106


Fourth Power 0.05765 0.04536 0.03435 0.02405 0.01727 0.01200 0.008825 0.006414 0.004748 0.003527 0.002577 0.001836 0.001359 0.001050 0.000982 0.000835 0.000689 0.000563 0.000484 0.000455 0.000363 0.000332 0.000286 0.000237 0.000211 0.000194 0.000157 0.000126 0.0001239 0.0001000 0.0000815 0.0000701 0.0000656 0.0000522 0.0000410 0.0000316 0.0000269 0.0000254 0.0000202 0.0000158 0.0000153 0.0000121 0.00000915 0.00000850 0.00000677 0.00000576 0.00000509 0.00000488 0.00000410 0.00000342 0.00000283 0.00000231 0.00000187 0.00000150 0.00000147 0.00000119 0.00000101 0.000000924 0.000000707 0.000000669 0.000000457 0.000000443 0.000000332 0.000000280 0.000000234


SPRING DESIGN

Spring Failure.—Spring failure may be breakage, high permanent set, or loss of load. The causes are listed in groups in Table 22. Group 1 covers causes that occur most frequently; Group 2 covers causes that are less frequent; and Group 3 lists causes that occur occasionally. Table 22. Causes of Spring Failure

Group 1

Group 2

Cause

Comments and Recommendations

High stress

The majority of spring failures are due to high stresses caused by large deflections and high loads. High stresses should be used only for statically loaded springs. Low stresses lengthen fatigue life.

Improper electroplating methods and acid cleaning of springs, without Hydrogen proper baking treatment, cause spring steels to become brittle, and are a embrittlement frequent cause of failure. Nonferrous springs are immune. Sharp bends and holes

Sharp bends on extension, torsion, and flat springs, and holes or notches in flat springs, cause high concentrations of stress, resulting in failure. Bend radii should be as large as possible, and tool marks avoided.

Fatigue

Repeated deflections of springs, especially above 1,000,000 cycles, even with medium stresses, may cause failure. Low stresses should be used if a spring is to be subjected to a very high number of operating cycles.

Shock loading

Impact, shock, and rapid loading cause far higher stresses than those computed by the regular spring formulas. High-carbon spring steels do not withstand shock loading as well as do alloy steels.

Corrosion

Slight rusting or pitting caused by acids, alkalis, galvanic corrosion, stress corrosion cracking, or corrosive atmosphere weakens the material and causes higher stresses in the corroded area.

Faulty heat treatment

Keeping spring materials at the hardening temperature for longer periods than necessary causes an undesirable growth in grain structure, resulting in brittleness, even though the hardness may be correct.

Faulty material

Poor material containing inclusions, seams, slivers, and flat material with rough, slit, or torn edges is a cause of early failure. Overdrawn wire, improper hardness, and poor grain structure also cause early failure.

High temperature

High operating temperatures reduce spring temper (or hardness) and lower the modulus of elasticity, thereby causing lower loads, reducing the elastic limit, and increasing corrosion. Corrosion-resisting or nickel alloys should be used.

Low temperature Group 3

Temperatures below −40 degrees F reduce the ability of carbon steels to withstand shock loads. Carbon steels become brittle at −70 degrees F. Corrosion-resisting, nickel, or nonferrous alloys should be used.

Friction

Close fits on rods or in holes result in a wearing away of material and occasional failure. The outside diameters of compression springs expand during deflection but they become smaller on torsion springs.

Other causes

Enlarged hooks on extension springs increase the stress at the bends. Carrying too much electrical current will cause failure. Welding and soldering frequently destroy the spring temper. Tool marks, nicks, and cuts often raise stresses. Deflecting torsion springs outwardly causes high stresses and winding them tightly causes binding on supporting rods. High speed of deflection, vibration, and surging due to operation near natural periods of vibration or their harmonics cause increased stresses.



353

Table 23. Arbor Diameters for Springs Made from Music Wire Spring Outside Diameter (inch)

Wire Dia. (inch)

1⁄ 16

0.008

0.039

0.060

0.078

0.093

0.107

0.119

0.129

0.010

0.037

0.060

0.080

0.099

0.115

0.129

0.142

0.012

0.034

0.059

0.081

0.101

0.119

0.135

0.150

0.163

0.014

0.031

0.057

0.081

0.102

0.121

0.140

0.156

0.172

0.187

0.200

0.213

0.234

…

0.016

0.028

0.055

0.079

0.102

0.123

0.142

0.161

0.178

0.194

0.209

0.224

0.250

0.271

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

11⁄ 32

3⁄ 8

7⁄ 16

1⁄ 2

…

…

…

…

…

…

0.154

0.164

…

…

…

…

0.177

0.189

0.200

…

…

Arbor Diameter (inch)

0.018

…

0.053

0.077

0.101

0.124

0.144

0.161

0.182

0.200

0.215

0.231

0.259

0.284

0.020

…

0.049

0.075

0.096

0.123

0.144

0.165

0.184

0.203

0.220

0.237

0.268

0.296

0.022

…

0.046

0.072

0.097

0.122

0.145

0.165

0.186

0.206

0.224

0.242

0.275

0.305

0.024

…

0.043

0.070

0.095

0.120

0.144

0.166

0.187

0.207

0.226

0.245

0.280

0.312

0.026

…

…

0.067

0.093

0.118

0.143

0.166

0.187

0.208

0.228

0.248

0.285

0.318

0.028

…

…

0.064

0.091

0.115

0.141

0.165

0.187

0.208

0.229

0.250

0.288

0.323

0.030

…

…

0.061

0.088

0.113

0.138

0.163

0.187

0.209

0.229

0.251

0.291

0.328

0.032

…

…

0.057

0.085

0.111

0.136

0.161

0.185

0.209

0.229

0.251

0.292

0.331

0.034

…

…

…

0.082

0.109

0.134

0.159

0.184

0.208

0.229

0.251

0.292

0.333

0.036

…

…

…

0.078

0.106

0.131

0.156

0.182

0.206

0.229

0.250

0.294

0.333

0.038

…

…

…

0.075

0.103

0.129

0.154

0.179

0.205

0.227

0.251

0.293

0.335

0.041

…

…

…

…

0.098

0.125

0.151

0.176

0.201

0.226

0.250

0.294

0.336

0.0475

…

…

…

…

0.087

0.115

0.142

0.168

0.194

0.220

0.244

0.293

0.337

0.054

…

…

…

…

…

0.103

0.132

0.160

0.187

0.212

0.245

0.287

0.336

0.0625

…

…

…

…

…

…

0.108

0.146

0.169

0.201

0.228

0.280

0.330

0.072

…

…

…

…

…

…

…

0.129

0.158

0.186

0.214

0.268

0.319

0.080

…

…

…

…

…

…

…

…

0.144

0.173

0.201

0.256

0.308

0.0915

…

…

…

…

…

…

…

…

…

…

0.181

0.238

0.293

0.1055

…

…

…

…

…

…

…

…

…

…

…

0.215

0.271

0.1205

…

…

…

…

…

…

…

…

…

…

…

…

0.215

0.125

…

…

…

…

…

…

…

…

…

…

…

…

0.239

Wire Dia. (inch)

Spring Outside Diameter (inches) 9⁄ 16

5⁄ 8

11⁄ 16

3⁄ 4

13⁄ 16

7⁄ 8

15⁄ 16

1

11⁄8

11⁄4

13⁄8

11⁄2

13⁄4

2

Arbor Diameter (inches)

0.022

0.332

0.357

0.380

…

…

…

…

…

…

…

…

…

…

…

0.024

0.341

0.367

0.393

0.415

…

…

…

…

…

…

…

…

…

… …

0.026

0.350

0.380

0.406

0.430

…

…

…

…

…

…

…

…

…

0.028

0.356

0.387

0.416

0.442

0.467

…

…

…

…

…

…

…

…

…

0.030

0.362

0.395

0.426

0.453

0.481

0.506

…

…

…

…

…

…

…

…

0.032

0.367

0.400

0.432

0.462

0.490

0.516

0.540

…

…

…

…

…

…

…

0.034

0.370

0.404

0.437

0.469

0.498

0.526

0.552

0.557

…

…

…

…

…

…

0.036

0.372

0.407

0.442

0.474

0.506

0.536

0.562

0.589

…

…

…

…

…

…

0.038

0.375

0.412

0.448

0.481

0.512

0.543

0.572

0.600

0.650

…

…

…

…

…

0.041

0.378

0.416

0.456

0.489

0.522

0.554

0.586

0.615

0.670

0.718

…

…

…

…

0.0475

0.380

0.422

0.464

0.504

0.541

0.576

0.610

0.643

0.706

0.763

0.812

…

…

…

0.054

0.381

0.425

0.467

0.509

0.550

0.589

0.625

0.661

0.727

0.792

0.850

0.906

…

…

0.0625

0.379

0.426

0.468

0.512

0.556

0.597

0.639

0.678

0.753

0.822

0.889

0.951

1.06

1.17

0.072

0.370

0.418

0.466

0.512

0.555

0.599

0.641

0.682

0.765

0.840

0.911

0.980

1.11

1.22

0.080

0.360

0.411

0.461

0.509

0.554

0.599

0.641

0.685

0.772

0.851

0.930

1.00

1.13

1.26

0.0915

0.347

0.398

0.448

0.500

0.547

0.597

0.640

0.685

0.776

0.860

0.942

1.02

1.16

1.30

0.1055

0.327

0.381

0.433

0.485

0.535

0.586

0.630

0.683

0.775

0.865

0.952

1.04

1.20

1.35

0.1205

0.303

0.358

0.414

0.468

0.520

0.571

0.622

0.673

0.772

0.864

0.955

1.04

1.22

1.38

0.125

0.295

0.351

0.406

0.461

0.515

0.567

0.617

0.671

0.770

0.864

0.955

1.05

1.23

1.39



DISC SPRINGS

DISC SPRINGS Performance of Disc Springs Introduction.—Disc springs, also known as Belleville springs, are conically formed from washers and have rectangular cross section. The disc spring concept was invented by a Frenchman Louis Belleville in 1865. His springs were relatively thick and had a small amount of cone height or “dish”, which determined axial deflection. At that time, these springs were used in the buffer parts of railway rolling stock, for recoil mechanisms of guns, and some other applications. The use of disc springs will be advantageous when space is limited and high force is required, as these conditions cannot be satisfied by using coil springs. Load-deflection characteristics of disc springs are linear and regressive depending on their dimensions and the type of stacking. A large number of standard sizes are available from disc spring manufacturers and distributors, so that custom sizes may not be required. Therefore, disc springs are widely used today in virtually all branches of engineering with possibilities of new applications. Disc Spring Nomenclature.—Disc spring manufacturers assign their own part number for each disc spring, but the catalog numbers for disc springs are similar, so each item can often be identified regardless of the manufacturer. The disc spring identification number is a numerical code that provides basic dimensions in millimeters. Identification numbers representing the primary dimensions of the disc spring and consist of one, two, or three numbers separated from each other by dash marks or spaces. Disc spring manufacturers in the United States also provide dimensions in inches. Dimensions of several typical disc springs are shown in the following table. Basic nomenclature is illustrated in Fig. 1. Catalog Number (mm)

Outside Diameter D (mm)

Inside Diameter d (mm)

Thickness t (mm)

Equivalent Catalog Number (inch)

8–4.2–0.4 50–25.4–2 200–102–12

8 50 200

4.2 25.4 102

0.4 2 12

0.315–0.165– 0.0157 1.97–1.00–0.0787 7.87–4.02–0.472

Additional dimensions shown in catalogs are cone (dish) height h at unloaded condition, and overall height H = h + t, that combines the cone height and the thickness of a disc spring. d

H t

h D Fig. 1. Disc Spring Nomenclature

Disc Spring Group Classification.—Forces and stresses generated by compression depend on disc spring thickness much more than on any other dimensions. Standard DIN 2093 divides all disc springs into three groups in accordance with their thickness: Group 1 includes all disc springs with thickness less than 1.25 mm (0.0492 inch). Group 2 includes all disc springs with thickness between 1.25 mm and 6.0 mm (0.0492 inch and 0.2362 inch). Group 3 includes disc springs with thickness greater than 6.0 mm (0.2362 inch). There are 87 standard disc spring items, which are manufactured in accordance with Standard DIN 2093 specifications for dimensions and quality requirements. There are 30 standard disc spring items in Group 1. The smallest and the largest disc springs in this


Machinery's Handbook 27th Edition DISC SPRING MATERIALS

355

group are 8–4.2–0.2 and 40–20.4–1 respectively. Group 2 has 45 standard disc spring items. The smallest and the largest disc springs are 22.5–11.2–1.25 and 200–102–5.5 respectfully. Group 3 includes 12 standard disc spring items. The smallest and the largest disc springs of this group are 125–64–8 and 250–127–14 respectively. Summary of Disc Spring Sizes Specified in DIN 2093 OD Classification Group 1 Group 2 Group 3

ID

Thickness

Min.

Max

Min.

Max

Min.

Max

6 mm (0.236 in) 20 mm (0.787 in) 125 mm (4.921 in)

40 mm (1.575 in) 225 mm (8.858 in) 250 mm (9.843 in)

3.2 mm (0.126 in) 10.2 mm (0.402 in) 61 mm (2.402 in)

20.4 mm (0.803 in) 112 mm (4.409 in) 127 mm (5.000 in)

0.2 mm (0.008 in) 1.25 mm (0.049 in) 6.5 mm (0.256 in)

1.2 mm (0.047 in) 6 mm (0.236 in) 16 mm (0.630 in)

The number of catalog items by disc spring dimensions depends on the manufacturer. Currently, the smallest disc spring is 6–3.2–0.3 and the largest is 250–127–16. One of the U.S. disc spring manufacturers, Key Bellevilles, Inc. offers 190 catalog items. The greatest number of disc spring items can be found in Christian Bauer GmbH + Co. catalog. There are 291 disc spring catalog items in all three groups. Disc Spring Contact Surfaces.—Disc springs are manufactured with and without contact (also called load-bearing) surfaces. Contact surfaces are small flats at points 1 and 3 in Fig. 2, adjacent to the corner radii of the spring. The width of the contact surfaces w depends on the outside diameter D of the spring, and its value is approximately w = D⁄150. F

w

d

1

H t' 3

w F

D Fig. 2. Disc Spring with Contact Surfaces

Disc springs of Group 1 and Group 2, that are contained in the DIN 2093 Standard, do not have contact surfaces, although some Group 2 disc springs not included in DIN 2093 are manufactured with contact surfaces. All disc springs of Group 3 (standard and nonstandard) are manufactured with contact surfaces. Almost all disc springs with contact surfaces are manufactured with reduced thickness. Disc springs without contact surfaces have a corner radii r whose value depends on the spring thickness, t. One disc spring manufacturers recommends the following relationship: r=t ⁄ 6 Disc Spring Materials .—A wide variety of materials are available for disc springs, but selection of the material depends mainly on application. High-carbon steels are used only for Group 1 disc springs. AISI 1070 and AISI 1095 carbon steels are used in the U.S. Similar high-carbon steels such as DIN 1.1231 and DIN 1.1238 (Germany), and BS 060 A67 and BS 060 A78 (Great Britain) are used in other countries. The most common materials for Groups 2 and 3 springs operating under normal conditions are chromium-vanadium alloy steels such as AISI 6150 used in the U.S. Similar alloys such as DIN 1.8159 and DIN



DISC SPRING STACKING

1.7701 (Germany) and BS 735 A50 (Great Britain) are used in foreign countries. Some disc spring manufacturers in the U.S. also use chromium alloy steel AISI 5160. The hardness of disc springs in Groups 2 and 3 should be 42 to 52 HRC. The hardness of disc springs in Group 1 tested by the Vickers method should be 412 to 544 HV. If disc springs must withstand corrosion and high temperatures, stainless steels and heatresistant alloys are used. Most commonly used stainless steels in the United States are AISI types 301, 316, and 631, which are similar to foreign material numbers DIN 1.4310, DIN 1.4401, and DIN 1.4568, respectively. The operating temperature range for 631 stainless steel is −330 to 660ºF (−200 to 350ºC). Among heat-resistant alloys, Inconel 718 and Inconel X750 (similar to DIN 2.4668 and DIN 2.4669, respectively) are the most popular. Operating temperature range for Inconel 718 is −440 to 1290ºF (−260 to 700ºC). When disc springs are stacked in large numbers and their total weight becomes a major concern, titanium α-β alloys can be used to reduce weight. In such cases, Ti-6Al-4V alloy is used. If nonmagnetic and corrosion resistant properties are required and material strength is not an issue, phosphor bronzes and beryllium-coppers are the most popular copper alloys for disc springs. Phosphor bronze C52100, which is similar to DIN material number 2.1030, is used at the ordinary temperature range. Beryllium-coppers C17000 and C17200, similar to material numbers DIN 2.1245 and DIN 2.1247 respectively, works well at very low temperatures. Strength properties of disc spring materials are characterized by moduli of elasticity and Poisson’s ratios. These are summarized in Table 1. Table 1. Strength Characteristics of Disc Spring Materials Modulus of Elasticity Material All Steels Heat-resistant Alloys α-β Titanium Alloys (Ti-6Al-4V) Phosphor Bronze (C52100) Beryllium-copper (C17000) Beryllium-copper (C17200)

106 psi

N⁄mm2

28–31

193,000–213,700

17 16 17 18

117,200 110,300 117,200 124,100

Poisson’s Ratio 0.30 0.28–0.29 0.32 0.35 0.30 0.30

Stacking of Disc Springs.—Individual disc springs can be arranged in series and parallel stacks. Disc springs in series stacking, Fig. 3, provide larger deflection Stotal under the same load F as a single disc spring would generate. Disc springs in parallel stacking, Fig. 4, generate higher loads Ftotal with the same deflection s, that a single disc spring would have. n =number of disc springs in stack s =deflection of single spring Stotal = total deflection of stack of n springs F =load generated by a single spring Ftotal = total load generated by springs in stack L0 =length of unloaded spring stack Series: For n disc springs arranged in series as in Fig. 3, the following equations are applied: F total = F S total = s × n L0 = H × n = ( t ÷ h ) × n


(1)

Machinery's Handbook 27th Edition DISC SPRING STACKING

357

F

L0

L1,2

t

H

h F

d D

Fig. 3. Disc Springs in Series Stacking L1, 2 indices indicate length of spring stack under minimum and maximum load

Parallel: Parallel stacking generates a force that is directly proportional to number of springs arranged in parallel. Two springs in parallel will double the force, three springs in parallel will triple the force, and so on. However, it is a common practice to use two springs in parallel in order to keep the frictional forces between the springs as low as possible. Otherwise, the actual spring force cannot be accurately determined due to deviation from its theoretical value. For n disc springs arranged in parallel as in Fig. 4, the following equations are applied: F total = F × n S total = s L 0 = H + t ( n – 1 ) = ( h + t ) + tn – t = h + tn

(2)

d

L0

t h

D

H

Fig. 4. Disc Springs in Parallel Stacking

Parallel-Series: When both higher force and greater deflection are required, disc springs must be arranged in a combined parallel-series stacking as illustrated in Fig. 5. F

L0

L 1,2 H t

h d D

F

Fig. 5. Disc Springs in Parallel-Series Stacking

Normally, two springs in parallel are nested in series stacking. Two springs in parallel, called a pair, double the force, and the number of pairs, np, determines the total deflection, Stotal.



DISC SPRING FORCES AND STRESSES

For np disc spring pairs arranged in series, the following equations are applied: F total = 2 × F S total = s × n p L 0 = H × n p = ( 2t + h ) × n p

(3)

Disc Spring Forces and Stresses Several methods of calculating forces and stresses for given disc spring configurations exist, some very complicated, others of limited accuracy. The theory which is widely used today for force and stress calculations was developed more than 65 years ago by Almen and Laszlo. The theory is based on the following assumptions: cross sections are rectangular without radii, over the entire range of spring deflection; no stresses occur in the radial direction; disc springs are always under elastic deformation during deflection; and d u e t o s m a l l cone angles of unloaded disc springs (between 3.5° and 8.6°), mathematical simplifications are applied. The theory provides accurate results for disc springs with the following ratios: outsideto-inside diameter, D ⁄ d = 1.3 to 2.5; and cone height-to-thickness, h ⁄ t is up to 1.5. Force Generated by Disc Springs Without Contact Surfaces.—Disc springs in Group 1 and most of disc springs in Group 2 are manufactured without contact (load-bearing) surfaces, but have corner radii. A single disc spring force applied to points 1 and 3 in Fig. 6 can be found from Equation (4) in which corner radii are not considered: 3 4⋅E⋅s s F = ------------------------------------------ ⎛⎝ h – ---⎞⎠ ⋅ ( h – s ) ⋅ t + t 2 2 2 ( 1 – µ ) ⋅ K1 ⋅ D

(4)

where F = disc spring force; E = modulus of elasticity of spring material; µ = Poisson’s ratio of spring material; K1 = constant depending on outside-to-inside diameter ratio; D = disc spring nominal outside diameter; h = cone (dish) height; s = disc spring deflection; and, t = disc spring thickness. D F 1

H

2

t

3

F

h d Fig. 6. Schematic of Applied Forces

It has been found that the theoretical forces calculated using Equation (4) are lower than the actual (measured) spring forces, as illustrated in Fig. 7. The difference between theoretical (trace 1) and measured force values (trace 3) was significantly reduced (trace 2) when the actual outside diameter of the spring in loaded condition was used in the calculations.


Machinery's Handbook 27th Edition DISC SPRING FORCES AND STRESSES

359


6000

3

2

5500

1

5000 4500

Force (pounds)

4000 3500 3000 2500 2000 1500 1000 500 0 0.01

0

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

0.10

Deflection (inch)

Fig. 7. Force–Deflection Relationships (80–36–3.6 Disc Springs) 1 – Theoretical Force Calculated by Equation (4) 2 – Theoretical Force Calculated by Equation (10) 3 – Measured Force

The actual outside diameter Da of a disc spring contact circle is smaller than the nominal outside diameter D due to cone angle α and corner radius r, as shown in Fig. 8. Diameter Da cannot be measured, but can be calculated by Equation (9) developed by the author. D/2 d/2

t r r h Da / 2 D/2

t

r

r

a b Da / 2 Fig. 8. Conventional Shape of Disc Spring



DISC SPRING FORCES AND STRESSES

From Fig. 8, Da D (5) ------ = ---- – ( a + b ) 2 2 where a = t × sinα and b = r × cosα. Substitution of a and b values into Equation (5) gives: Da (6) ------ = D ---- – ( t sin α + r cos α ) 2 2 The cone angle α is found from: h = -----------2h tan α = ------------D d D –d ---- – --2 2

2h -⎞ α = atan ⎛ -----------⎝ D – d⎠

(7)

Substituting α from Equation (7) and r = t ⁄ 6 into Equation (6) gives: D ⎧ 2h -⎞ + 1--- cos atan ⎛ -----------2h -⎞ ⎫ ------a = D ---- – t ⎨ sin atan ⎛ -----------⎝ D – d⎠ ⎬ ⎝ D – d⎠ 2 2 ⎩ 6 ⎭

(8)

⎧ 2h -⎞ + 1--- cos atan ⎛ -----------2h -⎞ ⎫ D a = D – 2t ⎨ sin atan ⎛ -----------⎝ D – d⎠ ⎝ D – d⎠ ⎬ 6 ⎩ ⎭

(9)

Finally,

Substituting Da from Equation (9) for D in Equation (4) yields Equation (10), that provides better accuracy for calculating disc spring forces. 4⋅E⋅s s F = ------------------------------------------ ⎛ h – ---⎞ ⋅ ( h – s ) ⋅ t + t 3 2⎠ ( 1 – µ 2 ) ⋅ K 1 ⋅ D a2 ⎝

(10)

The constant K1 depends on disc spring outside diameter D, inside diameter d, and their ratio δ = D⁄d : – 1⎞ 2 ⎛ δ----------⎝ δ ⎠ K 1 = ---------------------------------------δ + 1- – ------2 -⎞ π ⋅ ⎛ ----------⎝ δ – 1 ln δ⎠

(11)

Table 2 compares the spring force of a series of disc springs deflected by 75% of their cone height, i.e., s = 0.75h, as determined from manufacturers catalogs calculated in accordance with Equation (4), calculated forces by use of Equation (10), and measured forces. Table 2. Comparison Between Calculated and Measured Disc Spring Forces Disc Spring Catalog Item 50 – 22.4 – 2.5 S = 1.05 mm 60 – 30.5 – 2.5 S = 1.35 mm 60 – 30.5 – 3 S = 1.275 mm 70 – 35.5 – 3 S = 1.575 mm 70 – 35.5 – 3.5 S = 1.35 mm

Schnorr Handbook for Disc Springs 8510 N 1913 lbf 8340 N 1875 lbf 13200 N 2967 lbf 12300 N 2765 lbf

Christian Bauer Disc Spring Handbook 8510 N 1913 lbf 8342 N 1875 lbf 13270 N 2983 lbf 12320 N 2770 lbf 16180 N 3637 lbf

Key Bellevilles Disc Spring Catalog 8616 N 1937 lbf 8465 N 1903 lbf 13416 N 3016 lbf 12397 N 2787 lbf

Spring Force Calculated by Equation (10)

Measured Disc Spring Force

9020 N 2028 lbf 8794 N 1977 lbf 14052 N 3159 lbf 12971 N 2916 lbf 17170 N 3860 lbf

9563 N 2150 lbf 8896 N 2000 lbf 13985 N 3144 lbf 13287 N 2987 lbf 17304 N 3890 lbf

Comparison made at 75% deflection, in Newtons (N) and pounds (lbf)


Machinery's Handbook 27th Edition DISC SPRING FORCES AND STRESSES

361

The difference between disc spring forces calculated by Equation (10) and the measured forces varies from −5.7% (maximum) to +0.5% (minimum). Disc spring forces calculated by Equation (4) and shown in manufacturers catalogs are less than measured forces by − 11% (maximum) to −6% (minimum). Force Generated by Disc Spring with Contact Surfaces.—Some of disc springs in Group 2 and all disc springs in Group 3 are manufactured with small contact (load-bearing) surfaces or flats in addition to the corner radii. These flats provide better contact between disc springs, but, at the same time, they reduce the springs outside diameter and generate higher spring force because in Equation (4) force F is inversely proportional to the square of outside diameter D2. To compensate for the undesired force increase, the disc spring thickness is reduced from t to t′. Thickness reduction factors t′⁄t are approximately 0.94 for disc spring series A and B, and approximately 0.96 for series C springs. With such reduction factors, the disc spring force at 75% deflection is the same as for equivalent disc spring without contact surfaces. Equation (12), which is similar to Equation (10), has an additional constant K4 that correlates the increase in spring force due to contact surfaces. If disc springs do not have contact surfaces, then K42 = K4 = 1. 2

4 ⋅ E ⋅ K4 ⋅ s 3 2 s F = ----------------------------------------- K 4 ⋅ ⎛ h′ – ---⎞ ⋅ ( h′ – s ) ⋅ t′ + ( t′ ) ⎝ ⎠ 2 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da

(12)

where t′ = reduced thickness of a disc spring h′ = cone height adjusted to reduced thickness: h′= H − t′ (h′ > h) K4 = constant applied to disc springs with contact surfaces. K42 can be calculated as follows: 2

2 – b + b – 4acK 4 = -------------------------------------(13) 2a where a = t′(H − 4t′ + 3t) (5H − 8 t′ + 3t); b = 32(t′)3 ; and, c = −t [5(H – t)2 + 32t2]. Disc Spring Functional Stresses.—Disc springs are designed for both static and dynamic load applications. In static load applications, disc springs may be under constant or fluctuating load conditions that change up to 5,000 or 10,000 cycles over long time intervals. Dynamic loads occur when disc springs are under continuously changing deflection between pre-load (approximately 15% to 20% of the cone height) and the maximum deflection values over short time intervals. Both static and dynamic loads cause compressive and tensile stresses. The position of critical stress points on a disc spring cross section are shown in Fig. 9.

Do

F

F 0

t

1

1

0

2

2

3

3

F

h s

H

F d D

Fig. 9. Critical Stress Points s is deflection of spring by force F; h − s is a cone height of loaded disc spring

Compressive stresses are acting at points 0 and 1, that are located on the top surface of the disc spring. Point 0 is located on the cross-sectional mid-point diameter, and point 1 is located on the top inside diameter. Tensile stresses are acting at points 2 and 3, which are located on the bottom surface of the disc spring. Point 2 is on the bottom inside diameter, and point 3 is on the bottom outside diameter. The following equations are used to calcu-



DISC SPRING FATIGUE LIFE

late stresses. The minus sign “−” indicates that compressive stresses are acting in a direction opposite to the tensile stresses. 4E ⋅ t ⋅ s ⋅ K 4 3 σ 0 = – --- ⋅ ----------------------------------------π ( 1 – µ2 ) ⋅ K ⋅ D2 1 a

Point 0:

(14)

Point 1:

4E ⋅ K 4 ⋅ s ⋅ K 4 ⋅ K 2 ⋅ ⎛ h – --s-⎞ + K 3 ⋅ t ⎝ 2⎠ σ 1 = – --------------------------------------------------------------------------------------------2 2 ( 1 – µ ) ⋅ K1 ⋅ Da

(15)

Point 2:

s 4E ⋅ K 4 ⋅ s ⋅ K 3 ⋅ t – K 2 ⋅ K 4 ⋅ ⎛ h – ---⎞ ⎝ 2⎠ σ 2 = --------------------------------------------------------------------------------------------2 2 ( 1 – µ ) ⋅ K1 ⋅ Da

(16)

Point 3:

4E ⋅ K 4 ⋅ s ⋅ K 4 ⋅ ( 2K 3 – K 2 ) ⋅ ⎛ h – --s-⎞ + K 3 ⋅ t ⎝ 2⎠ σ 3 = -----------------------------------------------------------------------------------------------------------------2 2 ( 1 – µ ) ⋅ K1 ⋅ Da ⋅ δ

(17)

K2 and K3 are disc spring dimensional constants, defined as follows: δ–1 6 ⎛⎝ ----------- – 1⎞⎠ ln δ K 2 = -----------------------------π ⋅ ln δ

(18)

⋅ ( δ – 1 )K 3 = 3----------------------π ⋅ ln δ

(19)

where δ = D ⁄d is the outside-to-inside diameter ratio. In static application, if disc springs are fully flattened (100% deflection), compressive stress at point 0 should not exceed the tensile strength of disc spring materials. For most spring steels, the permissible value is σ0 ≤ 1600 N⁄mm2 or 232,000 psi. In dynamic applications, certain limitations on tensile stress values are recommended to obtain controlled fatigue life of disc springs utilized in various stacking. Maximum tensile stresses at points 2 and 3 depend on the Group number of the disc springs. Stresses σ2 and σ3 should not exceed the following values: Maximum allowable tensile stresses at points 2 and 3

Group 1

Group 2

Group 3

1300 N ⁄ mm2 (188,000 psi)

1250 N ⁄ mm2 (181,000 psi)

1200 N ⁄ mm2 (174,000 psi)

Fatigue Life of Disc Springs.—Fatigue life is measured in terms of the maximum number of cycles that dynamically loaded disc springs can sustain prior to failure. Dynamically loaded disc springs are divided into two groups: disc springs with unlimited fatigue life, which exceeds 2 × 106 cycles without failure, and disc springs with limited fatigue life between 104 cycles and less then 2 × 106 cycles. Typically, fatigue life is estimated from three diagrams, each representing one of the three Groups of disc springs (Figs. 10, 11, and 12). Fatigue life is found at the intersection of the vertical line representing minimum tensile stress σmin with the horizontal line, which represents maximum tensile stress σmax. The point of intersection of these two lines defines fatigue life expressed in number of cycles N that can be sustained prior to failure. Example: For Group 2 springs in Fig. 11, the intersection point of the σmin = 500 N⁄mm2 line with the σmax = 1200 N⁄mm2 line, is located on the N = 105 cycles line. The estimated fatigue life is 105 cycles.


Machinery's Handbook 27th Edition DISC SPRING FATIGUE LIFE

363


1400

A

B

C

Maximun Tensile Stress (N /mm2)

1200

1000

800

600

Number of Loading Cycles 400

A B C

200

100,000 500,000 2,000,000

0 0

200

400

600

800

1000

1200

1400

Minimum Tensile Stress (N / mm2)

Fig. 10. Group 1 Diagram for Estimating Fatigue Life of Disc Springs (0.2 ≤ t < 1.25 mm) LIVE GRAPH Click here to view

1400

A

B

C


1200

1000

800

600


A B C

200

100,000 500,000 2,000,000

0 0

200

400

600

800

1000

1200

1400


Fig. 11. Group 2 Diagram for Estimating Fatigue Life of Disc Springs (1.25 ≤ t ≤ 6 mm) LIVE GRAPH Click here to view

1400

A


1200

B

C

1000

800

600


A B C

200

100,000 500,000 2,000,000

0 0

200

400

600

800

1000

1200

1400


Fig. 12. Group 3 Diagram for Estimating Fatigue Life of Disc Springs (6 < t ≤ 16 mm)



DISC SPRING FATIGUE LIFE

When the intersection points of the minimum and maximum stress lines fall inside the areas of each cycle line, only the approximate fatigue life can be estimated by extrapolating the distance from the point of intersection to the nearest cycle line. The extrapolation cannot provide accurate values of fatigue life, because the distance between the cycle lines is expressed in logarithmic scale, and the distance between tensile strength values is expressed in linear scale (Figs. 10, 11, and 12), therefore linear-to-logarithmic scales ratio is not applicable. When intersection points of minimum and maximum stress lines fall outside the cycle lines area, especially outside the N = 105 cycles line, the fatigue life cannot be estimated. Thus, the use of the fatigue life diagrams should be limited to such cases when the minimum and maximum tensile stress lines intersect exactly with each of the cycle lines. To calculate fatigue life of disc springs without the diagrams, the following equations developed by the author can be used. Disc Springs in Group 1 Disc Springs in Group 2 Disc Springs in Group 3

N = 10

10.29085532 – 0.00542096 ( σ max – 0.5σ min )

(20)

N = 10

10.10734911 – 0.00537616 ( σ max – 0.5σ min )

(21)

N = 10

13.23985664 – 0.01084192 ( σ max – 0.5σ min )

(22)

As can be seen from Equations (20), (21), and (22), the maximum and minimum tensile stress range affects the fatigue life of disc springs. Since tensile stresses at Points 2 and 3 have different values, see Equations (16) and (17), it is necessary to determine at which critical point the minimum and maximum stresses should be used for calculating fatigue life. The general method is based on the diagram, Fig. 9, from which Point 2 or Point 3 can be found in relationship with disc spring outside-to-inside diameters ratio D⁄d and disc spring cone height-to-thickness ratio h/r. This method requires intermediate calculations of D⁄d and h/t ratios and is applicable only to disc springs without contact surfaces. The method is not valid for Group 3 disc springs or for disc springs in Group 2 that have contact surfaces and reduced thickness. A simple and accurate method, that is valid for all disc springs, is based on the following statements: if (σ2 max – 0.5 σ2 min) > (σ3 max – 0.5 σ3 min), then Point 2 is used, otherwise if (σ3 max – 0.5 σ3 min) > (σ2 max – 0.5 σ2 min), then Point 3 is used The maximum and minimum tensile stress range for disc springs in Groups 1, 2, and 3 is found from the following equations. For disc springs in Group 1: 10.29085532 – log N σ max – 0.5σ min = ------------------------------------------------0.00542096 For disc springs in Group 2: – log N σ max – 0.5σ min = 10.10734911 ------------------------------------------------0.00537616 For disc springs in Group 3:

(23)

(24)

– log N σ max – 0.5σ min = 13.23985664 ------------------------------------------------(25) 0.01084192 Thus, Equations (23), (24), and (25) can be used to design any spring stack that provides required fatigue life. The following example illustrates how a maximum-minimum stress range is calculated in relationship with fatigue life of a given disc spring stack.


Machinery's Handbook 27th Edition DISC SPRING RECOMMENDED DIMENSION RATIOS

365

Example:A dynamically loaded stack, which utilizes disc springs in Group 2, must have the fatigue life of 5 × 105 cycles. The maximum allowable tensile stress at Points 2 or 3 is 1250 N⁄mm2. Find the minimum tensile stress value to sustain N = 5 × 105 cycles. Solution: Substitution of σmax = 1250 and N = 5 × 105 in Equation (24) gives: 5

10.10734911 – log ( 5 × 10 ) – 5.69897- = 820 1250 – 0.5σ min = -------------------------------------------------------------------- = 10.10734911 -------------------------------------------------------0.00537616 0.00537616 1250 – 820 from which σ min = --------------------------- = 860 N/mm 2 (124,700 psi) 0.5 Recommended Dimensional Characteristics of Disc Springs.—Dimensions of disc springs play a very important role in their performance. It is imperative to check selected disc springs for dimensional ratios, that should fall within the following ranges: 1) Diameters ratio, δ = D⁄d = 1.7 to 2.5. 2) Cone height-to-thickness ratio, h⁄t = 0.4 to 1.3. 3) Outside diameter-to-thickness ratio, D⁄t = 18 to 40. Small values of δ correspond with small values of the other two ratios. The h⁄t ratio determines the shape of force-deflection characteristic graphs, that may be nearly linear or strongly curved. If h⁄t = 0.4 the graph is almost linear during deflection of a disc spring up to its flat position. If h⁄t = 1.6 the graph is strongly curved and its maximum point is at 75% deflection. Disc spring deflection from 75% to 100% slightly reduces spring force. Within the h⁄t = 0.4 – 1.3 range, disc spring forces increase with the increase in deflection and reach maximum values at 100% deflection. In a stack of disc springs with a ratio h⁄t > 1.3 deflection of individual springs may be unequal, and only one disc spring should be used if possible. Example Applications of Disc Springs Example 1, Disc Springs in Group 2 (no contact surfaces): A mechanical device that works under dynamic loads must sustain a minimum of 1,000,000 cycles. The applied load varies from its minimum to maximum value every 30 seconds. The maximum load is approximately 20,000N (4,500 lbf). A 40-mm diameter guide rod is a receptacle for the disc springs. The rod is located inside a hollow cylinder. Deflection of the disc springs under minimum load should not exceed 5.5 mm (0.217 inch) including a 20 per cent preload deflection. Under maximum load, the deflection is limited to 8 mm (0.315 inch) maximum. Available space for the disc spring stack inside the cylinder is 35 to 40 mm (1.38 to 1.57 inch) in length and 80 to 85 mm (3.15 to 3.54 inch) in diameter. Select the disc spring catalog item, determine the number of springs in the stack, the spring forces, the stresses at minimum and maximum deflection, and actual disc spring fatigue life. Solution: 1) Disc spring standard inside diameter is 41 mm (1.61 inch) to fit the guide rod. The outside standard diameter is 80 mm (3.15 in) to fit the cylinder inside diameter. Disc springs with such diameters are available in various thickness: 2.25, 3.0, 4.0, and 5.0 mm (0.089, 0.118, 0.157, and 0.197 inch). The 2.25- and 3.0-mm thick springs do not fit the applied loads, since the maximum force values for disc springs with such thickness are 7,200N and 13,400N (1,600 lbf and 3,000 lbf) respectively. A 5.0-mm thick disc spring should not be used because its D⁄t ratio, 80⁄5 = 16, is less than 18 and is considered as unfavorable. Disc spring selection is narrowed to an 80–41–4 catalog item. 2) Checking 80 – 41 – 4 disc spring for dimensional ratios: h⁄ = 2.2⁄ = 0.55 D⁄ = 80⁄ = 20 δ = D⁄d = 80⁄41 = 1.95 t 4 t 4 Because the dimensional ratios are favorable, the 80–41–4 disc springs are selected.



DISC SPRING EXAMPLE

3) The number of springs in the stack is found from Equation (1): n = Lo ⁄ (t + h) = 40 ⁄ (4 + 2.2) = 40⁄6.2 = 6.45. Rounding n to the nearest integer gives n = 6. The actual length of unloaded spring stack is Lo = 6.2 × 6 = 37.2 mm (1.465 inch) and it satisfies the Lo< 40 mm condition. 4) Calculating the cone angle α from Equation (7) and actual outside diameter Da from Equation (9) gives: 2 × 2.2-⎞ = atan ( 0.11282 ) = 6.4° α = atan ⎛ ----------------⎝ 80 – 41⎠ D a = 80 – 2 × 4 ⎛ sin [ atan ( 0.11282 ) ] + 1--- cos [ atan ( 0.11282 ) ]⎞ ⎝ ⎠ 6 D a = 77.78 mm (3.062 in) 5) Calculating constant K1 from Equation (11): D- = 1.95122 δ = --d 2

– 1-⎞ ⎛ 1.95122 --------------------------⎝ 1.95122 ⎠ K 1 = ------------------------------------------------------------------------------ = 0.6841 + 1 – ----------------------------2 π ⋅ 1.95122 ---------------------------1.95122 – 1 ln ( 1.95122 ) 6) Calculating minimum and maximum forces, Fmin and Fmax from Equation (10): Based on the design requirements, the disc spring stack is deflecting by 5.5 mm (0.217 in) under minimum load, and each individual disc spring is deflecting by 5.5 ⁄ 6 ≅ 0.92 mm (0.036 in). A single disc spring deflection smin = 0.9 mm (0.035 in) is used to calculate Fmin. Under maximum load, the disc spring stack is permitted maximum deflection of 8 mm (0.315 in), and each individual disc spring deflects by 8 ⁄ 6 ≅ 1.33 mm (0.0524 in). A disc spring deflection smax = 1.32 mm (0.052 in) will be used to calculate Fmax. If disc springs are made of AISI 6150 alloy steel, then modulus of elasticity E = 206,000 N⁄mm2 (30 × 106 psi) and Poisson’s ratio µ = 0.3. 4 ⋅ 206000 F min = ------------------------------------------------------------------- ⎛ 2.2 – 0.9 -------⎞ ⋅ ( 2.2 – 0.9 ) ⋅ 4 + 4 3 0.9 2⎠ ( 1 – 0.3 2 ) ( 0.6841 ) ( 77.78 ) 2 ⎝ F min = 14390N (3235 lbf) 1.32 4 ⋅ 206000 - ⎛ 2.2 – ----------⎞ ⋅ ( 2.2 – 1.32 ) ⋅ 4 + 4 3 1.32 F max = -----------------------------------------------------------------2 ⎠ ( 1 – 0.3 2 ) ( 0.6841 ) ( 77.78 ) 2 ⎝ F max = 20050N (4510 lbf) 7) Calculating constant K2, Equation (18): D 80 δ = ---- = ------ = 1.95122 d 41 – 1 – 1⎞ 1.95122 – 1- – 1⎞ 6 ⎛ δ----------6 ⎛ ----------------------------⎝ ln δ ⎠ ⎝ ln ( 1.95122 ) ⎠ K 2 = ------------------------------ = ------------------------------------------------ = 1.2086 π ⋅ ln δ π ⋅ ln ( 1.95122 ) 8) Calculating constant K3 (Equation (19)): 3 ⋅ (δ – 1) 3 ⋅ ( 1.95122 – 1 ) K 3 = ------------------------ = ---------------------------------------- = 1.3589 π ⋅ ln δ π ⋅ ln ( 1.95122 )


Machinery's Handbook 27th Edition DISC SPRING EXAMPLE

367

9) Compressive stress σ0 at point 0 due to maximum deflection, Equation (14): 4E ⋅ t ⋅ s ⋅ K 4 4 ⋅ 206000 ⋅ 4 ⋅ 1.32 ⋅ 1 σ 0 = – --3- ⋅ ----------------------------------------- = – --3- ⋅ ---------------------------------------------------------------π ( 1 – µ2 ) ⋅ K ⋅ D2 π ( 1 – 0.3 2 ) ⋅ 0.6841 ⋅ 77.78 2 1 a σ 0 = 1103N/mm2 = 160000psi Because the compressive stress at point 0 does not exceed 1600 N⁄mm2, its current value satisfies the design requirement. 10) Tensile stress σ2 at point 2 due to minimum deflection s = 0.9 mm, Equation (16): σ 2min

s 4E ⋅ K 4 ⋅ s ⋅ K 3 ⋅ t – K 2 ⋅ K 4 ⋅ ⎛ h – ---⎞ ⎝ 2⎠ = --------------------------------------------------------------------------------------------- = 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da

4 ⋅ 206000 ⋅ 1 ⋅ 0.9 ⋅ 1.3589 ⋅ 4 – 1.2086 ⋅ 1 ⋅ ⎛ 2.2 – 0.9 -------⎞ ⎝ 2⎠ -------------------------------------------------------------------------------------------------------------------------------------------- = 654 N/mm2 2 2 ( 1 – 0.3 ) ⋅ 0.6841 ⋅ 77.78 11) Tensile stress σ2 at point 2 due to maximum deflection s = 1.32 mm, Equation (16): σ 2max

4E ⋅ K 4 ⋅ s ⋅ K 3 ⋅ t – K 2 ⋅ K 4 ⋅ ⎛ h – --s-⎞ ⎝ 2⎠ = --------------------------------------------------------------------------------------------- = 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da

1.32 4 ⋅ 206000 ⋅ 1 ⋅ 1.32 ⋅ 1.3589 ⋅ 4 – 1.2086 ⋅ 1 ⋅ ⎛⎝ 2.2 – ----------⎞⎠ 2 -------------------------------------------------------------------------------------------------------------------------------------------------- = 1032 N/mm2 2 2 ( 1 – 0.3 ) ⋅ 0.6841 ⋅ 77.78 Thus, σ2 min = 654 N⁄mm2 (94,850 psi) and σ2 max = 1032 N⁄mm2 (149,700 psi). 12) Tensile stress σ3 at point 3 due to minimum deflection s = 0.9 mm, Equation (17): 4E ⋅ K 4 ⋅ s ⋅ K 4 ⋅ ( 2K 3 – K 2 ) ⋅ ⎛ h – --s-⎞ + K 3 ⋅ t ⎝ 2⎠ σ 3min = ------------------------------------------------------------------------------------------------------------------ = 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da ⋅ δ 4 ⋅ 206000 ⋅ 1 ⋅ 0.9 ⋅ 1 ⋅ ( 2 ⋅ 1.3589 – 1.2086 ) ⋅ ⎛ 2.2 – 0.9 -------⎞ + 1.3589 ⋅ 4 ⎝ 2⎠ 2 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- = 815N/mm 2 2 ( 1 – 0.3 ) ⋅ 0.6841 ⋅ 77.78 ⋅ 1.95122

13) Tensile stress σ3 at point 3 due to maximum deflection s = 1.32 mm, Equation (17): 4E ⋅ K 4 ⋅ s ⋅ K 4 ⋅ ( 2K 3 – K 2 ) ⋅ ⎛ h – --s-⎞ + K 3 ⋅ t ⎝ 2⎠ σ 3max = ------------------------------------------------------------------------------------------------------------------ = 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da ⋅ δ 1.32-⎞ + 1.3589 ⋅ 4 4 ⋅ 206000 ⋅ 1 ⋅ 1.32 ⋅ 1 ⋅ ( 2 ⋅ 1.3589 – 1.2086 ) ⋅ ⎛⎝ 2.2 – --------2 ⎠ 2 ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- = 1149 N/mm 2 2 ( 1 – 0.3 ) ⋅ 0.6841 ⋅ 77.78 ⋅ 1.95122

Thus, σ3 min = 815 N⁄mm2 (118,200 psi) and σ3 max = 1149 N⁄mm2 (166,600 psi). 14) Functional tensile stress range at critical points 2 and 3. Point 2: σ2 max – 0.5σ2 min = 1032 – 0.5 × 654 = 705 N⁄mm2 Point 3: σ3 max – 0.5σ3 min = 1149 – 0.5 × 815 = 741.5 N⁄mm2 Because σ3 max – 0.5σ3 min > σ2 max – 0.5 σ2 min, the tensile stresses at point 3 are used for fatigue life calculations.



DISC SPRING EXAMPLE

15) Fatigue life of selected disc springs, Equation (21): N = 10[10.10734911 – 0.00537616 (1149 – 0.5 × 815)] = 1010.10734911 – 3.98642264 = 10 6.12092647 N = 1,321,000 cycles. Thus, the calculated actual fatigue life exceeds required minimum number of cycles by 32%. In conclusion, the six 80–41–4 disc springs arranged in series stacking, satisfy the requirements and will provide a 32 % longer fatigue life than required by the design criteria. Example 2:A company wishes to use Group 3 disc springs with contact surfaces on couplings to absorb bumping impacts between railway cars. Given: D =200 mm, disc spring outside diameter d =102 mm, disc spring inside diameter t =14 mm, spring standard thickness t′ =13.1 mm, spring reduced thickness h =4.2 mm, cone height of unloaded spring n =22, number of springs in series stacking Si =33.9 mm, initial deflection of the pack Sa =36.0 mm, additional deflection of the pack Find the fatigue life in cycles and determine if the selected springs are suitable for the application. The calculations are performed in the following sequence: 1) Determine the minimum smin and maximum smax deflections of a single disc spring: ( Si + Sa ) 33.9 + 36 )- = 3.18mm s max = -------------------- = (-------------------------n 22 Si 33.9- = 1.54mm s min = ---- = --------n 22 2) Use Equations (16) and (17) to calculate tensile stresses σ2 and σ3 at smin and smax deflections: σ2min= 674 N⁄mm2, σ2max= 1513 N⁄mm2, σ3min= 707 N⁄mm2, σ3max= 1379 N⁄mm2 3) Determine critical stress points: σ2max − 0.5σ2min = 1513 − 0.5 × 674 = 1176 N⁄mm2 σ3max − 0.5σ3min = 1379 − 0.5 × 707 = 1025.5 N⁄mm2 Because (σ2max − 0.5σ2min) > (σ3max − 0.5σ3min), then tensile stresses at Point 2 are used to calculate fatigue life. 4) Fatigue life N is calculated using Equation (22): N = 10 [13.23985664 − (0.01084192 × 1176)] = 10 0.49 = 3 cycles The selected disc springs at the above-mentioned minimum and maximum deflection values will not sustain any number of cycles. It is imperative to check the selected disc springs for dimensional ratios: Outside-to-inside diameters ratio, 200⁄102 = 1.96; within recommended range. Cone height-to-thickness ratio is 4.2⁄13.1 = 0.3; out of range, the minimum ratio is 0.4. Outside diameter-to-thickness ratio is 200 ⁄13.1 = 15; out of range, the minimum ratio is 18. Thus, only one of the dimensional ratios satisfies the requirements for the best disc spring performance.


Machinery's Handbook 27th Edition WIRE ROPE

369

WIRE ROPE, CHAIN, ROPE, AND HOOKS Strength and Properties of Wire Rope Wire Rope Construction.—Essentially, a wire rope is made up of a number of strands laid helically about a metallic or non-metallic core. Each strand consists of a number of wires also laid helically about a metallic or non-metallic center. Various types of wire rope have been developed to meet a wide range of uses and operating conditions. These types are distinguished by the kind of core; the number of strands; the number, sizes, and arrangement of the wires in each strand; and the way in which the wires and strands are wound or laid about each other. The following descriptive material is based largely on information supplied by the Bethlehem Steel Co. Rope Wire Materials: Materials used in the manufacture of rope wire are, in order of increasing strength: iron, phosphor bronze, traction steel, plow steel, improved plow steel, and bridge rope steel. Iron wire rope is largely used for low-strength applications such as elevator ropes not used for hoisting, and for stationary guy ropes. Phosphor bronze wire rope is used occasionally for elevator governor-cable rope and for certain marine applications as life lines, clearing lines, wheel ropes and rigging. Traction steel wire rope is used primarily as hoist rope for passenger and freight elevators of the traction drive type, an application for which it was specifically designed. Ropes made of galvanized wire or wire coated with zinc by the electro-deposition process are used in certain applications where additional protection against rusting is required. As will be noted from the tables of wire-rope sizes and strengths, the breaking strength of galvanized wire rope is 10 per cent less than that of ungalvanized (bright) wire rope. Bethanized (zinc-coated) wire rope can be furnished to bright wire rope strength when so specified. Galvanized carbon steel, tinned carbon steel, and stainless steel are used for small cords and strands ranging in diameter from 1⁄64 to 3⁄8 inch and larger. Marline clad wire rope has each strand wrapped with a layer of tarred marline. The cladding provides hand protection for workers and wear protection for the rope. Rope Cores: Wire-rope cores are made of fiber, cotton, asbestos, polyvinyl plastic, a small wire rope (independent wire-rope core), a multiple-wire strand (wire-strand core) or a cold-drawn wire-wound spring. Fiber (manila or sisal) is the type of core most widely used when loads are not too great. It supports the strands in their relative positions and acts as a cushion to prevent nicking of the wires lying next to the core. Cotton is used for small ropes such as sash cord and aircraft cord. Asbestos cores can be furnished for certain special operations where the rope is used in oven operations. Polyvinyl plastics cores are offered for use where exposure to moisture, acids, or caustics is excessive. A wire-strand core often referred to as WSC, consists of a multiple-wire strand that may be the same as one of the strands of the rope. It is smoother and more solid than the independent wire rope core and provides a better support for the rope strands. The independent wire rope core, often referred to as IWRC, is a small 6 × 7 wire rope with a wire-strand core and is used to provide greater resistance to crushing and distortion of the wire rope. For certain applications it has the advantage over a wire-strand core in that it stretches at a rate closer to that of the rope itself. Wire ropes with wire-strand cores are, in general, less flexible than wire ropes with independent wire-rope or non-metallic cores.



WIRE ROPE

Ropes with metallic cores are rated 71⁄2 per cent stronger than those with non-metallic cores. Wire-Rope Lay: The lay of a wire rope is the direction of the helical path in which the strands are laid and, similarly, the lay of a strand is the direction of the helical path in which the wires are laid. If the wires in the strand or the strands in the rope form a helix similar to the threads of a right-hand screw, i.e., they wind around to the right, the lay is called right hand and, conversely, if they wind around to the left, the lay is called left hand. In the regular lay, the wires in the strands are laid in the opposite direction to the lay of the strands in the rope. In right-regular lay, the strands are laid to the right and the wires to the left. In leftregular lay, the strands are laid to the left, the wires to the right. In Lang lay, the wires and strands are laid in the same direction, i.e., in right Lang lay, both the wires and strands are laid to the right and in left Lang they are laid to the left. Alternate lay ropes having alternate right and left laid strands are used to resist distortion and prevent clamp slippage, but because other advantages are missing, have limited use. The regular lay wire rope is most widely used and right regular lay rope is customarily furnished. Regular lay rope has less tendency to spin or untwist when placed under load and is generally selected where long ropes are employed and the loads handled are frequently removed. Lang lay ropes have greater flexibility than regular lay ropes and are more resistant to abrasion and fatigue. In preformed wire ropes the wires and strands are preshaped into a helical form so that when laid to form the rope they tend to remain in place. In a non-preformed rope, broken wires tend to “wicker out” or protrude from the rope and strands that are not seized tend to spring apart. Preforming also tends to remove locked-in stresses, lengthen service life, and make the rope easier to handle and to spool. Strand Construction: Various arrangements of wire are used in the construction of wire rope strands. In the simplest arrangement six wires are grouped around a central wire thus making seven wires, all of the same size. Other types of construction known as “fillerwire,” Warrington, Seale, etc. make use of wires of different sizes. Their respective patterns of arrangement are shown diagrammatically in the table of wire weights and strengths. Specifying Wire Rope.—In specifying wire rope the following information will be required: length, diameter, number of strands, number of wires in each strand, type of rope construction, grade of steel used in rope, whether preformed or not preformed, type of center, and type of lay. The manufacturer should be consulted in selecting the best type of wire rope for a new application. Properties of Wire Rope.—Important properties of wire rope are strength, wear resistance, flexibility, and resistance to crushing and distortion. Strength: The strength of wire rope depends upon its size, kind of material of which the wires are made and their number, the type of core, and whether the wire is galvanized or not. Strengths of various types and sizes of wire ropes are given in the accompanying tables together with appropriate factors to apply for ropes with steel cores and for galvanized wire ropes. Wear Resistance: When wire rope must pass back and forth over surfaces that subject it to unusual wear or abrasion, it must be specially constructed to give satisfactory service. Such construction may make use of 1) relatively large outer wires; 2) Lang lay in which wires in each strand are laid in the same direction as the strand; and 3) flattened strands. The object in each type is to provide a greater outside surface area to take the wear or abrasion. From the standpoint of material, improved plow steel has not only the highest tensile strength but also the greatest resistance to abrasion in regularly stocked wire rope.



371

Flexibility: Wire rope that undergoes repeated and severe bending, such as in passing around small sheaves and drums, must have a high degree of flexibility to prevent premature breakage and failure due to fatigue. Greater flexibility in wire rope is obtained by 1) using small wires in larger numbers; 2) using Lang lay; and 3) preforming, that is, the wires and strands of the rope are shaped during manufacture to fit the position they will assume in the finished rope. Resistance to Crushing and Distortion: Where wire rope is to be subjected to transverse loads that may crush or distort it, care should be taken to select a type of construction that will stand up under such treatment. Wire rope designed for such conditions may have 1) large outer wires to spread the load per wire over a greater area; and 2) an independent wire core or a high-carbon cold-drawn wound spring core. Standard Classes of Wire Rope.—Wire rope is commonly designated by two figures, the first indicating the number of strands and the second, the number of wires per strand, as: 6 × 7, a six-strand rope having seven wires per strand, or 8 × 19, an eight-strand rope having 19 wires per strand. When such numbers are used as designations of standard wire rope classes, the second figure in the designation may be purely nominal in that the number of wires per strand for various ropes in the class may be slightly less or slightly more than the nominal as will be seen from the following brief descriptions. (For ropes with a wire strand core, a second group of two numbers may be used to indicate the construction of the wire core, as 1 × 21, 1 × 43, and so on.) 6 × 7 Class (Standard Coarse Laid Rope): Wire ropes in this class are for use where resistance to wear, as in dragging over the ground or across rollers, is an important requirement. Heavy hauling, rope transmissions, and well drilling are common applications. These wire ropes are furnished in right regular lay and occasionally in Lang lay. The cores may be of fiber, independent wire rope, or wire strand. Since this class is a relatively stiff type of construction, these ropes should be used with large sheaves and drums. Because of the small number of wires, a larger factor of safety may be called for.

Fig. 1a. 6 × 7 with fiber core

Fig. 1b. 6 × 7 with 1 × 7 WSC

Fig. 1c. 6 × 7 with 1 × 19 WSC

Fig. 1d. 6 × 7 with IWRC

As shown in Figs. 1a through Figs. 1d, this class includes a 6 × 7 construction with fiber core: a 6 × 7 construction with 1 × 7 wire strand core (sometimes called 7 × 7); a 6 × 7 construction with 1 × 19 wire strand core; and a 6 × 7 construction with independent wire rope core. Table 1 provides strength and weight data for this class. Two special types of wire rope in this class are: aircraft cord, a 6 × 6 or 7 × 7 Bethanized wire rope of high tensile strength and sash cord, a 6 × 7 iron rope used for a variety of purposes where strength is not an important factor.



WIRE ROPE Table 1. Weights and Strengths of 6 × 7 (Standard Coarse Laid) Wire Ropes, Preformed and Not Preformed

Dia., Inches 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8

Approx. Weight per Ft., Pounds

Breaking Strength, Tons of 2000 Lbs. Impr. Mild Plow Plow Plow Steel Steel Steel

Dia., Inches


3⁄ 4 7⁄ 8

0.84 1.15


0.094 0.15

2.64 4.10

2.30 3.56

2.00 3.10

22.7 30.7

19.8 26.7

17.2 23.2

0.21

5.86

5.10

4.43

1

1.50

39.7

34.5

30.0

0.29

7.93

6.90

6.00

11⁄8

1.90

49.8

43.3

37.7

0.38

10.3

8.96

7.79

11⁄4

2.34

61.0

53.0

46.1

0.48

13.0

11.3

9.82

13⁄8

2.84

73.1

63.6

55.3

0.59

15.9

13.9

12.0

11⁄2

3.38

86.2

75.0

65.2

For ropes with steel cores, add 71⁄2 per cent to above strengths. For galvanized ropes, deduct 10 per cent from above strengths. Source: Rope diagrams, Bethlehem Steel Co. All data, U.S. Simplified Practice Recommendation 198–50.

6 × 19 Class (Standard Hoisting Rope): This rope is the most popular and widely used class. Ropes in this class are furnished in regular or Lang lay and may be obtained preformed or not preformed. Cores may be of fiber, independent wire rope, or wire strand. As can be seen from Table 2 and Figs. 2a through 2h, there are four common types: 6 × 25 filler wire construction with fiber core (not illustrated), independent wire core, or wire strand core (1 × 25 or 1 × 43); 6 × 19 Warrington construction with fiber core; 6 × 21 filler wire construction with fiber core; and 6 × 19, 6 × 21, and 6 × 17 Seale construction with fiber core. Table 2. Weights and Strengths of 6 × 19 (Standard Hoisting) Wire Ropes, Preformed and Not Preformed Breaking Strength, Tons of 2000 Lbs. Impr. Mild Plow Plow Plow Steel Steel Steel


Dia., Inches


1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

0.10 0.16

2.74

2.39

2.07

11⁄4

2.50

64.6

56.2

48.8

4.26

3.71

3.22

13⁄8

3.03

77.7

67.5

58.8

0.23

6.10

5.31

4.62

11⁄2

3.60

92.0

80.0

69.6

15⁄8 13⁄4 17⁄8

4.23

107

4.90

124

108

5.63

141

6.40

160

123 139

107 121 …

1 11⁄8

Dia., Inches


0.31

8.27

7.19

6.25

0.40

10.7

9.35

8.13

93.4

81.2 93.6

0.51

13.5

11.8

10.2

0.63

16.7

14.5

12.6

0.90

23.8

20.7

18.0

2 21⁄8

7.23

179

156

1.23

32.2

28.0

24.3

21⁄4

8.10

200

174

…

1.60

41.8

36.4

31.6

21⁄2

10.00

244

212

…

2.03

52.6

45.7

39.8

23⁄4

12.10

292

254

…

The 6 × 25 filler wire with fiber core not illustrated. For ropes with steel cores, add 71⁄2 per cent to above strengths. For galvanized ropes, deduct 10 per cent from above strengths. Source: Rope diagrams, Bethlehem Steel Co. All data, U.S. Simplified Practice Recommendation 198–50.

6 × 37 Class (Extra Flexible Hoisting Rope): For a given size of rope, the component wires are of smaller diameter than those in the two classes previously described and hence have less resistance to abrasion. Ropes in this class are furnished in regular and Lang lay with fiber core or independent wire rope core, preformed or not preformed.



373

Fig. 2a. 6 × 25 filler wire with WSC (1 × 25)

Fig. 2b. 6 × 25 filler wire with IWRC

Fig. 2c. 6 × 19 Seale with fiber core

Fig. 2d. 6 × 21 Seale with fiber core

Fig. 2e. 6 × 25 filler wire with WSC (1 × 43)

Fig. 2f. 6 × 19 Warrington with fiber core

Fig. 2g. 6 × 17 Seale with fiber core

Fig. 2h. 6 × 21 filler wire with fiber core

Table 3. Weights and Strengths of 6 × 37 (Extra Flexible Hoisting) Wire Ropes, Preformed and Not Preformed

Dia., Inches


1⁄ 4 5⁄ 16

Breaking Strength, Tons of 2000 Lbs.

Breaking Strength, Tons of 2000 Lbs.

Impr. Plow Steel

Plow Steel

Dia., Inches


0.10

2.59

2.25

11⁄2

3.49

0.16

4.03

3.50

15⁄8

4.09

103

3⁄ 8

0.22

5.77

5.02

13⁄4

4.75

119

103

7⁄ 16

0.30

7.82

6.80

17⁄8

5.45

136

118

1⁄ 2

0.39

10.2

8.85

2

6.20

154

134

9⁄ 16

0.49

12.9

11.2

21⁄8

7.00

173

150

5⁄ 8

0.61

15.8

13.7

21⁄4

7.85

193

168

3⁄ 4

0.87

22.6

19.6

21⁄2

9.69

236

205

7⁄ 8

1.19

30.6

26.6

23⁄4

11.72

284

247

1 11⁄8

1.55 1.96

39.8 50.1

34.6 43.5

3 31⁄4

14.0 16.4

335 390

291 339

11⁄4

2.42

61.5

53.5

31⁄2

19.0

449

390

13⁄8

2.93

74.1

64.5

…

…

…

…

Impr. Plow Steel 87.9

Plow Steel 76.4 89.3

For ropes with steel cores, add 71⁄2 per cent to above strengths. For galvanized ropes, deduct 10 per cent from above strengths. Source: Rope diagrams, Bethlehem Steel Co. All data, U. S. Simplified Practice Recommendation 198-50.

As shown in Table 3 and Figs. 3a through 3h, there are four common types: 6 × 29 filler wire construction with fiber core and 6 × 36 filler wire construction with independent wire rope core, a special rope for construction equipment; 6 × 35 (two operations) construction with fiber core and 6 × 41 Warrington Seale construction with fiber core, a standard crane rope in this class of rope construction; 6 × 41 filler wire construction with fiber core or independent wire core, a special large shovel rope usually furnished in Lang lay; and 6 × 46



WIRE ROPE

Fig. 3a. 6 × 29 filler wire with fiber core

Fig. 3b. 6 × 36 filler wire with IWRC

Fig. 3c. 6 × 35 with fiber core

Fig. 3d. 6 × 41 Warrington-Seale with fiber core

Fig. 3e. 6 × 41 filler wire with fiber core

Fig. 3f. 6 × 41 filler wire with IWRC

Fig. 3g. 6 × 46 filler wire with fiber core

Fig. 3h. 6 × 46 filler wire with IWRC

filler wire construction with fiber core or independent wire rope core, a special large shovel and dredge rope. 8 × 19 Class (Special Flexible Hoisting Rope): This rope is stable and smooth-running, and is especially suitable, because of its flexibility, for high speed operation with reverse bends. Ropes in this class are available in regular lay with fiber core. As shown in Table 4 and Figs. 4a through 4d, there are four common types: 8 × 25 filler wire construction, the most flexible but the least wear resistant rope of the four types; Warrington type in 8 × 19 construction, less flexible than the 8 × 25; 8 × 21 filler wire construction, less flexible than the Warrington; and Seale type in 8 × 19 construction, which has the greatest wear resistance of the four types but is also the least flexible. Table 4. Weights and Strengths of 8 × 19 (Special Flexible Hoisting) Wire Ropes, Preformed and Not Preformed

Dia., Inches


1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8

0.09 0.14 0.20 0.28 0.36 0.46 0.57

Breaking Strength, Tons of 2000 Lbs. Impr. Plow Plow Steel Steel 2.35 3.65 5.24 7.09 9.23 11.6 14.3

2.04 3.18 4.55 6.17 8.02 10.1 12.4

Dia., Inches


3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

0.82 1.11 1.45 1.84 2.27 2.74 3.26

Breaking Strength, Tons of 2000 Lbs. Impr. Plow Plow Steel Steel 20.5 27.7 36.0 45.3 55.7 67.1 79.4

17.8 24.1 31.3 39.4 48.4 58.3 69.1

For ropes with steel cores, add 71⁄2 per cent to above strengths. For galvanized ropes, deduct 10 per cent from above strengths. Source: Rope diagrams, Bethlehem Steel Co. All data, U. S. Simplified Practice Recommendation 198-50.



Fig. 4a. 8 × 25 filler wire with fiber core

Fig. 4b. 8 × 19 Warrington with fiber core

375

Fig. 4c. 8 × 21 filler wire with fiber core

Fig. 4d. 8 × 19 Seale with fiber core

Also in this class, but not shown in Table 4 are elevator ropes made of traction steel and iron. 18 × 7 Non-rotating Wire Rope: This rope is specially designed for use where a minimum of rotating or spinning is called for, especially in the lifting or lowering of free loads with a single-part line. It has an inner layer composed of 6 strands of 7 wires each laid in left Lang lay over a fiber core and an outer layer of 12 strands of 7 wires each laid in right regular lay. The combination of opposing lays tends to prevent rotation when the rope is stretched. However, to avoid any tendency to rotate or spin, loads should be kept to at least one-eighth and preferably one-tenth of the breaking strength of the rope. Weights and strengths are shown in Table 5. Table 5. Weights and Strengths of Standard 18 × 7 Nonrotating Wire Rope, Preformed and Not Preformed

Recommended Sheave and Drum Diameters Single layer on drum Multiple layers on drum Mine service

36 rope diameters 48 rope diameters 60 rope diameters

Fig. 5.

Dia., Inches 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Approx. Weight per Ft., Pounds 0.061 0.108 0.169 0.24 0.33 0.43 0.55 0.68 0.97

Breaking Strength, Tons of 2000 Lbs. Impr. Plow Plow Steel Steel 1.42 1.24 2.51 2.18 3.90 3.39 5.59 4.86 7.58 6.59 9.85 8.57 12.4 10.8 15.3 13.3 21.8 19.0

Dia., Inches 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 …

Approx. Weight per Ft., Pounds 1.32 1.73 2.19 2.70 3.27 3.89 4.57 5.30 …

Breaking Strength, Tons of 2000 Lbs. Impr. Plow Plow Steel Steel 29.5 25.7 38.3 33.3 48.2 41.9 59.2 51.5 71.3 62.0 84.4 73.4 98.4 85.6 114 98.8 … …

For galvanized ropes, deduct 10 per cent from above strengths. Source: Rope diagrams, sheave and drum diameters, and data for 3⁄16, 1⁄4 and 5⁄16-inch sizes, Bethlehem Steel Co. All other data, U. S. Simplified Practice Recommendation 198-50.

Flattened Strand Wire Rope: The wires forming the strands of this type of rope are wound around triangular centers so that a flattened outer surface is provided with a greater area than in the regular round rope to withstand severe conditions of abrasion. The triangu-



WIRE ROPE

lar shape of the strands also provides superior resistance to crushing. Flattened strand wire rope is usually furnished in Lang lay and may be obtained with fiber core or independent wire rope core. The three types shown in Table 6 and Figs. 6a through 6c are flexible and are designed for hoisting work.

Fig. 6a. 6 × 25 with fiber core

Fig. 6b. 6 × 30 with fiber core

Fig. 6c. 6 × 27 with fiber core

Table 6. Weights and Strengths of Flattened Strand Wire Rope, Preformed and Not Preformed

Dia., Inches 3⁄ a 8 1⁄ a 2 9⁄ a 16 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4

Approx. Weight per Ft., Pounds 0.25 0.45 0.57 0.70 1.01 1.39 1.80 2.28 2.81

Breaking Strength, Tons of 2000 Lbs. Impr. Mild Plow Plow Steel Steel 6.71 … 11.8 8.94 14.9 11.2 18.3 13.9 26.2 19.8 35.4 26.8 46.0 34.8 57.9 43.8 71.0 53.7

Dia., Inches 13⁄8 11⁄2 15⁄8 13⁄4 2 21⁄4 21⁄2 23⁄4 …

Approx. Weight per Ft., Pounds 3.40 4.05 4.75 5.51 7.20 9.10 11.2 13.6 …

Breaking Strength, Tons of 2000 Lbs. Impr. Mild Plow Plow Steel Steel 85.5 … 101 … 118 … 136 … 176 … 220 … 269 … 321 … … …

a These sizes in Type B only.

Type H is not in U.S. Simplified Practice Recommendation. Source: Rope diagrams, Bethlehem Steel Co. All other data, U.S. Simplified Practice Recommendation 198-50.

Flat Wire Rope: This type of wire rope is made up of a number of four-strand rope units placed side by side and stitched together with soft steel sewing wire. These four-strand units are alternately right and left lay to resist warping, curling, or rotating in service. Weights and strengths are shown in Table 7. Simplified Practice Recommendations.—Because the total number of wire rope types is large, manufacturers and users have agreed upon and adopted a U.S. Simplified Practice Recommendation to provide a simplified listing of those kinds and sizes of wire rope which are most commonly used and stocked. These, then, are the types and sizes which are most generally available. Other types and sizes for special or limited uses also may be found in individual manufacturer's catalogs. Sizes and Strengths of Wire Rope.—The data shown in Tables 1 through 7 have been taken from U.S. Simplified Practice Recommendation 198-50 but do not include those wire ropes shown in that Simplified Practice Recommendation which are intended primarily for marine use. Wire Rope Diameter: The diameter of a wire rope is the diameter of the circle that will just enclose it, hence when measuring the diameter with calipers, care must be taken to obtain the largest outside dimension, taken across the opposite strands, rather than the smallest dimension across opposite “valleys” or “flats.” It is standard practice for the nominal diameter to be the minimum with all tolerances taken on the plus side. Limits for diam-



377

eter as well as for minimum breaking strength and maximum pitch are given in Federal Specification for Wire Rope, RR-R—571a. Wire Rope Strengths: The strength figures shown in the accompanying tables have been obtained by a mathematical derivation based on actual breakage tests of wire rope and represent from 80 to 95 per cent of the total strengths of the individual wires, depending upon the type of rope construction. Table 7. Weights and Strengths of Standard Flat Wire Rope, Not Preformed This rope consists of a number of 4-strand rope units placed side by side and stitched together with soft steel sewing wire.

Flat Wire Rope Width and Thickness, Inches

No. of Ropes


Breaking Strength, Tons of 2000 Lbs. Mild Plow PlowSteel Steel

1⁄ × 4 1⁄ × 4 1⁄ × 4 1⁄ × 4

11⁄2

7

0.69

16.8

14.6

2

9

0.88

21.7

18.8

21⁄2

11

1.15

26.5

23.0

3

13

1.34

31.3

27.2

5⁄ × 16 5⁄ × 16 5⁄ × 16 5⁄ × 16 5⁄ × 16 5⁄ × 16

11⁄2

5

0.77

18.5

16.0

2

7

1.05

25.8

22.4

21⁄2 3

9

1.33

33.2

28.8

11

1.61

40.5

35.3

31⁄2

13

1.89

47.9

41.7

4

15

2.17

55.3

48.1

3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8 3⁄ × 8

2

6

1.25

31.4

27.3

1⁄ × 2 1⁄ × 2 1⁄ × 2

21⁄2

8

1.64

41.8

36.4

3

9

1.84

47.1

40.9

11

2.23

57.5

50.0

31⁄2 4

12

2.44

62.7

54.6

41⁄2

14

2.83

73.2

63.7

5

15

3.03

78.4

68.2

51⁄2

17

3.42

88.9

77.3

6

18

3.63

94.1

81.9

21⁄2

6

2.13

54.5

47.4

3

7

2.47

63.6

55.4

31⁄2

8

2.82

72.7

63.3

Width and Thickness, Inches

No. of Ropes


1⁄ × 2 1⁄ × 2 1⁄ × 2 1⁄ × 2 1⁄ × 2 1⁄ × 2

4

5⁄ × 8 5⁄ × 8 5⁄ × 8 5⁄ × 8 5⁄ × 8 5⁄ × 8 5⁄ × 8 5⁄ × 8

31⁄2

6

3.40

4

7

3.95

Breaking Strength, Tons of 2000 Lbs. Mild Plow Plow Steel Steel

9

3.16

81.8

71.2

41⁄2

10

3.82

90.9

79.1

5

12

4.16

109

51⁄2

13

4.50

118

103

6

14

4.85

127

111

7

16

5.85

145

126

85.8 100

41⁄2

8

4.50

114

5

9

5.04

129

94.9

74.6 87.1 99.5 112

51⁄2

10

5.59

143

124

6

11

6.14

157

137

7

13

7.23

186

162

8

15

8.32

214

186

3⁄ × 4 3⁄ × 4 3⁄ × 4 3⁄ × 4

5

8

6.50

165

143

6

9

7.31

185

161

7

10

8.13

206

179

8

11

9.70

227

197

7⁄ × 8 7⁄ × 8 7⁄ × 8 7⁄ × 8

5

7

7.50

190

165

6

8

8.56

217

188

7

9

9.63

244

212

8

10

271

236

10.7

Source: Rope diagram, Bethlehem Steel Co.; all data, U.S. Simplified Practice Recommendation 198–50.

Safe Working Loads and Factors of Safety.—The maximum load for which a wire rope is to be used should take into account such associated factors as friction, load caused by bending around each sheave, acceleration and deceleration, and, if a long length of rope is to be used for hoisting, the weight of the rope at its maximum extension. The condition of the rope — whether new or old, worn or corroded — and type of attachments should also be considered. Factors of safety for standing rope usually range from 3 to 4; for operating rope, from 5 to 12. Where there is the element of hazard to life or property, higher values are used.



WIRE ROPE

Installing Wire Rope.—The main precaution to be taken in removing and installing wire rope is to avoid kinking which greatly lessens the strength and useful life. Thus, it is preferable when removing wire rope from the reel to have the reel with its axis in a horizontal position and, if possible, mounted so that it will revolve and the wire rope can be taken off straight. If the rope is in a coil, it should be unwound with the coil in a vertical position as by rolling the coil along the ground. Where a drum is to be used, the rope should be run directly onto it from the reel, taking care to see that it is not bent around the drum in a direction opposite to that on the reel, thus causing it to be subject to reverse bending. On flat or smooth-faced drums it is important that the rope be started from the proper end of the drum. A right lay rope that is being overwound on the drum, that is, it passes over the top of the drum as it is wound on, should be started from the right flange of the drum (looking at the drum from the side that the rope is to come) and a left lay rope from the left flange. When the rope is under wound on the drum, a right lay rope should be started from the left flange and a left lay rope from the right flange, so that the rope will spool evenly and the turns will lie snugly together.

Sheaves and drums should be properly aligned to prevent undue wear. The proper position of the main or lead sheave for the rope as it comes off the drum is governed by what is called the fleet angle or angle between the rope as it stretches from drum to sheave and an imaginary center-line passing through the center of the sheave groove and a point halfway between the ends of the drum. When the rope is at one end of the drum, this angle should not exceed one and a half to two degrees. With the lead sheave mounted with its groove on this center-line, a safe fleet angle is obtained by allowing 30 feet of lead for each two feet of drum width. Sheave and Drum Dimensions: Sheaves and drums should be as large as possible to obtain maximum rope life. However, factors such as the need for lightweight equipment for easy transport and use at high speeds, may call for relatively small sheaves with consequent sacrifice in rope life in the interest of overall economy. No hard and fast rules can be laid down for any particular rope if the utmost in economical performance is to be obtained. Where maximum rope life is of prime importance, the following recommendations of Federal Specification RR-R-571a for minimum sheave or drum diameters D in terms of rope diameter d will be of interest. For 6 × 7 rope (six strands of 7 wires each) D = 72d; for 6 × 19 rope, D = 45d; for 6 × 25 rope, D = 45d; for 6 × 29 rope, D = 30d; for 6 × 37 rope, D = 27d; and for 8 × 19 rope, D = 31d. Too small a groove for the rope it is to carry will prevent proper seating of the rope in the bottom of the groove and result in uneven distribution of load on the rope. Too large a groove will not give the rope sufficient side support. Federal Specification RR-R-571a recommends that sheave groove diameters be larger than the nominal rope diameters by the following minimum amounts: For ropes of 1⁄4- to 5⁄16-inch diameters, 1⁄64 inch larger; for 3⁄8- to 3⁄ -inch diameter ropes, 1⁄ inch larger; for 13⁄ - to 11⁄ -inch diameter ropes, 3⁄ inch larger; for 4 32 16 8 64 13⁄16- to 11⁄2-inch ropes, 1⁄16 inch larger; for 19⁄16- to 21⁄4-inch ropes, 3⁄32 inch larger; and for 25⁄16 and larger diameter ropes, 1⁄8 inch larger. For new or regrooved sheaves these values should be doubled; in other words for 1⁄4- to 5⁄16-inch diameter ropes, the groove diameter should be 1⁄ inch larger, and so on. 32



379

Drum or Reel Capacity: The length of wire rope, in feet, that can be spooled onto a drum or reel, is computed by the following formula, where A =depth of rope space on drum, inches: A = (H − D − 2Y) ÷ 2 B =width between drum flanges, inches D =diameter of drum barrel, inches H =diameter of drum flanges, inches K =factor from Table 8 for size of line selected Y =depth not filled on drum or reel where winding is to be less than full capacity L =length of wire rope on drum or reel, feet: L = ( A + D ) × A × B × K Table 8. Factors K Used in Calculating Wire Rope Drum and Reel Capacities Rope Dia., In. 3⁄ 32 1⁄ 8 9⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16

Factor K 23.4 13.6 10.8 8.72 6.14 4.59 3.29

Rope Dia., In.

Factor K

Rope Dia., In.

Factor K

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8

0.925

13⁄8

0.127

0.741

11⁄2

0.107

0.607

15⁄8

0.0886

0.506

0.0770

0.428

13⁄4 17⁄8

0.354

2

0.0597

0.308

21⁄8

0.0532

0.0675

2.21

1

0.239

21⁄4

0.0476

1.58

11⁄8

0.191

23⁄8

0.0419

1.19

11⁄4

0.152

21⁄2

0.0380

Note: The values of “K” allow for normal oversize of ropes, and the fact that it is practically impossible to “thread-wind” ropes of small diameter. However, the formula is based on uniform rope winding and will not give correct figures if rope is wound non-uniformly on the reel. The amount of tension applied when spooling the rope will also affect the length. The formula is based on the same number of wraps of rope in each layer, which is not strictly correct, but does not result in appreciable error unless the width (B) of the reel is quite small compared with the flange diameter (H).

Example:Find the length in feet of 9⁄16-inch diameter rope required to fill a drum having the following dimensions: B = 24 inches, D = 18 inches, H = 30 inches, A = ( 30 – 18 – 0 ) ÷ 2 = 6 inches L = ( 6 + 18 ) × 6 × 24 × 0.741 = 2560.0 or 2560 feet The above formula and factors K allow for normal oversize of ropes but will not give correct figures if rope is wound non-uniformly on the reel. Load Capacity of Sheave or Drum: To avoid excessive wear and groove corrugation, the radial pressure exerted by the wire rope on the sheave or drum must be kept within certain maximum limits. The radial pressure of the rope is a function of rope tension, rope diameter, and tread diameter of the sheave and can be determined by the following equation: 2T P = -----------D×d where P =Radial pressure in pounds per square inch (see Table 9) T =Rope tension in pounds D =Tread diameter of sheave or drum in inches d =Rope diameter in inches According to the Bethlehem Steel Co. the radial pressures shown in Table 9 are recommended as maximums according to the material of which the sheave or drum is made.



WIRE ROPE Table 9. Maximum Radial Pressures for Drums and Sheaves

Type of Wire Rope 6×7 6 × 19 6 × 37

Drum or Sheave Material Manganese Cast Cast Iron Steel Steela Recommended Maximum Radial Pressures, psi 300b

550b

1500b

500b 600

900b 1075

2500b 3000

Drum or Sheave Material Manganese Cast Cast Iron Steel Steela Recommended Maximum Radial Pressures, psi

Type of Wire Rope 6 × 8 Flattened Strand 6 × 25 Flattened Strand 6 × 30 Flattened Strand

450 800 800

850 1450 1450

2200 4000 4000

a 11 to 13 per cent manganese. b These values are for regular lay rope. Lang lay rope values may be increased by 15 per cent.

Minimum Sheave- and Drum-Groove Dimensions for Wire Rope Applications Nominal Rope Diameter 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

Groove Radius New 0.135 0.167 0.201 0.234 0.271 0.303 0.334 0.401 0.468 0.543 0.605 0.669 0.736 0.803

Worn 0.129 0.160 0.190 0.220 0.256 0.288 0.320 0.380 0.440 0.513 0.577 0.639 0.699 0.759

Nominal Rope Diameter 15⁄8 13⁄4 17⁄8 2 21⁄8 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4

Groove Radius New 0.876 0.939 1.003 1.085 1.137 1.210 1.271 1.338 1.404 1.481 1.544 1.607 1.664 1.731

Worn 0.833 0.897 0.959 1.025 1.079 1.153 1.199 1.279 1.339 1.409 1.473 1.538 1.598 1.658

Nominal Rope Diameter 33⁄8 31⁄2 33⁄4 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6

Groove Radius New 1.807 1.869 1.997 2.139 2.264 2.396 2.534 2.663 2.804 2.929 3.074 3.198

Worn 1.730 1.794 1.918 2.050 2.178 2.298 2.434 2.557 2.691 2.817 2.947 3.075

All dimensions in inches. Data taken from Wire Rope Users Manual, 2nd ed., American Iron and Steel Institute, Washington, D. C. The values given in this table are applicable to grooves in sheaves and drums but are not generally suitable for pitch design, since other factors may be involved.

Rope Loads due to Bending: When a wire rope is bent around a sheave, the resulting bending stress sb in the outer wire, and equivalent bending load Pb (amount that direct tension load on rope is increased by bending) may be computed by the following formulas: sb = Edw ÷ D; Pb = sbA, where A = d2Q. E is the modulus of elasticity of the wire rope (varies with the type and condition of rope from 10,000,000 to 14,000,000. An average value of 12,000,000 is frequently used), d is the diameter of the wire rope, dw is the diameter of the component wire (for 6 × 7 rope, dw = 0.106d; for 6 × 19 rope, 0.063d; for 6 × 37 rope, 0.045d; and for 8 × 19 rope, dw = 0.050d). D is the pitch diameter of the sheave in inches, A is the metal cross-sectional area of the rope, and Q is a constant, values for which are: 6 × 7 (Fiber Core) rope, 0.380; 6 × 7 (IWRC or WSC), 0.437; 6 × 19 (Fiber Core), 0.405; 6 × 19 (IWRC or WSC), 0.475; 6 × 37 (Fiber Core), 0.400; 6 × 37 (IWRC), 0.470; 8 × 19 (Fiber Core), 0.370; and Flattened Strand Rope, 0.440. Example:Find the bending stress and equivalent bending load due to the bending of a 6 × 19 (Fiber Core) wire rope of 1⁄2-inch diameter around a 24-inch pitch diameter sheave. 2

d w = 0.063 × 0.5 = 0.0315 in. A = 0.5 × 0.405 = 0.101 sq. in. s b = 12 ,000 ,000 × 0.0315 ÷ 24 = 15 ,750 lbs. per sq. in. P b = 15 ,750 × 0.101 = 1590 lbs.



381

Cutting and Seizing of Wire Rope.—Wire rope can be cut with mechanical wire rope shears, an abrasive wheel, an electric resistance cutter (used for ropes of smaller diameter only), or an acetylene torch. This last method fuses the ends of the wires in the strands. It is important that the rope be seized on either side of where the cut is to be made. Any annealed low carbon steel wire may be used for seizing, the recommended sizes being as follows: For a wire rope of 1⁄4- to 15⁄16-inch diameter, use a seizing wire of 0.054-inch (No. 17 Steel Wire Gage); for a rope of 1- to 15⁄8-inch diameter, use a 0.105-inch wire (No. 12); and for rope of 13⁄4- to 31⁄2-inch diameter, use a 0.135-inch wire (No. 10). Except for preformed wire ropes, a minimum of two seizings on either side of a cut is recommended. Four seizings should be used on either side of a cut for Lang lay rope, a rope with a steel core, or a nonspinning type of rope. The following method of seizing is given in Federal Specification for wire rope, RR-R571a. Lay one end of the seizing wire in the groove between two strands of wire rope and wrap the other end tightly in a close helix over the portion in the groove. A seizing iron (round bar 1⁄2 to 5⁄8 inch diameter by 18 inches long) should be used to wrap the seizing tightly. This bar is placed at right angles to the rope next to the first turn or two of the seizing wire. The seizing wire is brought around the back of the seizing iron and wrapped loosely around the wire rope in the opposite direction to that of the seizing coil. As the seizing iron is now rotated around the rope it will carry the seizing wire snugly and tightly into place. When completed, both ends of the seizing should be twisted together tightly. Maintenance of Wire Rope.—Heavy abrasion, overloading, and bending around sheaves or drums that are too small in diameter are the principal reasons for the rapid deterioration of wire rope. Wire rope in use should be inspected periodically for evidence of wear and damage by corrosion. Such inspections should take place at progressively shorter intervals over the useful life of the rope as wear tends to accelerate with use. Where wear is rapid, the outside of a wire rope will show flattened surfaces in a short time. If there is any hazard involved in the use of the rope, it may be prudent to estimate the remaining strength and service life. This assessment should be done for the weakest point where the most wear or largest number of broken wires are in evidence. One way to arrive at a conclusion is to set an arbitrary number of broken wires in a given strand as an indication that the rope should be removed from service and an ultimate strength test run on the worn sample. The arbitrary figure can then be revised and rechecked until a practical working formula is arrived at. A piece of waste rubbed along the wire rope will help to reveal broken wires. The effects of corrosion are not easy to detect because the exterior wires may appear to be only slightly rusty, and the damaging effects of corrosion may be confined to the hidden inner wires where it cannot be seen. To prevent damage by corrosion, the rope should be kept well lubricated. Use of zinc coated wire rope may be indicated for some applications. Periodic cleaning of wire rope by using a stiff brush and kerosene or with compressed air or live steam and relubricating will help to lengthen rope life and reduce abrasion and wear on sheaves and drums. Before storing after use, wire rope should be cleaned and lubricated. Lubrication of Wire Rope.—Although wire rope is thoroughly lubricated during manufacture to protect it against corrosion and to reduce friction and wear, this lubrication should be supplemented from time to time. Special lubricants are supplied by wire rope manufacturers. These lubricants vary somewhat with the type of rope application and operating condition. Where the preferred lubricant can not be obtained from the wire rope manufacturer, an adhesive type of lubricant similar to that used for open gearing will often be found suitable. At normal temperatures, some wire rope lubricants may be practically solid and will require thinning before application. Thinning may be done by heating to 160 to 200 degrees F. or by diluting with gasoline or some other fluid that will allow the lubricant to penetrate the rope. The lubricant may be painted on the rope or the rope may be passed through a box or tank filled with the lubricant.



WIRE ROPE

Replacement of Wire Rope.—When an old wire rope is to be replaced, all drums and sheaves should be examined for wear. All evidence of scoring or imprinting of grooves from previous use should be removed and sheaves with flat spots, defective bearings, and broken flanges, should be repaired or replaced. It will frequently be found that the area of maximum wear is located relatively near one end of the rope. By cutting off that portion, the remainder of the rope may be salvaged for continued use. Sometimes the life of a rope can be increased by simply changing it end for end at about one-half the estimated normal life. The worn sections will then no longer come at the points that cause the greatest wear. Wire Rope Slings and Fittings Slings.—A few of the simpler sling arrangements or hitches as they are called, are shown in the accompanying illustration. Normally 6 × 19 Class wire rope is recommended where a diameter in the 1⁄4-inch to 11⁄8-inch range is to be used and 6 × 37 Class wire rope where a diameter in the 11⁄4-inch and larger range is to be used. However, the 6 × 19 Class may be used even in the larger sizes if resistance to abrasion is of primary importance and the 6 × 37 Class in the smaller sizes if greater flexibility is desired. The straight lift hitch, Fig. 7a, is a straight connector between crane hook and load. The basket hitch may be used with two hooks so that the sides are vertical as shown at Fig. 7b or with a single hook with sides at various angles with the vertical as shown at Fig. 7c, Fig. 7d, and Fig. 7e. As the angle with the vertical increases, a greater tension is placed on the rope so that for any given load, a sling of greater lifting capacity must be used. The choker hitch, shown at Fig. 7f, is widely used for lifting bundles of items such as bars, poles, pipe, and similar objects. The choker hitch holds these items firmly, but the load must be balanced so that it rides safely. Since additional stress is imposed on the rope due to the choking action, the capacity of this type of hitch is 25 per cent less than that of the comparable straight lift. If two choker hitches are used at an angle, these angles must also be taken into consideration as with the basket hitches. Wire Rope Fittings.—Many varieties of swaged fittings are available for use with wire rope and several industrial and aircraft types are shown in the accompanying illustration. Swaged fittings on wire rope have an efficiency (ability to hold the wire rope) of approximately 100 per cent of the catalogue rope strength. These fittings are attached to the end or body of the wire rope by the application of high pressure through special dies that cause the material of the fitting to “flow” around the wires and strands of the rope to form a union that is as strong as the rope itself. The more commonly used types, of swaged fittings range from 1⁄8- to 5⁄8-inch diameter sizes in industrial types and from the 1⁄16- to 5⁄8-inch sizes in aircraft types. These fittings are furnished attached to the wire strand, rope, or cable. Applying Clips and Attaching Sockets.—In attaching U-bolt clips for fastening the end of a wire rope to form a loop, it is essential that the saddle or base of the clip bears against the longer or “live” end of the rope loop and the U-bolt against the shorter or “dead” end. The “U” of the clips should never bear against the live end of the rope because the rope may be cut or kinked. A wire-rope thimble should be used in the loop eye of the rope to prevent kinking when rope clips are used. The strength of a clip fastening is usually less than 80 percent of the strength of the rope. Table 10 gives the proper size, number, and spacing for each size of wire rope. In attaching commercial sockets of forged steel to wire rope ends, the following procedure is recommended. The wire rope is seized at the end and another seizing is applied at a distance from the end equal to the length of the basket of the socket. As explained in a previous section, soft iron wire is used and particularly for the larger sizes of wire rope, it is important to use a seizing iron to secure a tight winding. For large ropes, the seizing should be several inches long.



383

Wire Rope Slings and Fittings

Fig. 7a. Straight Lift One leg vertical Load capacity is 100% of a single rope.

Fig. 7b. Basket Hitch Two legs vertical Load capacity is 200% of the single rope in Fig. 7a.

Fig. 7d. Basket Hitch Fig. 7e. Basket Hitch Two legs at 45° with the vertical Two legs at 60° with the vertical Load capacity is 141% of Load capacity is 100% of the single rope in Fig. 7a. the single rope in Fig. 7a.

Fig. 7c. Basket Hitch Two legs at 30° with the vertical Load capacity is 174% of the single rope in Fig. 7a.

Fig. 7f. Choker Hitch One leg vertical, with slipthrough loop Rated capacity is 75% of the single rope in Fig. 7a.

The end seizing is now removed and the strands are separated so that the fiber core can be cut back to the next seizing. The individual wires are then untwisted and “broomed out” and for the distance they are to be inserted in the socket are carefully cleaned with benzine, naphtha, or unleaded gasoline. The wires are then dipped into commercial muriatic (hydrochloric) acid and left (usually one to three minutes) until the wires are bright and clean or, if zinc coated, until the zinc is removed. After cleaning, the wires are dipped into a hot soda solution (1 pound of soda to 4 gallons of water at 175 degrees F. minimum) to neutralize the acid. The rope is now placed in a vise. A temporary seizing is used to hold the wire ends



A

Vertical B C

A

Independent Wire Rope Core Choker 60° Bridle 45°Bridle B C A B C A B C


WIRE ROPE

Fiber Core 30°Bridle Vertical Choker 60° Bridle 45° Bridle 30° Bridle A B C A B C A B C A B C A B C A B C Single Leg, 6 × 19 Wire Rope 1⁄ 0.59 0.56 0.53 0.44 0.42 0.40 … … … … … … … … … 0.55 0.51 0.49 0.41 0.38 0.37 … … … … … … … … … 4 3⁄ 1.3 1.2 1.1 0.98 0.93 0.86 … … … … … … … … … 1.2 1.1 1.1 0.91 0.85 0.80 … … … … … … … … … 8 1⁄ 2.3 2.2 2.0 1.7 1.6 1.5 … … … … … … … … … 2.1 2.0 1.8 1.6 1.5 1.4 … … … … … … … … … 2 5⁄ 3.6 3.4 3.0 2.7 2.5 2.2 … … … … … … … … … 3.3 3.1 2.8 2.5 2.3 2.1 … … … … … … … … … 8 3⁄ 5.1 4.9 4.2 3.8 3.6 3.1 … … … … … … … … … 4.8 4.4 3.9 3.6 3.3 2.9 … … … … … … … … … 4 7⁄ 6.9 6.6 5.5 5.2 4.9 4.1 … … … … … … … … … 6.4 5.9 5.1 4.8 4.5 3.9 … … … … … … … … … 8 1 9.0 8.5 7.2 6.7 6.4 5.4 … … … … … … … … … 8.4 7.7 6.7 6.3 5.8 5.0 … … … … … … … … … 1 1 ⁄8 11 10 9.0 8.5 7.8 6.8 … … … … … … … … … 10 9.5 8.4 7.9 7.1 6.3 … … … … … … … … … Single Leg, 6 × 37 Wire Rope 11⁄4 13 12 10 9.9 9.2 7.9 … … … … … … … … … 12 11 9.8 9.2 8.3 7.4 … … … … … … … … … 13⁄8 16 15 13 12 11 9.6 … … … … … … … … … 15 13 12 11 10 8.9 … … … … … … … … … 11⁄2 19 17 15 14 13 11 … … … … … … … … … 17 16 14 13 12 10 … … … … … … … … … 3 1 ⁄4 26 24 20 19 18 15 … … … … … … … … … 24 21 19 18 16 14 … … … … … … … … … 2 33 30 26 25 23 20 … … … … … … … … … 31 28 25 23 21 18 … … … … … … … … … 21⁄4 41 38 33 31 29 25 … … … … … … … … … … … … … … … … … … … … … … … … Two-Leg Bridle or Basket Hitch, 6 × 19 Wire Rope Sling 1⁄ 1.2 1.1 1.0 … … … 1.0 0.97 0.92 0.83 0.79 0.75 0.59 0.56 0.53 1.1 1.0 0.99 … … … 0.95 0.88 0.85 0.77 0.72 0.70 0.55 0.51 0.49 4 3⁄ 2.0 2.5 2.3 … … … 2.3 2.1 2.0 1.8 1.8 1.8 1.3 1.2 1.1 2.4 2.2 2.1 … … … 2.1 1.9 1.8 1.7 1.6 1.5 1.2 1.1 1.1 8 1⁄ 4.0 4.4 3.9 … … … 4.0 3.6 3.4 3.2 3.1 2.8 2.3 2.2 2.0 4.3 3.9 3.7 … … … 3.7 3.4 3.2 3.0 2.8 2.6 2.1 2.0 1.8 2 5⁄ 7.2 6.6 6.0 … … … 6.2 5.9 5.2 5.1 4.8 4.2 3.6 3.4 3.0 6.7 6.2 5.6 … … … 6.2 5.3 4.8 4.7 4.4 4.0 3.3 3.1 2.8 8 3⁄ 10 9.7 8.4 … … … 8.9 8.4 7.3 7.2 6.9 5.9 5.1 4.9 4.2 9.5 8.8 7.8 … … … 8.2 7.6 6.8 6.7 6.2 5.5 4.8 4.4 3.9 4 7⁄ 14 13 11 … … … 12 11 9.6 9.8 9.3 7.8 6.9 6.6 5.5 13 12 10 … … … 11 10 8.9 9.1 8.4 7.3 6.4 5.9 5.1 8 1 18 17 14 … … … 15 15 12 13 12 10 9.0 8.5 7.2 17 15 13 … … … 14 13 11 12 11 9.4 8.4 7.7 6.7 1 1 ⁄8 23 21 18 … … … 19 18 16 16 15 13 11 10 9.0 21 19 17 … … … 18 16 14 15 13 12 10 9.5 8.4 Two-Leg Bridle or Basket Hitch, 6 × 37 Wire Rope Sling 11⁄4 26 24 21 … … … 23 21 18 19 17 15 13 12 10 25 22 20 … … … 21 19 17 17 16 14 12 11 9.8 13⁄8 32 29 25 … … … 28 25 22 22 21 18 16 15 13 30 27 24 … … … 26 23 20 21 19 17 15 13 12 1 1 ⁄2 38 35 30 … … … 33 30 26 27 25 21 19 17 15 35 32 28 … … … 30 27 24 25 22 20 17 16 14 3 1 ⁄4 51 47 41 … … … 44 41 35 36 33 29 26 24 20 46 43 39 … … … 41 37 33 34 30 27 24 21 19 2 66 61 53 … … … 57 53 46 47 43 37 33 30 26 62 55 49 … … … 53 43 43 43 39 35 31 26 25 21⁄4 83 76 66 … … … 72 66 67 58 54 47 41 38 33 … … … … … … … … … … … … … … … A–socket or swaged terminal attachment; B–mechanical sleeve attachment; C–hand-tucked splice attachment. Data from Longshoring Industry, OSHA Safety and Health Standards Digest, OSHA 2232, 1985.

Dia. (in.)

384

Rated Capacities for Improved Plow Steel Wire Rope and Wire Rope Slings (in tons of 2,000 lbs)


385

Industrial Types

Round Eye

Rod Eye

Clevis

Hoist-Hook

Button-Stop

Threaded Stud

Swaged Closed Socket Swaged Open Socket Aircraft Types

Single-Shank Ball

Double-Shank Ball

Eye

Fork

Strap-Eye

Strap-Fork

Wire Rope Fittings

together until the socket is placed over the rope end. The temporary seizing is then removed and the socket located so that the ends of the wires are about even with the upper end of the basket. The opening around the rope at the bottom of the socket is now sealed with putty. Table 10. Clips Required for Fastening Wire Rope End Rope Dia., In.

U-Bolt Dia., In.

3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8

11⁄ 32 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4

Min. No. of Clips 2 2 2 2 2 3 3

Clip Spacing, In. 3 31⁄4 31⁄4 4 41⁄2 5 53⁄4

Rope Dia., In.

U-Bolt Dia., In.

3⁄ 4 7⁄ 8

7⁄ 8

1

11⁄8 11⁄4 17⁄16 11⁄2 123⁄32

11⁄8 11⁄4 13⁄8 11⁄2

1

Min. No. of Clips 4 4 4 5 5 6 6

Clip Spacing, In.

Rope Dia., In.

U-Bolt Dia., In.

63⁄4 8

15⁄8 13⁄4 2

13⁄4 115⁄16 21⁄8 25⁄8 27⁄8 … …

83⁄4 93⁄4 103⁄4 111⁄2 121⁄2

21⁄4 21⁄2 … …

Min. No. of Clips 6 7 8 8 8 … …

Clip Spacing, In. 131⁄4 141⁄2 161⁄2 161⁄2 173⁄4 … …

A special high grade pure zinc is used to fill the socket. Babbit metal should not be used as it will not hold properly. For proper fluidity and penetration, the zinc is heated to a tem-



CRANE CHAIN AND HOOKS

perature in the 830- to 900-degree F. range. If a pyrometer is not available to measure the temperature of the molten zinc, a dry soft pine stick dipped into the zinc and quickly withdrawn will show only a slight discoloration and no zinc will adhere to it. If the wood chars, the zinc is too hot. The socket is now permitted to cool and the resulting joint is ready for use. When properly prepared, the strength of the joint should be approximately equal to that of the rope itself. Crane Chain and Hooks Material for Crane Chains.—The best material for crane and hoisting chains is a good grade of wrought iron, in which the percentage of phosphorus, sulfur, silicon, and other impurities is comparatively low. The tensile strength of the best grades of wrought iron does not exceed 46,000 pounds per square inch, whereas mild steel with about 0.15 per cent carbon has a tensile strength nearly double this amount. The ductility and toughness of wrought iron, however, is greater than that of ordinary commercial steel, and for this reason it is preferable for chains subjected to heavy intermittent strains, because wrought iron will always give warning by bending or stretching, before breaking. Another important reason for using wrought iron in preference to steel is that a perfect weld can be effected more easily. Heat-treated alloy steel is also widely used for chains. This steel contains carbon, 0.30 per cent, max; phosphorus, 0.045 per cent, max; and sulfur, 0.045 per cent, max. The selection and amounts of alloying elements are left to the individual manufacturers. Strength of Chains.—When calculating the strength of chains it should be observed that the strength of a link subjected to tensile stresses is not equal to twice the strength of an iron bar of the same diameter as the link stock, but is a certain amount less, owing to the bending action caused by the manner in which the load is applied to the link. The strength is also reduced somewhat by the weld. The following empirical formula is commonly used for calculating the breaking load, in pounds, of wrought-iron crane chains: W = 54 ,000D 2 in which W = breaking load in pounds and D = diameter of bar (in inches) from which links are made. The working load for chains should not exceed one-third the value of W, and, it is often one-fourth or one-fifth of the breaking load. When a chain is wound around a casting and severe bending stresses are introduced, a greater factor of safety should be used. Care of Hoisting and Crane Chains.—Chains used for hoisting heavy loads are subject to deterioration, both apparent and invisible. The links wear, and repeated loading causes localized deformations to form cracks that spread until the links fail. Chain wear can be reduced by occasional lubrication. The life of a wrought-iron chain can be prolonged by frequent annealing or normalizing unless it has been so highly or frequently stressed that small cracks have formed. If this condition is present, annealing or normalizing will not “heal” the material, and the links will eventually fracture. To anneal a wrought-iron chain, heat it to cherry-red and allow it to cool slowly. Annealing should be done every six months, and oftener if the chain is subjected to unusually severe service. Maximum Allowable Wear at Any Point of Link Chain Size (in.) 1⁄ (9⁄ ) 4 32 3⁄ 8 1⁄ 2 5⁄ 8

Maximum Allowable Wear (in.) 3⁄ 64 5⁄ 64 7⁄ 64 9⁄ 64

Chain Size (in.)

Maximum Allowable Wear (in.)

3⁄ 4 7⁄ 8

1 11⁄8

5⁄ 32 11⁄ 64 3⁄ 16 7⁄ 32

Chain Size (in.) 11⁄4 13⁄8 11⁄2 13⁄4

Maximum Allowable Wear (in.) 1⁄ 4 3⁄ 32 5⁄ 16 11⁄ 32

Source: Longshoring Industry, OSHA 2232, 1985.

Chains should be examined periodically for twists, as a twisted chain will wear rapidly. Any links that have worn excessively should be replaced with new ones, so that every link will do its full share of work during the life of the chain, without exceeding the limit of


Machinery's Handbook 27th Edition SAFE WORKING LOAD FOR ROPE AND CHAIN

387

safety. Chains for hoisting purposes should be made with short links, so that they will wrap closely around the sheaves or drums without bending. The diameter of the winding drums should be not less than 25 or 30 times the diameter of the iron used for the links. The accompanying table lists the maximum allowable wear for various sizes of chains. Safe Loads for Ropes and Chains.—Safe loads recommended for wire rope or chain slings depend not only upon the strength of the sling but also upon the method of applying it to the load, as shown by the accompanying table giving safe loads as prepared by OSHA. The loads recommended in this table are more conservative than those usually specified, in order to provide ample allowance for some unobserved weakness in the sling, or the possibility of excessive strains due to misjudgment or accident. Safe Working Loads in Pounds for Manila Rope and Chains

1 11⁄16 11⁄8 11⁄4 15⁄16 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄8

3240 204 1835 … 346 2865 6600 467 4200 … 605 5600 … 775 … 11,240 915 7400 … 1190 9200 16,500 1520 11,400 23,000 1870 16,600 … 2250 … 28,600 2660 22,400 38,600 3120 29,400 … 3400 … 44,400 4200 34,600 57,400 4600 42,600 … 5200 … 67,000 … 51,800 79,400 6200 61,600 85,000 7800 72,400 95,800 9000 84,000 … … 95,800 … 10,800 109,600 … 12,400 …

Sling at 30°

5640 170 … 282 11,400 380 … 493 … 635 19,500 798 … 973 28,500 1240 39,800 1520 … 1830 49,800 2170 67,000 2540 … 2800 77,000 3400 99,400 3800 … 4200 116,000 … 137,000 5000 147,000 6400 163,000 7400 … … … 8800 … 10,200

1500 4540 120 1060 2340 … 200 1655 3370 9300 270 2385 4600 … 350 3250 … … 450 … 6000 15,800 530 4200 7600 … 690 5400 9400 23,300 880 6600 13,400 32,400 1080 9600 … … 1300 … 18,400 40,600 1540 13,000 24,000 54,600 1800 17,000 … … 2000 … 28,400 63,000 2400 20,000 35,000 81,000 2700 24,800 … … 3000 … 42,200 94,000 … 30,000 50,400 112,000 3600 35,600 59,000 119,000 4500 41,800 68,600 124,000 5200 48,400 78,200 … … 55,200 89,600 … 6200 63,200 … … 7200 …

Alloy Steel

Crane Chain Manila Rope

Alloy Steel

Wrought Iron

Crane Chain Manila Rope

Alloy Steel

Wrought Iron

Manila Rope

1060 1655 2385 3250 … 4200 5400 6600 9600 … 13,000 17,000 … 20,000 24,800 … 30,000 35,600 41,800 48,400 55,200 63,200 …

Alloy Steel

120 200 270 350 450 530 690 880 1080 1300 1540 1800 2000 2400 2700 3000 … 3600 4500 5200 … 6200 7200

Sling at 45°

Crane Chain

Wrought Iron

Sling at 60°

Crane Chain Wrought Iron

1⁄ a 4 5⁄ a 16 3⁄ 8 7⁄ a 16 15⁄ 32 1⁄ 2 9⁄ a 16 5⁄ 8 3⁄ 4 13⁄ 16 7⁄ 8

Rope or Chain Vertical

Manila Rope

Diameter of Rope, or Chain Link, Inch

3240 … 6600 … … 11,240 … 16,500 23,000 … 28,600 38,600 … 44,400 57,400 … 67,000 79,400 85,000 95,800 … … …

a These sizes of wrought chain are no longer manufactured in the United States.

Data from Longshoring Industry, OSHA Safety and Health Standards Digest, OSHA 2232, 1985.

The working load limit is defined as the maximum load in pounds that should ever be applied to chain, when the chain is new or in “as new” condition, and when the load is uniformly applied in direct tension to a straight length of chain. This limit is also affected by the number of chains used and their configuration. The accompanying table shows the working load limit for various configurations of heat-treated alloy steel chain using a 4 to 1 design factor, which conforms to ISO practice.



STRENGTH OF ROPE Working Load Limit for Heat-Treated Alloy Steel Chain, pounds Single Leg

Double Leg

Triple and Quad Leg

Chain Size (in.) 1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

3,600

6,200

5,050

3,600

9,300

7,600

5,400

6,400

11,000

9,000

6,400

16,550

13,500

9,500

11,400

19,700

16,100

11,400

29,600

24,200

17,100

17,800

30,800

25,150

17,800

46,250

37,750

26,700

25,650

44,400

36,250

25,650

66,650

54,400

38,450

34,900

60,400

49,300

34,900

90,650

74,000

52,350

Source: The Crosby Group.

Protection from Sharp Corners: When the load to be lifted has sharp corners or edges, as are often encountered with castings, and with structural steel and other similar objects, pads or wooden protective pieces should be applied at the corners, to prevent the slings from being abraded or otherwise damaged where they come in contact with the load. These precautions are especially important when the slings consist of wire cable or fiber rope, although they should also be used even when slings are made of chain. Wooden cornerpieces are often provided for use in hoisting loads with sharp angles. If pads of burlap or other soft material are used, they should be thick and heavy enough to sustain the pressure, and distribute it over a considerable area, instead of allowing it to be concentrated directly at the edges of the part to be lifted. Strength of Manila Rope

Dia. (in.) 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 13⁄ 16 7⁄ 8

1 11⁄16 11⁄8 11⁄4

Circumference (in.) 5⁄ 8 3⁄ 4

1 11⁄8 11⁄4 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4

Weight of 100 feet of Ropea (lb)

New Rope Tensile Strengthb (lb)

Working Loadc (lb)

1.50 2.00 2.90 4.10 5.25 7.50 10.4 13.3 16.7 19.5 22.4 27.0 31.2 36.0 41.6

406 540 900 1220 1580 2380 3100 3960 4860 5850 6950 8100 9450 10,800 12,200

41 54 90 122 176 264 388 496 695 835 995 1160 1350 1540 1740

Dia. (in.)

Circumference (in.)



Working Loadc (lb)

15⁄16 11⁄2 15⁄8 13⁄4 2 21⁄8 21⁄4 21⁄2 25⁄8 27⁄8 3 31⁄4 31⁄2 4 …

4 41⁄2 5 51⁄2 6 61⁄2 7 71⁄2 8 81⁄2 9 10 11 12 …

47.8 60.0 74.5 89.5 108 125 146 167 191 215 242 298 366 434 …

13,500 16,700 20,200 23,800 28,000 32,400 37,000 41,800 46,800 52,000 57,500 69,500 82,000 94,500 …

1930 2380 2880 3400 4000 4620 5300 5950 6700 7450 8200 9950 11,700 13,500 …

a Average value is shown; maximum is 5 per cent higher. b Based on tests of new and unused rope of standard construction in accordance with Cordage Institute Standard Test Methods. c These values are for rope in good condition with appropriate splices, in noncritical applications, and under normal service conditions. These values should be reduced where life, limb, or valuable propety are involved, or for exceptional service conditions such as shock loads or sustained loads.

Data from Cordage Institute Rope Specifications for three-strand laid and eight-strand plaited manila rope (standard construction).


Machinery's Handbook 27th Edition STRENGTH OF ROPE

389

Strength of Nylon and Double Braided Nylon Rope

Dia. (in.) 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 13⁄ 16 7⁄ 8

Circumference (in.) 5⁄ 8 3⁄ 4



Working Loadc (lb)

Dia. (in.)

Nylon Rope 75 15⁄16


New Rope Tensile Strengtha (lb)

Working Loadc (lb)

4

45.0

38,800

4,320

55.0

47,800

5,320

66.5

58,500

6,500

83.0

70,000

7,800

95.0

83,000

9,200

Circumference (in.)

1.00

900

1.50

1,490

124

11⁄2

1

2.50

2,300

192

15⁄8

41⁄2 5

11⁄8

3.50

3,340

278

11⁄4

5.00

4,500

410

13⁄4 2

51⁄2 6

11⁄2

6.50

5,750

525

21⁄8

95,500

10,600

8.15

7,200

720

21⁄4

61⁄2 7

109

13⁄4 2

129

113,000

12,600

10.5

9,350

935

21⁄2

126,000

14,000

14.5

12,800

1,420

25⁄8

71⁄2 8

149

21⁄4

168

146,000

16,200

21⁄2

17.0

15,300

1,700

18,000

18,000

2,000

81⁄2 9

162,000

20.0

27⁄8 3

189 210

180,000

20,000

1

23⁄4 3

26.4

22,600

2,520

25,200

11⁄16

31⁄4

29.0

26,000

11⁄8

31⁄2

34.0

11⁄4

33⁄4

40.0

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 13⁄ 16 7⁄ 8

3⁄ 4 1

10

264

226,000

2,880

31⁄4 31⁄2

11

312

270,000

30,000

29,800

3,320

4

12

380

324,000

36,000

33,800

3,760

…

…

…

…

…

Double Braided Nylon Rope (Nylon Cover—Nylon Core) 1.56 1,650 150 4 43.1 15⁄16

44,700

5,590

2.44

2,570

234

13⁄8

41⁄4

47.3

49,000

6,130

11⁄8

3.52

3,700

336

11⁄2

56.3

58,300

7,290

15⁄16

4.79

5,020

502

15⁄8

41⁄2 5

66.0

68,300

8,540

51⁄2

11⁄2 13⁄4

6.25

6,550

655

13⁄4

79,200

9,900

7.91

8,270

919

2

6

100

103,000

12,900

9.77

61⁄2 7

113

117,000

14,600

127

131,000

18,700

71⁄2 8

156

161,000

23,000

172

177,000

25,300

225 264

231,000 271,000

33,000 38,700

76.6

10,200

1,130

21⁄8

21⁄4

14.1

14,700

1,840

21⁄4

21⁄2

16.5

17,200

2,150

21⁄2

19.1

19,900

2,490

1 11⁄16

23⁄4 3 31⁄4

25.0 28.2

26,000 29,300

3,250 3,660

25⁄8 3 31⁄4

9 10

11⁄8

31⁄2

31.6

32,800

4,100

329

338,000

48,300

33⁄4

39.1

40,600

5,080

31⁄2 4

11

11⁄4

12

400

410,000

58,600

2

a Average value is shown. Maximum for nylon rope is 5 per cent higher; tolerance for double braided nylon rope is ± 5 per cent. b Based on tests of new and unused rope of standard construction in accordance with Cordage Institute Standard Test Methods. For double braided nylon rope these values are minimums and are based on a large number of tests by various manufacturers; these values represent results two standard deviations below the mean. The minimum tensile strength is determined by the formula 1057 × (linear density)0.995. c These values are for rope in good condition with appropriate splices, in noncritical applications, and under normal service conditions. These values should be reduced where life, limb, or valuable property are involved, or for exceptional service conditions such as shock loads or sustained loads. Data from Cordage Institute Specifications for nylon rope (three-strand laid and eight-strand plaited, standard construction) and double braided nylon rope.



CRANE CHAIN

Loads Lifted by Crane Chains.—To find the approximate weight a chain will lift when rove as a tackle, multiply the safe load given in the table Close-link Hoisting, Sling and Crane Chain by the number of parts or chains at the movable block, and subtract one-quarter for frictional resistance. To find the size of chain required for lifting a given weight, divide the weight by the number of chains at the movable block, and add one-third for friction; next find in the column headed “Average Safe Working Load” the corresponding load, and then the corresponding size of chain in the column headed “Size.” With the heavy chain or where the chain is unusually long, the weight of the chain itself should also be considered.

Close-link Hoisting, Sling and Crane Chain

Size 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1 11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 113⁄16 17⁄8 115⁄16 2 21⁄16 21⁄8 23⁄16 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3

Standard Pitch, P Inches 25⁄ 32 27⁄ 32 31⁄ 32 15⁄32 111⁄32 115⁄32 123⁄32 113⁄16 115⁄16 21⁄16 23⁄16 27⁄16 21⁄2 25⁄8 23⁄4 31⁄16 31⁄8 33⁄8 39⁄16 311⁄16 37⁄8

Average Weight per Foot, Pounds

4 41⁄4 41⁄2 43⁄4

3⁄ 4 1 11⁄2 2 21⁄2 31⁄4 4 5 61⁄4 7 8 9 10 12 13 141⁄2 16 171⁄2 19 211⁄2 23 25 28 30 31

5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2 63⁄4 67⁄8 7 71⁄8 71⁄4 71⁄2 73⁄4

33 35 38 40 43 47 50 53 581⁄2 65 70 73 76 86

Outside Length, L Inches 15⁄16 11⁄2 13⁄4 21⁄16 23⁄8 25⁄8 3 31⁄4 31⁄2 33⁄4 4 43⁄8 45⁄8 47⁄8 51⁄8 59⁄16 53⁄4 61⁄8 67⁄16 611⁄16 7 73⁄8 73⁄4 81⁄8 81⁄2 87⁄8 91⁄4 95⁄8 10 103⁄8 103⁄4 111⁄8 111⁄2 117⁄8 121⁄4 125⁄8 13 131⁄2 14

Outside Width, W Inches 7⁄ 8 11⁄16 11⁄4 13⁄8 111⁄16 17⁄8 21⁄16 21⁄4 21⁄2 211⁄16 27⁄8 31⁄16 31⁄4 35⁄16 33⁄4 37⁄8 41⁄8 41⁄4 49⁄16 43⁄4 5 55⁄16 51⁄2 511⁄16 57⁄8 61⁄16 63⁄8 69⁄16 63⁄4 615⁄16 71⁄8 75⁄16 75⁄8 8 83⁄8 83⁄4 91⁄8 91⁄2 97⁄8

Average Safe Working Load, Pounds 1,200 1,700 2,500 3,500 4,500 5,500 6,700 8,100 10,000 10,500 12,000 13,500 15,200 17,200 19,500 22,000 23,700 26,000 28,500 30,500 33,500 35,500 38,500 39,500 41,500

Proof Test, Poundsa 2,500 3,500 5,000 7,000 9,000 11,000 14,000 17,000 20,000 23,000 26,000 29,000 32,000 35,000 40,000 46,000 51,000 54,000 58,000 62,000 67,000 70,500 77,000 79,000 83,000

44,500 47,500 50,500 54,000 57,500 61,000 64,500 68,200 76,000 84,200 90,500 96,700 103,000 109,000

89,000 95,000 101,000 108,000 115,000 122,000 129,000 136,500 152,000 168,500 181,000 193,500 206,000 218,000

a Chains tested to U.S. Government and American Bureau of Shipping requirements.


Approximate Breaking Load, Pounds 5,000 7,000 10,000 14,000 18,000 22,000 27,000 32,500 40,000 42,000 48,000 54,000 61,000 69,000 78,000 88,000 95,000 104,000 114,000 122,000 134,000 142,000 154,000 158,000 166,000 178,000 190,000 202,000 216,000 230,000 244,000 258,000 273,000 304,000 337,000 362,000 387,000 412,000 436,000

Machinery's Handbook 27th Edition SPROCKET WHEELS AND WINDING DRUMS FOR CHAIN

391

Winding Drum Scores for Chain

Chain Size

A

3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

11⁄2 111⁄16 17⁄8 21⁄16 25⁄16 21⁄2 211⁄16 27⁄8 31⁄8 35⁄16 31⁄2

1

Chain Size

B

C

D

3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2

9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

3⁄ 16 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16

1 11⁄16 11⁄8 13⁄16

A

3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

11⁄4 17⁄16 19⁄16 13⁄4 17⁄8 21⁄16 23⁄16 23⁄8 21⁄2 211⁄16 213⁄16

1

B

C

11⁄ 32 3⁄ 8 7⁄ 16 15⁄ 32 17⁄ 32 9⁄ 16 5⁄ 8 21⁄ 32 23⁄ 32 3⁄ 4 13⁄ 16

3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2

D 1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄8 21⁄4

All dimensions are in inches.

Sprocket Wheels for Ordinary Link Chains Size of Chain

3⁄ 16

1⁄ 4

5⁄ 16

3⁄ 8

7⁄

Length of Link

13⁄8

11⁄2

13⁄4

2

21⁄4

1

16

1⁄ 2

9⁄ 16

5⁄

8

11⁄ 16

3⁄ 4

13⁄ 16

7⁄ 8

21⁄2

27⁄8

31⁄4

31⁄2

33⁄4

4

41⁄4

15⁄

41⁄2

43⁄4 31⁄2

16

1

Width of Link

13⁄

13⁄16

13⁄8

19⁄16

13⁄4

115⁄16

21⁄8

25⁄16

21⁄2

211⁄16

3

31⁄4

X

1⁄

16

3⁄

32

3⁄

32

3⁄

32

3⁄

32

3⁄ 32

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

y

3⁄

32

3⁄

32

3⁄

32

3⁄

32

3⁄

32

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

1⁄ 16

…

10.14 11.56 12.98 14.40 15.83 17.26 18.68 20.06 21.54 22.97 24.40 25.83 27.26 28.69 30.12 31.55 32.97 34.41 35.84 37.27 38.70 40.04

10.71 12.20 13.72 15.21 16.71 18.20 19.72 21.23 22.74 24.24 25.75 27.26 28.77 30.28 31.79 33.30 34.81 36.32 37.83 39.34 40.85 …

11.27 12.85 14.43 16.01 17.55 19.17 20.76 22.35 23.93 25.52 27.11 28.70 30.29 31.88 33.46 35.04 36.63 38.23 39.82 41.41 … …

11.84 13.50 15.15 16.81 18.47 20.13 21.80 23.46 25.13 26.80 28.47 30.14 31.80 33.46 35.13 36.83 38.48 40.15 … … … …

12.40 14.13 15.87 17.61 19.35 21.09 22.84 24.58 26.33 28.08 29.83 31.57 33.31 35.06 36.81 38.56 40.30 … … … … …

No. of Angle α Teeth 7 12°51′ 8 11°15′ 9 10°0′ 10 9°0′ 11 8°11′ 12 7°30′ 13 6°55′ 14 6°25′ 15 6°0′ 16 5°37′ 17 5°17′ 18 5°0′ 19 4°44′ 20 4°30′ 21 4°17′ 22 4°6′ 23 3°55′ 24 3°45′ 25 3°36′ 26 3°28′ 27 3°20′ 28 3°13′

16

D = Pitch Diameter in Inches 4.50 5.13 5.76 6.40 7.03 7.66 8.29 8.93 9.57 10.20 10.84 11.47 12.11 12.75 13.38 14.02 14.66 15.29 15.93 16.56 17.20 17.84

4.50 5.13 5.76 6.40 7.03 7.66 8.29 8.93 9.57 10.20 10.84 11.47 12.11 12.75 13.38 14.02 14.66 15.29 15.93 16.56 17.20 17.84

5.06 5.77 6.48 7.18 7.91 8.62 9.33 10.05 10.76 11.47 12.19 12.91 13.62 14.34 15.05 15.77 16.49 17.20 17.92 18.62 19.34 20.06

5.63 6.42 7.21 8.00 8.79 9.59 10.38 11.17 11.96 12.76 13.56 14.36 15.16 15.96 16.74 17.53 18.32 19.11 19.90 20.70 21.50 22.29

6.18 7.06 7.74 8.79 9.67 10.53 11.41 12.28 13.16 14.03 14.90 15.78 16.65 17.53 18.40 19.27 20.15 21.02 21.90 22.77 23.65 24.52

6.76 7.71 8.65 9.61 10.55 11.49 12.45 13.40 14.35 15.30 16.26 17.21 18.16 19.12 20.07 21.03 21.98 22.94 23.89 24.85 25.80 26.75

7.88 8.97 10.08 11.19 12.30 13.41 14.52 15.63 16.74 17.85 18.97 20.08 21.19 22.30 23.42 24.53 25.64 26.76 27.87 28.98 30.10 31.21

9.01 10.27 11.53 12.80 14.07 15.33 16.60 17.90 19.14 20.41 21.68 22.95 24.22 25.50 26.77 28.03 29.31 30.58 31.85 33.13 34.40 35.67

9.58 10.91 12.26 13.61 14.95 16.29 17.65 18.99 20.34 21.69 23.04 24.34 25.73 27.09 28.44 29.79 31.14 32.49 33.84 35.20 36.55 37.90



HOOKS, SHACKLES, AND EYES Sprocket Wheels for Ordinary Link Chains (Continued)

Additional Tables Dimensions of Forged Round Pin, Screw Pin, and Bolt Type Chain Shackles and Bolt Type Anchor Shackles

Working Load Nominal Limit (tons) Shackle Size 1⁄ 2 3⁄ 4

1 11⁄2 2 31⁄4 43⁄4 61⁄2 81⁄2 91⁄2 12 131⁄2 17 25 35

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2 13⁄4 2

A

B

C

D

7⁄ 8 11⁄32 11⁄4 17⁄16 15⁄8 2 23⁄8 213⁄16 33⁄16 39⁄16 315⁄16 43⁄8 413⁄16 53⁄4 63⁄4

15⁄ 16 17⁄ 32 21⁄ 32 23⁄ 32 13⁄ 16 11⁄16 11⁄4 17⁄16 111⁄16 113⁄16 21⁄32 21⁄4 23⁄8 27⁄8 31⁄4

5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

11⁄ 16 13⁄ 16 31⁄ 32 11⁄16 13⁄16 19⁄16 17⁄8 21⁄8 23⁄8 25⁄8

1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 2 21⁄4

3 35⁄16 35⁄8 41⁄8 5

E … … … … 17⁄8 23⁄8 213⁄16 35⁄16 33⁄4 41⁄4 411⁄16 53⁄16 53⁄4 7 73⁄4

F … … … … 15⁄8 2 23⁄8 213⁄16 33⁄16 39⁄16 315⁄16 43⁄8 413⁄16 53⁄4 63⁄4

G … … … … 13⁄ 16 11⁄16 11⁄4 17⁄16 111⁄16 113⁄16 21⁄32 21⁄4 23⁄8 27⁄8 31⁄4

All dimensions are in inches. Load limits are in tons of 2000 pounds. Source:The Crosby Group.


H … … … … 5⁄ 8 3⁄ 4 7⁄ 8 1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 2 21⁄4

I … … … … 13⁄16 19⁄16 17⁄8 21⁄8 23⁄8 25⁄8 3 35⁄16 35⁄8 41⁄8 5

Machinery's Handbook 27th Edition HOOKS, SHACKLES, AND EYES

Eye Hook With Latch Assembled

Eye Hook

393

Swivel Hook With Latch Assembled

Swivel Hook

Dimensions of Crane Hooks Feature

Capacity of Hook in Tons (tons of 2000 lbs) 1.1

A B D E G H K L R T O

1.47 0.75 2.88 0.94 0.75 0.81 0.56 4.34 3.22 0.81 0.88

1.75 0.91 3.19 1.03 0.84 0.94 0.62 4.94 3.66 0.81 0.97

2.03 1.12 3.62 1.06 1.00 1.16 0.75 5.56 4.09 0.84 1.00

2.41 1.25 4.09 1.22 1.12 1.31 0.84 6.40 4.69 1.19 1.12

2.94 1.56 4.94 1.50 1.44 1.62 1.12 7.91 5.75 1.38 1.34

A B C D E L R S T O

2 0.94 1.25 2.88 0.94 5.56 4.47 0.38 0.81 0.88

2.50 1.31 1.50 3.19 1.03 6.63 5.28 0.50 0.81 0.97

3 1.63 1.75 3.63 1.06 7.63 6.02 0.63 0.84 1

3 1.56 1.75 4.09 1.22 8.13 6.38 0.63 1.19 1.13

3.50 1.75 2 4.94 1.5 9.59 7.41 0.75 1.38 1.34

1.65

2.2

3.3

4.95

7.7

12.1

16.5

24.2

33

40.7

49.5

6.62 3.50 11.00 3.38 3.00 3.50 2.38 17.09 12.50 2.88 3.00

7.00 3.50 13.62 4.00 3.66 4.62 3.00 19.47 14.06 3.44 3.62

8.50 4.50 14.06 4.25 4.56 5.00 3.75 24.75 18.19 3.88 3.75

9.31 4.94 15.44 4.75 5.06 5.50 4.12 27.38 20.12 4.75 4.25

7 4.19 4 11 3.38 21.06 16.56 1.5 2.88 3

7 4.19 4 13.63 4 23.22 18.06 1.5 3.44 3.63

… … … … … … … … … …

… … … … … … … … … …

Dimensions for Eye Hooks 3.81 4.69 5.38 2.00 2.44 2.84 6.50 7.56 8.69 1.88 2.25 2.50 1.81 2.25 2.59 2.06 2.62 2.94 1.38 1.62 1.94 10.09 12.44 13.94 7.38 9.06 10.06 1.78 2.12 2.56 1.69 2.06 2.25 Dimensions for Swivel Hooks 4.50 5 5.63 2.31 2.38 2.69 2.50 2.75 3.13 6.5 7.56 8.69 1.88 2.25 2.5 12.41 14.50 15.88 9.59 11.13 12.03 1 1.13 1.25 1.78 2.13 2.56 1.69 2.06 2.25

Source: The Crosby Group. All dimensions are in inches. Hooks are made of alloy steel, quenched and tempered. For swivel hooks, the data are for a bail of carbon steel. The ultimate load is four times the working load limit (capacity). The swivel hook is a positioning device and is not intended to rotate under load; special load swiveling hooks must be used in such applications. Method of Making an Eye-splice.— When a loop is formed at the end of a rope by splicing the free end to the main or standing part of the rope, this is known as an eye-splice. The end of the rope is first unlaid about as far as it would be for making a short splice. After bending the end around to form a loop of the required size, the middle strand a, Fig. 8a, is tucked under a strand on the main part of the rope. The strand b is next inserted from the rear side under the strand on the main part which is just above the strand under which a was inserted. Since strand b is pushed under the strand on the main part from the rear side, it will come out at the point where strand a went in, as Fig. 8b. The third strand c is now passed over the strand under which strand a was inserted, and then under the next successive one, as Fig. 8c. These three strands are next pulled taut and then about one-third of the fiber should be cut from them; they are next tucked away by passing a strand over its adjoining one and under the next successive strand. The reason for cutting away part of the fiber or yarns is to reduce the size of the splice and give it a neater appearance. By gradually thinning out the fiber, the over-lapping strands may be given a gradual taper, as Fig. 8d which shows the completed eye-splice.



HOOKS, SHACKLES, AND EYES

Hot Dip Galvanized, Forged Steel Eye-bolts Shank

Eye Dia.

D

C

1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

2 4 21⁄4 41⁄4 21⁄2 41⁄2

A

6 31⁄4 6 8 10 12 4 6 8 10 12

B

1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

1 1 11⁄4 11⁄4 11⁄2 11⁄2 11⁄2

1 1 1 1 1 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4

2 2 2 2 2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2

Safe Shank Loada (tons) D C Regular Pattern 0.25 0.25 0.4 0.4 0.6 0.6 0.6 1.1 1.1 1.1 1.1 1.1 1.75 1.75 1.75 1.75 1.75

3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8 7⁄ 8

1 1 1 1 11⁄4 11⁄4 11⁄4 …

41⁄2 6 8 10 10 10 5 8 10 6 9 10 10 8 10 10 …

Eye Dia.

Safe Loada (tons)

A

B

11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4

3 3 3 3 3 3 31⁄2 31⁄2 31⁄2

2 2 2 2 21⁄2 21⁄2 21⁄2

4 4 4 4 5 5 5 …

2.6 2.6 2.6 2.6 2.6 2.6 3.6 3.6 3.6 5 5 5 5 7.6 7.6 7.6 …

21⁄4 23⁄4 23⁄4 31⁄4 33⁄4 33⁄4 41⁄2 41⁄2 51⁄2

1.75 2.6 2.6 3.6 5 5 7.6 7.6 10.7

…

Shoulder Pattern 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8

1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

2 4 21⁄4 41⁄4 21⁄2 41⁄2 31⁄4

1 1 11⁄4

6 4

7⁄ 8 7⁄ 8 11⁄8 11⁄8 13⁄8 13⁄8 13⁄4 13⁄4 21⁄4

0.25 0.25 0.4 0.4 0.6 0.6 1.1 1.1 1.75

5⁄ 8 3⁄ 4 3⁄ 4 7⁄ 8

1 1 11⁄4 11⁄4 11⁄2

6 41⁄2 6 5 6 9 8 12 15

11⁄4 11⁄2 11⁄2 13⁄4 2 2 21⁄2 21⁄2 3

a The ultimate or breaking load is 5 times the safe working load.

All dimensions are in inches. Safe loads are in tons of 2000 pounds. Source:The Crosby Group.

Fig. 8a. Eye -Splice

Fig. 8b. Eye -Splice

Fig. 8c. Eye -Splice

Fig. 8d. Eye -Splice


Machinery's Handbook 27th Edition HOOKS, SHACKLES, AND EYES

395

Eye Nuts and Lift Eyes

Eye Nut

Lifting Eye

Eye Nuts The general function of eye nuts is similar to that of eye-bolts. Eye nuts are utilized for a variety of applications in either the swivel or tapped design. Working Load M A C D E F S T Limit (lbs)a 1⁄ 1 1 11 3 21 1 1 520 1 ⁄4 ⁄4 1 ⁄16 ⁄32 ⁄2 ⁄4 1 ⁄16 4 5⁄ 3⁄ 21⁄ 1⁄ 1⁄ 850 11⁄4 11⁄16 111⁄16 16 4 32 2 4 3⁄ 3⁄ 9⁄ 5⁄ 1 1,250 11⁄4 15⁄8 21⁄16 8 4 16 16 7⁄ 13⁄ 3⁄ 2 1 1,700 11⁄2 21⁄2 11⁄4 16 16 8 1⁄ 13⁄ 3⁄ 2 1 2,250 11⁄4 11⁄2 21⁄2 2 16 8 5⁄ 1⁄ 2 1 3,600 21⁄2 11⁄2 33⁄16 13⁄16 8 2 3⁄ 5⁄ 3 5,200 13⁄4 23⁄8 13⁄8 11⁄8 37⁄8 4 8 7⁄ 3⁄ 2 7,200 31⁄2 15⁄8 15⁄16 45⁄16 25⁄8 8 4 7⁄ 1 4 5 10,000 21⁄4 31⁄16 17⁄8 19⁄16 8 7⁄ 4 5 12,300 31⁄16 17⁄8 19⁄16 21⁄4 11⁄8 8 1 15,500 53⁄4 41⁄2 21⁄2 31⁄2 115⁄16 17⁄8 11⁄4 5 2 2 18,500 33⁄4 61⁄4 23⁄4 11⁄8 13⁄8 4 22,500 23⁄8 55⁄8 31⁄8 21⁄4 11⁄4 63⁄4 11⁄2 4 10 40,000 2 7 4 11⁄2 33⁄8 61⁄4 a Data for eye nuts are for hot dip galvanized, quenched, and tempered forged steel.

Lifting Eyes A

C

11⁄4 15⁄8 2

1

21⁄2 3 31⁄2 4 41⁄2 55⁄8

3⁄ 4

11⁄4 11⁄2 13⁄4 2 21⁄4 21⁄2 31⁄8

D

E

F

G

H

L

S

T

11⁄16 11⁄4 11⁄2 2

19⁄ 32 3⁄ 4

1⁄ 2 9⁄ 16 13⁄ 16

3⁄ 8 1⁄ 2 5⁄ 8 11⁄ 16 7⁄ 8 15⁄ 16 11⁄16 11⁄4 11⁄2

5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

11⁄ 16 15⁄ 16 11⁄4 11⁄2 13⁄4

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

23⁄8 3

23⁄8 25⁄8 31⁄16 31⁄2 4

1 13⁄16 13⁄8 15⁄8 17⁄8 115⁄16 23⁄8

1 11⁄8 15⁄16 19⁄16 17⁄8 23⁄8

1 11⁄8 13⁄8

2 21⁄16 21⁄2 215⁄16

1 11⁄4

33⁄4 411⁄16 55⁄8 65⁄16 71⁄16 81⁄4 911⁄16

a Data for lifting eyes are for quenched and tempered forged steel.

All dimensions are in inches. Source:The Crosby Group.


Working Load Limit Threaded (lbs)a 850 1,250 2,250 3,600 5,200 7,200 10,000 12,500 18,000

Machinery's Handbook 27th Edition TABLE OF CONTENTS PROPERTIES, TREATMENT, AND TESTING OF MATERIALS THE ELEMENTS, HEAT, MASS, AND WEIGHT 398 399 399 402 403 403 405 405 407 409 409 410 410 410

STANDARD STEELS

The Elements Latent Heat Specific Heat Coefficient of Thermal Expansion Ignition Temperatures Thermal Properties of Metals Adjusting Length for Temperature Length and Radius Change Due to Temperature Specific Gravity Weights and Volumes of Fuels Weight of Natural Piles Earth or Soil Weight Molecular Weight Mol

PROPERTIES OF WOOD, CERAMICS, PLASTICS, METALS, WATER, AND AIR 411 Properties of Wood 411 Mechanical Properties 412 Weight of Wood 413 Density of Wood 413 Machinability of Wood Properties of 415 Ceramics 416 Plastics 417 Investment Casting Alloys 419 Powdered Metals 420 Elastic Properties of Materials 421 Tensile Strength of Spring Wire 421 Temperature Effects on Strength 422 Pressure and Flow of Water 422 Water Pressure 423 Flow of Water in Pipes 424 Buoyancy 425 Flow through Nozzle 427 Friction Loss 428 Properties of Air 428 Volumes and Weights 429 Density of Air 430 Expansion and Compression 432 Horsepower Required to Compress Air 432 Continuity Equation 436 Flow of Air in Pipes 436 Flow of Compressed Air in Pipes

438 Properties, Compositions, and Applications 438 Standard Steel Classification 440 Numbering Systems 440 Unified Numbering System 441 Standard Steel Numbering System 441 Binary, Ternary and Quarternary 441 Damascus Steel 442 AISI-SAE Numbers for Steels 443 AISI-SAE Designation System 444 Composition of Carbon Steels 446 Composition of Alloy Steels 448 Composition of Stainless Steels 449 Thermal Treatments of Steel 450 Applications of Steels 452 Carbon Steels 455 Carburizing Grade Alloy Steels 456 Hardenable Grade Alloy Steels 457 Characteristics of Stainless Steels 460 Chromium-Nickel Austenitic Steels 462 High-Strength, Low-Alloy Steels 464 Mechanical Properties of Steels

TOOL STEELS 475 475 478 479 481 482 488 488 490 491 493 493 494 494 495 497 497 499 499 501 502 502 502

Overview Properties of Tool Steels Tool Faults, Failures and Cures Tool Steel Properties Classification Tool Steel Selection High-Speed Tool Steels Molybdenum-Type Tungsten-Type Hot-Work Tool Steels Tungsten-Types Molybdenum-Types Cold-Work Tool Steels Oil-Hardening Types Air-Hardening Types Shock-Resisting Tool Steels Mold Steels Special-Purpose Tool Steels Water-Hardening Tool Steels Forms of Tool Steel Tolerances of Dimensions Allowances for Machining Decarburization Limits

396


Machinery's Handbook 27th Edition TABLE OF CONTENTS PROPERTIES, TREATMENT, AND TESTING OF MATERIALS HARDENING, TEMPERING, AND ANNEALING 503 503 507 509 511 511 512 513 513 515 516 516 517 517 518 518 519 521 522 526 526 527 527 527 529 529 532 533 534 536 537 538 538 541 543 544 547 547 548 548 548 549 549 549 550

NONFERROUS ALLOYS 554 Strength of Nonferrous Metals 555 Copper and Copper Alloys 555 Cast Copper Alloys 560 Wrought Copper Alloys 569 Copper–Silicon and Copper– Beryllium Alloys 569 Everdur 571 Aluminum and Aluminum Alloys 571 Characteristics 572 Temper Designations 575 Alloy Designation Systems 575 Composition of Casting Alloys 576 Properties of Casting Alloys 578 Composition of Wrought Alloys 580 Properties of Wrought Alloys 584 Clad Aluminum Alloys 584 Principal Alloy Groups 585 Type Metal 586 Magnesium Alloys 586 Alloy and Temper Designation 589 Nickel and Nickel Alloys 589 Characteristics 589 Properties of Nickel Alloys 589 Titanium and Titanium Alloys 591 Mechanical Properties Table

Heat Treatment Of Standard Steels Heat-Treating Definitions Hardness and Hardenability Case Hardening Slow Cooling Rapid Cooling or Quenching Heat-Treating Furnaces Physical Properties Hardening Hardening Temperatures Heating Steel in Liquid Baths Salt Baths Quenching Baths Hardening or Quenching Baths Quenching in Water Quenching in Molten Salt Bath Tanks for Quenching Baths Tempering Color as Temperature Indicator Case Hardening Carburization Pack-Hardening Cyanide Hardening Nitriding Process Flame Hardening Induction Hardening SAE Carbon Steels SAE Alloy Steels Metallography Chromium-Ni Austenitic Steels Stainless Chromium Steels Heat Treating High-Speed Steels Tungsten High-Speed Steels Molybdenum High-Speed Steels Nitriding High-Speed Steel Subzero Treatment of Steel Testing the Hardness of Metals Brinell Hardness Test Rockwell Hardness Test Shore’s Scleroscope Vickers Hardness Test Knoop Hardness Numbers Monotron Hardness Indicator Keep’s Test Comparative Hardness Scales

PLASTICS 592 Properties of Plastics 592 Characteristics of Plastics 593 Plastics Materials 593 Structures 593 Mixtures 594 Physical Properties 596 Mechanical Properties 601 Strength and Modulus 602 Time Related Properties 603 Thermal Properties 605 Electrical Properties 607 Chemical Resistance 607 Design Analysis 607 Structural Analysis 609 Design Stresses 610 Thermal Stresses 611 Design for Injection Moldings 615 Design for Assembly 620 Assembly with Fasteners 621 Machining Plastics 624 Development of Prototypes 625 Plastics Gearing

397



PROPERTIES, TREATMENT, AND TESTING OF MATERIALS

THE ELEMENTS, HEAT, MASS, AND WEIGHT Table 1. The Elements — Symbols, Atomic Numbers and Weights, Melting Points Name of Element

Sym bol

Actinium Aluminum Americium Antimony Argon Arsenic Astatine Barium Berkelium Beryllium Bismuth Boron Bromine Cadmium Calcium Californium Carbon Cerium Cesium Chlorine Chromium Cobalt Copper Curium Dysprosium Einsteinium Erbium Europium Fermium Fluorine Francium Gadolinium Gallium Germanium Gold Hafnium Helium Holmium Hydrogen Indium Iodine Iridium Iron Krypton Lanthanum Lawrencium Lead Lithium Lutetium Magnesium Manganese Mendelevium Mercury Molybdenum Neodymium

Ac Al Am Sb A As At Ba Bk Be Bi B Br Cd Ca Cf C Ce Cs Cl Cr Co Cu Cm Dy Es Er Eu Fm F Fr Gd Ga Ge Au Hf He Ho H In I Ir Fe Kr La Lw Pb Li Lu Mg Mn Md Hg Mo Nd

Atomic Num. Weight 89 13 95 51 18 33 85 56 97 4 83 5 35 48 20 98 6 58 55 17 24 27 29 96 66 99 68 63 100 9 87 64 31 32 79 72 2 67 1 49 53 77 26 36 57 103 82 3 71 12 25 101 80 42 60

227.028 26.9815 (243) 121.75 39.948 74.9216 (210) 137.33 (247) 9.01218 208.980 10.81 79.904 112.41 40.08 (251) 12.011 140.12 132.9054 35.453 51.996 58.9332 63.546 (247) 162.5 (252) 167.26 151.96 (257) 18.9984 (223) 157.25 69.72 72.59 196.967 178.49 4.00260 164.930 1.00794 114.82 126.905 192.22 55.847 83.80 138.906 (260) 207.2 6.941 174.967 24.305 54.9380 (258) 200.59 95.94 144.24

Melting Point, °C

Name of Element

Sym bol

Atomic Num. Weight

1050 660.37 994 ± 4 630.74 −189.2 817a 302 725 … 1278 ± 5 271.3 2079 −7.2 320.9 839 ± 2 … 3652c 798 ± 2 28.4 ± 0.01 −100.98 1857 ± 20 1495 1083.4 ± 0.2 1340 ± 40 1409 … 1522 822 ± 5 … −219.62 27b 1311 ± 1 29.78 937.4 1064.434 2227 ± 20 −272.2d 1470 −259.14 156.61 113.5 2410 1535 −156.6 920 ± 5 … 327.502 180.54 1656 ± 5 648.8 ± 0.5 1244 ± 2 … −38.87 2617 1010

Neon Neptunium Nickel Niobium Nitrogen Nobelium Osmium Oxygen Palladium Phosphorus Platinum Plutonium Polonium Potassium Praseodymium Promethium Protactinium Radium Radon Rhenium Rhodium Rubidium Ruthenium Samarium Scandium Selenium Silicon Silver Sodium Strontium Sulfur Tantalum Technetium Tellurium Terbium Thallium Thorium Thulium Tin Titanium Tungsten Unnilhexium Unnilnonium Unniloctium Unnilpentium Unnilquadium Unnilseptium Uranium Vanadium Xenon Ytterbium Yttrium Zinc Zirconium

Ne Np Ni Nb N No Os O Pd P Pt Pu Po K Pr Pm Pa Ra Rn Re Rh Rb Ru Sm Sc Se Si Ag Na Sr S Ta Tc Te Tb Tl Th Tm Sn Ti W Unh Unn Uno Unp Unq Uns U V Xe Yb Y Zn Zr

10 93 28 41 7 102 76 8 46 15 78 94 84 19 59 61 91 88 86 75 45 37 44 62 21 34 14 47 11 38 16 73 43 52 65 81 90 69 50 22 74 106 109 108 105 104 107 92 23 54 70 39 30 40

20.1179 237.048 58.69 92.9064 14.0067 (259) 190.2 15.9994 106.42 30.9738 195.08 (244) (209) 39.0938 140.908 (145) 231.0359 226.025 (222) 186.207 102.906 85.4678 101.07 150.36 44.9559 78.96 28.0855 107.868 22.9898 87.62 32.06 180.9479 (98) 127.60 158.925 204.383 232.038 168.934 118.71 47.88 183.85 (266) (266) (265) (262) (261) (261) 238.029 50.9415 131.29 173.04 88.9059 65.39 91.224

Melting Point, °C −248.67 640 ± 1 1453 2468 ± 10 −209.86 … 3045 ± 30 −218.4 1554 44.1 1772 641 254 63.25 931 ± 4 1080b 1600 700 −71 3180 1965 ± 3 38.89 2310 1072 ± 5 1539 217 1410 961.93 97.81 ± 0.03 769 112.8 2996 2172 449.5 ± 0.3 1360 ± 4 303.5 1750 1545 ± 15 231.9681 1660 ± 10 3410 ± 20 … … … … … … 1132 ± 0.8 1890 ± 10 −111.9 824 ± 5 1523 ± 8 419.58 1852 ± 2

a At 28 atm. b Approximate. c Sublimates. d At 26 atm.

Notes: Values in parentheses are atomic weights of the most stable known isotopes. Melting points at standard pressure except as noted.


Machinery's Handbook 27th Edition HEAT

399

Heat and Combustion Related Properties Latent Heat.—When a body changes from the solid to the liquid state or from the liquid to the gaseous state, a certain amount of heat is used to accomplish this change. This heat does not raise the temperature of the body and is called latent heat. When the body changes again from the gaseous to the liquid, or from the liquid to the solid state, it gives out this quantity of heat. The latent heat of fusion is the heat supplied to a solid body at the melting point; this heat is absorbed by the body although its temperature remains nearly stationary during the whole operation of melting. The latent heat of evaporation is the heat that must be supplied to a liquid at the boiling point to transform the liquid into a vapor. The latent heat is generally given in British thermal units per pound. When it is said that the latent heat of evaporation of water is 966.6, this means that it takes 966.6 heat units to evaporate 1 pound of water after it has been raised to the boiling point, 212°F. When a body changes from the solid to the gaseous state without passing through the liquid stage, as solid carbon dioxide does, the process is called sublimation. Table 2. Latent Heat of Fusion Substance Bismuth Beeswax Cast iron, gray Cast iron, white

Btu per Pound 22.75 76.14 41.40 59.40

Substance Paraffine Phosphorus Lead Silver

Btu per Pound 63.27 9.06 10.00 37.92

Substance Sulfur Tin Zinc Ice

Btu per Pound 16.86 25.65 50.63 144.00

Table 3. Latent Heat of Evaporation Liquid Alcohol, ethyl Alcohol, methyl Ammonia

Btu per Pound 371.0 481.0 529.0

Liquid Carbon bisulfide Ether Sulfur dioxide

Btu per Pound 160.0 162.8 164.0

Liquid Turpentine Water

Btu per Pound 133.0 966.6

Table 4. Boiling Points of Various Substances at Atmospheric Pressure Substance Aniline Alcohol Ammonia Benzine Bromine Carbon bisulfide

Boiling Point, °F 363 173 −28 176 145 118

Substance Chloroform Ether Linseed oil Mercury Napthaline Nitric acid Oil of turpentine

Boiling Point, °F 140 100 597 676 428 248 315

Substance Saturated brine Sulfur Sulfuric acid Water, pure Water, sea Wood alcohol

Boiling Point, °F 226 833 590 212 213.2 150

Specific Heat.—The specific heat of a substance is the ratio of the heat required to raise the temperature of a certain weight of the given substance 1°F, to the heat required to raise the temperature of the same weight of water 1°F. As the specific heat is not constant at all temperatures, it is generally assumed that it is determined by raising the temperature from 62 to 63°F. For most substances, however, specific heat is practically constant for temperatures up to 212°F. In metric units, specific heat is defined as the ratio of the heat needed to raise the temperature of a mass by 1°C, to the heat needed to raise the temperature of the same mass of water by 1°C. In the metic system, heat is measued in calories (cal), mass is in grams (g), and measurements usually taken at 15°C. Because specific heat is a dimensionless ratio, the values given in the table that follows are valid in both the US system and the metric system.



HEAT Table 5. Average Specific Heats (Btu/lb-°F) of Various Substances

Substance Alcohol (absolute) Alcohol (density 0.8) Aluminum Antimony Benzine Brass Brickwork Cadmium Carbon Charcoal Chalk Coal Coke Copper, 32° to 212° F Copper, 32° to 572° F Corundum Ether Fusel oil Glass Gold Graphite Ice Iron, cast Iron, wrought, 32° to 212° F 32° to 392° F 32° to 572° F 32° to 662° F Iron, at high temperatures: 1382° to 1832° F 1750° to 1840° F 1920° to 2190° F Kerosene

Specific Heat 0.700 0.622 0.214 0.051 0.450 0.094 0.200 0.057 0.204 0.200 0.215 0.240 0.203 0.094 0.101 0.198 0.503 0.564 0.194 0.031 0.201 0.504 0.130 0.110 0.115 0.122 0.126 0.213 0.218 0.199 0.500

Specific Heat 0.031 0.037 0.217 0.222 0.210 0.200 0.033 0.310 0.109 0.400 0.350 0.32 0.189 0.032 0.188 0.195 0.191 0.056 0.231 0.117 0.116 0.200 0.178 0.330 0.056 0.064 0.472 1.000 0.650 0.570 0.467 0.095

Substance Lead Lead (fluid) Limestone Magnesia Marble Masonry, brick Mercury Naphtha Nickel Oil, machine Oil, olive Paper Phosphorus Platinum Quartz Sand Silica Silver Soda Steel, high carbon Steel, mild Stone (generally) Sulfur Sulfuric acid Tin (solid) Tin (fluid) Turpentine Water Wood, fir Wood, oak Wood, pine Zinc

Table 6. Specific Heat of Gases (Btu/lb-°F) Gas Acetic acid Air Alcohol Ammonia Carbonic acid Carbonic oxide Chlorine

Constant Pressure 0.412 0.238 0.453 0.508 0.217 0.245 0.121

Constant Volume … 0.168 0.399 0.399 0.171 0.176 …

Gas Chloroform Ethylene Hydrogen Nitrogen Oxygen Steam

Constant Pressure 0.157 0.404 3.409 0.244 0.217 0.480

Constant Volume … 0.332 2.412 0.173 0.155 0.346

Heat Loss from Uncovered Steam Pipes.—The loss of heat from a bare steam or hotwater pipe varies with the temperature difference of the inside the pipe and that of the surrounding air. The loss is 2.15 Btu per hour, per square foot of pipe surface, per degree F of temperature difference when the latter is 100 degrees; for a difference of 200 degrees, the loss is 2.66 Btu; for 300 degrees, 3.26 Btu; for 400 degrees, 4.03 Btu; for 500 degrees, 5.18 Btu. Thus, if the pipe area is 1.18 square feet per foot of length, and the temperature difference 300°F, the loss per hour per foot of length = 1.18 × 300 × 3.26 = 1154 Btu.


Machinery's Handbook 27th Edition THERMAL PROPERTIES OF MATERIALS

401

Table 7. Values of Thermal Conductivity (k) and of Conductance (C) of Common Building and Insulating Materials Thickness, in.

Type of Material BUILDING Batt: Mineral Fiber Mineral Fiber Mineral Fiber Mineral Fiber Block: Cinder Cinder Cinder Block: Concrete Concrete Concrete Board: Asbestos Cement

Hardwood Finish Tile Glass: Architectural Mortar: Cement Plaster: Sand Sand and Gypsum Stucco Roofing: Asphalt Roll Shingle, asb. cem. Shingle, asphalt Shingle, wood

k or Ca

Max. Temp.,° F

Density, lb per cu. ft.

ka

… Avg.

… 1.61

… …

… …

… …

7⁄ 16

0.09

1.49

…

…

…

0.05

Stone:

…

…

…

…

…

6–7 81⁄2 … 4 8 12 … 4 8 12 … 1⁄ 4

0.04 0.03

Lime or Sand Wall Tile:

1 …

12.50 …

… …

… …

… …

4 8 12 Avg.

0.9 0.54 0.40 0.7

… … … …

… … … …

… … … …

… 1 1 1 …

Brick: Common Face Concrete (poured) Floor: Wood Subfloor

Thickness, in.

3–31⁄2 31⁄2–61⁄2

1⁄ 2 3⁄ 4

Plaster Plywood

Type of Material BUILDING (Continued) Siding: Metalb Wood, Med. Density

… 2–23⁄4

Mineral Fiber

k or Ca

3⁄ 4 3⁄ 4

… 0.14

… 0.90 0.58 0.53 … 1.40 0.90 0.78 … 16.5

Hollow Clay, 1-Cell Hollow Clay, 2-Cell Hollow Clay, 3-Cell Hollow Gypsum INSULATING Blanket, Mineral Fiber: Felt Rock or Slag Glass Textile

… … … … …

… … … … …

… 400 1200 350 350

… 3 to 8 6 to 12 0.65 0.65

… 0.26 0.26c 0.33 0.31

2.22

Blanket, Hairfelt

…

…

180

10

0.29

1.07

Board, Block and Pipe

…

…

…

…

…

Insulation: Amosite Asbestos Paper Glass or Slag (for Pipe) Glass or Slag (for Pipe) Glass, Cellular

… … … … … …

… … … … … …

… 1500 700 350 1000 800

… 15 to 18 30 3 to 4 10 to 15 9

… 0.32c 0.40c 0.23 0.33c 0.40

… 5.0 9.0 12.0 … 1.06 1.47

Magnesia (85%)

…

…

600

11 to 12

Avg. … … … 1 … 3⁄ 8

20.0 … 10.00 … 5.0 … 13.30

Mineral Fiber Polystyrene, Beaded Polystyrene, Rigid Rubber, Rigid Foam Wood Felt Loose Fill: Cellulose

… … … … … … …

… … … … … … …

100 170 170 150 180 … …

15 1 1.8 4.5 20 … 2.5 to 3

0.35c 0.29 0.28 0.25 0.22 0.31 … 0.27

1⁄ 2

11.10

…

…

…

2 to 5

0.28

… … … … … …

… … … … … …

… … … … 1800 1200

5 to 8 7.6 7 to 8.2 … 24 to 30 30 to 40

0.37 0.17 0.47 … 0.49c 0.75c

1 … Avg. Avg. Avg. Avg.

5.0 … 6.50 4.76 2.27 1.06

Mineral Fiber Perlite Silica Aerogel Vermiculite Mineral Fiber Cement: Clay Binder Hydraulic Binder

a Units are in Btu/hr-ft2-°F. Where thickness is given as 1 inch, the value given is thermal conductivity (k); for other thicknesses the value given is thermal conductance (C). All values are for a test mean temperature of 75°F, except those designated with c, which are for 100°F. b Over hollowback sheathing. c Test mean temperature 100°F, see footnote a . Source: American Society of Heating, Refrigerating and Air-Conditioning Engineers, Inc.: Handbook of Fundamentals.



THERMAL PROPERTIES OF MATERIALS Table 8. Typical Values of Coefficient of Linear Thermal Expansion for Thermoplastics and Other Commonly Used Materials Materiala

in/in/deg F × 10−5

cm/cm/deg C × 10−5

Liquid Crystal—GR Glass Steel Concrete

0.3 0.4 0.6 0.8

0.6 0.7 1.1 1.4

Copper Bronze Brass Aluminum Polycarbonate—GR Nylon—GR TP polyester—GR Magnesium Zinc ABS—GR

0.9 1.0 1.0 1.2 1.2 1.3 1.4 1.4 1.7 1.7

1.6 1.8 1.8 2.2 2.2 2.3 2.5 2.5 3.1 3.1

Materiala

in/in/deg F × 10−5

cm/cm/deg C × 10−5

1.7 1.8 2.0 2.0

3.1 3.2 3.6 3.6

2.2 3.0 3.6 3.8 4.0 4.5 4.8 4.8 6.9 7.2

4.0 5.4 6.5 6.8 7.2 8.1 8.5 8.6 12.4 13.0

ABS—GR Polypropylene—GR Epoxy—GR Polyphenylene sulfide—GR Acetal—GR Epoxy Polycarbonate Acrylic ABS Nylon Acetal Polypropylene TP Polyester Polyethylene

a GR = Typical glass fiber-reinforced material. Other plastics materials shown are unfilled.

Table 9. Linear Expansion of Various Substances between 32 and 212°F Expansion of Volume = 3 × Linear Expansion Linear Expansion for 1°F

Substance Brick Cement, Portland Concrete Ebonite Glass, thermometer Glass, hard Granite Marble, from to

0.0000030 0.0000060 0.0000080 0.0000428 0.0000050 0.0000040 0.0000044 0.0000031 0.0000079

Linear Expansion for 1°F

Substance Masonry, brick from to Plaster Porcelain Quartz, from to Slate Sandstone Wood, pine

0.0000026 0.0000050 0.0000092 0.0000020 0.0000043 0.0000079 0.0000058 0.0000065 0.0000028

Table 10. Coefficients of Heat Transmission Metal

Btu per Second

Metal

Btu per Second

Aluminum Antimony Brass, yellow Brass, red Copper

0.00203 0.00022 0.00142 0.00157 0.00404

German silver Iron Lead Mercury Steel, hard

0.00050 0.00089 0.00045 0.00011 0.00034

Metal Steel, soft Silver Tin Zinc …

Btu per Second 0.00062 0.00610 0.00084 0.00170 …

Heat transmitted, in British thermal units, per second, through metal 1 inch thick, per square inch of surface, for a temperature difference of 1°F

Table 11. Coefficients of Heat Radiation Surface Cast-iron, new Cast-iron, rusted Copper, polished Glass Iron, ordinary Iron, sheet-, polished Oil

Btu per Hour 0.6480 0.6868 0.0327 0.5948 0.5662 0.0920 1.4800

Surface Sawdust Sand, fine Silver, polished Tin, polished Tinned iron, polished Water …

Btu per Hour 0.7215 0.7400 0.0266 0.0439 0.0858 1.0853 …

Heat radiated, in British thermal units, per square foot of surface per hour, for a temperature difference of 1° F


Machinery's Handbook 27th Edition PROPERTIES OF MATERIALS

403

Table 12. Freezing Mixtures Temperature Change,°F Mixture

From

To

Common salt (NaCl), 1 part; snow, 3 parts Common salt (NaCl), 1 part; snow, 1 part Calcium chloride (CaCl2), 3 parts; snow, 2 parts

32 32 32

±0 −0.4 −27

Calcium chloride (CaCl2), 2 parts; snow, 1 part

32

−44

Sal ammoniac (NH4Cl), 5 parts; saltpeter (KNO3), 5 parts; water,16 parts

50

+10

Sal ammoniac (NH4Cl), 1 part; saltpeter (KNO3), 1 part; water,1 part

46

−11

Ammonium nitrate (NH4NO3), 1 part; water, 1 part

50

+3

Potassium hydrate (KOH), 4 parts; snow, 3 parts

32

−35

Ignition Temperatures.—The following temperatures are required to ignite the different substances specified: Phosphorus, transparent, 120°F; bisulfide of carbon, 300°F; gun cotton, 430°F; nitro-glycerine, 490°F; phosphorus, amorphous, 500°F; rifle powder, 550°F; charcoal, 660°F; dry pine wood, 800°F; dry oak wood, 900°F. Table 13. Typical Thermal Properties of Various Metals Material and Alloy Designation a

Density, ρ lb/in3

Melting Point, °F solidus

liquidus

Conductivity, k, Btu/hr-ft-°F

Specific Heat, C, Btu/lb/°F

Coeff. of Expansion, α µin/in-°F

82.5 99.4 109.2 111 80 73 104 70

0.23 0.22 0.22 0.22 0.22 0.23 0.23 0.23

12.8 13.1 12.9 12.9 13.2 13.2 13.0 13.1

61 226 205 62 187 218 109 92 70 67 71 67 67 67 67 71 67 40 50 31.4 33.9 21.8 17

0.09 0.09 0.09 0.10 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09 0.09

11.8 9.8 9.9 9.9 9.8 9.8 10.2 10.4 11.1 11.3 11.6 11.2 11.3 11.4 11.4 11.6 11.8 9.9 9.6 9.0 9.2 9.0 9.0

Aluminum Alloys 2011 2017 2024 3003 5052 5086 6061 7075

0.102 0.101 0.100 0.099 0.097 0.096 0.098 0.101

Manganese Bronze C11000 (Electrolytic tough pitch) C14500 (Free machining Cu) C17200, C17300 (Beryllium Cu) C18200 (Chromium Cu) C18700 (Leaded Cu) C22000 (Commercial bronze, 90%) C23000 (Red brass, 85%) C26000 (Cartridge brass, 70%) C27000 (Yellow brass) C28000 (Muntz metal, 60%) C33000 (Low-leaded brass tube) C35300 (High-leaded brass) C35600 (Extra-high-leaded brass) C36000 (Free machining brass) C36500 (Leaded Muntz metal) C46400 (Naval brass) C51000 (Phosphor bronze, 5% A) C54400 (Free cutting phos. bronze) C62300 (Aluminum bronze, 9%) C62400 (Aluminum bronze, 11%) C63000 (Ni-Al bronze) Nickel-Silver

0.302 0.321 0.323 0.298 0.321 0.323 0.318 0.316 0.313 0.306 0.303 0.310 0.306 0.307 0.307 0.304 0.304 0.320 0.321 0.276 0.269 0.274 0.314

995 995 995 1190 1100 1085 1080 890

1190 1185 1180 1210 1200 1185 1200 1180

Copper-Base Alloys 1590 1941 1924 1590 1958 1750 1870 1810 1680 1660 1650 1660 1630 1630 1630 1630 1630 1750 1700 1905 1880 1895 1870

1630 1981 1967 1800 1967 1975 1910 1880 1750 1710 1660 1720 1670 1660 1650 1650 1650 1920 1830 1915 1900 1930 2030



PROPERTIES OF MATERIALS Table 13. Typical Thermal Properties of Various Metals (Continued)

Material and Alloy Designation a

Density, ρ lb/in3

Melting Point, °F

Conductivity, k, Btu/hr-ft-°F

Specific Heat, C, Btu/lb/°F

43.3 7.5 7.5 6.5 10 12.6 10.1 10.1

0.11 0.10 0.10 0.10 0.10 0.10 0.10 0.10

8.5 6.9 6.2 7.2 8.7 7.7 7.6 7.6

9.4 9.4 9.2 9.4 6.5 8.8 9.0 8.2 9.4 8.3 9.3 9.3 9.3 9.4 14.4 15.6 14.4 14.4 13.8 14.8 15.1 13.8 14.0 14.0 12.1 21.2

0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.12 0.11 0.12 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.12 0.11

9.4 9.6 9.0 9.6 9.6 9.6 8.3 8.8 8.8 9.2 9.2 9.2 9.3 9.6 5.5 6.0 5.8 5.7 6.2 5.7 5.8 5.2 5.7 5.6 5.8 6.2

0.265

29.5

0.12

7.5

0.25 0.25 0.25 0.25 0.25 0.25 0.25

28.0

28.0

0.25 0.16 0.16 0.15 0.15 0.12 0.12

9.0 4.5 6.3

0.12 0.13 0.19

solidus

liquidus

Coeff. of Expansion, α µin/in-°F

Nickel-Base Alloys Nickel 200, 201, 205 Hastelloy C-22 Hastelloy C-276 Inconel 718 Monel Monel 400 Monel K500 Monel R405

0.321 0.314 0.321 0.296 0.305 0.319 0.306 0.319

S30100 S30200, S30300, S30323 S30215 S30400, S30500 S30430 S30800 S30900, S30908 S31000, S31008 S31600, S31700 S31703 S32100 S34700 S34800 S38400 S40300, S41000, S41600, S41623 S40500 S41400 S42000, S42020 S42200 S42900 S43000, S43020, S43023 S43600 S44002, S44004 S44003 S44600 S50100, S50200

0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.280 0.270 0.280

2615 2475 2415 2300 2370 2370 2400 2370

2635 2550 2500 2437 2460 2460 2460 2460

Stainless Steels 2550 2550 2500 2550 2550 2550 2550 2550 2500 2500 2550 2550 2550 2550 2700 2700 2600 2650 2675 2650 2600 2600 2500 2500 2600 2700

2590 2590 2550 2650 2650 2650 2650 2650 2550 2550 2600 2650 2650 2650 2790 2790 2700 2750 2700 2750 2750 2750 2700 2750 2750 2800

Cast Iron and Steel Malleable Iron, A220 (50005, 60004, 80002) Grey Cast Iron Ductile Iron, A536 (120–90–02) Ductile Iron, A536 (100–70–03) Ductile Iron, A536 (80–55–06) Ductile Iron, A536 (65–45–120) Ductile Iron, A536 (60–40–18) Cast Steel, 3%C

liquidus approximately, 2100 to 2200, depending on composition

liquidus, 2640

20.0 18.0 20.8

5.8 5.9–6.2 5.9–6.2 5.9–6.2 5.9–6.2 5.9–6.2 7.0

Titanium Alloys Commercially Pure Ti-5Al-2.5Sn Ti-8Mn

0.163 0.162 0.171

3000 2820 2730

3040 3000 2970

5.1 5.3 6.0

a Alloy designations correspond to the AluminumAssociation numbers for aluminum alloys and to the unified numbering system (UNS) for copper and stainless steel alloys. A220 and A536 are ASTM specified irons.


Machinery's Handbook 27th Edition LENGTH/TEMPERATURE CHANGES

405

Adjusting Lengths for Reference Temperature.—The standard reference temperature for industrial length measurements is 20 degrees Celsius (68 degrees Fahrenheit). For other temperatures, corrections should be made in accordance with the difference in thermal expansion for the two parts, especially when the gage is made of a different material than the part to be inspected. Example:An aluminum part is to be measured with a steel gage when the room temperature is 30 °C. The aluminum part has a coefficient of linear thermal expansion, αPart = 24.7 × 10−6 mm/mm-°C, and for the steel gage, αGage = 10.8 × 10−6 mm/mm-°C. At the reference temperature, the specified length of the aluminum part is 20.021 mm. What is the length of the part at the measuring (room) temperature? ∆L, the change in the measured length due to temperature, is given by: ∆L = L ( T R – T 0 ) ( α Part – α Gage ) = 20.021 ( 30 – 20 ) ( 24.7 – 10.8 ) × 10 = 2782.919 × 10

–6

–6

mm

≈ 0.003 mm

where L = length of part at reference temperature; TR = room temperature (temperature of part and gage); and, T0 = reference temperature. Thus, the temperature corrected length at 30°C is L + ∆L = 20.021 + 0.003 = 20.024 mm. Length Change Due to Temperature.—Table 14 gives changes in length for variations from the standard reference temperature of 68°F (20°C) for materials of known coefficients of expansion, α. Coefficients of expansion are given in tables on pages 402, 403, 415, 416, 427, and elsewhere. Example:In Table 14, for coefficients between those listed, add appropriate listed values. For example, a length change for a coefficient of 7 is the sum of values in the 5 and 2 columns. Fractional interpolation also is possible. Thus, in a steel bar with a coefficient of thermal expansion of 6.3 × 10−6 = 0.0000063 in/in = 6.3 µin/in of length/°F, the increase in length at 73°F is 25 + 5 + 1.5 = 31.5 µin/in of length. For a steel with the same coefficient of expansion, the change in length, measured in degrees C, is expressed in microns (micrometers)/meter (µm/m) of length. Alternatively, and for temperatures beyond the scope of the table, the length difference due to a temperature change is equal to the coefficient of expansion multiplied by the change in temperature, i.e., 䉭L = α䉭T. Thus, for the previous example, 䉭L = 6.3 × (73 − 68) = 6.3 × 5 = 31.5 µin/in. Change in Radius of Thin Circular Ring with Temperature.—Consider a circular ring of initial radius r, that undergoes a temperature change 䉭T. Initially, the circumference of the ring is c = 2πr. If the coefficient of expansion of the ring material is α, the change in circumference due to the temperature change is 䉭c = 2πr α䉭T The new circumference of the ring will be: cn = c + 䉭c = 2πr + 2πrα䉭T = 2πr(1 + α䉭T) Note: An increase in temperature causes 䉭c to be positive, and a decrease in temperature causes 䉭c to be negative. As the circumference increases, the radius of the circle also increases. If the new radius is R, the new circumference 2πR. For a given change in temperature, 䉭T, the change in radius of the ring is found as follows: c n = 2πR = 2πr ( 1 + α ∆T )

R = r + rα ∆T

∆r = R – r = rα ∆T



LENGTH/TEMPERATURE CHANGES Table 14. Differences in Length in Inches/Inch (Microns/Meter) for Changes from the Standard Temperature of 68°F (20°C)

Temperature Deg. F C 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98

−10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50

Coefficient of Thermal Expansion of Material per Degree F (C) × 106 3 4 5 10 15 20 25 for °F in microinches/inch of length (µin/in) Total Change in Length from Standard Temperature { for °C or °K in microns/meter of length (µm/m) 1

2

−30 −29 −28 −27 −26 −25 −24 −23 −22 −21 −20 −19 −18 −17 −16 −15 −14 −13 −12 −11 −10 −9 −8 −7 −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

−60 −58 −56 −54 −52 −50 −48 −46 −44 −42 −40 −38 −36 −34 −32 −30 −28 −26 −24 −22 −20 −18 −16 −14 −12 −10 −8 −6 −4 −2 0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60

−90 −87 −84 −81 −78 −75 −72 −69 −66 −63 −60 −57 −54 −51 −48 −45 −42 −39 −36 −33 −30 −27 −24 −21 −18 −15 −12 −9 −6 −3 0 3 6 9 12 15 18 21 24 27 30 33 36 39 42 45 48 51 54 57 60 63 66 69 72 75 78 81 84 87 90

−120 −116 −112 −108 −104 −100 −96 −92 −88 −84 −80 −76 −72 −68 −64 −60 −56 −52 −48 −44 −40 −36 −32 −28 −24 −20 −16 −12 −8 −4 0 4 8 12 16 20 24 28 32 36 40 44 48 52 56 60 64 68 72 76 80 84 88 92 96 100 104 108 112 116 120

−150 −145 −140 −135 −130 −125 −120 −115 −110 −105 −100 −95 −90 −85 −80 −75 −70 −65 −60 −55 −50 −45 −40 −35 −30 −25 −20 −15 −10 −5 0 5 10 15 20 25 30 35 40 45 50 55 60 65 70 75 80 85 90 95 100 105 110 115 120 125 130 135 140 145 150

−300 −290 −280 −270 −260 −250 −240 −230 −220 −210 −200 −190 −180 −170 −160 −150 −140 −130 −120 −110 −100 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

−450 −435 −420 −405 −390 −375 −360 −345 −330 −315 −300 −285 −270 −255 −240 −225 −210 −195 −180 −165 −150 −135 −120 −105 −90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90 105 120 135 150 165 180 195 210 225 240 255 270 285 300 315 330 345 360 375 390 405 420 435 450

−600 −580 −560 −540 −520 −500 −480 −460 −440 −420 −400 −380 −360 −340 −320 −300 −280 −260 −240 −220 −200 −180 −160 −140 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380 400 420 440 460 480 500 520 540 560 580 600


−750 −725 −700 −675 −650 −625 −600 −575 −550 −525 −500 −475 −450 −425 −400 −375 −350 −325 −300 −275 −250 −225 −200 −175 −150 −125 −100 −75 −50 −25 0 25 50 75 100 125 150 175 200 225 250 275 300 325 350 375 400 425 450 475 500 525 550 575 600 625 650 675 700 725 750

30

−900 −870 −840 −810 −780 −750 −720 −690 −660 −630 −600 −570 −540 −510 −480 −450 −420 −390 −360 −330 −300 −270 −240 −210 −180 −150 −120 −90 −60 −30 0 30 60 90 120 150 180 210 240 270 300 330 360 390 420 450 480 510 540 570 600 630 660 690 720 750 780 810 840 870 900

Machinery's Handbook 27th Edition SPECIFIC GRAVITY

407

Properties of Mass and Weight Specific Gravity.—Specific gravity is a number indicating how many times a certain volume of a material is heavier than an equal volume of water. The density of water differs slightly at different temperatures, so the usual custom is to make comparisons on the basis that the water has a temperature of 62°F. The weight of 1 cubic inch of pure water at 62°F is 0.0361 pound. If the specific gravity of any material is known, the weight of a cubic inch of the material, therefore, can be found by multiplying its specific gravity by 0.0361. To find the weight per cubic foot of a material, multiply the specific gravity by 62.355. If the weight of a cubic inch of a material is known, the specific gravity is found by dividing the weight per cubic inch by 0.0361. Example:Given the specific gravity of cast iron is 7.2. Then, the weight of 5 cubic inches of cast iron = 7.2 × 0.0361 × 5 = 1.2996 pounds. Example:Given the weight of a cubic inch of gold is 0.697 pound. Then, the specific gravity of gold = 0.697 ÷ 0.0361 = 19.31 If the weight per cubic foot of a material is known, the specific gravity is found by multiplying this weight by 0.01604. Table 15. Average Specific Gravity of Various Substances Specific Gravity

a Weight

Substance

lb/ft3

Substance

Specific Gravity

aWeight

lb/ft3

Specific Gravity

aWeight

Substance ABS Acrylic Aluminum bronze Aluminum, cast Aluminum, wrought Asbestos Asphaltum Borax Brick, common Brick, fire Brick, hard Brick, pressed Brickwork, in cement Brickwork, in mortar CPVC Cement, Portland (set) Chalk Charcoal Coal, anthracite Coal, bituminous Concrete Earth, loose Earth, rammed Emery

1.05 1.19 7.8 2.6 2.7 2.4 1.4 1.8 1.8 2.3 2.0 2.2 1.8 1.6 1.55 3.1 2.3 0.4 1.5 1.3 2.2 … … 4.0

66 74 486 160 167 150 87 112 112 143 125 137 112 100 97 193 143 25 94 81 137 75 100 249

Glass Glass, crushed Gold, 22 carat fine Gold, pure Granite Gravel Gypsum Ice Iron, cast Iron, wrought Iron slag Lead Limestone Marble Masonry Mercury Mica Mortar Nickel, cast Nickel, rolled Nylon 6, Cast PTFE Phosphorus Plaster of Paris

2.6 … 17.5 19.3 2.7 … 2.4 0.9 7.2 7.7 2.7 11.4 2.6 2.7 2.4 13.56 2.8 1.5 8.3 8.7 1.16 2.19 1.8 1.8

162 74 1091 1204 168 109 150 56 447 479 168 711 162 168 150 845.3 175 94 517 542 73 137 112 112

Platinum Polycarbonate Polyethylene Polypropylene Polyurethane Quartz Salt, common Sand, dry Sand, wet Sandstone Silver Slate Soapstone Steel Sulfur Tar, bituminous Tile Trap rock Water at 62°F White metal Zinc, cast Zinc, sheet … …

21.5 1.19 0.97 0.91 1.05 2.6 … … … 2.3 10.5 2.8 2.7 7.9 2.0 1.2 1.8 3.0 1.0 7.3 6.9 7.2 … …

1342 74 60 57 66 162 48 100 125 143 656 175 168 491 125 75 112 187 62.355 457 429 450 … …

lb/ft3

a The weight per cubic foot is calculated on the basis of the specific gravity except for those substances that occur in bulk, heaped, or loose form. In these instances, only the weights per cubic foot are given because the voids present in representative samples make the values of the specific gravities inaccurate.

Specific Gravity of Gases.—The specific gravity of gases is the number that indicates their weight in comparison with that of an equal volume of air. The specific gravity of air is 1, and the comparison is made at 32°F. Values are given in Table 16. Specific Gravity of Liquids.—The specific gravity of liquids is the number that indicates how much a certain volume of the liquid weighs compared with an equal volume of water, the same as with solid bodies. Specific gravity of various liquids is given in Table 17. The density of liquid is often expressed in degrees on the hydrometer, an instrument for determining the density of liquids, provided with graduations made to an arbitrary scale. The hydrometer consists of a glass tube with a bulb at one end containing air, and arranged with a weight at the bottom so as to float in an upright position in the liquid, the density of



SPECIFIC GRAVITY Table 16. Specific Gravity of Gases At 32°F Gas

Sp. Gr. 1.000 0.920 1.601 0.592 1.520 0.967 2.423

Aira Acetylene Alcohol vapor Ammonia Carbon dioxide Carbon monoxide Chlorine

Gas Ether vapor Ethylene Hydrofluoric acid Hydrochloric acid Hydrogen Illuminating gas Mercury vapor

Sp. Gr. 2.586 0.967 2.370 1.261 0.069 0.400 6.940

Gas Marsh gas Nitrogen Nitric oxide Nitrous oxide Oxygen Sulfur dioxide Water vapor

Sp. Gr. 0.555 0.971 1.039 1.527 1.106 2.250 0.623

a 1 cubic foot of air at 32°F and atmospheric pressure weighs 0.0807 pound.

which is to be measured. The depth to which the hydrometer sinks in the liquid is read off on the graduated scale. The most commonly used hydrometer is the Baumé, see Table 18. The value of the degrees of the Baumé scale differs according to whether the liquid is heavier or lighter than water. The specific gravity for liquids heavier than water equals 145 ÷ (145 − degrees Baumé). For liquids lighter than water, the specific gravity equals 140 ÷ (130 + degrees Baumé). Table 17. Specific Gravity of Liquids Liquid Acetic acid Alcohol, commercial Alcohol, pure Ammonia Benzine Bromine Carbolic acid Carbon disulfide Cotton-seed oil Ether, sulfuric

Sp. Gr. 1.06 0.83 0.79 0.89 0.69 2.97 0.96 1.26 0.93 0.72

Liquid Fluoric acid Gasoline Kerosene Linseed oil Mineral oil Muriatic acid Naphtha Nitric acid Olive oil Palm oil

Sp. Gr. 1.50 0.70 0.80 0.94 0.92 1.20 0.76 1.50 0.92 0.97

Liquid Petroleum oil Phosphoric acid Rape oil Sulfuric acid Tar Turpentine oil Vinegar Water Water, sea Whale oil

Sp. Gr. 0.82 1.78 0.92 1.84 1.00 0.87 1.08 1.00 1.03 0.92

Table 18. Degrees on Baumé’s Hydrometer Converted to Specific Gravity Deg. Baumé 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

Specific Gravity for Liquids Heavier than Lighter than Water Water 1.000 1.007 1.014 1.021 1.028 1.036 1.043 1.051 1.058 1.066 1.074 1.082 1.090 1.099 1.107 1.115 1.124 1.133 1.142 1.151 1.160 1.169 1.179 1.189 1.198 1.208 1.219

… … … … … … … … … … 1.000 0.993 0.986 0.979 0.972 0.966 0.959 0.952 0.946 0.940 0.933 0.927 0.921 0.915 0.909 0.903 0.897

Deg. Baumé 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53

Specific Gravity for Liquids Heavier than Lighter Water than Water 1.229 1.239 1.250 1.261 1.272 1.283 1.295 1.306 1.318 1.330 1.343 1.355 1.368 1.381 1.394 1.408 1.422 1.436 1.450 1.465 1.480 1.495 1.510 1.526 1.542 1.559 1.576

0.892 0.886 0.881 0.875 0.870 0.864 0.859 0.854 0.849 0.843 0.838 0.833 0.828 0.824 0.819 0.814 0.809 0.805 0.800 0.796 0.791 0.787 0.782 0.778 0.773 0.769 0.765

Deg. Baumé 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80

Specific Gravity for Liquids Heavier Lighter than Water than Water 1.593 1.611 1.629 1.648 1.667 1.686 1.706 1.726 1.747 1.768 1.790 1.813 1.836 1.859 1.883 1.908 1.933 1.959 1.986 2.014 2.042 2.071 2.101 2.132 2.164 2.197 2.230


0.761 0.757 0.753 0.749 0.745 0.741 0.737 0.733 0.729 0.725 0.721 0.718 0.714 0.710 0.707 0.704 0.700 0.696 0.693 0.689 0.686 0.683 0.679 0.676 0.673 0.669 0.666

Machinery's Handbook 27th Edition WEIGHT OF PILES

409 lb/ft3;

Average Weights and Volumes of Solid Fuels.—Anthracite coal, 55–65 34–41 ft3/ton (2240 lb); 67 lb/bushel. Bituminous coal, 50–55 lb/ft3; 41–45 ft3/ton (2240 lb); 60 lb/bushel.Charcoal, 8–18.5 lb/ft3; 120–124 ft3/ton (2240 lb); 20 lb/bushel. Coke, 28 lb/ft3; 80 ft3/ton (2240 lb); 40 lb/bushel. How to Estimate the Weight of Natural Piles.—To calculate the upper and lower limits of the weight of a substance piled naturally on a circular plate, so as to form a cone of material, use the equation: W = MD 3 (1) where W = weight, lb; D = diameter of plate, ft. (Fig. 1a); and, M = materials factor, whose upper and lower limits are given in Table 19b. For a rectangular plate, calculate the weight of material piled naturally by means of the following equation: W = MRA 3 (2) where A and B = the length and width in ft., respectively, of the rectangular plate in Fig. 1b, with B ≤ A; and, R = is a factor given in Table 19a as a function of the ratio B/A. Example:Find the upper and lower limits of the weight of dry ashes piled naturally on a plate 10 ft. in diameter. Using Equation (1), M = 4.58 from Table 19b, the lower limit W = 4.58 × 103 = 4,580 lb. For M = 5.89, the upper limit W = 5.89 × 103 = 5,890 lb. Example:What weight of dry ashes rests on a rectangular plate 10 ft. by 5 ft.? For B/A = 5/10 = 0.5, R = 0.39789 from Table 19a. Using Equation (2), for M = 4.58, the lower limit W = 4.58 × 0.39789 × 103 = 1,822 lb. For M = 5.89, the upper limit W = 5.89 × 0.39789 × 103 = 2,344lb.

B

A D

Fig. 1a. Conical Pile

Fig. 1b. Rectangular Pile

Table 19a. Factor R as a function of B/A (B ≤ A) B/A

R

B/A

R

B/A

R

B/A

R

B/A

R

B/A

R

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.10 0.11 0.12 0.13 0.14 0.15 0.16 0.17

0.00019 0.00076 0.00170 0.00302 0.00470 0.00674 0.00914 0.01190 0.01501 0.01846 0.02226 0.02640 0.03088 0.03569 0.04082 0.04628 0.05207

0.18 0.19 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.28 0.29 0.30 0.31 0.32 0.33 0.34

0.05817 0.06458 0.07130 0.07833 0.08566 0.09329 0.10121 0.10942 0.11792 0.12670 0.13576 0.14509 0.15470 0.16457 0.17471 0.18511 0.19576

0.35 0.36 0.37 0.38 0.39 0.40 0.41 0.42 0.43 0.44 0.45 0.46 0.47 0.48 0.49 0.50 0.51

0.20666 0.21782 0.22921 0.24085 0.25273 0.26483 0.27717 0.28973 0.30252 0.31552 0.32873 0.34216 0.35579 0.36963 0.38366 0.39789 0.41231

0.52 0.53 0.54 0.55 0.56 0.57 0.58 0.59 0.60 0.61 0.62 0.63 0.64 0.65 0.66 0.67 0.68

0.42691 0.44170 0.45667 0.47182 0.48713 0.50262 0.51826 0.53407 0.55004 0.56616 0.58243 0.59884 0.61539 0.63208 0.64891 0.66586 0.68295

0.69 0.70 0.71 0.72 0.73 0.74 0.75 0.76 0.77 0.78 0.79 0.80 0.81 0.82 0.83 0.84 0.85

0.70015 0.71747 0.73491 0.75245 0.77011 0.78787 0.80572 0.82367 0.84172 0.85985 0.87807 0.89636 0.91473 0.93318 0.95169 0.97027 0.98891

0.86 0.87 0.88 0.89 0.90 0.91 0.92 0.93 0.94 0.95 0.96 0.97 0.98 0.99 1.00 … …

1.00761 1.02636 1.04516 1.06400 1.08289 1.10182 1.12078 1.13977 1.15879 1.17783 1.19689 1.21596 1.23505 1.25414 1.27324 … …



WEIGHT OF PILES Table 19b. Limits of Factor M for Various Materials Material

Factor M

Material

Factor M

Material

Factor M

Almonds, whole Aluminum chips Aluminum silicate Ammonium chloride Asbestos, shred Ashes, dry Ashes, damp Asphalt, crushed Bakelite, powdered Baking powder Barium carbonate Bauxite, mine run Beans, navy, dry Beets, sugar, shredded Bicarbonate of soda Borax Boric acid Bronze chips Buckwheat Calcium lactate Calcium oxide (lime) Carbon, ground Casein Cashew nuts Cast iron chips Cement, Portland Cinders, coal Clay, blended for tile Coal, anthracite, chestnut Coal, bituminous, sized Coal, ground Cocoa, powdered Coconut, shredded Coffee beans

2.12–3.93 0.92–1.96 3.7–6.41 3.93–6.81 2.62–3.27 4.58–5.89 6.24–7.80 3.4–5.89 3.93–5.24 3.1–5.37 9.42 5.9–6.69 3.63 0.47–0.55 3.10 3.78–9.16 4.16–7.20 3.93–6.54 2.8–3.17 3.4–3.8 3.30 2.51 2.72–4.71 4.19–4.84 17.02–26.18 6.8–13.09 3.02–5.24 5.89 2.43 2.64–4.48 2.90 3.93–4.58 2.62–2.88 2.42–5.89

Coffee, ground Coke, pulverized Copper oxide, powdered Cork, granulated Corn on cob Corn sugar Cottonseed, dry, de–linted Diatoinaceous earth Dicalcium phosphate Ebonite, crushed Epsoin salts Feldspar, ground Fish scrap Flour Flue dust Flourspar (Flourite) Graphite, flake Gravel Gypsum, calcined Hominy Hops, dry Kaolin clay Lead silicate, granulated Lead sulphate, pulverized Lime ground Limestone, crushed Magnesium chloride Malt, dry, ground Manganese sulphate Marble, crushed Mica, ground Milk, whole, powdered Oats Orange peel, dry

1.89–3.27 2.21 20.87 1.57–1.96 1.29–1.33 2.34–4.06 1.66–5.24 0.83–1.83 5.63 4.91–9.16 3.02–6.54 8.51–9.16 5.24–6.54 5.61–10.43 2.65–3.40 10.73–14.40 3.02–5.24 6.8–13.18 6.04–6.59 2.8–6.54 4.58 12.32–21.34 25.26 24.09 7.85 6.42–11.78 4.32 1.66–2.88 5.29–9.16 6.8–12.44 1.24–1.43 2.62 1.74–2.86 1.96

Peanuts, unshelled Peanuts, shelled Peas, dry Potassium carbonate Potasiuin sulphate Pumice Rice, bran Rubber, scrap, ground Salt, dry, coarse Salt, dry, fine Saltpeter Salt rock, crushed Sand, very fine Sawdust, dry Sesame seed Shellac, powdered Slag, furnace, granular Soap powder Sodium nitrate Sodium sulphite Sodium sulphate Soybeans Steel chips, crushed Sugar, refined Sulphur Talcum powder Tin oxide, ground Tobacco stems Trisodium phosphate Walnut shells, crushed Wood chips, fir Zinc sulphate … …

1.13–3.14 2.65–5.89 2.75–3.05 3.85–6.68 5.5–6.28 5.24–5.89 1.51–2.75 2.11–4.58 3.02–8.38 5.29–10.47 6.05–10.47 4.58 7.36–9 0.95–2.85 2.04–4.84 2.34–4.06 4.53–8.51 1.51–3.27 3.96–4.66 10.54 6.92 3.48–6.28 7.56–19.63 3.78–7.2 4.5–6.95 4.37–5.9 9.17 1.96–3.27 4.53–7.85 2.65–5.24 2.49–2.88 8.85–11.12 … …

Earth or Soil Weight.—Loose earth has a weight of approximately 75 pounds per cubic foot and rammed earth, 100 pounds per cubic foot. The solid crust of the earth, according to an estimate, is composed approximately of the following elements: Oxygen, 44.0 to 48.7 per cent; silicon, 22.8 to 36.2 per cent; aluminum, 6.1 to 9.9 per cent; iron, 2.4 to 9.9 per cent; calcium, 0.9 to 6.6 per cent; magnesium, 0.1 to 2.7 per cent; sodium, 2.4 to 2.5 per cent; potassium, 1.7 to 3.1 per cent. Molecular Weight.—The smallest mass of a chemical combination which can be conceived of as existing and yet preserving its chemical properties is known as a molecule. The molecular weight of a chemical compound is equal to the sum of the atomic weights of the atoms contained in the molecule, and are calculated from the atomic weights, when the symbol of the compound is known. The atomic weight of silver is 107.88; of nitrogen, 14.01; and of oxygen, 16; hence, the molecular weight of silver-nitrate, the chemical formula of which is AgNO3 equals 107.88 + 14.01 + (3 × 16) = 169.89. Mol.—The term “mol” is used as a designation of quantity in electro-chemistry, and indicates the number of grams of a substance equal to its molecular weight. For example, one mol of siliver-nitrate equals 169.89 grams, the molecular weight of silver-nitrate being 169.89.


Machinery's Handbook 27th Edition WOOD

411

PROPERTIES OF WOOD, CERAMICS, PLASTICS, METALS, WATER, AND AIR Properties of Wood Mechanical Properties of Wood.—Wood is composed of cellulose, lignin, ash-forming minerals, and extractives formed into a cellular structure. (Extractives are substances that can be removed from wood by extraction with such solvents as water, alcohol, acetone, benzene, and ether.) Variations in the characteristics and volumes of the four components and differences in the cellular structure result in some woods being heavy and some light, some stiff and some flexible, and some hard and some soft. For a single species, the properties are relatively constant within limits; therefore, selection of wood by species alone may sometimes be adequate. However, to use wood most effectively in engineering applications, the effects of physical properties or specific characteristics must be considered. The mechanical properties listed in the accompanying Table 1 were obtained from tests on small pieces of wood termed “clear” and “straight grained” because they did not contain such characteristics as knots, cross grain, checks, and splits. However, these test pieces did contain such characteristics as growth rings that occur in consistent patterns within the piece. Since wood products may contain knots, cross grain, etc., these characteristics must be taken into account when assessing actual properties or when estimating actual performance. In addition, the methods of data collection and analysis have changed over the years during which the data in Table 1 have been collected; therefore, the appropriateness of the data should be reviewed when used for critical applications such as stress grades of lumber. Wood is an orthotropic material; that is, its mechanical properties are unique and independent in three mutually perpendicular directions—longitudinal, radial, and tangential. These directions are illustrated in the following figure.

Modulus of Rupture: The modulus of rupture in bending reflects the maximum load-carrying capacity of a member and is proportional to the maximum moment borne by the member. The modulus is an accepted criterion of strength, although it is not a true stress because the formula used to calculate it is valid only to the proportional limit. Work to Maximum Load in Bending: The work to maximum load in bending represents the ability to absorb shock with some permanent deformation and more or less injury to a specimen; it is a measure of the combined strength and toughness of the wood under bending stress. Maximum Crushing Strength: The maximum crushing strength is the maximum stress sustained by a compression parallel-to-grain specimen having a ratio of length to least diameter of less than 11. Compression Perpendicular to Grain: Strength in compression perpendicular to grain is reported as the stress at the proportional limit because there is no clearly defined ultimate stress for this property.



WOOD

Shear Strength Parallel to Grain: Shear strength is a measure of the ability to resist internal slipping of one part upon another along the grain. The values listed in the table are averages of the radial and tangential shears. Tensile Strength Perpendicular to Grain: The tensile strength perpendicular to the grain is a measure of the resistance of wood to forces acting across the grain that tend to split the material. Averages of radial and tangential measurements are listed. Table 1. Mechanical Properties of Commercially Important U.S. Grown Woods Static Bending

Use the first number in each column for GREEN wood; use the second number for DRY wood.

Modulus of Rupture (103 psi)

Basswood, American Cedar, N. white Cedar, W. red Douglas Fir, coasta Douglas Fir, interior W. Douglas Fir, interior N. Douglas Fir, interior S. Fir, balsam Hemlock, Eastern Hemlock, Mountain Hemlock, Western Pine, E. white Pine, Virginia Pine, W. white Redwood, old-growth Redwood, young-growth Spruce, Engelmann Spruce, red Spruce, white

5.0 4.2 5.2 7.7 7.7 7.4 6.8 5.5 6.4 6.3 6.6 4.9 7.3 4.7 7.5 5.9 4.7 6.0 5.0

Work to Max Load (in.-lb/in.3)

8.7 5.3 6.5 5.7 7.5 5.0 12.4 7.6 12.6 7.2 13.1 8.1 11.9 8.0 9.2 4.7 8.9 6.7 11.5 11.0 11.3 6.9 9.9 5.2 13.0 10.9 9.7 5.0 10.0 7.4 7.9 5.7 9.3 5.1 10.8 6.9 9.4 6.0

7.2 4.8 5.8 9.9 10.6 10.5 9.0 5.1 6.8 10.4 8.3 8.3 13.7 8.8 6.9 5.2 6.4 8.4 7.7

Maximum Crushing Strength (103 psi)

Compression Strength Perpendicular to Grain (psi)

2.22 1.90 2.77 3.78 3.87 3.47 3.11 2.63 3.08 2.88 3.36 2.44 3.42 2.43 4.20 3.11 2.18 2.72 2.35

170 230 240 380 420 360 340 190 360 370 280 220 390 190 420 270 200 260 210

4.73 3.96 4.56 7.23 7.43 6.90 6.23 5.28 5.41 6.44 7.20 5.66 6.71 5.04 6.15 5.22 4.48 5.54 5.18

370 310 460 800 760 770 740 404 650 860 550 580 910 470 700 520 410 550 430

Shear Strength Parallel to Grain (psi) 600 620 770 900 940 950 950 662 850 930 860 680 890 680 800 890 640 750 640

990 850 990 1,130 1,290 1,400 1,510 944 1,060 1,540 1,290 1,170 1,350 1,040 940 1,110 1,200 1,290 970

Tensile Strength Perp. to Grain (psi) 280 240 230 300 290 340 250 180 230 330 290 250 400 260 260 300 240 220 220

350 240 220 340 350 390 330 180 … … 340 420 380 … 240 250 350 350 360

a Coast: grows west of the summit of the Cascade Mountains in OR and WA. Interior west: grows in CA and all counties in OR and WA east of but adjacent to the Cascade summit. Interior north: grows in remainder of OR and WA and ID, MT, and WY. Interior south: grows in UT, CO, AZ, and NM.

Results of tests on small, clear, straight-grained specimens. Data for dry specimens are from tests of seasoned material adjusted to a moisture content of 12%. Source:U.S. Department of Agriculture:Wood Handbook.

Weight of Wood.—The weight of seasoned wood per cord is approximately as follows, assuming about 70 cubic feet of solid wood per cord: beech, 3300 pounds; chestnut, 2600 pounds; elm, 2900 pounds; maple, 3100 pounds; poplar, 2200 pounds; white pine, 2200 pounds; red oak, 3300 pounds; white oak, 3500 pounds. For additional weights of green and dry woods, see Table 2. Weight per Foot of Wood, Board Measure.—The following is the weight in pounds of various kinds of woods, commercially known as dry timber, per foot board measure: white oak, 4.16; white pine, 1.98; Douglas fir, 2.65; short-leaf yellow pine, 2.65; red pine, 2.60; hemlock, 2.08; spruce, 2.08; cypress, 2.39; cedar, 1.93; chestnut, 3.43; Georgia yellow pine, 3.17; California spruce, 2.08. For other woods, divide the weight/ft3 from Table 2 by 12 to obtain the approximate weight per board foot. Effect of Pressure Treatment on Mechanical Properties of Wood.—The strength of wood preserved with creosote, coal-tar, creosote-coal-tar mixtures, creosote-petroleum mixtures, or pentachlorophenol dissolved in petroleum oil is not reduced. However, waterborne salt preservatives contain chemicals such as copper, arsenic, chromium, and ammonia, which have the potential of affecting mechanical properties of treated wood and


Machinery's Handbook 27th Edition WOOD

413

causing mechanical fasteners to corrode. Preservative salt-retention levels required for marine protection may reduce bending strength by 10 per cent or more. Density of Wood.—The following formula can be used to find the density of wood in lb/ft3 as a function of its moisture content. M⎞ G ⎞ ⎛ 1 + -------ρ = 62.4 ⎛ -------------------------------------------⎝ 1 + G × 0.009 × M⎠ ⎝ 100⎠ where ρ is the density, G is the specific gravity of wood, and M is the moisture content expressed in per cent.

35 54 53 56 45 46 45 50 50 41 62 63 61 48 58 47 54 50 45 56

30 35 44 37 25 27 35 34 28 29 45 51 … 36 48 34 40 38 33 44

Species Oak, red Oak, white Pine, lodgepole Pine, northern white Pine, Norway Pine, ponderosa Pines, southern yellow: Pine, loblolly Pine, longleaf Pine, shortleaf Pine, sugar Pine, western white Poplar, yellow Redwood Spruce, eastern Spruce, Engelmann Spruce, Sitka Sycamore Tamarack Walnut, black

Green

Species Douglas fir, Rocky Mt. region Elm, American Elm, rock Elm, slippery Fir, balsam Fir, commercial white Gum, black Gum, red Hemlock, eastern Hemlock, western Hickory, pecan Hickory, true Honeylocust Larch, western Locust, black Maple, bigleaf Maple, black Maple, red Maple, silver Maple, sugar

Airdry

28 34 41 38 26 26 45 44 38 31 33 22 23 23 35 30 28 24 32 34

Green

46 52 48 46 43 42 54 57 50 36 37 28 26 27 45 55 49 46 51 38

Airdry

Green

Species Alder, red Ash, black Ash, commercial white Ash, Oregon Aspen Basswood Beech Birch Birch, paper Cedar, Alaska Cedar, eastern red Cedar, northern white Cedar, southern white Cedar, western red Cherry, black Chestnut Cottonwood, eastern Cottonwood, northern black Cypress, southern Douglas fir, coast region

Airdry

Table 2. Weights of American Woods, in Pounds per Cubic Foot

64 63 39 36 42 45

44 47 29 25 34 28

53 55 52 52 35 38 50 34 39 33 52 47 58

36 41 36 25 27 28 28 28 23 28 34 37 38

Source: United States Department of Agriculture

Machinability of Wood.—The ease of working wood with hand tools generally varies directly with the specific gravity of the wood; the lower the specific gravity, the easier the wood is to cut with a sharp tool. A rough idea of the specific gravity of various woods can be obtained from the preceding table by dividing the weight of wood in lb/ft3 by 62.355. A wood species that is easy to cut does not necessarily develop a smooth surface when it is machined. Three major factors, other than specific gravity, influence the smoothness of the surface obtained by machining: interlocked and variable grain, hard deposits in the grain, and reaction wood. Interlocked and variable grain is a characteristic of many tropical and some domestic species; this type of grain structure causes difficulty in planing quarter sawn boards unless careful attention is paid to feed rates, cutting angles, and sharpness of the knives. Hard deposits of calcium carbonate, silica, and other minerals in the grain tend to dull cutting edges quickly, especially in wood that has been dried to the usual in service moisture content. Reaction wood results from growth under some physical stress such as occurs in leaning trunks and crooked branches. Generally, reaction wood occurs as tension wood in hardwoods and as compression wood in softwoods. Tension wood is particularly troublesome, often resulting in fibrous and fuzzy surfaces, especially in woods of lower density. Reaction wood may also be responsible for pinching saw blades, resulting in burning and dulling of teeth. The Table 3 rates the suitability of various domestic hardwoods for machining. The data for each species represent the percentage of pieces machined that successfully met the listed quality requirement for the processes. For example, 62 per cent of the black walnut



WOOD

pieces planed came out perfect, but only 34 per cent of the pieces run on the shaper achieved good to excellent results. Table 3. Machinability and Related Properties of Various Domestic Hardwoods Planing

Shaping

Type of Wood

Perfect

Good to Excellent

Alder, red Ash Aspen Basswood Beech Birch Birch, paper Cherry, black Chestnut Cottonwood Elm, soft Hackberry Hickory Magnolia Maple, bigleaf Maple, hard Maple, soft Oak, red Oak, white Pecan Sweetgum Sycamore Tanoak Tupelo, black Tupelo, water Walnut, black Willow Yellow-poplar

61 75 26 64 83 63 47 80 74 21 33 74 76 65 52 54 41 91 87 88 51 22 80 48 55 62 52 70

20 55 7 10 24 57 22 80 28 3 13 10 20 27 56 72 25 28 35 40 28 12 39 32 52 34 5 13

Turning Boring Quality Required Fair to Good to Excellent Excellent 88 79 65 68 90 80 … 88 87 70 65 77 84 79 8 82 76 84 85 89 86 85 81 75 79 91 58 81

Mortising

Sanding

Fair to Excellent

Good to Excellent

52 58 60 51 92 97 … 100 70 52 75 72 98 32 80 95 34 95 99 98 53 96 100 24 33 98 24 63

… 75 … 17 49 34 … … 64 19 66 … 80 37 … 38 37 81 83 … 23 21 … 21 34 … 24 19

64 94 78 76 99 97 … 100 91 70 94 99 100 71 100 99 80 99 95 100 92 98 100 82 62 100 71 87

The data above represent the percentage of pieces attempted that meet the quality requirement listed.

Nominal and Minimum Sizes of Sawn Lumber Type of Lumber

Thickness (inches) Nominal, Tn

3⁄ 4

Face Widths (inches) Green

Nominal, Wn

Dry

Green

2 to 4

Wn − 1⁄2

Wn − 7⁄16

5 to 7

Wn − 1⁄2

Wn − 3⁄8

8 to 16

Wn − 3⁄4

Wn − 1⁄2

2 to 4

Wn − 1⁄2

Wn − 7⁄16

11⁄4

1

11⁄2

11⁄4

25⁄ 32 11⁄32 19⁄32

2

11⁄2

19⁄16

1 Boards

Dry

21⁄2

2

21⁄16

5 to 6

Wn − 1⁄2

Wn − 3⁄8

Dimension

3

21⁄2

29⁄16

8 to 16

Wn − 3⁄4

Wn − 1⁄2

Lumber

31⁄2

3

31⁄16

…

…

…

4

31⁄2

39⁄16

…

…

…

41⁄2

4

41⁄16

…

…

…

…

Tn − 1⁄2

5 and up

…

Wn − 1⁄2

Timbers

5 and up

Source: National Forest Products Association: Design Values for Wood Construction. Moisture content: dry lumber ≤ 19%; green lumber > 19%. Dimension lumber refers to lumber 2 to 4 inches thick (nominal) and 2 inches or greater in width. Timbers refers to lumber of approximately square cross-section, 5 × 5 inches or larger, and a width no more than 2 inches greater than the thickness.



Tabulated Properties of Ceramics, Plastics, and Metals Typical Properties of Ceramics Materials Material Machinable Glass Ceramic

Glass-Mica

Machining Grades

Aluminum Silicate Alumina Silicate Silica Foam TiO2 (Titania) Lava (Grade A) Zirconium Phosphate ZrO2 ZrO2·SiO2 (Zircon)

2MgO·2Al2O3·5SiO2 (Cordierite)

(Alumina)

Flexural Strength (103 psi)

Mohs’s Hardnessc

Operating Temperature (°F)

Tensile Strength (103 psi)

Compressive Strength (103 psi)

Thermal Conductivityd (Btu-ft-hr-ft2-°F)

0.09 0.11 0.10 0.09–0.10 0.10 0.13–0.17 0.14 0.10 0.08 0.08 0.03 0.14

1000 400 380 400 380 300–325 350 80 100 70 80 100

4.1–7.0 6 5.2 10.5–11.2 9.4 11–11.5 10.3 2.5 2.9 … 0.3 4.61

15 14 12.5–13 11 9–10 9 4.5 10 … 0.4 20

48 Ra 5.5 5.0 90 Rh 90 Rh 90 Rh 90 Rh 1–2 6.0 … NA 8

1472 700 1100 750 1100 700–750 1300 1000 2100 2370 2000 1800

… … … 6 5 6–6.5 6 … … … … 7.5

50 40 32 40–45 32 33–35 30 12 25 … 1.4 100

0.85 0.24 0.34 0.24–0.29 0.34 0.29–0.31 0.3 0.92 0.75 0.38 0.10 …

0.08 0.11 0.21

80 NA …

1.83 0.5 6.1

9 7.5 102

6 NA 1300 V

2000 2800 …

2.5 … …

40 30 261

0.92 0.4 (approx.) 1.69

0.11

2MgO·SiO2 (Forsterite) MgO·SiO2 (Steatite)

Al2O3

Coeff. of Expansionb (10−6 in./in.-°F)

94% 96% 99.5% 99.9%

220

1.94

16

10

90

…

7.5

1825

0.11

240

5.56

20

7.5

1825

10

85

4.58

0.09–0.10

210–240

3.83–5.44

18–21

7.5

1825

8.5–10

80–90

3.17–3.42

0.06 0.08 0.09 0.13

60 100–172 200 210

0.33 1.22–1.28 1.33 3.33

3.4 8–12 15 44

6.5 7–7.5 8 9

2000 2000 2000 2700

2.5 3.5–3.7 4 20

18.5 30–40 50 315

1.00 1.00 1.83 16.00

0.13–0.14 0.14 0.14

210 200 …

3.5–3.7 3.72 3.75

48–60 70 72

9 9 9

2600–2800 2700 2900

25 28 …

375 380 400

20.3–20.7 21.25 …


415

a Obtain specific gravity by dividing density in lb/in.3 by 0.0361; for density in lb/ft3, multiply lb/in.3 by 1728; for g/cm3, multiply density in lb/in.3 by 27.68; for kg/m3, multiply density in lb/in.3 by 27,679.9. b To convert coefficient of expansion to 10−6 in./in.-°C, multiply table value by 1.8. c Mohs’s Hardness scale is used unless otherwise indicated as follows: Ra and Rh for Rockwell A and H scales, respectively; V for Vickers hardness. d To convert conductivity from Btu-ft/hr-ft2-°F to cal-cm/sec-cm2-°C, divide by 241.9.

PROPERTIES OF CERAMICS

Molding Grades

Densitya (lb/in.3)

Dielectric Strength (V/mil)


Material

Specific Gravity

0.038 0.037 0.056 0.051 0.051 0.043 0.043 0.056 0.067 0.050 0.042 0.047 0.041 0.042 0.049 0.079 0.050 0.064 0.050 0.043 0.046 0.035 0.034 0.030 0.051 0.047 0.033 0.045 0.038

1.05 1.03 1.55 1.41 1.41 1.19 1.19 1.55 1.87 1.39 1.16 1.30 1.14 1.16 1.36 2.19 1.39 1.77 1.38 1.19 1.27 0.97 0.94 0.83 1.41 1.30 0.91 1.25 1.05

… … … 380 … 500 500 … … … 295 … 600 … 1300 480 500 260 … 380 480 475 710 … 560 380 600 425 …

Coeff. of Expansionb (10−6 in/in-°F)

Tensile Modulus (103 psi)

Izod Impact (ft-lb/in of notch)

Flexural Modulus (ksi at 73°F)

% Elongation

Hardnessc

Max. Operating Temp. (°F)

53.0 … … 47.0 58.0 35.0 15.0 34.0 11.1 … 45.0 … 45.0 … 39.0 50.0 29.5 60.0 11.1 37.5 … 20.0 19.0 … … … 96.0 31.0 …

275 200 1000 437 310 400 750 400 … 1350 380 … 390 … 500 225 550 320 … 345 430 156 110 220 300 … 155 360 …

7 … 0.9 2 … 0.5 14 3 8 2.8 1.4 … 1 2.2 0.5 3 0.8 3 2.4 14 1.1 6 No Break 2.5 1.5 0.5 0.75 1.2 …

300 330 715 400 320 400 800 400 1 1400 450 … … … 400 80 400 200 1000 340 480 160 130 … … 550 200 390 …

… … … 13 … 2.7 2.1 4 … … 20 … 240 … 70 350 31–40 80 … 110 … 900 450 … … … 120 50 465–520

105 Rr 105 Rr 94 Rm 94 Rm 94 Rm 94 Rm 94 Rm … 101 Rm 119 Rr 100 Rr … 118 Rr … … … 110 Rr 100 Rr 100 Rm 74 Rm … … 64 Rr … … … 92 Rr 120 Rr …

200 … … … 200 180 311 212 260 … 210 … 230 … 230 … 170 180 248 290 … 180 176 … … … 150 325 …

a To obtain specific gravity, divide density in lb/in3 by 0.0361; for density in lb/ft3, multiply lb/in3 by 1728; for g/cm3, multiply density in lb/in3 by 27.68; for kg/m3, multiply density in lb/in3 by 27,679.9. b To convert coefficient of expansion to 10−6 in/in-°C, multiply table value by 1.8. c Hardness value scales are as follows: Rm for Rockwell M scale; Rr for Rockwell R scale.


PROPERTIES OF PLASTICS

ABS, Extrusion Grade ABS, High Impact Acetal, 20% Glass Acetal, Copolymer Acetyl, Homopolymer Acrylic Azdel CPVC Fiber Glass Sheet Nylon 6, 30% Glass Nylon 6, Cast Nylon 6⁄6, Cast Nylon 6⁄6, Extruded Nylon 60L, Cast PET, unfilled PTFE (Teflon) PVC PVDF Phenolics Polycarbonate Polyetherimide Polyethylene, HD Polyethylene, UHMW Polymethylpentene Polymid, unfilled Polyphenylene Sulfide Polypropylene Polysulfone Polyurethane

Densitya (lb/in3)

416

Typical Properties of Plastics Materials Dielectric Strength (V/mil)

Machinery's Handbook 27th Edition PROPERTIES OF INVESTMENT CASTING ALLOYS

417

Mechanical Properties of Various Investment Casting Alloys Alloy Designation

Material Condition


0.2% Yield Strengtha (103 psi)

% Elongation

Hardness

22–30 28–36 27–40 28–39 25–32 36–45 24–38 25–45 48–55

3–7 3–10 3–9 1–8 4–8 2–5 1.5–5 2–5 3–5

… … … … … … … … …

30–40 45–55 40–50 60–70 25–40 60–70 18 18–30 11–20 14–25 32 … 40–45 90–130 40–140 50–55 … … 20–40

10–20 6–10 6–10 5–8 16–24 8–16 20 20–35 15–25 20–30 24 4–50 15–20 3–8 1–15 18–23 1–4 15–20 20–30

80–85 Rb 91–96 Rb 91–96 Rb 93–98 Rb 60–65 Rb 95–100 Rb … 40–50 Rb … 30–35 Rb … 35–42 Rb 50–55 Rb 90–95 Rb 60 Rb–38 Rc 75–80 Rb 25–44 Rc 80–85 Rb 70–78 Rb

30–35 25–40 20–30 0–15 20–30 0–15 20–25 0–10 20–25 0–10 5–10 0–3 12–20 0–3 5–10 5–20 5–20 5–10 5–20 5–20 10–20 5–10 10–20 7–20 5–20

50–55 Rb 80 Rb 75 Rb 20–50 Rc 80 Rb 25–52 Rc 100 Rb 25–57 Rc 100 Rb 30–60 Rc 25 Rc 30–60 Rc 30 Rc 37–50 Rc 30–58 Rc 23–49 Rc 29–57 Rc 25–58 Rc 25–48 Rc 20–55 Rc 20–32 Rc 30–60 Rc 20–45 Rc 25–50 Rc 30–60 Rc

Aluminum 356 A356 A357 355, C355 D712 (40E) A354 RR-350 Precedent 71 KO-1

As Cast As Cast As Cast As Cast As Cast As Cast As Cast As Cast As Cast

32–40 38–40 33–50 35–50 34–40 47–55 32–45 35–55 56–60

Copper-Base Alloysa Al Bronze C (954) Al Bronze D (955) Manganese Bronze, A Manganese Bronze, C Silicon Bronze Tin Bronze Lead. Yellow Brass (854) Red Brass Silicon Brass Pure Copper Beryllium Cu 10C (820) Beryllium Cu 165C (824) Beryllium Cu 20C (825) Beryllium Cu 275C (828) Chrome Copper

As Cast Heat-Treated As Cast Heat-Treated … … … … … … … … As Cast Hardened … As Cast Hardened As Cast …

75–85 90–105 90–100 110–120 65–75 110–120 45 40–50 30–50 30–40 70 20–30 45–50 90–100 70–155 70–80 110–160 80–90 33–50

Carbon and Low-Alloy Steels and Iron IC 1010 IC 1020 IC 1030 IC 1035 IC 1045 IC 1050 IC 1060 IC 1090 IC 2345 IC 4130 IC 4140 IC 4150 IC 4330 IC 4340 IC 4620 IC 6150, IC 8740 IC 8620 IC 8630 IC 8640

Annealed Annealed Annealed Hardened Annealed Hardened Annealed Hardened Annealed Hardened Annealed Hardened Annealed Hardened Hardened Hardened Hardened Hardened Hardened Hardened Hardened Hardened Hardened Hardened Hardened

50–60 60–70 65–75 85–150 70–80 90–150 80–90 100–180 90–110 125–180 100–120 120–200 110–150 130–180 130–200 130–170 130–200 140–200 130–190 130–200 110–150 140–200 100–130 120–170 130–200

30–35 40–45 45–50 60–150 45–55 85–150 50–60 90–180 50–65 100–180 55–70 100–180 70–80 130–180 110–180 100–130 100–155 120–180 100–175 100–180 90–130 120–180 80–110 100–130 100–180



PROPERTIES OF INVESTMENT CASTING ALLOYS Mechanical Properties of Various Investment Casting Alloys (Continued) Material Condition

Alloy Designation


0.2% Yield Strengtha (103 psi)

% Elongation

Hardness

140–200 110–150 140–180 100–140 37–43 40–50 70–80

0–10 7–20 1–7 6–12 30–35 18–24 3–10

… … 30–65 Rc 25–48 Rc 55 Rb 143–200 Bhn 243–303 Bhn

75–160 75–160 130–210 75–105 140–160 150–165 110–145 75–85 100–120

5–12 3–8 0–5 5–20 6–20 6–12 5–15 20–30 10–25

94 Rb–45 Rc 94 Rb–45 Rc 30–52 Rc 20–40 Rc 34–44 Rc … 26–38 Rc 94–100 Rb 28–32 Rc

40–50 32–36 30–35 30–45 30–40 25–35 30–40

35–50 30–40 35–45 35–60 30–45 35–45 35–45

90 Rb (max) 90 Rb (max) 90 Rb (max) 90 Rb (max) 90 Rb (max) 90 Rb (max) 90 Rb (max)

50–60 45–55 45–55 41–45 … 25–30 35–40 40–55 32–38 55–65 85–100 60–80 33–40 25–35

8–12 8–12 8–12 10–15 12–20 30–40 10–20 15–30 25–35 5–10 0 10–20 25–35 25–40

90–100 Rb 90–100 Rb 90 Rb–25 Rc 85–96 Rb … 50–60 Rb 80–90 Rb 10–20 Rc 65–75 Rb 20–28 Rc 32–38 Rc 20–30 Rc 67–78 Rb 65–85 Rb

65–95 60–75 75–90 60–70 70–80 50–60

8–20 15–25 6–10 15–20 8–15 15–30

24–32 Rc 20–25 Rc 20–30 Rc 30–36 Rc 25–34 Rc 90–100 Rb

Carbon and Low-Alloy Steels and Iron (Continued) IC 8665 IC 8730 IC 52100 IC 1722AS 1.2% Si Iron Ductile Iron, Ferritic Ductile Iron, Pearlitic

Hardened Hardened Hardened Hardened … Annealed Normalized

170–220 120–170 180–230 130–170 50–60 60–80 100–120

Hardenable Stainless Steel CA-15 IC 416 CA-40 IC 431 IC 17–4 Am-355 IC 15–5 CD-4M Cu

Hardened Hardened Hardened Hardened Hardened Hardened Hardened Annealed Hardened

CF-3, CF-3M, CF-8, CF-8M, IC 316F CF-8C CF-16F CF-20 CH-20 CN-7M IC 321, CK-20

Annealed Annealed Annealed Annealed Annealed Annealed Annealed

95–200 95–200 200–225 110–160 150–190 200–220 135–170 100–115 135–145

Austenitic Stainless Steels 70–85 70–85 65–75 65–75 70–80 65–75 65–75

Nickel-Base Alloys Alloy B Alloy C

RH Monel Monel E M-35 Monel

Annealed As Cast Annealed AC to 24°C AC to 816°C As Cast As Cast Annealed As Cast Annealed Hardened As Cast As Cast As Cast

Cobalt 21 Cobalt 25 Cobalt 31 Cobalt 36 F75 N-155

As Cast As Cast As Cast As Cast As Cast Sol. Anneal

Alloy Xb Invar (Fe–Ni alloy) In 600 (Inconel) In 625 (Inconel) Monel 410 S Monel

75–85 80–95 75–95 63–70 35–45 50–60 65–75 80–100 65–75 100–110 120–140 100–110 65–80 65–80

Cobalt-Base Alloys 95–130 90–120 105–130 90–105 95–110 90–100

a For copper alloys, yield strength is determined by 0.5% extension under load or 0.2% offset method. A number in parentheses following a copper alloy indicates the UNS designation of that alloy (for example, Al Bronze C (954) identifies the alloy as UNS C95400). b AC = air cooled to temperature indicated. Source: Investment Casting Institute. Mechanical properties are average values of separately cast test bars, and are for reference only. Items marked … indicates data are not available. Alloys identified by IC followed by an SAE designation number (IC 1010 steel, for example) are generally similar to the SAE material although properties and chemical composition may be different.


Machinery's Handbook 27th Edition PROPERTIES OF POWDER METAL ALLOYS

419

Typical Properties of Compressed and Sintered Powdered Metal Alloys Strength (103 psi) Alloy Number a and Nominal Composition (%)

Density (g/cc)

Hardness

Transverse Rupture

Ultimate Tensile

Yield

% Elongation

Copper Base … CZP-3002

100Cu 70Cu, 1.5Pb, Bal. Zn

CNZ-1818 63Cu, 17.5Ni, Bal. Zn CTG-1004 10Sn, 4.4C, Bal. Cu CTG-1001 10Sn, 1C, Bal. Cu

7.7–7.9

81–82 Rh

54–68

24–34

…

10–26

8

75 Rh

…

33.9

…

24

7.9

90 Rh

73

34

20

11

7

67 Rh

20

9.4

6.5

6

6.5

45 Rh

25.8

15.1

9.6

9.7

Iron Base (Balance of composition, Fe) FC-2015

23.5Cu, 1.5C

FC-0800

8Cu, 0.4C

6.5

65 Rb

80

52.4

48.5

0

6.3–6.8

39–55 Rb

75–100

38–54

32–47

1 or less

FX-2008

20Cu, 1C

FN-0408

4Ni, 1–2Cu, 0.75C

7.3

93 Rb

164.2

72.3

57.7

2

6.3–7

64–84 Rb

70–107

37–63

30–47

1–1.6

F-0000

100Fe

6.5

FN-0005

0.45C, 0.50 MnS

6.4–6.8

26 Rf

37.7

15.7

11

5.7

66–78 Rf

44–61

…

…

F-0000

0.02C, 0.45P

6.6–7.2

35–50 Rb

…

90–125

…

29–38

3.9–5.5

F-0008

0.6–0.9C

6.2–7

FC-0508

0.6–0.9C, 4–6Cu

5.9–6.8

50–70 Rb

61–100

35–57

30–40

3

>3

1200–1800

2500–3000

Milling of Plastics: Peripheral cutting with end mills is used for edge preparation, slotting and similar milling operations, and end cutting can also be used for facing operations. Speeds for milling range from 800 to 1400 ft/min for peripheral end milling of many thermoplastics and from 400 to 800 ft/min for many thermosets. However, slower speeds are generally used for other milling operations, with some thermoplastics being machined at 300–500 ft/min, and some thermosets at 150–300 ft/min. Adequate support and suitable feed rates are very important. A table feed that is too low will generate excessive heat and cause surface cracks, loss of dimensional accuracy, and poor surface finish. Too high a feed rate will produce a rough surface. High-speed steel tools (M2, M3, M7, or T15) are generally used, but for glass-reinforced nylon, silicone, polyimide, and allyl, carbide (C2) is recommended. New Techniques: Lasers can be used for machining plastics, especially sheet laminates, although their use may generate internal stresses. Ultrasonic machining has no thermal, chemical, or electrical reaction with the workpiece and can produce holes down to 0.003 in. diameter, tight tolerances (0.0005 in.), and very smooth finishes (0.15 µin. with No. 600 boron carbide abrasive powder). Water-jet cutting using pressures up to 60,000 lb/in.2 is widely used for plastics and does not introduce stresses into the material. Tolerances of ± 0.004 in. can be held, depending on the equipment available. Process variables, pressures, feed rates, and the nozzle diameter depend on the material being cut. This method does not work with hollow parts unless they can be filled with a solid core. Development of Prototypes.—Prototypes are made for testing of properties such as stress and fatigue resistance, to find ways to improve quality and reliability, to improve tooling, and to reduce time to market. Prototyping may answer questions about finish, sink marks that result from contraction, witness lines from mold joints, ejector pin marks, knit or weld lines, texturing, moldability, shrinkage, mechanical strength, pull-out resistance of inserts, electrical properties, and problems of mating with other parts. Prototypes of moldings are made in five major steps including design; refining the design; making a model (physical or computer); making a mold; and producing parts. The model may be made from wood, plaster, plastics (by machining), or a metal. Some 90 per cent of prototypes are made by modern CAD/CAM methods that allow holding of dimensional tolerances of 2–3 per cent of drawing specifications. Prototypes can also be made by a process called stereo lithography that uses a tank of photosensitive liquid polymer, an x-y scanning, ultraviolet laser with a beam diameter of 0.010 in., a z-axis elevator platform, and a controlling computer. The platform height is adjusted so that a suitable thickness of liquid polymer covers its surface. The laser beam is focused on the liquid surface and hardens the polymer at this point by heating. The CAD representation of the prototype is described by a model in which thin (0.005– 0.020 in.) cross sections can be isolated. Data representing the lowest level of the prototype are used to move the platform so that a layer of the polymer corresponding to the lowest “slice” is hardened. The platform is then lowered, the liquid polymer flows over the hard-


Machinery's Handbook 27th Edition PLASTICS GEAR DESIGN

625

ened layer, and the platform is again raised, less an amount equal to the next “slice.” The process is repeated for successive “slices” of the prototype, which is thus built up gradually to form a hollow, three-dimensional shape corresponding to the model in the CAD program. The part thus produced is fairly brittle but can be used for visual examination, design verification, and marketing evaluation, and can be replicated from other materials such as plastics or metals by casting or other methods. Finishing and decorating methods used for plastics parts include spray painting, vacuum metallizing, hot stamping, silk screening, and plating. Conductive coatings may be applied to inside surfaces, usually by flame- or arc-spraying, to dissipate static electricity and provide electromagnetic shielding. Thorough cleaning is essential. Materials such as polyethylene, polypropylene, and acetal have waxlike surfaces that may not be painted easily or may need pretreatment or special primers. Many amorphous plastics are easy to paint. Suitable coatings include polyurethane-, epoxy-, acrylic-, alkyd-, and vinyl-based paints. Oven curing may distort parts made from non-heat-resistant materials. Vacuum metallizing and sputter-plating require application of a special base coat and a protective clear top coat before and after treatment. Resistance heating or an electron beam can be used to melt the metallizing materials such as aluminum, silver, copper, and gold, which usually are pure elements. Sputter plating uses a plasma to produce the metallic vapor and can use brass as well as the metals mentioned. Chromium plating requires etched surfaces to ensure good adhesion. Plastics may be polished by buffing methods similar to those used on metals, but experiments to determine the effect of frictional heat are recommended. Surfaces can be heated to 300–400 deg. F by buffing, and some plastics soften and melt at these temperatures. Heating sometimes causes plastics to give off toxic gases, so masks should be worn to filter out such gases and dust. Parting lines, imperfections, scratches, saw lines, and scars resulting from fabrication can be treated with abrasives prior to buffing. Wet or dry abrasives such as silicon carbide or aluminum oxide are generally used, in grain sizes of 60 to as fine as 320. Some buffing compounds are ineffective on plastics. Scratch lines should be presented at a slight angle to the buff surface for best results. Light, tallow-free grease will help keep the abrasive surface free from buildup, and speeds of 5,000 to 6,000 surface feet per minute are recommended. For low-melting point plastics, soft cotton buffs are best, with surface speeds of 4,000 to 5,000 feet per minute, using a wet or greasy tripoli or silica compound. For finishing, only rouge may be needed for a satisfactory finish. If a cleaning solvent is used it should be checked to see that it does not dissolve the plastics, and it should be used only in a wellventilated area. Acrylics such as Acrylite or Plexiglass may also be ‘flame polished,’ under advice from the materials supplier. Plastics Gearing.—Plastics gears may be cut from blanks, as with metal gears, or molded to shape in an injection-molding machine, for lower production costs, though tooling may cost more. Cut plastics gears may be of similar design to their metal counterparts, but molded gears are usually of modified form to suit the material characteristics. Plastics materials also may be preferred for gears because of superior sliding properties with reduced noise and need for lubrication, chemical or electrical properties, or resistance to wear. However, plastics gear teeth slide more smoothly and easily against metal teeth than do plastics against plastics, and wear is less. For power transmission, plastics gear teeth are usually of involute form. See also Non-metallic Gearing on page 2149. Most plastics gears are made from nylons and acetals, although acrylonitrile-butadienestyrenes (ABS), polycarbonates, polysulfones, phenylene oxides, poly-urethanes, and thermoplastic polyesters can also be used. Additives used in plastics gears include glass fiber for added strength, and fibers, beads, and powders for reduced thermal expansion and improved dimensional stability. Other materials, such as molybdenum disulfide, tetrafluoroethylene (TFE), and silicones, may be added as lubricants to improve wear resistance.



PLASTICS GEAR DESIGN

Choice of plastics gear material depends on requirements for size and nature of loads to be transmitted, speeds, required life, working environment, type of cooling, lubrication, and operating precision. Because of cost, plastics gears are sometimes not enclosed in sealed housings, so are often given only a single coating of lubricant grease. Overloading of lubricated plastics gear teeth will usually cause tooth fracture, and unlubricated teeth often suffer excessive wear. Thermoplastics strength varies with temperature, with higher temperatures reducing root stress and permitting tooth deformation. In calculating power to be transmitted by spur, helical, and straight bevel gearing, the following formulas should be used with the factors given in Tables 7, 8, and 9. For internal and external spur gears, S s FYV HP = ---------------------------------------(28) 55 ( 600 + V )PC s For internal and external helical gears, S s FYV HP = ---------------------------------------------423 ( 78 + V )P n C s

(29)

S s FYV ( C – F ) HP = -------------------------------------------55 ( 600 + V )PCC s

(30)

For straight bevel gears,

where Ss = safe stress in bending (from Table 8); F = face width in inches; Y = tooth form factor (from Table 7); C = pitch cone distance in inches; Cs = service factor (from Table 9); P = diametral pitch; Pn = normal diametral pitch; and V = velocity at pitch circle diameter in ft/min. Table 7. Tooth Form Factors Y for Plastics Gears 20-deg Internal Full Depth

Number of Teeth

141⁄2-deg Involute or Cycloidal

20-deg Full Depth Involute

20-deg Stub Tooth Involute

Pinion

Gear

12 13 14 15 16 17 18 19 20 21 22 24 26 28 30 34 38 43

0.210 0.220 0.226 0.236 0.242 0.251 0.261 0.273 0.283 0.289 0.292 0.298 0.307 0.314 0.320 0.327 0.336 0.346

0.245 0.261 0.276 0.289 0.259 0.302 0.308 0.314 0.320 0.327 0.330 0.336 0.346 0.352 0.358 0.371 0.383 0.396

0.311 0.324 0.339 0.348 0.361 0.367 0.377 0.386 0.393 0.399 0.405 0.415 0.424 0.430 0.437 0.446 0.456 0.462

0.327 0.327 0.330 0.330 0.333 0.342 0.349 0.358 0.364 0.371 0.374 0.383 0.393 0.399 0.405 0.415 0.424 0.430

… … … … … … … … … … … … … 0.691 0.679 0.660 0.644 0.628


Machinery's Handbook 27th Edition PLASTICS GEAR DESIGN

627

Table 7. (Continued) Tooth Form Factors Y for Plastics Gears 141⁄2-deg Involute or Cycloidal 0.352 0.358 0.364 0.371 0.377 0.383 0.390

Number of Teeth 50 60 75 100 150 300 Rack

20-deg Full Depth Involute 0.480 0.421 0.434 0.446 0.459 0.471 0.484

20-deg Stub Tooth Involute 0.474 0.484 0.496 0.506 0.518 0.534 0.550

20-deg Internal Full Depth Pinion 0.437 0.446 0.452 0.462 0.468 0.478 …

Gear 0.613 0.597 0.581 0.565 0.550 0.534 …

These values assume a moderate temperature increase and some initial lubrication. With bevel gearing, divide the number of teeth by the cosine of the pitch angle and use the data in the table. For example, if a 20-deg PA bevel gear has 40 teeth and a pitch angle of 58 deg, 40 divided by the cosine of 58 deg = 40 ÷ 0.529919 ∼ 75, and Y = 0.434.

Table 8. Safe Bending Stress (lb/in2) Values for Plastics Gears Safe Stress Plastics Type

Unfilled

Glass-filled

ABS

3,000

6,000

Acetal

5,000

7,000

Nylon

6,000

12,000

Polycarbonate

6,000

9,000

Polyester

3,500

8,000

Polyurethane

2,500

…

Table 9. Service Factors for Plastics Gears Type of Load

8–10 Hr/Day

24 Hr/Day

Intermittent, 3 Hr/Day

Occasional, 1⁄ Hr/Day 2

Steady

1.00

1.25

0.80

0.50

Light shock

1.25

1.5

1.00

0.80

Medium shock

1.5

1.75

1.25

1.00

Heavy shock

1.75

2.00

1.5

1.25

Example:As an example, assume that a material is to be selected for a spur gear that must transmit 1⁄8 hp at 350 rpm, for 8 hrs/day under a steady load. The gear is to have 75 teeth, 32 diametral pitch, 20 deg pressure angle, 0.375 in. face width, and a pitch diameter of 2.3438 in. Using Equation (28), S s FYV 55 ( 600 + V )PC s HP HP = ---------------------------------------- or S s = ------------------------------------------------55 ( 600 + V )PC s FYV hp = 0.125, Y = 0.434 and rpm × π × D = ----------------------------------------------------350 × 3.1416 × 2.3438- = 215 ft ⁄ min V = -----------------------------12 12



PLASTICS GEAR DESIGN

therefore, ( 600 + 215 )32 × 1.00 × 0.125 = 5,124 lb ⁄ in. 2 S s = 55 -----------------------------------------------------------------------------0.375 × 0.434 × 215 From Table 8 it is apparent that the gear could be molded from several materials. Available physical and chemical characteristics must now be considered in relation to the operating environment for the gear. Strengths of plastics materials decrease with increasing temperatures and not all plastics resist the effects of some liquids, including some lubricants. Some plastics deteriorate when in sunlight for long periods; some are more dimensionally stable than others; and wear resistance varies from one to another. Manufacturers’ data sheets will answer some of these questions. Backlash: Plastics gears should be so dimensioned that they will provide sufficient backlash at the highest temperatures likely to be encountered in service. Dimensional allowances must also be made for gears made of hygroscopic plastics that may be exposed to damp service conditions. Teeth of heavily loaded gears usually have tip relief to reduce effects of deflection, and have full fillet radii to reduce stress concentrations. Such modifications to tooth form are also desirable in plastics gears. If the pinion in a pair of gears has a small number of teeth, undercutting may result. Undercutting weakens teeth, causes undue wear, and may affect continuity of action. The undercutting can be reduced by using the long-short addendum system, which involves increasing the addendum of the pinion teeth and reducing that of the gear teeth. The modified addendum method will also reduce the amount of initial wear that takes place during the initial stages of contact between the teeth. Accuracy: The Gear Handbook, AGMA 390-03a-1980, Part 2, Gear Classification, provides a system whereby results of gear accuracy measurements are expressed in terms of maximum tooth-to-tooth and composite tolerances. This system uses AGMA quality numbers related to maximum tolerances, by pitch and diameter, and is equally applicable to plastics gears as to metal gears. AGMA quality numbers must be chosen for a pair of mating gears early in the design process, and the finished gears must be inspected by being run in close mesh with a master gear in a center-distance measuring instrument to make sure that the errors do not exceed the specified tolerances. To prevent failure from fatigue and wear caused by excessive flexing of the teeth, plastics gears must be made to the same standards of acccuracy as metal gears. Solidification shrinkage of plastics requires that dimensions of molds for gears be larger than the dimensions of the parts to be produced from them. The amount of the shrinkage is usually added to the mold dimension (with the mold at operating temperature). However, this procedure cannot be followed for the tooth profile as it would introduce large errors in the pressure angle. Increases in pressure angle cause gear teeth to become wider at the root and more pointed. Sliding conditions are improved and the teeth are stronger, so that higher loading values can be used. Shrinkage allowances have the greatest effect on the accuracy of the molded gears, so tooth profiles must be calculated extremely carefully in terms of mold profile. If a tooth is merely made larger by using a standard hobbing cutter to cut the tool whereby the teeth in the mold are electroeroded, differential shrinkage caused by the molded tooth being thicker at the root than at the tip will distort the shape of the molded tooth, making it thinner at the tip and thicker at the root. With two mating gears, these faulty shapes will affect the pressure angle resulting in binding, wear, and general malfunction. If the tooth thickness limits for a molded gear are to be held to +0.000 in., −0.001 in., the outside diameter must be permitted to vary up to 0.0027 in. for 20-deg, and 0.0039 in. for 141⁄2-deg pressure angle gears. All high-accuracy gears should be specified with AGMA quality numbers and inspected with center-distance measuring machines if the required accuracy is to be achieved.


Machinery's Handbook 27th Edition TABLE OF CONTENTS DIMENSIONING, GAGING, AND MEASURING DRAFTING PRACTICES 630 630 630 630 633 634 638 640 642

MEASURING INSTRUMENTS AND INSPECTION METHODS

ANSI Drafting Practices Sizes of Drawing Sheets Symbols for Section Lining Geometric Dimensioning ANSI and ISO Symbols Definitions Datum Referencing Positional Tolerance Checking Drawings

ALLOWANCES AND TOLERANCES FOR FITS 645 645 647 648 649 651 651 652 652 652 656 658 660 662 665 665 666 667 670 670 672 674 674 676 678 679 680 680 682 682 683 685 687 689 689 690

Basic Dimensions Tolerances Force fits Expansion and Shrinkage Fits Temperatures for Shrinkage Fits ANSI Standard Limits and Fits Definitions Preferred Basic Sizes Standard Tolerances ANSI Standard Fits Modified Standard Fits Running and Sliding Fits Clearance Locational Fits Transition Locational Fits ANSI Metric Limits and Fits Definitions Tolerances Designation Preferred Metric Fits Hole Basis Fits Clearance Fits Transition and Interference Fits Shaft Basis Fits Clearance Fits Transition and Interference Fits Gagemakers Tolerances ISO Metric Limits and Fits Definitions Calculated Limits of Tolerance Tolerance for Selected Holes Tolerance for Selected Shafts Clearances Deviations for Shafts Deviations for Holes Preferred Numbers ANSI Preferred Numbers Preferred Metric Sizes

692 693 695 695 695 696 697 698 698 699 706 713 713 714 715 717 717 717 718 719 721 723

Verniers and Micrometers Dual Metric-Inch Vernier Metric Micrometer Sine-bar Types of Sine-bars Setting a Sine-bar Using Sine-bar Tables Measuring Tapers with V-block Dimensioning Tapers Constants for 5-inch Sine-bar Constants for 100-mm Sine-bar Angles and Tapers Measuring Dovetail Slides Tapers per Foot Figuring Tapers Measurement over Pins and Rolls Measurement over Pins Checking a V-shaped Groove Checking Radius of Arc Checking Shaft Conditions Out-of-Roundness and Lobing Measurements Using Light

SURFACE TEXTURE 724 ANSI Surface Texture 726 Definitions 727 Sampling Lengths 728 Roughness Parameters 729 Waviness Parameters 729 Surface Roughness to Tolerances 730 Instruments for Measurement 731 Roughness Measurements 731 Surface Texture Symbols 734 Roughness Average Values 735 Lay Symbols 735 Surface Texture of Castings 735 Metric Dimensions on Drawings 738 ISO Surface Finish 738 Surface Finish Symbology 740 Roughness Lengths 743 Gage Blocks 743 Precision Gage Blocks 744 Gage Block Sets

629



DIMENSIONING, GAGING, AND MEASURING

DRAFTING PRACTICES American National Standard Drafting Practices Several American National Standards for use in preparing engineering drawings and related documents are referred to for use. Sizes of Drawing Sheets.—Recommended trimmed sheet sizes, based on ANSI Y14.11980 (R1987), are shown in the following table. Size, inches

Metric Size, mm

A

81⁄2 × 11

D

22 × 34

A0

841 × 1189

A3

297 × 420

B

11 × 17

E

34 × 44

A1

594 × 841

A4

210 × 297

C

17 × 22

F

28 × 40

A2

420 × 594

The standard sizes shown by the left-hand section of the table are based on the dimensions of the commercial letter head, 81⁄2 × 11 inches, in general use in the United States. The use of the basic sheet size 81⁄2 × 11 inches and its multiples permits filing of small tracings and folded blueprints in commercial standard letter files with or without correspondence. These sheet sizes also cut without unnecessary waste from the present 36-inch rolls of paper and cloth. For drawings made in the metric system of units or for foreign correspondence, it is recommended that the metric standard trimmed sheet sizes be used. (Right-hand section of table.) These sizes are based on the width-to-length ratio of 1 to

2.

Line Conventions and Drawings.—American National Standard Y14.2M-1979 (R1987) establishes line and lettering practices for engineering drawings. The line conventions and the symbols for section lining are as shown on Tables 1 and 2. Approximate width of THICK lines for metric drawings are 0.6 mm, and for inch drawings, 0.032 inch. Approximate width of THIN lines for metric drawings are 0.3 mm, and for inch drawings, 0.016 inch. These approximate line widths are intended to differentiate between THICK and THIN lines and are not values for control of acceptance or rejection of the drawings. Surface-Texture Symbols.—A detailed explanation of the use of surface-texture symbols from American National Standard Y14.36M-1996 begins on page 731. Geometric Dimensioning and Tolerancing.—ANSI/ASME Y14.5M-1994, “Dimensioning and Tolerancing,” covers dimensioning, tolerancing, and similar practices for engineering drawings and related documentation. The mathematical definitions of dimensioning and tolerancing principles are given in the standard ANSI/ASME Y14.5.1M-1994. ISO standards ISO 8015 and ISO 26921 contain a detailed explanation of ISO geometric dimensioning and tolerancing practices. Geometric dimensioning and tolerancing provides a comprehensive system for symbolically defining the geometrical tolerance zone within which features must be contained. It provides an accurate transmission of design specifications among the three primary users of engineering drawings; design, manufacturing and quality assurance. Some techniques introduced in ANSI/ASME Y14.5M-1994 have been accepted by ISO. These techniques include projected tolerance zone, three-plane datum concept, total runout tolerance, multiple datums, and datum targets. Although this Standard follows ISO practice closely, there are still differences between ISO and U.S. practice. (A comparison of the symbols used in ISO standards and Y14.5M is given on page 633.)


Machinery's Handbook 27th Edition DRAFTING PRACTICES

631

Table 1. American National Standard for Engineering Drawings ANSI/ASME Y14.2M-1992 Visible Line

THICK

Hidden Line

THIN

Section Line

THIN

Center Line

THIN THIN

Symmetry Line

Leader Extension Line Dimension Line Extension Line And Leader

Dimension Line THIN 3.50

THICK Cutting-Plane Line or Viewing-Plane Line

THICK

THICK Short Breaks Break Line

THIN Long Breaks

Phantom Line

THIN THIN

Stitch Line

THIN ................................................... Chain Line

THICK



DRAFTING PRACTICES Table 2. American National Standard Symbols for Section Lining ANSI Y14.2M-1979 (R1987) Cast and Malleable iron (Also for general use of all materials)

Titanium and refractory material

Steel

Electric windings, electro magnets, resistance, etc.

Bronze, brass, copper, and compositions

Concrete

White metal, zinc, lead, babbitt, and alloys

Marble, slate, glass, porcelain, etc.

Magnesium, aluminum, and aluminum alloys

Earth

Rubber, plastic electrical insulation

Rock

Cork, felt, fabric, leather, fiber

Sand

Sound insulation

Water and other liquids

Thermal insulation

Wood-across grain Wood-with grain



Table 3. Comparison of ANSI and ISO Geometric Symbols ASME Y14.5M-1994 Symbol for

ANSI Y14.5M

ISO

Symbol for

ANSI Y14.5

ISO

Symbol for

ANSI Y14.5M

ISO

Circular Runouta

Feature Control Frame

Flatness

Total Runouta

Datum Featurea

Circularity

At Maximum Material Condition

All Around - Profile

Cylindricity

At Least Material Condition

Conical Taper

Profile of a Line

Regardless of Feature Size

Profile of a Surface

Projected Tolerance Zone

Counterbore/Spotface

Angularity

Diameter

Countersink

Perpendicularity

Basic Dimension

Parallelism

Reference Dimension

Position

Datum Target

Dimension Not to Scale

15

15

Concentricity/Coaxiality

Target Point

Number of Times/Places

8X

8X

Symmetry

Dimension Origin

Arc Length

Radius

R

Betweena

NONE

NONE

GEOMETRIC SYMBOLS

Straightness

Slope

Depth/Deep (50)

(50)

Square (Shape)

R

Spherical Radius

SR

SR

Sperical Diameter

None

Controlled Radius

CR

None

Statical Tolerance

None

633

a Arrowheads may be filled in.



GEOMETRIC DIMENSIONING

One major area of disagreement is the ISO “principle of independency” versus the “Taylor principle.” Y14.5M and standard U.S. practice both follow the Taylor principle, in which a geometric tolerancing zone may not extend beyond the boundary (or envelope) of perfect form at MMC (maximum material condition). This boundary is prescribed to control variations as well as the size of individual features. The U.S. definition of independency further defines features of size as being independent and not required to maintain a perfect relationship with other features. The envelope principle is optional in treatment of these principles. A summary of the application of ANSI/ASME geometric control symbols and their use with basic dimensions and modifiers is given in Table 1. Table 1. Application of Geometric Control Symbols Type Geometric Characteristics

Pertains To

Basic Dimensions

Feature Modifier

Datum Modifier

Form

Straightness Circularity Flatness

ONLY individual feature

NO datum Modifier not applicable

Runout Location Orientation Profile

Cylindricity Profile (Line) Profile (Surface)

Individual or related

Angularity

Yes if related Yes RFS implied unless MMC or LMC is stated

Perpendicularity Parallelism Position Concentricity Symmetry Circular Runout

ALWAYS related feature(s)

RFS implied unless MMC or LMC is stated

Yes

Only RFS

Only RFS

Total Runout

Five types of geometric control, when datums are indicated, when basic dimensions are required, and when MMC and LMC modifiers may be used.

ANSI/ASME Y14.5M features metric SI units (the International System of Units), but customary units may be used without violating any principles. On drawings where all dimensions are either in millimeters or in inches, individual identification of linear units is not required. However, the drawing should contain a note stating UNLESS OTHERWISE SPECIFIED, ALL DIMENSIONS ARE IN MILLIMETERS (or IN INCHES, as applicable). According to this Standard, all dimensions are applicable at a temperature of 20 C (68 F) unless otherwise specified. Compensation may be made for measurements taken at other temperatures. Angular units are expressed in degrees and decimals of a degree (35.4) or in degrees (°), minutes (′), and seconds (″), as in 35° 25′ 10″. A 90-degree angle is implied where center lines and depicting features are shown on a drawing at right angles and no angle is specified. A 90-degree BASIC angle applies where center lines of features in a pattern or surface shown at right angles on a drawing are located or defined by basic dimensions and no angle is specified. Definitions.—The following terms are defined as their use applies to ANSI/ASME Y14.5M. Datum Feature: The feature of a part that is used to establish a datum. Datum Identifier: The graphic symbol on a drawing used to indicate the datum feature.


Machinery's Handbook 27th Edition GEOMETRIC DIMENSIONING Leader may be appropriately directed to a feature.

Datum letter

A

A

0.25

M

Datum triangle may be filled or not filled.

A

635

Combined feature control frame and datum identifier

A B C A

A

Fig. 1. Datum Feature Symbol

Datum Plane: The individual theoretical planes of the reference frame derived from a specified datum feature. A datum is the origin from which the location or other geometric characteristics of features of a part are established. Datum Reference Frame: Sufficient features on a part are chosen to position the part in relationship to three planes. The three planes are mutually perpendicular and together called the datum reference frame. The planes follow an order of precedence and allow the part to be immobilized. This immobilization in turn creates measurable relationships among features. Datum Simulator: Formed by the datum feature contacting a precision surface such as a surface plate, gage surface or by a mandrel contacting the datum. Thus, the plane formed by contact restricts motion and constitutes the specific reference surface from which measurements are taken and dimensions verified. The datum simulator is the practical embodiment of the datum feature during manufacturing and quality assurance. Datum Target: A specified point, line, or area on a part, used to establish a datum. Degrees of Freedom: The six directions of movement or translation are called degrees of freedom in a three-dimensional environment. They are up-down, left-right, fore-aft, roll, pitch and yaw. Up Right Aft

Yaw

Pitch

Fore Roll

Left Down

Fig. 2. Degrees of Freedom (Movement) That Must be Controlled, Depending on the Design Requirements.



GEOMETRIC DIMENSIONING

Dimension, Basic: A numerical value used to describe the theoretically exact size, orientation, location, or optionally, profile, of a feature or datum or datum target. Basic dimensions are indicated by a rectangle around the dimension and are not toleranced directly or by default. The specific dimensional limits are determined by the permissible variations as established by the tolerance zone specified in the feature control frame. A dimension is only considered basic for the geometric control to which it is related. 38

Fig. 3. Basic Dimensions

Dimension Origin: Symbol used to indicate the origin and direction of a dimension between two features. The dimension originates from the symbol with the dimension tolerance zone being applied at the other feature. 20

0.3 4.2 4.1 8

0.3 20

30

0.3

0.1˚ Dimension origin symbol Fig. 4. Dimension Origin Symbol

Dimension, Reference: A dimension, usually without tolerance, used for information purposes only. Considered to be auxiliary information and not governing production or inspection operations. A reference dimension is a repeat of a dimension or is derived from a calculation or combination of other values shown on the drawing or on related drawings. Feature Control Frame: Specification on a drawing that indicates the type of geometric control for the feature, the tolerance for the control, and the related datums, if applicable. Geometric control symbol

0.25 A-B Co-datum (both primary)

Primary datum reference

Tolerance

Tolerance modifier

M

A

B

C Tertiary datum reference Secondary datum reference

Fig. 5. Feature Control Frame and Datum Order of Precedence

Feature: The general term applied to a physical portion of a part, such as a surface, hole, pin, tab, or slot. Least Material Condition (LMC): The condition in which a feature of size contains the least amount of material within the stated limits of size, for example, upper limit or maximum hole diameter and lower limit or minimum shaft diameter.


Machinery's Handbook 27th Edition GEOMETRIC DIMENSIONING

637

Limits, Upper and Lower (UL and LL): The arithmetic values representing the maximum and minimum size allowable for a dimension or tolerance. The upper limit represents the maximum size allowable. The lower limit represents the minimum size allowable. Maximum Material Condition (MMC): The condition in which a feature of size contains the maximum amount of material within the stated limits of size. For example, the lower limit of a hole is the minimum hole diameter. The upper limit of a shaft is the maximum shaft diameter. Position: Formerly called true position, position is the theoretically exact location of a feature established by basic dimensions. Regardless of Feature Size (RFS): The term used to indicate that a geometric tolerance or datum reference applies at any increment of size of the feature within its tolerance limits. RFS is the default condition unless MMC or LMC is specified. The concept is now the default in ANSI/ASME Y14.5M-1994, unless specifically stated otherwise. Thus the symbol for RFS is no longer supported in ANSI/ASME Y14.5M-1994. Size, Actual: The term indicating the size of a feature as produced. Size, Feature of: A feature that can be described dimensionally. May include a cylindrical or spherical surface, or a set of two opposed parallel surfaces associated with a size dimension. Tolerance Zone Symmetry: In geometric tolerancing, the tolerance value stated in the feature control frame is always a single value. Unless otherwise specified, it is assumed that the boundaries created by the stated tolerance are bilateral and equidistant about the perfect form control specified. However, if desired, the tolerance may be specified as unilateral or unequally bilateral. (See Figs. 6 through 8) Tolerance, Bilateral: A tolerance where variation is permitted in both directions from the specified dimension. Bilateral tolerances may be equal or unequal. Tolerance, Geometric: The general term applied to the category of tolerances used to control form, profile, orientation, location, and runout. Tolerance, Unilateral: A tolerance where variation is permitted in only one direction from the specified dimension. True Geometric Counterpart: The theoretically perfect plane of a specified datum feature. Virtual Condition: A constant boundary generated by the collective effects of the feature size, its specified MMC or LMC material condition, and the geometric tolerance for that condition. 0.1

0.25

M

A

10 R75 38

A

Bilateral zone with 0.1 of the 0.25 tolerance outside perfect form. Fig. 6. Application of a bilateral geometric tolerance



GEOMETRIC TOLERANCING

0.25

M

A

10 R75 38

A

Unilateral zone with all of the 0.25 tolerance outside perfect form. Fig. 7. Application of a unilateral geometric tolerance zone outside perfect form

0.25

M

A

10 R75 38

A

Unilateral zone with all of the 0.25 tolerance inside perfect form. Fig. 8. Application of a unilateral geometric tolerance zone inside a perfect form

Datum Referencing.—A datum indicates the origin of a dimensional relationship between a toleranced feature and a designated feature or features on a part. The designated feature serves as a datum feature, whereas its true geometric counterpart establishes the datum plane. Because measurements cannot be made from a true geometric counterpart, which is theoretical, a datum is assumed to exist in, and be simulated by the associated processing equipment. For example, machine tables and surface plates, although not true planes, are of such quality that they are used to simulate the datums from which measurements are taken and dimensions are verified. When magnified, flat surfaces of manufactured parts are seen to have irregularities, so that contact is made with a datum plane formed at a number of surface extremities or high points. Sufficient datum features, those most important to the design of the part, are chosen to position the part in relation to a set of three mutually perpendicular planes, the datum reference frame. This reference frame exists only in theory and not on the part. Therefore, it is necessary to establish a method for simulating the theoretical reference frame from existing features of the part. This simulation is accomplished by positioning the part on appropriate datum features to adequately relate the part to the reference frame and to restrict the degrees of freedom of the part in relation to it. These reference frame planes are simulated in a mutually perpendicular relationship to provide direction as well as the origin for related dimensions and measurements. Thus, when the part is positioned on the datum reference frame (by physical contact between each datum feature and its counterpart in the associated processing equipment), dimensions related to the datum reference frame by a feature control frame are thereby mutually perpendicular. This theoretical reference frame constitutes the three-plane dimensioning system used for datum referencing.


Machinery's Handbook 27th Edition GEOMETRIC TOLERANCING

639

Target area (where applicable)

12 P1 Datum reference letter 18

18 12

12 P1

or

P1 Target number

18

18 Target C2 is on the hidden or far side of the part.

12 C2 18 18

Fig. 9. Datum target symbols

Depending on the degrees of freedom that must be controlled, a simple reference frame may suffice. At other times, additional datum reference frames may be necessary where physical separation occurs or the functional relationship. Depending on the degrees of freedom that must be controlled, a single datum of features require that datum reference frames be applied at specific locations on the part. Each feature control frame must contain the datum feature references that are applicable. Datum Targets: Datum targets are used to establish a datum plane. They may be points, lines or surface areas. Datum targets are used when the datum feature contains irregularities, the surface is blocked by other features or the entire surface cannot be used. Examples where datum targets may be indicated include uneven surfaces, forgings and castings, weldments, non-planar surfaces or surfaces subject to warping or distortion. The datum target symbol is located outside the part outline with a leader directed to the target point, area or line. The targets are dimensionally located on the part using basic or toleranced dimensions. If basic dimensions are used, established tooling or gaging tolerances apply. A solid leader line from the symbol to the target is used for visible or near side locations with a dashed leader line used for hidden or far side locations. The datum target symbol is divided horizontally into two halves. The top half contains the target point area if applicable; the bottom half contains a datum feature identifying letter and target number. Target



GEOMETRIC TOLERANCING

numbers indicate the quantity required to define a primary, secondary, or tertiary datum. If indicating a target point or target line, the top half is left blank. Datum targets and datum features may be combined to form the datum reference frame, Fig. 9. Datum Target points: A datum target point is indicated by the symbol “X,” which is dimensionally located on a direct view of the surface. Where there is no direct view, the point location is dimensioned on multiple views. Datum Target Lines: A datum target line is dimensionally located on an edge view of the surface using a phantom line on the direct view. Where there is no direct view, the location is dimensioned on multiple views. Where the length of the datum target line must be controlled, its length and location are dimensioned. Datum Target Areas: Where it is determined that an area or areas of flat contact are necessary to ensure establishment of the datum, and where spherical or pointed pins would be inadequate, a target area of the desired shape is specified. Examples include the need to span holes, finishing irregularities, or rough surface conditions. The datum target area may be indicated with the “X” symbol as with a datum point, but the area of contact is specified in the upper half of the datum target symbol. Datum target areas may additionally be specified by defining controlling dimensions and drawing the contact area on the feature with section lines inside a phantom outline of the desired shape. Positional Tolerance.—A positional tolerance defines a zone within which the center, axis, or center plane of a feature of size is permitted to vary from true (theoretically exact) position. Basic dimensions establish the true position from specified datum features and between interrelated features. A positional tolerance is indicated by the position symbol, a tolerance, and appropriate datum references placed in a feature control frame. Modifiers: In certain geometric tolerances, modifiers in the form of additional symbols may be used to further refine the level of control. The use of the MMC and LMC modifiers has been common practice for many years. However, several new modifiers were introduced with the 1994 U.S. national standard. Some of the new modifiers include free state, tangent plane and statistical tolerancing, Fig. 10.

F

M

L

T

P

ST

Free State

MMC

LMC

Tangent Plane

Projected Tolerance Zone

Statistical Tolerance

Fig. 10. Tolerance modifiers

Projected Tolerance Zone: Application of this concept is recommended where any variation in perpendicularity of the threaded or press-fit holes could cause fasteners such as screws, studs, or pins to interfere with mating parts. An interference with subsequent parts can occur even though the hole axes are inclined within allowable limits. This interference occurs because, without a projected tolerance zone, a positional tolerance is applied only to the depth of threaded or press-fit holes. Unlike the floating fastener application involving clearance holes only, the attitude of a fixed fastener is restrained by the inclination of the produced hole into which it assembles. Projected tolerance zone symbol

0.25 M P 14 A

B

C

Minimum height of projected tolerance zone Fig. 11. Projected tolerance zone callout


Machinery's Handbook 27th Edition GEOMETRIC TOLERANCING

641

With a projected tolerance zone equal to the thickness of the mating part, the inclinational error is accounted for in both parts. The minimum extent and direction of the projected tolerance zone is shown as a value in the feature control frame. The zone may be shown in a drawing view as a dimensioned value with a heavy chain line drawn closely adjacent to an extension of the center line of the hole. 4x M6x1-6H

A

0.25

M P

14 A

B

C

This on the drawing

0.25 positional True position tolerance zone axis

Axis of threaded hole projected tolerance 14 minimum zone height

Means this

True position axis Axis of threaded hole Fig. 12. Projected tolerance zone application

Statistical Tolerance: The statistical tolerancing symbol is a modifier that may be used to indicate that a tolerance is controlled statistically as opposed to being controlled arithmetically. With arithmetic control, assembly tolerances are typically divided arithmetically among the individual components of the assembly. This division results in the assumption that assemblies based on “worst case” conditions would be guaranteed to fit because the worst case set of parts fit — so that anything better would fit as well. When this technique is restrictive, statistical tolerancing, via the symbol, may be specified in the feature control frame as a method of increasing tolerances for individual parts. This procedure may reduce manufacturing costs because its use changes the assumption that statistical process control may make a statistically significant quantity of parts fit, but not absolutely all. The technique should only be used when sound statistical methods are employed.



CHECKING DRAWINGS

Tangent Plane: When it is desirable to control the surface of a feature by the contacting or high points of the surface, a tangent plane symbol is added as a modifier to the tolerance in the feature control frame, Fig. 13. This on the drawing 0.1 T A

A

Means this 0.1 Tolerance zone

Controlled surface

Tangent plane generated by high points Fig. 13. Tangent plane modifier

Free State: The free state modifier symbol is used when the geometric tolerance applies to the feature in its “free state,” or after removal of any forces used in the manufacturing process. With removal of forces the part may distort due to gravity, flexibility, spring back, or other release of internal stresses developed during fabrication. Typical applications include parts with extremely thin walls and non-rigid parts made of rubber or plastics. The modifier is placed in the tolerance portion of the feature control frame and follows any other modifier. The above examples are just a few of the numerous concepts and related symbols covered by ANSI/ASME Y14.5M-1994. Refer to the standard for a complete discussion with further examples of the application of geometric dimensioning and tolerancing principles. Checking Drawings.—In order that the drawings may have a high standard of excellence, a set of instructions, as given in the following, has been issued to the checkers, and also to the draftsmen and tracers in the engineering department of a well-known machine-building company. Inspecting a New Design: When a new design is involved, first inspect the layouts carefully to see that the parts function correctly under all conditions, that they have the proper relative proportions, that the general design is correct in the matters of strength, rigidity, bearing areas, appearance, convenience of assembly, and direction of motion of the parts, and that there are no interferences. Consider the design as a whole to see if any improvements can be made. If the design appears to be unsatisfactory in any particular, or improvements appear to be possible, call the matter to the attention of the chief engineer. Checking for Strength: Inspect the design of the part being checked for strength, rigidity, and appearance by comparing it with other parts for similar service whenever possible, giving preference to the later designs in such comparison, unless the later designs are known to be unsatisfactory. If there is any question regarding the matter, compute the stresses and deformations or find out whether the chief engineer has approved the stresses or deformations that will result from the forces applied to the part in service. In checking parts that are to go on a machine of increased size, be sure that standard parts used in similar machines and proposed for use on the larger machine, have ample strength and rigidity under the new and more severe service to which they will be put. Materials Specified: Consider the kind of material required for the part and the various possibilities of molding, forging, welding, or otherwise forming the rough part from this material. Then consider the machining operations to see whether changes in form or design will reduce the number of operations or the cost of machining. See that parts are designed with reference to the economical use of material, and whenever possible, utilize standard sizes of stock and material readily obtainable from local


Machinery's Handbook 27th Edition CHECKING DRAWINGS

643

dealers. In the case of alloy steel, special bronze, and similar materials, be sure that the material can be obtained in the size required. Method of Making Drawing: Inspect the drawing to see that the projections and sections are made in such a way as to show most clearly the form of the piece and the work to be done on it. Make sure that any worker looking at the drawing will understand what the shape of the piece is and how it is to be molded or machined. Make sure that the delineation is correct in every particular, and that the information conveyed by the drawing as to the form of the piece is complete. Checking Dimensions: Check all dimensions to see that they are correct. Scale all dimensions and see that the drawing is to scale. See that the dimensions on the drawing agree with the dimensions scaled from the lay-out. Wherever any dimension is out of scale, see that the dimension is so marked. Investigate any case where the dimension, the scale of the drawing, and the scale of the lay-out do not agree. All dimensions not to scale must be underlined on the tracing. In checking dimensions, note particularly the following points: See that all figures are correctly formed and that they will print clearly, so that the workers can easily read them correctly. See that the overall dimensions are given. See that all witness lines go to the correct part of the drawing. See that all arrow points go to the correct witness lines. See that proper allowance is made for all fits. See that the tolerances are correctly given where necessary. See that all dimensions given agree with the corresponding dimensions of adjacent parts. Be sure that the dimensions given on a drawing are those that the machinist will use, and that the worker will not be obliged to do addition or subtraction to obtain the necessary measurements for machining or checking his work. Avoid strings of dimensions where errors can accumulate. It is generally better to give a number of dimensions from the same reference surface or center line. When holes are to be located by boring on a horizontal spindle boring machine or other similar machine, give dimensions to centers of bored holes in rectangular coordinates and from the center lines of the first hole to be bored, so that the operator will not be obliged to add measurements or transfer gages. Checking Assembly: See that the part can readily be assembled with the adjacent parts. If necessary, provide tapped holes for eyebolts and cored holes for tongs, lugs, or other methods of handling. Make sure that, in being assembled, the piece will not interfere with other pieces already in place and that the assembly can be taken apart without difficulty. Check the sum of a number of tolerances; this sum must not be great enough to permit two pieces that should not be in contact to come together. Checking Castings: In checking castings, study the form of the pattern, the methods of molding, the method of supporting and venting the cores, and the effect of draft and rough molding on clearances. Avoid undue metal thickness, and especially avoid thick and thin sections in the same casting. Indicate all metal thicknesses, so that the molder will know what chaplets to use for supporting the cores. See that ample fillets are provided, and that they are properly dimensioned. See that the cores can be assembled in the mold without crushing or interference. See that swelling, shrinkage, or misalignment of cores will not make trouble in machining. See that the amount of extra material allowed for finishing is indicated.



CHECKING DRAWINGS

See that there is sufficient extra material for finishing on large castings to permit them to be “cleaned up,” even though they warp. In such castings, make sure that the metal thickness will be sufficient after finishing, even though the castings do warp. Make sure that sufficient sections are shown so that the pattern makers and molders will not be compelled to make assumptions about the form of any part of the casting. These details are particularly important when a number of sections of the casting are similar in form, while others differ slightly. Checking Machined Parts: Study the sequences of operations in machining and see that all finish marks are indicated. See that the finish marks are placed on the lines to which dimensions are given. See that methods of machining are indicated where necessary. Give all drill, reamer, tap, and rose bit sizes. See that jig and gage numbers are indicated at the proper places. See that all necessary bosses, lugs, and openings are provided for lifting, handling, clamping, and machining the piece. See that adequate wrench room is provided for all nuts and bolt heads. Avoid special tools, such as taps, drills, reamers, etc., unless such tools are specifically authorized. Where parts are right- and left-hand, be sure that the hand is correctly designated. When possible, mark parts as symmetrical, so as to avoid having them right- and left-hand, but do not sacrifice correct design or satisfactory operation on this account. When heat-treatment is required, the heat-treatment should be specified. Check the title, size of machine, the scale, and the drawing number on both the drawing and the drawing record card. Tapers for Machine Tool Spindles.—Various standard tapers have been used for the taper holes in the spindles of machine tools, such as drilling machines, lathes, milling machines, or other types requiring a taper hole for receiving either the shank of a cutter, an arbor, a center, or any tool or accessory requiring a tapering seat. The Morse taper represents a generally accepted standard for drilling machines. Morse Tapers Morse Taper 0 1

Taper per Foot 0.62460 0.59858

Morse Taper 2 3


Morse Taper 4 5


The headstock and tailstock spindles of lathes also have the Morse taper in most cases; but the Jarno, the Reed (which is the short Jarno), and the Brown & Sharpe have also been used. Milling machine spindles formerly had Brown & Sharpe tapers in most cases. In 1927, the milling machine manufacturers of the National Machine Tool Builders’ Association adopted a standard taper of 31⁄2 inches per foot. This comparatively steep taper has the advantage of insuring instant release of arbors or adapters. National Machine Tool Builders’ Association Tapers Taper Numbera

Large End Diameter

Taper Numbera

Large End Diameter

30

11⁄4

50

23⁄4

40

13⁄4

60

41⁄4

a Standard taper of 31⁄ inches per foot 2

The British Standard for milling machine spindles is also 31⁄2 inches taper per foot and includes these large end diameters: 13⁄8 inches, 13⁄4 inches, 23⁄4 inches, and 31⁄4 inches.


Machinery's Handbook 27th Edition ALLOWANCES AND TOLERANCES

645

ALLOWANCES AND TOLERANCES FOR FITS Limits and Fits Fits between cylindrical parts, i.e., cylindrical fits, govern the proper assembly and performance of many mechanisms. Clearance fits permit relative freedom of motion between a shaft and a hole—axially, radially, or both. Interference fits secure a certain amount of tightness between parts, whether these are meant to remain permanently assembled or to be taken apart from time to time. Or again, two parts may be required to fit together snugly—without apparent tightness or looseness. The designer's problem is to specify these different types of fits in such a way that the shop can produce them. Establishing the specifications requires the adoption of two manufacturing limits for the hole and two for the shaft, and, hence, the adoption of a manufacturing tolerance on each part. In selecting and specifying limits and fits for various applications, it is essential in the interests of interchangeable manufacturing that 1) standard definitions of terms relating to limits and fits be used; 2) preferred basic sizes be selected wherever possible to reduce material and tooling costs; 3) limits be based upon a series of preferred tolerances and allowances; and 4) a uniform system of applying tolerances (preferably unilateral) be used. These principles have been incorporated in both the American and British standards for limits and fits. Information about these standards is given beginning on page 651. Basic Dimensions.—The basic size of a screw thread or machine part is the theoretical or nominal standard size from which variations are made. For example, a shaft may have a basic diameter of 2 inches, but a maximum variation of minus 0.010 inch may be permitted. The minimum hole should be of basic size wherever the use of standard tools represents the greatest economy. The maximum shaft should be of basic size wherever the use of standard purchased material, without further machining, represents the greatest economy, even though special tools are required to machine the mating part. Tolerances.—Tolerance is the amount of variation permitted on dimensions or surfaces of machine parts. The tolerance is equal to the difference between the maximum and minimum limits of any specified dimension. For example, if the maximum limit for the diameter of a shaft is 2.000 inches and its minimum limit 1.990 inches, the tolerance for this diameter is 0.010 inch. The extent of these tolerances is established by determining the maximum and minimum clearances required on operating surfaces. As applied to the fitting of machine parts, the word tolerance means the amount that duplicate parts are allowed to vary in size in connection with manufacturing operations, owing to unavoidable imperfections of workmanship. Tolerance may also be defined as the amount that duplicate parts are permitted to vary in size to secure sufficient accuracy without unnecessary refinement. The terms “tolerance” and “allowance” are often used interchangeably, but, according to common usage, allowance is a difference in dimensions prescribed to secure various classes of fits between different parts. Unilateral and Bilateral Tolerances.—The term “unilateral tolerance” means that the total tolerance, as related to a basic dimension, is in one direction only. For example, if the basic dimension were 1 inch and the tolerance were expressed as 1.000 − 0.002, or as 1.000 + 0.002, these would be unilateral tolerances because the total tolerance in each is in one direction. On the contrary, if the tolerance were divided, so as to be partly plus and partly minus, it would be classed as “bilateral.” +0.001 Thus, 1.000 −0.001 is an example of bilateral tolerance, because the total tolerance of 0.002 is given in two directions—plus and minus. When unilateral tolerances are used, one of the three following methods should be used to express them:



ALLOWANCES AND TOLERANCES

1) Specify, limiting dimensions only as Diameter of hole: 2.250, 2.252 Diameter of shaft: 2.249, 2.247 2) One limiting size may be specified with its tolerances as Diameter of hole: 2.250 + 0.002, −0.000 Diameter of shaft: 2.249 + 0.000, −0.002 3) The nominal size may be specified for both parts, with a notation showing both allowance and tolerance, as Diameter of hole: 21⁄4 + 0.002, −0.000 Diameter of shaft: 21⁄4 − 0.001, −0.003 Bilateral tolerances should be specified as such, usually with plus and minus tolerances of equal amount. An example of the expression of bilateral tolerances is +0.001 −0.001 Application of Tolerances.—According to common practice, tolerances are applied in such a way as to show the permissible amount of dimensional variation in the direction that is less dangerous. When a variation in either direction is equally dangerous, a bilateral tolerance should be given. When a variation in one direction is more dangerous than a variation in another, a unilateral tolerance should be given in the less dangerous direction. For nonmating surfaces, or atmospheric fits, the tolerances may be bilateral, or unilateral, depending entirely upon the nature of the variations that develop in manufacture. On mating surfaces, with few exceptions, the tolerances should be unilateral. Where tolerances are required on the distances between holes, usually they should be bilateral, as variation in either direction is normally equally dangerous. The variation in the distance between shafts carrying gears, however, should always be unilateral and plus; otherwise, the gears might run too tight. A slight increase in the backlash between gears is seldom of much importance. One exception to the use of unilateral tolerances on mating surfaces occurs when tapers are involved; either bilateral or unilateral tolerances may then prove advisable, depending upon conditions. These tolerances should be determined in the same manner as the tolerances on the distances between holes. When a variation either in or out of the position of the mating taper surfaces is equally dangerous, the tolerances should be bilateral. When a variation in one direction is of less danger than a variation in the opposite direction, the tolerance should be unilateral and in the less dangerous direction. Locating Tolerance Dimensions.—Only one dimension in the same straight line can be controlled within fixed limits. That dimension is the distance between the cutting surface of the tool and the locating or registering surface of the part being machined. Therefore, it is incorrect to locate any point or surface with tolerances from more than one point in the same straight line. Every part of a mechanism must be located in each plane. Every operating part must be located with proper operating allowances. After such requirements of location are met, all other surfaces should have liberal clearances. Dimensions should be given between those points or surfaces that it is essential to hold in a specific relation to each other. This restriction applies particularly to those surfaces in each plane that control the location of other component parts. Many dimensions are relatively unimportant in this respect. It is good practice to establish a common locating point in each plane and give, as far as possible, all such dimensions from these common locating points. The locating points on the drawing, the locatingor registering points used for machining the surfaces and the locating points for measuring should all be identical. The initial dimensions placed on component drawings should be the exact dimensions that would be used if it were possible to work without tolerances. Tolerances should be 2 ± 0.001 or

2


Machinery's Handbook 27th Edition FITS

647

given in that direction in which variations will cause the least harm or danger. When a variation in either direction is equally dangerous, the tolerances should be of equal amount in both directions, or bilateral. The initial clearance, or allowance, between operating parts should be as small as the operation of the mechanism will permit. The maximum clearance should be as great as the proper functioning of the mechanism will permit. Direction of Tolerances on Gages.—The extreme sizes for all plain limit gages shall not exceed the extreme limits of the part to be gaged. All variations in the gages, whatever their cause or purpose, shall bring these gages within these extreme limits. The data for gage tolerances on page 678 cover gages to inspect workpieces held to tolerances in the American National Standard ANSI B4.4M-1981. Allowance for Forced Fits.—The allowance per inch of diameter usually ranges from 0.001 inch to 0.0025 inch, 0.0015 being a fair average. Ordinarily the allowance per inch decreases as the diameter increases; thus the total allowance for a diameter of 2 inches might be 0.004 inch, whereas for a diameter of 8 inches the total allowance might not be over 0.009 or 0.010 inch. The parts to be assembled by forced fits are usually made cylindrical, although sometimes they are slightly tapered. The advantages of the taper form are that the possibility of abrasion of the fitted surfaces is reduced; that less pressure is required in assembling; and that the parts are more readily separated when renewal is required. On the other hand, the taper fit is less reliable, because if it loosens, the entire fit is free with but little axial movement. Some lubricant, such as white lead and lard oil mixed to the consistency of paint, should be applied to the pin and bore before assembling, to reduce the tendency toward abrasion. Pressure for Forced Fits.—The pressure required for assembling cylindrical parts depends not only upon the allowance for the fit, but also upon the area of the fitted surfaces, the pressure increasing in proportion to the distance that the inner member is forced in. The approximate ultimate pressure in tons can be determined by the use of the following formula in conjunction with the accompanying table of Pressure Factors for Forced Fits. Assuming that A = area of surface in contact in “fit”; a = total allowance in inches; P = ultimate pressure required, in tons; F = pressure factor based upon assumption that the diameter of the hub is twice the diameter of the bore, that the shaft is of machine steel, and that the hub is of cast iron: ×a×F P = A ---------------------2 Pressure Factors for Forced Fits Diameter, Inches

Pressure Factor

Diameter, Inches

Pressure Factor

1 11⁄4

500

31⁄2

395

33⁄4

123

132

Diameter, Inches

Pressure Factor

6 61⁄4

75 72

11⁄2

325

61⁄2

69

276

4 41⁄4

115

13⁄4

108

63⁄4

66

2 21⁄4

240

41⁄2

101

64

212

43⁄4

96

7 71⁄4

21⁄2

189

91

71⁄2

59

61

23⁄4

171

5 51⁄4

86

73⁄4

57

3 31⁄4

156

51⁄2

82

55

143

53⁄4

78

8 81⁄2

52

Diameter, Inches

Pressure Factor

9 91⁄2

48.7

10 101⁄2

43.5

11 111⁄2

39.3

12 121⁄2

35.9

13 131⁄2

46.0

Diameter, Inches 14 141⁄2

Pressure Factor 30.5 29.4

15 151⁄2

28.3

16 161⁄2

26.5 24.8

34.4

17 171⁄2

33.0

18

23.4

31.7

…

…

41.3 37.5

27.4 25.6 24.1

Allowance for Given Pressure.—By transposing the preceding formula, the approxi2P mate allowance for a required ultimate tonnage can be determined. Thus, a = ------- . The AF



FITS

average ultimate pressure in tons commonly used ranges from 7 to 10 times the diameter in inches. Expansion Fits.—In assembling certain classes of work requiring a very tight fit, the inner member is contracted by sub-zero cooling to permit insertion into the outer member and a tight fit is obtained as the temperature rises and the inner part expands. To obtain the sub-zero temperature, solid carbon dioxide or “dry ice” has been used but its temperature of about 109 degrees F. below zero will not contract some parts sufficiently to permit insertion in holes or recesses. Greater contraction may be obtained by using high purity liquid nitrogen which has a temperature of about 320 degrees F. below zero. During a temperature reduction from 75 degrees F. to −321 degrees F., the shrinkage per inch of diameter varies from about 0.002 to 0.003 inch for steel; 0.0042 inch for aluminum alloys; 0.0046 inch for magnesium alloys; 0.0033 inch for copper alloys; 0.0023 inch for monel metal; and 0.0017 inch for cast iron (not alloyed). The cooling equipment may vary from an insulated bucket to a special automatic unit, depending upon the kind and quantity of work. One type of unit is so arranged that parts are precooled by vapors from the liquid nitrogen before immersion. With another type, cooling is entirely by the vapor method. Shrinkage Fits.—General practice seems to favor a smaller allowance for shrinkage fits than for forced fits, although in many shops the allowances are practically the same for each, and for some classes of work, shrinkage allowances exceed those for forced fits. The shrinkage allowance also varies to a great extent with the form and construction of the part that has to be shrunk into place. The thickness or amount of metal around the hole is the most important factor. The way in which the metal is distributed also has an influence on the results. Shrinkage allowances for locomotive driving wheel tires adopted by the American Railway Master Mechanics Association are as follows: Center diameter, inches Allowances, inches

38

44

50

56

62

66

0.040

0.047

0.053

0.060

0.066

0.070

Whether parts are to be assembled by forced or shrinkage fits depends upon conditions. For example, to press a tire over its wheel center, without heating, would ordinarily be a rather awkward and difficult job. On the other hand, pins, etc., are easily and quickly forced into place with a hydraulic press and there is the additional advantage of knowing the exact pressure required in assembling, whereas there is more or less uncertainty connected with a shrinkage fit, unless the stresses are calculated. Tests to determine the difference in the quality of shrinkage and forced fits showed that the resistance of a shrinkage fit to slippage for an axial pull was 3.66 times greater than that of a forced fit, and in rotation or torsion, 3.2 times greater. In each comparative test, the dimensions and allowances were the same. Allowances for Shrinkage Fits.—The most important point to consider when calculating shrinkage fits is the stress in the hub at the bore, which depends chiefly upon the shrinkage allowance. If the allowance is excessive, the elastic limit of the material will be exceeded and permanent set will occur, or, in extreme conditions, the ultimate strength of the metal will be exceeded and the hub will burst. The intensity of the grip of the fit and the resistance to slippage depends mainly upon the thickness of the hub; the greater the thickness, the stronger the grip, and vice versa. Assuming the modulus of elasticity for steel to be 30,000,000, and for cast iron, 15,000,000, the shrinkage allowance per inch of nominal diameter can be determined by the following formula, in which A = allowance per inch of diameter; T = true tangential tensile stress at inner surface of outer member; C = factor taken from one of the accompanying Tables 1, 2, and 3. For a cast-iron hub and steel shaft: T(2 + C) A = --------------------------30 ,000 ,000


(1)

Machinery's Handbook 27th Edition SHRINKAGE FIT

649

When both hub and shaft are of steel: T(1 + C) A = --------------------------(2) 30 ,000 ,000 If the shaft is solid, the factor C is taken from Table 1; if it is hollow and the hub is of steel, factor C is taken from Table 2; if it is hollow and the hub is of cast iron, the factor is taken from Table 3. Table 1. Factors for Calculating Shrinkage Fit Allowances for Steel Shafts and Steel or Cast Iron Hubs Ratio of Diameters D2 -----D1

1.5 1.6 1.8 2.0 2.2 2.4 2.6

Steel Hub

Cast-iron Hub

Ratio of Diameters

0.234 0.263 0.311 0.348 0.377 0.399 0.417

2.8 3.0 3.2 3.4 3.6 3.8 4.0

C 0.227 0.255 0.299 0.333 0.359 0.380 0.397

D2 -----D1

Steel Hub

Cast-iron Hub C

0.410 0.421 0.430 0.438 0.444 0.450 0.455

0.432 0.444 0.455 0.463 0.471 0.477 0.482

Values of factor C for solid steel shafts of nominal diameter D1, and hubs of steel or cast iron of nominal external and internal diameters D2 and D1, respectively.

Example 1:A steel crank web 15 inches outside diameter is to be shrunk on a 10-inch solid steel shaft. Required the allowance per inch of shaft diameter to produce a maximum tensile stress in the crank of 25,000 pounds per square inch, assuming the stresses in the crank to be equivalent to those in a ring of the diameter given. The ratio of the external to the internal diameters equals 15 ÷ 10 = 1.5; T = 25,000 pounds; from Table 1, C = 0.227. Substituting in Formula (2): ,000 × ( 1 + 0.227 -) = 0.001 inch A = 25 -------------------------------------------------30 ,000 ,000 Example 2:Find the allowance per inch of diameter for a 10-inch shaft having a 5-inch axial through hole, other conditions being the same as in Example 1. The ratio of external to internal diameters of the hub equals 15 ÷ 10 = 1.5, as before, and the ratio of external to internal diameters of the shaft equals 10 ÷ 5 = 2. From Table 2, we find that factor C = 0.455; T = 25,000 pounds. Substituting these values in Formula (2): 25 ,000 ( 1 + 0.455 ) A = --------------------------------------------- = 0.0012 inch 30 ,000 ,000 The allowance is increased, as compared with Example 1, because the hollow shaft is more compressible. Example 3:If the crank web in Example 1 is of cast iron and 4000 pounds per square inch is the maximum tensile stress in the hub, what is the allowance per inch of diameter? D2 ------ = 1.5 T = 4000 D1 In Table 1, we find that C = 0.234. Substituting in Formula (1), for cast-iron hubs, A = 0.0003 inch, which, owing to the lower tensile strength of cast iron, is about one-third the shrinkage allowance in Example 1, although the stress is two-thirds of the elastic limit. Temperatures for Shrinkage Fits.—The temperature to which the outer member in a shrinkage fit should be heated for clearance in assembling the parts depends on the total



SHRINKAGE FIT Table 2. Factors for Calculating Shrinkage Fit Allowances for Hollow Steel Shafts and Steel Hubs

D2 -----D1

D1 -----D0

Ca

D ------2 D1

D1 -----D0

Ca

D2 -----D1

D ------1 D0

Ca

1.5

2.0 2.5 3.0 3.5

0.455 0.357 0.313 0.288

2.4

2.0 2.5 3.0 3.5

0.760 0.597 0.523 0.481

3.4

2.0 2.5 3.0 3.5

0.876 0.689 0.602 0.555

1.6

2.0 2.5 3.0 3.5

0.509 0.400 0.350 0.322

2.6

2.0 2.5 3.0 3.5

0.793 0.624 0.546 0.502

3.6

2.0 2.5 3.0 3.5

0.888 0.698 0.611 0.562

1.8

2.0 2.5 3.0 3.5

0.599 0.471 0.412 0.379

2.8

2.0 2.5 3.0 3.5

0.820 0.645 0.564 0.519

3.8

2.0 2.5 3.0 3.5

0.900 0.707 0.619 0.570

2.0

2.0 2.5 3.0 3.5

0.667 0.524 0.459 0.422

3.0

2.0 2.5 3.0 3.5

0.842 0.662 0.580 0.533

4.0

2.0 2.5 3.0 3.5

0.909 0.715 0.625 0.576

2.2

2.0 2.5 3.0 3.5

0.718 0.565 0.494 0.455

3.2

2.0 2.5 3.0 3.5

0.860 0.676 0.591 0.544

…

… … … …

… … … …

a Values of factor C for hollow steel shafts of external and internal diameters D and D , respectively, 1 0 and steel hubs of nominal external diameter D2.

Table 3. Factors for Calculating Shrinkage Fit Allowances for Hollow Steel Shafts and Cast-iron Hubs D2 -----D1

D1 -----D0

Ca

D ------2 D1

D1 -----D0

Ca

D2 -----D1

D ------1 D0

Ca

1.5

2.0 2.5 3.0 3.5

0.468 0.368 0.322 0.296

2.4

2.0 2.5 3.0 3.5

0.798 0.628 0.549 0.506

3.4

2.0 2.5 3.0 3.5

0.926 0.728 0.637 0.587

1.6

2.0 2.5 3.0 3.5

0.527 0.414 0.362 0.333

2.6

2.0 2.5 3.0 3.5

0.834 0.656 0.574 0.528

3.6

2.0 2.5 3.0 3.5

0.941 0.740 0.647 0.596

1.8

2.0 2.5 3.0 3.5

0.621 0.488 0.427 0.393

2.8

2.0 2.5 3.0 3.5

0.864 0.679 0.594 0.547

3.8

2.0 2.5 3.0 3.5

0.953 0.749 0.656 0.603

2.0

2.0 2.5 3.0 3.5

0.696 0.547 0.479 0.441

3.0

2.0 2.5 3.0 3.5

0.888 0.698 0.611 0.562

4.0

2.0 2.5 3.0 3.5

0.964 0.758 0.663 0.610

2.2

2.0 2.5 3.0 3.5

0.753 0.592 0.518 0.477

3.2

2.0 2.5 3.0 3.5

0.909 0.715 0.625 0.576

…

… … … …

… … … …

a Values of factor C for hollow steel shafts and cast-iron hubs.

Notation as in Table 2.


Machinery's Handbook 27th Edition ANSI STANDARD LIMITS AND FITS

651

expansion required and on the coefficient α of linear expansion of the metal (i.e., the increase in length of any section of the metal in any direction for an increase in temperature of 1 degree F). The total expansion in diameter that is required consists of the total allowance for shrinkage and an added amount for clearance. The value of the coefficient α is, for nickel-steel, 0.000007; for steel in general, 0.0000065; for cast iron, 0.0000062. As an example, take an outer member of steel to be expanded 0.005 inch per inch of internal diameter, 0.001 being the shrinkage allowance and the remainder for clearance. Then α × t ° = 0.005 0.005 - = 769 degrees F t = -----------------------0.0000065 The value t is the number of degrees F that the temperature of the member must be raised above that of the room temperature. ANSI Standard Limits and Fits This American National Standard for Preferred Limits and Fits for Cylindrical Parts, ANSI B4.1-1967 (R1999), presents definitions of terms applying to fits between plain (non threaded) cylindrical parts and makes recommendations on preferred sizes, allowances, tolerances, and fits for use wherever they are applicable. This standard is in accord with the recommendations of American-British-Canadian (ABC) conferences up to a diameter of 20 inches. Experimental work is being carried on with the objective of reaching agreement in the range above 20 inches. The recommendations in the standard are presented for guidance and for use where they might serve to improve and simplify products, practices, and facilities. They should have application for a wide range of products. As revised in 1967, and reaffirmed in 1999, the definitions in ANSI B4.1 have been expanded and some of the limits in certain classes have been changed. Factors Affecting Selection of Fits.—Many factors, such as length of engagement, bearing load, speed, lubrication, temperature, humidity, and materials must be taken into consideration in the selection of fits for a particular application, and modifications in the ANSI recommendations may be required to satisfy extreme conditions. Subsequent adjustments may also be found desirable as a result of experience in a particular application to suit critical functional requirements or to permit optimum manufacturing economy. Definitions.—The following terms are defined in this standard: Nominal Size: The nominal size is the designation used for the purpose of general identification. Dimension: A dimension is a geometrical characteristic such as diameter, length, angle, or center distance. Size: Size is a designation of magnitude. When a value is assigned to a dimension, it is referred to as the size of that dimension. (It is recognized that the words “dimension” and “size” are both used at times to convey the meaning of magnitude.) Allowance: An allowance is a prescribed difference between the maximum material limits of mating parts. (See definition of Fit). It is a minimum clearance (positive allowance) or maximum interference (negative allowance) between such parts. Tolerance: A tolerance is the total permissible variation of a size. The tolerance is the difference between the limits of size. Basic Size: The basic size is that size from which the limits of size are derived by the application of allowances and tolerances. Design Size: The design size is the basic size with allowance applied, from which the limits of size are derived by the application of tolerances. Where there is no allowance, the design size is the same as the basic size. Actual Size: An actual size is a measured size. Limits of Size: The limits of size are the applicable maximum and minimum sizes.



PREFERRED BASIC SIZES

Maximum Material Limit: A maximum material limit is that limit of size that provides the maximum amount of material for the part. Normally it is the maximum limit of size of an external dimension or the minimum limit of size of an internal dimension.* Minimum Material Limit: A minimum material limit is that limit of size that provides the minimum amount of material for the part. Normally it is the minimum limit of size of an external dimension or the maximum limit of size of an internal dimension.* Tolerance Limit: A tolerance limit is the variation, positive or negative, by which a size is permitted to depart from the design size. Unilateral Tolerance: A unilateral tolerance is a tolerance in which variation is permitted in only one direction from the design size. Bilateral Tolerance: A bilateral tolerance is a tolerance in which variation is permitted in both directions from the design size. Unilateral Tolerance System: A design plan that uses only unilateral tolerances is known as a Unilateral Tolerance System. Bilateral Tolerance System: A design plan that uses only bilateral tolerances is known as a Bilateral Tolerance System. Fits.— Fit: Fit is the general term used to signify the range of tightness that may result from the application of a specific combination of allowances and tolerances in the design of mating parts. Actual Fit: The actual fit between two mating parts is the relation existing between them with respect to the amount of clearance or interference that is present when they are assembled. (Fits are of three general types: clearance, transition, and interference.) Clearance Fit: A clearance fit is one having limits of size so specified that a clearance always results when mating parts are assembled. Interference Fit: An interference fit is one having limits of size so specified that an interference always results when mating parts are assembled. Transition Fit: A transition fit is one having limits of size so specified that either a clearance or an interference may result when mating parts are assembled. Basic Hole System: A basic hole system is a system of fits in which the design size of the hole is the basic size and the allowance, if any, is applied to the shaft. Basic Shaft System: A basic shaft system is a system of fits in which the design size of the shaft is the basic size and the allowance, if any, is applied to the hole. Preferred Basic Sizes.—In specifying fits, the basic size of mating parts shall be chosen from the decimal series or the fractional series in Table 4. Prefered Series for Tolerances and Allowances.—All fundamental tolerances and allowances of all shafts and holes have been taken from the series given in Table 5. Standard Tolerances.—The series of standard tolerances shown in Table 6 are so arranged that for any one grade they represent approximately similar production difficulties throughout the range of sizes. This table provides a suitable range from which appropriate tolerances for holes and shafts can be selected and enables standard gages to be used. The tolerances shown in Table 6 have been used in the succeeding tables for different classes of fits. Table 7 graphically illustrates the range of tolearance grades that various machining processes may produce under normal conditions. ANSI Standard Fits.—Tables 8a through 12 inclusive show a series of standard types and classes of fits on a unilateral hole basis, such that the fit produced by mating parts in any one class will produce approximately similar performance throughout the range of sizes. These tables prescribe the fit for any given size, or type of fit; they also prescribe the * An example of exceptions: an exterior corner radius where the maximum radius is the minimum mate-

rial limit and the minimum radius is the maximum material limit.


Machinery's Handbook 27th Edition STANDARD FITS

653

Table 4. Preferred Basic Sizes ANSI B4.1-1967 (R1999) Decimala

Fractionala

0.010

2.00

8.50

1⁄ 64

0.015625

21⁄4

2.2500

91⁄2

9.5000

0.012

2.20

9.00

1⁄ 32

0.03125

21⁄2

2.5000

10

10.0000 10.5000

0.016

2.40

9.50

1⁄ 16

0.0625

23⁄4

2.7500

101⁄2

0.020

2.60

10.00

3⁄ 32

0.09375

3

3.0000

11

11.0000

0.025

2.80

10.50

1⁄ 8

0.1250

31⁄4

3.2500

111⁄2

11.5000

0.032

3.00

11.00

5⁄ 32

0.15625

31⁄2

3.5000

12

12.0000

0.040

3.20

11.50

3⁄ 16

0.1875

33⁄4

3.7500

121⁄2

12.5000

0.05

3.40

12.00

1⁄ 4

0.2500

4

4.0000

13

13.0000

0.06

3.60

12.50

5⁄ 16

0.3125

41⁄4

4.2500

131⁄2

13.5000

0.08

3.80

13.00

3⁄ 8

0.3750

41⁄2

4.5000

14

14.0000

0.10

4.00

13.50

7⁄ 16

0.4375

43⁄4

4.7500

141⁄2

14.5000

0.12

4.20

14.00

1⁄ 2

0.5000

5

5.0000

15

15.0000

0.16

4.40

14.50

9⁄ 16

0.5625

51⁄4

5.2500

151⁄2

15.5000

0.20

4.60

15.00

5⁄ 8

0.6250

51⁄2

5.5000

16

16.0000

0.24

4.80

15.50

11⁄ 16

0.6875

53⁄4

5.7500

161⁄2

16.5000

0.30

5.00

16.00

3⁄ 4

0.7500

6

6.0000

17

17.0000

0.40

5.20

16.50

7⁄ 8

0.8750

61⁄2

6.5000

171⁄2

17.5000

0.50 0.60

5.40 5.60

17.00 17.50

1

1.0000 1.2500

7 71⁄2

7.0000 7.5000

18

11⁄4

181⁄2

18.0000 18.5000

0.80

5.80

18.00

11⁄2

1.5000

8

8.0000

19

19.0000

1.00

6.00

18.50

13⁄4

1.7500

81⁄2

8.5000

191⁄2

19.5000

1.20 1.40 1.60 1.80

6.50 7.00 7.50 8.00

19.00 19.50 20.00 …

2 … … …

2.0000 … … …

9 … … …

9.0000 … … …

20 … … …

20.0000 … … …

a All dimensions are in inches.

Table 5. Preferred Series of Tolerances and Allowances a ANSI B4.1-1967 (R1999) 0.1 … 0.15 … … 0.2 … 0.25 …

1 1.2 1.4 1.6 1.8 2 2.2 2.5 2.8

10 12 14 16 18 20 22 25 28

100 125 … 160 … 200 … 250 …

0.3 … 0.4 … 0.5 0.6 0.7 0.8 0.9

3 3.5 4 4.5 5 6 7 8 9

30 35 40 45 50 60 70 80 …

… … … … … … … … …

a All values in thousandths of an inch

standard limits for the mating parts that will produce the fit. The fits listed in these tables contain all those that appear in the approved American-British-Canadian proposal. Selection of Fits: In selecting limits of size for any application, the type of fit is determined first, based on the use or service required from the equipment being designed; then the limits of size of the mating parts are established, to insure that the desired fit will be produced. Theoretically, an infinite number of fits could be chosen, but the number of standard fits shown in the accompanying tables should cover most applications. Designation of Standard Fits: Standard fits are designated by means of the following symbols which, facilitate reference to classes of fit for educational purposes. The symbols are not intended to be shown on manufacturing drawings; instead, sizes should be specified on drawings.



STANDARD FITS Table 6. ANSI Standard Tolerances ANSI B4.1-1967 (R1999) Nominal Size, Inches

Over

To

0 0.12 0.24 0.40 0.71 1.19 1.97 3.15 4.73 7.09 9.85 12.41 15.75 19.69 30.09 41.49 56.19 76.39 100.9 131.9 171.9

0.12 0.24 0.40 0.71 1.19 1.97 3.15 4.73 7.09 9.85 12.41 15.75 19.69 30.09 41.49 56.19 76.39 100.9 131.9 171.9 200

Grade 4

5

6

7

8

9

10

11

12

13

Tolerances in thousandths of an incha 0.12 0.15 0.15 0.2 0.25 0.3 0.3 0.4 0.5 0.6 0.6 0.7 0.8 0.9 1.0 1.2 1.6 2.0 2.5 3 4

0.15 0.20 0.25 0.3 0.4 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.0 1.2 1.6 2.0 2.5 3 4 5 6

0.25 0.3 0.4 0.4 0.5 0.6 0.7 0.9 1.0 1.2 1.2 1.4 1.6 2.0 2.5 3 4 5 6 8 10

0.4 0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.5 3 4 5 6 8 10 12 16

0.6 0.7 0.9 1.0 1.2 1.6 1.8 2.2 2.5 2.8 3.0 3.5 4 5 6 8 10 12 16 20 25

1.0 1.2 1.4 1.6 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6 6 8 10 12 16 20 25 30 40

1.6 1.8 2.2 2.8 3.5 4.0 4.5 5 6 7 8 9 10 12 16 20 25 30 40 50 60

2.5 3.0 3.5 4.0 5.0 6 7 9 10 12 12 14 16 20 25 30 40 50 60 80 100

4 5 6 7 8 10 12 14 16 18 20 22 25 30 40 50 60 80 100 125 160

6 7 9 10 12 16 18 22 25 28 30 35 40 50 60 80 100 125 160 200 250

a All tolerances above heavy line are in accordance with American-British-Canadian (ABC) agreements.

Table 7. Relation of Machining Processes to Tolerance Grades ANSI B4.1-1967 (R1999) MACHINING OPERATION

TOLERANCE GRADES 4

5

6

7

8

9

10

Lapping & Honing Cylindrical Grinding Surface Grinding This chart may be used as a general guide to determine the machining processes that will under normal conditions, produce work withen the tolerance grades indicated. (See also Relation of Surface Roughness to Tolerances starting on page 729.

Diamond Turning Diamond Boring Broaching Reaming Turning Boring Milling Planing & Shaping Drilling

The letter symbols used to designate standard fits are as follows: RC = Running or Sliding Clearance Fit LC = Locational Clearance Fit LT = Transition Clearance or Interference Fit LN = Locational Interference Fit FN = Force or Shrink Fit


11

12

13

Machinery's Handbook 27th Edition STANDARD FITS

655

These letter symbols are used in conjunction with numbers representing the class of fit; thus FN 4 represents a Class 4, force fit. Each of these symbols (two letters and a number) represents a complete fit for which the minimum and maximum clearance or interference and the limits of size for the mating parts are given directly in the tables. Description of Fits.—The classes of fits are arranged in three general groups: running and sliding fits, locational fits, and force fits. Running and Sliding Fits (RC): Running and sliding fits, for which limits of clearance are given in Table 8a, are intended to provide a similar running performance, with suitable lubrication allowance, throughout the range of sizes. The clearances for the first two classes, used chiefly as slide fits, increase more slowly with the diameter than for the other classes, so that accurate location is maintained even at the expense of free relative motion. These fits may be described as follows: RC 1 Close sliding fits are intended for the accurate location of parts that must assemble without perceptible play. RC 2 Sliding fits are intended for accurate location, but with greater maximum clearance than class RC 1. Parts made to this fit move and turn easily but are not intended to run freely, and in the larger sizes may seize with small temperature changes. RC 3 Precision running fits are about the closest fits that can be expected to run freely, and are intended for precision work at slow speeds and light journal pressures, but are not suitable where appreciable temperature differences are likely to be encountered. RC 4 Close running fits are intended chiefly for running fits on accurate machinery with moderate surface speeds and journal pressures, where accurate location and minimum play are desired. RC 5 and RC 6 Medium running fits are intended for higher running speeds, or heavy journal pressures, or both. RC 7 Free running fits are intended for use where accuracy is not essential, or where large temperature variations are likely to be encountered, or under both these conditions. RC 8 and RC 9 Loose running fits are intended for use where wide commercial tolerances may be necessary, together with an allowance, on the external member. Locational Fits (LC, LT, and LN): Locational fits are fits intended to determine only the location of the mating parts; they may provide rigid or accurate location, as with interference fits, or provide some freedom of location, as with clearance fits. Accordingly, they are divided into three groups: clearance fits (LC), transition fits (LT), and interference fits (LN). These are described as follows: LC Locational clearance fits are intended for parts which are normally stationary, but that can be freely assembled or disassembled. They range from snug fits for parts requiring accuracy of location, through the medium clearance fits for parts such as spigots, to the looser fastener fits where freedom of assembly is of prime importance. LT Locational transition fits are a compromise between clearance and interference fits, for applications where accuracy of location is important, but either a small amount of clearance or interference is permissible. LN Locational interference fits are used where accuracy of location is of prime importance, and for parts requiring rigidity and alignment with no special requirements for bore pressure. Such fits are not intended for parts designed to transmit frictional loads from one part to another by virtue of the tightness of fit. These conditions are covered by force fits. Force Fits: (FN): Force or shrink fits constitute a special type of interference fit, normally characterized by maintenance of constant bore pressures throughout the range of sizes. The interference therefore varies almost directly with diameter, and the difference



MODIFIED STANDARD FITS

between its minimum and maximum value is small, to maintain the resulting pressures within reasonable limits. These fits are described as follows: FN 1 Light drive fits are those requiring light assembly pressures, and produce more or less permanent assemblies. They are suitable for thin sections or long fits, or in cast-iron external members. FN 2 Medium drive fits are suitable for ordinary steel parts, or for shrink fits on light sections. They are about the tightest fits that can be used with high-grade cast-iron external members. FN 3 Heavy drive fits are suitable for heavier steel parts or for shrink fits in medium sections. FN 4 and FN 5 Force fits are suitable for parts that can be highly stressed, or for shrink fits where the heavy pressing forces required are impractical. Graphical Representation of Limits and Fits.—A visual comparison of the hole and shaft tolerances and the clearances or interferences provided by the various types and classes of fits can be obtained from the diagrams on page 657. These diagrams have been drawn to scale for a nominal diameter of 1 inch. Use of Standard Fit Tables.—Example 1:A Class RC 1 fit is to be used in assembling a mating hole and shaft of 2-inch nominal diameter. This class of fit was selected because the application required accurate location of the parts with no perceptible play (see Description of Fits, RC 1 close sliding fits). From the data in Table 8a, establish the limits of size and clearance of the hole and shaft. Maximum hole = 2 + 0.0005 = 2.0005; minimum hole = 2 inches Maximum shaft = 2 − 0.0004 = 1.9996; minimum shaft = 2 − 0.0007 = 1.9993 inches Minimum clearance = 0.0004; maximum clearance = 0.0012 inch Modified Standard Fits.—Fits having the same limits of clearance or interference as those shown in Tables 8a to 12 may sometimes have to be produced by using holes or shafts having limits of size other than those shown in these tables. These modifications may be accomplished by using either a Bilateral Hole System (Symbol B) or a Basic Shaft System (Symbol S). Both methods will result in nonstandard holes and shafts. Bilateral Hole Fits (Symbol B): The common situation is where holes are produced with fixed tools such as drills or reamers; to provide a longer wear life for such tools, a bilateral tolerance is desired. The symbols used for these fits are identical with those used for standard fits except that they are followed by the letter B. Thus, LC 4B is a clearance locational fit, Class 4, except that it is produced with a bilateral hole. The limits of clearance or interference are identical with those shown in Tables 8a to 12 for the corresponding fits. The hole tolerance, however, is changed so that the plus limit is that for one grade finer than the value shown in the tables and the minus limit equals the amount by which the plus limit was lowered. The shaft limits are both lowered by the same amount as the lower limit of size of the hole. The finer grade of tolerance required to make these modifications may be obtained from Table 6. For example, an LC 4B fit for a 6-inch diameter hole would have tolerance limits of +4.0, −2.0 ( + 0.0040 inch, − 0.0020 inch); the shaft would have tolerance limits of −2.0, −6.0 ( −0.0020 inch, −0.0060 inch). Basic Shaft Fits (Symbol S): For these fits, the maximum size of the shaft is basic. The limits of clearance or interference are identical with those shown in Tables 8a to 12 for the corresponding fits and the symbols used for these fits are identical with those used for standard fits except that they are followed by the letter S. Thus, LC 4S is a clearance locational fit, Class 4, except that it is produced on a basic shaft basis.



; ; ;;; ;;; ;;; ;;; ;; ;;;;;;; MODIFIED STANDARD FITS

657

The limits for hole and shaft as given in Tables 8a to 12 are increased for clearance fits (decreased for transition or interference fits) by the value of the upper shaft limit; that is, by the amount required to change the maximum shaft to the basic size. Graphical Representation of ANSI Standard Limits and Fits ANSI B4.1-1967 (R1999)

Hole Tolerance

6 4 2 0 –2 –4 –6 –8 –10 12 10 8 6 4 2 0 –2 –4 –6 –8 –10 –12 –14 –16 –18 –20 –22

Shaft Tolerance

RC9

RC8

RC2

RC1

RC3

RC4

RC6

RC5

RC7

Running or Sliding Fits

LC11

LC10

LC9

LC7

LC4

LC1

LC2

LC3

LC5

LC8

LC6

;;;;;;;; ; ;;;;;;;; ;; ;;;; ;;

2 1 0 –1

Clearance Locational Fits

LT1

LT2

LT3

LT4

LT6

LT5

Transition Fits

FN3

LN3

LN2 2 LN1 1 0 Interference Locational Fits

2 1 0 –1

FN1

FN2

FN3

FN3

Force or Shrink Fits

Diagrams show disposition of hole and shaft tolerances (in thousandths of an inch) with respect to basic size (0) for a diameter of 1 inch.



658

Table 8a. American National Standard Running and Sliding Fits ANSI B4.1-1967 (R1999) Nominal Size Range, Inches Over

Class RC 1

Class RC 2

Class RC 3

Class RC 4

Standard Tolerance Limits




Clearancea

Hole H5

Shaft g4

Clearancea

Hole H6

0.1

+0.2

−0.1

0.1

+0.25

0.45

−0.1

0.3

+0.4

0

−0.25

0.55

0

−0.3

0.95

0

0.15

+0.2

−0.15

0.15

+0.3

−0.15

0.4

+0.5

To

0 – 0.12

0.24 – 0.40 0.40 – 0.71 0.71 – 1.19 1.19 – 1.97 1.97 – 3.15 3.15 – 4.73 4.73 – 7.09 7.09 – 9.85 9.85 – 12.41 12.41 – 15.75 15.75 – 19.69

Clearancea

Hole H7

Shaft f6

Clearancea

Hole H8

Shaft f7

−0.3

0.3

+0.6

−0.3

−0.55

1.3

0

−0.7

−0.4

0.4

+0.7

−0.4

Values shown below are in thousandths of an inch

0.5

0

−0.3

0.65

0

−0.35

1.12

0

−0.7

1.6

0

−0.9

0.2

+0.25

−0.2

0.2

+0.4

−0.2

0.5

+0.6

−0.5

0.5

+0.9

−0.5

0.6

0

−0.35

0.85

0

−0.45

1.5

0

−0.9

2.0

0

−1.1

0.25

+0.3

−0.25

0.25

+0.4

−0.25

0.6

+0.7

−0.6

0.6

+1.0

−0.6

0.75

0

−0.45

0.95

0

−0.55

1.7

0

−1.0

2.3

0

−1.3

0.3

+0.4

−0.3

0.3

+0.5

−0.3

0.8

+0.8

−0.8

0.8

+1.2

−0.8

0.95

0

−0.55

1.2

0

−0.7

2.1

0

−1.3

2.8

0

−1.6

0.4

+0.4

−0.4

0.4

+0.6

−0.4

1.0

+1.0

−1.0

1.0

+1.6

−1.0

1.1

0

−0.7

1.4

0

−0.8

2.6

0

−1.6

3.6

0

−2.0

0.4

+0.5

−0.4

0.4

+0.7

−0.4

1.2

+1.2

−1.2

1.2

+1.8

−1.2

1.2

0

−0.7

1.6

0

−0.9

3.1

0

−1.9

4.2

0

−2.4

0.5

+0.6

−0.5

0.5

+0.9

−0.5

1.4

+1.4

−1.4

1.4

+2.2

−1.4

1.5

0

−0.9

2.0

0

−1.1

3.7

0

−2.3

5.0

0

−2.8

0.6

+0.7

−0.6

0.6

+1.0

−0.6

1.6

+1.6

−1.6

1.6

+2.5

−1.6 −3.2

1.8

0

−1.1

2.3

0

−1.3

4.2

0

−2.6

5.7

0

0.6

+0.8

−0.6

0.6

+1.2

−0.6

2.0

+1.8

−2.0

2.0

+2.8

−2.0

2.0

0

−1.2

2.6

0

−1.4

5.0

0

−3.2

6.6

0

−3.8

0.8

+0.9

−0.8

0.8

+1.2

−0.8

2.5

+2.0

−2.5

2.5

+3.0

−2.5

2.3

0

−1.4

2.9

0

−1.7

5.7

0

−3.7

7.5

0

−4.5

1.0

+1.0

−1.0

1.0

+1.4

−1.0

3.0

+2.2

−3.0

3.0

+3.5

−3.0

2.7

0

−1.7

3.4

0

−2.0

6.6

0

−4.4

8.7

0

−5.2

1.2

+1.0

−1.2

1.2

+1.6

−1.2

4.0

+2.5

−4.0

4.0

+4.0

−4.0

3.0

0

−2.0

3.8

0

−2.2

8.1

0

−5.6

10.5

0

−6.5


RUNNING AND SLIDING FITS

0.12 – 0.24

Shaft g5


Table 8b. American National Standard Running and Sliding Fits ANSI B4.1-1967 (R1999) Class RC 5 Nominal Size Range, Inches Over

Class RC 6

Standard Tolerance Limits Clearancea

Hole H8

Shaft e7

Clearancea

Hole H9

To

0 – 0.12 0.12 – 0.24

0.40 – 0.71 0.71 – 1.19 1.19 – 1.97 1.97 – 3.15 3.15 – 4.73 4.73 – 7.09 7.09 – 9.85 9.85 – 12.41 12.41 – 15.75 15.75 – 19.69

Shaft e8

Class RC 8


Hole H9

Shaft d8

Class RC 9



Hole H10

Shaft c9

Clearancea

Hole H11

Shaft

+1.6 0 +1.8 0 +2.2 0 +2.8 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6.0 0 +7.0 0 +8.0 0 +9.0 0 +10.0 0

− 2.5 − 3.5 − 2.8 − 4.0 − 3.0 − 4.4 − 3.5 − 5.1 − 4.5 − 6.5 − 5.0 − 7.5 − 6.0 − 9.0 − 7.0 −10.5 − 8.0 −12.0 −10.0 −14.5 −12.0 −17.0 −14.0 −20.0 −16.0 −22.0

4.0 8.1 4.5 9.0 5.0 10.7 6.0 12.8 7.0 15.5 8.0 18.0 9.0 20.5 10.0 24.0 12.0 28.0 15.0 34.0 18.0 38.0 22.0 45.0 25.0 51.0

+2.5 0 +3.0 0 +3.5 0 +4.0 0 +5.0 0 +6.0 0 +7.0 0 +9.0 0 +10.0 0 +12.0 0 +12.0 0 +14.0 0 +16.0 0

− 4.0 − 5.6 − 4.5 − 6.0 − 5.0 − 7.2 − 6.0 − 8.8 − 7.0 −10.5 − 8.0 −12.0 − 9.0 −13.5 −10.0 −15.0 −12.0 −18.0 −15.0 −22.0 −18.0 −26.0 −22.0 −31.0 −25.0 −35.0

Values shown below are in thousandths of an inch 0.6 1.6 0.8 2.0 1.0 2.5 1.2 2.9 1.6 3.6 2.0 4.6 2.5 5.5 3.0 6.6 3.5 7.6 4.0 8.6 5.0 10.0 6.0 11.7 8.0 14.5

+0.6 0 +0.7 0 +0.9 0 +1.0 0 +1.2 0 +1.6 0 +1.8 0 +2.2 0 +2.5 0 +2.8 0 +3.0 0 +3.5 0 +4.0 0

− 0.6 − 1.0 − 0.8 − 1.3 − 1.0 − 1.6 − 1.2 − 1.9 − 1.6 − 2.4 − 2.0 − 3.0 − 2.5 − 3.7 − 3.0 − 4.4 − 3.5 − 5.1 − 4.0 − 5.8 − 5.0 − 7.0 − 6.0 − 8.2 − 8.0 −10.5

0.6 2.2 0.8 2.7 1.0 3.3 1.2 3.8 1.6 4.8 2.0 6.1 2.5 7.3 3.0 8.7 3.5 10.0 4.0 11.3 5.0 13.0 6.0 15.5 8.0 18.0

+1.0 0 +1.2 0 +1.4 0 +1.6 0 +2.0 0 +2.5 0 +3.0 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6.0 0 +6.0 0

− 0.6 − 1.2 − 0.8 − 1.5 − 1.0 − 1.9 − 1.2 − 2.2 − 1.6 − 2.8 − 2.0 − 3.6 − 2.5 − 4.3 − 3.0 − 5.2 − 3.5 − 6.0 − 4.0 − 6.8 − 5.0 − 8.0 − 6.0 − 9.5 − 8.0 −12.0

1.0 2.6 1.2 3.1 1.6 3.9 2.0 4.6 2.5 5.7 3.0 7.1 4.0 8.8 5.0 10.7 6.0 12.5 7.0 14.3 8.0 16.0 10.0 19.5 12.0 22.0

+1.0 0 +1.2 0 +1.4 0 +1.6 0 +2.0 0 +2.5 0 +3.0 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6.0 0 +6.0 0

− 1.0 − 1.6 − 1.2 − 1.9 − 1.6 − 2.5 − 2.0 − 3.0 − 2.5 − 3.7 − 3.0 − 4.6 − 4.0 − 5.8 − 5.0 − 7.2 − 6.0 − 8.5 − 7.0 − 9.8 − 8.0 −11.0 −10.0 −13.5 −12.0 −16.0

2.5 5.1 2.8 5.8 3.0 6.6 3.5 7.9 4.5 10.0 5.0 11.5 6.0 13.5 7.0 15.5 8.0 18.0 10.0 21.5 12.0 25.0 14.0 29.0 16.0 32.0

RUNNING AND SLIDING FITS

0.24 – 0.40

Class RC 7


a Pairs of values shown represent minimum and maximum amounts of clearance resulting from application of standard tolerance limits.


659

Tolerance limits given in body of table are added to or subtracted from basic size (as indicated by + or − sign) to obtain maximum and minimum sizes of mating parts. All data above heavy lines are in accord with ABC agreements. Symbols H5, g4, etc. are hole and shaft designations in ABC system. Limits for sizes above 19.69 inches are also given in the ANSI Standard.


660

Table 9a. American National Standard Clearance Locational Fits ANSI B4.1-1967 (R1999) Class LC 1 Nominal Size Range, Inches Over

Class LC 2


Hole H6

Shaft h5

0

+0.25

0

Clearancea

Hole H7

Shaft h6

0

+0.4

0

To

0– 0.12

0.24– 0.40 0.40– 0.71 0.71– 1.19 1.19– 1.97 1.97– 3.15 3.15– 4.73 4.73– 7.09 7.09– 9.85 9.85– 12.41 12.41– 15.75 15.75– 19.69

Class LC 4


Hole H8

Shaft h7

Class LC 5


Hole H10

Shaft h9


Hole H7

Shaft g6

Values shown below are in thousandths of an inch 0.45 0 0.5 0 0.65 0 0.7 0 0.9 0 1.0 0 1.2 0 1.5 0 1.7 0 2.0 0 2.1 0 2.4 0 2.6

0

−0.2

+0.3

0

0

−0.2

+0.4 0

0 −0.25

+0.4

0

0

−0.3

+0.5

0

0

−0.4

+0.6

0

0

−0.4

+0.7

0

0

−0.5

+0.9

0

0

−0.6

+1.0

0

0

−0.7

+1.2

0

0

−0.8

+1.2

0

0

−0.9

+1.4

0

0

−1.0

+1.6

0

0

−1.0

0.65 0 0.8 0 1.0 0 1.1 0 1.3 0 1.6 0 1.9 0 2.3 0 2.6 0 3.0 0 3.2 0 3.6 0 4.1

0

−0.25

+0.5

0

0

−0.3

+0.6

0

0

−0.4

+0.7

0

0

−0.4

+0.8

0

0

0

+0.6

0

1

0

−0.4

0

+0.7

0

0

−0.5

1.2 0 1.5

+0.9

0

0

−0.6

+1.0

0

0

−0.7

0

+1.2

0

−0.5

2

0

−0.8

+1.0

0

0

+1.6

0

0 1.7

0

−0.6

0

−1

+1.2

0

0

+1.8

0

0

−0.7

3

0

−1.2

+1.4

0

0

+2.2

0

0

−0.9

+1.6

0

0

−1.0

+1.8

0

0

−1.2

+2.0

0

0

2.6

0 2.6 0 3.0 0 3.6 0 4.4 0 5.5 0 6.5 0 7.5 0

+1.6

0

0.1

+0.4

−0.1

0

−1.0

0.75

0

−0.35

+1.8

0

0.15

+0.5

−0.15

0

−1.2

0.95

0

−0.45

+2.2

0

0.2

+0.6

−0.2

0

−1.4

1.2

0

−0.6

+2.8

0

0.25

+0.7

−0.25

0

−1.6

1.35

0

−0.65

+3.5

0

0.3

+0.8

−0.3

0

−2.0

1.6

0

−0.8

+4.0

0

0.4

+1.0

−0.4

0

−2.5

2.0

0

−1.0

+4.5

0

0.4

+1.2

−0.4

0

−3

2.3

0

−1.1

+5.0

0

0.5

+1.4

−0.5

0

−1.4

0

−3.5

2.8

0

−1.4

+2.5

0

0

+6.0

0

0.6

+1.6

−0.6

0

−1.6

10.0

0

−4

3.2

0

−1.6

+2.8

0

0

+7.0

0

0.6

+1.8

−0.6

0

−1.8

11.5

0

−4.5

3.6

0

−1.8

0

+3.0

0

0

+8.0

0

0.7

+2.0

−0.7

−1.2

5

0

−2.0

13.0

0

−5

3.9

0

−1.9

+2.2

0

0

+3.5

0

0

+9.0

0

0.7

+2.2

−0.7

0

−1.4

0

−2.2

15.0

0

−6

4.3

0

−2.1

+2.5

0

+4

0

0

+10.0

0

0.8

+2.5

−0.8

0

−1.6

0

−2.5

16.0

0

−6

4.9

0

−2.4

3.6 0 4.1 0 4.6

5.7 0 6.5

8.5


CLEARANCE LOCATIONAL FITS

0.12– 0.24

Class LC 3



Table 9b. American National Standard Clearance Locational Fits ANSI B4.1-1967 (R1999) Class LC 6 Nominal Size Range, Inches Over

Class LC 7

Std. Tolerance Limits Clearancea

Hole H9

Shaft f8

Class LC 8


Hole H10

Shaft e9

Clearancea

To

0 – 0.12 0.12 − 0.24

0.40 – 0.71 0.71 – 1.19 1.19 – 1.97 1.97 – 3.15 3.15 – 4.73 4.73 – 7.09 7.09 − 9.85 9.85 – 12.41 12.41 – 15.75 15.75– 19.69

Hole H10

Shaft d9


Hole H11

Shaft c10

Clearancea

Class LC 10

Class LC 11

Std. Tolerance Limits


Hole H12

Shaft

Clearancea

Hole H13

5 17 6 20 7 25 8 28 10 34 12 44 14 50 16 60 18 68 22 78 28 88 30 100 35 115

+6 0 +7 0 +9 0 +10 0 +12 0 +16 0 +18 0 +22 0 +25 0 +28 0 +30 0 +35 0 +40 0

Shaft

Values shown below are in thousandths of an inch 0.3 1.9 0.4 2.3 0.5 2.8 0.6 3.2 0.8 4.0 1.0 5.1 1.2 6.0 1.4 7.1 1.6 8.1 2.0 9.3 2.2 10.2 2.5 12.0 2.8 12.8

+1.0 0 +1.2 0 +1.4 0 +1.6 0 +2.0 0 +2.5 0 +3.0 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6.0 0 +6.0 0

−0.3 −0.9 −0.4 −1.1 −0.5 −1.4 −0.6 −1.6 −0.8 −2.0 −1.0 −2.6 −1.0 −3.0 −1.4 −3.6 −1.6 −4.1 −2.0 −4.8 −2.2 −5.2 −2.5 −6.0 −2.8 −6.8

0.6 3.2 0.8 3.8 1.0 4.6 1.2 5.6 1.6 7.1 2.0 8.5 2.5 10.0 3.0 11.5 3.5 13.5 4.0 15.5 4.5 17.5 5.0 20.0 5.0 21.0

+1.6 0 +1.8 0 +2.2 0 +2.8 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6.0 0 +7.0 0 +8.0 0 +9.0 0 +10.0 0

− 0.6 − 1.6 − 0.8 − 2.0 − 1.0 − 2.4 − 1.2 − 2.8 − 1.6 − 3.6 − 2.0 − 4.5 − 2.5 − 5.5 − 3.0 − 6.5 − 3.5 − 7.5 − 4.0 − 8.5 − 4.5 − 9.5 − 5 −11 − 5 −11

1.0 2.0 1.2 4.2 1.6 5.2 2.0 6.4 2.5 8.0 3.6 9.5 4.0 11.5 5.0 13.5 6 16 7 18.5 7 20 8 23 9 25

+1.6 0 +1.8 0 +2.2 0 +2.8 0 +3.5 0 +4.0 0 +4.5 0 +5.0 0 +6 0 +7 0 +8 0 +9 0 +10 0

− 1.0 − 2.0 − 1.2 − 2.4 − 1.6 − 3.0 − 2.0 − 3.6 − 2.5 − 4.5 − 3.0 − 5.5 − 4.0 − 7.0 − 5.0 − 8.5 − 6 −10 − 7 −11.5 − 7 −12 − 8 −14 − 9 −15

2.5 6.6 2.8 7.6 3.0 8.7 3.5 10.3 4.5 13.0 5.0 15.0 6.0 17.5 7 21 8 24 10 29 12 32 14 37 16 42

+2.5 0 +3.0 0 +3.5 0 +4.0 0 +5.0 0 +6 0 +7 0 +9 0 +10 0 +12 0 +12 0 +14 0 +16 0

− 2.5 − 4.1 − 2.8 − 4.6 − 3.0 − 5.2 − 3.5 − 6.3 − 4.5 − 8.0 − 5.0 − 9.0 − 6.0 −10.5 − 7 −12 − 8 −14 −10 −17 −12 −20 −14 −23 −16 −26

4 12 4.5 14.5 5 17 6 20 7 23 8 28 10 34 11 39 12 44 16 52 20 60 22 66 25 75

+4 0 +5 0 +6 0 +7 0 +8 0 +10 0 +12 0 +14 0 +16 0 +18 0 +20 0 +22 0 +25 0

− 4 − 8 − 4.5 − 9.5 − 5 −11 − 6 −13 − 7 −15 − 8 −18 −10 −22 −11 −25 −12 −28 −16 −34 −20 −40 −22 −44 −25 −50

− 5 − 11 − 6 −13 − 7 −16 − 8 −18 −10 −22 −12 −28 −14 −32 −16 −38 −18 −43 −22 −50 −28 −58 −30 −65 −35 −75

CLEARANCE LOCATIONAL FITS

0.24 − 0.40

Class LC 9


a Pairs of values shown represent minimum and maximum amounts of interference resulting from application of standard tolerance limits.


661

Tolerance limits given in body of table are added or subtracted to basic size (as indicated by + or − sign) to obtain maximum and minimum sizes of mating parts. All data above heavy lines are in accordance with American-British-Canadian (ABC) agreements. Symbols H6, H7, s6, etc. are hole and shaft designations in ABC system. Limits for sizes above 19.69 inches are not covered by ABC agreements but are given in the ANSI Standard.


Nominal Size Range, Inches Over

Class LT 2

Std. Tolerance Limits Fita

Hole H7

Shaft js6

Class LT 3


Hole H8

Shaft js7

Fita

To

0 – 0.12

0.24 – 0.40 0.40 – 0.71 0.71 – 1.19 1.19 – 1.97 1.97 – 3.15 3.15 – 4.73 4.73 – 7.09 7.09 – 9.85 9.85 – 12.41 12.41 – 15.75 15.75 – 19.69

Hole H7

Shaft k6

Class LT 5


Hole H8

Shaft k7

Class LT 6



Fita

Hole H7

Shaft n6

Fita

Hole H7

Shaft n7

−0.5 +0.15 −0.6 +0.2 −0.8 +0.2 −0.9 +0.2 −1.1 +0.2 −1.3 +0.3 −1.5 +0.4 −1.9 +0.4 −2.2 +0.4 −2.6 +0.4 −2.6 +0.6 −3.0 +0.6 −3.4 +0.7

+0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.5 +0.25 +0.6 +0.3 +0.8 +0.4 +0.9 +0.5 +1.1 +0.6 +1.3 +0.7 +1.5 +0.8 +1.9 +1.0 +2.2 +1.2 +2.6 +1.4 +2.6 +1.4 +3.0 +1.6 +3.4 +1.8

−0.65 +0.15 −0.8 +0.2 −1.0 +0.2 −1.2 +0.2 −1.4 +0.2 −1.7 +0.3 −2.0 +0.4 −2.4 +0.4 −2.8 +0.4 −3.2 +0.4 −3.4 +0.6 −3.8 +0.6 −4.3 +0.7

+0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.65 +0.25 +0.8 +0.3 +1.0 +0.4 +1.2 +0.5 +1.4 +0.6 +1.7 +0.7 +2.0 +0.8 +2.4 +1.0 +2.8 +1.2 +3.2 +1.4 +3.4 +1.4 +3.8 +1.6 +4.3 +1.8

Values shown below are in thousandths of an inch −0.12 +0.52 −0.15 +0.65 −0.2 +0.8 −0.2 +0.9 −0.25 +1.05 −0.3 +1.3 −0.3 +1.5 −0.4 +1.8 −0.5 +2.1 −0.6 +2.4 −0.6 +2.6 −0.7 +2.9 −0.8 +3.3

+0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.12 −0.12 +0.15 −0.15 +0.2 −0.2 +0.2 −0.2 +0.25 −0.25 +0.3 −0.3 +0.3 −0.3 +0.4 −0.4 +0.5 −0.5 +0.6 −0.6 +0.6 −6.6 +0.7 −0.7 +0.8 −0.8

−0.2 +0.8 −0.25 +0.95 −0.3 +1.2 −0.35 +1.35 −0.4 +1.6 −0.5 +2.1 −0.6 +2.4 −0.7 +2.9 −0.8 +3.3 −0.9 +3.7 −1.0 +4.0 −1.0 +4.5 −1.2 +5.2

+0.6 0 +0.7 0 +0.9 0 +1.0 0 +1.2 0 +1.6 0 +1.8 0 +2.2 0 +2.5 0 +2.8 0 +3.0 0 +3.5 0 +4.0 0

+0.2 −0.2 +0.25 −0.25 +0.3 −0.3 +0.35 −0.35 +0.4 −0.4 +0.5 −0.5 +0.6 −0.6 +0.7 −0.7 +0.8 −0.8 +0.9 −0.9 +1.0 −1.0 +1.0 −1.0 +1.2 −1.2

−0.5 +0.5 −0.5 +0.6 −0.6 +0.7 −0.7 +0.9 −0.8 +1.1 −1.0 +1.3 −1.1 +1.5 −1.4 +1.6 −1.4 +1.8 −1.6 +2.0 −1.8 +2.3

+0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.5 +0.1 +0.5 +0.1 +0.6 +0.1 +0.7 +0.1 +0.8 +0.1 +1.0 +0.1 +1.1 +0.1 +1.4 +0.2 +1.4 +0.2 +1.6 +0.2 +1.8 +0.2

−0.7 +0.8 −0.8 +0.9 −0.9 +1.1 −1.1 +1.5 −1.3 +1.7 −1.5 +2.1 −1.7 +2.4 −2.0 +2.6 −2.2 +2.8 −2.4 +3.3 −2.7 +3.8

+0.9 0 +1.0 0 +1.2 0 +1.6 0 +1.8 0 +2.2 0 +2.5 0 +2.8 0 +3.0 0 +3.5 0 +4.0 0

+0.7 +0.1 +0.8 +0.1 +0.9 +0.1 +1.1 +0.1 +1.3 +0.1 +1.5 +0.1 +1.7 +0.1 +2.0 +0.2 +2.2 +0.2 +2.4 +0.2 +2.7 +0.2

a Pairs of values shown represent maximum amount of interference (−) and maximum amount of clearance (+) resulting from application of standard tolerance limits. All data above heavy lines are in accord with ABC agreements. Symbols H7, js6, etc., are hole and shaft designations in the ABC system.


TRANSITION LOCATIONAL FITS

0.12 – 0.24

Class LT 4


662

Table 10. ANSI Standard Transition Locational Fits ANSI B4.1-1967 (R1999) Class LT 1


Table 11. ANSI Standard Force and Shrink Fits ANSI B4.1-1967 (R1999) Class FN 1 Nominal Size Range, Inches Over

Interferencea

Hole H6

0.12– 0.24

Shaft

Interferencea

Hole H7

Shaft s6

+0.5

0.2

+0.4

+0.85

0.40– 0.56 0.56– 0.71 0.71– 0.95 0.95– 1.19 1.58

1.58– 1.97 1.97– 2.56 2.56– 3.15 3.15– 3.94 3.94– 4.73

Class FN 4

Standard Tolerance Limits Interferencea

Hole H7

Shaft t6

Class FN 5


Hole H7

Shaft u6


Hole H8

Shaft x7

Values shown below are in thousandths of an inch 0.3

+0.4

+0.95

0.3

+0.6

+1.3

0.5

0

+0.3

0.85

0

+0.6

0.95

0

+0.7

1.3

0

+0.9

0.1

+0.3

+0.6

0.2

+0.5

+1.0

0.4

+0.5

+1.2

0.5

+0.7

+1.7

0.6

0

+0.4

1.0

0

+0.7

1.2

0

+0.9

1.7

0

+1.2

0.1

+0.4

+0.75

0.4

+0.6

+1.4

0.6

+0.6

+1.6

0.5

+0.9

+2.0

0.75

0

+0.5

1.4

0

+1.0

1.6

0

+1.2

2.0

0

+1.4

0.05

+0.25

+0.8

0.5

+0.7

+1.6

0.7

+0.7

+1.8

0.6

+1.0

+2.3

0

+0.5

1.6

0

+1.2

1.8

0

+1.4

2.3

0

+1.6

0.2

+0.4

+0.9

0.5

+0.7

+1.6

0.7

+0.7

+1.8

0.8

+1.0

+2.5

0.9

0

+0.6

1.6

0

+1.2

1.8

0

+1.4

2.5

0

+1.8

0.2

+0.5

+1.1

0.6

+0.8

+1.9

0.8

+0.8

+2.1

1.0

+1.2

+3.0

1.1

0

+0.7

1.9

0

+1.4

2.1

0

+1.6

3.0

0

+2.2

0.3

+0.5

+1.2

0.6

+0.8

+1.9

0.8

+0.8

+2.1

+1.0

+0.8

+2.3

1.3

+1.2

+3.3

1.2

0

+0.8

1.9

0

+1.4

2.1

0

+1.6

2.3

0

+1.8

3.3

0

+2.5

0.3

+0.6

+1.3

0.8

+1.0

+2.4

1.0

+1.0

+2.6

1.5

+1.0

+3.1

1.4

+1.6

+4.0

1.3

0

+0.9

2.4

0

+1.8

2.6

0

+2.0

3.1

0

+2.5

4.0

0

+3.0

0.4

+0.6

+1.4

0.8

+1.0

+2.4

1.2

+1.0

+2.8

1.8

+1.0

+3.4

2.4

+1.6

+5.0

1.4

0

+1.0

2.4

0

+1.8

2.8

0

+2.2

3.4

0

+2.8

5.0

0

+4.0

0.6

+0.7

+1.8

0.8

+1.2

+2.7

1.3

+1.2

+3.2

2.3

+1.2

+4.2

3.2

+1.8

+6.2

1.8

0

+1.3

2.7

0

+2.0

3.2

0

+2.5

4.2

0

+3.5

6.2

0

+5.0

0.7

+0.7

+1.9

1.0

+1.2

+2.9

1.8

+1.2

+3.7

2.8

+1.2

+4.7

4.2

+1.8

+7.2

1.9

0

+1.4

2.9

0

+2.2

3.7

0

+3.0

4.7

0

+4.0

7.2

0

+6.0

0.9

+0.9

+2.4

1.4

+1.4

+3.7

2.1

+1.4

+4.4

3.6

+1.4

+5.9

4.8

+2.2

+8.4

2.4

0

+1.8

3.7

0

+2.8

4.4

0

+3.5

5.9

0

+5.0

8.4

0

+7.0

1.1

+0.9

+2.6

1.6

+1.4

+3.9

2.6

+1.4

+4.9

4.6

+1.4

+6.9

5.8

+2.2

+9.4

2.6

0

+2.0

3.9

0

+3.0

4.9

0

+4.0

6.9

0

+6.0

9.4

0

+8.0

0.1


663

+0.4

0.8

FORCE AND SHRINK FITS

0.24– 0.40

Class FN 3


To

0– 0.12

1.19–

Class FN 2



Nominal Size Range, Inches Over

Class FN 2


Hole H6

Shaft

Interferencea

Hole H7

Shaft s6

+2.9

1.9

+1.6

+4.5

To 5.52

5.52–

6.30

6.30–

7.09

7.09–

7.88

7.88–

8.86

8.86–

9.85

9.85– 11.03 11.03– 12.41 12.41– 13.98 13.98– 15.75 15.75– 17.72 17.72– 19.69

Class FN 4


Hole H7

Shaft t6

Class FN 5


Hole H7

Shaft u6


Hole H8

Shaft x7

Values shown below are in thousandths of an inch 3.4

+1.6

+6.0

5.4

+1.6

+8.0

7.5

+2.5

+11.6

2.9

0

+2.2

4.5

0

+3.5

6.0

0

+5.0

8.0

0

+7.0

11.6

0

+10.0

1.5

+1.0

+3.2

2.4

+1.6

+5.0

3.4

+1.6

+6.0

5.4

+1.6

+8.0

9.5

+2.5

+13.6

3.2

0

+2.5

5.0

0

+4.0

6.0

0

+5.0

8.0

0

+7.0

13.6

0

+12.0

1.8

+1.0

+3.5

2.9

+1.6

+5.5

4.4

+1.6

+7.0

6.4

+1.6

+9.0

9.5

+2.5

3.5

0

+2.8

5.5

0

+4.5

7.0

0

+6.0

9.0

0

+8.0

13.6

0

+12.0

1.8

+1.2

+3.8

3.2

+1.8

+6.2

5.2

+1.8

+8.2

7.2

+1.8

+10.2

11.2

+2.8

+15.8

3.8

0

+3.0

6.2

0

+5.0

8.2

0

+7.0

10.2

0

+9.0

15.8

0

+14.0

2.3

+1.2

+4.3

3.2

+1.8

+6.2

5.2

+1.8

+8.2

8.2

+1.8

+11.2

13.2

+2.8

+17.8

4.3

0

+3.5

6.2

0

+5.0

8.2

0

+7.0

11.2

0

+10.0

17.8

0

+16.0

2.3

+1.2

+4.3

4.2

+1.8

+7.2

6.2

+1.8

+9.2

10.2

+1.8

+13.2

13.2

+2.8

+17.8

4.3

0

+3.5

7.2

0

+6.0

9.2

0

+8.0

13.2

0

+12.0

17.8

0

+16.0

2.8

+1.2

+4.9

4.0

+2.0

+7.2

7.0

+2.0

+10.2

10.0

+2.0

+13.2

15.0

+3.0

+20.0

4.9

0

+4.0

7.2

0

+6.0

10.2

0

+9.0

13.2

0

+12.0

20.0

0

+18.0

2.8

+1.2

+4.9

5.0

+2.0

+8.2

7.0

+2.0

+10.2

12.0

+2.0

+15.2

17.0

+3.0

+22.0

4.9

0

+4.0

8.2

0

+7.0

10.2

0

+9.0

15.2

0

+14.0

22.0

0

+20.0 +24.2

1.2

+1.0

+13.6

3.1

+1.4

+5.5

5.8

+2.2

+9.4

7.8

+2.2

+11.4

13.8

+2.2

+17.4

18.5

+3.5

5.5

0

+4.5

9.4

0

+8.0

11.4

0

+10.0

17.4

0

+16.0

24.2

0

+22.0

3.6

+1.4

+6.1

5.8

+2.2

+9.4

9.8

+2.2

+13.4

15.8

+2.2

+19.4

21.5

+3.5

+27.2

6.1

0

+5.0

9.4

0

+8.0

13.4

0

+12.0

19.4

0

+18.0

27.2

0

+25.0

4.4

+1.6

+7.0

6.5

+2.5

+10.6

+9.5

+2.5

+13.6

17.5

+2.5

+21.6

24.0

+4.0

+30.5

7.0

0

+6.0

10.6

0

+9.0

13.6

0

+12.0

21.6

0

+20.0

30.5

0

+28.0

4.4

+1.6

+7.0

7.5

+2.5

+11.6

11.5

+2.5

+15.6

19.5

+2.5

+23.6

26.0

+4.0

+32.5

7.0

0

+6.0

11.6

0

+10.0

15.6

0

+14.0

23.6

0

+22.0

32.5

0

+30.0

a Pairs of values shown represent minimum and maximum amounts of interference resulting from application of standard tolerance limits.

All data above heavy lines are in accordance with American-British-Canadian (ABC) agreements. Symbols H6, H7, s6, etc., are hole and shaft designations in the ABC system. Limits for sizes above 19.69 inches are not covered by ABC agreements but are given in the ANSI standard.


FORCE AND SHRINK FITS

4.73–

Class FN 3


664

Table 11. (Continued) ANSI Standard Force and Shrink Fits ANSI B4.1-1967 (R1999) Class FN 1

Machinery's Handbook 27th Edition INTERFERENCE LOCATIONAL FITS

665

Table 12. ANSI Standard Interference Location Fits ANSI B4.1-1967 (R1999) Class LN 1 Nominal Size Range, Inches Over

Limits of Interference

Hole H6

To 0– 0.12

0.12– 0.24 0.24– 0.40 0.40– 0.71 0.71– 1.19 1.19– 1.97 1.97– 3.15 3.15– 4.73 4.73– 7.09 7.09– 9.85 9.85– 12.41 12.41– 15.75 15.75– 19.69

Class LN 2

Standard Limits Shaft n5


Class LN 3

Standard Limits Hole H7

Shaft p6


Standard Limits Hole H7

Shaft r6

+0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.75 +0.5 +0.9 +0.6 +1.2 +0.8 +1.4 +1.0 +1.7 +1.2 +2.0 +1.4 +2.3 +1.6 +2.9 +2.0 +3.5 +2.5 +4.2 +3.0 +4.7 +3.5 +5.9 +4.5 +6.6 +5.0

Values shown below are given in thousandths of an inch 0 0.45 0 0.5 0 0.65 0 0.8 0 1.0 0 1.1 0.1 1.3 0.1 1.6 0.2 1.9 0.2 2.2 0.2 2.3 0.2 2.6 0.2 2.8

+0.25 0 +0.3 0 +0.4 0 +0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.9 0 +1.0 0 +1.2 0 +1.2 0 +1.4 0 +1.6 0

+0.45 +0.25 +0.5 +0.3 +0.65 +0.4 +0.8 +0.4 +1.0 +0.5 +1.1 +0.6 +1.3 +0.8 +1.6 +1.0 +1.9 +1.2 +2.2 +1.4 +2.3 +1.4 +2.6 +1.6 +2.8 +1.8

0 0.65 0 0.8 0 1.0 0 1.1 0 1.3 0 1.6 0.2 2.1 0.2 2.5 0.2 2.8 0.2 3.2 0.2 3.4 0.3 3.9 0.3 4.4

+0.4 0 +0.5 0 +0.6 0 +0.7 0 +0.8 0 +1.0 0 +1.2 0 +1.4 0 +1.6 0 +1.8 0 +2.0 0 +2.2 0 +2.5 0

+0.65 +0.4 +0.8 +0.5 +1.0 +0.6 +1.1 +0.7 +1.3 +0.8 +1.6 +1.0 +2.1 +1.4 +2.5 +1.6 +2.8 +1.8 +3.2 +2.0 +3.4 +2.2 +3.9 +2.5 +4.4 +2.8

0.1 0.75 0.1 0.9 0.2 1.2 0.3 1.4 0.4 1.7 0.4 2.0 0.4 2.3 0.6 2.9 0.9 3.5 1.2 4.2 1.5 4.7 2.3 5.9 2.5 6.6

All data in this table are in accordance with American-British-Canadian (ABC) agreements. Limits for sizes above 19.69 inches are not covered by ABC agreements but are given in the ANSI Standard. Symbols H7, p6, etc., are hole and shaft designations in the ABC system. Tolerance limits given in body of table are added or subtracted to basic size (as indicated by + or − sign) to obtain maximum and minimum sizes of mating parts.

American National Standard Preferred Metric Limits and Fits This standard ANSI B4.2-1978 (R1999) describes the ISO system of metric limits and fits for mating parts as approved for general engineering usage in the United States. It establishes: 1) the designation symbols used to define dimensional limits on drawings, material stock, related tools, gages, etc.; 2) the preferred basic sizes (first and second choices); 3) the preferred tolerance zones (first, second, and third choices); 4 ) t h e p r e ferred limits and fits for sizes (first choice only) up to and including 500 millimeters; and 5) the definitions of related terms. The general terms “hole” and “shaft” can also be taken to refer to the space containing or contained by two parallel faces of any part, such as the width of a slot, or the thickness of a key. Definitions.—The most important terms relating to limits and fits are shown in Fig. 1 and are defined as follows: Basic Size: The size to which limits of deviation are assigned. The basic size is the same for both members of a fit. For example, it is designated by the numbers 40 in 40H7. Deviation: The algebraic difference between a size and the corresponding basic size.



ANSI STANDARD PREFERRED METRIC LIMITS AND FITS

Upper Deviation: The algebraic difference between the maximum limit of size and the corresponding basic size. Lower Deviation: The algebraic difference between the minimum limit of size and the corresponding basic size. Fundamental Deviation: That one of the two deviations closest to the basic size. For example, it is designated by the letter H in 40H7. Tolerance: The difference between the maximum and minimum size limits on a part. Tolerance Zone: A zone representing the tolerance and its position in relation to the basic size.

Fig. 1. Illustration of Definitions

International Tolerance Grade: (IT): A group of tolerances that vary depending on the basic size, but that provide the same relative level of accuracy within a given grade. For example, it is designated by the number 7 in 40H7 or as IT7. Hole Basis: The system of fits where the minimum hole size is basic. The fundamental deviation for a hole basis system is H. Shaft Basis: The system of fits where the maximum shaft size is basic. The fundamental deviation for a shaft basis system is h. Clearance Fit: The relationship between assembled parts when clearance occurs under all tolerance conditions. Interference Fit: The relationship between assembled parts when interference occurs under all tolerance conditions. Transition Fit: The relationship between assembled parts when either a clearance or an interference fit can result, depending on the tolerance conditions of the mating parts. Tolerances Designation.—An “International Tolerance grade” establishes the magnitude of the tolerance zone or the amount of part size variation allowed for external and internal dimensions alike (see Fig. 1). Tolerances are expressed in grade numbers that are consistent with International Tolerance grades identified by the prefix IT, such as IT6, IT11, etc. A smaller grade number provides a smaller tolerance zone.


Machinery's Handbook 27th Edition PREFERRED METRIC FITS

667

A fundamental deviation establishes the position of the tolerance zone with respect to the basic size (see Fig. 1). Fundamental deviations are expressed by tolerance position letters. Capital letters are used for internal dimensions and lowercase or small letters for external dimensions. Symbols.—By combining the IT grade number and the tolerance position letter, the tolerance symbol is established that identifies the actual maximum and minimum limits of the part. The toleranced size is thus defined by the basic size of the part followed by a symbol composed of a letter and a number, such as 40H7, 40f7, etc. A fit is indicated by the basic size common to both components, followed by a symbol corresponding to each component, the internal part symbol preceding the external part symbol, such as 40H8/f7. Some methods of designating tolerances on drawings are: 40.039⎞ 40H8 ⎛

40H8

⎛ 40.039⎞ 40H8 ⎝ 40.000⎠

⎝ 40.000⎠

The values in parentheses indicate reference only.

Preferred Metric Fits.—First-choice tolerance zones are used to establish preferred fits in ANSI B4.2, Preferred Metric Limits and Fits, as shown in Figs. 2 and 3. A complete listing of first-, second-, and thirdchoice tolerance zones is given in the Standard. Hole basis fits have a fundamental deviation of H on the hole, and shaft basis fits have a fundamental deviation of h on the shaft and are shown in Fig. 2 for hole basis and Fig. 3 for shaft basis fits. A description of both types of fits, that have the same relative fit condition, is given in Table 1. Normally, the hole basis system is preferred; however, when a common shaft mates with several holes, the shaft basis system should be used. The hole basis and shaft basis fits shown in the table Description of Preferred Fits on page 669 are combined with the first-choice preferred metric sizes from Table 1 on page 690, to form Tables 2, 3, 4, and 5, in which specific limits as well as the resultant fits are tabulated. If the required size is not found tabulated in Tables 2 through 5 then the preferred fit can be calculated from numerical values given in an appendix of ANSI B4.2-1978 (R1999). It is anticipated that other fit conditions may be necessary to meet special requirements, and a preferred fit can be loosened or tightened simply by selecting a standard tolerance zone as given in the Standard. Information on how to calculate limit dimensions, clearances, and interferences, for nonpreferred fits and sizes can be found in an appendix of this Standard. Conversion of Fits: It may sometimes be neccessary or desirable to modify the tolereance zone on one or both of two mating parts, yet still keep the total tolerance and fit condition the same. Examples of this appear in Table 1 on page 669 when converting from a hole basis fit to a shaft basis fit. The corresponding fits are identical yet the individual tolerance zones are different. To convert from one type of fit to another, reverse the fundamental devations between the shaft and hole keeping the IT grade the same on each individual part. The examples below represent preferred fits from Table 1 for a 60-mm basic size. These fits have the same maximum clearance (0.520) and the same minimum clearance (0.140). Hole basis, loose running fit, values from Table 2 Hole 60H11

⎛ 60.190⎞ ⎝ 60.000⎠

Hole 60C11

⎛ 60.330⎞ ⎝ 60.140⎠

Shaft 60c11

⎛ 59.860⎞ ⎝ 59.670⎠

Fit 60H11/c11

⎛ 0.520⎞ ⎝ 0.140⎠

Hole basis, loose running fit, values from Table 4 Shaft 60h11

⎛ 60.000⎞ ⎝ 59.810⎠

Fit 60C11/h11


⎛ 0.520⎞ ⎝ 0.140⎠

Machinery's Handbook 27th Edition PREFERRED METRIC FITS

Shaft Tolerance u6

H11

s6 p6

n6

H9

Maximum Interference

K6

H8

H7 g6

Minimum Tolerance Shaft Tolerance

Maximum Clearance

Hole Tolerance

668

H7 h6

H7

H7

H7

H7

Basic Size

H7

Minimum Interference Hole Tolerance

f7

d9

c11

Transition

Clearance

Interference

Minimum tolerance

C11

D9

F8 G7 h7

Shaft tolerance

Maximum clearance

Hole tolerance

Fig. 2. Preferred Hole Basis Fits

h6

H7 h6

h6 h6

h9

Shaft tolerance

K7 h6

Basic size

h6

h6 N7

Maximum interference

P7 S7

h11

U7

Minimum interference Hole tolerance

Clearance

Transition

Interference

Fig. 3. Preferred Shaft Basis Fits



Table 1. Description of Preferred Fits

Transition Fits Interference Fits

DESCRIPTION

Shaft Basis

H11/c11

C11/h11

H9/d9

D9/h9

Free running fit not for use where accuracy is essential, but good for large temperature variations, high running speeds, or heavy journal pressures.

H8/f7

F8/h7

Close Running fit for running on accurate machines and for accurate moderate speeds and journal pressures.

H7/g6

G7/h6

H7/h6

H7/h6

H7/k6

K7/h6

Locational transition fit for accurate location, a compromise between clearance and interferance.

H7/n6

N7/h6

Locational transition fit for more accurate location where greater interferance is permissible.

H7/p6a

P7/h6

Locational interference fit for parts requiring rigidity and alignment with prime accuracy of location but without special bore pressure requirements.

H7/s6

S7/h6

Medium drive fit for ordinary steel parts or shrink fits on light sections, the tightest fit usable with cast iron.

H7/u6

U7/h6

Force fit suitable for parts which can be highly stressed or for shrink fits where the heavy pressing forces required are impractical.

Loose running fit for wide commercial tolerances or allowances on external members.

↑ More Clearance

Sliding fit not intended to run freely, but to move and turn freely and locate accurately. Locational clearance fit provides snug fit for locating stationary parts; but can be freely assembled and disassembled.


More Interferance ↓

669

a Transition fit for basic sizes in range from 0 through 3 mm.

PREFERRED METRIC FITS

Clearance Fits

ISO SYMBOL Hole Basis


670

Table 2. American National Standard Preferred Hole Basis Metric Clearance Fits ANSI B4.2-1978 (R1999) Loose Running Basic Sizea 1

2 2.5 3 4 5 6 8 10 12 16 20 25

Shaft C11

1.060 1.000 1.260 1.200 1.660 1.600 2.060 2.000 2.560 2.500 3.060 3.000 4.075 4.000 5.075 5.000 6.075 6.000 8.090 8.000 10.090 10.000 12.110 12.000 16.110 16.000 20.130 20.000 25.130 25.000

0.940 0.880 1.140 1.080 1.540 1.480 1.940 1.880 2.440 2.380 2.940 2.880 3.930 3.855 4.930 4.855 5.930 5.855 7.920 7.830 9.920 9.830 11.905 11.795 15.905 15.795 19.890 19.760 24.890 24.760

Free Running

Close Running

Sliding

Locational Clearance

Fitb

Hole H9

Shaft d9

Fitb

Hole H8

Shaft f7

Fitb

Hole H7

Shaft g6

Fitb

Hole H7

Shaft h6

Fitb

0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.220 0.070 0.220 0.070 0.220 0.070 0.260 0.080 0.260 0.080 0.315 0.095 0.315 0.095 0.370 0.110 0.370 0.110

1.025 1.000 1.225 1.200 1.625 1.600 2.025 2.000 2.525 2.500 3.025 3.000 4.030 4.000 5.030 5.000 6.030 6.000 8.036 8.000 10.036 10.000 12.043 12.000 16.043 16.000 20.052 20.000 25.052 25.000

0.980 0.995 1.180 1.155 1.580 1.555 1.980 1.955 2.480 2.455 2.980 2.955 3.970 3.940 4.970 4.940 5.970 5.940 7.960 7.924 9.960 9.924 11.956 11.907 15.950 15.907 19.935 19.883 24.935 24.883

0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.090 0.030 0.090 0.030 0.090 0.030 0.112 0.040 0.112 0.040 0.136 0.050 0.136 0.050 0.169 0.065 0.169 0.065

1.014 1.000 1.214 1.200 1.614 1.600 2.014 2.000 2.514 2.500 3.014 3.000 4.018 4.000 5.018 5.000 6.018 6.000 8.022 8.000 10.022 10.000 12.027 12.000 16.027 16.000 20.033 20.000 25.033 25.000

0.994 0.984 1.194 1.184 1.594 1.584 1.994 1.984 2.494 2.484 2.994 2.984 3.990 3.978 4.990 4.978 5.990 5.978 7.987 7.972 9.987 9.972 11.984 11.966 15.984 15.966 19.980 19.959 24.980 24.959

0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.040 0.010 0.040 0.010 0.040 0.010 0.050 0.013 0.050 0.013 0.061 0.016 0.061 0.016 0.074 0.020 0.074 0.020

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

0.998 0.992 1.198 1.192 1.598 1.592 1.998 1.992 2.498 2.492 2.998 2.992 3.996 3.988 4.996 4.988 5.996 5.988 7.995 7.986 9.995 9.986 11.994 11.983 15.994 15.983 19.993 19.980 24.993 24.980

0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.024 0.004 0.024 0.004 0.024 0.004 0.029 0.005 0.029 0.005 0.035 0.006 0.035 0.006 0.041 0.007 0.041 0.007

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.020 0.000 0.020 0.000 0.020 0.000 0.024 0.000 0.024 0.000 0.029 0.000 0.029 0.000 0.034 0.000 0.034 0.000


HOLE BASIS METRIC CLEARANCE FITS

1.2 1.6

Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min

Hole H11


Table 2. (Continued) American National Standard Preferred Hole Basis Metric Clearance Fits ANSI B4.2-1978 (R1999) Loose Running Basic Sizea 30 40

60 80 100 120 160 200 250 300 400 500

Shaft C11 29.890 29.760 39.880 39.720 49.870 49.710 59.860 59.670 79.850 79.660 99.830 99.610 119.820 119.600 159.790 159.540 199.760 199.470 249.720 249.430 299.670 299.350 399.600 399.240 499.520 499.120

Free Running Fitb 0.370 0.110 0.440 0.120 0.450 0.130 0.520 0.140 0.530 0.150 0.610 0.170 0.620 0.180 0.710 0.210 0.820 0.240 0.860 0.280 0.970 0.330 1.120 0.400 1.280 0.480

Hole H9 30.052 30.000 40.062 40.000 50.062 50.000 60.074 60.000 80.074 80.000 100.087 100.000 120.087 120.000 160.100 160.000 200.115 200.000 250.115 250.000 300.130 300.000 400.140 400.000 500.155 500.000

Shaft d9 29.935 29.883 39.920 39.858 49.920 49.858 59.900 59.826 79.900 79.826 99.880 99.793 119.880 119.793 159.855 159.755 199.830 199.715 249.830 249.715 299.810 299.680 399.790 399.650 499.770 499.615

Close Running Fitb 0.169 0.065 0.204 0.080 0.204 0.080 0.248 0.100 0.248 0.100 0.294 0.120 0.294 0.120 0.345 0.145 0.400 0.170 0.400 0.170 0.450 0.190 0.490 0.210 0.540 0.230

Hole H8 30.033 30.000 40.039 40.000 50.039 50.000 60.046 60.000 80.046 80.000 100.054 100.000 120.054 120.000 160.063 160.000 200.072 200.000 250.072 250.000 300.081 300.000 400.089 400.000 500.097 500.000

Shaft f7 29.980 29.959 39.975 39.950 49.975 49.950 59.970 59.940 79.970 79.940 99.964 99.929 119.964 119.929 159.957 159.917 199.950 199.904 249.950 249.904 299.944 299.892 399.938 399.881 499.932 499.869

Sliding Fitb 0.074 0.020 0.089 0.025 0.089 0.025 0.106 0.030 0.106 0.030 0.125 0.036 0.125 0.036 0.146 0.043 0.168 0.050 0.168 0.050 0.189 0.056 0.208 0.062 0.228 0.068

Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft g6 29.993 29.980 39.991 39.975 49.991 49.975 59.990 59.971 79.990 79.971 99.988 99.966 119.988 119.966 159.986 159.961 199.985 199.956 249.985 249.956 299.983 299.951 399.982 399.946 499.980 499.940

Locational Clearance Fitb 0.041 0.007 0.050 0.009 0.050 0.009 0.059 0.010 0.059 0.010 0.069 0.012 0.069 0.012 0.079 0.014 0.090 0.015 0.090 0.015 0.101 0.017 0.111 0.018 0.123 0.020

Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb 0.034 0.000 0.041 0.000 0.041 0.000 0.049 0.000 0.049 0.000 0.057 0.000 0.057 0.000 0.065 0.000 0.075 0.000 0.075 0.000 0.084 0.000 0.093 0.000 0.103 0.000

HOLE BASIS METRIC CLEARANCE FITS

50

Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min Max Min

Hole H11 30.130 30.000 40.160 40.000 50.160 50.000 60.190 60.000 80.190 80.000 100.220 100.000 120.220 120.000 160.250 160.000 200.290 200.000 250.290 250.000 300.320 300.000 400.360 400.000 500.400 500.000

a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b All fits shown in this table have clearance.

All dimensions are in millimeters.

671



672

Table 3. American National Standard Preferred Hole Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999) Locational Transition Basic Sizea 1 1.2

2 2.5 3 4 5 6 8 10 12 16 20 25

Locational Interference

Medium Drive

Force

Shaft k6

Fitb

Hole H7

Shaft n6

Fitb

Hole H7

Shaft p6

Fitb

Hole H7

Shaft s6

Fitb

Hole H7

Shaft u6

Fitb

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.006 1.000 1.206 1.200 1.606 1.600 2.006 2.000 2.506 2.500 3.006 3.000 4.009 4.001 5.009 5.001 6.009 6.001 8.010 8.001 10.010 10.001 12.012 12.001 16.012 16.001 20.015 20.002 25.015 25.002

+0.010 −0.006 +0.010 −0.006 +0.010 −0.006 +0.010 −0.006 +0.010 −0.006 +0.010 −0.006 +0.011 −0.009 +0.011 −0.009 +0.011 −0.009 +0.014 −0.010 +0.014 −0.010 +0.017 −0.012 +0.017 −0.012 +0.019 −0.015 +0.019 −0.015

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.010 1.004 1.210 1.204 1.610 1.604 2.010 2.004 2.510 2.504 3.010 3.004 4.016 4.008 5.016 5.008 6.016 6.008 8.019 8.010 10.019 10.010 12.023 12.012 16.023 16.012 20.028 20.015 25.028 25.015

+0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.004 −0.016 +0.004 −0.016 +0.004 −0.016 +0.005 −0.019 +0.005 −0.019 +0.006 −0.023 +0.006 −0.023 +0.006 −0.028 +0.006 −0.028

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.012 1.006 1.212 1.206 1.612 1.606 2.012 2.006 2.512 2.506 3.012 3.006 4.020 4.012 5.020 5.012 6.020 6.012 8.024 8.015 10.024 10.015 12.029 12.018 16.029 16.018 20.035 20.022 25.035 25.022

+0.004 −0.012 +0.004 −0.012 +0.004 −0.012 +0.004 −0.012 +0.004 −0.012 +0.004 −0.012 0.000 −0.020 0.000 −0.020 0.000 −0.020 0.000 −0.024 0.000 −0.024 0.000 −0.029 0.000 −0.029 −0.001 −0.035 −0.001 −0.035

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.020 1.014 1.220 1.214 1.620 1.614 2.020 2.014 2.520 2.514 3.020 3.014 4.027 4.019 5.027 5.019 6.027 6.019 8.032 8.023 10.032 10.023 12.039 12.028 16.039 16.028 20.048 20.035 25.048 25.035

−0.004 −0.020 −0.004 −0.020 −0.004 −0.020 −0.004 −0.020 −0.004 −0.020 −0.004 −0.020 −0.007 −0.027 −0.007 −0.027 −0.007 −0.027 −0.008 −0.032 −0.008 −0.032 −0.010 −0.039 −0.010 −0.039 −0.014 −0.048 −0.014 −0.048

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.024 1.018 1.224 1.218 1.624 1.618 2.024 2.018 2.524 2.518 3.024 3.018 4.031 4.023 5.031 5.023 6.031 6.023 8.037 8.028 10.034 10.028 12.044 12.033 16.044 16.033 20.054 20.041 25.061 25.048

−0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.011 −0.031 −0.011 −0.031 −0.011 −0.031 −0.013 −0.037 −0.013 −0.037 −0.015 −0.044 −0.015 −0.044 −0.020 −0.054 −0.027 −0.061


HOLE BASIS METRIC TRANSITION FITS

1.6


Locational Transition

Hole H7


Table 3. (Continued) American National Standard Preferred Hole Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999) Locational Transition Basic Sizea 30 40

60 80 100 120 160 200 250 300 400 500

Shaft k6 30.015 30.002 40.018 40.002 50.018 50.002 60.021 60.002 80.021 80.002 100.025 100.003 120.025 120.003 160.028 160.003 200.033 200.004 250.033 250.004 300.036 300.004 400.040 400.004 500.045 500.005

Fitb +0.019 −0.015 +0.023 −0.018 +0.023 −0.018 +0.028 −0.021 +0.028 −0.021 +0.032 −0.025 +0.032 −0.025 +0.037 −0.028 +0.042 −0.033 +0.042 −0.033 +0.048 −0.036 +0.053 −0.040 +0.058 −0.045

Locational Transition Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft n6 30.028 30.015 40.033 40.017 50.033 50.017 60.039 60.020 80.039 80.020 100.045 100.023 120.045 120.023 160.052 160.027 200.060 200.031 250.060 250.031 300.066 300.034 400.073 400.037 500.080 500.040

Fitb +0.006 −0.028 +0.008 −0.033 +0.008 −0.033 +0.010 −0.039 +0.010 −0.039 +0.012 −0.045 +0.012 −0.045 +0.013 −0.052 +0.015 −0.060 +0.015 −0.060 +0.018 −0.066 +0.020 −0.073 +0.023 −0.080

Locational Interference Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft p6 30.035 30.022 40.042 40.026 50.042 50.026 60.051 60.032 80.051 80.032 100.059 100.037 120.059 120.037 160.068 160.043 200.079 200.050 250.079 250.050 300.088 300.056 400.098 400.062 500.108 500.068

Fitb −0.001 −0.035 −0.001 −0.042 −0.001 −0.042 −0.002 −0.051 −0.002 −0.051 −0.002 −0.059 −0.002 −0.059 −0.003 −0.068 −0.004 −0.079 −0.004 −0.079 −0.004 −0.088 −0.005 −0.098 −0.005 −0.108

Medium Drive Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft s6 30.048 30.035 40.059 40.043 50.059 50.043 60.072 60.053 80.078 80.059 100.093 100.071 120.101 120.079 160.125 160.100 200.151 200.122 250.169 250.140 300.202 300.170 400.244 400.208 500.292 500.252

Force Fitb −0.014 −0.048 −0.018 −0.059 −0.018 −0.059 −0.023 −0.072 −0.029 −0.078 −0.036 −0.093 −0.044 −0.101 −0.060 −0.125 −0.076 −0.151 −0.094 −0.169 −0.118 −0.202 −0.151 −0.244 −0.189 −0.292

Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft u6 30.061 30.048 40.076 40.060 50.086 50.070 60.106 60.087 80.121 80.102 100.146 100.124 120.166 120.144 160.215 160.190 200.265 200.236 250.313 250.284 300.382 300.350 400.471 400.435 500.580 500.540

Fitb −0.027 −0.061 −0.035 −0.076 −0.045 −0.086 −0.057 −0.106 −0.072 −0.121 −0.089 −0.146 −0.109 −0.166 −0.150 −0.215 −0.190 −0.265 −0.238 −0.313 −0.298 −0.382 −0.378 −0.471 −0.477 −0.580

HOLE BASIS METRIC TRANSITION FITS

50


Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b A plus sign indicates clearance; a minus sign indicates interference.


673



674

Table 4. American National Standard Preferred Shaft Basis Metric Clearance Fits ANSI B4.2-1978 (R1999) Loose Running Basic Sizea 1

1.6 2 2.5 3 4 5 6 8 10 12 16 20 25

Shaft h11

1.120 1.060 1.320 1.260 1.720 1.660 2.120 2.060 2.620 2.560 3.120 3.060 4.145 4.070 5.145 5.070 6.145 6.070 8.170 8.080 10.170 10.080 12.205 12.095 16.205 16.095 20.240 20.110 25.240 25.110

1.000 0.940 1.200 1.140 1.600 1.540 2.000 1.940 2.500 2.440 3.000 2.940 4.000 3.925 5.000 4.925 6.000 5.925 8.000 7.910 10.000 9.910 12.000 11.890 16.000 15.890 20.000 19.870 25.000 24.870

Free Running

Close Running

Sliding

Locational Clearance

Fitb

Hole D9

Shaft h9

Fitb

Hole F8

Shaft h7

Fitb

Hole G7

Shaft h6

Fitb

Hole H7

Shaft h6

Fitb

0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.180 0.060 0.220 0.070 0.220 0.070 0.220 0.070 0.260 0.080 0.260 0.080 0.315 0.095 0.315 0.095 0.370 0.110 0.370 0.110

1.045 1.020 1.245 1.220 1.645 1.620 2.045 2.020 2.545 2.520 3.045 3.020 4.060 4.030 5.060 5.030 6.060 6.030 8.076 8.040 10.076 10.040 12.093 12.050 16.093 16.050 20.117 20.065 25.117 25.065

1.000 0.975 1.200 1.175 1.600 1.575 2.000 1.975 2.500 2.475 3.000 2.975 4.000 3.970 5.000 4.970 6.000 5.970 8.000 7.964 10.000 9.964 12.000 11.957 16.000 15.957 20.000 19.948 25.000 24.948

0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.070 0.020 0.090 0.030 0.090 0.030 0.090 0.030 0.112 0.040 0.112 0.040 0.136 0.050 0.136 0.050 0.169 0.065 0.169 0.065

1.020 1.006 1.220 1.206 1.620 1.606 2.020 2.006 2.520 2.506 3.020 3.006 4.028 4.010 5.028 5.010 6.028 6.010 8.035 8.013 10.035 10.013 12.043 12.016 16.043 16.016 20.053 20.020 25.053 25.020

1.000 0.990 1.200 1.190 1.600 1.590 2.000 1.990 2.500 2.490 3.000 2.990 4.000 3.988 5.000 4.988 6.000 5.988 8.000 7.985 10.000 9.985 12.000 11.982 16.000 15.982 20.000 19.979 25.000 24.979

0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.030 0.006 0.040 0.010 0.040 0.010 0.040 0.010 0.050 0.013 0.050 0.013 0.061 0.016 0.061 0.016 0.074 0.020 0.074 0.020

1.012 1.002 1.212 1.202 1.612 1.602 2.012 2.002 2.512 2.502 3.012 3.002 4.016 4.004 5.016 5.004 6.016 6.004 8.020 8.005 10.020 10.005 12.024 12.006 16.024 16.006 20.028 20.007 25.028 25.007

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.018 0.002 0.024 0.004 0.024 0.004 0.024 0.004 0.029 0.005 0.029 0.005 0.035 0.006 0.035 0.006 0.041 0.007 0.041 0.007

1.010 1.000 1.210 1.200 1.610 1.600 2.010 2.000 2.510 2.500 3.010 3.000 4.012 4.000 5.012 5.000 6.012 6.000 8.015 8.000 10.015 10.000 12.018 12.000 16.018 16.000 20.021 20.000 25.021 25.000

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.016 0.000 0.020 0.000 0.020 0.000 0.020 0.000 0.024 0.000 0.024 0.000 0.029 0.000 0.029 0.000 0.034 0.000 0.034 0.000


SHAFT BASIS METRIC CLEARANCE FITS

1.2


Hole C11


Table 4. (Continued) American National Standard Preferred Shaft Basis Metric Clearance Fits ANSI B4.2-1978 (R1999) Loose Running Basic Sizea 30 40

60 80 100 120 160 200 250 300 400 500

Shaft h11 30.000 29.870 40.000 39.840 50.000 49.840 60.000 59.810 80.000 79.810 100.000 99.780 120.000 119.780 160.000 159.750 200.000 199.710 250.000 249.710 300.000 299.680 400.000 399.640 500.000 499.600

Free Running Fitb 0.370 0.110 0.440 0.120 0.450 0.130 0.520 0.140 0.530 0.150 0.610 0.170 0.620 0.180 0.710 0.210 0.820 0.240 0.860 0.280 0.970 0.330 1.120 0.400 1.280 0.480

Hole D9 30.117 30.065 40.142 40.080 50.142 50.080 60.174 60.100 80.174 80.100 100.207 100.120 120.207 120.120 160.245 160.145 200.285 200.170 250.285 250.170 300.320 300.190 400.350 400.210 500.385 500.230

Shaft h9 30.000 29.948 40.000 39.938 50.000 49.938 60.000 59.926 80.000 79.926 100.000 99.913 120.000 119.913 160.000 159.900 200.000 199.885 250.000 249.885 300.000 299.870 400.000 399.860 500.000 499.845

Close Running Fitb 0.169 0.065 0.204 0.080 0.204 0.080 0.248 0.100 0.248 0.100 0.294 0.120 0.294 0.120 0.345 0.145 0.400 0.170 0.400 0.170 0.450 0.190 0.490 0.210 0.540 0.230

Hole F8 30.053 30.020 40.064 40.025 50.064 50.025 60.076 60.030 80.076 80.030 100.090 100.036 120.090 120.036 160.106 160.043 200.122 200.050 250.122 250.050 300.137 300.056 400.151 400.062 500.165 500.068

Shaft h7 30.000 29.979 40.000 39.975 50.000 49.975 60.000 59.970 80.000 79.970 100.000 99.965 120.000 119.965 160.000 159.960 200.000 199.954 250.000 249.954 300.000 299.948 400.000 399.943 500.000 499.937

Sliding Fitb 0.074 0.020 0.089 0.025 0.089 0.025 0.106 0.030 0.106 0.030 0.125 0.036 0.125 0.036 0.146 0.043 0.168 0.050 0.168 0.050 0.189 0.056 0.208 0.062 0.228 0.068

Hole G7 30.028 30.007 40.034 40.009 50.034 50.009 60.040 60.010 80.040 80.010 100.047 100.012 120.047 120.012 160.054 160.014 200.061 200.015 250.061 250.015 300.069 300.017 400.075 400.018 500.083 500.020

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Locational Clearance Fitb 0.041 0.007 0.050 0.009 0.050 0.009 0.059 0.010 0.059 0.010 0.069 0.012 0.069 0.012 0.079 0.014 0.090 0.015 0.090 0.015 0.101 0.017 0.111 0.018 0.123 0.020

Hole H7 30.021 30.000 40.025 40.000 50.025 50.000 60.030 60.000 80.030 80.000 100.035 100.000 120.035 120.000 160.040 160.000 200.046 200.000 250.046 250.000 300.052 300.000 400.057 400.000 500.063 500.000

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb 0.034 0.000 0.041 0.000 0.041 0.000 0.049 0.000 0.049 0.000 0.057 0.000 0.057 0.000 0.065 0.000 0.075 0.000 0.075 0.000 0.084 0.000 0.093 0.000 0.103 0.000

SHAFT BASIS METRIC CLEARANCE FITS

50


Hole C11 30.240 30.110 40.280 40.120 50.290 50.130 60.330 60.140 80.340 80.150 100.390 100.170 120.400 120.180 160.460 160.210 200.530 200.240 250.570 250.280 300.650 300.330 400.760 400.400 500.880 500.480

a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b All fits shown in this table have clearance.


675



676

Table 5. American National Standard Preferred Shaft Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999) Locational Transition Basic Sizea 1

1.6 2 2.5 3 4 5 6 8 10 12 16 20 25

Locational Interference

Medium Drive

Force

Shaft h6

Fitb

Hole N7

Shaft h6

Fitb

Hole P7

Shaft h6

Fitb

Hole S7

Shaft h6

Fitb

Hole U7

Shaft h6

Fitb

1.000 0.990 1.200 1.190 1.600 1.590 2.000 1.990 2.500 2.490 3.000 2.990 4.003 3.991 5.003 4.991 6.003 5.991 8.005 7.990 10.005 9.990 12.006 11.988 16.006 15.988 20.006 19.985 25.006 24.985

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

+0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.006 −0.010 +0.011 −0.009 +0.011 −0.009 +0.011 −0.009 +0.014 −0.010 +0.014 −0.010 +0.017 −0.012 +0.017 −0.012 +0.019 −0.015 +0.019 −0.015

0.996 0.986 1.196 1.186 1.596 1.586 1.996 1.986 2.496 2.486 2.996 2.986 3.996 3.984 4.996 4.984 5.996 5.984 7.996 7.981 9.996 9.981 11.995 11.977 15.995 15.977 19.993 19.972 24.993 24.972

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

+0.002 −0.014 +0.002 −0.014 +0.002 −0.014 +0.002 −0.014 +0.002 −0.014 +0.002 −0.014 +0.004 −0.016 +0.004 −0.016 +0.004 −0.016 +0.005 −0.019 +0.005 −0.019 +0.006 −0.023 +0.006 −0.023 +0.006 −0.028 +0.006 −0.028

0.994 0.984 1.194 1.184 1.594 1.584 1.994 1.984 2.494 2.484 2.994 2.984 3.992 3.980 4.992 4.980 5.992 5.980 7.991 7.976 9.991 9.976 11.989 11.971 15.989 15.971 19.986 19.965 24.986 24.965

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

0.000 −0.016 0.000 −0.016 0.000 −0.016 0.000 −0.016 0.000 −0.016 0.000 −0.016 0.000 −0.020 0.000 −0.020 0.000 −0.020 0.000 −0.024 0.000 −0.024 0.000 −0.029 0.000 −0.029 −0.001 −0.035 −0.001 −0.035

0.986 0.976 1.186 1.176 1.586 1.576 1.986 1.976 2.486 2.476 2.986 2.976 3.985 3.973 4.985 4.973 5.985 5.973 7.983 7.968 9.983 9.968 11.979 11.961 15.979 15.961 19.973 19.952 24.973 24.952

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

−0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.008 −0.024 −0.007 −0.027 −0.007 −0.027 −0.007 −0.027 −0.008 −0.032 −0.008 −0.032 −0.010 −0.039 −0.010 −0.039 −0.014 −0.048 −0.014 −0.048

0.982 0.972 1.182 1.172 1.582 1.572 1.982 1.972 2.482 2.472 2.982 2.972 3.981 3.969 4.981 4.969 5.981 5.969 7.978 7.963 9.978 9.963 11.974 11.956 15.974 15.956 19.967 19.946 24.960 24.939

1.000 0.994 1.200 1.194 1.600 1.594 2.000 1.994 2.500 2.494 3.000 2.994 4.000 3.992 5.000 4.992 6.000 5.992 8.000 7.991 10.000 9.991 12.000 11.989 16.000 15.989 20.000 19.987 25.000 24.987

−0.012 −0.028 −0.012 −0.028 −0.012 −0.028 −0.012 −0.028 −0.012 −0.028 −0.012 −0.028 −0.011 −0.031 −0.011 −0.031 −0.011 −0.031 −0.013 −0.037 −0.013 −0.037 −0.015 −0.044 −0.015 −0.044 −0.020 −0.054 −0.027 −0.061


SHAFT BASIS METRIC TRANSITION FITS

1.2


Locational Transition

Hole K7


Table 5. (Continued) American National Standard Preferred Shaft Basis Metric Transition and Interference Fits ANSI B4.2-1978 (R1999) Locational Transition Basic Sizea 30 40

60 80 100 120 160 200 250 300 400 500

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.00 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb +0.019 −0.015 +0.023 −0.018 +0.023 −0.018 +0.028 −0.021 +0.028 −0.021 +0.032 −0.025 +0.032 −0.025 +0.037 −0.028 +0.042 −0.033 +0.042 −0.033 +0.048 −0.036 +0.053 −0.040 +0.058 −0.045

Locational Transition Hole N7 29.993 29.972 39.992 39.967 49.992 49.967 59.991 59.961 79.991 79.961 99.990 99.955 119.990 119.955 159.988 159.948 199.986 199.940 249.986 249.940 299.986 299.934 399.984 399.927 499.983 499.920

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb +0.006 −0.028 +0.008 −0.033 +0.008 −0.033 +0.010 −0.039 +0.010 −0.039 +0.012 −0.045 +0.012 −0.045 +0.013 −0.052 +0.015 −0.060 +0.015 −0.060 +0.018 −0.066 +0.020 −0.073 +0.023 −0.080

Locational Interference Hole P7 29.986 29.965 39.983 39.958 49.983 49.958 59.979 59.949 79.979 79.949 99.976 99.941 119.976 119.941 159.972 159.932 199.967 199.921 249.967 249.921 299.964 299.912 399.959 399.902 499.955 499.892

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb −0.001 −0.035 −0.001 −0.042 −0.001 −0.042 −0.002 −0.051 −0.002 −0.051 −0.002 −0.059 −0.002 −0.059 −0.003 −0.068 −0.004 −0.079 −0.004 −0.079 −0.004 −0.088 −0.005 −0.098 −0.005 −0.108

Medium Drive Hole S7 29.973 29.952 39.966 39.941 49.966 49.941 59.958 59.928 79.952 79.922 99.942 99.907 119.934 119.899 159.915 159.875 199.895 199.849 249.877 249.831 299.850 299.798 399.813 399.756 499.771 499.708

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Force Fitb −0.014 −0.048 −0.018 −0.059 −0.018 −0.059 −0.023 −0.072 −0.029 −0.078 −0.036 −0.093 −0.044 −0.101 −0.060 −0.125 −0.076 −0.151 −0.094 −0.169 −0.118 −0.202 −0.151 −0.244 −0.189 −0.292

Hole U7 29.960 29.939 39.949 39.924 49.939 49.914 59.924 59.894 79.909 79.879 99.889 99.854 119.869 119.834 159.825 159.785 199.781 199.735 249.733 249.687 299.670 299.618 399.586 399.529 499.483 499.420

Shaft h6 30.000 29.987 40.000 39.984 50.000 49.984 60.000 59.981 80.000 79.981 100.000 99.978 120.000 119.978 160.000 159.975 200.000 199.971 250.000 249.971 300.000 299.968 400.000 399.964 500.000 499.960

Fitb −0.027 −0.061 −0.035 −0.076 −0.045 −0.086 −0.087 −0.106 −0.072 −0.121 −0.089 −0.146 −0.109 −0.166 −0.150 −0.215 −0.190 −0.265 −0.238 −0.313 −0.298 −0.382 −0.378 −0.471 −0.477 −0.580

SHAFT BASIS METRIC TRANSITION FITS

50


Hole K7 30.006 29.985 40.007 39.982 50.007 49.982 60.009 59.979 80.009 79.979 100.010 99.975 120.010 119.975 160.012 159.972 200.013 199.967 250.013 249.967 300.016 299.964 400.017 399.960 500.018 499.955

a The sizes shown are first-choice basic sizes (see Table 1). Preferred fits for other sizes can be calculated from data given in ANSI B4.2-1978 (R1999). b A plus sign indicates clearance; a minus sign indicates interference.


677



GAGEMAKERS TOLERANCES Table 6. American National Standard Gagemakers Tolerances ANSI B4.4M-1981 (R1987)

Gagemakers Tolerance ISO SymClass bola ZM 0.05 IT11 YM

0.05 IT9

XM

0.05 IT8

XXM

0.05 IT7

XXX M

0.05 IT6

Workpiece Tolerance IT Grade Recommended Gage Usage IT11 Low-precision gages recommended to be used to inspect workpieces held to internal (hole) tolerances C11 and H11 and to external (shaft) tolerances c11 and h11. IT9 Gages recommended to be used to inspect workpieces held to internal (hole) tolerances D9 and H9 and to external (shaft) tolerances d9 and h9. IT8 Precision gages recommended to be used to inspect workpieces held to internal (hole) tolerances F8 and H8. IT7 Recommended to be used for gages to inspect workpieces held to internal (hole) tolerances G7, H7, K7, N7, P7, S7, and U7, and to external (shaft) tolerances f7 and h7. IT6 High-precision gages recommended to be used to inspect workpieces held to external (shaft) tolerances g6, h6, k6, n6, p6, s6, and u6.

a Gagemakers tolerance is equal to 5 per cent of workpiece tolerance or 5 per cent of applicable IT grade value. See Table 7.

For workpiece tolerance class values, see previous Tables 2 through 5, incl.

Table 7. American National Standard Gagemakers Tolerances ANSI B4.4M-1981 (R1987) Basic Size Over 0 3 6 10 18 30 50 80 120 180 250 315 400

To 3 6 10 18 30 50 80 120 180 250 315 400 500

Class ZM

Class YM

Class XM

Class XXM

Clas XXXM

(0.05 IT11) 0.0030 0.0037 0.0045 0.0055 0.0065 0.0080 0.0095 0.0110 0.0125 0.0145 0.0160 0.0180 0.0200

(0.05 IT9) 0.0012 0.0015 0.0018 0.0021 0.0026 0.0031 0.0037 0.0043 0.0050 0.0057 0.0065 0.0070 0.0077

(0.05 IT8) 0.0007 0.0009 0.0011 0.0013 0.0016 0.0019 0.0023 0.0027 0.0031 0.0036 0.0040 0.0044 0.0048

(0.05 IT7) 0.0005 0.0006 0.0007 0.0009 0.0010 0.0012 0.0015 0.0017 0.0020 0.0023 0.0026 0.0028 0.0031

(0.05 IT6) 0.0003 0.0004 0.0005 0.0006 0.0007 0.0008 0.0010 0.0011 0.0013 0.0015 0.0016 0.0018 0.0020

All dimensions are in millimeters. For closer gagemakers tolerance classes than Class XXXM, specify 5 per cent of IT5, IT4, or IT3 and use the designation 0.05 IT5, 0.05 IT4, etc.

Fig. 4. Relationship between Gagemakers Tolerance, Wear Allowance and Workpiece Tolerance


Machinery's Handbook 27th Edition TOLERANCE APPLICATION

679

Applications.—Many factors such as length of engagement, bearing load, speed, lubrication, operating temperatures, humidity, surface texture, and materials must be taken into account in fit selections for a particular application. Choice of other than the preferred fits might be considered necessary to satisfy extreme conditions. Subsequent adjustments might also be desired as the result of experience in a particular application to suit critical functional requirements or to permit optimum manufacturing economy. Selection of a departure from these recommendations will depend upon consideration of the engineering and economic factors that might be involved; however, the benefits to be derived from the use of preferred fits should not be overlooked. A general guide to machining processes that may normally be expected to produce work within the tolerances indicated by the IT grades given in ANSI B4.2-1978 (R1999) is shown in Table 8. Practical usage of the various IT tolerance grades is shown in Table 9. Table 8. Relation of Machining Processes to IT Tolerance Grades IT Grades 4

5

6

7

8

9

10

11

Lapping & Honing Cylindrical Grinding Surface Grinding Diamond Turning Diamond Boring Broaching Powder Metal sizes Reaming Turning Powder Metal sintered Boring Milling Planing & Shaping Drilling Punching Die Casting

Table 9. Practical Use of International Tolerance Grades For Measurig Tools For Material IT Grades 01 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 For Fits For Large Manufacturing Tolerances

British Standard for Metric ISO Limits and Fits Based on ISO Recommendation R286, this British Standard BS 4500:1969 is intended to provide a comprehensive range of metric limits and fits for engineering purposes, and meets the requirements of metrication in the United Kingdom. Sizes up to 3,150 mm are covered by the Standard, but the condensed information presented here embraces dimensions up to 500 mm only. The system is based on a series of tolerances graded to suit all classes of work from the finest to the most coarse, and the different types of fits that can be obtained range from coarse clearance to heavy interference. In the Standard, only cylindrical parts, designated holes and shafts are referred to explicitly, but it is emphasized that the recommendations apply equally well to other sections, and the general term hole or shaft



BRITISH STANDARD METRIC ISO LIMITS AND FITS

can be taken to mean the space contained by or containing two parallel faces or tangent planes of any part, such as the width of a slot, or the thickness of a key. It is also strongly emphasized that the grades series of tolerances are intended for the most general application, and should be used wherever possible whether the features of the component involved are members of a fit or not. Definitions.—The definitions given in the Standard include the following: Limits of Size: The maximum and minimum sizes permitted for a feature. Basic Size: The reference size to which the limits of size are fixed. The basic size is the same for both members of a fit. Upper Deviation: The algebraical difference between the maximum limit of size and the corresponding basic size. It is designated as ES for a hole, and as es for a shaft, which stands for the French term écart supérieur. Lower Deviation: The algebraical difference between the minimum limit of size and the corresponding basic size. It is designated as EI for a hole, and as ei for a shaft, which stands for the French term écart inférieur. Zero Line: In a graphical representation of limits and fits, the straight line to which the deviations are referred. The zero line is the line of zero deviation and represents the basic size. Tolerance: The difference between the maximum limit of size and the minimum limit of size. It is an absolute value without sign. Tolerance Zone: In a graphical representation of tolerances, the zone comprised between the two lines representing the limits of tolerance and defined by its magnitude (tolerance) and by its position in relation to the zero line. Fundamental Deviation: That one of the two deviations, being the one nearest to the zero line, which is conventionally chosen to define the position of the tolerance zone in relation to the zero line. Shaft-Basis System of Fits: A system of fits in which the different clearances and interferences are obtained by associating various holes with a single shaft. In the ISO system, the basic shaft is the shaft the upper deviation of which is zero. Hole-Basis System of Fits: A system of fits in which the different clearances and interferences are obtained by associating various shafts with a single hole. In the ISO system, the basic hole is the hole the lower deviation of which is zero. Selected Limits of Tolerance, and Fits.—The number of fit combinations that can be built up with the ISO system is very large. However, experience shows that the majority of fits required for usual engineering products can be provided by a limited selection of tolerances. Limits of tolerance for selected holes are shown in Table 1, and for shafts, in Table 2. Selected fits, based on combinations of the selected hole and shaft tolerances, are given in Table 3. Tolerances and Fundamental Deviations.—There are 18 tolerance grades intended to meet the requirements of different classes of work, and they are designated IT01, IT0, and IT1 to IT16. (IT stands for ISO series of tolerances.) Table 4 shows the standardized numerical values for the 18 tolerance grades, which are known as standard tolerances. The system provides 27 fundamental deviations for sizes up to and including 500 mm, and Tables 5a and 5b contain the values for shafts and Tables 6a and 6b for holes. Uppercase (capital) letters designate hole deviations, and the same letters in lower case designate shaft deviations. The deviation js (Js for holes) is provided to meet the need for symmetrical bilateral tolerances. In this instance, there is no fundamental deviation, and the tolerance zone, of whatever magnitude, is equally disposed about the zero line. Calculated Limits of Tolerance.—The deviations and fundamental tolerances provided by the ISO system can be combined in any way that appears necessary to give a required fit. Thus, for example, the deviations H (basic hole) and f (clearance shaft) could be associated, and with each of these deviations any one of the tolerance grades IT01 to IT16 could


Machinery's Handbook 27th Edition BRITISH STANDARD METRIC ISO LIMITS AND FITS

681

be used. All the limits of tolerance that the system is capable of providing for sizes up to and including 500 mm can be calculated from the standard tolerances given in Table 4, and the fundamental deviations given in Tables 5a, 5b, 6a and 6b. The range includes limits of tolerance for shafts and holes used in small high-precision work and horology. The system provides for the use of either hole-basis or shaft-basis fits, and the Standard includes details of procedures for converting from one type of fit to the other. The limits of tolerance for a shaft or hole are designated by the appropriate letter indicating the fundamental deviation, followed by a suffix number denoting the tolerance grade. This suffix number is the numerical part of the tolerance grade designation. Thus, a hole tolerance with deviation H and tolerance grade IT7 is designated H7. Likewise, a shaft with deviation p and tolerance grade IT6 is designated p6. The limits of size of a component feature are defined by the basic size, say, 45 mm, followed by the appropriate tolerance designation, for example, 45 H7 or 45 p6. A fit is indicated by combining the basic size common to both features with the designation appropriate to each of them, for example, 45 H7-p6 or 45 H7/p6. When calculating the limits of size for a shaft, the upper deviation es, or the lower deviation ei, is first obtained from Tables 5a or 5b, depending on the particular letter designation, and nominal dimension. If an upper deviation has been determined, the lower deviation ei = es − IT. The IT value is obtained from Table 4 for the particular tolerance grade being applied. If a lower deviation has been obtained from Tables 5a or 5b, the upper deviation es = ei + IT. When the upper deviation ES has been determined for a hole from Tables 6a or 6b, the lower deviation EI = ES − IT. If a lower deviation EI has been obtained from Table 6a, then the upper deviation ES = EI + IT. The upper deviations for holes K, M, and N with tolerance grades up to and including IT8, and for holes P to ZC with tolerance grades up to and including IT7 must be calculated by adding the delta (∆) values given in Table 6b as indicated. Example 1:The limits of size for a part of 133 mm basic size with a tolerance designation g9 are derived as follows: From Table 5a, the upper deviation (es) is − 0.014 mm. From Table 4, the tolerance grade (IT9) is 0.100 mm. The lower deviation (ei) = es − IT = 0.114 mm, and the limits of size are thus 132.986 and 132.886 mm. Example 2:The limits of size for a part 20 mm in size, with tolerance designation D3, are derived as follows: From Table 6a, the lower deviation (EI) is + 0.065 mm. From Table 4, the tolerance grade (IT3) is 0.004 mm. The upper deviation (ES) = EI + IT = 0.069 mm, and thus the limits of size for the part are 20.069 and 20.065 mm. Example 3:The limits of size for a part 32 mm in size, with tolerance designation M5, which involves a delta value, are obtained as follows: From Table 6a, the upper deviation ES is − 0.009 mm + ∆ = −0.005 mm. (The delta value given at the end of Table 6b for this size and grade IT5 is 0.004 mm.) From Table 4, the tolerance grade (IT5) is 0.011 mm. The lower deviation (EI) = ES − IT = − 0.016 mm, and thus the limits of size for the part are 31.995 and 31.984 mm. Where the designations h and H or js and Js are used, it is only necessary to refer to Table 4. For h and H, the fundamental deviation is always zero, and the disposition of the tolerance is always negative ( − ) for a shaft, and positive ( + ) for a hole. Example 4:The limits for a part 40 mm in size, designated h8 are derived as follows: From Table 4, the tolerance grade (IT8) is 0.039 mm, and the limits are therefore 40.000 and 39.961 mm. Example 5:The limits for a part 60 mm in size, designated js7 or Js7 are derived as follows: From Table 4, the tolerance grade (IT7) is 0.030 mm, and this value is divided equally about the basic size to give limits of 60.015 and 59.985 mm.



BRITISH STANDARD METRIC ISO LIMITS AND FITS Table 1. British Standard Limits of Tolerance for Selected Holes (Upper and Lower Deviations) BS 4500:1969

Nominal Sizes, mm

H7

H8

H9

H11

Over

Up to and Including

ES +

EI

ES +

EI

ES +

EI

ES +

EI

…

3

10

0

14

0

25

0

60

0

3

6

12

0

18

0

30

0

75

0

6

10

15

0

22

0

36

0

90

0

10

18

18

0

27

0

43

0

110

0

18

30

21

0

33

0

52

0

130

0

30

50

25

0

39

0

62

0

160

0

50

80

30

0

46

0

74

0

190

0

80

120

35

0

54

0

87

0

220

0

120

180

40

0

63

0

100

0

250

0

180

250

46

0

72

0

115

0

290

0

250

315

52

0

81

0

130

0

320

0

315

400

57

0

89

0

140

0

360

0

400

500

63

0

97

0

155

0

400

0

ES = Upper deviation, EI = Lower deviation. The dimensions are given in 0.001 mm, except for the nominal sizes, which are in millimeters.

Table 2. British Standard Limits of Tolerance for Selected Shafts (Upper and Lower Deviations) BS 4500:1969 Nominal Sizes, mm

d10

e9

f7

g6

h6

k6

n6

p6

s6

es −

…

3

60

120

20

60

14

39

6

16

2

8

0

6

6

0

10

4

12

6

20

14

3

6

70

145

30

78

20

50

10

22

4

12

0

8

9

1

16

8

20

12

27

19

6

10

80

170

40

98

25

61

13

28

5

14

0

9

10

1

19

10

24

15

32

23

10

18

95

205

50

120

32

75

16

34

6

17

0

11

12

1

23

12

29

18

39

28

18

30

110

240

65

149

40

92

20

41

7

20

0

13

15

2

28

15

35

22

48

35

30

40

120

280

80

180

50

112

25

50

9

25

0

16

18

2

33

17

42

26

59

43

40

50

130

290

80

180

50

112

25

50

9

25

0

16

18

2

33

17

42

26

59

43

50

65

140

330

100

220

60

134

30

60

10

29

0

19

21

2

39

20

51

32

72

53

65

80

150

340

100

220

60

134

30

60

10

29

0

19

21

2

39

20

51

32

78

59

80

100

170

390

120

260

72

159

36

71

12

34

0

22

25

3

45

23

59

37

93

71

100

120

180

400

120

260

72

159

36

71

12

34

0

22

25

3

45

23

59

37

101

79

120

140

200

450

145

305

85

185

43

83

14

39

0

25

28

3

52

27

68

43

117

92

140

160

210

460

145

305

85

185

43

83

14

39

0

25

28

3

52

27

68

43

125

100

160

180

230

480

145

305

85

185

43

83

14

39

0

25

28

3

52

27

68

43

133

108

180

200

240

530

170

355

100

215

50

96

15

44

0

29

33

4

60

31

79

50

151

122

200

225

260

550

170

355

100

215

50

96

15

44

0

29

33

4

60

31

79

50

159

130

225

250

280

570

170

355

100

215

50

96

15

44

0

29

33

4

60

31

79

50

169

140

250

280

300

620

190

400

110

240

56

108

17

49

0

32

36

4

66

34

88

56

190

158

280

315

330

650

190

400

110

240

56

108

17

49

0

32

36

4

66

34

88

56

202

170

315

355

360

720

210

440

125

265

62

119

18

54

0

36

40

4

73

37

98

62

226

190

355

400

400

760

210

440

125

265

62

119

18

54

0

36

40

4

73

37

98

62

244

208

400

450

440

840

230

480

135

290

68

131

20

60

0

40

45

5

80

40

108

68

272

232

450

500

480

880

230

480

135

290

68

131

20

60

0

40

45

5

80

40

108

68

292

252

Over

Up to and Incl.

c11 ei −

es −

ei −

es −

ei −

es −

ei −

es −

ei −

es −

ei −

es +

ei +

es +

ei +

es +

ei +

es +

ei +

es = Upper deviation, ei = Lower deviation. The dimensions are given in 0.001 mm, except for the nominal sizes, which are in millimeters.



Table 3. British Standard Selected Fits, Minimum and Maximum Clearances BS 4500:1969 Nominal Sizes, mm

H11—c11

H9—d10

H9—e9

H8—f7

H7—g6

H7—h6

H7—k6

H7—n6

H7—p6

H7—s6

Up to and Incl.

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

…

3

60

180

20

85

14

64

6

30

2

18

0

16

−6

+10

−10

+6

−12

+4

−20

−4

3

6

70

220

30

108

20

80

10

40

4

24

0

20

−9

+11

−16

+4

−20

0

−27

−7

6

10

80

260

40

134

25

97

13

50

5

29

0

24

−10

+14

−19

+5

−24

0

−32

−8

10

18

95

315

50

163

32

118

16

61

6

35

0

29

−12

+17

−23

+6

−29

0

−39

−10

18

30

110

370

65

201

40

144

20

74

7

41

0

34

−15

+19

−28

+6

−35

−1

−48

−14

30

40

120

440

80

242

50

174

25

89

9

50

0

41

−18

+23

−33

+8

−42

−1

−59

−18

40

50

130

450

80

242

50

174

25

89

9

50

0

41

−18

+23

−33

+8

−42

−1

−59

−18

50

65

140

520

100

294

60

208

30

106

10

59

0

49

−21

+28

−39

+10

−51

−2

−72

−23

65

80

150

530

100

294

60

208

30

106

10

59

0

49

−21

+28

−39

+10

−51

−2

−78

−29

80

100

170

610

120

347

72

246

36

125

12

69

0

57

−25

+32

−45

+12

−59

−2

−93

−36

100

120

180

620

120

347

72

246

36

125

12

69

0

57

−25

+32

−45

+12

−59

−2

−101

−44 −52

120

140

200

700

145

405

85

285

43

146

14

79

0

65

−28

+37

−52

+13

−68

−3

−117

140

160

210

710

145

405

85

285

43

146

14

79

0

65

−28

+37

−52

+13

−68

−3

−125

−60

160

180

230

730

145

405

85

285

43

146

14

79

0

65

−28

+37

−52

+13

−68

−3

−133

−68

180

200

240

820

170

470

100

330

50

168

15

90

0

75

−33

+42

−60

+15

−79

−4

−151

−76

200

225

260

840

170

470

100

330

50

168

15

90

0

75

−33

+42

−60

+15

−79

−4

−159

−84

225

250

280

860

170

470

100

330

50

168

15

90

0

75

−33

+42

−60

+15

−79

−4

−169

−94

250

280

300

940

190

530

110

370

56

189

17

101

0

84

−36

+48

−66

+18

−88

−4

−190

−126

280

315

330

970

190

530

110

370

56

189

17

101

0

84

−36

+48

−66

+18

−88

−4

−202

−112

315

355

360

1080

210

580

125

405

62

208

18

111

0

93

−40

−53

−73

+20

−98

−5

−226

−133

355

400

400

1120

210

580

125

405

62

208

18

111

0

93

−40

−53

−73

+20

−98

−5

−244

−151

400

450

440

1240

230

635

135

445

68

228

20

123

0

103

−45

+58

−80

+23

−108

−5

−272

−169

450

500

480

1280

230

635

135

445

68

228

20

123

0

103

−45

+58

−80

+23

−108

−5

−292

−189

Minus (−) sign indicates negative clearance, i.e., interference.


683

The dimensions are given in 0.001 mm, except for the nominal sizes, which are in millimeters.


Over


Nominal Sizes, mm

684

Table 4. British Standard Limits and Fits BS 4500:1969 Tolerance Grades

To

IT 01

IT 0

IT 1

IT 2

IT 3

IT 4

IT 5

IT 6

IT 7

IT 8

IT 9

IT 10

IT 11

IT 12

IT 13

IT 14 a

IT 15 a

IT 16 a

…

3

0.3

0.5

0.8

1.2

2

3

4

6

10

14

25

40

60

100

140

250

400

600

3

6

0.4

0.6

1

1.5

2.5

4

5

8

12

18

30

48

75

120

180

300

480

750

6

10

0.4

0.6

1

1.5

2.5

4

6

9

15

22

36

58

90

150

220

360

580

900

10

18

0.5

0.8

1.2

2

3

5

8

11

18

27

43

70

110

180

270

430

700

1100

18

30

0.6

1

1.5

2.5

4

6

9

13

21

33

52

84

130

210

330

520

840

1300

30

50

0.6

1

1.5

2.5

4

7

11

16

25

39

62

100

160

250

390

620

1000

1600

50

80

0.8

1.2

2

3

5

8

13

19

30

46

74

120

190

300

460

740

1200

1900

80

120

1

1.5

2.5

4

6

10

15

22

35

54

87

140

220

350

540

870

1400

2200

120

180

1.2

2

3.5

5

8

12

18

25

40

63

100

160

250

400

630

1000

1600

2500

180

250

2

3

4.5

7

10

14

20

29

46

72

115

185

290

460

720

1150

1850

2900

250

315

2.5

4

6

8

12

16

23

32

52

81

130

210

320

520

810

1300

2100

3200

315

400

3

5

7

9

13

18

25

36

57

89

140

230

360

570

890

1400

2300

3600

400

500

4

6

8

10

15

20

27

40

63

97

155

250

400

630

970

1550

2500

4000

a Not applicable to sizes below 1 mm.

The dimensions are given in 0.001 mm, except for the nominal sizes which are in millimeters.



Over


Table 5a. British Standard Fundamental Deviations for Shafts BS 4500:1969 Grade Nominal Sizes, mm

01 to 16

5–6

Fundamental (Upper) Deviation es

7

8

≤3 >7

4–7

Fundamental (Lower) Deviation ei

To

aa

ba

c

cd

d

e

ef

f

fg

g

h

… 3 6 10 14 18 24 30 40 50 65 80 100 120 140 160 180 200 225 250 280 315 355 400 450

3 6 10 14 18 24 30 40 50 65 80 100 120 140 160 180 200 225 250 280 315 355 400 450 500

−270 −270 −280 −290 −290 −300 −300 −310 −320 −340 −360 −380 −410 −460 −520 −580 −660 −740 −820 −920 −1050 −1200 −1350 −1500 −1650

−140 −140 −150 −150 −150 −160 −160 −170 −180 −190 −200 −220 −240 −260 −280 −310 −340 −380 −420 −480 −540 −600 −680 −760 −840

−60 −70 −80 −95 −95 −110 −110 −120 −130 −140 −150 −170 −180 −200 −210 −230 −240 −260 −280 −300 −330 −360 −400 −440 −480

−34 −46 −56 … … … … … … … … … … … … … … … … … … … … … …

−20 −30 −40 −50 −50 −65 −65 −80 −80 −100 −100 −120 −120 −145 −145 −145 −170 −170 −170 −190 −190 −210 −210 −230 −230

−14 −20 −25 −32 −32 −40 −40 −50 −50 −60 −60 −72 −72 −85 −85 −85 −100 −100 −100 −110 −110 −125 −125 −135 −135

−10 −14 −18 … … … … … … … … … … … … … … … … … … … … … …

−6 −10 −13 −16 −16 −20 −20 −25 −25 −30 −30 −36 −36 −43 −43 −43 −50 −50 −50 −56 −56 −62 −62 −68 −68

−4 −6 −8 … … … … … … … … … … … … … … … … … … … … … …

−2 −4 −5 −6 −6 −7 −7 −9 −9 −10 −10 −12 −12 −14 −14 −14 −15 −15 −15 −17 −17 −18 −18 −20 −20

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

js b

±IT/2

j −2 −2 −2 −3 −3 −4 −4 −5 −5 −7 −7 −9 −9 −11 −11 −11 −13 −13 −13 −16 −16 −18 −18 −20 −20

−4 −4 −5 −6 −6 −8 −8 −10 −10 −12 −12 −15 −15 −18 −18 −18 −21 −21 −21 −26 −26 −28 −28 −32 −32

k −6 … … … … … … … … … … … … … … … … … … … … … … … …

0 +1 +1 +1 +1 +2 +2 +2 +2 +2 +2 +3 +3 +3 +3 +3 +4 +4 +4 +4 +4 +4 +4 +5 +5

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0


Over

a Not applicable to sizes up to 1 mm.


685

b In grades 7 to 11, the two symmetrical deviations ±IT/2 should be rounded if the IT value in micrometers is an odd value by replacing it with the even value immediately below. For example, if IT = 175, replace it by 174.


686

Table 5b. British Standard Fundamental Deviations for Shafts BS 4500:1969 Grade Nominal Sizes, mm

01 to 16 Fundamental (Lower) Deviation ei To

m

n

p

r

s

t

u

v

x

y

z

za

zb

zc

…

3

+2

+4

+6

+10

+14

…

+18

…

+20

…

+26

+32

+40

+60

3

6

+4

+8

+12

+15

+19

…

+23

…

+28

…

+35

+42

+50

+80

6

10

+6

+10

+15

+19

+23

…

+28

…

+34

…

+42

+52

+67

+97

10

14

+7

+12

+18

+23

+28

…

+33

…

+40

…

+50

+64

+90

+130

14

18

+7

+12

+18

+23

+28

…

+33

+39

+45

…

+60

+77

+108

+150

18

24

+8

+15

+22

+28

+35

…

+41

+47

+54

+63

+73

+98

+136

+188 +218

24

30

+8

+15

+22

+28

+35

+41

+48

+55

+64

+75

+88

+118

+160

30

40

+9

+17

+26

+34

+43

+48

+60

+68

+80

+94

+112

+148

+200

+274

40

50

+9

+17

+26

+34

+43

+54

+70

+81

+97

+114

+136

+180

+242

+325

50

65

+11

+20

+32

+41

+53

+66

+87

+102

+122

+144

+172

+226

+300

+405

65

80

+11

+20

+32

+43

+59

+75

+102

+120

+146

+174

+210

+274

+360

+480

80

100

+13

+23

+37

+51

+71

+91

+124

+146

+178

+214

+258

+335

+445

+585

100

120

+13

+23

+37

+54

+79

+104

+144

+172

+210

+254

+310

+400

+525

+690

120

140

+15

+27

+43

+63

+92

+122

+170

+202

+248

+300

+365

+470

+620

+800

140

160

+15

+27

+43

+65

+100

+134

+190

+228

+280

+340

+415

+535

+700

+900

160

180

+15

+27

+43

+68

+108

+146

+210

+252

+310

+380

+465

+600

+780

+1000

180

200

+17

+31

+50

+77

+122

+166

+236

+284

+350

+425

+520

+670

+880

+1150

200

225

+17

+31

+50

+80

+130

+180

+258

+310

+385

+470

+575

+740

+960

+1250

225

250

+17

+31

+50

+84

+140

+196

+284

+340

+425

+520

+640

+820

+1050

+1350

250

280

+20

+34

+56

+94

+158

+218

+315

+385

+475

+580

+710

+920

+1200

+1550

280

315

+20

+34

+56

+98

+170

+240

+350

+425

+525

+650

+790

+1000

+1300

+1700

315

355

+21

+37

+62

+108

+190

+268

+390

+475

+590

+730

+900

+1150

+1500

+1900

355

400

+21

+37

+62

+114

+208

+294

+435

+530

+660

+820

+1000

+1300

+1650

+2100

400

450

+23

+40

+68

+126

+232

+330

+490

+595

+740

+920

+1100

+1450

+1850

+2400

450

500

+23

+40

+68

+132

+252

+360

+540

+660

+820

+1000

+1250

+1600

+2100

+2600

The dimensions are in 0.001 mm, except the nominal sizes, which are in millimeters.



Over


Table 6a. British Standard Fundamental Deviations for Holes BS 4500:1969 Grade Nominal Sizes, mm

01 to 16

6

7

8

Fundamental (Lower) Deviation EI

≤8

>8

≤8a

>8

≤8

>8b

Fundamental (Upper) Deviation ES

To

Ab

Bb

C

CD

D

E

EF

F

FG

G

H

… 3 6 10 14 18 24 30 40 50 65 80 100 120 140 160 180 200 225 250 280 315 355 400 450

3 6 10 14 18 24 30 40 50 65 80 100 120 140 160 180 200 225 250 280 315 355 400 450 500

+270 +270 +280 +290 +290 +300 +300 +310 +320 +340 +360 +380 +410 +460 +520 +580 +660 +740 +820 +920 +1050 +1200 +1350 +1500 +1650

+140 +140 +150 +150 +150 +160 +160 +170 +180 +190 +200 +220 +240 +260 +280 +310 +340 +380 +420 +480 +540 +600 +680 +760 +840

+60 +70 +80 +95 +95 +110 +110 +120 +130 +140 +150 +170 +180 +200 +210 +230 +240 +260 +280 +300 +330 +360 +400 +440 +480

+34 +46 +56 … … … … … … … … … … … … … … … … … … … … … …

+20 +30 +40 +50 +50 +65 +65 +80 +80 +100 +100 +120 +120 +145 +145 +145 +170 +170 +170 +190 +190 +210 +210 +230 +230

+14 +20 +25 +32 +32 +40 +40 +50 +50 +60 +60 +72 +72 +85 +85 +85 +100 +100 +100 +110 +110 +125 +125 +135 +135

+10 +14 +18 … … … … … … … … … … … … … … … … … … … … … …

+6 +10 +13 +16 +16 +20 +20 +25 +25 +30 +30 +36 +36 +43 +43 +43 +50 +50 +50 +56 +56 +62 +62 +68 +68

+4 +6 +8 … … … … … … … … … … … … … … … … … … … … … …

+2 +4 +5 +6 +6 +7 +7 +9 +9 +10 +10 +12 +12 +14 +14 +14 +15 +15 +15 +17 +17 +18 +18 +20 +20

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Jsc

±IT/2

Kd

J +2 +5 +5 +6 +6 +8 +8 +10 +10 +13 +13 +16 +16 +18 +18 +18 +22 +22 +22 +25 +25 +29 +29 +33 +33

+4 +6 +8 +10 +10 +12 +12 +14 +14 +18 +18 +22 +22 +26 +26 +26 +30 +30 +30 +36 +36 +39 +39 +43 +43

+6 +10 +12 +15 +15 +20 +20 +24 +24 +28 +28 +34 +34 +41 +41 +41 +47 +47 +47 +55 +55 +60 +60 +66 +66

0 −1+∆ −1+∆ −1+∆ −1+∆ −2+∆ −2+∆ −2+∆ −2+∆ −2+∆ −2+∆ −3+∆ −3+∆ −3+∆ −3+∆ −3+∆ −4+∆ −4+∆ −4+∆ −4+∆ −4+∆ −4+∆ −4+∆ −5+4 −5+4

Md 0 … … … … … … … … … … … … … … … … … … … … … … … …

−2 −4+∆ −6+∆ −7+∆ −7+∆ −8+∆ −8+∆ −9+∆ −9+∆ −11+∆ −11+∆ −13+∆ −13+∆ −15+∆ −15+∆ −15+∆ −17+∆ −17−∆ −17+∆ −20+∆ −20+∆ −21+∆ −21+∆ −23+∆ −23+∆

Nd −2 −4 −6 −7 −7 −8 −8 −9 −9 −11 −11 −13 −13 −15 −15 −15 −17 −17 −17 −20 −20 −21 −21 −23 −23

−4 −8+∆ −10+∆ −12+∆ −12+∆ −15+∆ −15+∆ −17+∆ −17+∆ −20+∆ −20+∆ −23+∆ −23+∆ −27+∆ −27+∆ −27+∆ −31+∆ −31+∆ −31+∆ −34+∆ −34+∆ −37+∆ −37+∆ −40+∆ −40+∆

−4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

a Special case: for M6, ES = −9 for sizes from 250 to 315 mm, instead of −11. b Not applicable to sizes up to 1 mm.


687

c In grades 7 to 11, the two symmetrical deviations ±IT/2 should be rounded if the IT value in micrometers is an odd value, by replacing it with the even value below. For example, if IT = 175, replace it by 174. d When calculating deviations for holes K, M, and N with tolerance grades up to and including IT8, and holes F to ZC with tolerance grades up to and including IT7, the delta (∆) values are added to the upper deviation ES. For example, for 25 P7, ES = −0.022 + 0.008 = −0.014 mm.


Over


688

Table 6b. British Standard Fundamental Deviations for Holes BS 4500:1969 Grade Nominal Sizes, mm

≤7

Values for delta (∆)d

>7 Fundamental (Upper) Deviation ES

To

…

3

P to ZC

Grade

P

R

S

T

U

V

X

Y

Z

− 6

−10

−14

…

−18

…

−20

…

−26

ZA −32

ZB −40

ZC −60

3

4

5

6

7

8

0

0

0

0

0

0

3

6

−12

−15

−19

…

−23

…

−28

…

−35

−42

−50

−80

1

1.5

1

3

4

6

6

10

−15

−19

−23

…

−28

…

−34

…

−42

−52

−67

−97

1

1.5

2

3

6

7 9

10

14

−18

−23

−28

…

−33

…

−40

…

−50

−64

−90

−130

1

2

3

3

7

14

18

−18

−23

−28

…

−33

−39

−45

…

−60

−77

−108

−150

1

2

3

3

7

9

18

24

−22

−28

−35

…

−41

−47

−54

−63

−73

−98

−136

−188

1.5

2

3

4

8

12

24

30

−22

−28

−35

−41

−48

−55

−64

−75

−88

−118

−160

−218

1.5

2

3

4

8

12

30

40

−26

−34

−43

−48

−60

−68

−80

−94

−112

−148

−200

−274

1.5

3

4

5

9

14

40

50

−26

−34

−43

−54

−70

−81

−97

−114

−136

−180

−242

−325

1.5

3

4

5

9

14

50

65

−32

−41

−53

−66

−87

−102

−122

−144

−172

−226

−300

−405

2

3

5

6

11

16

65

80

80

100

100

120

120

140

Same deviation as for grades above 7 increased by ∆

−32

−43

−59

−75

−102

−120

−146

−174

−210

−274

−360

−480

2

3

5

6

11

16

−37

−51

−71

−91

−124

−146

−178

−214

−258

−335

−445

−585

2

4

5

7

13

19

−37

−54

−79

−104

−144

−172

−210

−254

−310

−400

−525

−690

2

4

5

7

13

19

−43

−63

−92

−122

−170

−202

−248

−300

−365

−470

−620

−800

3

4

6

7

15

23

140

160

−43

−65

−100

−134

−190

−228

−280

−340

−415

−535

−700

−900

3

4

6

7

15

23

160

180

−43

−68

−108

−146

−210

−252

−310

−380

−465

−600

−780

−1000

3

4

6

7

15

23

180

200

−50

−77

−122

−166

−226

−284

−350

−425

−520

−670

−880

−1150

3

4

6

9

17

26

200

225

−50

−80

−130

−180

−258

−310

−385

−470

−575

−740

−960

−1250

3

4

6

9

17

26

225

250

−50

−84

−140

−196

−284

−340

−425

−520

−640

−820

−1050

−1350

3

4

6

9

17

26

250

280

−56

−94

−158

−218

−315

−385

−475

−580

−710

−920

−1200

−1550

4

4

7

9

20

29

280

315

−56

−98

−170

−240

−350

−425

−525

−650

−790

−1000

−1300

−1700

4

4

7

9

20

29

315

355

−62

−108

−190

−268

−390

−475

−590

−730

−900

−1150

−1500

−1800

4

5

7

11

21

32

355

400

−62

−114

−208

−294

−435

−530

−660

−820

−1000

−1300

−1650

−2100

4

5

7

11

21

32

400

450

−68

−126

−232

−330

−490

−595

−740

−920

−1100

−1450

−1850

−2400

5

5

7

13

23

34

450

500

−68

−132

−252

−360

−540

−660

−820

−1000

−1250

−1600

−2100

−2600

5

5

7

13

23

34

The dimensions are given in 0.001 mm, except the nominal sizes, which are in millimeters.



Over

Machinery's Handbook 27th Edition PREFERRED NUMBERS

689

Preferred Numbers Preferred numbers are series of numbers selected to be used for standardization purposes in preference to any other numbers. Their use will lead to simplified practice and they should be employed whenever possible for individual standard sizes and ratings, or for a series, in applications similar to the following: 1) Important or characteristic linear dimensions, such as diameters and lengths, areas, volume, weights, capacities. 2) Ratings of machinery and apparatus in horsepower, kilowatts, kilovolt-amperes, voltages, currents, speeds, power-factors, pressures, heat units, temperatures, gas or liquidflow units, weight-handling capacities, etc. 3) Characteristic ratios of figures for all kinds of units. American National Standard for Preferred Numbers.—This ANSI Standard Z17.11973 covers basic series of preferred numbers which are independent of any measurement system and therefore can be used with metric or customary units. The numbers are rounded values of the following five geometric series of numbers: 10N/5, 10N/10, 10N/20, 10N/40, and 10N/80, where N is an integer in the series 0, 1, 2, 3, etc. The designations used for the five series are respectively R5, R10, R20, R40, and R80, where R stands for Renard (Charles Renard, originator of the first preferred number system) and the number indicates the root of 10 on which the particular series is based. The R5 series gives 5 numbers approximately 60 per cent apart, the R10 series gives 10 numbers approximately 25 per cent apart, the R20 series gives 20 numbers approximately 12 per cent apart, the R40 series gives 40 numbers approximately 6 per cent apart, and the R80 series gives 80 numbers approximately 3 per cent apart. The number of sizes for a given purpose can be minimized by using first the R5 series and adding sizes from the R10 and R20 series as needed. The R40 and R80 series are used principally for expressing tolerances in sizes based on preferred numbers. Preferred numbers below 1 are formed by dividing the given numbers by 10, 100, etc., and numbers above 10 are obtained by multiplying the given numbers by 10, 100, etc. Sizes graded according to the system may not be exactly proportional to one another due to the fact that preferred numbers may differ from calculated values by +1.26 per cent to −1.01 per cent. Deviations from preferred numbers are used in some instances — for example, where whole numbers are needed, such as 32 instead of 31.5 for the number of teeth in a gear. Basic Series of Preferred Numbers ANSI Z17.1-1973 Series Designation R5

R10

R20

R40

R40

R80

R80

R80

R80

1.00 1.03 1.06 1.09 1.12 1.15 1.18 1.22 1.25 1.28 1.32 1.36 1.40 1.45 1.50 1.55 1.60 1.65 1.70 1.75

1.80 1.85 1.90 1.95 2.00 2.06 2.12 2.18 2.24 2.30 2.36 2.43 2.50 2.58 2.65 2.72 2.80 2.90 3.00 3.07

3.15 3.25 3.35 3.45 3.55 3.65 3.75 3.87 4.00 4.12 4.25 4.37 4.50 4.62 4.75 4.87 5.00 5.15 5.20 5.45

5.60 5.80 6.00 6.15 6.30 6.50 6.70 6.90 7.10 7.30 7.50 7.75 8.00 8.25 8.50 8.75 9.00 9.25 9.50 9.75

Preferred Numbers 1.00 1.60 2.50 4.00 6.30 … … … … … … … … … … … … … … …

1.00 1.25 1.60 2.00 2.50 3.15 4.00 5.00 6.30 8.00 … … … … … … … … … …

1.00 1.12 1.25 1.40 1.60 1.80 2.00 2.24 2.50 2.80 3.15 3.55 4.00 4.50 5.00 5.60 6.30 7.10 8.00 9.00

1.00 1.06 1.12 1.18 1.25 1.32 1.40 1.50 1.60 1.70 1.80 1.90 2.00 2.12 2.24 2.36 2.50 2.65 2.80 3.00

3.15 3.35 3.55 3.75 4.00 4.25 4.50 4.75 5.00 5.30 5.60 6.00 6.30 6.70 7.10 7.50 8.00 8.50 9.00 9.50



PREFERRED METRIC SIZES

Preferred Metric Sizes.—American National Standard ANSI B32.4M-1980 (R1994), presents series of preferred metric sizes for round, square, rectangular, and hexagonal metal products. Table 1 gives preferred metric diameters from 1 to 320 millimeters for round metal products. Wherever possible, sizes should be selected from the Preferred Series shown in the table. A Second Preference series is also shown. A Third Preference Series not shown in the table is: 1.3, 2.1, 2.4, 2.6, 3.2, 3.8, 4.2, 4.8, 7.5, 8.5, 9.5, 36, 85, and 95. Most of the Preferred Series of sizes are derived from the American National Standard “10 series” of preferred numbers (see American National Standard for Preferred Numbers on page 689). Most of the Second Preference Series are derived from the “20 series” of preferred numbers. Third Preference sizes are generally from the “40 series” of preferred numbers. For preferred metric diameters less than 1 millimeter, preferred across flat metric sizes of square and hexagon metal products, preferred across flat metric sizes of rectangular metal products, and preferred metric lengths of metal products, reference should be made to the Standard. Table 1. American National Standard Preferred Metric Sizes ANSI B4.2-1978 (R1999) Basic Size, mm

Basic Size, mm

Basic Size, mm

Basic Size, mm

1st Choice

2nd Choice

1st Choice

2nd Choice

1st Choice

2nd Choice

1st Choice

2nd Choice

1 … 1.2 … 1.6 … 2 … 2.5 … 3 … 4 … 5 …

… 1.1 … 1.4 … 1.8 … 2.2 … 2.8 … 3.5 … 4.5 … 5.5

6 … 8 … 10 … 12 … 16 … 20 … 25 … 30 …

… 7 … 9 … 11 … 14 … 18 … 22 … 28 … 35

40 … 50 … 60 … 80 … 100 … 120 … 160 … 200 …

… 45 … 55 … 70 … 90 … 110 … 140 … 180 … 220

250 … 300 … 400 … 500 … 600 … 800 … 1000 … … …

… 280 … 350 … 450 … 550 … 700 … 900 … … … …

British Standard Preferred Numbers and Preferred Sizes.—This British Standard, PD 6481:1977 1983, gives recommendations for the use of preferred numbers and preferred sizes for functional characteristics and dimensions of various products. The preferred number system is internationally standardized in ISO 3. It is also referred to as the Renard, or R, series (see American National Standard for Preferred Numbers, on page 689). The series in the preferred number system are geometric series, that is, there is a constant ratio between each figure and the succeeding one, within a decimal framework. Thus, the R5 series has five steps between 1 and 10, the R10 series has 10 steps between 1 and 10, the R20 series, 20 steps, and the R40 series, 40 steps, giving increases between steps of approximately 60, 25, 12, and 6 per cent, respectively. The preferred size series have been developed from the preferred number series by rounding off the inconvenient numbers in the basic series and adjusting for linear measurement in millimeters. These series are shown in Table 2. After taking all normal considerations into account, it is recommended that (a) for ranges of values of the primary functional characteristics (outputs and capacities) of a series of


Machinery's Handbook 27th Edition BRITISH STANDARD PREFERRED SIZES

691

products, the preferred number series R5 to R40 (see page 689) should be used, and (b) whenever linear sizes are concerned, the preferred sizes as given in the following table should be used. The presentation of preferred sizes gives designers and users a logical selection and the benefits of rational variety reduction. The second-choice size given should only be used when it is not possible to use the first choice, and the third choice should be applied only if a size from the second choice cannot be selected. With this procedure, common usage will tend to be concentrated on a limited range of sizes, and a contribution is thus made to variety reduction. However, the decision to use a particular size cannot be taken on the basis that one is first choice and the other not. Account must be taken of the effect on the design, the availability of tools, and other relevant factors. Table 2. British Standard Preferred Sizes, PD 6481: 1977 (1983) Choice 1st

2nd

Choice 3rd

1st

2nd

1

1st

2nd

5.2 1.1

5.5

1.2

5.8 1.3 1.4

6.2 1.5

6.5

9

2.2

2.6

14 3.2 3.5

15

3.8

17

4 4.5

20

95

56

110

21 22

250 165 168 172 175

112 115

275 280

178

285

180

290

118 120

265 270

108

64

255 260

170

58 62

245

162

102 105

235 240

160

100

60

4.8

152 158

98

54

225 230

155

55

19

148

88

52

215 220

150

92

18 4.2

142

90

48

205 210

145

42

16

198 200

140

82

50

192 195

135

80

46

188

132

76

3rd

190

138

45 13

2nd

128

85 44

1st

130

38

12

2.8 3

125

78

10

Choice 3rd 122

74

35

9.5

2nd

75

40

11

1st

72

32

8.5

2.4

70

36

2

2.5

26

Choice 3rd 66

28

8

2.1

65

34 7.5

1.9

23 24

2nd

68

7

1.8

1st

30 6.8

1.7

Choice 3rd

25

6

1.6

5

Choice 3rd

182 185

295 300

For dimensions above 300, each series continues in a similar manner, i.e., the intervals between each series number are the same as between 200 and 300.



MEASURING INSTRUMENTS

MEASURING INSTRUMENTS AND INSPECTION METHODS Verniers and Micrometers Reading a Vernier.—A general rule for taking readings with a vernier scale is as follows: Note the number of inches and sub-divisions of an inch that the zero mark of the vernier scale has moved along the true scale, and then add to this reading as many thousandths, or hundredths, or whatever fractional part of an inch the vernier reads to, as there are spaces between the vernier zero and that line on the vernier which coincides with one on the true scale. For example, if the zero line of a vernier which reads to thousandths is slightly beyond the 0.5 inch division on the main or true scale, as shown in Fig. 1, and graduation line 10 on the vernier exactly coincides with one on the true scale, the reading is 0.5 + 0.010 or 0.510 inch. In order to determine the reading or fractional part of an inch that can be obtained by a vernier, multiply the denominator of the finest sub-division given on the true scale by the total number of divisions on the vernier. For example, if one inch on the true scale is divided into 40 parts or fortieths (as in Fig. 1), and the vernier into twenty-five parts, the vernier will read to thousandths of an inch, as 25 × 40 = 1000. Similarly, if there are sixteen divisions to the inch on the true scale and a total of eight on the vernier, the latter will enable readings to be taken within one-hundred-twenty-eighths of an inch, as 8 × 16 = 128.

Fig. 1.

Fig. 2.

If the vernier is on a protractor, note the whole number of degrees passed by the vernier zero mark and then count the spaces between the vernier zero and that line which coincides with a graduation on the protractor scale. If the vernier indicates angles within five minutes or one-twelfth degree (as in Fig. 2), the number of spaces multiplied by 5 will, of course, give the number of minutes to be added to the whole number of degrees. The reading of the protractor set as illustrated would be 14 whole degrees (the number passed by the zero mark on the vernier) plus 30 minutes, as the graduation 30 on the vernier is the only one to


Machinery's Handbook 27th Edition MEASURING INSTRUMENTS

693

the right of the vernier zero which exactly coincides with a line on the protractor scale. It will be noted that there are duplicate scales on the vernier, one being to the right and the other to the left of zero. The left-hand scale is used when the vernier zero is moved to the left of the zero of the protractor scale, whereas the right-hand graduations are used when the movement is to the right. Reading a Metric Vernier.—The smallest graduation on the bar (true or main scale) of the metric vernier gage shown in Fig. 1, is 0.5 millimeter. The scale is numbered at each twentieth division, and thus increments of 10, 20, 30, 40 millimeters, etc., are indicated. There are 25 divisions on the vernier scale, occupying the same length as 24 divisions on the bar, which is 12 millimeters. Therefore, one division on the vernier scale equals one twenty-fifth of 12 millimeters = 0.04 × 12 = 0.48 millimeter. Thus, the difference between one bar division (0.50 mm) and one vernier division (2.48 mm) is 0.50 − 0.48 = 0.02 millimeter, which is the minimum measuring increment that the gage provides. To permit direct readings, the vernier scale has graduations to represent tenths of a millimeter (0.1 mm) and fiftieths of a millimeter (0.02 mm).

Fig. 1.

To read a vernier gage, first note how many millimeters the zero line on the vernier is from the zero line on the bar. Next, find the graduation on the vernier scale which exactly coincides with a graduation line on the bar, and note the value of the vernier scale graduation. This value is added to the value obtained from the bar, and the result is the total reading. In the example shown in Fig. 1, the vernier zero is just past the 40.5 millimeters graduation on the bar. The 0.18 millimeter line on the vernier coincides with a line on the bar, and the total reading is therefore 40.5 + 0.18 = 40.68 mm. Dual Metric-Inch Vernier.—The vernier gage shown in Fig. 2 has separate metric and inch 50-division vernier scales to permit measurements in either system. A 50-division vernier has more widely spaced graduations than the 25-division vernier shown on the previous pages, and is thus easier to read. On the bar, the smallest metric graduation is 1 millimeter, and the 50 divisions of the vernier occupy the same length as 49 divisions on the bar, which is 49 mm. Therefore, one division on the vernier scale equals one-fiftieth of 49 millimeters = 0.02 × 49 = 0.98 mm. Thus, the difference between one bar division (1.0 mm) and one vernier division (0.98 mm) is 0.02 mm, which is the minimum measuring increment the gage provides. The vernier scale is graduated for direct reading to 0.02 mm. In the figure, the vernier zero is just past the 27 mm graduation on the bar, and the 0.42 mm graduation on the vernier coincides with a line on the bar. The total reading is therefore 27.42 mm. The smallest inch graduation on the bar is 0.05 inch, and the 50 vernier divisions occupy the same length as 49 bar divisions, which is 2.45 inches. Therefore, one vernier division



MEASURING INSTRUMENTS

equals one-fiftieth of 2.45 inches = 0.02 × 2.45 = 0.049 inch. Thus, the difference between the length of a bar division and a vernier division is 0.050-0.049 = 0.001 inch. The vernier scale is graduated for direct reading to 0.001 inch. In the example, the vernier zero is past the 1.05 graduation on the bar, and the 0.029 graduation on the vernier coincides with a line on the bar. Thus, the total reading is 1.079 inches.

Fig. 2.

Reading a Micrometer.—The spindle of an inch-system micrometer has 40 threads per inch, so that one turn moves the spindle axially 0.025 inch (1 ÷ 40 = 0.025), equal to the distance between two graduations on the frame. The 25 graduations on the thimble allow the 0.025 inch to be further divided, so that turning the thimble through one division moves the spindle axially 0.001 inch (0.025 ÷ 25 = 0.001). To read a micrometer, count the number of whole divisions that are visible on the scale of the frame, multiply this number by 25 (the number of thousandths of an inch that each division represents) and add to the product the number of that division on the thimble which coincides with the axial zero line on the frame. The result will be the diameter expressed in thousandths of an inch. As the numbers 1, 2, 3, etc., opposite every fourth sub-division on the frame, indicate hundreds of thousandths, the reading can easily be taken mentally. Suppose the thimble were screwed out so that graduation 2, and three additional sub-divisions, were visible (as shown in Fig. 3), and that graduation 10 on the thimble coincided with the axial line on the frame. The reading then would be 0.200 + 0.075 + 0.010, or 0.285 inch.

Fig. 3. Inch Micrometer

Fig. 4. Inch Micrometer with Vernier

Some micrometers have a vernier scale on the frame in addition to the regular graduations, so that measurements within 0.0001 part of an inch can be taken. Micrometers of this type are read as follows: First determine the number of thousandths, as with an ordinary micrometer, and then find a line on the vernier scale that exactly coincides with one on the thimble; the number of this line represents the number of ten-thousandths to be added to the number of thousandths obtained by the regular graduations. The reading shown in the illustration, Fig. 4, is 0.270 + 0.0003 = 0.2703 inch.


Machinery's Handbook 27th Edition SINE-BAR

695

Micrometers graduated according to the English system of measurement ordinarily have a table of decimal equivalents stamped on the sides of the frame, so that fractions such as sixty-fourths, thirty-seconds, etc., can readily be converted into decimals. Reading a Metric Micrometer.—The spindle of an ordinary metric micrometer has 2 threads per millimeter, and thus one complete revolution moves the spindle through a distance of 0.5 millimeter. The longitudinal line on the frame is graduated with 1 millimeter divisions and 0.5 millimeter sub-divisions. The thimble has 50 graduations, each being 0.01 millimeter (one-hundredth of a millimeter). To read a metric micrometer, note the number of millimeter divisions visible on the scale of the sleeve, and add the total to the particular division on the thimble which coincides with the axial line on the sleeve. Suppose that the thimble were screwed out so that graduation 5, and one additional 0.5 sub-division were visible (as shown in Fig. 5), and that graduation 28 on the thimble coincided with the axial line on the sleeve. The reading then would be 5.00 + 0.5 + 0.28 = 5.78 mm. Some micrometers are provided with a vernier scale on the sleeve in addition to the regular graduations to permit measurements within 0.002 millimeter to be made. Micrometers of this type are read as follows: First determine the number of whole millimeters (if any) and the number of hundredths of a millimeter, as with an ordinary micrometer, and then find a line on the sleeve vernier scale which exactly coincides

Fig. 5. Metric Micrometer

with one on the thimble. The number of this coinciding vernier line represents the number of two-thousandths of a millimeter to be added to the reading already obtained. Thus, for example, a measurement of 2.958 millimeters would be obtained by reading 2.5 millimeters on the sleeve, adding 0.45 millimeter read from the thimble, and then adding 0.008 millimeter as determined by the vernier. Note: 0.01 millimeter = 0.000393 inch, and 0.002 millimeter = 0.000078 inch (78 millionths). Therefore, metric micrometers provide smaller measuring increments than comparable inch unit micrometers—the smallest graduation of an ordinary inch reading micrometer is 0.001 inch; the vernier type has graduations down to 0.0001 inch. When using either a metric or inch micrometer, without a vernier, smaller readings than those graduated may of course be obtained by visual interpolation between graduations. Sine-bar The sine-bar is used either for very accurate angular measurements or for locating work at a given angle as, for example, in surface grinding templets, gages, etc. The sine-bar is especially useful in measuring or checking angles when the limit of accuracy is 5 minutes or less. Some bevel protractors are equipped with verniers which read to 5 minutes but the setting depends upon the alignment of graduations whereas a sine-bar usually is located by positive contact with precision gage-blocks selected for whatever dimension is required for obtaining a given angle. Types of Sine-bars.—A sine-bar consists of a hardened, ground and lapped steel bar with very accurate cylindrical plugs of equal diameter attached to or near each end. The form illustrated by Fig. 3 has notched ends for receiving the cylindrical plugs so that they are held firmly against both faces of the notch. The standard center-to-center distance C between the plugs is either 5 or 10 inches. The upper and lower sides of sine-bars are parallel to the center line of the plugs within very close limits. The body of the sine-bar ordi-



SINE-BAR

narily has several through holes to reduce the weight. In the making of the sine-bar shown in Fig. 4, if too much material is removed from one locating notch, regrinding the shoulder at the opposite end would make it possible to obtain the correct center distance. That is the reason for this change in form. The type of sine-bar illustrated by Fig. 5 has the cylindrical disks or plugs attached to one side. These differences in form or arrangement do not, of course, affect the principle governing the use of the sine-bar. An accurate surface plate or master flat is always used in conjunction with a sine-bar in order to form the base from which the vertical measurements are made.

Fig. 1.

Fig. 2.

Fig. 3.

Fig. 4.

Setting a Sine-bar to a Given Angle.—To find the vertical distance H, for setting a sinebar to the required angle, convert the angle to decimal form on a pocket calculator, take the sine of that angle, and multiply by the distance between the cylinders. For example, if an angle of 31 degrees, 30 minutes is required, the equivalent angle is 31 degrees plus 30⁄60 = 31 + 0.5, or 31.5 degrees. (For conversions from minutes and seconds to decimals of degrees and vice versa, see page 96). The sine of 31.5 degrees is 0.5225 and multiplying this value by the sine-bar length gives 2.613 in. for the height H, Fig. 1 and 3, of the gage blocks. Finding Angle when Height H of Sine-bar is Known.—To find the angle equivalent to a given height H, reverse the above procedure. Thus, if the height H is 1.4061 in., dividing by 5 gives a sine of 0.28122, which corresponds to an angle of 16.333 degrees, or 16 degrees 20 minutes. Checking Angle of Templet or Gage by Using Sine-bar.—Place templet or gage on sine-bar as indicated by dotted lines, Fig. 1. Clamps may be used to hold work in place. Place upper end of sine-bar on gage blocks having total height H corresponding to the required angle. If upper edge D of work is parallel with surface plate E, then angle A of work equals angle A to which sine-bar is set. Parallelism between edge D and surface plate may be tested by checking the height at each end with a dial gage or some type of indicating comparator. Measuring Angle of Templet or Gage with Sine-bar.—To measure such an angle, adjust height of gage blocks and sine-bar until edge D, Fig. 1, is parallel with surface plate E; then find angle corresponding to height H, of gage blocks. For example, if height H is


Machinery's Handbook 27th Edition SINE-BAR

697

2.5939 inches when D and E are parallel, the calculator will show that the angle A of the work is 31 degrees, 15 minutes. Checking Taper per Foot with Sine-bar.—As an example, assume that the plug gage in Fig. 2 is supposed to have a taper of 61⁄8 inches per foot and taper is to be checked by using a 5-inch sine-bar. The table of Tapers per Foot and Corresponding Angles on page 714 shows that the included angle for a taper of 6 1⁄8 inches per foot is 28 degrees 38 minutes 1 second, or 28.6336 degrees from the calculator. For a 5-inch sine-bar, the calculator gives a value of 2.396 inch for the height H of the gage blocks. Using this height, if the upper surface F of the plug gage is parallel to the surface plate the angle corresponds to a taper of 6 1⁄8 inches per foot. Setting Sine-bar having Plugs Attached to Side.—If the lower plug does not rest directly on the surface plate, as in Fig. 3, the height H for the sine-bar is the difference between heights x and y, or the difference between the heights of the plugs; otherwise, the procedure in setting the sine-bar and checking angles is the same as previously described. Checking Templets Having Two Angles.—Assume that angle a of templet, Fig. 4, is 9 degrees, angle b 12 degrees, and that edge G is parallel to the surface plate. For an angle b of 12 degrees, the calculator shows that the height H is 1.03956 inches. For an angle a of 9 degrees, the difference between measurements x and y when the sine-bar is in contact with the upper edge of the templet is 0.78217 inch. Using Sine-bar Tables to Set 5-inch and 100-mm Sine-bars to Given Angle.—T h e table starting on page page 699 gives constants for a 5-inch sine-bar, and starting on page 706 are given constants for a 100-mm sine-bar. These constants represent the vertical height H for setting a sine-bar of the corresponding length to the required angle. Using Sine-bar Tables with Sine-bars of Other Lengths.—A sine-bar may sometimes be preferred that is longer (or shorter) than that given in available tables because of its longer working surface or because the longer center distance is conducive to greater precision. To use the sine-bar tables with a sine-bar of another length to obtain the vertical distances H, multiply the value obtained from the table by the fraction (length of sine-bar used ÷ length of sine-bar specified in table). Example: Use the 5-inch sine-bar table to obtain the vertical height H for setting a 10inch sine-bar to an angle of 39°. The sine of 39 degrees is 0.62932, hence the vertical height H for setting a 10-inch sine-bar is 6.2932 inches. Solution: The height H given for 39° in the 5-inch sine-bar table (page 703) is 3.14660. The corresponding height for a 10-inch sine-bar is 10⁄5 × 3.14660 = 6.2932 inches. Using a Calculator to Determine Sine-bar Constants for a Given Angle.—T h e c o n stant required to set a given angle for a sine-bar of any length can be quickly determined by using a scientific calculator. The required formaulas are as follows: a) angle A given in degrees and calculator is set to measure angles in radian

π ⎞ H = L × sin ⎛ A × -------⎝ 180⎠

or

a) angle A is given in radian, or b) angle A is given in degrees and calculator is set to measure angles in degrees

H = L × sin ( A )

where L =length of the sine-bar A =angle to which the sine-bar is to be set H = vertical height to which one end of sine-bar must be set to obtain angle A π = 3.141592654 In the previous formulas, the height H and length L must be given in the same units, but may be in either metric or US units. Thus, if L is given in mm, then H is in mm; and, if L is given in inches, then H is in inches.



TAPERS

Measuring Tapers with Vee-block and Sine-bar.—The taper on a conical part may be checked or found by placing the part in a vee-block which rests on the surface of a sineplate or sine-bar as shown in the accompanying diagram. The advantage of this method is that the axis of the vee-block may be aligned with the sides of the sine-bar. Thus when the tapered part is placed in the vee-block it will be aligned perpendicular to the transverse axis of the sine-bar.

The sine-bar is set to angle B = (C + A/2) where A/2 is one-half the included angle of the tapered part. If D is the included angle of the precision vee-block, the angle C is calculated from the formula: sin ( A ⁄ 2 )sin C = ----------------------sin ( D ⁄ 2 ) If dial indicator readings show no change across all points along the top of the taper surface, then this checks that the angle A of the taper is correct. If the indicator readings vary, proceed as follows to find the actual angle of taper: 1) Adjust the angle of the sine-bar until the indicator reading is constant. Then find the new angle B′ as explained in the paragraph Measuring Angle of Templet or Gage with Sine-bar on page 696; and 2) Using the angle B′ calculate the actual half-angle A′/2 of the taper from the formula:. ′ sin B ′ tan A ----- = --------------------------------2 D csc ---- + cos B ′ 2 The taper per foot corresponding to certain half-angles of taper may be found in the table on page 714. Dimensioning Tapers.—At least three methods of dimensioning tapers are in use. Standard Tapers: Give one diameter or width, the length, and insert note on drawing designating the taper by number. Special Tapers: In dimensioning a taper when the slope is specified, the length and only one diameter should be given or the diameters at both ends of the taper should be given and length omitted. Precision Work: In certain cases where very precise measurements are necessary the taper surface, either external or internal, is specified by giving a diameter at a certain distance from a surface and the slope of the taper.


Machinery's Handbook 27th Edition 5-INCH SINE-BAR CONSTANTS

699

Constants for 5-inch Sine-bar Constants for Setting a 5-inch Sine-bar for 1° to 7° Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0° 0.00000 0.00145 0.00291 0.00436 0.00582 0.00727 0.00873 0.01018 0.01164 0.01309 0.01454 0.01600 0.01745 0.01891 0.02036 0.02182 0.02327 0.02473 0.02618 0.02763 0.02909 0.03054 0.03200 0.03345 0.03491 0.03636 0.03782 0.03927 0.04072 0.04218 0.04363 0.04509 0.04654 0.04800 0.04945 0.05090 0.05236 0.05381 0.05527 0.05672 0.05818 0.05963 0.06109 0.06254 0.06399 0.06545 0.06690 0.06836 0.06981 0.07127 0.07272 0.07417 0.07563 0.07708 0.07854 0.07999 0.08145 0.08290 0.08435 0.08581 0.08726

1° 0.08726 0.08872 0.09017 0.09162 0.09308 0.09453 0.09599 0.09744 0.09890 0.10035 0.10180 0.10326 0.10471 0.10617 0.10762 0.10907 0.11053 0.11198 0.11344 0.11489 0.11634 0.11780 0.11925 0.12071 0.12216 0.12361 0.12507 0.12652 0.12798 0.12943 0.13088 0.13234 0.13379 0.13525 0.13670 0.13815 0.13961 0.14106 0.14252 0.14397 0.14542 0.14688 0.14833 0.14979 0.15124 0.15269 0.15415 0.15560 0.15705 0.15851 0.15996 0.16141 0.16287 0.16432 0.16578 0.16723 0.16868 0.17014 0.17159 0.17304 0.17450

2° 0.17450 0.17595 0.17740 0.17886 0.18031 0.18177 0.18322 0.18467 0.18613 0.18758 0.18903 0.19049 0.19194 0.19339 0.19485 0.19630 0.19775 0.19921 0.20066 0.20211 0.20357 0.20502 0.20647 0.20793 0.20938 0.21083 0.21228 0.21374 0.21519 0.21664 0.21810 0.21955 0.22100 0.22246 0.22391 0.22536 0.22681 0.22827 0.22972 0.23117 0.23263 0.23408 0.23553 0.23699 0.23844 0.23989 0.24134 0.24280 0.24425 0.24570 0.24715 0.24861 0.25006 0.25151 0.25296 0.25442 0.25587 0.25732 0.25877 0.26023 0.26168

3° 0.26168 0.26313 0.26458 0.26604 0.26749 0.26894 0.27039 0.27185 0.27330 0.27475 0.27620 0.27766 0.27911 0.28056 0.28201 0.28346 0.28492 0.28637 0.28782 0.28927 0.29072 0.29218 0.29363 0.29508 0.29653 0.29798 0.29944 0.30089 0.30234 0.30379 0.30524 0.30669 0.30815 0.30960 0.31105 0.31250 0.31395 0.31540 0.31686 0.31831 0.31976 0.32121 0.32266 0.32411 0.32556 0.32702 0.32847 0.32992 0.33137 0.33282 0.33427 0.33572 0.33717 0.33863 0.34008 0.34153 0.34298 0.34443 0.34588 0.34733 0.34878

4° 0.34878 0.35023 0.35168 0.35313 0.35459 0.35604 0.35749 0.35894 0.36039 0.36184 0.36329 0.36474 0.36619 0.36764 0.36909 0.37054 0.37199 0.37344 0.37489 0.37634 0.37779 0.37924 0.38069 0.38214 0.38360 0.38505 0.38650 0.38795 0.38940 0.39085 0.39230 0.39375 0.39520 0.39665 0.39810 0.39954 0.40099 0.40244 0.40389 0.40534 0.40679 0.40824 0.40969 0.41114 0.41259 0.41404 0.41549 0.41694 0.41839 0.41984 0.42129 0.42274 0.42419 0.42564 0.42708 0.42853 0.42998 0.43143 0.43288 0.43433 0.43578

5° 0.43578 0.43723 0.43868 0.44013 0.44157 0.44302 0.44447 0.44592 0.44737 0.44882 0.45027 0.45171 0.45316 0.45461 0.45606 0.45751 0.45896 0.46040 0.46185 0.46330 0.46475 0.46620 0.46765 0.46909 0.47054 0.47199 0.47344 0.47489 0.47633 0.47778 0.47923 0.48068 0.48212 0.48357 0.48502 0.48647 0.48791 0.48936 0.49081 0.49226 0.49370 0.49515 0.49660 0.49805 0.49949 0.50094 0.50239 0.50383 0.50528 0.50673 0.50818 0.50962 0.51107 0.51252 0.51396 0.51541 0.51686 0.51830 0.51975 0.52120 0.52264

6° 0.52264 0.52409 0.52554 0.52698 0.52843 0.52987 0.53132 0.53277 0.53421 0.53566 0.53710 0.53855 0.54000 0.54144 0.54289 0.54433 0.54578 0.54723 0.54867 0.55012 0.55156 0.55301 0.55445 0.55590 0.55734 0.55879 0.56024 0.56168 0.56313 0.56457 0.56602 0.56746 0.56891 0.57035 0.57180 0.57324 0.57469 0.57613 0.57758 0.57902 0.58046 0.58191 0.58335 0.58480 0.58624 0.58769 0.58913 0.59058 0.59202 0.59346 0.59491 0.59635 0.59780 0.59924 0.60068 0.60213 0.60357 0.60502 0.60646 0.60790 0.60935


7° 0.60935 0.61079 0.61223 0.61368 0.61512 0.61656 0.61801 0.61945 0.62089 0.62234 0.62378 0.62522 0.62667 0.62811 0.62955 0.63099 0.63244 0.63388 0.63532 0.63677 0.63821 0.63965 0.64109 0.64254 0.64398 0.64542 0.64686 0.64830 0.64975 0.65119 0.65263 0.65407 0.65551 0.65696 0.65840 0.65984 0.66128 0.66272 0.66417 0.66561 0.66705 0.66849 0.66993 0.67137 0.67281 0.67425 0.67570 0.67714 0.67858 0.68002 0.68146 0.68290 0.68434 0.68578 0.68722 0.68866 0.69010 0.69154 0.69298 0.69443 0.69587


5-INCH SINE-BAR CONSTANTS Constants for Setting a 5-inch Sine-bar for 8° to 15°

Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

8° 0.69587 0.69731 0.69875 0.70019 0.70163 0.70307 0.70451 0.70595 0.70739 0.70883 0.71027 0.71171 0.71314 0.71458 0.71602 0.71746 0.71890 0.72034 0.72178 0.72322 0.72466 0.72610 0.72754 0.72898 0.73042 0.73185 0.73329 0.73473 0.73617 0.73761 0.73905 0.74049 0.74192 0.74336 0.74480 0.74624 0.74768 0.74911 0.75055 0.75199 0.75343 0.75487 0.75630 0.75774 0.75918 0.76062 0.76205 0.76349 0.76493 0.76637 0.76780 0.76924 0.77068 0.77211 0.77355 0.77499 0.77643 0.77786 0.77930 0.78074 0.78217

9° 0.78217 0.78361 0.78505 0.78648 0.78792 0.78935 0.79079 0.79223 0.79366 0.79510 0.79653 0.79797 0.79941 0.80084 0.80228 0.80371 0.80515 0.80658 0.80802 0.80945 0.81089 0.81232 0.81376 0.81519 0.81663 0.81806 0.81950 0.82093 0.82237 0.82380 0.82524 0.82667 0.82811 0.82954 0.83098 0.83241 0.83384 0.83528 0.83671 0.83815 0.83958 0.84101 0.84245 0.84388 0.84531 0.84675 0.84818 0.84961 0.85105 0.85248 0.85391 0.85535 0.85678 0.85821 0.85965 0.86108 0.86251 0.86394 0.86538 0.86681 0.86824

10° 0.86824 0.86967 0.87111 0.87254 0.87397 0.87540 0.87683 0.87827 0.87970 0.88113 0.88256 0.88399 0.88542 0.88686 0.88829 0.88972 0.89115 0.89258 0.89401 0.89544 0.89687 0.89830 0.89973 0.90117 0.90260 0.90403 0.90546 0.90689 0.90832 0.90975 0.91118 0.91261 0.91404 0.91547 0.91690 0.91833 0.91976 0.92119 0.92262 0.92405 0.92547 0.92690 0.92833 0.92976 0.93119 0.93262 0.93405 0.93548 0.93691 0.93834 0.93976 0.94119 0.94262 0.94405 0.94548 0.94691 0.94833 0.94976 0.95119 0.95262 0.95404

11° 0.95404 0.95547 0.95690 0.95833 0.95976 0.96118 0.96261 0.96404 0.96546 0.96689 0.96832 0.96974 0.97117 0.97260 0.97403 0.97545 0.97688 0.97830 0.97973 0.98116 0.98258 0.98401 0.98544 0.98686 0.98829 0.98971 0.99114 0.99256 0.99399 0.99541 0.99684 0.99826 0.99969 1.00112 1.00254 1.00396 1.00539 1.00681 1.00824 1.00966 1.01109 1.01251 1.01394 1.01536 1.01678 1.01821 1.01963 1.02106 1.02248 1.02390 1.02533 1.02675 1.02817 1.02960 1.03102 1.03244 1.03387 1.03529 1.03671 1.03814 1.03956

12° 1.03956 1.04098 1.04240 1.04383 1.04525 1.04667 1.04809 1.04951 1.05094 1.05236 1.05378 1.05520 1.05662 1.05805 1.05947 1.06089 1.06231 1.06373 1.06515 1.06657 1.06799 1.06941 1.07084 1.07226 1.07368 1.07510 1.07652 1.07794 1.07936 1.08078 1.08220 1.08362 1.08504 1.08646 1.08788 1.08930 1.09072 1.09214 1.09355 1.09497 1.09639 1.09781 1.09923 1.10065 1.10207 1.10349 1.10491 1.10632 1.10774 1.10916 1.11058 1.11200 1.11342 1.11483 1.11625 1.11767 1.11909 1.12050 1.12192 1.12334 1.12476

13° 1.12476 1.12617 1.12759 1.12901 1.13042 1.13184 1.13326 1.13467 1.13609 1.13751 1.13892 1.14034 1.14175 1.14317 1.14459 1.14600 1.14742 1.14883 1.15025 1.15166 1.15308 1.15449 1.15591 1.15732 1.15874 1.16015 1.16157 1.16298 1.16440 1.16581 1.16723 1.16864 1.17006 1.17147 1.17288 1.17430 1.17571 1.17712 1.17854 1.17995 1.18136 1.18278 1.18419 1.18560 1.18702 1.18843 1.18984 1.19125 1.19267 1.19408 1.19549 1.19690 1.19832 1.19973 1.20114 1.20255 1.20396 1.20538 1.20679 1.20820 1.20961

14° 1.20961 1.21102 1.21243 1.21384 1.21525 1.21666 1.21808 1.21949 1.22090 1.22231 1.22372 1.22513 1.22654 1.22795 1.22936 1.23077 1.23218 1.23359 1.23500 1.23640 1.23781 1.23922 1.24063 1.24204 1.24345 1.24486 1.24627 1.24768 1.24908 1.25049 1.25190 1.25331 1.25472 1.25612 1.25753 1.25894 1.26035 1.26175 1.26316 1.26457 1.26598 1.26738 1.26879 1.27020 1.27160 1.27301 1.27442 1.27582 1.27723 1.27863 1.28004 1.28145 1.28285 1.28426 1.28566 1.28707 1.28847 1.28988 1.29129 1.29269 1.29410


15° 1.29410 1.29550 1.29690 1.29831 1.29971 1.30112 1.30252 1.30393 1.30533 1.30673 1.30814 1.30954 1.31095 1.31235 1.31375 1.31516 1.31656 1.31796 1.31937 1.32077 1.32217 1.32357 1.32498 1.32638 1.32778 1.32918 1.33058 1.33199 1.33339 1.33479 1.33619 1.33759 1.33899 1.34040 1.34180 1.34320 1.34460 1.34600 1.34740 1.34880 1.35020 1.35160 1.35300 1.35440 1.35580 1.35720 1.35860 1.36000 1.36140 1.36280 1.36420 1.36560 1.36700 1.36840 1.36980 1.37119 1.37259 1.37399 1.37539 1.37679 1.37819


701

Constants for Setting a 5-inch Sine-bar for 16° to 23° Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

16° 1.37819 1.37958 1.38098 1.38238 1.38378 1.38518 1.38657 1.38797 1.38937 1.39076 1.39216 1.39356 1.39496 1.39635 1.39775 1.39915 1.40054 1.40194 1.40333 1.40473 1.40613 1.40752 1.40892 1.41031 1.41171 1.41310 1.41450 1.41589 1.41729 1.41868 1.42008 1.42147 1.42287 1.42426 1.42565 1.42705 1.42844 1.42984 1.43123 1.43262 1.43402 1.43541 1.43680 1.43820 1.43959 1.44098 1.44237 1.44377 1.44516 1.44655 1.44794 1.44934 1.45073 1.45212 1.45351 1.45490 1.45629 1.45769 1.45908 1.46047 1.46186

17° 1.46186 1.46325 1.46464 1.46603 1.46742 1.46881 1.47020 1.47159 1.47298 1.47437 1.47576 1.47715 1.47854 1.47993 1.48132 1.48271 1.48410 1.48549 1.48687 1.48826 1.48965 1.49104 1.49243 1.49382 1.49520 1.49659 1.49798 1.49937 1.50075 1.50214 1.50353 1.50492 1.50630 1.50769 1.50908 1.51046 1.51185 1.51324 1.51462 1.51601 1.51739 1.51878 1.52017 1.52155 1.52294 1.52432 1.52571 1.52709 1.52848 1.52986 1.53125 1.53263 1.53401 1.53540 1.53678 1.53817 1.53955 1.54093 1.54232 1.54370 1.54509

18° 1.54509 1.54647 1.54785 1.54923 1.55062 1.55200 1.55338 1.55476 1.55615 1.55753 1.55891 1.56029 1.56167 1.56306 1.56444 1.56582 1.56720 1.56858 1.56996 1.57134 1.57272 1.57410 1.57548 1.57687 1.57825 1.57963 1.58101 1.58238 1.58376 1.58514 1.58652 1.58790 1.58928 1.59066 1.59204 1.59342 1.59480 1.59617 1.59755 1.59893 1.60031 1.60169 1.60307 1.60444 1.60582 1.60720 1.60857 1.60995 1.61133 1.61271 1.61408 1.61546 1.61683 1.61821 1.61959 1.62096 1.62234 1.62371 1.62509 1.62647 1.62784

19° 1.62784 1.62922 1.63059 1.63197 1.63334 1.63472 1.63609 1.63746 1.63884 1.64021 1.64159 1.64296 1.64433 1.64571 1.64708 1.64845 1.64983 1.65120 1.65257 1.65394 1.65532 1.65669 1.65806 1.65943 1.66081 1.66218 1.66355 1.66492 1.66629 1.66766 1.66903 1.67041 1.67178 1.67315 1.67452 1.67589 1.67726 1.67863 1.68000 1.68137 1.68274 1.68411 1.68548 1.68685 1.68821 1.68958 1.69095 1.69232 1.69369 1.69506 1.69643 1.69779 1.69916 1.70053 1.70190 1.70327 1.70463 1.70600 1.70737 1.70873 1.71010

20° 1.71010 1.71147 1.71283 1.71420 1.71557 1.71693 1.71830 1.71966 1.72103 1.72240 1.72376 1.72513 1.72649 1.72786 1.72922 1.73059 1.73195 1.73331 1.73468 1.73604 1.73741 1.73877 1.74013 1.74150 1.74286 1.74422 1.74559 1.74695 1.74831 1.74967 1.75104 1.75240 1.75376 1.75512 1.75649 1.75785 1.75921 1.76057 1.76193 1.76329 1.76465 1.76601 1.76737 1.76873 1.77010 1.77146 1.77282 1.77418 1.77553 1.77689 1.77825 1.77961 1.78097 1.78233 1.78369 1.78505 1.78641 1.78777 1.78912 1.79048 1.79184

21° 1.79184 1.79320 1.79456 1.79591 1.79727 1.79863 1.79998 1.80134 1.80270 1.80405 1.80541 1.80677 1.80812 1.80948 1.81083 1.81219 1.81355 1.81490 1.81626 1.81761 1.81897 1.82032 1.82168 1.82303 1.82438 1.82574 1.82709 1.82845 1.82980 1.83115 1.83251 1.83386 1.83521 1.83657 1.83792 1.83927 1.84062 1.84198 1.84333 1.84468 1.84603 1.84738 1.84873 1.85009 1.85144 1.85279 1.85414 1.85549 1.85684 1.85819 1.85954 1.86089 1.86224 1.86359 1.86494 1.86629 1.86764 1.86899 1.87034 1.87168 1.87303

22° 1.87303 1.87438 1.87573 1.87708 1.87843 1.87977 1.88112 1.88247 1.88382 1.88516 1.88651 1.88786 1.88920 1.89055 1.89190 1.89324 1.89459 1.89594 1.89728 1.89863 1.89997 1.90132 1.90266 1.90401 1.90535 1.90670 1.90804 1.90939 1.91073 1.91207 1.91342 1.91476 1.91610 1.91745 1.91879 1.92013 1.92148 1.92282 1.92416 1.92550 1.92685 1.92819 1.92953 1.93087 1.93221 1.93355 1.93490 1.93624 1.93758 1.93892 1.94026 1.94160 1.94294 1.94428 1.94562 1.94696 1.94830 1.94964 1.95098 1.95232 1.95366


23° 1.95366 1.95499 1.95633 1.95767 1.95901 1.96035 1.96169 1.96302 1.96436 1.96570 1.96704 1.96837 1.96971 1.97105 1.97238 1.97372 1.97506 1.97639 1.97773 1.97906 1.98040 1.98173 1.98307 1.98440 1.98574 1.98707 1.98841 1.98974 1.99108 1.99241 1.99375 1.99508 1.99641 1.99775 1.99908 2.00041 2.00175 2.00308 2.00441 2.00574 2.00708 2.00841 2.00974 2.01107 2.01240 2.01373 2.01506 2.01640 2.01773 2.01906 2.02039 2.02172 2.02305 2.02438 2.02571 2.02704 2.02837 2.02970 2.03103 2.03235 2.03368



Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

24° 2.03368 2.03501 2.03634 2.03767 2.03900 2.04032 2.04165 2.04298 2.04431 2.04563 2.04696 2.04829 2.04962 2.05094 2.05227 2.05359 2.05492 2.05625 2.05757 2.05890 2.06022 2.06155 2.06287 2.06420 2.06552 2.06685 2.06817 2.06950 2.07082 2.07214 2.07347 2.07479 2.07611 2.07744 2.07876 2.08008 2.08140 2.08273 2.08405 2.08537 2.08669 2.08801 2.08934 2.09066 2.09198 2.09330 2.09462 2.09594 2.09726 2.09858 2.09990 2.10122 2.10254 2.10386 2.10518 2.10650 2.10782 2.10914 2.11045 2.11177 2.11309

25° 2.11309 2.11441 2.11573 2.11704 2.11836 2.11968 2.12100 2.12231 2.12363 2.12495 2.12626 2.12758 2.12890 2.13021 2.13153 2.13284 2.13416 2.13547 2.13679 2.13810 2.13942 2.14073 2.14205 2.14336 2.14468 2.14599 2.14730 2.14862 2.14993 2.15124 2.15256 2.15387 2.15518 2.15649 2.15781 2.15912 2.16043 2.16174 2.16305 2.16436 2.16567 2.16698 2.16830 2.16961 2.17092 2.17223 2.17354 2.17485 2.17616 2.17746 2.17877 2.18008 2.18139 2.18270 2.18401 2.18532 2.18663 2.18793 2.18924 2.19055 2.19186

26° 2.19186 2.19316 2.19447 2.19578 2.19708 2.19839 2.19970 2.20100 2.20231 2.20361 2.20492 2.20622 2.20753 2.20883 2.21014 2.21144 2.21275 2.21405 2.21536 2.21666 2.21796 2.21927 2.22057 2.22187 2.22318 2.22448 2.22578 2.22708 2.22839 2.22969 2.23099 2.23229 2.23359 2.23489 2.23619 2.23749 2.23880 2.24010 2.24140 2.24270 2.24400 2.24530 2.24660 2.24789 2.24919 2.25049 2.25179 2.25309 2.25439 2.25569 2.25698 2.25828 2.25958 2.26088 2.26217 2.26347 2.26477 2.26606 2.26736 2.26866 2.26995

27° 2.26995 2.27125 2.27254 2.27384 2.27513 2.27643 2.27772 2.27902 2.28031 2.28161 2.28290 2.28420 2.28549 2.28678 2.28808 2.28937 2.29066 2.29196 2.29325 2.29454 2.29583 2.29712 2.29842 2.29971 2.30100 2.30229 2.30358 2.30487 2.30616 2.30745 2.30874 2.31003 2.31132 2.31261 2.31390 2.31519 2.31648 2.31777 2.31906 2.32035 2.32163 2.32292 2.32421 2.32550 2.32679 2.32807 2.32936 2.33065 2.33193 2.33322 2.33451 2.33579 2.33708 2.33836 2.33965 2.34093 2.34222 2.34350 2.34479 2.34607 2.34736

28° 2.34736 2.34864 2.34993 2.35121 2.35249 2.35378 2.35506 2.35634 2.35763 2.35891 2.36019 2.36147 2.36275 2.36404 2.36532 2.36660 2.36788 2.36916 2.37044 2.37172 2.37300 2.37428 2.37556 2.37684 2.37812 2.37940 2.38068 2.38196 2.38324 2.38452 2.38579 2.38707 2.38835 2.38963 2.39091 2.39218 2.39346 2.39474 2.39601 2.39729 2.39857 2.39984 2.40112 2.40239 2.40367 2.40494 2.40622 2.40749 2.40877 2.41004 2.41132 2.41259 2.41386 2.41514 2.41641 2.41769 2.41896 2.42023 2.42150 2.42278 2.42405

29° 2.42405 2.42532 2.42659 2.42786 2.42913 2.43041 2.43168 2.43295 2.43422 2.43549 2.43676 2.43803 2.43930 2.44057 2.44184 2.44311 2.44438 2.44564 2.44691 2.44818 2.44945 2.45072 2.45198 2.45325 2.45452 2.45579 2.45705 2.45832 2.45959 2.46085 2.46212 2.46338 2.46465 2.46591 2.46718 2.46844 2.46971 2.47097 2.47224 2.47350 2.47477 2.47603 2.47729 2.47856 2.47982 2.48108 2.48235 2.48361 2.48487 2.48613 2.48739 2.48866 2.48992 2.49118 2.49244 2.49370 2.49496 2.49622 2.49748 2.49874 2.50000

30° 2.50000 2.50126 2.50252 2.50378 2.50504 2.50630 2.50755 2.50881 2.51007 2.51133 2.51259 2.51384 2.51510 2.51636 2.51761 2.51887 2.52013 2.52138 2.52264 2.52389 2.52515 2.52640 2.52766 2.52891 2.53017 2.53142 2.53268 2.53393 2.53519 2.53644 2.53769 2.53894 2.54020 2.54145 2.54270 2.54396 2.54521 2.54646 2.54771 2.54896 2.55021 2.55146 2.55271 2.55397 2.55522 2.55647 2.55772 2.55896 2.56021 2.56146 2.56271 2.56396 2.56521 2.56646 2.56771 2.56895 2.57020 2.57145 2.57270 2.57394 2.57519


31° 2.57519 2.57644 2.57768 2.57893 2.58018 2.58142 2.58267 2.58391 2.58516 2.58640 2.58765 2.58889 2.59014 2.59138 2.59262 2.59387 2.59511 2.59635 2.59760 2.59884 2.60008 2.60132 2.60256 2.60381 2.60505 2.60629 2.60753 2.60877 2.61001 2.61125 2.61249 2.61373 2.61497 2.61621 2.61745 2.61869 2.61993 2.62117 2.62241 2.62364 2.62488 2.62612 2.62736 2.62860 2.62983 2.63107 2.63231 2.63354 2.63478 2.63602 2.63725 2.63849 2.63972 2.64096 2.64219 2.64343 2.64466 2.64590 2.64713 2.64836 2.64960


703


32° 2.64960 2.65083 2.65206 2.65330 2.65453 2.65576 2.65699 2.65822 2.65946 2.66069 2.66192 2.66315 2.66438 2.66561 2.66684 2.66807 2.66930 2.67053 2.67176 2.67299 2.67422 2.67545 2.67668 2.67791 2.67913 2.68036 2.68159 2.68282 2.68404 2.68527 2.68650 2.68772 2.68895 2.69018 2.69140 2.69263 2.69385 2.69508 2.69630 2.69753 2.69875 2.69998 2.70120 2.70243 2.70365 2.70487 2.70610 2.70732 2.70854 2.70976 2.71099 2.71221 2.71343 2.71465 2.71587 2.71709 2.71831 2.71953 2.72076 2.72198 2.72320

33° 2.72320 2.72441 2.72563 2.72685 2.72807 2.72929 2.73051 2.73173 2.73295 2.73416 2.73538 2.73660 2.73782 2.73903 2.74025 2.74147 2.74268 2.74390 2.74511 2.74633 2.74754 2.74876 2.74997 2.75119 2.75240 2.75362 2.75483 2.75605 2.75726 2.75847 2.75969 2.76090 2.76211 2.76332 2.76453 2.76575 2.76696 2.76817 2.76938 2.77059 2.77180 2.77301 2.77422 2.77543 2.77664 2.77785 2.77906 2.78027 2.78148 2.78269 2.78389 2.78510 2.78631 2.78752 2.78873 2.78993 2.79114 2.79235 2.79355 2.79476 2.79596

34° 2.79596 2.79717 2.79838 2.79958 2.80079 2.80199 2.80319 2.80440 2.80560 2.80681 2.80801 2.80921 2.81042 2.81162 2.81282 2.81402 2.81523 2.81643 2.81763 2.81883 2.82003 2.82123 2.82243 2.82364 2.82484 2.82604 2.82723 2.82843 2.82963 2.83083 2.83203 2.83323 2.83443 2.83563 2.83682 2.83802 2.83922 2.84042 2.84161 2.84281 2.84401 2.84520 2.84640 2.84759 2.84879 2.84998 2.85118 2.85237 2.85357 2.85476 2.85596 2.85715 2.85834 2.85954 2.86073 2.86192 2.86311 2.86431 2.86550 2.86669 2.86788

35° 2.86788 2.86907 2.87026 2.87146 2.87265 2.87384 2.87503 2.87622 2.87741 2.87860 2.87978 2.88097 2.88216 2.88335 2.88454 2.88573 2.88691 2.88810 2.88929 2.89048 2.89166 2.89285 2.89403 2.89522 2.89641 2.89759 2.89878 2.89996 2.90115 2.90233 2.90351 2.90470 2.90588 2.90707 2.90825 2.90943 2.91061 2.91180 2.91298 2.91416 2.91534 2.91652 2.91771 2.91889 2.92007 2.92125 2.92243 2.92361 2.92479 2.92597 2.92715 2.92833 2.92950 2.93068 2.93186 2.93304 2.93422 2.93540 2.93657 2.93775 2.93893

36° 2.93893 2.94010 2.94128 2.94246 2.94363 2.94481 2.94598 2.94716 2.94833 2.94951 2.95068 2.95185 2.95303 2.95420 2.95538 2.95655 2.95772 2.95889 2.96007 2.96124 2.96241 2.96358 2.96475 2.96592 2.96709 2.96827 2.96944 2.97061 2.97178 2.97294 2.97411 2.97528 2.97645 2.97762 2.97879 2.97996 2.98112 2.98229 2.98346 2.98463 2.98579 2.98696 2.98813 2.98929 2.99046 2.99162 2.99279 2.99395 2.99512 2.99628 2.99745 2.99861 2.99977 3.00094 3.00210 3.00326 3.00443 3.00559 3.00675 3.00791 3.00908

37° 3.00908 3.01024 3.01140 3.01256 3.01372 3.01488 3.01604 3.01720 3.01836 3.01952 3.02068 3.02184 3.02300 3.02415 3.02531 3.02647 3.02763 3.02878 3.02994 3.03110 3.03226 3.03341 3.03457 3.03572 3.03688 3.03803 3.03919 3.04034 3.04150 3.04265 3.04381 3.04496 3.04611 3.04727 3.04842 3.04957 3.05073 3.05188 3.05303 3.05418 3.05533 3.05648 3.05764 3.05879 3.05994 3.06109 3.06224 3.06339 3.06454 3.06568 3.06683 3.06798 3.06913 3.07028 3.07143 3.07257 3.07372 3.07487 3.07601 3.07716 3.07831

38° 3.07831 3.07945 3.08060 3.08174 3.08289 3.08403 3.08518 3.08632 3.08747 3.08861 3.08976 3.09090 3.09204 3.09318 3.09433 3.09547 3.09661 3.09775 3.09890 3.10004 3.10118 3.10232 3.10346 3.10460 3.10574 3.10688 3.10802 3.10916 3.11030 3.11143 3.11257 3.11371 3.11485 3.11599 3.11712 3.11826 3.11940 3.12053 3.12167 3.12281 3.12394 3.12508 3.12621 3.12735 3.12848 3.12962 3.13075 3.13189 3.13302 3.13415 3.13529 3.13642 3.13755 3.13868 3.13982 3.14095 3.14208 3.14321 3.14434 3.14547 3.14660


39° 3.14660 3.14773 3.14886 3.14999 3.15112 3.15225 3.15338 3.15451 3.15564 3.15676 3.15789 3.15902 3.16015 3.16127 3.16240 3.16353 3.16465 3.16578 3.16690 3.16803 3.16915 3.17028 3.17140 3.17253 3.17365 3.17478 3.17590 3.17702 3.17815 3.17927 3.18039 3.18151 3.18264 3.18376 3.18488 3.18600 3.18712 3.18824 3.18936 3.19048 3.19160 3.19272 3.19384 3.19496 3.19608 3.19720 3.19831 3.19943 3.20055 3.20167 3.20278 3.20390 3.20502 3.20613 3.20725 3.20836 3.20948 3.21059 3.21171 3.21282 3.21394



Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

40° 3.21394 3.21505 3.21617 3.21728 3.21839 3.21951 3.22062 3.22173 3.22284 3.22395 3.22507 3.22618 3.22729 3.22840 3.22951 3.23062 3.23173 3.23284 3.23395 3.23506 3.23617 3.23728 3.23838 3.23949 3.24060 3.24171 3.24281 3.24392 3.24503 3.24613 3.24724 3.24835 3.24945 3.25056 3.25166 3.25277 3.25387 3.25498 3.25608 3.25718 3.25829 3.25939 3.26049 3.26159 3.26270 3.26380 3.26490 3.26600 3.26710 3.26820 3.26930 3.27040 3.27150 3.27260 3.27370 3.27480 3.27590 3.27700 3.27810 3.27920 3.28030

41° 3.28030 3.28139 3.28249 3.28359 3.28468 3.28578 3.28688 3.28797 3.28907 3.29016 3.29126 3.29235 3.29345 3.29454 3.29564 3.29673 3.29782 3.29892 3.30001 3.30110 3.30219 3.30329 3.30438 3.30547 3.30656 3.30765 3.30874 3.30983 3.31092 3.31201 3.31310 3.31419 3.31528 3.31637 3.31746 3.31854 3.31963 3.32072 3.32181 3.32289 3.32398 3.32507 3.32615 3.32724 3.32832 3.32941 3.33049 3.33158 3.33266 3.33375 3.33483 3.33591 3.33700 3.33808 3.33916 3.34025 3.34133 3.34241 3.34349 3.34457 3.34565

42° 3.34565 3.34673 3.34781 3.34889 3.34997 3.35105 3.35213 3.35321 3.35429 3.35537 3.35645 3.35753 3.35860 3.35968 3.36076 3.36183 3.36291 3.36399 3.36506 3.36614 3.36721 3.36829 3.36936 3.37044 3.37151 3.37259 3.37366 3.37473 3.37581 3.37688 3.37795 3.37902 3.38010 3.38117 3.38224 3.38331 3.38438 3.38545 3.38652 3.38759 3.38866 3.38973 3.39080 3.39187 3.39294 3.39400 3.39507 3.39614 3.39721 3.39827 3.39934 3.40041 3.40147 3.40254 3.40360 3.40467 3.40573 3.40680 3.40786 3.40893 3.40999

43° 3.40999 3.41106 3.41212 3.41318 3.41424 3.41531 3.41637 3.41743 3.41849 3.41955 3.42061 3.42168 3.42274 3.42380 3.42486 3.42592 3.42697 3.42803 3.42909 3.43015 3.43121 3.43227 3.43332 3.43438 3.43544 3.43649 3.43755 3.43861 3.43966 3.44072 3.44177 3.44283 3.44388 3.44494 3.44599 3.44704 3.44810 3.44915 3.45020 3.45126 3.45231 3.45336 3.45441 3.45546 3.45651 3.45757 3.45862 3.45967 3.46072 3.46177 3.46281 3.46386 3.46491 3.46596 3.46701 3.46806 3.46910 3.47015 3.47120 3.47225 3.47329

44° 3.47329 3.47434 3.47538 3.47643 3.47747 3.47852 3.47956 3.48061 3.48165 3.48270 3.48374 3.48478 3.48583 3.48687 3.48791 3.48895 3.48999 3.49104 3.49208 3.49312 3.49416 3.49520 3.49624 3.49728 3.49832 3.49936 3.50039 3.50143 3.50247 3.50351 3.50455 3.50558 3.50662 3.50766 3.50869 3.50973 3.51077 3.51180 3.51284 3.51387 3.51491 3.51594 3.51697 3.51801 3.51904 3.52007 3.52111 3.52214 3.52317 3.52420 3.52523 3.52627 3.52730 3.52833 3.52936 3.53039 3.53142 3.53245 3.53348 3.53451 3.53553

45° 3.53553 3.53656 3.53759 3.53862 3.53965 3.54067 3.54170 3.54273 3.54375 3.54478 3.54580 3.54683 3.54785 3.54888 3.54990 3.55093 3.55195 3.55297 3.55400 3.55502 3.55604 3.55707 3.55809 3.55911 3.56013 3.56115 3.56217 3.56319 3.56421 3.56523 3.56625 3.56727 3.56829 3.56931 3.57033 3.57135 3.57236 3.57338 3.57440 3.57542 3.57643 3.57745 3.57846 3.57948 3.58049 3.58151 3.58252 3.58354 3.58455 3.58557 3.58658 3.58759 3.58861 3.58962 3.59063 3.59164 3.59266 3.59367 3.59468 3.59569 3.59670

46° 3.59670 3.59771 3.59872 3.59973 3.60074 3.60175 3.60276 3.60376 3.60477 3.60578 3.60679 3.60779 3.60880 3.60981 3.61081 3.61182 3.61283 3.61383 3.61484 3.61584 3.61684 3.61785 3.61885 3.61986 3.62086 3.62186 3.62286 3.62387 3.62487 3.62587 3.62687 3.62787 3.62887 3.62987 3.63087 3.63187 3.63287 3.63387 3.63487 3.63587 3.63687 3.63787 3.63886 3.63986 3.64086 3.64186 3.64285 3.64385 3.64484 3.64584 3.64683 3.64783 3.64882 3.64982 3.65081 3.65181 3.65280 3.65379 3.65478 3.65578 3.65677


47° 3.65677 3.65776 3.65875 3.65974 3.66073 3.66172 3.66271 3.66370 3.66469 3.66568 3.66667 3.66766 3.66865 3.66964 3.67063 3.67161 3.67260 3.67359 3.67457 3.67556 3.67655 3.67753 3.67852 3.67950 3.68049 3.68147 3.68245 3.68344 3.68442 3.68540 3.68639 3.68737 3.68835 3.68933 3.69031 3.69130 3.69228 3.69326 3.69424 3.69522 3.69620 3.69718 3.69816 3.69913 3.70011 3.70109 3.70207 3.70305 3.70402 3.70500 3.70598 3.70695 3.70793 3.70890 3.70988 3.71085 3.71183 3.71280 3.71378 3.71475 3.71572


705


48° 3.71572 3.71670 3.71767 3.71864 3.71961 3.72059 3.72156 3.72253 3.72350 3.72447 3.72544 3.72641 3.72738 3.72835 3.72932 3.73029 3.73126 3.73222 3.73319 3.73416 3.73513 3.73609 3.73706 3.73802 3.73899 3.73996 3.74092 3.74189 3.74285 3.74381 3.74478 3.74574 3.74671 3.74767 3.74863 3.74959 3.75056 3.75152 3.75248 3.75344 3.75440 3.75536 3.75632 3.75728 3.75824 3.75920 3.76016 3.76112 3.76207 3.76303 3.76399 3.76495 3.76590 3.76686 3.76782 3.76877 3.76973 3.77068 3.77164 3.77259 3.77355

49° 3.77355 3.77450 3.77546 3.77641 3.77736 3.77831 3.77927 3.78022 3.78117 3.78212 3.78307 3.78402 3.78498 3.78593 3.78688 3.78783 3.78877 3.78972 3.79067 3.79162 3.79257 3.79352 3.79446 3.79541 3.79636 3.79730 3.79825 3.79919 3.80014 3.80109 3.80203 3.80297 3.80392 3.80486 3.80581 3.80675 3.80769 3.80863 3.80958 3.81052 3.81146 3.81240 3.81334 3.81428 3.81522 3.81616 3.81710 3.81804 3.81898 3.81992 3.82086 3.82179 3.82273 3.82367 3.82461 3.82554 3.82648 3.82742 3.82835 3.82929 3.83022

50° 3.83022 3.83116 3.83209 3.83303 3.83396 3.83489 3.83583 3.83676 3.83769 3.83862 3.83956 3.84049 3.84142 3.84235 3.84328 3.84421 3.84514 3.84607 3.84700 3.84793 3.84886 3.84978 3.85071 3.85164 3.85257 3.85349 3.85442 3.85535 3.85627 3.85720 3.85812 3.85905 3.85997 3.86090 3.86182 3.86274 3.86367 3.86459 3.86551 3.86644 3.86736 3.86828 3.86920 3.87012 3.87104 3.87196 3.87288 3.87380 3.87472 3.87564 3.87656 3.87748 3.87840 3.87931 3.88023 3.88115 3.88207 3.88298 3.88390 3.88481 3.88573

51° 3.88573 3.88665 3.88756 3.88847 3.88939 3.89030 3.89122 3.89213 3.89304 3.89395 3.89487 3.89578 3.89669 3.89760 3.89851 3.89942 3.90033 3.90124 3.90215 3.90306 3.90397 3.90488 3.90579 3.90669 3.90760 3.90851 3.90942 3.91032 3.91123 3.91214 3.91304 3.91395 3.91485 3.91576 3.91666 3.91756 3.91847 3.91937 3.92027 3.92118 3.92208 3.92298 3.92388 3.92478 3.92568 3.92658 3.92748 3.92839 3.92928 3.93018 3.93108 3.93198 3.93288 3.93378 3.93468 3.93557 3.93647 3.93737 3.93826 3.93916 3.94005

52° 3.94005 3.94095 3.94184 3.94274 3.94363 3.94453 3.94542 3.94631 3.94721 3.94810 3.94899 3.94988 3.95078 3.95167 3.95256 3.95345 3.95434 3.95523 3.95612 3.95701 3.95790 3.95878 3.95967 3.96056 3.96145 3.96234 3.96322 3.96411 3.96500 3.96588 3.96677 3.96765 3.96854 3.96942 3.97031 3.97119 3.97207 3.97296 3.97384 3.97472 3.97560 3.97649 3.97737 3.97825 3.97913 3.98001 3.98089 3.98177 3.98265 3.98353 3.98441 3.98529 3.98616 3.98704 3.98792 3.98880 3.98967 3.99055 3.99143 3.99230 3.99318

53° 3.99318 3.99405 3.99493 3.99580 3.99668 3.99755 3.99842 3.99930 4.00017 4.00104 4.00191 4.00279 4.00366 4.00453 4.00540 4.00627 4.00714 4.00801 4.00888 4.00975 4.01062 4.01148 4.01235 4.01322 4.01409 4.01495 4.01582 4.01669 4.01755 4.01842 4.01928 4.02015 4.02101 4.02188 4.02274 4.02361 4.02447 4.02533 4.02619 4.02706 4.02792 4.02878 4.02964 4.03050 4.03136 4.03222 4.03308 4.03394 4.03480 4.03566 4.03652 4.03738 4.03823 4.03909 4.03995 4.04081 4.04166 4.04252 4.04337 4.04423 4.04508

54° 4.04508 4.04594 4.04679 4.04765 4.04850 4.04936 4.05021 4.05106 4.05191 4.05277 4.05362 4.05447 4.05532 4.05617 4.05702 4.05787 4.05872 4.05957 4.06042 4.06127 4.06211 4.06296 4.06381 4.06466 4.06550 4.06635 4.06720 4.06804 4.06889 4.06973 4.07058 4.07142 4.07227 4.07311 4.07395 4.07480 4.07564 4.07648 4.07732 4.07817 4.07901 4.07985 4.08069 4.08153 4.08237 4.08321 4.08405 4.08489 4.08572 4.08656 4.08740 4.08824 4.08908 4.08991 4.09075 4.09158 4.09242 4.09326 4.09409 4.09493 4.09576


55° 4.09576 4.09659 4.09743 4.09826 4.09909 4.09993 4.10076 4.10159 4.10242 4.10325 4.10409 4.10492 4.10575 4.10658 4.10741 4.10823 4.10906 4.10989 4.11072 4.11155 4.11238 4.11320 4.11403 4.11486 4.11568 4.11651 4.11733 4.11816 4.11898 4.11981 4.12063 4.12145 4.12228 4.12310 4.12392 4.12475 4.12557 4.12639 4.12721 4.12803 4.12885 4.12967 4.13049 4.13131 4.13213 4.13295 4.13377 4.13459 4.13540 4.13622 4.13704 4.13785 4.13867 4.13949 4.14030 4.14112 4.14193 4.14275 4.14356 4.14437 4.14519


100-MILLIMETER SINE-BAR CONSTANTS Constants for 100-millimeter Sine-bar Constants for Setting a 100-mm Sine-bar for 0° to 7°

Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

0° 0.000000 0.029089 0.058178 0.087266 0.116355 0.145444 0.174533 0.203622 0.232710 0.261799 0.290888 0.319977 0.349065 0.378154 0.407242 0.436331 0.465420 0.494508 0.523596 0.552685 0.581773 0.610861 0.639950 0.669038 0.698126 0.727214 0.756302 0.785390 0.814478 0.843566 0.872654 0.901741 0.930829 0.959916 0.989004 1.018091 1.047179 1.076266 1.105353 1.134440 1.163527 1.192613 1.221700 1.250787 1.279873 1.308960 1.338046 1.367132 1.396218 1.425304 1.454390 1.483476 1.512561 1.541646 1.570732 1.599817 1.628902 1.657987 1.687072 1.716156 1.745241

1° 1.745241 1.774325 1.803409 1.832493 1.861577 1.890661 1.919744 1.948828 1.977911 2.006994 2.036077 2.065159 2.094242 2.123324 2.152407 2.181489 2.210570 2.239652 2.268733 2.297815 2.326896 2.355977 2.385057 2.414138 2.443218 2.472298 2.501378 2.530457 2.559537 2.588616 2.617695 2.646774 2.675852 2.704930 2.734009 2.763086 2.792164 2.821241 2.850318 2.879395 2.908472 2.937548 2.966624 2.995700 3.024776 3.053851 3.082927 3.112001 3.141076 3.170151 3.199224 3.228298 3.257372 3.286445 3.315518 3.344591 3.373663 3.402735 3.431807 3.460879 3.489950

2° 3.489950 3.519021 3.548091 3.577162 3.606232 3.635301 3.664371 3.693440 3.722509 3.751578 3.780646 3.809714 3.838781 3.867848 3.896915 3.925982 3.955048 3.984114 4.013179 4.042244 4.071309 4.100374 4.129438 4.158502 4.187566 4.216629 4.245691 4.274754 4.303816 4.332878 4.361939 4.391000 4.420060 4.449121 4.478180 4.507240 4.536299 4.565357 4.594416 4.623474 4.652532 4.681589 4.710645 4.739702 4.768757 4.797813 4.826868 4.855923 4.884977 4.914031 4.943084 4.972137 5.001190 5.030242 5.059294 5.088346 5.117396 5.146447 5.175497 5.204546 5.233596

3° 5.233596 5.262644 5.291693 5.320741 5.349788 5.378835 5.407881 5.436927 5.465973 5.495018 5.524063 5.553107 5.582151 5.611194 5.640237 5.669279 5.698321 5.727362 5.756403 5.785443 5.814483 5.843522 5.872561 5.901600 5.930638 5.959675 5.988712 6.017748 6.046784 6.075819 6.104854 6.133888 6.162922 6.191956 6.220988 6.250021 6.279052 6.308083 6.337114 6.366144 6.395174 6.424202 6.453231 6.482259 6.511286 6.540313 6.569339 6.598365 6.627390 6.656415 6.685439 6.714462 6.743485 6.772508 6.801529 6.830551 6.859571 6.888591 6.917611 6.946630 6.975647

4° 6.975647 7.004666 7.033682 7.062699 7.091714 7.120730 7.149745 7.178759 7.207772 7.236785 7.265797 7.294809 7.323820 7.352830 7.381840 7.410849 7.439858 7.468865 7.497873 7.526879 7.555886 7.584891 7.613896 7.642900 7.671903 7.700905 7.729908 7.758909 7.787910 7.816910 7.845910 7.874909 7.903907 7.932905 7.961901 7.990898 8.019893 8.048887 8.077881 8.106875 8.135867 8.164860 8.193851 8.222842 8.251831 8.280821 8.309810 8.338798 8.367785 8.396770 8.425757 8.454741 8.483727 8.512710 8.541693 8.570675 8.599656 8.628636 8.657617 8.686596 8.715574

5° 8.715574 8.744553 8.773529 8.802505 8.831481 8.860456 8.889430 8.918404 8.947375 8.976348 9.005319 9.034289 9.063258 9.092227 9.121195 9.150162 9.179129 9.208094 9.237060 9.266023 9.294987 9.323949 9.352911 9.381871 9.410831 9.439791 9.468750 9.497706 9.526664 9.555620 9.584576 9.613530 9.642484 9.671437 9.700389 9.729341 9.758290 9.787240 9.816189 9.845137 9.874084 9.903030 9.931975 9.960920 9.989863 10.018806 10.047749 10.076690 10.105630 10.134569 10.163508 10.192446 10.221383 10.250319 10.279254 10.308188 10.337122 10.366054 10.394986 10.423916 10.452847

6° 10.452847 10.481776 10.510704 10.539631 10.568558 10.597483 10.626408 10.655332 10.684254 10.713176 10.742096 10.771017 10.799935 10.828855 10.857771 10.886688 10.915604 10.944518 10.973432 11.002344 11.031256 11.060166 11.089077 11.117986 11.146894 11.175800 11.204707 11.233611 11.262516 11.291419 11.320322 11.349223 11.378123 11.407023 11.435922 11.464819 11.493715 11.522612 11.551505 11.580400 11.609291 11.638184 11.667073 11.695964 11.724852 11.753740 11.782627 11.811512 11.840398 11.869281 11.898164 11.927045 11.955926 11.984805 12.013684 12.042562 12.071439 12.100314 12.129189 12.158062 12.186934


7° 12.186934 12.215807 12.244677 12.273546 12.302414 12.331282 12.360147 12.389013 12.417877 12.446741 12.475602 12.504464 12.533323 12.562182 12.591040 12.619897 12.648753 12.677608 12.706462 12.735313 12.764166 12.793015 12.821865 12.850713 12.879560 12.908405 12.937251 12.966094 12.994938 13.023779 13.052620 13.081459 13.110297 13.139134 13.167971 13.196806 13.225639 13.254473 13.283303 13.312135 13.340963 13.369792 13.398619 13.427444 13.456269 13.485093 13.513916 13.542737 13.571558 13.600377 13.629195 13.658011 13.686828 13.715641 13.744455 13.773267 13.802078 13.830888 13.859696 13.888504 13.917311

Machinery's Handbook 27th Edition 100-MILLIMETER SINE-BAR CONSTANTS

707

Constants for Setting a 100-mm Sine-bar for 8° to 15° Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

8° 13.917311 13.946115 13.974920 14.003723 14.032524 14.061324 14.090124 14.118922 14.147718 14.176514 14.205309 14.234102 14.262894 14.291684 14.320475 14.349262 14.378049 14.406837 14.435621 14.464404 14.493186 14.521968 14.550748 14.579526 14.608303 14.637080 14.665854 14.694628 14.723400 14.752172 14.780942 14.809710 14.838478 14.867244 14.896008 14.924772 14.953535 14.982296 15.011056 15.039814 15.068572 15.097328 15.126082 15.154835 15.183589 15.212339 15.241088 15.269837 15.298584 15.327330 15.356073 15.384818 15.413560 15.442300 15.471039 15.499778 15.528514 15.557248 15.585982 15.614716 15.643447

9° 15.643447 15.672176 15.700907 15.729633 15.758359 15.787084 15.815807 15.844529 15.873250 15.901969 15.930688 15.959404 15.988119 16.016832 16.045546 16.074257 16.102966 16.131676 16.160383 16.189089 16.217793 16.246496 16.275198 16.303898 16.332596 16.361296 16.389990 16.418684 16.447378 16.476070 16.504761 16.533449 16.562140 16.590824 16.619509 16.648193 16.676876 16.705557 16.734236 16.762913 16.791590 16.820265 16.848938 16.877609 16.906282 16.934952 16.963619 16.992287 17.020950 17.049614 17.078276 17.106937 17.135597 17.164253 17.192909 17.221565 17.250219 17.278872 17.307520 17.336170 17.364819

10° 17.364819 17.393463 17.422110 17.450752 17.479393 17.508034 17.536674 17.565311 17.593946 17.622580 17.651215 17.679844 17.708475 17.737103 17.765730 17.794355 17.822979 17.851603 17.880222 17.908842 17.937458 17.966076 17.994690 18.023304 18.051914 18.080526 18.109135 18.137741 18.166346 18.194950 18.223553 18.252153 18.280754 18.309351 18.337948 18.366541 18.395136 18.423727 18.452316 18.480906 18.509493 18.538078 18.566662 18.595243 18.623825 18.652405 18.680981 18.709558 18.738132 18.766705 18.795275 18.823847 18.852413 18.880980 18.909544 18.938108 18.966669 18.995230 19.023787 19.052345 19.080900

11° 19.080900 19.109453 19.138006 19.166555 19.195105 19.223652 19.252197 19.280741 19.309282 19.337824 19.366364 19.394899 19.423435 19.451969 19.480503 19.509033 19.537561 19.566090 19.594616 19.623138 19.651661 19.680183 19.708702 19.737219 19.765734 19.794249 19.822762 19.851271 19.879780 19.908289 19.936794 19.965298 19.993801 20.022301 20.050800 20.079296 20.107794 20.136286 20.164778 20.193268 20.221758 20.250244 20.278730 20.307213 20.335695 20.364176 20.392654 20.421131 20.449606 20.478079 20.506550 20.535021 20.563488 20.591955 20.620419 20.648882 20.677343 20.705801 20.734259 20.762716 20.791170

12° 20.791170 20.819622 20.848074 20.876522 20.904968 20.933413 20.961857 20.990299 21.018738 21.047176 21.075613 21.104048 21.132481 21.160910 21.189341 21.217768 21.246193 21.274618 21.303040 21.331459 21.359877 21.388294 21.416710 21.445122 21.473532 21.501944 21.530350 21.558756 21.587158 21.615562 21.643963 21.672359 21.700758 21.729153 21.757544 21.785934 21.814325 21.842712 21.871098 21.899481 21.927864 21.956244 21.984621 22.012997 22.041372 22.069744 22.098114 22.126484 22.154850 22.183216 22.211578 22.239941 22.268299 22.296656 22.325012 22.353367 22.381718 22.410067 22.438416 22.466763 22.495106

13° 22.495106 22.523447 22.551790 22.580128 22.608463 22.636799 22.665133 22.693462 22.721790 22.750118 22.778444 22.806767 22.835087 22.863405 22.891726 22.920040 22.948353 22.976665 23.004974 23.033281 23.061586 23.089891 23.118193 23.146492 23.174789 23.203087 23.231380 23.259672 23.287962 23.316252 23.344538 23.372820 23.401104 23.429384 23.457661 23.485937 23.514212 23.542484 23.570755 23.599022 23.627289 23.655554 23.683815 23.712074 23.740334 23.768589 23.796844 23.825096 23.853346 23.881594 23.909840 23.938086 23.966328 23.994566 24.022804 24.051041 24.079275 24.107506 24.135736 24.163965 24.192190

14° 24.192190 24.220413 24.248636 24.276855 24.305073 24.333288 24.361502 24.389713 24.417923 24.446129 24.474335 24.502539 24.530739 24.558937 24.587135 24.615330 24.643522 24.671715 24.699902 24.728088 24.756271 24.784456 24.812635 24.840813 24.868988 24.897163 24.925335 24.953505 24.981672 25.009838 25.038002 25.066162 25.094322 25.122478 25.150633 25.178785 25.206938 25.235085 25.263231 25.291374 25.319517 25.347658 25.375795 25.403931 25.432064 25.460196 25.488325 25.516453 25.544577 25.572699 25.600819 25.628939 25.657055 25.685167 25.713280 25.741390 25.769497 25.797602 25.825705 25.853807 25.881905


15° 25.881905 25.910002 25.938097 25.966188 25.994278 26.022366 26.050451 26.078535 26.106615 26.134695 26.162773 26.190845 26.218918 26.246988 26.275057 26.303122 26.331184 26.359247 26.387306 26.415361 26.443417 26.471470 26.499519 26.527567 26.555613 26.583656 26.611696 26.639736 26.667770 26.695807 26.723839 26.751867 26.779896 26.807920 26.835943 26.863964 26.891983 26.920000 26.948013 26.976025 27.004034 27.032042 27.060045 27.088047 27.116049 27.144045 27.172041 27.200035 27.228025 27.256014 27.284000 27.311985 27.339966 27.367945 27.395922 27.423899 27.451870 27.479839 27.507807 27.535774 27.563736


100-MILLIMETER SINE-BAR CONSTANTS Constants for Setting a 100-mm Sine-bar for 16° to 23°

Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

16° 27.563736 27.591696 27.619656 27.647610 27.675568 27.703518 27.731466 27.759413 27.787357 27.815298 27.843239 27.871176 27.899113 27.927044 27.954975 27.982903 28.010828 28.038750 28.066669 28.094591 28.122507 28.150421 28.178331 28.206240 28.234146 28.262049 28.289951 28.317852 28.345749 28.373644 28.401535 28.429424 28.457312 28.485195 28.513081 28.540960 28.568838 28.596712 28.624586 28.652456 28.680323 28.708189 28.736053 28.763914 28.791773 28.819628 28.847481 28.875332 28.903179 28.931028 28.958872 28.986712 29.014551 29.042387 29.070219 29.098051 29.125879 29.153708 29.181532 29.209352 29.237171

17° 29.237171 29.264988 29.292801 29.320612 29.348425 29.376230 29.404034 29.431835 29.459635 29.487431 29.515224 29.543015 29.570807 29.598593 29.626377 29.654158 29.681936 29.709713 29.737488 29.765261 29.793030 29.820797 29.848560 29.876320 29.904079 29.931835 29.959589 29.987343 30.015091 30.042837 30.070581 30.098322 30.126060 30.153795 30.181532 30.209263 30.236990 30.264715 30.292439 30.320160 30.347878 30.375593 30.403309 30.431019 30.458725 30.486431 30.514133 30.541832 30.569530 30.597227 30.624920 30.652609 30.680296 30.707981 30.735662 30.763342 30.791018 30.818695 30.846365 30.874035 30.901701

18° 30.901701 30.929363 30.957024 30.984682 31.012341 31.039993 31.067644 31.095291 31.122936 31.150579 31.178219 31.205856 31.233494 31.261126 31.288755 31.316381 31.344006 31.371626 31.399244 31.426865 31.454477 31.482088 31.509697 31.537302 31.564903 31.592505 31.620102 31.647699 31.675291 31.702881 31.730467 31.758051 31.785631 31.813210 31.840790 31.868362 31.895933 31.923500 31.951065 31.978628 32.006187 32.033745 32.061302 32.088852 32.116402 32.143948 32.171490 32.199032 32.226570 32.254108 32.281639 32.309170 32.336697 32.364220 32.391743 32.419262 32.446777 32.474293 32.501804 32.529312 32.556816

19° 32.556816 32.584320 32.611816 32.639317 32.666813 32.694302 32.721790 32.749275 32.776760 32.804241 32.831718 32.859192 32.886665 32.914135 32.941601 32.969067 32.996525 33.023983 33.051437 33.078896 33.106342 33.133789 33.161236 33.188675 33.216114 33.243549 33.270981 33.298416 33.325840 33.353264 33.380688 33.408104 33.435520 33.462933 33.490349 33.517754 33.545158 33.572559 33.599960 33.627354 33.654747 33.682137 33.709530 33.736912 33.764294 33.791672 33.819050 33.846420 33.873791 33.901161 33.928528 33.955887 33.983246 34.010601 34.037956 34.065304 34.092651 34.119999 34.147343 34.174679 34.202015

20° 34.202015 34.229347 34.256680 34.284004 34.311333 34.338654 34.365971 34.393288 34.420597 34.447906 34.475216 34.502518 34.529823 34.557121 34.584415 34.611706 34.638996 34.666283 34.693565 34.720848 34.748127 34.775398 34.802670 34.829941 34.857204 34.884468 34.911728 34.938988 34.966240 34.993492 35.020741 35.047985 35.075226 35.102463 35.129704 35.156937 35.184166 35.211395 35.238617 35.265839 35.293056 35.320271 35.347488 35.374695 35.401901 35.429104 35.456306 35.483501 35.510696 35.537891 35.565079 35.592262 35.619446 35.646626 35.673801 35.700974 35.728142 35.755314 35.782478 35.809639 35.836796

21° 35.836796 35.863953 35.891102 35.918251 35.945400 35.972542 35.999683 36.026817 36.053951 36.081081 36.108212 36.135334 36.162460 36.189579 36.216694 36.243805 36.270912 36.298019 36.325123 36.352226 36.379322 36.406418 36.433506 36.460594 36.487679 36.514759 36.541840 36.568916 36.595989 36.623058 36.650124 36.677185 36.704247 36.731304 36.758358 36.785408 36.812458 36.839500 36.866543 36.893581 36.920616 36.947647 36.974678 37.001705 37.028725 37.055744 37.082760 37.109772 37.136784 37.163792 37.190796 37.217796 37.244793 37.271790 37.298779 37.325768 37.352753 37.379734 37.406712 37.433689 37.460659

22° 37.460659 37.487629 37.514595 37.541557 37.568520 37.595474 37.622429 37.649376 37.676323 37.703266 37.730206 37.757145 37.784081 37.811012 37.837940 37.864864 37.891785 37.918701 37.945614 37.972530 37.999439 38.026344 38.053246 38.080143 38.107037 38.133930 38.160820 38.187706 38.214588 38.241470 38.268345 38.295216 38.322086 38.348953 38.375816 38.402679 38.429535 38.456387 38.483238 38.510082 38.536926 38.563766 38.590607 38.617439 38.644272 38.671097 38.697922 38.724743 38.751560 38.778374 38.805187 38.831993 38.858799 38.885597 38.912395 38.939190 38.965981 38.992771 39.019554 39.046337 39.073112


23° 39.073112 39.099888 39.126659 39.153427 39.180195 39.206955 39.233715 39.260468 39.287220 39.313965 39.340710 39.367451 39.394192 39.420929 39.447659 39.474388 39.501110 39.527832 39.554550 39.581268 39.607979 39.634686 39.661392 39.688091 39.714790 39.741486 39.768173 39.794865 39.821548 39.848232 39.874908 39.901581 39.928253 39.954922 39.981586 40.008247 40.034904 40.061558 40.088207 40.114857 40.141499 40.168140 40.194778 40.221413 40.248043 40.274670 40.301292 40.327911 40.354530 40.381145 40.407757 40.434361 40.460964 40.487564 40.514160 40.540752 40.567341 40.593929 40.620510 40.647091 40.673664


709


24° 40.673664 40.700237 40.726807 40.753372 40.779934 40.806492 40.833046 40.859600 40.886147 40.912689 40.939232 40.965767 40.992306 41.018837 41.045364 41.071888 41.098408 41.124924 41.151436 41.177948 41.204453 41.230957 41.257458 41.283951 41.310444 41.336933 41.363419 41.389900 41.416378 41.442856 41.469326 41.495792 41.522259 41.548717 41.575176 41.601631 41.628082 41.654526 41.680969 41.707409 41.733845 41.760277 41.786709 41.813133 41.839558 41.865974 41.892391 41.918800 41.945210 41.971615 41.998016 42.024414 42.050804 42.077194 42.103580 42.129963 42.156345 42.182724 42.209095 42.235462 42.261826

25° 42.261826 42.288189 42.314545 42.340900 42.367252 42.393600 42.419945 42.446285 42.472618 42.498951 42.525280 42.551605 42.577930 42.604248 42.630566 42.656876 42.683182 42.709488 42.735786 42.762085 42.788380 42.814667 42.840954 42.867237 42.893513 42.919788 42.946060 42.972332 42.998592 43.024853 43.051109 43.077362 43.103615 43.129860 43.156105 43.182343 43.208576 43.234806 43.261036 43.287258 43.313480 43.339695 43.365910 43.392120 43.418324 43.444527 43.470726 43.496918 43.523109 43.549301 43.575481 43.601662 43.627838 43.654011 43.680180 43.706345 43.732506 43.758667 43.784821 43.810970 43.837116

26° 43.837116 43.863258 43.889397 43.915531 43.941666 43.967796 43.993919 44.020039 44.046154 44.072269 44.098377 44.124481 44.150589 44.176685 44.202778 44.228870 44.254955 44.281040 44.307117 44.333199 44.359268 44.385338 44.411400 44.437462 44.463520 44.489571 44.515621 44.541668 44.567711 44.593750 44.619781 44.645813 44.671841 44.697861 44.723885 44.749901 44.775909 44.801918 44.827923 44.853924 44.879917 44.905910 44.931904 44.957886 44.983868 45.009846 45.035820 45.061787 45.087753 45.113720 45.139679 45.165630 45.191582 45.217529 45.243473 45.269409 45.295345 45.321281 45.347206 45.373131 45.399052

27° 45.399052 45.424969 45.450878 45.476788 45.502697 45.528595 45.554493 45.580387 45.606274 45.632160 45.658043 45.683918 45.709797 45.735664 45.761532 45.787392 45.813251 45.839104 45.864956 45.890804 45.916649 45.942486 45.968323 45.994152 46.019978 46.045803 46.071621 46.097439 46.123253 46.149059 46.174862 46.200661 46.226460 46.252251 46.278042 46.303825 46.329605 46.355381 46.381153 46.406921 46.432686 46.458447 46.484207 46.509960 46.535709 46.561455 46.587193 46.612930 46.638664 46.664394 46.690121 46.715843 46.741558 46.767273 46.792980 46.818687 46.844387 46.870090 46.895782 46.921471 46.947159

28° 46.947159 46.972839 46.998516 47.024189 47.049862 47.075527 47.101189 47.126846 47.152500 47.178150 47.203796 47.229439 47.255077 47.280712 47.306343 47.331966 47.357590 47.383205 47.408821 47.434433 47.460041 47.485641 47.511238 47.536831 47.562420 47.588009 47.613590 47.639168 47.664742 47.690311 47.715878 47.741440 47.766994 47.792549 47.818100 47.843647 47.869186 47.894726 47.920258 47.945786 47.971313 47.996834 48.022350 48.047863 48.073372 48.098877 48.124378 48.149876 48.175369 48.200859 48.226341 48.251823 48.277298 48.302773 48.328239 48.353703 48.379162 48.404621 48.430073 48.455521 48.480965

29° 48.480965 48.506401 48.531837 48.557270 48.582699 48.608120 48.633541 48.658955 48.684364 48.709770 48.735172 48.760571 48.785969 48.811359 48.836742 48.862125 48.887505 48.912876 48.938244 48.963612 48.988976 49.014332 49.039684 49.065033 49.090378 49.115715 49.141052 49.166386 49.191715 49.217037 49.242359 49.267673 49.292984 49.318291 49.343597 49.368893 49.394188 49.419479 49.444763 49.470047 49.495323 49.520596 49.545868 49.571133 49.596394 49.621651 49.646904 49.672153 49.697395 49.722637 49.747875 49.773106 49.798332 49.823555 49.848774 49.873989 49.899200 49.924408 49.949612 49.974808 50.000000

30° 50.000000 50.025192 50.050377 50.075558 50.100735 50.125908 50.151077 50.176239 50.201397 50.226555 50.251705 50.276852 50.301998 50.327137 50.352268 50.377399 50.402523 50.427647 50.452763 50.477879 50.502987 50.528091 50.553192 50.578285 50.603378 50.628464 50.653545 50.678627 50.703701 50.728771 50.753838 50.778900 50.803955 50.829010 50.854061 50.879105 50.904144 50.929180 50.954208 50.979237 51.004261 51.029278 51.054295 51.079304 51.104309 51.129311 51.154308 51.179298 51.204288 51.229275 51.254253 51.279228 51.304199 51.329163 51.354126 51.379082 51.404037 51.428989 51.453934 51.478874 51.503807


31° 51.503807 51.528740 51.553669 51.578590 51.603512 51.628426 51.653336 51.678242 51.703140 51.728039 51.752930 51.777817 51.802704 51.827583 51.852455 51.877327 51.902191 51.927055 51.951912 51.976768 52.001614 52.026459 52.051300 52.076134 52.100964 52.125790 52.150612 52.175430 52.200245 52.225052 52.249859 52.274658 52.299454 52.324245 52.349033 52.373814 52.398594 52.423367 52.448135 52.472900 52.497658 52.522415 52.547169 52.571915 52.596657 52.621395 52.646126 52.670856 52.695580 52.720303 52.745018 52.769730 52.794434 52.819138 52.843834 52.868526 52.893215 52.917904 52.942581 52.967258 52.991928



Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

32° 52.991928 53.016594 53.041256 53.065914 53.090565 53.115211 53.139858 53.164497 53.189137 53.213768 53.238392 53.263012 53.287628 53.312241 53.336849 53.361454 53.386051 53.410645 53.435234 53.459820 53.484402 53.508976 53.533546 53.558121 53.582684 53.607243 53.631794 53.656342 53.680889 53.705425 53.729961 53.754494 53.779018 53.803539 53.828056 53.852570 53.877079 53.901581 53.926086 53.950581 53.975067 53.999554 54.024036 54.048512 54.072983 54.097450 54.121910 54.146370 54.170822 54.195271 54.219715 54.244152 54.268589 54.293022 54.317448 54.341869 54.366287 54.390697 54.415104 54.439507 54.463905

33° 54.463905 54.488297 54.512688 54.537071 54.561451 54.585827 54.610195 54.634560 54.658928 54.683285 54.707634 54.731983 54.756325 54.780663 54.804996 54.829323 54.853649 54.877968 54.902283 54.926594 54.950897 54.975197 54.999493 55.023792 55.048077 55.072361 55.096638 55.120911 55.145176 55.169441 55.193699 55.217953 55.242203 55.266449 55.290688 55.314922 55.339153 55.363380 55.387608 55.411823 55.436035 55.460243 55.484444 55.508644 55.532837 55.557026 55.581207 55.605389 55.629562 55.653732 55.677895 55.702057 55.726212 55.750370 55.774513 55.798656 55.822792 55.846924 55.871052 55.895172 55.919292

34° 55.919292 55.943405 55.967514 55.991615 56.015717 56.039810 56.063900 56.087982 56.112068 56.136143 56.160213 56.184280 56.208340 56.232395 56.256447 56.280495 56.304535 56.328571 56.352604 56.376633 56.400654 56.424675 56.448685 56.472702 56.496704 56.520702 56.544697 56.568687 56.592670 56.616650 56.640625 56.664597 56.688560 56.712521 56.736477 56.760429 56.784374 56.808315 56.832256 56.856190 56.880116 56.904037 56.927956 56.951866 56.975777 56.999676 57.023575 57.047470 57.071358 57.095242 57.119118 57.142994 57.166862 57.190731 57.214592 57.238445 57.262295 57.286140 57.309978 57.333817 57.357643

35° 57.357643 57.381470 57.405293 57.429108 57.452919 57.476723 57.500523 57.524323 57.548119 57.571903 57.595684 57.619461 57.643234 57.667000 57.690762 57.714520 57.738274 57.762020 57.785763 57.809502 57.833233 57.856960 57.880684 57.904408 57.928120 57.951828 57.975533 57.999229 58.022926 58.046612 58.070297 58.093975 58.117649 58.141319 58.164982 58.188641 58.212296 58.235947 58.259594 58.283234 58.306870 58.330498 58.354122 58.377743 58.401360 58.424969 58.448574 58.472172 58.495770 58.519360 58.542942 58.566525 58.590099 58.613674 58.637238 58.660801 58.684357 58.707905 58.731449 58.754990 58.778526

36° 58.778526 58.802055 58.825584 58.849102 58.872620 58.896130 58.919636 58.943134 58.966637 58.990128 59.013615 59.037094 59.060570 59.084042 59.107506 59.130966 59.154423 59.177872 59.201317 59.224758 59.248196 59.271626 59.295052 59.318478 59.341892 59.365303 59.388710 59.412109 59.435505 59.458893 59.482281 59.505661 59.529037 59.552406 59.575771 59.599133 59.622486 59.645836 59.669186 59.692528 59.715862 59.739193 59.762516 59.785835 59.809151 59.832462 59.855766 59.879066 59.902359 59.925652 59.948933 59.972214 59.995487 60.018761 60.042027 60.065285 60.088539 60.111790 60.135033 60.158272 60.181503

37° 60.181503 60.204731 60.227955 60.251175 60.274387 60.297596 60.320797 60.343994 60.367195 60.390381 60.413563 60.436741 60.459915 60.483082 60.506245 60.529400 60.552551 60.575699 60.598839 60.621979 60.645107 60.668236 60.691357 60.714478 60.737587 60.760693 60.783794 60.806889 60.829979 60.853065 60.876144 60.899220 60.922287 60.945354 60.968414 60.991467 61.014515 61.037560 61.060604 61.083637 61.106667 61.129688 61.152706 61.175720 61.198727 61.221729 61.244728 61.267719 61.290707 61.313686 61.336662 61.359634 61.382603 61.405567 61.428524 61.451473 61.474419 61.497360 61.520294 61.543224 61.566151

38° 61.566151 61.589069 61.611984 61.634892 61.657795 61.680695 61.703587 61.726475 61.749363 61.772240 61.795113 61.817982 61.840843 61.863697 61.886551 61.909397 61.932236 61.955074 61.977905 62.000729 62.023548 62.046364 62.069172 62.091984 62.114780 62.137577 62.160362 62.183147 62.205925 62.228699 62.251465 62.274227 62.296986 62.319736 62.342484 62.365223 62.387959 62.410690 62.433418 62.456139 62.478855 62.501564 62.524269 62.546967 62.569660 62.592350 62.615032 62.637711 62.660381 62.683048 62.705711 62.728367 62.751019 62.773670 62.796310 62.818943 62.841576 62.864201 62.886818 62.909431 62.932041


39° 62.932041 62.954643 62.977242 62.999836 63.022423 63.045002 63.067581 63.090153 63.112724 63.135284 63.157837 63.180389 63.202934 63.225471 63.248005 63.270535 63.293056 63.315575 63.338089 63.360596 63.383095 63.405594 63.428085 63.450573 63.473053 63.495529 63.517998 63.540462 63.562923 63.585377 63.607822 63.630264 63.652702 63.675137 63.697563 63.719982 63.742397 63.764809 63.787220 63.809620 63.832012 63.854401 63.876785 63.899162 63.921535 63.943901 63.966263 63.988621 64.010971 64.033318 64.055656 64.077988 64.100319 64.122650 64.144966 64.167282 64.189590 64.211891 64.234184 64.256477 64.278763


711


40° 64.278763 64.301041 64.323318 64.345589 64.367851 64.390106 64.412361 64.434608 64.456856 64.479095 64.501328 64.523552 64.545769 64.567986 64.590195 64.612396 64.634598 64.656792 64.678978 64.701164 64.723335 64.745506 64.767677 64.789841 64.811996 64.834145 64.856285 64.878426 64.900558 64.922684 64.944809 64.966919 64.989037 65.011139 65.033241 65.055336 65.077423 65.099503 65.121590 65.143661 65.165726 65.187790 65.209846 65.231895 65.253937 65.275978 65.298012 65.320038 65.342064 65.364075 65.386093 65.408096 65.430099 65.452095 65.474083 65.496071 65.518044 65.540016 65.561989 65.583946 65.605904

41° 65.605904 65.627853 65.649803 65.671738 65.693672 65.715599 65.737526 65.759438 65.781357 65.803261 65.825165 65.847061 65.868950 65.890831 65.912712 65.934586 65.956451 65.978310 66.000168 66.022018 66.043861 66.065704 66.087532 66.109367 66.131187 66.153008 66.174820 66.196625 66.218422 66.240219 66.262009 66.283791 66.305565 66.327339 66.349106 66.370865 66.392624 66.414368 66.436119 66.457855 66.479591 66.501320 66.523041 66.544754 66.566467 66.588165 66.609863 66.631561 66.653244 66.674927 66.696602 66.718277 66.739944 66.761604 66.783257 66.804909 66.826546 66.848183 66.869820 66.891441 66.913063

42° 66.913063 66.934677 66.956284 66.977890 66.999481 67.021072 67.042664 67.064240 67.085823 67.107391 67.128952 67.150513 67.172058 67.193611 67.215149 67.236679 67.258209 67.279732 67.301254 67.322762 67.344269 67.365768 67.387268 67.408760 67.430244 67.451721 67.473190 67.494659 67.516121 67.537575 67.559021 67.580467 67.601906 67.623337 67.644760 67.666183 67.687599 67.709007 67.730415 67.751808 67.773201 67.794586 67.815971 67.837341 67.858711 67.880074 67.901436 67.922783 67.944130 67.965469 67.986809 68.008133 68.029457 68.050781 68.072090 68.093399 68.114693 68.135986 68.157280 68.178558 68.199837

43° 68.199837 68.221107 68.242371 68.263634 68.284889 68.306137 68.327377 68.348610 68.369850 68.391075 68.412292 68.433502 68.454712 68.475914 68.497108 68.518303 68.539482 68.560661 68.581833 68.603004 68.624161 68.645317 68.666466 68.687614 68.708755 68.729889 68.751015 68.772133 68.793251 68.814354 68.835457 68.856560 68.877647 68.898735 68.919815 68.940887 68.961952 68.983017 69.004074 69.025131 69.046173 69.067207 69.088242 69.109268 69.130295 69.151306 69.172318 69.193321 69.214317 69.235313 69.256294 69.277275 69.298248 69.319221 69.340187 69.361145 69.382095 69.403038 69.423981 69.444908 69.465836

44° 69.465836 69.486763 69.507675 69.528587 69.549492 69.570389 69.591278 69.612167 69.633049 69.653923 69.674797 69.695656 69.716515 69.737366 69.758209 69.779045 69.799881 69.820709 69.841530 69.862343 69.883156 69.903961 69.924759 69.945549 69.966339 69.987114 70.007889 70.028656 70.049423 70.070175 70.090927 70.111671 70.132408 70.153145 70.173866 70.194588 70.215302 70.236015 70.256721 70.277420 70.298111 70.318794 70.339470 70.360146 70.380814 70.401474 70.422127 70.442780 70.463425 70.484062 70.504692 70.525314 70.545937 70.566551 70.587158 70.607765 70.628357 70.648949 70.669533 70.690109 70.710678

45° 70.710678 70.731247 70.751808 70.772362 70.792908 70.813446 70.833984 70.854515 70.875038 70.895561 70.916069 70.936577 70.957077 70.977570 70.998055 71.018539 71.039017 71.059486 71.079948 71.100403 71.120857 71.141304 71.161743 71.182182 71.202606 71.223030 71.243446 71.263855 71.284256 71.304657 71.325043 71.345428 71.365814 71.386185 71.406555 71.426910 71.447266 71.467613 71.487961 71.508301 71.528633 71.548958 71.569275 71.589592 71.609894 71.630196 71.650490 71.670776 71.691063 71.711334 71.731606 71.751869 71.772133 71.792389 71.812630 71.832870 71.853104 71.873337 71.893555 71.913773 71.933983

46° 71.933983 71.954185 71.974380 71.994576 72.014755 72.034935 72.055107 72.075279 72.095444 72.115601 72.135750 72.155891 72.176025 72.196159 72.216278 72.236397 72.256508 72.276619 72.296715 72.316811 72.336899 72.356979 72.377052 72.397125 72.417191 72.437248 72.457298 72.477341 72.497383 72.517410 72.537437 72.557457 72.577469 72.597481 72.617485 72.637474 72.657463 72.677452 72.697433 72.717400 72.737366 72.757324 72.777275 72.797226 72.817162 72.837097 72.857025 72.876945 72.896866 72.916771 72.936676 72.956573 72.976463 72.996353 73.016228 73.036102 73.055969 73.075829 73.095680 73.115532 73.135368


47° 73.135368 73.155205 73.175034 73.194855 73.214676 73.234482 73.254288 73.274086 73.293884 73.313667 73.333450 73.353226 73.372986 73.392746 73.412506 73.432251 73.451996 73.471733 73.491463 73.511185 73.530899 73.550613 73.570320 73.590019 73.609711 73.629395 73.649078 73.668755 73.688416 73.708084 73.727737 73.747383 73.767029 73.786659 73.806290 73.825920 73.845535 73.865143 73.884758 73.904350 73.923943 73.943535 73.963112 73.982689 74.002251 74.021812 74.041367 74.060921 74.080460 74.099998 74.119530 74.139053 74.158569 74.178085 74.197586 74.217087 74.236580 74.256065 74.275543 74.295013 74.314484



Min. 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

48° 74.314484 74.333946 74.353401 74.372849 74.392288 74.411728 74.431152 74.450577 74.470001 74.489410 74.508812 74.528214 74.547600 74.566986 74.586365 74.605736 74.625107 74.644463 74.663818 74.683167 74.702507 74.721840 74.741173 74.760498 74.779816 74.799118 74.818428 74.837723 74.857010 74.876297 74.895576 74.914848 74.934113 74.953369 74.972618 74.991867 75.011108 75.030342 75.049568 75.068794 75.088005 75.107216 75.126419 75.145615 75.164803 75.183983 75.203156 75.222328 75.241493 75.260651 75.279800 75.298943 75.318085 75.337219 75.356346 75.375458 75.394577 75.413681 75.432777 75.451874 75.470963

49° 75.470963 75.490044 75.509117 75.528183 75.547241 75.566299 75.585350 75.604385 75.623428 75.642456 75.661484 75.680496 75.699509 75.718513 75.737511 75.756500 75.775482 75.794464 75.813431 75.832397 75.851357 75.870308 75.889259 75.908203 75.927132 75.946060 75.964981 75.983894 76.002800 76.021706 76.040596 76.059486 76.078369 76.097244 76.116112 76.134972 76.153831 76.172684 76.191528 76.210365 76.229195 76.248016 76.266838 76.285645 76.304451 76.323250 76.342041 76.360825 76.379601 76.398376 76.417145 76.435898 76.454651 76.473404 76.492142 76.510880 76.529602 76.548325 76.567039 76.585747 76.604446

50° 76.604446 76.623138 76.641830 76.660507 76.679184 76.697853 76.716515 76.735168 76.753822 76.772469 76.791100 76.809731 76.828354 76.846970 76.865578 76.884186 76.902779 76.921371 76.939957 76.958534 76.977104 76.995667 77.014229 77.032784 77.051331 77.069862 77.088394 77.106926 77.125443 77.143951 77.162460 77.180962 77.199455 77.217941 77.236420 77.254890 77.273354 77.291817 77.310272 77.328720 77.347160 77.365593 77.384026 77.402443 77.420860 77.439262 77.457664 77.476059 77.494446 77.512833 77.531204 77.549576 77.567932 77.586296 77.604645 77.622986 77.641319 77.659653 77.677971 77.696289 77.714600

51° 77.714600 77.732903 77.751198 77.769485 77.787766 77.806046 77.824318 77.842575 77.860840 77.879089 77.897331 77.915565 77.933800 77.952019 77.970238 77.988449 78.006653 78.024849 78.043045 78.061226 78.079399 78.097572 78.115738 78.133896 78.152054 78.170197 78.188332 78.206467 78.224586 78.242706 78.260818 78.278923 78.297020 78.315109 78.333199 78.351273 78.369347 78.387413 78.405472 78.423523 78.441566 78.459610 78.477638 78.495667 78.513680 78.531693 78.549698 78.567696 78.585693 78.603676 78.621651 78.639626 78.657593 78.675552 78.693504 78.711449 78.729393 78.747322 78.765244 78.783165 78.801079

52° 78.801079 78.818985 78.836884 78.854774 78.872658 78.890533 78.908409 78.926277 78.944138 78.961990 78.979836 78.997673 79.015503 79.033325 79.051147 79.068962 79.086761 79.104561 79.122353 79.140137 79.157921 79.175690 79.193451 79.211220 79.228966 79.246712 79.264450 79.282181 79.299904 79.317627 79.335335 79.353043 79.370735 79.388428 79.406113 79.423790 79.441460 79.459129 79.476791 79.494438 79.512085 79.529716 79.547348 79.564972 79.582588 79.600204 79.617805 79.635399 79.652992 79.670578 79.688156 79.705719 79.723289 79.740845 79.758392 79.775940 79.793472 79.811005 79.828529 79.846046 79.863556

53° 79.863556 79.881058 79.898552 79.916039 79.933525 79.950996 79.968468 79.985931 80.003387 80.020836 80.038277 80.055710 80.073143 80.090561 80.107979 80.125381 80.142784 80.160179 80.177567 80.194946 80.212318 80.229683 80.247047 80.264404 80.281754 80.299088 80.316422 80.333748 80.351067 80.368385 80.385689 80.402985 80.420280 80.437561 80.454842 80.472115 80.489380 80.506638 80.523895 80.541138 80.558372 80.575607 80.592827 80.610046 80.627258 80.644463 80.661659 80.678848 80.696030 80.713211 80.730377 80.747543 80.764694 80.781853 80.798988 80.816124 80.833252 80.850380 80.867493 80.884598 80.901703

54° 80.901703 80.918793 80.935883 80.952965 80.970039 80.987106 81.004166 81.021217 81.038269 81.055305 81.072342 81.089363 81.106384 81.123398 81.140404 81.157402 81.174393 81.191376 81.208351 81.225327 81.242287 81.259247 81.276199 81.293144 81.310081 81.327011 81.343933 81.360847 81.377754 81.394661 81.411552 81.428444 81.445320 81.462196 81.479065 81.495926 81.512779 81.529625 81.546471 81.563301 81.580132 81.596947 81.613762 81.630569 81.647362 81.664154 81.680939 81.697723 81.714493 81.731255 81.748009 81.764763 81.781502 81.798248 81.814972 81.831696 81.848412 81.865120 81.881821 81.898521 81.915207


55° 81.915207 81.931885 81.948563 81.965225 81.981888 81.998543 82.015190 82.031830 82.048462 82.065086 82.081711 82.098320 82.114922 82.131523 82.148109 82.164696 82.181274 82.197845 82.214401 82.230957 82.247513 82.264053 82.280586 82.297119 82.313637 82.330154 82.346664 82.363159 82.379654 82.396141 82.412621 82.429092 82.445557 82.462013 82.478470 82.494911 82.511353 82.527779 82.544205 82.560623 82.577034 82.593437 82.609833 82.626221 82.642601 82.658974 82.675346 82.691704 82.708061 82.724403 82.740746 82.757080 82.773399 82.789726 82.806038 82.822342 82.838638 82.854927 82.871216 82.887489 82.903755

Machinery's Handbook 27th Edition ANGLES AND TAPERS

713

Accurate Measurement of Angles and Tapers When great accuracy is required in the measurement of angles, or when originating tapers, disks are commonly used. The principle of the disk method of taper measurement is that if two disks of unequal diameters are placed either in contact or a certain distance apart, lines tangent to their peripheries will represent an angle or taper, the degree of which depends upon the diameters of the two disks and the distance between them.

The gage shown in the accompanying illustration, which is a form commonly used for originating tapers or measuring angles accurately, is set by means of disks. This gage consists of two adjustable straight edges A and A1, which are in contact with disks B and B1. The angle α or the taper between the straight edges depends, of course, upon the diameters of the disks and the center distance C, and as these three dimensions can be measured accurately, it is possible to set the gage to a given angle within very close limits. Moreover, if a record of the three dimensions is kept, the exact setting of the gage can be reproduced quickly at any time. The following rules may be used for adjusting a gage of this type, and cover all problems likely to arise in practice. Disks are also occasionally used for the setting of parts in angular positions when they are to be machined accurately to a given angle: the rules are applicable to these conditions also. Measuring Dovetail Slides.—Dovetail slides that must be machined accurately to a given width are commonly gaged by using pieces of cylindrical rod or wire and measuring as indicated by the dimensions x and y of the accompanying illustrations.

The rod or wire used should be small enough so that the point of contact e is somewhat below the corner or edge of the dovetail. To obtain dimension x for measuring male dovetails, add 1 to the cotangent of one-half the dovetail angle α, multiply by diameter D of the rods used, and add the product to dimension α. x = D ( 1 + cot 1⁄2 α ) + a

c = h × cot α

To obtain dimension y for measuring a female dovetail, add 1 to the cotangent of one-half the dovetail angle α, multiply by diameter D of the rod used, and subtract the result from dimension b. Expressing these rules as formulas: y = b – D ( 1 + cot 1⁄2 α )



ANGLES AND TAPERS Tapers per Foot and Corresponding Angles

Taper per Foot 1⁄ 64 1⁄ 32 1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 11⁄ 16 23⁄ 32 3⁄ 4 25⁄ 32 13⁄ 16 27⁄ 32 7⁄ 8 29⁄ 32 15⁄ 16 31⁄ 32

Included Angle

Angle with Center Line

Taper per Foot

0.149208°

0°

4′

29″ 0°

2′

14″

0.298415

0

8

57

4

29

17⁄8 115⁄16

0

Included Angle

Angle with Center Line

9.230863°

8°

56′

9.527283

9

13 51

4″

4°

28′

4

36

2″ 56

0.447621

0

17

54

0

8

57

2

10.119738

9

31 38

4

45

49

0.596826

0

26

51

0

13

26

21⁄8

10.711650

10

7 11

5

3

36

0.746028

0

35

49

0

17

54

21⁄4

11.302990

10

42 42

5

21

21

0.895228

0

44

46

0

22

23

23⁄8

11.893726

11

18 11

5

39

5

1.044425

0

53

43

0

26

51

21⁄2

12.483829

11

53 37

5

56

49

1.193619

1

2

40

0

31

20

25⁄8

13.073267

12

29

2

6

14

31

1.342808

1

11

37

0

35

49

23⁄4

13.662012

13

4 24

6

32

12

1.491993

1

20

34

0

40

17

14.250033

13

39 43

6

49

52

1.641173

1

29

31

0

44

46

27⁄8 3

30

1.790347

1

38

28

0

49

14

1.939516

1

47

25

0

53

43

2.088677

1

56

22

0

58

11

2.237832

2

5

19

1

2

40

2.386979

2

14

16

1

7

8

2.536118

2

23

13

1

11

37

2.685248

2

32

10

1

16

5

2.834369

2

41

7

1

20

33

14.837300

14

15

0

7

7

31⁄8 31⁄4 33⁄8 31⁄2 35⁄8 33⁄4 37⁄8

15.423785

14

50 14

7

25

7

16.009458

15

25 26

7

42

43

16.594290

16

0 34

8

0

17

17.178253

16

35 39

8

17

50

17.761318

17

10 42

8

35

21

18.343458

17

45 41

8

52

50

18.924644

18

20 36

9

10

18

4

19.504850

18

55 29

9

27

44

30 17

2.983481

2

50

4

1

25

2

41⁄8

20.084047

19

3.132582

2

59

1

1

29

30

41⁄4

20.662210

20

21.239311 21.815324

9

45

9

3

10

2

31

20

39 44

10

19

52

21

14 22

10

37

11

22.390223

21

48 55

10

54

28

22.963983

22

23 25

11

11

42

23.536578

22

57 50

11

28

55

5

3.281673

3

7

57

1

33

59

3.430753

3

16

54

1

38

27

3.579821

3

25

51

1

42

55

3.728877

3

34

47

1

47

24

3.877921

3

43

44

1

51

52

43⁄8 41⁄2 45⁄8 43⁄4 47⁄8

4.026951

3

52

41

1

56

20

5

24.107983

23

32 12

11

46

6

4.175968

4

1

37

2

0

49

51⁄8

24.678175

24

6 29

12

3

14

4.324970

4

10

33

2

5

17

51⁄4

25.247127

24

40 41

12

20

21

4.473958

4

19

30

2

9

45

53⁄8

25.814817

25

14 50

12

37

25

4.622931

4

28

26

2

14

13

51⁄2

26.381221

25

48 53

12

54

27

4.771888

4

37

23

2

18

41

55⁄8

26.946316

26

22 52

13

11

26

27.510079

26

56 47

13

28

23

28.072487

27

30 36

13

45

18

4 21

14

2

10

1

5.069753

4

46

19

2

23

9

11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 113⁄16

5.367550

5

4

11

2

32

6

53⁄4 57⁄8

5.665275

5

22

3

2

41

2

6

28.633518

28

5.962922

5

39

55

2

49

57

61⁄8

29.193151

28

38

1

14

19

0

6.260490

5

57

47

2

58

53

61⁄4

29.751364

29

11 35

14

35

48

6.557973

6

15

38

3

7

49

63⁄8

30.308136

29

45

5

14

52

32

6.855367

6

33

29

3

16

44

61⁄2

30.863447

30

18 29

15

9

15

7.152669

6

51

19

3

25

40

65⁄8

31.417276

30

51 48

15

25

54

7.449874

7

9

10

3

34

35

63⁄4

31.969603

31

25

15

42

31

7.746979

7

27

0

3

43

30

31

58 11

15

59

5

7

44

49

3

52

25

67⁄8 7

32.520409

8.043980

33.069676

32

31 13

16

15

37

33.617383

33

34.163514

33

9.230863

34

8.340873

8

2

38

4

1

19

8.637654

8

20

27

4

10

14

0.149208

8

38

16

4

19

8

71⁄8 71⁄4 73⁄8

2

4 11

16

32

5

3

16

48

31

9 49

17

4

54

37

Taper per foot represents inches of taper per foot of length. For conversions into decimal degrees and radians see Conversion Tables of Angular Measure on page 96.


Machinery's Handbook 27th Edition ANGLES AND TAPERS

715

Rules for Figuring Tapers Given To Find The taper per foot. The taper per inch. The taper per inch. The taper per foot. End diameters and length The taper per foot. of taper in inches. Large diameter and Diameter at small end in length of taper in inches inches, and taper per foot. Small diameter and Diameter at large end in length of taper in inches. inches, and taper per foot. The taper per foot and Distance between two two diameters in inches. given diameters in inches. The taper per foot. Amount of taper in a certain length in inches.

Rule Divide the taper per foot by 12. Multiply the taper per inch by 12. Subtract small diameter from large; divide by length of taper; and multiply quotient by 12. Divide taper per foot by 12; multiply by length of taper; and subtract result from large diameter. Divide taper per foot by 12; multiply by length of taper; and add result to small diameter. Subtract small diameter from large; divide remainder by taper per foot; and multiply quotient by 12. Divide taper per foot by 12; multiply by given length of tapered part.

To find angle α for given taper T in inches per foot.—

d

D C

α = 2 arctan ( T ⁄ 24 )

Example:What angle α is equivalent to a taper of 1.5 inches per foot? α = 2 × arctan ( 1.5 ⁄ 24 ) = 7.153° To find taper per foot T given angle α in degrees.— T = 24 tan ( α ⁄ 2 ) inches per foot Example:What taper T is equivalent to an angle of 7.153°? T = 24 tan ( 7.153 ⁄ 2 ) = 1.5 inches per foot To find angle α given dimensions D, d, and C.— Let K be the difference in the disk diameters divided by twice the center distance. K = (D − d)/(2C), then α = 2 arcsin K Example:If the disk diameters d and D are 1 and 1.5 inches, respectively, and the center distance C is 5 inches, find the included angle α. K = ( 1.5 – 1 ) ⁄ ( 2 × 5 ) = 0.05

α = 2 × arcsin 0.05 = 5.732°

To find taper T measured at right angles to a line through the disk centers given dimensions D, d, and distance C.— Find K using the formula in the previous example, then T = 24K ⁄ 1 – K 2 inches per foot Example:If disk diameters d and D are 1 and 1.5 inches, respectively, and the center distance C is 5 inches, find the taper per foot. K = ( 1.5 – 1 ) ⁄ ( 2 × 5 ) = 0.05

24 × 0.05 T = ------------------------------- = 1.2015 inches per foot 1 – ( 0.05 ) 2



ANGLES AND TAPERS

To find center distance C for a given taper T in inches per foot.— D–d 1 + ( T ⁄ 24 ) 2 C = ------------- × ---------------------------------- inches 2 T ⁄ 24 Example:Gage is to be set to 3⁄4 inch per foot, and disk diameters are 1.25 and 1.5 inches, respectively. Find the required center distance for the disks. – 1.25- × ---------------------------------------1 + ( 0.75 ⁄ 24 ) 2- = 4.002 inches C = 1.5 ----------------------0.75 ⁄ 24 2 To find center distance C for a given angle α and dimensions D and d.— C = ( D – d ) ⁄ 2 sin ( α ⁄ 2 ) inches Example:If an angle α of 20° is required, and the disks are 1 and 3 inches in diameter, respectively, find the required center distance C. C = ( 3 – 1 ) ⁄ ( 2 × sin 10 ° ) = 5.759 inches To find taper T measured at right angles to one side .—When one side is taken as a base line and the taper is measured at right angles to that side, calculate K as explained above and use the following formula for determining the taper T:

D d

C

1 – K 2 inches per foot T = 24K ------------------1 – 2K 2

Example:If the disk diameters are 2 and 3 inches, respectively, and the center I distance is 5 inches, what is the taper per foot measured at right angles to one side? 3 – 2- = 0.1 K = ----------2×5

1 – ( 0.1 ) 2 T = 24 × 0.1 × ------------------------------------- = 2.4367 in. per ft. 1 – [ 2 × ( 0.1 ) 2 ]

To find center distance C when taper T is measured from one side.— D–d C = ----------------------------------------------------- inches 2 – 2 ⁄ 1 + ( T ⁄ 12 ) 2 Example:If the taper measured at right angles to one side is 6.9 inches per foot, and the disks are 2 and 5 inches in diameter, respectively, what is center distance C? 5–2 C = ---------------------------------------------------------- = 5.815 inches. 2 – 2 ⁄ 1 + ( 6.9 ⁄ 12 ) 2 To find diameter D of a large disk in contact with a small disk of diameter d given angle α.—

d

D

+ sin ( α ⁄ 2 )- inches D = d×1 -------------------------------1 – sin ( α ⁄ 2 )

Example:The required angle α is 15°. Find diameter D of a large disk that is in contact with a standard 1-inch reference disk.


Machinery's Handbook 27th Edition MEASUREMENT OVER PINS

717

+ sin 7.5° = 1.3002 inches D = 1 × 1--------------------------1 – sin 7.5° Measurement over Pins and Rolls Measurement over Pins.—When the distance across a bolt circle is too large to measure using ordinary measuring tools, then the required distance may be found from the distance across adacent or alternate holes using one of the methods that follow: c θ

θ

= 3 ---- 60 n -----

y

x

d

c

= 3 ---- 60 n -----

x

d

θ = 3 ------6---0 n

x

Fig. 1a.

Fig. 1b.

d

Fig. 1c.

Even Number of Holes in Circle: To measure the unknown distance x over opposite plugs in a bolt circle of n holes (n is even and greater than 4), as shown in Fig. 1a, where y is the distance over alternate plugs, d is the diameter of the holes, and θ = 360°/n is the angle between adjacent holes, use the following general equation for obtaining x: – d- + d x = y---------sin θ Example:In a die that has six 3/4-inch diameter holes equally spaced on a circle, where the distance y over alternate holes is 41⁄2 inches, and the angle θ between adjacent holes is 60°, then 4.500 – 0.7500 x = ------------------------------------ + 0.7500 = 5.0801 sin 60° In a similar problem, the distance c over adjacent plugs is given, as shown in Fig. 1b. If the number of holes is even and greater than 4, the distance x over opposite plugs is given in the following formula: –θ ⎛ sin ⎛ 180 ------------------⎞ ⎞ ⎜ ⎝ 2 ⎠⎟ x = 2 ( c – d ) ⎜ -------------------------------⎟ + d sin θ ⎜ ⎟ ⎝ ⎠ where d and θ are as defined above. Odd Number of Holes in Circle: In a circle as shown in Fig. 1c, where the number of holes n is odd and greater than 3, and the distance c over adjacent holes is given, then θ equals 360/n and the distance x across the most widely spaced holes is given by: c---------–d 2 x = ----------+d θ sin --4 Checking a V-shaped Groove by Measurement Over Pins.—In checking a groove of the shape shown in Fig. 2, it is necessary to measure the dimension X over the pins of radius R. If values for the radius R, dimension Z, and the angles α and β are known, the problem is



MEASUREMENT WITH ROLLS

to determine the distance Y, to arrive at the required overall dimension for X. If a line AC is drawn from the bottom of the V to the center of the pin at the left in Fig. 2, and a line CB from the center of this pin to its point of tangency with the side of the V, a right-angled triangle is formed in which one side, CB, is known and one angle CAB, can be determined. A line drawn from the center of a circle to the point of intersection of two tangents to the circle bisects the angle made by the tangent lines, and angle CAB therefore equals 1⁄2 (α + β). The length AC and the angle DAC can now be found, and with AC known in the rightangled triangle ADC, AD, which is equal to Y can be found.

Fig. 2.

The value for X can be obtained from the formula + β- cos α – β- + 1⎞ X = Z + 2R ⎛ csc α ----------------------⎝ ⎠ 2 2 For example, if R = 0.500, Z = 1.824, α = 45 degrees, and β = 35 degrees, 45° + 35° 45° – 35° X = 1.824 + ( 2 × 0.5 ) ⎛⎝ csc ------------------------ cos ----------------------- + 1⎞⎠ 2 2 X = 1.824 + csc 40° cos 5° + 1 X = 1.824 + 1.5557 × 0.99619 + 1 X = 1.824 + 1.550 + 1 = 4.374 Checking Radius of Arc by Measurement Over Rolls.—The radius R of large-radius concave and convex gages of the type shown in Figs. 3a, 3b and 3c can be checked by measurement L over two rolls with the gage resting on the rolls as shown. If the diameter of the rolls D, the length L, and the height H of the top of the arc above the surface plate (for the concave gage, Fig. 3a) are known or can be measured, the radius R of the workpiece to be checked can be calculated trigonometrically, as follows. Referring to Fig. 3a for the concave gage, if L and D are known, cb can be found, and if H and D are known, ce can be found. With cb and ce known, ab can be found by means of a diagram as shown in Fig. 3c. In diagram Fig. 3c, cb and ce are shown at right angles as in Fig. 3a. A line is drawn connecting points b and e and line ce is extended to the right. A line is now drawn from point b perpendicular to be and intersecting the extension of ce at point f. A semicircle can now be drawn through points b, e, and f with point a as the center. Triangles bce and bcf are similar and have a common side. Thus ce:bc::bc:cf. With ce and bc known, cf can be found from this proportion and hence ef which is the diameter of the semicircle and radius ab. Then R = ab + D/2.


Machinery's Handbook 27th Edition CHECKING SHAFT CONDITIONS

Fig. 3a.

719

Fig. 3b.

Fig. 3c.

The procedure for the convex gage is similar. The distances cb and ce are readily found and from these two distances ab is computed on the basis of similar triangles as before. Radius R is then readily found. The derived formulas for concave and convex gages are as follows: Formulas:

( L – D )2 + H ---R = ---------------------8(H – D) 2

(Concave gage Fig. 3a)

( L – D )2 R = --------------------(Convex gage Fig. 3b) 8D For example: For Fig. 3a, let L = 17.8, D = 3.20, and H = 5.72, then ( 17.8 – 3.20 ) 2 5.72 ( 14.60 ) 2 R = ----------------------------------- + ---------- = -------------------- + 2.86 8 ( 5.72 – 3.20 ) 2 8 × 2.52 213.16 R = ---------------- + 2.86 = 13.43 20.16 For Fig. 3b, let L = 22.28 and D = 3.40, then 22.28 – 3.40 ) 2- = 356.45 R = (--------------------------------------------------- = 13.1 8 × 3.40 27.20 Checking Shaft Conditions Checking for Various Shaft Conditions.—An indicating height gage, together with Vblocks can be used to check shafts for ovality, taper, straightness (bending or curving), and concentricity of features (as shown exaggerated in Fig. 4). If a shaft on which work has



CHECKING SHAFT CONDITIONS

been completed shows lack of concentricity. it may be due to the shaft having become bent or bowed because of mishandling or oval or tapered due to poor machine conditions. In checking for concentricity, the first step is to check for ovality, or out-of-roundness, as in Fig. 4a. The shaft is supported in a suitable V-block on a surface table and the dial indicator plunger is placed over the workpiece, which is then rotated beneath the plunger to obtain readings of the amount of eccentricity. This procedure (sometimes called clocking, owing to the resemblance of the dial indicator to a clock face) is repeated for other shaft diameters as necessary, and, in addition to making a written record of the measurements, the positions of extreme conditions should be marked on the workpiece for later reference.

Fig. 4.

To check for taper, the shaft is supported in the V-block and the dial indicator is used to measure the maximum height over the shaft at various positions along its length, as shown in Fig. 4b, without turning the workpiece. Again, the shaft should be marked with the reading positions and values, also the direction of the taper, and a written record should be made of the amount and direction of any taper discovered. Checking for a bent shaft requires that the shaft be clocked at the shoulder and at the farther end, as shown in Fig. 4c. For a second check the shaft is rotated only 90° or a quarter turn. When the recorded readings are compared with those from the ovality and taper checks, the three conditions can be distinguished.


Machinery's Handbook 27th Edition OUT OF ROUNDNESS, LOBING

721

To detect a curved or bowed condition, the shaft should be suspended in two V-blocks with only about 1⁄8 inch of each end in each vee. Alternatively, the shaft can be placed between centers. The shaft is then clocked at several points, as shown in Fig. 4d, but preferably not at those locations used for the ovality, taper, or crookedness checks. If the single element due to curvature is to be distinguished from the effects of ovality, taper, and crookedness, and its value assessed, great care must be taken to differentiate between the conditions detected by the measurements. Finally, the amount of eccentricity between one shaft diameter and another may be tested by the setup shown in Fig. 4e. With the indicator plunger in contact with the smaller diameter, close to the shoulder, the shaft is rotated in the V-block and the indicator needle position is monitored to find the maximum and minimum readings. Curvature, ovality, or crookedness conditions may tend to cancel each other, as shown in Fig. 5, and one or more of these degrees of defectiveness may add themselves to the true eccentricity readings, depending on their angular positions. Fig. 5a shows, for instance, how crookedness and ovality tend to cancel each other, and also shows their effect in falsifying the reading for eccentricity. As the same shaft is turned in the V-block to the position shown in Fig. 5b, the maximum curvature reading could tend to cancel or reduce the maximum eccentricity reading. Where maximum readings for ovality, curvature, or crookedness occur at the same angular position, their values should be subtracted from the eccentricity reading to arrive at a true picture of the shaft condition. Confirmation of eccentricity readings may be obtained by reversing the shaft in the V-block, as shown in Fig. 5c, and clocking the larger diameter of the shaft.

Fig. 5.

Out-of-Roundness—Lobing.—With the imposition of finer tolerances and the development of improved measurement methods, it has become apparent that no hole,' cylinder, or sphere can be produced with a perfectly symmetrical round shape. Some of the conditions are diagrammed in Fig. 6, where Fig. 6a shows simple ovality and Fig. 6b shows ovality occurring in two directions. From the observation of such conditions have come the terms lobe and lobing. Fig. 6c shows the three-lobed shape common with centerless-ground components, and Fig. 6d is typical of multi-lobed shapes. In Fig. 6e are shown surface waviness, surface roughness, and out-of-roundness, which often are combined with lobing.



OUT OF ROUNDNESS, LOBING

Fig. 6.

In Figs. 6a through 6d, the cylinder (or hole) diameters are shown at full size but the lobes are magnified some 10,000 times to make them visible. In precision parts, the deviation from the round condition is usually only in the range of millionths of an inch, although it occasionally can be 0.0001 inch, 0.0002 inch, or more. For instance, a 3-inch-diameter part may have a lobing condition amounting to an inaccuracy of only 30 millionths (0.000030 inch). Even if the distortion (ovality, waviness, roughness) is small, it may cause hum, vibration, heat buildup, and wear, possibly leading to eventual failure of the component or assembly. Plain elliptical out-of-roundness (two lobes), or any even number of lobes, can be detected by rotating the part on a surface plate under a dial indicator of adequate resolution, or by using an indicating caliper or snap gage. However, supporting such a part in a Vblock during measurement will tend to conceal roundness errors. Ovality in a hole can be detected by a dial-type bore gage or internal measuring machine. Parts with odd numbers of lobes require an instrument that can measure the envelope or complete circumference. Plug and ring gages will tell whether a shaft can be assembled into a bearing, but not whether there will be a good fit, as illustrated in Fig. 6e. A standard, 90-degree included-angle V-block can be used to detect and count the number of lobes, but to measure the exact amount of lobing indicated by R-r in Fig. 7 requires a V-block with an angle α, which is related to the number of lobes. This angle α can be calculated from the formula 2α = 180° − 360°/N, where N is the number of lobes. Thus, for a three-lobe form, α becomes 30 degrees, and the V-block used should have a 60-degree included angle. The distance M, which is obtained by rotating the part under the comparator plunger, is converted to a value for the radial variation in cylinder contour by the formula M = (R − r) (1 + csc α).

Fig. 7.

Using a V-block (even of appropriate angle) for parts with odd numbers of lobes will give exaggerated readings when the distance R − r (Fig. 7) is used as the measure of the amount of out-of-roundness. The accompanying table shows the appropriate V-block angles for various odd numbers of lobes, and the factors (1 + csc α) by which the readings are increased over the actual out-of-roundness values.


Machinery's Handbook 27th Edition MEASUREMENTS USING LIGHT

723

Table of Lobes, V-block Angles and Exaggeration Factors in Measuring Out-of-round Conditions in Shafts Number of Lobes 3 5 7 9

Included Angle of V-block (deg) 60 108 128.57 140

Exaggeration Factor (1 + csc α) 3.00 2.24 2.11 2.06

Measurement of a complete circumference requires special equipment, often incorporating a precision spindle running true within two millionths (0.000002) inch. A stylus attached to the spindle is caused to traverse the internal or external cylinder being inspected, and its divergences are processed electronically to produce a polar chart similar to the wavy outline in Fig. 6e. The electronic circuits provide for the variations due to surface effects to be separated from those of lobing and other departures from the “true” cylinder traced out by the spindle. Measurements Using Light Measuring by Light-wave Interference Bands.—Surface variations as small as two millionths (0.000002) inch can be detected by light-wave interference methods, using an optical flat. An optical flat is a transparent block, usually of plate glass, clear fused quartz, or borosilicate glass, the faces of which are finished to extremely fine limits (of the order of 1 to 8 millionths [0.000001 to 0.000008] inch, depending on the application) for flatness. When an optical flat is placed on a “flat” surface, as shown in Fig. 8, any small departure from flatness will result in formation of a wedge-shaped layer of air between the work surface and the underside of the flat. Light rays reflected from the work surface and the underside of the flat either interfere with or reinforce each other. Interference of two reflections results when the air gap measures exactly half the wavelength of the light used, and produces a dark band across the work surface when viewed perpendicularly, under monochromatic helium light. A light band is produced halfway between the dark bands when the rays reinforce each other. With the 0.0000232-inch-wavelength helium light used, the dark bands occur where the optical flat and the work surface are separated by 11.6 millionths (0.0000116) inch, or multiples thereof.

;; ;;

7 fringes × .0000116 = .0000812′′

.0000812′′

.0000116′′

Fig. 8.

For instance, at a distance of seven dark bands from the point of contact, as shown in Fig. 8, the underface of the optical flat is separated from the work surface by a distance of 7 × 0.0000116 inch or 0.0000812 inch. The bands are separated more widely and the indications become increasingly distorted as the viewing angle departs from the perpendicular. If the bands appear straight, equally spaced and parallel with each other, the work surface is flat. Convex or concave surfaces cause the bands to curve correspondingly, and a cylindrical tendency in the work surface will produce unevenly spaced, straight bands.



SURFACE TEXTURE

SURFACE TEXTURE American National Standard Surface Texture (Surface Roughness, Waviness, and Lay) American National Standard ANSI/ASME B46.1-1995 is concerned with the geometric irregularities of surfaces of solid materials, physical specimens for gaging roughness, and the characteristics of stylus instrumentation for measuring roughness. The standard defines surface texture and its constituents: roughness, waviness, lay, and flaws. A set of symbols for drawings, specifications, and reports is established. To ensure a uniform basis for measurements the standard also provides specifications for Precision Reference Specimens, and Roughness Comparison Specimens, and establishes requirements for stylustype instruments. The standard is not concerned with luster, appearance, color, corrosion resistance, wear resistance, hardness, subsurface microstructure, surface integrity, and many other characteristics that may be governing considerations in specific applications. The standard is expressed in SI metric units but U.S. customary units may be used without prejudice. The standard does not define the degrees of surface roughness and waviness or type of lay suitable for specific purposes, nor does it specify the means by which any degree of such irregularities may be obtained or produced. However, criteria for selection of surface qualities and information on instrument techniques and methods of producing, controlling and inspecting surfaces are included in Appendixes attached to the standard. The Appendix sections are not considered a part of the standard: they are included for clarification or information purposes only. Surfaces, in general, are very complex in character. The standard deals only with the height, width, and direction of surface irregularities because these characteristics are of practical importance in specific applications. Surface texture designations as delineated in this standard may not be a sufficient index to performance. Other part characteristics such as dimensional and geometrical relationships, material, metallurgy, and stress must also be controlled. Definitions of Terms Relating to the Surfaces of Solid Materials.—The terms and ratings in the standard relate to surfaces produced by such means as abrading, casting, coating, cutting, etching, plastic deformation, sintering, wear, and erosion. Error of form is considered to be that deviation from the nominal surface caused by errors in machine tool ways, guides, insecure clamping or incorrect alignment of the workpiece or wear, all of which are not included in surface texture. Out-of-roundness and outof-flatness are examples of errors of form. See ANSI/ASME B46.3.1-1988 for measurement of out-of-roundness. Flaws are unintentional, unexpected, and unwanted interruptions in the topography typical of a part surface and are defined as such only when agreed upon by buyer and seller. If flaws are defined, the surface should be inspected specifically to determine whether flaws are present, and rejected or accepted prior to performing final surface roughness measurements. If defined flaws are not present, or if flaws are not defined, then interruptions in the part surface may be included in roughness measurements. Lay is the direction of the predominant surface pattern, ordinarily determined by the production method used. Roughness consists of the finer irregularities of the surface texture, usually including those irregularities that result from the inherent action of the production process. These irregularities are considered to include traverse feed marks and other irregularities within the limits of the roughness sampling length. Surface is the boundary of an object that separates that object from another object, substance or space. Surface, measured is the real surface obtained by instrumental or other means.


Machinery's Handbook 27th Edition SURFACE TEXTURE

725

Flaw

Lay

Waviness Spacing

Waviness Height

Valleys Roughness Average — Ra

Peaks

Mean Line

Roughness Spacing

Fig. 1. Pictorial Display of Surface Characteristics

Surface, nominal is the intended surface contour (exclusive of any intended surface roughness), the shape and extent of which is usually shown and dimensioned on a drawing or descriptive specification. Surface, real is the actual boundary of the object. Manufacturing processes determine its deviation from the nominal surface. Surface texture is repetitive or random deviations from the real surface that forms the three-dimensional topography of the surface. Surface texture includes roughness, waviness, lay and flaws. Fig. 1 is an example of a unidirectional lay surface. Roughness and waviness parallel to the lay are not represented in the expanded views. Waviness is the more widely spaced component of surface texture. Unless otherwise noted, waviness includes all irregularities whose spacing is greater than the roughness sampling length and less than the waviness sampling length. Waviness may result from



SURFACE TEXTURE

such factors as machine or work deflections, vibration, chatter, heat-treatment or warping strains. Roughness may be considered as being superposed on a ‘wavy’ surface. Definitions of Terms Relating to the Measurement of Surface Texture.—T e r m s regarding surface texture pertain to the geometric irregularities of surfaces and include roughness, waviness and lay. Profile is the contour of the surface in a plane measured normal, or perpendicular, to the surface, unless another other angle is specified. Graphical centerline. See Mean Line. Height (z) is considered to be those measurements of the profile in a direction normal, or perpendicular, to the nominal profile. For digital instruments, the profile Z(x) is approximated by a set of digitized values. Height parameters are expressed in micrometers (µm). Height range (z) is the maximum peak-to-valley surface height that can be detected accurately with the instrument. It is measurement normal, or perpendicular, to the nominal profile and is another key specification. Mean line (M) is the line about which deviations are measured and is a line parallel to the general direction of the profile within the limits of the sampling length. See Fig. 2. The mean line may be determined in one of two ways. The filtered mean line is the centerline established by the selected cutoff and its associated circuitry in an electronic roughness average measuring instrument. The least squares mean line is formed by the nominal profile but by dividing into selected lengths the sum of the squares of the deviations minimizes the deviation from the nominal form. The form of the nominal profile could be a curve or a straight line. Peak is the point of maximum height on that portion of a profile that lies above the mean line and between two intersections of the profile with the mean line. Profile measured is a representation of the real profile obtained by instrumental or other means. When the measured profile is a graphical representation, it will usually be distorted through the use of different vertical and horizontal magnifications but shall otherwise be as faithful to the profile as technically possible. Profile, modified is the measured profile where filter mechanisms (including the instrument datum) are used to minimize certain surface texture characteristics and emphasize others. Instrument users apply profile modifications typically to differentiate surface roughness from surface waviness. Profile, nominal is the profile of the nominal surface; it is the intended profile (exclusive of any intended roughness profile). Profile is usually drawn in an x-z coordinate system. See Fig. 2. Measure profile

Z

X Nominal profile Fig. 2. Nominal and Measured Profiles

Profile, real is the profile of the real surface. Profile, total is the measured profile where the heights and spacing may be amplified differently but otherwise no filtering takes place. Roughness profile is obtained by filtering out the longer wavelengths characteristic of waviness. Roughness spacing is the average spacing between adjacent peaks of the measured profile within the roughness sampling length.



727

Roughness topography is the modified topography obtained by filtering out the longer wavelengths of waviness and form error. Sampling length is the nominal spacing within which a surface characteristic is determined. The range of sampling lengths is a key specification of a measuring instrument. Spacing is the distance between specified points on the profile measured parallel to the nominal profile. Spatial (x) resolution is the smallest wavelength which can be resolved to 50% of the actual amplitude. This also is a key specification of a measuring instrument. System height resolution is the minimum height that can be distinguished from background noise of the measurement instrument. Background noise values can be determined by measuring approximate rms roughness of a sample surface where actual roughness is significantly less than the background noise of the measuring instrument. It is a key instrumentation specification. Topography is the three-dimensional representation of geometric surface irregularities. Topography, measured is the three-dimensional representation of geometric surface irregularities obtained by measurement. Topography, modified is the three-dimensional representation of geometric surface irregularities obtained by measurement but filtered to minimize certain surface characteristics and accentuate others. Valley is the point of maximum depth on that portion of a profile that lies below the mean line and between two intersections of the profile with the mean line. Waviness, evaluation length (L), is the length within which waviness parameters are determined. Waviness, long-wavelength cutoff (lcw) the spatial wavelength above which the undulations of waviness profile are removed to identify form parameters. A digital Gaussian filter can be used to separate form error from waviness but its use must be specified. Waviness profile is obtained by filtering out the shorter roughness wavelengths characteristic of roughness and the longer wavelengths associated with the part form parameters. Waviness sampling length is a concept no longer used. See waviness long-wavelength cutoff and waviness evaluation length. Waviness short-wavelength cutoff (lsw) is the spatial wavelength below which roughness parameters are removed by electrical or digital filters. Waviness topography is the modified topography obtained by filtering out the shorter wavelengths of roughness and the longer wavelengths associated with form error. Waviness spacing is the average spacing between adjacent peaks of the measured profile within the waviness sampling length. Sampling Lengths.—Sampling length is the normal interval for a single value of a surface parameter. Generally it is the longest spatial wavelength to be included in the profile measurement. Range of sampling lengths is an important specification for a measuring instrument.

Sampling Length

l

l

l

l

l

Evaluation length, L

Traverse Length Fig. 3. Traverse Length

Roughness sampling length (l) is the sampling length within which the roughness average is determined. This length is chosen to separate the profile irregularities which are des-



SURFACE TEXTURE

ignated as roughness from those irregularities designated as waviness. It is different from evaluation length (L) and the traversing length. See Fig. 3. Evaluation length (L) is the length the surface characteristics are evaluated. The evaluation length is a key specification of a measuring instrument. Traversing length is profile length traversed to establish a representative evaluation length. It is always longer than the evaluation length. See Section 4.4.4 of ANSI/ASME B46.1-1995 for values which should be used for different type measurements. Cutoff is the electrical response characteristic of the measuring instrument which is selected to limit the spacing of the surface irregularities to be included in the assessment of surface texture. Cutoff is rated in millimeters. In most electrical averaging instruments, the cutoff can be user selected and is a characteristic of the instrument rather than of the surface being measured. In specifying the cutoff, care must be taken to choose a value which will include all the surface irregularities to be assessed. Waviness sampling length (l) is a concept no longer used. See waviness long-wavelength cutoff and waviness evaluation length. Roughness Parameters.—Roughness is the fine irregularities of the surface texture resulting from the production process or material condition. Roughness average (Ra), also known as arithmetic average (AA) is the arithmetic average of the absolute values of the measured profile height deviations divided by the evaluation length, L. This is shown as the shaded area of Fig. 4 and generally includes sampling lengths or cutoffs. For graphical determinations of roughness average, the height deviations are measured normal, or perpendicular, to the chart center line. Y'

Mean line

X

f a b

c

d

e

g

h

i

j

p k

l

m n

q

r

s

t u

o

v

w

X'

Y

Fig. 4.

Roughness average is expressed in micrometers (µm). A micrometer is one millionth of a meter (0.000001 meter). A microinch (µin) is one millionth of an inch (0.000001 inch). One microinch equals 0.0254 micrometer (1 µin. = 0.0254 µm). Roughness Average Value (Ra) From Continuously Averaging Meter Reading m a y b e made of readings from stylus-type instruments of the continuously averaging type. To ensure uniform interpretation, it should be understood that the reading that is considered significant is the mean reading around which the needle tends to dwell or fluctuate with a small amplitude. Roughness is also indicated by the root-mean-square (rms) average, which is the square root of the average value squared, within the evaluation length and measured from the mean line shown in Fig. 4, expressed in micrometers. A roughness-measuring instrument calibrated for rms average usually reads about 11 per cent higher than an instrument calibrated for arithmetical average. Such instruments usually can be recalibrated to read arithmetical average. Some manufacturers consider the difference between rms and AA to be small enough that rms on a drawing may be read as AA for many purposes. Roughness evaluation length (L), for statistical purposes should, whenever possible, consist of five sampling lengths (l). Use of other than five sampling lengths must be clearly indicated.



729

Waviness Parameters.—Waviness is the more widely spaced component of surface texture. Roughness may be thought of as superimposed on waviness. Waviness height (Wt) is the peak-to-valley height of the modified profile with roughness and part form errors removed by filtering, smoothing or other means. This value is typically three or more times the roughness average. The measurement is taken normal, or perpendicular, to the nominal profile within the limits of the waviness sampling length. Waviness evaluation length (Lw) is the evaluation length required to determine waviness parameters. For waviness, the sampling length concept is no longer used. Rather, only waviness evaluation length (Lw) and waviness long-wavelength cutoff (lew) are defined. For better statistics, the waviness evaluation length should be several times the waviness long-wavelength cutoff. Relation of Surface Roughness to Tolerances.—Because the measurement of surface roughness involves the determination of the average linear deviation of the measured surface from the nominal surface, there is a direct relationship between the dimensional tolerance on a part and the permissible surface roughness. It is evident that a requirement for the accurate measurement of a dimension is that the variations introduced by surface roughness should not exceed the dimensional tolerances. If this is not the case, the measurement of the dimension will be subject to an uncertainty greater than the required tolerance, as illustrated in Fig. 5. Roughness Height

Roughness Mean Line

Profile Height

Uncertainty In Measurement

Roughness Mean Line

Roughness Height

Profile Height

Fig. 5.

The standard method of measuring surface roughness involves the determination of the average deviation from the mean surface. On most surfaces the total profile height of the surface roughness (peak-to-valley height) will be approximately four times (4×) the measured average surface roughness. This factor will vary somewhat with the character of the surface under consideration, but the value of four may be used to establish approximate profile heights. From these considerations it follows that if the arithmetical average value of surface roughness specified on a part exceeds one eighth of the dimensional tolerance, the whole tolerance will be taken up by the roughness height. In most cases, a smaller roughness specification than this will be found; but on parts where very small dimensional tolerances are given, it is necessary to specify a suitably small surface roughness so useful dimensional measurements can be made. The tables on pages pages 652 and 679 show the relations between machining processes and working tolerances. Values for surface roughness produced by common processing methods are shown in Table 1. The ability of a processing operation to produce a specific surface roughness depends on many factors. For example, in surface grinding, the final surface depends on the peripheral speed of the wheel, the speed of the traverse, the rate of feed, the grit size, bonding material and state of dress of the wheel, the amount and type of lubrication at the



SURFACE TEXTURE Table 1. Surface Roughness Produced by Common Production Methods

Process

Roughness Average, Ra – Micrometers µm (Microinches µin.) 50 25 12.5 6.3 3.2 1.6 0.80 0.40 0.20 (2000) (1000) (500) (250) (125) (63) (32) (16) (8)

Flame Cutting Snagging Sawing Planing, Shaping Drilling Chemical Milling Elect. Discharge Mach. Milling Broaching Reaming Electron Beam Laser Electro-Chemical Boring, Turning Barrel Finishing Electrolytic Grinding Roller Burnishing Grinding Honing Electro-Polish Polishing Lapping Superfinishing Sand Casting Hot Rolling Forging Perm. Mold Casting Investment Casting Extruding Cold Rolling, Drawing Die Casting The ranges shown above are typical of the processes listed Higher or lower values may be obtained under special conditions

KEY

0.10 (4)

0.05 (2)

0.025 (1)

0.012 (0.5)

Average Application Less Frequent Application

point of cutting, and the mechanical properties of the piece being ground. A small change in any of the above factors can have a marked effect on the surface produced. Instrumentation for Surface Texture Measurement.—Instrumentation used for measurement of surface texture, including roughness and waviness generally falls into six types. These include: Type I, Profiling Contact Skidless Instruments: Used for very smooth to very rough surfaces. Used for roughness and may measure waviness. Can generate filtered or unfiltered profiles and may have a selection of filters and parameters for data analysis. Examples include: 1) skidless stylus-type with LVDT (linear variable differential transformer) vertical transducers; 2) skidless-type using an interferometric transducer; 3)skidless stylustype using capacitance transducer. Type II, Profiling Non-contact Instruments: Capable of full profiling or topographical analysis. Non-contact operation may be advantageous for softness but may vary with sample type and reflectivity. Can generate filtered or unfiltered profiles but may have difficulty with steeply inclined surfaces. Examples include: 1) interferometric microscope; 2) optical focus sending; 3) Nomarski differential profiling; 4) laser triangulation; 5) scanning electron microscope (SEM) stereoscopy; 6) confocal optical microscope. Type III, Scanned Probe Microscope: Feature high spatial resolution (at or near the atomic scale) but area of measurement may be limited. Examples include: 1) scanning tunneling microscope (STM) and 2) atomic force microscope (AFM).



731

Type IV, Profiling Contact Skidded Instruments: Uses a skid as a datum to eliminate longer wavelengths; thus cannot be used for waviness or errors of form. May have a selection of filters and parameters and generates an output recording of filtered and skid-modified profiles. Examples include: 1) skidded, stylus-type with LVDT vertical measuring transducer and 2) fringe-field capacitance (FFC) transducer. Type V, Skidded Instruments with Parameters Only: Uses a skid as a datum to eliminate longer wavelengths; thus cannot be used for waviness or errors of form. Does not generate a profile. Filters are typically 2RC type and generate Ra but other parameters may be available. Examples include: 1) skidded, stylus-type with piezoelectric measuring transducer and 2) skidded, stylus-type with moving coil measuring transducer. Type VI, Area Averaging Methods: Used to measure averaged parameters over defined areas but do not generate profiles. Examples include: 1) parallel plate capacitance (PPC) method; 2) total integrated scatter (TIS); 3) angle resolved scatter (ARS)/bi-directional reflectance distribution function (BRDF). Selecting Cutoff for Roughness Measurements.—In general, surfaces will contain irregularities with a large range of widths. Surface texture instruments are designed to respond only to irregularity spacings less than a given value, called cutoff. In some cases, such as surfaces in which actual contact area with a mating surface is important, the largest convenient cutoff will be used. In other cases, such as surfaces subject to fatigue failure only the irregularities of small width will be important, and more significant values will be obtained when a short cutoff is used. In still other cases, such as identifying chatter marks on machined surfaces, information is needed on only the widely space irregularities. For such measurements, a large cutoff value and a larger radius stylus should be used. The effect of variation in cutoff can be understood better by reference to Fig. 6. The profile at the top is the true movement of a stylus on a surface having a roughness spacing of about 1 mm and the profiles below are interpretations of the same surface with cutoff value settings of 0.8 mm, 0.25 mm and 0.08 mm, respectively. It can be seen that the trace based on 0.8 mm cutoff includes most of the coarse irregularities and all of the fine irregularities of the surface. The trace based on 0.25 mm excludes the coarser irregularities but includes the fine and medium fine. The trace based on 0.08 mm cutoff includes only the very fine irregularities. In this example the effect of reducing the cutoff has been to reduce the roughness average indication. However, had the surface been made up only of irregularities as fine as those of the bottom trace, the roughness average values would have been the same for all three cutoff settings. In other words, all irregularities having a spacing less than the value of the cutoff used are included in a measurement. Obviously, if the cutoff value is too small to include coarser irregularities of a surface, the measurements will not agree with those taken with a larger cutoff. For this reason, care must be taken to choose a cutoff value which will include all of the surface irregularities it is desired to assess. To become proficient in the use of continuously averaging stylus-type instruments the inspector or machine operator must realize that for uniform interpretation, the reading which is considered significant is the mean reading around which the needle tends to dwell or fluctuate under small amplitude. Drawing Practices for Surface Texture Symbols.—American National Standard ANSI/ASME Y14.36M-1996 establishes the method to designate symbolic controls for surface texture of solid materials. It includes methods for controlling roughness, waviness, and lay, and provides a set of symbols for use on drawings, specifications, or other documents. The standard is expressed in SI metric units but U.S. customary units may be used without prejudice. Units used (metric or non-metric) should be consistent with the other units used on the drawing or documents. Approximate non-metric equivalents are shown for reference.



SURFACE TEXTURE

Fig. 6. Effects of Various Cutoff Values

Surface Texture Symbol.—The symbol used to designate control of surface irregularities is shown in Fig. 7b and Fig. 7d. Where surface texture values other than roughness average are specified, the symbol must be drawn with the horizontal extension as shown in Fig. 7f. Use of Surface Texture Symbols: When required from a functional standpoint, the desired surface characteristics should be specified. Where no surface texture control is specified, the surface produced by normal manufacturing methods is satisfactory provided it is within the limits of size (and form) specified in accordance with ANSI/ASME Y14.5M-1994, Dimensioning and Tolerancing. It is considered good practice to always specify some maximum value, either specifically or by default (for example, in the manner of the note shown in Fig. 2). Material Removal Required or Prohibited: The surface texture symbol is modified when necessary to require or prohibit removal of material. When it is necessary to indicate that a surface must be produced by removal of material by machining, specify the symbol shown in Fig. 7b. When required, the amount of material to be removed is specified as shown in Fig. 7c, in millimeters for metric drawings and in inches for non-metric drawings. Tolerance for material removal may be added to the basic value shown or specified in a general note. When it is necessary to indicate that a surface must be produced without material removal, specify the machining prohibited symbol as shown in Fig. 7d. Proportions of Surface Texture Symbols: The recommended proportions for drawing the surface texture symbol are shown in Fig. 7f. The letter height and line width should be the same as that for dimensions and dimension lines.



733

Surface Texture Symbols and Construction Symbol

Meaning Basic Surface Texture Symbol. Surface may be produced by any method except when the bar or circle (Fig. 7b or 7d) is specified.

Fig. 7a.

Fig. 7b.

Fig. 7c.

Material Removal By Machining Is Required. The horizontal bar indicates that material removal by machining is required to produce the surface and that material must be provided for that purpose. Material Removal Allowance. The number indicates the amount of stock to be removed by machining in millimeters (or inches). Tolerances may be added to the basic value shown or in general note.

Fig. 7d.

Material Removal Prohibited. The circle in the vee indicates that the surface must be produced by processes such as casting, forging, hot finishing, cold finishing, die casting, powder metallurgy or injection molding without subsequent removal of material.

Fig. 7e.

Surface Texture Symbol. To be used when any surface characteristics are specified above the horizontal line or the right of the symbol. Surface may be produced by any method except when the bar or circle (Fig. 7b and 7d) is specified.

Fig. 7f.

Applying Surface Texture Symbols.—The point of the symbol should be on a line representing the surface, an extension line of the surface, or a leader line directed to the surface, or to an extension line. The symbol may be specified following a diameter dimension. Although ANSI/ASME Y14.5M-1994, “Dimensioning and Tolerancing” specifies that normally all textual dimensions and notes should be read from the bottom of the drawing, the surface texture symbol itself with its textual values may be rotated as required. Regardless, the long leg (and extension) must be to the right as the symbol is read. For parts requiring extensive and uniform surface roughness control, a general note may be added to the drawing which applies to each surface texture symbol specified without values as shown in Fig. 8. When the symbol is used with a dimension, it affects the entire surface defined by the dimension. Areas of transition, such as chamfers and fillets, shall conform with the roughest adjacent finished area unless otherwise indicated. Surface texture values, unless otherwise specified, apply to the complete surface. Drawings or specifications for plated or coated parts shall indicate whether the surface texture values apply before plating, after plating, or both before and after plating. Only those values required to specify and verify the required texture characteristics should be included in the symbol. Values should be in metric units for metric drawing and non-metric units for non-metric drawings. Minority units on dual dimensioned drawings are enclosed in brackets.



SURFACE TEXTURE

Fig. 8. Application of Surface Texture Symbols

Roughness and waviness measurements, unless otherwise specified, apply in a direction which gives the maximum reading; generally across the lay. Cutoff or Roughness Sampling Length, (l): Standard values are listed in Table 2. When no value is specified, the value 0.8 mm (0.030 in.) applies. Table 2. Standard Roughness Sampling Length (Cutoff) Values mm 0.08 0.25 0.80

in. 0.003 0.010 0.030

mm 2.5 8.0 25.0

in. 0.1 0.3 1.0

Roughness Average (Ra): The preferred series of specified roughness average values is given in Table 3. Table 3. Preferred Series Roughness Average Values (Ra) µm

µin

µm

µin

µm

µin

0.012

0.5

0.025a

1a

160 200

2a 3

16a 20 25

4.0 5.0

0.050a 0.075a 0.10a 0.125 0.15

0.40a 0.50 0.63 0.80a 1.00 1.25

32a 40 50

6.3a 8.0 10.0

250a 320 400

0.20a 0.25 0.32

8a 10 13

1.60a 2.0 2.5

63a 80 100

12.5a 15 20

500a 600 800

3.2a

125a

25a …

1000a …

4a 5 6

a Recommended



735

Waviness Height (Wt): The preferred series of maximum waviness height values is listed in Table 3. Waviness height is not currently shown in U.S. or ISO Standards. It is included here to follow present industry practice in the United States. Table 4. Preferred Series Maximum Waviness Height Values mm

in.

mm

in.

mm

in.

0.0005 0.0008 0.0012 0.0020 0.0025 0.005

0.00002 0.00003 0.00005 0.00008 0.0001 0.0002

0.008 0.012 0.020 0.025 0.05 0.08

0.0003 0.0005 0.0008 0.001 0.002 0.003

0.12 0.20 0.25 0.38 0.50 0.80

0.005 0.008 0.010 0.015 0.020 0.030

Lay: Symbols for designating the direction of lay are shown and interpreted in Table 5. Example Designations.—Table 6 illustrates examples of designations of roughness, waviness, and lay by insertion of values in appropriate positions relative to the symbol. Where surface roughness control of several operations is required within a given area, or on a given surface, surface qualities may be designated, as in Fig. 9a. If a surface must be produced by one particular process or a series of processes, they should be specified as shown in Fig. 9b. Where special requirements are needed on a designated surface, a note should be added at the symbol giving the requirements and the area involved. An example is illustrated in Fig. 9c. Surface Texture of Castings.—Surface characteristics should not be controlled on a drawing or specification unless such control is essential to functional performance or appearance of the product. Imposition of such restrictions when unnecessary may increase production costs and in any event will serve to lessen the emphasis on the control specified for important surfaces. Surface characteristics of castings should never be considered on the same basis as machined surfaces. Castings are characterized by random distribution of non-directional deviations from the nominal surface. Surfaces of castings rarely need control beyond that provided by the production method necessary to meet dimensional requirements. Comparison specimens are frequently used for evaluating surfaces having specific functional requirements. Surface texture control should not be specified unless required for appearance or function of the surface. Specification of such requirements may increase cost to the user. Engineers should recognize that different areas of the same castings may have different surface textures. It is recommended that specifications of the surface be limited to defined areas of the casting. Practicality of and methods of determining that a casting’s surface texture meets the specification shall be coordinated with the producer. The Society of Automotive Engineers standard J435 “Automotive Steel Castings” describes methods of evaluating steel casting surface texture used in the automotive and related industries. Metric Dimensions on Drawings.—The length units of the metric system that are most generally used in connection with any work relating to mechanical engineering are the meter (39.37 inches) and the millimeter (0.03937 inch). One meter equals 1000 millimeters. On mechanical drawings, all dimensions are generally given in millimeters, no matter how large the dimensions may be. In fact, dimensions of such machines as locomotives and large electrical apparatus are given exclusively in millimeters. This practice is adopted to avoid mistakes due to misplacing decimal points, or misreading dimensions as when other units are used as well. When dimensions are given in millimeters, many of them can be given without resorting to decimal points, as a millimeter is only a little more than 1⁄32 inch. Only dimensions of precision need be given in decimals of a millimeter; such dimensions are generally given in hundredths of a millimeter—for example, 0.02 millimeter,



SURFACE TEXTURE Table 5. Lay Symbols Lay Symbol

Meaning

Example Showing Direction of Tool Marks

Lay approximately parallel to the line representing the surface to which the symbol is applied.

Lay approximately perpendicular to the line representing the surface to which the symbol is applied.

X

Lay angular in both directions to line representing the surface to which the symbol is applied.

M

Lay multidirectional

C

Lay approximately circular relative to the center of the surface to which the symbol is applied.

R

Lay approximately radial relative to the center of the surface to which the symbol is applied.

P

Lay particulate, non-directional, or protuberant

which is equal to 0.0008 inch. As 0.01 millimeter is equal to 0.0004 inch, dimensions are seldom given with greater accuracy than to hundredths of a millimeter. Scales of Metric Drawings: Drawings made to the metric system are not made to scales of 1⁄2, 1⁄4, 1⁄8, etc., as with drawings made to the English system. If the object cannot be drawn full size, it may be drawn 1⁄2, 1⁄5, 1⁄10 , 1⁄20, 1⁄50 , 1⁄100 , 1⁄200 , 1⁄500 , or 1⁄1000 size. If the object is too small and has to be drawn larger, it is drawn 2, 5, or 10 times its actual size.



737

Table 6. Application of Surface Texture Values to Symbol Roughness average rating is placed at the left of the long leg. The specification of only one rating shall indicate the maximum value and any lesser value shall be acceptable. Specify in micrometers (microinch).

Material removal by machining is required to produce the surface. The basic amount of stock provided forf material removal is specified at the left of the short leg of the symbol. Specify in millimeters (inch).

The specification of maximum and minimum roughness average values indicates permissible range of roughness. Specify in micrometers (microinch).

Removal of material is prohibited.

Maximum waviness height rating is the first rating place above the horizontal extension. Any lesser rating shall be acceptable. Specify in millimeters (inch). Maximum waviness spacing rating is the second rating placed above the horizontal extension and to the right of the waviness height rating. Any lesser rating shall be acceptable. Specify in millimeters (inch).

Lay designation is indicated by the lay symbol placed at the right of the long leg. Roughness sampling length or cutoff rating is placed below the horizontal extension. When no value is shown, 0.80 mm (0.030 inch) applies. Specify in millimeters (inch). Where required maximum roughness spacing shall be placed at the right of the lay symbol. Any lesser rating shall be acceptable. Specify in millimeters (inch).

Table 7. Examples of Special Designations

Fig. 9a.

Fig. 9b.

Fig. 9c.



ISO SURFACE FINISH ISO Surface Finish

Differences Between ISO and ANSI Surface Finish Symbology.—ISO surface finish standards are comprised of numerous individual standards that taken as a whole form a set of standards roughly comparable in scope to American National Standard ANSI/ASME Y14.36M. The primary standard dealing with surface finish, ISO 1302:1992, is concerned with the methods of specifying surface texture symbology and additional indications on engineering drawings. The parameters in ISO surface finish standards relate to surfaces produced by abrading, casting, coating, cutting, etching, plastic deformation, sintering, wear, erosion, and some other methods. ISO 1302 defines how surface texture and its constituents, roughness, waviness, and lay, are specified on the symbology. Surface defects are specifically excluded from consideration during inspection of surface texture, but definitions of flaws and imperfections are discussed in ISO 8785. As with American National Standard ASME Y14.36M, ISO 1302 is not concerned with luster, appearance, color, corrosion resistance, wear resistance, hardness, sub-surface microstructure, surface integrity, and many other characteristics that may govern considerations in specific applications. Visually, the ISO surface finish symbol is similar to the ANSI symbol, but the proportions of the symbol in relationship to text height differs from ANSI, as do some of the parameters as described in Fig. 10. Examples of the application of the ISO surface finish symbol are illustrated in Table 10. The ISO 1302 standard does not define the degrees of surface roughness and waviness or type of lay for specific purposes, nor does it specify the means by which any degree of such irregularities may be obtained or produced. Also, errors of form such as out-of-roundness and out-of-flatness are not addressed in the ISO surface finish standards. Other ISO Standards Related To Surface Finish ISO 468:1982

“Surface roughness — parameters. Their values and general rules for specifying requirements.” ISO 4287:1997 “Surface texture: Profile method — Terms, definitions and surface texture parameters.” ISO 4288:1996 “Surface texture: Profile method — Rules and procedures for the assessment of surface texture.” Includes specifications for precision reference specimens, and roughness comparison specimens, and establishes requirements for stylus-type instruments.” ISO 8785:1998 “Surface imperfections — Terms, definitions and parameters.” ISO 10135-1:CD “Representation of parts produced by shaping processes — Part 1: Molded parts.”

Rules for Comparing Measured Values to Specified Limits.—Max rule: When a maximum requirement is specified for a surface finish parameter on a drawing (e.g. Rz1.5max), none of the inspected values may extend beyond the upper limit over the entire surface. MAX must be added to the parametric symbol in the surface finish symbology on the drawing. 16% rule: When upper and lower limits are specified, no more than 16% of all measured values of the selected parameter within the evaluation length may exceed the upper limit. No more than 16% of all measured values of the selected parameter within the evaluation length may be less than the lower limit.


Machinery's Handbook 27th Edition ISO SURFACE FINISH Production method

Roughness value in micrometers preceded by parameter symbol

Basic symbol for surface under consideration or to a specification explained elsewhere in a note

a

Machine allowance

Roughness value other than Ra (micrometers)

b c/f

e Basic symbol for a surface to be machined

739

d Surface pattern

Basic symbol for material removal prohibited and left in the state from a previous manufacturing process

In future versions of 1302, all roughness values will be allowed at location 'a' only Waviness height preceded by parametric symbol or sampling length (millimeters)

a2 x'

c / f1

a1

x

Basic symbol with all round circle added to indicate the surface specification applies to all surfaces in that view

e

Text height h (ISO 3098-1)

d'

b

f2

d

h

2.5

3.5

5

7

10

14

Line width for symbols

d and d'

0.25

0.35

0.5

0.7

1

1.2

2

Height for segment

x

3.5

5

7

10

14

20

28

8

11

15

21

30

42

60

Height for symbol segment

x'

20

Fig. 10. ISO Surface Finish Symbol

ISO Surface Parameter Symbols Rp = max height profile Rv = max profile valley depth Rz* = max height of the profile Rc = mean height of profile Rt = total height of the profile Ra = arithmetic mean deviation of the profile Rq = root mean square deviation of the profile Rsk = skewness of the profile Rku = kurtosis of the profile RSm = mean width of the profile R∆q = root mean square slope of the profile Rmr = material ration of the profile

Rδc = profile section height difference Ip = sampling length – primary profile lw = sampling length – waviness profile lr = sampling length – roughness profile ln = evaluation length Z(x) = ordinate value dZ /dX = local slope Zp = profile peak height Zv = profile valley depth Zt = profile element height Xs = profile element width Ml = material length of profile

Exceptions to the 16% rule: Where the measured values of roughness profiles being inspected follow a normal distribution, the 16% rule may be overridden. This is allowed when greater than 16% of the measured values exceed the upper limit, but the total roughness profile conforms with the sum of the arithmetic mean and standard deviation (µ + σ). Effectively this means that the greater the value of σ, the further µ must be from the upper limit (see Fig. 11). Basic rules for determining cut-off wavelength: When the sampling length is specified on the drawing or in documentation, the cut-off wavelength λc is equal to the sample length. When no sampling length is specified, the cut-off wavelength is estimated using Table 8.



ISO SURFACE FINISH

Upper limit of surface texture parameter

Fig. 11.

Basic rules for measurement of roughness parameters: For non-periodic roughness the parameter Ra, Rz, Rz1max or RSm are first estimated using visual inspection, comparison to specimens, graphic analysis, etc. The sampling length is then selected from Table 8, based on the use of Ra, Rz, Rz1max or RSm. Then with instrumentation, a representative sample is taken using the sampling length chosen above.

Ra, µm

Rz, Rz1max, µm

RSm, µm

Sampling length, lr (mm)

Curves for Periodic and Non-periodic Profiles

Evaluation length, ln (mm)

Table 8. Sampling Lengths Curves for Non-periodic Profiles such as Ground Surfaces

(0.006) < Ra ≤ 0.02

(0.025) < Rz, Rz1max ≤ 0.1

0.013 < RSm ≤ 0.04

0.08

0.4

0.02 < Ra ≤ 0.1

0.1 < Rz, Rz1max ≤ 0.5

0.04 < RSm ≤ 0.13

0.25

1.25

0.1 < Ra ≤ 2

0.5 < Rz, Rz1max ≤ 10

0.13 < RSm ≤ 0.4

0.8

4

2 < Ra ≤ 10

10 < Rz, Rz1max ≤ 50

0.4 < RSm ≤ 1.3

2.5

12.5

10 < Ra ≤ 80

50 < Rz, Rz1max ≤ 200

1.3 < RSm ≤ 4

8

40

For Ra, Rq, Rsk, Rku, R∆q

For Rz, Rv, Rp, Rc, Rt

For R-parameters and RSm

The measured values are then compared to the ranges of values in Table 8 for the particular parameter. If the value is outside the range of values for the estimated sampling length, the measuring instrument is adjusted for the next higher or lower sampling length and the measurement repeated. If the final setting corresponds to Table 8, then both the sampling length setting and Ra, Rz, Rz1max or RSm values are correct and a representative measurement of the parameter can be taken. For periodic roughness, the parameter RSm is estimated graphically and the recommended cut-off values selected using Table 8. If the value is outside the range of values for the estimated sampling length, the measuring instrument is adjusted for the next higher or lower sampling length and the measurement repeated. If the final setting corresponds to Table 8, then both the sampling length setting and RSm values are correct and a representative measurement of the parameter can be taken. Table 9. Preferred Roughness Values and Roughness Grades Roughness values, Ra µm µin 50 25 12.5 6.3 3.2 1.6

2000 1000 500 250 125 63

Previous Grade Number from ISO 1302 N12 N11 N10 N9 N8 N7

Roughness values, Ra µm µin 0.8 0.4 0.2 0.1 0.05 0.025

Previous Grade Number from ISO 1302

32 16 8 4 2 1


N6 N5 N4 N3 N2 N1

Machinery's Handbook 27th Edition ISO SURFACE FINISH

741

Table 10. Examples of ISO Applications of Surface Texture Symbology Interpretation

Example

Surface roughness is produced by milling and between upper limit of Ra = 50 µm and Ra = 6.3 µm; direction of lay is crossed in oblique directions relative to plane of projection; sampling length is 5 mm. Surface roughness of Rz = 6.3 µm is the default for all surfaces as indicated by the Rz = 6.3 specification, plus basic symbol within parentheses. Any deviating specification is called out with local notes such as the Ra = 0.8 µm specification. Surface roughness is produced by grinding to Ra = 1.2 µm and limited to Ry = 6.3 µm max; direction of lay is perpendicular relative to the plane of projection; sampling length is 2.4 mm.

Ra 50 Ra 6.3

5 X

Rz 6.3

( )

Ra 0.8

ground Ra 1.2

2.4/Ry 6.3 MAX

Fe/Ni20pCr

Surface treatment without any machining; nickel-chrome plated to Rz = 1 µm on all surfaces.

Rz 1

Fe/Ni10bCr 0,8 2,5/Rz 16 2,5/Rz 6.3

Ra 3.2

R3

Surface is nickel-chrome plated to roughness of Ra = 3.2 µm with a sampling length of 0.8 mm; limited to Rz = 16 µm to Rz = 6.3 µm with a sampling length of 2.5 mm.

milled

Ra 1.6

Ra 0.8

Surface roughness of Rz = 6.3 µm is the default for all surfaces except the inside diameter which is Ra = 0.8 mm.

Surface texture symbology may be combined with dimension leaders and witness (extension) lines.

Ra 0.8 2x45˚



ISO SURFACE FINISH

Table 10. (Continued) Examples of ISO Applications of Surface Texture Symbology Interpretation

Example

Ra 1. 6

Ra

Rz 4.0

R3

43

45

Surface texture symbology may be applied to extended extension lines or on extended projection lines.

0.8

Rz 40

Surface roughness is produced by milling and between upper limit of Ra = 50 µm and Ra = 6.3 µm; direction of lay is crossed in oblique directions relative to plane of projection; sampling length is 5 mm.

3x Ø5

Ground Fe/Cr 50 Ry 6.2 Ry 1.6

Ø45

Surface treatment without any machining; nickel-chrome plated to Rz = 1 µm on all surfaces.

30 Chromium plated

a2 Surface texture characteristics may be specified both before and after surface treatment.

Ø

Built-up surface The symbol may be expanded with additional lines for textual information where there is insufficient room on the drawing.

a1

Ground


Machinery's Handbook 27th Edition PRECISION GAGE BLOCKS

743

Gage Blocks Precision Gage Blocks.—Precision gage blocks are usually purchased in sets comprising a specific number of blocks of different sizes. The nominal gage lengths of individual blocks in a set are determined mathematically so that particular desired lengths can be obtained by combining selected blocks. They are made to several different tolerance grades which categorize them as master blocks, calibration blocks, inspection blocks, and workshop blocks. Master blocks are employed as basic reference standards; calibration blocks are used for high precision gaging work and calibrating inspection blocks; inspection blocks are used as toolroom standards and for checking and setting limit and comparator gages, for example. The workshop blocks are working gages used as shop standards for a variety of direct precision measurements and gaging applications, including sine-bar settings. Federal Specification GGG-G-15C, Gage Blocks (see below), lists typical sets, and gives details of materials, design, and manufacturing requirements, and tolerance grades. When there is in a set no single block of the exact size that is wanted, two or more blocks are combined by “wringing” them together. Wringing is achieved by first placing one block crosswise on the other and applying some pressure. Then a swiveling motion is used to twist the blocks to a parallel position, causing them to adhere firmly to one another. When combining blocks for a given dimension, the object is to use as few blocks as possible to obtain the dimension. The procedure for selecting blocks is based on successively eliminating the right-hand figure of the desired dimension. Example:Referring to gage block set number 1 in Table 1, determine the blocks required to obtain 3.6742 inches. Step 1: Eliminate 0.0002 by selecting a 0.1002 block. Subtract 0.1002 from 3.6743 = 3.5740. Step 2: Eliminate 0.004 by selecting a 0.124 block. Subtract 0.124 from 3.5740 = 3.450. Step 3: Eliminate 0.450 with a block this size. Subtract 0.450 from 3.450 = 3.000. Step 4: Select a 3.000 inch block. The combined blocks are 0.1002 + 0.124 + 0.450 + 3.000 = 3.6742 inches. Federal Specification for Gage Blocks, Inch and Metric Sizes.—This Specification, GGG-G-15C, March 20, 1975, which supersedes GGG-G-15B, November 6, 1970, covers design, manufacturing, and purchasing details for precision gage blocks in inch and metric sizes up to and including 20 inches and 500 millimeters gage lengths. The shapes of blocks are designated Style 1, which is rectangular; Style 2, which is square with a center accessory hole, and Style 3, which defines other shapes as may be specified by the purchaser. Blocks may be made from steel, chromium-plated steel, chromium carbide, or tungsten carbide. There are four tolerance grades, which are designated Grade 0.5 (formerly Grade AAA in the GGG-G-15A issue of the Specification); Grade 1 (formerly Grade AA); Grade 2 (formerly Grade A +); and Grade 3 (a compromise between former Grades A and B). Grade 0.5 blocks are special reference gages used for extremely high precision gaging work, and are not recommended for general use. Grade 1 blocks are laboratory reference standards used for calibrating inspection gage blocks and high precision gaging work. Grade 2 blocks are used as inspection and toolroom standards, and Grade 3 blocks are used as shop standards. Inch and metric sizes of blocks in specific sets are given in Tables 1 and 2, which is not a complete list of available sizes. It should be noted that some gage blocks must be ordered as specials, some may not be available in all materials, and some may not be available from all manufacturers. Gage block set number 4 (88 blocks), listed in the Specification, is not given in Table 1. It is the same as set number 1 (81 blocks) but contains seven additional blocks measuring 0.0625, 0.078125, 0.093750, 0.100025, 0.100050, 0.100075, and 0.109375 inch. In Table 2, gage block set number 3M (112 blocks) is not given. It is similar to set number 2M (88 blocks), and the chief difference is the inclusion of a larger number of blocks in the 0.5 millimeter increment series up to 24.5 mm. Set numbers 5M (88 blocks), 6M (112 blocks), and 7M (17 blocks) also are not listed.



PRECISION GAGE BLOCKS Table 1. Gage Block Sets—Inch Sizes Federal Specification GGG-G-15C Set Number 1 (81 Blocks)

.1001

First Series: 0.0001 Inch Increments (9 Blocks) .1003 .1004 .1005 .1006 .1007

.1002

.101 .111 .121 .131 .141

.102 .112 .122 .132 .142

.103 .113 .123 .133 .143

.050 .550

.100 .600

.150 .650

Second Series: 0.001 Inch Increments (49 Blocks) .104 .105 .106 .107 .114 .115 .116 .117 .124 .125 .126 .127 .134 .135 .136 .137 .144 .145 .146 .147 Third Series: 0.050 Inch Increments (19 Blocks) .200 .250 .300 .350 .700 .750 .800 .850

.1008

.1009

.108 .118 .128 .138 .148

.109 .119 .129 .139 .149

.110 .120 .130 .140

.400 .900

.450 .950

.500

Fourth Series: 1.000 Inch Increments (4 Blocks) 2.000 3.000

1.000

4.000

Set Number 5 (21 Blocks) .0101


.0102

.010

.011

Second Series: 0.001 Inch Increments (11 Blocks) .013 .014 .015 .016 .017 One Block 0.01005 Inch

.012

.0108 .018

.0109

.019

.020

Set Number 6 (28 Blocks) .0201

.0202

.021

.022

.010

.020

First Series: 0.0001 Inch Increments (9 Blocks) .0203 .0204 .0205 .0206 .0207 Second Series: 0.001 Inch Increments (9 Blocks) .023 .024 .025 .026 .027 Third Series: 0.010 Inch Increments (9 Blocks) .030 .040 .050 .060 .070 One Block 0.02005 Inch

.0208

.0209

.028

.029

.080

.090

Long Gage Block Set Number 7 (8 Blocks) 5

6

7

Whole Inch Series (8 Blocks) 8 10 12

16

20

Set Number 8 (36 Blocks) .1001 .100 .120


.1002 .101

.102 .130

Second Series: 0.001 Inch Increments (11 Blocks) .103 .104 .105 .106 .107

.1008 .108

Third Series: 0.010 Inch Increments (8 Blocks) .140 .150 .160 .170

.109

.180

Fourth Series: 0.100 Inch Increments (4 Blocks) .300 .400

.200 1

Whole Inch Series (3 Blocks) 2 One Block 0.050 Inch

.1009 .110 .190

.500 4

Set Number 9 (20 Blocks) .0501 .050

.0502 .051

First Series: 0.0001 Inch Increments (9 Blocks) .0503 .0504 .0505 .0506 .0507 Second Series: 0.001 Inch Increments (10 Blocks) .052 .053 .054 .055 .056 .057 One Block 0.05005 Inch

.0508

.0509

.058

.059

Set number 4 is not shown, and the Specification does not list a set 2 or 3. Arranged here in incremental series for convenience of use.


Machinery's Handbook 27th Edition PRECISION GAGE BLOCKS

745

Table 2. Gage Block Sets—Metric Sizes Federal Specification GGG-G-15C Set Number 1M (45 Blocks) First Series: 0.001 Millimeter Increments (9 Blocks) 1.001

1.002

1.003

1.004

1.005

1.006

1.007

1.008

1.009

1.08

1.09

1.80

1.90

7.0

8.0

9.0

70

80

90

1.008

1.009

Second Series: 0.01 Millimeter Increments (9 Blocks) 1.01

1.02

1.03

1.04

1.05

1.06

1.07

Third Series: 0.10 Millimeter Increments (9 Blocks) 1.10

1.20

1.30

1.40

1.50

1.60

1.70

Fourth Series: 1.0 Millimeter Increments (9 Blocks) 1.0

2.0

3.0

4.0

5.0

6.0

Fifth Series: 10 Millimeter Increments (9 Blocks) 10

20

30

40

50

60

Set Number 2M (88 Blocks) First Series: 0.001 Millimeter Increments (9 Blocks) 1.001

1.002

1.003

1.004

1.005

1.006

1.007


1.02

1.03

1.04

1.05

1.06

1.07

1.08

1.09

1.10

1.11

1.12

1.13

1.14

1.15

1.16

1.17

1.18

1.19

1.20

1.21

1.22

1.23

1.24

1.25

1.26

1.27

1.28

1.29

1.30

1.31

1.32

1.33

1.34

1.35

1.36

1.37

1.38

1.39

1.40

1.41

1.42

1.43

1.44

1.45

1.46

1.47

1.48

1.49

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.5

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10

20

30

80

90


Fourth Series: 10 Millimeter Increments (10 Blocks) 40

50

60

70

100

One Block 1.0005 mm Set Number 4M (45 Blocks) First Series: 0.001 Millimeter Increments (9 Blocks) 2.001

2.002

2.003

2.004

2.005

2.006

2.007

2.008

2.009

2.08

2.09

2.7

2.8

2.9

7.0

8.0

9.0

70

80

90


2.02

2.03

2.04

2.05

2.06

2.07


2.2

2.3

2.4

2.5

2.6

Fourth Series: 1 Millimeter Increments (9 Blocks) 1.0

2.0

3.0

4.0

5.0

6.0

Fifth Series: 10 Millimeter Increments (9 Blocks) 10

20

30

40

50

60

Long Gage Block Set Number 8M (8 Blocks) Whole Millimeter Series (8 Blocks) 125

150

175

200

250

300

400

500

Set numbers 3M, 5M, 6M, and 7M are not listed. Arranged here in incremental series for convenience of use. Note: Gage blocks measuring 1.09 millimeters and under in set number 1M, blocks measuring 1.5 millimeters and under in set number 2M, and block measuring 1.0 millimeter in set number 4M are not available in tolerance grade 0.5.


Machinery's Handbook 27th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING CUTTING TOOLS

FORMING TOOLS (Continued)

749 Terms and Definitions 749 Tool Contour 752 Relief Angles 753 Rake Angles 754 Nose Radius 755 Chipbreakers 756 Planing Tools 756 Indexable Inserts 757 Identification System 758 Indexable Insert Tool Holders 759 Standard Shank Sizes 760 Letter Symbols 761 Indexable Insert Holders 764 Sintered Carbide Tools 764 Sintered Carbide Blanks 764 Single Point Tools 764 Single-Point, Sintered-CarbideTipped Tools 767 Tool Nose Radii 767 Tool Angle Tolerances 767 Carbide Tipped Tools 767 Style A 768 Style B 769 Style C 769 Style D 770 Style E 770 Styles ER and EL 771 Style F 772 Style G

Constants for Diameters Corrected Diameters Arrangement of Circular Tools Circular Cut-Off Tools

796 796 797 798 799 800

Selection of Milling Cutters Number of Teeth Hand of Milling Cutters Plain Milling Cutters Side Milling Cutters Staggered Teeth,T-Slot Milling Cutters Metal Slitting Saws Milling Cutter Terms Shell Mills Multiple- and Two-Flute SingleEnd Helical End Mills Regular-, Long-, and Extra LongLength, Mills Two-Flute, High Helix, Regular-, Long-, and Extra Long-Length, Mills Roughing, Single-End End Mills Concave, Convex, and CornerRounding Arbor-Type Cutters Roller Chain Sprocket Keys and Keyways Woodruff Keyseat Cutters Spline-Shaft Milling Cutter Cutter Grinding Wheel Speeds and Feeds Clearance Angles Rake Angles for Milling Cutters Eccentric Type Radial Relief Indicator Drop Method Relieving Attachments Distance to Set Tooth

MILLING CUTTERS

801 801 803 804 805 806 807 815

CEMENTED CARBIDES 773 Cemented Carbide 773 Carbides and Carbonitrides 774 Properties of Tungsten-CarbideBased Cutting-Tool 778 ISO Classifications of Hardmetals 778 Ceramics 781 Superhard Materials 782 Machining Data 783 Hardmetal Tooling 783 Cutting Blades

FORMING TOOLS 784 784 787 788 789

789 789 794 795

Dovetail Forming Tools Straight Forming Tools Circular Forming Tools Circular Forming Tools Formula Top Rake

817 819 820 824 824 825 825 826 826 829 830 831

REAMERS 832 833 833 833 835 835

Hand Reamers Irregular Tooth Spacing in Reamers Threaded-end Hand Reamers Fluted and Rose Chucking Reamers Vertical Adjustment of Tooth-rest Reamer Terms and Definitions

746


Machinery's Handbook 27th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING REAMERS

TAPS AND THREADING DIES

(Continued)

839 839 840 842 843 844 845 846 849 851 852

Direction of Rotation and Helix Dimensions of Centers Reamer Difficulties Expansion Chucking Reamers Hand Reamers Expansion Hand Reamers Driving Slots and Lugs Chucking Reamers Shell Reamers Center Reamers Taper Pipe Reamers

892 Taps 892 Types of Taps 892 Definitions of Tap Terms 896 Fraction-Size Taps 898 Machine Screw Taps 899 Ground Thread Limits 900 Taper Pipe Taps 901 Straight Pipe Taps 903 Straight Fluted Taps 905 Spiral-Pointed Taps 910 ANSI Standard Taps 911 Pulley Taps 911 Spark Plug Taps 913 Spiral Pointed Ground Thread Taps 914 Taper and Straight Pipe Taps 916 Thread Series Designations 917 Pitch Diameter Tolerance 917 Eccentricity Tolerances 919 Acme and Square-Threaded Taps 919 Acme Threads Taps 921 Proportions 921 Drill Hole Sizes for Acme Threads 922 Screwing Taps for ISO Metric Threads 925 Tapping Square Threads

TWIST DRILLS AND COUNTERBORES 854 855 875 876 877 878 878 878 879 880 881 882 884 884 884 885 886 886 887 887 889 890 891 891

Definitions of Twist Drill Terms Types of Drills Split-Sleeve, Collet Type Drill Drivers Three- and Four-Flute Straight Shank Core Drills Twist Drills and Centering Tools British Standard Combined Drills Drill Drivers British Standard Metric Twist Drills Gauge and Letter Sizes Morse Taper Shank Twist Drills Tolerance on Diameter Parallel Shank Jobber Series Twist Drills Stub Drills Steels for Twist Drills Accuracy of Drilled Holes Counterboring Interchangeable Cutters Three Piece Counterbores Sintered Carbide Boring Tools Style Designations Square Boring Tools Carbide-Tipped Square Boring Tools Solid Carbide Round Boring Tools Boring Machines, Origin

STANDARD TAPERS 926 Standard Tapers 926 Morse Taper 926 Brown & Sharpe Taper 926 Jarno Taper 934 British Standard Tapers 935 Morse Taper Sleeves 936 Brown & Sharpe Taper Shank 937 Jarno Taper Shanks 937 Machine Tool Spindles 938 Plug and Ring Gages 939 Jacobs Tapers and Threads 940 Spindle Noses 942 Tool Shanks 943 Draw-in Bolt Ends 944 Spindle Nose 945 Collets 945 Collets for Lathes, Mills, Grinders, and Fixtures

747


Machinery's Handbook 27th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING ARBORS, CHUCKS, AND SPINDLES

TOOL WEAR AND SHARPENING

948 Portable Tool Spindles 948 Circular Saw Arbors 948 Spindles for Geared Chucks 948 Spindle Sizes 948 Straight Grinding Wheel Spindles 949 Square Drives for Portable Air 950 Threaded and Tapered Spindles 950 Abrasion Tool Spindles 951 Hexagonal Chucks for Portable Air 952 Mounted Wheels and Points 954 Shapes of Mounted Wheels and Points

BROACHES AND BROACHING

973

Sharpening Twist Drills Relief Grinding of the Tool Flanks Drill Point Thinning Sharpening Carbide Tools Silicon Carbide Wheels Diamond Wheels Diamond Wheel Grit Sizes Diamond Wheel Grades Diamond Concentration Dry Versus Wet Grinding of Carbide Tools Coolants for Carbide Tool Grinding Peripheral Versus Flat Side Grinding Lapping Carbide Tools Chip Breaker Grinding Summary of Miscellaneous Points

JIGS AND FIXTURES 975 Jig Bushings 975 Materials 975 American National Standard 976 Head Type Press Fit Wearing Bushings 979 Specifications for Press Fit Wearing Bushings 979 Slip Type Renewable Wearing Bushings 981 Fixed Type Renewable Wearing Bushings 982 Headless Type Liner Bushings 984 Locking Mechanisms 985 Jig Bushing Definitions 985 Jig Plate Thickness 985 Jig Bushing Designation System 985 Jig Boring 985 Definition of Jig and Fixture 985 Jig Borers 986 Jig-Boring Practice 987 Transfer of Tolerances 989 Determining Hole Coordinates 989 Hole Coordinate Dimension Factors 991 Spacing Off the Circumferences of Circles 993 Hole Coordinate Tables

FILES AND BURS

966

973

974 974 974

955 The Broaching Process 955 Types of Broaches 956 Pitch of Broach Teeth 957 Designing Data for Surface Broaches 957 Broaching Pressure 958 Depth of Cut per Tooth 959 Face Angle or Rake 959 Clearance Angle 959 Land Width 959 Depth of Broach Teeth 959 Radius of Tooth Fillet 959 Total Length of Broach 959 Chip Breakers 960 Shear Angle 960 Types of Broaching Machines 960 Ball-Broaching 961 Broaching Difficulties

962 963 963 965

969 969 970 971 971 972 972 972 972 973

Definitions of File Terms File Characteristics Classes of Files Effectiveness of Rotary Files and Burs Speeds of Rotary Files and Burs

748


Machinery's Handbook 27th Edition TOOLING AND TOOLMAKING

749

CUTTING TOOLS Terms and Definitions Tool Contour.—Tools for turning, planing, etc., are made in straight, bent, offset, and other forms to place the cutting edges in convenient positions for operating on differently located surfaces. The contour or shape of the cutting edge may also be varied to suit different classes of work. Tool shapes, however, are not only related to the kind of operation, but, in roughing tools particularly, the contour may have a decided effect upon the cutting efficiency of the tool. To illustrate, an increase in the side cutting-edge angle of a roughing tool, or in the nose radius, tends to permit higher cutting speeds because the chip will be thinner for a given feed rate. Such changes, however, may result in chattering or vibrations unless the work and the machine are rigid; hence, the most desirable contour may be a compromise between the ideal form and one that is needed to meet practical requirements. Terms and Definitions.—The terms and definitions relating to single-point tools vary somewhat in different plants, but the following are in general use.

Fig. 1. Terms Applied to Single-point Turning Tools

Single-point Tool: This term is applied to tools for turning, planing, boring, etc., which have a cutting edge at one end. This cutting edge may be formed on one end of a solid piece of steel, or the cutting part of the tool may consist of an insert or tip which is held to the body of the tool by brazing, welding, or mechanical means. Shank: The shank is the main body of the tool. If the tool is an inserted cutter type, the shank supports the cutter or bit. (See diagram, Fig. 1.) Nose: A general term sometimes used to designate the cutting end but usually relating more particularly to the rounded tip of the cutting end. Face: The surface against which the chips bear, as they are severed in turning or planing operations, is called the face. Flank: The flank is that end surface adjacent to the cutting edge and below it when the tool is in a horizontal position as for turning. Base: The base is the surface of the tool shank that bears against the supporting toolholder or block. Side Cutting Edge: The side cutting edge is the cutting edge on the side of the tool. Tools such as shown in Fig. 1 do the bulk of the cutting with this cutting edge and are, therefore, sometimes called side cutting edge tools. End Cutting Edge: The end cutting edge is the cutting edge at the end of the tool. On side cutting edge tools, the end cutting edge can be used for light plunging and facing cuts. Cutoff tools and similar tools have only one cutting edge located on the end. These



CUTTING TOOLS

tools and other tools that are intended to cut primarily with the end cutting edge are sometimes called end cutting edge tools. Rake: A metal-cutting tool is said to have rake when the tool face or surface against which the chips bear as they are being severed, is inclined for the purpose of either increasing or diminishing the keenness or bluntness of the edge. The magnitude of the rake is most conveniently measured by two angles called the back rake angle and the side rake angle. The tool shown in Fig. 1 has rake. If the face of the tool did not incline but was parallel to the base, there would be no rake; the rake angles would be zero. Positive Rake: If the inclination of the tool face is such as to make the cutting edge keener or more acute than when the rake angle is zero, the rake angle is defined as positive. Negative Rake: If the inclination of the tool face makes the cutting edge less keen or more blunt than when the rake angle is zero, the rake is defined as negative. Back Rake: The back rake is the inclination of the face toward or away from the end or the end cutting edge of the tool. When the inclination is away from the end cutting edge, as shown in Fig. 1, the back rake is positive. If the inclination is downward toward the end cutting edge the back rake is negative. Side Rake: The side rake is the inclination of the face toward or away from the side cutting edge. When the inclination is away from the side cutting edge, as shown in Fig. 1, the side rake is positive. If the inclination is toward the side cutting edge the side rake is negative. Relief: The flanks below the side cutting edge and the end cutting edge must be relieved to allow these cutting edges to penetrate into the workpiece when taking a cut. If the flanks are not provided with relief, the cutting edges will rub against the workpiece and be unable to penetrate in order to form the chip. Relief is also provided below the nose of the tool to allow it to penetrate into the workpiece. The relief at the nose is usually a blend of the side relief and the end relief. End Relief Angle: The end relief angle is a measure of the relief below the end cutting edge. Side Relief Angle: The side relief angle is a measure of the relief below the side cutting edge. Back Rake Angle: The back rake angle is a measure of the back rake. It is measured in a plane that passes through the side cutting edge and is perpendicular to the base. Thus, the back rake angle can be defined by measuring the inclination of the side cutting edge with respect to a line or plane that is parallel to the base. The back rake angle may be positive, negative, or zero depending upon the magnitude and direction of the back rake. Side Rake Angle: The side rake angle is a measure of the side rake. This angle is always measured in a plane that is perpendicular to the side cutting edge and perpendicular to the base. Thus, the side rake angle is the angle of inclination of the face perpendicular to the side cutting edge with reference to a line or a plane that is parallel to the base. End Cutting Edge Angle: The end cutting edge angle is the angle made by the end cutting edge with respect to a plane perpendicular to the axis of the tool shank. It is provided to allow the end cutting edge to clear the finish machined surface on the workpiece. Side Cutting Edge Angle: The side cutting edge angle is the angle made by the side cutting edge and a plane that is parallel to the side of the shank. Nose Radius: The nose radius is the radius of the nose of the tool. The performance of the tool, in part, is influenced by nose radius so that it must be carefully controlled. Lead Angle: The lead angle, shown in Fig. 2, is not ground on the tool. It is a tool setting angle which has a great influence on the performance of the tool. The lead angle is bounded by the side cutting edge and a plane perpendicular to the workpiece surface when the tool is in position to cut; or, more exactly, the lead angle is the angle between the side cutting edge and a plane perpendicular to the direction of the feed travel.


Machinery's Handbook 27th Edition CUTTING TOOLS

751

Fig. 2. Lead Angle on Single-point Turning Tool

Solid Tool: A solid tool is a cutting tool made from one piece of tool material. Brazed Tool: A brazed tool is a cutting tool having a blank of cutting-tool material permanently brazed to a steel shank. Blank: A blank is an unground piece of cutting-tool material from which a brazed tool is made. Tool Bit: A tool bit is a relatively small cutting tool that is clamped in a holder in such a way that it can readily be removed and replaced. It is intended primarily to be reground when dull and not indexed. Tool-bit Blank: The tool-bit blank is an unground piece of cutting-tool material from which a tool bit can be made by grinding. It is available in standard sizes and shapes. Tool-bit Holder: Usually made from forged steel, the tool-bit holder is used to hold the tool bit, to act as an extended shank for the tool bit, and to provide a means for clamping in the tool post. Straight-shank Tool-bit Holder: A straight-shank tool-bit holder has a straight shank when viewed from the top. The axis of the tool bit is held parallel to the axis of the shank. Offset-shank Tool-bit Holder: An offset-shank tool-bit holder has the shank bent to the right or left, as seen in Fig. 3. The axis of the tool bit is held at an angle with respect to the axis of the shank. Side cutting Tool: A side cutting tool has its major cutting edge on the side of the cutting part of the tool. The major cutting edge may be parallel or at an angle with respect to the axis of the tool. Indexable Inserts: An indexable insert is a relatively small piece of cutting-tool material that is geometrically shaped to have two or several cutting edges that are used until dull. The insert is then indexed on the holder to apply a sharp cutting edge. When all the cutting edges have been dulled, the insert is discarded. The insert is held in a pocket or against other locating surfaces on an indexable insert holder by means of a mechanical clamping device that can be tightened or loosened easily. Indexable Insert Holder: Made of steel, an indexable insert holder is used to hold indexable inserts. It is equipped with a mechanical clamping device that holds the inserts firmly in a pocket or against other seating surfaces. Straight-shank Indexable Insert Holder: A straight-shank indexable insert tool-holder is essentially straight when viewed from the top, although the cutting edge of the insert may be oriented parallel, or at an angle to, the axis of the holder. Offset-shank Indexable Insert Holder: An offset-shank indexable insert holder has the head end, or the end containing the insert pocket, offset to the right or left, as shown in Fig. 3.



CUTTING TOOLS

Fig. 3. Top: Right-hand Offset-shank, Indexable Insert Holder Bottom: Right-hand Offset-shank Tool-bit Holder

End cutting Tool: An end cutting tool has its major cutting edge on the end of the cutting part of the tool. The major cutting edge may be perpendicular or at an angle, with respect to the axis of the tool. Curved Cutting-edge Tool: A curved cutting-edge tool has a continuously variable side cutting edge angle. The cutting edge is usually in the form of a smooth, continuous curve along its entire length, or along a large portion of its length. Right-hand Tool: A right-hand tool has the major, or working, cutting edge on the righthand side when viewed from the cutting end with the face up. As used in a lathe, such a tool is usually fed into the work from right to left, when viewed from the shank end. Left-hand Tool: A left-hand tool has the major or working cutting edge on the left-hand side when viewed from the cutting end with the face up. As used in a lathe, the tool is usually fed into the work from left to right, when viewed from the shank end. Neutral-hand Tool: A neutral-hand tool is a tool to cut either left to right or right to left; or the cut may be parallel to the axis of the shank as when plunge cutting. Chipbreaker: A groove formed in or on a shoulder on the face of a turning tool back of the cutting edge to break up the chips and prevent the formation of long,continuous chips which would be dangerous to the operator and also bulky and cumbersome to handle. A chipbreaker of the shoulder type may be formed directly on the tool face or it may consist of a separate piece that is held either by brazing or by clamping. Relief Angles.—The end relief angle and the side relief angle on single-point cutting tools are usually, though not invariably, made equal to each other. The relief angle under the nose of the tool is a blend of the side and end relief angles. The size of the relief angles has a pronounced effect on the performance of the cutting tool. If the relief angles are too large, the cutting edge will be weakened and in danger of breaking when a heavy cutting load is placed on it by a hard and tough material. On finish cuts, rapid wear of the cutting edge may cause problems with size control on the part. Relief angles that are too small will cause the rate of wear on the flank of the tool below the cutting edge to increase, thereby significantly reducing the tool life. In general, when cutting hard and tough materials, the relief angles should be 6 to 8 degrees for high-speed steel tools and 5 to 7 degrees for carbide tools. For medium steels, mild steels, cast iron, and other average work the recommended values of the relief angles are 8 to 12 degrees for high-speed steel tools and 5 to 10 degrees for carbides. Ductile materials having a relatively low modulus of elasticity should be cut using larger relief angles. For example, the relief angles recommended for turning copper, brass, bronze, aluminum, ferritic malleable



753

iron, and similar metals are 12 to 16 degrees for high-speed steel tools and 8 to 14 degrees for carbides. Larger relief angles generally tend to produce a better finish on the finish machined surface because less surface of the worn flank of the tool rubs against the workpiece. For this reason, single-point thread-cutting tools should be provided with relief angles that are as large as circumstances will permit. Problems encountered when machining stainless steel may be overcome by increasing the size of the relief angle. The relief angles used should never be smaller than necessary. Rake Angles.—Machinability tests have confirmed that when the rake angle along which the chip slides, called the true rake angle, is made larger in the positive direction, the cutting force and the cutting temperature will decrease. Also, the tool life for a given cutting speed will increase with increases in the true rake angle up to an optimum value, after which it will decrease again. For turning tools which cut primarily with the side cutting edge, the true rake angle corresponds rather closely with the side rake angle except when taking shallow cuts. Increasing the side rake angle in the positive direction lowers the cutting force and the cutting temperature, while at the same time it results in a longer tool life or a higher permissible cutting speed up to an optimum value of the side rake angle. After the optimum value is exceeded, the cutting force and the cutting temperature will continue to drop; however, the tool life and the permissible cutting speed will decrease. As an approximation, the magnitude of the cutting force will decrease about one per cent per degree increase in the side rake angle. While not exact, this rule of thumb does correspond approximately to test results and can be used to make rough estimates. Of course, the cutting force also increases about one per cent per degree decrease in the side rake angle. The limiting value of the side rake angle for optimum tool life or cutting speed depends upon the work material and the cutting tool material. In general, lower values can be used for hard and tough work materials. Cemented carbides are harder and more brittle than high-speed steel; therefore, the rake angles usually used for cemented carbides are less positive than for high-speed steel. Negative rake angles cause the face of the tool to slope in the opposite direction from positive rake angles and, as might be expected, they have an opposite effect. For side cutting edge tools, increasing the side rake angle in a negative direction will result in an increase in the cutting force and an increase in the cutting temperature of approximately one per cent per degree change in rake angle. For example, if the side rake angle is changed from 5 degrees positive to 5 degrees negative, the cutting force will be about 10 per cent larger. Usually the tool life will also decrease when negative side rake angles are used, although the tool life will sometimes increase when the negative rake angle is not too large and when a fast cutting speed is used. Negative side rake angles are usually used in combination with negative back rake angles on single-point cutting tools. The negative rake angles strengthen the cutting edges enabling them to sustain heavier cutting loads and shock loads. They are recommended for turning very hard materials and for heavy interrupted cuts. There is also an economic advantage in favor of using negative rake indexable inserts and tool holders inasmuch as the cutting edges provided on both the top and bottom of the insert can be used. On turning tools that cut primarily with the side cutting edge, the effect of the back rake angle alone is much less than the effect of the side rake angle although the direction of the change in cutting force, cutting temperature, and tool life is the same. The effect that the back rake angle has can be ignored unless, of course, extremely large changes in this angle are made. A positive back rake angle does improve the performance of the nose of the tool somewhat and is helpful in taking light finishing cuts. A negative back rake angle strengthens the nose of the tool and is helpful when interrupted cuts are taken. The back rake angle has a very significant effect on the performance of end cutting edge tools, such as cut-off tools. For these tools, the effect of the back rake angle is very similar to the effect of the side rake angle on side cutting edge tools.



CUTTING TOOLS

Side Cutting Edge and Lead Angles.—These angles are considered together because the side cutting edge angle is usually designed to provide the desired lead angle when the tool is being used. The side cutting edge angle and the lead angle will be equal when the shank of the cutting tool is positioned perpendicular to the workpiece, or, more correctly, perpendicular to the direction of the feed. When the shank is not perpendicular, the lead angle is determined by the side cutting edge and an imaginary line perpendicular to the feed direction. The flow of the chips over the face of the tool is approximately perpendicular to the side cutting edge except when shallow cuts are taken. The thickness of the undeformed chip is measured perpendicular to the side cutting edge. As the lead angle is increased, the length of chip in contact with the side cutting edge is increased, and the chip will become longer and thinner. This effect is the same as increasing the depth of cut and decreasing the feed, although the actual depth of cut and feed remain the same and the same amount of metal is removed. The effect of lengthening and thinning the chip by increasing the lead angle is very beneficial as it increases the tool life for a given cutting speed or that speed can be increased. Increasing the cutting speed while the feed and the tool life remain the same leads to faster production. However, an adverse effect must be considered. Chatter can be caused by a cutting edge that is oriented at a high lead angle when turning and sometimes, when turning long and slender shafts, even a small lead angle can cause chatter. In fact, an unsuitable lead angle of the side cutting edge is one of the principal causes of chatter. When chatter occurs, often simply reducing the lead angle will cure it. Sometimes, very long and slender shafts can be turned successfully with a tool having a zero degree lead angle (and having a small nose radius). Boring bars, being usually somewhat long and slender, are also susceptible to chatter if a large lead angle is used. The lead angle for boring bars should be kept small, and for very long and slender boring bars a zero degree lead angle is recommended. It is impossible to provide a rule that will determine when chatter caused by a lead angle will occur and when it will not. In making a judgment, the first consideration is the length to diameter ratio of the part to be turned, or of the boring bar. Then the method of holding the workpiece must be considered — a part that is firmly held is less apt to chatter. Finally, the overall condition and rigidity of the machine must be considered because they may be the real cause of chatter. Although chatter can be a problem, the advantages gained from high lead angles are such that the lead angle should be as large as possible at all times. End Cutting Edge Angle.—The size of the end cutting edge angle is important when tool wear by cratering occurs. Frequently, the crater will enlarge until it breaks through the end cutting edge just behind the nose, and tool failure follows shortly. Reducing the size of the end cutting edge angle tends to delay the time of crater breakthrough. When cratering takes place, the recommended end cutting edge angle is 8 to 15 degrees. If there is no cratering, the angle can be made larger. Larger end cutting edge angles may be required to enable profile turning tools to plunge into the work without interference from the end cutting edge. Nose Radius.—The tool nose is a very critical part of the cutting edge since it cuts the finished surface on the workpiece. If the nose is made to a sharp point, the finish machined surface will usually be unacceptable and the life of the tool will be short. Thus, a nose radius is required to obtain an acceptable surface finish and tool life. The surface finish obtained is determined by the feed rate and by the nose radius if other factors such as the work material, the cutting speed, and cutting fluids are not considered. A large nose radius will give a better surface finish and will permit a faster feed rate to be used. Machinability tests have demonstrated that increasing the nose radius will also improve the tool life or allow a faster cutting speed to be used. For example, high-speed steel tools were used to turn an alloy steel in one series of tests where complete or catastrophic tool failure was used as a criterion for the end of tool life. The cutting speed for a 60-minute tool



755

life was found to be 125 fpm when the nose radius was 1⁄16 inch and 160 fpm when the nose radius was 1⁄4 inch. A very large nose radius can often be used but a limit is sometimes imposed because the tendency for chatter to occur is increased as the nose radius is made larger. A nose radius that is too large can cause chatter and when it does, a smaller nose radius must be used on the tool. It is always good practice to make the nose radius as large as is compatible with the operation being performed. Chipbreakers.—Many steel turning tools are equipped with chipbreaking devices to prevent the formation of long continuous chips in connection with the turning of steel at the high speeds made possible by high-speed steel and especially cemented carbide tools. Long steel chips are dangerous to the operator, and cumbersome to handle, and they may twist around the tool and cause damage. Broken chips not only occupy less space, but permit a better flow of coolant to the cutting edge. Several different forms of chipbreakers are illustrated in Fig. 4. Angular Shoulder Type: The angular shoulder type shown at A is one of the commonly used forms. As the enlarged sectional view shows, the chipbreaking shoulder is located back of the cutting edge. The angle a between the shoulder and cutting edge may vary from 6 to 15 degrees or more, 8 degrees being a fair average. The ideal angle, width W and depth G, depend upon the speed and feed, the depth of cut, and the material. As a general rule, width W, at the end of the tool, varies from 3⁄32 to 7⁄32 inch, and the depth G may range from 1⁄ to 1⁄ inch. The shoulder radius equals depth G. If the tool has a large nose radius, the 64 16 corner of the shoulder at the nose end may be beveled off, as illustrated at B, to prevent it from coming into contact with the work. The width K for type B should equal approximately 1.5 times the nose radius. Parallel Shoulder Type: Diagram C shows a design with a chipbreaking shoulder that is parallel with the cutting edge. With this form, the chips are likely to come off in short curled sections. The parallel form may also be applied to straight tools which do not have a side cutting-edge angle. The tendency with this parallel shoulder form is to force the chips against the work and damage it.

Fig. 4. Different Forms of Chipbreakers for Turning Tools

Groove Type: This type (diagram D) has a groove in the face of the tool produced by grinding. Between the groove and the cutting edge, there is a land L. Under ideal conditions, this width L, the groove width W, and the groove depth G, would be varied to suit the feed, depth of cut and material. For average use, L is about 1⁄32 inch; G, 1⁄32 inch; and W, 1⁄16 inch. There are differences of opinion concerning the relative merits of the groove type and



CUTTING TOOLS

the shoulder type. Both types have proved satisfactory when properly proportioned for a given class of work. Chipbreaker for Light Cuts: Diagram E illustrates a form of chipbreaker that is sometimes used on tools for finishing cuts having a maximum depth of about 1⁄32 inch. This chipbreaker is a shoulder type having an angle of 45 degrees and a maximum width of about 1⁄16 inch. It is important in grinding all chipbreakers to give the chip-bearing surfaces a fine finish, such as would be obtained by honing. This finish greatly increases the life of the tool. Planing Tools.—Many of the principles which govern the shape of turning tools also apply in the grinding of tools for planing. The amount of rake depends upon the hardness of the material, and the direction of the rake should be away from the working part of the cutting edge. The angle of clearance should be about 4 or 5 degrees for planer tools, which is less than for lathe tools. This small clearance is allowable because a planer tool is held about square with the platen, whereas a lathe tool, the height and inclination of which can be varied, may not always be clamped in the same position. Carbide Tools: Carbide tools for planing usually have negative rake. Round-nose and square-nose end-cutting tools should have a “negative back rake” (or front rake) of 2 or 3 degrees. Side cutting tools may have a negative back rake of 10 degrees, a negative side rake of 5 degrees, and a side cutting-edge angle of 8 degrees. Indexable Inserts Introduction.—A large proportion of the cemented carbide, single-point cutting tools are indexable inserts and indexable insert tool holders. Dimensional specifications for solid sintered carbide indexable inserts are given in American National Standard ANSI B212.12-1991 (R2002). Samples of the many insert shapes are shown in Table 3. Most modern, cemented carbide, face milling cutters are of the indexable insert type. Larger size end milling cutters, side milling or slotting cutters, boring tools, and a wide variety of special tools are made to use indexable inserts. These inserts are primarily made from cemented carbide, although most of the cemented oxide cutting tools are also indexable inserts. The objective of this type of tooling is to provide an insert with several cutting edges. When an edge is worn, the insert is indexed in the tool holder until all the cutting edges are used up, after which it is discarded. The insert is not intended to be reground. The advantages are that the cutting edges on the tool can be rapidly changed without removing the tool holder from the machine, tool-grinding costs are eliminated, and the cost of the insert is less than the cost of a similar, brazed carbide tool. Of course, the cost of the tool holder must be added to the cost of the insert; however, one tool holder will usually last for a long time before it, too, must be replaced. Indexable inserts and tool holders are made with a negative rake or with a positive rake. Negative rake inserts have the advantage of having twice as many cutting edges available as comparable positive rake inserts, because the cutting edges on both the top and bottom of negative rake inserts can be used, while only the top cutting edges can be used on positive rake inserts. Positive rake inserts have a distinct advantage when machining long and slender parts, thin-walled parts, or other parts that are subject to bending or chatter when the cutting load is applied to them, because the cutting force is significantly lower as compared to that for negative rake inserts. Indexable inserts can be obtained in the following forms: utility ground, or ground on top and bottom only; precision ground, or ground on all surfaces; prehoned to produce a slight rounding of the cutting edge; and precision molded, which are unground. Positive-negative rake inserts also are available. These inserts are held on a negative-rake tool holder and have a chipbreaker groove that is formed to produce an effective positive-rake angle while cutting. Cutting edges may be available on the top surface only, or on both top and bottom surfaces. The positive-rake chipbreaker surface may be ground or precision molded on the insert.



757

Many materials, such as gray cast iron, form a discontinuous chip. For these materials an insert that has plain faces without chipbreaker grooves should always be used. Steels and other ductile materials form a continuous chip that must be broken into small segments when machined on lathes and planers having single-point, cemented-carbide and cemented-oxide cutting tools; otherwise, the chips can cause injury to the operator. In this case a chipbreaker must be used. Some inserts are made with chipbreaker grooves molded or ground directly on the insert. When inserts with plain faces are used, a cemented-carbide plate-type chipbreaker is clamped on top of the insert. Identification System for Indexable Inserts.—The size of indexable inserts is determined by the diameter of an inscribed circle (I.C.), except for rectangular and parallelogram inserts where the length and width dimensions are used. To describe an insert in its entirety, a standard ANSI B212.4-2002 identification system is used where each position number designates a feature of the insert. The ANSI Standard includes items now commonly used and facilitates identification of items not in common use. Identification consists of up to ten positions; each position defines a characteristic of the insert as shown below: 1 T

2 N

3 M

4 G

5 5

6 4

7 3

8a

9a

10a A

a Eighth, Ninth, and Tenth Positions are used only when required.

1) Shape: The shape of an insert is designated by a letter: R for round; S, square; T, triangle; A, 85° parallelogram; B, 82° parallelogram; C, 80° diamond; D, 55° diamond; E, 75° diamond; H, hexagon; K, 55° parallelogram; L, rectangle; M, 86° diamond; O, octagon; P, pentagon; V, 35° diamond; and W, 80° trigon. 2) Relief Angle (Clearances): The second position is a letter denoting the relief angles; N for 0°; A, 3°; B, 5°; C, 7°; P, 11°; D, 15°; E, 20°; F, 25°; G, 30°; H, 0° & 11°*; J, 0° & 14°*; K, 0° & 17°*; L, 0° & 20°*; M, 11° & 14°*; R, 11° & 17°*; S, 11° & 20°*. When mounted on a holder, the actual relief angle may be different from that on the insert. 3) Tolerances: The third position is a letter and indicates the tolerances which control the indexability of the insert. Tolerances specified do not imply the method of manufacture.

Symbol A B C D E F G

Tolerance (± from nominal) Inscribed Thicknes, Circle, Inch Inch 0.001 0.001 0.001 0.005 0.001 0.001 0.001 0.005 0.001 0.001 0.0005 0.001 0.001 0.005

Symbol H J K L M U N

Tolerance (± from nominal) Inscribed Thickness, Circle, Inch Inch 0.0005 0.001 0.002–0.005 0.001 0.002–0.005 0.001 0.002–0.005 0.001 0.005 0.002–0.004a 0.005 0.005–0.010a 0.001 0.002–0.004a

a Exact tolerance is determined by size of insert. See ANSI B212.12.

4) Type: The type of insert is designated by a letter. A, with hole; B, with hole and countersink; C, with hole and two countersinks; F, chip grooves both surfaces, no hole; G, same as F but with hole; H, with hole, one countersink, and chip groove on one rake surface; J, with hole, two countersinks and chip grooves on two rake surfaces; M, with hole and chip groove on one rake surface; N, without hole; Q, with hole and two countersinks; R, without hole but with chip groove on one rake surface; T, with hole, one countersink, and chip * Second angle is secondary facet angle, which may vary by ± 1°.



CUTTING TOOLS

groove on one rake face; U, with hole, two countersinks, and chip grooves on two rake faces; and W, with hole and one countersink. Note: a dash may be used after position 4 to separate the shape-describing portion from the following dimensional description of the insert and is not to be considered a position in the standard description. 5) Size: The size of the insert is designated by a one- or a two-digit number. For regular polygons and diamonds, it is the number of eighths of an inch in the nominal size of the inscribed circle, and will be a one- or two-digit number when the number of eighths is a whole number. It will be a two-digit number, including one decimal place, when it is not a whole number. Rectangular and parallelogram inserts require two digits: the first digit indicates the number of eighths of an inch width and the second digit, the number of quarters of an inch length. 6) Thickness: The thickness is designated by a one- or two-digit number, which indicates the number of sixteenths of an inch in the thickness of the insert. It is a one-digit number when the number of sixteenths is a whole number; it is a two-digit number carried to one decimal place when the number of sixteenths of an inch is not a whole number. 7) Cutting Point Configuration: The cutting point, or nose radius, is designated by a number representing 1⁄64ths of an inch; a flat at the cutting point or nose, is designated by a letter: 0 for sharp corner; 1, 1⁄64 inch radius; 2, 1⁄32 inch radius; 3, 3⁄64inch radius; 4, 1⁄16 inch radius; 5, 5⁄64 inch radius; 6, 3⁄32 inch radius; 7, 7⁄64 inch radius; 8, 1⁄8 inch radius; A, square insert with 45° chamfer; D, square insert with 30° chamfer; E, square insert with 15° chamfer; F, square insert with 3° chamfer; K, square insert with 30° double chamfer; L, square insert with 15° double chamfer; M, square insert with 3° double chamfer; N, truncated triangle insert; and P, flatted corner triangle insert. 8) Special Cutting Point Definition: The eighth position, if it follows a letter in the 7th position, is a number indicating the number of 1⁄64ths of an inch measured parallel to the edge of the facet. 9) Hand: R, right; L, left; to be used when required in ninth position. 10) Other Conditions: The tenth position defines special conditions (such as edge treatment, surface finish) as follows: A, honed, 0.0005 inch to less than 0.003 inch; B, honed, 0.003 inch to less than 0.005 inch; C, honed, 0.005 inch to less than 0.007 inch; J, polished, 4 microinch arithmetic average (AA) on rake surfaces only; T, chamfered, manufacturer's standard negative land, rake face only. Indexable Insert Tool Holders.—Indexable insert tool holders are made from a good grade of steel which is heat treated to a hardness of 44 to 48 Rc for most normal applications. Accurate pockets that serve to locate the insert in position and to provide surfaces against which the insert can be clamped are machined in the ends of tool holders. A cemented carbide seat usually is provided, and is held in the bottom of the pocket by a screw or by the clamping pin, if one is used. The seat is necessary to provide a flat bearing surface upon which the insert can rest and, in so doing, it adds materially to the ability of the insert to withstand the cutting load. The seating surface of the holder may provide a positive-, negative-, or a neutral-rake orientation to the insert when it is in position on the holder. Holders, therefore, are classified as positive, negative, or neutral rake. Four basic methods are used to clamp the insert on the holder: 1) Clamping, usually top clamping; 2) Pin-lock clamping; 3) Multiple clamping using a clamp, usually a top clamp, and a pin lock; and 4) Clamping the insert with a machine screw. All top clamps are actuated by a screw that forces the clamp directly against the insert. When required, a cemented-carbide, plate-type chipbreaker is placed between the clamp and the insert. Pin-lock clamps require an insert having a hole: the pin acts against the walls of the hole to clamp the insert firmly against the seating surfaces of the holder. Multiple or combination clamping, simultaneously using both a pin-lock and a top clamp, is recommended when taking heavier or interrupted cuts. Holders are available on which all the above-mentioned methods of clamping may be used. Other holders are made with only a



759

top clamp or a pin lock. Screw-on type holders use a machine screw to hold the insert in the pocket. Most standard indexable insert holders are either straight-shank or offset-shank, although special holders are made having a wide variety of configurations. The common shank sizes of indexable insert tool holders are shown in Table 1. Not all styles are available in every shank size. Positive- and negative-rake tools are also not available in every style or shank size. Some manufacturers provide additional shank sizes for certain tool holder styles. For more complete details the manufacturers' catalogs must be consulted. Table 1. Standard Shank Sizes for Indexable Insert Holders

Shank Dimensions for Indexable Insert Holders Basic Shank Size 1⁄ × 1⁄ × 41⁄ 2 2 2 5⁄ × 5⁄ × 41⁄ 8 8 2 5⁄ × 11⁄ × 6 8 4 3⁄ × 3⁄ × 41⁄ 4 4 2 3⁄ × 1 × 6 4 3⁄ × 11⁄ × 6 4 4

A In.

Ca

B mm

In.

mm

In.

mm

0.500

12.70

0.500

12.70

4.500

114.30

0.625

15.87

0.625

15.87

4.500

114.30

0.625

15.87

1.250

31.75

6.000

152.40

0.750

19.05

0.750

19.05

4.500

114.30

0.750

19.05

1.000

25.40

6.000

152.40

0.750

19.05

1.250

31.75

6.000

152.40

1×1×6 1 × 11⁄4 × 6

1.000 1.000

25.40 25.40

1.000 1.250

25.40 31.75

6.000 6.000

152.40 152.40

1 × 11⁄2 × 6

1.000

25.40

1.500

38.10

6.000

152.40

11⁄4 × 11⁄4 × 7

1.250

31.75

1.250

31.75

7.000

177.80

11⁄4 × 11⁄2 × 8

1.250

31.75

1.500

38.10

8.000

203.20

13⁄8 × 21⁄16 × 63⁄8

1.375

34.92

2.062

52.37

6.380

162.05

11⁄2 × 11⁄2 × 7

1.500

38.10

1.500

38.10

7.000

177.80

13⁄4 × 13⁄4 × 91⁄2 2×2×8

1.750

44.45

1.750

44.45

9.500

241.30

2.000

50.80

2.000

50.80

8.000

203.20

a Holder length; may vary by manufacturer. Actual shank length depends on holder style.

Identification System for Indexable Insert Holders.—The following identification system conforms to the American National Standard, ANSI B212.5-2002, Metric Holders for Indexable Inserts. Each position in the system designates a feature of the holder in the following sequence: 1 2 3 4 5 — 6 — 7 — 8a — 9 — 10a C T N A R — 85 — 25 — D — 16 — Q 1) Method of Holding Horizontally Mounted Insert: The method of holding or clamping is designated by a letter: C, top clamping, insert without hole; M, top and hole clamping, insert with hole; P, hole clamping, insert with hole; S, screw clamping through hole, insert with hole; W, wedge clamping. 2) Insert Shape: The insert shape is identified by a letter: H, hexagonal; O, octagonal; P, pentagonal; S, square; T, triangular; C, rhombic, 80° included angle; D, rhombic, 55° included angle; E, rhombic, 75° included angle; M, rhombic, 86° included angle; V, rhombic, 35° included angle; W, hexagonal, 80° included angle; L, rectangular; A, parallelogram, 85° included angle; B, parallelogram, 82° included angle; K, parallelogram, 55° included angle; R, round. The included angle is always the smaller angle.



CUTTING TOOLS

3) Holder Style: The holder style designates the shank style and the side cutting edge angle, or end cutting edge angle, or the purpose for which the holder is used. It is designated by a letter: A, for straight shank with 0° side cutting edge angle; B, straight shank with 15° side cutting edge angle; C, straight-shank end cutting tool with 0° end cutting edge angle; D, straight shank with 45° side cutting edge angle; E, straight shank with 30° side cutting edge angle; F, offset shank with 0° end cutting edge angle; G, offset shank with 0° side cutting edge angle; J, offset shank with negative 3° side cutting edge angle; K, offset shank with 15° end cutting edge angle; L, offset shank with negative 5° side cutting edge angle and 5° end cutting edge angle; M, straight shank with 40° side cutting edge angle; N, straight shank with 27° side cutting edge angle; R, offset shank with 15° side cutting edge angle; S, offset shank with 45° side cutting edge angle; T, offset shank with 30° side cutting edge angle; U, offset shank with negative 3° end cutting edge angle; V, straight shank with 171⁄2° side cutting edge angle; W, offset shank with 30° end cutting edge angle; Y, offset shank with 5° end cutting edge angle. 4) Normal Clearances: The normal clearances of inserts are identified by letters: A, 3°; B, 5°; C, 7°; D, 15°; E, 20°; F, 25°; G, 30°; N, 0°; P, 11°. 5) Hand of tool: The hand of the tool is designated by a letter: R for right-hand; L, lefthand; and N, neutral, or either hand. 6) Tool Height for Rectangular Shank Cross Sections: The tool height for tool holders with a rectangular shank cross section and the height of cutting edge equal to shank height is given as a two-digit number representing this value in millimeters. For example, a height of 32 mm would be encoded as 32; 8 mm would be encoded as 08, where the one-digit value is preceded by a zero. 7) Tool Width for Rectangular Shank Cross Sections: The tool width for tool holders with a rectangular shank cross section is given as a two-digit number representing this value in millimeters. For example, a width of 25 mm would be encoded as 25; 8 mm would be encoded as 08, where the one-digit value is preceded by a zero. 8) Tool Length: The tool length is designated by a letter: A, 32 mm; B, 40 mm; C, 50 mm; D, 60 mm; E, 70 mm; F, 80 mm; G, 90 mm; H, 100 mm; J, 110 mm; K, 125 mm; L, 140 mm; M, 150 mm; N, 160 mm; P, 170 mm; Q, 180 mm; R, 200 mm; S, 250 mm; T, 300 mm; U, 350 mm; V, 400 mm; W, 450 mm; X, special length to be specified; Y, 500 mm. 9) Indexable Insert Size: The size of indexable inserts is encoded as follows: For insert shapes C, D, E, H. M, O, P, R, S, T, V, the side length (the diameter for R inserts) in millimeters is used as a two-digit number, with decimals being disregarded. For example, the symbol for a side length of 16.5 mm is 16. For insert shapes A, B, K, L, the length of the main cutting edge or of the longer cutting edge in millimeters is encoded as a two-digit number, disregarding decimals. If the symbol obtained has only one digit, then it should be preceded by a zero. For example, the symbol for a main cutting edge of 19.5 mm is 19; for an edge of 9.5 mm, the symbol is 09. 10) Special Tolerances: Special tolerances are indicated by a letter: Q, back and end qualified tool; F, front and end qualified tool; B, back, front, and end qualified tool. A qualified tool is one that has tolerances of ± 0.08 mm for dimensions F, G, and C. (See Table 2.) Table 2. Letter Symbols for Qualification of Tool Holders Position 10 ANSI B212.5-2002

Qualification of Tool Holder

Q

Back and end qualified tool

Letter Symbol F

Front and end qualified tool

B

Back, front, and end qualified tool



761

Selecting Indexable Insert Holders.—A guide for selecting indexable insert holders is provided by Table 3b. Some operations such as deep grooving, cut-off, and threading are not given in this table. However, tool holders designed specifically for these operations are available. The boring operations listed in Table 3b refer primarily to larger holes, into which the holders will fit. Smaller holes are bored using boring bars. An examination of this table shows that several tool-holder styles can be used and frequently are used for each operation. Selection of the best holder for a given job depends largely on the job and there are certain basic facts that should be considered in making the selection. Rake Angle: A negative-rake insert has twice as many cutting edges available as a comparable positive-rake insert. Sometimes the tool life obtained when using the second face may be less than that obtained on the first face because the tool wear on the cutting edges of the first face may reduce the insert strength. Nevertheless, the advantage of negative-rake inserts and holders is such that they should be considered first in making any choice. Positive-rake holders should be used where lower cutting forces are required, as when machining slender or small-diameter parts, when chatter may occur, and for machining some materials, such as aluminum, copper, and certain grades of stainless steel, when positivenegative rake inserts can sometimes be used to advantage. These inserts are held on negative-rake holders that have their rake surfaces ground or molded to form a positive-rake angle. Insert Shape: The configuration of the workpiece, the operation to be performed, and the lead angle required often determine the insert shape. When these factors need not be considered, the insert shape should be selected on the basis of insert strength and the maximum number of cutting edges available. Thus, a round insert is the strongest and has a maximum number of available cutting edges. It can be used with heavier feeds while producing a good surface finish. Round inserts are limited by their tendency to cause chatter, which may preclude their use. The square insert is the next most effective shape, providing good corner strength and more cutting edges than all other inserts except the round insert. The only limitation of this insert shape is that it must be used with a lead angle. Therefore, the square insert cannot be used for turning square shoulders or for back-facing. Triangle inserts are the most versatile and can be used to perform more operations than any other insert shape. The 80-degree diamond insert is designed primarily for heavy turning and facing operations, using the 100-degree corners, and for turning and back-facing square shoulders using the 80-degree corners. The 55- and 35-degree diamond inserts are intended primarily for tracing. Lead Angle: Tool holders should be selected to provide the largest possible lead angle, although limitations are sometimes imposed by the nature of the job. For example, when tuning and back-facing a shoulder, a negative lead angle must be used. Slender or smalldiameter parts may deflect, causing difficulties in holding size, or chatter when the lead angle is too large. End Cutting Edge Angle: When tracing or contour turning, the plunge angle is determined by the end cutting edge angle. A 2-deg minimum clearance angle should be provided between the workpiece surface and the end cutting edge of the insert. Table 3a provides the maximum plunge angle for holders commonly used to plunge when tracing where insert shape identifiers are S = square, T = triangle, D = 55-deg diamond, V = 35-deg diamond. When severe cratering cannot be avoided, an insert having a small, end cutting edge angle is desirable to delay the crater breakthrough behind the nose. For very heavy cuts a small, end cutting edge angle will strengthen the corner of the tool. Tool holders for numerical control machines are discussed in the NC section, beginning page 1309.



CUTTING TOOLS Table 3a. Maximum Plunge Angle for Tracing or Contour Turning

Tool Holder Style E D and S H J

Maximum Plunge Angle 58° 43° 71° 25°

Insert Shape T S D T

Tool Holder Style J J N N

Maximum Plunge Angle 30° 50° 55° 58°–60°

Insert Shape D V T D

R

A

R

B

T

B

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

䊉

N

䊉

䊉

䊉

N

䊉

䊉

Bore

䊉

Plane

Chamfer

Groove

Trace

Turn and Backface

Turn and Face

N

T

A

B

Face

A

Turn

T

N-Negative P-Positive

A

Application

Rake

Insert Shape

Tool

Tool Holder Style

Table 3b. Indexable Insert Holder Application Guide

䊉

䊉

䊉

䊉

P

䊉

䊉

N

䊉

䊉

䊉

䊉

P

䊉

䊉

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

N

䊉

䊉

䊉

䊉

P

䊉

䊉

䊉

䊉

T

䊉

S

B

C

C

T

䊉

䊉


䊉


763

Bore

Plane

䊉

䊉

䊉

䊉

䊉

䊉

P

䊉

䊉

䊉

䊉

䊉

䊉

䊉

N

䊉

䊉

䊉

䊉

䊉

P

䊉

䊉

䊉

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

Groove

䊉

Trace

N

Turn and Backface

Chamfer

G

Turn and Face

F

Face

E

Turn

S


D

Application

Rake

Insert Shape

Tool

Tool Holder Style

Table 3b. (Continued) Indexable Insert Holder Application Guide

T

T

T

G

R

G

C

H

D

J

T

J

D

J

V

K

S

䊉

N

䊉

䊉

P

䊉

䊉

N

䊉

䊉

N

䊉

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉



CARBIDE TIPS AND TOOLS

N

D

S

S

W

Plane

Bore

Chamfer

䊉

䊉

N

Groove

䊉

Trace

T

䊉

Turn and Backface

N

N

Turn and Face

C

Face

L

Turn

C


K

Application

Rake

Insert Shape

Tool

Tool Holder Style

Table 3b. (Continued) Indexable Insert Holder Application Guide

䊉

N

䊉

䊉

䊉

P

䊉

䊉

䊉

N

䊉

䊉

䊉

N

䊉

䊉

䊉

䊉

䊉

䊉

䊉

P

䊉

䊉

䊉

䊉

䊉

䊉

䊉

N

䊉

䊉

S

Sintered Carbide Blanks and Cutting Tools Sintered Carbide Blanks.—As shown in Table 4, American National Standard ANSI B212.1-2002 provides standard sizes and designations for eight styles of sintered carbide blanks. These blanks are the unground solid carbide from which either solid or tipped cutting tools are made. Tipped cutting tools are made by brazing a blank onto a shank to produce the cutting tool; these tools differ from carbide insert cutting tools which consist of a carbide insert held mechanically in a tool holder. A typical single-point carbide-tipped cutting tool is shown in Fig. 1 on page 766. Single-Point, Sintered-Carbide-Tipped Tools.—American National Standard ANSI B212.1-2002 covers eight different styles of single-point, carbide-tipped general purpose tools. These styles are designated by the letters A to G inclusive. Styles A, B, F, G, and E with offset point are either right- or left-hand cutting as indicated by the letters R or L. Dimensions of tips and shanks are given in Tables 5 to 12. For dimensions and tolerances not shown, and for the identification system, dimensions, and tolerances of sintered carbide boring tools, see the Standard. A number follows the letters of the tool style and hand designation and for square shank tools, represents the number of sixteenths of an inch of width, W, and height, H. With rectangular shanks, the first digit of the number indicates the number of eighths of an inch in the shank width, W, and the second digit the number of quarters of an inch in the shank


Machinery's Handbook 27th Edition CARBIDE TIPS AND TOOLS

765

Table 4. American National Standard Sizes and Designations for Carbide Blanks ANSI B212.1-2002 Styleb Blank Dimensionsa T

W

L

1⁄ 16 1⁄ 16 1⁄ 16 1⁄ 16 1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 5⁄ 32 5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 8 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 5⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 8 3⁄ 8 5⁄ 8 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 3⁄ 4

5⁄ 8 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 4 5⁄ 16 1⁄ 2 3⁄ 8 1⁄ 2 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 3⁄ 8 3⁄ 4 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 16 1⁄ 2 3⁄ 4 5⁄ 8 1⁄ 2 3⁄ 4 1⁄ 2 3⁄ 4 3⁄ 4 9⁄ 16 3⁄ 4 5⁄ 8 7⁄ 16 5⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 5⁄ 8 13⁄ 16 1⁄ 2 3⁄ 4 3⁄ 4

1000

Styleb 2000

Blank Designation 1010

2010

1015

2015

1020

2020

1025

2025

1030

2030

1035

2035

1040

2040

1050

2050

1060

2060

1070

2070

1080

2080

1090

2090

1100

2100

1105

2105

1080

2080

1110

2110

1120

2120

1130

2130

1140

2140

1150

2150

1160

2160

1110

2110

1170

2170

1180

2180

1190

2190

1200

2200

1210

2210

1215

2215

1220

2220

1230

2230

1240

2240

1250

2250

1260

2260

1270

2270

1280

2280

1290

2290

1300

2300

1310

2310

1320

2320

1330

2330

1340

2340

Blank Dimensionsa T

W

L

1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 3⁄ 8 1⁄ 2

3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 3⁄ 4

9⁄ 16 3⁄ 4 5⁄ 8 3⁄ 4

1

1000

3000

4000

Blank Designation 0350

1350

3350

4350

0360

1360

3360

4360

0370

1370

3370

4370

0380

1380

3380

4380

0390

1390

3390

4390

0400

1400

3400

4400

0405

1405

3405

4405

0410

1410

3410

4410

0415

1415

3415

4415

0420

1420

3420

4420

0430

1430

3430

4430

0440

1440

3440

4440

1

0450

1450

3450

4450

1

0460

1460

3460

4460

3⁄ 4

0470

1470

3470

4470

0475

1475

3475

4475

11⁄4

0480

1480

3480

4480

3⁄ 4

1 5⁄ 8 3⁄ 4

1 1

7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 1⁄ 2 3⁄ 4

0000

5⁄ 8 15⁄ 16 3⁄ 4

1

0490

1490

3490

4490

1

0500

1500

3500

4500

1

0510

1510

3510

4510

11⁄4

0515

1515

3515

4515

11⁄4

0520

1520

3520

4520

11⁄2

0525

1525

3525

4525

0530

1530

3530

4530

0540

1540

3540

4540

0490

1490

3490

4490

0550

1550

3550

4550

1 11⁄4 3⁄ 4 11⁄2

Styleb T 1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 3⁄ 32 1⁄ 8 5⁄ 32 5⁄ 32 3⁄ 16 1⁄ 4

W 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 5⁄ 16 1⁄ 4 1⁄ 2 3⁄ 8 5⁄ 8 3⁄ 4

1

L 5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 8 1⁄ 2 3⁄ 4 5⁄ 8 3⁄ 4 3⁄ 4

F …

5000 5030

6000 …

70000 …

…

…

7060

5080

6080

…

1⁄ 16

… …

5100

6100

…

…

5105

…

…

3⁄ 32 1⁄ 16

…

…

7170

…

…

7060

…

5200

6200

…

1⁄ 8

…

…

7230

…

5240

6240

…

…

5340

6340

…

…

5410

…

…

a All dimensions are in inches. b See Fig. 1 on page

766 for a description of styles.

height, H. One exception is the 11⁄2 × 2-inch size which has been arbitrarily assigned the number 90. A typical single-point carbide tipped cutting tool is shown in Fig. 2. The side rake, side relief, and the clearance angles are normal to the side-cutting edge, rather than the shank, to facilitate its being ground on a tilting-table grinder. The end-relief and clearance angles are




Fig. 1. Eight styles of sintered carbide blanks (see Table 4.)

Side Rake

Side Relief Angle

Side Clearance Angle

Tip Width

Tip Overhang Nose Radius

End Cutting Edge Angle (ECEA) Shank Width Side Cutting Edge Angle (SCEA) Overall length Tip length

Tip Thickness

Back Rake

Cutting Height Tip Overhang End Relief Angle End Clearance Angle

Shank Height

Fig. 2. A typical single-point carbide tipped cutting tool.

normal to the end-cutting edge. The back-rake angle is parallel to the side-cutting edge. The tip of the brazed carbide blank overhangs the shank of the tool by either 1⁄32 or 1⁄16 inch, depending on the size of the tool. For tools in Tables 5, 6, 7, 8, 11 and , the maximum overhang is 1⁄32 inch for shank sizes 4, 5, 6, 7, 8, 10, 12 and 44; for other shank sizes in these tables, the maximum overhang is 1⁄16 inch. In Tables 9 and 10 all tools have maximum overhang of 1⁄32 inch.



767

Single-point Tool Nose Radii: The tool nose radii recommended in the American National Standard are as follows: For square-shank tools up to and including 3⁄8-inch square tools, 1⁄64 inch; for those over 3⁄8-inch square through 11⁄4-inches square, 1⁄32 inch; and for those above 11⁄4-inches square, 1⁄16 inch. For rectangular-shank tools with shank section of 1⁄2 × 1 inch through 1 × 11⁄2 inches, the nose radii are 1⁄32 inch, and for 1 × 2 and 11⁄2 × 2 inch shanks, the nose radius is 1⁄16 inch. Single-point Tool Angle Tolerances: The tool angles shown on the diagrams in the Tables 5 through 12 are general recommendations. Tolerances applicable to these angles are ± 1 degree on all angles except end and side clearance angles; for these the tolerance is ± 2 degrees. Table 5. American National Standard Style A Carbide Tipped Tools ANSI B212.1-2002

Designation Style ARa

Shank Dimensions

Style ALa

Width A

Height B

1⁄ 4

Tip Dimensions Tip Designationa

Length C

Thickness T

Width W

Length L

Square Shank AR 4

AL 4

1⁄ 4

2

AR 5

AL 5

5⁄ 16

2040

3⁄ 32

3⁄ 16

5⁄ 16

5⁄ 16

21⁄4

2070

3⁄ 32

1⁄ 4

1⁄ 2

AR 6

AL 6

3⁄ 8

AR 7

AL 7

7⁄ 16

3⁄ 8

21⁄2

2070

3⁄ 32

1⁄ 4

1⁄ 2

3

2070

3⁄ 32

1⁄ 4

AR 8

AL 8

1⁄ 2

1⁄ 2

1⁄ 2

31⁄2

2170

1⁄ 8

5⁄ 16

AR 10

AL 10

5⁄ 8

5⁄ 8

5⁄ 8

4

2230

5⁄ 32

3⁄ 8

3⁄ 4

AR 12

AL 12

AR 16

AL 16

1

3⁄ 4

3⁄ 4

41⁄2

2310

3⁄ 16

7⁄ 16

1

6

{

P3390, P4390

1⁄ 4

9⁄ 16

1

AR 20

AL 20

AR 24

AL 24

11⁄4

11⁄4

7

{

P3460, P4460

5⁄ 16

5⁄ 8

1

11⁄2

11⁄2

8

{

P3510, P4510

3⁄ 8

5⁄ 8

1

7⁄ 16

13⁄ 16

Rectangular Shank AR 44

AL 44

1⁄ 2

1

6

AR 54

AL 54

5⁄ 8

1

6

AR 55

AL 55

5⁄ 8

11⁄4

7

AR 64

AL 64

3⁄ 4

1

6

AR 66

AL 66

3⁄ 4

11⁄2

8

AR 85

AL 85

1

11⁄4

7

AR 86

AL 86

1

11⁄2

AR 88

AL 88

1

2

AL 90

11⁄2

AR 90

2

P2260

3⁄ 16

5⁄ 16

5⁄ 8

P3360, P4360

1⁄ 4

3⁄ 8

3⁄ 4

{

P3360, P4360

1⁄ 4

3⁄ 8

3⁄ 4

{

P3380, P4380

1⁄ 4

1⁄ 2

3⁄ 4

{

P3430, P4430

5⁄ 16

7⁄ 16

{

P3460, P4460

5⁄ 16

5⁄ 8

1

{

15⁄ 16

8

{

P3510, P4510

3⁄ 8

5⁄ 8

1

10

{

P3510, P4510

3⁄ 8

5⁄ 8

1

P3540, P4540

1⁄ 2

3⁄ 4

11⁄4

10

{

a

“A” is straight shank, 0 deg., SCEA (side-cutting-edge angle). “R” is right-cut. “L” is left-cut. Where a pair of tip numbers is shown, the upper number applies to AR tools, the lower to AL tools. All dimensions are in inches.



CARBIDE TIPS AND TOOLS Table 6. American National Standard Style B Carbide Tipped Tools with 15-degree Side-cutting-edge Angle ANSI B212.1-2002 7° ±1°

6° ± 1° To sharp corner

10° ± 2°

15° ± 1°

W

Overhang

F Ref

T

A L

R

15° ± 1° C

0° ± 1° H

Tool designation and carbide grade

Overhang 7° ±1°

10° ± 2°

B

Style GR right hand (shown) Style GE left hand (not shown) Designation Style BR Style BL

Width A

Shank Dimensions Height Length B C

Tip Designationa

Tip Dimensions Thickness Width T W

Length L

Square Shank BR 4 BR 5 BR 6 BR 7 BR 8 BR 10 BR 12 BR 16 BR 20 BR 24

BL 4 BL 5 BL 6 BL 7 BL 8 BL 10 BL 12 BL 16 BL 20 BL 24

BR 44 BR 54 BR 55 BR 64 BR 66 BR 85 BR 86 BR 88 BR 90

BL 44 BL 54 BL 55 BL 64 BL 66 BL 85 BL 86 BL 88 BL 90

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄4 11⁄2

1 11⁄4 11⁄2

1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

1 1 11⁄4 1 11⁄2 11⁄4 11⁄2 2 2

2 21⁄4 21⁄2 3 31⁄2 4 41⁄2 6 7 8

{ { {

2015 2040 2070 2070 2170 2230 2310 3390, 4390 3460, 4460 3510, 4510

1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8

5⁄ 32 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8

3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2

5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2 7⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4

1⁄ 4 5⁄ 16 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4 13⁄ 16

1 1 1

Rectangular Shank

1 1 1 11⁄2

6 6 7 6 8 7 8 10 10

{ { { { { { { {

2260 3360, 4360 3360, 4360 3380, 4380 3430, 4430 3460, 4460 3510, 4510 3510, 4510 3540, 4540

5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 15⁄ 16

1 1 1 11⁄4

a Where a pair of tip numbers is shown, the upper number applies to BR tools, the lower to BL tools. All dimensions are in inches.

Brazing Carbide Tips to Steel Shanks.—Sintered carbide tips or blanks are attached to steel shanks by brazing. Shanks usually are made of low-alloy steels having carbon contents ranging from 0.40 to 0.60 per cent. Shank Preparation: The carbide tip usually is inserted into a milled recess or seat. When a recess is used, the bottom should be flat to provide a firm even support for the tip. The corner radius of the seat should be somewhat smaller than the radius on the tip to avoid contact and insure support along each side of the recess. Cleaning: All surfaces to be brazed must be absolutely clean. Surfaces of the tip may be cleaned by grinding lightly or by sand-blasting. Brazing Materials and Equipment: The brazing metal may be copper, naval brass such as Tobin bronze, or silver solder. A flux such as borax is used to protect the clean surfaces and prevent oxidation. Heating may be done in a furnace or by oxy-acetylene torch or an oxy-hydrogen torch. Copper brazing usually is done in a furnace, although an oxy-hydrogen torch with excess hydrogen is sometimes used. Brazing Procedure: One method using a torch is to place a thin sheet material, such as copper foil, around and beneath the carbide tip, the top of which is covered with flux. The flame is applied to the under side of the tool shank, and, when the materials melt, the tip is pressed firmly into its seat with tongs or with the end of a rod. Brazing material in the form of wire or rod may be used to coat or tin the surfaces of the recess after the flux melts and runs freely. The tip is then inserted, flux is applied to the top, and heating continued until the coatings melt and run freely. The tip, after coating with flux, is placed in the recess and the shank end is heated. Then a small piece of silver solder, having a melting point of 1325 degrees F., is placed on top of the tip. When this solder melts, it runs over the nickel-coated surfaces while the tip is held firmly into its seat. The brazed tool should be cooled slowly to avoid cracking due to unequal contraction between the steel and carbide.



769

Table 7. American National Standard Style C Carbide Tipped Tools ANSI B212.1-2002 3°I2° 0.015 × 45° Maximum permissible

Overhang W 5° ± 2° Both sides 0° ± 1°

A

F

C Tool designation and carbide grade

90° ± 1° 0° ± 1°

T

L

B

H Overhang

7° ± 1°

Note – Tool must pass thru slot of nominal width “A”

10° ± 2° Designation

Width, A

Shank Dimensions Height, B Length, C

Tip Designnation

Thickness, T

1 11⁄4

2 21⁄4 21⁄2 3 31⁄2 4 41⁄2 6 7

1030 1080 1090 1105 1200 1240 1340 1410 1480

1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16

1 1 11⁄4 1 11⁄2 11⁄2

6 6 7 6 8 8

1320 1400 1400 1405 1470 1475

3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

C4 C5 C6 C7 C8 C 10 C 12 C 16 C 20

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄4 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

C 44 C 54 C 55 C 64 C 66 C 86

1

Tip Dimensions Width, W

Length, L

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

5⁄ 16 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

1 11⁄4 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

1

All dimensions are in inches. Square shanks above horizontal line; rectangular below.

Table 8. American National Standard Style D, 80-degree Nose-angle Carbide Tipped Tools ANSI B212.1-2002 10° ± 2° Both sides 7° ± 1° Overhang

Note – Tool must pass thru slot of nominal width “A” R

W 0° ± 1°

40° ± 1° A

F

40° ± 1° C±

To sharp corner 0° ± 1°

T

L

1 8

Tool designation and carbide grade

H Designation D4 D5 D6 D7 D8 D 10 D 12 D 16

Width, A

1

B

Shank Dimensions Height, B Length, C

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1

2 21⁄4 21⁄2 3 31⁄2 4 41⁄2 6

+0.000 –0.010

+0.000 –0.010

Tip Designation

Thickness, T

5030 5080 5100 5105 5200 5240 5340 5410

1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4

Tip Dimensions Width, W 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1



Length, L 5⁄ 16 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4



Table 9. American National Standard Style E, 60-degree Nose-angle, Carbide Tipped Tools ANSI B212.1-2002

Designation

Width A

Shank Dimensions Height B

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

E4 E5 E6 E8 E 10 E 12

Tip Designation

Thickness T

Tip Dimensions Width W

Length L

2

6030

21⁄4

6080

21⁄2

6100

1⁄ 16 3⁄ 32 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

5⁄ 16 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4

Length C

31⁄2

6200

4

6240

41⁄2

6340


Table 10. American National Standard Styles ER and EL, 60-degree Nose-angle, Carbide Tipped Tools with Offset Point ANSI B212.1-2002

Designation Style Style ER EL ER 4

EL 4

ER 5

EL 5

ER 6

EL 6

ER 8

EL 8

ER 10

EL 10

ER 12

EL 12

Width A

Shank Dimensions Height Length B C

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

Tip Designation

2

1020

21⁄4

7060

21⁄2

7060

31⁄2

7170

4

7170

41⁄2

7230

Thick. T

Tip Dimensions Width Length W L

1⁄ 16 3⁄ 32 3⁄ 32 1⁄ 8 1⁄ 8 5⁄ 32



3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8

1⁄ 4 3⁄ 8 3⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4


771

Table 11. American National Standard Style F, Offset, End-cutting Carbide Tipped Tools ANSI B212.1-2002

Designation

Style FR

Style FL

Shank Dimensions

Width A

Height B

Length C

Tip Dimensions

Offset G

Length of Offset E

Tip Designation

Thickness T

Width W

Length L

1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8

5⁄ 16 3⁄ 8 7⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8

5⁄ 8 3⁄ 4 13⁄ 16

3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 1⁄ 2

5⁄ 16 3⁄ 8 1⁄ 2 7⁄ 16 5⁄ 8 5⁄ 8 3⁄ 4

5⁄ 8 3⁄ 4 3⁄ 4 15⁄ 16

Square Shank 1⁄ 2 5⁄ 8 3⁄ 4

31⁄2

FL 12

1⁄ 2 5⁄ 8 3⁄ 4

FL 16

1

1

6

FR 20

FL 20

11⁄4

11⁄4

7

FR 24

FL 24

11⁄2

11⁄2

8

FR 8

FL 8

FR 10

FL 10

FR 12 FR 16

4 41⁄2

1⁄ 4 3⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

3⁄ 4

{

P4170, P3170

1

{

P1230, P3230

11⁄8

{

P4310, P3310

13⁄8

{

P4390, P3390

11⁄2

{

P4460, P3460

11⁄2

{

P4510, P3510

1 1 1

Rectangular Shank FR 44

FL 44

FR 55

FL 55

FR 64

FL 64

FR 66

FL 66

1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

FR 85

FL 85

FR 86 FR 90

1

6

11⁄4

7

1

6

11⁄2

8

1

11⁄4

7

FL 86

1

11⁄2

8

FL 90

11⁄2

2

10

1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

7⁄ 8

{

P4260, P1260

11⁄8

{

P4360, P3360

13⁄16

{

P4380, P3380

11⁄4

{

P4430, P3430

11⁄2

{

P4460, P3460

11⁄2

{

P4510, P3510

15⁄8

{

P4540, P3540

1 1 11⁄4

All dimensions are in inches. Where a pair of tip numbers is shown, the upper number applies to FR tools, the lower number to FL tools.

Carbide Tools.—Cemented or sintered carbides are used in the machine building and various other industries, chiefly for cutting tools but also for certain other tools or parts subject to considerable abrasion or wear. Carbide cutting tools, when properly selected to obtain the right combination of strength and hardness, are very effective in machining all classes of iron and steel, non-ferrous alloys, non-metallic materials, hard rubber, synthetic resins, slate, marble, and other materials which would quickly dull steel tools either because of hardness or abrasive action. Carbide cutting tools are not only durable, but capable of exceptionally high cutting speeds. See CEMENTED CARBIDES starting on page 773 for more on these materials. Tungsten carbide is used extensively in cutting cast iron, nonferrous metals which form short chips in cutting; plastics and various other non-metallic materials. A grade having a hardness of 87.5 Rockwell A might be used where a strong grade is required, as for roughing cuts, whereas for light high-speed finishing or other cuts, a hardness of about 92 might be preferable. When tungsten carbide is applied to steel, craters or chip cavities are formed



CARBIDE TIPS AND TOOLS Table 12. American National Standard Style G, Offset, Side-cutting, Carbide Tipped Tools ANSI B212.1-2002

Designation

Shank Dimensions

Tip Dimensions

Style GR

Style GL

Width A

Height B

Length C

Offset G

GR 8

GL 8 GL 10

GR 12

GL 12

1⁄ 2 5⁄ 8 3⁄ 4

31⁄2

GR 10

1⁄ 2 5⁄ 8 3⁄ 4

GR 16

GL 16

1

1

6

GR 20

GL 20

11⁄4

11⁄4

7

GR 24

GL 24

11⁄2

11⁄2

8

1⁄ 4 3⁄ 8 3⁄ 8 1⁄ 2 3⁄ 4 3⁄ 4

Length of Offset E

Tip Designation

Thickness T

Width W

Length L

1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8

5⁄ 16 3⁄ 8 7⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8

5⁄ 8 3⁄ 4 13⁄ 16

3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 1⁄ 2

5⁄ 16 3⁄ 8 1⁄ 2 7⁄ 16 5⁄ 8 5⁄ 8 3⁄ 4

Square Shank 4 41⁄2

11⁄16

{

P3170, P4170

13⁄8

{

P3230, P4230

11⁄2

{

P3310, P2310

111⁄16

{

P3390, P4390

113⁄16

{

P3460, P4460

113⁄16

{

P3510, P4510

1 1 1

Rectangular Shank 1

6

11⁄4

7

GL 66

1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

GR 85

GL 85

GR 86 GR 90

GR 44

GL 44

GR 55

GL 55

GR 64

GL 64

GR 66

1

6

11⁄2

8

1

11⁄4

7

GL 86

1

11⁄2

8

GL 90

11⁄2

2

10

1⁄ 4 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 3⁄ 4

11⁄16

{

P3260, P4260

13⁄8

{

P3360, P4360

17⁄16

{

P3380, P4380

15⁄8

{

P3430, P4430

111⁄16

{

P3460, P4460

111⁄16

{

P3510, P4510

21⁄16

{

P3540, P4540

5⁄ 8 3⁄ 4 3⁄ 4 15⁄ 16

1 1 11⁄4

All dimensions are in inches. Where a pair of tip numbers is shown, the upper number applies to GR tools, the lower number to GL tools.

back of the cutting edge; hence other carbides have been developed which offer greater resistance to abrasion. Tungsten-titanium carbide (often called “titanium carbide”) is adapted to cutting either heat-treated or unheattreated steels, cast steel, or any tough material which might form chip cavities. It is also applicable to bronzes, monel metal, aluminum alloys, etc. Tungsten-tantalum carbide or “tantalum carbide” cutting tools are also applicable to steels, bronzes or other tough materials. A hardness of 86.8 Rockwell A is recommended by one manufacturer for roughing steel, whereas a grade for finishing might have a hardness ranging from 88.8 to 91.5 Rockwell A.


Machinery's Handbook 27th Edition CEMENTED CARBIDES AND OTHER HARD MATERIALS

773

CEMENTED CARBIDES Cemented Carbides and Other Hard Materials Carbides and Carbonitrides.—Though high-speed steel retains its importance for such applications as drilling and broaching, most metal cutting is carried out with carbide tools. For materials that are very difficult to machine, carbide is now being replaced by carbonitrides, ceramics, and superhard materials. Cemented (or sintered) carbides and carbonitrides, known collectively in most parts of the world as hard metals, are a range of very hard, refractory, wear-resistant alloys made by powder metallurgy techniques. The minute carbide or nitride particles are “cemented” by a binder metal that is liquid at the sintering temperature. Compositions and properties of individual hardmetals can be as different as those of brass and high-speed steel. All hardmetals are cermets, combining ceramic particles with a metallic binder. It is unfortunate that (owing to a mistranslation) the term cermet has come to mean either all hardmetals with a titanium carbide (TiC) base or simply cemented titanium carbonitrides. Although no single element other than carbon is present in all hard-metals, it is no accident that the generic term is “tungsten carbide.” The earliest successful grades were based on carbon, as are the majority of those made today, as listed in Table 1. The outstanding machining capabilities of high-speed steel are due to the presence of very hard carbide particles, notably tungsten carbide, in the iron-rich matrix. Modern methods of making cutting tools from pure tungsten carbide were based on this knowledge. Early pieces of cemented carbide were much too brittle for industrial use, but it was soon found that mixing tungsten carbide powder with up to 10 per cent of metals such as iron, nickel, or cobalt, allowed pressed compacts to be sintered at about 1500°C to give a product with low porosity, very high hardness, and considerable strength. This combination of properties made the materials ideally suitable for use as tools for cutting metal. Cemented carbides for cutting tools were introduced commercially in 1927, and although the key discoveries were made in Germany, many of the later developments have taken place in the United States, Austria, Sweden, and other countries. Recent years have seen two “revolutions” in carbide cutting tools, one led by the United States and the other by Europe. These were the change from brazed to clamped carbide inserts and the rapid development of coating technology. When indexable tips were first introduced, it was found that so little carbide was worn away before they were discarded that a minor industry began to develop, regrinding the socalled “throwaway” tips and selling them for reuse in adapted toolholders. Hardmetal consumption, which had grown dramatically when indexable inserts were introduced, leveled off and began to decline. This situation was changed by the advent and rapid acceptance of carbide, nitride, and oxide coatings. Application of an even harder, more wear-resistant surface to a tougher, more shock-resistant substrate allowed production of new generations of longer-lasting inserts. Regrinding destroyed the enhanced properties of the coatings, so was abandoned for coated tooling. Brazed tools have the advantage that they can be reground over and over again, until almost no carbide is left, but the tools must always be reset after grinding to maintain machining accuracy. However, all brazed tools suffer to some extent from the stresses left by the brazing process, which in unskilled hands or with poor design can shatter the carbide even before it has been used to cut metal. In present conditions it is cheaper to use indexable inserts, which are tool tips of precise size, clamped in similarly precise holders, needing no time-consuming and costly resetting but usable only until each cutting edge or corner has lost its initial sharpness (see Introduction and related topics starting on page 756 and Indexable Insert Holders for NC on page 1309. The absence of brazing stresses and the “one-use” concept also means that harder, longer-lasting grades can be used.



CEMENTED CARBIDES AND OTHER HARD MATERIALS

Table 1. Typical Properties of Tungsten-Carbide-Based Cutting-Tool Hardmetals Density (g/cm3)

Hardness (Vickers)

Transverse Rupture Strength (N/mm2)

8.5 11.4 11.5 11.7 12.1 12.9 13.3 13.4 13.1 13.4 13.3 13.6 14.0 15.2 15.0 14.9 14.8 14.4 14.1

1900 1820 1740 1660 1580 1530 1490 1420 1250 1590 1540 1440 1380 1850 1790 1730 1650 1400 1320

1100 1300 1400 1500 1600 1700 1850 1950 2300 1800 1900 2000 2100 1450 1550 1700 1950 2250 2500

Composition (%) ISO Application Code

WC

P01 P05 P10 P15 P20 P25 P30 P40 P50 M10 M20 M30 M40 K01 K05 K10 K20 K30 K40

50 78 69 78 79 82 84 85 78 85 82 86 84 97 95 92 94 91 89

TiC 35 16 15 12 8 6 5 5 3 5 5 4 4

TaC 7 8 3 5 4 2 3 4 5 2 1 2

Co 6 6 8 7 8 8 9 10 16 6 8 10 10 3 4 6 6 9 11

A complementary development was the introduction of ever-more complex chip-breakers, derived from computer-aided design and pressed and sintered to precise shapes and dimensions. Another advance was the application of hot isostatic pressing (HIP), which has moved hardmetals into applications that were formerly uneconomic. This method allows virtually all residual porosity to be squeezed out of the carbide by means of inert gas at high pressure, applied at about the sintering temperature. Toughness, rupture strength, and shock resistance can be doubled or tripled by this method, and the reject rates of very large sintered components are reduced to a fraction of their previous levels. Further research has produced a substantial number of excellent cutting-tool materials based on titanium carbonitride. Generally called “cermets,” as noted previously, carbonitride-based cutting inserts offer excellent performance and considerable prospects for the future. Compositions and Structures: Properties of hardmetals are profoundly influenced by microstructure. The microstructure in turn depends on many factors including basic chemical composition of the carbide and matrix phases; size, shape, and distribution of carbide particles; relative proportions of carbide and matrix phases; degree of intersolubility of carbides; excess or deficiency of carbon; variations in composition and structure caused by diffusion or segregation; production methods generally, but especially milling, carburizing, and sintering methods, and the types of raw materials; post sintering treatments such as hot isostatic pressing; and coatings or diffusion layers applied after initial sintering. Tungsten Carbide/Cobalt (WC/Co): The first commercially available cemented carbides consisted of fine angular particles of tungsten carbide bonded with metallic cobalt. Intended initially for wire-drawing dies, this composition type is still considered to have the greatest resistance to simple abrasive wear and therefore to have many applications in machining. For maximum hardness to be obtained from closeness of packing, the tungsten carbide grains should be as small as possible, preferably below 1 µm swaging 0.00004 in.) and considerably less for special purposes. Hardness and abrasion resistance increase as the cobalt content is lowered, provided that a minimum of cobalt is present (2 per cent can be



775

enough, although 3 per cent is the realistic minimum) to ensure complete sintering. In general, as carbide grain size or cobalt content or both are increased—frequently in unison— tougher and less hard grades are obtained. No porosity should be visible, even under the highest optical magnification. WC/Co compositions used for cutting tools range from about 2 to 13 per cent cobalt, and from less than 0.5 to more than 5 µm (0.00002–0.0002 in.) in grain size. For stamping tools, swaying dies, and other wear applications for parts subjected to moderate or severe shock, cobalt content can be as much as 30 per cent, and grain size a maximum of about 10 µm (0.0004 in.). In recent years, “micrograin” carbides, combining submicron (less than 0.00004 in.) carbide grains with relatively high cobalt content have found increasing use for machining at low speeds and high feed rates. An early use was in high-speed woodworking cutters such as are used for planing. For optimum properties, porosity should be at a minimum, carbide grain size as regular as possible, and carbon content of the tungsten carbide phase close to the theoretical (stoichiometric) value. Many tungsten carbide/cobalt compositions are modified by small but important additions—from 0.5 to perhaps 3 per cent of tantalum, niobium, chromium, vanadium, titanium, hafnium, or other carbides. The basic purpose of these additions is generally inhibition of grain growth, so that a consistently fine structure is maintained. Tungsten – Titanium Carbide/Cobalt (WC/TiC/Co): These grades are used for tools to cut steels and other ferrous alloys, the purpose of the TiC content being to resist the hightemperature diffusive attack that causes chemical breakdown and cratering. Tungsten carbide diffuses readily into the chip surface, but titanium carbide is extremely resistant to such diffusion. A solid solution or “mixed crystal” of WC in TiC retains the anticratering property to a great extent. Unfortunately, titanium carbide and TiC-based solid solutions are considerably more brittle and less abrasion resistant than tungsten carbide. TiC content, therefore, is kept as low as possible, only sufficient TiC being provided to avoid severe cratering wear. Even 2 or 3 per cent of titanium carbide has a noticeable effect, and as the relative content is substantially increased, the cratering tendency becomes more severe. In the limiting formulation the carbide is tungsten-free and based entirely on TiC, but generally TiC content extends to no more than about 18 per cent. Above this figure the carbide becomes excessively brittle and is very difficult to braze, although this drawback is not a problem with throwaway inserts. WC/TiC/Co grades generally have two distinct carbide phases, angular crystals of almost pure WC and rounded TiC/WC mixed crystals. Among progressive manufacturers, although WC/TiC/Co hardmetals are very widely used, in certain important respects they are obsolescent, having been superseded by the WC/TiC/Ta(Nb)C/Co series in the many applications where higher strength combined with crater resistance is an advantage. TiC, TiN, and other coatings on tough substrates have also diminished the attractions of highTiC grades for high-speed machining of steels and ferrous alloys. Tungsten-Titanium-Tantalum (-Niobium) Carbide/Cobalt: Except for coated carbides, tungsten-titanium-tantalum (-niobium) grades could be the most popular class of hardmetals. Used mainly for cutting steel, they combine and improve upon most of the best features of the longer-established WC/TiC/Co compositions. These carbides compete directly with carbonitrides and silicon nitride ceramics, and the best cemented carbides of this class can undertake very heavy cuts at high speeds on all types of steels, including austenitic stainless varieties. These tools also operate well on ductile cast irons and nickel-base superalloys, where great heat and high pressures are generated at the cutting edge. However, they do not have the resistance to abrasive wear possessed by micrograin straight tungsten carbide grades nor the good resistance to cratering of coated grades and titanium carbidebased cermets.




Titanium Carbide/Molybdenum/Nickel (TiC/Mo/Ni): The extreme indentation hardness and crater resistance of titanium carbide, allied to the cheapness and availability of its main raw material (titanium dioxide, TiO2), provide a strong inducement to use grades based on this carbide alone. Although developed early in the history of hardmetals, these carbides were difficult to braze satisfactorily and consequently were little used until the advent of clamped, throwaway inserts. Moreover, the carbides were notoriously brittle and could take only fine cuts in minimal-shock conditions. Titanium-carbide-based grades again came into prominence about 1960, when nickelmolybdenum began to be used as a binder instead of nickel. The new grades were able to perform a wider range of tasks including interrupted cutting and cutting under shock conditions. The very high indentation hardness values recorded for titanium carbide grades are not accompanied by correspondingly greater resistance to abrasive wear, the apparently less hard tungsten carbide being considerably superior in this property. Moreover, carbonitrides, advanced tantalum-containing multicarbides, and coated variants generally provide better all-round cutting performances. Titanium-Base Carbonitrides: Development of titanium-carbonitride-based cuttingtool materials predates the use of coatings of this type on more conventional hardmetals by many years. Appreciable, though uncontrolled, amounts of carbonitride were often present, if only by accident, when cracked ammonia was used as a less expensive substitute for hydrogen in some stages of the production process in the 1950's and perhaps for two decades earlier. Much of the recent, more scientific development of this class of materials has taken place in the United States, particularly by Teledyne Firth Sterling with its SD3 grade and in Japan by several companies. Many of the compositions currently in use are extremely complex, and their structures—even with apparently similar compositions—can vary enormously. For instance, Mitsubishi characterizes its Himet NX series of cermets as TiC/WC/Ta(Nb)C/Mo2C/TiN/Ni/Co/Al, with a structure comprising both large and medium-size carbide particles (mainly TiC according to the quoted density) in a superalloy-type matrix containing an aluminum-bearing intermetallic compound. Steel- and Alloy-Bonded Titanium Carbide: The class of material exemplified by FerroTic, as it is known, consists primarily of titanium carbide bonded with heat-treatable steel, but some grades also contain tungsten carbide or are bonded with nickel- or copper-base alloys. These cemented carbides are characterized by high binder contents (typically 50– 60 per cent by volume) and lower hardnesses, compared with the more usual hardmetals, and by the great variation in properties obtained by heat treatment. In the annealed condition, steel-bonded carbides have a relatively soft matrix and can be machined with little difficulty, especially by CBN (superhard cubic boron nitride) tools. After heat treatment, the degree of hardness and wear resistance achieved is considerably greater than that of normal tool steels, although understandably much less than that of traditional sintered carbides. Microstructures are extremely varied, being composed of 40–50 per cent TiC by volume and a matrix appropriate to the alloy composition and the stage of heat treatment. Applications include stamping, blanking and drawing dies, machine components, and similar items where the ability to machine before hardening reduces production costs substantially. Coating: As a final stage in carbide manufacture, coatings of various kinds are applied mainly to cutting tools, where for cutting steel in particular it is advantageous to give the rank and clearance surfaces characteristics that are quite different from those of the body of the insert. Coatings of titanium carbide, nitride, or carbonitride; of aluminum oxide; and of other refractory compounds are applied to a variety of hardmetal substrates by chemical or physical vapor deposition (CVD or PVD) or by newer plasma methods.



777

The most recent types of coatings include hafnium, tantalum, and zirconium carbides and nitrides; alumina/titanium oxide; and multiple carbide/carbonitride/nitride/oxide, oxynitride or oxycarbonitride combinations. Greatly improved properties have been claimed for variants with as many as 13 distinct CVD coatings. A markedly sharper cutting edge compared with other CVD-coated hardmetals is claimed, permitting finer cuts and the successful machining of soft but abrasive alloys. The keenest edges on coated carbides are achieved by the techniques of physical vapor deposition. In this process, ions are deposited directionally from the electrodes, rather than evenly on all surfaces, so the sharpness of cutting edges is maintained and may even be enhanced. PVD coatings currently available include titanium nitride and carbonitride, their distinctive gold color having become familiar throughout the world on high-speed steel tooling. The high temperatures required for normal CVD tends to soften heat-treated high-speed steel. PVD-coated hardmetals have been produced commercially for several years, especially for precision milling inserts. Recent developments in extremely hard coatings, generally involving exotic techniques, include boron carbide, cubic boron nitride, and pure diamond. Almost the ultimate in wear resistance, the commercial applications of thin plasma-generated diamond surfaces at present are mainly in manufacture of semiconductors, where other special properties are important. For cutting tools the substrate is of equal importance to the coating in many respects, its critical properties including fracture toughness (resistance to crack propagation), elastic modulus, resistance to heat and abrasion, and expansion coefficient. Some manufacturers are now producing inserts with graded composition, so that structures and properties are optimized at both surface and interior, and coatings are less likely to crack or break away. Specifications: Compared with other standardized materials, the world of sintered hardmetals is peculiar. For instance, an engineer who seeks a carbide grade for the finishmachining of a steel component may be told to use ISO Standard Grade P10 or Industry Code C7. If the composition and nominal properties of the designated tool material are then requested, the surprising answer is that, in basic composition alone, the tungsten carbide content of P10 (or of the now superseded C7) can vary from zero to about 75, titanium carbide from 8 to 80, cobalt 0 to 10, and nickel 0 to 15 per cent. There are other possible constituents, also, in this so-called standard alloy, and many basic properties can vary as much as the composition. All that these dissimilar materials have in common, and all that the so-called standards mean, is that their suppliers—and sometimes their suppliers alone—consider them suitable for one particular and ill-defined machining application (which for P10 or C7 is the finish machining of steel). This peculiar situation arose because the production of cemented carbides in occupied Europe during World War II was controlled by the German Hartmetallzentrale, and no factory other than Krupp was permitted to produce more than one grade. By the end of the war, all German-controlled producers were equipped to make the G, S, H, and F series to German standards. In the postwar years, this series of carbides formed the basis of unofficial European standardization. With the advent of the newer multicarbides, the previous identities of grades were gradually lost. The applications relating to the old grades were retained, however, as a new German DIN standard, eventually being adopted, in somewhat modified form, by the International Standards Organization (ISO) and by ANSI in the United States. The American cemented carbides industry developed under diverse ownership and solid competition. The major companies actively and independently developed new varieties of hardmetals, and there was little or no standardization, although there were many attempts to compile equivalent charts as a substitute for true standardization. Around 1942, the Buick division of GMC produced a simple classification code that arranged nearly 100 grades derived from 10 manufacturers under only 14 symbols (TC-1 to TC-14). In spite of serious deficiencies, this system remained in use for many years as an American industry



HARDMETAL CUTTING TOOL INSERTS

standard; that is, Buick TC-1 was equivalent to industry code C1. Buick itself went much further, using the tremendous influence, research facilities, and purchasing potential of its parent company to standardize the products of each carbide manufacturer by properties that could be tested, rather than by the indeterminate recommended applications. Many large-scale carbide users have developed similar systems in attempts to exert some degree of in-house standardization and quality control. Small and medium-sized users, however, still suffer from so-called industry standards, which only provide a starting point for grade selection. ISO standard 513, summarized in Table 2, divides all machining grades into three colorcoded groups: straight tungsten carbide grades (letter K, color red) for cutting gray cast iron, nonferrous metals, and nonmetallics; highly alloyed grades (letter, P. color blue) for machining steel; and less alloyed grades (letter M, color yellow, generally with less TiC than the corresponding P series), which are multipurpose and may be used on steels, nickel-base superalloys, ductile cast irons, and so on. Each grade within a group is also given a number to represent its position in a range from maximum hardness to maximum toughness (shock resistance). Typical applications are described for grades at more or less regular numerical intervals. Although coated grades scarcely existed when the ISO standard was prepared, it is easy to classify coated as uncoated carbides—or carbonitrides, ceramics, and superhard materials—according to this system. In this situation, it is easy to see how one plant will prefer one manufacturer's carbide and a second plant will prefer that of another. Each has found the carbide most nearly ideal for the particular conditions involved. In these circumstances it pays each manufacturer to make grades that differ in hardness, toughness, and crater resistance, so that they can provide a product that is near the optimum for a specific customer's application. Although not classified as a hard metal, new particle or powder metallurgical methods of manufacture, coupled with new coating technology have led in recent years to something of an upsurge in the use of high speed steel. Lower cost is a big factor, and the development of such coatings as titanium nitride, cubic boron nitride, and pure diamond, has enabled some high speed steel tools to rival tools made from tungsten and other carbides in their ability to maintain cutting accuracy and prolong tool life. Multiple layers may be used to produce optimum properties in the coating, with adhesive strength where there is contact with the substrate, combined with hardness at the cutting surface to resist abrasion. Total thickness of such coating, even with multiple layers, is seldom more than 15 microns (0.000060 in.). Importance of Correct Grades: A great diversity of hardmetal types is required to cope with all possible combinations of metals and alloys, machining operations, and working conditions. Tough, shock-resistant grades are needed for slow speeds and interrupted cutting, harder grades for high-speed finishing, heat-resisting alloyed grades for machining superalloys, and crater-resistant compositions, including most of the many coated varieties, for machining steels and ductile iron. Ceramics.—Moving up the hardness scale, ceramics provide increasing competition for cemented carbides, both in performance and in cost-effectiveness, though not yet in reliability. Hardmetals themselves consist of ceramics—nonmetallic refractory compounds, usually carbides or carbonitrides—with a metallic binder of much lower melting point. In such systems, densification generally takes place by liquid-phase sintering. Pure ceramics have no metallic binder, but may contain lower-melting-point compounds or ceramic mixtures that permit liquid-phase sintering to take place. Where this condition is not possible, hot pressing or hot isostatic pressing can often be used to make a strong, relatively porefree component or cutting insert. This section is restricted to those ceramics that compete directly with hardmetals, mainly in the cutting-tool category as shown in Table 3. Ceramics are hard, completely nonmetallic substances that resist heat and abrasive wear. Increasingly used as clamped indexable tool inserts, ceramics differ significantly from tool



Table 2. ISO Classifications of Hardmetals (Cemented Carbides and Carbonitrides) by Application Main Types of Chip Removal Symbol and Color

Ferrous with long chips

Steel, steel castings

P10

Steel, steel casting

P20

Steel, steel castings, ductile cast iron with long chips Steel, steel castings, ductile cast iron with long chips Steel, steel castings with sand inclusions and cavities

P40

Ferrous metals with long or short chips, and non ferrous metals

Steel, steel castings of medium or low tensile strength, with sand inclusions and cavities

M10

Steel, steel castings, manganese steel, gray cast iron, alloy cast iron Steel, steel castings, austenitic or manganese steel, gray cast iron Steel, steel castings, austenitic steel, gray cast iron, high-temperature-resistant alloys Mild, free-cutting steel, low-tensile steel, nonferrous metals and light alloys Very hard gray cast iron, chilled castings over 85 Shore, high-silicon aluminum alloys, hardened steel, highly abrasive plastics, hard cardboard, ceramics Gray cast iron over 220 Brinell, malleable cast iron with short chips, hardened steel, siliconaluminum and copper alloys, plastics, glass, hard rubber, hard cardboard, porcelain, stone Gray cast iron up to 220 Brinell, nonferrous metals, copper, brass, aluminum Low-hardness gray cast iron, low-tensile steel, compressed wood Softwood or hard wood, nonferrous metals

M20

M40 Ferrous metals with short chips, non-ferrous metals and non-metallic materials

K01

K10

K20 K30 K40

Use and Working Conditions Finish turning and boring; high cutting speeds, small chip sections, accurate dimensions, fine finish, vibration-free operations Turning, copying, threading, milling; high cutting speeds; small or medium chip sections Turning, copying, milling; medium cutting speeds and chip sections, planing with small chip sections Turning, milling, planing; medium or large chip sections, unfavorable machining conditions Turning, planing, slotting; low cutting speeds, large chip sections, with possible large cutting angles, unfavorable cutting conditions, and work on automatic machines Operations demanding very tough carbides; turning, planing, slotting; low cutting speeds, large chip sections, with possible large cutting angles, unfavorable conditions and work on automatic machines Turning; medium or high cutting speeds, small or medium chip sections

of cut

of carbide ↑ speed ↑ wear

Turning, milling; medium cutting speeds and chip sections Turning, milling, planing; medium cutting speeds, medium or large chip sections Turning, parting off; particularly on automatic machines Turning, finish turning, boring, milling, scraping

Turning, milling, drilling, boring, broaching, scraping

Turning, milling, planing, boring, broaching, demanding very tough carbide Turning, milling, planing, slotting, unfavorable conditions, and possibility of large cutting angles Turning, milling, planing, slotting, unfavorable conditions, and possibility of large cutting angles


↓ feed ↓ toughness

779

P50

M30

K Red

Specific Material to be Machined

P01

P30

M Yellow

Direction of Decrease in Characteristic

Groups of Applications Designation (Grade)

CEMENTED CARBIDES AND OTHER HARD MATERI-

P Blue

Broad Categories of Materials to be Machined



steels, which are completely metallic. Ceramics also differ from cermets such as cemented carbides and carbonitrides, which comprise minute ceramic particles held together by metallic binders. Table 3. Typical Properties of Cutting Tool Ceramics Group Typical composition types Density (g/cm3) Transverse rupture strength (N/mm2) Compressive strength (kN/mm2) Hardness (HV)

Alumina

Alumina/TiC

Silicon Nitride

Al2O3 or Al2O3/ZrO2

70⁄30 Al2O3/TiC

Si3N4/Y2O3 plus

4.0 700 4.0

4.25 750 4.5

3.27

PCD

3.4

800 4.0

PCBN

3.1 800

4.7

3.8

1750

1800

1600 50

28

Young's modulus (kN/mm2)

380

370

300

925

680

Modulus of rigidity (kN/mm2) Poisson's ratio

150

160

150

430

280

Hardness HK

(kN/mm2)

Thermal expansion coefficient (10−6/K) Thermal conductivity (W/m K) Fracture toughness (K1cMN/m3⁄2)

0.24 8.5 23 2.3

0.22 7.8 17 3.3

0.20 3.2 22 5.0

0.09 3.8 120 7.9

0.22 4.9 100 10

Alumina-based ceramics were introduced as cutting inserts during World War II, and were for many years considered too brittle for regular machine-shop use. Improved machine tools and finer-grain, tougher compositions incorporating zirconia or silicon carbide “whiskers” now permit their use in a wide range of applications. Silicon nitride, often combined with alumina (aluminum oxide), yttria (yttrium oxide), and other oxides and nitrides, is used for much of the high-speed machining of superalloys, and newer grades have been formulated specifically for cast iron—potentially a far larger market. In addition to improvements in toolholders, great advances have been made in machine tools, many of which now feature the higher powers and speeds required for the efficient use of ceramic tooling. Brittleness at the cutting edge is no longer a disadvantage, with the improvements made to the ceramics themselves, mainly in toughness, but also in other critical properties. Although very large numbers of useful ceramic materials are now available, only a few combinations have been found to combine such properties as minimum porosity, hardness, wear resistance, chemical stability, and resistance to shock to the extent necessary for cutting-tool inserts. Most ceramics used for machining are still based on high-purity, finegrained alumina (aluminum oxide), but embody property-enhancing additions of other ceramics such as zirconia (zirconium oxide), titania (titanium oxide), titanium carbide, tungsten carbide, and titanium nitride. For commercial purposes, those more commonly used are often termed “white” (alumina with or without zirconia) or “black” (roughly 70⁄30 alumina/titanium carbide). More recent developments are the distinctively green alumina ceramics strengthened with silicon carbide whiskers and the brown-tinged silicon nitride types. Ceramics benefit from hot isostatic pressing, used to remove the last vestiges of porosity and raise substantially the material's shock resistance, even more than carbide-based hardmetals. Significant improvements are derived by even small parts such as tool inserts, although, in principle, they should not need such treatment if raw materials and manufacturing methods are properly controlled. Oxide Ceramics: Alumina cutting tips have extreme hardness—more than HV 2000 or HRA 94—and give excellent service in their limited but important range of uses such as the machining of chilled iron rolls and brake drums. A substantial family of alumina-based materials has been developed, and fine-grained alumina-based composites now have suf-



781

ficient strength for milling cast iron at speeds up to 2500 ft/min (800 m/min). Resistance to cratering when machining steel is exceptional. Oxide/Carbide Ceramics: A second important class of alumina-based cutting ceramics combines aluminum oxide or alumina-zirconia with a refractory carbide or carbides, nearly always 30 per cent TiC. The compound is black and normally is hot pressed or hot isostatically pressed (HIPed). As shown in Table 3, the physical and mechanical properties of this material are generally similar to those of the pure alumina ceramics, but strength and shock resistance are generally higher, being comparable with those of higher-toughness simple alumina-zirconia grades. Current commercial grades are even more complex, combining alumina, zirconia, and titanium carbide with the further addition of titanium nitride. Silicon Nitride Base: One of the most effective ceramic cutting-tool materials developed in the UK is Syalon (from SiAlON or silicon-aluminum-oxynitride) though it incorporates a substantial amount of yttria for efficient liquid-phase sintering). The material combines high strength with hot hardness, shock resistance, and other vital properties. Syalon cutting inserts are made by Kennametal and Sandvik and sold as Kyon 2000 and CC680, respectively. The brown Kyon 200 is suitable for machining high-nickel alloys and cast iron, but a later development, Kyon 3000 has good potential for machining cast iron. Resistance to thermal stress and thermal shock of Kyon 2000 are comparable to those of sintered carbides. Toughness is substantially less than that of carbides, but roughly twice that of oxide-based cutting-tool materials at temperatures up to 850°C. Syon 200 can cut at high edge temperatures and is harder than carbide and some other ceramics at over 700°C, although softer than most at room temperature. Whisker-Reinforced Ceramics: To improve toughness, Greenleaf Corp. has reinforced alumina ceramics with silicon carbide single-crystal “whiskers” that impart a distinctive green color to the material, marketed as WG300. Typically as thin as human hairs, the immensely strong whiskers improve tool life under arduous conditions. Whisker-reinforced ceramics and perhaps hardmetals are likely to become increasingly important as cutting and wear-resistant materials. Their only drawback seems to be the carcinogenic nature of the included fibers, which requires stringent precautions during manufacture. Superhard Materials.—Polycrystalline synthetic diamond (PCD) and cubic boron nitride (PCBN), in the two columns at the right in Table 3, are almost the only cuttinginsert materials in the “superhard” category. Both PCD and PCBN are usually made with the highest practicable concentration of the hard constituent, although ceramic or metallic binders can be almost equally important in providing overall strength and optimizing other properties. Variations in grain size are another critical factor in determining cutting characteristics and edge stability. Some manufacturers treat CBN in similar fashion to tungsten carbide, varying the composition and amount of binder within exceptionally wide limits to influence the physical and mechanical properties of the sintered compact. In comparing these materials, users should note that some inserts comprise solid polycrystalline diamond or CBN and are double-sized to provide twice the number of cutting edges. Others consist of a layer, from 0.020 to 0.040 in. (0.5 to 1 mm) thick, on a tough carbide backing. A third type is produced with a solid superhard material almost surrounded by sintered carbide. A fourth type, used mainly for cutting inserts, comprises solid hard metal with a tiny superhard insert at one or more (usually only one) cutting corners or edges. Superhard cutting inserts are expensive—up to 30 times the cost of equivalent shapes or sizes in ceramic or cemented carbide—but their outstanding properties, exceptional performance and extremely long life can make them by far the most cost-effective for certain applications. Diamond: Diamond is the hardest material found or made. As harder, more abrasive ceramics and other materials came into widespread use, diamond began to be used for grinding-wheel grits. Cemented carbide tools virtually demanded diamond grinding wheels for fine edge finishing. Solid single-crystal diamond tools were and are used to a




small extent for special purposes, such as microtomes, for machining of hard materials, and for exceptionally fine finishes. These diamonds are made from comparatively large, high-quality gem-type diamonds, have isotropic properties, and are very expensive. By comparison, diamond abrasive grits cost only a few dollars a carat. Synthetic diamonds are produced from graphite using high temperatures and extremely high pressures. The fine diamond particles produced are sintered together in the presence of a metal “catalyst” to produce high-efficiency anisotropic cutting tool inserts. These tools comprise either a solid diamond compact or a layer of sintered diamond on a carbide backing, and are made under conditions similar to, though less severe than, those used in diamond synthesis. Both natural and synthetic diamond can be sintered in this way, although the latter method is the most frequently used. Polycrystalline diamond (PCD) compacts are immensely hard and can be used to machine many substances, from highly abrasive hardwoods and glass fiber to nonferrous metals, hardmetals, and tough ceramics. Important classes of tools that are also available with cubic boron nitride inserts include brazed-tip drills, single-point turning tools, and face-milling cutters. Boron Nitride: Polycrystalline diamond has one big limitation: it cannot be used to machine steel or any other ferrous material without rapid chemical breakdown. Boron nitride does not have this limitation. Normally soft and slippery like graphite, the soft hexagonal crystals (HBN) become cubic boron nitride (CBN) when subjected to ultrahigh pressures and temperatures, with a structure similar to and hardness second only to diamond. As a solid insert of polycrystalline cubic boron nitride (PCBN), the compound machines even the hardest steel with relative immunity from chemical breakdown or cratering. Backed by sintered carbide, inserts of PCBN can readily be brazed, increasing the usefulness of the material and the range of tooling in which it can be used. With great hardness and abrasion resistance, coupled with extreme chemical stability when in contact with ferrous alloys at high temperatures, PCBN has the ability to machine both steels and cast irons at high speeds for long operating cycles. Only its currently high cost in relation to hardmetals prevents its wider use in mass-production machining. Similar in general properties to PCBN, the recently developed “Wurbon” consists of a mixture of ultrafine (0.02 µm grain size) hexagonal and cubic boron nitride with a “wurtzite” structure, and is produced from soft hexagonal boron nitride in a microsecond by an explosive shock-wave. Basic Machining Data: Most mass-production metalcutting operations are carried out with carbide-tipped tools but their correct application is not simple. Even apparently similar batches of the same material vary greatly in their machining characteristics and may require different tool settings to attain optimum performance. Depth of cut, feed, surface speed, cutting rate, desired surface finish, and target tool life often need to be modified to suit the requirements of a particular component. For the same downtime, the life of an insert between indexings can be less than that of an equivalent brazed tool between regrinds, so a much higher rate of metal removal is possible with the indexable or throwaway insert. It is commonplace for the claims for a new coating to include increases in surface-speed rates of 200–300 per cent, and for a new insert design to offer similar improvements. Many operations are run at metal removal rates that are far from optimum for tool life because the rates used maximize productivity and cost-effectiveness. Thus any recommendations for cutting speeds and feeds must be oversimplified or extremely complex, and must be hedged with many provisos, dependent on the technical and economic conditions in the manufacturing plant concerned. A preliminary grade selection should be made from the ISO-based tables and manufacturers' literature consulted for recommendations on the chosen grades and tool designs. If tool life is much



783

greater than that desired under the suggested conditions, speeds, feeds, or depths of cut may be increased. If tools fail by edge breakage, a tougher (more shock-resistant) grade should be selected, with a numerically higher ISO code. Alternatively, increasing the surface speed and decreasing the feed may be tried. If tools fail prematurely from what appears to be abrasive wear, a harder grade with numerically lower ISO designation should be tried. If cratering is severe, use a grade with higher titanium carbide content; that is, switch from an ISO K to M or M to P grade, use a P grade with lower numerical value, change to a coated grade, or use a coated grade with a (claimed) more-resistant surface layer. Built-Up Edge and Cratering: The big problem in cutting steel with carbide tools is associated with the built-up edge and the familar phenomenon called cratering. Research has shown that the built-up edge is continuous with the chip itself during normal cutting. Additions of titanium, tantalum, and niobium to the basic carbide mixture have a remarkable effect on the nature and degree of cratering, which is related to adhesion between the tool and the chip. Hardmetal Tooling for Wood and Nonmetallics.—Carbide-tipped circular saws are now conventional for cutting wood, wood products such as chipboard, and plastics, and tipped bandsaws of large size are also gaining in popularity. Tipped handsaws and mechanical equivalents are seldom needed for wood, but they are extremely useful for cutting abrasive building boards, glass-reinforced plastics, and similar material. Like the hardmetal tips used on most other woodworking tools, saw tips generally make use of straight (unalloyed) tungsten carbide/cobalt grades. However, where excessive heat is generated as with the cutting of high-silica hardwoods and particularly abrasive chipboards, the very hard but tough tungsten-titanium-tantalum-niobium carbide solid-solution grades, normally reserved for steel finishing, may be preferred. Saw tips are usually brazed and reground a number of times during service, so coated grades appear to have little immediate potential in this field. Cutting Blades and Plane Irons: These tools comprise long, thin, comparatively wide slabs of carbide on a minimal-thickness steel backing. Compositions are straight tungsten carbide, preferably micrograin (to maintain a keen cutting edge with an included angle of 30° or less), but with relatively high amounts of cobalt, 11–13 per cent, for toughness. Considerable expertise is necessary to braze and grind these cutters without inducing or failing to relieve the excessive stresses that cause distortion or cracking. Other Woodworking Cutters: Routers and other cutters are generally similar to those used on metals and include many indexable-insert designs. The main difference with wood is that rotational and surface speeds can be the maximum available on the machine. Highspeed routing of aluminum and magnesium alloys was developed largely from machines and techniques originally designed for work on wood. Cutting Other Materials: The machining of plastics, fiber-reinforced plastics, graphite, asbestos, and other hard and abrasive constructional materials mainly requires abrasion resistance. Cutting pressures and power requirements are generally low. With thermoplastics and some other materials, particular attention must be given to cooling because of softening or degradation of the work material that might be caused by the heat generated in cutting. An important application of cemented carbides is the drilling and routing of printed circuit boards. Solid tungsten carbide drills of extremely small sizes are used for this work.



FORMING TOOLS

FORMING TOOLS When curved surfaces or those of stepped, angular or irregular shape are required in connection with turning operations, especially on turret lathes and “automatics,” forming tools are used. These tools are so made that the contour of the cutting edge corresponds to the shape required and usually they may be ground repeatedly without changing the shape of the cutting edge. There are two general classes of forming tools—the straight type and the circular type. The circular forming tool is generally used on small narrow forms, whereas the straight type is more suitable for wide forming operations. Some straight forming tools are clamped in a horizontal position upon the cut-off slide, whereas the others are held in a vertical position in a special holder. A common form of holder for these vertical tools is one having a dovetail slot in which the forming tool is clamped; hence they are often called “dovetail forming tools.” In many cases, two forming tools are used, especially when a very smooth surface is required, one being employed for roughing and the other for finishing. There was an American standard for forming tool blanks which covered both straight or dovetailed, and circular forms. The formed part of the finished blanks must be shaped to suit whatever job the tool is to be used for. This former standard includes the important dimensions of holders for both straight and circular forms. Dimensions of Steps on Straight or Dovetail Forming Tools.—The diagrams at the top of the accompanying Table 1 illustrate a straight or “dovetail” forming tool. The upper or cutting face lies in the same plane as the center of the work and there is no rake. (Many forming tools have rake to increase the cutting efficiency, and this type will be referred to later.) In making a forming tool, the various steps measured perpendicular to the front face (as at d) must be proportioned so as to obtain the required radial dimensions on the work. For example, if D equals the difference between two radial dimensions on the work, then: Step d = D × cosine front clearance angle Angles on Straight Forming Tools.—In making forming tools to the required shape or contour, any angular surfaces (like the steps referred to in the previous paragraph) are affected by the clearance angle. For example, assume that angle A on the work (see diagram at top of accompanying table) is 20 degrees. The angle on the tool in plane x-x, in that case, will be slightly less than 20 degrees. In making the tool, this modified or reduced angle is required because of the convenience in machining and measuring the angle square to the front face of the tool or in the plane x–x. If the angle on the work is measured from a line parallel to the axis (as at A in diagram), then the reduced angle on the tool as measured square to the front face (or in plane x–x) is found as follows: tan reduced angle on tool = tan A × cos front clearance angle If angle A on the work is larger than, say, 45 degrees, it may be given on the drawing as indicated at B. In this case, the angle is measured from a plane perpendicular to the axis of the work. When the angle is so specified, the angle on the tool in plane x–x may be found as follows: tan B tan reduced angle on tool = ---------------------------------------------cos clearance angle Table Giving Step Dimensions and Angles on Straight or Dovetailed Forming Tools.—The accompanying table gives the required dimensions and angles within its range, direct or without calculation.


Machinery's Handbook 27th Edition FORMING TOOLS

785

Table 1. Dimensions of Steps and Angles on Straight Forming Tools

D

x A

d

C B

x

C Radial Depth of Step D

When C = 10°

Depth d of step on tool When C = 15°

When C = 20°

Radial Depth of Step D

When C = 10°

Depth d of step on tool When C = 15°

When C = 20°

0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.020 0.030

0.00098 0.00197 0.00295 0.00393 0.00492 0.00590 0.00689 0.00787 0.00886 0.00984 0.01969 0.02954

0.00096 0.00193 0.00289 0.00386 0.00483 0.00579 0.00676 0.00772 0.00869 0.00965 0.01931 0.02897

0.00094 0.00187 0.00281 0.00375 0.00469 0.00563 0.00657 0.00751 0.00845 0.00939 0.01879 0.02819

0.040 0.050 0.060 0.070 0.080 0.090 0.100 0.200 0.300 0.400 0.500 …

0.03939 0.04924 0.05908 0.06893 0.07878 0.08863 0.09848 0.19696 0.29544 0.39392 0.49240 …

0.03863 0.04829 0.05795 0.06761 0.07727 0.08693 0.09659 0.19318 0.28977 0.38637 0.48296 …

0.03758 0.04698 0.05638 0.06577 0.07517 0.08457 0.09396 0.18793 0.28190 0.37587 0.46984 …

Upper section of table gives depth d of step on forming tool for a given dimension D that equals the actual depth of the step on the work, measured radially and along the cutting face of the tool (see diagram at left). First, locate depth D required on work; then find depth d on tool under tool clearance angle C. Depth d is measured perpendicular to front face of tool. Angle A in Plane of Tool Cutting Face 5° 10 15 20 25 30 35 40 45

Angle on tool in plane x–x When C = 10° 4° 9 14 19 24 29 34 39 44

55′ 51 47 43 40 37 35 34 34

When C = 15° 4° 9 14 19 24 29 34 39 44

50′ 40 31 22 15 9 4 1 0

When C = 20° 4° 9 14 18 23 28 33 38 43

42′ 24 8 53 40 29 20 15 13

Angle A in Plane of Tool Cutting Face 50° 55 60 65 70 75 80 85 …

Angle on tool in plane x–x When C = 10° 49° 54 59 64 69 74 79 84

34′ 35 37 40 43 47 51 55 …

When C = 15° 49° 54 59 64 69 74 79 84

1′ 4 8 14 21 30 39 49 …

When C = 20° 48° 53 58 63 68 74 79 84

14′ 18 26 36 50 5 22 41 …

Lower section of table gives angles as measured in plane x–x perpendicular to front face of forming tool (see diagram on right). Find in first column the angle A required on work; then find reduced angle in plane x–x under given clearance angle C.

To Find Dimensions of Steps: The upper section of Table 1 is used in determining the dimensions of steps. The radial depth of the step or the actual cutting depth D (see left-hand diagram) is given in the first column of the table. The columns that follow give the corresponding depths d for a front clearance angle of 10, 15, or 20 degrees. To illustrate the use of the table, suppose a tool is required for turning the part shown in Fig. 1, which has diameters of 0.75, 1.25, and 1.75 inches, respectively. The difference between the largest and the smallest radius is 0.5 inch, which is the depth of one step. Assume that the clearance angle is 15 degrees. First, locate 0.5 in the column headed “Radial Depth of Step D”; then find depth d in the column headed “when C = 15°.” As will be seen, this depth is 0.48296



FORMING TOOLS

inch. Practically the same procedure is followed in determining the depth of the second step on the tool. The difference in the radii in this case equals0.25. This value is not given directly in the table, so first find the depth equivalent to 0.200 and add to it the depth equivalent to 0.050. Thus, we have 0.19318 + 0.04829 = 0.24147. In using Table 1, it is assumed that the top face of the tool is set at the height of the work axis. To Find Angle: The lower section of Table 1 applies to angles when they are measured relative to the axis of the work. The application of the table will again be illustrated by using the part shown in Fig. 1. The angle used here is 40 degrees (which is also the angle in the plane of the cutting face of the tool). If the clearance angle is 15 degrees, the angle measured in plane x–x square to the face of the tool is shown by the table to be 39° 1′- a reduction of practically 1 degree.

y R

13 4"

3 4"

11 4"

r F

x D

40˚ Fig. 1.

E Fig. 2.

If a straight forming tool has rake, the depth x of each step (see Fig. 2), measured perpendicular to the front or clearance face, is affected not only by the clearance angle, but by the rake angle F and the radii R and r of the steps on the work. First, it is necessary to find three angles, designated A, B, and C, that are not shown on the drawing. Angle A = 180° – rake angle F r sin A sin B = -------------R Angle C = 180° – ( A + B ) R sin C y = ---------------sin A Angle D of tool = 90° – ( E + F ) Depth x = y sin D If the work has two or more shoulders, the depth x for other steps on the tool may be determined for each radius r. If the work has curved or angular forms, it is more practical to use a tool without rake because its profile, in the plane of the cutting face, duplicates that of the work. Example:Assume that radius R equals 0.625 inch and radius r equals 0.375 inch, so that the step on the work has a radial depth of 0.25 inch. The tool has a rake angle F of 10 degrees and a clearance angle E of 15 degrees. Then angle A = 180 − 10 = 170 degrees.



787

0.375 × 0.17365 sin B = --------------------------------------- = 0.10419 Angle B = 5°59′ nearly. 0.625 Angle C = 180 – ( 170° + 5°59′ ) = 4°1′ 0.625 × 0.07005 Dimension y = --------------------------------------- = 0.25212 0.17365 Angle D = 90° – ( 15 + 10 ) = 65 degrees Depth x of step = 0.25212 × 0.90631 = 0.2285 inch Circular Forming Tools.—To provide sufficient peripheral clearance on circular forming tools, the cutting face is offset with relation to the center of the tool a distance C, as shown in Fig. 3. Whenever a circular tool has two or more diameters, the difference in the radii of the steps on the tool will not correspond exactly to the difference in the steps on the work. The form produced with the tool also changes, although the change is very slight, unless the amount of offset C is considerable. Assume that a circular tool is required to produce the piece A having two diameters as shown. A

C

r

R

D1

D

Fig. 3.

If the difference D1 between the large and small radii of the tool were made equal to dimension D required on the work, D would be a certain amount oversize, depending upon the offset C of the cutting edge. The following formulas can be used to determine the radii of circular forming tools for turning parts to different diameters: Let R = largest radius of tool in inches; D = difference in radii of steps on work; C = amount cutting edge is offset from center of tool; r = required radius in inches; then 2

⎛ R 2 – C 2 – D⎞ + C 2 ⎝ ⎠ If the small radius r is given and the large radius R is required, then r =

(1)

2

⎛ r 2 – C 2 + D⎞ + C 2 (2) ⎝ ⎠ To illustrate, if D (Fig. 3) is to be 1⁄8 inch, the large radius R is 11⁄8 inches, and C is 5⁄32 inch, what radius r would be required to compensate for the offset C of the cutting edge? Inserting these values in Formula (1): R =

r =

2

2

2

2

( 1 1⁄8 ) – ( 5⁄32 ) – ( 1⁄8 ) + ( 5⁄32 ) = 1.0014 inches

The value of r is thus found to be 1.0014 inches; hence, the diameter = 2 × 1.0014 = 2.0028 inches instead of 2 inches, as it would have been if the cutting edge had been exactly on the center line. Formulas for circular tools used on different makes of screw machines can be simplified when the values R and C are constant for each size of machine. The accompanying Table 2, Formulas for Circular Forming Tools, gives the standard values of R and C for circular tools used on different automatics. The formulas for determining the



FORMING TOOLS Table 2. Formulas for Circular Forming Tools a

Make of Machine

Brown & Sharpe

Acme

Size of Machine

Radius R, Inches

Offset C, Inches

No. 00

0.875

0.125

r =

( 0.8660 – D ) 2 + 0.0156

No. 0

1.125

0.15625

r =

( 1.1141 – D ) + 0.0244

No. 2

1.50

0.250

r =

( 1.4790 – D ) + 0.0625

No. 6

2.00

0.3125

r =

( 1.975 – D ) + 0.0976

No. 51

0.75

0.09375

r =

( 1.7441 – D ) + 0.0088

No. 515

0.75

0.09375

r =

( 0.7441 – D ) + 0.0088

No. 52

1.0

0.09375

r =

( 0.9956 – D ) + 0.0088

No. 53

1.1875

0.125

r =

( 1.1809 – D ) + 0.0156

No. 54

1.250

0.15625

r =

( 1.2402 – D ) + 0.0244

No. 55

1.250

0.15625

r =

( 1.2402 – D ) + 0.0244

No. 56

1.50

0.1875

r =

( 1.4882 – D ) + 0.0352

1⁄ ″ 4

0.625

0.03125

r =

( 0.6242 – D ) + 0.0010

3⁄ ″ 8

0.084375

0.0625

r =

( 0.8414 – D ) + 0.0039

1.15625

0.0625

r =

( 1.1546 – D ) + 0.0039

1.1875

0.0625

r =

( 1.1859 – D ) + 0.0039

2″

1.375 1.375

0.0625 0.0625

r =

( 1.3736 – D ) + 0.0039

r =

( 1.6202 – D ) + 0.0156

5⁄ ″ 8 7⁄ ″ 8

Cleveland

11⁄4″

Radius r, Inches

2 2

2

2 2 2 2 2 2 2 2 2 2 2

2

21⁄4″

1.625

0.125

23⁄4″

1.875

0.15625

31⁄4″

1.875

0.15625

r =

( 1.8685 – D ) + 0.0244

41⁄4″

2.50

0.250

r =

( 2.4875 – D ) + 0.0625

2.625

0.250

r =

( 2.6131 – D ) + 0.0625

6″

2

2

2 2

a For notation, see Fig. 3

radius r (see column at right-hand side of table) contain a constant that represents the value 2

2

of the expression R – C in Formula (1). Table 3, Constant for Determining Diameters of Circular Forming Tools has been compiled to facilitate proportioning tools of this type and gives constants for computing the various diameters of forming tools, when the cutting face of the tool is 1⁄8, 3⁄16, 1⁄4, or 5⁄16 inch below the horizontal center line. As there is no standard distance for the location of the cutting face, the table has been prepared to correspond with distances commonly used. As an example, suppose the tool is required for a part having three diameters of 1.75, 0.75, and 1.25 inches, respectively, as shown in Fig. 1, and that the largest diameter of the tool is 3 inches and the cutting face is 1⁄4 inch below the horizontal center line. The first step would



789

be to determine approximately the respective diameters of the forming tool and then correct the diameters by the use of the table. To produce the three diameters shown in Fig. 1, with a 3-inch forming tool, the tool diameters would be approximately 2, 3, and 2.5 inches, respectively. The first dimension (2 inches) is 1 inch less in diameter than that of the tool, and the necessary correction should be given in the column “Correction for Difference in Diameter”; but as the table is only extended to half-inch differences, it will be necessary to obtain this particular correction in two steps. On the line for 3-inch diameter and under corrections for 1⁄2 inch, we find 0.0085; then in line with 21⁄2 and under the same heading, we find 0.0129, hence the total correction would be 0.0085 + 0.0129 = 0.0214 inch. This correction is added to the approximate diameter, making the exact diameter of the first step 2 + 0.0214 = 2.0214 inches. The next step would be computed in the same way, by noting on the 3-inch line the correction for 1⁄2 inch and adding it to the approximate diameter of the second step, giving an exact diameter of 2.5 + 0.0085 + 2.5085 inches. Therefore, to produce the part shown in Fig. 1, the tool should have three steps of 3, 2.0214, and 2.5085 inches, respectively, provided the cutting face is 1⁄4 inch below the center. All diameters are computed in this way, from the largest diameter of the tool. Tables 4a, 4b, and 4c, Corrected Diameters of Circular Forming Tools, are especially applicable to tools used on Brown & Sharpe automatic screw machines. Directions for using these tables are given on page 789. Circular Tools Having Top Rake.—Circular forming tools without top rake are satisfactory for brass, but tools for steel or other tough metals cut better when there is a rake angle of 10 or 12 degrees. For such tools, the small radius r (see Fig. 3) for an outside radius R may be found by the formula r =

2

2

P + R – 2PR cos θ

To find the value of P, proceed as follows: sin φ = small radius on work × sin rake angle ÷ large radius on work. Angle β = rake angle − φ. P = large radius on work × sin β ÷ sin rake angle. Angle θ = rake angle + δ. Sin δ = vertical height C from center of tool to center of work ÷ R. It is assumed that the tool point is to be set at the same height as the work center.

Using Tables for “Corrected Diameters of Circular Forming Tools”.—Tables 4a, 4b, and 4c are especially applicable to Brown & Sharpe automatic screw machines. The maximum diameter D of forming tools for these machines should be as follows: For No. 00 machine, 13⁄4 inches; for No. 0 machine, 21⁄4 inches; for No. 2 machine, 3 inches. To find the other diameters of the tool for any piece to be formed, proceed as follows: Subtract the smallest diameter of the work from the diameter of the work that is to be formed by the required tool diameter; divide the remainder by 2; locate the quotient obtained in the column headed “Length c on Tool,” and opposite the figure thus located and in the column headed by the number of the machine used, read off directly the diameter to which the tool is to be made. The quotient obtained, which is located in the column headed “Length c on Tool,” is the length c, as shown in Fig. 4. Example:A piece of work is to be formed on a No. 0 machine to two diameters, one being

1⁄ inch and one 0.550 inch; find the diameters of the tool. The maximum tool diameter is 21⁄ 4 4 inches, or the diameter that will cut the 1⁄4-inch diameter of the work. To find the other diameter, proceed according to the rule given: 0.550 − 1⁄4 = 0.300; 0.300 ÷ 2 = 0.150. In

Table 4b, opposite 0.150, we find that the required tool diameter is 1.9534 inches. These tables are for tools without rakes.



Cutting Face 3⁄16 Inch Below Center



Correction for Difference in Diameter




Radius of Tool

1⁄ Inch 8

1⁄ Inch 4

1⁄ Inch 2

1⁄ Inch 8

1⁄ Inch 4

1⁄ Inch 2

1⁄ Inch 8

1⁄ Inch 4

1⁄ Inch 2

1⁄ Inch 8

1⁄ Inch 4

1⁄ Inch 2

1

0.500

…

…

…

…

…

…

…

…

…

…

…

…

11⁄8

0.5625

0.0036

…

…

0.0086

…

…

0.0167

…

…

0.0298

…

…

11⁄4

0.625

0.0028

0.0065

…

0.0067

0.0154

…

0.0128

0.0296

…

0.0221

0.0519

…

13⁄8

0.6875

0.0023

…

…

0.0054

…

…

0.0102

…

…

0.0172

…

…

11⁄2

0.750

0.0019

0.0042

0.0107

0.0045

0.0099

0.0253

0.0083

0.0185

0.0481

0.0138

0.0310

0.0829

15⁄8

0.8125

0.0016

…

…

0.0037

…

…

0.0069

…

…

0.0114

…

…

13⁄4

0.875

0.0014

0.0030

…

0.0032

0.0069

…

0.0058

0.0128

…

0.0095

0.0210

…

17⁄8

0.9375

0.0012

…

…

0.0027

…

…

0.0050

…

…

0.0081

…

…

2

1.000

0.0010

0.0022

0.0052

0.0024

0.0051

0.0121

0.0044

0.0094

0.0223

0.0070

0.0152

0.0362

21⁄8

1.0625

0.0009

…

…

0.0021

…

…

0.0038

…

…

0.0061

…

…

21⁄4

1.125

0.0008

0.0017

…

0.0018

0.0040

…

0.0034

0.0072

…

0.0054

0.0116

…

23⁄8

1.1875

0.0007

…

…

0.0016

…

…

0.0029

…

…

0.0048

…

…

21⁄2

1.250

0.0006

0.0014

0.0031

0.0015

0.0031

0.0071

0.0027

0.0057

0.0129

0.0043

0.0092

0.0208

25⁄8

1.3125

0.0006

…

…

0.0013

…

…

0.0024

…

…

0.0038

…

…

23⁄4

1.375

0.0005

0.0011

…

0.0012

0.0026

…

0.0022

0.0046

…

0.0035

0.0073

…

27⁄8

1.4375

0.0005

…

…

0.0011

…

…

0.0020

…

…

0.0032

…

…

3

1.500

0.0004

0.0009

0.0021

0.0010

0.0021

0.0047

0.0018

0.0038

0.0085

0.0029

0.0061

0.0135

31⁄8

1.5625

0.00004

…

…

0.0009

…

…

0.0017

…

…

0.0027

…

…

31⁄4

1.625

0.0003

0.0008

…

0.0008

0.0018

…

0.0015

0.0032

…

0.0024

0.0051

…

33⁄8

1.6875

0.0003

…

…

0.0008

…

…

0.0014

…

…

0.0023

…

…

31⁄2

1.750

0.0003

0.0007

0.0015

0.0007

0.0015

0.0033

0.0013

0.0028

0.0060

0.0021

0.0044

0.0095

35⁄8

1.8125

0.0003

…

…

0.0007

…

…

0.0012

…

…

0.0019

…

…

33⁄4

1.875

0.0002

0.0006

…

0.0.0006

0.0013

…

0.0011

0.0024

…

0.0018

0.0038

…


FORMING TOOLS

Dia. of Tool

790

Table 3. Constant for Determining Diameters of Circular Forming Tools Cutting Face 1⁄8 Inch Below Center


791

Table 4a. Corrected Diameters of Circular Forming Tools Length c on Tool

Number of B. & S. Automatic Screw Machine No. 00 No. 0 No. 2

0.001 0.002 0.003 0.004 0.005 0.006

1.7480 1.7460 1.7441 1.7421 1.7401 1.7381

2.2480 2.2460 2.2441 2.2421 2.2401 2.2381

2.9980 2.9961 2.9941 2.9921 2.9901 2.9882

0.007 0.008 0.009 0.010 0.011 0.012 0.013 0.014 0.015 1⁄ 64 0.016 0.017 0.018 0.019 0.020 0.021 0.022

1.7362 1.7342 1.7322 1.7302 1.7282 1.7263 1.7243 1.7223 1.7203 1.7191

2.2361 2.2341 2.2321 2.2302 2.2282 2.2262 2.2243 2.2222 2.2203 2.2191

2.9862 2.9842 2.9823 2.9803 2.9783 2.9763 2.9744 2.9724 2.9704 2.9692

1.7184 1.7164 1.7144 1.7124 1.7104 1.7085 1.7065

2.2183 2.2163 2.2143 2.2123 2.2104 2.2084 2.2064

2.9685 2.9665 2.9645 2.9625 2.9606 2.9586 2.9566

0.023 0.024 0.025 0.026 0.027 0.028 0.029 0.030 0.031 1⁄ 32 0.032 0.033 0.034 0.035 0.036 0.037

1.7045 1.7025 1.7005 1.6986 1.6966 1.6946 1.6926 1.6907 1.6887 1.6882

2.2045 2.2025 2.2005 2.1985 2.1965 2.1945 2.1925 2.1906 2.1886 2.1881

2.9547 2.9527 2.9507 2.9488 2.9468 2.9448 2.9428 2.9409 2.9389 2.9384

1.6867 1.6847 1.6827 1.6808 1.6788 1.6768

2.1866 2.1847 2.1827 2.1807 2.1787 2.1767

2.9369 2.9350 2.9330 2.9310 2.9290 2.9271

0.038 0.039 0.040 0.041 0.042 0.043 0.044 0.045 0.046 3⁄ 64 0.047 0.048 0.049 0.050 0.051 0.052 0.053

1.6748 1.6729 1.6709 1.6689 1.6669 1.6649 1.6630 1.6610 1.6590 1.6573

2.1747 2.1727 2.1708 2.1688 2.1668 2.1649 2.1629 2.1609 2.1589 2.1572

2.9251 2.9231 2.9211 2.9192 2.9172 2.9152 2.9133 2.9113 2.9093 2.9076

1.6570 1.6550 1.6531 1.6511 1.6491 1.6471 1.6452

2.1569 2.1549 2.1529 2.1510 2.1490 2.1470 2.1451

2.9073 2.9054 2.9034 2.9014 2.8995 2.8975 2.8955

0.054 0.055 0.056

1.6432 1.6412 1.6392

2.1431 2.1411 2.1391

0.057

1.6373

2.1372

Length c on Tool 0.058 0.059 0.060 0.061 0.062 1⁄ 16 0.063 0.064 0.065 0.066 0.067 0.068 0.069 0.070 0.071 0.072

Number of B. & S. Automatic Screw Machine No. 00 No. 0 No. 2 1.6353 1.6333 1.6313 1.6294 1.6274 1.6264

2.1352 2.1332 2.1312 2.1293 2.1273 2.1263

2.8857 2.8837 2.8818 2.8798 2.8778 2.8768

1.6254 1.6234 1.6215 1.6195 1.6175 1.6155 1.6136 1.6116 1.6096 1.6076

2.1253 2.1233 2.1213 2.1194 2.1174 2.1154 2.1134 2.1115 2.1095 2.1075

2.8759 2.8739 2.8719 2.8699 2.8680 2.8660 2.8640 2.8621 2.8601 2.8581

1.6057 1.6037 1.6017 1.5997 1.5978 1.5958 1.5955

2.1055 2.1035 2.1016 2.0996 2.0976 2.0956 2.0954

2.8561 2.8542 2.8522 2.8503 2.8483 2.8463 2.8461

1.5938 1.5918 1.5899 1.5879 1.5859 1.5839 1.5820 1.5800 1.5780 1.5760

2.0937 2.0917 2.0897 2.0877 2.0857 2.0838 2.0818 2.0798 2.0778 2.0759

2.8443 2.8424 2.8404 2.8384 2.8365 2.8345 2.8325 2.8306 2.8286 2.8266

1.5740 1.5721 1.5701 1.5681 1.5661 1.5647

2.0739 2.0719 2.0699 2.0679 2.0660 2.0645

2.8247 2.8227 2.8207 2.8187 2.8168 2.8153

1.5642 1.5622 1.5602 1.5582 1.5563 1.5543 1.5523 1.5503 1.5484 1.5464

2.0640 2.0620 2.0600 2.0581 2.0561 2.0541 2.0521 2.0502 2.0482 2.0462

2.8148 2.8128 2.8109 2.8089 2.8069 2.8050 2.8030 2.8010 2.7991 2.7971

1.5444 1.5425 1.5405 1.5385 1.5365 1.5346 1.5338

2.0442 2.0422 2.0403 2.0383 2.0363 2.0343 2.0336

2.7951 2.7932 2.7912 2.7892 2.7873 2.7853 2.7846

2.8936 2.8916 2.8896

0.104 0.105 0.106 0.107 0.108 0.109 7⁄ 64 0.110 0.111 0.112

1.5326 1.5306 1.5287

2.0324 2.0304 2.0284

2.7833 2.7814 2.7794

2.8877

0.113

1.5267

2.0264

2.7774

0.073 0.074 0.075 0.076 0.077 0.078 5⁄ 64 0.079 0.080 0.081 0.082 0.083 0.084 0.085 0.086 0.087 0.088 0.089 0.090 0.091 0.092 0.093 3⁄ 32 0.094 0.095 0.096 0.097 0.098 0.099 0.100 0.101 0.102 0.103



FORMING TOOLS Table 4a. Corrected Diameters of Circular Forming Tools (Continued)

Length c on Tool 0.113 0.114

Number of B. & S. Automatic Screw Machine No. 00 No. 0 No. 2 1.5267 2.0264 2.7774 1.5247 2.0245 2.7755

0.115 0.116 0.117 0.118 0.119 0.120 0.121 0.122 0.123 0.124 0.125 0.126 0.127 0.128 0.129 0.130 0.131

1.5227 1.5208 1.5188 1.5168 1.5148 1.5129 1.5109 1.5089 1.5070 1.5050 1.5030 1.5010 1.4991 1.4971 1.4951 1.4932 1.4912

2.0225 2.0205 2.0185 2.0166 2.0146 2.0126 2.0106 2.0087 2.0067 2.0047 2.0027 2.0008 1.9988 1.9968 1.9948 1.9929 1.9909

2.7735 2.7715 2.7696 2.7676 2.7656 2.7637 2.7617 2.7597 2.7578 2.7558 2.7538 2.7519 2.7499 2.7479 2.7460 2.7440 2.7420

0.132 0.133 0.134 0.135 0.136 0.137 0.138 0.139 0.140 9⁄ 64 0.141 0.142 0.143 0.144 0.145 0.146 0.147

1.4892 1.4872 1.4853 1.4833 1.4813 1.4794 1.4774 1.4754 1.4734 1.4722

1.9889 1.9869 1.9850 1.9830 1.9810 1.9790 1.9771 1.9751 1.9731 1.9719

2.7401 2.7381 2.7361 2.7342 2.7322 2.7302 2.7282 2.7263 2.7243 2.7231

1.4715 1.4695 1.4675 1.4655 1.4636 1.4616 1.4596

1.9711 1.9692 1.9672 1.9652 1.9632 1.9613 1.9593

2.7224 2.7204 2.7184 2.7165 2.7145 2.7125 2.7106

0.148 0.149 0.150 0.151 0.152 0.153 0.154 0.155 0.156 5⁄ 32 0.157 0.158 0.159 0.160 0.161 0.162

1.4577 1.4557 1.4537 1.4517 1.4498 1.4478 1.4458 1.4439 1.4419 1.4414

1.9573 1.9553 1.9534 1.9514 1.9494 1.9474 1.9455 1.9435 1.9415 1.9410

2.7086 2.7066 2.7047 2.7027 2.7007 2.6988 2.6968 2.6948 2.6929 2.6924

1.4399 1.4380 1.4360 1.4340 1.4321 1.4301

1.9395 1.9376 1.9356 1.9336 1.9317 1.9297

2.6909 2.6889 2.6870 2.6850 2.6830 2.6811

0.163 0.164 0.165 0.166 0.167 0.168 0.169 0.170

1.4281 1.4262 1.4242 1.4222 1.4203 1.4183 1.4163 1.4144

1.9277 1.9257 1.9238 1.9218 1.9198 1.9178 1.9159 1.9139

2.6791 2.6772 2.6752 2.6732 2.6713 2.6693 2.6673 2.6654

Length c on Tool 0.171 11⁄ 64 0.172 0.173 0.174 0.175 0.176 0.177 0.178 0.179 0.180 0.181 0.182 0.183 0.184 0.185 0.186 0.187 3⁄ 16 0.188 0.189 0.190 0.191 0.192 0.193 0.194 0.195 0.196 0.197

Number of B. & S. Automatic Screw Machine No. 00 No. 0 No. 2 1.4124 1.9119 2.6634 1.4107 1.9103 2.6617 1.4104 1.4084 1.4065 1.4045 1.4025 1.4006 1.3986 1.3966 1.3947 1.3927 1.3907 1.3888 1.3868 1.3848 1.3829 1.3809 1.3799

1.9099 1.9080 1.9060 1.9040 1.9021 1.9001 1.8981 1.8961 1.8942 1.8922 1.8902 1.8882 1.8863 1.8843 1.8823 1.8804 1.8794

2.6614 2.6595 2.6575 2.6556 2.6536 2.6516 2.6497 2.6477 2.6457 2.6438 2.6418 2.6398 2.6379 2.6359 2.6339 2.6320 2.6310

1.3789 1.3770 1.3750 1.3730 1.3711 1.3691 1.3671 1.3652 1.3632 1.3612

1.8784 1.8764 1.8744 1.8725 1.8705 1.8685 1.8665 1.8646 1.8626 1.8606

2.6300 2.6281 2.6261 2.6241 2.6222 2.6202 2.6182 2.6163 2.6143 2.6123

0.198 0.199 0.200 0.201 0.202 0.203 13⁄ 64 0.204 0.205 0.206 0.207 0.208 0.209 0.210 0.211 0.212 0.213

1.3592 1.3573 1.3553 … … … …

1.8587 1.8567 1.8547 1.8527 1.8508 1.8488 1.8486

2.6104 2.6084 2.6064 2.6045 2.6025 2.6006 2.6003

… … … … … … … … … …

1.8468 1.8449 1.8429 1.8409 1.8390 1.8370 1.8350 1.8330 1.8311 1.8291

2.5986 2.5966 2.5947 2.5927 2.5908 2.5888 2.5868 2.5849 2.5829 2.5809

0.214 0.215 0.216 0.217 0.218 7⁄ 32 0.219 0.220 0.221 0.222 0.223 0.224 0.225 0.226

… … … … … …

1.8271 1.8252 1.8232 1.8212 1.8193 1.8178

2.5790 2.5770 2.5751 2.5731 2.5711 2.5697

… … … … … … … …

1.8173 1.8153 1.8133 1.8114 1.8094 1.8074 1.8055 1.8035

2.5692 2.5672 2.5653 2.5633 2.5613 2.5594 2.5574 2.5555



793

Table 4b. Corrected Diameters of Circular Forming Tools Number of B. & S. Screw Machine

Number of B. & S. Screw Machine

Length c on Tool

No. 0

No. 2

Length c on Tool

No. 0

No. 2

0.227 0.228 0.229 0.230

1.8015 1.7996 1.7976 1.7956

2.5535 2.5515 2.5496 2.5476

0.284 0.285 0.286 0.287

1.6894 1.6874 1.6854 1.6835

2.4418 2.4398 2.4378 2.4359

0.231 0.232 0.233 0.234 15⁄ 64 0.235 0.236 0.237 0.238 0.239

1.7936 1.7917 1.7897 1.7877 1.7870

2.5456 2.5437 2.5417 2.5398 2.5390

0.288 0.289 0.290 0.291 0.292

1.6815 1.6795 1.6776 1.6756 1.6736

1.7858 1.7838 1.7818 1.7799 1.7779

2.5378 2.5358 2.5339 2.5319 2.5300

0.240 0.241 0.242 0.243 0.244 0.245 0.246

1.7759 1.7739 1.7720 1.7700 1.7680 1.7661 1.7641

2.5280 2.5260 2.5241 2.5221 2.5201 2.5182 2.5162

0.293 0.294 0.295 0.296 19⁄ 64 0.297 0.298 0.299 0.300 0.301 0.302 0.303

0.247 0.248 0.249 0.250 0.251 0.252 0.253 0.254 0.255 0.256

1.7621 1.7602 1.7582 1.7562 1.7543 1.7523 1.7503 1.7484 1.7464 1.7444

2.5143 2.5123 2.5104 2.5084 2.5064 2.5045 2.5025 2.5005 2.4986 2.4966

0.257 0.258 0.259 0.260 0.261 0.262 0.263 0.264 0.265 17⁄ 64 0.266 0.267 0.268 0.269 0.270 0.271 0.272

1.7425 1.7405 1.7385 1.7366 1.7346 1.7326 1.7306 1.7287 1.7267 1.7255

2.4947 2.4927 2.4908 2.4888 2.4868 2.4849 2.4829 2.4810 2.4790 2.4778

0.304 0.305 0.306 0.307 0.308 0.309 0.310 0.311 0.312 5⁄ 16 0.313 0.314 0.315 0.316 0.317 0.318 0.319 0.320 0.321 0.322

1.7248 1.7228 1.7208 1.7189 1.7169 1.7149 1.7130

2.4770 2.4751 2.4731 2.4712 2.4692 2.4673 2.4653

0.273 0.274 0.275 0.276 0.277

1.7110 1.7090 1.7071 1.7051 1.7031

0.278 0.279 0.280 0.281 9⁄ 32 0.282 0.283

Length c on Tool

Number 2 B. & S. Machine 2.3303 2.3284 2.3264 2.3250

2.4340 2.4320 2.4300 2.4281 2.4261

0.341 0.342 0.343 11⁄ 32 0.344 0.345 0.346 0.347 0.348

1.6717 1.6697 1.6677 1.6658 1.6641

2.4242 2.4222 2.4203 2.4183 2.4166

0.349 0.350 0.351 0.352 0.353

2.3147 2.3127 2.3108 2.3088 2.3069

1.6638 1.6618 1.6599 1.6579 … … …

2.4163 2.4144 2.4124 2.4105 2.4085 2.4066 2.4046

2.3049 2.3030 2.3010 2.2991 2.2971 2.2952 2.2945

… … … … … … … … … …

2.4026 2.4007 2.3987 2.3968 2.3948 2.3929 2.3909 2.3890 2.3870 2.3860

0.354 0.355 0.356 0.357 0.358 0.359 23⁄ 64 0.360 0.361 0.362 0.363 0.364 0.365 0.366 0.367 0.368 0.369

… … … … … … … … … …

2.3851 2.3831 2.3811 2.3792 2.3772 2.3753 2.3733 2.3714 2.3694 2.3675

0.370 0.371 0.372 0.373 0.374 0.375 0.376 0.377 0.378 0.379

2.2737 2.2718 2.2698 2.2679 2.2659 2.2640 2.2620 2.2601 2.2581 2.2562

… … … … … … …

2.3655 2.3636 2.3616 2.3596 2.3577 2.3557 2.3555

0.380 0.381 0.382 0.383 0.384 0.385 0.386

2.2542 2.2523 2.2503 2.2484 2.2464 2.2445 2.2425

2.4633 2.4614 2.4594 2.4575 2.4555

0.323 0.324 0.325 0.326 0.327 0.328 21⁄ 64 0.329 0.330 0.331 0.332 0.333

… … … … …

2.3538 2.3518 2.3499 2.3479 2.3460

2.2406 2.2386 2.2367 2.2347 2.2335

1.7012 1.6992 1.6972 1.6953 1.6948

2.4535 2.4516 2.4496 2.4477 2.4472

0.334 0.335 0.336 0.337 0.338

… … … … …

2.3440 2.3421 2.3401 2.3381 2.3362

0.387 0.388 0.389 0.390 25⁄ 64 0.391 0.392 0.393 0.394 0.395

2.2328 2.2308 2.2289 2.2269 2.2250

1.6933

2.4457

0.339

0.396

2.2230

2.4438

0.340

… …

2.3342

1.6913

2.3323

0.397

2.2211


2.3245 2.3225 2.3206 2.3186 2.3166

2.2932 2.2913 2.2893 2.2874 2.2854 2.2835 2.2815 2.2796 2.2776 2.2757


FORMING TOOLS Table 4c. Corrected Diameters of Circular Forming Tools

Length c on Tool

Number 2 B. & S. Machine

Length c on Tool


0.398 0.399 0.400 0.401 0.402 0.403

2.2191 2.2172 2.2152 2.2133 2.2113 2.2094

0.423 0.424 0.425 0.426 0.427 0.428

2.1704 2.1685 2.1666 2.1646 2.1627 2.1607

0.404 0.405 0.406 13⁄ 32 0.407 0.408 0.409 0.410 0.411 0.412

2.2074 2.2055 2.2035 2.2030

0.429 0.430 0.431 0.432

2.2016 2.1996 2.1977 2.1957 2.1938 2.1919

0.413 0.414 0.415 0.416 0.417 0.418

2.1899 2.1880 2.1860 2.1841 2.1821 2.1802

0.433 0.434 0.435 0.436 0.437 7⁄ 16 0.438 0.439 0.440 0.441 0.442 0.443

0.419 0.420 0.421 27⁄ 64 0.422

2.1782 2.1763 2.1743 2.1726

0.444 0.445 0.446 0.447

2.1724

0.448

Length c on Tool


Length c on Tool


2.1199 2.1179 2.1160 2.1140 2.1121 2.1118

0.474 0.475 0.476 0.477 0.478 0.479

2.0713 2.0694 2.0674 2.0655 2.0636 2.0616

2.1588 2.1568 2.1549 2.1529

0.449 0.450 0.451 0.452 0.453 29⁄ 64 0.454 0.455 0.456 0.457

2.1101 2.1082 2.1063 2.1043

0.480 0.481 0.482 0.483

2.0597 2.0577 2.0558 2.0538

2.1510 2.1490 2.1471 2.1452 2.1432 2.1422

0.458 0.459 0.460 0.461 0.462 0.463

2.1024 2.1004 2.0985 2.0966 2.0946 2.0927

0.484 0.485 0.486 0.487 0.488 0.489

2.0519 2.0500 2.0480 2.0461 2.0441 2.0422

2.1413 2.1393 2.1374 2.1354 2.1335 2.1315

2.0907 2.0888 2.0868 2.0849 2.0830 2.0815

0.490 0.491 0.492 0.493 0.494 0.495

2.0403 2.0383 2.0364 2.0344 2.0325 2.0306

2.1296 2.1276 2.1257 2.1237

0.464 0.465 0.466 0.467 0.468 15⁄ 32 0.469 0.470 0.471 0.472

2.0810 2.0791 2.0771 2.0752

0.496 0.497 0.498 0.499

2.0286 2.0267 2.0247 2.0228

2.1218

0.473

2.0733

0.500

2.0209

Dimensions of Forming Tools for B. & S. Automatic Screw Machines

W D T h

No. of Machine

Max. Dia., D

h

T

W

00

13⁄4

1⁄ 8

3⁄ –16 8

1⁄ 4

0

21⁄4

5⁄ 32

1⁄ –14 2

5⁄ 16

2

3

1⁄ 4

5⁄ –12 8

3⁄ 8

6

4

5⁄ 16

3⁄ –12 4

3⁄ 8

c Fig. 4.

Arrangement of Circular Tools.—When applying circular tools to automatic screw machines, their arrangement has an important bearing on the results obtained. The various ways of arranging the circular tools, with relation to the rotation of the spindle, are shown at A, B, C, and D in Fig. 5. These diagrams represent the view obtained when looking toward the chuck. The arrangement shown at A gives good results on long forming operations on brass and steel because the pressure of the cut on the front tool is downward; the support is more rigid than when the forming tool is turned upside down on the front slide, as shown at B; here the stock, turning up toward the tool, has a tendency to lift the crossslide, causing chattering; therefore, the arrangement shown at A is recommended when a high-quality finish is desired. The arrangement at B works satisfactorily for short steel pieces that do not require a high finish; it allows the chips to drop clear of the work, and is especially advantageous when making screws, when the forming and cut-off tools operate after the die, as no time is lost in reversing the spindle. The arrangement at C is recommended for heavy cutting on large work, when both tools are used for forming the piece; a



795

rigid support is then necessary for both tools and a good supply of oil is also required. The arrangement at D is objectionable and should be avoided; it is used only when a left-hand thread is cut on the piece and when the cut-off tool is used on the front slide, leaving the heavy cutting to be performed from the rear slide. In all “cross-forming” work, it is essential that the spindle bearings be kept in good condition, and that the collet or chuck has a parallel contact upon the bar that is being formed.

Front

Back Back

A

Front

B

Form

Cut-Off Cut-Off

Front

Form

Front

Back C

Form

Back D

Cut-Off

Form and Cut-Off

Form

Fig. 5.

Feeds and Speeds for Forming Tools.—Approximate feeds and speeds for forming tools are given in the table beginning on page 1132. The feeds and speeds are average values, and if the job at hand has any features out of the ordinary, the figures given should be altered accordingly. Dimensions for Circular Cut-Off Tools x a

T

1" 32

r r

D

1⁄ 16

T 0.031

x 0.013

Norway Iron, Machine Steel a = 15 Deg. T x 0.039 0.010

1⁄ 8

0.044

0.019

0.055

0.015

0.062

0.013

3⁄ 16

0.052

0.022

0.068

0.018

0.076

0.016

1⁄ 4

0.062

0.026

0.078

0.021

0.088

0.019

Dia. of Stock

R

Soft Brass, Copper a = 23 Deg.

Drill Rod, Tool Steel a = 12 Deg. T x 0.043 0.009

5⁄ 16

0.069

0.029

0.087

0.023

0.098

0.021

3⁄ 8

0.076

0.032

0.095

0.025

0.107

0.023

7⁄ 16

0.082

0.035

0.103

0.028

0.116

0.025

1⁄ 2

0.088

0.037

0.110

0.029

0.124

0.026

9⁄ 16

0.093

0.039

0.117

0.031

0.131

0.028

5⁄ 8

0.098

0.042

0.123

0.033

0.137

0.029

11⁄ 16

0.103

0.044

0.129

0.035

0.145

0.031

3⁄ 4

0.107

0.045

0.134

0.036

0.152

0.032

13⁄ 16

0.112

0.047

0.141

0.038

0.158

0.033

7⁄ 8

0.116

0.049

0.146

0.039

0.164

0.035

15⁄ 16

0.120

0.051

0.151

0.040

0.170

0.036

1

0.124

0.053

0.156

0.042

0.175

0.037

The length of the blade equals radius of stock R + x + r + 1⁄32 inch (for notation, see illustration above); r = 1⁄16 inch for 3⁄8- to 3⁄4-inch stock, and 3⁄32 inch for 3⁄4- to 1-inch stock.



MILLING CUTTERS

MILLING CUTTERS Selection of Milling Cutters The most suitable type of milling cutter for a particular milling operation depends on such factors as the kind of cut to be made, the material to be cut, the number of parts to be machined, and the type of milling machine available. Solid cutters of small size will usually cost less, initially, than inserted blade types; for long-run production, inserted-blade cutters will probably have a lower overall cost. Depending on either the material to be cut or the amount of production involved, the use of carbide-tipped cutters in preference to high-speed steel or other cutting tool materials may be justified. Rake angles depend on both the cutter material and the work material. Carbide and cast alloy cutting tool materials generally have smaller rake angles than high-speed steel tool materials because of their lower edge strength and greater abrasion resistance. Soft work materials permit higher radial rake angles than hard materials; thin cutters permit zero or practically zero axial rake angles; and wide cutters operate smoother with high axial rake angles. See Rake Angles for Milling Cutters on page 826. Cutting edge relief or clearance angles are usually from 3 to 6 degrees for hard or tough materials, 4 to 7 degrees for average materials, and 6 to 12 degrees for easily machined materials. See Clearance Angles for Milling Cutter Teeth on page 825. The number of teeth in the milling cutter is also a factor that should be given consideration, as explained in the next paragraph. Number of Teeth in Milling Cutters.—In determining the number of teeth a milling cutter should have for optimum performance, there is no universal rule. There are, however, two factors that should be considered in making a choice: 1 ) T h e number of teeth should never be so great as to reduce the chip space between the teeth to a point where a free flow of chips is prevented; and 2) The chip space should be smooth and without sharp corners that would cause clogging of the chips in the space. For milling ductile materials that produce a continuous and curled chip, a cutter with large chip spaces is preferable. Such coarse tooth cutters permit an easier flow of the chips through the chip space than would be obtained with fine tooth cutters, and help to eliminate cutter “chatter.” For cutting operations in thin materials, fine tooth cutters reduce cutter and workpiece vibration and the tendency for the cutter teeth to “straddle” the workpiece and dig in. For slitting copper and other soft nonferrous materials, teeth that are either chamfered or alternately flat and V-shaped are best. As a general rule, to give satisfactory performance the number of teeth in milling cutters should be such that no more than two teeth at a time are engaged in the cut. Based on this rule, the following formulas are recommended: For face milling cutters, T = 6.3D -----------W

(1)

cos AT = 12.6D --------------------------D + 4d

(2)

For peripheral milling cutters,

where T = number of teeth in cutter; D = cutter diameter in inches; W = width of cut in inches; d = depth of cut in inches; and A = helix angle of cutter. To find the number of teeth that a cutter should have when other than two teeth in the cut at the same time is desired, Formulas (1) and (2) should be divided by 2 and the result multiplied by the number of teeth desired in the cut.


Machinery's Handbook 27th Edition MILLING CUTTERS

797

Example:Determine the required number of teeth in a face mill where D = 6 inches and W = 4 inches. Using Formula (1), 6.3 × 6 T = ---------------- = 10 teeth, approximately 4 Example:Determine the required number of teeth in a plain milling cutter where D = 4 inches and d = 1⁄4 inch. Using Formula (2), 12.6 × 4 × cos 0 ° T = ---------------------------------------- = 10 teeth, approximately 4 + ( 4 × 1⁄4 ) In high speed milling with sintered carbide, high-speed steel, and cast non-ferrous cutting tool materials, a formula that permits full use of the power available at the cutter but prevents overloading of the motor driving the milling machine is: K×H T = ---------------------------------F×N×d×W

(3)

where T = number of cutter teeth; H = horsepower available at the cutter; F = feed per tooth in inches; N = revolutions per minute of cutter; d = depth of cut in inches; W = width of cut in inches; and K = a constant which may be taken as 0.65 for average steel, 1.5 for cast iron, and 2.5 for aluminum. These values are conservative and take into account dulling of the cutter in service. Example:Determine the required number of teeth in a sintered carbide tipped face mill for high speed milling of 200 Brinell hardness alloy steel if H = 10 horsepower; F = 0.008 inch; N = 272 rpm; d = 0.125 inch; W = 6 inches; and K for alloy steel is 0.65. Using Formula (3), 0.65 × 10 T = --------------------------------------------------------= 4 teeth, approximately 0.008 × 272 × 0.125 × 6 American National Standard Milling Cutters.—According to American National Standard ANSI/ASME B94.19-1997 milling cutters may be classified in two general ways, which are given as follows: By Type of Relief on Cutting Edges: Milling cutters may be described on the basis of one of two methods of providing relief for the cutting edges. Profile sharpened cutters are those on which relief is obtained and which are resharpened by grinding a narrow land back of the cutting edges. Profile sharpened cutters may produce flat, curved, or irregular surfaces. Form relieved cutters are those which are so relieved that by grinding only the faces of the teeth the original form is maintained throughout the life of the cutters. Form relieved cutters may produce flat, curved or irregular surfaces. By Method of Mounting: Milling cutters may be described by one of two methods used to mount the cutter. Arbor type cutters are those which have a hole for mounting on an arbor and usually have a keyway to receive a driving key. These are sometimes called Shell type. Shank type cutters are those which have a straight or tapered shank to fit the machine tool spindle or adapter. Explanation of the “Hand” of Milling Cutters.—In the ANSI Standard the terms “right hand” and “left hand” are used to describe hand of rotation, hand of cutter and hand of flute helix. Hand of Rotation or Hand of Cut: is described as either “right hand” if the cutter revolves counterclockwise as it cuts when viewed from a position in front of a horizontal milling machine and facing the spindle or “left hand” if the cutter revolves clockwise as it cuts when viewed from the same position.



MILLING CUTTERS

American National Standard Plain Milling Cutters ANSI/ASME B94.19-1997 Cutter Diameter Nom.

Max.

Min.

Range of Face Widths, Nom.a

Hole Diameter Nom.

Max.

Min.

1

1.00075

1.0000

1

1.00075

1.0000

Light-duty Cuttersb 3⁄ , 1⁄ , 5⁄ , 3⁄ , 16 4 16 8

21⁄2

2.515

2.485

1⁄ , 5⁄ , 3⁄ , 2 8 4

1, 11⁄2 ,

2 and 3 3⁄ , 1⁄ , 5⁄ , 3⁄ , 16 4 16 8

3

3.015

2.985

3

3.015

2.985

1, 11⁄4 , 11⁄2 , 2

11⁄4

1.2510

1.2500

3.985

and 3 1⁄ , 5⁄ and 3⁄ 4 16 8

1

1.00075

1.0000 1.2500

5⁄ , 3⁄ , 8 4

and 11⁄2

1⁄ , 5⁄ , 3⁄ , 2 8 4

4

4.015

3⁄ , 1⁄ , 5⁄ , 3⁄ , 8 2 8 4

4

4.015

3.985

1, 11⁄2 , 2, 3

11⁄4

1.2510

1

1.00075

1.0000

1

1.0010

1.0000

21⁄2

2.515

2.485

and 4 Heavy-duty Cuttersc 2

21⁄2

2.515

2.485

4

3

3.015

2.985

2, 21⁄2 , 3, 4 and 6

11⁄4

1.2510

1.2500

4

4.015

3.985

2, 3, 4 and 6

11⁄2

1.5010

1.5000

11⁄4

1.2510

1.2500

11⁄2

1.5010

1.5000

3

3.015

2.985

High-helix Cuttersd 4 and 6

4

4.015

3.985

8

on Face Widths: Up to 1 inch, inclusive, ± 0.001 inch; over 1 to 2 inches, inclusive, +0.010, −0.000 inch; over 2 inches, +0.020, −0.000 inch. b Light-duty plain milling cutters with face widths under 3⁄ inch have straight teeth. Cutters with 3⁄ 4 4 inch face and wider have helix angles of not less than 15 degrees nor greater than 25 degrees. c Heavy-duty plain milling cutters have a helix angle of not less than 25 degrees nor greater than 45 degrees. d High-helix plain milling cutters have a helix angle of not less than 45 degrees nor greater than 52 degrees. a Tolerances

All dimensions are in inches. All cutters are high-speed steel. Plain milling cutters are of cylindrical shape, having teeth on the peripheral surface only.

Hand of Cutter: Some types of cutters require special consideration when referring to their hand. These are principally cutters with unsymmetrical forms, face type cutters, or cutters with threaded holes. Symmetrical cutters may be reversed on the arbor in the same axial position and rotated in the cutting direction without altering the contour produced on the work-piece, and may be considered as either right or left hand. Unsymmetrical cutters reverse the contour produced on the work-piece when reversed on the arbor in the same axial position and rotated in the cutting direction. A single-angle cutter is considered to be a right-hand cutter if it revolves counterclockwise, or a left-hand cutter if it revolves clockwise, when cutting as viewed from the side of the larger diameter. The hand of rotation of a single angle milling cutter need not necessarily be the same as its hand of cutter. A single corner rounding cutter is considered to be a right-hand cutter if it revolves counterclockwise, or a left-hand cutter if it revolves clockwise, when cutting as viewed from the side of the smaller diameter.



799

American National Standard Side Milling Cutters ANSI/ASME B94.19-1997 Cutter Diameter Nom.

Max.

Min.

Range of Face Widths Nom.a

Hole Diameter Nom.

Max.

Min.

Side Cuttersb 2

2.015

1.985

3⁄ , 1⁄ , 3⁄ 16 4 8

5⁄ 8

0.62575

0.6250

21⁄2

2.515

2.485

1⁄ , 3⁄ , 1⁄ 4 8 2

7⁄ 8

0.87575

0.8750

3

3.015

2.985

1⁄ , 5⁄ , 3⁄ , 7⁄ , 1⁄ 4 16 8 16 2

1

1.00075

1.0000

4

4.015

3.985

1⁄ , 3⁄ , 1⁄ , 5⁄ , 3⁄ , 7⁄ 4 8 2 8 4 8

1

1.00075

1.0000

4

4.015

3.985

1⁄ , 5⁄ , 3⁄ 2 8 4

11⁄4

1.2510

1.2500

5

5.015

4.985

1⁄ , 5⁄ , 3⁄ 2 8 4

5

5.015

4.985

1⁄ , 5⁄ , 3⁄ , 2 8 4

6

6.015

5.985

6

6.015

5.985

7

7.015

6.985

7

7.015

6.985

8

8.015

7.985

3⁄ , 4

8.015

7.985

3⁄ , 4

8

1

1⁄ 2

1.00075

1.0000

11⁄4

1.2510

1.2500

1

1.00075

1.0000

11⁄4

1.2510

1.2500

3⁄ 4

11⁄4

1.2510

1.2500

3⁄ 4

11⁄2

1.5010

1.5000

1

11⁄4

1.2510

1.2500

1

11⁄2

1.5010

1.5000

0.87575

0.8750

1⁄ , 5⁄ , 3⁄ , 2 8 4

1

21⁄2

2.515

2.485

Staggered-tooth Side Cuttersc 1⁄ , 5⁄ , 3⁄ , 1⁄ 4 16 8 2

3

3.015

2.985

3⁄ , 1⁄ , 5⁄ , 3⁄ 16 4 16 8

3

3.015

2.985

1⁄ , 5⁄ , 3⁄ 2 8 4

4

4.015

3.985

5

5.015

4.985

6

6.015

5.985

3⁄ , 1⁄ , 5⁄ , 3⁄ , 7⁄ , 8 2 8 4 8

8

8.015

7.985

3⁄ , 1⁄ , 5⁄ , 3⁄ , 8 2 8 4

1⁄ , 5⁄ , 3⁄ , 7⁄ , 1⁄ , 4 16 8 16 2 5⁄ , 3⁄ 8 4

1

and 7⁄8

1⁄ , 5⁄ , 3⁄ 2 8 4

1

1

7⁄ 8

1

1.00075

1.0000

11⁄4

1.2510

1.2500

11⁄4

1.2510

1.2500

11⁄4

1.2510

1.2500

11⁄4

1.2510

1.2500

11⁄2

1.5010

1.5000

11⁄4

4

4.015

3.985

Half Side Cuttersd 3⁄ 4

1.2510

1.2500

5

5.015

4.985

3⁄ 4

11⁄4

1.2510

1.2500

6

6.015

5.985

3⁄ 4

11⁄4

1.2510

1.2500

a Tolerances on Face Widths: For side cutters, +0.002, −0.001 inch; for staggered-tooth side cutters

up to 3⁄4 inch face width, inclusive, +0.000 −0.0005 inch, and over 3⁄4 to 1 inch, inclusive, +0.000 − 0.0010 inch; and for half side cutters, +0.015, −0.000 inch. b Side milling cutters have straight peripheral teeth and side teeth on both sides. c Staggered-tooth side milling cutters have peripheral teeth of alternate right- and left-hand helix and alternate side teeth. d Half side milling cutters have side teeth on one side only. The peripheral teeth are helical of the same hand as the cut. Made either with right-hand or left-hand cut. All dimensions are in inches. All cutters are high-speed steel. Side milling cutters are of cylindrical shape, having teeth on the periphery and on one or both sides.

Hand of Flute Helix: Milling cutters may have straight flutes which means that their cutting edges are in planes parallel to the cutter axis. Milling cutters with flute helix in one direction only are described as having a right-hand helix if the flutes twist away from the observer in a clockwise direction when viewed from either end of the cutter or as having a left-hand helix if the flutes twist away from the observer in a counterclockwise direction when viewed from either end of the cutter. Staggered tooth cutters are milling cutters with every other flute of opposite (right and left hand) helix. An illustration describing the various milling cutter elements of both a profile cutter and a form-relieved cutter is given on page 801.



MILLING CUTTERS American National Standard Staggered Teeth, T-Slot Milling Cutters with Brown & Sharpe Taper and Weldon Shanks ANSI/ASME B94.19-1997

Cutter Dia., D

Bolt Size 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1

Neck Dia., N

Face Width, W

9⁄ 16 21⁄ 32 25⁄ 32 31⁄ 32 11⁄4 115⁄32 127⁄32

15⁄ 64 17⁄ 64 21⁄ 64 25⁄ 64 31⁄ 64 5⁄ 8 53⁄ 64

17⁄ 64 21⁄ 64 13⁄ 32 17⁄ 32 21⁄ 32 25⁄ 32 11⁄32

With B. & S. Tapera,b Length, Taper L No.

With Weldon Shank Length, Dia., L S

…

…

219⁄32

…

…

211⁄16

…

…

5 51⁄4

7

67⁄8

9

71⁄4

9

31⁄4 37⁄16 315⁄16 47⁄16 413⁄16

7

a For dimensions of Brown & Sharpe taper shanks, see information given on page

1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 4

1 1 11⁄4

936.

b Brown & Sharpe taper shanks have been removed from ANSI/ASME B94.19 they are included for

reference only. All dimensions are in inches. All cutters are high-speed steel and only right-hand cutters are standard. Tolerances: On D, +0.000, −0.010 inch; on W, +0.000, −0.005 inch; on N, +0.000, −0.005 inch; on L, ± 1⁄16 inch; on S, −00001 to −0.0005 inch.

American National Standard Form Relieved Corner Rounding Cutters with Weldon Shanks ANSI/ASME B94.19-1997

Rad., R

Dia., D

Dia., d

S

L

1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16

7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8

3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2

21⁄2

1 11⁄8

21⁄2 3 3 3 3 31⁄4

Rad., R 3⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

Dia., D 11⁄4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

Dia., d 3⁄ 8 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8

S

L

1⁄ 2 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8

31⁄2

1

4 41⁄8

1

31⁄8 31⁄4 31⁄2 33⁄4

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters are standard. Tolerances: On D, ±0.010 inch; on diameter of circle, 2R, ±0.001 inch for cutters up to and including 1⁄8 -inch radius, +0.002, −0.001 inch for cutters over 1⁄8 -inch radius; on S, −0.0001 to −0.0005 inch; and on L, ± 1⁄16 inch.



801

American National Standard Metal Slitting Saws ANSI/ASME B94.19-1997 Cutter Diameter Nom.

Max.

21⁄2

2.515

3

3.015

4

4.015

5 5 6 6 8 8

5.015 5.015 6.015 6.015 8.015 8.015

21⁄2 3 4 5 5 6 6 8 8

2.515 3.015 4.015 5.015 5.015 6.015 6.015 8.015 8.015

3 4 5 6

3.015 4.015 5.015 6.015

6 8 10 12

6.015 8.015 10.015 12.015

Min.

Range of Face Widths Nom.a

Hole Diameter Nom.

Plain Metal Slitting Sawsb 1⁄ , 3⁄ , 1⁄ , 3⁄ , 1⁄ 7⁄ 2.485 32 64 16 32 8 8 1⁄ , 3⁄ , 1⁄ , 3⁄ , 32 64 16 32 2.985 1 1⁄ and 5⁄ 8 32 1⁄ , 3⁄ , 1⁄ , 3⁄ , 1⁄ , 32 64 16 32 8 3.985 1 5⁄ and 3⁄ 32 16 1⁄ , 3⁄ , 1⁄ 1 4.985 16 32 8 1⁄ 11⁄4 4.985 8 1 3 1 ⁄16 , ⁄32 , ⁄8 1 5.985 1⁄ , 3⁄ 11⁄4 5.985 8 16 1⁄ 1 7.985 8 1⁄ 11⁄4 7.985 8 Metal Slitting Saws with Side Teethc 1 3 1 7⁄ ⁄16 , ⁄32 , ⁄8 2.485 8 1⁄ , 3⁄ , 1⁄ , 5⁄ 2.985 1 16 32 8 32 1 3 1 5 3 ⁄16 , ⁄32 , ⁄8 , ⁄32 , ⁄16 1 3.985 1⁄ , 3⁄ , 1⁄ , 5⁄ , 3⁄ 4.985 1 16 32 8 32 16 1⁄ 1⁄ 1 4.985 8 4 1⁄ , 3⁄ , 1⁄ , 3⁄ 5.985 1 16 32 8 16 1⁄ , 3⁄ 1⁄ 1 5.985 8 16 4 1⁄ 7.985 1 8 1⁄ , 3⁄ 11⁄4 7.985 8 16 Metal Slitting Saws with Staggered Peripheral and Side Teethd 3⁄ 2.985 1 16 3⁄ 1 3.985 16 3⁄ , 1⁄ 4.985 1 16 4 3⁄ , 1⁄ 5.985 1 16 4 3⁄ , 1⁄ 11⁄4 5.985 16 4 3⁄ , 1⁄ 11⁄4 7.985 16 4 3⁄ , 1⁄ 11⁄4 9.985 16 4 1 5 ⁄4 , ⁄16 11⁄2 11.985

Max.

Min.

0.87575

0.8750

1.00075

1.0000

1.00075

1.0000

1.00075 1.2510 1.00075 1.2510 1.00075 1.2510

1.0000 1.2500 1.0000 1.2500 1.0000 1.2500

0.87575 1.00075 1.00075 1.00075 1.2510 1.00075 1.2510 1.00075 1.2510

0.8750 1.0000 1.0000 1.0000 1.2500 1.0000 1.2500 1.0000 1.2500

1.00075 1.00075 1.00075 1.00075

1.0000 1.0000 1.0000 1.0000

1.2510 1.2510 1.2510 1.5010

1.2500 1.2500 1.2500 1.5000

a Tolerances on face widths are plus or minus 0.001 inch. b Plain metal slitting saws are relatively thin plain milling cutters having peripheral teeth only. They are furnished with or without hub and their sides are concaved to the arbor hole or hub. c Metal slitting saws with side teeth are relatively thin side milling cutters having both peripheral and side teeth. d Metal slitting saws with staggered peripheral and side teeth are relatively thin staggered tooth milling cutters having peripheral teeth of alternate right- and left-hand helix and alternate side teeth.

All dimensions are in inches. All saws are high-speed steel. Metal slitting saws are similar to plain or side milling cutters but are relatively thin.

Milling Cutter Terms



MILLING CUTTERS Milling Cutter Terms (Continued)

American National Standard Single- and Double-Angle Milling Cutters ANSI/ASME B94.19-1997 Cutter Diameter Nom.

Max.

Hole Diameter Min.

Nominal Face Widtha

Nom.

Max.

Min.

Single-angle Cuttersb 3⁄ -24 8

UNF-2B RH

3⁄ -24 8

UNF-2B LH

c11⁄ 4

1.265

1.235

7⁄ 16

c15⁄ 8

1.640

1.610

9⁄ 16

23⁄4

2.765

2.735

1⁄ 2

1

1.00075

1.0000

3

3.015

2.985

1⁄ 2

11⁄4

1.2510

1.2500

23⁄4

2.765

2.735

1

1.00075

1.0000

1⁄ -20 2

UNF-2B RH

Double-angle Cuttersd 1⁄ 2

a Face width tolerances are plus or minus 0.015 inch. b Single-angle milling cutters have peripheral teeth, one cutting edge of which lies in a conical surface and the other in the plane perpendicular to the cutter axis. There are two types: one has a plain keywayed hole and has an included tooth angle of either 45 or 60 degrees plus or minus 10 minutes; the other has a threaded hole and has an included tooth angle of 60 degrees plus or minus 10 minutes. Cutters with a right-hand threaded hole have a right-hand hand of rotation and a right-hand hand of cutter. Cutters with a left-hand threaded hole have a left-hand hand of rotation and a left-hand hand of cutter. Cutters with plain keywayed holes are standard as either right-hand or left-hand cutters. c These cutters have threaded holes, the sizes of which are given under “Hole Diameter.” d Double-angle milling cutters have symmetrical peripheral teeth both sides of which lie in conical surfaces. They are designated by the included angle, which may be 45, 60 or 90 degrees. Tolerances are plus or minus 10 minutes for the half angle on each side of the center.

All dimensions are in inches. All cutters are high-speed steel.



803

American National Standard Shell Mills ANSI/ASME B94.19-1997

Dia., D inches

Width, W inches

Dia., H inches

11⁄4

1

11⁄2

11⁄8

13⁄4

11⁄4

2

13⁄8

1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 4

21⁄4

11⁄2

1

21⁄2

15⁄8

1

23⁄4

15⁄8

1

3

13⁄4

11⁄4

31⁄2

17⁄8 21⁄4 21⁄4 21⁄4 21⁄4

11⁄4 11⁄2 11⁄2 11⁄2

4 41⁄2 5 6

2

Length, B inches 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

1 1 1 1

Width, C inches

Depth, E inches

Radius, F inches

Dia., J inches

1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4

5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 7⁄ 32 7⁄ 32 7⁄ 32 9⁄ 32 9⁄ 32 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16

1⁄ 64 1⁄ 64 1⁄ 32 1⁄ 32 1⁄ 32 1⁄ 32 1⁄ 32 1⁄ 32 1⁄ 32 1⁄ 16 1⁄ 16 1⁄ 16 1⁄ 16

11⁄ 16 11⁄ 16 15⁄ 16 15⁄ 16 11⁄4 13⁄8 11⁄2 121⁄32 111⁄16 21⁄32 21⁄16 29⁄16 213⁄16

Dia., K degrees 5⁄ 8 5⁄ 8 7⁄ 8 7⁄ 8 13⁄16 13⁄16 13⁄16 11⁄2 11⁄2 17⁄8 17⁄8 17⁄8 21⁄2

Angle, L inches 0 0 0 0 0 0 5 5 5 5 10 10 15

All cutters are high-speed steel. Right-hand cutters with right-hand helix and square corners are standard. Tolerances: On D, +1⁄64 inch; on W, ±1⁄64 inch; on H, +0.0005 inch; on B, +1⁄64 inch; on C, at least +0.008 but not more than +0.012 inch; on E, +1⁄64 inch; on J, ±1⁄64 inch; on K, ±1⁄64 inch.

End Mill Terms

Enlarged Section of End Mill Tooth



MILLING CUTTERS End Mill Terms (Continued)

Enlarged Section of End Mill

American National Standard Multiple- and Two-Flute Single-End Helical End Mills with Plain Straight and Weldon Shanks ANSI/ASME B94.19-1997

Cutter Diameter, D Nom. 1⁄ 8 3⁄ 16 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

Max. .130

Shank Diameter, S Min.

Max.

Min.

Multiple-flute with Plain Straight Shanks .125 .125 .1245

.1925

.1875

.1875

.1870

.255

.250

.250

.2495

.380

.375

.375

.3745

.505

.500

.500

.4995

.755

.750

.750

.7495

Length of Cut, W 5⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 15⁄ 16 1 1 ⁄4

Length Overall, L 11⁄4 13⁄8 111⁄16 113⁄16 21⁄4 25⁄8

Two-flute for Keyway Cutting with Weldon Shanks 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

.125

.1235

.375

.3745

.1875

.1860

.375

.3745

.250

.2485

.375

.3745

3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 9⁄ 16

25⁄16 25⁄16 25⁄16 25⁄16

.3125

.3110

.375

.3745

.375

.3735

.375

.3745

.500

.4985

.500

.4995

1

3

.625

.6235

.625

.6245

15⁄16

37⁄16

.750

.7485

.750

.7495

15⁄16

39⁄16

.875

.8735

.875

.8745

11⁄2

33⁄4

25⁄16

1

1.000

.9985

1.000

.9995

15⁄8

41⁄8

11⁄4

1.250

1.2485

1.250

1.2495

15⁄8

41⁄8

11⁄2

1.500

1.4985

1.250

1.2495

15⁄8

41⁄8

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. The helix angle is not less than 10 degrees for multiple-flute cutters with plain straight shanks; the helix angle is optional with the manufacturer for two-flute cutters with Weldon shanks. Tolerances: On W, ±1⁄32 inch; on L, ±1⁄16 inch.



805

ANSI Regular-, Long-, and Extra Long-Length, Multiple-Flute Medium Helix Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997

As Indicated By The Dimensions Given Below, Shank Diameter S May Be Larger, Smaller, Or The Same As The Cutter Diameter D Cutter Dia., D 1⁄ b 8 3⁄ b 16 1⁄ b 4 5⁄ b 16 3⁄ b 8 7⁄ 16 1⁄ 2 1⁄ b 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 5⁄ b 8 11⁄ 16 3⁄ b 4 13⁄ 16 7⁄ 8

1 7⁄ 8

1 11⁄8 11⁄4

Regular Mills S 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

Long Mills

L

Na

25⁄16

4

…

23⁄8

4

…

27⁄16

4

21⁄2

4

21⁄2

4

1

211⁄16

4

1

211⁄16

11⁄4

31⁄4

13⁄8 13⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 17⁄8 17⁄8 17⁄8 17⁄8 17⁄8 2 2

W 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

S

W …

…

…

4

3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2

4

…

33⁄8 33⁄8 35⁄8 35⁄8 33⁄4 33⁄4 33⁄4

4 4 4

4

L …

Extra Long Mills Na

S

…

…

…

…

…

…

W

Na

L …

…

…

…

11⁄4

31⁄16

4

13⁄4

39⁄16

4

2

33⁄4

4

4

3⁄ 8 3⁄ 8 3⁄ 8

13⁄8

31⁄8

4

11⁄2

31⁄4

21⁄2

41⁄4

13⁄4

33⁄4

4

4

…

…

…

…

2

4

4

1⁄ 2

3

5

4

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

5⁄ 8

21⁄2

45⁄8

4

5⁄ 8

4

61⁄8

4

…

…

…

…

…

…

…

…

4

3⁄ 4

3

51⁄4

4

3⁄ 4

4

61⁄4

4

4

…

…

…

…

…

…

…

…

4

…

…

…

…

…

…

…

…

4

…

…

…

…

…

…

…

…

6

…

…

…

…

…

…

…

…

4

6

7⁄ 8

31⁄2

4

7⁄ 8

5

6

1

4

4

1

6

71⁄4 81⁄2

4

4

53⁄4 61⁄2

41⁄8

4

…

…

…

…

…

…

…

…

41⁄8

4

…

…

…

…

…

…

…

…

41⁄4

6

1

4

61⁄2

6

…

…

…

…

41⁄4

6

1

4

61⁄2

6

11⁄4

6

81⁄2

6

4

1

1

2

41⁄2

4

…

…

…

…

…

…

…

…

11⁄8

1

2

41⁄2

6

…

…

…

…

…

…

…

…

11⁄4

1

2

41⁄2

6

…

…

…

…

…

…

…

…

2

41⁄2 41⁄2 41⁄2 41⁄2 41⁄2 41⁄2

6

…

…

…

…

…

…

…

…

61⁄2 61⁄2 61⁄2 61⁄2 61⁄2

6

…

…

…

…

6

…

…

…

…

6

11⁄4

8

101⁄2

6

6

…

…

…

…

8

…

…

…

…

13⁄8 11⁄2 11⁄4 11⁄2 13⁄4

1

2

11⁄4

2

11⁄4

2

11⁄4

2

2

11⁄4

2

1

6

1

4

6

11⁄4

4

6

11⁄4

4

6

11⁄4

4

8

11⁄4

4

a N = Number of flutes. b In this size of regular mill a left-hand cutter with left-hand helix is also standard.

All dimensions are in inches. All cutters are high-speed steel. Helix angle is greater than 19 degrees but not more than 39 degrees. Right-hand cutters with right-hand helix are standard. Tolerances: On D, +0.003 inch; on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; on L, ±1⁄16 inch.



MILLING CUTTERS ANSI Two-Flute, High Helix, Regular-, Long-, and Extra Long-Length, Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Cutter Dia., D

Regular Mill

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

S

W

3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

5⁄ 8 3⁄ 4 3⁄ 4

11⁄4 15⁄8 15⁄8 17⁄8

1

2

11⁄4

11⁄4

2

11⁄2

11⁄4 11⁄4

2 2

Extra Long Mill

S

W

L

S

W

27⁄16

3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4

11⁄4

31⁄16

39⁄16

31⁄8 31⁄4 33⁄4

3⁄ 8 3⁄ 8 3⁄ 8

13⁄4

13⁄8 11⁄2 13⁄4

2 21⁄2

33⁄4 41⁄4

…

…

…

2

4

3

5

21⁄2

45⁄8

4

61⁄8

3

51⁄4

…

21⁄2 21⁄2 211⁄16 31⁄4 33⁄4 37⁄8 41⁄8 41⁄2 41⁄2 41⁄2 41⁄2

1

1

2

Long Mill L

…

1⁄ 2 5⁄ 8 3⁄ 4

4

61⁄4

…

… 81⁄2

1

4

… 61⁄2

1

6

11⁄4

4

61⁄2

11⁄4

6

81⁄2

4

61⁄2 61⁄2

11⁄4

8

101⁄2

…

…

11⁄4 11⁄4

4

…

L

…

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 39 degrees. Tolerances: On D, +0.003 inch; on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; and on L, ±1⁄16 inch.

Combination Shanks for End Mills ANSI/ASME B94.19-1997 Right-hand Cut

Left-hand Cut

G K 1/2 K 90° H

E B

F C

12°

45° D

A J

Dia. A

45°

L

.015

Central With “K”

M

La

B

C

D

E

F

G

H

J

K

M

11⁄2

211⁄16

13⁄16

.515

1.406

11⁄2

.515

1.371

1.302

.377

2 21⁄2

31⁄4

123⁄32

.700

1.900

13⁄4

.700

1.809

1.772

.440

31⁄2

115⁄16

.700

2.400

2

.700

2.312

9⁄ 16 5⁄ 8 3⁄ 4

2.245

.503

7⁄ 16 1⁄ 2 9⁄ 16

a Length of shank.

All dimensions are in inches. Modified for use as Weldon or Pin Drive shank.



807

ANSI Roughing, Single-End End Mills with Weldon Shanks, High-Speed Steel ANSI/ASME B94.19-1997

Diameter Cutter D

Length Shank S

1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4

1 1 11⁄4 11⁄4 11⁄2 11⁄2 13⁄4 13⁄4

1 1 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4

Cut W 1 11⁄4 2 11⁄4 15⁄8 21⁄2 11⁄2 15⁄8 3 2 4 2 4 2 4 2 4

Diameter Overall L 3 31⁄4 4 33⁄8 33⁄4 45⁄8 33⁄4 37⁄8 51⁄4 41⁄2 61⁄2 41⁄2 61⁄2 41⁄2 61⁄2 41⁄2 61⁄2

Length

Cutter D

Shank S

Cut W

Overall L

2 2 2 2 2 2 2 2 2 21⁄2 21⁄2 21⁄2 21⁄2 3 3 3 3

2 2 2 2 2 2 2 2 2 2 2 2 2 21⁄2 21⁄2 21⁄2 21⁄2

2 3 4 5 6 7 8 10 12 4 6 8 10 4 6 8 10

53⁄4 63⁄4 73⁄4 83⁄4 93⁄4 103⁄4 113⁄4 133⁄4 153⁄4 73⁄4 93⁄4 113⁄4 133⁄4 73⁄4 93⁄4 113⁄4 133⁄4

All dimensions are in inches. Right-hand cutters with right-hand helix are standard. Tolerances: Outside diameter, +0.025, −0.005 inch; length of cut, +1⁄8 , −1⁄32 inch.

American National Standard Heavy Duty, Medium Helix Single-End End Mills, 21⁄2 -inch Combination Shank, High-Speed Steel ANSI/ASME B94.19-1997

Dia. of Cutter, D 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 3 3

No. of Flutes 3 3 6 6 6 6 6 2 2

Length of Cut, W 8 10 4 6 8 10 12 4 6

Length Overall, L 12 14 8 10 12 14 16 73⁄4 93⁄4

Dia. of Cutter, D

No. of Flutes

3 3 3 3 3 3 3 3 …

3 3 3 8 8 8 8 8 …

Length of Cut, W 4 6 8 4 6 8 10 12 …

Length Overall, L 73⁄4 93⁄4 113⁄4 73⁄4 93⁄4 113⁄4 133⁄4 153⁄4 …

All dimensions are in inches. For shank dimensions see page 806. Right-hand cutters with righthand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On D, +0.005 inch; on W, ±1⁄32 inch; on L, ±1⁄16 inch.



MILLING CUTTERS

ANSI Stub-, Regular-, and Long-Length, Four-Flute, Medium Helix, Plain-End, Double-End Miniature End Mills with 3⁄16 -Inch Diameter Straight Shanks ANSI/ASME B94.19-1997

Stub Length

Regular Length

Dia. D

W

L

W

L

1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16

3⁄ 32 9⁄ 64 3⁄ 16 15⁄ 64 9⁄ 32

2 2 2 2 2

3⁄ 16 9⁄ 32 3⁄ 8 7⁄ 16 1⁄ 2

21⁄4 21⁄4 21⁄4 21⁄4 21⁄4

Dia. D

Long Length W

B

1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16

3⁄ 8 1⁄ 2 3⁄ 4 7⁄ 8

L

7⁄ 32 9⁄ 32 3⁄ 4 7⁄ 8

1

21⁄2 25⁄8 31⁄8 31⁄4 33⁄8

1

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On D, + 0.003 inch (if the shank is the same diameter as the cutting portion, however, then the tolerance on the cutting diameter is − 0.0025 inch.); on W, + 1⁄32 , − 1⁄64 inch; and on L, ±1⁄16 inch.

American National Standard 60-Degree Single-Angle Milling Cutters with Weldon Shanks ANSI/ASME B94.19-1997

Dia., D

S

W

L

Dia., D

S

W

L

3⁄ 4 13⁄8

3⁄ 8 5⁄ 8

5⁄ 16 9⁄ 16

21⁄8

17⁄8

7⁄ 8

31⁄4

27⁄8

21⁄4

13⁄ 16 11⁄16

1

33⁄4

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters are standard. Tolerances: On D, ± 0.015 inch; on S, − 0.0001 to − 0.0005 inch; on W, ± 0.015 inch; and on L, ±1⁄16 inch.



809

American National Standard Stub-, Regular-, and Long-Length, Two-Flute, Medium Helix, Plain- and Ball-End, Double-End Miniature End Mills with 3⁄16 -Inch Diameter Straight Shanks ANSI/ASME B94.19-1997

Stub Length

Regular Length

Dia., C and D

W

L

W

L

W

L

W

L

1⁄ 32 3⁄ 64 1⁄ 16 5⁄ 64 3⁄ 32 7⁄ 64 1⁄ 8 9⁄ 64 5⁄ 32 11⁄ 64 3⁄ 16

3⁄ 64 1⁄ 16 3⁄ 32 1⁄ 8 9⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 15⁄ 64 1⁄ 4 9⁄ 32

2

…

…

21⁄4

…

…

2

…

…

21⁄4

…

…

2

3⁄ 32

2

21⁄4

3⁄ 16

2

…

…

…

9⁄ 64 …

…

9⁄ 32 …

21⁄4 …

2

3⁄ 16 …

…

21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4

21⁄4 …

2

3⁄ 32 9⁄ 64 3⁄ 16 15⁄ 64 9⁄ 32 21⁄ 64 3⁄ 8 13⁄ 32 7⁄ 16 1⁄ 2 1⁄ 2

3⁄ 8 …

21⁄4 …

7⁄ 16 …

21⁄4 …

1⁄ 2

21⁄4

Plain End

Ball End

2 2

Plain End

2 2

2

15⁄ 64

2

2

…

…

2

9⁄ 32

Long Length, Plain End

Dia., D

Ba

W

L

1⁄ 16 3⁄ 32 1⁄ 8

3⁄ 8 1⁄ 2 3⁄ 4

7⁄ 32 9⁄ 32 3⁄ 4

21⁄2 25⁄8 31⁄8

2 Dia., D 5⁄ 32 3⁄ 16

Ball End

Long Length, Plain End Ba

W

L

7⁄ 8

7⁄ 8

1

1

31⁄4 33⁄8

a B is the length below the shank.

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On C and D, − 0.0015 inch for stub and regular length; + 0.003 inch for long length (if the shank is the same diameter as the cutting portion, however, then the tolerance on the cutting diameter is − 0.0025 inch.); on W, + 1⁄32 , − 1⁄64 inch; and on L, ± 1⁄16 inch.

American National Standard Multiple Flute, Helical Series End Mills with Brown & Sharpe Taper Shanks

Dia., D

W

L

Taper No.

Dia., D

W

L

Taper No.

1⁄ 2 3⁄ 4

15⁄ 16 11⁄4 5 1 ⁄8

415⁄16 51⁄4 55⁄8

7 7 7

11⁄4 11⁄2 2

2

71⁄4 71⁄2 8

9 9 9

1

21⁄4 23⁄4

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is not less than 10 degrees. No. 5 taper is standard without tang; Nos. 7 and 9 are standard with tang only. Tolerances: On D, +0.005 inch; on W, ±1⁄32 inch; and on L ±1⁄16 inch. For dimensions of B & S taper shanks, see information given on page 936.



MILLING CUTTERS

American National Standard Stub- and Regular-Length, Two-Flute, Medium Helix, Plain- and Ball-End, Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Regular Length — Plain End Dia., D 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8

1 7⁄ 8 1 11⁄8 11⁄4 1 11⁄8 11⁄4 13⁄8 11⁄2 11⁄4 11⁄2 13⁄4 2

S 3⁄ 8 3⁄8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 1 1 1 1 1 11⁄4 11⁄4 11⁄4 11⁄4

W 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 9⁄ 16 13⁄ 16 13⁄ 16

1 11⁄8 11⁄8 15⁄16 15⁄16 15⁄16 15⁄16 15⁄16 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8

Stub Length — Plain End

L 25⁄16 25⁄16 25⁄16 25⁄16 25⁄16 21⁄2 21⁄2 3 31⁄8 31⁄8 35⁄16 35⁄16 37⁄16 37⁄16 37⁄16 35⁄8 35⁄8 35⁄8 33⁄4 33⁄4 37⁄8 37⁄8 41⁄8 41⁄8 41⁄8 41⁄8 41⁄8 41⁄8 41⁄8 41⁄8 41⁄8

Cutter Dia., D

Shank Dia., S

1⁄ 8 3⁄ 16 1⁄ 4

Length of Cut. W

3⁄ 8 3⁄ 8 3⁄ 8

3⁄ 16 9⁄ 32 3⁄ 8

Length Overall. L 21⁄8 23⁄16 21⁄4

Regular Length — Ball End

Dia., C and D 1⁄ 8 3⁄ 16 1⁄ 4

Shank Dia., S 3⁄ 8 3⁄ 8 3⁄ 8

Length of Cut. W 3⁄ 8 1⁄ 2 5⁄ 8

Length Overall. L 25⁄16 3 2 ⁄8 27⁄16

5⁄ 16 3⁄ 8 7⁄ 16

3⁄ 8 3⁄ 8 1⁄ 2

3⁄ 4 3⁄ 4

1

21⁄2 21⁄2 3

1⁄ 2 9⁄ 16 5⁄ 8

1⁄ 2 1⁄ 2 1⁄ 2

1 11⁄8 11⁄8

3 31⁄8 31⁄8

5⁄ 8 3⁄ 4 3⁄ 4

5⁄ 8 1⁄ 2 3⁄ 4

13⁄8 15⁄16 15⁄8

31⁄2 35⁄16 37⁄8

7⁄ 8 1 1 1 ⁄8

7⁄ 8

1 1

2 21⁄4 21⁄4

41⁄4 43⁄4 43⁄4

11⁄4 11⁄2

11⁄4 11⁄4

21⁄2 21⁄2

5 5

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On C and D, −0.0015 inch for stub-length mills, + 0.003 inch for regular-length mills; on S, −0.0001 to −0.0005 inch; on W, ± 1⁄32 inch; and on L, ± 1⁄16 inch. The following single-end end mills are available in premium high speed steel: ball end, two flute, with D ranging from 1⁄8 to 11⁄2 inches; ball end, multiple flute, with D ranging from 1⁄8 to 1 inch; and plain end, two flute, with D ranging from 1⁄8 to 11⁄2 inches.



811

American National Standard Long-Length Single-End and Stub-, and Regular Length, Double-End, Plain- and Ball-End, Medium Helix, Two-Flute End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Dia., C and D 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄4

Single End Long Length — Plain End S

Ba

W

… … 3⁄ 8 3⁄ 8 3⁄ 8 … 1⁄ 2 5⁄ 8 3⁄ 4 1 11⁄4

… … 11⁄2 13⁄4 13⁄4 … 27⁄32 223⁄32 311⁄32 431⁄32 431⁄32

… … 5⁄ 8 3⁄ 4 3⁄ 4 … 1 13⁄8 15⁄8 21⁄2 3

Long Length — Ball End

L

Ba

S 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4

… … 31⁄16 35⁄16 35⁄16 … 4 45⁄8 53⁄8 71⁄4 71⁄4

W

13⁄ 16 11⁄8 1 1 ⁄2 13⁄4 13⁄4 17⁄8 21⁄4 23⁄4 33⁄8

1 …

3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

1 1 13⁄8 15⁄8 21⁄2 …

5 …

L 23⁄8 211⁄16 31⁄16 35⁄16 35⁄16 311⁄16 4 45⁄8 53⁄8 71⁄4 …

a B is the length below the shank.

Dia., C and D 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8

1

S

Stub Length — Plain End W

3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8

3⁄ 16 15⁄ 64 9⁄ 32 21⁄ 64 3⁄ 8

… … … … … … … … … … … … … …

… … … … … … … … … … … … … …

L 23⁄4 23⁄4 23⁄4 27⁄8 27⁄8 … … … … … … … … … … … … … …

Double End Regular Length — Plain End S W 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 7⁄ 8

1

3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 13⁄ 16 13⁄ 16 13⁄ 16 13⁄ 16 11⁄8 11⁄8 15⁄16 15⁄16 19⁄16 15⁄8

L 31⁄16 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 33⁄4 33⁄4 33⁄4 33⁄4 41⁄2 41⁄2 5 5 51⁄2 57⁄8

S

Regular Length — Ball End W L

3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 1⁄ 2 … 1⁄ 2 … 5⁄ 8 … 3⁄ 4 … 1

3⁄ 8 … 7⁄ 16 … 1⁄ 2 … 9⁄ 16 … 9⁄ 16 … 13⁄ 16 … 13⁄ 16 … 11⁄8 … 15⁄16 … 15⁄8

31⁄16 … 31⁄8 … 31⁄8 … 31⁄8 … 31⁄8 … 33⁄4 … 33⁄4 … 41⁄2 … 5 … 57⁄8

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On C and D, + 0.003 inch for single-end mills, −0.0015 inch for double-end mills; on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; and on L, ±1⁄16 inch.



MILLING CUTTERS American National Standard Regular-, Long-, and Extra Long-Length, Three-and Four-Flute, Medium Helix, Center Cutting, Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Dia., D 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 11⁄2

Regular Length W

S 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 5⁄ 8 5⁄ 8 3⁄ 4 7⁄ 8

3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4 11⁄4 15⁄8 15⁄8 15⁄8 17⁄8

1 1 11⁄4 11⁄4

25⁄16 23⁄8 27⁄16 21⁄2 21⁄2 31⁄4 33⁄4 33⁄4 37⁄8 41⁄8 41⁄2 41⁄2 41⁄2 41⁄2

2 2 2 2

Four Flute Long Length S W

L … …

… … 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 5⁄ 8

… 3⁄ 4 7⁄ 8 1 … 11⁄4 …

L

… …

S

Extra Long Length W L

… …

11⁄4 13⁄8 11⁄2

33⁄16 31⁄8 31⁄4

2 21⁄2 … 3 31⁄2 4 … 4 …

4 45⁄8 … 51⁄4 53⁄4 61⁄2 … 61⁄2 …

… … 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 5⁄ 8

… … 13⁄4 2 21⁄2 3 4 … 4 5 6 … 6 …

… 3⁄ 4 7⁄ 8 1 … 11⁄4 …

39⁄16 33⁄4 41⁄4 5 61⁄8 … 61⁄4 71⁄4 81⁄2 … 81⁄2 …

Three Flute Dia., D 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 3⁄ 4 5⁄ 8 3⁄ 4 7⁄ 8

1 3⁄ 4 7⁄ 8

1 1 1

S W Regular Length 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 7⁄ 8

1

3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

1 1 11⁄4 13⁄8 13⁄8 13⁄8 15⁄8 15⁄8 15⁄8 17⁄8 17⁄8 15⁄8 17⁄8 17⁄8 17⁄8 2

L 25⁄16 23⁄8 27⁄16 21⁄2 21⁄2 211⁄16 211⁄16 31⁄4 33⁄8 33⁄8 33⁄8 35⁄8 33⁄4 33⁄4 4 4 37⁄8 41⁄8 41⁄8 41⁄8 41⁄2

Dia., D 11⁄8 11⁄4 11⁄2 11⁄4 11⁄2 13⁄4 2

S W Regular Length (cont.) 1 1 1 11⁄4 11⁄4 11⁄4 11⁄4

L

2 2 2 2 2 2 2

41⁄2 41⁄2 41⁄2 41⁄2 41⁄2 41⁄2 41⁄2

11⁄4 13⁄8 11⁄2 13⁄4 2 21⁄2 3 4 4 4 4 4

311⁄16 31⁄8 31⁄4 33⁄4 4 45⁄8 51⁄4 61⁄2 61⁄2 61⁄2 61⁄2 61⁄2

Long Length 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄4 11⁄2 13⁄4 2

1 11⁄4 11⁄4 11⁄4 11⁄4

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On D, +0.003 inch; on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; and on L, ±1⁄16 inch. The following center-cutting, single-end end mills are available in premium high speed steel: regular length, multiple flute, with D ranging from 1⁄8 to 11⁄2 inches; long length, multiple flute, with D ranging from 3⁄8 to 11⁄4 inches; and extra long-length, multiple flute, with D ranging from 3⁄8 to 11⁄4 inches.



813

American National Standard Stub- and Regular-length, Four-flute, Medium Helix, Double-end End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Dia., D

S

W

Dia., D

L

S

W

Dia., D

L

S

W

L

Stub Length 1⁄ 8

3⁄ 8

3⁄ 16

23⁄4

3⁄ 16

3⁄ 8

5⁄ 32

3⁄ 8

15⁄ 64

23⁄4

7⁄ 32

3⁄ 8

9⁄ 32 21⁄ 64

23⁄4

1⁄ 4

3⁄ 8

3⁄ 8

27⁄8

27⁄8

…

…

…

…

Regular Length 1⁄ a 8

3⁄ 8

3⁄ 8

31⁄16

11⁄ 32

3⁄ 8

3⁄ 4

31⁄2

5⁄ a 8

5⁄ 8

13⁄8

5

5⁄ a 32

3⁄ 8

7⁄ 16

31⁄8

3⁄ a 8

3⁄ 8

3⁄ 4

31⁄2

11⁄ 16

3⁄ 4

15⁄8

55⁄8

3⁄ a 16

3⁄ 8

1⁄ 2

31⁄4

13⁄ 32

1⁄ 2

1

41⁄8

3⁄ a 4

3⁄ 4

15⁄8

55⁄8

7⁄ 32

3⁄ 8

9⁄ 16

31⁄4

7⁄ 16

1⁄ 2

1

41⁄8

13⁄ 16

7⁄ 8

17⁄8

61⁄8

1⁄ a 4

3⁄ 8

5⁄ 8

33⁄8

15⁄ 32

1⁄ 2

1

41⁄8

7⁄ 8

7⁄ 8

17⁄8

61⁄8

9⁄ 32

3⁄ 8

11⁄ 16

33⁄8

1⁄ a 2

1⁄ 2

1

41⁄8

1

17⁄8

63⁄8

5⁄ a 16

3⁄ 8

3⁄ 4

31⁄2

9⁄ 16

5⁄ 8

13⁄8

5

…

…

…

1 …

a In this size of regular mill a left-hand cutter with a left-hand helix is also standard.

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On D, +0.003 inch (if the shank is the same diameter as the cutting portion, however, then the tolerance on the cutting diameter is −0.0025 inch); on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; and on L, ±1⁄16 inch.

American National Standard Stub- and Regular-Length, Four-Flute, Medium Helix, Double-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997

Dia., D

S

W

L

Dia., D

S

Three Flute

W

L

Four Flute

1⁄ 8

3⁄ 8

3⁄ 8

31⁄16

1⁄ 8

3⁄ 8

3⁄ 8

31⁄16

3⁄ 16

3⁄ 8

1⁄ 2

31⁄4

3⁄ 16

3⁄ 8

1⁄ 2

31⁄4

1⁄ 4

3⁄ 8

5⁄ 8

33⁄8

1⁄ 4

3⁄ 8

5⁄ 8

33⁄8

5⁄ 16

3⁄ 8

3⁄ 4

31⁄2

5⁄ 16

3⁄ 8

3⁄ 4

31⁄2

3⁄ 8

3⁄ 8

3⁄ 4

31⁄2

3⁄ 8

3⁄ 8

3⁄ 4

7⁄ 16

1⁄ 2

1

41⁄8

1⁄ 2

1⁄ 2

1

41⁄8

1⁄ 2

1⁄ 2

1

41⁄8

5⁄ 8

5⁄ 8

13⁄8

5

9⁄ 16

5⁄ 8

13⁄8

5

3⁄ 4

3⁄ 4

15⁄8

55⁄8

5⁄ 8

5⁄ 8

13⁄8

5

7⁄ 8

7⁄ 8

17⁄8

61⁄8

3⁄ 4

3⁄ 4

15⁄8

55⁄8

1

1

17⁄8

63⁄8

1

1

17⁄8

63⁄8

…

…

…

…

31⁄2

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On D, +0.0015 inch; on S, −0.0001 to −0.0005 inch; on W, ±1⁄32 inch; and on L, ±1⁄16 inch.



MILLING CUTTERS

American National Standard Plain- and Ball-End, Heavy Duty, Medium Helix, Single-End End Mills with 2-Inch Diameter Shanks ANSI/ASME B94.19-1997

W

Plain End L

2

2

53⁄4

2

3

2

4

2

…

…

2

6

93⁄4

8 4

113⁄4 73⁄4

…

…

6

93⁄4 113⁄4

2, 4, 6

…

…

…

6

…

…

…

Dia., C and D

2 21⁄2 21⁄2 21⁄2 21⁄2

8

W

Ball End L

2, 4, 6

…

…

63⁄4

2, 3

…

…

73⁄4

2, 3, 4, 6

4

73⁄4

6

…

5

83⁄4

2, 4

2, 3, 4, 6

6

93⁄4

6

6

8

113⁄4

6

2, 3, 4, 6

…

…

…

…

5

83⁄4

4

No. of Flutes

No. of Flutes … …

All dimensions are in inches. All cutters are high-speed steel. Right-hand cutters with right-hand helix are standard. Helix angle is greater than 19 degrees but not more than 39 degrees. Tolerances: On C and D, + 0.005 inch for 2, 3, 4 and 6 flutes: on W, ± 1⁄16 inch; and on L, ± 1⁄16 inch.

Dimensions of American National Standard Weldon Shanks ANSI/ASME B94.19-1997 Shank Dia.

Flat Length

Shank

Xa

Lengthb

Dia.

Flat Length

Xa

Lengthb 0.515

3⁄ 8

19⁄16

0.325

0.280

1

29⁄32

0.925

1⁄ 2

125⁄32

0.440

0.330

11⁄4

29⁄32

1.156

0.515

5⁄ 8

129⁄32

0.560

0.400

11⁄2

211⁄16

1.406

0.515

3⁄ 4

21⁄32

0.675

0.455

2

31⁄4

1.900

0.700

7⁄ 8

21⁄32

0.810

0.455

21⁄2

31⁄2

2.400

0.700

a X is distance from bottom of flat to opposite side of shank. b Minimum.

All dimensions are in inches. Centerline of flat is at half-length of shank except for 11⁄2 -, 2- and 21⁄2 -inch shanks where it is 13⁄16 , 127⁄32 and 115⁄16 from shank end, respectively. Tolerance on shank diameter, − 0.0001 to − 0.0005 inch.



815

Amerian National Standard Form Relieved, Concave, Convex, and Corner-Rounding Arbor-Type Cutters ANSI/ASME B94.19-1997

Concave

Convex

Diameter C or Radius R Nom.

Max.

Min.

Cutter Dia. Da

Corner-rounding

Width W ± .010b

Diameter of Hole H Nom.

Max.

Min.

1.00000

Concave Cuttersc 1⁄ 8

0.1270

0.1240

21⁄4

1⁄ 4

1

1.00075

3⁄ 16

0.1895

0.1865

21⁄4

3⁄ 8

1

1.00075

1.00000

1⁄ 4

0.2520

0.2490

21⁄2

7⁄ 16

1

1.00075

1.00000

5⁄ 16

0.3145

0.3115

23⁄4

9⁄ 16

1

1.00075

1.00000

3⁄ 8

0.3770

0.3740

23⁄4

5⁄ 8

1

1.00075

1.00000

7⁄ 16

0.4395

0.4365

3

3⁄ 4

1

1.00075

1.00000

1⁄ 2

0.5040

0.4980

3

13⁄ 16

1

1.00075

1.00000

5⁄ 8

0.6290

0.6230

31⁄2

1

11⁄4

1.251

1.250

3⁄ 4

0.7540

0.7480

33⁄4

13⁄16

11⁄4

1.251

1.250

0.8730

4

13⁄8

11⁄4

1.251

1.250

0.9980

41⁄4

19⁄16

11⁄4

1.251

1.250

1.00000

7⁄ 8

1

0.8790 1.0040

Convex Cuttersc 1⁄ 8

0.1270

0.1230

21⁄4

1⁄ 8

1

1.00075

3⁄ 16

0.1895

0.1855

21⁄4

3⁄ 16

1

1.00075

1.00000

1⁄ 4

0.2520

0.2480

21⁄2

1⁄ 4

1

1.00075

1.00000

5⁄ 16

0.3145

0.3105

23⁄4

5⁄ 16

1

1.00075

1.00000

3⁄ 8

0.3770

0.3730

23⁄4

3⁄ 8

1

1.00075

1.00000

7⁄ 16

0.4395

0.4355

3

7⁄ 16

1

1.00075

1.00000

1⁄ 2

0.5020

0.4980

3

1⁄ 2

1

1.00075

1.00000

5⁄ 8

0.6270

0.6230

31⁄2

5⁄ 8

11⁄4

1.251

1.250

3⁄ 4

0.7520

0.7480

33⁄4

3⁄ 4

11⁄4

1.251

1.250

0.8730

4

7⁄ 8

11⁄4

1.251

1.250

0.9980

41⁄4

11⁄4

1.251

1.250

7⁄ 8

1

0.8770 1.0020

1

Corner-rounding Cuttersd 1⁄ 8

0.1260

0.1240

21⁄2

1

1.00075

1.00000

1⁄ 4

0.2520

0.2490

3

13⁄ 32

1

1.00075

1.00000

3⁄ 8

0.3770

0.3740

33⁄4

9⁄ 16

11⁄4

1.251

1.250

1⁄ 2

0.5020

0.4990

41⁄4

3⁄ 4

11⁄4

1.251

1.250

5⁄ 8

0.6270

0.6240

41⁄4

15⁄ 16

11⁄4

1.251

1.250

a Tolerances on cutter diameter are + 1⁄ , − 1⁄ 16 16 b Tolerance does not apply to convex cutters.

1⁄ 4

inch for all sizes.

c Size of cutter is designated by specifying diameter C of circular form. d Size of cutter is designated by specifying radius R of circular form.

All dimensions in inches. All cutters are high-speed steel and are form relieved. Right-hand corner rounding cutters are standard, but left-hand cutter for 1⁄4 -inch size is also standard. For key and keyway dimensions for these cutters, see page 819.



MILLING CUTTERS

American National Standard Roughing and Finishing Gear Milling Cutters for Gears with 141⁄2 -Degree Pressure Angles ANSI/ASME B94.19-1997

ROUGHING

FINISHING Dia. of Cutter, D

Dia. of Hole, H

5

33⁄8

6

37⁄8

1 11⁄2

13⁄4

6

31⁄2

11⁄4

41⁄2

11⁄2

6

31⁄8

4

41⁄4

11⁄4

7

33⁄8

1 11⁄4

11⁄2

4

35⁄8

27⁄8

5

43⁄8

1 13⁄4

7

13⁄4

8

31⁄4

1 11⁄4

5

41⁄4 33⁄4

11⁄2 11⁄4

8

27⁄8

1

…

…

…

11⁄2 11⁄4

14

1 11⁄2

16

21⁄8 21⁄2 21⁄8 23⁄8

Dia. of Cutter, D

Dia. of Hole, H

Dia. of Cutter, D

Dia. of Hole, H

1

81⁄2

2

3

51⁄4

11⁄2

11⁄4

73⁄4

3

43⁄4

11⁄4

11⁄2

4

43⁄4

13⁄4

7 61⁄2

2 13⁄4 13⁄4

4

2

61⁄2

13⁄4

2 21⁄2

53⁄4 61⁄8

3

53⁄4 55⁄8

11⁄2 13⁄4

1 11⁄4

81⁄2 73⁄4

11⁄2

7 61⁄2

Diametral Pitch

Diametral Pitch

Diametral Pitch

Roughing Gear Milling Cutters

21⁄2

5

Finishing Gear Milling Cutters

13⁄4

2

6

2 13⁄4

6 6

13⁄4

7

2

61⁄2

13⁄4

7

2 21⁄2

53⁄4

11⁄2

7

61⁄8

13⁄4

8

21⁄2

53⁄4

11⁄2

8

3

55⁄8 51⁄4 43⁄4 43⁄4 41⁄2 41⁄4 35⁄8 43⁄8 41⁄4 33⁄4 33⁄8 41⁄4

13⁄4 11⁄2 11⁄4 13⁄4 11⁄2 11⁄4

8

1 13⁄4 11⁄2

3 3 4 4 4 4 5 5 5 5 6

9

37⁄8 31⁄2 31⁄8 35⁄8 33⁄8 27⁄8 31⁄2 31⁄4 27⁄8 31⁄8 23⁄4

16 18

11⁄4

18

1 11⁄2

20

11⁄4

22

1 11⁄4

22

7⁄ 8

1 7⁄ 8

1 7⁄ 8

2 23⁄8

1

2 21⁄4

1

24

2 21⁄4

1

1 11⁄4

24

13⁄4

26

13⁄4

1

28

13⁄4

20

7⁄ 8 7⁄ 8

36

13⁄4

12

27⁄8

11⁄4

40

13⁄4

11⁄4

12

1

48

13⁄4

1 13⁄4

12

25⁄8 21⁄4 21⁄2

7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

…

…

…

…

…

…

9 10 10

3 23⁄4

10

23⁄8

11

25⁄8

11

23⁄8

14

7⁄ 8

1 7⁄ 8

7⁄ 8

1

30

13⁄4

32

13⁄4

All dimensions are in inches. All gear milling cutters are high-speed steel and are form relieved. For keyway dimensions see page 819. Tolerances: On outside diameter, + 1⁄16 , −1⁄16 inch; on hole diameter, through 1-inch hole diameter, +0.00075 inch, over 1-inch and through 2-inch hole diameter, +0.0010 inch. For cutter number relative to numbers of gear teeth, see page 2052. Roughing cutters are made with No. 1 cutter form only.



817

American National Standard Gear Milling Cutters for Mitre and Bevel Gears with 141⁄2 -Degree Pressure Angles ANSI/ASME B94.19-1997 Diametral Pitch 3 4 5 6 7 8

Diameter of Cutter, D 4 35⁄8 33⁄8 31⁄8 27⁄8 27⁄8

Diameter of Hole, H 11⁄4 11⁄4 11⁄4 1 1 1

Diameter of Cutter, D

Diametral Pitch

23⁄8 21⁄4 21⁄8 21⁄8 2 13⁄4

10 12 14 16 20 24

Diameter of Hole, H 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

All dimensions are in inches. All cutters are high-speed steel and are form relieved. For keyway dimensions see page 819. For cutter selection see page 2091. Tolerances: On outside diameter, +1⁄16 , −1⁄16 inch; on hole diameter, through 1-inch hole diameter, +0.00075 inch, for 11⁄4 -inch hole diameter, +0.0010 inch. To select the cutter number for bevel gears with the axis at any angle, double the back cone radius and multiply the result by the diametral pitch. This procedure gives the number of equivalent spur gear teeth and is the basis for selecting the cutter number from the table on page 2054.

American National Standard Roller Chain Sprocket Milling Cutters

American National Standard Roller Chain Sprocket Milling Cutters ANSI/ASME B94.19-1997 Chain Pitch

Dia. of Roll

No. of Teeth in Sprocket

1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

0.130 0.130 0.130 0.130 0.130 0.130 0.200 0.200 0.200 0.200 0.200 0.200 0.313 0.313 0.313 0.313 0.313 0.313 0.400 0.400 0.400 0.400 0.400 0.400

6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over

Dia. of Cutter, D 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 3 3 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄4 31⁄4 31⁄4 31⁄4

Width of Cutter, W 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 9⁄ 32 9⁄ 32 15⁄ 32 15⁄ 32 15⁄ 32 7⁄ 16 7⁄ 16 13⁄ 32 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 23⁄ 32 11⁄ 16 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 23⁄ 32 11⁄ 16


Dia. of Hole, H 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1


MILLING CUTTERS American National Standard Roller Chain Sprocket Milling Cutters ANSI/ASME B94.19-1997(Continued) Chain Pitch 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 1 1 1 1 1 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 2 2 2 2 2 2 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 3 3 3 3 3 3

Dia. of Roll 0.469 0.469 0.469 0.469 0.469 0.469 0.625 0.625 0.625 0.625 0.625 0.750 0.750 0.750 0.750 0.750 0.875 0.875 0.875 0.875 0.875 0.875 1.000 1.000 1.000 1.000 1.000 1.000 1.125 1.125 1.125 1.125 1.125 1.125 1.406 1.406 1.406 1.406 1.406 1.406 1.563 1.563 1.563 1.563 1.563 1.563 1.875 1.875 1.875 1.875 1.875 1.875

No. of Teeth in Sprocket 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 18–34 35 and over 6 7–8 9–11 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over 6 7–8 9–11 12–17 18–34 35 and over

Dia. of Cutter, D 31⁄4 31⁄4 33⁄8 33⁄8 33⁄8 33⁄8 37⁄8 4 41⁄8 41⁄4 41⁄4 41⁄4 43⁄8 41⁄2 45⁄8 45⁄8 43⁄8 41⁄2 45⁄8 45⁄8 43⁄4 43⁄4 5 51⁄8 51⁄4 53⁄8 51⁄2 51⁄2 53⁄8 51⁄2 55⁄8 53⁄4 57⁄8 57⁄8 57⁄8 6 61⁄4 63⁄8 61⁄2 61⁄2 63⁄8 65⁄8 63⁄4 67⁄8 7 71⁄8 71⁄2 73⁄4 77⁄8 8 8 81⁄4

Width of Cutter, W 29⁄ 32 29⁄ 32 29⁄ 32 7⁄ 8 27⁄ 32 13⁄ 16 11⁄2 11⁄2 115⁄32 113⁄32 111⁄32 113⁄16 113⁄16 125⁄32 111⁄16 15⁄8 113⁄16 113⁄16 125⁄32 13⁄4 111⁄16 15⁄8 23⁄32 23⁄32 21⁄16 21⁄32 131⁄32 17⁄8 213⁄32 213⁄32 23⁄8 25⁄16 21⁄4 25⁄32 211⁄16 211⁄16 221⁄32 219⁄32 215⁄32 213⁄32 3 3 215⁄16 229⁄32 23⁄4 211⁄16 319⁄32 319⁄32 317⁄32 315⁄32 311⁄32 37⁄32

Dia. of Hole, H 1 1 1 1 1 1 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 2 2 2 2 2 2

All dimensions are in inches. All cutters are high-speed steel and are form relieved. For keyway dimensions see page 819. Tolerances: Outside diameter, +1⁄16 , −1⁄16 inch; hole diameter, through 1-inch diameter, + 0.00075 inch, above 1-inch diameter and through 2-inch diameter, + 0.0010 inch. For tooth form, see ANSI sprocket tooth form table on page 2458.



American National Standard Keys and Keyways for Milling Cutters and Arbors ANSI/ASME B94.19-1997

Nom. Size Key (Square)

CUTTER HOLE AND KEYWAY

Arbor and Keyseat A Max.

A Min.

B Max.

ARBOR AND KEY

Hole and Keyway B Min.

C Max.

C Min.

Arbor and Key

Da Min.

H Nom.

Corner Radius

E Max.

E Min.

F Max.

F Min.

1⁄ 2

3⁄ 32

0.0947

0.0937

0.4531

0.4481

0.106

0.099

0.5578

3⁄ 64

0.020

0.0932

0.0927

0.5468

0.5408

5⁄ 8

1⁄ 8

0.1260

0.1250

0.5625

0.5575

0.137

0.130

0.6985

1⁄ 16

1⁄ 32

0.1245

0.1240

0.6875

0.6815

3⁄ 4

1⁄ 8

0.1260

0.1250

0.6875

0.6825

0.137

0.130

0.8225

1⁄ 16

1⁄ 32

0.1245

0.1240

0.8125

0.8065

7⁄ 8

1⁄ 8

0.1260

0.1250

0.8125

0.8075

0.137

0.130

0.9475

1⁄ 16

1⁄ 32

0.1245

0.1240

0.9375

0.9315

1⁄ 4

0.2510

0.2500

0.8438

0.8388

0.262

0.255

1.1040

3⁄ 32

3⁄ 64

0.2495

0.2490

1.0940

1.0880

11⁄4

5⁄ 16

0.3135

0.3125

1.0630

1.0580

0.343

0.318

1.3850

1⁄ 8

1⁄ 16

0.3120

0.3115

1.3750

1.3690

11⁄2

3⁄ 8

0.3760

0.3750

1.2810

1.2760

0.410

0.385

1.6660

5⁄ 32

1⁄ 16

0.3745

0.3740

1.6560

1.6500

13⁄4

7⁄ 16

0.4385

0.4375

1.5000

1.4950

0.473

0.448

1.9480

3⁄ 16

1⁄ 16

0.4370

0.4365

1.9380

1.9320

2

1⁄ 2

0.5010

0.5000

1.6870

1.6820

0.535

0.510

2.1980

3⁄ 16

1⁄ 16

0.4995

0.4990

2.1880

2.1820

21⁄2

5⁄ 8

0.6260

0.6250

2.0940

2.0890

0.660

0.635

2.7330

7⁄ 32

1⁄ 16

0.6245

0.6240

2.7180

2.7120

3

3⁄ 4

0.7510

0.7500

2.5000

2.4950

0.785

0.760

3.2650

1⁄ 4

3⁄ 32

0.7495

0.7490

3.2500

3.2440

31⁄2

7⁄ 8

0.8760

0.8750

3.0000

2.9950

0.910

0.885

3.8900

3⁄ 8

3⁄ 32

0.8745

0.8740

3.8750

3.8690

1

4

1

1.0010

1.0000

3.3750

3.3700

1.035

1.010

4.3900

3⁄ 8

3⁄ 32

0.9995

0.9990

4.3750

4.3690

41⁄2

11⁄8

1.1260

1.1250

3.8130

3.8080

1.160

1.135

4.9530

7⁄ 16

1⁄ 8

1.1245

1.1240

4.9380

4.9320

5

11⁄4

1.2510

1.2500

4.2500

4.2450

1.285

1.260

5.5150

1⁄ 2

1⁄ 8

1.2495

1.2490

5.5000

5.4940

819

a D max. is 0.010 inch larger than D min.

MILLING CUTTERS

ARBOR AND KEYSEAT Nom.Arbor and Cutter Hole Dia.

All dimensions given in inches.



MILLING CUTTERS

American National Standard Woodruff Keyseat Cutters—Shank-Type StraightTeeth and Arbor-Type Staggered-Teeth ANSI/ASME B94.19-1997

Shank-type Cutters

Cutter Number

Nom. Dia.of Cutter, D

Width of Face, W

Length Overall, Cutter L Number

Nom. Dia. of Cutter, D

Width of Face, W

Length Overall, Cutter L Number


Width of Face, W

Length Overall, L

202

1⁄ 4

1⁄ 16

21⁄16

506

3⁄ 4

5⁄ 32

25⁄32

809

1 1⁄8

1⁄ 4

2 1⁄4

202 1⁄2

5⁄ 16

1⁄ 16

21⁄16

606

3⁄ 4

3⁄ 16

23⁄16

1009

1 1⁄8

5⁄ 16

2 5⁄16

302 1⁄2

5⁄ 16

3⁄ 32

23⁄32

806

3⁄ 4

1⁄ 4

21⁄4

610

11⁄4

3⁄ 16

23⁄16

203

3⁄ 8

1⁄ 16

21⁄16

507

7⁄ 8

5⁄ 32

25⁄32

710

11⁄4

7⁄ 32

27⁄32

303

3⁄ 8

3⁄ 32

23⁄32

607

7⁄ 8

3⁄ 16

23⁄16

810

11⁄4

1⁄ 4

21⁄4

403

3⁄ 8

1⁄ 8

21⁄8

707

7⁄ 8

7⁄ 32

27⁄32

1010

11⁄4

5⁄ 16

25⁄16

204

1⁄ 2

1⁄ 16

21⁄16

807

7⁄ 8

1⁄ 4

21⁄4

1210

11⁄4

3⁄ 8

23⁄8

304

1⁄ 2

3⁄ 32

23⁄32

608

1

3⁄ 16

23⁄16

811

13⁄8

1⁄ 4

21⁄4

404

1⁄ 2

1⁄ 8

21⁄8

708

1

7⁄ 32

27⁄32

1011

13⁄8

5⁄ 16

25⁄16

305

5⁄ 8

3⁄ 32

23⁄32

808

1

1⁄ 4

21⁄4

1211

13⁄8

3⁄ 8

23⁄8

405

5⁄ 8

1⁄ 8

21⁄8

1008

1

5⁄ 16

25⁄16

812

11⁄2

1⁄ 4

21⁄4

505

5⁄ 8

5⁄ 32

25⁄32

1208

1

3⁄ 8

23⁄8

1012

11⁄2

5⁄ 16

25⁄16

605

5⁄ 8

3⁄ 16

23⁄16

609

11⁄8

3⁄ 16

23⁄16

1212

11⁄2

3⁄ 8

23⁄8

406

3⁄ 4

1⁄ 8

21⁄8

709

11⁄8

7⁄ 32

27⁄32

…

…

…

…

Width of Face, W

Dia. of Hole, H

Arbor-type Cutters

Cutter Number


Width of Face, W

617

21⁄8

3⁄ 16

3⁄ 4

1022

23⁄4

5⁄ 16

1

1628

31⁄2

1⁄ 2

1

817

21⁄8

1⁄ 4

3⁄ 4

1222

23⁄4

3⁄ 8

1

1828

31⁄2

9⁄ 16

1

1017

21⁄8

5⁄ 16

3⁄ 4

1422

23⁄4

7⁄ 16

1

2028

31⁄2

5⁄ 8

1

1217

21⁄8

3⁄ 8

3⁄ 4

1622

23⁄4

1⁄ 2

1

2428

31⁄2

3⁄ 4

1

822

23⁄4

1⁄ 4

1228

31⁄2

3⁄ 8

1

…

…

…

…

Dia. of Hole, Cutter H Number

1


Width of Face, W

Dia. of Hole, Cutter H Number


All dimensions are given in inches. All cutters are high-speed steel. Shank type cutters are standard with right-hand cut and straight teeth. All sizes have 1⁄2 -inch diameter straight shank. Arbor type cutters have staggered teeth. For Woodruff key and key-slot dimensions, see pages 2369 through 2371. Tolerances: Face with W for shank type cutters: 1⁄16 - to 5⁄32 -inch face, + 0.0000, −0.0005; 3⁄16 to 7⁄32 , − 0.0002, − 0.0007; 1⁄4 , −0.0003, −0.0008; 5⁄16 , −0.0004, −0.0009; 3⁄8 , − 0.0005, −0.0010 inch. Face width W for arbor type cutters; 3⁄16 inch face, −0.0002, −0.0007; 1⁄4 , −0.0003, −0.0008; 5⁄16 , −0.0004, −0.0009; 3⁄8 and over, −0.0005, −0.0010 inch. Hole size H: +0.00075, −0.0000 inch. Diameter D for shank type cutters: 1⁄4 - through 3⁄4 -inch diameter, +0.010, +0.015, 7⁄8 through 11⁄8 , +0.012, +0.017; 11⁄4



821

through 11⁄2 , +0.015, +0.020 inch. These tolerances include an allowance for sharpening. For arbor type cutters diameter D is furnished 1⁄32 inch larger than listed and a tolerance of ±0.002 inch applies to the oversize diameter.

Setting Angles for Milling Straight Teeth of Uniform Land Width in End Mills, Angular Cutters, and Taper Reamers.—The accompanying tables give setting angles for the dividing head when straight teeth, having a land of uniform width throughout their length, are to be milled using single-angle fluting cutters. These setting angles depend upon three factors: the number of teeth to be cut; the angle of the blank in which the teeth are to be cut; and the angle of the fluting cutter. Setting angles for various combinations of these three factors are given in the tables. For example, assume that 12 teeth are to be cut on the end of an end mill using a 60-degree cutter. By following the horizontal line from 12 teeth, read in the column under 60 degrees that the dividing head should be set to an angle of 70 degrees and 32 minutes.

The following formulas, which were used to compile these tables, may be used to calculate the setting-angles for combinations of number of teeth, blank angle, and cutter angle not covered by the tables. In these formulas, A = setting-angle for dividing head, B = angle of blank in which teeth are to be cut, C = angle of fluting cutter, N = number of teeth to be cut, and D and E are angles not shown on the accompanying diagram and which are used only to simplify calculations. tan D = cos ( 360° ⁄ N ) × cot B (1) sin E = tan ( 360° ⁄ N ) × cot C × sin D

(2)

Setting-angle A = D – E

(3)

Example:Suppose 9 teeth are to be cut in a 35-degree blank using a 55-degree singleangle fluting cutter. Then, N = 9, B = 35°, and C = 55°. tan D = cos ( 360° ⁄ 9 ) × cot 35° = 0.76604 × 1.4281 = 1.0940; and D = 47°34′ sin E = tan ( 360° ⁄ 9 ) × cot 55° × sin 47°34′ = 0.83910 × 0.70021 × 0.73806 = 0.43365; and E = 25°42′ Setting angle A = 47°34′ – 25°42′ = 21°52′ For end mills and side mills the angle of the blank B is 0 degrees and the following simplified formula may be used to find the setting angle A cos A = tan ( 360° ⁄ N ) × cot C (4) Example:If in the previous example the blank angle was 0 degrees, cos A = tan (360°/9) × cot 55° = 0.83910 × 0.70021 = 0.58755, and setting-angle A = 54°1′



MILLING CUTTERS Angles of Elevation for Milling Straight Teeth in 0-, 5-, 10-, 15-, 20-, 25-, 30-, and 35-degree Blanks Using Single-Angle Fluting Cutters

No. of Teeth

Angle of Fluting Cutter 90°

80°

70°

60°

50°

90°

80°

70°

0° Blank (End Mill)

60°

50°

5° Blank

6

…

72° 13′

50° 55′

…

…

80°

4′

62° 34′

41° 41′

8

…

79

51

68

39

54° 44′

32° 57′

82

57

72

52

61

47

48°

0′

25°

40′

10

…

82

38

74

40

65

12

52

26

83

50

76

31

68

35

59

11

46

4

12

…

84

9

77

52

70

32

61

2

84

14

78

25

72

10

64

52

55

5

14

…

85

8

79

54

73

51

66

10

84

27

79

36

74

24

68

23

60

28

16

…

85

49

81

20

76

10

69

40

84

35

80

25

75

57

70

49

64

7

18

…

86

19

82

23

77

52

72

13

84

41

81

1

77

6

72

36

66

47

20

…

86

43

83

13

79

11

74

11

84

45

81

29

77

59

73

59

68

50

22

…

87

2

83

52

80

14

75

44

84

47

81

50

78

40

75

4

70

26

24

…

87

18

84

24

81

6

77

0

84

49

82

7

79

15

75

57

71

44

10° Blank

…

…

15° Blank

6

70° 34′

53° 50′

34° 5′

…

…

61° 49′

46° 12′

28 ° 4′

8

76

0

66

9

55

19

41° 56′

20° 39′

69

15

59

46

49

21

36°

…

10

77

42

70

31

62

44

53

30

40

42

71

40

64

41

57

8

12

78

30

72

46

66

37

59

26

49

50

72

48

67

13

61

14

78

56

74

9

69

2

63

6

55

19

73

26

68

46

63

16

79

12

75

5

70 41

65

37

59

1

73

50

18

79

22

75

45

71

53

67

27

61

43

74

20

79

30

76

16

72

44

68

52

63

47

74

22

79

35

76

40

73

33

69

59

65

25

74

24

79

39

76

59

74

9

70

54

66

44

74

… 34′ 17°

34′

48

12

36

18

13

54

14

45

13

46

57

59

50

38

69 49

65 30

60

33

54 20

5

70

33

66

46

62

26

57

16

71

6

67

44

63

52

59

3

24

71

32

68

29

65

0

60

40

30

71

53

69

6

65

56

61

59

20° Blank

0

25° Blank

6

53° 57′

39° 39′

23° 18′

47° 0′

34° 6′

19° 33′

…

…

8

62

46

53

45

43

53

31°

… 53′

14° 31′

…

56

36

48

8

38

55

27° 47′

11° 33′

10

65

47

59

4

51

50

43

18

32

1

60

2

53

40

46

47

38

43

27

47

12

67

12

61

49

56

2

49

18

40

40

61

42

56

33

51

2

44

38

36

10

14

68

0

63

29

58 39

53

4

46

0

62

38

58 19

53 41

48

20

41 22

16

68

30

64

36

60

26

55

39

49

38

63

13

59

29

55

29

50

53

44

18

68

50

65

24

61

44

57

32

52

17

63

37

60

19

56

48

52

46

47

34

20

69

3

65

59

62

43

58

58

54

18

63

53

60

56

57

47

54

11

49

33

22

69

14

66

28

63

30

60

7

55

55

64

5

61

25

58

34

55

19

51

9

24

69

21

66

49

64

7

61

2

57

12

64

14

61

47

59

12

56

13

52

26

6

40° 54′

29° 22′

16° 32′

8

50

46

42

55

34

24

24°

10

54

29

48

30

42

3

12

56

18

51

26

46

14

57

21

53

15

16

58

0

54

18

58

26

20

58

44

22

58

24

59

30° Blank

57

35° Blank …

…

35° 32′

25° 19′

…

…

14°

3′

12′ 10°

14′

45

17

38

5

30

18

21°

4′

8°

41′

34

31

24

44

49

7

43

33

37

35

30

38

21

40

14

40

12

32

32

51

3

46

30

41

39

36

2

28

55

48

52

43

49

37

27

52

9

48

19

44

12

39

28

33

33

27

50

39

46

19

40

52

52

50

49

20

45

56

41

51

36

45

55

18

51

57

48

7

43

20

53

18

50

21

47

12

43

36

39 8

55

55

52

56

49

30

45

15

53

38

50

59

48

10

44

57

40

57

57

56

24

53

42

50

36

46

46

53

53

51

29

48

56

46

1

42

24

8

56

48

54

20

51

30

48

0

54

4

51

53

49

32

46

52

43

35



823

Angles of Elevation for Milling Straight Teeth in 40-, 45-, 50-, 55-, 60-, 65-, 70-, and 75-degree Blanks Using Single-Angle Fluting Cutters No. of Teeth


80°

70°

60°

50°

90°

80°

70°

40° Blank

60°

50°

45° Blank …

…

6

30° 48′

21° 48′

11° 58′

26° 34′

18° 43′

10° 11′

8

40

7

33

36

26

33

18°

16′

7°

23′

35

16

29

25

23

8

10

43

57

38

51

33

32

27

3

18

55

38

58

34

21

29

12

45

54

41

43

37

14

32

3

25

33

40

54

37

5

14

47

3

43

29

39

41

35

19

29

51

42

1

38

16

47

45

44

39

41

21

37

33

32

50

42

44

18

48

14

45

29

42

34

39

13

35

5

43

20

48

35

46

7

43

30

40

30

36

47

43

22

48

50

46

36

44

13

41

30

38

8

24

49

1

46

58

44

48

42

19

39

15

…

…

15° 48′

5°

58′

24

23

40

16

10

33

0

28

18

22

13

46

35

17

31

18

26

9

39

54

36

52

33

24

28

57

13

40

42

38

1

34

56

30

1

34

41

18

38

53

36

8

32

37

43

49

41

46

39

34

37

5

34

53

44

0

42

7

40

7

37

50

35

55

50° Blank

55° Blank …

…

…

6

22° 45′

15° 58′

8°

38′

19° 17′

13° 30′

7°

15′

…

8

30

41

25

31

19

59

13°

33′

5°

20′

26

21

21

52

17

3

11° 30′

4°

17′

10

34

10

30

2

25

39

20

32

14

9

29

32

25

55

22

3

17

36

11

52

12

36

0

32

34

28

53

24

42

19

27

31

14

28

12

24

59

21

17

16

32

14

37

5

34

9

31

1

27

26

22

58

32

15

29

39

26

53

23

43

19

40

16

37

47

35

13

32

29

29

22

25

30

32

54

30

38

28

12

25

26

21

54

18

38

15

35

58

33

33

30

46

27

21

33

21

31

20

29

10

26

43

23

35

20

38

35

36

32

34

21

31

52

28

47

33

40

31

51

29

54

27

42

24

53

22

38

50

36

58

34

59

32

44

29

57

33

54

32

15

30

29

28

28

25

55

24

39

1

37

19

35

30

33

25

30

52

34

5

32

34

30

57

29

7

26

46

60° Blank

65° Blank …

…

…

…

6

16°

6′

11°

12′

6°

2′

13°

7′

9°

8′

4°

53′

8

22

13

18

24

14

19

9°

37′

3°

44′

18

15

15

6

11

42

7°

50′

3°

1′

10

25

2

21

56

18

37

14

49

10

5

20

40

18

4

15

19

12

9

8

15

12

26

34

23

57

21

10

17

59

14

13

21

59

19

48

17

28

14

49

11

32

14

27

29

25

14

22

51

20

6

16

44

22

48

20

55

18

54

16

37

13

48

16

28

5

26

7

24

1

21

37

18

40

23

18

21

39

19

53

17

53

15

24

18

28

29

26

44

24

52

22

44

20

6

23

40

22

11

20

37

18

50

16

37

20

28

46

27

11

25

30

23

35

21

14

23

55

22

35

21

10

19

33

17

34

22

29

0

27

34

26

2

24

17

22

8

24

6

22

53

21

36

20

8

18

20

24

29

9

27

50

26

26

24

50

22

52

24

15

23

8

21

57

20

36

18

57

34′

1° 45′

70° Blank 6

10° 18′

7°

9′

3°

48′

8

14

26

11

55

9

14

10

16

25

14

21

12

12

17

30

15

45

13

14

18

9

16

38

15

16

18

35

17

15

15

18

18

53

17

42

16

20

19

6

18

1

22

19

15

18

16

24

19

22

18

29

75° Blank …

…

…

…

7°

38′

5°

19′

2°

50′

10

44

8

51

6

51

30

12

14

10

40

9

1

7

8

4

49

8

13

4

11

45

10

21

8

45

6

47

10

55

13

34

12

26

11

13

9

50

8

7

12

13

13

54

12

54

11

50

10

37

9

7

59

13

13

14

8

13

14

12

17

11

12

9

51

15

35

13

59

14

18

13

29

12

38

11

39

10

27

16

3

14

35

14

25

13

41

12

53

12

0

10

54

16

25

15

5

14

31

13

50

13

7

12

18

11

18

6°

9′

2°

21′

8

9

53

11

37

6

45

9

1 50

13

11

14

13

26

14

16

53

17

15

17

33


4°


CUTTER GRINDING Angles of Elevation for Milling Straight Teeth in 80- and 85-degree Blanks Using Single-Angle Fluting Cutters

No.of Teeth


80°

70°

60°

50°

90°

80°

80° Blank 6 8 10 12 14 16 18 20 22 24

5° 7 8 8 9 9 9 9 9 9

2′ 6 7 41 2 15 24 31 36 40

3° 5 7 7 8 8 8 8 9 9

30′ 51 5 48 16 35 48 58 6 13

1° 4 5 6 7 7 8 8 8 8

52′ 31 59 52 28 51 10 24 35 43

70°

60°

50°

… 1° 29′ 2 21 2 53 3 15 3 30 3 43 3 52 3 59 4 5

… 0° 34′ 1 35 2 15 2 42 3 1 3 16 3 28 3 37 3 45

85° Blank … 3° 2′ 4 44 5 48 6 32 7 3 7 26 7 44 7 59 8 11

… 1° 8′ 3 11 4 29 5 24 6 3 6 33 6 56 7 15 7 30

2° 3 4 4 4 4 4 4 4 4

30′ 32 3 20 30 37 42 46 48 50

1° 2 3 3 4 4 4 4 4 4

44′ 55 32 53 7 17 24 29 33 36

0° 2 2 3 3 3 4 4 4 4

55′ 15 59 25 43 56 5 12 18 22

Spline-Shaft Milling Cutter.—The most efficient method of forming splines on shafts is by hobbing, but special milling cutters may also be used. Since the cutter forms the space between adjacent splines, it must be made to suit the number of splines and the root diameter of the shaft. The cutter angle B equals 360 degrees divided by the number of splines. The following formulas are for determining the chordal width C at the root of the splines or the chordal width across the concave edge of the cutter. In these formulas, A = angle between center line of spline and a radial line passing through the intersection of the root circle and one side of the spline; W = width of spline; d = root diameter of splined shaft; C = chordal width at root circle between adjacent splines; N = number of splines.

sin A = W ----d

C = d × sin ⎛ 180 --------- – A⎞ ⎝ N ⎠

Splines of involute form are often used in preference to the straight-sided type. Dimensions of the American Standard involute splines and hobs are given in the section on splines. Cutter Grinding Wheels for Sharpening Milling Cutters.—Milling cutters may be sharpened either by using the periphery of a disk wheel or the face of a cup wheel. The latter grinds the lands of the teeth flat, whereas the periphery of a disk wheel leaves the teeth slightly concave back of the cutting edges. The concavity produced by disk wheels reduces the effective clearance angle on the teeth, the effect being more pronounced for wheels of small diameter than for wheels of large diameter. For this reason, large diameter wheels are preferred when sharpening milling cutters with disk type wheels. Irrespective of what type of wheel is used to sharpen a milling cutter, any burrs resulting from grinding should be carefully


Machinery's Handbook 27th Edition CUTTER GRINDING

825

removed by a hand stoning operation. Stoning also helps to reduce the roughness of grinding marks and improves the quality of the finish produced on the surface being machined. Unless done very carefully, hand stoning may dull the cutting edge. Stoning may be avoided and a sharper cutting edge produced if the wheel rotates toward the cutting edge, which requires that the operator maintain contact between the tool and the rest while the wheel rotation is trying to move the tool away from the rest. Though slightly more difficult, this method will eliminate the burr. Specifications of Grinding Wheels for Sharpening Milling Cutters Cutter Material Carbon Tool Steel

Operation Roughing Finishing

Abrasive Material

Grinding Wheel Grain Size 46–60 100

Grade K H

Bond Vitrified Vitrified

60 100 80 100 46 100–120

K,H H F,G,H H H,K,L,N H

Vitrified Vitrified Vitrified Vitrified Vitrified Vitrified

60

G

Vitrified

Diamond Diamond

100 Up to 500

a a

Resinoid Resinoid

Cubic Boron Nitride

80–100 100–120

R,P S,T

Resinoid Resinoid

Aluminum Oxide

High-speed Steel: 18-4-1

{

18-4-2

{

Cast Non-Ferrous Tool Material

Sintered Carbide

Carbon Tool Steel and High-Speed Steelb

Roughing Finishing Roughing Finishing Roughing Finishing Roughing after Brazing Roughing Finishing Roughing Finishing

Aluminum Oxide

Aluminum Oxide Silicon Carbide

a Not indicated in diamond wheel markings. b For hardnesses above Rockwell C 56.

Wheel Speeds and Feeds for Sharpening Milling Cutters.—Relatively low cutting speeds should be used when sharpening milling cutters to avoid tempering and heat checking. Dry grinding is recommended in all cases except when diamond wheels are employed. The surface speed of grinding wheels should be in the range of 4500 to 6500 feet per minute for grinding milling cutters of high-speed steel or cast non-ferrous tool material. For sintered carbide cutters, 5000 to 5500 feet per minute should be used. The maximum stock removed per pass of the grinding wheel should not exceed about 0.0004 inch for sintered carbide cutters; 0.003 inch for large high-speed steel and cast nonferrous tool material cutters; and 0.0015 inch for narrow saws and slotting cutters of highspeed steel or cast non-ferrous tool material. The stock removed per pass of the wheel may be increased for backing-off operations such as the grinding of secondary clearance behind the teeth since there is usually a sufficient body of metal to carry off the heat. Clearance Angles for Milling Cutter Teeth.—The clearance angle provided on the cutting edges of milling cutters has an important bearing on cutter performance, cutting efficiency, and cutter life between sharpenings. It is desirable in all cases to use a clearance angle as small as possible so as to leave more metal back of the cutting edges for better heat dissipation and to provide maximum support. Excessive clearance angles not only weaken the cutting edges, but also increase the likelihood of “chatter” which will result in poor finish on the machined surface and reduce the life of the cutter. According to The Cincinnati Milling Machine Co., milling cutters used for general purpose work and having diameters from 1⁄8 to 3 inches should have clearance angles from 13 to 5 degrees, respectively, decreasing proportionately as the diameter increases. General purpose cutters over 3



CUTTER GRINDING

inches in diameter should be provided with a clearance angle of 4 to 5 degrees. The land width is usually 1⁄64 , 1⁄32 , and 1⁄16 inch, respectively, for small, medium, and large cutters. The primary clearance or relief angle for best results varies according to the material being milled about as follows: low carbon, high carbon, and alloy steels, 3 to 5 degrees; cast iron and medium and hard bronze, 4 to 7 degrees; brass, soft bronze, aluminum, magnesium, plastics, etc., 10 to 12 degrees. When milling cutters are resharpened, it is customary to grind a secondary clearance angle of 3 to 5 degrees behind the primary clearance angle to reduce the land width to its original value and thus avoid interference with the surface to be milled. A general formula for plain milling cutters, face mills, and form relieved cutters which gives the clearance angle C, in degrees, necessitated by the feed per revolution F, in inches, the width of land L, in inches, the depth of cut d, in inches, the cutter diameter D, in inches, and the Brinell hardness number B of the work being cut is: F - d ( D – d )⎞ C = 45860 --------------- ⎛ 1.5L + ------⎠ DB ⎝ πD Rake Angles for Milling Cutters.—In peripheral milling cutters, the rake angle is generally defined as the angle in degrees that the tooth face deviates from a radial line to the cutting edge. In face milling cutters, the teeth are inclined with respect to both the radial and axial lines. These angles are called radial and axial rake, respectively. The radial and axial rake angles may be positive, zero, or negative. Positive rake angles should be used whenever possible for all types of high-speed steel milling cutters. For sintered carbide tipped cutters, zero and negative rake angles are frequently employed to provide more material back of the cutting edge to resist shock loads. Rake Angles for High-speed Steel Cutters: Positive rake angles of 10 to 15 degrees are satisfactory for milling steels of various compositions with plain milling cutters. For softer materials such as magnesium and aluminum alloys, the rake angle may be 25 degrees or more. Metal slitting saws for cutting alloy steel usually have rake angles from 5 to 10 degrees, whereas zero and sometimes negative rake angles are used for saws to cut copper and other soft non-ferrous metals to reduce the tendency to “hog in.” Form relieved cutters usually have rake angles of 0, 5, or 10 degrees. Commercial face milling cutters usually have 10 degrees positive radial and axial rake angles for general use in milling cast iron, forged and alloy steel, brass, and bronze; for milling castings and forgings of magnesium and free-cutting aluminum and their alloys, the rake angles may be increased to 25 degrees positive or more, depending on the operating conditions; a smaller rake angle is used for abrasive or difficult to machine aluminum alloys. Cast Non-ferrous Tool Material Milling Cutters: Positive rake angles are generally provided on milling cutters using cast non-ferrous tool materials although negative rake angles may be used advantageously for some operations such as those where shock loads are encountered or where it is necessary to eliminate vibration when milling thin sections. Sintered Carbide Milling Cutters: Peripheral milling cutters such as slab mills, slotting cutters, saws, etc., tipped with sintered carbide, generally have negative radial rake angles of 5 degrees for soft low carbon steel and 10 degrees or more for alloy steels. Positive axial rake angles of 5 and 10 degrees, respectively, may be provided, and for slotting saws and cutters, 0 degree axial rake may be used. On soft materials such as free-cutting aluminum alloys, positive rake angles of 10 to so degrees are used. For milling abrasive or difficult to machine aluminum alloys, small positive or even negative rake angles are used. Eccentric Type Radial Relief.—When the radial relief angles on peripheral teeth of milling cutters are ground with a disc type grinding wheel in the conventional manner the ground surfaces on the lands are slightly concave, conforming approximately to the radius of the wheel. A flat land is produced when the radial relief angle is ground with a cup wheel. Another entirely different method of grinding the radial angle is by the eccentric method, which produces a slightly convex surface on the land. If the radial relief angle at



827

the cutting edge is equal for all of the three types of land mentioned, it will be found that the land with the eccentric relief will drop away from the cutting edge a somewhat greater distance for a given distance around the land than will the others. This is evident from a study of Table 1 entitled, Indicator Drops for Checking the Radial Relief Angle on Peripheral Teeth. This feature is an advantage of the eccentric type relief which also produces an excellent finish. Table 1. Indicator Drops for Checking the Radial Relief Angle on Peripheral Teeth Cutter Diameter, Inch 1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

Indicator Drops, Inches For Flat and Concave Relief For Eccentric Relief Min. Max. Min. Max.

Rec. Range of Radial Relief Angles, Degrees

Checking Distance, Inch

Rec. Max. Primary Land Width, Inch

20–25

.005

.0014

.0019

.0020

.0026

16–20

.005

.0012

.0015

.0015

.0019

.007

15–19

.010

.0018

.0026

.0028

.0037

.015

13–17

.010

.0017

.0024

.0024

.0032

.015

12–16

.010

.0016

.0023

.0022

.0030

.015

11–15

.010

.0015

.0022

.0020

.0028

.015

10–14

.015

.0017

.0028

.0027

.0039

.020

10–14

.015

.0018

.0029

.0027

.0039

.020

10–13

.015

.0019

.0027

.0027

.0035

.020

10–13

.015

.0020

.0028

.0027

.0035

.020

10–13

.015

.0020

.0029

.0027

.0035

.020

9–12

.020

.0022

.0032

.0032

.0044

.025

9–12

.020

.0022

.0033

.0032

.0043

.025

9–12

.020

.0023

.0034

.0032

.0043

.025

.007

9–12

.020

.0024

.0034

.0032

.0043

.025

9–12

.020

.0024

.0035

.0032

.0043

.025

8–11

.020

.0022

.0032

.0028

.0039

.025

8–11

.030

.0029

.0045

.0043

.0059

.035

8–11

.030

.0030

.0046

.0043

.0059

.035

8–11

.030

.0031

.0047

.0043

.0059

.035

8–11

.030

.0032

.0048

.0043

.0059

.035

1 11⁄8

7–10 7–10 7–10

.030 .030 .030

.0027 .0028 .0029

.0043 .0044 .0045

.0037 .0037 .0037

.0054 .0054 .0053

.035 .035 .035

11⁄4

6–9

.030

.0024

.0040

.0032

.0048

.035

13⁄8

6–9

.030

.0025

.0041

.0032

.0048

.035

11⁄2

6–9

.030

.0026

.0041

.0032

.0048

.035

15⁄8

6–9

.030

.0026

.0042

.0032

.0048

.035

13⁄4

6–9

.030

.0026

.0042

.0032

.0048

.035

17⁄8 2 21⁄4

6–9 6–9 5–8

.030 .030 .030

.0027 .0027 .0022

.0043 .0043 .0038

.0032 .0032 .0026

.0048 .0048 .0042

.035 .035 .040

21⁄2

5–8

.030

.0023

.0039

.0026

.0042

.040

23⁄4 3 31⁄2 4 5 6 7 8 10 12

5–8 5–8 5–8 5–8 4–7 4–7 4–7 4–7 4–7 4–7

.030 .030 .030 .030 .030 .030 .030 .030 .030 .030

.0023 .0023 .0024 .0024 .0019 .0019 .0020 .0020 .0020 .0020

.0039 .0039 .0040 .0040 .0035 .0035 .0036 .0036 .0036 .0036

.0026 .0026 .0026 .0026 .0021 .0021 .0021 .0021 .0021 .0021

.0042 .0042 .0042 .0042 .0037 .0037 .0037 .0037 .0037 .0037

.040 .040 .047 .047 .047 .047 .060 .060 .060 .060



CUTTER GRINDING

The setup for grinding an eccentric relief is shown in Fig. 1. In this setup the point of contact between the cutter and the tooth rest must be in the same plane as the centers, or axes, of the grinding wheel and the cutter. A wide face is used on the grinding wheel, which is trued and dressed at an angle with respect to the axis of the cutter. An alternate method is to tilt the wheel at this angle. Then as the cutter is traversed and rotated past the grinding wheel while in contact with the tooth rest, an eccentric relief will be generated by the angular face of the wheel. This type of relief can only be ground on the peripheral teeth on milling cutters having helical flutes because the combination of the angular wheel face and the twisting motion of the cutter is required to generate the eccentric relief. Therefore, an eccentric relief cannot be ground on the peripheral teeth of straight fluted cutters. Table 2 is a table of wheel angles for grinding an eccentric relief for different combinations of relief angles and helix angles. When angles are required that cannot be found in this table, the wheel angle, W, can be calculated by using the following formula, in which R is the radial relief angle and H is the helix angle of the flutes on the cutter. tan W = tan R × tan H Table 2. Grinding Wheel Angles for Grinding Eccentric Type Radial Relief Angle Radial Relief Angle, R, Degrees

Helix Angle of Cutter Flutes, H, Degrees 12

18

20

30

40

45

50

52

Wheel Angle, W, Degrees

1

0°13′

0°19′

0°22′

0°35′

0°50′

1°00′

1°12′

1°17′

2

0°26′

0°39′

0°44′

1°09′

1°41′

2°00′

2°23′

2°34′

3

0°38′

0°59′

1°06′

1°44′

2°31′

3°00′

3°34′

3°50′

4

0°51′

1°18′

1°27′

2°19′

3°21′

4°00′

4°46′

5°07′

5

1°04′

1°38′

1°49′

2°53′

4°12′

5°00′

5°57′

6°23′

6

1°17′

1°57′

2°11′

3°28′

5°02′

6°00′

7°08′

7°40′

7

1°30′

2°17′

2°34′

4°03′

5°53′

7°00′

8°19′

8°56′

8

1°43′

2°37′

2°56′

4°38′

6°44′

8°00′

9°30′

10°12′

9

1°56′

2°57′

3°18′

5°13′

7°34′

9°00′

10°41′

11°28′

10

2°09′

3°17′

3°40′

5°49′

8°25′

10°00′

11°52′

12°43′

11

2°22′

3°37′

4°03′

6°24′

9°16′

11°00′

13°03′

13°58′

12

2°35′

3°57′

4°25′

7°00′

10°07′

12°00′

14°13′

15°13′ 16°28′

13

2°49′

4°17′

4°48′

7°36′

10°58′

13°00′

15°23′

14

3°02′

4°38′

5°11′

8°11′

11°49′

14°00′

16°33′

17°42′

15

3°16′

4°59′

5°34′

8°48′

12°40′

15°00′

17°43′

18°56′ 20°09′

16

3°29′

5°19′

5°57′

9°24′

13°32′

16°00′

18°52′

17

3°43′

5°40′

6°21′

10°01′

14°23′

17°00′

20°01′

21°22′

18

3°57′

6°02′

6°45′

10°37′

15°15′

18°00′

21°10′

22°35′ 23°47′

19

4°11′

6°23′

7°09′

11°15′

16°07′

19°00′

22°19′

20

4°25′

6°45′

7°33′

11°52′

16°59′

20°00′

23°27′

24°59′

21

4°40′

7°07′

7°57′

12°30′

17°51′

21°00′

24°35′

26°10′ 27°21′

22

4°55′

7°29′

8°22′

13°08′

18°44′

22°00′

25°43′

23

5°09′

7°51′

8°47′

13°46′

19°36′

23°00′

26°50′

28°31′

24

5°24′

8°14′

9°12′

14°25′

20°29′

24°00′

27°57′

29°41′

25

5°40′

8°37′

9°38′

15°04′

21°22′

25°00′

29°04′

30°50′



829

Indicator Drop Method of Checking Relief and Rake Angles.—The most convenient and inexpensive method of checking the relief and rake angles on milling cutters is by the indicator drop method. Three tables, Tables 1, 3 and 4, of indicator drops are provided in this section, for checking radial relief angles on the peripheral teeth, relief angles on side and end teeth, and rake angles on the tooth faces.

Fig. 1. Setup for Grinding Eccentric Type Radial Relief Angle

Table 3. Indicator Drops for Checking Relief Angles on Side Teeth and End Teeth Given Relief Angle Checking Distance, Inch

1°

.005

.00009

.00017

.00026

.00035

.010

.00017

.00035

.00052

.0007

.015

.00026

.0005

.00079

.031

.00054

.0011

.047

.00082

.0016

.062

.00108

.0022

2°

3°

4°

5°

6°

7°

8°

9°

.0004

.0005

.0006

.0007

.0008

.0009

.0011

.0012

.0014

.0016

.0010

.0013

.0016

.0018

.0021

.0024

.0016

.0022

.0027

.0033

.0038

.0044

.0049

.0025

.0033

.0041

.0049

.0058

.0066

.0074

.0032

.0043

.0054

.0065

.0076

.0087

.0098

Indicator Drop, inch

Fig. 2. Setup for Checking the Radial Relief Angle by Indicator Drop Method

The setup for checking the radial relief angle is illustrated in Fig. 2. Two dial test indicators are required, one of which should have a sharp pointed contact point. This indicator is positioned so that the axis of its spindle is vertical, passing through the axis of the cutter. The cutter may be held by its shank in the spindle of a tool and cutter grinder workhead, or



CUTTER GRINDING

between centers while mounted on a mandrel. The cutter is rotated to the position where the vertical indicator contacts a cutting edge. The second indicator is positioned with its spindle axis horizontal and with the contact point touching the tool face just below the cutting edge. With both indicators adjusted to read zero, the cutter is rotated a distance equal to the checking distance, as determined by the reading on the second indicator. Then the indicator drop is read on the vertical indicator and checked against the values in the tables. The indicator drops for radial relief angles ground by a disc type grinding wheel and those ground with a cup wheel are so nearly equal that the values are listed together; values for the eccentric type relief are listed separately, since they are larger. A similar procedure is used to check the relief angles on the side and end teeth of milling cutters; however, only one indicator is used. Also, instead of rotating the cutter, the indicator or the cutter must be moved a distance equal to the checking distance in a straight line. Table 4. Indicator Drops for Checking Rake Angles on Milling Cutter Face

Set indicator to read zero on horizontal plane passing through cutter axis. Zero cutting edge against indicator.

Move cutter or indicator measuring distance.

Measuring Distance, inch Rate Angle, Deg. 1 2 3 4 5 6 7 8 9 10

.031

.062

.094

Measuring Distance, inch .125

Indicator Drop, inch .0005 .0011 .0016 .0022 .0027 .0033 .0038 .0044 .0049 .0055

.0011 .0022 .0032 .0043 .0054 .0065 .0076 .0087 .0098 .0109

.0016 .0033 .0049 .0066 .0082 .0099 .0115 .0132 .0149 .0166

.0022 .0044 .0066 .0087 .0109 .0131 .0153 .0176 .0198 .0220

Rate Angle, Deg.

.031

11 12 13 14 15 16 17 18 19 20

.0060 .0066 .0072 .0077 .0083 .0089 .0095 .0101 .0107 .0113

.062

.094

.125

Indicator Drop, inch .0121 .0132 .0143 .0155 .0166 .0178 .0190 .0201 .0213 .0226

.0183 .0200 .0217 .0234 .0252 .0270 .0287 .0305 .0324 .0342

.0243 .0266 .0289 .0312 .0335 .0358 .0382 .0406 .0430 .0455

Relieving Attachments.—A relieving attachment is a device applied to lathes (especially those used in tool-rooms) for imparting a reciprocating motion to the tool-slide and tool, in order to provide relief or clearance for the cutting edges of milling cutters, taps, hobs, etc. For example, in making a milling cutter of the formed type, such as is used for cutting gears, it is essential to provide clearance for the teeth and so form them that they may he ground repeatedly without changing the contour or shape of the cutting edge. This may be accomplished by using a relieving attachment. The tool for “backing off” or giving clearance to the teeth corresponds to the shape required, and it is given a certain amount of reciprocating movement, so that it forms a surface back of each cutting edge, which is of uniform cross-section on a radial plane but eccentric to the axis of the cutter sufficiently to provide the necessary clearance for the cutting edges.



831

Various Set-ups Used in Grinding the Clearance Angle on Milling Cutter Teeth

Wheel Above Center

In-Line Centers

Wheel Below Center

Cup Wheel

Distance to Set Center of Wheel Above the Cutter Center (Disk Wheel) Desired Clearance Angle, Degrees

Dia. of Wheel, Inches

1

3

.026

.052

.079

.105

.131

.157

.183

.209

4

.035

.070

.105

.140

.174

.209

.244

.278

5

.044

.087

.131

.174

.218

.261

.305

6

.052

.105

.157

.209

.261

.314

7

.061

.122

.183

.244

.305

8

.070

.140

.209

.279

9

.079

.157

.236

10

.087

.175

.262

2

3

4

10

11

12

.235

.260

.286

.312

.313

.347

.382

.416

.348

.391

.434

.477

.520

.366

.417

.469

.521

.572

.624

.366

.427

.487

.547

.608

.668

.728

.349

.418

.488

.557

.626

.695

.763

.832

.314

.392

.470

.548

.626

.704

.781

.859

.936

.349

.436

.523

.609

.696

.782

.868

.954

1.040

aDistance

5

6

7

8

9

to Offset Wheel Center Above Cutter Center, Inches

a Calculated from the formula: Offset = Wheel Diameter × 1⁄ 2

× Sine of Clearance Angle.

Distance to Set Center of Wheel Below the Cutter Center (Disk Wheel) Dia. of Cutter, Inches

Desired Clearance Angle, Degrees 1

2

3

4 aDistance

5

6

7

8

9

10

11

12

to Offset Wheel Center Below Cutter Center, Inches

2

.017

.035

.052

.070

.087

.105

.122

.139

.156

.174

.191

.208

3

.026

.052

.079

.105

.131

.157

.183

.209

.235

.260

.286

.312

4

.035

.070

.105

.140

.174

.209

.244

.278

.313

.347

.382

.416

5

.044

.087

.131

.174

.218

.261

.305

.348

.391

.434

.477

.520

6

.052

.105

.157

.209

.261

.314

.366

.417

.469

.521

.572

.624

7

.061

.122

.183

.244

.305

.366

.427

.487

.547

.608

.668

.728

8

.070

.140

.209

.279

.349

.418

.488

.557

.626

.695

.763

.832

9

.079

.157

.236

.314

.392

.470

.548

.626

.704

.781

.859

.936

10

.087

.175

.262

.349

.436

.523

.609

.696

.782

.868

.954

1.040

a Calculated from the formula: Offset = Cutter Diameter × 1⁄ 2

× Sine of Clearance Angle.

Distance to Set Tooth Rest Below Center Line of Wheel and Cutter.—W h e n the clearance angle is ground with a disk type wheel by keeping the center line of the wheel in line with the center line of the cutter, the tooth rest should be lowered by an amount given by the following formula: Wheel Diam. × Cutter Dia. × Sine of One-half the Clearance Angle Offset = ----------------------------------------------------------------------------------------------------------------------------------------------------------------Wheel Dia. + Cutter Dia. Distance to Set Tooth Rest Below Cutter Center When Cup Wheel is Used.—W h e n the clearance is ground with a cup wheel, the tooth rest is set below the center of the cutter the same amount as given in the table for Distance to Set Center of Wheel Below the Cutter Center (Disk Wheel).



REAMERS

REAMERS Hand Reamers.—Hand reamers are made with both straight and helical flutes. Helical flutes provide a shearing cut and are especially useful in reaming holes having keyways or grooves, as these are bridged over by the helical flutes, thus preventing binding or chattering. Hand reamers are made in both solid and expansion forms. The American standard dimensions for solid forms are given in the accompanying table. The expansion type is useful whenever, in connection with repair or other work, it is necessary to enlarge a reamed hole by a few thousandths of an inch. The expansion form is split through the fluted section and a slight amount of expansion is obtained by screwing in a tapering plug. The diameter increase may vary from 0.005 to 0.008 inch for reamers up to about 1 inch diameter and from 0.010 to 0.012 inch for diameters between 1 and 2 inches. Hand reamers are tapered slightly on the end to facilitate starting them properly. The actual diameter of the shanks of commercial reamers may be from 0.002 to 0.005 inch under the reamer size. That part of the shank that is squared should be turned smaller in diameter than the shank itself, so that, when applying a wrench, no burr may be raised that may mar the reamed hole if the reamer is passed clear through it. When fluting reamers, the cutter is so set with relation to the center of the reamer blank that the tooth gets a slight negative rake; that is, the cutter should be set ahead of the center, as shown in the illustration accompanying the table giving the amount to set the cutter ahead of the radial line. The amount is so selected that a tangent to the circumference of the reamer at the cutting point makes an angle of approximately 95 degrees with the front face of the cutting edge. Amount to Set Cutter Ahead of Radial Line to Obtain Negative Front Rake Fluting Cutter a B C 95

A Reamer Blank

Size of Reamer

a, Inches

1⁄ 4

0.011

3⁄ 8

Size of Reamer 7⁄ 8

a, Inches

Size of Reamer

a, Inches

0.038

2

0.087 0.098

0.016

1

0.044

21⁄4

1⁄ 2

0.022

11⁄4

0.055

21⁄2

0.109

5⁄ 8

0.027

11⁄2

0.066

23⁄4

0.120

3⁄ 4

0.033

13⁄4

0.076

3

0.131

When fluting reamers, it is necessary to “break up the flutes”; that is, to space the cutting edges unevenly around the reamer. The difference in spacing should be very slight and need not exceed two degrees one way or the other. The manner in which the breaking up of the flutes is usually done is to move the index head to which the reamer is fixed a certain amount more or less than it would be moved if the spacing were regular. A table is given showing the amount of this additional movement of the index crank for reamers with different numbers of flutes. When a reamer is provided with helical flutes, the angle of spiral should be such that the cutting edges make an angle of about 10 or at most 15 degrees with the axis of the reamer. The relief of the cutting edges should be comparatively slight. An eccentric relief, that is, one where the land back of the cutting edge is convex, rather than flat, is used by one or two manufacturers, and is preferable for finishing reamers, as the reamer will hold its size longer. When hand reamers are used merely for removing stock, or simply for enlarging holes, the flat relief is better, because the reamer has a keener cutting edge. The width of the land of the cutting edges should be about 1⁄32 inch for a 1⁄4-inch, 1⁄16 inch for a 1-inch, and 3⁄32 inch for a 3-inch reamer.


Machinery's Handbook 27th Edition REAMERS

833

Irregular Spacing of Teeth in Reamers Number of flutes in reamer Index circle to use

4

6

39

39

Before cutting 2d flute 3d flute 4th flute 5th flute 6th flute 7th flute 8th flute 9th flute 10th flute 11th flute 12th flute 13th flute 14th flute 15th flute 16th flute

8 less 4 more 6 less … … … … … … … … … … … …

8

10

12

14

39 39 39 49 Move Spindle the Number of Holes below More or Less than for Regular Spacing 4 less 3 less 2 less 4 less 3 less 5 more 5 more 3 more 4 more 2 more 7 less 2 less 5 less 1 less 2 less 6 more 4 more 2 more 3 more 4 more 5 less 6 less 2 less 4 less 1 less … 2 more 3 more 4 more 3 more … 3 less 2 less 3 less 2 less … … 5 more 2 more 1 more … … 1 less 2 less 3 less … … … 3 more 3 more … … … 4 less 2 less … … … … 2 more … … … … 3 less … … … … … … … … … …

16 20

2 less 2 more 1 less 2 more 2 less 1 more 2 less 2 more 2 less 1 more 2 less 2 more 1 less 2 more 2 less

Threaded-end Hand Reamers.—Hand reamers are sometimes provided with a thread at the extreme point in order to give them a uniform feed when reaming. The diameter on the top of this thread at the point of the reamer is slightly smaller than the reamer itself, and the thread tapers upward until it reaches a dimension of from 0.003 to 0.008 inch, according to size, below the size of the reamer; at this point, the thread stops and a short neck about 1⁄16inch wide separates the threaded portion from the actual reamer, which is provided with a short taper from 3⁄16 to 7⁄16 inch long up to where the standard diameter is reached. The length of the threaded portion and the number of threads per inch for reamers of this kind are given in the accompanying table. The thread employed is a sharp V-thread. Dimensions for Threaded-End Hand Reamers Dia. of Thread at Point of Reamer

Sizes of Reamers

Length of Threaded Part

No. of Threads per Inch

1⁄ –5⁄ 8 16

3⁄ 8

32

Full diameter −0.006

11⁄ –1⁄ 32 2

7⁄ 16

28

17⁄ –3⁄ 32 4

1⁄ 2

24

25⁄ –1 32

9⁄ 16

18

Dia. of Thread at Point of Reamer

Sizes of Reamers

Length of Threaded Part

No. of Threads per Inch

11⁄32–11⁄2

9⁄ 16

18

Full diameter −0.010

−0.006

117⁄32–2

9⁄ 16

18

−0.012

−0.008

21⁄32–21⁄2

9⁄ 16

18

−0.015

−0.008

217⁄32–3

9⁄ 16

18

−0.020

Fluted Chucking Reamers.—Reamers of this type are used in turret lathes, screw machines, etc., for enlarging holes and finishing them smooth and to the required size. The best results are obtained with a floating type of holder that permits a reamer to align itself with the hole being reamed. These reamers are intended for removing a small amount of metal, 0.005 to 0.010 inch being common allowances. Fluted chucking reamers are provided either with a straight shank or a standard taper shank. (See table for standard dimensions.)



REAMERS Fluting Cutters for Reamers 55

D

30

85

85

A

A

C

B

C

B 15 70

D

Reamer Dia. 1⁄ 8 3⁄ 16 1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1

Fluting Cutter Dia. A 13⁄4 13⁄4 13⁄4 2 2 2 2 21⁄4

Fluting Cutter Thickness B

Hole Dia. in Cutter C

3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

1

Radius between Cutting Faces D

Reamer Dia. 11⁄4

nonea nonea 1⁄ 64 1⁄ 64 1⁄ 32 1⁄ 32 3⁄ 64 3⁄ 64

11⁄2 13⁄4

Fluting Cutter Dia. A

Fluting Cutter Thickness B

Hole Dia. in Cutter C

21⁄4

9⁄ 16 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8

1

21⁄4 21⁄4

2

21⁄2

21⁄4

21⁄2

21⁄2

21⁄2

23⁄4 3

21⁄2 21⁄2

1

1 1 1 1 1 1 1

Radius between Cutting Faces D 1⁄ 16 1⁄ 16 5⁄ 64 5⁄ 64 5⁄ 64 3⁄ 16 3⁄ 16 3⁄ 16

a Sharp corner, no radius

Rose Chucking Reamers.—The rose type of reamer is used for enlarging cored or other holes. The cutting edges at the end are ground to a 45-degree bevel. This type of reamer will remove considerable metal in one cut. The cylindrical part of the reamer has no cutting edges, but merely grooves cut for the full length of the reamer body, providing a way for the chips to escape and a channel for lubricant to reach the cutting edges. There is no relief on the cylindrical surface of the body part, but it is slightly back-tapered so that the diameter at the point with the beveled cutting edges is slightly larger than the diameter farther back. The back-taper should not exceed 0.001 inch per inch. This form of reamer usually produces holes slightly larger than its size and it is, therefore, always made from 0.005 to 0.010 inch smaller than its nominal size, so that it may be followed by a fluted reamer for finishing. The grooves on the cylindrical portion are cut by a convex cutter having a width equal to from one-fifth to one-fourth the diameter of the rose reamer itself. The depth of the groove should be from one-eighth to one-sixth the diameter of the reamer. The teeth at the end of the reamer are milled with a 75-degree angular cutter; the width of the land of the cutting edge should be about one-fifth the distance from tooth to tooth. If an angular cutter is preferred to a convex cutter for milling the grooves on the cylindrical portion, because of the higher cutting speed possible when milling, an 80-degree angular cutter slightly rounded at the point may be used. Cutters for Fluting Rose Chucking Reamers.—The cutters used for fluting rose chucking reamers on the end are 80-degree angular cutters for 1⁄4- and 5⁄16-inch diameter reamers; 75-degree angular cutters for 3⁄8- and 7⁄16-inch reamers; and 70-degree angular cutters for all larger sizes. The grooves on the cylindrical portion are milled with convex cutters of approximately the following sizes for given diameters of reamers: 5⁄32-inch convex cutter


;; ;


835

Dimensions of Formed Reamer Fluting Cutters

A

B Dia. = D

C

C

The making and maintenance of cutters of the formed type involves greater expense than the use of angular cutters of which dimensions are given on the previous page; but the form of flute produced by the formed type of cutter is preferred by many reamer users. The claims made for the formed type of flute are that the chips can be more readily removed from the reamer, and that the reamer has greater strength and is less likely to crack or spring out of shape in hardening.

G

E

H

F

6

Reamer Size 1⁄ –3⁄ 8 16 1⁄ –5⁄ 4 16 3⁄ –7⁄ 8 16 1⁄ –11⁄ 2 16 3⁄ –1 4 11⁄16–11⁄2 19⁄16–21⁄8 21⁄4–3

1⁄ -inch 2

No. of Teeth in Reamer

Cutter Dia. D

6

13⁄4

6

13⁄4

6

17⁄8 2

6–8 8 10 12 14

21⁄8 21⁄4 23⁄8 25⁄8

Cutter Width A

Hole Dia. B

Bearing Width C

Bevel Length E

Radius F

Radius F

3⁄ 16 1⁄ 4 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

…

0.125

0.016

…

0.152

0.022

1⁄ 8 1⁄ 8 5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16

0.178

0.029

0.205

0.036

0.232

0.042

0.258

0.049

0.285

0.056

0.312

0.062

7⁄ 32 9⁄ 32 1⁄ 2 9⁄ 16 11⁄ 16 3⁄ 4 27⁄ 32 7⁄ 8

Tooth Depth H

No. of Cutter Teeth

0.21

14

0.25

13

0.28

12

0.30

12

0.32

12

0.38

11

0.40

11

0.44

10

5⁄ -inch 16

for reamers; cutter for 1-inch reamers; 3⁄8-inch cutter for 11⁄2-inch reamers; 13⁄ -inch cutters for 2-inch reamers; and 15⁄ -inch cutters for 21⁄ -inch reamers. The smaller 32 32 2 sizes of reamers, from 1⁄4 to 3⁄8 inch in diameter, are often milled with regular double-angle reamer fluting cutters having a radius of 1⁄64 inch for 1⁄4-inch reamer, and 1⁄32 inch for 5⁄16- and 3⁄ -inch sizes. 8 Reamer Terms and Definitions.—Reamer: A rotary cutting tool with one or more cutting elements used for enlarging to size and contour a previously formed hole. Its principal support during the cutting action is obtained from the workpiece. (See Fig. 1.) Actual Size: The actual measured diameter of a reamer, usually slightly larger than the nominal size to allow for wear. Angle Of Taper: The included angle of taper on a taper tool or taper shank. Arbor Hole: The central mounting hole in a shell reamer. Axis: the imaginary straight line which forms the longitudinal centerline of a reamer, usually established by rotating the reamer between centers. Back Taper: A slight decrease in diameter, from front to back, in the flute length of reamers. Bevel: An unrelieved angular surface of revolution (not to be confused with chamfer). Body: The fluted full diameter portion of a reamer, inclusive of the chamfer, starting taper, and bevel. Chamfer: The angular cutting portion at the entering end of a reamer (see also Secondary Chamfer).



REAMERS Vertical Adjustment of Tooth-rest for Grinding Clearance on Reamers Hand Reamer for Steel. Cutting Clearance Land 0.006 inch Wide

Size of Reamer 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄8 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2 35⁄8 33⁄4 37⁄8 4 41⁄8 41⁄4 43⁄8 41⁄2 45⁄8 43⁄4 47⁄8 5

Hand Reamer for Cast Iron and Bronze. Cutting Clearance Land 0.025 inch Wide

Chucking Reamer for Cast Iron and Bronze. Cutting Clearance Land 0.025 inch Wide

For Cutting Clearance

For Second Clearance





0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012 0.012

0.052 0.062 0.072 0.082 0.092 0.102 0.112 0.122 0.132 0.142 0.152 0.162 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172 0.172

0.032 0.032 0.035 0.040 0.040 0.040 0.045 0.045 0.048 0.050 0.052 0.056 0.056 0.059 0.063 0.063 0.065 0.065 0.065 0.070 0.072 0.075 0.078 0.081 0.084 0.087 0.090 0.093 0.096 0.096 0.096 0.096 0.100 0.100 0.104 0.106 0.110

0.072 0.072 0.095 0.120 0.120 0.120 0.145 0.145 0.168 0.170 0.192 0.196 0.216 0.219 0.223 0.223 0.225 0.225 0.225 0.230 0.232 0.235 0.238 0.241 0.244 0.247 0.250 0.253 0.256 0.256 0.256 0.256 0.260 0.260 0.264 0.266 0.270

0.040 0.040 0.040 0.045 0.045 0.045 0.050 0.050 0.055 0.060 0.060 0.060 0.064 0.064 0.064 0.068 0.072 0.075 0.077 0.080 0.080 0.083 0.083 0.087 0.090 0.093 0.097 0.100 0.104 0.104 0.106 0.108 0.108 0.110 0.114 0.116 0.118

0.080 0.090 0.100 0.125 0.125 0.125 0.160 0.160 0.175 0.200 0.200 0.200 0.224 0.224 0.224 0.228 0.232 0.235 0.237 0.240 0.240 0.240 0.243 0.247 0.250 0.253 0.257 0.260 0.264 0.264 0.266 0.268 0.268 0.270 0.274 0.276 0.278

Rose Chucking Reamers for Steel For Cutting Clearance on Angular Edge at End 0.080 0.090 0.100 0.125 0.125 0.125 0.160 0.175 0.175 0.200 0.200 0.200 0.225 0.225 0.225 0.230 0.230 0.235 0.240 0.240 0.240 0.240 0.245 0.245 0.250 0.250 0.255 0.255 0.260 0.260 0.265 0.265 0.265 0.270 0.275 0.275 0.275

Chamfer Angle: The angle between the axis and the cutting edge of the chamfer measured in an axial plane at the cutting edge. Chamfer Length: The length of the chamfer measured parallel to the axis at the cutting edge. Chamfer Relief Angle: See under Relief. Chamfer Relief: See under Relief. Chip Breakers: Notches or grooves in the cutting edges of some taper reamers designed. to break the continuity of the chips. Circular Land: See preferred term Margin.



837

Illustration of Terms Applying to Reamers

Machine Reamer

Hand Reamer

Hand Reamer, Pilot and Guide

Chucking Reamer, Straight and Taper Shank

Clearance: The space created by the relief behind the cutting edge or margin of a reamer. Core: The central portion of a reamer below the flutes which joins the lands. Core Diameter: The diameter at a given point along the axis of the largest circle which does not project into the flutes. Cutter Sweep: The section removed by the milling cutter or grinding wheel in entering or leaving a flute. Cutting Edge: The leading edge of the relieved land in the direction of rotation for cutting. Cutting Face: The leading side of the relieved land in the direction of rotation for cutting on which the chip impinges. External Center: The pointed end of a reamer. The included angle varies with manufacturing practice. Flutes: Longitudinal channels formed in the body of the reamer to provide cutting edges, permit passage of chips, and allow cutting fluid to reach the cutting edges. Angular Flute: A flute which forms a cutting face lying in a plane intersecting the reamer axis at an angle. It is unlike a helical flute in that it forms a cutting face which lies in a single plane. Helical Flute: Sometimes called spiral flute, a flute which is formed in a helical path around the axis of a reamer. Spiral flute: 1) On a taper reamer, a flute of constant lead; or, 2) in reference to a straight reamer, see preferred term helical flute. Straight Flute: A flute which forms a cutting edge lying in an axial plane. Flute Length: The length of the flutes not including the cutter sweep.



REAMERS

Guide: A cylindrical portion following the flutes of a reamer to maintain alignment. Heel: The trailing edge of the land in the direction of rotation for cutting. Helix Angle: The angle which a helical cutting edge at a given point makes with an axial plane through the same point. Hook: A concave condition of a cutting face. The rake of a hooked cutting face must be determined at a given point. Internal Center: A 60 degree countersink with clearance at the bottom, in one or both ends of a tool, which establishes the tool axis. Irregular Spacing: A deliberate variation from uniform spacing of the reamer cutting edges. Land: The section of the reamer between adjacent flutes. Land Width: The distance between the leading edge of the land and the heel measured at a right angle to the leading edge. Lead of Flute: The axial advance of a helical or spiral cutting edge in one turn around the reamer axis. Length: The dimension of any reamer element measured parallel to the reamer axis. Limits: The maximum and minimum values designated for a specific element. Margin: The unrelieved part of the periphery of the land adjacent to the cutting edge. Margin Width: The distance between the cutting edge and the primary relief measured at a right angle to the cutting edge. Neck: The section of reduced diameter connecting shank to body, or connecting other portions of the reamer. Nominal Size: The designated basic size of a reamer overall length–the extreme length of the complete reamer from end to end, but not including external centers or expansion screws. Periphery: The outside circumference of a reamer. Pilot: A cylindrical portion preceding the entering end of the reamer body to maintain alignment. Rake: The angular relationship between the cutting face, or a tangent to the cutting face at a given point and a given reference plane or line. Axial Rake: Applies to angular (not helical or spiral) cutting faces. It is the angle between a plane containing the cutting face, or tangent to the cutting face at a given point, and the reamer axis. Helical Rake: Applies only to helical and spiral cutting faces (not angular). It is the angle between a plane, tangent to the cutting face at a given point on the cutting edge, and the reamer axis. Negative Rake: Describes a cutting face in rotation whose cutting edge lags the surface of the cutting face. Positive Rake: Describes a cutting face in rotation whose cutting edge leads the surface of the cutting face. Radial Rake Angle: The angle in a transverse plane between a straight cutting face and a radial line passing through the cutting edge. Relief: The result of the removal of tool material behind or adjacent to the cutting edge to provide clearance and prevent rubbing (heel drag). Axial Relief: The relief measured in the axial direction between a plane perpendicular to the axis and the relieved surface. It can be measured by the amount of indicator drop at a given radius in a given amount of angular rotation. Cam Relief : The relief from the cutting edge to the heel of the land produced by a cam action. Chamfer Relief Angle: The axial relief angle at the outer corner of the chamfer. It is measured by projection into a plane tangent to the periphery at the outer corner of the chamfer. Chamfer Relief: The axial relief on the chamfer of the reamer. Eccentric Relief: A convex relieved surface behind the cutting edge.



839

Flat Relief: A relieved surface behind the cutting edge which is essentially flat. Radial Relief: Relief in a radial direction measured in the plane of rotation. It can be measured by the amount of indicator drop at a given radius in a given amount of angular rotation. Primary Relief: The relief immediately behind the cutting edge or margin. Properly called relief. Secondary Relief: An additional relief behind the primary relief. Relief Angle: The angle, measured in a transverse plane, between the relieved surface and a plane tangent to the periphery at the cutting edge. Secondary Chamfer: A slight relieved chamfer adjacent to and following the initial chamfer on a reamer. Shank: The portion of the reamer by which it is held and driven. Squared Shank: A cylindrical shank having a driving square on the back end. Starting Radius: A relieved radius at the entering end of a reamer in place of a chamfer. Starting Taper: A slight relieved taper on the front end of a reamer. Straight Shank: A cylindrical shank. Tang: The flatted end of a taper shank which fits a slot in the socket. Taper per Foot: The difference in diameter between two points 12 in. apart measured along the axis. Taper Shank: A shank made to fit a specific (conical) taper socket. Direction of Rotation and Helix.—The terms “right hand” and “left hand” are used to describe both direction of rotation and direction of flute helix or reamers. Hand of Rotation (or Hand of Cut): Right-hand Rotation (or Right-hand Cut): W h e n viewed from the cutting end, the reamer must revolve counterclockwise to cut Left-hand Rotation (or Left-hand Cut): When viewed from the cutting end, the reamer must revolve clockwise to cut Hand of Flute Helix: Right-hand Helix: When the flutes twist away from the observer in a clockwise direction when viewed from either end of the reamer. Left-hand helix: When the flutes twist away from the observer in a counterclockwise direction when viewed from either end of the reamer. The standard reamers on the tables that follow are all right-hand rotation.

;; ; ; ;;

Dimensions of Centers for Reamers and Arbors

A

B 60

C

D

Arbor. Dia. A 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16

Large Center Dia. B 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32

Drill No. C 55 52 48 43 39 33 30 29

Hole Depth D 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32

Arbor Dia. A 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1 11⁄8 11⁄4 13⁄8 11⁄2 … 15⁄8 13⁄4 17⁄8 2 21⁄8 21⁄4 23⁄8

Large Center Dia. B 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 33⁄ 64 17⁄ 32 35⁄ 64 9⁄ 16

Drill No. C 25 20 17 12 8 5 3 2 1

Hole Depth D 7⁄ 16 1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 21⁄ 32 11⁄ 16

Arbor Dia. A 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2

…

Letter

…

35⁄8

37⁄ 64 19⁄ 32 39⁄ 64 5⁄ 8 41⁄ 64 21⁄ 32 43⁄ 64

A

23⁄ 32 23⁄ 32 3⁄ 4 3⁄ 4 25⁄ 32 13⁄ 16 27⁄ 32

33⁄4

B C E F G H

37⁄8 4 41⁄4 41⁄2 43⁄4 5

Large Center Dia. B 11⁄ 16 45⁄ 64 23⁄ 32 47⁄ 64 3⁄ 4 49⁄ 64 25⁄ 32 51⁄ 64 13⁄ 16 53⁄ 64 27⁄ 32 55⁄ 64 7⁄ 8 29⁄ 32 15⁄ 16 31⁄ 32

1


Drill No. C J

Hole Depth D 27⁄ 32

K

7⁄ 8 29⁄ 32 29⁄ 32 15⁄ 16 31⁄ 32 31⁄ 32

L M N N O O

1

P

1

Q

11⁄16

R

11⁄16

R

11⁄16

S

11⁄8

T

11⁄8

V

13⁄16

W

11⁄4

X

11⁄4


REAMERS Straight Shank Center Reamers and Machine Countersinks ANSI B94.2-1983 (R1988) D

D S

S A

A

Center Reamers (Short Countersinks) Dia. of Cut

Approx. Length Overall, A

Length of Shank, S

Machine Countersinks

Dia. of Shank, D

Dia. of Cut

Approx. Length Overall, A

Length of Shank, S

Dia. of Shank, D

1⁄ 4

11⁄2

3⁄ 4

3⁄ 16

1⁄ 2

37⁄8

21⁄4

1⁄ 2

3⁄ 8

13⁄4

7⁄ 8

1⁄ 4

5⁄ 8

4

21⁄4

1⁄ 2

1⁄ 2

2

1

3⁄ 8

3⁄ 4

41⁄8

21⁄4

1⁄ 2

5⁄ 8

21⁄4

1

3⁄ 8

7⁄ 8

41⁄4

21⁄4

1⁄ 2

3⁄ 4

25⁄8

11⁄4

1⁄ 2

1

43⁄8

21⁄4

1⁄ 2

All dimensions are given in inches. Material is high-speed steel. Reamers and countersinks have 3 or 4 flutes. Center reamers are standard with 60, 82, 90, or 100 degrees included angle. Machine countersinks are standard with either 60 or 82 degrees included angle. Tolerances: On overall length A, the tolerance is ±1⁄8 inch for center reamers in a size range of from 1⁄ to 3⁄ inch, incl., and machine countersinks in a size range of from 1⁄ to 5⁄ inch. incl.; ± 3⁄ inch for 4 8 2 8 16 center reamers, 1⁄2 to 3⁄4 inch, incl.; and machine countersinks, 3⁄4 to 1 inch, incl. On shank diameter D, the tolerance is −0.0005 to −0.002 inch. On shank length S, the tolerance is ±1⁄16 inch.

Reamer Difficulties.—Certain frequently occurring problems in reaming require remedial measures. These difficulties include the production of oversize holes, bellmouth holes, and holes with a poor finish. The following is taken from suggestions for correction of these difficulties by the National Twist Drill and Tool Co. and Winter Brothers Co.* Oversize Holes: The cutting of a hole oversize from the start of the reaming operations usually indicates a mechanical defect in the setup or reamer. Thus, the wrong reamer for the workpiece material may have been used or there may be inadequate workpiece support, inadequate or worn guide bushings, or misalignment of the spindles, bushings, or workpiece or runout of the spindle or reamer holder. The reamer itself may be defective due to chamfer runout or runout of the cutting end due to a bent or nonconcentric shank. When reamers gradually start to cut oversize, it is due to pickup or galling, principally on the reamer margins. This condition is partly due to the workpiece material. Mild steels, certain cast irons, and some aluminum alloys are particularly troublesome in this respect. Corrective measures include reducing the reamer margin widths to about 0.005 to 0.010 inch, use of hard case surface treatments on high-speed-steel reamers, either alone or in combination with black oxide treatments, and the use of a high-grade finish on the reamer faces, margins, and chamfer relief surfaces. Bellmouth Holes: The cutting of a hole that becomes oversize at the entry end with the oversize decreasing gradually along its length always reflects misalignment of the cutting portion of the reamer with respect to the hole. The obvious solution is to provide improved guiding of the reamer by the use of accurate bushings and pilot surfaces. If this solution is not feasible, and the reamer is cutting in a vertical position, a flexible element may be employed to hold the reamer in such a way that it has both radial and axial float, with the hope that the reamer will follow the original hole and prevent the bellmouth condition. In horizontal setups where the reamer is held fixed and the workpiece rotated, any misalignment exerts a sideways force on the reamer as it is fed to depth, resulting in the forma* “Some Aspects of Reamer Design and Operation,” Metal Cuttings, April 1963.



841

tion of a tapered hole. This type of bellmouthing can frequently be reduced by shortening the bearing length of the cutting portion of the reamer. One way to do this is to reduce the reamer diameter by 0.010 to 0.030 inch, depending on size and length, behind a short fulldiameter section, 1⁄8 to 1⁄2 inch long according to length and size, following the chamfer. The second method is to grind a high back taper, 0.008 to 0.015 inch per inch, behind the short full-diameter section. Either of these modifications reduces the length of the reamer tooth that can cause the bellmouth condition. Poor Finish: The most obvious step toward producing a good finish is to reduce the reamer feed per revolution. Feeds as low as 0.0002 to 0.0005 inch per tooth have been used successfully. However, reamer life will be better if the maximum feasible feed is used. The minimum practical amount of reaming stock allowance will often improve finish by reducing the volume of chips and the resulting heat generated on the cutting portion of the chamfer. Too little reamer stock, however, can be troublesome in that the reamer teeth may not cut freely but will deflect or push the work material out of the way. When this happens, excessive heat, poor finish, and rapid reamer wear can occur. Because of their superior abrasion resistance, carbide reamers are often used when fine finishes are required. When properly conditioned, carbide reamers can produce a large number of good-quality holes. Careful honing of the carbide reamer edges is very important. American National Standard Fluted Taper Shank Chucking Reamers— Straight and Helical Flutes, Fractional Sizes ANSI B94.2-1983 (R1988)

No. of Morse Taper Shanka

No. of Flutes

21⁄2

2

8 to 10

25⁄8

2

8 to 10

10

25⁄8

2

8 to 10

10

25⁄8

3

8 to 10

10

25⁄8

3

8 to 10

Length Overall A

Flute Length B


No. of Flutes

Reamer Dia.

1⁄ 4

6

11⁄2

1

4 to 6

27⁄ 32

91⁄2

5⁄ 16

6

11⁄2

1

4 to 6

7⁄ 8

10

3⁄ 8

7

13⁄4

1

4 to 6

29⁄ 32

7

13⁄4

6 to 8

15⁄ 16 31⁄ 32

Reamer Dia.

7⁄ 16

1

Length Overall A

Flute Length B

1⁄ 2

8

2

1

6 to 8

17⁄ 32

8

2

1

6 to 8

1

101⁄2

23⁄4

3

8 to 12

9⁄ 16

8

2

1

6 to 8

11⁄16

101⁄2

23⁄4

3

8 to 12

19⁄ 32

8

2

1

6 to 8

11⁄8

11

27⁄8

3

8 to 12

5⁄ 8

9

21⁄4

2

6 to 8

13⁄16

11

27⁄8

3

8 to 12

21⁄ 32

9

21⁄4

2

6 to 8

1 1⁄4

11 1⁄2

3

4

8 to 12

11⁄ 16

9

21⁄4

2

6 to 8

15⁄16

111⁄2

3

4

8 to 12

23⁄ 32

9

21⁄4

2

6 to 8

13⁄8

12

31⁄4

4

10 to 12

3⁄ 4

91⁄2

21⁄2

2

6 to 8

17⁄16

12

31⁄4

4

10 to 12

25⁄ 32

91⁄2

21⁄2

2

8 to 10

11⁄2

121⁄2

31⁄2

4

10 to 12

13⁄ 16

91⁄2

21⁄2

2

8 to 10

…

…

…

…

…

a American National Standard self-holding tapers (see Table 7a on page 933.)

All dimensions are given in inches. Material is high-speed steel. Helical flute reamers with right-hand helical flutes are standard. Tolerances: On reamer diameter, 1⁄4-inch size, +.0001 to +.0004 inch; over 1⁄4- to 1-inch size, + .0001 to +.0005 inch; over 1-inch size, +.0002 to +.0006 inch. On length overall A and flute length B, 1⁄ - to 1-inch size, incl., ±1⁄ inch; 11⁄ -to 11⁄ -inch size, incl., 3⁄ inch. 4 16 16 2 32



REAMERS Expansion Chucking Reamers—Straight and Taper Shanks ANSI B94.2-1983 (R1988) D

B A Dia of Reamer 3⁄ 8

Length, A

Flute Length,B

7

3⁄ 4

13⁄ 32

7

3⁄ 4

7⁄ 16

7

7⁄ 8

15⁄ 32

7

7⁄ 8

1⁄ 2

8

17⁄ 32

Shank Dia., D Max.

Min.

Dia.of Reamer

Length, A

Shank Dia.,D

Flute Length,B

Max.

Min.

101⁄2

15⁄8

0.8745

0.8730

0.3095

13⁄32

0.3105

0.3095

11⁄8

11

13⁄4

0.8745

0.8730

0.3730

0.3720

15⁄32

11

13⁄4

0.8745

0.8730

0.3730

0.3720

13⁄16

11

13⁄4

0.9995

0.9980

1

0.4355

0.4345

17⁄32

11

13⁄4

0.9995

0.9980

8

1

0.4355

0.4345

11⁄4

111⁄2

17⁄8

0.9995

0.9980

9⁄ 16

8

11⁄8

0.4355

0.4345

15⁄16

111⁄2

17⁄8

0.9995

0.9980

19⁄ 32

8

11⁄8

0.4355

0.4345

13⁄8

12

2

0.9995

0.9980

5⁄ 8

9

11⁄4

0.5620

0.5605

17⁄16

12

2

1.2495

1.2480

21⁄ 32

9

11⁄4

0.5620

0.5605

11⁄2

121⁄2

21⁄8

1.2495

1.2480

11⁄ 16

9

11⁄4

0.5620

0.5605

19⁄16a

121⁄2

21⁄8

1.2495

1.2480

23⁄ 32

9

11⁄4

0.5620

0.5605

15⁄8

13

21⁄4

1.2495

1.2480

3⁄ 4

91⁄2

13⁄8

0.6245

0.6230

111⁄16a

13

21⁄4

1.2495

1.2480

25⁄ 32

91⁄2

13⁄8

0.6245

0.6230

13⁄4

131⁄2

23⁄8

1.2495

1.2480

13⁄ 16

91⁄2

13⁄8

0.6245

0.6230

113⁄16a

131⁄2

23⁄8

1.4995

1.4980

27⁄ 32

91⁄2

13⁄8

0.6245

0.6230

17⁄8

14

21⁄2

1.4995

1.4980

0.7480

115⁄16a

14

21⁄2

1.4995

1.4980

1.4995

1.4980

7⁄ 8

0.3105

10

11⁄2

29⁄ 32

10

11⁄2

0.7495

0.7480

2

14

21⁄2

15⁄ 16

10

11⁄2

0.7495

0.7480

21⁄8b

141⁄2

23⁄4

…

…

31⁄ 32

10

11⁄2

0.7495

0.7480

21⁄4b

141⁄2

23⁄4

…

…

1

101⁄2

15⁄8

0.8745

0.8730

23⁄8b

15

3

…

…

11⁄32

101⁄2

15⁄8

0.8745

0.8730

21⁄2b

15

3

…

…

11⁄16

101⁄2

15⁄8

0.8745

0.8730

…

…

…

…

…

0.7495

a Straight shank only. b Taper shank only.

All dimensions in inches. Material is high-speed steel. The number of flutes is as follows: 3⁄8- to 15⁄32inch sizes, 4 to 6; 1⁄2- to 31⁄32-inch sizes, 6 to 8; 1- to 111⁄16-inch sizes, 8 to 10; 13⁄4- to 115⁄16-inch sizes, 8 to 12; 2 - to 21⁄4-inch sizes, 10 to 12; 23⁄8- and 21⁄2-inch sizes, 10 to 14. The expansion feature of these reamers provides a means of adjustment that is important in reaming holes to close tolerances. When worn undersize, they may be expanded and reground to the original size. Tolerances: On reamer diameter, 8⁄8- to 1-inch sizes, incl., +0.0001 to +0.0005 inch; over 1-inch size, + 0.0002 to + 0.0006 inch. On length A and flute length B, 3⁄8- to 1-inch sizes, incl., ±1⁄16 inch; 11⁄32to 2-inch sizes, incl., ±3⁄32 inch; over 2-inch sizes, ±1⁄8 inch. Taper is Morse taper: No. 1 for sizes 3⁄8 to 19⁄32 inch, incl.; No. 2 for sizes 5⁄8 to 29⁄32 incl.; No. 3 for sizes 15⁄ to 17⁄ , incl.; No. 4 for sizes 11⁄ to 15⁄ , incl.; and No. 5 for sizes 13⁄ to 21⁄ , incl. For amount of taper, 16 32 4 8 4 2 see Table 1b on page 928.



843

Hand Reamers—Straight and Helical Flutes ANSI B94.2-1983 (R1988)

Straight Flutes 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 11⁄ 16 23⁄ 32 3⁄ 4

… 7⁄ 8 … 1

11⁄8 11⁄4 13⁄8 11⁄2

Reamer Diameter Helical Decimal Flutes Equivalent … 0.1250 … 0.1562 … 0.1875 … 0.2188 1⁄ 0.2500 4 … 0.2812 5⁄ 0.3125 16 … 0.3438 3⁄ 0.3750 8 … 0.4062 7⁄ 0.4375 16 … 0.4688 1⁄ 0.5000 2 … 0.5312 9⁄ 0.5625 16 … 0.5938 5⁄ 0.6250 8 … 0.6562 11⁄ 0.6875 16 … 0.7188 3⁄ 0.7500 4 13⁄ 0.8125 16 7⁄ 0.8750 8 15⁄ 0.9375 16 1 1.0000 1.1250 11⁄8 1.2500 11⁄4 3 1.3750 1 ⁄8 1 1.5000 1 ⁄2

Length Overall A 3 31⁄4 31⁄2 33⁄4 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2 63⁄4 7 73⁄8 73⁄4 81⁄8 83⁄8 91⁄8 93⁄4 101⁄4 107⁄8 115⁄8 121⁄4 125⁄8 13

Flute Length B

Square Length C

11⁄2 15⁄8 13⁄4 17⁄8

5⁄ 32 7⁄ 32 7⁄ 32 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 11⁄ 16 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

2 21⁄8 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2 311⁄16 37⁄8 41⁄16 43⁄16 49⁄16 47⁄8 51⁄8 57⁄16 513⁄16 61⁄8 65⁄16 61⁄2

1 1 1 1 11⁄8

Size of Square 0.095 0.115 0.140 0.165 0.185 0.210 0.235 0.255 0.280 0.305 0.330 0.350 0.375 0.400 0.420 0.445 0.470 0.490 0.515 0.540 0.560 0.610 0.655 0.705 0.750 0.845 0.935 1.030 1.125

No. of Flutes 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 12 10 to 12 10 to 14

All dimensions in inches. Material is high-speed steel. The nominal shank diameter D is the same as the reamer diameter. Helical-flute hand reamers with left-hand helical flutes are standard. Reamers are tapered slightly on the end to facilitate proper starting. Tolerances: On diameter of reamer, up to 1⁄4-inch size, incl., + .0001 to + .0004 inch; over 1⁄4-to 1inch size, incl., +.0001 to + .0005 inch; over 1-inch size, +.0002 to +.0006 inch. On length overall A and flute length B, 1⁄8- to 1-inch size, incl., ± 1⁄16 inch; 11⁄8- to 11⁄2-inch size, incl., ±3⁄32 inch. On length of square C, 1⁄8- to 1 inch size, incl., ±1⁄32 inch; 11⁄8-to 11⁄2-inch size, incl., ±1⁄16 inch. On shank diameter D, 1⁄ - to 1-inch size, incl., −.001 to −.005 inch; 11⁄ - to 11⁄ -inch size, incl., −.0015 to − .006 inch. On size 8 8 2 of square, 1⁄8- to 1⁄2-inch size, incl., −.004 inch; 17⁄32- to 1-inch size, incl., −.006 inch; 11⁄8- to 11⁄2-inch size, incl., −.008 inch.



REAMERS American National Standard Expansion Hand Reamers—Straight and Helical Flutes, Squared Shank ANSI B94.2-1983 (R1988)

Reamer Dia. 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8

Length Overall A Max Min 43⁄8 43⁄8 53⁄8 53⁄8 61⁄2 61⁄2 7

1

75⁄8 8 9 10

11⁄8 11⁄4

101⁄2 11

33⁄4 4 41⁄4 41⁄2 5 53⁄8 53⁄4 61⁄4 61⁄2 71⁄2 83⁄8 9 93⁄4

Flute Length Length of B Square Max Min C Straight Flutes 13⁄4 17⁄8 2 2 21⁄2 21⁄2 3 3 31⁄2 4 41⁄2 43⁄4 5

11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 17⁄8 21⁄4 21⁄2 25⁄8 31⁄8 31⁄8 31⁄2 41⁄4

Shank Dia. D

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8

1 1 1

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4

Size of Square

Number of Flutes

0.185 0.235 0.280 0.330 0.375 0.420 0.470 0.515 0.560 0.655 0.750 0.845 0.935

6 to 8 6 to 8 6 to 9 6 to 9 6 to 9 6 to 9 6 to 9 6 to 10 6 to 10 8 to 10 8 to 10 8 to 12 8 to 12

0.185 0.235 0.280 0.330 0.375 0.470 0.560 0.655 0.750 0.935

6 to 8 6 to 8 6 to 9 6 to 9 6 to 9 6 to 9 6 to 10 6 to 10 6 to 10 8 to 12

Helical Flutes 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄4

43⁄8 43⁄8 61⁄8 61⁄4 61⁄2 8

37⁄8 4 41⁄4 41⁄2 5 6

85⁄8 93⁄8 101⁄4 113⁄8

61⁄2 71⁄2 83⁄8 93⁄4

13⁄4 13⁄4 2 2 21⁄2 3 31⁄2 4 41⁄2 5

11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 21⁄4 25⁄8 31⁄8 31⁄8 41⁄4

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 1

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄4

All dimensions are given in inches. Material is carbon steel. Reamers with helical flutes that are left hand are standard. Expansion hand reamers are primarily designed for work where it is necessary to enlarge reamed holes by a few thousandths. The pilots and guides on these reamers are ground undersize for clearance. The maximum expansion on these reamers is as follows: .006 inch for the 1⁄4- to 7⁄16inch sizes. .010 inch for the 1⁄2- to 7⁄8-inch sizes and .012 inch for the 1- to 11⁄4-inch sizes. Tolerances: On length overall A and flute length B, ±1⁄16 inch for 1⁄4- to 1-inch sizes, ± 3⁄32 inch for 11⁄8to 11⁄4-inch sizes; on length of square C, ±1⁄32 inch for 1⁄4- to 1-inch sizes, ± 1⁄16 inch for 11⁄8-to 11⁄4-inch sizes; on shank diameter D −.001 to −.005 inch for 1⁄4- to 1-inch sizes, −.0015 to −.006 inch for 11⁄8- to 11⁄4-inch sizes; on size of square, −.004 inch for 1⁄4- to 1⁄2-inch sizes. −.006 inch for 9⁄16- to 1-inch sizes, and −.008 inch for 11⁄8- to 11⁄4-inch sizes.



845

Taper Shank Jobbers Reamers—Straight Flutes ANSI B94.2-1983 (R1988)

Reamer Diameter Fractional Dec. Equiv. 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1 11⁄16 11⁄8 13⁄16 11⁄4 13⁄8 11⁄2

0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000 1.0625 1.1250 1.1875 1.2500 1.3750 1.5000

Length Overall A 53⁄16 51⁄2 513⁄16 61⁄8 67⁄16 63⁄4 79⁄16 8 83⁄8 813⁄16 93⁄16 10 103⁄8 105⁄8 107⁄8 111⁄8 129⁄16 1213⁄16 131⁄8

Length of Flute B


No. of Flutes

1 1 1 1 1 1 2 2 2 2 2 3 3 3 3 3 4 4 4

6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 12 8 to 12 10 to 12 10 to 12

2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 37⁄8 43⁄16 49⁄16 47⁄8 51⁄8 57⁄16 55⁄8 513⁄16 6 61⁄8 65⁄16 61⁄2

a American National Standard self-holding tapers (Table 7a on page 933.)

All dimensions in inches. Material is high-speed steel. Tolerances: On reamer diameter, 1⁄4-inch size, +.0001 to +.0004 inch; over 1⁄4- to 1-inch size, incl., +.0001 to +.0005 inch; over 1-inch size, +.0002 to +.0006 inch. On overall length A and length of flute B, 1⁄4- to 1-inch size, incl., ±1⁄16 inch; and 11⁄16- to 11⁄2-inch size, incl., ±3⁄32 inch.

American National Standard Driving Slots and Lugs for Shell Reamers or Shell Reamer Arbors ANSI B94.2-1983 (R1988)

Arbor Size No. 4 5 6 7 8 9

Fitting Reamer Sizes 3⁄ 4 13⁄ to 1 16 11⁄16 to 11⁄4 15⁄16 to 15⁄8 111⁄16 to 2 21⁄16 to 21⁄2

Driving Slot Width Depth W J 5⁄ 3⁄ 32 16 3⁄ 1⁄ 16 4 3⁄ 1⁄ 16 4 1⁄ 5⁄ 4 16 5⁄ 1⁄ 4 16 5⁄ 3⁄ 16 8

Lug on Arbor Width Depth L M 9⁄ 5⁄ 64 32 11⁄ 7⁄ 64 32 11⁄ 7⁄ 64 32 15⁄ 9⁄ 64 32 15⁄ 9⁄ 64 32 19⁄ 11⁄ 64 32

Reamer Hole Dia. at Large End 0.375 0.500 0.625 0.750 1.000 1.250

All dimension are given in inches. The hole in shell reamers has a taper of 1⁄8 inch per foot, with arbors tapered to correspond. Shell reamer arbor tapers are made to permit a driving fit with the reamer.



REAMERS Straight Shank Chucking Reamers—Straight Flutes, Wire Gage Sizes ANSI B94.2-1983 (R1988)

Reamer Diameter Wire Gage

Inch

Lgth. Overall A

Shank Dia. D

Lgth. of Flute B

Max

Min

No. of Flutes

Reamer Diameter Wire Gage

Inch

Lgth. Overall A

Shank Dia. D

Lgth. of Flute B

Max

Min

No. of Flutes

60

.0400

21⁄2

1⁄ 2

.0390

.0380

4

49

.0730

3

3⁄ 4

.0660

.0650

4

59

.0410

21⁄2

1⁄ 2

.0390

.0380

4

48

.0760

3

3⁄ 4

.0720

.0710

4

58

.0420

21⁄2

1⁄ 2

.0390

.0380

4

47

.0785

3

3⁄ 4

.0720

.0710

4

57

.0430

21⁄2

1⁄ 2

.0390

.0380

4

46

.0810

3

3⁄ 4

.0771

.0701

4

56

.0465

21⁄2

1⁄ 2

.0455

.0445

4

45

.0820

3

3⁄ 4

.0771

.0761

4

55

.0520

21⁄2

1⁄ 2

.0510

.0500

4

44

.0860

3

3⁄ 4

.0810

.0800

4

54

.0550

21⁄2

1⁄ 2

.0510

.0500

4

43

.0890

3

3⁄ 4

.0810

.0800

4

53

.0595

21⁄2

1⁄ 2

.0585

.0575

4

42

.0935

3

3⁄ 4

.0880

.0870

4

52

.0635

21⁄2

1⁄ 2

.0585

.0575

4

41

.0960

31⁄2

7⁄ 8

.0928

.0918

4 to 6

51

.0670

3

3⁄ 4

.0660

.0650

4

40

.0980

31⁄2

7⁄ 8

.0928

.0918

4 to 6

50

.0700

3

3⁄ 4

.0660

.0650

4

39

.0995

31⁄2

7⁄ 8

.0928

.0918

4 to 6

38

.1015

31⁄2

7⁄ 8

.0950

.0940

4 to 6

19

.1660

41⁄2

11⁄8

.1595

.1585

4 to 6

37

.1040

31⁄2

7⁄ 8

.0950

.0940

4 to 6

18

.1695

41⁄2

11⁄8

.1595

.1585

4 to 6

36

.1065

31⁄2

7⁄ 8

.1030

.1020

4 to 6

17

.1730

41⁄2

11⁄8

.1645

.1635

4 to 6

35

.1100

31⁄2

7⁄ 8

.1030

.1020

4 to 6

16

.1770

41⁄2

11⁄8

.1704

.1694

4 to 6

34

.1110

31⁄2

7⁄ 8

.1055

.1045

4 to 6

15

.1800

41⁄2

11⁄8

.1755

.1745

4 to 6

33

.1130

31⁄2

7⁄ 8

.1055

.1045

4 to 6

14

.1820

41⁄2

11⁄8

.1755

.1745

4 to 6

32

.1160

31⁄2

7⁄ 8

.1120

.1110

4 to 6

13

.1850

41⁄2

11⁄8

.1805

.1795

4 to 6

31

.1200

31⁄2

7⁄ 8

.1120

.1110

4 to 6

12

.1890

41⁄2

11⁄8

.1805

.1795

4 to 6

30

.1285

31⁄2

7⁄ 8

.1190

.1180

4 to 6

11

.1910

5

11⁄4

.1860

.1850

4 to 6

29

.1360

4

1

.1275

.1265

4 to 6

10

.1935

5

11⁄4

.1860

.1850

4 to 6

28

.1405

4

1

.1350

.1340

4 to 6

9

.1960

5

11⁄4

.1895

.1885

4 to 6

27

.1440

4

1

.1350

.1340

4 to 6

8

.1990

5

11⁄4

.1895

.1885

4 to 6

26

.1470

4

1

.1430

.1420

4 to 6

7

.2010

5

11⁄4

.1945

.1935

4 to 6

25

.1495

4

1

.1430

.1420

4 to 6

6

.2040

5

11⁄4

.1945

.1935

4 to 6

24

.1520

4

1

.1460

.1450

4 to 6

5

.2055

5

11⁄4

.2016

.2006

4 to 6

23

.1540

4

1

.1460

.1450

4 to 6

4

.2090

5

11⁄4

.2016

.2006

4 to 6

22

.1570

4

1

.1510

.1500

4 to 6

3

.2130

5

11⁄4

.2075

.2065

4 to 6

21

.1590

41⁄2

11⁄8

.1530

.1520

4 to 6

2

2210

6

11⁄2

.2173

.2163

4 to 6

20

.1610

41⁄2

11⁄8

.1530

.1520

4 to 6

1

.2280

6

11⁄2

.2173

.2163

4 to 6

All dimensions in inches. Material is high-speed steel. Tolerances: On diameter of reamer, plus .0001 to plus .0004 inch. On overall length A, plus or minus 1⁄16 inch. On length of flute B, plus or minus 1⁄16 inch.



847

Straight Shank Chucking Reamers—Straight Flutes, Letter Sizes ANSI B94.2-1983 (R1988)

Reamer Diameter Letter Inch A B C D E F G H I J K L M

Lgth. Overall A

Lgth. of Flute B

6 6 6 6 6 6 6 6 6 6 6 6 6

11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2

0.2340 0.2380 0.2420 0.2460 0.2500 0.2570 0.2610 0.2660 0.2720 0.2770 0.2810 0.2900 0.2950

Shank Dia. D Max Min 0.2265 0.2329 0.2329 0.2329 0.2405 0.2485 0.2485 0.2485 0.2485 0.2485 0.2485 0.2792 0.2792

.2255 .2319 .2319 .2319 .2395 .2475 .2475 .2475 .2475 .2475 .2475 .2782 .2782

No. of Flutes 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6

Reamer Diameter Letter Inch N O P Q R S T U V W X Y Z

Lgth. Overall A

Lgth. of Flute B

6 6 6 6 6 7 7 7 7 7 7 7 7

11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4

0.3020 0.3160 0.3230 0.3320 0.3390 0.3480 0.3580 0.3680 0.3770 0.3860 0.3970 0.4040 0.4130

Shank Dia. D Max Min 0.2792 0.2792 0.2792 0.2792 0.2792 0.3105 0.3105 0.3105 0.3105 0.3105 0.3105 0.3105 0.3730

0.2782 0.2782 0.2782 0.2782 0.2782 0.3095 0.3095 0.3095 0.3095 0.3095 0.3095 0.3095 0.3720

No. of Flutes 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 6 to 8

All dimensions in inches. Material is high-speed steel. Tolerances: On diameter of reamer, for sizes A to E, incl., plus .0001 to plus .0004 inch and for sizes F to Z, incl., plus .0001 to plus .0005 inch. On overall length A, plus or minus 1⁄16 inch. On length of flute B, plus or minus 1⁄16 inch.

Straight Shank Chucking Reamers— Straight Flutes, Decimal Sizes ANSI B94.2-1983 (R1988)

Lgth. Reamer Overall Dia. A 0.1240 0.1260 0.1865 0.1885 0.2490 0.2510 0.3115

31⁄2 31⁄2 41⁄2 41⁄2 6 6 6

Lgth. of Flute B 7⁄ 8 7⁄ 8 11⁄8 11⁄8 11⁄2 11⁄2 11⁄2

Shank Diameter D Max. 0.1190 0.1190 0.1805 0.1805 0.2405 0.2405 0.2792

Min. 0.1180 0.1180 0.1795 0.1795 0.2395 0.2395 0.2782

No. of Flutes

Lgth. Reamer Overall Dia. A

4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6

0.3135 0.3740 0.3760 0.4365 0.4385 0.4990 0.5010

6 7 7 7 7 8 8

Lgth. of Flute B 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 2 2

Shank Diameter D Max. 0.2792 0.3105 0.3105 0.3730 0.3730 0.4355 0.4355

Min. 0.2782 0.3095 0.3095 0.3720 0.3720 0.4345 0.4345

No. of Flutes 4 to 6 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8

All dimensions in inches. Material is high-speed steel. Tolerances: On diameter of reamer, for 0.124 to 0.249-inch sizes, plus .0001 to plus .0004 inch and for 0.251 to 0.501-inch sizes, plus .0001 to plus .0005 inch. On overall length A, plus or minus 1⁄16 inch. On length of flute B, plus or minus 1⁄16 inch.



REAMERS

American National Standard Straight Shank Rose Chucking and Chucking Reamers—Straight and Helical Flutes, Fractional Sizes ANSI B94.2-1983 (R1988)

Reamer Diameter Chucking Rose Chucking 3⁄ a … 64 1⁄ … 16 5⁄ … 64 3⁄ … 32 7⁄ … 64 1⁄ 1⁄ a 8 8 9⁄ … 64 5⁄ … 32 11⁄ … 64 3⁄ 3⁄ a 16 16 13⁄ … 64 7⁄ … 32 15⁄ … 64 1⁄ 1⁄ a 4 4 17⁄ … 64 9⁄ … 32 19⁄ … 64 5⁄ 5⁄ a 16 16 21⁄ … 64 11⁄ … 32 23⁄ … 64 3⁄ 3⁄ a 8 8 25⁄ … 64 13⁄ … 32 27⁄ … 64 7⁄ 7⁄ a 16 16 29⁄ … 64 15⁄ … 32 31⁄ … 64 1⁄ 1⁄ a 2 2 17⁄ … 32 9⁄ … 16 19⁄ … 32 5⁄ … 8 21⁄ … 32 11⁄ … 16 23⁄ … 32 3⁄ … 4 25⁄ … 32 13⁄ … 16 27⁄ … 32 7⁄ … 8 29⁄ … 32 15⁄ … 16 31⁄ … 32 1 … 1 … 1 ⁄16 … 11⁄8 … 13⁄16 … 11⁄4 … 15⁄16b … 13⁄8 … 17⁄16b 1 … 1 ⁄2

Length Overall A 21⁄2 21⁄2 3 3 31⁄2 31⁄2 4 4 41⁄2 41⁄2 5 5 6 6 6 6 6 6 6 6 7 7 7 7 7 7 7 7 8 8 8 8 8 9 9 9 9 91⁄2 91⁄2 91⁄2 91⁄2 10 10 10 10 101⁄2 101⁄2 11 11 111⁄2 111⁄2 12 12 121⁄2

Flute Length B 1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8

1 1 11⁄8 11⁄8 11⁄4 11⁄4 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 2 2 2 2 2 21⁄4 21⁄4 21⁄4 21⁄4 21⁄2 21⁄2 21⁄2 21⁄2 25⁄8 25⁄8 25⁄8 25⁄8 23⁄4 23⁄4 27⁄8 27⁄8 3 3 31⁄4 31⁄4 31⁄2

Shank Dia. D Max Min 0.0455 0.0445 0.0585 0.0575 0.0720 0.0710 0.0880 0.0870 0.1030 0.1020 0.1190 0.1180 0.1350 0.1340 0.1510 0.1500 0.1645 0.1635 0.1805 0.1795 0.1945 0.1935 0.2075 0.2065 0.2265 0.2255 0.2405 0.2395 0.2485 0.2475 0.2485 0.2475 0.2792 0.2782 0.2792 0.2782 0.2792 0.2782 0.2792 0.2782 0.3105 0.3095 0.3105 0.3095 0.3105 0.3095 0.3105 0.3095 0.3730 0.3720 0.3730 0.3720 0.3730 0.3720 0.3730 0.3720 0.4355 0.4345 0.4355 0.4345 0.4355 0.4345 0.4355 0.4345 0.4355 0.4345 0.5620 0.5605 0.5620 0.5605 0.5620 0.5605 0.5620 0.5605 0.6245 0.6230 0.6245 0.6230 0.6245 0.6230 0.6245 0.6230 0.7495 0.7480 0.7495 0.7480 0.7495 0.7480 0.7495 0.7480 0.8745 0.8730 0.8745 0.8730 0.8745 0.8730 0.9995 0.9980 0.9995 0.9980 0.9995 0.9980 0.9995 0.9980 1.2495 1.2480 1.2495 1.2480

a Reamer with straight flutes is standard only.


No. of Flutes 4 4 4 4 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 6 to 8 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 10 8 to 12 8 to 12 8 to 12 8 to 12 8 to 12 10 to 12 10 to 12 10 to 12 10 to 12


849

b Reamer with helical flutes is standard only.

All dimensions are given in inches. Material is high-speed steel. Chucking reamers are end cutting on the chamfer and the relief for the outside diameter is ground in back of the margin for the full length of land. Lands of rose chucking reamers are not relieved on the periphery but have a relatively large amount of back taper. Tolerances: On reamer diameter, up to 1⁄4-inch size, incl., + .0001 to + .0004 inch; over 1⁄4-to 1-inch size, incl., + .0001 to + .0005 inch; over 1-inch size, + .0002 to + .0006 inch. On length overall A and flute length B, up to 1-inch size, incl., ±1⁄16 inch; 11⁄16- to 11⁄2-inch size, incl., ±3⁄32 inch. Helical flutes are right- or left-hand helix, right-hand cut, except sizes 11⁄16 through 11⁄2 inches, which are right-hand helix only.

Shell Reamers—Straight and Helical Flutes ANSI B94.2-1983 (R1988)

Length Overall A

Diameter of Reamer 3⁄ 4 7⁄ 8 15⁄ a 16

1 11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 113⁄16 17⁄8 115⁄16 2

21⁄4 21⁄2 21⁄2 21⁄2 23⁄4 23⁄4 23⁄4 23⁄4

11⁄2 13⁄4 13⁄4 13⁄4

3 3 3 3 3 3

21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄4 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4

31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 33⁄4 33⁄4 33⁄4 33⁄4 33⁄4 33⁄4

21⁄16a 21⁄8 23⁄16a 21⁄4 23⁄8a 21⁄2a

Flute Length B

2 2 2 2

Hole Diameter Large End H

Fitting Arbor No.

Number of Flutes

0.375 0.500 0.500 0.500 0.625 0.625 0.625 0.625 0.750 0.750 0.750 0.750 0.750 0.750 1.000 1.000 1.000 1.000 1.000 1.000 1.250 1.250 1.250 1.250 1.250 1.250

4 5 5 5 6 6 6 6 7 7 7 7 7 7 8 8 8 8 8 8 9 9 9 9 9 9

8 to 10 8 to 10 8 to 10 8 to 10 8 to 12 8 to 12 8 to 12 8 to 12 8 to 12 8 to 12 8 to 12 10 to 14 10 to 14 10 to 14 10 to 14 12 to 14 12 to 14 12 to 14 12 to 14 12 to 14 12 to 16 12 to 16 12 to 16 12 to 16 14 to 16 14 to 16

a Helical flutes only.

All dimensions are given in inches. Material is high-speed steel. Helical flute shell reamers with left-hand helical flutes are standard. Shell reamers are designed as a sizing or finishing reamer and are held on an arbor provided with driving lugs. The holes in these reamers are ground with a taper of 1⁄ inch per foot. 8 Tolerances: On diameter of reamer, 3⁄4- to 1-inch size, incl., + .0001 to + .0005 inch; over 1-inch size, + .0002 to + .0006 inch. On length overall A and flute length B, 3⁄4- to 1-inch size, incl., ± 1⁄16 inch; 11⁄16- to 2-inch size, incl., ± 3⁄32 inch; 21⁄16- to 21⁄2-inch size, incl., ± 1⁄8 inch.



REAMERS American National Standard Arbors for Shell Reamers— Straight and Taper Shanks ANSI B94.2-1983 (R1988)

Arbor Size No. 4 5 6

Overall Length A 9 91⁄2 10

Approx. Length of Taper L

Reamer Size

Taper Shank No.a

21⁄4 21⁄2 23⁄4

3⁄ 4 13⁄ to 1 16 1 1 ⁄16 to 11⁄4

2 2 3

Straight Shank Dia. D 1⁄ 2 5⁄ 8 3⁄ 4

Arbor Size No. 7 8 9

Overall Length A

Approx. Length of Taper L

11 12 13

3 31⁄2 33⁄4

Reamer Size

Taper Shank No.a

Straight Shank Dia. D

15⁄16 to 15⁄8 111⁄16 to 2 21⁄16 to 21⁄2

3 4 4

7⁄ 8 11⁄8 3 1 ⁄8

a American National Standard self-holding tapers (see Table 7a on page 933.)

All dimensions are given in inches. These arbors are designed to fit standard shell reamers (see table). End which fits reamer has taper of 1⁄8 inch per foot.

Stub Screw Machine Reamers—Helical Flutes ANSI B94.2-1983 (R1988)

Series No.

Diameter Range

Length Length Dia. of of OverFlute Shank all A

B

Size of Hole

Flute No.

Series No.

D

H

1⁄ 2

1⁄ 8

1⁄ 16

4

12

4

13

Length Length Dia. of of OverFlute Shank all

Size of Hole

A

B

D

H

Flute No.

.3761- .407

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

.4071- .439

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

.4391- .470

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

11⁄4

1⁄ 2

3⁄ 16

6

Diameter Range

00

.0600-.066

13⁄4

0

.0661-.074

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

.0741-.084

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

2

.0841-.096

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

4

15

.4701- .505

21⁄2

3

.0961-.126

2

3⁄ 4

1⁄ 8

1⁄ 16

4

16

.5051- .567

3

11⁄2

5⁄ 8

1⁄ 4

6

4

.1261-.158

21⁄4

1

1⁄ 4

3⁄ 32

4

17

.5671- .630

3

11⁄2

5⁄ 8

1⁄ 4

6

5

.1581-.188

21⁄4

1

1⁄ 4

3⁄ 32

4

18

.6301- .692

3

11⁄2

5⁄ 8

1⁄ 4

6

6

.1881-.219

21⁄4

1

1⁄ 4

3⁄ 32

6

19

.6921- .755

3

11⁄2

3⁄ 4

5⁄ 16

8

7

.2191-.251

21⁄4

1

1⁄ 4

3⁄ 32

6

20

.7551- .817

3

11⁄2

3⁄ 4

5⁄ 16

8

8

.2511-.282

21⁄4

1

3⁄ 8

1⁄ 8

6

21

.8171- .880

3

11⁄2

3⁄ 4

5⁄ 16

8

9

.2821-.313

21⁄4

1

3⁄ 8

1⁄ 8

6

22

.8801- .942

3

11⁄2

3⁄ 4

5⁄ 16

8

10

.3131-.344

21⁄2

11⁄4

3⁄ 8

1⁄ 8

6

23

.9421-1.010

3

11⁄2

3⁄ 4

5⁄ 16

8

11

.3441-.376

21⁄2

11⁄4

3⁄ 8

1⁄ 8

6

…

…

…

…

…

…

…

1

4

14

All dimensions in inches. Material is high-speed steel. These reamers are standard with right-hand cut and left-hand helical flutes within the size ranges shown. Tolerances: On diameter of reamer, for sizes 00 to 7, incl., plus .0001 to plus .0004 inch and for sizes 8 to 23, incl., plus .0001 to plus .0005 inch. On overall length A, plus or minus 1⁄16 inch. On length of flute B, plus or minus 1⁄16 inch. On diameter of shank D, minus .0005 to minus .002 inch.



851

American National Standard Morse Taper Finishing Reamers ANSI B94.2-1983 (R1988)

Taper No.a 0

Small End Dia. (Ref.) 0.2503

Large End Dia. (Ref.) 0.3674

1

0.3674

2

0.5696

3 4 5

Taper No.a 0 1

Straight Flutes and Squared Shank Length Flute Square Overall Length Length A B C 33⁄4

21⁄4

0.5170

5

3

0.7444

6

31⁄2

0.7748

0.9881

71⁄4

41⁄4

1.0167

1.2893

81⁄2

51⁄4

93⁄4 61⁄4 Straight and Spiral Flutes and Taper Shank Small Large Length Flute End Dia. End Dia. Overall Length (Ref.) (Ref.) A B 0.2503 0.3674 21⁄4 511⁄32 5 0.3674 0.5170 3 6 ⁄16 1.4717

1.8005

5⁄ 16 7⁄ 16 5⁄ 8 7⁄ 8

1 11⁄8 Taper Shank No.a 0

Shank Dia. D

Square Size 0.235

5⁄ 16 7⁄ 16 5⁄ 8 7⁄ 8 11⁄8 11⁄2

0.330 0.470 0.655 0.845 1.125

Squared and Taper Shank Number of Flutes 4 to 6 incl.

1

6 to 8 incl.

2

0.5696

0.7444

73⁄8

31⁄2

2

6 to 8 incl.

3

0.7748

0.9881

87⁄8

41⁄4

3

8 to 10 incl.

4

1.0167

1.2893

107⁄8

51⁄4

4

8 to 10 incl.

5

1.4717

1.8005

131⁄8

61⁄4

5

10 to 12 incl.

a Morse. For amount of taper see Table 1b on page 928.

All dimension are given in inches. Material is high-speed steel. The chamfer on the cutting end of the reamer is optional. Squared shank reamers are standard with straight flutes. Tapered shank reamers are standard with straight or spiral flutes. Spiral flute reamers are standard with left-had spiral flutes. Tolerances: On overall length A and flute length B, in taper numbers 0 to 3, incl., ±1⁄16 inch, in taper numbers 4 and 5, ±3⁄32 inch. On length of square C, in taper numbers 0 to 3, incl., ±1⁄32 inch; in taper numbers 4 and 5, ±1⁄16 inch. On shank diameter D, − .0005 to − .002 inch. On size of square, in taper numbers 0 and 1, − .004 inch; in taper numbers 2 and 3, − .006 inch; in taper numbers 4 and 5, − .008 inch.

Center Reamers.—A “center reamer” is a reamer the teeth of which meet in a point. By their use small conical holes may be reamed in the ends of parts to be machined as on lathe centers. When large holes—usually cored—must be center-reamed, a large reamer is ordinarily used in which the teeth do not meet in a point, the reamer forming the frustum of a cone. Center reamers for such work are called “bull” or “pipe” center reamers. Bull Center Reamer: A conical reamer used for reaming the ends of large holes—usually cored—so that they will fit on a lathe center. The cutting part of the reamer is generally in the shape of a frustum of a cone. It is also known as a pipe center reamer.



REAMERS Taper Pipe Reamers—Spiral Flutes ANSI B94.2-1983 (R1988)

Nom. Size 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1 11⁄4 11⁄2 2

Diameter Large Small End End 0.362 0.316 0.472 0.406 0.606 0.540 0.751 0.665 0.962 0.876 1.212 1.103 1.553 1.444 1.793 1.684 2.268 2.159

Length Overall A

Flute Length B

21⁄8 27⁄16 29⁄16 31⁄8 31⁄4 33⁄4 4

3⁄ 4 11⁄16 11⁄16 13⁄8 13⁄8 13⁄4 13⁄4 13⁄4 13⁄4

41⁄4 41⁄2

Square Length C

Shank Diaeter D 0.4375 0.5625 0.7000 0.6875 0.9063 1.1250 1.3125 1.5000 1.8750

3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 11⁄ 16 13⁄ 16 15⁄ 16

1 11⁄8

Size of Square 0.328 0.421 0.531 0.515 0.679 0.843 0.984 1.125 1.406

No. of Flutes 4 to 6 4 to 6 4 to 6 4 to 6 6 to 10 6 to 10 6 to 10 6 to 10 8 to 12

All dimensions are given in inches. These reamers are tapered3⁄4 inch per foot and are intended for reaming holes to be tapped with American National Standard Taper Pipe Thread taps. Material is high-speed steel. Reamers are standard with left-hand spiral flutes. Tolerances: On length overall A and flute length B, 1⁄8- to 3⁄4-inch size, incl., ±1⁄16 inch; 1- to 11⁄2-inch size, incl., ±3⁄32 inch; 2-inch size, ±1⁄8 inch. On length of square C, 1⁄8- to 3⁄4-inch size, incl., ±1⁄32 inch; 1to 2-inch size, incl., ±1⁄16 inch. On shank diameter D, 1⁄8-inch size, − .0015 inch; 1⁄4- to 1-inch size, incl., − .002 inch; 11⁄4- to 2-inch size, incl., − .003 inch. On size of square, 1⁄8-inch size, − .004 inch; 1⁄4- to 3⁄4inch size, incl., − .006 inch; 1- to 2-inch size, incl., − .008 inch.

B & S Taper Reamers—Straight and Spiral Flutes, Squared Shank Taper No.a 1 2 3 4 5 6 7 8 9 10

Dia., Small End 0.1974 0.2474 0.3099 0.3474 0.4474 0.4974 0.5974 0.7474 0.8974 1.0420

Dia., Large End 0.3176 0.3781 0.4510 0.5017 0.6145 0.6808 0.8011 0.9770 1.1530 1.3376

Overall Length

Square Length

43⁄4 51⁄8 51⁄2 57⁄8 63⁄8 67⁄8 71⁄2 81⁄8 87⁄8 93⁄4

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 13⁄ 16 7⁄ 8

1

Flute Length

Dia. of Shank

27⁄8 31⁄8 33⁄8 311⁄16 4 43⁄8 47⁄8 51⁄2 61⁄8 67⁄8

9⁄ 32 11⁄ 32 13⁄ 32 7⁄ 16 9⁄ 16 5⁄ 8 3⁄ 4 13⁄ 16

1 11⁄8

Size of Square 0.210 0.255 0.305 0.330 0.420 0.470 0.560 0.610 0.750 0.845

No. of Flutes 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 4 to 6 6 to 8 6 to 8 6 to 8 6 to 8

a For taper per foot, see Table 10 on page 936.

These reamers are no longer ANSI Standard. All dimensions are given in inches. Material is high-speed steel. The chamfer on the cutting end of the reamer is optional. All reamers are finishing reamers. Spiral flute reamers are standard with lefthand spiral flutes. (Tapered reamers, especially those with left-hand spirals, should not have circular lands because cutting must take place on the outer diameter of the tool.) B & S taper reamers are designed for use in reaming out Brown & Sharpe standard taper sockets. Tolerances: On length overall A and flute length B, taper nos. 1 to 7, incl., ±1⁄16 inch; taper nos. 8 to 10, incl., ±3⁄32 inch. On length of square C, taper nos. 1 to 9, incl., ±1⁄32 inch; taper no. 10, ±1⁄16 inch. On shank diameter D, − .0005 to − .002 inch. On size of square, taper nos. 1 to 3, incl., − .004 inch; taper nos. 4 to 9, incl., − .006 inch; taper no. 10, − .008 inch.



853

American National Standard Die-Maker's Reamers ANSI B94.2-1983 (R1988)

Letter Size AAA AA A B C D E F

Diameter Small Large End End 0.055 0.070 0.065 0.080 0.075 0.090 0.085 0.103 0.095 0.113 0.105 0.126 0.115 0.136 0.125 0.148

Length A

B

Letter Size

21⁄4 21⁄4 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 3

11⁄8 11⁄8 11⁄8 13⁄8 13⁄8 15⁄8 15⁄8 13⁄4

G H I J K L M N

Diameter Small Large End End 0.135 0.158 0.145 0.169 0.160 0.184 0.175 0.199 0.190 0.219 0.205 0.234 0.220 0.252 0.235 0.274

Length A

B

Letter Size

3 31⁄4 31⁄4 31⁄4 31⁄2 31⁄2 4 41⁄2

13⁄4 17⁄8 17⁄8 17⁄8 21⁄4 21⁄4 21⁄2 3

O P Q R S T U …

Diameter Small Large End End 0.250 0.296 0.275 0.327 0.300 0.358 0.335 0.397 0.370 0.435 0.405 0.473 0.440 0.511 … …

Length A

B

5 51⁄2 6 61⁄2 63⁄4 7 71⁄4 …

31⁄2 4 41⁄2 43⁄4 5 51⁄4 51⁄2 …

All dimensions in inches. Material is high-speed steel. These reamers are designed for use in diemaking, have a taper of 3⁄4 degree included angle or 0.013 inch per inch, and have 2 or 3 flutes. Reamers are standard with left-hand spiral flutes. Tip of reamer may have conical end. Tolerances: On length overall A and flute length B, ±1⁄16 inch.

Taper Pin Reamers — Straight and Left-Hand Spiral Flutes, Squared Shank; and Left-Hand High-Spiral Flutes, Round Shank ANSI B94.2-1983 (R1988)

No. of Taper Pin Reamer 8⁄0b 7⁄0 6⁄0 5⁄0 4⁄0 3⁄0 2⁄0 0 1 2 3 4 5 6 7 8 9 10

Diameter at Large End of Reamer (Ref.) 0.0514 0.0666 0.0806 0.0966 0.1142 0.1302 0.1462 0.1638 0.1798 0.2008 0.2294 0.2604 0.2994 0.3540 0.4220 0.5050 0.6066 0.7216

Diameter at Small End of Reamer (Ref.) 0.0351 0.0497 0.0611 0.0719 0.0869 0.1029 0.1137 0.1287 0.1447 0.1605 0.1813 0.2071 0.2409 0.2773 0.3297 0.3971 0.4805 0.5799

Overall Lengthof Reamer A

Length of Flute B

15⁄8 113⁄16 115⁄16 23⁄16 25⁄16 25⁄16 29⁄16 215⁄16 215⁄16 33⁄16 311⁄16 41⁄16 45⁄16 57⁄16 65⁄16 73⁄16 85⁄16 95⁄16

25⁄ 32 13⁄ 16 15⁄ 16 13⁄16 15⁄16 15⁄16 19⁄16 111⁄16 111⁄16 115⁄16 25⁄16 29⁄16 213⁄16 311⁄16 47⁄16 53⁄16 61⁄16 613⁄16

Length of Square Ca … 5⁄ 32 5⁄ 32 5⁄ 32 5⁄ 32 5⁄ 32 7⁄ 32 7⁄ 32 7⁄ 32 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 9⁄ 16 5⁄ 8

Diameter of Shank D

Size of Squarea

1⁄ 16 5⁄ 64 3⁄ 32 7⁄ 64 1⁄ 8 9⁄ 64 5⁄ 32 11⁄ 64 3⁄ 16 13⁄ 64 15⁄ 64 17⁄ 64 5⁄ 16 23⁄ 64 13⁄ 32 7⁄ 16 9⁄ 16 5⁄ 8

… 0.060 0.070 0.080 0.095 0.105 0.115 0.130 0.140 0.150 0.175 0.200 0.235 0.270 0.305 0.330 0.420 0.470

a Not applicable to high-spiral flute reamers. b Not applicable to straight and left-hand spiral fluted, squared shank reamers.

All dimensions in inches. Reamers have a taper of1⁄4 inch per foot and are made of high-speed steel. Straight flute reamers of carbon steel are also standard. The number of flutes is as follows; 3 or 4, for 7⁄0 to 4⁄0 sizes; 4 to 6, for 3⁄0 to 0 sizes; 5 or 6, for 1 to 5 sizes; 6 to 8, for 6 to 9 sizes; 7 or 8, for the 10 size in the case of straight- and spiral-flute reamers; and 2 or 3, for 8⁄0 to 8 sizes; 2 to 4, for the 9 and 10 sizes in the case of high-spiral flute reamers. Tolerances: On length overall A and flute length B, ±1⁄16 inch. On length of square C, ±1⁄32 inch. On shank diameter D, −.001 to −.005 inch for straight- and spiral-flute reamers and −.0005 to −.002 inch for high-spiral flute reamers. On size of square, −.004 inch for 7⁄0 to 7 sizes and −.006 inch for 8 to 10 sizes.



TWIST DRILLS

TWIST DRILLS AND COUNTERBORES Twist drills are rotary end-cutting tools having one or more cutting lips and one or more straight or helical flutes for the passage of chips and cutting fluids. Twist drills are made with straight or tapered shanks, but most have straight shanks. All but the smaller sizes are ground with “back taper,” reducing the diameter from the point toward the shank, to prevent binding in the hole when the drill is worn. Straight Shank Drills: Straight shank drills have cylindrical shanks which may be of the same or of a different diameter than the body diameter of the drill and may be made with or without driving flats, tang, or grooves. Taper Shank Drills: Taper shank drills are preferable to the straight shank type for drilling medium and large size holes. The taper on the shank conforms to one of the tapers in the American Standard (Morse) Series. American National Standard.—American National Standard B94.11M-1993 covers nomenclature, definitions, sizes and tolerances for High Speed Steel Straight and Taper Shank Drills and Combined Drills and Countersinks, Plain and Bell types. It covers both inch and metric sizes. Dimensional tables from the Standard will be found on the following pages. Definitions of Twist Drill Terms.—The following definitions are included in the Standard. Axis: The imaginary straight line which forms the longitudinal center of the drill. Back Taper: A slight decrease in diameter from point to back in the body of the drill. Body: The portion of the drill extending from the shank or neck to the outer corners of the cutting lips. Body Diameter Clearance: That portion of the land that has been cut away so it will not rub against the wall of the hole. Chisel Edge: The edge at the ends of the web that connects the cutting lips. Chisel Edge Angle: The angle included between the chisel edge and the cutting lip as viewed from the end of the drill. Clearance Diameter: The diameter over the cutaway portion of the drill lands. Drill Diameter: The diameter over the margins of the drill measured at the point. Flutes: Helical or straight grooves cut or formed in the body of the drill to provide cutting lips, to permit removal of chips, and to allow cutting fluid to reach the cutting lips. Helix Angle: The angle made by the leading edge of the land with a plane containing the axis of the drill. Land: The peripheral portion of the drill body between adjacent flutes. Land Width: The distance between the leading edge and the heel of the land measured at a right angle to the leading edge. Lips—Two Flute Drill: The cutting edges extending from the chisel edge to the periphery. Lips—Three or Four Flute Drill (Core Drill): The cutting edges extending from the bottom of the chamfer to the periphery. Lip Relief: The axial relief on the drill point. Lip Relief Angle: The axial relief angle at the outer corner of the lip. It is measured by projection into a plane tangent to the periphery at the outer corner of the lip. (Lip relief angle is usually measured across the margin of the twist drill.) Margin: The cylindrical portion of the land which is not cut away to provide clearance. Neck: The section of reduced diameter between the body and the shank of a drill. Overall Length: The length from the extreme end of the shank to the outer corners of the cutting lips. It does not include the conical shank end often used on straight shank drills, nor does it include the conical cutting point used on both straight and taper shank drills. (For core drills with an external center on the cutting end it is the same as for two-flute


Machinery's Handbook 27th Edition TWIST DRILLS

855

drills. For core drills with an internal center on the cutting end, the overall length is to the extreme ends of the tool.) Point: The cutting end of a drill made up of the ends of the lands, the web, and the lips. In form, it resembles a cone, but departs from a true cone to furnish clearance behind the cutting lips. Point Angle: The angle included between the lips projected upon a plane parallel to the drill axis and parallel to the cutting lips. Shank: The part of the drill by which it is held and driven. Tang: The flattened end of a taper shank, intended to fit into a driving slot in the socket. Tang Drive: Two opposite parallel driving flats on the end of a straight shank. Web: The central portion of the body that joins the end of the lands. The end of the web forms the chisel edge on a two-flute drill. Web Thickness: The thickness of the web at the point unless another specific location is indicated. Web Thinning: The operation of reducing the web thickness at the point to reduce drilling thrust. Point Angle

Neck Dia. Taper Shank Tang Straight Shank Axis

Neck Length

Lip Relief Angle Rake or Helix Angle

Straight Shank Shank Dia.

Shank Length

Shank Length

Drill Dia.

Clearance Dia. Body Dia. Clearance Chisel Edge Angle

Flutes Body Length Over-All Length

Flute Length

Flute Length

Margin Lip Web Chisel Edge

Land

ANSI Standard Twist Drill Nomenclature

Types of Drills.—Drills may be classified based on the type of shank, number of flutes or hand of cut. Straight Shank Drills: Those having cylindrical shanks which may be the same or different diameter than the body of the drill. The shank may be with or without driving flats, tang, grooves, or threads. Taper Shank Drills: Those having conical shanks suitable for direct fitting into tapered holes in machine spindles, driving sleeves, or sockets. Tapered shanks generally have a driving tang. Two-Flute Drills: The conventional type of drill used for originating holes. Three-Flute Drills (Core Drills): Drill commonly used for enlarging and finishing drilled, cast or punched holes. They will not produce original holes. Four-Flute Drills (Core Drills): Used interchangeably with three-flute drills. They are of similar construction except for the number of flutes. Right-Hand Cut: When viewed from the cutting point, the counterclockwise rotation of a drill in order to cut. Left-Hand Cut: When viewed from the cutting point, the clockwise rotation of a drill in order to cut. Teat Drill: The cutting edges of a teat drill are at right angles to the axis, and in the center there is a small teat of pyramid shape which leads the drill and holds it in position. This form is used for squaring the bottoms of holes made by ordinary twist drills or for drilling the entire hole, especially if it is not very deep and a square bottom is required. For instance, when drilling holes to form clearance spaces at the end of a keyseat, preparatory to cutting it out by planing or chipping, the teat drill is commonly used.



TWIST DRILLS

Table 1. ANSI Straight Shank Twist Drills — Jobbers Length through 17.5 mm, Taper Length through 12.7 mm, and Screw Machine Length through 25.4 mm Diameter ANSI/ASME B94.11M-1993 Drill Diameter, Da Fraction No. or Ltr.

Jobbers Length

Equivalent mm

Decimal In.

mm

Screw Machine Length

Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

97

0.15

0.0059

0.150

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

96

0.16

0.0063

0.160

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

95

0.17

0.0067

0.170

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

94

0.18

0.0071

0.180

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

93

0.19

0.0075

0.190

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

92

0.20

0.0079

0.200

1⁄ 16

1.6

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0083

0.211

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0087

0.221

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

89

0.0091

0.231

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

88

0.0095

0.241

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0098

0.250

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0100

0.254

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

0.267

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.280

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.292

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.300

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.305

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.318

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.320

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.330

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.343

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.350

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.368

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.380

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.396

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.400

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.406

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.420

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.450

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.0180

0.457

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.48

0.0189

0.480

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.50

0.0197

0.500

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

76

0.0200

0.508

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

75

0.0210

0.533

1⁄ 4

6

1

25

…

…

…

…

…

…

…

…

0.0217

0.550

1⁄ 4

6

1

25

…

…

…

…

…

…

…

…

0.0225

0.572

1⁄ 4

6

1

25

…

…

…

…

…

…

…

…

0.0236

0.600

5⁄ 16

8

11⁄8

29

…

…

…

…

…

…

…

…

91 90

0.22

0.25 87 86 85

0.0105 0.28

84

0.0110 0.0115

0.30 83

0.0118 0.0120

82

0.0125 0.32

81

0.0126 0.0130

80

0.0135 0.35

79

0.0138 0.0145

0.38 1⁄ 64

0.0150 0.0156

0.40 78

0.0157 0.0160

0.42 0.45 77

0.55 74 0.60

0.0165 0.0177



857

Table 1. (Continued) ANSI Straight Shank Twist Drills — Jobbers Length through 17.5 mm, Taper Length through 12.7 mm, and Screw Machine Length through 25.4 mm Diameter ANSI/ASME B94.11M-1993 Drill Diameter, Da Fraction No. or Ltr.

Jobbers Length

Equivalent Decimal In.


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

0.610

5⁄ 16

8

11⁄8

29

…

…

…

…

…

…

…

…

0.635

5⁄ 16

8

11⁄8

29

…

…

…

…

…

…

…

…

0.650

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.660

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.700

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.711

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.742

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.750

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.787

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.0312

0.792

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.0315

0.800

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

67

0.0320

0.813

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

66

0.0330

0.838

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.0335

0.850

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

0.0350

0.889

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

0.0354

0.899

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

64

0.0360

0.914

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

63

0.0370

0.940

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

0.0374

0.950

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

62

0.0380

0.965

5⁄ 8

16

11⁄2

38

…

…

…

…

…

…

…

…

61

0.0390

0.991

11⁄ 16

17

15⁄8

41

…

…

…

…

…

…

…

…

0.0394

1.000

11⁄ 16

17

15⁄8

41

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

60

0.0400

1.016

11⁄ 16

17

15⁄8

41

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

59

0.0410

1.041

11⁄ 16

17

15⁄8

41

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

0.0413

1.050

11⁄ 16

17

15⁄8

41

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

58

0.0420

1.067

11⁄ 16

17

15⁄8

41

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

57

0.0430

1.092

3⁄ 4

19

13⁄4

44

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

1.10

0.0433

1.100

3⁄ 4

19

13⁄4

44

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

1.15

0.0453

1.150

3⁄ 4

19

13⁄4

44

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

56

0.0465

1.181

3⁄ 4

19

13⁄4

44

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

3⁄ 64

0.0469

1.191

3⁄ 4

19

13⁄4

44

11⁄8

29

21⁄4

57

1⁄ 2

13

13⁄8

35

1.20

0.0472

1.200

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

1.25

0.0492

1.250

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

1.30

0.0512

1.300

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0520

1.321

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0531

1.350

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0550

1.397

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

1.40

0.0551

1.400

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

1.45

0.0571

1.450

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

1.50

0.0591

1.500

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0595

1.511

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0610

1.550

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0625

1.588

7⁄ 8

22

17⁄8

48

13⁄4

44

3

76

5⁄ 8

16

15⁄8

41

0.0630

1.600

7⁄ 8

22

17⁄8

48

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0635

1.613

7⁄ 8

22

17⁄8

48

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0650

1.650

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

mm

73

0.0240

72

0.0250 0.65

71

0.0256 0.0260

0.70 70

0.0276 0.0280

69

0.0292 0.75

68

0.0295 0.0310

1⁄ 32

0.80

0.85 65 0.90

0.95

1.00

1.05

55 1.35 54

53 1.55 1⁄ 16

1.60 52 1.65

mm



TWIST DRILLS


Jobbers Length

Equivalent mm 1.70

51

Decimal In. 0.0669 0.0670

1.75 50

0.0689 0.0700

1.80 1.85 49

0.0709 0.0728 0.0730

1.90 48

0.0748 0.0760

mm 1.700 1.702 1.750 1.778 1.800 1.850 1.854 1.900 1.930


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Inch

mm

Inch

mm

Inch

mm

Inch

mm

1

25

2

51

2

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

51

33⁄4

95

11⁄ 16

95

11⁄ 16

1 1 1 1 1 1 1 1

25 25 25 25 25 25 25 25

2 2 2 2 2 2 2 2

51 51 51 51 51 51 51 51

2 2 2 2 2 2 2 2

Inch

Overall L

mm

Inch

mm

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

17

111⁄16

43

0.0768

1.950

1

25

2

51

2

51

33⁄4

5⁄ 64

0.0781

1.984

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

47

0.0785

1.994

1

25

2

51

21⁄4

57

41⁄4

108

11⁄ 16

17

111⁄16

43

2.00

0.0787

2.000

1

25

2

51

21⁄4

57

41⁄4

108

11⁄ 16

17

111⁄16

43

2.05

0.0807

2.050

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

46

0.0810

2.057

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

45

0.0820

2.083

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.10

0.0827

2.100

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.15

0.0846

2.150

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

0.0860

2.184

11⁄8

29

21⁄8

54

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.20

0.0866

2.200

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.25

0.0886

2.250

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

0.0890

2.261

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.30

0.0906

2.300

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

2.35

0.0925

2.350

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

42

0.0935

2.375

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

3⁄ 32

0.0938

2.383

11⁄4

32

21⁄4

57

21⁄4

57

41⁄4

108

3⁄ 4

19

13⁄4

44

0.0945

2.400

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.0960

2.438

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.0965

2.450

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.0980

2.489

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.0984

2.500

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

39

0.0995

2.527

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

38

0.1015

2.578

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.1024

2.600

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.1040

2.642

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

0.1063

2.700

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

36

0.1065

2.705

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

7⁄ 64

0.1094

2.779

11⁄2

38

25⁄8

67

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

35

0.1100

2.794

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1102

2.800

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

34

0.1110

2.819

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

33

0.1130

2.870

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1142

2.900

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1160

2.946

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1181

3.000

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1200

3.048

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

1.95

44

43

2.40 41 2.46 40 2.50

2.60 37 2.70

2.80

2.90 32 3.00 31



859


Jobbers Length



Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

3.100

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

3.175

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

3.200

15⁄8

41

23⁄4

76

53⁄8

137

15⁄ 16

3.264

15⁄8

41

23⁄4

76

53⁄8

137

15⁄ 16

3.300

13⁄4

44

27⁄8

76

53⁄8

137

15⁄ 16

3.400

13⁄4

44

27⁄8

76

53⁄8

137

15⁄ 16

3.454

13⁄4

44

27⁄8

76

53⁄8

137

15⁄ 16

3.500

13⁄4

44

27⁄8

76

53⁄8

137

15⁄ 16

3.569

13⁄4

44

27⁄8

76

53⁄8

137

15⁄ 16

0.1406

3.571

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

0.1417

3.600

17⁄8

48

3

76

3

76

53⁄8

137

0.1440

3.658

17⁄8

48

3

76

3

76

53⁄8

0.1457

3.700

17⁄8

48

3

76

3

76

26

0.1470

3.734

17⁄8

48

3

76

3

25

0.1495

3.797

17⁄8

48

3

76

0.1496

3.800

17⁄8

48

3

0.1520

3.861

2

51

0.1535

3.900

2

23

0.1540

3.912

5⁄ 32

0.1562

22

mm

mm

Overall L

mm

Inch

mm

22

17⁄8

48

22

17⁄8

48

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

24

115⁄16

49

1

25

21⁄16

52

137

1

25

21⁄16

52

53⁄8

137

1

25

21⁄16

52

76

53⁄8

137

1

25

21⁄16

52

3

76

53⁄8

137

1

25

21⁄16

52

76

3

76

53⁄8

137

1

25

21⁄16

52

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

3.967

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

0.1570

3.988

2

51

31⁄8

79

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

0.1575

4.000

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

21

0.1590

4.039

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

20

0.1610

4.089

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

4.10

0.1614

4.100

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

4.20

0.1654

4.200

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

0.1660

4.216

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

0.1693

4.300

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

18

0.1695

4.305

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

11⁄ 64

0.1719

4.366

21⁄8

54

31⁄4

83

33⁄8

86

53⁄4

146

11⁄16

27

21⁄8

54

17

0.1730

4.394

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1732

4.400

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1770

4.496

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1772

4.500

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1800

4.572

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1811

4.600

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1820

4.623

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1850

4.700

25⁄16

59

31⁄2

89

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1875

4.762

25⁄16

59

31⁄2

89

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

0.1890

4.800

25⁄16

59

31⁄2

89

35⁄8

92

6

152

13⁄16

30

21⁄4

57

0.1910

4.851

25⁄16

59

31⁄2

89

35⁄8

92

6

152

13⁄16

30

21⁄4

57

0.1929

4.900

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

10

0.1935

4.915

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

9

0.1960

4.978

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

0.1969

5.000

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

0.1990

5.054

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

3.10 1⁄ 8

0.1250 3.20

30 3.40 29 28

0.1339 0.1378 0.1405

9⁄ 64

3.60 27 3.70

3.80 24 3.90

4.00

19 4.30

4.40 16 4.50 15 4.60 14 4.70

3⁄ 16

4.80

11 4.90

5.00 8

0.1299 0.1360

3.50

12

0.1260 0.1285

3.30

13

0.1220

70 70 73 73 73 73 73

3 3 3 3 3 3 3



TWIST DRILLS


Jobbers Length



Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

5.100

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

5.105

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

5.159

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

5.182

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

5.200

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

5.220

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

5.300

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

5.309

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

5.400

21⁄2

64

33⁄4

95

35⁄8

152

11⁄4

32

23⁄8

60

0.2130

5.410

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2165

5.500

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2188

5.558

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2205

5.600

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

0.2210

5.613

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

0.2244

5.700

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

0.2280

5.791

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

5.80

0.2283

5.800

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

5.90

0.2323

5.900

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

A

0.2340

5.944

25⁄8

67

37⁄8

98

…

…

…

…

15⁄16

33

27⁄16

62

15⁄ 64

0.2344

5.954

25⁄8

67

37⁄8

98

33⁄4

95

61⁄8

156

15⁄16

33

27⁄16

62

0.2362

6.000

23⁄4

70

4

102

33⁄4

95

61⁄8

156

13⁄8

35

21⁄2

64

0.2380

6.045

23⁄4

70

4

102

…

…

…

…

13⁄8

35

21⁄2

64

0.2402

6.100

23⁄4

70

4

102

33⁄4

95

61⁄8

156

13⁄8

35

21⁄2

64

0.2420

6.147

23⁄4

70

4

102

…

…

…

…

13⁄8

35

21⁄2

64

0.2441

6.200

23⁄4

70

4

102

33⁄4

95

61⁄8

156

13⁄8

35

21⁄2

64

0.2460

6.248

23⁄4

70

4

102

…

…

…

…

13⁄8

35

21⁄2

64

0.2480

6.300

23⁄4

70

4

102

33⁄4

95

61⁄8

156

13⁄8

35

21⁄2

64

0.2500

6.350

23⁄4

70

4

102

33⁄4

95

61⁄8

156

13⁄8

35

21⁄2

64

6.40

0.2520

6.400

27⁄8

73

41⁄8

105

37⁄8

98

61⁄4

159

17⁄16

37

25⁄8

67

6.50

0.2559

6.500

27⁄8

73

41⁄8

105

37⁄8

98

61⁄4

159

17⁄16

37

25⁄8

67

0.2570

6.528

27⁄8

73

41⁄8

105

…

…

…

…

17⁄16

37

25⁄8

67

0.2598

6.600

27⁄8

73

41⁄8

105

…

…

…

…

17⁄16

37

25⁄8

67

0.2610

6.629

27⁄8

73

41⁄8

105

…

…

…

…

17⁄16

37

25⁄8

67

0.2638

6.700

27⁄8

73

41⁄8

105

…

…

…

…

17⁄16

37

25⁄8

67

17⁄ 64

0.2656

6.746

27⁄8

73

41⁄8

105

37⁄8

98

61⁄4

159

17⁄16

37

25⁄8

67

H

0.2660

6.756

27⁄8

73

41⁄8

105

…

…

…

…

11⁄2

38

211⁄16

68

6.80

0.2677

6.800

27⁄8

73

41⁄8

105

37⁄8

98

61⁄4

159

11⁄2

38

211⁄16

68

6.90

0.2717

6.900

27⁄8

73

41⁄8

105

…

…

…

…

11⁄2

38

211⁄16

68

0.2720

6.909

27⁄8

73

41⁄8

105

…

…

…

…

11⁄2

38

211⁄16

68

0.2756

7.000

27⁄8

73

41⁄8

105

37⁄8

98

61⁄4

159

11⁄2

38

211⁄16

68

0.2770

7.036

27⁄8

73

41⁄8

105

…

…

…

…

11⁄2

38

211⁄16

68

0.2795

7.100

215⁄16

75

41⁄4

108

…

…

…

…

11⁄2

38

211⁄16

68

K

0.2810

7.137

215⁄16

75

41⁄4

108

…

…

…

…

11⁄2

38

211⁄16

68

9⁄ 32

0.2812

7.142

215⁄16

75

41⁄4

108

37⁄8

98

61⁄4

159

11⁄2

38

211⁄16

68

7.20

0.2835

7.200

215⁄16

75

41⁄4

108

4

102

63⁄8

162

19⁄16

40

23⁄4

70

7.30

0.2874

7.300

215⁄16

75

41⁄4

108

…

…

…

19⁄16

40

23⁄4

70

mm 5.10

7

0.2008 0.2010

13⁄ 64

0.2031

6

0.2040 5.20

5

0.2047 0.2055

5.30 4

0.2087 0.2090

5.40 3 5.50 7⁄ 32

5.60 2 5.70 1

6.00 B 6.10 C 6.20 D 6.30 E, 1⁄4

F 6.60 G 6.70

I 7.00 J 7.10

0.2126

…

92 92 92 92 92 92 92 92

6 6 6 6 6 6 6 6


Inch

mm


861


Jobbers Length



Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

7.366

215⁄16

75

41⁄4

108

…

…

…

…

19⁄16

40

23⁄4

70

7.400

31⁄16

78

43⁄8

111

…

…

…

…

19⁄16

40

23⁄4

70

7.493

31⁄16

78

43⁄8

111

…

…

…

…

19⁄16

40

23⁄4

70

7.500

31⁄16

78

43⁄8

102

63⁄8

162

19⁄16

40

23⁄4

70

7.541

31⁄16

78

43⁄8

102

63⁄8

162

19⁄16

40

23⁄4

70

7.600

31⁄16

78

43⁄8

41

213⁄16

71

7.671

31⁄16

78

43⁄8

41

213⁄16

71

7.700

33⁄16

81

41⁄2

41

213⁄16

71

7.800

33⁄16

81

41⁄2

71

0.3110

7.900

33⁄16

81

41⁄2

114

0.3125

7.938

33⁄16

81

41⁄2

114

0.3150

8.000

33⁄16

81

41⁄2

0.3160

8.026

33⁄16

81

8.10

0.3189

8.100

35⁄16

8.20

0.3228

8.200

0.3230

mm

L

0.2900 7.40

M

0.2913 0.2950

7.50 19⁄ 64

0.2953 0.2969

111 111

4 4

Inch

mm

111

…

…

…

…

15⁄8

111

…

…

…

…

15⁄8

114

…

…

…

…

15⁄8

102

63⁄8

162

15⁄8

41

213⁄16

…

…

…

15⁄8

41

213⁄16

71

4

102

63⁄8

162

15⁄8

41

213⁄16

71

114

41⁄8

105

61⁄2

165

111⁄16

43

215⁄16

75

41⁄2

114

…

…

…

…

111⁄16

43

215⁄16

75

84

45⁄8

117

…

…

…

…

111⁄16

43

215⁄16

75

35⁄16

84

45⁄8

117

41⁄8

105

61⁄2

165

111⁄16

43

215⁄16

75

8.204

35⁄16

84

45⁄8

117

…

…

…

…

111⁄16

43

215⁄16

75

0.3268

8.300

35⁄16

84

45⁄8

117

…

…

…

…

111⁄16

43

215⁄16

75

0.3281

8.334

35⁄16

84

45⁄8

117

41⁄8

105

61⁄2

165

111⁄16

43

215⁄16

75

0.3307

8.400

37⁄16

87

43⁄4

121

…

…

…

…

111⁄16

43

3

76

0.3320

8.433

37⁄16

87

43⁄4

121

…

…

…

…

111⁄16

43

3

76

8.50

0.3346

8.500

37⁄16

87

43⁄4

121

41⁄8

105

61⁄2

165

111⁄16

43

3

76

8.60

0.3386

8.600

37⁄16

87

43⁄4

121

…

…

…

…

111⁄16

43

3

76

0.3390

8.611

37⁄16

87

43⁄4

121

…

…

…

…

111⁄16

43

3

76

0.3425

8.700

37⁄16

87

43⁄4

121

…

…

…

…

111⁄16

43

3

76

0.3438

8.733

37⁄16

87

43⁄4

121

41⁄8

105

61⁄2

165

111⁄16

43

3

76

8.80

0.3465

8.800

31⁄2

89

47⁄8

124

41⁄4

108

63⁄4

171

13⁄4

44

31⁄16

78

0.3480

8.839

31⁄2

89

47⁄8

124

…

…

…

…

13⁄4

44

31⁄16

78

8.90

0.3504

8.900

31⁄2

89

47⁄8

124

…

…

…

…

13⁄4

44

31⁄16

78

9.00

0.3543

9.000

31⁄2

89

47⁄8

124

41⁄4

108

63⁄4

171

13⁄4

44

31⁄16

78

0.3580

9.093

31⁄2

89

47⁄8

124

…

…

…

…

13⁄4

44

31⁄16

78

0.3583

9.100

31⁄2

89

47⁄8

124

…

…

…

…

13⁄4

44

31⁄16

78

0.3594

9.129

31⁄2

89

47⁄8

124

41⁄4

108

63⁄4

171

13⁄4

44

31⁄16

78

9.20

0.3622

9.200

35⁄8

92

5

127

41⁄4

108

63⁄4

171

113⁄16

46

31⁄8

79

9.30

0.3661

9.300

35⁄8

92

5

127

…

…

…

…

113⁄16

46

31⁄8

79

0.3680

9.347

35⁄8

92

5

127

…

…

…

…

113⁄16

46

31⁄8

79

9.40

0.3701

9.400

35⁄8

92

5

127

…

…

…

…

113⁄16

46

31⁄8

79

9.50

0.3740

9.500

35⁄8

92

5

127

41⁄4

108

63⁄4

171

113⁄16

46

31⁄8

79

3⁄ 8

0.3750

9.525

35⁄8

92

5

127

41⁄4

108

63⁄4

171

113⁄16

46

31⁄8

79

V

0.3770

9.576

35⁄8

92

5

127

…

…

…

…

17⁄8

48

31⁄4

83

9.60

0.3780

9.600

33⁄4

95

51⁄8

130

…

…

…

…

17⁄8

48

31⁄4

83

9.70

0.3819

9.700

33⁄4

95

51⁄8

130

…

…

…

…

17⁄8

48

31⁄4

83

9.80

0.3858

9.800

33⁄4

95

51⁄8

130

43⁄8

111

178

17⁄8

48

31⁄4

83

0.3860

9.804

33⁄4

95

51⁄8

130

…

…

…

…

17⁄8

48

31⁄4

83

0.3898

9.900

33⁄4

95

51⁄8

130

…

…

…

…

17⁄8

48

31⁄4

83

0.3906

9.921

33⁄4

95

51⁄8

130

43⁄8

111

7

178

17⁄8

48

31⁄4

83

0.3937

10.000

33⁄4

95

51⁄8

130

43⁄8

111

7

178

115⁄16

49

35⁄16

84

7.60 N

0.2992 0.3020

7.70 7.80 7.90 5⁄ 16

8.00 O

P 8.30 21⁄ 64

8.40 Q

R 8.70 11⁄ 32

S

T 9.10 23⁄ 64

U

W 9.90 25⁄ 64

10.00

0.3031 0.3071

114

4 …

7



TWIST DRILLS


Decimal In.


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

10.084

33⁄4

95

51⁄8

130

…

…

…

…

115⁄16

49

35⁄16

84

10.200

37⁄8

98

51⁄4

133

43⁄8

111

178

115⁄16

49

35⁄16

84

10.262

37⁄8

98

51⁄4

133

…

…

…

115⁄16

49

35⁄16

84

10.317

37⁄8

98

51⁄4

133

43⁄8

111

178

115⁄16

49

35⁄16

84

10.490

37⁄8

98

51⁄4

133

…

…

…

51

33⁄8

86

10.500

37⁄8

98

51⁄4

133

45⁄8

117

71⁄4

51

33⁄8

86

10.716

315⁄16

100

53⁄8

137

45⁄8

117

71⁄4

51

33⁄8

86

10.800

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

52

37⁄16

87

11.000

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

87

0.4375

11.112

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

11.20

0.4409

11.200

43⁄16

106

55⁄8

143

43⁄4

121

11.50

0.4528

11.500

43⁄16

106

55⁄8

143

43⁄4

0.4531

11.509

43⁄16

106

55⁄8

143

0.4646

11.800

45⁄16

110

53⁄4

0.4688

11.908

45⁄16

110

12.00

0.4724

12.000

43⁄8

12.20

0.4803

12.200

0.4844

mm

X

0.3970 10.20

Y

0.4016 0.4040

13⁄ 32

0.4062

Z

0.4130 10.50

27⁄ 64

0.4134 0.4219

mm

7 … 7

… 184

2 2

Inch

mm

184

2

184

21⁄16

184

21⁄16

52

37⁄16

184

21⁄16

52

37⁄16

87

71⁄2

190

21⁄8

54

39⁄16

90

121

71⁄2

190

21⁄8

54

39⁄16

90

43⁄4

121

71⁄2

190

21⁄8

54

39⁄16

90

146

43⁄4

121

71⁄2

190

21⁄8

54

35⁄8

92

53⁄4

146

43⁄4

121

71⁄2

190

21⁄8

54

35⁄8

92

111

57⁄8

149

43⁄4

121

73⁄4

197

23⁄16

56

311⁄16

94

43⁄8

111

57⁄8

149

43⁄4

121

73⁄4

197

23⁄16

56

311⁄16

94

12.304

43⁄8

111

57⁄8

149

43⁄4

121

73⁄4

197

23⁄16

56

311⁄16

94

0.4921

12.500

41⁄2

114

6

152

43⁄4

121

73⁄4

197

21⁄4

57

33⁄4

95

0.5000

12.700

41⁄2

114

6

152

43⁄4

121

73⁄4

197

21⁄4

57

33⁄4

95

12.80

0.5039

12.800

41⁄2

114

6

152

…

…

…

…

23⁄8

60

37⁄8

98

13.00

0.5118

13.000

41⁄2

114

6

152

…

…

…

…

23⁄8

60

37⁄8

98

0.5156

13.096

413⁄16

122

65⁄8

168

…

…

…

…

23⁄8

60

37⁄8

98

0.5197

13.200

413⁄16

122

65⁄8

168

…

…

…

…

23⁄8

60

37⁄8

98

0.5312

13.492

413⁄16

122

65⁄8

168

…

…

…

…

23⁄8

60

37⁄8

98

13.50

0.5315

13.500

413⁄16

122

65⁄8

168

…

…

…

…

23⁄8

60

37⁄8

98

13.80

0.5433

13.800

413⁄16

122

65⁄8

168

…

…

…

…

21⁄2

64

4

102

0.5469

13.891

413⁄16

122

65⁄8

168

…

…

…

…

21⁄2

64

4

102

14.00

0.5512

14.000

413⁄16

122

65⁄8

168

…

…

…

…

21⁄2

64

4

102

14.25

0.5610

14.250

413⁄16

122

65⁄8

168

…

…

…

…

21⁄2

64

4

102

0.5625

14.288

413⁄16

122

65⁄8

168

…

…

…

…

21⁄2

64

4

102

14.50

0.5709

14.500

413⁄16

122

65⁄8

168

…

…

…

…

25⁄8

67

41⁄8

105

0.5781

14.684

413⁄16

122

65⁄8

168

…

…

…

…

25⁄8

67

41⁄8

105

14.75

0.5807

14.750

53⁄16

132

71⁄8

181

…

…

…

…

25⁄8

67

41⁄8

105

15.00

0.5906

15.000

53⁄16

132

71⁄8

181

…

…

…

…

25⁄8

67

41⁄8

105

0.5938

15.083

53⁄16

132

71⁄8

181

…

…

…

…

25⁄8

67

41⁄8

105

0.6004

15.250

53⁄16

132

71⁄8

181

…

…

…

…

23⁄4

70

41⁄4

108

0.6094

15.479

53⁄16

132

71⁄8

181

…

…

…

…

23⁄4

70

41⁄4

108

15.50

0.6102

15.500

53⁄16

132

71⁄8

181

…

…

…

…

23⁄4

70

41⁄4

108

15.75

0.6201

15.750

53⁄16

132

71⁄8

181

…

…

…

…

23⁄4

70

41⁄4

108

0.6250

15.875

53⁄16

132

71⁄8

181

…

…

…

…

23⁄4

70

41⁄4

108

16.00

0.6299

16.000

53⁄16

132

71⁄8

181

…

…

…

…

27⁄8

73

41⁄2

114

16.25

0.6398

16.250

53⁄16

132

71⁄8

181

…

…

…

…

27⁄8

73

41⁄2

114

0.6406

16.271

53⁄16

132

71⁄8

181

…

…

…

…

27⁄8

73

41⁄2

144

0.6496

16.500

53⁄16

132

71⁄8

181

…

…

…

…

27⁄8

73

41⁄2

114

0.6562

16.669

53⁄16

132

71⁄8

181

…

…

…

…

27⁄8

73

41⁄2

114

10.80 11.00 7⁄ 16

29⁄ 64

11.80 15⁄ 32

31⁄ 64

12.50 1⁄ 2

33⁄ 64

13.20 17⁄ 32

35⁄ 64

9⁄ 16

37⁄ 64

19⁄ 32

15.25 39⁄ 64

5⁄ 8

41⁄ 64

16.50 21⁄ 32

Jobbers Length

Equivalent

0.4252 0.4331



863


Jobbers Length

Equivalent mm

Decimal In.

16.75

0.6594


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Overall L

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

16.750

55⁄8

143

75⁄8

194

…

…

…

…

27⁄8

73

41⁄2

114

0.6693

17.000

55⁄8

143

75⁄8

194

…

…

…

…

27⁄8

73

41⁄2

114

0.6719

17.066

55⁄8

143

75⁄8

194

…

…

…

…

27⁄8

73

41⁄2

114

0.6791

17.250

55⁄8

143

75⁄8

194

…

…

…

…

27⁄8

73

41⁄2

114

0.6875

17.462

55⁄8

143

75⁄8

194

…

…

…

…

27⁄8

73

41⁄2

114

0.6890

17.500

55⁄8

143

75⁄8

194

…

…

…

…

3

76

43⁄4

121

0.7031

17.859

…

…

…

…

…

…

…

…

3

76

43⁄4

121

0.7087

18.000

…

…

…

…

…

…

…

…

3

76

43⁄4

121

0.7188

18.258

…

…

…

…

…

…

…

…

3

76

43⁄4

121

0.7283

18.500

…

…

…

…

…

…

…

…

31⁄8

79

5

127

0.7344

18.654

…

…

…

…

…

…

…

…

31⁄8

79

5

127

0.7480

19.000

…

…

…

…

…

…

…

…

31⁄8

79

5

127

3⁄ 4

0.7500

19.050

…

…

…

…

…

…

…

…

31⁄8

79

5

127

49⁄ 64

0.7656

19.446

…

…

…

…

…

…

…

…

31⁄4

83

51⁄8

130

0.7677

19.500

…

…

…

…

…

…

…

…

31⁄4

83

51⁄8

130

0.7812

19.845

…

…

…

…

…

…

…

…

31⁄4

83

51⁄8

130

0.7879

20.000

…

…

…

…

…

…

…

…

33⁄8

86

51⁄4

133

0.7969

20.241

…

…

…

…

…

…

…

…

33⁄8

86

51⁄4

133

0.8071

20.500

…

…

…

…

…

…

…

…

33⁄8

86

51⁄4

133

0.8125

20.638

…

…

…

…

…

…

…

…

33⁄8

86

51⁄4

133

0.8268

21.000

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

53⁄ 64

0.8281

21.034

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

27⁄ 32

0.8438

21.433

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

0.8465

21.500

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

0.8594

21.829

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

0.8661

22.000

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

0.8750

22.225

…

…

…

…

…

…

…

…

31⁄2

89

53⁄8

137

0.8858

22.500

…

…

…

…

…

…

…

…

35⁄8

92

55⁄8

143

0.8906

22.621

…

…

…

…

…

…

…

…

35⁄8

92

55⁄8

143

0.9055

23.000

…

…

…

…

…

…

…

…

35⁄8

92

55⁄8

143

29⁄ 32

0.9062

23.017

…

…

…

…

…

…

…

…

35⁄8

92

55⁄8

143

59⁄ 64

0.9219

23.416

…

…

…

…

…

…

…

…

33⁄4

95

53⁄4

146

0.9252

23.500

…

…

…

…

…

…

…

…

33⁄4

95

53⁄4

146

0.9375

23.812

…

…

…

…

…

…

…

…

33⁄4

95

53⁄4

146

0.9449

24.000

…

…

…

…

…

…

…

…

37⁄8

98

57⁄8

149

0.9531

24.209

…

…

…

…

…

…

…

…

37⁄8

98

57⁄8

149

0.9646

24.500

…

…

…

…

…

…

…

…

37⁄8

98

57⁄8

149

0.9688

24.608

…

…

…

…

…

…

…

…

37⁄8

98

57⁄8

149

0.9843

25.000

…

…

…

…

…

…

…

…

4

102

6

152

63⁄ 64

0.9844

25.004

…

…

…

…

…

…

…

…

4

102

6

152

1

1.0000

25.400

…

…

…

…

…

…

…

…

4

102

6

152

17.00 43⁄ 64

17.25 11⁄ 16

17.50 45⁄ 64

18.00 23⁄ 32

18.50 47⁄ 64

19.00

19.50 25⁄ 32

20.00 51⁄ 64

20.50 13⁄ 16

21.00

21.50 55⁄ 64

22.00 7⁄ 8

22.50 57⁄ 64

23.00

23.50 15⁄ 16

24.00 61⁄ 64

24.50 31⁄ 32

25.00

mm

a Fractional inch, number, letter, and metric sizes.


Inch

mm


TWIST DRILLS

Nominal Shank Size is Same as Nominal Drill Size

Table 2. ANSI Straight Shank Twist Drills — Taper Length — Over 1⁄2 in. (12.7 mm) Dia., Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Diameter of Drill D Frac.

mm 12.80 13.00

33⁄ 64

13.20 17⁄ 32

13.50 13.80 35⁄ 64

14.00 14.25 9⁄ 16

14.50 37⁄ 64

14.75 15.00 19⁄ 32

15.25 39⁄ 64

15.50 15.75 5⁄ 8

16.00 16.25 41⁄ 64

16.50 21⁄ 32

16.75 17.00 43⁄ 64

17.25 11⁄ 16

17.50 45⁄ 64

18.00 23⁄ 32

18.50 47⁄ 64

19.00 3⁄ 4 49⁄ 64

19.50 25⁄ 32

Decimal Inch Equiv.

Millimeter Equiv.

0.5039 0.5117 0.5156 0.5197 0.5312 0.5315 0.5433 0.5419 0.5512 0.5610 0.5625 0.5709 0.5781 0.5807 0.5906 0.5938 0.6004 0.6094 0.6102 0.6201 0.6250 0.6299 0.6398 0.6406 0.6496 0.6562 0.6594 0.6693 0.6719 0.6791 0.6875 0.6890 0.7031 0.7087 0.7188 0.7283 0.7344 0.7480 0.7500 0.7656 0.7677 0.7812

12.800 13.000 13.096 13.200 13.492 13.500 13.800 13.891 14.000 14.250 14.288 14.500 14.684 14.750 15.000 15.083 15.250 15.479 15.500 15.750 15.875 16.000 16.250 16.271 16.500 16.667 16.750 17.000 17.066 17.250 17.462 17.500 17.859 18.000 18.258 18.500 18.654 19.000 19.050 19.446 19.500 19.842

Flute Length F Inch mm 43⁄4 43⁄4 43⁄4 43⁄4 43⁄4 43⁄4 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 51⁄8 51⁄8 51⁄8 51⁄8 51⁄8 53⁄8 53⁄8 53⁄8 53⁄8 53⁄8 55⁄8 55⁄8 55⁄8 55⁄8 57⁄8 57⁄8 57⁄8 57⁄8 6 6 6

121 121 121 121 121 121 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 130 130 130 130 130 137 137 137 137 137 143 143 143 143 149 149 149 149 152 152 152

Overall Length L Inch mm 8 8 8 8 8 8 81⁄4 81⁄4 81⁄4 81⁄4 81⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 83⁄4 9 9 9 9 9 91⁄4 91⁄4 91⁄4 91⁄4 91⁄4 91⁄2 91⁄2 91⁄2 91⁄2 93⁄4 93⁄4 93⁄4 93⁄4 97⁄8 97⁄8 97⁄8

203 203 203 203 203 203 210 210 210 210 210 222 222 222 222 222 222 222 222 222 222 228 228 228 228 228 235 235 235 235 235 241 241 241 241 247 247 247 247 251 251 251

Length of Body B Inch mm 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 51⁄4 51⁄4 51⁄4 51⁄4 51⁄4 51⁄2 51⁄2 51⁄2 51⁄2 51⁄2 53⁄4 53⁄4 53⁄4 53⁄4 6 6 6 6 61⁄8 61⁄8 61⁄8

124 124 124 124 124 124 127 127 127 127 127 127 127 127 127 127 127 127 127 127 127 133 133 133 133 133 140 140 140 140 140 146 146 146 146 152 152 152 152 156 156 156

Minimum Length of Shk. S Inch mm 25⁄8 25⁄8 25⁄8 25⁄8 25⁄8 25⁄8 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8

66 66 66 66 66 66 70 70 70 70 70 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 79


Maximum Length ofNeck N Inch mm 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

13 13 13 13 13 13 13 13 13 13 13 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16


865

Table 2. (Continued) ANSI Straight Shank Twist Drills — Taper Length — Over 1⁄2 in. (12.7 mm) Dia., Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Diameter of Drill D Frac.

mm 20.00

51⁄ 64

20.50 13⁄ 16

21.00 53⁄ 64 27⁄ 32

21.50 55⁄ 64

22.00 7⁄ 8

22.50 57⁄ 64

23.00 29⁄ 32 59⁄ 64

23.50 15⁄ 16

24.00 61⁄ 64

24.50 31⁄ 32

25.00 63⁄ 64

1 25.50 11⁄64 26.00 11⁄32 26.50 13⁄64 11⁄16 27.00 15⁄64 27.50 13⁄32 28.00 17⁄64 28.50 11⁄8 19⁄64 29.00 15⁄32 29.50 111⁄64 30.00 13⁄16 30.50 113⁄64 17⁄32 31.00 115⁄64 31.50

Decimal Inch Equiv.

Millimeter Equiv.

0.7874 0.7969 0.8071 0.8125 0.8268 0.8281 0.8438 0.8465 0.8594 0.8661 0.8750 0.8858 0.8906 0.9055 0.9062 0.9219 0.9252 0.9375 0.9449 0.9531 0.9646 0.9688 0.9843 0.9844 1.0000 1.0039 1.0156 1.0236 1.0312 1.0433 1.0469 1.0625 1.0630 1.0781 1.0827 1.0938 1.1024 1.1094 1.1220 1.1250 1.1406 1.1417 1.1562 1.1614 1.1719 1.1811 1.1875 1.2008 1.2031 1.2188 1.2205 1.2344 1.2402

20.000 20.241 20.500 20.638 21.000 21.034 21.433 21.500 21.829 22.000 22.225 22.500 22.621 23.000 23.017 23.416 23.500 23.812 24.000 24.209 24.500 24.608 25.000 25.004 25.400 25.500 25.796 26.000 26.192 26.560 26.591 26.988 27.000 27.384 27.500 27.783 28.000 28.179 28.500 28.575 28.971 29.000 29.367 29.500 29.766 30.000 30.162 30.500 30.559 30.958 31.000 31.354 31.500

Flute Length F Inch mm 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 63⁄8 63⁄8 63⁄8 63⁄8 63⁄8 63⁄8 63⁄8 61⁄2 61⁄2 61⁄2 61⁄2 65⁄8 65⁄8 65⁄8 65⁄8 67⁄8 67⁄8 67⁄8 71⁄8 71⁄8 71⁄8 71⁄8 71⁄4 71⁄4 71⁄4 73⁄8 73⁄8 73⁄8 73⁄8 71⁄2 71⁄2 71⁄2 77⁄8 77⁄8 77⁄8

156 156 156 156 156 156 156 156 156 156 156 156 156 156 156 156 156 156 162 162 162 162 162 162 162 165 165 165 165 168 168 168 168 175 175 175 181 181 181 181 184 184 184 187 187 187 187 190 190 190 200 200 200

Overall Length L Inch mm 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 103⁄4 103⁄4 103⁄4 11 11 11 11 11 11 11 111⁄8 111⁄8 111⁄8 111⁄8 111⁄4 111⁄4 111⁄4 111⁄4 111⁄2 111⁄2 111⁄2 113⁄4 113⁄4 113⁄4 113⁄4 117⁄8 117⁄8 117⁄8 12 12 12 12 121⁄8 121⁄8 121⁄8 121⁄2 121⁄2 121⁄2

254 254 254 254 254 254 254 254 254 254 254 254 254 254 254 273 273 273 279 279 279 279 279 279 279 282 282 282 282 286 286 286 286 292 292 292 298 298 298 298 301 301 301 305 305 305 305 308 308 308 317 317 317

Length of Body B Inch mm 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 61⁄2 61⁄2 61⁄2 61⁄2 61⁄2 61⁄2 61⁄2 65⁄8 65⁄8 65⁄8 65⁄8 63⁄4 63⁄4 63⁄4 63⁄4 7 7 7 71⁄4 71⁄4 71⁄4 71⁄4 73⁄8 73⁄8 73⁄8 71⁄2 71⁄2 71⁄2 71⁄2 75⁄8 75⁄8 75⁄8 8 8 8

159 159 159 159 159 159 159 159 159 159 159 159 159 159 159 159 159 159 165 165 165 165 165 165 165 168 168 168 168 172 172 172 172 178 178 178 184 184 184 184 187 187 187 191 191 191 191 194 194 194 203 203 203

Minimum Length of Shk. S Inch mm 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8 37⁄8

79 79 79 79 79 79 79 79 79 79 79 79 79 79 79 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98 98


Maximum Length ofNeck N Inch mm 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16


TWIST DRILLS

Table 2. (Continued) ANSI Straight Shank Twist Drills — Taper Length — Over 1⁄2 in. (12.7 mm) Dia., Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Diameter of Drill D Frac.

mm

11⁄4 32.00 32.50 19⁄32 33.00 15⁄16 33.50 34.00 111⁄32 34.50 13⁄8 35.00 35.50 113⁄32 36.00 36.50 17⁄16 37.00 115⁄32 37.50 38.00 11⁄2 19⁄16 15⁄8 13⁄4

Decimal Inch Equiv.

Millimeter Equiv.

1.2500 1.2598 1.2795 1.2812 1.2992 1.3125 1.3189 1.3386 1.3438 1.3583 1.3750 1.3780 1.3976 1.4062 1.4173 1.4370 1.4375 1.4567 1.4688 1.4764 1.4961 1.5000 1.5625 1.6250 1.7500

31.750 32.000 32.500 32.542 33.000 33.338 33.500 34.000 34.133 34.500 34.925 35.000 35.500 35.717 36.000 36.500 36.512 37.000 37.308 37.500 38.000 38.100 39.688 41.275 44.450

Flute Length F Inch mm 77⁄8 81⁄2 81⁄2 81⁄2 85⁄8 85⁄8 83⁄4 83⁄4 83⁄4 87⁄8 87⁄8 9 9 9 91⁄8 91⁄8 91⁄8 91⁄4 91⁄4 93⁄8 93⁄8 93⁄8 95⁄8 97⁄8 101⁄2

200 216 216 216 219 219 222 222 222 225 225 229 229 229 232 232 232 235 235 238 238 238 244 251 267

Overall Length L Inch mm 121⁄2 141⁄8 141⁄8 141⁄8 141⁄4 141⁄4 143⁄8 143⁄8 143⁄8 141⁄2 141⁄2 145⁄8 145⁄8 145⁄8 143⁄4 143⁄4 143⁄4 147⁄8 147⁄8 15 15 15

317 359 359 359 362 362 365 365 365 368 368 372 372 372 375 375 375 378 378 381 381 381 387 397 413

151⁄4 155⁄8 161⁄4

Length of Body B Inch mm 8 85⁄8 85⁄8 85⁄8 83⁄4 83⁄4 87⁄8 87⁄8 87⁄8 9 9 91⁄8 91⁄8 91⁄8 91⁄4 91⁄4 91⁄4 93⁄8 93⁄8 91⁄2 91⁄2 91⁄2 93⁄4 10 105⁄8

203 219 219 219 222 222 225 225 225 229 229 232 232 232 235 235 235 238 238 241 241 241 247 254 270

Minimum Length of Shk. S Inch mm 37⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8 47⁄8

Maximum Length ofNeck N Inch mm 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

98 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124 124

16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 16 19 19

Table 3. American National Standard Tangs for Straight Shank Drills ANSI/ASME B94.11M-1993 Nominal Diameter of Drill Shank, A Inches 1⁄ thru 3⁄ 8 16 over 3⁄16 thru 1⁄4 over 1⁄4 thru 5⁄16 over 5⁄16 thru 3⁄8 over 3⁄8 thru 15⁄32 over 15⁄32 thru 9⁄16 over 9⁄16 thru 21⁄32 over 21⁄32 thru 3⁄4 over 3⁄4 thru 7⁄8 over 7⁄8 thru 1 over 1 thru 13⁄16 over 13⁄16 thru 13⁄8

Thickness of Tang, J Inches Millimeters Min. Max. Min.

Millimeters

Max.

3.18 thru 4.76

0.094

0.090

2.39

2.29

over 4.76 thru 6.35

0.122

0.118

3.10

3.00

over 6.35 thru 7.94

0.162

0.158

4.11

4.01

over 7.94 thru 9.53

0.203

0.199

5.16

5.06

over 9.53 thru 11.91

0.243

0.239

6.17

6.07

over 11.91 thru 14.29

0.303

0.297

7.70

7.55

over 14.29 thru 16.67

0.373

0.367

9.47

9.32

over 16.67 thru 19.05

0.443

0.437

11.25

11.10

over 19.05 thru 22.23

0.514

0.508

13.05

12.90

over 22.23 thru 25.40

0.609

0.601

15.47

15.27

over 25.40 thru 30.16

0.700

0.692

17.78

17.58

over 30.16 thru 34.93

0.817

0.809

20.75

20.55

To fit split sleeve collet type drill drivers. See page 878.


Length of Tang, K Inches 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8

Millimeters 7.0 8.0 8.5 9.5 11.0 12.5 14.5 16.0 17.5 19.0 20.5 22.0


867

Table 4. American National Standard Straight Shank Twist Drills — Screw Machine Length — Over 1 in. (25.4 mm) Dia. ANSI/ASME B94.11M-1993

Diameter of Drill D Frac.

mm

Decimal Inch Equivalent

Millimeter Equivalent

25.50

1.0039

26.00 11⁄16 28.00 11⁄8

Flute Length

Overall Length

F

L

Shank Diameter A

Inch

mm

Inch

mm

Inch

mm

25.500

4

102

6

152

0.9843

25.00

1.0236

26.000

4

102

6

152

0.9843

25.00

1.0625

26.988

4

102

6

152

1.0000

25.40

1.1024

28.000

4

102

6

152

0.9843

25.00

1.1250

28.575

4

102

6

152

1.0000

25.40

1.1811

30.000

41⁄4

108

65⁄8

168

0.9843

25.00

13⁄16

1.1875

30.162

41⁄4

108

65⁄8

168

1.0000

25.40

11⁄4

1.2500

31.750

43⁄8

111

63⁄4

171

1.0000

25.40

32.00

1.2598

32.000

43⁄8

111

7

178

1.2402

31.50

1.3125

33.338

43⁄8

111

7

178

1.2500

31.75

34.00

1.3386

34.000

41⁄2

114

71⁄8

181

1.2402

31.50

1.3750

34.925

41⁄2

114

71⁄8

181

1.2500

31.75

1.4173

36.000

43⁄4

121

73⁄8

187

1.2402

31.50

1.4375

36.512

43⁄4

121

73⁄8

187

1.2500

31.75

1.4961

38.000

47⁄8

124

71⁄2

190

1.2402

31.50

11⁄2

1.5000

38.100

47⁄8

124

71⁄2

190

1.2500

31.75

19⁄16

1.5625

39.688

47⁄8

124

73⁄4

197

1.5000

38.10

1.5748

40.000

47⁄8

124

73⁄4

197

1.4961

38.00

1.6250

41.275

47⁄8

124

73⁄4

197

1.5000

38.10

42.00

1.6535

42.000

51⁄8

130

8

203

1.4961

38.00

1.6875

42.862

51⁄8

130

8

203

1.5000

38.10

44.00

1.7323

44.000

51⁄8

130

8

203

1.4961

38.00

1.7500

44.450

51⁄8

130

8

203

1.5000

38.10

1.8110

46.000

53⁄8

137

81⁄4

210

1.4961

38.00

113⁄16

1.8125

46.038

53⁄8

137

81⁄4

210

1.5000

38.10

17⁄8

1.8750

47.625

53⁄8

137

81⁄4

210

1.5000

38.10

1.8898

48.000

55⁄8

143

81⁄2

216

1.4961

38.00

1.9375

49.212

55⁄8

143

81⁄2

216

1.5000

38.10

1.9685

50.000

55⁄8

143

81⁄2

216

1.4961

38.00

2.0000

50.800

55⁄8

143

81⁄2

216

1.5000

38.10

30.00

15⁄16

13⁄8 36.00 17⁄16 38.00

40.00 15⁄8

111⁄16

13⁄4 46.00

48.00 115⁄16 50.00 2



TWIST DRILLS

Table 5. American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent Fraction

mm 3.00

1⁄ 8

3.20 3.50 9⁄ 64

3.80 5⁄ 32

4.00 4.20 11⁄ 64

4.50 3⁄ 16

4.80 5.00 13⁄ 64

5.20 5.50 7⁄ 32

5.80 15⁄ 64

6.00 6.20 1⁄ 4

6.50 17⁄ 64

6.80 7.00 9⁄ 32

7.20 7.50 19⁄ 64

7.80 5⁄ 16

8.00 8.20 21⁄ 64

8.50 11⁄ 32

8.80 9.00 23⁄ 64

9.20 9.50 3⁄ 8

9.80 25⁄ 64

10.00

Decimal Inch 0.1181 0.1250 0.1260 0.1378 0.1406 0.1496 0.1562 0.1575 0.1654 0.1719 0.1772 0.1875 0.1890 0.1969 0.2031 0.2047 0.2165 0.2183 0.2223 0.2344 0.2362 0.2441 0.2500 0.2559 0.2656 0.2677 0.2756 0.2812 0.2835 0.2953 0.2969 0.3071 0.3125 0.3150 0.3228 0.3281 0.3346 0.3438 0.3465 0.3543 0.3594 0.3622 0.3740 0.3750 0.3858 0.3906 0.3937

mm 3.000 3.175 3.200 3.500 3.571 3.800 3.967 4.000 4.200 4.366 4.500 4.762 4.800 5.000 5.159 5.200 5.500 5.558 5.800 5.954 6.000 6.200 6.350 6.500 6.746 6.800 7.000 7.142 7.200 7.500 7.541 7.800 7.938 8.000 8.200 8.334 8.500 8.733 8.800 9.000 9.129 9.200 9.500 9.525 9.800 9.921 10.000

Morse Taper No. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Regular Shank Flute Length Overall Length F L Inch mm Inch mm 7 1 48 130 1 ⁄8 5 ⁄8 48 130 17⁄8 51⁄8 54 137 53⁄8 21⁄8 54 137 53⁄8 21⁄8 1 3 54 137 2 ⁄8 5 ⁄8 54 137 53⁄8 21⁄8 54 137 21⁄8 53⁄8 64 146 53⁄4 21⁄2 1 3 64 146 5 ⁄4 2 ⁄2 1 3 64 146 2 ⁄2 5 ⁄4 64 146 53⁄4 21⁄2 64 146 21⁄2 53⁄4 70 6 152 23⁄4 3 70 6 152 2 ⁄4 70 6 152 23⁄4 70 6 152 23⁄4 70 6 152 23⁄4 70 6 152 23⁄4 7 1 73 156 6 ⁄8 2 ⁄8 73 156 27⁄8 61⁄8 73 156 61⁄8 27⁄8 73 156 61⁄8 27⁄8 7 1 73 156 2 ⁄8 6 ⁄8 1 159 3 76 6 ⁄4 3 76 159 61⁄4 159 3 76 61⁄4 159 3 76 61⁄4 1 3 76 159 6 ⁄4 1 3 79 162 6 ⁄8 3 ⁄8 79 162 63⁄8 31⁄8 79 162 31⁄8 63⁄8 79 162 63⁄8 31⁄8 1 3 79 162 3 ⁄8 6 ⁄8 1 1 83 165 6 ⁄2 3 ⁄4 83 165 61⁄2 31⁄4 83 165 31⁄4 61⁄2 83 165 61⁄2 31⁄4 1 1 83 165 3 ⁄4 6 ⁄2 89 171 63⁄4 31⁄2 89 171 63⁄4 31⁄2 89 171 31⁄2 63⁄4 1 3 89 171 6 ⁄4 3 ⁄2 1 3 89 171 6 ⁄4 3 ⁄2 89 171 31⁄2 63⁄4 92 7 178 35⁄8 92 7 178 35⁄8 92 7 178 35⁄8

Morse Taper No. … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 2 … 2 …

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 89 187 31⁄2 73⁄8 … … … … 92 190 35⁄8 71⁄2 … … … …



869

Table 5. (Continued) American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent Fraction

mm 10.20

13⁄ 32

10.50 27⁄ 64

10.80 11.00 7⁄ 16

11.20 11.50 29⁄ 64

11.80 15⁄ 32

12.00 12.20 31⁄ 64

12.50 1⁄ 2

12.80 13.00 33⁄ 64

13.20 17⁄ 32

13.50 13.80 35⁄ 64

14.00 14.25 9⁄ 16

14.50 37⁄ 64

14.75 15.00 19⁄ 32

15.25 39⁄ 64

15.50 15.75 5⁄ 8

16.00 16.25 41⁄ 64

16.50 21⁄ 32

16.75 17.00 43⁄ 64

17.25 11⁄ 16

17.50 45⁄ 64

18.00 23⁄ 32

18.50 47⁄ 64

Decimal Inch 0.4016 0.4062 0.4134 0.4219 0.4252 0.4331 0.4375 0.4409 0.4528 0.4531 0.4646 0.4688 0.4724 0.4803 0.4844 0.4921 0.5000 0.5034 0.5118 0.5156 0.5197 0.5312 0.5315 0.5433 0.5469 0.5572 0.5610 0.5625 0.5709 0.5781 0.5807 0.5906 0.5938 0.6004 0.6094 0.6102 0.6201 0.6250 0.6299 0.6398 0.6406 0.6496 0.6562 0.6594 0.6693 0.6719 0.6791 0.6875 0.6880 0.7031 0.7087 0.7188 0.7283 0.7344

mm 10.200 10.320 10.500 10.716 10.800 11.000 11.112 11.200 11.500 11.509 11.800 11.906 12.000 12.200 12.304 12.500 12.700 12.800 13.000 13.096 13.200 13.492 13.500 13.800 13.891 14.000 14.250 14.288 14.500 14.684 14.750 15.000 15.083 15.250 15.479 15.500 15.750 15.875 16.000 16.250 16.271 16.500 16.667 16.750 17.000 17.066 17.250 17.462 17.500 17.859 18.000 18.258 18.500 18.654

Morse Taper No. 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

Regular Shank Flute Length Overall Length F L Inch mm Inch mm 35⁄8 92 7 178 92 7 178 35⁄8 7 1 98 184 7 ⁄4 3 ⁄8 7 1 98 184 3 ⁄8 7 ⁄4 98 184 71⁄4 37⁄8 98 184 71⁄4 37⁄8 98 184 37⁄8 71⁄4 1 1 105 190 7 ⁄2 4 ⁄8 1 1 105 190 7 ⁄2 4 ⁄8 105 190 41⁄8 71⁄2 105 190 71⁄2 41⁄8 105 190 41⁄8 71⁄2 3 1 111 210 8 ⁄4 4 ⁄8 111 210 81⁄4 43⁄8 111 210 43⁄8 81⁄4 111 210 81⁄4 43⁄8 3 1 111 210 4 ⁄8 8 ⁄4 5 1 117 216 8 ⁄2 4 ⁄8 117 216 81⁄2 45⁄8 117 216 45⁄8 81⁄2 117 216 81⁄2 45⁄8 5 1 117 216 4 ⁄8 8 ⁄2 5 1 117 216 8 ⁄2 4 ⁄8 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 124 222 83⁄4 47⁄8 7 3 124 222 8 ⁄4 4 ⁄8 7 3 124 222 4 ⁄8 8 ⁄4 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 124 222 83⁄4 47⁄8 7 3 124 222 8 ⁄4 4 ⁄8 124 222 47⁄8 83⁄4 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 7 3 124 222 8 ⁄4 4 ⁄8 7 3 124 222 8 ⁄4 4 ⁄8 124 222 47⁄8 83⁄4 130 9 229 51⁄8 130 9 229 51⁄8 1 130 9 229 5 ⁄8 1 130 9 229 5 ⁄8 130 9 229 51⁄8 137 235 91⁄4 53⁄8 137 235 91⁄4 53⁄8 137 235 53⁄8 91⁄4 137 235 91⁄4 53⁄8 137 235 53⁄8 91⁄4 143 241 91⁄2 55⁄8 5 1 143 241 5 ⁄8 9 ⁄2 5 1 143 241 9 ⁄2 5 ⁄8 143 241 55⁄8 91⁄2 149 248 93⁄4 57⁄8 149 248 57⁄8 93⁄4

Morse Taper No. … 2 … 2 … … 2 … … 2 … 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 … … … … … … … … … … … … 3 … 3 … … 3 … 3 … 3 … 3 … 3

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm … … … … 92 190 35⁄8 71⁄2 … … … … 98 197 37⁄8 73⁄4 … … … … … … … … 98 197 37⁄8 73⁄4 … … … … … … … … 105 8 203 41⁄8 … … … … 105 8 203 41⁄8 3 3 111 197 4 ⁄8 7 ⁄4 111 197 43⁄8 73⁄4 111 197 43⁄8 73⁄4 111 197 43⁄8 73⁄4 3 3 111 197 4 ⁄8 7 ⁄4 5 117 8 203 4 ⁄8 117 8 203 45⁄8 117 8 203 45⁄8 117 8 203 45⁄8 5 117 8 203 4 ⁄8 5 117 8 203 4 ⁄8 124 210 47⁄8 81⁄4 124 210 47⁄8 81⁄4 124 210 47⁄8 81⁄4 7 1 124 210 4 ⁄8 8 ⁄4 7 1 124 210 4 ⁄8 8 ⁄4 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 130 248 51⁄8 93⁄4 … … … … 130 248 51⁄8 93⁄4 … … … … … … … … 3 137 10 254 5 ⁄8 … … … … 137 10 254 53⁄8 … … … … 143 260 55⁄8 101⁄4 … … … … 143 260 55⁄8 101⁄4 … … … … 149 267 57⁄8 101⁄2



TWIST DRILLS Table 5. (Continued) American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent

Fraction

mm 19.00

3⁄ 4 49⁄ 64

19.50 25⁄ 32

20.00 51⁄ 64

20.50 13⁄ 16

21.00 53⁄ 64 27⁄ 32

21.50 55⁄ 64

22.00 7⁄ 8

22.50 57⁄ 64

23.00 29⁄ 32 59⁄ 64

23.50 15⁄ 16

24.00 61⁄ 64

24.50 31⁄ 32

25.00 63⁄ 64

1 25.50 11⁄64 26.00 11⁄32 26.50 13⁄64 11⁄16 27.00 15⁄64 27.50 13⁄32 28.00 17⁄64 28.50 11⁄8 19⁄64 29.00 15⁄32 29.50 111⁄64 30.00 13⁄16 30.50 113⁄64

Decimal Inch 0.7480 0.7500 0.7656 0.7677 0.7812 0.7821 0.7969 0.8071 0.8125 0.8268 0.8281 0.8438 0.8465 0.8594 0.8661 0.8750 0.8858 0.8906 0.9055 0.9062 0.9219 0.9252 0.9375 0.9449 0.9531 0.9646 0.9688 0.9843 0.9844 1.0000 1.0039 1.0156 1.0236 1.0312 1.0433 1.0469 1.0625 1.0630 1.0781 1.0827 1.0938 1.1024 1.1094 1.1220 1.1250 1.1406 1.1417 1.1562 1.1614 1.1719 1.1811 1.1875 1.2008 1.2031

mm 19.000 19.050 19.446 19.500 19.843 20.000 20.241 20.500 20.638 21.000 21.034 21.433 21.500 21.829 22.000 22.225 22.500 22.621 23.000 23.017 23.416 23.500 23.813 24.000 24.209 24.500 24.608 25.000 25.004 25.400 25.500 25.796 26.000 26.192 26.500 26.591 26.988 27.000 27.384 27.500 27.783 28.000 28.179 28.500 28.575 28.971 29.000 29.367 29.500 29.797 30.000 30.162 30.500 30.559

Morse Taper No. 2 2 2 2 2 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

Regular Shank Flute Length Overall Length F L Inch mm Inch mm 57⁄8 93⁄4 149 248 149 248 57⁄8 93⁄4 7 6 152 251 9 ⁄8 7 251 6 152 9 ⁄8 6 152 251 97⁄8 156 273 103⁄4 61⁄8 156 273 61⁄8 103⁄4 1 3 156 273 10 ⁄4 6 ⁄8 1 3 156 273 6 ⁄8 10 ⁄4 156 273 103⁄4 61⁄8 156 273 61⁄8 103⁄4 156 273 61⁄8 103⁄4 1 3 156 273 10 ⁄4 6 ⁄8 156 273 61⁄8 103⁄4 156 273 103⁄4 61⁄8 156 273 61⁄8 103⁄4 1 3 156 273 10 ⁄4 6 ⁄8 1 3 156 273 6 ⁄8 10 ⁄4 156 273 103⁄4 61⁄8 156 273 61⁄8 103⁄4 156 273 61⁄8 103⁄4 1 3 156 273 10 ⁄4 6 ⁄8 1 3 156 273 6 ⁄8 10 ⁄4 162 11 279 63⁄8 162 11 279 63⁄8 162 11 279 63⁄8 3 162 11 279 6 ⁄8 3 162 11 279 6 ⁄8 162 11 279 63⁄8 162 11 279 63⁄8 165 283 111⁄8 61⁄2 1 1 165 283 6 ⁄2 11 ⁄8 165 283 111⁄8 61⁄2 165 283 61⁄2 111⁄8 168 286 111⁄4 65⁄8 5 1 168 286 6 ⁄8 11 ⁄4 5 1 168 286 6 ⁄8 11 ⁄4 168 286 111⁄4 65⁄8 175 318 67⁄8 121⁄2 175 318 121⁄2 67⁄8 7 1 175 318 6 ⁄8 12 ⁄2 1 3 181 324 12 ⁄4 7 ⁄8 181 324 71⁄8 123⁄4 181 324 123⁄4 71⁄8 181 324 71⁄8 123⁄4 1 7 184 327 7 ⁄4 12 ⁄8 184 327 127⁄8 71⁄4 184 327 71⁄4 127⁄8 187 13 330 73⁄8 3 187 13 330 7 ⁄8 187 13 330 73⁄8 187 13 330 73⁄8 190 333 131⁄8 71⁄2 190 333 71⁄2 131⁄8

Morse Taper No. … 3 3 … 3 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 … … … … … … … … … 4 … … … 4 … … 4 … 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm … … … … 149 267 57⁄8 101⁄2 5 6 152 270 10 ⁄8 … … … … 6 152 270 105⁄8 156 10 254 61⁄8 156 10 254 61⁄8 1 156 10 254 6 ⁄8 1 156 10 254 6 ⁄8 156 10 254 61⁄8 156 10 254 61⁄8 156 10 254 61⁄8 1 156 10 254 6 ⁄8 156 10 254 61⁄8 156 10 254 61⁄8 156 10 254 61⁄8 1 156 10 254 6 ⁄8 1 156 10 254 6 ⁄8 156 10 254 61⁄8 156 10 254 61⁄8 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 162 12 305 63⁄8 … … … … … … … … … … … … 165 308 61⁄2 121⁄8 … … … … … … … … 5 1 168 311 6 ⁄8 12 ⁄4 … … … … 175 292 67⁄8 111⁄2 175 292 67⁄8 111⁄2 175 292 67⁄8 111⁄2 1 3 181 298 7 ⁄8 11 ⁄4 181 298 71⁄8 113⁄4 181 298 71⁄8 113⁄4 181 298 71⁄8 113⁄4 1 7 184 302 7 ⁄4 11 ⁄8 184 302 71⁄4 117⁄8 184 302 71⁄4 117⁄8 187 12 305 73⁄8 3 187 12 305 7 ⁄8 187 12 305 73⁄8 187 12 305 73⁄8 190 308 71⁄2 121⁄8 190 308 71⁄2 121⁄8



871

Table 5. (Continued) American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent Fraction 17⁄32

mm 31.00

115⁄64 31.50 11⁄4 32.00 117⁄64 32.50 19⁄32 119⁄64 33.00 15⁄16 33.50 121⁄64 34.00 111⁄32 34.50 123⁄64 13⁄8 35.00 125⁄64 35.50 113⁄32 36.00 127⁄64 36.50 17⁄16 129⁄64 37.00 115⁄32 37.50 131⁄64 38.00 11⁄2 133⁄64 117⁄32 39.00 135⁄64 19⁄16 40.00 137⁄64 119⁄32 139⁄64 41.00 15⁄8 141⁄64 42.00 121⁄32 143⁄64 111⁄16 43.00 145⁄64 123⁄32 44.00

Decimal Inch 1.2188 1.2205 1.2344 1.2402 1.2500 1.2598 1.2656 1.2795 1.2812 1.2969 1.2992 1.3125 1.3189 1.3281 1.3386 1.3438 1.3583 1.3594 1.3750 1.3780 1.3906 1.3976 1.4062 1.4173 1.4219 1.4370 1.4375 1.4531 1.4567 1.4688 1.4764 1.4844 1.4961 1.5000 1.5156 1.5312 1.5354 1.5469 1.5625 1.5748 1.5781 1.5938 1.6094 1.6142 1.6250 1.6406 1.6535 1.6562 1.6719 1.6875 1.6929 1.7031 1.7188 1.7323

mm 30.958 31.000 31.354 31.500 31.750 32.000 32.146 32.500 32.542 32.941 33.000 33.338 33.500 33.734 34.000 34.133 34.500 34.529 34.925 35.000 35.321 35.500 35.717 36.000 36.116 36.500 36.512 36.909 37.000 37.308 37.500 37.704 38.000 38.100 38.496 38.892 39.000 39.291 39.688 40.000 40.084 40.483 40.879 41.000 41.275 41.671 42.000 42.067 42.466 42.862 43.000 43.259 43.658 44.000

Morse Taper No. 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 … 5 5 … 5 5 … 5 … 5 5 … 5 5 … 5 5 … 5 5

Regular Shank Flute Length Overall Length F L Inch mm Inch mm 71⁄2 131⁄8 190 333 200 343 131⁄2 77⁄8 7 1 200 343 7 ⁄8 13 ⁄2 7 1 200 343 13 ⁄2 7 ⁄8 200 343 77⁄8 131⁄2 216 359 141⁄8 81⁄2 216 359 81⁄2 141⁄8 1 1 216 359 14 ⁄8 8 ⁄2 1 1 216 359 8 ⁄2 14 ⁄8 219 362 85⁄8 141⁄4 219 362 141⁄4 85⁄8 219 362 85⁄8 141⁄4 3 3 222 365 14 ⁄8 8 ⁄4 222 365 83⁄4 143⁄8 222 365 143⁄8 83⁄4 222 365 83⁄4 143⁄8 7 1 225 368 14 ⁄2 8 ⁄8 7 1 225 368 8 ⁄8 14 ⁄2 225 368 87⁄8 141⁄2 371 9 229 145⁄8 9 229 371 145⁄8 5 371 9 229 14 ⁄8 5 9 229 371 14 ⁄8 232 375 143⁄4 91⁄8 232 375 91⁄8 143⁄4 232 375 143⁄4 91⁄8 1 3 232 375 9 ⁄8 14 ⁄4 1 7 235 378 9 ⁄4 14 ⁄8 235 378 147⁄8 91⁄4 235 378 91⁄4 147⁄8 238 15 381 93⁄8 3 238 15 381 9 ⁄8 238 15 381 93⁄8 238 15 381 93⁄8 … … … … 3 3 238 416 9 ⁄8 16 ⁄8 5 5 244 422 16 ⁄8 9 ⁄8 … … … … 244 422 95⁄8 165⁄8 251 429 167⁄8 97⁄8 … … … … 7 7 251 429 9 ⁄8 16 ⁄8 … … … … 10 254 17 432 10 254 17 432 … … … … 257 435 171⁄8 101⁄8 257 435 101⁄8 171⁄8 … … … … 257 435 101⁄8 171⁄8 1 1 257 435 17 ⁄8 10 ⁄8 … … … … 257 435 101⁄8 171⁄8 257 435 171⁄8 101⁄8

Morse Taper No. 3 3 3 3 3 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm 71⁄2 121⁄8 190 308 200 318 77⁄8 121⁄2 7 1 200 318 7 ⁄8 12 ⁄2 7 1 200 318 7 ⁄8 12 ⁄2 200 318 77⁄8 121⁄2 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 238 15 381 93⁄4 3 238 15 381 9 ⁄8 244 387 95⁄8 151⁄4 244 387 95⁄8 151⁄4 244 387 95⁄8 151⁄4 251 394 97⁄8 151⁄2 7 1 251 394 9 ⁄8 15 ⁄2 7 1 251 394 9 ⁄8 15 ⁄2 10 254 397 155⁄8 397 10 254 155⁄8 10 254 397 155⁄8 1 3 257 400 10 ⁄8 15 ⁄4 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 1 3 257 400 10 ⁄8 15 ⁄4 1 3 257 400 10 ⁄8 15 ⁄4 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 264 413 103⁄8 161⁄4



TWIST DRILLS Table 5. (Continued) American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent

Fraction 147⁄64 13⁄4

mm

45.00 125⁄32 46.00 113⁄16 127⁄32 47.00 17⁄8 48.00 129⁄32 49.00 115⁄16 50.00 131⁄32 2 51.00 21⁄32 52.00 21⁄16 53.00 23⁄32 21⁄8 54.00 25⁄32 55.00 23⁄16 56.00 27⁄32 57.00 21⁄4 58.00 25⁄16 59.00 60.00 23⁄8 61.00 27⁄16 62.00 63.00 21⁄2 64.00 65.00 29⁄16 66.00 25⁄8 67.00 68.00 211⁄16 69.00 23⁄4 70.00 71.00 213⁄16

Decimal Inch 1.7344 1.7500 1.7717 1.7812 1.8110 1.8125 1.8438 1.8504 1.8750 1.8898 1.9062 1.9291 1.9375 1.9625 1.9688 2.0000 2.0079 2.0312 2.0472 2.0625 2.0866 2.0938 2.1250 2.1260 2.1562 2.1654 2.1875 2.2000 2.2188 2.2441 2.2500 2.2835 2.3125 2.3228 2.3622 2.3750 2.4016 2.4375 2.4409 2.4803 2.5000 2.5197 2.5591 2.5625 2.5984 2.6250 2.6378 2.6772 2.6875 2.7165 2.7500 2.7559 2.7953 2.8125

mm 44.054 44.450 45.000 45.242 46.000 46.038 46.833 47.000 47.625 48.000 48.417 49.000 49.212 50.000 50.008 50.800 51.000 51.592 52.000 52.388 53.000 53.183 53.975 54.000 54.767 55.000 55.563 56.000 56.358 57.000 57.150 58.000 58.738 59.000 60.000 60.325 61.000 61.912 62.000 63.000 63.500 64.000 65.000 65.088 66.000 66.675 67.000 68.000 68.262 69.000 69.850 70.000 71.000 71.438

Morse Taper No. … 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5

Regular Shank Flute Length Overall Length F L Inch mm Inch mm … … … … 257 435 101⁄8 171⁄8 1 1 257 435 17 ⁄8 10 ⁄8 257 435 101⁄8 171⁄8 257 435 171⁄8 101⁄8 257 435 101⁄8 171⁄8 257 435 101⁄8 171⁄8 3 3 264 441 17 ⁄8 10 ⁄8 3 3 264 441 10 ⁄8 17 ⁄8 264 441 173⁄8 103⁄8 264 441 103⁄8 173⁄8 264 441 173⁄8 103⁄8 3 3 264 441 10 ⁄8 17 ⁄8 264 441 173⁄8 103⁄8 264 441 103⁄8 173⁄8 264 441 173⁄8 103⁄8 3 3 264 441 17 ⁄8 10 ⁄8 3 3 264 441 10 ⁄8 17 ⁄8 260 441 173⁄8 101⁄4 260 441 101⁄4 173⁄8 260 441 173⁄8 101⁄4 1 3 260 441 10 ⁄4 17 ⁄8 1 3 260 441 10 ⁄4 17 ⁄8 260 441 173⁄8 101⁄4 260 441 101⁄4 173⁄8 260 441 173⁄8 101⁄4 1 3 260 441 10 ⁄4 17 ⁄4 1 3 257 441 17 ⁄8 10 ⁄8 257 441 101⁄8 173⁄8 257 441 173⁄8 101⁄8 257 441 101⁄8 173⁄8 1 3 257 441 17 ⁄8 10 ⁄8 257 441 101⁄8 173⁄8 257 441 173⁄8 101⁄8 257 441 173⁄8 101⁄8 1 3 257 441 10 ⁄8 17 ⁄8 1 3 286 476 18 ⁄4 11 ⁄4 286 476 111⁄4 183⁄4 286 476 183⁄4 111⁄4 286 476 183⁄4 111⁄4 1 3 286 476 11 ⁄4 18 ⁄4 7 1 302 495 19 ⁄2 11 ⁄8 302 495 191⁄2 117⁄8 302 495 117⁄8 191⁄2 302 495 191⁄2 117⁄8 7 1 302 495 11 ⁄8 19 ⁄2 324 518 203⁄8 123⁄4 324 518 203⁄8 123⁄4 324 518 123⁄4 203⁄8 3 3 324 518 20 ⁄8 12 ⁄4 3 3 324 518 12 ⁄4 20 ⁄8 340 537 211⁄8 133⁄8 340 537 211⁄8 133⁄8 340 537 133⁄8 211⁄8

Morse Taper No. 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm 103⁄8 161⁄4 264 413 264 413 103⁄4 161⁄4 3 1 264 413 10 ⁄8 16 ⁄4 3 1 264 413 10 ⁄8 16 ⁄4 264 413 103⁄8 161⁄4 264 413 103⁄8 161⁄4 264 413 103⁄8 161⁄4 1 1 267 419 10 ⁄2 16 ⁄2 1 1 267 419 10 ⁄2 16 ⁄2 267 419 101⁄2 161⁄2 267 419 101⁄2 161⁄2 270 422 105⁄8 165⁄8 5 5 270 422 10 ⁄8 16 ⁄8 270 422 105⁄8 165⁄8 270 422 105⁄8 165⁄8 270 422 105⁄8 165⁄8 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …



873

Table 5. (Continued) American National Taper Shank Twist Drills Fractional and Metric Sizes ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent Fraction

mm 72.00 73.00

27⁄8 74.00 215⁄16 75.00 76.00 3 77.00 78.00 31⁄8 31⁄4 31⁄2

Decimal Inch

mm

2.8346 2.8740 2.8750 2.9134 2.9375 2.9528 2.9921 3.0000 3.0315 3.0709 3.1250 3.2500 3.5000

72.000 73.000 73.025 74.000 74.612 75.000 76.000 76.200 77.000 78.000 79.375 82.550 88.900

Morse Taper No. 5 5 5 5 5 5 5 5 6 6 6 6 …

Regular Shank Flute Length Overall Length F L Inch mm Inch mm 133⁄8 133⁄8 133⁄8 14 14 14 14 14 145⁄8 145⁄8 145⁄8 151⁄2 …

340 211⁄8 340 211⁄8 340 211⁄8 356 213⁄4 356 213⁄4 356 213⁄4 356 213⁄4 356 213⁄4 371 241⁄2 371 241⁄2 371 241⁄2 394 251⁄2 … …

Morse Taper No. … … … … … … … … 5 5 5 5 5

537 537 537 552 552 552 552 552 622 622 622 648 …

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm … … … … … … … … 141⁄4 141⁄4 141⁄4 151⁄4 161⁄4

… … … … … … … … 362 362 362 387 413

… … … … … … … … 22 22 22 23 24

… … … … … … … … 559 559 559 584 610

a Larger or smaller than regular shank.

Table 6. American National Standard Combined Drills and Countersinks — Plain and Bell Types ANSI/ASME B94.11M-1993 BELL TYPE

PLAIN TYPE

Size Designation

Body Diameter A Inches Millimeters 1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

00 0 1 2 3 4 5 6 7 8

Plain Type Drill Diameter D Inches Millimeters

3.18 3.18 3.18 4.76 6.35 7.94 11.11 12.70 15.88 19.05

.025 1⁄ 32 3⁄ 64 5⁄ 64 7⁄ 64 1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16

Drill Length C Millimeters

Inches

0.64 0.79 1.19 1.98 2.78 3.18 4.76 5.56 6.35 7.94

.030 .038

11⁄8 11⁄8 11⁄4 17⁄8 2

0.76 0.97 1.19 1.98 2.78 3.18 4.76 5.56 6.35 7.94

3⁄ 64 5⁄ 64 7⁄ 64 1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16

Overall Length L Millimeters

Inches

29 29 32 48 51 54 70 76 83 89

21⁄8 23⁄4 3 31⁄4 31⁄2

Bell Type

Size Designation 11 12 13 14 15 16 17 18

Body Diameter

Drill Diameter

Bell Diameter

Drill Length

A

D

E

C

Inches 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

mm 3.18 4.76 6.35 7.94 11.11 12.70 15.88 19.05

Overall Length L

Inches

mm

Inches

mm

Inches

mm

Inches

mm

3⁄ 64 1⁄ 16 3⁄ 32 7⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4

1.19

0.10

2.5

1.19

11⁄4

32

1.59

0.15

3.8

1.59

0.20

5.1

2.38

17⁄8 2

48

2.38 2.78

0.25

6.4

3⁄ 64 1⁄ 16 3⁄ 32 7⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4

2.78

21⁄8

54

3.97

23⁄4 3

70

4.76 5.56

31⁄4

83

6.35

31⁄2

89

3.97

0.35

8.9

4.76

0.40

10.2

5.56

0.50

12.7

6.35

0.60

15.2


51

76


TWIST DRILLS

Table 7. American National Standard Three- and Four-Flute Taper Shank Core Drills — Fractional Sizes Only ANSI/ASME B94.11M-1993 Drill Diameter, D Equivalent Inch 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 11⁄ 16 23⁄ 32 3⁄ 4 25⁄ 32 13⁄ 16 27⁄ 32 7⁄ 8 29⁄ 32 15⁄ 16 31⁄ 32

Three-Flute Drills Morse Taper No.

Overall Length

F

L

Decimal Inch

mm

A

Inch

0.2500

6.350

1

0.2812

7.142

1

0.3175

7.938

1

0.3438

8.733

1

0.3750

9.525

1

0.4062

10.319

1

0.4375

11.112

1

0.4688

11.908

1

0.5000

12.700

2

0.5312

13.492

2

0.5625

14.288

2

0.5938

15.083

2

0.6250

15.815

2

0.6562

16.668

2

0.6875

17.462

2

0.7188

18.258

2

0.7500

19.050

2

0.7812

19.842

Four-Flute Drills

Flute Length

Morse Taper No.

Flute Length

Overall Length

F

L

mm

Inch

mm

A

Inch

mm

Inch

mm

27⁄8 3

73

61⁄8

156

…

…

…

…

…

76

159

…

…

…

…

…

31⁄8 31⁄4 31⁄2 35⁄8 37⁄8 41⁄8 43⁄8 45⁄8 47⁄8 47⁄8 47⁄8 51⁄8 53⁄8 55⁄8 57⁄8

79

162

…

…

…

…

…

165

…

…

…

…

…

89

61⁄4 63⁄8 61⁄2 63⁄4

171

…

…

…

…

…

92

7

178

…

…

…

…

…

98

184

…

…

…

…

…

190

…

…

…

…

…

210

2

43⁄8

111

81⁄4

210

216

2

45⁄8

117

81⁄2

216

222

2

47⁄8

124

83⁄4

222

222

2

47⁄8

124

83⁄4

222

124

71⁄4 71⁄2 81⁄4 81⁄2 83⁄4 83⁄4 83⁄4

222

2

47⁄8

124

222

130

9

229

2

51⁄8

130

83⁄4 9

137

91⁄4

235

2

53⁄8

137

91⁄4

235

143

91⁄2

241

2

55⁄8

143

91⁄2

241

149

93⁄4

248

2

93⁄4

248

152

251

57⁄8 6

149 152

156

97⁄8 103⁄4 103⁄4 103⁄4 103⁄4 103⁄4

251

156

97⁄8 103⁄4 103⁄4 103⁄4 103⁄4 103⁄4

162

162

11

279

162

11

279

165

111⁄8

283

168

111⁄4

286

175

121⁄2

318

181

123⁄4

324

184

327

187

127⁄8 13

190

131⁄8

333

200

131⁄2

343

216

141⁄8

359

2

6

0.8125

20.638

3

0.8438

21.433

3

0.8750

22.225

3

0.9062

23.019

3

0.9375

23.812

3

0.9688

24.608

3

1

1.0000

25.400

3

11⁄32

1.0312

26.192

3

11⁄16

1.0625

26.988

3

13⁄32

1.0938

27.783

4

11⁄8

1.1250

28.575

4

15⁄32

1.1562

29.367

4

13⁄16

1.1875

30.162

4

17⁄32

1.2188

30.958

4

11⁄4

1.2500

31.750

4

61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 63⁄8 63⁄8 61⁄2 65⁄8 67⁄8 71⁄8 71⁄4 73⁄8 71⁄2 77⁄8

19⁄32

1.2812

32.542

…

…

83

105 111 117 124 124

156

2

273

3

273

3

273

3

273

3

273

3

11

279

3

162

11

279

3

165

111⁄8

283

3

168

111⁄4

286

3

175

121⁄2

318

4

181

123⁄4

324

4

184

327

4

187

127⁄8 13

330

4

190

131⁄8

333

4

200

131⁄2 …

343

4

…

4

156 156 156

…

61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 63⁄8 63⁄8 61⁄2 65⁄8 67⁄8 71⁄8 71⁄4 73⁄8 71⁄2 77⁄8 81⁄2

156 156 156 156


229

273 273 273 273 273

330


875

Table 7. American National Standard Three- and Four-Flute Taper Shank Core Drills — Fractional Sizes Only ANSI/ASME B94.11M-1993 Drill Diameter, D

Three-Flute Drills

Equivalent Inch 15⁄16

Decimal Inch 1.3125

Morse Taper No.

Four-Flute Drills

Flute Length

Overall Length

F

L

mm 33.338

A …

Inch …

mm …

Inch …

mm …

Morse Taper No.

Flute Length

Overall Length

F

A 4

Inch 85⁄8

111⁄32 13⁄8

1.3438

34.133

…

…

…

…

…

4

1.3750

34.925

…

…

…

…

…

4

83⁄4 87⁄8

113⁄32

1.4062

35.717

…

…

…

…

…

4

9 91⁄8 91⁄4 93⁄8 93⁄8 95⁄8 97⁄8

L mm 219

Inch 141⁄4

mm 362

222

365

225

143⁄8 141⁄2

229

145⁄8

371

232

375

235

143⁄4 147⁄8

238

15

381

238

416

368

17⁄16 115⁄32 11⁄2 117⁄32 19⁄16 119⁄32 15⁄8 121⁄32 111⁄16 123⁄32 13⁄4 125⁄32 113⁄16 127⁄32 17⁄8 129⁄32 115⁄16 131⁄32

1.4375

36.512

…

…

…

…

…

4

1.4688

37.306

…

…

…

…

…

4

1.5000

38.100

…

…

…

…

…

4

1.5312

38.892

…

…

…

…

…

5

1.5675

39.688

…

…

…

…

…

5

1.5938

40.483

…

…

…

…

…

5

251

163⁄8 165⁄8 167⁄8

1.6250

41.275

…

…

…

…

…

5

10

254

17

432

1.6562

42.067

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.6875

42.862

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.7188

43.658

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.7500

44.450

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.7812

45.244

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.8125

46.038

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.8438

46.833

…

…

…

…

…

5

101⁄8

257

171⁄8

435

1.8750

47.625

…

…

…

…

…

5

103⁄8

264

173⁄8

441

1.9062

48.417

…

…

…

…

…

5

103⁄8

264

173⁄8

441

1.9375

49.212

…

…

…

…

…

5

264

50.008

…

…

…

…

…

5

2

2.0000

50.800

…

…

…

…

…

5

21⁄8 21⁄4 23⁄8 21⁄2

2.1250

53.975

…

…

…

…

…

5

2.2500

57.150

…

…

…

…

…

5

2.3750

60.325

…

…

…

…

…

5

2.5000

63.500

…

…

…

…

…

5

173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 183⁄4

441

1.9688

103⁄8 103⁄8 103⁄8 101⁄4 101⁄8 101⁄8 111⁄4

244

264 264 260 257 257 286

378

422 429

441 441 441 441 441 476

Table 8. American National Standard Drill Drivers — Split-Sleeve, Collet Type ANSI B94.35-1972 (R1995)

Taper Number

G Overall Length

H Diameter at Gage Line

J Taper per Foota

K Length to Gage Line

0b

2.38

0.356

0.62460

2.22

0.16

1

2.62

0.475

0.59858

2.44

0.19

2

3.19

0.700

0.59941

2.94

0.25

L Driver Projection

a Taper rate in accordance with ANSI/ASME B5.10-1994 (R2002), Machine Tapers. b Size 0 is not an American National Standard but is included here to meet special needs.




TWIST DRILLS Table 9. ANSI Three- and Four-Flute Straight Shank Core Drills — Fractional Sizes Only ANSI/ASME B94.11M-1993

Drill Diameter, D

Three-Flute Drills

Equivalent Inch 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 11⁄ 16 23⁄ 32 3⁄ 4 25⁄ 32 13⁄ 16 27⁄ 32 7⁄ 8 29⁄ 32 15⁄ 16 31⁄ 32

Four-Flute Drills

Flute Length

Overall Length

Flute Length

F

L

F

Overall Length L

Decimal Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

0.2500

6.350

33⁄4

95

61⁄8

156

…

…

…

…

0.2812

7.142

98

61⁄4

159

…

…

…

…

0.3125

7.938

37⁄8 4

102

63⁄8

162

…

…

…

…

0.3438

8.733

41⁄8

105

61⁄2

165

…

…

…

…

0.3750

9.525

41⁄8

105

171

…

…

…

…

0.4062

10.317

43⁄8

111

63⁄4 7

178

…

…

…

…

0.4375

11.112

45⁄8

117

71⁄4

184

…

…

…

…

0.4688

11.908

43⁄4

121

71⁄2

190

…

…

…

…

0.5000

12.700

43⁄4

121

197

43⁄4

121

13.492

43⁄4

121

203

43⁄4

121

73⁄4 8

197

0.5312

73⁄4 8

203

0.5625

14.288

47⁄8

124

81⁄4

210

47⁄8

124

81⁄4

210

0.5938

15.083

124

222

124

15.875

124

124

83⁄4 83⁄4

222

0.6250

83⁄4 83⁄4

0.6562

16.667

130

9

229

130

9

229

137

91⁄4

235

137

91⁄4 91⁄2 93⁄4 97⁄8

235

0.6875

17.462

47⁄8 47⁄8 51⁄8 53⁄8

0.7188

18.258

…

…

…

…

0.7500

19.050

57⁄8

149

93⁄4

248

47⁄8 47⁄8 51⁄8 53⁄8 55⁄8 57⁄8

0.7812

19.842

…

…

…

…

6

152

0.8125

20.638

…

…

…

…

156

10

254

0.8438

21.433

…

…

…

…

156

10

254

0.8750

22.225

…

…

…

…

156

10

254

0.9062

23.017

…

…

…

…

156

10

254

0.9375

23.812

…

…

…

…

156

0.9688

24.608

…

…

…

…

61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 63⁄8 63⁄8 61⁄2 65⁄8 67⁄8 71⁄8 77⁄8

162

103⁄4 11

279

162

11

279

165

111⁄8

283

168

111⁄4

286

175

111⁄2

292

181

113⁄4

298

200

121⁄2

318

222

1

1.0000

25.400

…

…

…

…

11⁄32

1.0312

26.192

…

…

…

…

11⁄16

1.0625

26.988

…

…

…

…

13⁄32

1.0938

27.783

…

…

…

…

11⁄8

1.1250

28.575

…

…

…

…

11⁄4

1.2500

31.750

…

…

…

…

143 149


222

241 248 251

273


Table 10. Length of Point on Twist Drills and Centering Tools

Decimal Equivalent

Length of Point when Included Angle = 90°


Dia. of Drill


Decimal Equivalent

60

0.0400

0.020

0.012

37

0.1040

0.052

0.031

14

0.1820

0.091

0.055

3⁄ 8

0.3750

0.188

0.113

59

0.0410

0.021

0.012

36

0.1065

0.054

0.032

13

0.1850

0.093

0.056

25⁄ 64

0.3906

0.195

0.117

58

0.0420

0.021

0.013

35

0.1100

0.055

0.033

12

0.1890

0.095

0.057

13⁄ 32

0.4063

0.203

0.122

57

0.0430

0.022

0.013

34

0.1110

0.056

0.033

11

0.1910

0.096

0.057

27⁄ 64

0.4219

0.211

0.127

56

0.0465

0.023

0.014

33

0.1130

0.057

0.034

10

0.1935

0.097

0.058

7⁄ 16

0.4375

0.219

0.131

55

0.0520

0.026

0.016

32

0.1160

0.058

0.035

9

0.1960

0.098

0.059

29⁄ 64

0.4531

0.227

0.136

54

0.0550

0.028

0.017

31

0.1200

0.060

0.036

8

0.1990

0.100

0.060

15⁄ 32

0.4688

0.234

0.141

53

0.0595

0.030

0.018

30

0.1285

0.065

0.039

7

0.2010

0.101

0.060

31⁄ 64

0.4844

0.242

0.145

52

0.0635

0.032

0.019

29

0.1360

0.068

0.041

6

0.2040

0.102

0.061

1⁄ 2

0.5000

0.250

0.150

51

0.0670

0.034

0.020

28

0.1405

0.070

0.042

5

0.2055

0.103

0.062

33⁄ 64

0.5156

0.258

0.155

50

0.0700

0.035

0.021

27

0.1440

0.072

0.043

4

0.2090

0.105

0.063

17⁄ 32

0.5313

0.266

0.159

49

0.0730

0.037

0.022

26

0.1470

0.074

0.044

3

0.2130

0.107

0.064

35⁄ 64

0.5469

0.273

0.164

48

0.0760

0.038

0.023

25

0.1495

0.075

0.045

2

0.2210

0.111

0.067

9⁄ 16

0.5625

0.281

0.169

47

0.0785

0.040

0.024

24

0.1520

0.076

0.046

1

0.2280

0.114

0.068

37⁄ 64

0.5781

0.289

0.173

46

0.0810

0.041

0.024

23

0.1540

0.077

0.046

15⁄ 64

0.2344

0.117

0.070

19⁄ 32

0.5938

0.297

0.178

45

0.0820

0.041

0.025

22

0.1570

0.079

0.047

1⁄ 4

0.2500

0.125

0.075

39⁄ 64

0.6094

0.305

0.183

44

0.0860

0.043

0.026

21

0.1590

0.080

0.048

17⁄ 64

0.2656

0.133

0.080

5⁄ 8

0.6250

0.313

0.188

43

0.0890

0.045

0.027

20

0.1610

0.081

0.048

9⁄ 32

0.2813

0.141

0.084

41⁄ 64

0.6406

0.320

0.192

42

0.0935

0.047

0.028

19

0.1660

0.083

0.050

19⁄ 64

0.2969

0.148

0.089

21⁄ 32

0.6563

0.328

0.197

41

0.0960

0.048

0.029

18

0.1695

0.085

0.051

5⁄ 16

0.3125

0.156

0.094

43⁄ 64

0.6719

0.336

0.202

40

0.0980

0.049

0.029

17

0.1730

0.087

0.052

21⁄ 64

0.3281

0.164

0.098

11⁄ 16

0.6875

0.344

0.206

39

0.0995

0.050

0.030

16

0.1770

0.089

0.053

11⁄ 32

0.3438

0.171

0.103

23⁄ 32

0.7188

0.359

0.216

38

0.1015

0.051

0.030

15

0.1800

0.090

0.054

23⁄ 64

0.3594

0.180

0.108

3⁄ 4

0.7500

0.375

0.225

Size of Drill

Decimal Equivalent



Size or Dia. of Drill


877

Decimal Equivalent



TWIST DRILLS

Size of Drill



DRILL DRIVERS

British Standard Combined Drills and Countersinks (Center Drills).—BS 328: Part 2: 1972 (1990) provides dimensions of combined drills and countersinks for center holes. Three types of drill and countersink combinations are shown in this standard but are not given here. These three types will produce center holes without protecting chamfers, with protecting chamfers, and with protecting chamfers of radius form. Drill Drivers—Split-Sleeve, Collet Type.—American National Standard ANSI B94.351972 (R1995) covers split-sleeve, collet-type drivers for driving straight shank drills, reamers, and similar tools, without tangs from 0.0390-inch through 0.1220-inch diameter, and with tangs from 0.1250-inch through 0.7500-inch diameter, including metric sizes. For sizes 0.0390 through 0.0595 inch, the standard taper number is 1 and the optional taper number is 0. For sizes 0.0610 through 0.1875 inch, the standard taper number is 1, first optional taper number is 0, and second optional taper number is 2. For sizes 0.1890 through 0.2520 inch, the standard taper number is 1, first optional taper number is 2, and second optional taper number is 0. For sizes 0.2570 through 0.3750 inch, the standard taper number is 1 and the optional taper number is 2. For sizes 0.3860 through 0.5625 inch, the standard taper number is 2 and the optional taper number is 3. For sizes 0.5781 through 0.7500 inch, the standard taper number is 3 and the optional taper number is 4. The depth B that the drill enters the driver is 0.44 inch for sizes 0.0390 through 0.0781 inch; 0.50 inch for sizes 0.0785 through 0.0938 inch; 0.56 inch for sizes 0.0960 through 0.1094 inch; 0.62 inch for sizes 0.1100 through 0.1220 inch; 0.75 inch for sizes 0.1250 through 0.1875 inch; 0.88 inch for sizes 0.1890 through 0.2500 inch; 1.00 inch for sizes 0.2520 through 0.3125 inch; 1.12 inches for sizes 0.3160 through 0.3750 inch; 1.25 inches for sizes 0.3860 through 0.4688 inch; 1.31 inches for sizes 0.4844 through 0.5625 inch; 1.47 inches for sizes 0.5781 through 0.6562 inch; and 1.62 inches for sizes 0.6719 through 0.7500 inch. British Standard Metric Twist Drills.—BS 328: Part 1:1959 (incorporating amendments issued March 1960 and March 1964) covers twist drills made to inch and metric dimensions that are intended for general engineering purposes. ISO recommendations are taken into account. The accompanying tables give the standard metric sizes of Morse taper shank twist drills and core drills, parallel shank jobbing and long series drills, and stub drills. All drills are right-hand cutting unless otherwise specified, and normal, slow, or quick helix angles may be provided. A “back-taper” is ground on the diameter from point to shank to provide longitudinal clearance. Core drills may have three or four flutes, and are intended for opening up cast holes or enlarging machined holes, for example. The parallel shank jobber, and long series drills, and stub drills are made without driving tenons. Morse taper shank drills with oversize dimensions are also listed, and Table 11 shows metric drill sizes superseding gage and letter size drills, which are now obsolete in Britain. To meet special requirements, the Standard lists nonstandard sizes for the various types of drills. The limits of tolerance on cutting diameters, as measured across the lands at the outer corners of a drill, shall be h8, in accordance with BS 1916, Limits and Fits for Engineering (Part I, Limits and Tolerances), and Table 14 shows the values common to the different types of drills mentioned before. The drills shall be permanently and legibly marked whenever possible, preferably by rolling, showing the size, and the manufacturer's name or trademark. If they are made from high-speed steel, they shall be marked with the letters H.S. where practicable. Drill Elements: The following definitions of drill elements are given. Axis: The longitudinal center line. Body: That portion of the drill extending from the extreme cutting end to the commencement of the shank.



879

Shank: That portion of the drill by which it is held and driven. Flutes: The grooves in the body of the drill that provide lips and permit the removal of chips and allow cutting fluid to reach the lips. Web (Core): The central portion of the drill situated between the roots of the flutes and extending from the point end toward the shank; the point end of the web or core forms the chisel edge. Lands: The cylindrical-ground surfaces on the leading edges of the drill flutes. The width of the land is measured at right angles to the flute helix. Body Clearance: The portion of the body surface that is reduced in diameter to provide diametral clearance. Heel: The edge formed by the intersection of the flute surface and the body clearance. Point: The sharpened end of the drill, consisting of all that part of the drill that is shaped to produce lips, faces, flanks, and chisel edge. Face: That portion of the flute surface adjacent to the lip on which the chip impinges as it is cut from the work. Flank: The surface on a drill point that extends behind the lip to the following flute. Lip (Cutting Edge): The edge formed by the intersection of the flank and face. Relative Lip Height: The relative position of the lips measured at the outer corners in a direction parallel to the drill axis. Outer Corner: The corner formed by the intersection of the lip and the leading edge of the land. Chisel Edge: The edge formed by the intersection of the flanks. Chisel Edge Corner: The corner formed by the intersection of a lip and the chisel edge. Table 11. British Standard Drills — Metric Sizes Superseding Gauge and Letter Sizes BS 328: Part 1:1959, Appendix B Obsolete Drill Size 80 79 78 77 76 75 74 73 72 71 70 69 68 67 66 65 64 63 62 61 60 59

Recommended MetricSize (mm) 0.35 0.38 0.40 0.45 0.50 0.52 0.58 0.60 0.65 0.65 0.70 0.75 1⁄ in. 32 0.82 0.85 0.90 0.92 0.95 0.98 1.00 1.00 1.05

Obsolete Drill Size 58 57 56 55 54 53 52 51 50 49 48 47 46 45 44 43 42 41 40 39 38 37

Recommended Metric Size (mm) 1.05 1.10 3⁄ in. 64 1.30 1.40 1.50 1.60 1.70 1.80 1.85 1.95 2.00 2.05 2.10 2.20 2.25 3⁄ in. 32 2.45 2.50 2.55 2.60 2.65

Obsolete Drill Size

Recommended Metric Size (mm)

Obsolete Drill Size

36 35 34 33 32 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 15

2.70 2.80 2.80 2.85 2.95 3.00 3.30 3.50 9⁄ in. 64 3.70 3.70 3.80 3.90 3.90 4.00 4.00 4.10 4.20 4.30 4.40 4.50 4.60

14 13 12 11 10 9 8 7 6 5 4 3 2 1 A B C D E F G H

Recommended Metric Size (mm)

Obsolete Drill Size

4.60 4.70 4.80 4.90 4.90 5.00 5.10 5.10 5.20 5.20 5.30 5.40 5.60 5.80 15⁄ in. 64

6.00 6.10 6.20 1⁄ in. 4 6.50 6.60 17⁄ in. 64

I J K L M N O P Q R S T U V W X Y Z … … … …

Recommended Metric Size (mm) 6.90 7.00 9⁄ in. 32

7.40 7.50 7.70 8.00 8.20 8.40 8.60 8.80 9.10 9.30 3⁄ in. 8 9.80 10.10 10.30 10.50 … … … …

Gauge and letter size drills are now obsolete in the United Kingdom and should not be used in the production of new designs. The table is given to assist users in changing over to the recommended standard sizes.



TWIST DRILLS Table 12. British Standard Morse Taper Shank Twist Drills and Core Drills — Standard Metric Sizes BS 328: Part 1:1959

Diameter 3.00 3.20 3.50 3.80 4.00 4.20 4.50 4.80 5.00 5.20 5.50 5.80 6.00 6.20 6.50 6.80 7.00 7.20 7.50 7.80 8.00 8.20 8.50 8.80 9.00 9.20 9.50 9.80 10.00 10.20 10.50 10.80 11.00 11.20 11.50 11.80 12.00 12.20 12.50 12.80 13.00 13.20 13.50 13.80 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75 16.00 16.25 16.50

Flute Length

Overall Length

33 36 39

114 117 120

43

123

47

128

52

133

57

138

63

144

69

150

75

156

81

87

94

162

168

175

101

182

108

189

114

212

120

218

125

223

Diameter 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75 20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75 24.00 24.25 24.50 24.75 25.00 25.25 25.50 25.75 26.00 26.25 26.50 26.75 27.00 27.25 27.50 27.75 28.00 28.25 28.50 28.75 29.00 29.25 29.50 29.75 30.00

Flute Length

Overall Length

125

223

130

228

135

233

140

145

150

238

243

248

155

253

155

276

160

281

165

286

170

291

175

175

296

296

Diameter 30.25 30.50 30.75 31.00 31.25 31.50 31.75 32.00 32.50 33.00 33.50 34.00 34.50 35.00 35.50 36.00 36.50 37.00 37.50 38.00 38.50 39.00 39.50 40.00 40.50 41.00 41.50 42.00 42.50 43.00 43.50 44.00 44.50 45.00 45.50 46.00 46.50 47.00 47.50 48.00 48.50 49.00 49.50 50.00 50.50 51.00 52.00 53.00 54.00 55.00 56.00 57.00 58.00 59.00 60.00


Flute Length

Overall Length

180

301

185

306

185

334

190

339

195

344

200

349

205

354

210

359

215

364

220

369

225

374

225

412

230

417

235

422


881

Table 12. (Continued) British Standard Morse Taper Shank Twist Drills and Core Drills — Standard Metric Sizes BS 328: Part 1:1959 Diameter 61.00 62.00 63.00 64.00 65.00 66.00 67.00 68.00 69.00 70.00 71.00 72.00 73.00 74.00 75.00

Flute Length

Overall Length

240

427

245

432

250

437

250

437

255

442

Diameter 76.00 77.00 78.00 79.00 80.00 81.00 82.00 83.00 84.00 85.00 86.00 87.00 88.00 89.00 90.00

Flute Length 260

Overall Length 477

260

514

265

519

270

524

Diameter 91.00 92.00 93.00 94.00 95.00 96.00 97.00 98.00 99.00 100.00

Flute Length

Overall Length

275

529

280

534

All dimensions are in millimeters. Tolerances on diameters are given in the table below. Table 13, shows twist drills that may be supplied with the shank and length oversize, but they should be regarded as nonpreferred. The Morse taper shanks of these twist and core drills are as follows: 3.00 to 14.00 mm diameter, M.T. No. 1; 14.25 to 23.00 mm diameter, M.T. No. 2; 23.25 to 31.50 mm diameter, M.T. No. 3; 31.75 to 50.50 mm diameter, M.T. No. 4; 51.00 to 76.00 mm diameter, M.T. No. 5; 77.00 to 100.00 mm diameter, M.T. No. 6.

Table 13. British Standard Morse Taper Shank Twist Drills — Metric Oversize Shank and Length Series BS 328: Part 1:1959 Dia. Range

Overall Length

M. T. No.

Dia. Range

Overall Length

M. T. No.

Dia. Range

Overall Length

M. T. No.

12.00 to 13.20

199

2

22.50 to 23.00

276

3

45.50 to 47.50

402

5

13.50 to 14.00

206

2

26.75 to 28.00

319

4

48.00 to 50.00

407

5

18.25 to 19.00

256

3

29.00 to 30.00

324

4

50.50

412

5

19.25 to 20.00

251

3

30.25 to 31.50

329

4

64.00 to 67.00

499

6

20.25 to 21.00

266

3

40.50 to 42.50

392

5

68.00 to 71.00

504

6

21.25 to 22.25

271

3

43.00 to 45.00

397

5

72.00 to 75.00

509

6

Diameters and lengths are given in millimeters. For the individual sizes within the diameter ranges given, see Table 12. This series of drills should be regarded as non-preferred.

Table 14. British Standard Limits of Tolerance on Diameter for Twist Drills and Core Drills — Metric Series BS 328: Part 1:1959 Drill Size (Diameter measured across lands at outer corners)

Tolerance (h8)

0 to 1 inclusive

Plus 0.000 to Minus 0.014

Over 1 to 3 inclusive
















All dimensions are given in millimeters.



TWIST DRILLS

4

19

5

20

6

22

7

24

8

26

9

28

10

30

11

32

12

34

14

36

16

38

1.35 1.40 1.45 1.50

18

40

1.55 1.60 1.65 1.70

20

43

24

49

27

53

30

57

33

61

36

65

39

70

43

75

47

52

80

86

5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.90 9.00 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00 10.10

57

93

63

101

69

109

75

81

87

117

125

133

Diameter

Overall Length

Flute Length

Diameter

46

Overall Length

19

22

Flute Length

3.0

1.75 1.80 1.85 1.90 1.95 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.10 5.20 5.30

Overall Length

19

Flute Length

2.5

Diameter

Overall Length

0.20 0.22 0.25 0.28 0.30 0.32 0.35 0.38 0.40 0.42 0.45 0.48 0.50 0.52 0.55 0.58 0.60 0.62 0.65 0.68 0.70 0.72 0.75 0.78 0.80 0.82 0.85 0.88 0.90 0.92 0.95 0.98 1.00 1.05 1.10 1.15 1.20 1.25 1.30

Flute Length

Diameter

Table 15. British Standard Parallel Shank Jobber Series Twist Drills — Standard Metric Sizes BS 328: Part 1:1959

87

133

94

142

101

151

108

160

14.25 14.50 14.75 15.00

114

169

15.25 15.50 15.75 16.00

120

178

10.20 10.30 10.40 10.50 10.60 10.70 10.80 10.90 11.00 11.10 11.20 11.30 11.40 11.50 11.60 11.70 11.80 11.90 12.00 12.10 12.20 12.30 12.40 12.50 12.60 12.70 12.80 12.90 13.00 13.10 13.20 13.30 13.40 13.50 13.60 13.70 13.80 13.90 14.00

All dimensions are in millimeters. Tolerances on diameters are given in Table 14.



883

Table 16. British Standard Parallel Shank Long Series Twist Drills — Standard Metric Sizes BS 328: Part 1:1959 Diameter 2.00 2.05 2.10 2.15 2.20 2.25 2.30 2.35 2.40 2.45 2.50 2.55 2.60 2.65 2.70 2.75 2.80 2.85 2.90 2.95 3.00 3.10 3.20 3.30 3.40 3.50 3.60 3.70 3.80 3.90 4.00 4.10 4.20 4.30 4.40 4.50 4.60 4.70 4.80 4.90 5.00 5.10 5.20 5.30 5.40 5.50 5.60 5.70 5.80 5.90 6.00 6.10 6.20 6.30 6.40 6.50 6.60 6.70

Flute Length

Overall Length

56

85

59

90

62

95

66

100

69

106

73

112

78

119

82

126

87

132

91

97

139

148

Diameter 6.80 6.90 7.00 7.10 7.20 7.30 7.40 7.50 7.60 7.70 7.80 7.90 8.00 8.10 8.20 8.30 8.40 8.50 8.60 8.70 8.80 8.90 9.00 9.10 9.20 9.30 9.40 9.50 9.60 9.70 9.80 9.90 10.00 10.10 10.20 10.30 10.40 10.50 10.60 10.70 10.80 10.90 11.00 11.10 11.20 11.30 11.40 11.50 11.60 11.70 11.80 11.90 12.00 12.10 12.20 12.30 12.40 12.50 12.60

Flute Length

102

109

115

121

128

134

Overall Length

156

165

175

184

195

205

Diameter 12.70 12.80 12.90 13.00 13.10 13.20 13.30 13.40 13.50 13.60 13.70 13.80 13.90 14.00 14.25 14.50 14.75 15.00 15.25 15.50 15.75 16.00 16.25 16.50 16.75 17.00 17.25 17.50 17.75 18.00 18.25 18.50 18.75 19.00 19.25 19.50 19.75 20.00 20.25 20.50 20.75 21.00 21.25 21.50 21.75 22.00 22.25 22.50 22.75 23.00 23.25 23.50 23.75 24.00 24.25 24.50 24.75 25.00

All dimensions are in millimeters. Tolerances on diameters are given in Table 14.


Flute Length

Overall Length

134

205

140

214

144

220

149

227

154

235

158

241

162

247

166

254

171

261

176

268

180

275

185

282


TWIST DRILLS

49 52

22

55

24 26

58 62

3.80 4.00 4.20 4.50 4.80

66

31

70

34

74

37

79

40

84

Overall Length

18 20

28

Flute Length

46

62

Diameter

16

6.20 6.50 6.80 7.00 7.20 7.50 7.80 8.00 8.20 8.50 8.80 9.00 9.20

26

Overall Length

5.00 5.20 5.50 5.80 6.00

Flute Length

Diameter

20 24 26 30 32 36 38 40 43

Diameter

Overall Length

3 5 6 8 9 11 12 13 14

Overall Length

Flute Length

0.50 0.80 1.00 1.20 1.50 1.80 2.00 2.20 2.50 2.80 3.00 3.20 3.50

Flute Length

Diameter

Table 17. British Standard Stub Drills — Metric Sizes BS 328: Part 1:1959

9.50 9.80 10.00 10.20 10.50

40

84

14.00 14.50 15.00 15.50 16.00

54

107

10.80 11.00 11.20 11.50 11.80 12.00 12.20 12.50 12.80 13.00 13.20 13.50 13.80

43

47

89

95

51

102

54

107

16.50 17.00 17.50 18.00 18.50 19.00 19.50 20.00 21.00 22.00 23.00 24.00 25.00

56

111

58

115

60

119

62

123

64

127

66

131

68 70 72

136 141 146

75

151

All dimensions are given in millimeters. Tolerances on diameters are given in Table 14.

Steels for Twist Drills.—Twist drill steels need good toughness, abrasion resistance, and ability to resist softening due to heat generated by cutting. The amount of heat generated indicates the type of steel that should be used. Carbon Tool Steel may be used where little heat is generated during drilling. High-Speed Steel is preferred because of its combination of red hardness and wear resistance, which permit higher operating speeds and increased productivity. Optimum properties can be obtained by selection of alloy analysis and heat treatment. Cobalt High-Speed Steel alloys have higher red hardness than standard high-speed steels, permitting drilling of materials such as heat-resistant alloys and materials with hardness greater than Rockwell 38 C. These high-speed drills can withstand cutting speeds beyond the range of conventional high-speed-steel drills and have superior resistance to abrasion but are not equal to tungsten-carbide tipped tools. Accuracy of Drilled Holes.—Normally the diameter of drilled holes is not given a tolerance; the size of the hole is expected to be as close to the drill size as can be obtained. The accuracy of holes drilled with a two-fluted twist drill is influenced by many factors, which include: the accuracy of the drill point; the size of the drill; length and shape of the chisel edge; whether or not a bushing is used to guide the drill; the work material; length of the drill; runout of the spindle and the chuck; rigidity of the machine tool, workpiece, and the setup; and also the cutting fluid used, if any. The diameter of the drilled holes will be oversize in most materials. The table Oversize Diameters in Drilling on page 885 provides the results of tests reported by The United States Cutting Tool Institute in which the diameters of over 2800 holes drilled in steel and cast iron were measured. The values in this table indicate what might be expected under average shop conditions; however, when the drill point is accurately ground and the other machining conditions are correct, the resulting hole size is more likely to be between the mean and average minimum values given in this table. If the drill is ground and used incorrectly, holes that are even larger than the average maximum values can result.


Machinery's Handbook 27th Edition COUNTERBORES

885

Oversize Diameters in Drilling Drill Dia., Inch 1⁄ 16 1⁄ 8 1⁄ 4

Amount Oversize, Inch Average Max. Mean Average Min. 0.002 0.0045 0.0065

0.0015 0.003 0.004

Drill Dia., Inch

0.001 0.001 0.0025

1⁄ 2 3⁄ 4

1

Amount Oversize, Inch Average Max. Mean Average Min. 0.008 0.008 0.009

0.005 0.005 0.007

0.003 0.003 0.004

Courtesy of The United States Cutting Tool Institute

Some conditions will cause the drilled hole to be undersize. For example, holes drilled in light metals and in other materials having a high coefficient of thermal expansion such as plastics, may contract to a size that is smaller than the diameter of the drill as the material surrounding the hole is cooled after having been heated by the drilling. The elastic action of the material surrounding the hole may also cause the drilled hole to be undersize when drilling high strength materials with a drill that is dull at its outer corner. The accuracy of the drill point has a great effect on the accuracy of the drilled hole. An inaccurately ground twist drill will produce holes that are excessively over-size. The drill point must be symmetrical; i.e., the point angles must be equal, as well as the lip lengths and the axial height of the lips. Any alterations to the lips or to the chisel edge, such as thinning the web, must be done carefully to preserve the symmetry of the drill point. Adequate relief should be provided behind the chisel edge to prevent heel drag. On conventionally ground drill points this relief can be estimated by the chisel edge angle. When drilling a hole, as the drill point starts to enter the workpiece, the drill will be unstable and will tend to wander. Then as the body of the drill enters the hole the drill will tend to stabilize. The result of this action is a tendency to drill a bellmouth shape in the hole at the entrance and perhaps beyond. Factors contributing to bellmouthing are: an unsymmetrically ground drill point; a large chisel edge length; inadequate relief behind the chisel edge; runout of the spindle and the chuck; using a slender drill that will bend easily; and lack of rigidity of the machine tool, workpiece, or the setup. Correcting these conditions as required will reduce the tendency for bellmouthing to occur and improve the accuracy of the hole diameter and its straightness. Starting the hole with a short stiff drill, such as a center drill, will quickly stabilize the drill that follows and reduce or eliminate bellmouthing; this procedure should always be used when drilling in a lathe, where the work is rotating. Bellmouthing can also be eliminated almost entirely and the accuracy of the hole improved by using a close fitting drill jig bushing placed close to the workpiece. Although specific recommendations cannot be made, many cutting fluids will help to increase the accuracy of the diameters of drilled holes. Double margin twist drills, available in the smaller sizes, will drill a more accurate hole than conventional twist drills having only a single margin at the leading edge of the land. The second land, located on the trailing edge of each land, provides greater stability in the drill bushing and in the hole. These drills are especially useful in drilling intersecting off-center holes. Single and double margin step drills, also available in the smaller sizes, will produce very accurate drilled holes, which are usually less than 0.002 inch larger than the drill size. Counterboring.—Counterboring (called spot-facing if the depth is shallow) is the enlargement of a previously formed hole. Counterbores for screw holes are generally made in sets. Each set contains three counterbores: one with the body of the size of the screw head and the pilot the size of the hole to admit the body of the screw; one with the body the size of the head of the screw and the pilot the size of the tap drill; and the third with the body the size of the body of the screw and the pilot the size of the tap drill. Counterbores are usually provided with helical flutes to provide positive effective rake on the cutting edges. The four flutes are so positioned that the end teeth cut ahead of center to provide a shearing action and eliminate chatter in the cut. Three designs are most common: solid, two-piece, and three-piece. Solid designs have the body, cutter, and pilot all in one piece. Two-piece designs have an integral shank and counterbore cutter, with an interchangeable pilot, and provide true concentricity of the cutter diameter with the shank, but allowing use of various



COUNTERBORES

pilot diameters. Three-piece counterbores have separate holder, counterbore cutter, and pilot, so that a holder will take any size of counterbore cutter. Each counterbore cutter, in turn, can be fitted with any suitable size diameter of pilot. Counterbores for brass are fluted straight. Counterbores with Interchangeable Cutters and Guides

Range of Cutter Diameters, A

Range of Pilot Diameters, B

Total Length, C

Length of Cutter Body, D

Length of Pilot, E

Dia. of Shank, F

No. of Holder

No. of Morse Taper Shank

1

1 or 2

3⁄ -11⁄ 4 16

1⁄ -3⁄ 2 4

71⁄4

1

5⁄ 8

3⁄ 4

2

2 or 3

11⁄8-19⁄16

11⁄16-11⁄8

91⁄2

13⁄8

7⁄ 8

11⁄8

3

3 or 4

15⁄8-21⁄16

7⁄ -15⁄ 8 8

121⁄2

13⁄4

11⁄8

15⁄8

4

4 or 5

21⁄8-31⁄2

1-21⁄8

15

21⁄4

13⁄8

21⁄8

Solid Counterbores with Integral Pilot Pilot Diameters

Overall Length

Counterbore Diameters

Nominal

+1⁄64

+1⁄32

Straight Shank Diameter

Short

Long

13⁄ 32

1⁄ 4

17⁄ 64

9⁄ 32

3⁄ 8

31⁄2

51⁄2

1⁄ 2

5⁄ 16

21⁄ 64

11⁄ 32

3⁄ 8

31⁄2

51⁄2

19⁄ 32

3⁄ 8

25⁄ 64

13⁄ 32

1⁄ 2

4

6

11⁄ 16

7⁄ 16

29⁄ 64

15⁄ 32

1⁄ 2

4

6

25⁄ 32

1⁄ 2

33⁄ 64

17⁄ 32

1⁄ 2

5

7

0.110

0.060

0.076

…

7⁄ 64

21⁄2

…

0.133

0.073

0.089

…

1⁄ 8

21⁄2

…

0.155

0.086

0.102

…

5⁄ 32

21⁄2

…

0.176

0.099

0.115

…

11⁄ 64

21⁄2

…

0.198

0.112

0.128

…

3⁄ 16

21⁄2

…

0.220

0.125

0.141

…

3⁄ 16

21⁄2

…

0.241

0.138

0.154

…

7⁄ 32

21⁄2

…

0.285

0.164

0.180

…

1⁄ 4

21⁄2

…

0.327

0.190

0.206

…

9⁄ 32

23⁄4

…

0.372

0.216

0.232

…

5⁄ 16

23⁄4

…


Small counterbores are often made with three flutes, but should then have the size plainly stamped on them before fluting, as they cannot afterwards be conveniently measured. The flutes should be deep enough to come below the surface of the pilot. The counterbore should be relieved on the end of the body only, and not on the cylindrical surface. To facilitate the relieving process, a small neck is turned between the guide and the body for clearance. The amount of clearance on the cutting edges is, for general work, from 4 to 5 degrees. The accompanying table gives dimensions for straight shank counterbores. Three Piece Counterbores.—Data shown for the first two styles of counterbores are for straight shank designs. These tools are also available with taper shanks in most sizes. Sizes of taper shanks for cutter diameters of 1⁄4 to 9⁄16 in. are No. 1, for 19⁄32 to 7⁄8 in., No. 2; for 15⁄16 to 13⁄8 in., No. 3; for 11⁄2 to 2 in., No. 4; and for 21⁄8 to 21⁄2 in., No. 5.


Machinery's Handbook 27th Edition STANDARD CARBIDE BORING TOOLS

887

Counterbore Sizes for Hex-head Bolts and Nuts.—Table 2, page 1531, shows the maximum socket wrench dimensions for standard 1⁄4-, 1⁄2- and 3⁄4-inch drive socket sets. For a given socket size (nominal size equals the maximum width across the flats of nut or bolt head), the dimension K given in the table is the minimum counterbore diameter required to provide socket wrench clearance for access to the bolt or nut. Sintered Carbide Boring Tools.—Industrial experience has shown that the shapes of tools used for boring operations need to be different from those of single-point tools ordinarily used for general applications such as lathe work. Accordingly, Section 5 of American National Standard ANSI B212.1-2002 gives standard sizes, styles and designations for four basic types of sintered carbide boring tools, namely: solid carbide square; carbidetipped square; solid carbide round; and carbide-tipped round boring tools. In addition to these ready-to-use standard boring tools, solid carbide round and square unsharpened boring tool bits are provided. Style Designations for Carbide Boring Tools: Table 1 shows designations used to specify the styles of American Standard sintered carbide boring tools. The first letter denotes solid (S) or tipped (T). The second letter denotes square (S) or round (R). The side cutting edge angle is denoted by a third letter (A through H) to complete the style designation. Solid square and round bits with the mounting surfaces ground but the cutting edges unsharpened (Table 3) are designated using the same system except that the third letter indicating the side cutting edge angle is omitted. Table 1. American National Standard Sintered Carbide Boring Tools — Style Designations ANSI B212.1-2002 Side Cutting Edge Angle E Degrees

Designation

0 10 30 40 45 55 90 (0° Rake) 90 (10° Rake)

A B C D E F G H

Boring Tool Styles Solid Square (SS)

SSC SSE

Tipped Square (TS) TSA TSB TSC TSD TSE TSF

Solid Round (SR)

Tipped Round (TR)

SRC

TRC

SRE

TRE TRG TRH

Size Designation of Carbide Boring Tools: Specific sizes of boring tools are identified by the addition of numbers after the style designation. The first number denotes the diameter or square size in number of 1⁄32nds for types SS and SR and in number of 1⁄16ths for types TS and TR. The second number denotes length in number of 1⁄8ths for types SS and SR. For styles TRG and TRH, a letter “U” after the number denotes a semi-finished tool (cutting edges unsharpened). Complete designations for the various standard sizes of carbide boring tools are given in Tables 2 through 7. In the diagrams in the tables, angles shown without tolerance are ± 1°. Examples of Tool Designation:The designation TSC-8 indicates: a carbide-tipped tool (T); square cross-section (S); 30-degree side cutting edge angle (C); and 8⁄16 or 1⁄2 inch square size (8). The designation SRE-66 indicates: a solid carbide tool (S); round cross-section (R); 45 degree side cutting edge angle (E); 6⁄32 or 3⁄16 inch diameter (6); and 6⁄8 or 3⁄4 inch long (6). The designation SS-610 indicates: a solid carbide tool (S); square cross-section (S); 6⁄32 or 3⁄ inch square size (6); 10⁄ or 11⁄ inches long (10). 16 8 4 It should be noted in this last example that the absence of a third letter (from A to H) indicates that the tool has its mounting surfaces ground but that the cutting edges are unsharpened.



STANDARD CARBIDE BORING TOOLS

Table 2. ANSI Carbide-Tipped Round General-Purpose Square-End Boring Tools Style TRG with 0° Rake and Style TRH with 10° Rake ANSI B212.1-2002

Tool Designation

Finished

Semifinisheda

TRG-5

TRG-5U

TRH-5

TRH-5U

TRG-6

TRG-6U

TRH-6

TRH-6U

TRG-7

TRG-7U

TRH-7

TRH-7U

TRG-8

TRG-8U

TRH-8

TRH-8U

Shank Dimensions, Inches Dia. D

Length C

5⁄ 16

11⁄2

3⁄ 8

13⁄4

7⁄ 16

21⁄2

1⁄ 2

Tip Dimensions, Inches Rake Angle Deg.

Dim.Over Flat B

Nose Height H

Setback M (Min)

19⁄ 64

3⁄ 16

3⁄ 16

0

±.005

7⁄ 32

3⁄ 16

10

11⁄ 32

7⁄ 32

±.010

1⁄ 4

21⁄2

13⁄ 32

1⁄ 4

±.010

5⁄ 16

15⁄ 32

9⁄ 32

±.010

11⁄ 32

Tip No.

T

W

L

1025

1⁄ 16

1⁄ 4

1⁄ 4

1030

1⁄ 16

5⁄ 16

1⁄ 4

1080

3⁄ 32

5⁄ 16

3⁄ 8

1090

3⁄ 32

3⁄ 8

3⁄ 8

0

3⁄ 16

10 0

3⁄ 16

10 0

1⁄ 4

10

a Semifinished tool will be without Flat (B) and carbide unground on the end.

Table 3. Solid Carbide Square and Round Boring Tool Bits

Square Bits Tool Designation

Round Bits

A

B

SS-58

5⁄ 32

5⁄ 32

C 1

SS-610

3⁄ 16

3⁄ 16

SS-810

1⁄ 4

1⁄ 4

SS-1012

5⁄ 16

SS-1214

3⁄ 8

Tool Designation

Tool Designation

D

C

D

C

5⁄ 8

Tool Designation SR-88

1⁄ 4

1 11⁄4

D

C

SR-33

3⁄ 32

3⁄ 8

SR-55

5⁄ 32

11⁄4

SR-34

3⁄ 32

1⁄ 2

SR-64

3⁄ 16

1⁄ 2

SR-810

1⁄ 4

11⁄4

SR-44

1⁄ 8

1⁄ 2

SR-66

3⁄ 16

3⁄ 4

SR-1010

5⁄ 16

11⁄4

5⁄ 16

11⁄2

SR-46

1⁄ 8

3⁄ 4

SR-69

3⁄ 16

11⁄8

…

…

…

3⁄ 8

13⁄4

SR-48

1⁄ 8

1

SR-77

7⁄ 32

7⁄ 8

…

…

…

All dimensions are in inches. Tolerance on Length: Through 1 inch, + 1⁄32, − 0; over 1 inch, +1⁄16, −0.



Table 4. ANSI Solid Carbide Square Boring Tools Style SSC for 60° Boring Bar and Style SSE for 45° Boring Bar ANSI B212.1-2002

Table 5. ANSI Carbide-Tipped Round Boring Tools Style TRC for 60° Boring Bar and Style TRE for 45° Boring Bar ANSI B212.1-2002 6° ± 1° Tool Designation and Carbide Grade

6° ± 1°

G ± 1°

F Ref

W

G ± 1°

F Ref A +0.000 –0.002

1 C ± 16

A ±0.005 to sharp corner 2

E ± 1°

H ± 0.010 6° ± 1° Along angle “G” Optional Design

12° ± 1°

5⁄ 32

5⁄ 32

1

3⁄ 16

3⁄ 16

11⁄4

1⁄ 4

1⁄ 4

11⁄4

5⁄ 16

5⁄ 16

11⁄2

End Cutting Edge Angle G ,Deg.

Shoulder Angle F ,Deg.

30 45 30 45 30 45 30 45

38 53 38 53 38 53 38 53

60 45 60 45 60 45 60 45

TRC-5

60

TRE-5

45

TRC-6

60

TRE-6

45

TRC-7

60

TRE-7

45

TRC-8

60

TRE-8

45

D

C

5⁄ 16

11⁄2

3⁄ 8

13⁄4

7⁄ 16

21⁄2

1⁄ 2

21⁄2

B 19⁄ 64

±.005 11⁄ 32

±.010 13⁄ 32

±.010 15⁄ 32

±.010

H 7⁄ 32

9⁄ 32

5⁄ 16

3⁄ 8

Shoulder Angle F, Deg.

60 45 60 45 60 45 60 45

Side Cutting Edge Angle E,Deg.

Shank Dimensions, Inches

End Cut. Edge Angle G, Deg.

SSC-58 SSE-58 SSC-610 SSE-610 SSC-810 SSE-810 SSC-1012 SSE-1012

+0.000 –0.002

Bor. Bar Angle from Axis, Deg.

R

Shank Dimensions, Inches Width Height Length A B C

Tool Designation

6° ± 1° Along angle “G”

Side Cut. Edge Angle E, Deg.

12° ± 2° Along angle “G”

Tool Designation and Carbide Grade

Tool Designation

6° ± 1° L

1 C ± 64

Boring Bar Angle, Deg. from Axis

D/2 ± 1 to sharp corner 64

F ± 1°

B

0.010 R ± 0.003

T

30

38

60

R 1⁄ 64

Tip Dimensions, Inches Tip No.

T

W

L

2020

1⁄ 16

3⁄ 16

1⁄ 4

±.005

45

53

45

1⁄ 64

30

38

60

2040

3⁄ 32

3⁄ 16

5⁄ 16

±.005

45

53

45

2020

1⁄ 16

3⁄ 16

1⁄ 4

1⁄ 32

30

38

60

±.010

45

53

45

2060

3⁄ 32

1⁄ 4

3⁄ 8

1⁄ 4

3⁄ 8

5⁄ 16

3⁄ 8

1⁄ 32

30

38

60

2060

3⁄ 32

±.010

45

53

45

2080

3⁄ 32


8° ± 2° 6° ± 1°

R D +0.0005 –0.0015

889




Table 6. ANSI Carbide-Tipped Square Boring Tools — ANSI B212.1-2002 Styles TSA and TSB for 90° Boring Bar, Styles TSC and TSD for 60° Boring Bar, and Styles TSE and TSF for 45° Boring Bar

G ± 1° Shoulder angle Ref F

10° ± 1° 7° ± 1° 6° ± 1°

W

R Ref to Sharp Corner

A +0.000 –0.010

T 1 C ± 16

E ± 1° L

A

B

5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

C 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 3 3 3 3 3 3 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2

R

⎛ 1⁄64 ⎞ ⎜ ± ⎟ ⎜ ⎟ ⎝ 0.005⎠

⎛ 1⁄32 ⎞ ⎜ ± ⎟ ⎜ ⎟ ⎝ 0.010⎠

⎛ 1⁄32 ⎞ ⎜ ± ⎟ ⎜ ⎟ ⎝ 0.010⎠

Shoulder Angle F, Deg.

90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45

B +0.000 –0.010 End Cut. Edge Angle G, Deg.

Bor. Bar Angle from Axis, Deg.

TSA-5 TSB-5 TSC-5 TSD-5 TSE-5 TSF-5 TSA-6 TSB-6 TSC-6 TSD-6 TSE-6 TSF-6 TSA-7 TSB-7 TSC-7 TSD-7 TSE-7 TSF-7 TSA-8 TSB-8 TSC-8 TSD-8 TSE-8 TSF-8 TSA-10 TSB-10 TSC-10 TSD-10 TSE-10 TSF-10 TSA-12 TSB-12 TSC-12 TSD-12 TSE-12 TSF-12

Shank Dimensions, Inches

0° ± 1° Along angle “G” 10° ± 2° Along angle “G”

SideCut. Edge Angle E, Deg.

Tool Designation

12° ± 1° Tool Designation and Carbide Grade

0 10 30 40 45 55 0 10 30 40 45 55 0 10 30 40 45 55 0 10 30 40 45 55 0 10 30 40 45 55 0 10 30 40 45 55

8 8 38 38 53 53 8 8 38 38 53 53 8 8 38 38 53 53 8 8 38 38 53 53 8 8 38 38 53 53 8 8 38 38 53 53

90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45 90 90 60 60 45 45

Tip Dimensions, Inches Tip No. 2040 2040 2040 2040 2040 2040 2040 2040 2040 2040 2040 2040 2060 2060 2060 2060 2060 2060 2150 2150 2150 2150 2150 2150 2220 2220 2220 2220 2220 2220 2300 2300 2300 2300 2300 2300


T

W

L

3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 5⁄ 32 5⁄ 32 5⁄ 32 5⁄ 32 5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16

5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 7⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8

Machinery's Handbook 27th Edition STANDARD CARBIDE BORING TOOLS

891

Table 7. ANSI Solid Carbide Round Boring Tools — ANSI B212.1-2002 Style SRC for 60° Boring Bar and Style SRE for 45° Boring Bar

6° ± 1°

Tool Designation and Carbide Grade

G ± 1°

F Ref

6° ± 1°

0.010 R ± 0.003

D +0.0005 –0.0015 B +0.000 –0.005

D ±0.005 to sharp corner 2

E ± 1° 1

C ± 64

H 6° ± 1° Along angle “G”

Bor. Bar Angle Tool from Axis, Designation Deg.

Dia. D

Shank Dimensions, Inches Dim. Nose Over Height Flat B H

Length C

Side Cut. Edge Angle E ,Deg.

End Cut. Edge Angle G ,Deg.

Shoulder Angle F ,Deg.

30

38

60

45

53

45

30

38

60

45

53

45

SRC-33

60

3⁄ 32

3⁄ 8

0.088

0.070

SRE-33

45

3⁄ 32

3⁄ 8

0.088

0.070

SRC-44

60

1⁄ 8

1⁄ 2

0.118

0.094

SRE-44

45

1⁄ 8

1⁄ 2

0.118

0.094

+0.000 – 0.005

SRC-55

60

5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16

5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

0.149

0.117

±0.005

30

38

60

0.149

0.117

±0.005

45

53

45

0.177

0.140

±0.005

30

38

60

0.177

0.140

±0.005

45

53

45

1

0.240

0.187

±0.005

30

38

60

1

0.240

0.187

±0.005

45

53

45

11⁄4

0.300

0.235

±0.005

30

38

60

11⁄4

0.300

0.235

±0.005

45

53

45

SRE-55

45

SRC-66

60

SRE-66

45

SRC-88

60

SRE-88

45

SRC-1010

60

SRE-1010

45

+0.000 – 0.005

Boring Machines, Origin.—The first boring machine was built by John Wilkinson, in 1775. Smeaton had built one in 1769 which had a large rotary head, with inserted cutters, carried on the end of a light, overhanging shaft. The cylinder to be bored was fed forward against the cutter on a rude carriage, running on a track laid in the floor. The cutter head followed the inaccuracies of the bore, doing little more than to smooth out local roughness of the surface. Watt’s first steam cylinders were bored on this machine and he complained that one, 18 inches in diameter, was 3⁄8 inch out of true. Wilkinson thought of the expedient, which had escaped both Smeaton and Watt, of extending the boring-bar completely through the cylinder and giving it an out-board bearing, at the same time making it much larger and stiffer. With this machine cylinders 57 inches in diameter were bored which were within 1⁄16 inch of true. Its importance can hardly be overestimated as it insured the commercial success of Watt’s steam engine which, up to that time, had not passed the experimental stage.




TAPS AND THREADING DIES Taps General dimensions and tap markings given in the ASME B94.9 Standard for straight fluted taps, spiral pointed taps, spiral pointed only taps, spiral fluted taps, fast spiral fluted taps, thread forming taps, pulley taps, nut taps, and pipe taps are shown in the tables on the pages that follow. This Standard also gives the thread limits for taps with cut threads and ground threads. The thread limits for cut thread and ground thread taps for screw threads are given in Tables 1 through 5 and Tables 4a and 4b; thread limits for cut thread and ground thread taps for pipe threads are given in Tables 6a through 7c. Taps recommended for various classes of Unified screw threads are given in Tables 8a through 11 in numbered sizes and Table 9 for nuts in fractional sizes. Types of Taps.—Taps included in ASME B94.9 are categorized either by the style of fluting or by the specific application for which the taps are designed. The following types 1 through 6 are generally short in length, and were originally called “Hand Taps” but this design is generally used in machine applications. The remaining types have special lengths, which are detailed in the tables. The thread size specifications for these types may be fractional or machine screw inch sizes, or metric sizes. The thread form may be ground or cut (unground) as further defined in each table. Additionally, the cutting chamfer on the thread may be Bottoming (B), Plug (P), or Taper (T). (1) Straight Flute Taps: These taps have straight flutes of a number specified as either standard or optional, and are for general purpose applications. (2) Spiral Pointed Taps: These taps have straight flutes and the cutting face of the first few threads is ground at an angle to force the chips ahead and prevent clogging in the flutes. (3) Spiral Pointed Only Taps: These taps are made with the spiral point feature only without longitudinal flutes. These taps are especially suitable for tapping thin materials. (4) Spiral Fluted Taps: These taps have right-hand helical flutes with a helix angle of 25 to 35 deg. These features are designed to help draw chips from the hole or to bridge a keyway. (5) Fast Spiral Fluted Taps: These taps are similar to spiral fluted taps, except the helix angle is from 45 to 60 deg. (6) Thread Forming Taps: These taps are fluteless except as optionally designed with one or more lubricating grooves. The thread form on the tap is lobed, so that there are a finite number of points contacting the work thread form. The tap does not cut, but forms the thread by extrusion. (7) Pulley Taps: These taps have shanks that are extended in length by a standard amount for use where added reach is required. The shank is the same nominal diameter as the thread. (8) Nut Taps: These taps are designed for tapping nuts on a low-production basis. Approximately one-half to three-quarters of the threaded portion has a chamfered section, which distributes the cutting over many teeth and facilitates entering the hole to be tapped. The length overall, the length of the thread, and the length of the shank are appreciably longer than on a regular straight fluted tap. Nut taps have been removed from ASME B94.9 but are retained for reference. (9) Pipe Taps: These taps are used to produce standard straight or tapered pipe threads. Definitions of Tap Terms.—The definitions that follow are taken from ASME B94.9 but include only the more important terms. Some tap terms are the same as screw thread terms; therefore, see Definitions of Screw Threads starting on page 1727. Back Taper: A gradual decrease in the diameter of the thread form on a tap from the chamfered end of the land toward the back, which creates a slight radial relief in the threads.


Machinery's Handbook 27th Edition TAPS AND THREADING DIES

893

Base of Thread: Coincides with the cylindrical or conical surface from which the thread projects. Chamfer: Tapering of the threads at the front end of each land or chaser of a tap by cutting away and relieving the crest of the first few teeth to distribute the cutting action over several teeth. Chamfer Angle: Angle formed between the chamfer and the axis of the tap measured in an axial plane at the cutting edge. Chamfer Relief Angle: Complement of the angle formed between a tangent to the relieved surface at the cutting edge and a radial line to the same point on the cutting edge. Core Diameter: Diameter of a circle which is tangent to the bottom of the flutes at a given point on the axis. First Full Thread: First full thread on the cutting edge back of the chamfer. It is at this point that rake, hook, and thread elements are measured. Crest Clearance: Radial distance between the root of the internal thread and the crest of the external thread of the coaxially assembled design forms of mating threads. Class of Thread: Designation of the class that determines the specification of the size, allowance, and tolerance to which a given threaded product is to be manufactured. It is not applicable to the tools used for threading. Tap Terms Overall Length Shank Thread Length Length Chamfer Axis Length

Length of Sq.

Size of Square

Core Dia. Land Flute

;;; ;;;;;; ;;;;;;; Point Dia.

Style 1

2

3 Shank Dia.

90°

Thread Lead Angle

Pitch

Max. Tap Major Dia.

Min. Tap Major Dia.

Internal Center

Tap Crest Basic Crest

Basic Height of Thread

Basic Major Dia.

Angle of Thread Flank

Basic Pitch Dia.

Basic Minor Dia. Base of Thread Basic Root

Relieved to Cutting Edge

No Relief

Cutting Edge Cutting Face

External Center

Chamfer Angle

Concentric Margin Eccentric Relief

Heel

Eccentric

Concentric

Con-Eccentric Relief

Land

Negative Rake Angle

Zero Rake

Positive Rake Angle

Negative Rake

Radial

Positive Rake

Tangential Measurement Hook Angle (Chordal Measurement)

Hook




Flank Angle: Angle between the individual flank and the perpendicular to the axis of the thread, measured in an axial plane. A flank angle of a symmetrical thread is commonly termed the “half angle of thread.” Flank—Leading: 1) Flank of a thread facing toward the chamfered end of a threading tool; and 2) The leading flank of a thread is the one which, when the thread is about to be assembled with a mating thread, faces the mating thread. Flank—Trailing: The trailing flank of a thread is the one opposite the leading flank. Flutes: Longitudinal channels formed in a tap to create cutting edges on the thread profile and to provide chip spaces and cutting fluid passages. On a parallel or straight thread tap they may be straight, angular or helical; on a taper thread tap they may be straight, angular or spiral. Flute-Angular: A flute lying in a plane intersecting the tool axis at an angle. Flute-Helical: A flute with uniform axial lead and constant helix in a helical path around the axis of a cylindrical tap. Flute-Spiral: A flute with uniform axial lead in a spiral path around the axis of a conical tap. Flute Lead Angle: Angle at which a helical or spiral cutting edge at a given point makes with an axial plane through the same point. Flute-Straight: A flute which forms a cutting edge lying in an axial plane. Front Taper: A gradual increase in the diameter of the thread form on a tap from the leading end of the tool toward the back. Heel: Edge of the land opposite the cutting edge. Hook Angle: Inclination of a concave cutting face, usually specified either as Chordal Hook or Tangential Hook. Hook-Chordal Angle: Angle between the chord passing through the root and crest of a thread form at the cutting face, and a radial line through the crest at the cutting edge. Hook-Tangential Angle: Angle between a line tangent to a hook cutting face at the cutting edge and a radial line to the same point. Interrupted Thread Tap: A tap having an odd number of lands with alternate teeth in the thread helix removed. In some designs alternate teeth are removed only for a portion of the thread length. Land: One of the threaded sections between the flutes of a tap. Lead: Distance a screw thread advances axially in one complete turn. Lead Error: Deviation from prescribed limits. Lead Deviation: Deviation from the basic nominal lead. Progressive Lead Deviation: (1) On a straight thread the deviation from a true helix where the thread helix advances uniformly. (2) On a taper thread the deviation from a true spiral where the thread spiral advances uniformly. Length of Thread: The length of the thread of the tap includes the chamfered threads and the full threads but does not include an external center. It is indicated by the letter “B” in the illustrations at the heads of the tables. Limits: The limits of size are the applicable maximum and minimum sizes. Major Diameter: On a straight thread the major diameter is that of the major cylinder. On a taper thread the major diameter at a given position on the thread axis is that of the major cone at that position. Minor Diameter: On a straight thread the minor diameter is that of the minor cylinder. On a taper thread the minor diameter at a given position on the thread axis is that of the minor cone at that position. Pitch Diameter (Simple Effective Diameter): On a straight thread, the pitch diameter is the diameter of the imaginary coaxial cylinder, the surface of which would pass through the thread profiles at such points as to make the width of the groove equal to one-half the basic pitch. On a perfect thread this coincidence occurs at the point where the widths of the thread and groove are equal. On a taper thread, the pitch diameter at a given position on the thread axis is the diameter of the pitch cone at that position.



895

Point Diameter: Diameter at the cutting edge of the leading end of the chamfered section. Rake: Angular relationship of the straight cutting face of a tooth with respect to a radial line through the crest of the tooth at the cutting edge. Positive rake means that the crest of the cutting face is angularly ahead of the balance of the cutting face of the tooth. Negative rake means that the crest of the cutting face is angularly behind the balance of the cutting face of the tooth. Zero rake means that the cutting face is directly on a radial line. Relief: Removal of metal behind the cutting edge to provide clearance between the part being threaded and the threaded land. Relief-Center: Clearance produced on a portion of the tap land by reducing the diameter of the entire thread form between cutting edge and heel. Relief-Chamfer: Gradual decrease in land height from cutting edge to heel on the chamfered portion of the land on a tap to provide radial clearance for the cutting edge. Relief-Con-eccentric Thread: Radial relief in the thread form starting back of a concentric margin. Relief-Double Eccentric Thread: Combination of a slight radial relief in the thread form starting at the cutting edge and continuing for a portion of the land width, and a greater radial relief for the balance of the land. Relief-Eccentric Thread: Radial relief in the thread form starting at the cutting edge and continuing to the heel. Relief-Flatted Land: Clearance produced on a portion of the tap land by truncating the thread between cutting edge and heel. Relief-Grooved Land: Clearance produced on a tap land by forming a longitudinal groove in the center of the land. Relief-Radial: Clearance produced by removal of metal from behind the cutting edge. Taps should have the chamfer relieved and should have back taper, but may or may not have relief in the angle and on the major diameter of the threads. When the thread angle is relieved, starting at the cutting edge and continuing to the heel, the tap is said to have “eccentric” relief. If the thread angle is relieved back of a concentric margin (usually onethird of land width), the tap is said to have “con-eccentric” relief. Size-Actual: Measured size of an element on an individual part. Size-Basic: That size from which the limits of size are derived by the application of allowances and tolerances. Size-Functional: The functional diameter of an external or internal thread is the pitch diameter of the enveloping thread of perfect pitch, lead and flank angles, having full depth of engagement but clear at crests and roots, and of a specified length of engagement. It may be derived by adding to the pitch diameter in an external thread, or subtracting from the pitch diameter in an internal thread, the cumulative effects of deviations from specified profile, including variations in lead and flank angle over a specified length of engagement. The effects of taper, out-of-roundness, and surface defects may be positive or negative on either external or internal threads. Size-Nominal: Designation used for the purpose of general identification. Spiral Flute: See Flutes. Spiral Point: Angular fluting in the cutting face of the land at the chamfered end. It is formed at an angle with respect to the tap axis of opposite hand to that of rotation. Its length is usually greater than the chamfer length and its angle with respect to the tap axis is usually made great enough to direct the chips ahead of the tap. The tap may or may not have longitudinal flutes. Thread Lead Angle: On a straight thread, the lead angle is the angle made by the helix of the thread at the pitch line with a plane perpendicular to the axis. On a taper thread, the lead angle at a given axial position is the angle made by the conical spiral of the thread, with the plane perpendicular to the axis, at the pitch line.



TAPS AND THREADING DIES Table 1. ANSI Standard Fraction-Size Taps — Cut Thread Limits ASME B94.9-1999 Threads per Inch

Tap Size

Major Diameter

Pitch Diameter

NC UNC

NF UNF

NS UNS

Basic

Min.

Max.

Basic

Min.

Max.

1⁄ 8

…

…

40

0.1250

0.1266

0.1286

0.1088

0.1090

0.1105

5⁄ 32

…

…

32

0.1563

0.1585

0.1605

0.1360

0.1365

0.1380

3⁄ 16

…

…

24

0.1875

0.1903

0.1923

0.1604

0.1609

0.1624

3⁄ 16

…

…

32

0.1875

0.1897

0.1917

0.1672

0.1677

0.1692

1⁄ 4

20

…

…

0.2500

0.2532

0.2557

0.2175

0.2180

0.2200

1⁄ 4

…

28

…

0.2500

0.2524

0.2549

0.2268

0.2273

0.2288

5⁄ 16

18

…

…

0.3125

0.3160

0.3185

0.2764

0.2769

0.2789

5⁄ 16

…

24

…

0.3125

0.3153

0.3178

0.2854

0.2859

0.2874

3⁄ 8

16

…

…

0.3750

0.3789

0.3814

0.3344

0.3349

0.3369

3⁄ 8

…

24

…

0.3750

0.3778

0.3803

0.3479

0.3484

0.3499

7⁄ 16

14

…

…

0.4375

0.4419

0.4449

0.3911

0.3916

0.3941

7⁄ 16

…

20

…

0.4375

0.4407

0.4437

0.4050

0.4055

0.4075

1⁄ 2

13

…

…

0.5000

0.5047

0.5077

0.4500

0.4505

0.4530

1⁄ 2

…

20

…

0.5000

0.5032

0.5062

0.4675

0.4680

0.4700

9⁄ 16

12

…

…

0.5625

0.5675

0.5705

0.5084

0.5089

0.5114

9⁄ 16

…

18

…

0.5625

0.5660

0.5690

0.5264

0.5269

0.5289

5⁄ 8

11

…

…

0.6250

0.6304

0.6334

0.5660

0.5665

0.5690

5⁄ 8

…

18

…

0.6250

0.6285

0.6315

0.5889

0.5894

0.5914

3⁄ 4

10

…

…

0.7500

0.7559

0.7599

0.6850

0.6855

0.6885

3⁄ 4

…

16

…

0.7500

0.7539

0.7579

0.7094

0.7099

0.7124

7⁄ 8

9

…

…

0.8750

0.8820

0.8860

0.8028

0.8038

0.8068

7⁄ 8

…

14

…

0.8750

0.8799

0.8839

0.8286

0.8296

0.8321

1

8

…

…

1.0000

1.0078

1.0118

0.9188

0.9198

0.9228

1

…

12

…

1.0000

1.0055

1.0095

0.9459

0.9469

0.9494

1

…

…

14

1.0000

1.0049

1.0089

0.9536

0.9546

0.9571

11⁄8

7

…

…

1.1250

1.1337

1.1382

1.0322

1.0332

1.0367

11⁄8

…

12

…

1.1250

1.1305

1.1350

1.0709

1.0719

1.0749

11⁄4

7

…

…

1.2500

1.2587

1.2632

1.1572

1.1582

1.1617

11⁄4

…

12

…

1.2500

1.2555

1.2600

1.1959

1.1969

1.1999

13⁄8

6

…

…

1.3750

1.3850

1.3895

1.2667

1.2677

1.2712

13⁄8

…

12

…

1.3750

1.3805

1.3850

1.3209

1.3219

1.3249

11⁄2

6

…

…

1.5000

1.5100

1.5145

1.3917

1.3927

1.3962

11⁄2

…

12

…

1.5000

1.5055

1.5100

1.4459

1.4469

1.4499

13⁄4

5

…

…

1.7500

1.7602

1.7657

1.6201

1.6216

1.6256

2

41⁄2

…

…

2.0000

2.0111

2.0166

1.8557

1.8572

1.8612

All dimensions are given in inches. Lead Tolerance: Plus or minus 0.003 inch max. per inch of thread. Angle Tolerance: Plus or minus 35 min. in half angle or 53 min. in full angle for 41⁄2 to 51⁄2 thds. per in.; 40 min. half angle and 60 min. full angle for 6 to 9 thds.; 45 min. half angle and 68 min. full angle for 10 to 28 thds.; 60 min. half angle and 90 min. full angle for 30 to 64 thds. per in.



Table 2. ANSI Standard Fractional-Size Taps — Ground Thread Limits ASME B94.9-1999 Threads per Inch Size in.

1 1 1 11⁄8 11⁄8 11⁄4 11⁄4 13⁄8 13⁄8 11⁄2 11⁄2 13⁄4 2

NF UNF

NS UNS

20 … 18 … 16 … 14 … 13 … 12 … 11 … … … 10 … 9 … 8 … … 7 … 7 … 6 … 6 … … …

… 28 … 24 … 24 … 20 … 20 … 18 … 18 … … … 16 … 14 … 12 … … 12 … 12 … 12 … 12 5 4.5

… … … … … … … … … … … … … … 11 16 … … … … … … 14 … … … … … … … … … …

Major Diameter Basic 0.2500 0.2500 0.3125 0.3125 0.3750 0.3750 0.4375 0.4375 0.5000 0.5000 0.5625 0.5625 0.6250 0.6250 0.6875 0.6875 0.7500 0.7500 0.8750 0.8750 1.0000 1.0000 1.0000 1.1250 1.1250 1.2500 1.2500 1.3750 1.3750 1.5000 1.5000 1.7500 2.0000

Min. 0.2532 0.2523 0.3161 0.3152 0.3790 0.3777 0.4422 0.4407 0.5050 0.5032 0.5679 0.5661 0.6309 0.6286 0.6934 0.6915 0.7565 0.7540 0.8822 0.8797 1.0082 1.0054 1.0047 1.1343 1.1304 1.2593 1.2554 1.3859 1.3804 1.5109 1.5054 1.7630 2.0145

Basic Pitch Dia.

Max. 0.2565 0.2546 0.3197 0.3179 0.3831 0.3804 0.4468 0.4440 0.5100 0.5065 0.5733 0.5697 0.6368 0.6322 0.6993 0.6956 0.7630 0.7581 0.8894 0.8843 1.0163 1.0108 1.0093 1.1436 1.1358 1.2686 1.2608 1.3967 1.3858 1.5217 1.5108 1.7760 2.0289

0.2175 0.2268 0.2764 0.2854 0.3344 0.3479 0.3911 0.4050 0.4500 0.4675 0.5084 0.5264 0.5660 0.5889 0.6285 0.6469 0.6850 0.7094 0.8028 0.8286 0.9188 0.9459 0.9536 1.0322 1.0709 1.1572 1.1959 1.2667 1.3209 1.3917 1.4459 1.6201 1.8557

H1 Limit Min. Max. 0.2175 0.2268 0.2764 0.2854 0.3344 0.3479 … … 0.4500 0.4675 … … … … … … … 0.7094 … …

0.2180 0.2273 0.2769 0.2859 0.3349 0.3484 … … 0.4505 0.4680 … … … … … … … 0.7099 … …

H2 Limit Min. Max. 0.2180 0.2273 0.2769 0.2859 0.3349 0.3484 0.3916 … 0.4505 0.4680 … 0.5269 0.5665 0.5894 … … 0.6855 0.7099 … 0.8291

0.2185 0.2278 0.2774 0.2864 0.3354 0.3489 0.3921 … 0.4510 0.4685 … 0.5274 0.5670 0.5899 … … 0.6860 0.7104 … 0.8296

Notes: a H4 limit value; b H5 limit value; c H6 limit value; e H7 limit value; f H8 limit value. Minimum and maximum major diameters are: d 0.0010 larger than shown; g 0.0035 larger than shown; h 0.0020 larger than shown; i 0.0015 larger than shown.

Pitch Diameter H3 & H4 a Limits Min. Max. 0.2185 0.2278 0.2774 0.2864 0.3354 0.3489 0.3921 0.4060 0.4510 0.4685 0.5094 0.5274 0.5670 0.5899 0.6295 0.6479 0.6860 0.7104 0.8043 a 0.8301 a 0.9203 a 0.9474 a 0.9551 a 1.0337 a 1.0724 a 1.1587 a 1.1974 a 1.2682 a 1.3224 a 1.3932 a 1.4474 a 1.6216 a 1.8572 a

0.2190 0.2283 0.2779 0.2869 0.3359 0.3494 0.3926 0.4065 0.4515 0.4690 0.5099 0.5279 0.5675 0.5904 0.6300 0.6484 0.6865 0.7109 0.8048 a 0.8306 a 0.9208 a 0.9479 a 0.9556 a 1.0342 a 1.0729 a 1.1592 a 1.1979 a 1.2687 a 1.3229 a 1.3937 a 1.4479 a 1.6221 a 1.8577 a

H4 a, H5 b, H6 c Limits Min. Max. b, d

0.2195 0.2283 a 0.2784 b, d 0.2869 a 0.3364 b, d 0.3494 a 0.3931b, d 0.4070 b, d 0.4520 b, d 0.4695 b, d 0.5104 b, d 0.5284 b, d 0.5680 b, d 0.5909 b, d … … 0.6870 b, d 0.7114 b, d 0.8053 c … 0.9213 c … … … … … … … … … … … …

b, d

0.2200 0.2288 a 0.2789 b, d 0.2874 a 0.3369 b, d 0.3499 a 0.3936 b, d 0.4075 b, d 0.4525 b, d 0.4700 b, d 0.5109 b, d 0.5289 b, d 0.5685 b, d 0.5914 b, d … … 0.6875 b, d 0.7119 b, d 0.8058 c … 0.9218 c … … … … … … … … … … … …

H7 e, H8 f Limits Min. Max. … … 0.2794 e, h 0.2884 e, h 0.3374 e, h 0.3509 e, h 0.3946 f 0.4085 f 0.4536 f 0.4710 f 0.5114 e, h 0.5294 e, h 0.5690 e, h 0.5919 e, h … … 0.6880 e, i 0.7124 e, i … … … … … … … … … … … … … … …

… … 0.2799 e, h 0.2889 e, h 0.3379 e, h 0.3514 e, h 0.3951 f 0.4090 f 0.4240 f 0.4715 f 0.5119 e, h 0.5299 e, h 0.5695 e, h 0.5924 e, h … … 0.6885 e, i 0.7129 e, i … … … … … … … … … … … … … … …


897

All dimensions are given in inches. Limits listed in the above table are the most commonly used in industry. Not all styles of taps are available with all limits listed. For calculation of limits not listed see ASME B94.9-1999


1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 11⁄ 16 11⁄ 16 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8

NC UNC


Major Diameter

898

Table 3. ANSI Standard Machine Screw Taps — Ground Thread Limits ASME B94.9-1999 Threads per Inch

Pitch Diameter Limits H1 Limit

H3 a, H4 b, H5 c Limits

H2 Limit

Max.

Basic Pitch Dia.

Min.

Max.

Min.

Max.

Min.

0.0605

0.0616

0.0519

0.0519

0.0524

0.0524

0.0529

Notes:

0.0730

0.0736

0.0750

0.0629

0.0629

0.0634

0.0634

0.0639

0.0730

0.0736

0.0748

0.0640

0.0640

0.0645

0.0645

0.0650

0.0860

0.0867

0.0883

0.0744

0.0744

0.0749

0.0749

0.0754

H6 d, H7 e, H10 f Limits

Size

NC UNC

NF UNF

NS UNS

Basic

Min.

0

…

80

…

0.0600

1

64

…

…

1

…

72

…

2

56

…

…

2

…

64

…

0.0860

0.0866

0.0880

0.0759

…

…

0.0764

0.0769

3

48

…

…

0.0990

0.0999

0.1017

0.0855

…

…

0.0860

0.0865

3

…

56

…

0.0990

0.0997

0.1013

0.0874

0.0874

0.0879

0.0879

0.0884

4

40

…

…

0.1120

0.1134

0.1152

0.0958

0.0958

0.0963

0.0963

0.0968

0.0978 c, j

0.0983 c, j

…

…

4

…

48

…

0.1120

0.1129

0.1147

0.0985

0.0985

0.0990

0.0990

0.0995

0.1005 c, j

0.1010 c, j

…

…

4

…

…

36

0.1120

0.1135

0.1156

0.0940

0.0940

0.0945

0.0945

0.0950

0.0960 c, j

0.0965 c, j

…

…

5

40

…

…

0.1250

0.1264

0.1283

0.1088

0.1088

0.1093

0.1093

0.1098

0.1108 c, j

0.1113 c, j

…

…

5

…

44

…

0.1250

0.1263

0.1280

0.1102

…

…

0.1107

0.1112

0.1122 c, j

0.1127 c, j

…

6

32

…

…

0.1380

0.1401

0.1421

0.1177

0.1177

0.1182

0.1182

0.1187

0.1187 a 0.1197 c, g

0.1192 a 0.1202 g

0.1207 e, h 0.1222 f, i

Max.

Min.

Max.

a H3 d H6

limit value; b H4 limit value; c H5 limit value; limit value; e H7 limit value; f H10 limit value.

Minimum and maximum major diameters are: 0.0010 larger than shown; h 0.0020 larger than shown;i 0.0035 larger than shown; j 0.0015 larger than shown.

g

6

…

40

…

0.1380

0.1394

0.1413

0.1218

0.1218

0.1223

0.1223

0.1228

0.1238 c

0.1243 c

…

…

8

32

…

…

0.1640

0.1661

0.1681

0.1437

0.1437

0.1442

0.1442

0.1447

0.1447 a 0.1457 g

0.1452 a 0.1462 g

0.1467 e, h 0.1482 f, i

0.1472 e, h 0.1487 f, i

8

…

36

…

0.1640

0.1655

0.1676

0.1460

…

…

0.1465

0.1470

0.1480 g

0.1485 g

10

24

…

…

0.1900

0.1927

0.1954

0.1629

0.1629

0.1634

0.1634

0.1639

0.1639 a 0.1644 b

0.1644 a 0.1649 b

0.1654 d, g 0.1659 e, h

…

0.1659 d, g 0.1664 e, h

10

…

32

…

0.1900

0.1921

0.1941

0.1697

0.1697

0.1702

0.1702

0.1707

0.1707 a 0.1712 b

0.1712 a 0.1717 b

0.1722 d, g 0.1727 e, h 0.1742 f, i

0.1727 d, g 0.1732 e, h 0.1747 f, i

12

24

…

…

0.2160

0.2187

0.2214

0.1889

…

…

…

…

0.1899 a 0.0914 b

0.1904 a 0.1919 b

0.1914 d, g

0.1919 d, g

12

…

28

…

0.2160

0.2183

0.2206

0.1928

…

…

…

…

0.1938 a 0.1953 b

0.1943 a 0.1958 b

0.1953 d, g

0.1958 d, g

All dimensions are given in inches. Limits listed in table are most commonly used in industry. Not all style of taps are available with all limits listed.


…


… 0.1212 e, h 0.1227 f, i


899

Table 4a. ANSI Standard Metric Tap Ground Thread Limits in Inches — M Profile ASME B94.9-1999 Nominal Diam, mm 1.6 2 2.5 3 3.5 4 4.5 5 6 7 8 10 12 14 16 20 24 30 36 42 48

Pitch, mm 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1 1.25 1.5 1.75 2 2 2.5 3 3.5 4 4.5 5

Basic 0.06299 0.07874 0.09843 0.11811 0.13780 0.15748 0.17717 0.19685 0.23622 0.27559 0.31496 0.39370 0.47244 0.55118 0.62992 0.78740 0.94488 1.18110 1.41732 1.65354 1.88976

Major Diameter (Inches) Min 0.06409 0.08000 0.09984 0.11969 0.13969 0.15969 0.17953 0.19937 0.23937 0.27874 0.31890 0.39843 0.47795 0.55748 0.63622 0.79538 0.95433 1.19213 1.42992 1.66772 1.90551

Max 0.06508 0.08098 0.10083 0.12067 0.14067 0.16130 0.18114 0.20098 0.24098 0.28035 0.32142 0.40094 0.48047 0.56000 0.63874 0.79780 0.95827 1.19606 1.43386 1.71102 1.98819

Basic 0.05406 0.06850 0.08693 0.10531 0.12244 0.13957 0.15799 0.17638 0.21063 0.25000 0.28299 0.35535 0.42768 0.50004 0.57878 0.72346 0.86815 1.09161 1.31504 1.53846 1.76189

Pitch Diameter (Inches) Min 0.05500 0.06945 0.08787 0.10626 0.12370 0.14083 0.15925 0.17764 0.21220 0.25157 0.28433 0.35720 0.42953 0.50201 0.58075 0.72543 0.87063 1.09417 1.31760 1.54154 1.76496

Max 0.05559 0.07004 0.08846 0.10685 0.12449 0.14161 0.16004 0.17843 0.21319 0.25256 0.28555 0.35843 0.43075 0.50362 0.58236 0.72705 0.87224 1.09622 1.31965 1.54358 1.76701

Basic pitch diameter is the same as minimum pitch diameter of internal thread, Class 6H as shown in table starting on page 1798. Pitch diameter limits are designated in the Standard as D3 for 1.6 to 3 mm diameter sizes, incl.: D4 for 3.5 to 5 mm sizes, incl.; D5 for 6 and 8 mm sizes; D6 for 10 and 12 mm sizes; D7 for 14 to 20 mm sizes, incl.; D8 for 24 mm size; and D9 for 30 and 36 mm sizes. Angle tolerances are plus or minus 30 minutes in half angle for pitches ranging from 0.35 through 2.5 mm, incl. and plus or minus 25 minutes in half angle for pitches ranging from 3 to 4 mm, incl. A maximum deviation of plus or minus 0.0005 inch within any two threads not farther apart than one inch is permitted.

Table 4b. ANSI Standard Metric Tap Ground Thread Limits in Millimeters— M Profile ASME B94.9-1999 Nominal Diam, mm 1.6 2 2.5 3 3.5 4 4.5 5 6 7 8 10 12 14 16 20 24 30 36 42 48

Pitch, mm 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1 1.25 1.5 1.75 2 2 2.5 3 3.5 4 4.5 5

Basic 1.600 2.000 2.500 3.000 3.500 4.000 4.500 5.000 6.000 7.000 8.000 10.000 12.000 14.000 16.000 20.000 24.000 30.000 36.000 42.000 48.000

Major Diameter (mm) Min 1.628 2.032 2.536 3.040 3.548 4.056 4.560 5.064 6.080 7.080 8.100 10.120 12.140 14.160 16.160 20.200 24.240 30.280 36.320 42.360 48.400

Max

Basic

Pitch Diameter (mm) Min

Max

1.653 2.057 2.561 3.065 3.573 4.097 4.601 5.105 6.121 7.121 8.164 10.184 12.204 14.224 16.224 20.264 24.340 30.380 36.420 43.460 50.500

1.373 1.740 2.208 2.675 3.110 3.545 4.013 4.480 5.350 6.350 7.188 9.026 10.863 12.701 14.701 18.376 22.051 27.727 33.402 39.077 44.752

1.397 1.764 2.232 2.699 3.142 3.577 4.045 4.512 5.390 6.390 7.222 9.073 10.910 12.751 14.751 18.426 22.114 27.792 33.467 39.155 44.830

1.412 1.779 2.247 2.714 3.162 3.597 4.065 4.532 5.415 6.415 7.253 9.104 10.941 12.792 14.792 18.467 22.155 27.844 33.519 36.207 44.882

Basic pitch diameter is the same as minimum pitch diameter of internal thread, Class 6H as shown in table starting on page 1798. Pitch diameter limits are designated in the Standard as D3 for 1.6 to 3 mm diameter sizes, incl.: D4 for 3.5 to 5 mm sizes, incl.; D5 for 6 and 8 mm sizes; D6 for 10 and 12 mm sizes; D7 for 14 to 20 mm sizes, incl.; D8 for 24 mm size; D9 for 30 and 36 mm sizes; D10 for 42 and 48 mm sizes.



TAPS AND THREADING DIES Table 5. ANSI Standard Machine Screw Taps — Cut Threads Limits ASME B94.9-1999

Size 0 1 1 2 2 3 3 4 4 4 5 6 6 6 8 8 8 10 10 12 12 14

NC UNC

Threads per Inch NF NS UNF UNS

… 64 … 56 … 48 … … 40 … 40 32 … … 32 … … 24 … 24 … …

80 … 72 … 64 … 56 … … 48 … … … 40 … 36 … … 32 … 28 …

… … … … … … … 36 … … … … 36 … … … 40 … … … … 24

Major Diameter

Pitch Diameter

Basic

Min.

Max.

Basic

Min.

Max.

0.0600 0.0730 0.0730 0.0860 0.0860 0.0990 0.0990 0.1120 0.1120 0.1120 0.1250 0.1380 0.1380 0.1380 0.1640 0.1640 0.1640 0.1900 0.1900 0.2160 0.2160 0.2420

0.0609 0.0740 0.0740 0.0872 0.0870 0.1003 0.1002 0.1137 0.1136 0.1133 0.1266 0.1402 0.1397 0.1396 0.1662 0.1657 0.1656 0.1928 0.1922 0.2188 0.2184 0.2448

0.0624 0.0755 0.0755 0.0887 0.0885 0.1018 0.1017 0.1157 0.1156 0.1153 0.1286 0.1422 0.1417 0.1416 0.1682 0.1677 0.1676 0.1948 0.1942 0.2208 0.2204 0.2473

0.0519 0.0629 0.0640 0.0744 0.0759 0.0855 0.0874 0.0940 0.0958 0.0985 0.1088 0.1177 0.1200 0.1218 0.1437 0.1460 0.1478 0.1629 0.1697 0.1889 0.1928 0.2149

0.0521 0.0631 0.0642 0.0746 0.0761 0.0857 0.0876 0.0942 0.0960 0.0987 0.1090 0.1182 0.1202 0.1220 0.1442 0.1462 0.1480 0.1634 0.1702 0.1894 0.1933 0.2154

0.0531 0.0641 0.0652 0.0756 0.0771 0.0867 0.0886 0.0957 0.0975 0.1002 0.1105 0.1197 0.1217 0.1235 0.1457 0.1477 0.1495 0.1649 0.1717 0.1909 0.1948 0.2174

All dimensions are given in inches. Lead Tolerance: Plus or minus 0.003 inch per inch of thread. Angle Tolerance: Plus or minus 45 min. in half angle and 65 min. in full angle for 20 to 28 threads per inch; plus or minus 60 min. in half angle and 90 min. in full angle for 30 or more threads per inch.

Table 6a. ANSI Standard Taper Pipe Taps — Cut Thread Tolerances for NPT and Ground Thread Tolerances for NPT, NPTF, and ANPT ASME B94.9-1999

Nominal Size 1⁄ 16 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1 11⁄4 11⁄2 2 21⁄2 3 31⁄2 b 4b

Threads per Inch NPT, NPTF, or ANPT 27 27 18 18 14 14 111⁄2 111⁄2 111⁄2 111⁄2 8 8 8 8

Gage Measurementa Tolerance Plus or Minus Projection Cut Ground Inches Thread Thread 0.312 0.312 0.459 0.454 0.579 0.565 0.678 0.686 0.699 0.667 0.925 0.925 0.938 0.950

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0937 0.0937 0.0937 0.0937 0.0937 0.0937 1⁄ 8 1⁄ 8

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0937 0.0937 0.0937 0.0937 0.0937 0.0937 1⁄ 8 1⁄ 8

Taper per Inch on Diameter, Inches Cut Thread Ground Thread Min.

Max.

Min.

Max.

0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0612 0.0612 47⁄ c 64 47⁄ c 64

0.0703 0.0703 0.0703 0.0703 0.0677 0.0677 0.0677 0.0677 0.0677 0.0677 0.0664 0.0664 51⁄ c 64 51⁄ c 64

0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0612 0.0612 47⁄ c 64 47⁄ c 64

0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 25⁄ c 32 25⁄ c 32

a Distance that small end of tap projects through L1 taper ring gage (see ANSI B1.20.3). b

No longer included in ASME B94.9-1999 shown for reference only.

c Taper per foot, inches.

All dimensions are given in inches. Lead Tolerance: Plus or minus 0.003 inch per inch of cut thread and plus or minus 0.0005 inch per inch of ground thread. Angle Tolerance: Plus or minus 40 min. in half angle and 60 min. in full angle for 8 cut threads per inch; plus or minus 45 min. in half angle and 60 min. in full angle for 111⁄2 to 27 cut threads per inch; plus or minus 25 min. in half angle for 8 ground threads per inch; and plus and minus 30 min. in half angle for 111⁄2 to 27 ground threads per inch.



901

Table 6b. ANSI Taper Pipe Thread — Widths of Flats at Tap Crests and Roots for Cut Thread NPT and Ground Thread NPT, ANPT, and NPTF ASME B94.9-1999 Threads per Inch 27 18 14 111⁄2 8

Column I NPT—Cut and Ground Thread ANPT—Ground Thread

Tap Flat Width at { Major Diameter { Minor Diameter { Major Diameter { Minor Diameter { Major Diameter { Minor Diameter { Major Diameter { Minor Diameter { Major Diameter { Minor Diameter

a Minimum minor diameter

Column II NPTF—Cut and Ground Thread

Minimuma

Maximum

Minimuma

Maximum

0.0014 … 0.0021 … 0.0027 … 0.0033 … 0.0048 …

0.0041 0.0041 0.0057 0.0057 0.0064 0.0064 0.0073 0.0073 0.0090 0.0090

0.0040 … 0.0050 … 0.0050 … 0.0060 … 0.0080 …

0.0055 0.0040 0.0065 0.0050 0.0065 0.0050 0.0083 0.0060 0.0103 0.0080

falts are not specified. May be sharp as practicable.

All dimensions are given in inches. Note: Cut Thread taps made to Column I are marked NPT but are not recommended for ANPT applications. Ground Thread taps made to Column I are marked NPT and may be used for NPT and ANPT applications. Ground Thread taps made to Column II are marked NPTF and used for Dryseal application.

Table 7a. ANSI Standard Straight Pipe Taps (NPSF—Dryseal) Ground Thread Limits ASME B94.9-1999 Major Diameter Nominal Size, Inches 1⁄ 16 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

Threads per Inch 27 27 18 18 14 14

Min. G 0.3008 0.3932 0.5239 0.6593 0.8230 1.0335

Max. H 0.3018 0.3942 0.5249 0.6603 0.8240 1.0345

Pitch Diameter Plug at Gaging Notch E 0.2812 0.3736 0.4916 0.6270 0.7784 0.9889

Min. K 0.2772 0.3696 0.4859 0.6213 0.7712 0.9817

Max. L 0.2777 0.3701 0.4864 0.6218 0.7717 0.9822

Minora Dia. Flat, Max. 0.004 0.004 0.005 0.005 0.005 0.005

a As specified or sharper.

Formulas For American Dryseal (NPSF) Ground Thread Taps Major Diameter Pitch Diameter Min. Max. Min. Max. G H K L H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F H − 0.0010 K + Q − 0.0005 L − 0.0005 E−F

Nominal Size, Inches 1⁄ 16 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

Threads per Inch 27 18 14

Values to Use in Formulas F 0.0035 Pitch diameter of plug 0.0052 at gaging notch 0.0067 E

M Actual measured pitch diameter

Max. Minor Dia. M−Q M−Q M−Q M−Q M−Q M−Q Q 0.0251 0.0395 0.0533

All dimensions are given in inches. Lead Tolerance: Plus or minus 0.0005 inch within any two threads not farther apart than one inch. Angle Tolerance: Plus or minus 30 min. in half angle for 14 to 27 threads per inch.



TAPS AND THREADING DIES Table 7b. ANSI Standard Straight Pipe Taps (NPS) Cut Thread Limits ASME B94.9-1999 Threads per Inch, NPS, NPSC

Size at Gaging Notch

Min.

Max.

A

B

C

1⁄ 8

27

0.3736

0.3721

0.3751

0.0267

0.0296

0.0257

1⁄ 4

18

0.4916

0.4908

0.4938

3⁄ 8

18

0.6270

0.6257

0.6292

} 0.0408

0.0444

0.0401

1⁄ 2

14

0.7784

0.7776

0.7811

3⁄ 4

14

0.9889

0.9876

0.9916

111⁄2

1.2386

1.2372

1.2412

Nominal Size

1

Pitch Diameter

Values to Use in Formulas

} 0.0535

0.0571

0.0525

0.0658

0.0696

0.0647

The following are approximate formulas, in which M = measured pitch diameter in inches: Major dia., min. = M + A Major dia., max. = M + B Minor dia., max. = M − C

All dimensions are given in inches. Lead Tolerance: Plus or minus 0.003 inch per inch of thread. Angle Tolerance: All pitches, plus or minus 45 min. in half angle and 68 min. in full angle. Taps made to these specifications are to be marked NPS and used for NPSC thread form.

Table 7c. ANSI Standard Straight Pipe Taps (NPS) Ground Thread Limits ASME B94.9-1999

Nominal Size, Inches

Major Diameter Plug at Gaging Notch 0.3983 0.5286 0.6640 0.8260 1.0364 1.2966

Max. L 0.3751 0.4938 0.6292 0.7811 0.9916 1.2412

1⁄ 8

Formulas for NPS Ground Thread Tapsa Minor Threads Major Diameter Dia. per Inch Min. G Max. H Max. 27 H − 0.0010 (K + A) − 0.0010 M−B 18

A 0.0296 0.0444

B 0.0257 0.0401

to 3⁄4 1

H − 0.0010

(K + A) − 0.0020

M−B

0.0571

0.0525

H − 0.0015

(K + A) − 0.0021

M−B

111⁄2

1

Nominal Size

Min. G 0.4022 0.5347 0.6701 0.8347 1.0447 1.3062

Pitch Diameter

Max. H 0.4032 0.5357 0.6711 0.8357 1.0457 1.3077

Plug at Gaging Notch E 0.3736 0.4916 0.6270 0.7784 0.9889 1.2386

Min. K 0.3746 0.4933 0.6287 0.7806 0.9906 1.2402

1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1⁄ 4

Threads per Inch, NPS, NPSC, NPSM 27 18 18 14 14

14

0.0696 0.0647 111⁄2 The maximum Pitch Diameter of tap is based upon an allowance deducted from the maximum product pitch diameter of NPSC or NPSM, whichever is smaller. The minimum Pitch Diameter of tap is derived by subtracting the ground thread pitch diameter tolerance for actual equivalent size. a In the formulas, M equals the actual measured pitch diameter.

All dimensions are given in inches. Lead tolerance: Plus or minus 0.0005 inch within any two threads not farther apart than one inch. Angle Tolerance: All pitches, plus or minus 30 min. in half angle. Taps made to these specifications are to be marked NPS and used for NPSC and NPSM.



903

0 1 1 2 2 2 3 3 3 4 4 4 4 5 5 5 6 6 6 6 8 8 8 8 10 10 10 10 10 12 12

0.060 0.073 0.073 0.086 0.086 0.086 0.099 0.099 0.099 0.112 0.112 0.112 0.112 0.125 0.125 0.125 0.138 0.138 0.138 0.138 0.164 0.164 0.164 0.164 0.190 0.190 0.190 0.190 0.190 0.216 0.216

NC NF NS UNC UNF UNS … 64 … 56 56 … 48 48 … … 40 40 … 40 40 … 32 32 … … 32 32 32 … 24 24 … … 24 24 …

80 … 72 … … 64 … … 56 … … … 48 … … 44 … … 40 40 … … … 36 … … 32 32 32 … 28

… … … … … … … … … 36 … … … … … … … … … … … … … … … … … … … … …

No. of Flutes 2 2 2 2b 3 3 2b 3 3 3 2b 3 3 2b 3 3 2b 3 2b 3 2b 3b 4 4 2* 3b 2b 3b 4 4 4

H1

H2

H3

H7

TPB TPB TPB … TPB … … P … … P … … … P … P TPB … P P … TPB … … … P … TPB … …

PB P PB PB TPB TPB PB TPB TPB TPB PB TPB TPB PB TPB TPB PB TPB P TPB PB PB TPB TPB PB P PB PB TPB … …

… … … … … … … … … … … … … … … … PB TPB … … PB PB TPB … PB PB PB PB TPB TPB TPB

… … … … … … … … … … … … … … … … … PB … … … PB PB … … … … PB PB … …

Length Overall A 15⁄8 111⁄16 111⁄16 13⁄4 13⁄4 13⁄4 113⁄16 113⁄16 113⁄16 17⁄8 17⁄8 17⁄8 17⁄8 115⁄16 115⁄16 115⁄16 2 2 2 2 21⁄8 21⁄8 21⁄8 21⁄8 23⁄8 23⁄8 23⁄8 23⁄8 23⁄8 23⁄8 23⁄8

Diameter of Shank D

Basic Major Diameter

Length of Square C

Pitch Dia.Limits and Chamfersa

Threads per Inch Size

Length of Thread B

Table 8a. ANSI Standard Ground Thread Straight Fluted Taps Machine Screw Sizes ASME B94.9-1999

E

5⁄ 16 3⁄ 16 3⁄ 8 7⁄ 16 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8 11⁄ 16 11⁄ 16 11⁄ 16 11⁄ 16 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 15⁄ 16 15⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 9⁄ 32 9⁄ 32

0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.168 0.168 0.168 0.168 0.194 0.194 0.194 0.194 0.194 0.220 0.220

0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.131 0.131 0.131 0.131 0.152 0.152 0.152 0.152 0.152 0.165 0.165

a Chamfer designations are: T = taper, P = plug, and B = bottoming. b Optional number of flutes.

All dimensions are given in inches. These taps are standard as high-speed steel taps with ground threads, with standard and optional number of flutes and pitch diameter limits and chamfers as given in the table. These are style 1 taps and have external centers on thread and shank ends (may be removed on thread end of bottoming taps). For standard thread limits see Table 3. For eccentricity tolerances see Table 22. Tolerances: Numbers 0 to 12 size range — A, ± 1⁄32 ; B, ± 3⁄64 ; C, ± 1⁄32 ; D, − 0.0015; E, − 0.004.



TAPS AND THREADING DIES Table 8b. ANSI Standard Cut Thread Straight Fluted Taps Machine Screw Sizes ASME B94.9-1999

Size 0 1 2 3 4 5 6 8 10 12 14

Threads per Inch Carbon Steel HS Steel

Basic Major Diameter 0.060 0.073 0.086 0.099 0.112 0.125 0.138 0.164 0.190 0.216 0.242

NC UNC

NF UNF

NS UNS

NC UNC

NF UNF

Number of Flutes

…

80a 72a 64a 56a 48a …

… … … …

… … … …

36a …

40a 40a 32 32 24 24 …

… … … … … … … … 32 … …

2 2 3 3 3 3 3 4 4 4 4

64a 56 48a 40 40 32 32 24 24 …

40a 36a 32

36a 40a … …

28a …

24a

Length of Thread, B

Length Overall, A 15⁄8 111⁄16 13⁄4 113⁄16 17⁄8 115⁄16 2

Dimensions Length Diameter of Square, of Shank, D C

5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8 15⁄ 16

21⁄8 23⁄8 23⁄8 21⁄2

3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 9⁄ 32 5⁄ 16

1

Size of Square, E

0.141 0.141 0.141 0.141 0.141 0.141 0.141 0.168 0.194 0.220 0.255

0.110 0.110 0.110 0.110 0.110 0.110 0.110 0.131 0.152 0.165 0.191

a These taps are standard with plug chamfer only. All others are standard with taper, plug or bottom-

ing chamfer. Tolerances for General Dimensions Element

Range

Length Overall, A Length of Thread, B

Tolerance

0 to 14 incl

±1⁄32

0 to 12 incl

±3⁄64 ±1⁄16

14

Length of Square, C

Element

Tolerance −0.004 −0.005

14

Size of Square, E

±1⁄32

0 to 14 incl

Range 0 to 12 incl

Diameter of Shank, D

−0.004

0 to 14 incl

All dimensions are given in inches. Styles 1 and 2 cut thread taps have optional style centers on thread and shank ends. For standard thread limits see Table 5. For eccentricity tolerances see Table 22.

Table 9. ANSI Standard Nut Taps (formerly ANSI/ASME B94.9-1987)

Dia. of Tap

Threads per Inch NC,UNC

Number of Flutes

1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2

20 18 16 13

4 4 4 4

Element Overall Length, A Thread Length, B Square Length, C

Diameter Range 1⁄ 4 1⁄ 4 1⁄ 4

to 1⁄2 to 1⁄2 to 1⁄2

Length Overall, A 5 51⁄2 6 7

Length of Thread, B

Length of Square, C

15⁄8 113⁄16 2 21⁄2

9⁄ 16 5⁄ 8 11⁄ 16 7⁄ 8

Tolerances for General Dimensions Tolerance Element ±1⁄16 ±1⁄16 ±1⁄32

Shank Diameter,D Size of Square,E


Size of Square, E

0.185 0.240 0.294 0.400

0.139 0.180 0.220 0.300

Diameter Range 1⁄ 4 1⁄ 4

to 1⁄2 to 1⁄2

Tolerance −0.005 −0.004

All dimensions are given in inches. These ground thread high-speed steel taps are standard in H3 limit only. All taps have an internal center in thread end. For standard limits see Table 2. Chamfer J is made 1⁄2 ro 3⁄4 the thread length of B.



905

Table 10. ANSI Standard Spiral-Pointed Taps Machine Screw Sizes ASME B94.9-1999

High-Speed Steel Taps with Ground Threads Threads per Basic Inch Major NF NS Diam- NC UNC UNF UNS eter

Size

Pitch Dia. Limits and Chamfers†

No. of Flute s

H1

H2

H3

H7

Length Overall A

0

0.060

…

80

…

2

PB

PB

…

…

15⁄8

1

0.073

64

72

…

2

P

P

…

…

111⁄16

2

0.086

56

…

…

2

PB

PB

…

…

2

0.086

…

64

…

2

…

P

…

…

3

0.099

48

…

…

2

…

PB

…

…

3

0.099

…

56

…

2

P

P

…

…

4

0.112

…

…

36

2

…

P

…

…

4

0.112

40

…

…

2

P

PB

…

…

4

0.112

…

48

…

2

P

PB

…

…

5

0.125

40

…

…

2

P

PB

…

…

5

0.125

…

44

…

2

…

P

…

…

13⁄4 13⁄4 113⁄16 113⁄16 17⁄8 17⁄8 17⁄8 115⁄16 115⁄16

6

0.138

32

…

…

2

P

PB

PB

PB

2

6

0.138

…

40

…

2

…

PB

…

…

2 21⁄8 21⁄8 23⁄8 23⁄8 23⁄8 23⁄8

8

0.164

32

…

…

2

P

PB

PB

PB

8

0.164

…

36

…

2

…

P

…

…

10

0.190

24

…

…

2

P

PB

PB

P

10

0.190

…

32

…

2

PB

PB

PB

P

12

0.216

24

…

…

2

…

…

PB

…

12

0.216

…

28

…

2

…

…

P

…

Length of Thread B

Length of Square C

Diameter of Shank D

Size of Square E

5⁄ 16 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 11⁄ 16 11⁄ 16 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8 15⁄ 16 15⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 9⁄ 32 9⁄ 32

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.168

0.131

0.168

0.131

0.194

0.152

0.194

0.152

0.220

0.165

0.220

0.165

High-Speed and Carbon Steel Taps with Cut Threads Threads per Inch Carbon Steel HS Steel

Size


NC UNC

NF UNF

NC UNC

NF UNF

No. of Flutes

Length Overall, A

4

0.112

…

…

40

…

2

17⁄8

5

0.125

…

…

40

…

2

6

0.138

32

…

32

…

2

115⁄16 2

8

0.164

32

…

32

…

2

21⁄8

10

0.190

24

32

24

32

2

23⁄8

12

0.216

…

…

24

…

2

23⁄8

Length of Thread, B

Length of Square, C


Size of Square, E

9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8 15⁄ 16

3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 9⁄ 32

0.141

0.110

0.141

0.110

0.141

0.110

0.168

0.131

0.194

0.152

0.220

0.165

Tolerances for General Dimensions Tolerance

Tolerance

Size Range

Ground Thread

Cut Thread

Overall Length, A

0 to 12

Thread Length, B

0 to 12

Square Length, C

0 to 12

±1⁄32 ±3⁄64 ±1⁄32

±1⁄32 ±3⁄64 ±1⁄32

Element

Size Range

Ground Thread

Shank Diameter, D

0 to 12

−0.0015

−0.004

Size of Square, E

0 to 12

−0.004

−0.004

Element

Cut Thread

All dimensions are in inches. Chamfer designations are: P = plug and B = bottoming. Cut thread taps are standard with plug chamfer only. Style 1 ground thread taps have external centers on thread and shank ends (may be removed on thread end of bottoming taps). Style 1 cut thread taps have optional style centers on thread and shank ends. Standard thread limits for ground threads are given in Table 3 and for cut threads in Table 5. For eccentricity tolerances see Table 22.



TAPS AND THREADING DIES Table 11. ANSI Standard Spiral Pointed Only and Regular and Fast Spiral-Fluted Taps — Machine Screw Sizes ASME B94.9-1999 STYLE 1

Pitch Dia. Limits & Chamfersa

Length of Thread, B

Length of Square, C


Size of Square, E

Size


3b

0.099

48

…

2

PB

…

113⁄16

1⁄ 2

3⁄ 16

0.141

0.110

4

0.112

40

…

2

PB

…

17⁄8

9⁄ 16

3⁄ 16

0.141

0.110

5

0.125

40

…

2

PB

…

115⁄16

5⁄ 8

3⁄ 16

0.141

0.110

6

0.138

32

…

2

…

PB

2

11⁄ 16

3⁄ 16

0.141

0.110

8

0.164

32

…

2c, 3b

…

PB

21⁄8

3⁄ 4

1⁄ 4

0.168

0.131

10

0.190

24

32

2c, 3b

…

PB

23⁄8

7⁄ 8

1⁄ 4

0.194

0.152

12d

0.216

24

…

2c, 3b

…

PB

23⁄8

15⁄ 16

9⁄ 32

0.220

0.165

Threads per Inch NC UNC

NF UNF

No. of Flutes

H2

H3

Length Overall, A

a Bottom chamfer applies only to regular and fast spiral-fluted machine screw taps. b Applies only to fast spiral-fluted machine screw taps. c Does not apply to fast spiral-fluted machine screw taps. d Does not apply to regular spiral-fluted machine screw taps.

Tolerances for General Dimensions Element

Size Range

Tolerance

Element

Size Range

Tolerance

Overall Length, A

3 to 12

±1⁄32

Shank Diameter, D

3 to 12

−0.0015

Thread Length, B

3 to 12

±3⁄64

Square Length, C

3 to 12

±1⁄32

Size of Square, E

3 to 12

−0.004

All dimensions are given in inches. These standard taps are made of high-speed steel with ground threads. For standard thread limits see Table 3. For eccentricity tolerances see Table 22. Spiral Pointed Only Taps: These taps are standard with plug chamfer only. They are provided with a spiral point only; the balance of the threaded section is left unfluted. These Style 1 taps have external centers on thread and shank ends. Regular Spiral Fluted Taps: These taps have right-hand spiral flutes with a helix angle of from 25 to 35 degrees. Fast Spiral Fluted Taps: These taps have right-hand spiral flutes with a helix angle of from 45 to 60 degrees. Both regular and fast spiral-fluted Style 1 taps have external centers on thread and shank ends (may be removed on thread end of bottoming taps). Chamfer designations: P = plug and B = bottoming.



907

Table 12a. ANSI Standard Ground Thread Straight Fluted Taps Fractional Sizes ASME B94.9-1999

Pitch Diameter Limits and Chamfers

Threads per Inch

Dia. of Tap 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 11⁄ a 16 3⁄ 4 3⁄ 4 7⁄ b 8 7⁄ 8 1b

1 1c 11⁄8 11⁄4 13⁄8 11⁄2

No. of NC NF Flute UNC UNF s 20 … 4 … 28 4 18 … 4 … 24 4 16 … 4 … 24 4 14 20 4 13 … 4 … 20 4 12 … 4 … 18 4 11 … 4 … 18 4 … … 4 10 … 4 … 16 4 9 … 4 … 14 4 8 … 4 … 12 4 … … 4 7 12 4 4 7 12d 4 6 12d 4 6 12d

H1 TPB PB PB PB PB PB … P PB … … … … … … P … … … … … … … … …

H2 TPB PB PB P PB PB … … … … P P P … P P … P … … … … … … …

H3 TPB TBP TPB TPB TPB TPB TPB TPB TPB TPB TPB TPB TPB TPB TPB TPB … … … … … … … … …

H4 … PB … PB … PB … … … … … … … … … … TPB TPB TPB TPB TPB TPB TPB TPB TPB

H5 PB … PB … PB … PB PB P P P PB PB … PB PB … … … … … … … … …

Length Overall, A 2 1⁄2 2 1⁄2 223⁄32 223⁄32 215⁄16 215⁄16 35⁄32 3 3⁄8 33⁄8 319⁄32 319⁄32 313⁄16 313⁄16 41⁄32 41⁄4 41⁄4 411⁄16 411⁄16 51⁄8 51⁄8 51⁄8 57⁄16 53⁄4 61⁄16 63⁄8

Dimensions Length Length ofThread, of Square, C B 5⁄ 1 16 5 1 ⁄16 3⁄ 1 1⁄8 8 3⁄ 11⁄8 8 7⁄ 11⁄4 16 1 7 1 ⁄4 ⁄16 13⁄ 17⁄16 32 7⁄ 1 21⁄32 16 7⁄ 121⁄32 16 1⁄ 1 21⁄32 2 1⁄ 121⁄32 2 13 9⁄ 1 ⁄16 16 13 9 1 ⁄16 ⁄16 5⁄ 113⁄16 8 11⁄ 2 16 11⁄ 2 16 3⁄ 27⁄32 4 3⁄ 27⁄32 4 13⁄ 21⁄2 16 13⁄ 21⁄2 16 13⁄ 21⁄2 16 7⁄ 29⁄16 8 1 29⁄16 3 11⁄16 3 11⁄8

Dia.of Shank, D 0.255 0.255 0.318 0.318 0.381 0.381 0.323 0.367 0.367 0.429 0.429 0.480 0.480 0.542 0.590 0.590 0.697 0.697 0.800 0.800 0.800 0.896 1.021 1.108 1.233

Sizeof Square, E 0.191 0.191 0.238 0.238 0.286 0.286 0.242 0.275 0.275 0.322 0.322 0.360 0.360 0.406 0.442 0.442 0.523 0.523 0.600 0.600 0.600 0.672 0.766 0.831 0.925

a This size has 11 or 16 threads per

inch NS-UNS. are also available with plug chamfer in H6 pitch diameter limits. threads per inch NS-UNS. d In these sizes NF-UNF thread taps have six flutes. b These sizes

c This size has 14

Element

Diameter Range

Length Overall, A Length of Thread, B Length of Square, C

1⁄ to 1 incl 4 11⁄8 to 11⁄2 incl 1⁄ to 1⁄ incl 4 2 9⁄ to 11⁄ incl 16 2 1⁄ to 1 incl 4 11⁄8 to 11⁄2 incl

Tolerances for General Dimensions Tolerance Element ±1⁄32 ±1⁄16 ±1⁄16 ±3⁄32 ±1⁄32 ±1⁄16

Diameter Range

Tolerance


1⁄ to 5⁄ incl 4 8 11⁄ to 11⁄ incl 16 2

−0.0015 −0.002

Size of Square, E

1⁄ to 1⁄ incl 4 2 9⁄ to 1 incl 16 11⁄8 to 11⁄2 incl

−0.004 −0.006 −0.008

All dimensions are given in inches. These taps are standard in high-speed steel. Chamfer designations are: T = taper, P = plug, and B = bottoming. Style 2 taps, 3⁄8 inch and smaller, have external center on thread end (may be removed on bottoming taps) and external partial cone center on shank end with length of come approximately one-quarter of diameter of shank. Style 3 taps, larger than 3⁄8 inch, have internal center in thread and shank ends. For standared thread limits see Table 2. For eccentricity tolerances see Table 22.



TAPS AND THREADING DIES Table 12b. ANSI Standard Cut Thread Straight Fluted Taps Fractional Sizes ASME B94.9-1999

Threads Per Inch

Dimensions

Carbon Steel Dia. of Tap 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

NC UNC

NF UNF

HS Steel NS UNS

NC UNC

NF UNF

No. of Flutes

Length Overall, A

…

…

40

…

…

3

115⁄16

…

…

32

…

…

4

2 1⁄8

…

…

24, 32

…

…

4

23⁄8

20

28

…

20

28

4

21⁄2

1

18

24

…

18

24

4

223⁄32

11⁄8

16

24

…

16

24

4

215⁄16

11⁄4

20

…

14

20

4

35⁄32

17⁄16

13

20

…

13

20

4

12

18

…

12

…

4

11

18

…

11

18

4

121⁄32 121⁄32 113⁄16

10

16

…

10

16

4

9

14

…

9

14

4

1

8

…

…

4

7

12

14a …

8

11⁄8

…

…

4

11⁄4

7

12b

…

…

…

4

13⁄8

6a 6

12ba

…

…

…

4

…

…

…

4

5a

12ba …

…

…

…

6

41⁄2 a

…

…

…

…

6

13⁄4 2

5⁄ 8 3⁄ 4 7⁄ 8

14

33⁄8 319⁄32 313⁄16 41⁄4 411⁄16 51⁄8 57⁄16 53⁄4 61⁄16 63⁄8

11⁄2

Length of Thread, B

2 27⁄32 21⁄2 29⁄16 29⁄16 3

Length of Square, C 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 13⁄ 32 7⁄ 16 1⁄ 2 9⁄ 16 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8

Dia. of Shank, D

Size of Square, E

0.141

0.110

0.168

0.131

0.194

0.152

0.255

0.191

0.318

0.238

0.381

0.286

0.323

0.242

0.367

0.275

0.429

0.322

0.480

0.360

0.590

0.442

0.697

0.523

0.800

0.600

0.896

0.672

1

1.021

0.766

11⁄16

1.108

0.831

3

11⁄8

1.233

0.925

7

33⁄16

11⁄4

1.430

1.072

75⁄8

39⁄16

13⁄8

1.644

1.233

a Standard in plug chamfer only. b In these sizes NF-UNF thread taps have six flutes.

Elements

Range

Length Overall, A

Length of Thread, B

Length of Square, C

1⁄ to 1 16 11⁄8 to 2 1⁄ to 3⁄ 16 16 1⁄ to 1⁄ 4 2 9⁄ to 11⁄ 16 2 15⁄8 to 2 1⁄ to 1 16 11⁄8 to 2

Tolerances for General Dimensions Tolerance Elements ±1⁄32 ±1⁄16 ±3⁄64 ±1⁄16 ±3⁄32 ±1⁄8 ±1⁄32 ±1⁄16

Range

Tolerance


1⁄ to 3⁄ 16 16 1⁄ to 1 4 11⁄8 to 2

−0.004 −0.005 −0.007

Size of Square, E

1⁄ to 1⁄ 16 2 9⁄ to 1 16 1⁄ to 2 8

−0.004 −0.006 −0.008

All dimensions are given in inches. These taps are standard in carbon steel and high-speed steel. Except where indicated, these taps are standard with taper, plug, or bottoming chamfer. Cut thread taps, sizes 3⁄8 inch and smaller have optional style center on thread and shank ends; sizes larger than 3⁄8 inch have internal centers in thread and shank ends. For standard thread limits see Table 1. For eccentricity tolerances see Table 22.



909

Table 13. ANSI Standard Straight Fluted (Optional Number of Flutes) and Spiral Pointed Taps—Fractional Sizes ASME B94.9-1999

Dia. of Tap

Threads per Inch NC, UNC NF, UNF

1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2

20 20 … 18 18 … 16 … 14 … 13 …

1⁄ 4 1⁄ a 4 1⁄ 4 1⁄ a 4 5⁄ 16 5⁄ a 16 5⁄ 16 5⁄ a 16 3⁄ 8 3⁄ 8 7⁄ a 16 1⁄ 2 5⁄ a 8 3⁄ a 4

20 20 … … 18 18 … … 16 … 14 13 11 10

Pitch Diameter Length Length Limits and Chamfersab No. of Overall, of Thread, B Flutes H1 H2 H3 H4 H5 A Ground Thread High-Speed-Steel Straight Fluted Taps

Length of Square, C

Dia. of Shank, D

Size of Square, E

0.255 0.255 0.255 0.318 0.318 0.318 0.381 0.381 0.323 0.323 0.367 0.367

0.191 0.191 0.191 0.238 0.238 0.238 0.286 0.286 0.242 0.242 0.275 0.275

0.255 0.255 0.255 0.255 0.318 0.318 0.318 0.318 0.381 0.381 0.323 0.367 0.480 0.590

0.191 0.191 0.191 0.191 0.238 0.238 0.238 0.238 0.286 0.286 0.242 0.275 0.360 0.442

5⁄ 21⁄2 … 2 … … PB … … 1 16 5⁄ 21⁄2 … 3 P P PB … P 1 16 1 5⁄ 2 ⁄2 28 2, 3 … … PB … … 1 16 3⁄ 223⁄32 11⁄8 … 2 … … PB … … 8 3⁄ 223⁄32 11⁄8 … 3 … … PB … … 8 3⁄ 223⁄32 11⁄8 24 3 … … PB … … 8 7⁄ 215⁄16 11⁄4 … 3 … … PB … … 16 7⁄ 215⁄16 11⁄4 24 3 … … PB … … 16 13⁄ 35⁄32 17⁄16 … 3 … … P … … 32 13⁄ 35⁄32 17⁄16 20 3 … … P … … 32 7⁄ 121⁄32 33⁄8 … 3 … … PB … … 16 7⁄ 121⁄32 33⁄8 20 3 … … P … … 16 Ground Thread High-Speed-Steel and Cut Thread High-Speed-Steel Spiral Pointed Taps 5⁄ 21⁄2 … 2 P P PB … P 1 16 5⁄ 21⁄2 1 … 3 … … P … P 16 1 5⁄ 2 ⁄2 28 2 P P PB P … 1 16 5⁄ 21⁄2 1 28 3 … P … P … 16 3⁄ 223⁄32 11⁄8 … 2 P P PB … P 8 3⁄ 11⁄8 223⁄32 … 3 … … P … P 8 3⁄ 223⁄32 11⁄8 24 2 P P PB P … 8 3⁄ 11⁄8 223⁄32 24 3 … P P P … 8 7⁄ 215⁄16 11⁄4 … 3 P P P … P 16 7⁄ 215⁄16 11⁄4 24 3 P P P P … 16 13⁄ 17⁄16 35⁄32 20 3 … Pc P … P 32 7⁄ 121⁄32 33⁄8 3 P P P … P 20a 16 9⁄ 313⁄16 113⁄16 18 3 … … P … Pd 16 11⁄ 41⁄4 2 16 3 … … P … Pe 16

a Applies only to ground thread high-speed-steel taps. b Cut thread high-speed-steel taps are standard with plug chamfer only. c Applies only to 7⁄ -14 tap. 16 d Applies only to 5⁄ -11 tap. 8 e Applies ony to 3⁄ -10 tap. For eccentricity tolerances see Table 22. 4


Diameter Range

Tolerances for General Dimensions Tolerance Ground Thread Cut Thread Element

1⁄ 4

to 3⁄4

±1⁄32

1⁄ 4 5⁄ 8 1⁄ 4

to 1⁄2 to 3⁄4 to 3⁄4

±1⁄16 ±1⁄32 ±1⁄32

±1⁄32 ±1⁄16

ShankDiameter,D Size of Square,E

Diameter Range 1⁄ 4 1⁄ 4 5⁄ 8

Tolerance Ground Thread CutThread

5⁄ 8

−0.0015 −0.0020

−0.005 …

to 1⁄2 to 3⁄4

−0.0040 −0.0060

−0.004 …

to 3⁄ 4

All dimensions are given in inches. P = plug and B = bottoming. Ground thread taps — Style 2, 3⁄8 inch and smaller, have external center on thread end (may be removed on bottoming taps) and external partial cone center on shank end, with length of cone approximately 1⁄4 of shank diameter. Ground thread taps—Style 3, larger than 3⁄8 inch, have internal center in thread and shank ends. Cut threadtaps, 3⁄8 inch and smaller have optional style center on thread and shank ends; sizes larger than 3⁄8 inch have internal centers in thread and shank ends. For standard thread limits see Tables 1 and 2.



TAPS AND THREADING DIES Table 14. Other Types of ANSI Standard Taps ASME B94.9-1999

Threads per Inch

Dia. of Tap 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ e 16 1⁄ 2

Length Overall, A

Length of Thread, B

NC UNC

NF UNF

Number of Flutes

20

28a

2 b,c , 3 a

21⁄2

1

18

24a

223⁄32

11⁄8

16

24a

2d, 3a 3

14

20

3

13

20a

3

215⁄16 35⁄32 33⁄8

11⁄4 17⁄16 121⁄32

Length of Square, C 5⁄ 16 3⁄ 8 7⁄ 16 13⁄ 32 7⁄ 16

Dia. of Shank, D

Size of Square, E

0.255

0.191

0.318

0.238

0.381

0.286

0.323

0.242

0.367

0.275

a Does not apply to spiral pointed only taps. b Does not apply to spiral fluted taps with 28 threads per inch. c Does not apply to fast spiral fluted taps. d Applies only to spiral pointed only taps. e Applies only to fast spiral fluted taps.

Tolerances for General Dimensions Diameter Range


1⁄ 4 1⁄ 4 1⁄ 4

to to to

1⁄ 2 1⁄ 2 1⁄ 2

Diameter Range

Tolerance

Element

±1⁄32 ±1⁄16 ±1⁄32

Shank Diameter, D

1⁄ 4

to 1⁄2

Tolerance −0.0015

Size of Square, E

1⁄ 4

to 1⁄2

−0.004

All dimensions are given in inches. These standard taps are made of high-speed steel with ground threads. For standard thread limits see Table 2. Spiral Pointed Only Taps: These taps are standard with plulg chamfer only in H3 limit. They are provided with spiral point only. The balance of the threaded section is left unfluted. Spiral Fluted Taps: These taps are standard with plug or bottoming chamfer in H3 limit and have right-hand spiral flutes with a helix angle of from 25 to 35 degrees. Fast Spiral Fluted Taps: These taps are standard with plug or bottoming chamfer in H3 limit and have right-hand spiral flutes with a helix angle of from 45 to 60 degrees. Style 2 taps, 3⁄8 inch and smaller, have external center on thread end (may be removed on bottoming taps) and external partial cone center on shank end with cone length approximately 1⁄4 shank diameter. Style 3 taps larger than 3⁄8 inch have internal center in thread and shank ends. For standard thread limits see Table 2. For eccentricity tolerances see Table 22.



911

Table 15. ANSI Standard Pulley Taps ASME B94.9-1999

Threads per Dia. Inch Number of NC of Tap UNC Flutes

Length of Length Size Shank Length Length Dia. of of Close of of of Thread, Square, Shank, Tolerance, Square, Neck, B C D Kc Eb Ta

Length Overall, A

1⁄ 4

20

4

6, 8

1.00

0.31

0.2550

1.50

0.191

0.38

5⁄ 16

18

4

6, 8

1.13

0.38

0.3180

1.56

0.238

0.38

0.44

0.3810

1.63

0.286

0.38

3⁄ 8

16

4

6, 8, 10

1.25

7⁄ 16

14

4

6, 8

1.44

0.50

0.4440

1.69

0.333

0.44

1⁄ 2

13

4

6, 8, 10, 12

1.66

0.56

0.5070

1.69

0.380

0.50

5⁄ 8

11

4

6,8,10,12

1.81

0.69

0.6330

2.00

0.475

0.63

3⁄ 4

10

4

10, 12

2.00

0.75

0.7590

2.25

0.569

0.75

a T is minimum length of shank which is held to eccentricity tolerances. b Size of square is equal to 0.75D to the nearest 0.001 inch. c K neck optional with manufacturer.

Tolerances for General Dimensions Diameter Range

Element

Diameter Range

Tolerance

Element Shank Diameter, D

1⁄ 4

to 3⁄4

Size of Square, E

1⁄ 4 5⁄ 8

1⁄ 2 3⁄ 4

Overall Length, A

1⁄ 4

to 3⁄4

±0.06

Thread Length, B

1⁄ 4

to 3⁄4

±0.06

Square Length, C

1⁄ 4

to 3⁄4

±0.03

to to

Tolerance −0.0050 −0.004 −0.006

All dimensions are given in inches. These ground thread high-speed steel taps are standard with plug chamfer in H3 limit only. All taps have an internal center in thread end. For standard thread limits see Table 2. For eccentricity tolerances see Table 22.

Table 16. ANSI Standard Ground Thread Spark Plug Taps Metric Sizes ASME B94.9-1999 Tap Diameter, mm 14 18

Pitch, mm

Number of Flutes

1.25

4 4

1.50

Overall Length, In. A

Thread Length, In. B

Square Length, In. C

Shank Dia., In. D

Square Size, In. E

319⁄32

121⁄32

1⁄ 2

0.429

0.322

41⁄32

113⁄16

5⁄ 8

0.542

0.406

These are high-speed steel Style 3 taps and have internal center in thread and shank ends. They are standard with plug chamfer only, right-hand threads with 60-degree form of thread. Tolerances: Overall length, ± 1⁄32 inch; thread length, ± 3⁄32 inch; square length, ± 1⁄32 inch; shank diameter, 14 mm, −0.0015 inch, 18 mm, −0.0020 inch; and size of square, −0.0040 inch.



TAPS AND THREADING DIES Table 17a. ANSI Standard Ground Thread Straight Fluted Taps M Profile — Metric Sizes ASME B94.9-1999

Nom. Dia. mm.

Pitch mm

No. of Flutes

D3

Pitch Diameter Limits and Chamfers D4 D5 D6 D7 D8

1.6

0.35

2

PB

…

…

…

…

…

…

15⁄8

2

0.4

3

PB

…

…

…

…

…

…

13⁄4

2.5

0.45

3

PB

…

…

…

…

…

…

113⁄16

3

0.5

3

PB

…

…

…

…

…

…

3.5

0.6

3

…

PB

…

…

…

…

…

115⁄16 2

D9

4

0.7

4

…

PB

…

…

…

…

…

4.5

0.75

4

…

PB

…

…

…

…

…

5

0.8

4

…

PB

…

…

…

…

…

6

1

4

…

…

PB

…

…

…

…

7

1

4

…

…

PB

…

…

…

…

8

1.25

4

…

…

PB

…

…

…

…

10

1.5

4

…

…

…

PB

…

…

…

12

1.75

4

…

…

…

PB

…

…

…

2

4

…

…

…

…

PB

…

…

16

2

4

…

…

…

…

PB

…

…

20

2.5

4

…

…

…

…

PB

…

…

24

3

4

…

…

…

…

…

PB

…

30

3.5

4

…

…

…

…

…

…

PB

36

4

4

…

…

…

…

…

…

PB

14

Element Overall Length, A

Thread Length, B

Square Length, C

Nom. Dia. Range, mm M1.6 to M24, incl. M30 and M36 M1.6 to M5, incl. M6 to M12 incl. M14 to M36 M1.6 to M24, incl. M30 and M36

Length Overall A

21⁄8 23⁄8 23⁄8 21⁄2 223⁄32 223⁄32 215⁄16 33⁄8 319⁄32 313⁄16 415⁄32 429⁄32 57⁄16 61⁄16

Tolerances Toler., Inch Element ±1⁄32 ±1⁄16 ±3⁄64 ±1⁄16 ±3⁄32 ±1⁄32 ±1⁄16

Length of Thread B 5⁄ 16 7⁄ 16 1⁄ 2 5⁄ 8 11⁄ 16 3⁄ 4 7⁄ 8 7⁄ 8

1 11⁄8 11⁄8 11⁄4 121⁄32 121⁄32 113⁄16 2 27⁄32 29⁄16 3

Length of Square C 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 9⁄ 16 11⁄ 16 3⁄ 4

Dia. of Square D

Size of Square E

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.141

0.110

0.168

0.131

0.194

0.152

0.194

0.152

0.255

0.191

0.318

0.238

0.318

0.238

0.381

0.286

0.367

0.275

0.429

0.322

0.480

0.360

0.652

0.489

0.760

0.570

1

1.021

0.766

11⁄8

1.233

0.925

Nom. Dia. Range, mm

Toler., Inch

Shank Diameter, D

M1.6 to M14, incl. M16 to M36

−0.0015 −0.002

Size of Square, E

M1.6 to M12, incl. M14 to M24, incl. M30 and M36

−0.004 −0.006 −0.008

All dimensions are in inches except where otherwise stated. Chamfer Designation: P — Plug, B — Bottoming. These taps are high-speed steel. Style 1 taps, sizes M1.6 through M5, have external center on thread and shank ends (may be removed on thread end of bottoming taps). Style 2 taps, sizes M6, M7, M8, and M10, have external center on thread end (may be removed on bottoming taps) and external partial cone center on shank end with length of cone approximately 1⁄4 of diameter of shank. Style 3 taps, sizes larger than M10 have external center on thread and shank ends. For standard thread limits see Tables 4a and 4b. For eccentricity tolerances of tap elements see Table 22.



913

Table 17b. ANSI Standard Spiral Pointed Ground Thread Taps M Profile — Metric Sizes ASME B94.9-1999

Nom. Dia. mm.

Pitch mm

No. of Flutes

Length Overall

Length of Thread

Length of Square

Dia. of Square

D3

Pitch Diameter Limits and Styles D4

D5

D6

D7

A

B

C

D

Size of Square E

1.6

0.35

2

P

…

…

…

…

15⁄8

5⁄ 16

3⁄ 16

0.141

0.110

2

0.4

2

P

…

…

…

…

13⁄4

7⁄ 16

3⁄ 16

0.141

0.110

2.5

0.45

2

P

…

…

…

…

113⁄16

1⁄ 2

3⁄ 16

0.141

0.110

3

0.5

2

P

…

…

…

…

115⁄16

5⁄ 8

3⁄ 16

0.141

0.110

3.5

0.6

2

…

P

…

…

…

2

11⁄ 16

3⁄ 16

0.141

0.110

4

0.7

2

…

P

…

…

…

21⁄8

3⁄ 4

1⁄ 4

0.168

0.131

5

0.8

2

…

P

…

…

…

23⁄8

7⁄ 8

1⁄ 4

0.194

0.152

6

1

2

…

…

P

…

…

21⁄2

1

5⁄ 16

0.255

0.191

8

1.25

2

…

…

P

…

…

223⁄32

11⁄8

3⁄ 8

0.318

0.238

10

1.5

3

…

…

…

P

…

215⁄16

11⁄4

7⁄ 16

0.381

0.286

12

1.75

3

…

…

…

P

…

33⁄8

121⁄32

7⁄ 16

0.367

0.275

14

2

3

…

…

…

…

P

319⁄32

121⁄32

1⁄ 2

0.429

0.322

16

2

3

…

…

…

…

P

313⁄16

113⁄16

9⁄ 16

0.480

0.360

20

2.5

3

…

…

…

…

P

415⁄32

2

11⁄ 16

0.652

0.489

Tolerances Element

Nom. Dia. Range, mm

Toler., Inch

Overall Length, A

±1⁄32

M1.6 to M20, incl. M1.6 to M5, incl.

±3⁄64

Thread Length, B

M16 to M12 incl.

±1⁄16

M14 to M20

±3⁄32

Square Length, C

M1.6 to M20

±1⁄32

Nom. Dia. Range, mm Element

Toler., Inch

Shank Diameter, D

M1.6 to M14, incl. M16 to M20

−0.0015 −0.002

Size of Square, E

M1.6 to M12, incl. M14 to M20, incl.

−0.004 −0.006

All dimensions are in inches except where otherwise stated. Chamfer Designation: P — Plug. These taps are high-speed steel. Style 1 taps, sizes M1.6 through M5, have external center on thread and shank ends. Style 2 taps, sizes M6, M8 and M10, have external center on thread end and external partial cone center on shank end with length of cone approximately 1⁄4 of diameter of shank. Style 3 taps, sizes larger than M10 have external center on thread and shank ends. For standards thread limits see Table 4a and 4b. For eccentricity tolerances of tap elements see Table 22.



TAPS AND THREADING DIES Table 18. ANSI Standard Taper and Straight Pipe Taps ASME B94.9-1999

Nominal Size

Threads per Inch Carbon High-Speed Steel Steel

1⁄ a 16 1⁄ 8 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

… 27 27 18 18 14 14

27 27 27 18 18 14 14

1

111⁄2 111⁄2 111⁄2 111⁄2 8 8

111⁄2 111⁄2 111⁄2 111⁄2 … …

… … … … … … …

27 27 18 18 14 14

11⁄4 11⁄2 2 21⁄2 c 3c 1⁄ a 8 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1

Number of Flutes Regular 4 4 4 4 4 4 5 5 5 7 7 8 8

Length Interrupted Overall, A Taper Pipe Taps … 21⁄8 5 21⁄8 5 21⁄8 5 27⁄16 5 29⁄16 5 31⁄8 5 31⁄4 5 33⁄4 5 4

4 4 4 4 4 5 5

111⁄2

7 ba 7ba … …

41⁄4 41⁄2 51⁄2 6

Straight Pipe Taps … 21⁄8 … 21⁄8 … 27⁄16 … 29⁄16 … 31⁄8 … 31⁄4 … 33⁄4

Length of Thread, B

Dimensions Length of Diameter Square, C of Shank, D

11⁄ 16 3⁄ 4 3⁄ 4 11⁄16 11⁄16 13⁄8 13⁄8 13⁄4 13⁄4 13⁄4 13⁄4 29⁄16 25⁄8

3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 11⁄ 16 13⁄ 16 15⁄ 16

3⁄ 4 3⁄ 4 11⁄16 11⁄16 13⁄8 13⁄8 13⁄4

Size of Square, E

11⁄8 11⁄4 13⁄8

0.3125 0.3125 0.4375 0.5625 0.7000 0.6875 0.9063 1.1250 1.3125 1.5000 1.8750 2.2500 2.6250

0.234 0.234 0.328 0.421 0.531 0.515 0.679 0.843 0.984 1.125 1.406 1.687 1.968

3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 11⁄ 16 13⁄ 16

0.3125 0.4375 0.5625 0.7000 0.6875 0.9063 1.1250

0.234 0.328 0.421 0.531 0.515 0.679 0.843

1

a Ground thread taps only. b Standard in NPT form of thread only. c Cut thread taps only.

Element Overall Length, A

Diameter Range 1⁄ 16

to 1 to 3

3⁄ 4

1⁄ 16

Thread Length, B

Square Length, C

to 3⁄4 1 to 11⁄4 1 1 ⁄2 to 3 1⁄ 16

to 3⁄4 1 to 3

Tolerances for General Dimensions Tolerance Cut Thread Ground Thread Element ±1⁄32 ±1⁄16 ±1⁄16 ±3⁄32 ±1⁄8 ±1⁄32 ±1⁄16

±1⁄32 ± 1⁄16 ±1⁄16 ±3⁄32 ±1⁄8 ±1⁄32 ±1⁄16

Shank Diameter, D

Size of Square, E

Diameter Range 1⁄ to ⁄ 16 8 1⁄ to 1⁄ 8 2 1⁄ to 1 4 3⁄ to 3 4 11⁄4 to 2 1⁄ to 1⁄ 16 8 1⁄ to 3⁄ 4 4

1 to 3

Tolerance Cut Thread Ground Thread … −0.0015 −0.007 … … −0.002 −0.009 … −0.004 −0.006 −0.008

… −0.003 −0.004 −0.006 −0.008

All dimensions are given in inches. These taps have an internal center in the thread end. Taper Pipe Threads: The 1⁄8 -inch pipe tap is furnished with large size shank unless the small shank is specified. These taps have 2 to 31⁄2 threads chamfer. The first few threads on interrupted thread pipe taps are left full. The following styles and sizes are standard: 1⁄16 to 2 inches regular ground thread, NPT, NPTF, and ANPT: 1⁄8 to 2 inches interrupted ground thread, NPT, NPTF and ANPT: 1⁄8 to 3 inches carbon steel regular cut thread, NPT; 1⁄8 to 2 inches high-speed steel, regular cut thread, NPT; 1⁄8 to 11⁄4 inches high-speed steel interrupted cut thread, NPT. For standard thread limits see Tables 6a and 6b. Straight Pipe Threads: The 1⁄8 -inch pipe tap is furnished with large size shank unless the small size is specified. These taps are standard with plug chamfer only. The following styles and sizes are standard: ground threads — 1⁄8 to 1 inch, NPSC and NPSM; 1⁄8 to 3⁄4 inch, NPSF; cut threads — 1⁄8 to 1 inch, NPSC and NPSM. For standard thread limits see Tables 7a, 7b, and 7c. For eccentricity tolerances see Table 22.



915

Table 19. Taps Recommended for Classes 2B and 3B Unified Screw Threads Numbered and Fractional Sizes ASME B94.9-1999 Size

Threads per Inch NC NF UNC UNF

Recommended Tap For Class of Thread Class 2Ba

Class 3B

Pitch Diameter Limits For Class of Thread Min, All Max Max Classes (Basic) Class 2B Class 3B

Machine Screw Numbered Size Taps 0 1 1 2 2 3 3 4 4 5 5 6 6 8 8 10 10 12 12

… 64 … 56 … 48 … 40 … 40 … 32 … 32 … 24 … 24 …

80 … 72 … 64 … 56 … 48 … 44 … 40 … 36 … 32 … 28

G H2 G H2 G H2 G H2 G H2 G H2 G H2 G H2 G H2 G H2 G H2 G H3 G H2 G H3 G H2 G H3 G H3 G H3 G H3

1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8

20 … 18 … 16 … 14 … 13 … 12 … 11 … 10 … 9 … 8 …

… 28 … 24 … 24 … 20 … 20 … 18 … 18 … 16 … 14 … 12

G H5 G H4 G H5 G H4 G H5 G H4 G H5 G H5 G H5 G H5 G H5 G H5 G H5 G H5 G H5 G H5

1 1 1 11⁄8 11⁄8 11⁄4 11⁄4 13⁄8 13⁄8 11⁄2 11⁄2

14NS 7 … 7 … 6 … 6 …

… 12 … 12 … 12 … 12

G H6b G H6b G H6b G H6b G H6b G H8b G H6b G H8b G H6b G H8b G H6b G H8b G H6b

G H1 G H1 G H1 G H1 G H1 G H1 G H1 G H2 G H1 G H2 G H1 G H2 G H2 G H2 G H2 G H3 G H2 G H3 G H3 Fractional Size Taps G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H3 G H5 G H3 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4 G H4

0.0519 0.0629 0.0640 0.0744 0.0759 0.0855 0.0874 0.0958 0.0985 0.1088 0.1102 0.1177 0.1218 0.1437 0.1460 0.1629 0.1697 0.1889 0.1928

0.0542 0.0655 0.0665 0.0772 0.0786 0.0885 0.0902 0.0991 0.1016 0.1121 0.1134 0.1214 0.1252 0.1475 0.1496 0.1672 0.1736 0.1933 0.1970

0.0536 0.0648 0.0659 0.0765 0.0779 0.0877 0.0895 0.0982 0.1008 0.1113 0.1126 0.1204 0.1243 0.1465 0.1487 0.1661 0.1726 0.1922 0.1959

0.2175 0.2268 0.2764 0.2854 0.3344 0.3479 0.3911 0.4050 0.4500 0.4675 0.5084 0.5264 0.5660 0.5889 0.6850 0.7094 0.8028 0.8286 0.9188 0.9459 0.9536 1.0322 1.0709 1.1572 1.1959 1.2667 1.3209 1.3917 1.4459

0.2224 0.2311 0.2817 0.2902 0.3401 0.3528 0.3972 0.4104 0.4565 0.4731 0.5152 0.5323 0.5732 0.5949 0.6927 0.7159 0.8110 0.8356 0.9276 0.9535 0.9609 1.0416 1.0787 1.1668 1.2039 1.2771 1.3291 1.4022 1.4542

0.2211 0.2300 0.2803 0.2890 0.3387 0.3516 0.3957 0.4091 0.4548 0.4717 0.5135 0.5308 0.5714 0.5934 0.6907 0.7143 0.8089 0.8339 0.9254 0.9516 0.9590 1.0393 1.0768 1.1644 1.2019 1.2745 1.3270 1.3996 1.4522

a Cut thread taps in all fractional sizes and in numbered sizes 3 to 12 NC and NF may be used under normal conditions and in average materials to produce tapped holes in this classification. b Standard G H4 taps are also suitable for this class of thread.

All dimensions are given in inches. The above recommended taps normally produce the class of thread indicated in average materials when used with reasonable care. However, if the tap specified does not give a satisfactory gage fit in the work, a choice of some other limit tap will be necessary.




Standard System of Tap Marking.—Ground thread taps, inch screw threads, are marked with the nominal size, number of threads per inch, the proper symbol to identify the thread form, “HS” for high-speed steel, “G” for ground thread, and designators for tap pitch diameter and special features, such as left-hand and multi-start threads. Cut thread taps, inch screw threads, are marked with the nominal size, number of threads per inch, and the proper symbol to identify the thread form. High-speed steel taps are marked “HS,” but carbon steel taps need not be marked. Ground thread taps made with metric screw threads, M profile, are marked with “M,” followed by the nominal size and pitch in millimeters, separated by “x.” Marking also includes “HS” for high-speed steel, “G” for ground thread, designators for tap pitch diameter and special features, such as left-hand and multi-start threads. Thread symbol designators are listed in the accompanying table. Tap pitch diameter designators, systems of limits, special features, and examples for ground threads are given in the following section. Standard System Tap Thread Limits and Identification for Unified Inch Screw Threads, Ground Thread.—H or L Limits: For Unified inch screw threads, when the maximum tap pitch diameter is over basic pitch diameter by an even multiple of 0.0005 in. or the minimum tap pitch diameter limit is under basic pitch diameter by an even multiple of 0.0005 in., the taps are marked “H” or “L,” respectively, followed by a limit number, determined as follows: H limit number =Amount maximum tap PD limit is over basic PD divided by 0.0005 L limit number =Amount minimum tap PD limit is under basic PD divided by 0.0005 Table 20. Thread Series Designations Standard Tap Marking

Product Thread Designation

M M

M MJ

NC NC NPS NPSF NPSH

NC5IF NC5INF NPSC NPSF NPSH

NPSI NPSL NPS NPT NPTF NPTR

NPSI NPSL NPSM NPT NPTF NPTR

N NC NF NEF N NC NF NEF N NC NF NEF NS

UN UNC UNF UNEF UNJ UNJC UNJF UNJEF UNR UNRC UNRF UNREF UNS

Third Series Metric Screw Threads—M Profile, with basic ISO 68 profile Metric Screw Threads—M Profile, with rounded root of radius 0.15011P to 0.18042P Class 5 interference-fit thread Entire ferrous material range Entire nonferrous material range American Standard straight pipe threads in pipe couplings Dry seal American Standard fuel internal straight pipe threads American Standard straight hose coupling threads for joining to American Standard taper pipe threads Dryseal American Standard intermediate internal straight pipe threads American Standard straight pipe threads for loose-fitting mechanical joints with locknuts American Standard straight pipe threads for free-fitting mechanical joints for fixtures American Standard taper pipe threads for general use Dryseal American Standard taper pipe threads American Standard taper pipe threads for railing joints Unified Inch Screw Thread Constant-pitch series Coarse pitch series Fine pitch series Extra-fine pitch series Constant-pitch series, with rounded root of radius 0.15011P to 0.18042P (ext. thd. only) Coarse pitch series, with rounded root of radius 0.15011P to 0.18042 P (ext. thd. only) Fine pitch series, with rounded root of radius 0.15011P to 0.18042P (ext. thd. only) Extra-fine pitch series, with rounded root of radius 0.15011P to 0.18042P (ext. thd. only) Constant-pitch series, with rounded root of radius not less than 0.108P (ext. thd. only) Coarse thread series, with rounded root of radius not less than 0.108P (ext. thd. only) Fine pitch series, with rounded root of radius not less than 0.108P (ext. thd. only) Extra-fine pitch series, with rounded root of radius not less than 0.108P (ext. thd. only) Special diameter pitch, or length of engagement



917

The PD limits for various H limit numbers are given in Table 2. The PD limits for L limit numbers are determined as follows. The minimum tap PD equals the basic PD minus the number of half-thousandths (0.0005 in.) represented by the limit number. The maximum tap PD equals the minimum PD plus the PD tolerance given in Table 21. Table 21. PD Tolerance for Unified Inch Screw Threads Ground Thread ASME B94.9-1999 Threads per Inch

To 1 in., incl.

Over 1 in. to 11⁄2 in., incl.

Over 11⁄2 to 21⁄2 in., incl.

Over 2 1⁄2 in.

80-28 24-18 16-18 7-6 51⁄2 -4

0.0005 0.0005 0.0005 0.0010 0.0010

0.0010 0.0010 0.0010 0.0010 0.0015

0.0010 0.0015 0.0015 0.0020 0.0020

0.0015 0.0015 0.0020 0.0025 0.0025

Example: 3⁄8 -16 NC HS H1 Max. tap PD = 0.3349 Min. tap PD = 0.3344 Example: 3⁄8 -16 NC HS G L2 Min. tap PD = Basic PD − 0.0010 in. = 0.3344 − 0.0010 = 0.3334 Max. tap PD = Min. Tap PD + 0.0005 = 0.3334 + 0.0005 = 0.3339 Oversize or Undersize: When the maximum tap PD over basic PD or the minimum tap PD under basic PD is not an even multiple of 0.0005, the tap PD is usually designated as an amount oversize or undersize. The amount oversize is added to the basic PD to establish the minimum tap PD. The amount undersize is subtracted from the basic PD to establish the minimum tap PD. The PD tolerance in Table 21 is added to the minimum tap PD to establish the maximum tap PD for both. Example : 7⁄16 -14 NC plus 0.0017 HS G Min. tap PD = Basic PD + 0.0017 in. Max. tap PD = Min. tap PD + 0.0005 in. Whenever possible for oversize or other special tap PD requirements, the maximum and minimum tap PD requirements should be specified. Special Tap Pitch Diameter: Taps not made to H or L limit numbers, to Table 22, or to the formula for oversize or undersize taps, may be marked with the letter “S” enclosed by a circle or by some other special identifier. Example: 1⁄2 -16 NC HS G . Table 22. ANSI Standard Runout and Location Tolerance of Tap Elements ASME B94.9-1999 Range Sizes are Inclusive Hand, Mch. Screw Metric Pipe

Element Square (at central point) Shank Major Diameter Pitch Diameter (at first full thread) Chamferb

#0–1⁄2 ″

M1.6–M12

17⁄ –4″ 32 #0–5⁄16 ″ 11⁄ –4″ 32 #0–5⁄16 ″ 11⁄ –4″ 32 #0–5⁄16 ″ 11⁄ –4″ 32 #0–1⁄2 ″ 17⁄ –4″ 32

M14–M100 M1.6–M8 M10–M100 M1.6–M8 M10–M100 M1.6–M8 M10–M100 M1.6–M12 M14–M100

1⁄ –1⁄ ″ 16 8 1⁄ –4″ 4 1⁄ ″ 16 1⁄ –4″ 8 1⁄ ″ 16 1⁄ –4″ 8 1⁄ ″ 16 1⁄ –4″ 8 1⁄ –1⁄ ″ 16 8 1⁄ –4″ 4

Cut Thread

Ground Thread

Eccentricity

tiva

Eccentricity

tiva

Location, inch

…

…

…

…

0.0060

…

…

…

…

0.0030

0.0060

0.0005

0.0010

0.0080 …

0.0040

0.0080

0.0008

0.0016

…

0.0025

0.0050

0.0005

0.0010

…

0.0040

0.0080

0.0008

0.0016

…

0.0025

0.0050

0.0005

0.0010

…

0.0040

0.0080

0.0008

0.0016

…

0.0020

0.0040

0.0010

0.0020

…

0.0030

0.0060

0.0015

0.0030

…

a tiv = total indicator variation. This data no longer included in Standard, but for reference figures are given for both eccentricity and total indicator variation to avoid misunderstanding. b Chamfer should preferably be inspected by light projection to avoid errors due to indicator contact points dropping into the thread groove. All dimensions are given in inches.




Left-Hand Taps: Taps with left-hand threads are marked “LEFT HAND” or “LH.” Example:3⁄8 -16 NC LH HS G H3. Multiple-Start Threads: Taps with multiple-start threads are marked with the lead designated as a fraction, also “Double,” “Triple,” etc. The Unified Screw Thread form symbol is always designated as “NS” for multiple-start threads. Example:3⁄8 -16 NS Double 1⁄8 Lead HS G H5. Standard System of Ground Thread Tap Limits and Identification for Metric Screw Threads, M Profile.—All calculations for metric taps use millimeter values. When U.S. customary values are needed, they are translated from the three-place millimeter tap diameters only after the calculations are completed. Table 23. PD Tolerance for Metric Screw Threads M Profile—Ground Threads ASME B94.9-1999 M1.6 to M6.3, inclusive.

Over M6.3 to M25, inclusive

Over M25 to M90, inclusive

Over M90

0.3

0.015

0.015

0.020

0.020

0.35

0.015

0.015

0.020

0.020

0.4

0.015

0.015

0.020

0.025

0.45

0.015

0.020

0.020

0.025

0.5

0.015

0.020

0.025

0.025

0.6

0.020

0.020

0.025

0.025

0.7

0.020

0.020

0.025

0.025

0.75

0.020

0.025

0.025

0.031

0.8

0.020

0.025

0.025

0.031

0.9

0.020

0.025

0.025

0.031

1

0.025

0.025

0.031

0.031

1.25

0.025

0.031

0.031

0.041

1.5

0.025

0.031

0.031

0.041

1.75

…

0.031

0.041

0.041

2

…

0.041

0.041

0.041

2.5

…

0.041

0.041

0.052 0.052

Pitch, P (mm)

3

…

0.041

0.052

3.5

…

0.041

0.052

0.052

4

…

0.052

0.052

0.064

4.5

…

0.052

0.052

0.064

5

…

…

0.064

0.064

5.5

…

…

0.064

0.064

6

…

…

0.064

0.064

D or DU Limits: When the maximum tap pitch diameter is over basic pitch diameter by an even multiple of 0.013 mm (0.000512 in. reference), or the minimum tap pitch diameter limit is under basic pitch diameter by an even multiple of 0.013 mm, the taps are marked with the letters “D” or “DU,” respectively, followed by a limit number. The limit number is determined as follows: D limit number = Amount maximum tap PD limit is over basic PD divided by 0.013 DU limit number = Amount minimum tap PD limit is under basic PD divided by 0.013



919

The PD limits for various D limit numbers are given in Table 4b. The PD limits for DU limit numbers are determined as follows. The minimum tap PD equals the basic PD minus the number of millimeters represented by the limit number (multiples of 0.013 mm). The maximum tap PD equals the minimum tap PD plus the PD tolerance given in Table 23. Example:M1.6 × 0.35 HS G D3 Max. tap PD = 1.412 Min. tap PD = 1.397 M6 × 1 HS G DU4 Min. tap PD = Basic PD − 0.052 mm = 5.350 − 0.052 = 5.298 Max. tap PD = Min. tap PD + 0.025 mm = 5.323 Metric oversize or undersize taps, taps with special pitch diameters, and left-hand taps follow the marking system given for inch taps. Examples:M12 × 1.75 + 0.044 HS G M10 × 1.5 HS G M10 × 1.5 LH HS G D6 Multiple-Start Threads: Metric taps with multiple-start threads are marked with the lead designated in millimeters preceded by the letter “L,” the pitch in millimeters preceded by the letter “P,” and the words “(2 starts),” “(3 starts),” etc. Examples:M16 × L4-P2 (2 starts) HS G D8 M14 × L6-P2 (3 starts) HS G D7 Acme and Square-Threaded Taps These taps are usually made in sets, three taps in a set being the most common. For very fine pitches, two taps in a set will be found sufficient, whereas as many as five taps in a set are used for coarse pitches. The table on the next page gives dimensions for proportioning both Acme and square-threaded taps when made in sets. In cutting the threads of squarethreaded taps, one leading tap maker uses the following rules: The width of the groove between two threads is made equal to one-half the pitch of the thread, less 0.004 inch, making the width of the thread itself equal to one-half of the pitch, plus 0.004 inch. The depth of the thread is made equal to 0.45 times the pitch, plus 0.0025 inch. This latter rule produces a thread that for all the ordinarily used pitches for square-threaded taps has a depth less than the generally accepted standard depth, this latter depth being equal to one-half the pitch. The object of this shallow thread is to ensure that if the hole to be threaded by the tap is not bored out so as to provide clearance at the bottom of the thread, the tap will cut its own clearance. The hole should, however, always be drilled out large enough so that the cutting of the clearance is not required of the tap. The table, Dimensions of Acme Threads Taps in Sets of Three Taps, may also be used for the length dimensions for Acme taps. The dimensions in this table apply to single-threaded taps. For multiple-threaded taps or taps with very coarse pitch, relative to the diameter, the length of the chamfered part of the thread may be increased. Square-threaded taps are made to the same table as Acme taps, with the exception of the figures in column K, which for square-threaded taps should be equal to the nominal diameter of the tap, no oversize allowance being customary in these taps. The first tap in a set of Acme taps (not square-threaded taps) should be turned to a taper at the bottom of the thread for a distance of about one-quarter of the length of the threaded part. The taper should be so selected that the root diameter is about 1⁄32 inch smaller at the point than the proper root diameter of the tap. The first tap should preferably be provided with a short pilot at the point. For very coarse pitches, the first tap may be provided with spiral flutes at right angles to the angle of the thread. Acme and square-threaded taps should be relieved or backed off on the top of the thread of the chamfered portion on all the taps in the set. When the taps are used as machine taps, rather than as hand taps, they should be relieved in the angle of the thread, as well as on the top,



TAPS AND THREADING DIES Table 24. Dimensions of Acme Threads Taps in Sets of Three Taps A B

C

1ST TAP IN SET

D

E

ROOT DIA. – 0.010"

2ND TAP IN SET

F

G

ROOT DIA. – 0.010" K FINISHING TAP Nominal Dia.

H

A

B

C

1⁄ 2

41⁄4

17⁄8

23⁄8

1⁄ 2

17⁄8

5⁄ 8

9⁄ 16

47⁄8

21⁄8

23⁄4

9⁄ 16

23⁄16

3⁄ 4

2

1

13⁄4

0.582

5⁄ 8

51⁄2

23⁄8

31⁄8

5⁄ 8

21⁄2

7⁄ 8

21⁄4

11⁄8

2

0.645

11⁄ 16

6

21⁄2

31⁄2

313⁄16

213⁄16

15⁄ 16

29⁄16

11⁄4

21⁄4

0.707

3⁄ 4

61⁄2

211⁄16

313⁄16

11⁄ 16

31⁄8

1

213⁄16

13⁄8

27⁄16

0.770

13⁄ 16

67⁄8

213⁄16

41⁄16

3⁄ 4

35⁄16

11⁄16

3

17⁄16

2 5⁄8

0.832

7⁄ 8

71⁄4

3

41⁄4

3⁄ 4

31⁄2

11⁄8

31⁄8

11⁄2

23⁄4

0.895

15⁄ 16

79⁄16

31⁄8

47⁄16

13⁄ 16

35⁄8

13⁄16

31⁄4

19⁄16

27⁄8

0.957

77⁄8

31⁄4

45⁄8

13⁄ 16

313⁄16

11⁄4

33⁄8

15⁄8

3

1.020

1

D

I

E

F

G

H

I

K

13⁄4

7⁄ 8

11⁄2

0.520

11⁄8

81⁄2

39⁄16

415⁄16

7⁄ 8

41⁄16

15⁄16

35⁄8

13⁄4

33⁄16

1.145

11⁄4

9

33⁄4

51⁄4

15⁄ 16

45⁄16

13⁄8

37⁄8

17⁄8

33⁄8

1.270

13⁄8

91⁄2

4

51⁄2

1

41⁄2

17⁄16

41⁄16

2

31⁄2

1.395 1.520

11⁄2

10

41⁄4

53⁄4

1

43⁄4

11⁄2

41⁄4

21⁄8

35⁄8

15⁄8

101⁄2

41⁄2

6

1

5

11⁄2

41⁄2

21⁄8

37⁄8

1.645

13⁄4

11

43⁄4

61⁄4

11⁄16

53⁄16

19⁄16

411⁄16

21⁄4

4

1.770

17⁄8

113⁄8

47⁄8

61⁄2

11⁄16

57⁄16

19⁄16

415⁄16

21⁄4

41⁄4

1.895

2

113⁄4

5

63⁄4

11⁄8

55⁄8

15⁄8

51⁄8

23⁄8

43⁄8

2.020

21⁄4

121⁄2

51⁄4

71⁄4

11⁄8

61⁄8

13⁄16

51⁄2

21⁄2

43⁄4

2.270

21⁄2

131⁄4

51⁄2

73⁄4

13⁄4

69⁄16

17⁄8

57⁄8

25⁄8

51⁄8

2.520

23⁄4

14

53⁄4

81⁄4

11⁄4

7

2

61⁄4

23⁄4

51⁄2

2.770

3

15

61⁄4

83⁄4

11⁄4

71⁄2

2

63⁄4

3

53⁄4

3.020

for the whole length of the chamfered portion. Acme taps should also always be relieved on the front side of the thread to within 1⁄32 inch of the cutting edge. Adjustable Taps: Many adjustable taps are now used, especially for accurate work. Some taps of this class are made of a solid piece of tool steel that is split and provided with means of expanding sufficiently to compensate for wear. Most of the larger adjustable taps have inserted blades or chasers that are held rigidly, but are capable of radial adjustment. The use of taps of this general class enables standard sizes to be maintained readily.



921

Table 25. Proportions of Acme and Square-Threaded Taps Made in Sets R – 0.010"

B

A C L

R = root diameter of thread. T = double depth of full thread.

Kind of Tap

No. of Taps in Set

Order of Tap in Set 1st

2

3

Acme Thread Taps

4

5

2

3

SquareThreaded Taps

4

5

D = full diameter of tap.

A

B

R + 0.65T

R + 0.010

1⁄ L 8

to 1⁄6 L

C

2d

D

A on 1st tap − 0.005

1⁄ L 4

to 1⁄3 L

1st

R + 0.45T

R + 0.010

1⁄ L 8

to 1⁄6 L

2d

R + 0.80T


1⁄ L 6

to 1⁄4 L

3d

D

A on 2d tap − 0.005

1⁄ L 4

to 1⁄3 L

1st

R + 0.40T

R + 0.010

1⁄ L 8

2d

R + 0.70T


1⁄ L 6

3d

R + 0.90T

A on 2d tap − 0.005

1⁄ L 5

4th

D

A on 3d tap − 0.005

1⁄ L 4

1st

R + 0.37T

R + 0.010

1⁄ L 8

2d

R + 0.63T


1⁄ L 6

3d

R + 0.82T

A on 2d tap − 0.005

1⁄ L 5

4th

R + 0.94T

A on 3d tap − 0.005

1⁄ L 5

to 1⁄4 L

5th

D

A on 4th tap − 0.005

1⁄ L 4

to 1⁄3 L

1st

R + 0.67T

R

1⁄ L 8

to 1⁄6 L

2d

D


1⁄ L 4

to 1⁄3 L

1st

R + 0.41T

R

1⁄ L 8

to 1⁄6 L

2d

R + 0.080T


1⁄ L 6

to 1⁄4 L

3d

D

A on 2d tap − 0.005

1⁄ L 4

to 1⁄3 L

1st

R + 0.32T

R

1⁄ L 8

2d

R + 0.62T


1⁄ L 6

3d

R + 0.90T

A on 2d tap − 0.005

1⁄ L 5

4th

D

A on 3d tap − 0.005

1⁄ L 4

1st

R + 0.26T

R

1⁄ L 8

2d

R + 0.50T


1⁄ L 6

3d

R + 0.72T

A on 2d tap − 0.005

1⁄ L 5

4th

R + 0.92T

A on 3d tap − 0.005

1⁄ L 5

to 1⁄4 L

5th

D

A on 4th tap − 0.005

1⁄ L 4

to 1⁄3 L

to 1⁄3 L

to 1⁄3 L

Drill Hole Sizes for Acme Threads.—Many tap and die manufacturers and vendors make available to their customers computer programs designed to calculate drill hole sizes for all the Acme threads in their ranges from the basic dimensions. The large variety and combination of dimensions for such tools prevent inclusion of a complete set of tables of tap drills for Acme taps in this Handbook. The following formulas (dimensions in inches) for calculating drill hole sizes for Acme threads are derived from the American National Standard, ANSI/ASME B1.5-1997, Acme Screw Threads.




To select a tap drill size for an Acme thread, first calculate the maximum and minimum internal product minor diameters for the thread to be produced. (Dimensions for general purpose, centralizing, and stub Acme screw threads are given in the Threads and Threading section, starting on page 1825.) Then select a drill that will yield a finished hole somewhere between the established maximum and minimum product minor diameters. Consider staying close to the maximum product limit in selecting the hole size, to reduce the amount of material to be removed when cutting the thread. If there is no standard drill size that matches the hole diameter selected, it may be necessary to drill and ream, or bore the hole to size, to achieve the required hole diameter. Diameters of General-Purpose Acme Screw Threads of Classes 2G, 3G, and 4G may be calculated from: minimum diameter = basic major diameter − pitch maximum diameter = minimum minor diameter + 0.05 × pitch pitch = 1/number of threads per inch Example: 1⁄2 -10 Acme 2G, pitch = 1⁄10 = 0.1 minimum diameter = 0.5 − 0.1 = 0.4 maximum diameter = 0.4 + (0.05 × 0.1) = 0.405 drill selected = letter X or 0.3970 + 0.0046 (probable oversize) = 0.4016 Diameters of Acme Centralizing Screw Threads of Classes 2C, 3C, and 4C may be calculated from: minimum diameter = basic major diameter − 0.9 × pitch maximum diameter = minimum minor diameter + 0.05 × pitch pitch = 1/number of threads per inch Example: 1⁄2 -10 Acme 2C, pitch = 1⁄10 = 0.1 minimum diameter = 0.5 − (0.9 × 0.1) = 0.41 maximum diameter = 0.41 + (0.05 × 0.1) = 0.415 drill selected = 13⁄32 or 0.4062 + 0.0046 (probable oversize) = 0.4108. Diameters for Acme Centralizing Screw Threads of Classes 5C and 6C: These classes are not recommended for new designs, but may be calculated from: minimum diameter = [basic major diameter − (0.025 √ basic major diameter)] − 0.9 × pitch maximum diameter = minimum minor diameter + 0.05 × pitch pitch = 1/number of threads per inch Example: 1⁄2 -10 Acme 5C, pitch = 1⁄10 = 0.1 minimum diameter = [0.5 − (0.025 √ 0.5)] − (0.9 × 0.1) = 0.3923 maximum diameter = 0.3923 + (0.05 × 0.1) = 0.3973 drill selected = 25⁄64 or 0.3906 + 0.0046 (probable oversize) = 0.3952 British Standard Screwing Taps for ISO Metric Threads.—BS 949: Part 1:1976 provides dimensions and tolerances for screwing taps for ISO metric coarse-pitch series threads in accordance with BS 3643: Part 2; and for metric fine-pitch series threads in accordance with BS 3643: Part 3. Table 26 provides dimensional data for the cutting portion of cut-thread taps for coarseseries threads of ISO metric sizes. The sizes shown were selected from the first-choice combinations of diameter and pitch listed in BS 3643:Part 1:1981 (1998). Table 13 provides similar data for ground-thread taps for both coarse- and fine-pitch series threads of ISO metric sizes.



923

Table 26. British Standard Screwing Taps for ISO Metric Threads Dimensional Limits for the Threaded Portion of Cut Taps— Coarse Pitch Series BS 949: Part 1:1976 Major Diameter Designation

Pitch

Pitch Diameter

Minimuma

Basic

Max.

Tolerance on Thread Angle, Degrees

Min.

M1

0.25

1.030

0.838

0.875

0.848

4.0

M1.2

0.25

1.230

1.038

1.077

1.048

4.0

M1.6

0.35

1.636

1.373

1.417

1.385

3.4

M2

0.40

2.036

1.740

1.786

1.752

3.2

M2.5

0.45

2.539

2.208

2.259

2.221

3.0

M3

0.50

3.042

2.675

2.730

2.689

2.9

M4

0.70

4.051

3.545

3.608

3.562

2.4

M5

0.80

5.054

4.480

4.547

4.498

2.3

M6

1.00

6.060

5.350

5.424

5.370

2.0

M8

1.25

8.066

7.188

7.270

7.210

1.8

M10

1.50

10.072

9.026

9.116

9.050

1.6

M12

1.75

12.078

10.863

10.961

10.889

1.5

M16

2.00

16.084

14.701

14.811

14.729

1.4

M20

2.50

20.093

18.376

18.497

18.407

1.3

M24

3.00

24.102

22.051

22.183

22.085

1.2

M30

3.50

30.111

27.727

27.874

27.764

1.1

M36

4.00

36.117

33.402

33.563

33.441

1.0

a See notes under Table 27.

Table 27. British Standard Screwing Taps for ISO Metric Threads Dimensional Limits for the Threaded Portion of Ground Taps— Coarse-and Fine-Pitch BS 949: Part 1:1976 All Classes of Taps

Thread

Designation

Nominal Major Dia. (basic) d

Pitch p

Min. Major Dia. dmina

Basic Pitch Dia. d2

Class 1 Taps

Class 2 Taps

Class 3 Taps

d2min

d2max

Tolerance on 1⁄2 Thd Angle

Pitch Diameter

d2min

d2max

d2min

d2max

COARSE-PITCH THREAD SERIES M1

1

0.25

1.022

0.838

0.844

0.855

…

…

…

…

±60′

M1.2

1.2

0.25

1.222

1.038

1.044

1.055

…

…

…

…

±60′

M1.6

1.6

0.35

1.627

1.373

1.380

1.393

1.393

1.407

…

…

±50′

M2

2

0.40

2.028

1.740

1.747

1.761

1.761

1.776

…

…

±40′

M2.5

2.5

0.45

2.530

2.208

2.216

2.231

2.231

2.246

…

…

±38′

M3

3

0.50

3.032

2.675

2.683

2.699

2.699

2.715

2.715

2.731

±36′

M4

4

0.70

4.038

3.545

3.555

3.574

3.574

3.593

3.593

3.612

±30′

M5

5

0.80

5.040

4.480

4.490

4.510

4.510

4.530

4.530

4.550

±26′

M6

6

1.00

6.047

5.350

5.362

5.385

5.385

5.409

5.409

5.433

±24′

M8

8

1.25

8.050

7.188

7.201

7.226

7.226

7.251

7.251

7.276

±22′

M10

10

1.50

10.056

9.026

9.040

9.068

9.068

9.096

9.096

9.124

±20′

M12

12

1.75

12.064

10.863

10.879

10.911

10.911

10.943

10.943

10.975

±19′

M16

16

2.00

16.068

14.701

14.718

14.752

14.752

14.786

14.786

14.820

±18′

M20

20

2.50

20.072

18.376

18.394

18.430

18.430

18.466

18.466

18.502

±16′

M24

24

3.00

24.085

22.051

22.072

22.115

22.115

22.157

22.157

22.199

±14′




Table 27. (Continued) British Standard Screwing Taps for ISO Metric Threads Dimensional Limits for the Threaded Portion of Ground Taps— Coarse-and Fine-Pitch BS 949: Part 1:1976 All Classes of Taps

Thread

Class 1 Taps

Class 2 Taps

Class 3 Taps

d2max

d2min

d2max

Tolerance on 1⁄2 Thd Angle

M30

30

3.50

30.090

27.727

27.749

27.794

27.794

27.839

27.839

27.884

±13′

M36

36

4.00

36.094

33.402

33.426

33.473

33.473

33.520

33.520

33.567

±12′

Designation

Nominal Major Dia. (basic) d

Pitch p

Min. Major Dia. dmina

Basic Pitch Dia. d2

d2min

Pitch Diameter

d2max

d2min

FINE-PITCH THREAD SIZES M1 × 0.2

1

0.20

1.020

0.870

0.875

0.885

…

…

…

…

±70′

M1.2 × 0.2

1.2

0.20

1.220

1.070

1.075

1.085

…

…

…

…

±70′

M1.6 × 0.2

1.6

0.20

1.621

1.470

1.475

1.485

…

…

…

…

±70′

M2 × 0.25

2

0.25

2.024

1.838

1.844

1.856

…

…

…

…

±60′

M2.5 × 0.35

2.5

0.35

2.527

2.273

2.280

2.293

2.293

2.307

…

…

±50′

M3 × 0.35

3

0.35

3.028

2.773

2.780

2.794

2.794

2.809

…

…

±50′

M4 × 0.5

4

0.50

4.032

3.675

3.683

3.699

3.699

3.715

3.715

3.731

±36′

M5 × 0.5

5

0.50

5.032

4.675

4.683

4.699

4.699

4.715

4.715

4.731

±36′

M6 × 0.75

6

0.75

6.042

5.513

5.524

5.545

5.545

5.566

5.566

5.587

±28′

M8 × 1

8

1.00

8.047

7.350

7.362

7.385

7.385

7.409

7.409

7.433

±24′

M10 × 1.25

10

1.25

10.050

9.188

9.201

9.226

9.226

9.251

9.251

9.276

±22′

M12 × 1.25

12

1.25

12.056

11.188

11.202

11.230

11.230

11.258

11.258

11.286

±22′

M16 × 1.5

16

1.50

16.060

15.026

15.041

15.071

15.071

15.101

15.101

15.131

±20′

M20 × 1.5

20

1.50

20.060

19.026

19.041

19.071

19.071

19.101

19.101

19.131

±20′

M24 × 2

24

2.00

24.072

22.701

22.719

22.755

22.755

22.791

22.791

22.827

±18′

M30 × 2

30

2.00

30.072

28.701

28.719

28.755

28.755

28.791

28.791

28.827

±18′

a The

maximum tap major diameter, d max, is not specified and is left to the manufacturer's discre-

tion. All dimension are in millimeters. The thread sizes in the table have been selected from the preferred series shown in BS 3643:Part 1:1981 (1998). For other sizes, and for second and third choice combinations of diameters and pitches, see the Standard.

Tolerance Classes of Taps: Three tolerance classes (class 1, class 2, and class 3) are used for the designation of taps used for the production of nuts of the following classes: nut classes 4H, 5H, 6H, 7H, and 8H, all having zero minimum clearance; nut classes 4G, 5G, and 6G, all having positive minimum clearance. The tolerances for the three classes of taps are stated in terms of a tolerance unit t, the value of which is equal to the pitch diameter tolerance, TD2, grade 5, of the nut. Thus, t = TD2, grade 5, of the nut. Taps of the different classes vary in the limits of size of the tap pitch diameter. The tolerance on the tap pitch diameter, Td2, is the same for all three classes of taps (20 percent of t), but the position of the tolerance zone with respect to the basic pitch diameter depends upon the lower deviation value Em which is: for tap class 1, Em = +0.1t; for tap class 2, Em = + 0.3t; and for tap class 3, Em = +0.5t.



925

Nuts 8H

6G

7H

5G

6H

4G

5H

Taps Class 3

4H Class 2

t Class 1

0.7t 0.5t E1

0.3t Pitch diameter of basic profile 0.1t

The disposition of the tolerances described is shown in the accompanying illustration of nut class tolerances compared against tap class tolerances. The distance EI shown in this illustration is the minumum clearance, which is zero for H classes and positive for G classes of nuts. Choice of Tap Tolerance Class: Unless otherwise specified, class 1 taps are used for nuts of classes 4H and 5H; class 2 taps for nuts of classes 6H, 4G, and 5G; and class 3 taps for nuts of classes 7H, 8H, and 6G. This relationship of tap and nut classes is a general one, since the accuracy of tapping varies with a number of factors such as the material being tapped, the condition of the machine tool used, the tapping attachment used, the tapping speed, and the lubricant. Tap Major Diameter: Except when a screwed connection has to be tight against gaseous or liquid pressure, it is undesirable for the mating threads to bear on the roots and crests. By avoiding contact in these regions of the threads, the opposite flanks of the two threads are allowed to make proper load bearing contact when the connection is tightened. In general, the desired clearance between crests and roots of mating threads is obtained by increasing the major and minor diameters of the internal thread. Such an increase in the minor diameter is already provided on threads such as the ISO metric thread, in which there is a basic clearance between the crests of minimum size nuts and the roots of maximum size bolts. For this reason, and the fact that taps are susceptible to wear on the crests of their threads, a minimum size is specified for the major diameter of new taps which provides a reasonable margin for the wear of their crests and at the same time provides the desired clearance at the major diameter of the hole. These minimum major diameters for taps are shown in Tables 26 and 13. The maximum tap major diameter is not specified and is left to the manufacturer to take advantage of this concession to produce taps with as liberal a margin possible for wear on the major diameter. Tapping Square Threads.—If it is necessary to tap square threads, this should be done by using a set of taps that will form the thread by a progressive cutting action, the taps varying in size in order to distribute the work, especially for threads of comparatively coarse pitch. From three to five taps may be required in a set, depending upon the pitch. Each tap should have a pilot to steady it. The pilot of the first tap has a smooth cylindrical end from 0.003 to 0.005 inch smaller than the hole, and the pilots of following taps should have teeth.



STANDARD TAPERS

STANDARD TAPERS Standard Tapers Certain types of small tools and machine parts, such as twist drills, end mills, arbors, lathe centers, etc., are provided with taper shanks which fit into spindles or sockets of corresponding taper, thus providing not only accurate alignment between the tool or other part and its supporting member, but also more or less frictional resistance for driving the tool. There are several standards for “self-holding” tapers, but the American National, Morse, and the Brown & Sharpe are the standards most widely used by American manufacturers. The name self-holding has been applied to the smaller tapers—like the Morse and the Brown & Sharpe—because, where the angle of the taper is only 2 or 3 degrees, the shank of a tool is so firmly seated in its socket that there is considerable frictional resistance to any force tending to turn or rotate the tool relative to the socket. The term “self-holding” is used to distinguish relatively small tapers from the larger or self-releasing type. A milling machine spindle having a taper of 31⁄2 inches per foot is an example of a self-releasing taper. The included angle in this case is over 16 degrees and the tool or arbor requires a positive locking device to prevent slipping, but the shank may be released or removed more readily than one having a smaller taper of the self-holding type. Morse Taper.—Dimensions relating to Morse standard taper shanks and sockets may be found in an accompanying table. The taper for different numbers of Morse tapers is slightly different, but it is approximately 5⁄8 inch per foot in most cases. The table gives the actual tapers, accurate to five decimal places. Morse taper shanks are used on a variety of tools, and exclusively on the shanks of twist drills. Dimensions for Morse Stub Taper Shanks are given in Table 1a, and for Morse Standard Taper Shanks in Table 1b. Brown & Sharpe Taper.—This standard taper is used for taper shanks on tools such as end mills and reamers, the taper being approximately 1⁄2 inch per foot for all sizes except for taper No. 10, where the taper is 0.5161 inch per foot. Brown & Sharpe taper sockets are used for many arbors, collets, and machine tool spindles, especially milling machines and grinding machines. In many cases there are a number of different lengths of sockets corresponding to the same number of taper; all these tapers, however, are of the same diameter at the small end. Jarno Taper.—The Jarno taper was originally proposed by Oscar J. Beale of the Brown & Sharpe Mfg. Co. This taper is based on such simple formulas that practically no calculations are required when the number of taper is known. The taper per foot of all Jarno taper sizes is 0.600 inch on the diameter. The diameter at the large end is as many eighths, the diameter at the small end is as many tenths, and the length as many half inches as are indicated by the number of the taper. For example, a No. 7 Jarno taper is 7⁄8 inch in diameter at the large end; 7⁄10 , or 0.700 inch at the small end; and 7⁄2 , or 31⁄2 inches long; hence, diameter at large end = No. of taper ÷ 8; diameter at small end = No. of taper ÷ 10; length of taper = No. of taper ÷ 2. The Jarno taper is used on various machine tools, especially profiling machines and die-sinking machines. It has also been used for the headstock and tailstock spindles of some lathes. American National Standard Machine Tapers: This standard includes a self-holding series (Tables 2, 3, 4, 5 and 7a) and a steep taper series, Table 6. The self-holding taper series consists of 22 sizes which are listed in Table 7a. The reference gage for the self-holding tapers is a plug gage. Table 7b gives the dimensions and tolerances for both plug and ring gages applying to this series. Tables 2 through 5 inclusive give the dimensions for selfholding taper shanks and sockets which are classified as to (1) means of transmitting torque from spindle to the tool shank, and (2) means of retaining the shank in the socket. The steep machine tapers consist of a preferred series (bold-face type, Table 6) and an intermediate series (light-face type). A self-holding taper is defined as “a taper with an


Machinery's Handbook 27th Edition STANDARD TAPERS

927

angle small enough to hold a shank in place ordinarily by friction without holding means. (Sometimes referred to as slow taper.)” A steep taper is defined as “a taper having an angle sufficiently large to insure the easy or self-releasing feature.” The term “gage line” indicates the basic diameter at or near the large end of the taper. Table 1a. Morse Stub Taper Shanks

Small End of Plug, b D

Shank Dia. End of Socket, a A

No. of Taper

Taper per Foota

Taper per Inchb

1

0.59858

0.049882

0.4314

0.475

15⁄16

2

0.59941

0.049951

0.6469

0.700

Total Length, B

Tang

Depth, C

Thickness, E

Length, F

11⁄8

13⁄ 64

5⁄ 16

111⁄16

17⁄16

19⁄ 64

7⁄ 16

25⁄ 64

9⁄ 16

3

0.60235

0.050196

0.8753

0.938

2

13⁄4

4

0.62326

0.051938

1.1563

1.231

23⁄8

21⁄16

33⁄ 64

11⁄ 16

3

211⁄16

3⁄ 4

15⁄ 16

5

0.63151

0.052626

1.6526

1.748

Tang

Socket

Tang Slot

Min. Depth of Tapered Hole

Socket End to Tang Slot, M

No. of Taper

Radius of Mill, G

Diameter, H

1

3⁄ 16

13⁄ 32

7⁄ 8

2

7⁄ 32

39⁄ 64

11⁄16

15⁄32

17⁄64

3

9⁄ 32

13⁄ 16

11⁄4

13⁄8

15⁄16

11⁄16

13⁄ 32

11⁄8

4

3⁄ 8

13⁄32

17⁄16

19⁄16

11⁄2

13⁄16

17⁄ 32

13⁄8

5

9⁄ 16

119⁄32

113⁄16

115⁄16

17⁄8

17⁄16

25⁄ 32

13⁄4

Plug Depth, P

Drilled X 5⁄ 16

Reamed Y 29⁄ 32

Width, N

Length, O

25⁄ 32

7⁄ 32

23⁄ 32

15⁄ 16

5⁄ 16

15⁄ 16

a These are basic dimensions. b These dimensions are calculated for reference only.

All dimensions in inches. Radius J is 3⁄64 , 1⁄16 , 5⁄64 , 3⁄32 , and 1⁄8 inch respectively for Nos. 1, 2, 3, 4, and 5 tapers.



STANDARD TAPERS Table 1b. Morse Standard Taper Shanks

No. of Taper

Taper per Foot

Taper per Inch

Small End of Plug D

0

0.62460

0.05205

0.252

1 2

0.59858 0.59941

0.04988 0.04995

0.369 0.572

Diameter End of Socket A

Shank Length B

0.3561

Depth S

Depth of Hole H

211⁄32

27⁄32

21⁄32

0.475

29⁄16

27⁄16

25⁄32

0.700

31⁄8

215⁄16

239⁄64

311⁄16

31⁄4

3

0.60235

0.05019

0.778

0.938

37⁄8

4

0.62326

0.05193

1.020

1.231

47⁄8

45⁄8

41⁄8

5

0.63151

0.05262

1.475

1.748

61⁄8

57⁄8

51⁄4

6

0.62565

0.05213

2.116

2.494

89⁄16

81⁄4

721⁄64

3.270

115⁄8

111⁄4

105⁄64

Dia.

Width W

Length L

Keyway to End K

11⁄ 64

9⁄ 16

115⁄16

7

0.62400

0.05200

2.750

Plug Depth P

Thickness t

Length T

Radius R

2

0.1562

1⁄ 4

5⁄ 32

0.235

Tang or Tongue

Keyway

21⁄8

0.2031

3⁄ 8

3⁄ 16

0.343

0.218

3⁄ 4

21⁄16

29⁄16

0.2500

7⁄ 16

1⁄ 4

17⁄ 32

0.266

7⁄ 8

21⁄2

33⁄16

0.3125

9⁄ 16

9⁄ 32

23⁄ 32

0.328

13⁄16

31⁄16

0.4687

5⁄ 8

5⁄ 16

31⁄ 32

0.484

11⁄4

37⁄8

0.6250

3⁄ 4

3⁄ 8

113⁄32

0.656

11⁄2

415⁄16

0.7500

11⁄8

1⁄ 2

2

0.781

13⁄4

7

1.1250

13⁄8

3⁄ 4

25⁄8

1.156

25⁄8

91⁄2

41⁄16 53⁄16 71⁄4 10

Tolerances on rate of taper: all sizes 0.002 in. per foot. This tolerance may be applied on shanks only in the direction that increases the rate of taper, and on sockets only in the direction that decreases the rate of taper.



929

Table 2. American National Standard Taper Drive with Tang, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

No. of Taper 0.239 0.299 0.375 1 2 3 4 41⁄2 5 6

Diameter at Gage Line (1) A 0.23922 0.29968 0.37525 0.47500 0.70000 0.93800 1.23100 1.50000 1.74800 2.49400

No. of Taper 0.239 0.299 0.375 1 2 3 4 41⁄2 5 6

Radius J 0.03 0.03 0.05 0.05 0.06 0.08 0.09 0.13 0.13 0.16

Shank Total Gage Line Length to End of Shank of Shank B C 1.28 1.19 1.59 1.50 1.97 1.88 2.56 2.44 3.13 2.94 3.88 3.69 4.88 4.63 5.38 5.13 6.12 5.88 8.25 8.25 Socket Min. Depth of Hole K Drilled 1.06 1.31 1.63 2.19 2.66 3.31 4.19 4.62 5.31 7.41

Reamed 1.00 1.25 1.56 2.16 2.61 3.25 4.13 4.56 5.25 7.33

Tang

Thickness E 0.125 0.156 0.188 0.203 0.250 0.312 0.469 0.562 0.625 0.750

Length F 0.19 0.25 0.31 0.38 0.44 0.56 0.63 0.69 0.75 1.13

Radius of Mill Diameter G H 0.19 0.18 0.19 0.22 0.19 0.28 0.19 0.34 0.25 0.53 0.22 0.72 0.31 0.97 0.38 1.20 0.38 1.41 0.50 2.00 Tang Slot

Gage Line to Tang Slot M 0.94 1.17 1.47 2.06 2.50 3.06 3.88 4.31 4.94 7.00

Width N 0.141 0.172 0.203 0.218 0.266 0.328 0.484 0.578 0.656 0.781

Length O 0.38 0.50 0.63 0.75 0.88 1.19 1.25 1.38 1.50 1.75

Shank End to Back of Tang Slot P 0.13 0.17 0.22 0.38 0.44 0.56 0.50 0.56 0.56 0.50

All dimensions are in inches. (1) See Table 7b for plug and ring gage dimensions. Tolerances: For shank diameter A at gage line, + 0.002 − 0.000; for hole diameter A, + 0.000 − 0.002. For tang thickness E up to No. 5 inclusive, + 0.000 − 0.006; No. 6, + 0.000 − 0.008. For width N of tang slot up to No. 5 inclusive, + 0.006; − 0.000; No. 6, + 0.008 − 0.000. For centrality of tang E with center line of taper, 0.0025 (0.005 total indicator variation). These centrality tolerances also apply to the tang slot N. On rate of taper, all sizes 0.002 per foot. This tolerance may be applied on shanks only in the direction which increases the rate of taper and on sockets only in the direction which decreases the rate of taper. Tolerances for two-decimal dimensions are plus or minus 0.010, unless otherwise specified.



STANDARD TAPERS Table 3. American National Standard Taper Drive with Keeper Key Slot, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

Shank

Tang

No. of Taper

Dia. at Gage Line (1) A

Total Length B

Gage Line to End C

3

0.938

3.88

4

1.231

41⁄2 5

Socket Min. Depth of Hole K

Gage Line to Tang Slot M

Thickness E

Length F

Radius of Mill G

Drill

Ream

3.69

0.312

0.56

0.28

0.78

0.08

3.31

3.25

3.06

4.88

4.63

0.469

0.63

0.31

0.97

0.09

4.19

4.13

3.88

1.500

5.38

5.13

0.562

0.69

0.38

1.20

0.13

4.63

4.56

4.32

1.748

6.13

5.88

0.625

0.75

0.38

1.41

0.13

5.31

5.25

4.94

Diameter H

Radius J

6

2.494

8.56

8.25

0.750

1.13

0.50

2.00

0.16

7.41

7.33

7.00

7

3.270

11.63

11.25

1.125

1.38

0.75

2.63

0.19

10.16

10.08

9.50

Tang Slot

Keeper Slot in Shank

Keeper Slot in Socket

No. of Taper

Width N

Length O

Shank End to Back of Slot P

Gage Line to Bottom of Slot Y′

Length X

Width N′

Gage Line to Front of Slot Y

3

0.328

1.19

0.56

1.03

1.13

0.266

1.13

1.19

4

0.484

1.25

0.50

1.41

1.19

0.391

1.50

1.25

0.391

41⁄2

0.578

1.38

0.56

1.72

1.25

0.453

1.81

1.38

0.453

5

0.656

1.50

0.56

2.00

1.38

0.516

2.13

1.50

0.516

6

0.781

1.75

0.50

2.13

1.63

0.641

2.25

1.75

0.641

7

1.156

2.63

0.88

2.50

1.69

0.766

2.63

1.81

0.766

Length Z

Width N′ 0.266

All dimensions are in inches. (1) See Table 7b for plug and ring gage dimensions. Tolerances: For shank diameter A at gage line, +0.002, −0; for hole diameter A, +0, −0.002. For tang thickness E up to No. 5 inclusive, +0, −0.006; larger than No. 5, +0, −0.008. For width of slots N and N′ up to No. 5 inclusive, +0.006, −0; larger than No. 5, +0.008, −0. For centrality of tang E with center line of taper 0.0025 (0.005 total indicator variation). These centrality tolerances also apply to slots N and N′. On rate of taper, see footnote in Table 2. Tolerances for two-decimal dimensions are ±0.010 unless otherwise specified.



931

Table 4. American National Standard Nose Key Drive with Keeper Key Slot, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

Taper

A(1)

200 250 300 350 400 450 500 600 800 1000 1200

2.000 2.500 3.000 3.500 4.000 4.500 5.000 6.000 8.000 10.000 12.000

Taper 200 250 300 350 400 450 500 600 800 1000 1200 Taper 200 250 300 350 400 450 500 600 800 1000 1200

D 1.41 1.66 2.25 2.50 2.75 3.00 3.25 3.75 4.75 … … U 1.81 2.25 2.75 3.19 3.63 4.19 4.63 5.50 7.38 9.19 11.00

C

Q

I′

I

R

S

5.13 5.88 6.63 7.44 8.19 9.00 9.75 11.31 14.38 17.44 20.50

B′

Min 0.003 Max 0.035 for all sizes

0.25 0.25 0.25 0.31 0.31 0.38 0.38 0.44 0.50 0.63 0.75

1.38 1.38 1.63 2.00 2.13 2.38 2.50 3.00 3.50 4.50 5.38

1.63 2.06 2.50 2.94 3.31 3.81 4.25 5.19 7.00 8.75 10.50

1.010 1.010 2.010 2.010 2.010 3.010 3.010 3.010 4.010 4.010 4.010

0.562 0.562 0.562 0.562 0.562 0.812 0.812 0.812 1.062 1.062 1.062

D′a 0.375 0.375 0.375 0.375 0.375 0.500 0.500 0.500 0.500 … … V 1.00 1.00 1.00 1.25 1.25 1.50 1.50 1.75 2.00 2.50 3.00

W 3.44 3.69 4.06 4.88 5.31 5.88 6.44 7.44 9.56 11.50 13.75 M 4.50 5.19 5.94 6.75 7.50 8.00 8.75 10.13 12.88 15.75 18.50

X 1.56 1.56 1.56 2.00 2.25 2.44 2.63 3.00 4.00 4.75 5.75 N 0.656 0.781 1.031 1.031 1.031 1.031 1.031 1.281 1.781 2.031 2.531

N′ 0.656 0.781 1.031 1.031 1.031 1.031 1.031 1.281 1.781 2.031 2.031 O 1.56 1.94 2.19 2.19 2.19 2.75 2.75 3.25 4.25 5.00 6.00

R′ 1.000 1.000 2.000 2.000 2.000 3.000 3.000 3.000 4.000 4.000 4.000 P 0.94 1.25 1.50 1.50 1.50 1.75 1.75 2.06 2.75 3.31 4.00

S′ 0.50 0.50 0.50 0.50 0.50 0.75 0.75 0.75 1.00 1.00 1.00 Y 2.00 2.25 2.63 3.00 3.25 3.63 4.00 4.63 5.75 7.00 8.25

T 4.75 5.50 6.25 6.94 7.69 8.38 9.13 10.56 13.50 16.31 19.00 Z 1.69 1.69 1.69 2.13 2.38 2.56 2.75 3.25 4.25 5.00 6.00

a Thread is UNF-2B for hole; UNF-2A for screw. (1) See Table 7b for plug and ring gage dimensions. All dimensions are in inches. AE is 0.005 greater than one-half of A. Width of drive key R″ is 0.001 less than width R″ of keyway. Tolerances: For diameter A of hole at gage line, +0, −0.002; for diameter A of shank at gage line, +0.002, −0; for width of slots N and N′, +0.008, −0; for width of drive keyway R′ in socket, +0, − 0.001; for width of drive keyway R in shank, 0.010, −0; for centrality of slots N and N′ with center line of spindle, 0.007; for centrality of keyway with spindle center line: for R, 0.004 and for R′, 0.002 T.I.V. On rate of taper, see footnote in Table 2. Two-decimal dimensions, ±0.010 unless otherwise specified.



STANDARD TAPERS Table 5. American National Standard Nose Key Drive with Drawbolt, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

No. of Taper 200 250 300 350 400 450 500 600 800 1000 1200

Dia. at Gage Line Aa 2.000 2.500 3.000 3.500 4.000 4.500 5.000 6.000 8.000 10.000 12.000

Drive Key Screw Holes UNF 2B Center Line Hole UNF to Center 2A Screw of Screw D′ D 1.41 1.66 2.25 2.50 2.75 3.00 3.25 3.75 4.75 … …

0.38 0.38 0.38 0.38 0.38 0.50 0.50 0.50 0.50 … …

Sockets Drive Keyway

Width R″

Width R′

Depth S′

0.999 0.999 1.999 1.999 1.999 2.999 2.999 2.999 3.999 3.999 3.999

1.000 1.000 2.000 2.000 2.000 3.000 3.000 3.000 4.000 4.000 4.000

0.50 0.50 0.50 0.50 0.50 0.75 0.75 0.75 1.00 1.00 1.00

Gage Line to Front of Relief T 4.75 5.50 6.25 6.94 7.69 8.38 9.13 10.56 13.50 16.31 19.00

Dia. of Relief U

Depth of Relief V

Dia. of Draw Bolt Hole d

1.81 2.25 2.75 3.19 3.63 4.19 4.63 5.50 7.38 9.19 11.00

1.00 1.00 1.00 1.25 1.25 1.50 1.50 1.75 2.00 2.50 3.00

1.00 1.00 1.13 1.13 1.63 1.63 1.63 2.25 2.25 2.25 2.25

a See Table 7b for plug and ring gage dimensions.

Shanks Drawbar Hole

No. of Taper

Length from Gage Line B′

Dia. UNC-2B AL 7⁄ –9 8 7⁄ –9 8

Depth of Drilled Hole E

Depth of Thread AP

Dia. of Counter Bore G

2.44

1.75

0.91

1.75 2.00 2.00 3.00

0.91 1.03 1.03 1.53

Drive Keyway

Depth of 60° Chamfer J

Width R

Depth S

Center Line to Bottom of Keyway AE

4.78

0.13

1.010

0.562

1.005

5.53 6.19 7.00 7.50

0.13 0.19 0.19 0.31

1.010 2.010 2.010 2.010

0.562 0.562 0.562 0.562

1.255 1.505 1.755 2.005

Gage Line to First Thread AO

200

5.13

250 300 350 400

5.88 6.63 7.44 8.19

1–8 1–8 11⁄2 –6

2.44 2.75 2.75 4.00

450

9.00

11⁄2 –6

4.00

3.00

1.53

8.31

0.31

3.010

0.812

2.255

500

9.75

11⁄2 –6

4.00

3.00

1.53

9.06

0.31

3.010

0.812

2.505

600

11.31

5.31

4.00

2.03

10.38

0.50

3.010

0.812

3.005

800

14.38

5.31

4.00

2.03

13.44

0.50

4.010

1.062

4.005

1000

17.44

5.31

4.00

2.03

16.50

0.50

4.010

1.062

5.005

1200

20.50

2–41⁄2 2–41⁄2 2–41⁄2 2–41⁄2

5.31

4.00

2.03

19.56

0.50

4.010

1.062

6.005

All dimensions in inches. Exposed length C is 0.003 minimum and 0.035 maximum for all sizes. Drive Key D′ screw sizes are 3⁄8 –24 UNF-2A up to taper No. 400 inclusive and 1⁄2 –20 UNF-2A for larger tapers. Tolerances: For diameter A of hole at gage line, +0.000, −0.002 for all sizes; for diameter A of shank at gage line, +0.002, −0.000; for all sizes; for width of drive keyway R′ in socket, +0.000, − 0.001; for width of drive keyway R in shank, +0.010, −0.000; for centrality of drive keyway R′, with center line of shank, 0.004 total indicator variation, and for drive keyway R′, with center line of spindle, 0.002. On rate of taper, see footnote in Table 2. Tolerances for two-decimal dimensions are ±0.010 unless otherwise specified.



933

Table 6. ANSI Standard Steep Machine Tapers ANSI/ASME B5.10-1994 (R2002)

No. of Taper 5 10 15 20 25 30

Taper per Foota 3.500 3.500 3.500 3.500 3.500 3.500

Dia. at Gage Lineb 0.500 0.625 0.750 0.875 1.000 1.250

Length Along Axis 0.6875 0.8750 1.0625 1.3125 1.5625 1.8750

No. of Taper 35 40 45 50 55 60

Taper per Foota 3.500 3.500 3.500 3.500 3.500 3.500

Dia.at Gage Lineb 1.500 1.750 2.250 2.750 3.500 4.250

Length Along Axis 2.2500 2.5625 3.3125 4.0000 5.1875 6.3750

a This taper corresponds to an included angle of 16°, 35′, 39.4″. b The basic diameter at gage line is at large end of taper.

All dimensions given in inches. The tapers numbered 10, 20, 30, 40, 50, and 60 that are printed in heavy-faced type are designated as the “Preferred Series.” The tapers numbered 5, 15, 25, 35, 45, and 55 that are printed in light-faced type are designated as the “Intermediate Series.”

Table 7a. American National Standard Self-holding Tapers — Basic Dimensions ANSI/ASME B5.10-1994 (R2002) No. of Taper

Taper per Foot

Dia. at Gage Line a A

.239 .299 .375 1 2 3 4

0.50200 0.50200 0.50200 0.59858 0.59941 0.60235 0.62326

0.23922 0.29968 0.37525 0.47500 0.70000 0.93800 1.23100

41⁄2

0.62400

1.50000

5 6 7 200 250 300 350 400 450 500 600 800 1000 1200

0.63151 1.74800 0.62565 2.49400 0.62400 3.27000 0.750 2.000 0.750 2.500 0.750 3.000 0.750 3.500 0.750 4.000 0.750 4.500 0.750 5.000 0.750 6.000 0.750 8.000 0.750 10.000 0.750 12.000

Means of Driving and Holdinga

} Tang Drive With Shank Held in by Friction (See Table 2)

} Tang Drive With Shank Held in by Key (See Table 3)

} Key Drive With Shank Held in by Key (See Table 4) } Key Drive With Shank Held in by Draw-bolt (See Table 5)

a See illustrations above Tables 2 through 5.

All dimensions given in inches.


Origin of Series Brown & Sharpe Taper Series

Morse Taper Series

3⁄ 4

Inch per Foot Taper Series


STANDARD TAPERS Table 7b. American National Standard Plug and Ring Gages for the Self-Holding Taper Series ANSI/ASME B5.10-1994 (R2002)

Length Gage Line to End L

Depth of GagingNotch, Plug Gage L′

0.94 1.19 1.50 2.13 2.56 3.19 4.06 4.50 5.19 7.25 10.00 4.75 5.50 6.25 7.00 7.75 8.50 9.25 10.75 13.75 16.75 19.75

0.048 0.048 0.048 0.040 0.040 0.040 0.038 0.038 0.038 0.038 0.038 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032 0.032

Tolerances for Diameter Ab No. of Taper

Tapera per Foot

Diametera at Gage Line A

Class X Gage

Class Y Gage

Class Z Gage

Diameter at Small End A′

0.239 0.299 0.375 1 2 3 4 41⁄2 5 6 7 200 250 300 350 400 450 500 600 800 1000 1200

0.50200 0.50200 0.50200 0.59858 0.59941 0.60235 0.62326 0.62400 0.63151 0.62565 0.62400 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000 0.75000

0.23922 0.29968 0.37525 0.47500 0.70000 0.93800 1.23100 1.50000 1.74800 2.49400 3.27000 2.00000 2.50000 3.00000 3.50000 4.00000 4.50000 5.00000 6.00000 8.00000 10.00000 12.00000

0.00004 0.00004 0.00004 0.00004 0.00004 0.00006 0.00006 0.00006 0.00008 0.00008 0.00010 0.00008 0.00008 0.00010 0.00010 0.00010 0.00010 0.00013 0.00013 0.00016 0.00020 0.00020

0.00007 0.00007 0.00007 0.00007 0.00007 0.00009 0.00009 0.00009 0.00012 0.00012 0.00015 0.00012 0.00012 0.00015 0.00015 0.00015 0.00015 0.00019 0.00019 0.00024 0.00030 0.00030

0.00010 0.00010 0.00010 0.00010 0.00010 0.00012 0.00012 0.00012 0.00016 0.00016 0.00020 0.00016 0.00016 0.00020 0.00020 0.00020 0.00020 0.00025 0.00025 0.00032 0.00040 0.00040

0.20000 0.25000 0.31250 0.36900 0.57200 0.77800 1.02000 1.26600 1.47500 2.11600 2.75000 1.703 2.156 2.609 3.063 3.516 3.969 4.422 5.328 7.141 8.953 10.766

a The taper per foot and diameter A at gage line are basic dimensions. Dimensions in Column A′ are calculated for reference only. b Tolerances for diameter A are plus for plug gages and minus for ring gages.

All dimensions are in inches. The amount of taper deviation for Class X, Class Y, and Class Z gages are the same, respectively, as the amounts shown for tolerances on diameter A. Taper deviation is the permissible allowance from true taper at any point of diameter in the length of the gage. On taper plug gages, this deviation may be applied only in the direction which decreases the rate of taper. On taper ring gages, this deviation may be applied only in the direction which increases the rate of taper. Tolerances on two-decimal dimensions are ±0.010.

British Standard Tapers.—British Standard 1660: 1972, “Machine Tapers, Reduction Sleeves, and Extension Sockets,” contains dimensions for self-holding and self-releasing tapers, reduction sleeves, extension sockets, and turret sockets for tools having Morse and metric 5 per cent taper shanks. Adapters for use with 7⁄24 tapers and dimensions for spindle noses and tool shanks with self-release tapers and cotter slots are included in this Standard.



935

Table 8. Dimensions of Morse Taper Sleeves

A

B

C

D

H

I

K

L

M

2

1

39⁄16

0.700

5⁄ 8

E

1⁄ 4

F

7⁄ 16

G

23⁄16

0.475

21⁄16

3⁄ 4

0.213

3

1

315⁄16

0.938

1⁄ 4

5⁄ 16

9⁄ 16

23⁄16

0.475

21⁄16

3⁄ 4

0.213

3

2

47⁄16

0.938

3⁄ 4

5⁄ 16

9⁄ 16

25⁄8

0.700

21⁄2

7⁄ 8

0.260

4

1

47⁄8

1.231

1⁄ 4

15⁄ 32

5⁄ 8

23⁄16

0.475

21⁄16

3⁄ 4

0.213

4

2

47⁄8

1.231

1⁄ 4

15⁄ 32

5⁄ 8

25⁄8

0.700

21⁄2

7⁄ 8

0.260

4

3

53⁄8

1.231

3⁄ 4

15⁄ 32

5⁄ 8

31⁄4

0.938

31⁄16

13⁄16

0.322

5

1

61⁄8

1.748

1⁄ 4

5⁄ 8

3⁄ 4

23⁄16

0.475

21⁄16

3⁄ 4

0.213

5

2

61⁄8

1.748

1⁄ 4

5⁄ 8

3⁄ 4

25⁄8

0.700

21⁄2

7⁄ 8

0.260

5

3

61⁄8

1.748

1⁄ 4

5⁄ 8

3⁄ 4

31⁄4

0.938

31⁄16

13⁄16

0.322

5

4

65⁄8

1.748

3⁄ 4

5⁄ 8

3⁄ 4

41⁄8

1.231

37⁄8

11⁄4

0.478

6

1

85⁄8

2.494

3⁄ 8

3⁄ 4

11⁄8

23⁄16

0.475

21⁄16

3⁄ 4

0.213

6

2

85⁄8

2.494

3⁄ 8

3⁄ 4

11⁄8

25⁄8

0.700

21⁄2

7⁄ 8

0.260

6

3

85⁄8

2.494

3⁄ 8

3⁄ 4

11⁄8

31⁄4

0.938

31⁄16

13⁄16

0.322

6

4

85⁄8

2.494

3⁄ 8

3⁄ 4

11⁄8

41⁄8

1.231

37⁄8

11⁄4

0.478

6

5

85⁄8

2.494

3⁄ 8

3⁄ 4

11⁄8

51⁄4

1.748

415⁄16

11⁄2

0.635

7

3

115⁄8

3.270

3⁄ 8

11⁄8

13⁄8

31⁄4

0.938

31⁄16

13⁄16

0.322

7

4

115⁄8

3.270

3⁄ 8

11⁄8

13⁄8

41⁄8

1.231

37⁄8

11⁄4

0.478

7

5

115⁄8

3.270

3⁄ 8

11⁄8

13⁄8

51⁄4

1.748

415⁄16

11⁄2

0.635

7

6

121⁄2

3.270

11⁄4

11⁄8

13⁄8

73⁄8

2.494

7

13⁄4

0.760

Table 9. Morse Taper Sockets — Hole and Shank Sizes

Morse Taper

Morse Taper

Morse Taper

Size

Hole

Shank

Size

Hole

Shank

Size

Hole

Shank

1 by 2

No. 1

No. 2

2 by 5

No. 2

No. 5

4 by 4

No. 4

No. 4

1 by 3

No. 1

No. 3

3 by 2

No. 3

No. 2

4 by 5

No. 4

No. 5

1 by 4

No. 1

No. 4

3 by 3

No. 3

No. 3

4 by 6

No. 4

No. 6

1 by 5

No. 1

No. 5

3 by 4

No. 3

No. 4

5 by 4

No. 5

No. 4

2 by 3

No. 2

No. 3

3 by 5

No. 3

No. 5

5 by 5

No. 5

No. 5

2 by 4

No. 2

No. 4

4 by 3

No. 4

No. 3

5 by 6

No. 5

No. 6



STANDARD TAPERS Table 10. Brown & Sharpe Taper Shanks

Dia. of Plug at Small End

Plug Depth, P

Number of Taper

Taper per Foot (inch)

1c

.50200

.20000

15⁄ 16

2c

.50200

.25000

13⁄16

…

11⁄2

…

…

…

…

3c

4

5

.50200

.50240

.50160

D

.31250

.35000

.45000

Keyway from End of Spindle

Length of Keywaya

Width of Keyway

Length Diame- Thickter of ness of of Arbor Arbor Arbor Tongue Tongue Tongue

Mill. Mach. Standard

Miscell.

K

S

W

T

d

t

…

…

15⁄ 16

13⁄16

3⁄ 8

.135

3⁄ 16

.170

1⁄ 8

…

111⁄64

11⁄2

1⁄ 2

.166

1⁄ 4

.220

5⁄ 32

…

115⁄32

17⁄8

5⁄ 8

.197

5⁄ 16

.282

3⁄ 16

13⁄4

123⁄32

21⁄8

5⁄ 8

.197

5⁄ 16

.282

3⁄ 16

…

2

131⁄32

23⁄8

5⁄ 8

.197

5⁄ 16

.282

3⁄ 16

…

11⁄4

…

113⁄64

121⁄32

11⁄ 16

.228

11⁄ 32

.320

7⁄ 32

111⁄16

…

…

141⁄64

23⁄32

11⁄ 16

.228

11⁄ 32

.320

7⁄ 32

…

13⁄4

…

111⁄16

23⁄16

3⁄ 4

.260

3⁄ 8

.420

1⁄ 4

…

…

2

115⁄16

27⁄16

3⁄ 4

.260

3⁄ 8

.420

1⁄ 4

21⁄8

…

…

21⁄16

29⁄16

3⁄ 4

.260

3⁄ 8

.420

1⁄ 4

…

…

219⁄64

27⁄8

7⁄ 8

.291

7⁄ 16

.460

9⁄ 32

B & Sb Standard

Shank Depth

L

6

.50329

.50000

23⁄8 …

…

21⁄2

213⁄32

31⁄32

15⁄ 16

.322

15⁄ 32

.560

5⁄ 16

7

.50147

.60000

27⁄8

…

…

225⁄32

313⁄32

15⁄ 16

.322

15⁄ 32

.560

5⁄ 16

…

3

…

229⁄32

317⁄32

15⁄ 16

.322

15⁄ 32

.560

5⁄ 16

39⁄16

…

…

329⁄64

41⁄8

1

.353

1⁄ 2

.710

11⁄ 32

…

4

…

37⁄8

45⁄8

11⁄8

.385

9⁄ 16

.860

3⁄ 8

41⁄4

…

…

41⁄8

47⁄8

11⁄8

.385

9⁄ 16

.860

3⁄ 8

5

…

…

427⁄32

523⁄32

15⁄16

.447

21⁄ 32

1.010

7⁄ 16

…

511⁄16

…

517⁄32

613⁄32

15⁄16

.447

21⁄ 32

1.010

7⁄ 16

…

…

67⁄32

61⁄16

615⁄16

15⁄16

.447

21⁄ 32

1.010

7⁄ 16

515⁄16

…

…

525⁄32

621⁄32

15⁄16

.447

21⁄ 32

1.210

7⁄ 16

…

63⁄4

…

619⁄32

715⁄32

15⁄16

.447

21⁄ 32

1.210

7⁄ 16

71⁄8

71⁄8

…

615⁄16

715⁄16

11⁄2

.510

3⁄ 4

1.460

1⁄ 2

…

…

61⁄4

…

…

…

…

…

…

…

8

.50100

.75000

9

.50085

.90010

10

11 12

.51612

.50100 .49973

1.04465

1.24995 1.50010

13

.50020

1.75005

73⁄4

…

…

79⁄16

89⁄16

11⁄2

.510

3⁄ 4

1.710

1⁄ 2

14

.50000

2.00000

81⁄4

81⁄4

…

81⁄32

95⁄32

111⁄16

.572

27⁄ 32

1.960

9⁄ 16

921⁄32

111⁄16

.572

27⁄ 32

2.210

9⁄ 16

17⁄8

.635

15⁄ 16

2.450

5⁄ 8

15

.5000

2.25000

83⁄4

…

…

817⁄32

16

.50000

2.50000

91⁄4

…

…

9

17

.50000

2.75000

93⁄4

…

…

…

…

…

…

…

…

…

.50000

3.00000

101⁄4

…

…

…

…

…

…

…

…

…

18

101⁄4

a Special

lengths of keyway are used instead of standard lengths in some places. Standard lengths need not be used when keyway is for driving only and not for admitting key to force out tool. b “B & S Standard” Plug Depths are not used in all cases. c Adopted by American Standards Association.



937

Table 11. Jarno Taper Shanks

Number of Taper

Length A

Length B

2

11⁄8

1

3

15⁄8

11⁄2

4

23⁄16

2

Diameter C

Diameter D

Taper per foot

0.20

0.250

0.600

0.30

0.375

0.600

0.40

0.500

0.600

5

211⁄16

21⁄2

0.50

0.625

0.600

6

33⁄16

3

0.60

0.750

0.600

7

311⁄16

31⁄2

0.70

0.875

0.600

8

43⁄16

4

0.80

1.000

0.600

9

411⁄16

41⁄2

0.90

1.125

0.600

10

51⁄4

5

1.00

1.250

0.600

11

53⁄4

51⁄2

1.10

1.375

0.600

12

61⁄4

6

1.20

1.500

0.600

13

63⁄4

61⁄2

1.30

1.625

0.600

14

71⁄4

7

1.40

1.750

0.600

15

73⁄4

71⁄2

1.50

1.875

0.600

16

85⁄16

8

1.60

2.000

0.600

17

813⁄16

81⁄2

1.70

2.125

0.600

18

95⁄16

9

1.80

2.250

0.600

91⁄2

1.90

2.375

0.600

2.00

2.500

0.600

19 20

913⁄16 105⁄16

10

Tapers for Machine Tool Spindles.—Most lathe spindles have Morse tapers, most milling machine spindles have American Standard tapers, almost all smaller milling machine spindles have R8 tapers, and large vertical milling machine spindles have American Standard tapers. The spindles of drilling machines and the taper shanks of twist drills are made to fit the Morse taper. For lathes, the Morse taper is generally used, but lathes may have the Jarno, Brown & Sharpe, or a special taper. Of 33 lathe manufacturers, 20 use the Morse taper; 5, the Jarno; 3 use special tapers of their own; 2 use modified Morse (longer than the standard but the same taper); 2 use Reed (which is a short Jarno); 1 uses the Brown & Sharpe standard. For grinding machine centers, Jarno, Morse, and Brown & Sharpe tapers are used. Of ten grinding machine manufacturers, 3 use Brown & Sharpe; 3 use Morse; and 4 use Jarno. The Brown & Sharpe taper is used extensively for milling machine and dividing head spindles. The standard milling machine spindle adopted in 1927 by the milling machine manufacturers of the National Machine Tool Builders' Association (now The Association for Manufacturing Technology [AMT]), has a taper of 31⁄2 inches per foot. This comparatively steep taper was adopted to ensure easy release of arbors.



STANDARD TAPERS

Table 12. American National Standard Plug and Ring Gages for Steep Machine Tapers ANSI/ASME B5.10-1994 (R2002)

Class Z Gage

Diameter at Small Enda A′

Length Gage Line to Small End L

Tolerances for Diameter Ab No. of Taper

Taper per Foota (Basic)

Diameter at Gage Linea A

Class X Gage

Class Y Gage

Overall Length Dia. of Gage of Body Opening B C

5

3.500

0.500

0.00004

0.00007

0.00010

0.2995

0.6875

0.81

0.30

10

3.500

0.625

0.00004

0.00007

0.00010

0.3698

0.8750

1.00

0.36

15

3.500

0.750

0.00004

0.00007

0.00010

0.4401

1.0625

1.25

0.44

20

3.500

0.875

0.00006

0.00009

0.00012

0.4922

1.3125

1.50

0.48

25

3.500

1.000

0.00006

0.00009

0.00012

0.5443

1.5625

1.75

0.53

30

3.500

1.250

0.00006

0.00009

0.00012

0.7031

1.8750

2.06

0.70

35

3.500

1.500

0.00006

0.00009

0.00012

0.8438

2.2500

2.44

0.84

40

3.500

1.750

0.00008

0.00012

0.00016

1.0026

2.5625

2.75

1.00

45

3.500

2.250

0.00008

0.00012

0.00016

1.2839

3.3125

3.50

1.00

50

3.500

2.750

0.00010

0.00015

0.00020

1.5833

4.0000

4.25

1.00

55

3.500

3.500

0.00010

0.00015

0.00020

1.9870

5.1875

5.50

1.00

60

3.500

4.250

0.00010

0.00015

0.00020

2.3906

6.3750

6.75

2.00

a The taper per foot and diameter A at gage line are basic dimensions. Dimensions in Column A′ are

calculated for reference only. b Tolerances for diameter A are plus for plug gages and minus for ring gages. All dimensions are in inches. The amounts of taper deviation for Class X, Class Y, and Class Z gages are the same, respectively, as the amounts shown for tolerances on diameter A. Taper deviation is the permissible allowance from true taper at any point of diameter in the length of the gage. On taper plug gages, this deviation may be applied only in the direction which decreases the rate of taper. On taper ring gages, this deviation may be applied only in the direction which increases the rate of taper. Tolerances on two-decimal dimensions are ±0.010.



939

Table 13. Jacobs Tapers and Threads for Drill Chucks and Spindles

Taper Series No. 0 No. 1 No. 2 No. 2a No. 3

A 0.2500 0.3840 0.5590 0.5488 0.8110

B 0.22844 0.33341 0.48764 0.48764 0.74610

C 0.43750 0.65625 0.87500 0.75000 1.21875

Taper per Ft. 0.59145 0.92508 0.97861 0.97861 0.63898

Taper Series No. 4 No. 5 No. 6 No. 33 …

A 1.1240 1.4130 0.6760 0.6240 …

B 1.0372 1.3161 0.6241 0.5605 …

Taper per Ft. 0.62886 0.62010 0.62292 0.76194 …

C 1.6563 1.8750 1.0000 1.0000 …

a These dimensions are for the No. 2 “short” taper.

Thread Size 5⁄ –24 16 5⁄ –24 16 3⁄ –24 8 1⁄ –20 2 5⁄ –11 8 5⁄ –16 8 45⁄ –16 64 3⁄ –16 4

1–8 1–10 11⁄2 –8 Threada Size 5⁄ –24 16 3⁄ –24 8 1⁄ –20 2 5⁄ –11 8 5⁄ –16 8 45⁄ –16 64 3⁄ –16 4

1–8 1–10 11⁄2 –8

Diameter D

Diameter E

Dimension F

Max.

Min.

Max.

Min.

Max.

Min.

0.531 0.633 0.633 0.860 1.125 1.125 1.250 1.250 1.437 1.437 1.871

0.516 0.618 0.618 0.845 1.110 1.110 1.235 1.235 1.422 1.422 1.851

0.3245 0.3245 0.385 0.510 0.635 0.635 0.713 0.760 1.036 1.036 1.536

0.3195 0.3195 0.380 0.505 0.630 0.630 0.708 0.755 1.026 1.026 1.526

0.135 0.135 0.135 0.135 0.166 0.166 0.166 0.166 0.281 0.281 0.343

0.115 0.115 0.115 0.115 0.146 0.146 0.146 0.146 0.250 0.250 0.312

G Max

Min

Hb

0.3114 0.3739 0.4987 0.6234 0.6236 0.7016 0.7485 1.000 1.000 1.500

0.3042 0.3667 0.4906 0.6113 0.6142 0.6922 0.7391 0.9848 0.9872 1.4848

0.437c 0.562d 0.562 0.687 0.687 0.687 0.687 1.000 1.000 1.000

Plug Gage Pitch Dia. Go Not Go 0.2854 0.3479 0.4675 0.5660 0.5844 0.6625 0.7094 0.9188 0.9350 1.4188

0.2902 0.3528 0.4731 0.5732 0.5906 0.6687 0.7159 0.9242 0.9395 1.4242

Ring Gage Pitch Dia. Go Not Go 0.2843 0.3468 0.4662 0.5644 0.5830 0.6610 0.7079 0.9188 0.9350 1.4188

0.2806 0.3430 0.4619 0.5589 0.5782 0.6561 0.7029 0.9134 0.9305 1.4134

a Except for 1–8, 1–10, 11⁄ –8 all threads are now manufactured to the American National Standard 2 Unified Screw Thread System, Internal Class 2B, External Class 2A. Effective date 1976. b Tolerances for dimension H are as follows: 0.030 inch for thread sizes 5⁄ –24 to 3⁄ –16, inclusive 16 4 and 0.125 inch for thread sizes 1–8 to 11⁄2 –8, inclusive. c Length for Jacobs 0B5⁄16 chuck is 0.375 inch, length for 1B5⁄16 chuck is 0.437 inch. d Length for Jacobs No. 1BS chuck is 0.437 inch.

Usual Chuck Capacities for Different Taper Series Numbers: No. 0 taper, drill diameters, 0–5⁄32 inch; No. 1, 0–1⁄4 inch; No. 2, 0–1⁄2 inch; No. 2 “Short,” 0–5⁄16 inch; No. 3, 0–1⁄2 , 1⁄8 –5⁄8 , 3⁄16 –3⁄4 , or 1⁄4 – 13⁄ inch; No. 4, 1⁄ –3⁄ inch; No. 5, 3⁄ –1; No. 6, 0–1⁄ inch; No. 33, 0–1⁄ inch. 16 8 4 8 2 2 Usual Chuck Capacities for Different Thread Sizes: Size 5⁄16 –24, drill diameters 0–1⁄4 inch; size 3⁄8 – 3 1 3 5 1 1 24, drill diameters 0– ⁄8 , ⁄16 – ⁄8 , or ⁄64 – ⁄2 inch; size ⁄2 –20, drill diameters 0–1⁄2 , 1⁄16 –3⁄8 , or 5⁄64 –1⁄2 inch; size 5⁄8 –11, drill diameters 0–1⁄2 inch; size 5⁄8 –16, drill diameters 0–1⁄2 , 1⁄8– –5⁄8 , or 3⁄16 –3⁄4 inch; size 45⁄64 –16, drill diameters 0–1⁄2 inch; size 3⁄4 –16, drill diameters 0–1⁄2 or 3⁄16 –3⁄4 .



;; ;;

Face of column

E min M

Standard steep machine taper 3.500 inch per ft

X See Note 3

C

;;

D min

Slot and key location X .002 total M

Usable threads

45°

G

Optional Key Construction

Z

K

.015

H

J

.015

B

A gage

H

–X–

X .0004 See note 4

;;; ;;; ;;; Z

L min section Z-Z

F

45°

F′ F

G

Keyseat Key tight fit in slot when insert key is used

Preferred Key Construction


G′

STANDARD TAPERS

Max variation from gage line

940

;;;;;;;;; ;;;;;;;;; ;;;;;;;;; ;;;;;;;; ;;;;;;;; ;;;;;;;; ;;;;;;;; ;;;; ;;;; ;;;;

Table 1. Essential Dimensions of American National Standard Spindle Noses for Milling Machines ANSI B5.18-1972 (R1998)


Table 1. (Continued) Essential Dimensions of American National Standard Spindle Noses for Milling Machines ANSI B5.18-1972 (R1998)

Size No.

Gage Dia.of Taper A

30

Clearance Hole for Draw-in Bolt Min. D

Minimum Dimension Spindle End to Column E

Width of Driving Key F

Width of Keyseat F′

Maximum Height of Driving Key G

Minimum Depth of Keyseat G′

Distance fromCenter to Driving Keys H

Radius of Bolt Hole Circle J

Size of Threads for Bolt Holes UNC-2B K

Full Depth of Arbor Hole in Spindle Min. L

Depth of Usable Thread for Bolt Hole M

Pilot Dia. C

1.250

2.7493 2.7488

0.692 0.685

0.66

0.50

0.6255 0.6252

0.624 0.625

0.31

0.31

0.660 0.654

1.0625 (Note 1)

0.375–16

2.88

0.62

40

1.750

3.4993 3.4988

1.005 0.997

0.66

0.62

0.6255 0.6252

0.624 0.625

0.31

0.31

0.910 0.904

1.3125 (Note 1)

0.500–13

3.88

0.81

45

2.250

3.9993 3.9988

1.286 1.278

0.78

0.62

0.7505 0.7502

0.749 0.750

0.38

0.38

1.160 1.154

1.500 (Note 1)

0.500–13

4.75

0.81

50

2.750

5.0618 5.0613

1.568 1.559

1.06

0.75

1.0006 1.0002

0.999 1.000

0.50

0.50

1.410 1.404

2.000(Note 2)

0.625–11

5.50

1.00

60

4.250

8.7180 8.7175

2.381 2.371

1.38

1.50

1.0006 1.0002

0.999 1.000

0.50

0.50

2.420 2.414

3.500 (Note 2)

0.750–10

8.62

1.25


941

All dimensions are given in inches. Tolerances: Two-digit decimal dimensions ± 0.010 unless otherwise specified. A—Taper: Tolerance on rate of taper to be 0.001 inch per foot applied only in direction which decreases rate of taper. F′—Centrality of keyway with axis of taper 0.002 total at maximum material condition. (0.002 Total indicator variation) F—Centrality of solid key with axis of taper 0.002 total at maximum material condition. (0.002 Total indicator variation) Note 1: Holes spaced as shown and located within 0.006 inch diameter of true position. Note 2: Holes spaced as shown and located within 0.010 inch diameter of true position. Note 3: Maximum turnout on test plug: 0.0004 at 1 inch projection from gage line. 0.0010 at 12 inch projection from gage line. Note 4: Squareness of mounting face measured near mounting bolt hole circle.

STANDARD TAPERS

Dia.of Spindle B


STANDARD TAPERS

Table 2. Essential Dimensions of American National Standard Tool Shanks for Milling Machines ANSI B5.18-1972 (R1998)

Size of Thread for Draw-in Bolt UNC-2B M

Pilot Dia. R

Length of Pilot S

Minimum Length of Usable Thread T

Minimum Depth of Clearance Hole U

0.500–13

0.675 0.670

0.81

1.00

2.00

0.94 0.93

0.625–11

0.987 0.980

1.00

1.12

2.25

0.656 0.666

1.19 1.18

0.750–10

1.268 1.260

1.00

1.50

2.75

2.750

0.875 0.885

1.50 1.49

1.000–8

1.550 1.540

1.00

1.75

3.50

60

4.250

1.109 1.119

2.28 2.27

1.250–7

2.360 2.350

1.75

2.25

4.25

Size. No.

Distance from Rear of Flange to End of Arbor V

30

2.75

0.045 0.075

0.640 0.625

0.635 0.645

2.50

0.05 0.07

0.525 0.530

40

3.75

0.045 0.075

0.890 0.875

0.635 0.645

3.50

0.05 0.07

0.650 0.655

45

4.38

0.105 0.135

1.140 1.125

0.760 0.770

4.06

0.05 0.07

0.775 0.780

5.12

0.105 0.135

1.390 1.375

1.010 1.020

4.75

0.05 0.12

1.025 1.030

8.25

0.105 0.135

2.400 2.385

1.010 1.020

7.81

0.05 0.12

1.307 1.312

Tap Drill Size for Draw-in Thread O

Dia.of Neck P

1.250

0.422 0.432

0.66 0.65

40

1.750

0.531 0.541

45

2.250

Size No.

Gage Dia.of Taper N

30

50

50 60

Clearance of Flange from Gage Diameter W

Tool Shank Centerline to Driving Slot X

Width of Driving Slot Y

Distance from Gage Line to Bottom of C'bore Z

Depth of 60° Center K

Diameter of C'bore L

All dimensions are given in inches. Tolerances: Two digit decimal dimensions ± 0.010 inch unless otherwise specified. M—Permissible for Class 2B “NoGo” gage to enter five threads before interference. N—Taper tolerance on rate of taper to be 0.001 inch per foot applied only in direction which increases rate of taper. Y—Centrality of drive slot with axis of taper shank 0.004 inch at maximum material condition. (0.004 inch total indicator variation)



943

Table 3. American National Standard Draw-in Bolt Ends ANSI B5.18-1972 (R1998)

Length of Usable Thread Size of Thread on Large Diam- for Large End eter UNC-2A C M

Length of Small End A

Length of Usable Thread at Small End B

30

1.06

0.75

0.75

0.500–13

0.375–16

40

1.25

1.00

1.12

0.625–11

0.500–13

45

1.50

1.12

1.25

0.750–10

0.625–11

50

1.50

1.25

1.38

1.000–8

0.625–11

60

1.75

1.37

2.00

1.250–7

1.000–8

Size No.

Size of Thread for Small End UNC-2A D

All dimensions are given in inches.

Table 4. American National Standard Pilot Lead on Centering Plugs for Flatback Milling Cutters ANSI B5.18-1972 (R1998)



STANDARD TAPERS

Table 5. Essential Dimensions for American National Standard Spindle Nose with Large Flange ANSI B5.18-1972 (R1998)

;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;; ;; ;; ;; M2

American Standard Taper 3.500 Inch Per Ft X See Note 1 D min

Usable threads

;; E min

H2

.015 .015

F1 F

Dia. of Spindle Flange B

Pilot Dia. C

50A

2.750

8.7180 8.7175

1.568 1.559

Size No.

Distance from Center to Driving Keys Second Position

H1

H2

1st Position

Z

B

Keyseat Key tight fit in slot G′

Drive Key

Clearance Hole for Draw-in Bolt Min. D

Min. Dim. Spindle End to Column E

1.06

0.75

Radius of Bolt Hole Circles (See Note 3)

Width of Driving Key F 1.0006 1.0002

H2

J1

J2

K1

K2

Full Depth of Arbor Hole in Spindle Min. L

2.420 2.410

2.000

3.500

0.625–11

0.750–10

5.50

Inner

H1

J

J1

X .0004 See note 2 Face of Column

G1

50A

2nd Position

K

L min section Z-Z

Gage Diam. of Taper A

45° Z

A gage

Max variation from Gage Line

Size No.

X .002 Total M

45°

K Usable threads

M1

C

Slot and key location

-X-

Size of Threads for Bolt Holes UNC-2B

Outer

Height of Driving Key Max. G

Depth of Keyseat Min. G1

0.50

0.50 Depth of Usable Thread for Bolt Holes

M1

M2

1.00

1.25

Distance from Center to Driving Keys First Position H1 1.410 1.404

Width of Keyseat F1 0.999 1.000

All dimensions are given in inches. Tolerances: Two-digit decimal dimensions ± 0.010 unless otherwise specified. A—Tolerance on rate of taper to be 0.001 inch per foot applied only in direction which decreases rate of taper. F—Centrality of solid key with axis of taper 0.002 inch total at maximum material condition. (0.002 inch Total indicator variation) F1—Centrality of keyseat with axis of taper 0.002 inch total at maximum material condition. (0.002 inch Total indicator variation) Note 1: Maximum runout on test plug: 0.0004 at 1 inch projection from gage line. 0.0010 at 12 inch projection from gage line. Note 2: Squareness of mounting face measured near mounting bolt hole circle. Note 3: Holes located as shown and within 0.010 inch diameter of true position.


Machinery's Handbook 27th Edition COLLETS

945

Collets Collets for Lathes, Mills, Grinders, and Fixtures AC

A C

A C B

1

B

2

B

3

A C

A

AC B

B

4

5 6

A D

C

A D

A C

B

7

B

8

A

B

C B

9

A C

A C B

B

B

11

10

12

Collet Styles

Collets for Lathes, Mills, Grinders, and Fixtures Dimensions Collet

Max. Capacity (inches)

Style

Bearing Diam., A

Length, B

Thread, C

Round

Hex

Square

1A

1

0.650

2.563

0.640 × 26 RH

0.500

0.438

0.344

1AM

1

1.125

3.906

1.118 × 24 RH

1.000

0.875

0.719

1B

2

0.437

1.750

0.312 × 30 RH

0.313

0.219

0.188

1C

1

0.335

1.438

0.322 × 40 RH

0.250

0.219

0.172

1J

1

1.250

3.000

1.238 × 20 RH

1.063

0.875

0.750

1K

3

1.250

2.813

None

1.000

0.875

0.719

2A

1

0.860

3.313

0.850 × 20 RH

0.688

0.594

0.469

2AB

2

0.750

2.563

0.500 × 20 RH

0.625

0.484

0.391

2AM

1

0.629

3.188

0.622 × 24 RH

0.500

0.438

0.344

2B

2

0.590

2.031

0.437 × 26 RH

0.500

0.438

0.344

2C

1

0.450

1.812

0.442 × 30 RH

0.344

0.594

0.234

2H

1

0.826

4.250

0.799 × 20 RH

0.625

0.531

1.000

2J

1

1.625

3.250

1.611 × 18 RH

1.375

1.188

0.438

2L

1

0.950

3.000

0.938 × 20 RH

0.750

0.656

1.000

2M

4

2 Morse

2.875

0.375 × 16 RH

0.500

0.438

0.344

2NS

1

0.324

1.562

0.318 × 40 RH

0.250

0.203

0.172

2OS

1

0.299

1.250

0.263 × 40 RH

0.188

0.156

0.125

2S

1

0.750

3.234

0.745 × 18 RH

0.563

0.484

0.391

2VB

2

0.595

2.438

0.437 × 26 RH

0.500

0.438

0.344

3AM

1

0.750

3.188

0.742 × 24 RH

0.625

0.531

0.438

3AT

1

0.687

2.313

0.637 × 26 RH

0.500

0.438

0.344



COLLETS Collets for Lathes, Mills, Grinders, and Fixtures (Continued) Dimensions

Collet


Style

Bearing Diam., A

Length, B

Thread, C

Round

Hex

Square

3B

2

0.875

3.438

0.625 × 16 RH

0.750

0.641

0.531

3C

1

0.650

2.688

0.640 × 26 RH

0.500

0.438

0.344

3H

1

1.125

4.438

1.050 × 20 RH

0.875

0.750

0.625

3J

1

2.000

3.750

1.988 × 20 RH

1.750

1.500

1.250

3NS

1

0.687

2.875

0.647 × 20 RH

0.500

0.438

0.344

3OS

1

0.589

2.094

0.518 × 26 RH

0.375

0.313

0.266

3PN

1

0.650

2.063

0.645 × 24 RH

0.500

0.438

0.344

3PO

1

0.599

2.063

0.500 × 24 RH

0.375

0.313

0.266

3S

1

1.000

4.594

0.995 × 20 RH

0.750

0.656

0.531

3SC

1

0.350

1.578

0.293 × 36 RH

0.188

0.156

0.125

3SS

1

0.589

2.125

0.515 × 26 RH

0.375

0.313

0.266

4C

1

0.950

3.000

0.938 × 20 RH

0.750

0.656

0.531

4NS

1

0.826

3.500

0.800 × 20 RH

0.625

0.531

0.438

4OS

1

0.750

2.781

0.660 × 20 RH

0.500

0.438

0.344

4PN

1

1.000

2.906

0.995 × 16 RH

0.750

0.656

0.531

4S

1

0.998

3.250

0.982 × 20 RH

0.750

0.656

0.531

5C

1

1.250

3.281

1.238 × 20 RHa

1.063

0.906

0.750

5M

5

1.438

3.438

1.238 × 20 RH

0.875

0.750

0.625

5NS

1

1.062

4.219

1.050 × 20 RH

0.875

0.750

0.625

5OS

1

3.500

3.406

0.937 × 18 RH

0.750

0.641

0.516

5P

1

0.812

3.687

0.807 × 24 RH

0.625

0.531

0.438

5PN

1

1.312

3.406

1.307 × 16 RH

1.000

0.875

0.719

5SC

1

0.600

2.438

0.500 × 26 RH

0.375

0.328

0.266

5ST

1

1.250

3.281

1.238 × 20 RH

1.063

0.906

0.750

5V

1

0.850

3.875

0.775 × 18 RH

0.563

0.484

0.391

6H

1

1.375

4.750

1.300 × 10 RH

1.125

0.969

0.797

6K

1

0.842

3.000

0.762 × 26 RH

0.625

0.531

0.438 0.719

6L

1

1.250

4.438

1.178 × 20 RH

1.000

0.875

6NS

1

1.312

5.906

1.234 × 14 RH

1.000

0.859

0.703

6R

1

1.375

4.938

1.300 × 20 RH

1.125

0.969

0.781 0.344

7B

4

7 B&S

3.125

0.375 × 16 RH

0.500

0.406

7 B&S

4

7 B&S

2.875

0.375 × 16 RH

0.500

0.406

0.344

7P

1

1.125

4.750

1.120 × 20 RH

0.875

0.750

0.625

7R

6

1.062

3.500

None

0.875

0.750

0.625

8H

1

1.500

4.750

1.425 × 20 RH

1.250

1.063

0.875

8ST

1

2.375

5.906

2.354 × 12 RH

2.125

1.844

1.500

8WN

1

1.250

3.875

1.245 × 16 RH

1.000

0.875

0.719

9B

4

9 B&S

4.125

0.500 × 13 RH

0.750

0.641

0.531

10L

1

1.562

5.500

1.490 × 18 RH

1.250

1.063

0.875

10P

1

1.500

4.750

1.495 × 20 RH

1.250

1.063

0.875

16C

1

1.889

4.516

1.875 × 1.75 mm RHb

1.625

1.406

1.141

20W

1

0.787

2.719

0.775 × 6–1 cm

0.563

0.484

0.391

22J

1

2.562

4.000

2.550 × 18 RH

2.250

1.938

1.563

32S

1

0.703

2.563

0.690 × 24 RH

0.500

0.438

0.344

35J

1

3.875

5.000

3.861 × 18 RH

3.500

3.000

2.438

42S

1

1.250

3.688

1.236 × 20 RH

1.000

0.875

0.719

50V

8

1.250

4.000

1.125 × 24 RH

0.938

0.813

0.656

52SC

1

0.800

3.688

0.795 × 20 RH

0.625

0.531

0.438

115

1

1.344

3.500

1.307 × 20 LH

1.125

0.969

0.797


Machinery's Handbook 27th Edition COLLETS

947

Collets for Lathes, Mills, Grinders, and Fixtures (Continued) Dimensions Collet


Style

Bearing Diam., A

Length, B

Thread, C

Round

Hex

215

1

2.030

4.750

1.990 × 18 LH

1.750

1.500

Square 1.219

315

1

3.687

5.500

3.622 × 16 LH

3.250

2.813

2.250

B3

7

0.650

3.031

0.437 × 20 RH

0.500

0.438

0.344

D5

7

0.780

3.031

0.500 × 20 RH

0.625

0.531

0.438

GTM

7

0.625

2.437

0.437 × 20 RH

0.500

0.438

0.344

J&L

9

0.999

4.375

None

0.750

0.641

0.516

JC

8

1.360

4.000

None

1.188

1.000

0.813

LB

10

0.687

2.000

None

0.500

0.438

0.344

RO

11

1.250

2.938

0.875 × 16 RH

1.125

0.969

0.781

RO

12

1.250

4.437

0.875 × 16 RH

0.800

0.688

0.563

RO

12

1.250

4.437

0.875 × 16 RH

1.125

0.969

0.781

RO

11

1.250

2.938

0.875 × 16 RH

0.800

0.688

0.563

R8

7

0.950

4.000

0.437 × 20 RH

0.750

0.641

0.531

a Internal stop thread is 1.041 × 24 RH.

b Internal stop thread is 1.687 × 20 RH.

Dimensions in inches unless otherwise noted. Courtesy of Hardinge Brothers, Inc.

DIN 6388, Type B, and DIN 6499, ER Type Collets 30 C A B

Collet Standard Type B, DIN 6388

ER Type, DIN 6499

A B

L

L

ER Type

Type B Dimensions

Type

B (mm)

16

25.50

L (mm) 40

A (mm)

C

4.5–16

…

20

29.80

45

5.5–20

…

25

35.05

52

5.5–25

…

32

43.70

60

9.5–32

…

13.5

0.5–5

8°

ERA8

8.50

ERA11

11.50

18

0.5–7

8°

ERA16

17

27

0.5–10

8°

ERA20

21

31

0.5–13

8°

ERA25

26

35

0.5–16

8°

ERA32

33

40

2–20

8°

41

46

3–26

8°

41

39

26–30

8°

52

60

5–34

8°

ERA40 ERA50



PORTABLE GRINDING TOOLS

ARBORS, CHUCKS, AND SPINDLES Portable Tool Spindles Circular Saw Arbors.—ANSI Standard B107.4-1982 “Driving and Spindle Ends for Portable Hand, Air, and Air Electric Tools” calls for a round arbor of 5⁄8-inch diameter for nominal saw blade diameters of 6 to 8.5 inches, inclusive, and a 3⁄4-inch diameter round arbor for saw blade diameters of 9 to 12 inches, inclusive. Spindles for Geared Chucks.—Recommended threaded and tapered spindles for portable tool geared chucks of various sizes are as given in the following table: Recommended Spindle Sizes Recommended Spindles

Chuck Sizes, Inch 3⁄ and 1⁄ Light 16 4 1⁄ and 5⁄ Medium 4 16 3⁄ Light 8 3⁄ Medium 8 1⁄ Light 2 1⁄ Medium 2 5⁄ and 3⁄ Medium 8 4

3⁄ –24 8 3⁄ –24 8 3⁄ –24 8 1⁄ –20 2 1⁄ –20 2 5⁄ –16 8 5⁄ –16 8

Threaded

Tapera

or 1⁄2–20

2 Short

or 1⁄2 –20

2

1

or 5⁄8 –16

2

or 5⁄8 –16

33

or 3⁄4 –16

6

or 3⁄4 –16

3

a Jacobs number.

Vertical and Angle Portable Tool Grinder Spindles.—The 5⁄8–11 spindle with a length of 11⁄8 inches shown on page 950 is designed to permit the use of a jam nut with threaded cup wheels. When a revolving guard is used, the length of the spindle is measured from the wheel bearing surface of the guard. For unthreaded wheels with a 7⁄8-inch hole, a safety sleeve nut is recommended. The unthreaded wheel with 5⁄8-inch hole is not recommended because a jam nut alone may not resist the inertia effect when motor power is cut off. Straight Grinding Wheel Spindles for Portable Tools.—Portable grinders with pneumatic or induction electric motors should be designed for the use of organic bond wheels rated 9500 feet per minute. Light-duty electric grinders may be designed for vitrified wheels rated 6500 feet per minute. Recommended maximum sizes of wheels of both types are as given in the following table: Recommended Maximum Grinding Wheel Sizes for Portable Tools Maximum Wheel Dimensions 9500 fpm 6500 fpm Diameter Thickness Diameter Thickness D T D T

Spindle Size 3⁄ -24 × 11⁄ 8 8 1⁄ –13 × 13⁄ 2 4 5⁄ –11 × 21⁄ 8 8 5⁄ –11 × 31⁄ 8 8 5⁄ –11 × 31⁄ 8 8 3⁄ –10 × 31⁄ 4 4

21⁄2 4

1⁄ 2 3⁄ 4

8

1

8

1

6

2

…

…

8

11⁄2

…

…

8

2

…

…

4 5

1⁄ 2 3⁄ 4

Minimum T with the first three spindles is about 1⁄8 inch to accommodate cutting off wheels. Flanges are assumed to be according to ANSI B7.1 and threads to ANSI B1.1.


Machinery's Handbook 27th Edition PORTABLE TOOL SPINDLES

949

American Standard Square Drives for Portable Air and Electric Tools ASA B5.38-1958

DESIGN A

DESIGN B Male End

AM

DM

CM

Drive Size

Desig n.

Max.

Min.

BM Max.

Max.

Min.

Max.

Min.

EM Min.

FM Max.

RM Max.

1⁄ 4

A

0.252

0.247

0.330

0.312

0.265

0.165

0.153

…

0.078

0.015

3⁄ 8

A

0.377

0.372

0.500

0.438

0.406

0.227

0.215

…

0.156

0.031

1⁄ 2

A

0.502

0.497

0.665

0.625

0.531

0.321

0.309

…

0.187

0.031

5⁄ 8

A

0.627

0.622

0.834

0.656

0.594

0.321

0.309

…

0.187

0.047

3⁄ 4

B B B

0.752 1.002 1.503

0.747 0.997 1.498

1.000 1.340 1.968

0.938 1.125 1.625

0.750 1.000 1.562

0.415 0.602 0.653

0.403 0.590 0.641

0.216 0.234 0.310

… … …

0.047 0.063 0.094

1 11⁄2

DESIGN A

DESIGN B Female End

Drive Size 1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄2

AF

DF

Design

Max.

Min.

BF Min.

Max.

Min.

EF Min.

RF Max.

A

0.258

0.253

0.335

0.159

0.147

0.090

…

A

0.383

0.378

0.505

0.221

0.209

0.170

…

A

0.508

0.503

0.670

0.315

0.303

0.201

…

A

0.633

0.628

0.839

0.315

0.303

0.201

…

B B B

0.758 1.009 1.510

0.753 1.004 1.505

1.005 1.350 1.983

0.409 0.596 0.647

0.397 0.584 0.635

0.216 0.234 0.310

0.047 0.062 0.125

All dimensions in inches. Incorporating fillet radius (RM) at shoulder of male tang precludes use of minimum diameter crosshole in socket (EF), unless female drive end is chamfered (shown as optional). If female drive end is not chamfered, socket cross-hole diameter (EF) is increased to compensate for fillet radius RM, max. Minimum clearance across flats male to female is 0.001 inch through 3⁄4-inch size; 0.002 inch in 1and 11⁄2-inch sizes. For impact wrenches AM should be held as close to maximum as practical. CF, min. for both designs A and B should be equal to CM, max.



PORTABLE TOOL SPINDLES American Standard Threaded and Tapered Spindles for Portable Air and Electric Tools ASA B5.38-1958

Taper Spindle (Jacobs)

Threaded Spindle Nom. Dia. and Thd.

Max.

Min.

R

L

3⁄ –24 8

0.3479

0.3455

1⁄ 16

9⁄ c 16 9⁄ 16

1⁄ –20 2

0.4675

0.4649

1⁄ 16

5⁄ –16 8

0.5844

0.5812

3⁄ 32

11⁄ 16

0.7062

3⁄ 32

11⁄ 16

3⁄ –16 4

Master Plug Gage

Pitch Dia.

0.7094

EG

DG

DM

LM

1

0.335-0.333

0.656

0.38400 0.33341 0.65625

0.92508

2Sd 2 33 6 3

0.490-0.488 0.490-0.488 0.563-0.561 0.626-0.624 0.748-0.746

0.750 0.875 1.000 1.000 1.219

0.54880 0.55900 0.62401 0.67600 0.81100

0.97861 0.97861 0.76194 0.62292 0.63898

0.48764 0.48764 0.56051 0.62409 0.74610

LG

Taper per Footb

No.a

0.7500 0.87500 1.000 1.000 1.21875

a Jacobs taper number. b Calculated from E , D , L for the master plug gage. G G G c Also 7⁄ inch. 16 d 2S stands for 2 Short.

All dimensions in inches. Threads are per inch and right-hand. Tolerances: On R, plus or minus 1⁄64 inch; on L, plus 0.000, minus 0.030 inch.

American Standard Abrasion Tool Spindles for Portable Air and Electric Tools ASA B5.38-1958 Sanders and Polishers

Vertical and Angle Grinders

With Revolving Cup Guard

Stationary Guard


Machinery's Handbook 27th Edition PORTABLE TOOL SPINDLES

951

American Standard Abrasion Tool Spindles for Portable Air and Electric Tools ASA B5.38-1958 (Continued) Straight Wheel Grinders

Cone Wheel Grinders

H

R

3⁄ –24 UNF-2A 8 1⁄ –13 UNC-2A 2 5⁄ –11 UNC-2A 8 5⁄ –11 UNC-2A 8 3⁄ –10 UNC-2A 4

1⁄ 4 3⁄ 8 1⁄ 2

L 11⁄8 13⁄4 21⁄8

1

31⁄8

1

31⁄4

D

L

3⁄ –24 UNF-2A 8 1⁄ –13 UNC-2A 2 5⁄ –11 UNC-2A 8

9⁄ 16 11⁄ 16 15⁄ 16

All dimensions in inches. Threads are right-hand.

American Standard Hexagonal Chucks and Shanks for Portable Air and Electric Tools ASA B5.38-1958

H

H

Nominal Hexagon

Min.

Max.

B

L Max.

Nominal Hexagon

Min.

Max.

B

L Max.

1⁄ 4

0.253

0.255

3⁄ 8

15⁄ 16

5⁄ 8

0.630

0.632

11⁄ 32

15⁄8

5⁄ 16

0.314

0.316

13⁄ 64

1

3⁄ 4

0.755

0.758

11⁄ 32

17⁄8

7⁄ 16

0.442

0.444

17⁄ 64

11⁄8

…

…

…

…

…

Shanks

All dimensions in inches. Tolerances on B is plus or minus 0.005 inch.



MOUNTED WHEELS AND POINTS Mounted Wheels and Mounted Points

These wheels and points are used in hard-to-get-at places and are available with a vitrified bond. The wheels are available with aluminum oxide or silicon carbide abrasive grains. The aluminum oxide wheels are used to grind tough and tempered die steels and the silicon carbide wheels, cast iron, chilled iron, bronze, and other non-ferrous metals. The illustrations on pages 952 and 953 give the standard shapes of mounted wheels and points as published by the Grinding Wheel Institute. A note about the maximum operating speed for these wheels is given at the bottom of the first page of illustrations. Metric sizes are given on page 954.

5′′ 8

1′′ 4

1′′ 2

B 41 1′′ 8

B 43

B 44

B 71

B 81

B 52 1′′ 4

B 91

11′′ 16

B 53

5′′ 16

3′′ 4

B 97 3′′ 8

1′′ 2

5′′ 8 11′′ 16

1′′ 8

B 96 1′′ 2

B 61

3′′ 8

1′′ 4

1′′ 8

B 92 3′′ 8

5′′ 16

B 101 1′′ 8

3′′ 16

3′′ 8

3′′ 16

B 103

B 104 3′′ 8

B 111

B 112

1′′ 4

3′′ 8

B 121 B 122 B 123 B 124 D

D

1′′ 2

1′′ 2

B 132

3′′ 8

B 133

T

1′′ 2

B 135

D

D T

B 131

5′′ 8

5′′ 16

1′′ 2 1′′ 4

7′′ 16

1′′ 2

B 51

5′′ 8 3′′ 16

5′′ 8

3′′ 8

3′′ 4

5′′ 8

3′′ 4

7′′ 32

1′′ 2

B 62

3′′ 4

7′′ 16

B 42 3′′ 8

3′′ 8

5′′ 16

3′′ 4

5′′ 8

T T

Group W

Fig. 1a. Standard Shapes and Sizes of Mounted Wheels and Points ANSI B74.2-1982 See Table 1 for inch sizes of Group W shapes, and for metric sizes for all shapes

The maximum speeds of mounted vitrified wheels and points of average grade range from about 38,000 to 152,000 rpm for diameters of 1 inch down to 1⁄4 inch. However, the safe operating speed usually is limited by the critical speed (speed at which vibration or whip tends to become excessive) which varies according to wheel or point dimensions, spindle diameter, and overhang.



3′′ 4

1′′ A4

A5

A 12

A 13

1 1′′ 8

11′′ 16

1′′

1′′ 4

A 14

A 11 3′′ 4

7′′ 8

1 1′′ 8

2 1′′ 2 11′′ 16

7′′ 8

3′′ 4

A3

1′′ 116

A1

1 1′′ 4

1′′

3′′ 4

1 1′′ 8

1 1′′ 4

2′′

2 1′′ 2

2 3′′ 4

MOUNTED WHEELS AND POINTS

1′′ 4

1′′ A 15

A 21

A 23

A 24

1 3′′ 8 3′′ 8 5′′ 8

1′′

1′′

5′′ 8

1 1′′ 2

1′′ A 32

A 31

A 34

1′′ 4

3′′ 4

1′′ 3′′ 8

3′′ 8

1′′ 1 5′′ 8

3′′ 4

A 26

A 25

1 3′′ 8

1′′ A 35

A 36

A 37

A 38

A 39

Fig. 1b. Standard Shapes and Sizes of Mounted Wheels and Points ANSI B74.2-1982



MOUNTED WHEELS AND POINTS Table 1. Shapes and Sizes of Mounted Wheels and Points ANSI B74.2-1982 Abrasive Shape

Abrasive Shape Size Diameter Thickness mm mm

No.a

A1 A3 A4 A5 A 11 A 12 A 13 A 14 A 15 A 21 A 23 B 41 B 42 B 43 B 44 B 51 B 52 B 53 B 61 B 62 B 71 B 81 B 91 B 92 B 96

20 22 30 20 21 18 25 18 6 25 20 16 13 6 5.6 11 10 8 20 13 16 20 13 6 3

65 70 30 28 45 30 25 22 25 25 25 16 20 8 10 20 20 16 8 10 3 5 16 6 6

Abrasive Shape Size T D mm inch

Abrasive Shape No.a

D mm

W 144

3

6

W 145

3

10

W 146

3

13

W 152

5

6

W 153

5

10

W 154

5

13

W 158

6

3

W 160

6

6

W 162

6

10

W 163

6

13

W 164

6

20

W 174

10

6

W 175

10

10

W 176

10

13

W 177

10

20

W 178

10

25

W 179

10

30

W 181

13

1.5

W 182

13

3

W 183

13

6

W 184

13

10

W 185

13

13

W 186

13

20

W 187

13

25

W 188

13

40

W 189

13

50

W 195

16

20

a See shape diagrams in Figs. 1a

1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8

Abrasive Shape

Abrasive Shape Size Diameter Thickness mm mm

No.a

A 24 A 25 A 26 A 31 A 32 A 34 A 35 A 36 A 37 A 38 A 39 B 97 B 101 B 103 B 104 B 111 B 112 B 121 B 122 B 123 B 124 B 131 B 132 B 133 B 135

6 25 16 35 25 38 25 40 30 25 20 3 16 16 8 11 10 13 10 5 3 13 10 10 6

20 … … 26 20 10 10 10 6 25 20 10 18 5 10 18 13 … … … … 13 13 10 13

Abrasive Shape Size T D mm inch

T inch

Abrasive Shape No.a

D mm

1⁄ 4 3⁄ 8 1⁄ 2 1⁄ 4 3⁄ 8 1⁄ 2 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

W 196

16

26

W 197

16

50

W 200

20

3

W 201

20

6

W 202

20

10

W 203

20

13

W 204

20

20

W 205

20

25

W 207

20

40

W 208

20

50

5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

W 215

25

3

1

W 216

25

6

1

W 217

25

10

1

W 218

25

13

1

W 220

25

25

1

1

1

W 221

25

40

1

11⁄2

11⁄4

W 222

25

50

1

2

1⁄ 16 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

W 225

30

6

11⁄4

W 226

30

10

11⁄4

W 228

30

20

11⁄4

W 230

30

30

11⁄4

1⁄ 4 3⁄ 8 3⁄ 4 1 1 ⁄4

W 232

30

50

11⁄4

2

W 235

40

6

11⁄2

1

W 236

40

13

1⁄ 4 1⁄ 2

11⁄2

W 237

40

25

2

W 238

40

40

11⁄2 11⁄2 11⁄2

11⁄2

3⁄ 4

W 242

50

25

2

1

and 1b on pages 952 and 953.


T inch 1 2 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1 11⁄2 2 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2

1

Machinery's Handbook 27th Edition BROACHES AND BROACHING

955

BROACHES AND BROACHING The Broaching Process The broaching process may be applied in machining holes or other internal surfaces and also to many flat or other external surfaces. Internal broaching is applied in forming either symmetrical or irregular holes, grooves, or slots in machine parts, especially when the size or shape of the opening, or its length in proportion to diameter or width, make other machining processes impracticable. Broaching originally was utilized for such work as cutting keyways, machining round holes into square, hexagonal, or other shapes, forming splined holes, and for a large variety of other internal operations. The development of broaching machines and broaches finally resulted in extensive application of the process to external, flat, and other surfaces. Most external or surface broaching is done on machines of vertical design, but horizontal machines are also used for some classes of work. The broaching process is very rapid, accurate, and it leaves a finish of good quality. It is employed extensively in automotive and other plants where duplicate parts must be produced in large quantities and for dimensions within small tolerances. Types of Broaches.—A number of typical broaches and the operations for which they are intended are shown by the diagrams, Fig. 1. Broach A produces a round-cornered, square hole. Prior to broaching square holes, it is usually the practice to drill a round hole having a diameter d somewhat larger than the width of the square. Hence, the sides are not completely finished, but this unfinished part is not objectionable in most cases. In fact, this clearance space is an advantage during the broaching operation in that it serves as a channel for the broaching lubricant; moreover, the broach has less metal to remove. Broach B is for finishing round holes. Broaching is superior to reaming for some classes of work, because the broach will hold its size for a much longer period, thus insuring greater accuracy. Broaches C and D are for cutting single and double keyways, respectively. Broach C is of rectangular section and, when in use, slides through a guiding bushing which is inserted in the hole. Broach E is for forming four integral splines in a hub. The broach at F is for producing hexagonal holes. Rectangular holes are finished by broach G. The teeth on the sides of this broach are inclined in opposite directions, which has the following advantages: The broach is stronger than it would be if the teeth were opposite and parallel to each other; thin work cannot drop between the inclined teeth, as it tends to do when the teeth are at right angles, because at least two teeth are always cutting; the inclination in opposite directions neutralizes the lateral thrust. The teeth on the edges are staggered, the teeth on one side being midway between the teeth on the other edge, as shown by the dotted line. A double cut broach is shown at H. This type is for finishing, simultaneously, both sides f of a slot, and for similar work. Broach I is the style used for forming the teeth in internal gears. It is practically a series of gear-shaped cutters, the outside diameters of which gradually increase toward the finishing end of the broach, Broach J is for round holes but differs from style B in that it has a continuous helical cutting edge. Some prefer this form because it gives a shearing cut. Broach K is for cutting a series of helical grooves in a hub or bushing. In helical broaching, either the work or the broach is rotated to form the helical grooves as the broach is pulled through. In addition to the typical broaches shown in Fig. 1, many special designs are now in use for performing more complex operations. Two surfaces on opposite sides of a casting or forging are sometimes machined simultaneously by twin broaches and, in other cases, three or four broaches are drawn through a part at the same time, for finishing as many duplicate holes or surfaces. Notable developments have been made in the design of broaches for external or “surface” broaching. Burnishing Broach: This is a broach having teeth or projections which are rounded on the top instead of being provided with a cutting edge, as in the ordinary type of broach. The teeth are highly polished, the tool being used for broaching bearings and for operations on



BROACHING

Fig. 1. Types of Broaches

other classes of work where the metal is relatively soft. The tool compresses the metal, thus making the surface hard and smooth. The amount of metal that can be displaced by a smooth-toothed burnishing broach is about the same as that removed by reaming. Such broaches are primarily intended for use on babbitt, white metal, and brass, but may also be satisfactorily used for producing a glazed surface on cast iron. This type of broach is also used when it is only required to accurately size a hole. Pitch of Broach Teeth.—The pitch of broach teeth depends upon the depth of cut or chip thickness, length of cut, the cutting force required and power of the broaching machine. In the pitch formulas which follow L =length, in inches, of layer to be removed by broaching d =depth of cut per tooth as shown by Table 1 (For internal broaches, d = depth of cut as measured on one side of broach or one-half difference in diameters of successive teeth in case of a round broach) F =a factor. (For brittle types of material, F = 3 or 4 for roughing teeth, and 6 for finishing teeth. For ductile types of material, F = 4 to 7 for roughing teeth and 8 for finishing teeth.) b =width of inches, of layer to be removed by broaching P =pressure required in tons per square inch, of an area equal to depth of cut times width of cut, in inches (Table 2) T =usable capacity, in tons, of broaching machine = 70% of maximum tonnage


Machinery's Handbook 27th Edition BROACHING

957

Table 1. Designing Data for Surface Broaches Depth of Cut per Tooth, Inch Material to be Broached Steel, High Tensile Strength Steel, Medium Tensile Strength Cast Steel Malleable Iron Cast Iron, Soft Cast Iron, Hard Zinc Die Castings Cast Bronze Wrought Aluminum Alloys Cast Aluminum Alloys Magnesium Die Castings

Roughinga 0.0015–0.002 0.0025–0.005 0.0025–0.005 0.0025–0.005 0.006 –0.010 0.003 –0.005 0.005 –0.010 0.010 –0.025

Finishing 0.0005 0.0005 0.0005 0.0005 0.0005 0.0005 0.0010 0.0005

Face Angle or Rake, Degrees 10–12 14–18 10 7 10–15 5 12b 8

0.005 –0.010 0.005 –0.010 0.010 –0.015

0.0010 0.0010 0.0010

15b 12b 20b

Clearance Angle, Degrees Roughing Finishing 1.5–3 0.5–1 1.5–3 0.5–1 1.53 0.5 1.5–3 0.5 1.5–3 0.5 1.5–3 0.5 5 2 0 0 3 3 3

1 1 1

a The lower depth-of-cut values for roughing are recommended when work is not very rigid, the tolerance is small, a good finish is required, or length of cut is comparatively short. b In broaching these materials, smooth surfaces for tooth and chip spaces are especially recommended.

Table 2. Broaching Pressure P for Use in Pitch Formula (2)

Material to be Broached Steel, High Ten. Strength Steel, Med. Ten. Strength Cast Steel Malleable Iron Cast Iron Cast Brass Brass, Hot Pressed Zinc Die Castings Cast Bronze Wrought Aluminum Cast Aluminum Magnesium Alloy

Depth d of Cut per Tooth, Inch 0.024 0.010 0.004 0.002 0.001 Pressure P in Tons per Square Inch … … … 250 312 … … 158 185 243 … … 128 158 … … … 108 128 … … 115 115 143 … … 50 50 … … … 85 85 … … … 70 70 … … 35 35 … … … … 70 70 … … … 85 85 … … 35 35 … … …

Pressure P, Side-cutting Broaches 200-.004″cut 143-.006″cut 115-.006″ cut 100-.006″ cut 115-.020″ cut ............ ............ ............ ............ ............ ............ ............

The minimum pitch shown by Formula (1) is based upon the receiving capacity of the chip space. The minimum, however, should not be less than 0.2 inch unless a smaller pitch is required for exceptionally short cuts to provide at least two teeth in contact simultaneously, with the part being broached. A reduction below 0.2 inch is seldom required in surface broaching but it may be necessary in connection with internal broaching. Minimum pitch = 3 LdF

(1)

Whether the minimum pitch may be used or not depends upon the power of the available machine. The factor F in the formula provides for the increase in volume as the material is broached into chips. If a broach has adjustable inserts for the finishing teeth, the pitch of the finishing teeth may be smaller than the pitch of the roughing teeth because of the smaller depth d of the cut. The higher value of F for finishing teeth prevents the pitch from becoming too small, so that the spirally curled chips will not be crowded into too small a space.



BROACHING

The pitch of the roughing and finishing teeth should be equal for broaches without separate inserts (notwithstanding the different values of d and F) so that some of the finishing teeth may be ground into roughing teeth after wear makes this necessary. Allowable pitch = dLbP -------------T

(2)

If the pitch obtained by Formula (2) is larger than the minimum obtained by Formula (1), this larger value should be used because it is based upon the usable power of the machine. As the notation indicates, 70 per cent of the maximum tonnage T is taken as the usable capacity. The 30 per cent reduction is to provide a margin for the increase in broaching load resulting from the gradual dulling of the cutting edges. The procedure in calculating both minimum and allowable pitches will be illustrated by an example. Example:Determine pitch of broach for cast iron when L = 9 inches; d = 0.004; and F = 4. Minimum pitch = 3 9 × 0.004 × 4 = 1.14 Next, apply Formula (2). Assume that b = 3 and T = 10; for cast iron and depth d of 0.004, P = 115 (Table 2). Then, 0.004 × 9 × 3 × 115 Allowable pitch = ----------------------------------------------- = 1.24 10 This pitch is safely above the minimum. If in this case the usable tonnage of an available machine were, say, 8 tons instead of 10 tons, the pitch as shown by Formula (2) might be increased to about 1.5 inches, thus reducing the number of teeth cutting simultaneously and, consequently, the load on the machine; or the cut per tooth might be reduced instead of increasing the pitch, especially if only a few teeth are in cutting contact, as might be the case with a short length of cut. If the usable tonnage in the preceding example were, say, 15, then a pitch of 0.84 would be obtained by Formula (2); hence the pitch in this case should not be less than the minimum of approximately 1.14 inches. Depth of Cut per Tooth.—The term “depth of cut” as applied to surface or external broaches means the difference in the heights of successive teeth. This term, as applied to internal broaches for round, hexagonal or other holes, may indicate the total increase in the diameter of successive teeth; however, to avoid confusion, the term as here used means in all cases and regardless of the type of broach, the depth of cut as measured on one side. In broaching free cutting steel, the Broaching Tool Institute recommends 0.003 to 0.006 inch depth of cut for surface broaching; 0.002 to 0.003 inch for multispline broaching; and 0.0007 to 0.0015 inch for round hole broaching. The accompanying table contains data from a German source and applies specifically to surface broaches. All data relating to depth of cut are intended as a general guide only. While depth of cut is based primarily upon the machinability of the material, some reduction from the depth thus established may be required particularly when the work supporting fixture in surface broaching is not sufficiently rigid to resist the thrust from the broaching operation. In some cases, the pitch and cutting length may be increased to reduce the thrust force. Another possible remedy in surface broaching certain classes of work is to use a side-cutting broach instead of the ordinary depth cutting type. A broach designed for side cutting takes relatively deep narrow cuts which extend nearly to the full depth required. The side cutting section is followed by teeth arranged for depth cutting to obtain the required size and surface finish on the work. In general, small tolerances in surface broaching require a reduced cut per tooth to minimize work deflection resulting from the pressure of the cut. See Cutting Speed for Broaching starting on page 1074 for broaching speeds.



959

Terms Commonly Used in Broach Design

Face Angle or Rake.—The face angle (see diagram) of broach teeth affects the chip flow and varies considerably for different materials. While there are some variations in practice, even for the same material, the angles given in the accompanying table are believed to represent commonly used values. Some broach designers increase the rake angle for finishing teeth in order to improve the finish on the work. Clearance Angle.—The clearance angle (see illustration) for roughing steel varies from 1.5 to 3 degrees and for finishing steel from 0.5 to 1 degree. Some recommend the same clearance angles for cast iron and others, larger clearance angles varying from 2 to 4 or 5 degrees. Additional data will be found in Table 1. Land Width.—The width of the land usually is about 0.25 × pitch. It varies, however, from about one-fourth to one-third of the pitch. The land width is selected so as to obtain the proper balance between tooth strength and chip space. Depth of Broach Teeth.—The tooth depth as established experimentally and on the basis of experience, usually varies from about 0.37 to 0.40 of the pitch. This depth is measured radially from the cutting edge to the bottom of the tooth fillet. Radius of Tooth Fillet.—The “gullet” or bottom of the chip space between the teeth should have a rounded fillet to strengthen the broach, facilitate curling of the chips, and safeguard against cracking in connection with the hardening operation. One rule is to make the radius equal to one-fourth the pitch. Another is to make it equal 0.4 to 0.6 the tooth depth. A third method preferred by some broach designers is to make the radius equal onethird of the sum obtained by adding together the land width, one-half the tooth depth, and one-fourth of the pitch. Total Length of Broach.—After the depth of cut per tooth has been determined, the total amount of material to be removed by a broach is divided by this decimal to ascertain the number of cutting teeth required. This number of teeth multiplied by the pitch gives the length of the active portion of the broach. By adding to this dimension the distance over three or four straight teeth, the length of a pilot to be provided at the finishing end of the broach, and the length of a shank which must project through the work and the faceplate of the machine to the draw-head, the overall length of the broach is found. This calculated length is often greater than the stroke of the machine, or greater than is practical for a broach of the diameter required. In such cases, a set of broaches must be used. Chip Breakers.—The teeth of broaches frequently have rounded chip-breaking grooves located at intervals along the cutting edges. These grooves break up wide curling chips and prevent them from clogging the chip spaces, thus reducing the cutting pressure and strain on the broach. These chip-breaking grooves are on the roughing teeth only. They are staggered and applied to both round and flat or surface broaches. The grooves are formed by a round edged grinding wheel and usually vary in width from about 1⁄32 to 3⁄32 inch depending upon the size of broach. The more ductile the material, the wider the chip breaker grooves should be and the smaller the distance between them. Narrow slotting broaches may have the right- and left-hand corners of alternate teeth beveled to obtain chip-breaking action.



BROACHING

Shear Angle.—The teeth of surface broaches ordinarily are inclined so they are not at right angles to the broaching movement. The object of this inclination is to obtain a shearing cut which results in smoother cutting action and an improvement in surface finish. The shearing cut also tends to eliminate troublesome vibration. Shear angles for surface broaches are not suitable for broaching slots or any profiles that resist the outward movement of the chips. When the teeth are inclined, the fixture should be designed to resist the resulting thrusts unless it is practicable to incline the teeth of right- and left-hand sections in opposite directions to neutralize the thrust. The shear angle usually varies from 10 to 25 degrees. Types of Broaching Machines.—Broaching machines may be divided into horizontal and vertical designs, and they may be classified further according to the method of operation, as, for example, whether a broach in a vertical machine is pulled up or pulled down in forcing it through the work. Horizontal machines usually pull the broach through the work in internal broaching but short rigid broaches may be pushed through. External surface broaching is also done on some machines of horizontal design, but usually vertical machines are employed for flat or other external broaching. Although parts usually are broached by traversing the broach itself, some machines are designed to hold the broach or broaches stationary during the actual broaching operation. This principle has been applied both to internal and surface broaching. Vertical Duplex Type: The vertical duplex type of surface broaching machine has two slides or rams which move in opposite directions and operate alternately. While the broach connected to one slide is moving downward on the cutting stroke, the other broach and slide is returning to the starting position, and this returning time is utilized for reloading the fixture on that side; consequently, the broaching operation is practically continuous. Each ram or slide may be equipped to perform a separate operation on the same part when two operations are required. Pull-up Type: Vertical hydraulically operated machines which pull the broach or broaches up through the work are used for internal broaching of holes of various shapes, for broaching bushings, splined holes, small internal gears, etc. A typical machine of this kind is so designed that all broach handling is done automatically. Pull-down Type: The various movements in the operating cycle of a hydraulic pulldown type of machine equipped with an automatic broach-handling slide, are the reverse of the pull-up type. The broaches for a pull-down type of machine have shanks on each end, there being an upper one for the broach-handling slide and a lower one for pulling through the work. Hydraulic Operation: Modern broaching machines, as a general rule, are operated hydraulically rather than by mechanical means. Hydraulic operation is efficient, flexible in the matter of speed adjustments, low in maintenance cost, and the “smooth” action required for fine precision finishing may be obtained. The hydraulic pressures required, which frequently are 800 to 1000 pounds per square inch, are obtained from a motor-driven pump forming part of the machine. The cutting speeds of broaching machines frequently are between 20 and 30 feet per minute, and the return speeds often are double the cutting speed, or higher, to reduce the idle period. Ball-Broaching.—Ball-broaching is a method of securing bushings, gears, or other components without the need for keys, pins, or splines. A series of axial grooves, separated by ridges, is formed in the bore of the workpiece by cold plastic deformation of the metal when a tool, having a row of three rotating balls around its periphery, is pressed through the parts. When the bushing is pressed into a broached bore, the ridges displace the softer material of the bushing into the grooves—thus securing the assembly. The balls can be made of high-carbon chromium steel or carbide, depending on the hardness of the component.



961

Broaching Difficulties.—The accompanying table has been compiled from information supplied by the National Broach and Machine Co. and presents some of the common broaching difficulties, their causes and means of correction. Causes of Broaching Difficulties Broaching Difficulty

Possible Causes

Stuck broach

Insufficient machine capacity; dulled teeth; clogged chip gullets; failure of power during cutting stroke. To remove a stuck broach, workpiece and broach are removed from the machine as a unit; never try to back out broach by reversing machine. If broach does not loosen by tapping workpiece lightly and trying to slide it off its starting end, mount workpiece and broach in a lathe and turn down workpiece to the tool surface. Workpiece may be sawed longitudinally into several sections in order to free the broach. Check broach design, perhaps tooth relief (back off) angle is too small or depth of cut per tooth is too great.

Galling and pickup

Lack of homogeneity of material being broached—uneven hardness, porosity; improper or insufficient coolant; poor broach design, mutilated broach; dull broach; improperly sharpened broach; improperly designed or outworn fixtures. Good broach design will do away with possible chip build-up on tooth faces and excessive heating. Grinding of teeth should be accurate so that the correct gullet contour is maintained. Contour should be fair and smooth.

Broach breakage

Overloading; broach dullness; improper sharpening; interrupted cutting stroke; backing up broach with workpiece in fixture; allowing broach to pass entirely through guide hole; ill fitting and/or sharp edged key; crooked holes; untrue locating surface; excessive hardness of workpiece; insufficient clearance angle; sharp corners on pull end of broach. When grinding bevels on pull end of broach use wheel that is not too pointed.

Chatter

Too few teeth in cutting contact simultaneously; excessive hardness of material being broached; loose or poorly constructed tooling; surging of ram due to load variations. Chatter can be alleviated by changing the broaching speed, by using shear cutting teeth instead of right angle teeth, and by changing the coolant and the face and relief angles of the teeth.

Drifting or misalignment of tool during cutting stroke

Lack of proper alignment when broach is sharpened in grinding machine, which may be caused by dirt in the female center of the broach; inadequate support of broach during the cutting stroke, on a horizontal machine especially; body diameter too small; cutting resistance variable around I.D. of hole due to lack of symmetry of surfaces to be cut; variations in hardness around I.D. of hole; too few teeth in cutting contact.

Streaks in broached surface

Lands too wide; presence of forging, casting or annealing scale; metal pickup; presence of grinding burrs and grinding and cleaning abrasives.

Rings in the broached hole

Due to surging resulting from uniform pitch of teeth; presence of sharpening burrs on broach; tooth clearance angle too large; locating face not smooth or square; broach not supported for all cutting teeth passing through the work. The use of differential tooth spacing or shear cutting teeth helps in preventing surging. Sharpening burrs on a broach may be removed with a wood block.



FILES AND BURS

FILES AND BURS Files Definitions of File Terms.—The following file terms apply to hand files but not to rotary files and burs. Axis: Imaginary line extending the entire length of a file equidistant from faces and edges. Back: The convex side of a file having the same or similar cross-section as a half-round file. Bastard Cut: A grade of file coarseness between coarse and second cut of American pattern files and rasps. Blank: A file in any process of manufacture before being cut. Blunt: A file whose cross-sectional dimensions from point to tang remain unchanged. Coarse Cut: The coarsest of all American pattern file and rasp cuts. Coarseness: Term describing the relative number of teeth per unit length, the coarsest having the least number of file teeth per unit length; the smoothest, the most. American pattern files and rasps have four degrees of coarseness: coarse, bastard, second and smooth. Swiss pattern files usually have seven degrees of coarseness: 00, 0, 1, 2, 3, 4, 6 (from coarsest to smoothest). Curved tooth files have three degrees of coarseness: standard, fine and smooth. Curved Cut: File teeth which are made in curved contour across the file blank. Cut: Term used to describe file teeth with respect to their coarseness or their character (single, double, rasp, curved, special). Double Cut: A file tooth arrangement formed by two series of cuts, namely the overcut followed, at an angle, by the upcut. Edge: Surface joining faces of a file. May have teeth or be smooth. Face: Widest cutting surface or surfaces that are used for filing. Heel or Shoulder: That portion of a file that abuts the tang. Hopped: A term used among file makers to represent a very wide skip or spacing between file teeth. Length: The distance from the heel to the point. Overcut: The first series of teeth put on a double-cut file. Point: The front end of a file; the end opposite the tang. Rasp Cut: A file tooth arrangement of round-topped teeth, usually not connected, that are formed individually by means of a narrow, punch-like tool. Re-cut: A worn-out file which has been re-cut and re-hardened after annealing and grinding off the old teeth. Safe Edge: An edge of a file that is made smooth or uncut, so that it will not injure that portion or surface of the workplace with which it may come in contact during filing. Second Cut: A grade of file coarseness between bastard and smooth of American pattern files and rasps. Set: To blunt the sharp edges or corners of file blanks before and after the overcut is made, in order to prevent weakness and breakage of the teeth along such edges or corners when the file is put to use. Shoulder or Heel: See Heel or Shoulder. Single Cut: A file tooth arrangement where the file teeth are composed of single unbroken rows of parallel teeth formed by a single series of cuts. Smooth Cut: An American pattern file and rasp cut that is smoother than second cut. Tang: The narrowed portion of a file which engages the handle. Upcut: The series of teeth superimposed on the overcut, and at an angle to it, on a doublecut file.


Machinery's Handbook 27th Edition FILES AND BURS

963

File Characteristics.—Files are classified according to their shape or cross-section and according to the pitch or spacing of their teeth and the nature of the cut. Cross-section and Outline: The cross-section may be quadrangular, circular, triangular, or some special shape. The outline or contour may be tapered or blunt. In the former, the point is more or less reduced in width and thickness by a gradually narrowing section that extends for one-half to two-thirds of the length. In the latter the cross-section remains uniform from tang to point. Cut: The character of the teeth is designated as single, double, rasp or curved. The single cut file (or float as the coarser cuts are sometimes called) has a single series of parallel teeth extending across the face of the file at an angle of from 45 to 85 degrees with the axis of the file. This angle depends upon the form of the file and the nature of the work for which it is intended. The single cut file is customarily used with a light pressure to produce a smooth finish. The double cut file has a multiplicity of small pointed teeth inclining toward the point of the file arranged in two series of diagonal rows that cross each other. For general work, the angle of the first series of rows is from 40 to 45 degrees and of the second from 70 to 80 degrees. For double cut finishing files the first series has an angle of about 30 degrees and the second, from 80 to 87 degrees. The second, or upcut, is almost always deeper than the first or overcut. Double cut files are usually employed, under heavier pressure, for fast metal removal and where a rougher finish is permissible. The rasp is formed by raising a series of individual rounded teeth from the surface of the file blank with a sharp narrow, punch-like cutting tool and is used with a relatively heavy pressure on soft substances for fast removal of material. The curved tooth file has teeth that are in the form of parallel arcs extending across the face of the file, the middle portion of each arc being closest to the point of the file. The teeth are usually single cut and are relatively coarse. They may be formed by steel displacement but are more commonly formed by milling. With reference to coarseness of cut the terms coarse, bastard, second and smooth cuts are used, the coarse or bastard files being used on the heavier classes of work and the second or smooth cut files for the finishing or more exacting work. These degrees of coarseness are only comparable when files of the same length are compared, as the number or teeth per inch of length decreases as the length of the file increases. The number of teeth per inch varies considerably for different sizes and shapes and for files of different makes. The coarseness range for the curved tooth files is given as standard, fine and smooth. In the case of Swiss pattern files, a series of numbers is used to designate coarseness instead of names; Nos. 00, 0, 1, 2, 3, 4 and 6 being the most common with No. 00 the coarsest and No. 6 the finest. Classes of Files.—There are five main classes of files: mill or saw files; machinists' files; curved tooth files; Swiss pattern files; and rasps. The first two classes are commonly referred to as American pattern files. Mill or Saw Files: These are used for sharpening mill or circular saws, large crosscut saws; for lathe work; for draw filing; for filing brass and bronze; and for smooth filing generally. The number identifying the following files refers to the illustration in Fig. 1 1) Cantsaw files have an obtuse isosceles triangular section, a blunt outline, are single cut and are used for sharpening saws having “M”-shaped teeth and teeth of less than 60-degree angle; 2) Crosscut files have a narrow triangular section with short side rounded, a blunt outline, are single cut and are used to sharpen crosscut saws. The rounded portion is used to deepen the gullets of saw teeth and the sides are used to sharpen the teeth themselves. ; 3) Double ender fileshave a triangular section, are tapered from the middle to both ends, are tangless are single cut and are used reversibly for sharpening saws; 4) The mill file itself, is usually single cut, tapered in width, and often has two square cutting edges in addition to the cutting sides. Either or both edges may be rounded, however, for filing the gul-



FILES AND BURS

lets of saw teeth. The blunt mill file has a uniform rectangular cross-section from tip to tang; 5) The The triangular saw files or taper saw files have an equilateral triangular section, are tapered, are single cut and are used for filing saws with 60-degree angle teeth. They come in taper, slim taper, extra slim taper and double extra slim taper thicknesses Blunt triangular and blunt hand saw files are without taper; and 6) Web saw files have a diamond-shaped section, a blunt outline, are single cut and are used for sharpening pulpwood or web saws. . Machinists' Files: These files are used throughout industry where metal must be removed rapidly and finish is of secondary importance. Except for certain exceptions in the round and half-round shapes, all are double cut. 7) Flat files have a rectangular section, are tapered in width and thickness, are cut on both sides and edges and are used for general utility work; 8) Half round files have a circular segmental section, are tapered in width and thickness, have their flat side double cut, their rounded side mostly double but sometimes single cut, and are used to file rounded holes, concave corners, etc. in general filing work; 9) Hand files are similar to flat files but taper in thickness only. One edge is uncut or “safe.”; and 10) Knife files have a “knife-blade” section, are tapered in width only, are double cut, and are used by tool and die makers on work having acute angles. Machinist's general purpose files have a rectangular section, are tapered and have single cut teeth divided by angular serrations which produce short cutting edges. These edges help stock removal but still leave a smooth finish and are suitable for use on various materials including aluminum, bronze, cast iron, malleable iron, mild steels and annealed tool steels. 11) Pillar files are similar to hand files but are thicker and not as wide; 12) Round files have a circular section, are tapered, single cut, and are generally used to file circular openings or curved surfaces; 13) Square files have a square section, are tapered, and are used for filing slots, keyways and for general surface filing where a heavier section is preferred; 14) Three square files have an equilateral triangular section and are tapered on all sides. They are double cut and have sharp corners as contrasted with taper triangular files which are single cut and have somewhat rounded corners. They are used for filing accurate internal angles, for clearing out square corners, and for filing taps and cutters; and 15) Warding files have a rectangular section, and taper in width to a narrow point. They are used for general narrow space filing. . Wood files are made in the same sections as flat and half round files but with coarser teeth especially suited for working on wood.

1

2

9

4

3

10

11

6

5

12

13

7

14

8

15

Fig. 1. Styles of Mill or Saw Files

Curved Tooth Files: Regular curved tooth files are made in both rigid and flexible forms. The rigid type has either a tang for a conventional handle or is made plain with a hole at each end for mounting in a special holder. The flexible type is furnished for use in special holders only. The curved tooth files come in standard fine and smooth cuts and in parallel


Machinery's Handbook 27th Edition FILES AND BURS

965

flat, square, pillar, pillar narrow, half round and shell types. A special curved tooth file is available with teeth divided by long angular serrations. The teeth are cut in an “off center” arc. When moved across the work toward one edge of the file a fast cutting action is provided; when moved toward the other edge, a smoothing action; thus the file is made to serve a dual purpose. Swiss Pattern Files: These are used by tool and die makers, model makers and delicate instrument parts finishers. They are made to closer tolerances than the conventional American pattern files although with similar cross-sections. The points of the Swiss pattern files are smaller, the tapers are longer and they are available in much finer cuts. They are primarily finishing tools for removing burrs left from previous finishing operations truing up narrow grooves, notches and keyways, cleaning out corners and smoothing small parts. For very fine work, round and square handled needle files, available in numerous crosssectional shapes in overall lengths from 4 to 7 3⁄4 inches, are used. Die sinkers use die sinkers files and die sinkers rifflers. The files, also made in many different cross-sectional shapes, are 31⁄2 inches in length and are available in the cut Nos. 0, 1, 2, and 4. The rifflers are from 51⁄2 to 63⁄4 inches long, have cutting surfaces on either end, and come in numerous cross-sectional shapes in cut Nos. 0, 2, 3, 4 and 6. These rifflers are used by die makers for getting into corners, crevices, holes and contours of intricate dies and molds. Used in the same fashion as die sinkers rifflers, silversmiths rifflers, that have a much heavier crosssection, are available in lengths from 6 7⁄8 to 8 inches and in cuts Nos. 0, 1, 2, and 3. Blunt machine files in Cut Nos. 00, 0, and 2 for use in ordinary and bench filing machines are available in many different cross-sectional shapes, in lengths from 3 to 8 inches. Rasps: Rasps are employed for work on relatively soft substances such as wood, leather, and lead where fast removal or material is required. They come in rectangular and half round cross-sections, the latter with and without a sharp edge. Special Purpose Files: Falling under one of the preceding five classes of files, but modified to meet the requirements of some particular function, are a number of special purpose files. The long angle lathe file is used for filing work that is rotating in a lathe. The long tooth angle provides a clean shear, eliminates drag or tear and is self-clearing. This file has safe or uncut edges to protect shoulders of the work which are not to be filed. The foundry file has especially sturdy teeth with heavy set edges for the snagging of castings—the removing of fins, sprues, and other projections. The die casting file has extra strong teeth on corners and edges as well as sides for working on die castings of magnesium, zinc, or aluminum alloys. A special file for stainless steel is designed to stand up under the abrasive action of stainless steel alloys. Aluminum rasps and files are designed to eliminate clogging. A special tooth construction is used in one type of aluminum tile which breaks up the filings, allows the file to clear itself and overcomes chatter. A brass file is designed so that with a little pressure the sharp, high-cut teeth bite deep while with less pressure, their short uncut angle produces a smoothing effect. The lead float has coarse, single cut teeth at almost right angles to the file axis. These shear away the metal under ordinary pressure and produce a smoothing effect under light pressure. The shear tooth file has a coarse single cut with a long angle for soft metals or alloys, plastics, hard rubber and wood. Chain saw files are designed to sharpen all types of chain saw teeth. These files come in round, rectangular, square and diamond-shaped sections. The round and square sectioned files have either double or single cut teeth, the rectangular files have single cut teeth and the diamondshaped files have double cut teeth. Effectiveness of Rotary Files and Burs.—There it very little difference in the efficiency of rotary files or burs when used in electric tools and when used in air tools, provided the speeds have been reasonably well selected. Flexible-shaft and other machines used as a source of power for these tools have a limited number of speeds which govern the revolutions per minute at which the tools can be operated.



FILES AND BURS

The carbide bur may be used on hard or soft materials with equally good results. The principle difference in construction of the carbide bur is that its teeth or flutes are provided with a negative rather than a radial rake. Carbide burs are relatively brittle, and must be treated more carefully than ordinary burs. They should be kept cutting freely, in order to prevent too much pressure, which might result in crumbling of the cutting epics. At the same speeds, both high-speed steel and carbide burs remove approximately the same amount of metal. However, when carbide burs are used at their most efficient speeds, the rate of stock removal may be as much as four times that of ordinary burs. In certain cases, speeds much higher than those shown in the table can be used. It has been demonstrated that a carbide bur will last up to 100 times as long as a high-speed steel bur of corresponding size and shape. Approximate Speeds of Rotary Files and Burs Medium Cut, High-Speed Steel Bur or File Tool Diam., Inches

Mild Steel

1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

4600

Cast Iron Bronze Aluminum Speed, Revolutions per Minute 7000 15,000 20,000

Magnesium 30,000

Carbide Bur Medium Fine Cut Cut Any Material 45,000 30,000

3450

5250

11,250

15,000

22,500

30,000

20,000

2750

4200

9000

12,000

18,000

24,000

16,000

2300

3500

7500

10,000

15,000

20,000

13,350

2000

3100

6650

8900

13,350

18,000

12,000

1900

2900

6200

8300

12,400

16,000

10,650

1700

2600

5600

7500

11,250

14,500

9650

1 11⁄8

1600 1500

2400 2300

5150 4850

6850 6500

10,300 9750

13,000 …

8650 …

11⁄4

1400

2100

4500

6000

9000

…

…

As recommended by the Nicholson File Company.

Steel Wool.—Steel wool is made by shaving thin layers of steel from wire. The wire is pulled, by special machinery built for the purpose, past cutting tools or through cutting dies which shave off chips from the outside. Steel wool consists of long, relatively strong, and resilient steel shavings having sharp edges. This characteristic renders it an excellent abrasive. The fact that the cutting characteristics of steel wool vary with the size of the fiber, which is readily controlled in manufacture, has adapted it to many applications. Metals other than steel have been made into wool by the same processes as steel, and when so manufactured have the same general characteristics. Thus wool has been made from copper, lead, aluminum, bronze, brass, monel metal, and nickel. The wire from which steel wool is made may be produced by either the Bessemer, or the basic or acid openhearth processes. It should contain from 0.10 to 0.20 per cent carbon; from 0.50 to 1.00 per cent manganese; from 0.020 to 0.090 per cent sulphur; from 0.050 to 0.120 per cent phosphorus; and from 0.001 to 0.010 per cent silicon. When drawn on a standard tensilestrength testing machine, a sample of the steel should show an ultimate strength of not less than 120,000 pounds per square inch. Steel Wool Grades Description Super Fine Extra Fine Very Fine Fine

Grade 0000 000 00 0

Fiber Thickness Inch Millimeter 0.001 0.025 0.0015 0.035 0.0018 0.04 0.002 0.05

Description Medium Medium Coarse Coarse Extra Coarse

Grade 1 2 3 4

Fiber Thickness Inch Millimeter 0.0025 0.06 0.003 0.075 0.0035 0.09 0.004 0.10


Machinery's Handbook 27th Edition TOOL WEAR

967

TOOL WEAR AND SHARPENING Metal cutting tools wear constantly when they are being used. A normal amount of wear should not be a cause for concern until the size of the worn region has reached the point where the tool should be replaced. Normal wear cannot be avoided and should be differentiated from abnormal tool breakage or excessively fast wear. Tool breakage and an excessive rate of wear indicate that the tool is not operating correctly and steps should be taken to correct this situation. There are several basic mechanisms that cause tool wear. It is generally understood that tools wear as a result of abrasion which is caused by hard particles of work material plowing over the surface of the tool. Wear is also caused by diffusion or alloying between the work material and the tool material. In regions where the conditions of contact are favorable, the work material reacts with the tool material causing an attrition of the tool material. The rate of this attrition is dependent upon the temperature in the region of contact and the reactivity of the tool and the work materials with each other. Diffusion or alloying also occurs where particles of the work material are welded to the surface of the tool. These welded deposits are often quite visible in the form of a built-up edge, as particles or a layer of work material inside a crater or as small mounds attached to the face of the tool. The diffusion or alloying occurring between these deposits and the tool weakens the tool material below the weld. Frequently these deposits are again rejoined to the chip by welding or they are simply broken away by the force of collision with the passing chip. When this happens, a small amount of the tool material may remain attached to the deposit and be plucked from the surface of the tool, to be carried away with the chip. This mechanism can cause chips to be broken from the cutting edge and the formation of small craters on the tool face called pull-outs. It can also contribute to the enlargement of the larger crater that sometimes forms behind the cutting edge. Among the other mechanisms that can cause tool wear are severe thermal gradients and thermal shocks, which cause cracks to form near the cutting edge, ultimately leading to tool failure. This condition can be caused by improper tool grinding procedures, heavy interrupted cuts, or by the improper application of cutting fluids when machining at high cutting speeds. Chemical reactions between the active constituents in some cutting fluids sometimes accelerate the rate of tool wear. Oxidation of the heated metal near the cutting edge also contributes to tool wear, particularly when fast cutting speeds and high cutting temperatures are encountered. Breakage of the cutting edge caused by overloading, heavy shock loads, or improper tool design is not normal wear and should be corrected. The wear mechanisms described bring about visible manifestations of wear on the tool which should be understood so that the proper corrective measures can be taken, when required. These visible signs of wear are described in the following paragraphs and the corrective measures that might be required are given in the accompanying Tool TroubleShooting Check List. The best procedure when trouble shooting is to try to correct only one condition at a time. When a correction has been made it should be checked. After one condition has been corrected, work can then start to correct the next condition. Flank Wear: Tool wear occurring on the flank of the tool below the cutting edge is called flank wear. Flank wear always takes place and cannot be avoided. It should not give rise to concern unless the rate of flank wear is too fast or the flank wear land becomes too large in size. The size of the flank wear can be measured as the distance between the top of the cutting edge and the bottom of the flank wear land. In practice, a visual estimate is usually made instead of a precise measurement, although in many instances flank wear is ignored and the tool wear is “measured” by the loss of size on the part. The best measure of tool wear, however, is flank wear. When it becomes too large, the rubbing action of the wear land against the workpiece increases and the cutting edge must be replaced. Because conditions vary, it is not possible to give an exact amount of flank wear at which the tool should be replaced. Although there are many exceptions, as a rough estimate, high-speed steel



TOOL SHARPENING

tools should be replaced when the width of the flank wear land reaches 0.005 to 0.010 inch for finish turning and 0.030 to 0.060 inch for rough turning; and for cemented carbides 0.005 to 0.010 inch for finish turning and 0.020 to 0.040 inch for rough turning. Under ideal conditions which, surprisingly, occur quite frequently, the width of the flank wear land will be very uniform along its entire length. When the depth of cut is uneven, such as when turning out-of-round stock, the bottom edge of the wear land may become somewhat slanted, the wear land being wider toward the nose. A jagged-appearing wear land usually is evidence of chipping at the cutting edge. Sometimes, only one or two sharp depressions of the lower edge of the wear land will appear, to indicate that the cutting edge has chipped above these depressions. A deep notch will sometimes occur at the “depth of cut line,” or that part of the cutting opposite the original surface of the work. This can be caused by a hard surface scale on the work, by a work-hardened surface layer on the work, or when machining high-temperature alloys. Often the size of the wear land is enlarged at the nose of the tool. This can be a sign of crater breakthrough near the nose or of chipping in this region. Under certain conditions, when machining with carbides, it can be an indication of deformation of the cutting edge in the region of the nose. When a sharp tool is first used, the initial amount of flank wear is quite large in relation to the subsequent total amount. Under normal operating conditions, the width of the flank wear land will increase at a uniform rate until it reaches a critical size after which the cutting edge breaks down completely. This is called catastrophic failure and the cutting edge should be replaced before this occurs. When cutting at slow speeds with high-speed steel tools, there may be long periods when no increase in the flank wear can be observed. For a given work material and tool material, the rate of flank wear is primarily dependent on the cutting speed and then the feed rate. Cratering: A deep crater will sometimes form on the face of the tool which is easily recognizable. The crater forms at a short distance behind the side cutting edge leaving a small shelf between the cutting edge and the edge of the crater. This shelf is sometimes covered with the built-up edge and at other times it is uncovered. Often the bottom of the crater is obscured with work material that is welded to the tool in this region. Under normal operating conditions, the crater will gradually enlarge until it breaks through a part of the cutting edge. Usually this occurs on the end cutting edge just behind the nose. When this takes place, the flank wear at the nose increases rapidly and complete tool failure follows shortly. Sometimes cratering cannot be avoided and a slow increase in the size of the crater is considered normal. However, if the rate of crater growth is rapid, leading to a short tool life, corrective measures must be taken. Cutting Edge Chipping: Small chips are sometimes broken from the cutting edge which accelerates tool wear but does not necessarily cause immediate tool failure. Chipping can be recognized by the appearance of the cutting edge and the flank wear land. A sharp depression in the lower edge of the wear land is a sign of chipping and if this edge of the wear land has a jagged appearance it indicates that a large amount of chipping has taken place. Often the vacancy or cleft in the cutting edge that results from chipping is filled up with work material that is tightly welded in place. This occurs very rapidly when chipping is caused by a built-up edge on the face of the tool. In this manner the damage to the cutting edge is healed; however, the width of the wear land below the chip is usually increased and the tool life is shortened. Deformation: Deformation occurs on carbide cutting tools when taking a very heavy cut using a slow cutting speed and a high feed rate. A large section of the cutting edge then becomes very hot and the heavy cutting pressure compresses the nose of the cutting edge, thereby lowering the face of the tool in the area of the nose. This reduces the relief under the nose, increases the width of the wear land in this region, and shortens the tool life. Surface Finish: The finish on the machined surface does not necessarily indicate poor cutting tool performance unless there is a rapid deterioration. A good surface finish is,


Machinery's Handbook 27th Edition TOOL SHARPENING

969

however, sometimes a requirement. The principal cause of a poor surface finish is the built-up edge which forms along the edge of the cutting tool. The elimination of the builtup edge will always result in an improvement of the surface finish. The most effective way to eliminate the built-up edge is to increase the cutting speed. When the cutting speed is increased beyond a certain critical cutting speed, there will be a rather sudden and large improvement in the surface finish. Cemented carbide tools can operate successfully at higher cutting speeds, where the built-up edge does not occur and where a good surface finish is obtained. Whenever possible, cemented carbide tools should be operated at cutting speeds where a good surface finish will result. There are times when such speeds are not possible. Also, high-speed tools cannot be operated at the speed where the built-up edge does not form. In these conditions the most effective method of obtaining a good surface finish is to employ a cutting fluid that has active sulphur or chlorine additives. Cutting tool materials that do not alloy readily with the work material are also effective in obtaining an improved surface finish. Straight titanium carbide and diamond are the two principal tool materials that fall into this category. The presence of feed marks can mar an otherwise good surface finish and attention must be paid to the feed rate and the nose radius of the tool if a good surface finish is desired. Changes in the tool geometry can also be helpful. A small “flat,” or secondary cutting edge, ground on the end cutting edge behind the nose will sometimes provide the desired surface finish. When the tool is in operation, the flank wear should not be allowed to become too large, particularly in the region of the nose where the finished surface is produced. Sharpening Twist Drills.—Twist drills are cutting tools designed to perform concurrently several functions, such as penetrating directly into solid material, ejecting the removed chips outside the cutting area, maintaining the essentially straight direction of the advance movement and controlling the size of the drilled hole. The geometry needed for these multiple functions is incorporated into the design of the twist drill in such a manner that it can be retained even after repeated sharpening operations. Twist drills are resharpened many times during their service life, with the practically complete restitution of their original operational characteristics. However, in order to assure all the benefits which the design of the twist drill is capable of providing, the surfaces generated in the sharpening process must agree with the original form of the tool's operating surfaces, unless a change of shape is required for use on a different work material. The principal elements of the tool geometry which are essential for the adequate cutting performance of twist drills are shown in Fig. 1. The generally used values for these dimensions are the following: Point angle: Commonly 118°, except for high strength steels, 118° to 135°; aluminum alloys, 90° to 140°; and magnesium alloys, 70° to 118°. Helix angle: Commonly 24° to 32°, except for magnesium and copper alloys, 10° to 30°. Lip relief angle: Commonly 10° to 15°, except for high strength or tough steels, 7° to 12°. The lower values of these angle ranges are used for drills of larger diameter, the higher values for the smaller diameters. For drills of diameters less than 1⁄4 inch, the lip relief angles are increased beyond the listed maximum values up to 24°. For soft and free machining materials, 12° to 18° except for diameters less than 1⁄4 inch, 20° to 26°. Relief Grinding of the Tool Flanks.—In sharpening twist drills the tool flanks containing the two cutting edges are ground. Each flank consists of a curved surface which provides the relief needed for the easy penetration and free cutting of the tool edges. In grinding the flanks, Fig. 2, the drill is swung around the axis A of an imaginary cone while resting in a support which holds the drill at one-half the point angle B with respect to the face of the grinding wheel. Feed f for stock removal is in the direction of the drill axis. The relief angle is usually measured at the periphery of the twist drill and is also specified by that value. It is not a constant but should increase toward the center of the drill.



TOOL SHARPENING

The relief grinding of the flank surfaces will generate the chisel angle on the web of the twist drill. The value of that angle, typically 55°, which can be measured, for example, with the protractor of an optical projector, is indicative of the correctness of the relief grinding.

Fig. 1. The principal elements of tool geometry on twist drills.

Fig. 3. The chisel edge C after thinning the web by grinding off area T.

Fig. 2. In grinding the face of the twist drill the tool is swung around the axis A of an imaginary cone, while resting in a support tilted by half of the point angle β with respect to the face of the grinding wheel. Feed f for stock removal is in the direction of the drill axis.

Fig. 4. Split point or “crankshaft” type web thinning.

Drill Point Thinning.—The chisel edge is the least efficient operating surface element of the twist drill because it does not cut, but actually squeezes or extrudes the work material. To improve the inefficient cutting conditions caused by the chisel edge, the point width is often reduced in a drill-point thinning operation, resulting in a condition such as that shown in Fig. 3. Point thinning is particularly desirable on larger size drills and also on those which become shorter in usage, because the thickness of the web increases toward the shaft of the twist drill, thereby adding to the length of the chisel edge. The extent of point thinning is limited by the minimum strength of the web needed to avoid splitting of the drill point under the influence of cutting forces. Both sharpening operations—the relieved face grinding and the point thinning—should be carried out in special drill grinding machines or with twist drill grinding fixtures mounted on general-purpose tool grinding machines, designed to assure the essential accu-



971

racy of the required tool geometry. Off-hand grinding may be used for the important web thinning when a special machine is not available; however, such operation requires skill and experience. Improperly sharpened twist drills, e.g. those with unequal edge length or asymmetrical point angle, will tend to produce holes with poor diameter and directional control. For deep holes and also drilling into stainless steel, titanium alloys, high temperature alloys, nickel alloys, very high strength materials and in some cases tool steels, split point grinding, resulting in a “crankshaft” type drill point, is recommended. In this type of pointing, see Fig. 4, the chisel edge is entirely eliminated, extending the positive rake cutting edges to the center of the drill, thereby greatly reducing the required thrust in drilling. Points on modified-point drills must be restored after sharpening to maintain their increased drilling efficiency. Sharpening Carbide Tools.—Cemented carbide indexable inserts are usually not resharpened but sometimes they require a special grind in order to form a contour on the cutting edge to suit a special purpose. Brazed type carbide cutting tools are resharpened after the cutting edge has become worn. On brazed carbide tools the cutting-edge wear should not be allowed to become excessive before the tool is re-sharpened. One method of determining when brazed carbide tools need resharpening is by periodic inspection of the flank wear and the condition of the face. Another method is to determine the amount of production which is normally obtained before excessive wear has taken place, or to determine the equivalent period of time. One disadvantage of this method is that slight variations in the work material will often cause the wear rate not to be uniform and the number of parts machined before regrinding will not be the same each time. Usually, sharpening should not require the removal of more than 0.005 to 0.010 inch of carbide. General Procedure in Carbide Tool Grinding: The general procedure depends upon the kind of grinding operation required. If the operation is to resharpen a dull tool, a diamond wheel of 100 to 120 grain size is recommended although a finer wheel—up to 150 grain size—is sometimes used to obtain a better finish. If the tool is new or is a “standard” design and changes in shape are necessary, a 100-grit diamond wheel is recommended for roughing and a finer grit diamond wheel can be used for finishing. Some shops prefer to rough grind the carbide with a vitrified silicon carbide wheel, the finish grinding being done with a diamond wheel. A final operation commonly designated as lapping may or may not be employed for obtaining an extra-fine finish. Wheel Speeds: The speed of silicon carbide wheels usually is about 5000 feet per minute. The speeds of diamond wheels generally range from 5000 to 6000 feet per minute; yet lower speeds (550 to 3000 fpm) can be effective. Offhand Grinding: In grinding single-point tools (excepting chip breakers) the common practice is to hold the tool by hand, press it against the wheel face and traverse it continuously across the wheel face while the tool is supported on the machine rest or table which is adjusted to the required angle. This is known as “offhand grinding” to distinguish it from the machine grinding of cutters as in regular cutter grinding practice. The selection of wheels adapted to carbide tool grinding is very important. Silicon Carbide Wheels.—The green colored silicon carbide wheels generally are preferred to the dark gray or gray-black variety, although the latter are sometimes used. Grain or Grit Sizes: For roughing, a grain size of 60 is very generally used. For finish grinding with silicon carbide wheels, a finer grain size of 100 or 120 is common. A silicon carbide wheel such as C60-I-7V may be used for grinding both the steel shank and carbide tip. However, for under-cutting steel shanks up to the carbide tip, it may be advantageous to use an aluminum oxide wheel suitable for grinding softer, carbon steel. Grade: According to the standard system of marking, different grades from soft to hard are indicated by letters from A to Z. For carbide tool grinding fairly soft grades such as G, H, I, and J are used. The usual grades for roughing are I or J and for finishing H, I, and J. The



TOOL SHARPENING

grade should be such that a sharp free-cutting wheel will be maintained without excessive grinding pressure. Harder grades than those indicated tend to overheat and crack the carbide. Structure: The common structure numbers for carbide tool grinding are 7 and 8. The larger cup-wheels (10 to 14 inches) may be of the porous type and be designated as 12P. The standard structure numbers range from 1 to 15 with progressively higher numbers indicating less density and more open wheel structure. Diamond Wheels.—Wheels with diamond-impregnated grinding faces are fast and cool cutting and have a very low rate of wear. They are used extensively both for resharpening and for finish grinding of carbide tools when preliminary roughing is required. Diamond wheels are also adapted for sharpening multi-tooth cutters such as milling cutters, reamers, etc., which are ground in a cutter grinding machine. Resinoid bonded wheels are commonly used for grinding chip breakers, milling cutters, reamers or other multi-tooth cutters. They are also applicable to precision grinding of carbide dies, gages, and various external, internal and surface grinding operations. Fast, cool cutting action is characteristic of these wheels. Metal bonded wheels are often used for offhand grinding of single-point tools especially when durability or long life and resistance to grooving of the cutting face, are considered more important than the rate of cutting. Vitrified bonded wheels are used both for roughing of chipped or very dull tools and for ordinary resharpening and finishing. They provide rigidity for precision grinding, a porous structure for fast cool cutting, sharp cutting action and durability. Diamond Wheel Grit Sizes.—For roughing with diamond wheels a grit size of 100 is the most common both for offhand and machine grinding. Grit sizes of 120 and 150 are frequently used in offhand grinding of single point tools 1) for resharpening; 2) for a combination roughing and finishing wheel; and 3) for chipbreaker grinding. Grit sizes of 220 or 240 are used for ordinary finish grinding all types of tools (offhand and machine) and also for cylindrical, internal and surface finish grinding. Grits of 320 and 400 are used for “lapping” to obtain very fine finishes, and for hand hones. A grit of 500 is for lapping to a mirror finish on such work as carbide gages and boring or other tools for exceptionally fine finishes. Diamond Wheel Grades.—Diamond wheels are made in several different grades to better adapt them to different classes of work. The grades vary for different types and shapes of wheels. Standard Norton grades are H, J, and L, for resinoid bonded wheels, grade N for metal bonded wheels and grades J, L, N, and P, for vitrified wheels. Harder and softer grades than standard may at times be used to advantage. Diamond Concentration.—The relative amount (by carat weight) of diamond in the diamond section of the wheel is known as the “diamond concentration.” Concentrations of 100 (high), 50 (medium) and 25 (low) ordinarily are supplied. A concentration of 50 represents one-half the diamond content of 100 (if the depth of the diamond is the same in each case) and 25 equals one-fourth the content of 100 or one-half the content of 50 concentration. 100 Concentration: Generally interpreted to mean 72 carats of diamond/in.3 of abrasive section. (A 75 concentration indicates 54 carats/in.3.) Recommended (especially in grit sizes up to about 220) for general machine grinding of carbides, and for grinding cutters and chip breakers. Vitrified and metal bonded wheels usually have 100 concentration. 50 Concentration: In the finer grit sizes of 220, 240, 320, 400, and 500, a 50 concentration is recommended for offhand grinding with resinoid bonded cup-wheels.



973

25 Concentration: A low concentration of 25 is recommended for offhand grinding with resinoid bonded cup-wheels with grit sizes of 100, 120 and 150. Depth of Diamond Section: The radial depth of the diamond section usually varies from 1⁄ to 1⁄ inch. The depth varies somewhat according to the wheel size and type of bond. 16 4

Dry Versus Wet Grinding of Carbide Tools.—In using silicon carbide wheels, grinding should be done either absolutely dry or with enough coolant to flood the wheel and tool. Satisfactory results may be obtained either by the wet or dry method. However, dry grinding is the most prevalent usually because, in wet grinding, operators tend to use an inadequate supply of coolant to obtain better visibility of the grinding operation and avoid getting wet; hence checking or cracking in many cases is more likely to occur in wet grinding than in dry grinding. Wet Grinding with Silicon Carbide Wheels: One advantage commonly cited in connection with wet grinding is that an ample supply of coolant permits using wheels about one grade harder than in dry grinding thus increasing the wheel life. Plenty of coolant also prevents thermal stresses and the resulting cracks, and there is less tendency for the wheel to load. A dust exhaust system also is unnecessary. Wet Grinding with Diamond Wheels: In grinding with diamond wheels the general practice is to use a coolant to keep the wheel face clean and promote free cutting. The amount of coolant may vary from a small stream to a coating applied to the wheel face by a felt pad. Coolants for Carbide Tool Grinding.—In grinding either with silicon carbide or diamond wheels a coolant that is used extensively consists of water plus a small amount either of soluble oil, sal soda, or soda ash to prevent corrosion. One prominent manufacturer recommends for silicon carbide wheels about 1 ounce of soda ash per gallon of water and for diamond wheels kerosene. The use of kerosene is quite general for diamond wheels and usually it is applied to the wheel face by a felt pad. Another coolant recommended for diamond wheels consists of 80 per cent water and 20 per cent soluble oil. Peripheral Versus Flat Side Grinding.—In grinding single point carbide tools with silicon carbide wheels, the roughing preparatory to finishing with diamond wheels may be done either by using the flat face of a cup-shaped wheel (side grinding) or the periphery of a “straight” or disk-shaped wheel. Even where side grinding is preferred, the periphery of a straight wheel may be used for heavy roughing as in grinding back chipped or broken tools (see left-hand diagram). Reasons for preferring peripheral grinding include faster cutting with less danger of localized heating and checking especially in grinding broad surfaces. The advantages usually claimed for side grinding are that proper rake or relief angles are easier to obtain and the relief or land is ground flat. The diamond wheels used for tool sharpening are designed for side grinding. (See right-hand diagram.)



TOOL SHARPENING

Lapping Carbide Tools.—Carbide tools may be finished by lapping, especially if an exceptionally fine finish is required on the work as, for example, tools used for precision boring or turning non-ferrous metals. If the finishing is done by using a diamond wheel of very fine grit (such as 240, 320, or 400), the operation is often called “lapping.” A second lapping method is by means of a power-driven lapping disk charged with diamond dust, Norbide powder, or silicon carbide finishing compound. A third method is by using a hand lap or hone usually of 320 or 400 grit. In many plants the finishes obtained with carbide tools meet requirements without a special lapping operation. In all cases any feather edge which may be left on tools should be removed and it is good practice to bevel the edges of roughing tools at 45 degrees to leave a chamfer 0.005 to 0.010 inch wide. This is done by hand honing and the object is to prevent crumbling or flaking off at the edges when hard scale or heavy chip pressure is encountered. Hand Honing: The cutting edge of carbide tools, and tools made from other tool materials, is sometimes hand honed before it is used in order to strengthen the cutting edge. When interrupted cuts or heavy roughing cuts are to be taken, or when the grade of carbide is slightly too hard, hand honing is beneficial because it will prevent chipping, or even possibly, breakage of the cutting edge. Whenever chipping is encountered, hand honing the cutting edge before use will be helpful. It is important, however, to hone the edge lightly and only when necessary. Heavy honing will always cause a reduction in tool life. Normally, removing 0.002 to 0.004 inch from the cutting edge is sufficient. When indexable inserts are used, the use of pre-honed inserts is preferred to hand honing although sometimes an additional amount of honing is required. Hand honing of carbide tools in between cuts is sometimes done to defer grinding or to increase the life of a cutting edge on an indexable insert. If correctly done, so as not to change the relief angle, this procedure is sometimes helpful. If improperly done, it can result in a reduction in tool life. Chip Breaker Grinding.—For this operation a straight diamond wheel is used on a universal tool and cutter grinder, a small surface grinder, or a special chipbreaker grinder. A resinoid bonded wheel of the grade J or N commonly is used and the tool is held rigidly in an adjustable holder or vise. The width of the diamond wheel usually varies from 1⁄8 to 1⁄4 inch. A vitrified bond may be used for wheels as thick as 1⁄4 inch, and a resinoid bond for relatively narrow wheels. Summary of Miscellaneous Points.—In grinding a single-point carbide tool, traverse it across the wheel face continuously to avoid localized heating. This traverse movement should be quite rapid in using silicon carbide wheels and comparatively slow with diamond wheels. A hand traversing and feeding movement, whenever practicable, is generally recommended because of greater sensitivity. In grinding, maintain a constant, moderate pressure. Manipulating the tool so as to keep the contact area with the wheel as small as possible will reduce heating and increase the rate of stock removal. Never cool a hot tool by dipping it in a liquid, as this may crack the tip. Wheel rotation should preferably be against the cutting edge or from the front face toward the back. If the grinder is driven by a reversing motor, opposite sides of a cup wheel can be used for grinding right-and lefthand tools and with rotation against the cutting edge. If it is necessary to grind the top face of a single-point tool, this should precede the grinding of the side and front relief, and topface grinding should be minimized to maintain the tip thickness. In machine grinding with a diamond wheel, limit the feed per traverse to 0.001 inch for 100 to 120 grit; 0.0005 inch for 150 to 240 grit; and 0.0002 inch for 320 grit and finer.


Machinery's Handbook 27th Edition JIGS AND FIXTURES

975

JIGS AND FIXTURES Jig Bushings Material for Jig Bushings.—Bushings are generally made of a good grade of tool steel to ensure hardening at a fairly low temperature and to lessen the danger of fire cracking. They can also be made from machine steel, which will answer all practical purposes, provided the bushings are properly casehardened to a depth of about 1⁄16 inch. Sometimes, bushings for guiding tools may be made of cast iron, but only when the cutting tool is of such a design that no cutting edges come within the bushing itself. For example, bushings used simply to support the smooth surface of a boring-bar or the shank of a reamer might, in some instances, be made of cast iron, but hardened steel bushings should always be used for guiding drills, reamers, taps, etc., when the cutting edges come in direct contact with the guiding surfaces. If the outside diameter of the bushing is very large, as compared with the diameter of the cutting tool, the cost of the bushing can sometimes be reduced by using an outer cast-iron body and inserting a hardened tool steel bushing. When tool steel bushings are made and hardened, it is recommended that A-2 steel be used. The furnace should be set to 1750°F and the bushing placed in the furnace and held there approximately 20 minutes after the furnace reaches temperature. Remove the bushing and cool in still air. After the part cools to 100–150°F, immediately place in a tempering furnace that has been heated to 300°F. Remove the bushing after one hour and cool in still air. If an atmospherically controlled furnace is unavailable, the part should be wrapped in stainless foil to prevent scaling and oxidation at the 1750°F temperature. American National Standard Jig Bushings.—Specifications for the following types of jig bushings are given in American National Standard B94.33-1974 (R1986). Head Type Press Fit Wearing Bushings, Type H (Fig. 1 and Tables 1 and 3); Headless Type Press Fit Wearing Bushings, Type P (Fig. 2 and Tables 1 and 3); Slip Type Renewable Wearing Bushings, Type S (Fig. 3 and Tables 4 and 5); Fixed Type Renewable Wearing Bushings, Type F (Fig. 4 and Tables 5 and 6); Headless Type Liner Bushings, Type L (Fig. 5 and Table 7); and Head Type Liner Bushings, Type HL (Fig. 6 and Table 8). Specifications for locking mechanisms are also given in Table 9.

Fig. 1. Head Type Press FitWearing Bushings — Type H

Fig. 2. Headless Type Press Fit Wearing Bushings — Type P

Fig. 3. Slip Type Renewable Wearing Bushings—Type S

Fig. 4. Fixed Type Renewable Wearing Bushings — Type F

Fig. 5. Headless Type Liner Bushings — Type L

Fig. 6. Head Type Liner Bushings — Type HL



JIGS AND FIXTURES Table 1. American National Standard Head Type Press Fit Wearing Bushings — Type H ANSI B94.33-1974 (R1986)

Range of Hole Sizes A

Body Diameter B Unfinished Nom

Max

Min

Finished Max

Min

0.0135 up to and including 0.0625

0.156

0.166

0.161

0.1578

0.1575

0.0630 to 0.0995

0.203

0.213

0.208

0.2046

0.2043

0.1015 to 0.1405

0.250

0.260

0.255

0.2516

0.2513

0.1406 to 0.1875

0.312

0.327

0.322

0.3141

0.3138

0.189 to 0.2500

0.406

0.421

0.416

0.4078

0.4075

0.2570 to 0.3125

0.500

0.520

0.515

0.5017

0.5014

0.3160 to 0.4219

0.625

0.645

0.640

0.6267

0.6264

0.4375 to 0.5000

0.750

0.770

0.765

0.7518

0.7515

0.5156 to 0.6250

0.875

0.895

0.890

0.8768

0.8765

Body Length C 0.250 0.312 0.375 0.500 0.250 0.312 0.375 0.500 0.750 0.250 0.312 0.375 0.500 0.750 0.250 0.312 0.375 0.500 0.750 1.000 0.250 0.312 0.375 0.500 0.750 1.000 1.375 1.750 0.312 0.375 0.500 0.750 1.000 1.375 1.750 0.312 0.375 0.500 0.750 1.000 1.375 1.750 2.125 0.500 0.750 1.000 1.375 1.750 2.125 0.500 0.750 1.000 1.375 1.750 2.125 2.500

Radius D

Head Diam. E Max

Head Thickness F Max

0.016

0.250

0.094

0.016

0.312

0.094

0.016

0.375

0.094

0.031

0.438

0.125

0.031

0.531

0.156

0.047

0.625

0.219

0.047

0.812

0.219

0.062

0.938

0.219

0.062

0.125

0.250


Number H-10-4 H-10-5 H-10-6 H-10-8 H-13-4 H-13-5 H-13-6 H-13-8 H-13-12 H-16-4 H-16-5 H-16-6 H-16-8 H-16-12 H-20-4 H-20-5 H-20-6 H-20-8 H-20-12 H-20-16 H-26-4 H-26-5 H-26-6 H-26-8 H-26-12 H-26-16 H-26-22 H-26-28 H-32-5 H-32-6 H-32-8 H-32-12 H-32-16 H-32-22 H-32-28 H-40-5 H-40-6 H-40-8 H-40-12 H-40-16 H-40-22 H-40-28 H-40-34 H-48-8 H-48-12 H-48-16 H-48-22 H-29-28 H-48-34 H-56-8 H-56-12 H-56-16 H-56-22 H-56-28 H-56-34 H-56-40


977

Table 1. (Continued) American National Standard Head Type Press Fit Wearing Bushings — Type H ANSI B94.33-1974 (R1986) Range of Hole Sizes A

Radius D

Head Diam. E Max


0.094

1.250

0.312

0.094

1.625

0.375

0.094

2.000

0.375

0.094

2.500

0.375

Body Diameter B Unfinished

Finished

Nom

Max

Min

Max

Min

0.6406 to 0.7500

1.000

1.020

1.015

1.0018

1.0015

0.7656 to 1.0000

1.375

1.395

1.390

1.3772

1.3768

1.0156 to 1.3750

1.750

1.770

1.765

1.7523

1.7519

1.3906 to 1.7500

2.250

2.270

2.265

2.2525

2.2521

Body Length C 0.500 0.750 1.000 1.375 1.750 2.125 2.500 0.750 1.000 1.375 1.750 2.125 2.500 1.000 1.375 1.750 2.125 2.500 3.000 1.000 1.375 1.750 2.125 2.500 3.000

Number H-64-8 H-64-12 H-64-16 H-64-22 H-64-28 H-64-34 H-64-40 H-88-12 H-88-16 H-88-22 H-88-28 H-88-34 H-88-40 H-112-16 H-112-22 H-112-28 H-112-34 H-112-40 H-112-48 H-144-16 H-144-22 H-144-28 H-144-34 H-144-40 H-144-48

All dimensions are in inches. See also Table 3 for additional specifications.

Table 2. American National Standard Headless Type Press Fit Wearing Bushings — Type P ANSI B94.33-1974 (R1986) Range of Hole Sizes A

Nom

Body Diameter B Unfinished Finished Max Min Max Min


0.156

0.166

0.161

0.1578

0.1575

0.0630 to 0.0995

0.203

0.213

0.208

0.2046

0.2043

0.1015 to 0.1405

0.250

0.260

0.255

0.2516

0.2513

0.1406 to 0.1875

0.312

0.327

0.322

0.3141

0.3138

Body Length C 0.250 0.312 0.375 0.500 0.250 0.312 0.375 0.500 0.750 0.250 0.312 0.375 0.500 0.750 0.250 0.312 0.375 0.500 0.750 1.000

Radius D

0.016

0.016

0.016

0.031


Number P-10-4 P-10-5 P-10-6 P-10-8 P-13-4 P-13-5 P-13-6 P-13-8 P-13-12 P-16-4 P-16-5 P-16-6 P-16-8 P-16-12 P-20-4 P-20-5 P-20-6 P-20-8 P-20-12 P-20-16


JIGS AND FIXTURES Table 2. (Continued) American National Standard Headless Type Press Fit Wearing Bushings — Type P ANSI B94.33-1974 (R1986)

Nom

Body Diameter B Unfinished Finished Max Min Max Min

0.1890 to 0.2500

0.406

0.421

0.416

0.4078

0.4075

0.2570 to 0.3125

0.500

0.520

0.515

0.5017

0.5014

0.3160 to 0.4219

0.625

0.645

0.640

0.6267

0.6264

0.4375 to 0.5000

0.750

0.770

0.765

0.7518

0.7515

0.5156 to 0.6250

0.875

0.895

0.890

0.8768

0.8765

0.6406 to 0.7500

1.000

1.020

1.015

1.0018

1.0015

0.7656 to 1.0000

1.375

1.395

1.390

1.3772

1.3768

1.0156 to 1.3750

1.750

1.770

1.765

1.7523

1.7519

1.3906 to 1.7500

2.250

2.270

2.265

2.2525

2.2521


Body Length C 0.250 0.312 0.375 0.500 0.750 1.000 1.375 1.750 0.312 0.375 0.500 0.750 1.000 1.375 1.750 0.312 0.375 0.500 0.750 1.000 1.375 1.750 2.125 0.500 0.750 1.000 1.375 1.750 2.125 0.500 0.750 1.000 1.375 1.750 2.125 2.500 0.500 0.750 1.000 1.375 1.750 2.125 2.500 0.750 1.000 1.375 1.750 2.125 2.500 1.000 1.375 1.750 2.125 2.500 3.000 1.000 1.375 1.750 2.125 2.500 3.000

Radius D

0.031

0.047

0.047

0.062

0.062

0.062

0.094

0.094

0.094

All dimensions are in inches. See Table 3 for additional specifications.


Number P-26-4 P-26-5 P-26-6 P-26-8 P-26-12 P-26-16 P-26-22 P-26-28 P-32-5 P-32-6 P-32-8 P-32-12 P-32-16 P-32-22 P-32-28 P-40-5 P-40-6 P-40-8 P-40-12 P-40-16 P-40-22 P-40-28 P-40-34 P-48-8 P-48-12 P-48-16 P-48-22 P-48-28 P-48-34 P-56-8 P-56-12 P-56-16 P-56-22 P-56-28 P-56-34 P-56-40 P-64-8 P-64-12 P-64-16 P-64-22 P-64-28 P-64-34 P-64-40 P-88-12 P-88-16 P-88-22 P-88-28 P-88-34 P-88-40 P-112-16 P-112-22 P-112-28 P-112-34 P-112-40 P-112-48 P-144-16 P-144-22 P-144-28 P-144-34 P-144-40 P-144-48


979

Table 3. Specifications for Head Type H and Headless Type P Press Fit Wearing Bushings ANSI B94.33-1974 (R1986) All dimensions given in inches. Tolerance on dimensions where not otherwise specified shall be ±0.010 inch. Size and type of chamfer on lead end to be manufacturer's option. The length, C, is the overall length for the headless type and length underhead for the head type. The head design shall be in accordance with the manufacturer's practice. Diameter A must be concentric to diameter B within 0.0005 T.I.V. on finish ground bushings. The body diameter, B, for unfinished bushings is larger than the nominal diameter in order to provide grinding stock for fitting to jig plate holes. The grinding allowance is: 0.005 to 0.010 in. for sizes 0.156, 0.203 and 0.250 in. 0.010 to 0.015 in. for sizes 0.312 and 0.406 in. 0.015 to 0.020 in. for sizes 0.500 in. and up. Hole sizes are in accordance with American National Standard Twist Drill Sizes. The maximum and minimum values of the hole size, A, shall be as follows: Nominal Size of Hole Maximum Minimum Above 0.0135 to 0.2500 in., incl. Nominal + 0.0004 in. Nominal + 0.0001 in. Above 0.2500 to 0.7500 in., incl. Nominal + 0.0005 in. Nominal + 0.0001 in. Above 0.7500 to 1.5000 in., incl. Nominal + 0.0006 in. Nominal + 0.0002 in. Above 1.5000 in. Nominal + 0.0007 in. Nominal + 0.0003 in. Bushings in the size range from 0.0135 through 0.3125 will be counterbored to provide for lubrication and chip clearance. Bushings without counterbore are optional and will be furnished upon request. The size of the counterbore shall be inside diameter of the bushing + 0.031 inch. The included angle at the bottom of the counterbore shall be 118 deg, ± 2 deg. The depth of the counterbore shall be in accordance with the table below to provide adequate drill bearing. Drill Bushing Hole Size 0.0135 to 0.0630 to 0.1015 to 0.1406 to 0.1890 to 0.2570 to 0.0625 0.0995 0.1405 0.1875 0.2500 0.3125 P H P H P H P H P H P H Body Minimum Drill Bearing Length—Inch Length 0.250 X 0.250 X X X X X X X X X X 0.312 X 0.250 X X X X X X X X X X 0.375 0.250 0.250 X X X X X X X X X X 0.500 0.250 0.250 X 0.312 X 0.312 X 0.375 X X X X 0.750 + + 0.375 0.375 0.375 0.375 X 0.375 X X X X 1.000 + + + + + + 0.625 0.625 0.625 0.625 0.625 0.625 1.375 + + + + + + + + 0.625 0.625 0.625 0.625 1.750 + + + + + + + + 0.625 0.625 0.625 0.625

All dimensions are in inches. X indicates no counterbore. + indicates not American National Standard

Table 4. American National Standard Slip Type Renewable Wearing Bushings — Type S ANSI B94.33-1974 (R1986) Range of Hole Sizes A

Body Diameter B Nom

Max

Min


0.188

0.1875

0.1873

0.0492 to 0.1562

0.312

0.3125

0.3123

0.1570 to 0.3125

0.500

0.5000

0.4998

0.3160 to 0.5000

0.750

0.7500

0.7498

Length UnderHead C 0.250 0.312 0.375 0.500 0.312 0.500 0.750 1.000 0.312 0.500 0.750 1.000 1.375 1.750 0.500 0.750 1.000 1.375 1.750 2.125

Radius D

Head Diam. E Max


0.031

0.312

0.188

0.047

0.562

0.375

0.047

0.812

0.438

0.094

1.062

0.438


Number S-12-4 S-12-5 S-12-6 S-12-8 S-20-5 S-20-8 S-20-12 S-20-16 S-32-5 S-32-8 S-32-12 S-32-16 S-32-22 S-32-28 S-48-8 S-48-12 S-48-16 S-48-22 S-48-28 S-48-34


JIGS AND FIXTURES Table 4. (Continued) American National Standard Slip Type Renewable Wearing Bushings — Type S ANSI B94.33-1974 (R1986)


Body Diameter B Nom

Max

Min

0.5156 to 0.7500

1.000

1.0000

0.9998

0.7656 to 1.0000

1.375

1.3750

1.3747

1.0156 to 1.3750

1.750

1.7500

1.7497

1.3906 to 1.7500

2.250

2.2500

2.2496

Length UnderHead C 0.500 0.750 1.000 1.375 1.750 2.125 2.500 0.750 1.000 1.375 1.750 2.125 2.500 1.000 1.375 1.750 2.125 2.500 3.000 1.000 1.375 1.750 2.125 2.500 3.000

Radius D

Head Diam. E Max


0.094

1.438

0.438

0.094

1.812

0.438

0.125

2.312

0.625

0.125

2.812

0.625

Number S-64-8 S-64-12 S-64-16 S-64-22 S-64-28 S-64-34 S-64-40 S-88-12 S-88-16 S-88-22 S-88-28 S-88-34 S-88-40 S-112-16 S-112-22 S-112-28 S-112-34 S-112-40 S-112-48 S-144-16 S-144-22 S-144-28 S-144-34 S-144-40 S-144-48


Table 5. Specifications for Slip Type S and Fixed Type F Renewable Wearing Bushings ANSI B94.33-1974 (R1986) Tolerance on dimensions where not otherwise specified shall be plus or minus 0.010 inch. Hole sizes are in accordance with the American Standard Twist Drill Sizes. The maximum and minimum values of hole size, A, shall be as follows: Nominal Size of Hole Maximum Minimum Above 0.0135 to 0.2500 in. incl. Nominal + 0.0004 in. Nominal + 0.0001 in. Above 0.2500 to 0.7500 in. incl. Nominal + 0.0005 in. Nominal + 0.0001 in. Above 0.7500 to 1.5000 in. incl. Nominal + 0.0006 in. Nominal + 0.0002 in. Above 1.5000 Nominal + 0.0007 in. Nominal + 0.0003 in. The head design shall be in accordance with the manufacturer's practice. Head of slip type is usually knurled. When renewable wearing bushings are used with liner bushings of the head type, the length under the head will still be equal to the thickness of the jig plate, because the head of the liner bushing will be countersunk into the jig plate. Diameter A must be concentric to diameter B within 0.0005 T.I.R. on finish ground bushings. Size and type of chamfer on lead end to be manufacturer's option. Bushings in the size range from 0.0135 through 0.3125 will be counterbored to provide for lubrication and chip clearance. Bushings without counterbore are optional and will be furnished upon request. The size of the counterbore shall be inside diameter of the bushings plus 0.031 inch. The included angle at the bottom of the counterbore shall be 118 deg., plus or minus 2 deg. The depth of the counterbore shall be in accordance with the table below to provide adequate drill bearing. Drill Bearing Hole Size

Body Length 0.250 0.312 0.375 0.500 0.750 1.000 1.375 1.750

0.0135 to 0.0625 S F

0.0630 to 0.0995 S F

0.1015 to 0.1405 S F

0.1406 to 0.1875 S F

0.1890 to 0.2500 S F

0.2500 to 0.3125 S F

X 0.375 0.375 0.375 0.625 0.625 0.625 0.625

X X X X 0.625 0.625 0.625 0.625

Minimum Drill Bearing Length 0.250 0.250 0.250 0.250 0.250 0.312 + +

0.250 0.250 0.250 0.250 0.250 0.312 + +

0.375 0.375 0.375 0.375 0.375 0.375 + +

0.375 0.375 0.375 0.375 0.375 0.375 + +

X 0.375 0.375 0.375 0.375 0.375 + +

X 0.375 0.375 0.375 0.375 0.375 + +

X 0.375 0.375 0.375 0.375 0.625 0.625 0.625

X 0.375 0.375 0.375 0.375 0.625 0.625 0.625

X 0.375 0.375 0.375 0.625 0.625 0.625 0.625

All dimensions are in inches. X indicates no counterbore, + indicates not American National Standard length.


X X X X 0.625 0.625 0.625 0.625


981

Table 6. American National Standard Fixed Type Renewable Wearing Bushings — Type F ANSI B94.33-1974 (R1986) Range of Hole Sizes A 0.0135 up to and including 0.0469

0.0492 to 0.1562

Body Diameter B Nom

Max

Min

Length Under Head C

Radius D

Head Diam. E Max


0.250 0.188

0.312

0.1875

0.3125

0.1873

0.3123

0.312 0.375

0.031

0.312

0.188

0.500

0.5000

0.4998

0.5156 to 0.7500

0.750

0.7500

0.7498

F-12-8 F-20-5

0.500 0.750

0.047

0.562

0.250

1.0000

0.9998

1.375

1.3750

1.3747

F-20-16 F-32-5

0.750 1.000

F-32-8 0.047

0.812

0.250

1.3906 to 1.7500

1.750

2.250

1.7500

2.2500

1.7497

2.2496

F-32-12 F-32-16

1.375

F-32-22

1.750

F-32-28

0.500

F-48-8

1.000 1.375

F-48-12 0.094

1.062

0.250

F-48-16 F-48-22

1.750

F-48-28

2.125

F-48-34

0.500

F-64-8

0.750

F-64-12

1.375

F-64-16 0.094

1.438

0.375

F-64-22

1.750

F-64-28

2.125

F-64-34

2.500

F-64-40

0.750

F-88-12

1.375 1.750

F-88-16 0.094

1.812

0.375

F-88-22 F-88-28

2.125

F-88-34

2.500

F-88-40

1.000

F-112-16

1.375 1.0156 to 1.3750

F-20-12

0.312

1.000 0.7656 to 1.0000

F-20-8

1.000

1.000 1.000

F-12-6

0.312

0.750 0.3160 to 0.5000

F-12-5

0.500

0.500 0.1570 to 0.3125

Number F-12-4

1.750 2.125

F-112-22 0.125

2.312

0.375

F-112-28 F-112-34

2.500

F-112-40

3.000

F-112-48

1.000

F-144-16

1.375

F-144-22

1.750 2.125

0.125

2.812

0.375

F-144-28 F-144-34

2.500

F-144-40

3.000

F-144-48




JIGS AND FIXTURES Table 7. American National Standard Headless Type Liner Bushings — Type L ANSI B94.33-1974 (R1986)

Range of Hole Sizes in Renewable Bushings

Body Diameter B Unfinished

Inside Diameter A

Finished

Nom

Max

Min

Nom

Max

Min

Max

Min


0.188

0.1879

0.1876

0.312

0.3341

0.3288

0.3141

0.3138

0.0492 to 0.1562

0.312

0.3129

0.3126

0.500

0.520

0.515

0.5017

0.5014

0.1570 to 0.3125

0.500

0.5005

0.5002

0.750

0.770

0.765

0.7518

0.7515

0.3160 to 0.5000

0.750

0.7506

0.7503

1.000

1.020

1.015

1.0018

1.0015

0.5156 to 0.7500

1.000

1.0007

1.0004

1.375

1.395

1.390

1.3772

1.3768

0.7656 to 1.0000

1.375

1.3760

1.3756

1.750

1.770

1.765

1.7523

1.7519

1.0156 to 1.3750

1.750

1.7512

1.7508

2.250

2.270

2.265

2.2525

2.2521

1.3906 to 1.7500

2.250

2.2515

2.2510

2.750

2.770

2.765

2.7526

2.7522

Overall Length C 0.250 0.312 0.375 0.500 0.312 0.500 0.750 1.000 0.312 0.500 0.750 1.000 1.375 1.750 0.500 0.750 1.000 1.375 1.750 2.125 0.500 1.750 1.000 1.375 1.750 2.125 2.500 0.750 1.000 1.375 1.750 2.125 2.500 1.000 1.375 1.750 2.125 2.500 3.000 1.000 1.375 1.750 2.125 2.500 3.000

Radius D

0.031

0.047

0.062

0.062

0.094

0.094

0.094

0.125

Number L-20-4 L-20-5 L-20-6 L-20-8 L-32-5 L-32-8 L-32-12 L-32-16 L-48-5 L-48-8 L-48-12 L-48-16 L-48-22 L-48-28 L-64-8 L-64-12 L-64-16 L-64-22 L-64-28 L-64-34 L-88-8 L-88-12 L-88-16 L-88-22 L-88-28 L-88-34 L-88-40 L-112-12 L-112-16 L-112-22 L-112-28 L-112-34 L-112-40 L-144-16 L-144-22 L-144-28 L-144-34 L-144-40 L-144-48 L-176-16 L-176-22 L-176-28 L-176-34 L-176-40 L-176-48

All dimensions are in inches. Tolerances on dimensions where otherwise not specified are ± 0.010 in. The body diameter, B, for unfinished bushings is 0.015 to 0.020 in. larger than the nominal diameter in order to provide grinding stock for fitting to jig plate holes. Diameter A must be concentric to diameter B within 0.0005 T.I.R. on finish ground bushings.



983

Nom

Max

Unfinished

Min

Nom

Max

Min

Finished

Max

Min

Overall Length C

Head Dia. E


Body Diameter B

Inside Diameter A

Radius D

Range of Hole Sizes in Renewable Bushings

Table 8. American National Standard Head Type Liner Bushing — Type HL ANSI B94.33-1974 (R1986)

0.312 0.0135 to 0.1562

0.312

0.3129

0.3126

0.500 0.520 0.515

0.5017

0.5014

0.500 0.750

0.047 0.625 0.094

0.500

0.5005

0.5002

0.750 0.770 0.765

0.7518

0.7515

HL-32-16

0.312

HL-48-5

0.750 1.000

HL-48-8 0.062 0.875 0.094

0.5156 to 0.7500

0.750

0.7506

0.7503

1.000 1.020 1.015

1.0018

1.0015

1.0007

1.0004

1.375 1.395 1.390

1.3772

1.3768

HL-48-22 HL-48-28

0.500

HL-64-8

1.000 1.375

HL-64-12 0.062 1.125 0.125

1.375

1.3760

1.3756

1.750 1.770 1.765

1.7523

1.7519

1.750

1.7512

1.7508

2.250

2.27

2.265

2.2525

2.2521

HL-64-28 HL-64-34

0.500

HL-88-8

0.750

HL-88-12

1.375

HL-88-16 0.094 1.500 0.125

2.250

2.2515

2.2510

2.750 2.770 2.765

2.7526

2.7522

HL-88-22

1.750

HL-88-28

2.125

HL-88-34

2.500

HL-88-40

0.750

HL-112-12

1.375 1.750

HL-112-16 0.094 1.875 0.188

HL-112-22 HL-112-28

2.125

HL-112-34

2.500

HL-112-40

1.000

HL-144-16

1.750 2.125

HL-144-22 0.094 2.375 0.188

HL-144-28 HL-144-34

2.500

HL-144-40

3.000

HL-144-48

1.000

HL-176-16

1.375 1.3906 to 1.7500

HL-64-22

2.125

1.375 1.0156 to 1.3750

HL-64-16

1.750

1.000 0.7656 to 1.0000

HL-48-16

1.750

1.000 1.000

HL-48-12

1.375

0.750 0.3160 to 0.5000

HL-32-8 HL-32-12

1.000 0.500 0.1570 to 0.3125

Number HL-32-5

1.750 2.125

HL-176-22 0.125 2.875 0.188

HL-176-28 HL-176-34

2.500

HL-176-40

3.000

HL-176-48

All dimensions are in inches. See also footnotes to Table 7.



JIGS AND FIXTURES

Table 9. American National Standard Locking Mechanisms for Jig Bushings ANSI B94.33-1974 (R1986) Lock Screw for Use with Slip or Fixed Renewable Bushings

No.

A

B

C

D

E

F

LS-0 LS-1

0.438 0.625

0.188 0.375

0.312 0.625

0.188 0.250

0.105-0.100 0.138-0.132

LS-2

0.875

0.375

0.625

Per Manufacturer's Standard

0.375

0.200-0.194

LS-3

1.000

0.438

0.750

0.375

0.200-0.194

UNC Thread 8–32 5⁄ –18 16 5⁄ –18 16 3⁄ –16 8

Round Clamp Optional Only for Use with Fixed Renewable Bushing

Number

A

B

C

D

E

F

G

H

RC-1

0.625

0.312

0.484

0.150

0.203

0.125

0.531

0.328

RC-2

0.625

0.438

0.484

0.219

0.187

0.188

0.906

0.328

RC-3

0.750

0.500

0.578

0.281

0.219

0.188

1.406

0.391

Use With Socket Head Screw 5⁄ –18 16 5⁄ –18 16 3⁄ –16 8

Locking Mechanism Dimensions of Slip and Fixed Renewable Bushings

R

Locking Dim. of Lock Screw (Slip or Fixed)

Locking Dim. of Clamp (Fixed Only)

Max Head Diam. of Mating Liner Used to Clear Locking Device

0.266 0.500 0.625 0.750 0.922 1.109 1.391 1.641

0.105-0.100 0.138-0.132 0.138-0.132 0.138-0.132 0.200-0.194 0.200-0.194 0.200-0.194 0.200-0.194

… 0.125-0.115 0.125-0.115 0.125-0.115 0.187-0.177 0.187-0.177 0.187-0.177 0.187-0.177

… 0.625 0.875 1.125 1.500 1.875 2.375 2.875

G Head Thickness

Body OD

Max Diam. F When Used With Locking Device

Slip

Fixed

H ± 0.005

0.188 0.312 0.500 0.750 1.000 1.375 1.750 2.250

0.312 0.562 0.812 1.062 1.438 1.812 2.312 2.812

0.188 0.375 0.438 0.438 0.438 0.438 0.625 0.625

0.188 0.250 0.250 0.250 0.375 0.375 0.375 0.375

0.094 0.125 0.125 0.125 0.188 0.188 0.188 0.188

J

L Ma x

0.094 0.172 0.297 0.422 0.594 0.781 1.000 1.250

55° 65° 65° 50° 35° 30° 30° 25°



Clam p or Screw LS or RC 0 1 1 1 2 2 3 3

Machinery's Handbook 27th Edition JIG BUSHINGS

985

Jig Bushing Definitions.— Renewable Bushings: Renewable wearing bushings to guide the tool are for use in liners which in turn are installed in the jig. They are used where the bushing will wear out or become obsolete before the jig or where several bushings are to be interchangeable in one hole. Renewable wearing bushings are divided into two classes, “Fixed” and “Slip.” Fixed renewable bushings are installed in the liner with the intention of leaving them in place until worn out. Slip renewable bushings are interchangeable in a given size of liner and, to facilitate removal, they are usually made with a knurled head. They are most frequently used where two or more operations requiring different inside diameters are performed in a single jig, such as where drilling is followed by reaming, tapping, spot facing, counterboring, or some other secondary operation. Press Fit Bushings: Press fit wearing bushings to guide the tool are for installation directly in the jig without the use of a liner and are employed principally where the bushings are used for short production runs and will not require replacement. They are intended also for short center distances. Liner Bushings: Liner bushings are provided with and without heads and are permanently installed in a jig to receive the renewable wearing bushings. They are sometimes called master bushings. Jig Plate Thickness.—The standard length of the press fit portion of jig bushings as established are based on standardized uniform jig plate thicknesses of 5⁄16, 3⁄8, 1⁄2, 3⁄4, 1, 13⁄8, 13⁄4, 21⁄8, 21⁄2, and 3 inches. Jig Bushing Designation System.—Inside Diameter: The inside diameter of the hole is specified by a decimal dimension. Type Bushing: The type of bushing is specified by a letter: S for Slip Renewable, F for Fixed Renewable, L for Headless Liner, HL for Head Liner, P for Headless Press Fit, and H for Head Press Fit. Body Diameter: The body diameter is specified in multiples of 0.0156 inch. For example, a 0.500-inch body diameter = 0.500/0.0156 = 32. Body Length: The effective or body length is specified in multiples of 0.0625 inch. For example, a 0.500-inch length = 0.500/0.0625 = 8. Unfinished Bushings: All bushings with grinding stock on the body diameter are designated by the letter U following the number. Example:A slip renewable bushing having a hole diameter of 0.5000 inch, a body diameter of 0.750 inch, and a body length of 1.000 inch would be designated as .5000-S-48-16. Jig Boring Definition of Jig and Fixture.—The distinction between a jig and fixture is not easy to define, but, as a general rule, it is as follows: A jig either holds or is held on the work, and, at the same time, contains guides for the various cutting tools, whereas a fixture holds the work while the cutting tools are in operation, but does not contain any special arrangements for guiding the tools. A fixture, therefore, must be securely held or fixed to the machine on which the operation is performed—hence the name. A fixture is sometimes provided with a number of gages and stops, but not with bushings or other devices for guiding and supporting the cutting tools. Jig Borers.—Jig borers are used for precision hole-location work. For this reason, the coordinate measuring systems on these machines are designed to provide longitudinal and transverse movements that are accurate to 0.0001 in. One widely used method of obtaining this accuracy utilizes ultraprecision lead screws. Another measuring system employs precision end measuring rods and a micrometer head that are placed in a trough which is parallel to the table movement. However, the purpose of all coordinate measuring systems used is the same: to provide a method of aligning the spindle at the precise location where a hole is to be produced. Since the work table of a jig borer moves in two directions, the



JIG BORING

coordinate system of dimensioning is used, where dimensions are given from two perpendicular reference axes, usually the sides of the workpiece, frequently its upper left-hand corner. See Fig. 1C. Jig-Boring Practice.—The four basic steps to follow to locate and machine a hole on a jig borer are: Align and Clamp the Workpiece: The first consideration in placing the workpiece on the jig-borer table should be the relation of the coordinate measuring system of the jig borer to the coordinate dimensions on the drawing. Therefore, the coordinate measuring system is designed so that the readings of the coordinate measurements are direct when the table is moved toward the left and when it is moved toward the column of the jig borer. The result would be the same if the spindle were moved toward the right and away from the column, with the workpiece situated in such a position that one reference axis is located at the left and the other axis at the back, toward the column. If the holes to be bored are to pass through the bottom of the workpiece, then the workpiece must be placed on precision parallel bars. In order to prevent the force exerted by the clamps from bending the workpiece the parallel bars are placed directly under the clamps, which hold the workpiece on the table. The reference axes of the workpiece must also be aligned with respect to the transverse and longitudinal table movements before it is firmly clamped. This alignment can be done with a dial-test indicator held in the spindle of the jig borer and bearing against the longitudinal reference edge. As the table is traversed in the longitudinal direction, the workpiece is adjusted until the dial-test indicator readings are the same for all positions. Locate the Two Reference Axes of the Workpiece with Respect to the Spindle: T h e j i g borer table is now moved to position the workpiece in a precise and known location from where it can be moved again to the location of the holes to be machined. Since all the holes are dimensioned from the two reference axes, the most convenient position to start from is where the axis of the jig-borer spindle and the intersection of the two workpiece reference axes are aligned. This is called the starting position, which is similar to a zero reference position. When so positioned, the longitudinal and transverse measuring systems of the jig borer are set to read zero. Occasionally, the reference axes are located outside the body of the workpiece: a convenient edge or hole on the workpiece is picked up as the starting position, and the dimensions from this point to the reference axes are set on the positioning measuring system. Locate the Hole: Precise coordinate table movements are used to position the workpiece so that the spindle axis is located exactly where the hole is to be machined. When the measuring system has been set to zero at the starting position, the coordinate readings at the hole location will be the same as the coordinate dimensions of the hole center. The movements to each hole must be made in one direction for both the transverse and longitudinal directions, to eliminate the effect of any backlash in the lead screw. The usual table movements are toward the left and toward the column. The most convenient sequence on machines using micrometer dials as position indicators (machines with lead screws) is to machine the hole closest to the starting position first and then the next closest, and so on. On jig borers using end measuring rods, the opposite sequence is followed: The farthest hole is machined first and then the next farthest, and so on, since it is easier to remove end rods and replace them with shorter rods. Drill and Bore Hole to Size: The sequence of operations used to produce a hole on a jig borer is as follows: 1) a short, stiff drill, such as a center drill, that will not deflect when cutting should be used to spot a hole when the work and the axis of the machine tool spindle are located at the exact position where the hole is wanted; 2) the initial hole is made by a twist drill; and 3) a single-point boring tool that is set to rotate about the axis of the machine tool spindle is then used to generate a cut surface that is concentric to the axis of rotation.


Machinery's Handbook 27th Edition JIG BORING

987

Heat will be generated by the drilling operation, so it is good practice to drill all the holes first, and then allow the workpiece to cool before the holes are bored to size. Transfer of Tolerances.—All of the dimensions that must be accurately held on precision machines and engine parts are usually given a tolerance. And when such dimensions are changed from the conventional to the coordinate system of dimensioning, the tolerances must also be included. Because of their importance, the transfer of the tolerances must be done with great care, keeping in mind that the sum of the tolerances of any pair of dimensions in the coordinate system must not be larger than the tolerance of the dimension that they replaced in the conventional system. An example is given in Fig. 1. The first step in the procedure is to change the tolerances given in Fig. 1A to equal, bilateral tolerances given in Fig. 1B. For example, the dimension 2.125+.003−.001 has a total tolerance of 0.004. The equal, bilateral tolerance would be plus or minus one-half of this value, or ±.002. Then to keep the limiting dimensions the same, the basic dimension must be changed to 2.126, in order to give the required values of 2.128 and 2.124. When changing to equal, bilateral tolerances, if the upper tolerance is decreased (as in this example), the basic dimension must be increased by a like amount. The upper tolerance was decreased by 0.003 − 0.002 = 0.001; therefore, the basic dimension was increased by 0.001 to 2.126. Conversely, if the upper tolerance is increased, the basic dimension is decreased. The next step is to transfer the revised basic dimension to the coordinate dimensioning system. To transfer the 2.126 dimension, the distance of the applicable holes from the left reference axis must be determined. The first holes to the right are 0.8750 from the reference axis. The second hole is 2.126 to the right of the first holes. Therefore, the second hole is 0.8750 + 2.126 = 3.0010 to the right of the reference axis. This value is then the coordinate dimension for the second hole, while the 0.8750 value is the coordinate dimension of the first two, vertically aligned holes. This procedure is followed for all the holes to find their distances from the two reference axes. These values are given in Fig. 1C. The final step is to transfer the tolerances. The 2.126 value in Fig. 1B has been replaced by the 0.8750 and 3.0010 values in Fig. 1C. The 2.126 value has an available tolerance of ±0.002. Dividing this amount equally between the two replacement values gives 0.8750 ± 0.001 and 3.0010 ± 0.001. The sum of these tolerances is .002, and as required, does not exceed the tolerance that was replaced. Next transfer the tolerance of the 0.502 dimension. Divide the available tolerance, ±0.002, equally between the two replacement values to yield 3.0010 ±0.001 and 3.5030 ±0.001. The sum of these two tolerances equals the replaced tolerance, as required. However, the 1.125 value of the last hole to the right (coordinate dimension 4.6280 in.) has a tolerance of only ±0.001. Therefore, the sum of the tolerances on the 3.5030 and 4.6280 values cannot be larger than 0.001. Dividing this tolerance equally would give 3.5030 ± .0005 and 4.6280 ±0.0005. This new, smaller tolerance replaces the ± 0.001 tolerance on the 3.5030 value in order to satisfy all tolerance sum requirements. This example shows how the tolerance of a coordinate value is affected by more than one other dimensional requirement. The following discussion will summarize the various tolerances listed in Fig. 1C. For the 0.8750 ± 0.0010 dimension, the ± 0.0010 tolerance together with the ± 0.0010 tolerance on the 3.0010 dimension is required to maintain the ± 0.002 tolerance of the 2.126 dimension. The ± .0005 tolerances on the 3.5030 and 4.2680 dimensions are required to maintain the ± 0.001 tolerance of the 1.125 dimension, at the same time as the sum of the ± .0005 tolerance on the 3.5030 dimension and the ± 0.001 tolerance on the 3.0010 dimension does not exceed the ± 0.002 tolerance on the replaced 0.503 dimension. The ± 0.0005 tolerances on the 1.0000 and 2.0000 values maintain the ± 0.001 tolerance on the 1.0000 value given at the right in Fig. 1A. The ± 0.0045 tolerance on the 3.0000 dimension together with the ± 0.0005 tolerance on the 1.0000 value maintains the ± .005 tolerance on the 2.0000 dimension of Fig. 1A. It should be noted that the 2.000 ± .005 dimension in Fig. 1A was replaced by the 1.0000 and 3.0000 dimensions in Fig. 1C. Each of these values could have had a tol-



JIG BORING ±.005

1.000 ±.001

1.000

±.005

2.000

±.005

2.125

.875

+.003 –.001

1.125 +.004

.500 –.000

A

±.005

1.000 ±.001

1.000

±.005

2.000

±.002

±.005

±.001

2.126

.875

1.125 ±.002

B

Ref.

Ref.

.502

±.0005

1.000 ±.001

1.000

±.0005

2.000 ±.0045

±.0005

4.6280

±.0005

3.5030

±.0010

3.0010

.8750

±.0010

3.000

C

Fig. 1. (A) Conventional Dimensions, Mixed Tolerances; (B) Conventional Dimensions, All Equal, Bilateral Tolerances; and (C) Coordinate Dimensions



989

erance of ± 0.0025, except that the tolerance on the 1.0000 dimension on the left in Fig. 1A is also bound by the ± 0.001 tolerance on the 1.0000 dimension on the right, thus the ± 0.0005 tolerance value is used. This procedure requires the tolerance on the 3.0000 value to be increased to ± 0.0045. Determining Hole Coordinates On the following pages are given tables of the lengths of chords for spacing off the circumferences of circles. The object of these tables is to make possible the division of the periphery into a number of equal parts without trials with the dividers. The first table, Table 10, is calculated for circles having a diameter equal to 1. For circles of other diameters, the length of chord given in the table should be multiplied by the diameter of the circle. Table 10 may be used by toolmakers when setting “buttons” in circular formation. Assume that it is required to divide the periphery of a circle of 20 inches diameter into thirty-two equal parts. From the table the length of the chord is found to be 0.098017 inch, if the diameter of the circle were 1 inch. With a diameter of 20 inches the length of the chord for one division would be 20 × 0.098017 = 1.9603 inches. Another example in metric units: For a 100 millimeter diameter requiring 5 equal divisions, the length of the chord for one division would be 100 × 0.587785 = 58.7785 millimeters. Tables 11a and 11b starting on page 991 are additional tables for the spacing off of circles; the tables, in this case, being worked out for diameters from 1⁄16 inch to 14 inches. As an example, assume that it is required to divide a circle having a diameter of 61⁄2 inches into seven equal parts. Find first, in the column headed “6” and in line with 7 divisions, the length of the chord for a 6-inch circle, which is 2.603 inches. Then find the length of the chord for a 1⁄2-inch diameter circle, 7 divisions, which is 0.217. The sum of these two values, 2.603 + 0.217 = 2.820 inches, is the length of the chord required for spacing off the circumference of a 61⁄2-inch circle into seven equal divisions. As another example, assume that it is required to divide a circle having a diameter of 923⁄32 inches into 15 equal divisions. First find the length of the chord for a 9-inch circle, which is 1.871 inch. The length of the chord for a 23⁄32-inch circle can easily be estimated from the table by taking the value that is exactly between those given for 11⁄16 and 3⁄4 inch. The value for 11⁄16 inch is 0.143, and for 3⁄4 inch, 0.156. For 23⁄32, the value would be 0.150. Then, 1.871 + 0.150 = 2.021 inches. Hole Coordinate Dimension Factors for Jig Boring.—Tables of hole coordinate dimension factors for use in jig boring are given in Tables 12 through 15 starting on page 993. The coordinate axes shown in the figure accompanying each table are used to reference the tool path; the values listed in each table are for the end points of the tool path. In this machine coordinate system, a positive Y value indicates that the effective motion of the tool with reference to the work is toward the front of the jig borer (the actual motion of the jig borer table is toward the column). Similarly, a positive X value indicates that the effective motion of the tool with respect to the work is toward the right (the actual motion of the jig borer table is toward the left). When entering data into most computer-controlled jig borers, current practice is to use the more familiar Cartesian coordinate axis system in which the positive Y direction is “up” (i.e., pointing toward the column of the jig borer). The computer will automatically change the signs of the entered Y values to the signs that they would have in the machine coordinate system. Therefore, before applying the coordinate dimension factors given in the tables, it is important to determine the coordinate system to be used. If a Cartesian coordinate system is to be used for the tool path, then the sign of the Y values in the tables must be changed, from positive to negative and from negative to positive. For example, when programming for a three-hole type A circle using Cartesian coordinates, the Y values from Table 14 would be y1 = + 0.50000, y2 = −0.25000, and y3 = −0.25000.



JIG BORING Table 10. Lengths of Chords for Spacing Off the Circumferences of Circles with a Diameter Equal to 1 (English or metric units)

No. of Spaces 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40

Length of Chord 0.866025 0.707107 0.587785 0.500000 0.433884 0.382683 0.342020 0.309017 0.281733 0.258819 0.239316 0.222521 0.207912 0.195090 0.183750 0.173648 0.164595 0.156434 0.149042 0.142315 0.136167 0.130526 0.125333 0.120537 0.116093 0.111964 0.108119 0.104528 0.101168 0.098017 0.095056 0.092268 0.089639 0.087156 0.084806 0.082579 0.080467 0.078459

No. of Spaces 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78

Length of Chord 0.076549 0.074730 0.072995 0.071339 0.069756 0.068242 0.066793 0.065403 0.064070 0.062791 0.061561 0.060378 0.059241 0.058145 0.057089 0.056070 0.055088 0.054139 0.053222 0.052336 0.051479 0.050649 0.049846 0.049068 0.048313 0.047582 0.046872 0.046183 0.045515 0.044865 0.044233 0.043619 0.043022 0.042441 0.041876 0.041325 0.040789 0.040266

No. of Spaces 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116

Length of Chord 0.039757 0.039260 0.038775 0.038303 0.037841 0.037391 0.036951 0.036522 0.036102 0.035692 0.035291 0.034899 0.034516 0.034141 0.033774 0.033415 0.033063 0.032719 0.032382 0.032052 0.031728 0.031411 0.031100 0.030795 0.030496 0.030203 0.029915 0.029633 0.029356 0.029085 0.028818 0.028556 0.028299 0.028046 0.027798 0.027554 0.027315 0.027079

No. of Spaces 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154

Length of Chord 0.026848 0.026621 0.026397 0.026177 0.025961 0.025748 0.025539 0.025333 0.025130 0.024931 0.024734 0.024541 0.024351 0.024164 0.023979 0.023798 0.023619 0.023443 0.023269 0.023098 0.022929 0.022763 0.022599 0.022438 0.022279 0.022122 0.021967 0.021815 0.021664 0.021516 0.021370 0.021225 0.021083 0.020942 0.020804 0.020667 0.020532 0.020399

For circles of other diameters, multiply length given in table by diameter of circle. Example:In a drill jig, 8 holes, each 1⁄2 inch diameter, were spaced evenly on a 6-inch diameter circle. To test the accuracy of the jig, plugs were placed in adjacent holes, and the distance over the plugs was measured with a micrometer. What should be the micrometer reading? Solution: The micrometer reading equals the diameter of one plug plus 6 times the chordal distance between adjacent hole centers given in the table above. Thus, the reading should be 1⁄2 + (6 × 0382683) = 2.796098 inches.



Table 11a. Table for Spacing Off the Circumferences of Circles Diameter of Circle to be Spaced Off No. of Divisions

Degrees in Arc

1⁄ 16

1⁄ 8

3⁄ 16

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

9⁄ 16

5⁄ 8

11⁄ 16

3⁄ 4

13⁄ 16

7⁄ 8

15⁄ 16

Length of Chord 120 90 72 60

8 9 10 11

45 40 36

12 13

30

51 3⁄7

32 8⁄11 27 9⁄13

0.054 0.044 0.037 0.031 0.027

0.108 0.088 0.073 0.063 0.054

0.162 0.133 0.110 0.094 0.081

0.217 0.177 0.147 0.125 0.108

0.271 0.221 0.184 0.156 0.136

0.325 0.265 0.220 0.188 0.163

0.379 0.309 0.257 0.219 0.190

0.433 0.354 0.294 0.250 0.217

0.487 0.398 0.331 0.281 0.244

0.541 0.442 0.367 0.313 0.271

0.595 0.486 0.404 0.344 0.298

0.650 0.530 0.441 0.375 0.325

0.704 0.575 0.478 0.406 0.353

0.758 0.619 0.514 0.438 0.380

0.812 0.663 0.551 0.469 0.407

0.024 0.021 0.019 0.018

0.048 0.043 0.039 0.035

0.072 0.064 0.058 0.053

0.096 0.086 0.077 0.070

0.120 0.107 0.097 0.088

0.144 0.128 0.116 0.106

0.167 0.150 0.135 0.123

0.191 0.171 0.155 0.141

0.215 0.192 0.174 0.158

0.239 0.214 0.193 0.176

0.263 0.235 0.212 0.194

0.287 0.257 0.232 0.211

0.311 0.278 0.251 0.229

0.335 0.299 0.270 0.247

0.359 0.321 0.290 0.264

0.016 0.015

0.032 0.030

0.049 0.045

0.065 0.060

0.081 0.075

0.097 0.090

0.113 0.105

0.129 0.120

0.146 0.135

0.162 0.150

0.178 0.165

0.194 0.179

0.210 0.194

0.226 0.209

0.243 0.224

14

25 5⁄7

0.014

0.028

0.042

0.056

0.069

0.083

0.097

0.111

0.125

0.139

0.153

0.167

0.181

0.195

0.209

15 16

24

0.013 0.012

0.026 0.024

0.039 0.037

0.052 0.049

0.065 0.061

0.078 0.073

0.091 0.085

0.104 0.098

0.117 0.110

0.130 0.122

0.143 0.134

0.156 0.146

0.169 0.159

0.182 0.171

0.195 0.183

22 1⁄2

17

21 3⁄17

0.011

0.023

0.034

0.046

0.057

0.069

0.080

0.092

0.103

0.115

0.126

0.138

0.149

0.161

0.172

18 19

20

0.011 0.010

0.022 0.021

0.033 0.031

0.043 0.041

0.054 0.051

0.065 0.062

0.076 0.072

0.087 0.082

0.098 0.093

0.109 0.103

0.119 0.113

0.130 0.123

0.141 0.134

0.152 0.144

0.163 0.154

20 21

18 17 1⁄7

0.010 0.009

0.020 0.019

0.029 0.028

0.039 0.037

0.049 0.047

0.059 0.056

0.068 0.065

0.078 0.075

0.088 0.084

0.098 0.093

0.108 0.102

0.117 0.112

0.127 0.121

0.137 0.130

0.147 0.140

22

16 4⁄11

0.009

0.018

0.027

0.036

0.044

0.053

0.062

0.071

0.080

0.089

0.098

0.107

0.116

0.125

0.133

23

15 15⁄23

0.009

0.017

0.026

0.034

0.043

0.051

0.060

0.068

0.077

0.085

0.094

0.102

0.111

0.119

0.128

24 25

15

0.008 0.008

0.016 0.016

0.024 0.023

0.033 0.031

0.041 0.039

0.049 0.047

0.057 0.055

0.065 0.063

0.073 0.070

0.082 0.078

0.090 0.086

0.098 0.094

0.106 0.102

0.114 0.110

0.122 0.117

26

13 11⁄13

0.008

0.015

0.023

0.030

0.038

0.045

0.053

0.060

0.068

0.075

0.083

0.090

0.098

0.105

0.113

28

12 6⁄7

0.007

0.014

0.021

0.028

0.035

0.042

0.049

0.056

0.063

0.070

0.077

0.084

0.091

0.098

0.105

30 32

12

0.007 0.006

0.013 0.012

0.020 0.018

0.026 0.025

0.033 0.031

0.039 0.037

0.046 0.043

0.052 0.049

0.059 0.055

0.065 0.061

0.072 0.067

0.078 0.074

0.085 0.080

0.091 0.086

0.098 0.092

18 18⁄19

14

11

2⁄ 5

1⁄ 4

JIG BORING

3 4 5 6 7

991



992

Table 11b. Table for Spacing Off the Circumferences of Circles Diameter of Circle to be Spaced Off No. of Divisions

Degrees in Arc

1

2

3

4

5

6

7

8

9

10

11

12

13

14

Length of Chord 120 90 72 60

8 9 10 11

45 40 36

12 13

30

518⁄7

328⁄11 279⁄13

0.866 0.707 0.588 0.500 0.434

1.732 1.414 1.176 1.000 0.868

2.598 2.121 1.763 1.500 1.302

3.464 2.828 2.351 2.000 1.736

4.330 3.536 2.939 2.500 2.169

5.196 4.243 3.527 3.000 2.603

6.062 4.950 4.114 3.500 3.037

6.928 5.657 4.702 4.000 3.471

7.794 6.364 5.290 4.500 3.905

8.660 7.071 5.878 5.000 4.339

9.526 7.778 6.466 5.500 4.773

10.392 8.485 7.053 6.000 5.207

11.258 9.192 7.641 6.500 5.640

12.124 9.899 8.229 7.000 6.074

0.383 0.342 0.309 0.282

0.765 0.684 0.618 0.563

1.148 1.026 0.927 0.845

1.531 1.368 1.236 1.127

1.913 1.710 1.545 1.409

2.296 2.052 1.854 1.690

2.679 2.394 2.163 1.972

3.061 2.736 2.472 2.254

3.444 3.078 2.781 2.536

3.827 3.420 3.090 2.817

4.210 3.762 3.399 3.099

4.592 4.104 3.708 3.381

4.975 4.446 4.017 3.663

5.358 4.788 4.326 3.944

0.259 0.239

0.518 0.479

0.776 0.718

1.035 0.957

1.294 1.197

1.553 1.436

1.812 1.675

2.071 1.915

2.329 2.154

2.588 2.393

2.847 2.632

3.106 2.872

3.365 3.111

3.623 3.350

14

255⁄7

0.223

0.445

0.668

0.890

1.113

1.335

1.558

1.780

2.003

2.225

2.448

2.670

2.893

3.115

15 16

24

0.208 0.195

0.416 0.390

0.624 0.585

0.832 0.780

1.040 0.975

1.247 1.171

1.455 1.366

1.663 1.561

1.871 1.756

2.079 1.951

2.287 2.146

2.495 2.341

2.703 2.536

2.911 2.731

221⁄2

17

213⁄17

0.184

0.367

0.551

0.735

0.919

1.102

1.286

1.470

1.654

1.837

2.021

2.205

2.389

2.572

18 19

20

0.174 0.165

0.347 0.329

0.521 0.494

0.695 0.658

0.868 0.823

1.042 0.988

1.216 1.152

1.389 1.317

1.563 1.481

1.736 1.646

1.910 1.811

2.084 1.975

2.257 2.140

2.431 2.304

20 21

18 171⁄7

0.156 0.149

0.313 0.298

0.469 0.447

0.626 0.596

0.782 0.745

0.939 0.894

1.095 1.043

1.251 1.192

1.408 1.341

1.564 1.490

1.721 1.639

1.877 1.789

2.034 1.938

2.190 2.087

22

164⁄11

0.142

0.285

0.427

0.569

0.712

0.854

0.996

1.139

1.281

1.423

1.565

1.708

1.850

1.992

23

1515⁄23

0.136

0.272

0.408

0.545

0.681

0.817

0.953

1.089

1.225

1.362

1.498

1.634

1.770

1.906

24 25

15 142⁄5

0.131 0.125

0.261 0.251

0.392 0.376

0.522 0.501

0.653 0.627

0.783 0.752

0.914 0.877

1.044 1.003

1.175 1.128

1.305 1.253

1.436 1.379

1.566 1.504

1.697 1.629

1.827 1.755

26

1311⁄13

0.121

0.241

0.362

0.482

0.603

0.723

0.844

0.964

1.085

1.205

1.326

1.446

1.567

1.688

28

126⁄7

0.112

0.224

0.336

0.448

0.560

0.672

0.784

0.896

1.008

1.120

1.232

1.344

1.456

1.568

30 32

12

0.105 0.098

0.209 0.196

0.314 0.294

0.418 0.392

0.523 0.490

0.627 0.588

0.732 0.686

0.836 0.784

0.941 0.882

1.045 0.980

1.150 1.078

1.254 1.176

1.359 1.274

1.463 1.372

1818⁄19

111⁄4

See Determining Hole Coordinates on page 989 for explanatory matter.


JIG BORING

3 4 5 6 7


993

Table 12. Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles (English or Metric Units)

The diagram shows a type “A” circle for a 5-hole circle. Coordinates x, y are given in the table for hole circles of from 3 to 28 holes. Dimensions are for holes numbered in a counterclockwise direction (as shown). Dimensions given are based upon a hole circle of unit diameter. For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 3.

3 Holes x1 y1 x2 y2 x3 y3

0.50000 0.00000 0.06699 0.75000 0.93301 0.75000

4 Holes x1 y1 x2 y2 x3 y3 x4 y4

10 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10

0.50000 0.00000 0.20611 0.09549 0.02447 0.34549 0.02447 0.65451 0.20611 0.90451 0.50000 1.00000 0.79389 0.90451 0.97553 0.65451 0.97553 0.34549 0.79389 0.09549

5 Holes

0.50000 x1 0.00000 y1 0.00000 x2 0.50000 y2 0.50000 x3 1.00000 y3 1.00000 x4 0.50000 y4 x5 y5

11 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11

0.50000 0.00000 0.22968 0.07937 0.04518 0.29229 0.00509 0.57116 0.12213 0.82743 0.35913 0.97975 0.64087 0.97975 0.87787 0.82743 0.99491 0.57116 0.95482 0.29229 0.77032 0.07937

0.50000 0.00000 0.02447 0.34549 0.20611 0.90451 0.79389 0.90451 0.97553 0.34549

6 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6

12 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12

0.50000 0.00000 0.25000 0.06699 0.06699 0.25000 0.00000 0.50000 0.06699 0.75000 0.25000 0.93301 0.50000 1.00000 0.75000 0.93301 0.93301 0.75000 1.00000 0.50000 0.93801 0.25000 0.75000 0.06699

0.50000 0.00000 0.06699 0.25000 0.06699 0.75000 0.50000 1.00000 0.93301 0.75000 0.93301 0.25000

7 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7

13 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13

0.50000 0.00000 0.26764 0.05727 0.08851 0.21597 0.00365 0.43973 0.03249 0.67730 0.16844 0.87426 0.38034 0.98547 0.61966 0.98547 0.83156 0.87426 0.96751 0.67730 0.99635 0.43973 0.91149 0.21597 0.73236 0.05727

0.50000 0.00000 0.10908 0.18826 0.01254 0.61126 0.28306 0.95048 0.71694 0.95048 0.98746 0.61126 0.89092 0.18826

8 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8

14 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14

0.50000 0.00000 0.28306 0.04952 0.10908 0.18826 0.01254 0.38874 0.01254 0.61126 0.10908 0.81174 0.28306 0.95048 0.50000 1.00000 0.71694 0.95048 0.89092 0.81174 0.98746 0.61126 0.98746 0.38874 0.89092 0.18826 0.71694 0.04952

x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15

9 Holes

0.50000 x1 0.50000 0.00000 y1 0.00000 0.14645 x2 0.17861 0.14645 y2 0.11698 0.00000 x3 0.00760 0.50000 y3 0.41318 0.14645 x4 0.06699 0.85355 y4 0.75000 0.50000 x5 0.32899 1.00000 y5 0.96985 0.85355 x6 0.67101 0.85355 y6 0.96985 1.00000 x7 0.93301 0.50000 y7 0.75000 0.85355 x8 0.99240 0.14645 y8 0.41318 x9 0.82139 y9 0.11698 15 Holes 16 Holes 0.50000 0.00000 0.29663 0.04323 0.12843 0.16543 0.02447 0.34549 0.00274 0.55226 0.06699 0.75000 0.20611 0.90451 0.39604 0.98907 0.60396 0.98907 0.79389 0.90451 0.93301 0.75000 0.99726 0.55226 0.97553 0.34549 0.87157 0.16543 0.70337 0.04323


x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16

0.50000 0.00000 0.30866 0.03806 0.14645 0.14645 0.03806 0.30866 0.00000 0.50000 0.03806 0.69134 0.14645 0.85355 0.30866 0.96194 0.50000 1.00000 0.69134 0.96194 0.85355 0.85355 0.96194 0.69134 1.00000 0.50000 0.96194 0.30866 0.85355 0.14645 0.69134 0.03806


JIG BORING Table 12. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles (English or Metric Units)


17 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17

0.50000 0.00000 0.31938 0.03376 0.16315 0.13050 0.05242 0.27713 0.00213 0.45387 0.01909 0.63683 0.10099 0.80132 0.23678 0.92511 0.40813 0.99149 0.59187 0.99149 0.76322 0.92511 0.89901 0.80132 0.98091 0.63683 0.99787 0.45387 0.94758 0.27713 0.83685 0.13050 0.68062 0.03376

18 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18

24Holes x1 y1 x2 y2 x3

0.50000 0.00000 0.37059 0.01704 0.25000

0.50000 0.00000 0.32899 0.03015 0.17861 0.11698 0.06699 0.25000 0.00760 0.41318 0.00760 0.58682 0.06699 0.75000 0.17861 0.88302 0.32899 0.96985 0.50000 1.00000 0.67101 0.96985 0.82139 0.88302 0.93301 0.75000 0.99240 0.58682 0.99240 0.41318 0.93301 0.25000 0.82139 0.11698 0.67101 0.03015

19 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19

25 Holes x1 y1 x2 y2 x3

0.50000 0.00000 0.37566 0.01571 0.25912

0.50000 0.00000 0.33765 0.02709 0.19289 0.10543 0.08142 0.22653 0.01530 0.37726 0.00171 0.54129 0.04211 0.70085 0.13214 0.83864 0.26203 0.93974 0.41770 0.99318 0.58230 0.99318 0.73797 0.93974 0.86786 0.83864 0.95789 0.70085 0.99829 0.54129 0.98470 0.37726 0.91858 0.22658 0.80711 0.10543 0.66235 0.02709

20 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20


0.50000 x1 0.00000 y1 0.38034 x2 0.01453 y2 0.26764 x3

0.50000 0.00000 0.34549 0.02447 0.20611 0.09549 0.09549 0.20611 0.02447 0.34549 0.00000 0.50000 0.02447 0.65451 0.09549 0.79389 0.20611 0.90451 0.34549 0.97553 0.50000 1.00000 0.65451 0.97553 0.79389 0.90451 0.90451 0.79389 0.97553 0.65451 1.00000 0.50000 0.97553 0.34549 0.90451 0.20611 0.79389 0.09549 0.65451 0.02447

21 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21

27 Holes 0.50000 x1 0.00000 y1 0.38469 x2 0.01348 y2 0.27560 x3

0.50000 0.00000 0.35262 0.02221 0.21834 0.08688 0.10908 0.18826 0.03456 0.31733 0.00140 0.46263 0.01254 0.61126 0.06699 0.75000 0.15991 0.86653 0.28306 0.95048 0.42548 0.99442 0.57452 0.99442 0.71694 0.95048 0.84009 0.86653 0.93301 0.75000 0.98746 0.61126 0.99860 0.46263 0.96544 0.31733 0.89092 0.18826 0.78166 0.08688 0.64738 0.02221

22 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22

0.50000 0.00000 0.35913 0.02025 0.22968 0.07937 0.12213 0.17257 0.04518 0.29229 0.00509 0.42884 0.00509 0.57116 0.04518 0.70771 0.12213 0.82743 0.22968 0.92063 0.35913 0.97975 0.50000 1.00000 0.64087 0.97975 0.77032 0.92063 0.87787 0.82743 0.95482 0.70771 0.99491 0.57116 0.99491 0.42884 0.95482 0.29229 0.87787 0.17257 0.77032 0.07937 0.64087 0.02025

28 Holes 0.50000 0.00000 0.38874 0.01254 0.28306


23 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23

0.50000 0.00000 0.36510 0.01854 0.24021 0.07279 0.13458 0.15872 0.05606 0.26997 0.01046 0.39827 0.00117 0.53412 0.02887 0.66744 0.09152 0.78834 0.18446 0.88786 0.30080 0.95861 0.43192 0.99534 0.56808 0.99534 0.69920 0.95861 0.81554 0.88786 0.90848 0.78834 0.97113 0.66744 0.99883 0.53412 0.98954 0.39827 0.94394 0.26997 0.86542 0.15872 0.75979 0.07279 0.63490 0.01854


995

Table 12. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles (English or Metric Units)


24Holes y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24

0.06699 0.14645 0.14645 0.06699 0.25000 0.01704 0.37059 0.00000 0.50000 0.01704 0.62941 0.06699 0.75000 0.14645 0.85355 0.25000 0.93301 0.37059 0.98296 0.50000 1.00000 0.62941 0.98296 0.75000 0.93301 0.85355 0.85355 0.93301 0.75000 0.98296 0.62941 1.00000 0.50000 0.98296 0.37059 0.93301 0.25000 0.85355 0.14645 0.75000 0.6699 0.62941 0.01704

25 Holes y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25

0.06185 0.15773 0.13552 0.07784 0.23209 0.02447 0.34549 0.00099 0.46860 0.00886 0.59369 0.04759 0.71289 0.11474 0.81871 0.20611 0.90451 0.31594 0.96489 0.43733 0.99606 0.56267 0.99606 0.68406 0.96489 0.79389 0.90451 0.88526 0.81871 0.95241 0.71289 0.99114 0.59369 0.99901 0.46860 0.97553 0.34549 0.92216 0.23209 0.84227 0.13552 0.74088 0.06185 0.62434 0.01571

26 Holes y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26

0.05727 0.16844 0.12574 0.08851 0.21597 0.03249 0.32270 0.00365 0.43973 0.00365 0.56027 0.03249 0.67730 0.08851 0.78403 0.16844 0.87426 0.26764 0.94273 0.38034 0.98547 0.50000 1.00000 0.61966 0.98547 0.73236 0.94273 0.83156 0.87426 0.91149 0.78403 0.96751 0.67730 0.99635 0.56027 0.99635 0.43973 0.96751 0.32270 0.91149 0.21597 0.83156 0.12574 0.73236 0.05727 0.61966 0.01453

27 Holes y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27

0.05318 0.17861 0.11698 0.09894 0.20142 0.04089 0.30196 0.00760 0.41318 0.00085 0.52907 0.02101 0.64340 0.06699 0.75000 0.13631 0.84312 0.22525 0.91774 0.32899 0.96985 0.44195 0.99662 0.55805 0.99662 0.67101 0.96985 0.77475 0.91774 0.86369 0.84312 0.93301 0.75000 0.97899 0.64340 0.99915 0.52907 0.99240 0.41318 0.95911 0.30196 0.90106 0.20142 0.82139 0.11698 0.72440 0.05318 0.61531 0.01348

28 Holes y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 x28 y28

0.04952 0.18826 0.10908 0.10908 0.18826 0.04952 0.28306 0.01254 0.38874 0.00000 0.50000 0.01254 0.61126 0.04952 0.71694 0.10908 0.81174 0.18826 0.89092 0.28306 0.95048 0.38874 0.98746 0.50000 1.00000 0.61126 0.98746 0.71694 0.95048 0.81174 0.89092 0.89092 0.81174 0.95048 0.71694 0.98746 0.61126 1.00000 0.50000 0.98746 0.38874 0.95048 0.28306 0.89092 0.18826 0.81174 0.10908 0.71694 0.04952 0.61126 0.01254



JIG BORING Table 13. Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles (English or Metric Units)

The diagram shows a type “B” circle for a 5-hole circle. Coordinates x, y are given in the table for hole circles of from 3 to 28 holes. Dimensions are for holes numbered in a counterclockwise direction (as shown). Dimensions given are based upon a hole circle of unit diameter. For a hole circle of, say, 3-inch or 3-centimeter diameter, multiply table values by 3.


0.06699 0.25000 0.50000 1.00000 0.93301 0.25000


0.14645 0.14645 0.14645 0.85355 0.85355 0.85355 0.85355 0.14645


0.34549 0.02447 0.09549 0.20611 0.00000 0.50000 0.09549 0.79389 0.34549 0.97553 0.65451 0.97553 0.90451 0.79389 1.00000 0.50000 0.90451 0.20611 0.65451 0.02447

5 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5


0.35913 0.02025 0.12213 0.17257 0.00509 0.42884 0.04518 0.70771 0.22968 0.92063 0.50000 1.00000 0.77032 0.92063 0.95482 0.70771 0.99491 0.42884 0.87787 0.17257 0.64087 0.02025

0.20611 0.09549 0.02447 0.65451 0.50000 1.00000 0.97553 0.65451 0.79389 0.09549



0.37059 0.01704 0.14645 0.14645 0.01704 0.37059 0.01704 0.62941 0.14645 0.85355 0.37059 0.98296 0.62941 0.98296 0.85355 0.85355 0.98296 0.62941 0.98296 0.37059 0.85355 0.14645 0.62941 0.01704

0.25000 0.06699 0.00000 0.50000 0.25000 0.93301 0.75000 0.93301 1.00000 0.50000 0.75000 0.06699



0.38034 0.01453 0.16844 0.12574 0.03249 0.32270 0.00365 0.56027 0.08851 0.78403 0.26764 0.94273 0.50000 1.00000 0.73236 0.94273 0.91149 0.78403 0.99635 0.56027 0.96751 0.32270 0.83156 0.12574 0.61966 0.01453

0.28306 0.04952 0.01254 0.38874 0.10908 0.81174 0.50000 1.00000 0.89092 0.81174 0.98746 0.38874 0.71694 0.04952



0.38874 0.01254 0.18826 0.10908 0.04952 0.28306 0.00000 0.50000 0.04952 0.71694 0.18826 0.89092 0.38874 0.98746 0.61126 0.98746 0.81174 0.89092 0.95048 0.71694 1.00000 0.50000 0.95048 0.28306 0.81174 0.10908 0.61126 0.01254

0.30866 0.03806 0.03806 0.30866 0.03806 0.69134 0.30866 0.96194 0.69134 0.96194 0.96194 0.69134 0.96194 0.30866 0.69134 0.03806

9 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9

15 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15

0.39604 0.01093 0.20611 0.09549 0.06699 0.25000 0.00274 0.44774 0.02447 0.65451 0.12843 0.83457 0.29663 0.95677 0.50000 1.00000 0.70337 0.95677 0.87157 0.83457 0.97553 0.65451 0.99726 0.44774 0.93301 0.25000 0.79389 0.09549 0.60396 0.01093



0.32899 0.03015 0.06699 0.25000 0.00760 0.58682 0.17861 0.88302 0.50000 1.00000 0.82139 0.88302 0.99240 0.58682 0.93301 0.25000 0.67101 0.03015 16 Holes 0.40245 0.00961 0.22221 0.08427 0.08427 0.22221 0.00961 0.40245 0.00961 0.59755 0.08427 0.77779 0.22221 0.91573 0.40245 0.99039 0.59755 0.99039 0.77779 0.91573 0.91573 0.77779 0.99039 0.59755 0.99039 0.40245 0.91573 0.22221 0.77779 0.08427 0.59755 0.00961


997

Table 13. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles (English or Metric Units)



0.40813 0.00851 0.23678 0.07489 0.10099 0.19868 0.01909 0.36317 0.00213 0.54613 0.05242 0.72287 0.16315 0.86950 0.31938 0.96624 0.50000 1.00000 0.68062 0.96624 0.83685 0.86950 0.94758 0.72287 0.99787 0.54613 0.98091 0.36317 0.89901 0.19868 0.76322 0.07489 0.59187 0.00851


24 Holes

0.41318 0.00760 0.25000 0.06699 0.11698 0.17861 0.03015 0.32899 0.00000 0.50000 0.03015 0.67101 0.11698 0.82139 0.25000 0.93301 0.41318 0.99240 0.58682 0.99240 0.75000 0.93301 0.88302 0.82139 0.96985 0.67101 1.00000 0.50000 0.96985 0.32899 0.88302 0.17861 0.75000 0.06699 0.58682 0.00760


25 Holes

0.41770 0.00682 0.26203 0.06026 0.13214 0.16136 0.04211 0.29915 0.00171 0.45871 0.01530 0.62274 0.08142 0.77347 0.19289 0.89457 0.33765 0.97291 0.50000 1.00000 0.66235 0.97291 0.80711 0.89457 0.91858 0.77347 0.98470 0.62274 0.99829 0.45871 0.95789 0.29915 0.86786 0.16136 0.73797 0.06026 0.58230 0.00682


26 Holes

0.42178 0.00616 0.27300 0.05450 0.14645 0.14645 0.05450 0.27300 0.00616 0.42178 0.00616 0.57822 0.05450 0.72700 0.14645 0.85355 0.27300 0.94550 0.42178 0.99384 0.57822 0.99384 0.72700 0.94550 0.85355 0.85355 0.94550 0.72700 0.99384 0.57822 0.99384 0.42178 0.94550 0.27300 0.85355 0.14645 0.72700 0.05450 0.57822 0.00616


27 Holes

0.42548 0.00558 0.28306 0.04952 0.15991 0.13347 0.06699 0.25000 0.01254 0.38874 0.00140 0.53737 0.03456 0.68267 0.10908 0.81174 0.21834 0.91312 0.35262 0.97779 0.50000 1.00000 0.64738 0.97779 0.78166 0.91312 0.89092 0.81174 0.96544 0.68267 0.99860 0.53737 0.98746 0.38874 0.93301 0.25000 0.84009 0.13347 0.71694 0.04952 0.57452 0.00558


0.42884 0.00509 0.29229 0.04518 0.17257 0.12213 0.07937 0.22968 0.02025 0.35913 0.00000 0.50000 0.02025 0.64087 0.07937 0.77032 0.17257 0.87787 0.29229 0.95482 0.42884 0.99491 0.57116 0.99491 0.70771 0.95482 0.82743 0.87787 0.92063 0.77032 0.97975 0.64087 1.00000 0.50000 0.97975 0.35913 0.92063 0.22968 0.82743 0.12213 0.70771 0.04518 0.57116 0.00509

28 Holes

x1 y1 x2 y2 x3

0.43474 0.00428 0.30866 0.03806 0.19562

x1 y1 x2 y2 x3

0.43733 0.00394 0.31594 0.03511 0.20611

x1 y1 x2 y2 x3

0.43973 0.00365 0.32270 0.03249 0.21597

x1 y1 x2 y2 x3

0.44195 0.00338 0.32899 0.03015 0.22525

x1 y1 x2 y2 x3

0.44402 0.00314 0.33486 0.02806 0.23398

y3

0.10332

y3

0.09549

y3

0.08851

y3

0.08226

y3

0.07664



0.43192 0.00466 0.30080 0.04139 0.18446 0.11214 0.09152 0.21166 0.02887 0.33256 0.00117 0.46588 0.01046 0.60173 0.05606 0.73003 0.13458 0.84128 0.24021 0.92721 0.36510 0.98146 0.50000 1.00000 0.63490 0.98146 0.75979 0.92721 0.86542 0.84128 0.94394 0.73003 0.98954 0.60173 0.99883 0.46588 0.97113 0.33256 0.90848 0.21166 0.81554 0.11214 0.69920 0.04139 0.56808 0.00466


JIG BORING Table 13. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles (English or Metric Units)


x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24

24 Holes 0.10332 0.19562 0.03806 0.30866 0.00428 0.43474 0.00428 0.56526 0.03806 0.69134 0.10332 0.80438 0.19562 0.89668 0.30866 0.96194 0.43474 0.99572 0.56526 0.99572 0.69134 0.96194 0.80438 0.89668 0.89668 0.80438 0.96194 0.69134 0.99572 0.56526 0.99572 0.43474 0.96194 0.30866 0.89668 0.19562 0.80438 0.10332 0.69134 0.03806 0.56526 0.00428

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25

25 Holes 0.11474 0.18129 0.04759 0.28711 0.00886 0.40631 0.00099 0.53140 0.02447 0.65451 0.07784 0.76791 0.15773 0.86448 0.25912 0.93815 0.37566 0.98429 0.50000 1.00000 0.62434 0.98429 0.74088 0.93815 0.84227 0.86448 0.92216 0.76791 0.97553 0.65451 0.99901 0.53140 0.99114 0.40631 0.95241 0.28711 0.88526 0.18129 0.79389 0.09549 0.68406 0.03511 0.56267 0.00394

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26

26 Holes 0.12574 0.16844 0.05727 0.26764 0.01453 0.38034 0.00000 0.50000 0.01453 0.61966 0.05727 0.73236 0.12574 0.83156 0.21597 0.91149 0.32270 0.96751 0.43973 0.99635 0.56027 0.99635 0.67730 0.96751 0.78403 0.91149 0.87426 0.83156 0.94273 0.73236 0.98547 0.61966 1.00000 0.50000 0.98547 0.38034 0.94273 0.26764 0.87426 0.16844 0.78403 0.08851 0.67730 0.03249 0.56027 0.00365

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27

27 Holes 0.13631 0.15688 0.06699 0.25000 0.02101 0.35660 0.00085 0.47093 0.00760 0.58682 0.04089 0.69804 0.09894 0.79858 0.17861 0.88302 0.27560 0.94682 0.38469 0.98652 0.50000 1.00000 0.61531 0.98652 0.72440 0.94682 0.82139 0.88302 0.90106 0.79858 0.95911 0.69804 0.99240 0.58682 0.99915 0.47093 0.97899 0.35660 0.93301 0.25000 0.86369 0.15688 0.77475 0.08226 0.67101 0.03015 0.55805 0.00338

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 x28 y28

28 Holes 0.14645 0.14645 0.07664 0.23398 0.02806 0.33486 0.00314 0.44402 0.00314 0.55598 0.02806 0.66514 0.07664 0.76602 0.14645 0.85355 0.23398 0.92336 0.33486 0.97194 0.44402 0.99686 0.55598 0.99686 0.66514 0.97194 0.76602 0.92336 0.85355 0.85355 0.92336 0.76602 0.97194 0.66514 0.99686 0.55598 0.99686 0.44402 0.97194 0.33486 0.92336 0.23398 0.85355 0.14645 0.76602 0.07664 0.66514 0.02806 0.55598 0.00314



999

Table 14. Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units)



0.00000 −0.50000 −0.43301 +0.25000 +0.43301 +0.25000


0.00000 −0.50000 −0.50000 0.00000 0.00000 +0.50000 +0.50000 0.00000


0.00000 −0.50000 −0.29389 −0.40451 −0.47553 −0.15451 −0.47553 +0.15451 −0.29389 +0.40451 0.00000 +0.50000 +0.29389 +0.40451 +0.47553 +0.15451 +0.47553 −0.15451 +0.29389 −0.40451



0.00000 −0.5000 −0.27032 −0.42063 −0.45482 −0.20771 −0.49491 +0.07116 −0.37787 +0.32743 −0.14087 +0.47975 +0.14087 +0.47975 +0.37787 +0.32743 +0.49491 +0.07116 +0.45482 −0.20771 +0.27032 −0.42063

0.00000 −0.50000 −0.47553 −0.15451 −0.29389 +0.40451 +0.29389 +0.40451 +0.47553 −0.15451



0.00000 −0.50000 −0.25000 −0.43301 −0.43301 −0.25000 −0.50000 0.00000 −0.43301 +0.25000 −0.25000 +0.43301 0.00000 +0.50000 +0.25000 +0.43301 +0.43301 +0.25000 +0.50000 0.00000 +0.43301 −0.25000 +0.25000 −0.43301

0.00000 −0.50000 −0.43301 −0.25000 −0.43301 +0.25000 0.00000 +0.50000 +0.43301 +0.25000 +0.43301 −0.25000



0.00000 −0.50000 −0.23236 −0.44273 −0.41149 −2.28403 −0.49635 −0.06027 −0.46751 +0.17730 − 0.33156 +0.37426 −0.11966 +0.48547 +0.11966 +0.48547 +0.33156 +0.37426 +0.46751 +0.17730 +0.49635 −0.06027 +0.41149 −0.28403 +0.23236 −0.44273

0.00000 −0.50000 −0.39092 −0.31174 −0.48746 +0.11126 −0.21694 +0.45048 +0.21694 +0.45048 +0.48746 +0.11126 +0.39092 −0.31174



0.00000 −0.50000 −0.21694 −0.45048 −0.39092 −0.31174 −0.48746 −0.11126 −0.48746 +0.11126 −0.39092 +0.31174 −0.21694 +0.45048 0.00000 +0.50000 +0.21694 +0.45048 +0.39092 +0.31174 +0.48746 +0.11126 +0.48746 −0.11126 +0.39092 −0.31174 +0.21694 −0.45048

0.00000 −0.50000 −0.35355 −0.35355 −0.50000 0.00000 −0.35355 +0.35355 0.00000 +0.50000 +0.35355 +0.35355 +0.50000 0.00000 +0.35355 −0.35355


15 Holes x1 y1 x2 y2 x3 y3 x4 y4 x5

0.00000 −0.50000 −0.20337 −0.45677 −0.37157 −0.33457 −0.47553 −0.15451 −0.49726 y5 +0.05226 x6 −0.43301 y6 +0.25000 x7 −0.29389 y7 +0.40451 x8 −0.10396 y8 +0.48907 x9 +0.10396 y9 +0.48907 x10 +0.29389 y10 +0.40451 x11 +0.43301 y11 +0.25000 x12 +0.49726 y12 +0.05226 x13 +0.47553 y13 −0.15451 x14 +0.37157 y14 −0.33457 x15 +0.20337 y15 −0.45677



0.00000 −0.50000 −0.32139 −0.38302 −0.49240 −0.08682 −0.43301 +0.25000 −0.17101 +0.46985 +0.17101 +0.46985 +0.43301 +0.25000 +0.49240 −0.08682 +0.32139 −0.38302 16 Holes 0.00000 −0.50000 −0.19134 −0.46194 −0.35355 −0.35355 −0.46194 −0.19134 −0.50000 0.00000 −0.46194 +0.19134 −0.35355 +0.35355 −0.19134 +0.46194 0.00000 +0.50000 +0.19134 +0.46194 +0.35355 +0.35355 +0.46194 +0.19134 +0.50000 0.00000 +0.46194 −0.19134 +0.35355 −0.35355 +0.19134 −0.46194


JIG BORING

Table 14. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units)



0.00000 −0.50000 −0.18062 −0.46624 −0.33685 −0.36950 −0.44758 −0.22287 −0.49787 −0.04613 −0.48091 +0.13683 −0.39901 +0.30132 −0.26322 +0.42511 −0.09187 +0.49149 +0.09187 +0.49149 +0.26322 +0.42511 +0.39901 +0.30132 +0.48091 +0.13683 +0.49787 −0.04613 +0.44758 −0.22287 +0.33685 −0.36950 +0.18062 −0.46624


24 Holes

0.00000 −0.50000 −0.17101 −0.46985 +0.32139 −0.38302 −0.43301 −0.25000 −0.49240 −0.08682 −0.49420 +0.08682 −0.43301 +0.25000 −0.32139 +0.38302 −0.17101 +0.46985 0.00000 +0.50000 +0.17101 +0.46985 +0.32139 +0.38302 +0.43301 +0.25000 +0.49240 +0.08682 +0.49240 −0.08682 +0.43301 −0.25000 +0.32139 −0.38302 +0.17101 −0.46985


25 Holes

x1 y1 x2 y2 x3

0.00000 −0.50000 −0.12941 −0.48296 −0.25000

x1 y1 x2 y2 x3

y3

− 0.43301 y3

0.00000 −0.50000 −0.12434 −0.48429 −0.24088

0.00000 −0.50000 −0.16235 −0.47291 −0.30711 −0.39457 −0.41858 −0.27347 −0.48470 −0.12274 −0.49829 +0.04129 −0.45789 +0.20085 −0.36786 +0.33864 −0.23797 +0.43974 −0.08230 +0.49318 +0.08230 +0.49318 +0.23797 +0.43974 +0.36786 +0.33864 +0.45789 +0.20085 +0.49829 +0.04129 +0.48470 −0.12274 +0.41858 −0.27347 +0.30711 −0.39457 + 0.16235 −0.47291



−0.43815 y3

0.00000 −0.50000 −0.11966 −0.48547 −0.23236

0.000000 −0.50000 −0.15451 −0.47553 −0.29389 −0.40451 −0.40451 −0.29389 −0.47553 −0.15451 −0.50000 0.00000 −0.47553 +0.15451 −0.40451 +0.29389 −0.29389 +0.40451 −0.15451 +0.47553 0.00000 +0.50000 +0.15451 +0.47553 +0.29389 +0.40451 +0.40451 +0.29389 +0.47553 +0.15451 +0.50000 0.00000 +0.47553 −0.15451 +0.40451 −0.29389 +0.29389 −0.40451 +0.15451 −0.47553



−0.44273 y3

0.00000 −0.50000 −0.11531 −0.48652 −0.22440

0.00000 −0.50000 −0.14738 −0.47779 −0.28166 −0.41312 −0.39092 −0.31174 −.046544 −0.18267 −0.49860 −0.03737 −0.48746 +0.11126 −0.43301 +0.25000 −0.34009 +0.36653 −0.21694 +0.45048 −0.07452 +0.49442 +0.07452 +0.49442 +0.21694 +0.45048 +0.34009 +0.36653 +0.43301 +0.25000 +0.48746 +0.11126 +0.49860 −0.03737 +0.46544 −0.18267 +0.39092 −0.31174 +0.28166 −0.41312 +0.14738 −0.47779


0.00000 −0.50000 −0.14087 −0.47975 −0.27032 −0.42063 −0.37787 −0.32743 −0.45482 −0.20771 −0.49491 −0.07116 −0.49491 +0.07116 −0.45482 +0.20771 −0.37787 +0.32743 −0.27032 +0.42063 −0.14087 +0.47975 0.00000 +0.50000 +0.14087 +0.47975 +0.27032 +0.42063 +0.37787 +0.32743 +0.45482 +0.20771 +0.49491 +0.07116 +0.49491 −0.07116 +0.45482 −0.20771 +0.37787 −0.32743 +0.27032 −0.42063 +0.14087 −0.47975


0.00000 −0.50000 −0.11126 −0.48746 −0.21694

−0.44682 y3

−0.45048



0.00000 −0.50000 −0.13490 −0.48146 −0.25979 −0.42721 −0.36542 −0.34128 −0.44394 −0.23003 −0.48954 −0.10173 −0.49883 +0.03412 −0.47113 +0.16744 −0.40848 +0.28834 −0.31554 +0.38786 −0.19920 +0.45861 −0.06808 +0.49534 +0.06808 +0.49534 +0.19920 +0.45861 +0.31554 +0.38786 +0.40848 +0.28834 +0.47113 +0.16744 +0.49883 +0.03412 +0.48954 −0.10173 +0.44394 −0.23003 +0.36542 −0.34128 +0.25979 −0.42721 +0.13490 −0.48146


1001

Table 14. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “A” Hole Circles, Central Coordinates (English or Metric Units)


x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24

24 Holes −0.35355 −0.35355 −0.43301 −0.25000 −0.48296 −0.12941 −0.50000 0.00000 −0.48296 +0.12941 −0.43301 +0.25000 −0.35355 +0.35355 −0.25000 +0.43301 −0.12941 +0.48296 0.00000 +0.50000 +0.12941 +0.48296 +0.25000 +0.43301 +0.35355 +0.35355 +0.43301 +0.25000 +0.48296 +0.12941 +0.50000 0.00000 +0.48296 −0.12941 +0.43301 −0.25000 +0.35355 −0.35355 +0.25000 −0.43301 +0.12941 −0.48296

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25

25 Holes −0.34227 −0.36448 −0.42216 −0.26791 −0.47553 −0.15451 −0.49901 −0.03140 −0.49114 +0.09369 −0.45241 +0.21289 −0.38526 +0.31871 −0.29389 +0.40451 −0.18406 +0.46489 −0.06267 +0.49606 +0.06267 +0.49606 +0.18406 +0.46489 +0.29389 +0.40451 + 0.38526 +0.31871 +0.45241 +0.21289 +0.49114 +0.09369 +0.49901 −0.03140 +0.47553 −0.15451 +0.42216 −0.26791 +0.34227 −0.36448 +0.24088 −0.43815 +0.12434 −0.48429

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26

26 Holes −0.33156 −0.37426 −0.41149 −0.28403 −0.46751 −0.17730 −0.49635 −0.06027 −0.49635 +0.06027 −0.46751 +0.17730 −0.41149 +0.28403 −0.33156 +0.37426 −0.23236 +0.44273 −0.11966 +0.48547 0.00000 +0.50000 +0.11966 +0.48547 +0.23236 +0.44273 +0.33156 +0.37426 +0.41149 +0.28403 +0.46751 +0.17730 +0.49635 +0.06027 +0.49635 −0.06027 +0.46751 −0.17730 +0.41149 −0.28403 +0.33156 −0.37426 +0.23236 −0.44273 +0.11966 −0.48547

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27

27 Holes −0.32139 −0.38302 −0.40106 −0.29858 −0.45911 −0.19804 −0.49240 −0.08682 −0.49915 +0.02907 −0.47899 +0.14340 −0.43301 +0.25000 −0.36369 +0.34312 −0.27475 +0.41774 −0.17101 +0.46985 −0.05805 +0.49662 +0.05805 +0.49662 +0.17101 +0.46985 +0.27475 +0.41774 +0.36369 +0.34312 +0.43301 +0.25000 +0.47899 +0.14340 +0.49915 +0.02907 +0.49240 −0.08682 +0.45911 −0.19804 +0.40106 −0.29858 +0.32139 −0.38302 +0.22440 −0.44682 +0.11531 −0.48652

x4 y4 x5 y5 x6 y6 x7 y7 x8 y8 x9 y9 x10 y10 x11 y11 x12 y12 x13 y13 x14 y14 x15 y15 x16 y16 x17 y17 x18 y18 x19 y19 x20 y20 x21 y21 x22 y22 x23 y23 x24 y24 x25 y25 x26 y26 x27 y27 x28 y28

28 Holes −0.31174 −0.39092 −0.39092 −0.31174 −0.45048 −0.21694 −0.48746 −0.11126 −0.50000 0.00000 −0.48746 +0.11126 −0.45048 +0.21694 −0.39092 +0.31174 −0.31174 +0.39092 −0.21694 +0.45048 −0.11126 +0.48746 0.00000 +0.50000 +0.11126 +0.48746 +0.21694 +0.45048 +0.31174 +0.39092 +0.39092 +0.31174 +0.45048 +0.21694 +0.48746 +0.11126 +0.50000 0.00000 +0.48746 −0.11126 +0.45048 −0.21694 +0.39092 −0.31174 +0.31174 −0.39092 +0.21694 −0.45048 +0.11126 −0.48746



JIG BORING Table 15. Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units)



−0.43301 −0.25000 0.00000 +0.50000 +0.43301 −0.25000

10 Holes x1 −0.15451 y1 −0.47553 x2 −0.40451 y2 −0.29389 x3 −0.50000 y3 0.00000 x4 −0.40451 y4 +0.29389 x5 −0.15451 y5 +0.47553 x6 +0.15451 y6 +0.47553 x7 +0.40451 y7 +0.29389 x8 +0.50000 y8 0.00000 x9 +0.40451 y9 −0.29389 x10 +0.15451 y10 −0.47553


−0.35355 −0.35355 −0.35355 +0.35355 +0.35355 +0.35355 +0.35355 −0.35355

11 Holes x1 −0.14087 y1 −0.47975 x2 −0.37787 y2 −0.32743 x3 −0.49491 y3 −0.07116 x4 −0.45482 y4 +0.20771 x5 −0.27032 y5 +0.42063 x6 0.00000 y6 +0.50000 x7 +0.27032 y7 +0.42063 x8 +0.45482 y8 +0.20771 x9 +0.49491 y9 −0.07116 x10 +0.37787 y10 −0.32743 x11 +0.14087 y11 −0.47975


−0.29389 −0.40451 −0.47553 +0.15451 0.00000 +0.50000 +0.47553 +0.15451 +0.29389 −0.40451

12 Holes x1 −0.12941 y1 −0.48296 x2 −0.35355 y2 −0.35355 x3 −0.48296 y3 −0.12941 x4 −0.48296 y4 +0.12941 x5 −0.35355 y5 +0.35355 x6 −0.12941 y6 +0.48296 x7 +0.12941 y7 +0.48296 x8 +0.35355 y8 +0.35355 x9 +0.48296 y9 +0.12941 x10 +0.48296 y10 −0.12941 x11 +0.35355 y11 −0.35355 x12 +0.12941 y12 −0.48296


−0.25000 −0.43301 −0.50000 0.00000 −0.25000 +0.43301 +0.25000 +0.43301 +0.50000 0.00000 +0.25000 −0.43301

13 Holes x1 −0.11966 y1 −0.48547 x2 −0.33156 y2 −0.37426 x3 −0.46751 y3 −0.17730 x4 −0.49635 y4 +0.06027 x5 −0.41149 y5 +0.28403 x6 −0.23236 y6 +0.44273 x7 0.00000 y7 + 0.50000 x8 +0.23236 y8 +0.44273 x9 +0.41149 y9 +0.28403 x10 +0.49635 y10 +0.06027 x11 +0.46751 y11 −0.17730 x12 +0.33156 y12 −0.37426 x13 +0.11966 y13 −0.48547


−0.21694 −0.45048 −0.48746 −0.11126 −0.39092 +0.31174 0.00000 +0.50000 +0.39092 +0.31174 +0.48746 −0.11126 +0.21694 −0.45048

14 Holes x1 −0.11126 y1 −0.48746 x2 −0.31174 y2 −0.39092 x3 −0.45048 y3 −0.21694 x4 −0.50000 y4 0.00000 x5 −0.45048 y5 +0.21694 x6 −0.31174 y6 +0.39092 x7 −0.11126 y7 +0.48746 x8 +0.11126 y8 +0.48746 x9 +0.31174 y9 +0.39092 x10 +0.45048 y10 +0.21694 x11 +0.50000 y11 0.00000 x12 +0.45048 y12 −0.21694 x13 +0.31174 y13 −0.39092 x14 +0.11126 y14 − 0.48746


−0.19134 −0.46194 −0.46194 −0.19134 −0.46194 +0.19134 −0.19134 +0.46194 +0.19134 +0.46194 +0.46194 +0.19134 +0.46194 −0.19134 +0.19134 −0.46194

15 Holes x1 −0.10396 y1 −0.48907 x2 −0.29389 y2 −0.40451 x3 −0.43301 y3 −0.25000 x4 −0.49726 y4 −0.05226 x5 −0.47553 y5 +0.15451 x6 −0.37157 y6 +0.33457 x7 −0.20337 y7 +0.45677 x8 0.00000 y8 +0.50000 x9 +0.20337 y9 +0.45677 x10 +0.37157 y10 +0.33457 x11 +0.47553 y11 +0.15451 x12 +0.49726 y12 −0.05226 x13 +0.43301 y13 −0.25000 x14 +0.29389 y14 −0.40451 x15 +0.10396 y15 −0.48907



−0.17101 −0.46985 −0.43301 −0.25000 −0.49240 +0.08682 −0.32139 +0.38302 0.00000 +0.50000 +0.32139 +0.38302 +0.49240 +0.08682 +0.43301 −0.25000 +0.17101 −0.46985 16 Holes

x1 −0.09755 y1 −0.49039 x2 −0.27779 y2 −0.41573 x3 −0.41573 y3 −0.27779 x4 −0.49039 y4 −0.09755 x5 −0.49039 y5 +0.09755 x6 −0.41573 y6 +0.27779 x7 −0.27779 y7 +0.41573 x8 −0.09755 y8 +0.49039 x9 +0.09755 y9 +0.49039 x10 +0.27779 y10 +0.41573 x11 +0.41573 y11 +0.27779 x12 +0.49039 y12 +0.09755 x13 +0.49039 y13 −0.09755 x14 +0.41573 y14 −0.27779 x15 +0.27779 y15 −0.41573 x16 +0.09755 y16 −0.49039


1003

Table 15. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units)


17 Holes x1 −0.09187 y1 − 0.49149 x2 −0.26322 y2 −0.42511 x3 − 0.39901 y3 −0.30132 x4 −0.48091 y4 −0.13683 x5 −0.49787 y5 +0.04613 x6 −0.44758 y6 +0.22287 x7 −0.33685 y7 +0.36950 x8 −0.18062 y8 +0.46624 x9 0.00000 y9 +0.50000 x10 +0.18062 y10 +0.46624 x11 +0.33685 y11 +0.36950 x12 +0.44758 y12 +0.22287 x13 +0.49787 y13 +0.04613 x14 +0.48091 y14 −0.13683 x15 +0.39901 y15 −0.30132 x16 +0.26322 y16 −0.42511 x17 +0.09187 y17 − 0.49149

18 Holes x1 −0.08682 y1 −0.49240 x2 −0.25000 y2 −0.43301 x3 −0.38302 y3 −0.32139 x4 −0.46985 y4 −0.17101 x5 −0.50000 y5 0.00000 x6 −0.46985 y6 +0.17101 x7 −0.38302 y7 +0.32139 x8 −0.25000 y8 +0.43301 x9 −0.08682 y9 +0.49240 x10 +0.08682 y10 +0.49240 x11 +0.25000 y11 +0.43301 x12 +0.38302 y12 +0.32139 x13 +0.46985 y13 +0.17101 x14 +0.50000 y14 0.00000 x15 +0.46985 y15 −0.17101 x16 +0.38302 y16 −0.32139 x17 +0.25000 y17 −0.43301 x18 +0.08682 y18 −0.49240

24 Holes x1 −0.06526 y1 −0.49572 x2 −0.19134 y2 −0.46194 x3 −0.30438 y3

−0.39668

19 Holes x1 −0.08230 y1 −0.49318 x2 −0.23797 y2 −0.43974 x3 −0.36786 y3 −0.33864 x4 −0.45789 y4 −0.20085 x5 −0.49829 y5 −0.04129 x6 −0.48470 y6 +0.12274 x7 −0.41858 y7 +0.27347 x8 −0.30711 y8 +0.39457 x9 −0.16235 y9 +0.47291 x10 0.00000 y10 +0.50000 x11 +0.16235 y11 +0.47291 x12 +0.30711 y12 +0.39457 x13 +0.41858 y13 +0.27347 x14 +0.48470 y14 +0.12274 x15 +0.49829 y15 −0.04129 x16 +0.45789 y16 −0.20085 x17 +0.36786 y17 −0.33864 x18 +0.23797 y18 −0.43974 x19 +0.08230 y19 −0.49318

25 Holes

20 Holes x1 −0.07822 y1 −0.49384 x2 −0.22700 y2 −0.44550 x3 −0.35355 y3 −0.35355 x4 −0.44550 y4 −0.22700 x5 −0.49384 y5 −0.07822 x6 −0.49384 y6 +0.07822 x7 −0.44550 y7 +0.22700 x8 −0.35355 y8 +0.35355 x9 −0.22700 y9 +0.44550 x10 −0.07822 y10 +0.49384 x11 +0.07822 y11 +0.49384 x12 +0.22700 y12 +0.44550 x13 +0.35355 y13 +0.35355 x14 +0.44550 y14 +0.22700 x15 +0.49384 y15 +0.07822 x16 +0.49384 y16 −0.07822 x17 +0.44550 y17 −0.22700 x18 +0.35355 y18 −0.35355 x19 +0.22700 y19 −0.44550 x20 +0.07822 y20 −0.49384

26 Holes

21 Holes x1 −0.07452 y1 −0.49442 x2 −0.21694 y2 −0.45048 x3 −0.34009 y3 −0.36653 x4 −0.43301 y4 −0.25000 x5 −0.48746 y5 −0.11126 x6 −0.49860 y6 +0.03737 x7 −0.46544 y7 +0.18267 x8 −0.39092 y8 +0.31174 x9 −0.28166 y9 +0.41312 x10 −0.14738 y10 +0.47779 x11 0.00000 y11 +0.50000 x12 +0.14738 y12 +0.47779 x13 +0.28166 y13 +0.41312 x14 +0.39092 y14 +0.31174 x15 +0.46544 y15 +0.18267 x16 +0.49860 y16 +0.03737 x17 +0.48746 y17 −0.11126 x18 +0.43301 y18 −0.25000 x19 +0.34009 y19 −0.36653 x20 +0.21694 y20 −0.45048 x21 +0.07452 y21 −0.49442

27 Holes

28 Holes

−0.06267 −0.49606 −0.18406 −0.46489 −0.29389

x1 y1 x2 y2 x3

−0.06027 −0.49635 −0.17730 −0.46751 −0.28403

x1 y1 x2 y2 x3

−0.05805 −0.49662 −0.17101 −0.46985 −0.27475

x1 y1 x2 y2 x3

y3 −0.40451

y3

−0.41149

y3

−0.41774

y3 −0.42336

x1 y1 x2 y2 x3

22 Holes x1 −0.07116 y1 −0.49491 x2 −0.20771 y2 −0.45482 x3 −0.32743 y3 −0.37787 x4 −0.42063 y4 −0.27032 x5 −0.47975 y5 −0.14087 x6 −0.50000 y6 0.00000 x7 −0.47975 y7 +0.14087 x8 −0.42063 y8 +0.27032 x9 −0.32743 y9 +0.37787 x10 −0.20771 y10 +0.45482 x11 −0.07116 y11 +0.49491 x12 + 0.07116 y12 +0.49491 x13 +0.20771 y13 +0.45482 x14 +0.32743 y14 +0.37787 x15 +0.42063 y15 +0.27032 x16 +0.47975 y16 +0.14087 x17 +0.50000 y17 0.00000 x18 +0.47975 y18 −0.14087 x19 +0.42063 y19 −0.27032 x20 +0.32743 y20 −0.37787 x21 +0.20771 y21 −0.45482 x22 +0.07116 y22 −0.49491

−0.05598 −0.49686 −0.16514 −0.47194 −0.26602


23 Holes x1 −0.06808 y1 −0.49534 x2 −0.19920 y2 −0.45861 x3 −0.31554 y3 −0.38786 x4 −0.40848 y4 −0.28834 x5 −0.47113 y5 −0.16744 x6 −0.49883 y6 −0.03412 x7 −0.48954 y7 +0.10173 x8 −0.44394 y8 +0.23003 x9 −0.36542 y9 +0.34128 x10 −0.25979 y10 +0.42721 x11 −0.13490 y11 +0.48146 x12 0.00000 y12 +0.50000 x13 +0.13490 y13 +0.48146 x14 +0.25979 y14 +0.42721 x15 +0.36542 y15 +0.34128 x16 +0.44394 y16 +0.23003 x17 +0.48954 y17 +0.10173 x18 +0.49883 y18 −0.03412 x19 +0.47113 y19 −0.16744 x20 +0.40848 y20 −0.28834 x21 +0.31554 y21 −0.38786 x22 +0.19920 y22 −0.45861 x23 +0.06808 y23 −0.49534


JIG BORING

Table 15. (Continued) Hole Coordinate Dimension Factors for Jig Boring — Type “B” Hole Circles Central Coordinates (English or Metric units)


24 Holes x4 −0.39668 y4 −0.30438 x5 −0.46194 y5 −0.19134 x6 −0.49572 y6 −0.06526 x7 −0.49572 y7 +0.06526 x8 −0.46194 y8 +0.19134 x9 −0.39668 y9 +0.30438 x10 −0.30438 y10 +0.39668 x11 −0.19134 y11 +0.46194 x12 −0.06526 y12 +0.49572 x13 +0.06526 y13 +0.49572 x14 +0.19134 y14 +0.46194 x15 +0.30438 y15 +0.39668 x16 +0.39668 y16 +0.30438 x17 +0.46194 y17 +0.19134 x18 +0.49572 y18 +0.06526 x19 +0.49572 y19 −0.06526 x20 +0.46194 y20 −0.19134 x21 +0.39668 y21 −0.30438 x22 +0.30438 y22 −0.39668 x23 +0.19134 y23 −0.46194 x24 +0.06526 y24 −0.49572

25 Holes x4 −0.38526 y4 −0.31871 x5 −0.45241 y5 −0.21289 x6 −0.49114 y6 −0.09369 x7 −0.49901 y7 +0.03140 x8 −0.47553 y8 +0.15451 x9 −0.42216 y9 +0.26791 x10 −0.34227 y10 + 0.36448 x11 −0.24088 y11 +0.43815 x12 −0.12434 y12 +0.48429 x13 0.00000 y13 +0.50000 x14 +0.12434 y14 +0.48429 x15 +0.24088 y15 +0.43815 x16 +0.34227 y16 +0.36448 x17 +0.42216 y17 +0.26791 x18 +0.47553 y18 +0.15451 x19 +0.49901 y19 +0.03140 x20 +0.49114 y20 −0.09369 x21 +0.45241 y21 −0.21289 x22 +0.38526 y22 −0.31871 x23 +0.29389 y23 −0.40451 x24 +0.18406 y24 −0.46489 x25 +0.06267 y25 −0.49606

26 Holes x4 −0.37426 y4 −0.33156 x5 −0.44273 y5 −0.23236 x6 −0.48547 y6 −0.11966 x7 −0.50000 y7 0.00000 x8 −0.48547 y8 +0.11966 x9 −0.44273 y9 +0.23236 x10 −0.37426 y10 +0.33156 x11 −0.28403 y11 +0.41149 x12 −0.17730 y12 +0.46751 x13 −0.06027 y13 +0.49635 x14 +0.06027 y14 +0.49635 x15 +0.17730 y15 +0.46751 x16 +0.28403 y16 +0.41149 x17 +0.37426 y17 +0.33156 x18 +0.44273 y18 +0.23236 x19 +0.48547 y19 +0.11966 x20 +0.50000 y20 0.00000 x21 + 0.48547 y21 −0.11966 x22 +0.44273 y22 −0.23236 x23 +0.37426 y23 −0.33156 x24 +0.28403 y24 −0.41149 x25 +0.17730 y25 −0.46751 x26 +0.06027 y26 −0.49635

27 Holes x4 −0.36369 y4 −0.34312 x5 −0.43301 y5 − 0.25000 x6 −0.47899 y6 −0.14340 x7 −0.49915 y7 − 0.02907 x8 −0.49240 y8 +0.08682 x9 −0.45911 y9 +0.19804 x10 −0.40106 y10 +0.29858 x11 −0.32139 y11 +0.38302 x12 −0.22440 y12 +0.44682 x13 −0.11531 y13 +0.48652 x14 0.00000 y14 +0.50000 x15 +0.11531 y15 +0.48652 x16 +0.22440 y16 +0.44682 x17 +0.32139 y17 +0.38302 x18 +0.40106 y18 + 0.29858 x19 +0.45911 y19 +0.19804 x20 +0.49240 y20 +0.08682 x21 +0.49915 y21 −0.02907 x22 +0.47899 y22 − 0.14340 x23 +0.43301 y23 −0.25000 x24 +0.36369 y24 −0.34312 x25 +0.27475 y25 −0.41774 x26 +0.17101 y26 −0.46985 x27 +0.05805 y27 −0.49662

28 Holes x4 −0.35355 y4 −0.35355 x5 −0.42336 y5 −0.26602 x6 −0.47194 y6 −0.16514 x7 −0.49686 y7 −0.05598 x8 −0.49686 y8 +0.05598 x9 −0.47194 y9 +0.16514 x10 −0.42336 y10 +0.26602 x11 −0.35355 y11 +0.35355 x12 −0.26602 y12 +0.42336 x13 −0.16514 y13 +0.47194 x14 −0.05598 y14 +0.49686 x15 +0.05598 y15 +0.49686 x16 +0.16514 y16 +0.47194 x17 +0.26602 y17 +0.42336 x18 +0.35355 y18 +0.35355 x19 +0.42336 y19 +0.26602 x20 +0.47194 y20 +0.16514 x21 +0.49686 y21 +0.05598 x22 +0.49686 y22 −0.05598 x23 +0.47194 y23 −0.16514 x24 +0.42336 y24 −0.26602 x25 +0.35355 y25 −0.35355 x26 +0.26602 y26 −0.42336 x27 +0.16514 y27 −0.47194 x28 +0.05598 y28 −0.49686


Machinery's Handbook 27th Edition TABLE OF CONTENTS MACHINING OPERATIONS CUTTING SPEEDS AND FEEDS 1009 Indroduction to Speeds and Feeds 1009 Cutting Tool Materials 1013 Cutting Speeds 1014 Cutting Conditions 1014 Selecting Cutting Conditions 1014 Tool Troubleshooting 1016 Cutting Speed Formulas 1018 RPM for Various Cutting Speeds and Diameter

SPEED AND FEED TABLES 1022 1022 1026 1027 1031 1032 1033 1035 1037 1038 1039 1040 1043 1044 1045 1049 1050 1052 1054 1056 1057 1059 1060 1061 1066 1067 1068 1070 1071 1072 1072 1074 1075 1075 1077 1079 1080 1081

How to Use the Tables Principal Speed andFeed Tables Speed and Feed Tables for Turning Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals Speed and Tool Life Adjustments Copper Alloys Titanium and Titanium Alloys Superalloys Speed and Feed Tables for Milling Slit Milling Aluminium Alloys Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals High Speed Steel Cutters Speed Adjustment Factors Radial Depth of Cut Adjustments Tool Life Adjustments Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Tool Steels Stainless Steels Ferrous Cast Metals Light Metals Adjustment Factors for HSS Copper Alloys Tapping and Threading Cutting Speed for Broaching Spade Drills Spade Drill Geometry Spade Drilling Feed Rates Power Consumption Trepanning

ESTIMATING SPEEDS AND MACHINING POWER 1082 1082 1082 1082 1082 1084 1084 1085 1085 1088 1090 1090 1091 1091 1091

Planer Cutting Speeds Cutting Speed and Time Planing Time Speeds for Metal-Cutting Saws Turning Unusual Material Estimating Machining Power Power Constants Feed Factors Tool Wear Factors Metal Removal Rates Estimating Drilling Thrust, Torque, and Power Work Material Factor Chisel Edge Factors Feed Factors Drill Diameter Factors

MACHINING ECONOMETRICS 1093 Tool Wear And Tool Life Relationships 1093 Equivalent Chip Thickness (ECT) 1094 Tool-life Relationships 1098 The G- and H-curves 1099 Tool-life Envelope 1102 Forces and Tool-life 1104 Surface Finish and Tool-life 1106 Shape of Tool-life Relationships 1107 Minimum Cost 1108 Production Rate 1108 The Cost Function 1109 Global Optimum 1110 Economic Tool-life 1113 Machine Settings and Cost Calculations 1113 Nomenclature 1114 Cutting Formulas 1118 Tooling And Total Cost 1119 Optimized Data 1122 High-speed Machining Econometrics 1123 Chip Geometry in Milling 1125 Chip Thickness 1127 Forces and Tool-life 1128 High-speed Milling 1129 Econometrics Comparison

1005


Machinery's Handbook 27th Edition TABLE OF CONTENTS MACHINING OPERATIONS SCREW MACHINE FEEDS AND SPEEDS 1131 Automatic Screw Machine Tools 1131 Knurling 1131 Revolution for Knurling 1131 Cams for Threading 1132 Cutting Speeds and Feeds 1134 Spindle Revolutions 1135 Practical Points on Cam 1136 Stock for Screw Machine Products 1138 Band Saw Blade Selection 1139 Tooth Forms 1139 Types of Blades 1140 Band Saw Speed and Feed Rate 1141 Bimetal Band Saw Speeds 1142 Band Saw Blade Break-In

GRINDING FEEDS AND SPEEDS 1158 Basic Rules 1158 Wheel life T and Grinding Ratio 1159 ECT in Grinding 1160 Optimum Grinding Data 1162 Surface Finish, Ra 1163 Spark-out Time 1164 Grinding Cutting Forces 1165 Grinding Data 1166 Grindability Groups 1166 Side Feed, Roughing and Finishing 1167 Relative Grindability 1168 Grindability Overview 1168 Procedure to Determine Data 1174 Calibration of Recommendations 1176 Optimization

GRINDING AND OTHER ABRASIVE PROCESSES

CUTTING FLUIDS 1144 Types of Fluids 1144 Cutting Oils 1144 Water-Miscible Fluids 1145 Selection of Cutting Fluids 1146 Turning, Milling, Drilling and Tapping 1147 Machining 1148 Machining Magnesium 1149 Metalworking Fluids 1149 Classes of Metalworking Fluids 1149 Occupational Exposures 1150 Fluid Selection, Use, and Application 1151 Fluid Maintenance 1152 Respiratory Protection

MACHINING NONFERROUS METALS AND NON-METALLIC MATERIALS 1153 Machining Nonferrous Metals 1153 Aluminium 1154 Magnesium 1155 Zinc Alloy Die-Castings 1155 Monel and Nickel Alloys 1156 Copper Alloys 1156 Machining Non-metals 1156 Hard Rubber 1156 Formica Machining 1157 Micarta Machining 1157 Ultrasonic Machining

1177 Grinding Wheels 1177 Abrasive Materials 1178 Bond Properties 1178 Structure 1179 ANSI Markings 1179 Sequence of Markings 1180 ANSI Shapes and Sizes 1180 Selection of Grinding Wheel 1181 Standard Shapes Ranges 1188 Grinding Wheel Faces 1189 Classification of Tool Steels 1190 Hardened Tool Steels 1194 Constructional Steels 1195 Cubic Boron Nitride 1196 Dressing and Truing 1196 Tools and Methods for Dressing and Truing 1198 Guidelines for Truing and Dressing 1199 Diamond Truing and Crossfeeds 1200 Size Selection Guide 1200 Minimum Sizes for Single-Point Truing Diamonds

1006


Machinery's Handbook 27th Edition TABLE OF CONTENTS MACHINING OPERATIONS GRINDING AND OTHER ABRASIVE PROCESSES

GRINDING AND OTHER ABRASIVE PROCESSES

(Continued)

(Continued)

1201 Diamond Wheels 1201 Shapes 1202 Core Shapes and Designations 1202 Cross-sections and Designations 1203 Designations for Location 1204 Composition 1205 Designation Letters 1206 Selection of Diamond Wheels 1206 Abrasive Specification 1207 Handling and Operation 1207 Speeds and Feeds 1207 Grinding Wheel Safety 1207 Safety in Operating 1208 Handling, Storage and Inspection 1208 Machine Conditions 1208 Grinding Wheel Mounting 1209 Safe Operating Speeds 1210 Portable Grinders 1212 Cylindrical Grinding 1212 Plain, Universal, and LimitedPurpose Machines 1212 Traverse or Plunge Grinding 1212 Work Holding on Machines 1213 Work-Holding Methods 1213 Selection of Grinding Wheels 1214 Wheel Recommendations 1214 Operational Data 1215 Basic Process Data 1215 High-Speed 1216 Areas and Degrees of Automation 1216 Troubles and Their Correction 1220 Centerless Grinding 1221 Through-feed Method of Grinding 1221 In-feed Method 1221 End-feed Method 1221 Automatic Centerless Method 1221 Centerless Grinding 1222 Surface Grinding 1223 Principal Systems 1225 Grinding Wheel Recommendations 1226 Process Data for Surface Grinding 1226 Basic Process Data 1227 Faults and Possible Causes

1229 1229 1229 1229 1230 1230 1230 1230 1233 1233 1233 1234 1234 1235 1235 1235 1235 1236 1236 1237 1237 1237 1238 1238 1238 1238 1238 1239 1239 1239

Offhand Grinding Floor- and Bench-Stand Grinding Portable Grinding Swing-Frame Grinding Abrasive Belt Grinding Application of Abrasive Belts Selection Contact Wheels Abrasive Cutting Cutting-Off Difficulties Honing Process Rate of Stock Removal Formula for Rotative Speeds Factors in Rotative Speed Formulas Eliminating Undesirable Honing Conditions Tolerances Laps and Lapping Material for Laps Laps for Flat Surfaces Grading Abrasives Charging Laps Rotary Diamond Lap Grading Diamond Dust Cutting Properties Cutting Qualities Wear of Laps Lapping Abrasives Effect on Lapping Lubricants Lapping Pressures Wet and Dry Lapping Lapping Tests

KNURLS AND KNURLING 1240 Knurls and Knurling 1240 ANSI Standard 1240 Preferred Sizes 1240 Specifications 1241 Cylindrical Tools 1242 Flat Tools 1242 Specifications for Flat Dies 1242 Formulas to Knurled Work 1243 Tolerances 1244 Marking on Knurls and Dies 1244 Concave Knurls

1007


Machinery's Handbook 27th Edition TABLE OF CONTENTS MACHINING OPERATIONS MACHINE TOOL ACCURACY 1248 1249

Degrees of Accuracy Expected with NC Machine Tool Part Tolerances

NUMERICAL CONTROL 1254 1254 1254 1255 1258 1262 1262 1262 1263 1264 1264 1264 1267

Introduction CNC Technology Numerical Control vs. Manual Operations Numerical Control Standards Programmable Controller Closed-Loop System Open-Loop System Adaptive Control Flexible Manufacturing Systems Flexible Manufacturing Cell Flexible Manufacturing Module Axis Nomenclature Total Indicator Reading

NUMERICAL CONTROL PROGRAMMING 1269 Programming 1272 Postprocessors 1272 G-Code Programming 1272 Format Classification 1272 Letter Addresses 1274 Sequence Number (N-Word) 1274 Preparatory Word (G-Word) 1278 Miscellaneous Functions 1279 Feed Function (F-Word) 1280 Spindle Function (S-Word) 1280 Tool Function (T-Word) 1282 Linear Interpolation 1283 Circular Interpolation 1284 Helical and Parabolic Interpolation 1285 Subroutine 1287 Conditional Expressions 1287 Fixed (Canned) Cycles 1291 Turning Cycles 1291 Thread Cutting

NUMERICAL CONTROL PROGRAMMING (Continued)

1292 APT Programming 1294 APT Computational Statements 1294 APT Geometry Statements 1295 Points, Lines and Circles 1299 APT Motion Statements 1300 Contouring Cutter Movements 1301 Circles and Planes 1303 3-D Geometry 1304 APT Postprocessor Statements 1306 APT Example Program 1307 APT for Turning 1309 Indexable Insert Holders for NC 1310 Insert Radius Compensation 1312 Threading Tool Insert Radius 1313 V-Flange Tool Shanks 1314 Retention Knobs

CAD/CAM 1315 1317 1318 1322 1322 1324 1324 1325 1325

CAD/CAM Drawing Projections Drawing Tips and Traps Sizes of Lettering on Drawing Drawing Exchange Standards Rapid Automated Prototyping DNC Machinery Noise Measuring Machinery Noise

1008


Machinery's Handbook 27th Edition MACHINING OPERATIONS

1009

CUTTING SPEEDS AND FEEDS Indroduction to Speeds and Feeds Work Materials.—The large number of work materials that are commonly machined vary greatly in their basic structure and the ease with which they can be machined. Yet it is possible to group together certain materials having similar machining characteristics, for the purpose of recommending the cutting speed at which they can be cut. Most materials that are machined are metals and it has been found that the most important single factor influencing the ease with which a metal can be cut is its microstructure, followed by any cold work that may have been done to the metal, which increases its hardness. Metals that have a similar, but not necessarily the same microstructure, will tend to have similar machining characteristics. Thus, the grouping of the metals in the accompanying tables has been done on the basis of their microstructure. With the exception of a few soft and gummy metals, experience has shown that harder metals are more difficult to cut than softer metals. Furthermore, any given metal is more difficult to cut when it is in a harder form than when it is softer. It is more difficult to penetrate the harder metal and more power is required to cut it. These factors in turn will generate a higher cutting temperature at any given cutting speed, thereby making it necessary to use a slower speed, for the cutting temperature must always be kept within the limits that can be sustained by the cutting tool without failure. Hardness, then, is an important property that must be considered when machining a given metal. Hardness alone, however, cannot be used as a measure of cutting speed. For example, if pieces of AISI 11L17 and AISI 1117 steel both have a hardness of 150 Bhn, their recommended cutting speeds for high-speed steel tools will be 140 fpm and 130 fpm, respectively. In some metals, two entirely different microstructures can produce the same hardness. As an example, a fine pearlite microstructure and a tempered martensite microstructure can result in the same hardness in a steel. These microstructures will not machine alike. For practical purposes, however, information on hardness is usually easier to obtain than information on microstructure; thus, hardness alone is usually used to differentiate between different cutting speeds for machining a metal. In some situations, the hardness of a metal to be machined is not known. When the hardness is not known, the material condition can be used as a guide. The surface of ferrous metal castings has a scale that is more difficult to machine than the metal below. Some scale is more difficult to machine than others, depending on the foundry sand used, the casting process, the method of cleaning the casting, and the type of metal cast. Special electrochemical treatments sometimes can be used that almost entirely eliminate the effect of the scale on machining, although castings so treated are not frequently encountered. Usually, when casting scale is encountered, the cutting speed is reduced approximately 5 or 10 per cent. Difficult-to-machine surface scale can also be encountered when machining hot-rolled or forged steel bars. Metallurgical differences that affect machining characteristics are often found within a single piece of metal. The occurrence of hard spots in castings is an example. Different microstructures and hardness levels may occur within a casting as a result of variations in the cooling rate in different parts of the casting. Such variations are less severe in castings that have been heat treated. Steel bar stock is usually harder toward the outside than toward the center of the bar. Sometimes there are slight metallurgical differences along the length of a bar that can affect its cutting characteristics. Cutting Tool Materials.—The recommended cutting feeds and speeds in the accompanying tables are given for high-speed steel, coated and uncoated carbides, ceramics, cermets, and polycrystalline diamonds. More data are available for HSS and carbides because these materials are the most commonly used. Other materials that are used to make cutting tools are cemented oxides or ceramics, cermets, cast nonferrous alloys (Stellite), singlecrystal diamonds, polycrystalline diamonds, and cubic boron nitride.



SPEEDS AND FEEDS

Carbon Tool Steel: It is used primarily to make the less expensive drills, taps, and reamers. It is seldom used to make single-point cutting tools. Hardening in carbon steels is very shallow, although some have a small amount of vanadium and chromium added to improve their hardening quality. The cutting speed to use for plain carbon tool steel should be approximately one-half of the recommended speed for high-speed steel. High-Speed Steel: This designates a number of steels having several properties that enhance their value as cutting tool material. They can be hardened to a high initial or roomtemperature hardness ranging from 63 Rc to 65 Rc for ordinary high-speed steels and up to 70 Rc for the so-called superhigh-speed steels. They can retain sufficient hardness at temperatures up to 1,000 to 1,100°F to enable them to cut at cutting speeds that will generate these tool temperatures, and they will return to their original hardness when cooled to room temperature. They harden very deeply, enabling high-speed steels to be ground to the tool shape from solid stock and to be reground many times without sacrificing hardness at the cutting edge. High-speed steels can be made soft by annealing so that they can be machined into complex cutting tools such as drills, reamers, and milling cutters and then hardened. The principal alloying elements of high-speed steels are tungsten (W), molybdenum (Mo), chromium (Cr), vanadium (V), together with carbon (C). There are a number of grades of high-speed steel that are divided into two types: tungsten high-speed steels and molybdenum high-speed steels. Tungsten high-speed steels are designated by the prefix T before the number that designates the grade. Molybdenum high-speed steels are designated by the prefix letter M. There is little performance difference between comparable grades of tungsten or molybdenum high-speed steel. The addition of 5 to 12 per cent cobalt to high-speed steel increases its hardness at the temperatures encountered in cutting, thereby improving its wear resistance and cutting efficiency. Cobalt slightly increases the brittleness of high-speed steel, making it susceptible to chipping at the cutting edge. For this reason, cobalt high-speed steels are primarily made into single-point cutting tools that are used to take heavy roughing cuts in abrasive materials and through rough abrasive surface scales. The M40 series and T15 are a group of high-hardness or so-called super high-speed steels that can be hardened to 70 Rc; however, they tend to be brittle and difficult to grind. For cutting applications, they are usually heat treated to 67–68 Rc to reduce their brittleness and tendency to chip. The M40 series is appreciably easier to grind than T15. They are recommended for machining tough die steels and other difficult-to-cut materials; they are not recommended for applications where conventional high-speed steels perform well. Highspeed steels made by the powder-metallurgy process are tougher and have an improved grindability when compared with similar grades made by the customary process. Tools made of these steels can be hardened about 1 Rc higher than comparable high-speed steels made by the customary process without a sacrifice in toughness. They are particularly useful in applications involving intermittent cutting and where tool life is limited by chipping. All these steels augment rather than replace the conventional high-speed steels. Cemented Carbides: They are also called sintered carbides or simply carbides. They are harder than high-speed steels and have excellent wear resistance. Information on cemented carbides and other hard metal tools is included in the section CEMENTED CARBIDES starting on page 773. Cemented carbides retain a very high degree of hardness at temperatures up to 1400°F and even higher; therefore, very fast cutting speeds can be used. When used at fast cutting speeds, they produce good surface finishes on the workpiece. Carbides are more brittle than high-speed steel and, therefore, must be used with more care. Hundreds of grades of carbides are available and attempts to classify these grades by area of application have not been entirely successful. There are four distinct types of carbides: 1) straight tungsten carbides; 2) crater-resistant carbides; 3) titanium carbides; and 4) coated carbides.


Machinery's Handbook 27th Edition SPEEDS AND FEEDS

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Straight Tungsten Carbide: This is the most abrasion-resistant cemented carbide and is used to machine gray cast iron, most nonferrous metals, and nonmetallic materials, where abrasion resistance is the primary criterion. Straight tungsten carbide will rapidly form a crater on the tool face when used to machine steel, which reduces the life of the tool. Titanium carbide is added to tungsten carbide in order to counteract the rapid formation of the crater. In addition, tantalum carbide is usually added to prevent the cutting edge from deforming when subjected to the intense heat and pressure generated in taking heavy cuts. Crater-Resistant Carbides: These carbides, containing titanium and tantalum carbides in addition to tungsten carbide, are used to cut steels, alloy cast irons, and other materials that have a strong tendency to form a crater. Titanium Carbides: These carbides are made entirely from titanium carbide and small amounts of nickel and molybdenum. They have an excellent resistance to cratering and to heat. Their high hot hardness enables them to operate at higher cutting speeds, but they are more brittle and less resistant to mechanical and thermal shock. Therefore, they are not recommended for taking heavy or interrupted cuts. Titanium carbides are less abrasion-resistant and not recommended for cutting through scale or oxide films on steel. Although the resistance to cratering of titanium carbides is excellent, failure caused by crater formation can sometimes occur because the chip tends to curl very close to the cutting edge, thereby forming a small crater in this region that may break through. Coated Carbides: These are available only as indexable inserts because the coating would be removed by grinding. The principal coating materials are titanium carbide (TiC), titanium nitride (TiN), and aluminum oxide (Al2O3). A very thin layer (approximately 0.0002 in.) of coating material is deposited over a cemented carbide insert; the material below the coating is called the substrate. The overall performance of the coated carbide is limited by the substrate, which provides the required toughness and resistance to deformation and thermal shock. With an equal tool life, coated carbides can operate at higher cutting speeds than uncoated carbides. The increase may be 20 to 30 per cent and sometimes up to 50 per cent faster. Titanium carbide and titanium nitride coated carbides usually operate in the medium (200–800 fpm) cutting speed range, and aluminum oxide coated carbides are used in the higher (800–1600 fpm) cutting speed range. Carbide Grade Selection: The selection of the best grade of carbide for a particular application is very important. An improper grade of carbide will result in a poor performance—it may even cause the cutting edge to fail before any significant amount of cutting has been done. Because of the many grades and the many variables that are involved, the carbide producers should be consulted to obtain recommendations for the application of their grades of carbide. A few general guidelines can be given that are useful to form an orientation. Metal cutting carbides usually range in hardness from about 89.5 Ra (Rockwell A Scale) to 93.0 Ra with the exception of titanium carbide, which has a hardness range of 90.5 Ra to 93.5 Ra. Generally, the harder carbides are more wear-resistant and more brittle, whereas the softer carbides are less wear-resistant but tougher. A choice of hardness must be made to suit the given application. The very hard carbides are generally used for taking light finishing cuts. For other applications, select the carbide that has the highest hardness with sufficient strength to prevent chipping or breaking. Straight tungsten carbide grades should always be used unless cratering is encountered. Straight tungsten carbides are used to machine gray cast iron, ferritic malleable iron, austenitic stainless steel, high-temperature alloys, copper, brass, bronze, aluminum alloys, zinc alloy die castings, and plastics. Crater-resistant carbides should be used to machine plain carbon steel, alloy steel, tool steel, pearlitic malleable iron, nodular iron, other highly alloyed cast irons, ferritic stainless steel, martensitic stainless steel, and certain high-temperature alloys. Titanium carbides are recommended for taking high-speed finishing and semifinishing cuts on steel, especially the low-carbon, low-alloy steels, which are less abrasive and have a strong tendency to form a crater. They are also used to take light cuts on alloy cast iron and on



SPEEDS AND FEEDS

some high-nickel alloys. Nonferrous materials, such as some aluminum alloys and brass, that are essentially nonabrasive may also be machined with titanium carbides. Abrasive materials and others that should not be machined with titanium carbides include gray cast iron, titanium alloys, cobalt- and nickel-base superalloys, stainless steel, bronze, many aluminum alloys, fiberglass, plastics, and graphite. The feed used should not exceed about 0.020 inch per revolution. Coated carbides can be used to take cuts ranging from light finishing to heavy roughing on most materials that can be cut with these carbides. The coated carbides are recommended for machining all free-machining steels, all plain carbon and alloy steels, tool steels, martensitic and ferritic stainless steels, precipitation-hardening stainless steels, alloy cast iron, pearlitic and martensitic malleable iron, and nodular iron. They are also recommended for taking light finishing and roughing cuts on austenitic stainless steels. Coated carbides should not be used to machine nickel- and cobalt-base superalloys, titanium and titanium alloys, brass, bronze, aluminum alloys, pure metals, refractory metals, and nonmetals such as fiberglass, graphite, and plastics. Ceramic Cutting Tool Materials: These are made from finely powdered aluminum oxide particles sintered into a hard dense structure without a binder material. Aluminum oxide is also combined with titanium carbide to form a composite, which is called a cermet. These materials have a very high hot hardness enabling very high cutting speeds to be used. For example, ceramic cutting tools have been used to cut AISI 1040 steel at a cutting speed of 18,000 fpm with a satisfactory tool life. However, much lower cutting speeds, in the range of 1000 to 4000 fpm and lower, are more common because of limitations placed by the machine tool, cutters, and chucks. Although most applications of ceramic and cermet cutting tool materials are for turning, they have also been used successfully for milling. Ceramics and cermets are relatively brittle and a special cutting edge preparation is required to prevent chipping or edge breakage. This preparation consists of honing or grinding a narrow flat land, 0.002 to 0.006 inch wide, on the cutting edge that is made about 30 degrees with respect to the tool face. For some heavy-duty applications, a wider land is used. The setup should be as rigid as possible and the feed rate should not normally exceed 0.020 inch, although 0.030 inch has been used successfully. Ceramics and cermets are recommended for roughing and finishing operations on all cast irons, plain carbon and alloy steels, and stainless steels. Materials up to a hardness of 60 Rockwell C Scale can be cut with ceramic and cermet cutting tools. These tools should not be used to machine aluminum and aluminum alloys, magnesium alloys, titanium, and titanium alloys. Cast Nonferrous Alloy: Cutting tools of this alloy are made from tungsten, tantalum, chromium, and cobalt plus carbon. Other alloying elements are also used to produce materials with high temperature and wear resistance. These alloys cannot be softened by heat treatment and must be cast and ground to shape. The room-temperature hardness of cast nonferrous alloys is lower than for high-speed steel, but the hardness and wear resistance is retained to a higher temperature. The alloys are generally marketed under trade names such as Stellite, Crobalt, and Tantung. The initial cutting speed for cast nonferrous tools can be 20 to 50 per cent greater than the recommended cutting speed for high-speed steel as given in the accompanying tables. Diamond Cutting Tools: These are available in three forms: single-crystal natural diamonds shaped to a cutting edge and mounted on a tool holder on a boring bar; polycrystalline diamond indexable inserts made from synthetic or natural diamond powders that have been compacted and sintered into a solid mass, and chemically vapor-deposited diamond. Single-crystal and polycrystalline diamond cutting tools are very wear-resistant, and are recommended for machining abrasive materials that cause other cutting tool materials to wear rapidly. Typical of the abrasive materials machined with single-crystal and polycrystalline diamond tools and cutting speeds used are the following: fiberglass, 300 to 1000 fpm; fused silica, 900 to 950 fpm; reinforced melamine plastics, 350 to 1000 fpm; reinforced phenolic plastics, 350 to 1000 fpm; thermosetting plastics, 300 to 2000 fpm; Teflon,



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600 fpm; nylon, 200 to 300 fpm; mica, 300 to 1000 fpm; graphite, 200 to 2000 fpm; babbitt bearing metal, 700 fpm; and aluminum-silicon alloys, 1000 to 2000 fpm. Another important application of diamond cutting tools is to produce fine surface finishes on soft nonferrous metals that are difficult to finish by other methods. Surface finishes of 1 to 2 microinches can be readily obtained with single-crystal diamond tools, and finishes down to 10 microinches can be obtained with polycrystalline diamond tools. In addition to babbitt and the aluminum-silicon alloys, other metals finished with diamond tools include: soft aluminum, 1000 to 2000 fpm; all wrought and cast aluminum alloys, 600 to 1500 fpm; copper, 1000 fpm; brass, 500 to 1000 fpm; bronze, 300 to 600 fpm; oilite bearing metal, 500 fpm; silver, gold, and platinum, 300 to 2500 fpm; and zinc, 1000 fpm. Ferrous alloys, such as cast iron and steel, should not be machined with diamond cutting tools because the high cutting temperatures generated will cause the diamond to transform into carbon. Chemically Vapor-Deposited (CVD) Diamond: This is a new tool material offering performance characteristics well suited to highly abrasive or corrosive materials, and hard-tomachine composites. CVD diamond is available in two forms: thick-film tools, which are fabricated by brazing CVD diamond tips, approximately 0.020 inch (0.5 mm) thick, to carbide substrates; and thin-film tools, having a pure diamond coating over the rake and flank surfaces of a ceramic or carbide substrate. CVD is pure diamond, made at low temperatures and pressures, with no metallic binder phase. This diamond purity gives CVD diamond tools extreme hardness, high abrasion resistance, low friction, high thermal conductivity, and chemical inertness. CVD tools are generally used as direct replacements for PCD (polycrystalline diamond) tools, primarily in finishing, semifinishing, and continuous turning applications of extremely wear-intensive materials. The small grain size of CVD diamond (ranging from less than 1 µm to 50 µm) yields superior surface finishes compared with PCD, and the higher thermal conductivity and better thermal and chemical stability of pure diamond allow CVD tools to operate at faster speeds without generating harmful levels of heat. The extreme hardness of CVD tools may also result in significantly longer tool life. CVD diamond cutting tools are recommended for the following materials: a l u m i n u m and other ductile; nonferrous alloys such as copper, brass, and bronze; and highly abrasive composite materials such as graphite, carbon-carbon, carbon-filled phenolic, fiberglass, and honeycomb materials. Cubic Boron Nitride (CBN): Next to diamond, CBN is the hardest known material. It will retain its hardness at a temperature of 1800°F and higher, making it an ideal cutting tool material for machining very hard and tough materials at cutting speeds beyond those possible with other cutting tool materials. Indexable inserts and cutting tool blanks made from this material consist of a layer, approximately 0.020 inch thick, of polycrystalline cubic boron nitride firmly bonded to the top of a cemented carbide substrate. Cubic boron nitride is recommended for rough and finish turning hardened plain carbon and alloy steels, hardened tool steels, hard cast irons, all hardness grades of gray cast iron, and superalloys. As a class, the superalloys are not as hard as hardened steel; however, their combination of high strength and tendency to deform plastically under the pressure of the cut, or gumminess, places them in the class of hard-to-machine materials. Conventional materials that can be readily machined with other cutting tool materials should not be machined with cubic boron nitride. Round indexable CBN inserts are recommended when taking severe cuts in order to provide maximum strength to the insert. When using square or triangular inserts, a large lead angle should be used, normally 15°, and whenever possible, 45°. A negative rake angle should always be used, which for most applications is negative 5°. The relief angle should be 5° to 9°. Although cubic boron nitride cutting tools can be used without a coolant, flooding the tool with a water-soluble type coolant is recommended. Cutting Speed, Feed, Depth of Cut, Tool Wear, and Tool Life.—The cutting conditions that determine the rate of metal removal are the cutting speed, the feed rate, and the depth of cut. These cutting conditions and the nature of the material to be cut determine the



SPEEDS AND FEEDS

power required to take the cut. The cutting conditions must be adjusted to stay within the power available on the machine tool to be used. Power requirements are discussed in Estimating Machining Power later in this section. The cutting conditions must also be considered in relation to the tool life. Tool life is defined as the cutting time to reach a predetermined amount of wear, usually flank wear. Tool life is determined by assessing the time—the tool life—at which a given predetermined flank wear is reached (0.01, 0.015, 0.025, 0.03 inch, for example). This amount of wear is called the tool wear criterion, and its size depends on the tool grade used. Usually, a tougher grade can be used with a bigger flank wear, but for finishing operations, where close tolerances are required, the wear criterion is relatively small. Other wear criteria are a predetermined value of the machined surface roughness and the depth of the crater that develops on the rake face of the tool. The ANSI standard, Specification For Tool Life Testing With Single-Point Tools (ANSI B94.55M-1985), defines the end of tool life as a given amount of wear on the flank of a tool. This standard is followed when making scientific machinability tests with singlepoint cutting tools in order to achieve uniformity in testing procedures so that results from different machinability laboratories can be readily compared. It is not practicable or necessary to follow this standard in the shop; however, it should be understood that the cutting conditions and tool life are related. Tool life is influenced most by cutting speed, then by the feed rate, and least by the depth of cut. When the depth of cut is increased to about 10 times greater than the feed, a further increase in the depth of cut will have no significant effect on the tool life. This characteristic of the cutting tool performance is very important in determining the operating or cutting conditions for machining metals. Conversely, if the cutting speed or the feed is decreased, the increase in the tool life will be proportionately greater than the decrease in the cutting speed or the feed. Tool life is reduced when either feed or cutting speed is increased. For example, the cutting speed and the feed may be increased if a shorter tool life is accepted; furthermore, the reduction in the tool life will be proportionately greater than the increase in the cutting speed or the feed. However, it is less well understood that a higher feed rate (feed/rev × speed) may result in a longer tool life if a higher feed/rev is used in combination with a lower cutting speed. This principle is well illustrated in the speed tables of this section, where two sets of feed and speed data are given (labeled optimum and average) that result in the same tool life. The optimum set results in a greater feed rate (i.e., increased productivity) although the feed/rev is higher and cutting speed lower than the average set. Complete instructions for using the speed tables and for estimating tool life are given in How to Use the Feeds and Speeds Tables starting on page 1022. Selecting Cutting Conditions.—The first step in establishing the cutting conditions is to select the depth of cut. The depth of cut will be limited by the amount of metal that is to be machined from the workpiece, by the power available on the machine tool, by the rigidity of the workpiece and the cutting tool, and by the rigidity of the setup. The depth of cut has the least effect upon the tool life, so the heaviest possible depth of cut should always be used. The second step is to select the feed (feed/rev for turning, drilling, and reaming, or feed/tooth for milling). The available power must be sufficient to make the required depth of cut at the selected feed. The maximum feed possible that will produce an acceptable surface finish should be selected. The third step is to select the cutting speed. Although the accompanying tables provide recommended cutting speeds and feeds for many materials, experience in machining a certain material may form the best basis for adjusting the given cutting speeds to a particular job. However, in general, the depth of cut should be selected first, followed by the feed, and last the cutting speed.



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Table 16. Tool Troubleshooting Check List Tool Material Carbide

Problem Excessive flank wear—Tool life too short

HSS

Excessive cratering

Carbide

HSS

Cutting edge chipping

Carbide

Remedy 1. Change to harder, more wear-resistant grade 2. Reduce the cutting speed 3. Reduce the cutting speed and increase the feed to maintain production 4. Reduce the feed 5. For work-hardenable materials—increase the feed 6. Increase the lead angle 7. Increase the relief angles 1. Use a coolant 2. Reduce the cutting speed 3. Reduce the cutting speed and increase the feed to maintain production 4. Reduce the feed 5. For work-hardenable materials—increase the feed 6. Increase the lead angle 7. Increase the relief angle 1. Use a crater-resistant grade 2. Use a harder, more wear-resistant grade 3. Reduce the cutting speed 4. Reduce the feed 5. Widen the chip breaker groove 1. Use a coolant 2. Reduce the cutting speed 3. Reduce the feed 4. Widen the chip breaker groove 1. Increase the cutting speed 2. Lightly hone the cutting edge 3. Change to a tougher grade 4. Use negative-rake tools 5. Increase the lead angle 6. Reduce the feed 7. Reduce the depth of cut 8. Reduce the relief angles 9. If low cutting speed must be used, use a high-additive EP cutting fluid

HSS

1. Use a high additive EP cutting fluid 2. Lightly hone the cutting edge before using 3. Increase the lead angle 4. Reduce the feed 5. Reduce the depth of cut 6. Use a negative rake angle 7. Reduce the relief angles

Carbide and HSS

1. Check the setup for cause if chatter occurs 2. Check the grinding procedure for tool overheating 3. Reduce the tool overhang 1. Change to a grade containing more tantalum 2. Reduce the cutting speed 3. Reduce the feed 1. Increase the cutting speed 2. If low cutting speed must be used, use a high additive EP cutting fluid 4. For light cuts, use straight titanium carbide grade 5. Increase the nose radius 6. Reduce the feed 7. Increase the relief angles 8. Use positive rake tools

Cutting edge deformation

Carbide

Poor surface finish

Carbide



SPEEDS AND FEEDS Table 16. (Continued) Tool Troubleshooting Check List Tool Material HSS

Problem Poor surface finish (Continued)

Notching at the depth of cut line

Remedy 1. Use a high additive EP cutting fluid 2. Increase the nose radius 3. Reduce the feed 4. Increase the relief angles 5. Increase the rake angles

Diamond Carbide and HSS

1. Use diamond tool for soft materials 1. Increase the lead angle 2. Reduce the feed

Cutting Speed Formulas Most machining operations are conducted on machine tools having a rotating spindle. Cutting speeds are usually given in feet or meters per minute and these speeds must be converted to spindle speeds, in revolutions per minute, to operate the machine. Conversion is accomplished by use of the following formulas: For U.S. units:

For metric units:

V- rpm N = 12V ---------- = 3.82 --πD D

V- rpm N = 1000V ---------------- = 318.3 --πD D

where N is the spindle speed in revolutions per minute (rpm); V is the cutting speed in feet per minute (fpm) for U.S. units and meters per minute (m/min) for metric units. In turning, D is the diameter of the workpiece; in milling, drilling, reaming, and other operations that use a rotating tool, D is the cutter diameter in inches for U.S. units and in millimeters for metric units. π = 3.1416. Example:The cutting speed for turning a 4-inch (101.6-mm) diameter bar has been found to be 575 fpm (175.3 m/min). Using both the inch and metric formulas, calculate the lathe spindle speed. 12 × 575 = 549 rpm N = 12V ---------- = ------------------------πD 3.1416 × 4

1000 × 175.3 - = 549 rpm N = 1000V ---------------- = ----------------------------------πD 3.1416 × 101.6

When the cutting tool or workpiece diameter and the spindle speed in rpm are known, it is often necessary to calculate the cutting speed in feet or meters per minute. In this event, the following formulas are used. For U.S. units:

For metric units:

V = πDN ------------ fpm 12

πDN- m/min V = ----------1000

As in the previous formulas, N is the rpm and D is the diameter in inches for the U.S. unit formula and in millimeters for the metric formula. Example:Calculate the cutting speed in feet per minute and in meters per minute if the spindle speed of a 3⁄4-inch (19.05-mm) drill is 400 rpm. × 0.75 × 400- = 78.5 fpm V = πDN ------------ = π ---------------------------------12 12 πDN- = ------------------------------------π × 19.05 × 400- = 24.9 m/min V = ----------1000 1000



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Cutting Speeds and Equivalent RPM for Drills of Number and Letter Sizes Size No. 1 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 54 Size A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

30′

40′

50′

503 518 548 562 576 592 606 630 647 678 712 730 754 779 816 892 988 1032 1076 1129 1169 1226 1333 1415 1508 1637 1805 2084

670 691 731 749 768 790 808 840 863 904 949 973 1005 1039 1088 1189 1317 1376 1435 1505 1559 1634 1777 1886 2010 2183 2406 2778

838 864 914 936 960 987 1010 1050 1079 1130 1186 1217 1257 1299 1360 1487 1647 1721 1794 1882 1949 2043 2221 2358 2513 2729 3008 3473

491 482 473 467 458 446 440 430 421 414 408 395 389 380 363 355 345 338 329 320 311 304 297 289 284 277

654 642 631 622 611 594 585 574 562 552 544 527 518 506 484 473 460 451 439 426 415 405 396 385 378 370

818 803 789 778 764 743 732 718 702 690 680 659 648 633 605 592 575 564 549 533 519 507 495 481 473 462

Cutting Speed, Feet per Minute 60′ 70′ 80′ 90′ 100′ Revolutions per Minute for Number Sizes 1005 1173 1340 1508 1675 1037 1210 1382 1555 1728 1097 1280 1462 1645 1828 1123 1310 1498 1685 1872 1151 1343 1535 1727 1919 1184 1382 1579 1777 1974 1213 1415 1617 1819 2021 1259 1469 1679 1889 2099 1295 1511 1726 1942 2158 1356 1582 1808 2034 2260 1423 1660 1898 2135 2372 1460 1703 1946 2190 2433 1508 1759 2010 2262 2513 1559 1819 2078 2338 2598 1631 1903 2175 2447 2719 1784 2081 2378 2676 2973 1976 2305 2634 2964 3293 2065 2409 2753 3097 3442 2152 2511 2870 3228 3587 2258 2634 3010 3387 3763 2339 2729 3118 3508 3898 2451 2860 3268 3677 4085 2665 3109 3554 3999 4442 2830 3301 3773 4244 4716 3016 3518 4021 4523 5026 3274 3820 4366 4911 5457 3609 4211 4812 5414 6015 4167 4862 5556 6251 6945 Revolutions per Minute for Letter Sizes 982 1145 1309 1472 1636 963 1124 1284 1445 1605 947 1105 1262 1420 1578 934 1089 1245 1400 1556 917 1070 1222 1375 1528 892 1040 1189 1337 1486 878 1024 1170 1317 1463 862 1005 1149 1292 1436 842 983 1123 1264 1404 827 965 1103 1241 1379 815 951 1087 1223 1359 790 922 1054 1185 1317 777 907 1036 1166 1295 759 886 1012 1139 1265 725 846 967 1088 1209 710 828 946 1065 1183 690 805 920 1035 1150 676 789 902 1014 1127 659 769 878 988 1098 640 746 853 959 1066 623 727 830 934 1038 608 709 810 912 1013 594 693 792 891 989 576 672 769 865 962 567 662 756 851 945 555 647 740 832 925

110′

130′

150′

1843 1901 2010 2060 2111 2171 2223 2309 2374 2479 2610 2676 2764 2858 2990 3270 3622 3785 3945 4140 4287 4494 4886 5187 5528 6002 6619 7639

2179 2247 2376 2434 2495 2566 2627 2728 2806 2930 3084 3164 3267 3378 3534 3864 4281 4474 4663 4892 5067 5311 5774 6130 6534 7094 7820 9028

2513 2593 2741 2809 2879 2961 3032 3148 3237 3380 3559 3649 3769 3898 4078 4459 4939 5162 5380 5645 5846 6128 6662 7074 7539 8185 9023 10417

1796 1765 1736 1708 1681 1635 1610 1580 1545 1517 1495 1449 1424 1391 1330 1301 1266 1239 1207 1173 1142 1114 1088 1058 1040 1017

2122 2086 2052 2018 1968 1932 1903 1867 1826 1793 1767 1712 1683 1644 1571 1537 1496 1465 1427 1387 1349 1317 1286 1251 1229 1202

2448 2407 2368 2329 2292 2229 2195 2154 2106 2068 2039 1976 1942 1897 1813 1774 1726 1690 1646 1600 1557 1520 1484 1443 1418 1387

For fractional drill sizes, use the following table.



RPM FOR VARIOUS SPEEDS Revolutions per Minute for Various Cutting Speeds and Diameters

Dia., Inches 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1 11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 17⁄8 2 21⁄8 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2 35⁄8 33⁄4 37⁄8 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2 63⁄4 7 71⁄4 71⁄2 73⁄4 8

40

50

60

70

611 489 408 349 306 272 245 222 203 190 175 163 153 144 136 129 123 116 111 106 102 97.6 93.9 90.4 87.3 81.5 76.4 72.0 68.0 64.4 61.2 58.0 55.6 52.8 51.0 48.8 46.8 45.2 43.6 42.0 40.8 39.4 38.2 35.9 34.0 32.2 30.6 29.1 27.8 26.6 25.5 24.4 23.5 22.6 21.8 21.1 20.4 19.7 19.1

764 611 509 437 382 340 306 273 254 237 219 204 191 180 170 161 153 146 139 133 127 122 117 113 109 102 95.5 90.0 85.5 80.5 76.3 72.5 69.5 66.0 63.7 61.0 58.5 56.5 54.5 52.5 51.0 49.3 47.8 44.9 42.4 40.2 38.2 36.4 34.7 33.2 31.8 30.6 29.4 28.3 27.3 26.4 25.4 24.6 23.9

917 733 611 524 459 407 367 333 306 284 262 244 229 215 204 193 183 175 167 159 153 146 141 136 131 122 115 108 102 96.6 91.7 87.0 83.4 79.2 76.4 73.2 70.2 67.8 65.5 63.0 61.2 59.1 57.3 53.9 51.0 48.2 45.9 43.6 41.7 39.8 38.2 36.7 35.2 34.0 32.7 31.6 30.5 29.5 28.7

1070 856 713 611 535 475 428 389 357 332 306 285 267 251 238 225 214 204 195 186 178 171 165 158 153 143 134 126 119 113 107 102 97.2 92.4 89.1 85.4 81.9 79.1 76.4 73.5 71.4 69.0 66.9 62.9 59.4 56.3 53.5 50.9 48.6 46.5 44.6 42.8 41.1 39.6 38.2 36.9 35.6 34.4 33.4

Cutting Speed, Feet per Minute 80 90 100 120 Revolutions per Minute 1222 1376 1528 1834 978 1100 1222 1466 815 916 1018 1222 699 786 874 1049 611 688 764 917 543 611 679 813 489 552 612 736 444 500 555 666 408 458 508 610 379 427 474 569 349 392 438 526 326 366 407 488 306 344 382 458 287 323 359 431 272 306 340 408 258 290 322 386 245 274 306 367 233 262 291 349 222 250 278 334 212 239 265 318 204 230 254 305 195 220 244 293 188 212 234 281 181 203 226 271 175 196 218 262 163 184 204 244 153 172 191 229 144 162 180 216 136 153 170 204 129 145 161 193 122 138 153 184 116 131 145 174 111 125 139 167 106 119 132 158 102 114 127 152 97.6 110 122 146 93.6 105 117 140 90.4 102 113 136 87.4 98.1 109 131 84.0 94.5 105 126 81.6 91.8 102 122 78.8 88.6 98.5 118 76.4 86.0 95.6 115 71.8 80.8 89.8 108 67.9 76.3 84.8 102 64.3 72.4 80.4 96.9 61.1 68.8 76.4 91.7 58.2 65.4 72.7 87.2 55.6 62.5 69.4 83.3 53.1 59.8 66.4 80.0 51.0 57.2 63.6 76.3 48.9 55.0 61.1 73.3 47.0 52.8 58.7 70.4 45.3 50.9 56.6 67.9 43.7 49.1 54.6 65.5 42.2 47.4 52.7 63.2 40.7 45.8 50.9 61.1 39.4 44.3 49.2 59.0 38.2 43.0 47.8 57.4

140

160

180

200

2139 1711 1425 1224 1070 951 857 770 711 664 613 570 535 503 476 451 428 407 389 371 356 342 328 316 305 286 267 252 238 225 213 203 195 185 178 171 164 158 153 147 143 138 134 126 119 113 107 102 97.2 93.0 89.0 85.5 82.2 79.2 76.4 73.8 71.0 68.9 66.9

2445 1955 1629 1398 1222 1086 979 888 813 758 701 651 611 575 544 515 490 466 445 424 406 390 374 362 349 326 306 288 272 258 245 232 222 211 203 195 188 181 174 168 163 158 153 144 136 129 122 116 111 106 102 97.7 93.9 90.6 87.4 84.3 81.4 78.7 76.5

2750 2200 1832 1573 1375 1222 1102 999 914 853 788 733 688 646 612 580 551 524 500 477 457 439 421 407 392 367 344 324 306 290 275 261 250 238 228 219 211 203 196 189 184 177 172 162 153 145 138 131 125 120 114 110 106 102 98.3 94.9 91.6 88.6 86.0

3056 2444 2036 1748 1528 1358 1224 1101 1016 948 876 814 764 718 680 644 612 582 556 530 508 488 468 452 436 408 382 360 340 322 306 290 278 264 254 244 234 226 218 210 205 197 191 180 170 161 153 145 139 133 127 122 117 113 109 105 102 98.4 95.6


Machinery's Handbook 27th Edition RPM FOR VARIOUS SPEEDS

1019

Revolutions per Minute for Various Cutting Speeds and Diameters Dia., Inches 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1 11⁄16 11⁄8 13⁄16 11⁄4 15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 113⁄16 17⁄8 115⁄16 2 21⁄8 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄8 31⁄4 33⁄8 31⁄2 35⁄8 33⁄4 37⁄8 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4 6 61⁄4 61⁄2 63⁄4 7 71⁄4 71⁄2 73⁄4 8

225

250

275

300

3438 2750 2292 1964 1719 1528 1375 1250 1146 1058 982 917 859 809 764 724 687 654 625 598 573 550 528 509 491 474 458 443 429 404 382 362 343 327 312 299 286 274 264 254 245 237 229 221 214 202 191 180 171 163 156 149 143 137 132 127 122 118 114 111 107

3820 3056 2546 2182 1910 1698 1528 1389 1273 1175 1091 1019 955 899 849 804 764 727 694 664 636 611 587 566 545 527 509 493 477 449 424 402 382 363 347 332 318 305 293 283 272 263 254 246 238 224 212 201 191 181 173 166 159 152 146 141 136 131 127 123 119

4202 3362 2801 2401 2101 1868 1681 1528 1401 1293 1200 1120 1050 988 933 884 840 800 764 730 700 672 646 622 600 579 560 542 525 494 468 442 420 400 381 365 350 336 323 311 300 289 280 271 262 247 233 221 210 199 190 182 174 168 161 155 149 144 139 135 131

4584 3667 3056 2619 2292 2037 1834 1667 1528 1410 1310 1222 1146 1078 1018 965 917 873 833 797 764 733 705 679 654 632 611 591 573 539 509 482 458 436 416 398 381 366 352 339 327 316 305 295 286 269 254 241 229 218 208 199 190 183 176 169 163 158 152 148 143

Cutting Speed, Feet per Minute 325 350 375 400 Revolutions per Minute 4966 5348 5730 6112 3973 4278 4584 4889 3310 3565 3820 4074 2837 3056 3274 3492 2483 2675 2866 3057 2207 2377 2547 2717 1987 2139 2292 2445 1806 1941 2084 2223 1655 1783 1910 2038 1528 1646 1763 1881 1419 1528 1637 1746 1324 1426 1528 1630 1241 1337 1432 1528 1168 1258 1348 1438 1103 1188 1273 1358 1045 1126 1206 1287 993 1069 1146 1222 946 1018 1091 1164 903 972 1042 1111 863 930 996 1063 827 891 955 1018 794 855 916 978 764 822 881 940 735 792 849 905 709 764 818 873 685 737 790 843 662 713 764 815 640 690 739 788 620 668 716 764 584 629 674 719 551 594 636 679 522 563 603 643 496 534 573 611 472 509 545 582 451 486 520 555 431 465 498 531 413 445 477 509 397 427 458 488 381 411 440 470 367 396 424 452 354 381 409 436 342 368 395 421 331 356 382 407 320 345 369 394 310 334 358 382 292 314 337 359 275 297 318 339 261 281 301 321 248 267 286 305 236 254 272 290 225 242 260 277 215 232 249 265 206 222 238 254 198 213 229 244 190 205 220 234 183 198 212 226 177 190 204 218 171 184 197 210 165 178 190 203 160 172 185 197 155 167 179 191

425

450

500

550

6493 5195 4329 3710 3248 2887 2598 2362 2165 1998 1855 1732 1623 1528 1443 1367 1299 1237 1181 1129 1082 1039 999 962 927 895 866 838 811 764 721 683 649 618 590 564 541 519 499 481 463 447 433 419 405 383 360 341 324 308 294 282 270 259 249 240 231 223 216 209 203

6875 5501 4584 3929 3439 3056 2751 2501 2292 2116 1965 1834 1719 1618 1528 1448 1375 1309 1250 1196 1146 1100 1057 1018 982 948 917 887 859 809 764 724 687 654 625 598 572 549 528 509 490 474 458 443 429 404 382 361 343 327 312 298 286 274 264 254 245 237 229 222 215

7639 6112 5093 4365 3821 3396 3057 2779 2547 2351 2183 2038 1910 1798 1698 1609 1528 1455 1389 1329 1273 1222 1175 1132 1091 1054 1019 986 955 899 849 804 764 727 694 664 636 611 587 566 545 527 509 493 477 449 424 402 382 363 347 332 318 305 293 283 272 263 254 246 238

8403 6723 5602 4802 4203 3736 3362 3056 2802 2586 2401 2241 2101 1977 1867 1769 1681 1601 1528 1461 1400 1344 1293 1245 1200 1159 1120 1084 1050 988 933 884 840 800 763 730 700 672 646 622 600 579 560 542 525 494 466 442 420 399 381 365 349 336 322 311 299 289 279 271 262



RPM FOR VARIOUS SPEEDS

Revolutions per Minute for Various Cutting Speeds and Diameters (Metric Units) Cutting Speed, Meters per Minute Dia., mm

5

6

8

10

12

16

20

25

30

35

40

45

Revolutions per Minute 5

318

382

509

637

764

1019

1273

1592

1910

2228

2546

2865

6

265

318

424

530

637

849

1061

1326

1592

1857

2122

2387

8

199

239

318

398

477

637

796

995

1194

1393

1592

1790

10

159

191

255

318

382

509

637

796

955

1114

1273

1432

12

133

159

212

265

318

424

531

663

796

928

1061

1194

119

159

199

239

318

398

497

597

696

796

895

95.5

127

159

191

255

318

398

477

557

637

716

102

16

99.5

20

79.6

25

63.7

76.4

30

53.1

63.7

84.9

127

153

204

255

318

382

446

509

573

106

127

170

212

265

318

371

424

477

35

45.5

54.6

72.8

90.9

145

182

227

273

318

364

409

40

39.8

47.7

63.7

79.6

95.5

127

159

199

239

279

318

358 318

109

45

35.4

42.4

56.6

70.7

84.9

113

141

177

212

248

283

50

31.8

38.2

51

63.7

76.4

102

127

159

191

223

255

286

55

28.9

34.7

46.3

57.9

69.4

92.6

116

145

174

203

231

260

60

26.6

31.8

42.4

53.1

63.7

84.9

106

133

159

186

212

239

65

24.5

29.4

39.2

49

58.8

78.4

98

122

147

171

196

220

70

22.7

27.3

36.4

45.5

54.6

72.8

90.9

114

136

159

182

205

75

21.2

25.5

34

42.4

51

68

84.9

106

127

149

170

191

80

19.9

23.9

31.8

39.8

47.7

63.7

79.6

99.5

119

139

159

179

106

90

17.7

21.2

28.3

35.4

42.4

56.6

70.7

88.4

124

141

159

100

15.9

19.1

25.5

31.8

38.2

51

63.7

79.6

95.5

111

127

143

110

14.5

17.4

23.1

28.9

34.7

46.2

57.9

72.3

86.8

101

116

130

120

13.3

15.9

21.2

26.5

31.8

42.4

53.1

66.3

79.6

92.8

106

119

130

12.2

14.7

19.6

24.5

29.4

39.2

49

61.2

73.4

85.7

97.9

110

140

11.4

13.6

18.2

22.7

27.3

36.4

45.5

56.8

68.2

79.6

90.9

102

150

10.6

12.7

17

21.2

25.5

34

42.4

53.1

63.7

74.3

84.9

95.5

160

9.9

11.9

15.9

19.9

23.9

31.8

39.8

49.7

59.7

69.6

79.6

89.5

170

9.4

11.2

15

18.7

22.5

30

37.4

46.8

56.2

65.5

74.9

84.2

180

8.8

10.6

14.1

17.7

21.2

28.3

35.4

44.2

53.1

61.9

70.7

79.6

190

8.3

10

13.4

16.8

20.1

26.8

33.5

41.9

50.3

58.6

67

75.4

200

8

39.5

12.7

15.9

19.1

25.5

31.8

39.8

47.7

55.7

63.7

71.6

220

7.2

8.7

11.6

14.5

17.4

23.1

28.9

36.2

43.4

50.6

57.9

65.1

240

6.6

8

10.6

13.3

15.9

21.2

26.5

33.2

39.8

46.4

53.1

59.7

260

6.1

7.3

9.8

12.2

14.7

19.6

24.5

30.6

36.7

42.8

49

55.1

280

5.7

6.8

9.1

11.4

13.6

18.2

22.7

28.4

34.1

39.8

45.5

51.1

300

5.3

6.4

8.5

10.6

12.7

17

21.2

26.5

31.8

37.1

42.4

47.7

350

4.5

5.4

7.3

9.1

10.9

14.6

18.2

22.7

27.3

31.8

36.4

40.9

400

4

4.8

6.4

8

9.5

12.7

15.9

19.9

23.9

27.9

31.8

35.8

450

3.5

4.2

5.7

7.1

8.5

11.3

14.1

17.7

21.2

24.8

28.3

31.8

500

3.2

3.8

5.1

6.4

7.6

10.2

12.7

15.9

19.1

22.3

25.5

28.6


Machinery's Handbook 27th Edition RPM FOR VARIOUS SPEEDS

1021

Revolutions per Minute for Various Cutting Speeds and Diameters (Metric Units) Cutting Speed, Meters per Minute Dia., mm

50

55

60

65

70

75

80

85

90

95

100

200

Revolutions per Minute 5

3183

3501

3820

4138

4456

4775

5093

5411

5730

6048

6366

12,732

6

2653

2918

3183

3448

3714

3979

4244

4509

4775

5039

5305

10,610

8

1989

2188

2387

2586

2785

2984

3183

3382

3581

3780

3979

7958

10

1592

1751

1910

2069

2228

2387

2546

2706

2865

3024

3183

6366

12

1326

1459

1592

1724

1857

1989

2122

2255

2387

2520

2653

5305

16

995

1094

1194

1293

1393

1492

1591

1691

1790

1890

1989

3979

20

796

875

955

1034

1114

1194

1273

1353

1432

1512

1592

3183

25

637

700

764

828

891

955

1019

1082

1146

1210

1273

2546

30

530

584

637

690

743

796

849

902

955

1008

1061

2122

35

455

500

546

591

637

682

728

773

819

864

909

1818

40

398

438

477

517

557

597

637

676

716

756

796

1592

45

354

389

424

460

495

531

566

601

637

672

707

1415

50

318

350

382

414

446

477

509

541

573

605

637

1273

55

289

318

347

376

405

434

463

492

521

550

579

1157

60

265

292

318

345

371

398

424

451

477

504

530

1061

65

245

269

294

318

343

367

392

416

441

465

490

979

70

227

250

273

296

318

341

364

387

409

432

455

909

75

212

233

255

276

297

318

340

361

382

403

424

849

80

199

219

239

259

279

298

318

338

358

378

398

796

90

177

195

212

230

248

265

283

301

318

336

354

707

100

159

175

191

207

223

239

255

271

286

302

318

637

110

145

159

174

188

203

217

231

246

260

275

289

579

120

133

146

159

172

186

199

212

225

239

252

265

530

130

122

135

147

159

171

184

196

208

220

233

245

490

140

114

125

136

148

159

171

182

193

205

216

227

455

150

106

117

127

138

149

159

170

180

191

202

212

424

160

99.5

109

119

129

139

149

159

169

179

189

199

398

170

93.6

103

112

122

131

140

150

159

169

178

187

374

180

88.4

97.3

106

115

124

133

141

150

159

168

177

354

190

83.8

92.1

101

109

117

126

134

142

151

159

167

335

200

79.6

87.5

95.5

103

111

119

127

135

143

151

159

318

220

72.3

79.6

86.8

94

101

109

116

123

130

137

145

289

240

66.3

72.9

79.6

86.2

92.8

99.5

106

113

119

126

132

265

260

61.2

67.3

73.4

79.6

85.7

91.8

97.9

104

110

116

122

245

280

56.8

62.5

68.2

73.9

79.6

85.3

90.9

96.6

102

108

114

227

300

53.1

58.3

63.7

69

74.3

79.6

84.9

90.2

95.5

101

106

212

350

45.5

50

54.6

59.1

63.7

68.2

72.8

77.3

81.8

99.1

91

182

400

39.8

43.8

47.7

51.7

55.7

59.7

63.7

67.6

71.6

75.6

79.6

159

450

35.4

38.9

42.4

46

49.5

53.1

56.6

60.1

63.6

67.2

70.7

141

500

31.8

35

38.2

41.4

44.6

47.7

50.9

54.1

57.3

60.5

63.6

127



SPEEDS AND FEEDS

SPEED AND FEED TABLES How to Use the Feeds and Speeds Tables Introduction to the Feed and Speed Tables.—The principal tables of feed and speed values are listed in the table below. In this section, Tables 1 through 9 give data for turning, Tables 10 through 15e give data for milling, and Tables 17 through 23 give data for reaming, drilling, threading. The materials in these tables are categorized by description, and Brinell hardness number (Bhn) range or material condition. So far as possible, work materials are grouped by similar machining characteristics. The types of cutting tools (HSS end mill, for example) are identified in one or more rows across the tops of the tables. Other important details concerning the use of the tables are contained in the footnotes to Tables 1, 10 and 17. Information concerning specific cutting tool grades is given in notes at the end of each table. Principal Speed andFeed Tables Feeds and Speeds for Turning Table 1. Cutting Feeds and Speeds for Turning Plain Carbon and Alloy Steels Table 2. Cutting Feeds and Speeds for Turning Tool Steels Table 3. Cutting Feeds and Speeds for Turning Stainless Steels Table 4a. Cutting Feeds and Speeds for Turning Ferrous Cast Metals Table 4b. Cutting Feeds and Speeds for Turning Ferrous Cast Metals Table 5c. Cutting-Speed Adjustment Factors for Turning with HSS Tools Table 5a. Turning-Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle Table 5b. Tool Life Factors for Turning with Carbides, Ceramics, Cermets, CBN, and Polycrystalline Diamond Table 6. Cutting Feeds and Speeds for Turning Copper Alloys Table 7. Cutting Feeds and Speeds for Turning Titanium and Titanium Alloys Table 8. Cutting Feeds and Speeds for Turning Light Metals Table 9. Cutting Feeds and Speeds for Turning Superalloys Feeds and Speeds for Milling Table 10. Cutting Feeds and Speeds for Milling Aluminum Alloys Table 11. Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels Table 12. Cutting Feeds and Speeds for Milling Tool Steels Table 13. Cutting Feeds and Speeds for Milling Stainless Steels Table 14. Cutting Feeds and Speeds for Milling Ferrous Cast Metals Table 15a. Recommended Feed in Inches per Tooth (ft) for Milling with High Speed Steel Cutters Table 15b. End Milling (Full Slot) Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle Table 15c. End, Slit, and Side Milling Speed Adjustment Factors for Radial Depth of Cut Table 15d. Face Milling Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle Table 15e. Tool Life Adjustment Factors for Face Milling, End Milling, Drilling, and Reaming Table 16. Cutting Tool Grade Descriptions and Common Vendor Equivalents Feeds and Speeds for Drilling, Reaming, and Threading Table 17. Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Table 18. Feeds and Speeds for Drilling, Reaming, and Threading Tool Steels Table 19. Feeds and Speeds for Drilling, Reaming, and Threading Stainless Steels Table 20. Feeds and Speeds for Drilling, Reaming, and Threading Ferrous Cast Metals Table 21. Feeds and Speeds for Drilling, Reaming, and Threading Light Metals Table 22. Feed and Diameter Speed Adjustment Factors for HSS Twist Drills and Reamers Table 23. Feeds and Speeds for Drilling and Reaming Copper Alloys



1023

Each of the cutting speed tables in this section contains two distinct types of cutting speed data. The speed columns at the left of each table contain traditional Handbook cutting speeds for use with high-speed steel (HSS) tools. For many years, this extensive collection of cutting data has been used successfully as starting speed values for turning, milling, drilling, and reaming operations. Instructions and adjustment factors for use with these speeds are given in Table 5c (feed and depth-of-cut factors) for turning, and in Table 15a (feed, depth of cut, and cutter diameter) for milling. Feeds for drilling and reaming are discussed in Using the Feed and Speed Tables for Drilling, Reaming, and Threading. With traditional speeds and feeds, tool life may vary greatly from material to material, making it very difficult to plan efficient cutting operations, in particular for setting up unattended jobs on CNC equipment where the tool life must exceed cutting time, or at least be predictable so that tool changes can be scheduled. This limitation is reduced by using the combined feed/speed data contained in the remaining columns of the speed tables. The combined feed/speed portion of the speed tables gives two sets of feed and speed data for each material represented. These feed/speed pairs are the optimum and average data (identified by Opt. and Avg.); the optimum set is always on the left side of the column and the average set is on the right. The optimum feed/speed data are approximate values of feed and speed that achieve minimum-cost machining by combining a high productivity rate with low tooling cost at a fixed tool life. The average feed/speed data are expected to achieve approximately the same tool life and tooling costs, but productivity is usually lower, so machining costs are higher. The data in this portion of the tables are given in the form of two numbers, of which the first is the feed in thousandths of an inch per revolution (or per tooth, for milling) and the second is the cutting speed in feet per minute. For example, the feed/speed set 15⁄215 represents a feed of 0.015 in./rev at a speed of 215 fpm. Blank cells in the data tables indicate that feed/speed data for these materials were not available at the time of publication. Generally, the feed given in the optimum set should be interpreted as the maximum safe feed for the given work material and cutting tool grade, and the use of a greater feed may result in premature tool wear or tool failure before the end of the expected tool life. The primary exception to this rule occurs in milling, where the feed may be greater than the optimum feed if the radial depth of cut is less than the value established in the table footnote; this topic is covered later in the milling examples. Thus, except for milling, the speed and tool life adjustment tables, to be discussed later, do not permit feeds that are greater than the optimum feed. On the other hand, the speed and tool life adjustment factors often result in cutting speeds that are well outside the given optimum to average speed range. The combined feed/speed data in this section were contributed by Dr. Colding of Colding International Corp., Ann Arbor, MI. The speed, feed, and tool life calculations were made by means of a special computer program and a large database of cutting speed and tool life testing data. The COMP computer program uses tool life equations that are extensions of the F. W. Taylor tool life equation, first proposed in the early 1900s. The Colding tool life equations use a concept called equivalent chip thickness (ECT), which simplifies cutting speed and tool life predictions, and the calculation of cutting forces, torque, and power requirements. ECT is a basic metal cutting parameter that combines the four basic turning variables (depth of cut, lead angle, nose radius, and feed per revolution) into one basic parameter. For other metal cutting operations (milling, drilling, and grinding, for example), ECT also includes additional variables such as the number of teeth, width of cut, and cutter diameter. The ECT concept was first presented in 1931 by Prof. R. Woxen, who showed that equivalent chip thickness is a basic metal cutting parameter for high-speed cutting tools. Dr. Colding later extended the theory to include other tool materials and metal cutting operations, including grinding. The equivalent chip thickness is defined by ECT = A/CEL, where A is the cross-sectional area of the cut (approximately equal to the feed times the depth of cut), and CEL is the cutting edge length or tool contact rubbing length. ECT and several other terms related to tool



SPEEDS AND FEEDS

geometry are illustrated in Figs. 1 and 2. Many combinations of feed, lead angle, nose radius and cutter diameter, axial and radial depth of cut, and numbers of teeth can give the same value of ECT. However, for a constant cutting speed, no matter how the depth of cut, feed, or lead angle, etc., are varied, if a constant value of ECT is maintained, the tool life will also remain constant. A constant value of ECT means that a constant cutting speed gives a constant tool life and an increase in speed results in a reduced tool life. Likewise, if ECT were increased and cutting speed were held constant, as illustrated in the generalized cutting speed vs. ECT graph that follows, tool life would be reduced.

; ;; ; ;; ;;;;;;;;;;;;;;;;;;; ;;;;;;;;;;;; ; ; ; ; ; ; ; ; ; EC

CE

L

T

a

CELe

A'

r

A

f

a =depth of cut A = A′ = chip cross-sectional area CEL = CELe = engaged cutting edge length ECT = equivalent chip thickness =A′/CEL f =feed/rev r =nose radius LA = lead angle (U.S.) LA(ISO) = 90−LA

LA (ISO)

LA (U.S.) Fig. 1. Cutting Geometry, Equivalent Chip Thickness, and Cutting Edge Length

;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;;;;; ;;; ;;;;; ;;;;; ;;; ;;;;; ;;;;; ;;; ;;;;; ;;; ;;; ;;; ;;; CEL

;;; ;;; ;;; ;;; ;;; ;;;

A

A– A

LA (ISO)

A

LA (U.S.)

Rake Angle

Fig. 2. Cutting Geometry for Turning

In the tables, the optimum feed/speed data have been calculated by COMP to achieve a fixed tool life based on the maximum ECT that will result in successful cutting, without premature tool wear or early tool failure. The same tool life is used to calculate the average feed/speed data, but these values are based on one-half of the maximum ECT. Because the data are not linear except over a small range of values, both optimum and average sets are required to adjust speeds for feed, lead angle, depth of cut, and other factors.



1025

Tool life is the most important factor in a machining system, so feeds and speeds cannot be selected as simple numbers, but must be considered with respect to the many parameters that influence tool life. The accuracy of the combined feed/speed data presented is believed to be very high. However, machining is a variable and complicated process and use of the feed and speed tables requires the user to follow the instructions carefully to achieve good predictability. The results achieved, therefore, may vary due to material condition, tool material, machine setup, and other factors, and cannot be guaranteed. The feed values given in the tables are valid for the standard tool geometries and fixed depths of cut that are identified in the table footnotes. If the cutting parameters and tool geometry established in the table footnotes are maintained, turning operations using either the optimum or average feed/speed data (Tables 1 through 9) should achieve a constant tool life of approximately 15 minutes; tool life for milling, drilling, reaming, and threading data (Tables 10 through 14 and Tables 17 through 22) should be approximately 45 minutes. The reason for the different economic tool lives is the higher tooling cost associated with milling-drilling operations than for turning. If the cutting parameters or tool geometry are different from those established in the table footnotes, the same tool life (15 or 45 minutes) still may be maintained by applying the appropriate speed adjustment factors, or tool life may be increased or decreased using tool life adjustment factors. The use of the speed and tool life adjustment factors is described in the examples that follow. Both the optimum and average feed/speed data given are reasonable values for effective cutting. However, the optimum set with its higher feed and lower speed (always the left entry in each table cell) will usually achieve greater productivity. In Table 1, for example, the two entries for turning 1212 free-machining plain carbon steel with uncoated carbide are 17⁄805 and 8⁄1075. These values indicate that a feed of 0.017 in./rev and a speed of 805 ft/min, or a feed of 0.008 in./rev and a speed of 1075 ft/min can be used for this material. The tool life, in each case, will be approximately 15 minutes. If one of these feed and speed pairs is assigned an arbitrary cutting time of 1 minute, then the relative cutting time of the second pair to the first is equal to the ratio of their respective feed × speed products. Here, the same amount of material that can be cut in 1 minute, at the higher feed and lower speed (17⁄805), will require 1.6 minutes at the lower feed and higher speed (8⁄1075) because 17 × 805/(8 × 1075) = 1.6 minutes. LIVE GRAPH

1000

Click here to view

V = Cutting Speed (m/min)

Tool Life, T (min)

100

T=5 T = 15 T = 45 T = 120

10 0.01

0.1

1

Equivalent Chip Thickness, ECT (mm) Cutting Speed versus Equivalent Chip Thickness with Tool Life as a Parameter



SPEEDS AND FEEDS

Speed and Feed Tables for Turning.—Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text. Examples Using the Feed and Speed Tables for Turning: The examples that follow give instructions for determining cutting speeds for turning. In general, the same methods are also used to find cutting speeds for milling, drilling, reaming, and threading, so reading through these examples may bring some additional insight to those other metalworking processes as well. The first step in determining cutting speeds is to locate the work material in the left column of the appropriate table for turning, milling, or drilling, reaming, and threading. Example 1, Turning:Find the cutting speed for turning SAE 1074 plain carbon steel of 225 to 275 Brinell hardness, using an uncoated carbide insert, a feed of 0.015 in./rev, and a depth of cut of 0.1 inch. In Table 1, feed and speed data for two types of uncoated carbide tools are given, one for hard tool grades, the other for tough tool grades. In general, use the speed data from the tool category that most closely matches the tool to be used because there are often significant differences in the speeds and feeds for different tool grades. From the uncoated carbide hard grade values, the optimum and average feed/speed data given in Table 1 are 17⁄615 and 8⁄815, or 0.017 in./rev at 615 ft/min and 0.008 in./rev at 815 ft/min. Because the selected feed (0.015 in./rev) is different from either of the feeds given in the table, the cutting speed must be adjusted to match the feed. The other cutting parameters to be used must also be compared with the general tool and cutting parameters given in the speed tables to determine if adjustments need to be made for these parameters as well. The general tool and cutting parameters for turning, given in the footnote to Table 1, are depth of cut = 0.1 inch, lead angle = 15°, and tool nose radius = 3⁄64 inch. Table 5a is used to adjust the cutting speeds for turning (from Tables 1 through 9) for changes in feed, depth of cut, and lead angle. The new cutting speed V is found from V = Vopt × Ff × Fd, where Vopt is the optimum speed from the table (always the lower of the two speeds given), and Ff and Fd are the adjustment factors from Table 5a for feed and depth of cut, respectively. To determine the two factors Ff and Fd, calculate the ratio of the selected feed to the optimum feed, 0.015⁄0.017 = 0.9, and the ratio of the two given speeds Vavg and Vopt, 815⁄615 = 1.35 (approximately). The feed factor Fd = 1.07 is found in Table 5a at the intersection of the feed ratio row and the speed ratio column. The depth-of-cut factor Fd = 1.0 is found in the same row as the feed factor in the column for depth of cut = 0.1 inch and lead angle = 15°, or for a tool with a 45° lead angle, Fd = 1.18. The final cutting speed for a 15° lead angle is V = Vopt × Ff × Fd = 615 × 1.07 × 1.0 = 658 fpm. Notice that increasing the lead angle tends to permit higher cutting speeds; such an increase is also the general effect of increasing the tool nose radius, although nose radius correction factors are not included in this table. Increasing lead angle also increases the radial pressure exerted by the cutting tool on the workpiece, which may cause unfavorable results on long, slender workpieces. Example 2, Turning:For the same material and feed as the previous example, what is the cutting speed for a 0.4-inch depth of cut and a 45° lead angle? As before, the feed is 0.015 in./rev, so Ff is 1.07, but Fd = 1.03 for depth of cut equal to 0.4 inch and a 45° lead angle. Therefore, V = 615 × 1.07 × 1.03 = 676 fpm. Increasing the lead angle from 15° to 45° permits a much greater (four times) depth of cut, at the same feed and nearly constant speed. Tool life remains constant at 15 minutes. (Continued on page 1036)



Table 1. Cutting Feeds and Speeds for Turning Plain Carbon and Alloy Steels

Opt.

Avg.

Opt.

Avg.

Tool Material Coated Carbide Ceramic Hard Tough Hard Tough f = feed (0.001 in./rev), s = speed (ft/min) Opt. Avg. Opt. Avg. Opt. Avg. Opt. Avg.

Opt.

Avg.

f s f s

17 805 17 745

8 1075 8 935

36 405 36 345

17 555 17 470

17 1165 28 915

8 1295 13 1130

28 850 28 785

13 1200 13 1110

15 3340 15 1795

8 4985 8 2680

15 1670 15 1485

8 2500 8 2215

7 1610 7 1490

3 2055 3 1815

f s

17 730

8 990

36 300

17 430

17 1090

8 1410

28 780

13 1105

15 1610

8 2780

15 1345

8 2005

7 1355

3 1695

f s

17 615

8 815

36 300

17 405

17 865

8 960

28 755

13 960

13 1400

7 1965

13 1170

7 1640

f s

17 515

8 685

36 235

17 340

17 720

8 805

28 650

13 810

10 1430

5 1745

10 1070

5 1305

f s

17 745

8 935

36 345

17 470

28 915

13 1130

28 785

13 1110

15 1795

8 2680

15 1485

8 2215

7 1490

3 1815

f s f s f s

17 615 17 805 17 745 17 615

8 815 8 1075 8 935 8 815

36 300 36 405 36 345 36 300

17 405 17 555 17 470 17 405

17 865 17 1165 28 915 17 865

8 960 8 1295 13 1130 8 960

28 755 28 850 28 785 28 755

13 960 13 1200 13 1110 13 960

13 1400 15 3340 15 1795 13 1400

7 1965 8 4985 8 2680 7 1965

13 1170 15 1670 15 1485 13 1170

7 1640 8 2500 8 2215 7 1640

7 1610 7 1490

3 2055 3 1815

Uncoated Carbide Hard Tough

HSS Material AISI/SAE Designation Free-machining plain carbon steels (resulfurized): 1212, 1213, 1215

100–150

150

150–200

160

100–150

130

150–200

120

175–225

120

{

275–325

75

325–375

50

{

Plain carbon steels: 1006, 1008, 1009, 1010, 1012, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1513, 1514

40

100–150

140

150–200

145

200–250

110

100–125

120

125–175

110

175–225

90

225–275

70

f s


1027

375–425

Cermet

SPEEDS AND FEEDS

(Leaded): 11L17, 11L18, 12L13, 12L14

Speed (fpm)

{

1108, 1109, 1115, 1117, 1118, 1120, 1126, 1211 {

1132, 1137, 1139, 1140, 1144, 1146, 1151

Brinell Hardness


f s

Opt. 17 745

Avg. 8 935

Opt. 36 345

Avg. 17 470

Tool Material Coated Carbide Ceramic Hard Tough Hard Tough f = feed (0.001 in./rev), s = speed (ft/min) Opt. Avg. Opt. Avg. Opt. Avg. Opt. Avg. 28 13 28 13 15 8 15 8 915 1130 785 1110 1795 2680 1485 2215

f s

17 615

8 815

36 300

17 405

17 865

8 960

28 755

13 960

13 1400

7 1965

13 1170

7 1640

f s

17 515

8 685

36 235

17 340

17 720

8 805

28 650

13 810

10 1430

5 1745

10 1070

5 1305

f s

17 730

8 990

36 300

17 430

17 8 1090 1410

28 780

13 1105

15 1610

8 2780

15 1345

8 2005

7 1355

3 1695

f s

17 615

8 815

36 300

17 405

17 865

8 960

28 755

13 960

13 1400

7 1965

13 1170

7 1640

7 1365

3 1695

f s

17 515

8 685

36 235

17 340

17 720

8 805

28 650

13 810

10 1430

5 1745

10 1070

5 1305

17 525

8 705

36 235

17 320

17 505

8 525

28 685

13 960

15 1490

8 2220

15 1190

8 1780

7 1040

3 1310

17 355

8 445

36 140

17 200

17 630

8 850

28 455

13 650

10 1230

5 1510

10 990

5 1210

7 715

3 915

17 330

8 440

36 125

17 175

17 585

8 790

28 125

13 220

8 1200

4 1320

8 960

4 1060

7 575

3 740


HSS Material AISI/SAE Designation

Plain carbon steels (continued): 1055, 1060, 1064, 1065, 1070, 1074, 1078, 1080, 1084, 1086, 1090, 1095, 1548, 1551, 1552, 1561, 1566

Free-machining alloy steels, (resulfurized): 4140, 4150

Speed (fpm)

125–175

100

175–225

85

225–275

70

275–325

60

325–375

40

375–425

30

125–175

100

175–225

80

225–275

65

275–325

50

325–375

35

375–425

30

175–200

110

200–250

90

250–300

65

300–375

50

375–425

40

f s f s f s


Cermet Opt. 7 1490

Avg. 3 1815

SPEEDS AND FEEDS

Plain carbon steels (continued): 1027, 1030, 1033, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1045, 1046, 1048, 1049, 1050, 1052, 1524, 1526, 1527, 1541

Brinell Hardness

1028

Table 1. (Continued) Cutting Feeds and Speeds for Turning Plain Carbon and Alloy Steels



Opt. 17 730 17 615

Avg. 8 990 8 815

Opt. 36 300 36 300

Avg. 17 430 17 405

f s

17 515

8 685

36 235

17 340

17 720

8 805

28 650

13 810

10 1430

5 1745

10 1070

5 1305

17 525

8 705

36 235

17 320

17 505

8 525

28 685

13 960

15 1490

8 2220

15 1190


Free-machining alloy steels: (leaded): 41L30, 41L40, 41L47, 41L50, 43L47, 51L32, 52L100, 86L20, 86L40

Alloy steels: 4012, 4023, 4024, 4028, 4118, 4320, 4419, 4422, 4427, 4615, 4620, 4621, 4626, 4718, 4720, 4815, 4817, 4820, 5015, 5117, 5120, 6118, 8115, 8615, 8617, 8620, 8622, 8625, 8627, 8720, 8822, 94B17

Alloy steels: 1330, 1335, 1340, 1345, 4032, 4037, 4042, 4047, 4130, 4135, 4137, 4140, 4142, 4145, 4147, 4150, 4161, 4337, 4340, 50B44, 50B46, 50B50, 50B60, 5130, 5132, 5140, 5145, 5147, 5150, 5160, 51B60, 6150, 81B45, 8630, 8635, 8637, 8640, 8642, 8645, 8650, 8655, 8660, 8740, 9254, 9255, 9260, 9262, 94B30 E51100, E52100 use (HSS Speeds)

Brinell Hardness

Speed (fpm)

150–200

120

200–250

100

250–300

75

300–375

55

375–425

50

125–175

100

175–225

90

225–275

70

275–325

60

325–35

50

375–425

30 (20)

175–225

85 (70)

225–275

70 (65)

275–325

60 (50) 40 (30) 30 (20)

Opt. 7 1355 7 1355

Avg. 3 1695 3 1695

8 1780

7 1040

3 1310

f s f s f s

17 355

8 445

36 140

1 200

17 630

8 850

28 455

13 650

10 1230

5 1510

10 990

5 1210

7 715

3 915

17 330

8 440

36 135

17 190

17 585

8 790

28 240

13 350

9 1230

5 1430

8 990

5 1150

7 655

3 840

f s

17 330

8 440

36 125

17 175

17 585

8 790

28 125

13 220

8 1200

4 1320

8 960

4 1060

7 575

3 740

f s f s f s

17 525 17 355

8 705 8 445

36 235 36 140

17 320 17 200

17 505 17 630

8 525 8 850

28 685 28 455

13 960 13 650

15 1490 10 1230

8 2220 5 1510

15 1190 10 990

8 1780 5 1210

7 1020 7 715

3 1310 3 915

17 330

8 440

36 135

17 190

17 585

8 790

28 240

13 350

9 1230

5 1430

8 990

5 1150

7 655

3 840

f s

17 330

8 440

36 125

17 175

17 585

8 790

28 125

13 220

8 1200

4 1320

8 960

4 1060

7 575

3 740


1029

325–375 375–425

Cermet

SPEEDS AND FEEDS

f s f s

Tool Material Coated Carbide Ceramic Hard Tough Hard Tough f = feed (0.001 in./rev), s = speed (ft/min) Opt. Avg. Opt. Avg. Opt. Avg. Opt. Avg. 17 8 28 13 15 8 15 8 1090 1410 780 1105 1610 2780 1345 2005 17 8 28 13 13 7 13 7 865 960 755 960 1400 1965 1170 1640



Opt.

Avg.

Opt.

Avg.


f s

17 220

8 295

36 100

17 150

20 355

10 525

28 600

13 865

10 660

5 810

7 570

3 740

f s

17 165

8 185

36 55

17 105

17 325

8 350

28 175

13 260

8 660

4 730

7 445

3 560

17 55†

8 90

36 100

17 150

7

3

17 55†

8 90

8 705

36 235

17 320

17 505

8 525

28 685

8 440

36 125

17 175

17 585

8 790

28 125



Brinell Hardness 220–300

Speed (fpm) 65

300–350

50

350–400

35

43–48 Rc

25

48–52 Rc

10

250–325

60

f s

50–52 Rc

10

f s

200–250

70

f s

17 525

300–350

30

f s

17 330

Maraging steels (not AISI): 18% Ni, Grades 200, 250, 300, and 350

Nitriding steels (not AISI): Nitralloy 125, 135, 135 Mod., 225, and 230, Nitralloy N, Nitralloy EZ, Nitrex 1

f s

17 220

8 295

20 355

10 525

28 600

Cermet Opt.

Avg.

7 385

3 645

10 270

5 500

660

810

10 570

5 740

7 385‡

3 645

10 270

5 500

13 960

15 1490

8 2220

15 1190

8 1780

7 1040

3 1310

13 220

8 1200

4 1320

8 960

4 1060

7 575

3 740

13 865

Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbides, hard = 17, tough = 19, † = 15; coated carbides, hard = 11, tough = 14; ceramics, hard = 2, tough = 3, ‡ = 4; cermet = 7 .


SPEEDS AND FEEDS

Ultra-high-strength steels (not ASI): AMS alloys 6421 (98B37 Mod.), 6422 (98BV40), 6424, 6427, 6428, 6430, 6432, 6433, 6434, 6436, and 6442; 300M and D6ac

1030



Table 2. Cutting Feeds and Speeds for Turning Tool Steels Uncoated HSS Material AISI Designation

Hot work, chromium type: H10, H11, H12, H13, H14, H19

Hot work, tungsten type: H21, H22, H23, H24, H25, H26 Hot work, molybdenum type: H41, H42, H43

Speed (fpm)

150–200 175–225 175–225

100 70 70

200–250

45

200–250

70

200–250 225–275 150–200 200–250

55 45 80 65

325–375

50

48–50 Rc 50–52 Rc 52–56 Rc 150–200 200–250 150–200 200–250

20 10 — 60 50 55 45

Opt.

Avg.

Opt.

Avg.


Cermet Opt.

Avg.

f s

17 455

8 610

36 210

17 270

17 830

8 1110

28 575

13 805

13 935

7 1310

13 790

7 1110

7 915

3 1150

f s

17 445

8 490

36 170

17 235

17 705

8 940

28 515

13 770

13 660

7 925

13 750

7 1210

7 1150

3 1510

f s

17 165

8 185

36 55

17 105

17 325

8 350

28 175

13 260

8 660

4 730

7 445

3 560

17 55†

8 90

7 1150

3 1510

f s

7 385‡

3 645

10 270

5 500

13 750

7 1210

f s

17 445

8 490

36 170

17 235

17 705

8 940

28 515

13 770

13 660

7 925

Special purpose, low alloy: L2, L3, L6

150–200

75

f s

17 445

8 610

36 210

17 270

17 830

8 1110

28 575

13 805

13 935

7 1310

13 790

7 1110

7 915

3 1150

Mold: P2, P3, P4, P5, P6, P26, P21

100–150 150–200

90 80

f s

17 445

8 610

36 210

17 270

17 830

8 1110

28 575

13 805

13 935

7 1310

13 790

7 1110

7 915

3 1150

200–250

65 f s

17 445

8 490

36 170

17 235

17 705

8 940

28 515

13 770

13 660

7 925

13 750

7 1210

7 1150

3 1510

High-speed steel: M1, M2, M6, M10, T1, T2,T6 M3-1, M4 M7, M30, M33, M34, M36, M41, M42, M43, M44, M46, M47, T5, T8 T15, M3-2

225–275

55

225–275

45


1031

Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text.The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbides, hard = 17, tough = 19, † = 15; coated carbides, hard = 11, tough = 14; ceramics, hard = 2, tough = 3, ‡ = 4; cermet = 7.

SPEEDS AND FEEDS

Water hardening: W1, W2, W5 Shock resisting: S1, S2, S5, S6, S7 Cold work, oil hardening: O1, O2, O6, O7 Cold work, high carbon, high chromium: D2, D3, D4, D5, D7 Cold work, air hardening: A2, A3, A8, A9, A10 A4, A6 A7

Brinell Hardness



1032

Table 3. Cutting Feeds and Speeds for Turning Stainless Steels Tool Material Uncoated

Uncoated Carbide

HSS Material Free-machining stainless steel (Ferritic): 430F, 430FSe (Austenitic): 203EZ, 303, 303Se, 303MA, 303Pb, 303Cu, 303 Plus X

Stainless steels (Ferritic): 405, 409 429, 430, 434, 436, 442, 446, 502 (Austenitic): 201, 202, 301, 302, 304, 304L, 305, 308, 321, 347, 348 (Austenitic): 302B, 309, 309S, 310, 310S, 314, 316, 316L, 317, 330

(Martensitic): 403, 410, 420, 501

(Martensitic): 414, 431, Greek Ascoloy, 440A, 440B, 440C (Precipitation hardening):15-5PH, 17-4PH, 17-7PH, AF-71, 17-14CuMo, AFC-77, AM-350, AM-355, AM-362, Custom 455, HNM, PH13-8, PH14-8Mo, PH15-7Mo, Stainless W

Speed (fpm)

135–185

110

135–185 225–275 135–185 185–240 275–325 375–425

100 80 110 100 60 30

135–185

90

135–185 225–275

75 65

135–185

70

135–175 175–225 275–325 375–425 225–275 275–325 375–425 150–200 275–325 325–375 375–450

95 85 55 35 55–60 45–50 30 60 50 40 25

Coated Carbide Tough

Hard

Cermet

Tough

f = feed (0.001 in./rev), s = speed (ft/min) Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

f s

20 480

10 660

36 370

17 395

17 755

8 945

28 640

13 810

7 790

3 995

f s

13 520

7 640

36 310

17 345

28 625

13 815

7 695

3 875

f s

13 520

7 640

36 310

28 625

13 815

7 695

3 875

f s f s

13 210

7 260

36 85

17 135

28 130

13 165

20 480

10 660

36 370

17 395

28 640

13 810

7 790

3 995

f s

13 520

7 640

36 310

17 345

28 625

13 165

7 695

3 875

f s

13 210

7 260

36 85

17 135

28 130

13 165

13 200†

7 230

f s

13 520

7 640

36 310

17 345

28 625

13 815

13 695

7 875

f s

13 195

7 240

36 85

17 155

17 755

8 945

See footnote to Table 1 for more information. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbides, hard = 17, tough = 19; coated carbides, hard = 11, tough = 14; cermet = 7, † = 18.


SPEEDS AND FEEDS

(Martensitic): 416, 416Se, 416 Plus X, 420F, 420FSe, 440F, 440FSe

Brinell Hardness

Hard


Table 4a. Cutting Feeds and Speeds for Turning Ferrous Cast Metals Tool Material Uncoated Carbide HSS

Material

Brinell Hardness

Coated Carbide

Tough

Hard

Ceramic

Tough

Hard

Tough

Cermet

CBN

f = feed (0.001 in./rev), s = speed (ft/min)

Speed (fpm)

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Gray Cast Iron 120–150

ASTM Class 25

160–200

120 90

ASTM Class 30, 35, and 40

190–220

80

ASTM Class 45 and 50

220–260

60


250–320

35

ASTM Type 1, 1b, 5 (Ni resist)

100–215

70

ASTM Type 2, 3, 6 (Ni resist)

120–175

65

ASTM Type 2b, 4 (Ni resist)

150–250

50

(Ferritic): 32510, 35018

110–160

130

(Pearlitic): 40010, 43010, 45006, 45008, 48005, 50005

160–200

95

200–240

75

(Martensitic): 53004, 60003, 60004

200–255

70

(Martensitic): 70002, 70003

220–260

60

(Martensitic): 80002

240–280

50


250–320

30

f s

28 240

13 365

28 665

13 1040

28 585

13 945

15 1490

8 2220

15 1180

8 1880

8 395

4 510

24 8490

11 36380

f s

28 160

13 245

28 400

13 630

28 360

13 580

11 1440

6 1880

11 1200

6 1570

8 335

4 420

24 1590

11 2200

f s

28 110

13 175

28 410

13 575

15 1060

8 1590

15 885

8 1320

8 260

4 325

f s

28 180

13 280

28 730

13 940

28 660

13 885

15 1640

8 2450

15 1410

8 2110

f s

28 125

13 200

28 335

13 505

28 340

13 510

13 1640

7 2310

13 1400

7 1970

f s

28 100

13 120

28 205

13 250

11 1720

6 2240

11 1460

6 1910

Malleable Iron

SPEEDS AND FEEDS

ASTM Class 20

Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust the given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text.


1033

The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbides, tough = 15; Coated carbides, hard = 11, tough = 14; ceramics, hard = 2, tough = 3; cermet = 7; CBN = 1.


1034

Table 4b. Cutting Feeds and Speeds for Turning Ferrous Cast Metals Tool Material Uncoated Carbide

Uncoated HSS Brinell Hardness

Material

Hard

Coated Carbide

Tough

Hard

Ceramic

Tough

Hard

Tough

Cermet

f = feed (0.001 in./rev), s = speed (ft/min) Speed (fpm)

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Nodular (Ductile) Iron (Ferritic): 60-40-18, 65-45-12 (Ferritic-Pearlitic): 80-55-06

{

(Martensitic): 120-90-02

{

100 80

225–260

65

240–300

45

270–330

30

300–400

15

100–150

110

125–175

100

175–225 225–300

90 70

150–200

90

200–250

80

250–300

60

175–225

80

225–250

70

250–300

55

300–350

45

350–400

30

f s

28 200

13 325

28 490

13 700

28 435

13 665

15 970

8 1450

15 845

8 1260

8 365

4 480

f s

28 130

13 210

28 355

13 510

28 310

13 460

11 765

6 995

11 1260

6 1640

8 355

4 445

f s

28 40

13 65

28 145

13 175

10 615

5 750

10 500

5 615

8 120

4 145

Cast Steels (Low-carbon): 1010, 1020 (Medium-carbon): 1030, 1040, 1050

{

(Low-carbon alloy): 1320, 2315, 2320, 4110, 4120, 4320, 8020, 8620

{

(Medium-carbon alloy): 1330, 1340, 2325, 2330, 4125, 4130, 4140, 4330, 4340, 8030, 80B30, 8040, 8430, 8440, 8630, 8640, 9525, 9530, 9535

{

f s

17 370

8 490

36 230

17 285

17 665

8 815

28 495

13 675

15 2090

8 3120

7 625

3 790

f s

17 370

8 490

36 150

17 200

17 595

8 815

28 410

13 590

15 1460

8 2170

7 625

3 790

f s

17 310

8 415

36 115

17 150

17 555

8 760

15 830

8 1240

f s

28 70†

13 145

15 445

8 665

f s

28 115†

13 355

28 335

13 345

15 955

8 1430

The combined feed/speed data in this table are based on tool grades (identified in Table 16) as shown: uncoated carbides, hard = 17; tough = 19, † = 15; coated carbides, hard = 11; tough = 14; ceramics, hard = 2; tough = 3; cermet = 7. Also, see footnote to Table 4a.


SPEEDS AND FEEDS

(Pearlitic-Martensitic): 100-70-03

140–190 190–225


Table 5a. Turning-Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle Ratio of the two cutting speeds given in the tables 1.00

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

1.0 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

Depth of Cut and Lead Angle

Vavg/Vopt 1.10

1.25

1.35

1.50

1.75

2.00

1 in. (25.4 mm)

0.4 in. (10.2 mm)

0.2 in. (5.1 mm)

0.1 in. (2.5 mm)

15°

15°

15°

15°

45°

45°

Feed Factor, Ff 1.0 1.02 1.03 1.05 1.08 1.10 1.09 1.06 1.00 0.80

1.0 1.05 1.09 1.13 1.20 1.25 1.28 1.32 1.34 1.20

1.0 1.07 1.10 1.22 1.25 1.35 1.44 1.52 1.60 1.55

1.0 1.09 1.15 1.22 1.35 1.50 1.66 1.85 2.07 2.24

45°

0.04 in. (1.0 mm)

45°

15°

45°

1.18 1.17 1.15 1.15 1.14 1.14 1.13 1.12 1.10 1.06

1.29 1.27 1.25 1.24 1.23 1.23 1.21 1.18 1.15 1.10

1.35 1.34 1.31 1.30 1.29 1.28 1.26 1.23 1.19 1.12

Depth of Cut and Lead Angle Factor, Fd 1.0 1.10 1.20 1.32 1.50 1.75 2.03 2.42 2.96 3.74

1.0 1.12 1.25 1.43 1.66 2.00 2.43 3.05 4.03 5.84

0.74 0.75 0.77 0.77 0.78 0.78 0.78 0.81 0.84 0.88

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

0.79 0.80 0.81 0.82 0.82 0.82 0.84 0.85 0.89 0.91

1.03 1.03 1.03 1.03 1.03 1.03 1.03 1.02 1.02 1.01

0.85 0.86 0.87 0.87 0.88 0.88 0.89 0.90 0.91 0.92

1.08 1.08 1.07 1.08 1.07 1.07 1.06 1.06 1.05 1.03

1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0

Use with Tables 1 through 9. Not for HSS tools. Tables 1 through 9 data, except for HSS tools, are based on depth of cut = 0.1 inch, lead angle = 15 degrees, and tool life = 15 minutes. For other depths of cut, lead angles, or feeds, use the two feed/speed pairs from the tables and calculate the ratio of desired (new) feed to optimum feed (largest of the two feeds given in the tables), and the ratio of the two cutting speeds (Vavg/Vopt). Use the value of these ratios to find the feed factor Ff at the intersection of the feed ratio row and the speed ratio column in the left half of the table. The depth-of-cut factor Fd is found in the same row as the feed factor in the right half of the table under the column corresponding to the depth of cut and lead angle. The adjusted cutting speed can be calculated from V = Vopt × Ff × Fd, where Vopt is the smaller (optimum) of the two speeds from the speed table (from the left side of the column containing the two feed/speed pairs). See the text for examples.

Table 5b. Tool Life Factors for Turning with Carbides, Ceramics, Cermets, CBN, and Polycrystalline Diamond Tool Life, T (minutes) 15 45 90 180

Turning with Carbides: Workpiece < 300 Bhn

Turning with Carbides: Workpiece > 300 Bhn; Turning with Ceramics: Any Hardness

Turning with Mixed Ceramics: Any Workpiece Hardness

fs

fm

fl

fs

fm

fl

fs

fm

fl

1.0 0.86 0.78 0.71

1.0 0.81 0.71 0.63

1.0 0.76 0.64 0.54

1.0 0.80 0.70 0.61

1.0 0.75 0.63 0.53

1.0 0.70 0.56 0.45

1.0 0.89 0.82 0.76

1.0 0.87 0.79 0.72

1.0 0.84 0.75 0.67

1035

Except for HSS speed tools, feeds and speeds given in Tables 1 through 9 are based on 15-minute tool life. To adjust speeds for another tool life, multiply the cutting speed for 15-minute tool life V15 by the tool life factor from this table according to the following rules: for small feeds where feed ≤ 1⁄2 fopt, the cutting speed for desired tool life is VT = fs × V15; for medium feeds where 1⁄2 fopt < feed < 3⁄4 fopt, VT = fm × V15; and for larger feeds where 3⁄4 fopt ≤ feed ≤ fopt, VT = fl × V15. Here, fopt is the largest (optimum) feed of the two feed/speed values given in the speed tables.


SPEEDS AND FEEDS

Ratio of Chosen Feed to Optimum Feed


SPEEDS AND FEEDS Table 5c. Cutting-Speed Adjustment Factors for Turning with HSS Tools Feed

Feed Factor

Depth-of-Cut Factor

Depth of Cut

in.

mm

Ff

in.

mm

Fd

0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.013 0.014 0.015 0.016 0.018 0.020 0.022 0.025 0.028 0.030 0.032 0.035 0.040 0.045 0.050 0.060

0.05 0.08 0.10 0.13 0.15 0.18 0.20 0.23 0.25 0.28 0.30 0.33 0.36 0.38 0.41 0.46 0.51 0.56 0.64 0.71 0.76 0.81 0.89 1.02 1.14 1.27 1.52

1.50 1.50 1.50 1.44 1.34 1.25 1.18 1.12 1.08 1.04 1.00 0.97 0.94 0.91 0.88 0.84 0.80 0.77 0.73 0.70 0.68 0.66 0.64 0.60 0.57 0.55 0.50

0.005 0.010 0.016 0.031 0.047 0.062 0.078 0.094 0.100 0.125 0.150 0.188 0.200 0.250 0.312 0.375 0.438 0.500 0.625 0.688 0.750 0.812 0.938 1.000 1.250 1.250 1.375

0.13 0.25 0.41 0.79 1.19 1.57 1.98 2.39 2.54 3.18 3.81 4.78 5.08 6.35 7.92 9.53 11.13 12.70 15.88 17.48 19.05 20.62 23.83 25.40 31.75 31.75 34.93

1.50 1.42 1.33 1.21 1.15 1.10 1.07 1.04 1.03 1.00 0.97 0.94 0.93 0.91 0.88 0.86 0.84 0.82 0.80 0.78 0.77 0.76 0.75 0.74 0.73 0.72 0.71

For use with HSS tool data only from Tables 1 through 9. Adjusted cutting speed V = VHSS × Ff × Fd, where VHSS is the tabular speed for turning with high-speed tools.

Example 3, Turning:Determine the cutting speed for turning 1055 steel of 175 to 225 Brinell hardness using a hard ceramic insert, a 15° lead angle, a 0.04-inch depth of cut and 0.0075 in./rev feed. The two feed/speed combinations given in Table 5a for 1055 steel are 15⁄1610 and 8⁄2780, corresponding to 0.015 in./rev at 1610 fpm and 0.008 in./rev at 2780 fpm, respectively. In Table 5a, the feed factor Ff = 1.75 is found at the intersection of the row corresponding to feed/fopt = 7.5⁄15 = 0.5 and the column corresponding to Vavg/Vopt = 2780⁄1610 = 1.75 (approximately). The depth-of-cut factor Fd = 1.23 is found in the same row, under the column heading for a depth of cut = 0.04 inch and lead angle = 15°. The adjusted cutting speed is V = 1610 × 1.75 × 1.23 = 3466 fpm. Example 4, Turning:The cutting speed for 1055 steel calculated in Example 3 represents the speed required to obtain a 15-minute tool life. Estimate the cutting speed needed to obtain a tool life of 45, 90, and 180 minutes using the results of Example 3. To estimate the cutting speed corresponding to another tool life, multiply the cutting speed for 15-minute tool life V15 by the adjustment factor from the Table 5b, Tool Life Factors for Turning. This table gives three factors for adjusting tool life based on the feed used, fs for feeds less than or equal to 1⁄2 fopt, 3⁄4 fm for midrange feeds between 1⁄2 and 3⁄4 fopt and fl for large feeds greater than or equal to 3⁄4 fopt and less than fopt. In Example 3, fopt is 0.015 in./rev and the selected feed is 0.0075 in./rev = 1⁄2 fopt. The new cutting speeds for the various tool lives are obtained by multiplying the cutting speed for 15-minute tool life V15 by the factor



1037

for small feeds fs from the column for turning with ceramics in Table 5b. These calculations, using the cutting speed obtained in Example 3, follow. Tool Life 15 min 45 min 90 min 180 min

Cutting Speed V15 = 3466 fpm V45 = V15 × 0.80 = 2773 fpm V90 = V15 × 0.70 = 2426 fpm V180 = V15 × 0.61 = 2114 fpm

Depth of cut, feed, and lead angle remain the same as in Example 3. Notice, increasing the tool life from 15 to 180 minutes, a factor of 12, reduces the cutting speed by only about one-third of the V15 speed. Table 6. Cutting Feeds and Speeds for Turning Copper Alloys Group 1 Architectural bronze (C38500); Extra-high-headed brass (C35600); Forging brass (C37700); Freecutting phosphor bronze, B2 (C54400); Free-cutting brass (C36000); Free-cutting Muntz metal (C37000); High-leaded brass (C33200; C34200); High-leaded brass tube (C35300); Leaded commercial bronze (C31400); Leaded naval brass (C48500); Medium-leaded brass (C34000) Group 2 Aluminum brass, arsenical (C68700); Cartridge brass, 70% (C26000); High-silicon bronze, B (C65500); Admiralty brass (inhibited) (C44300, C44500); Jewelry bronze, 87.5% (C22600); Leaded Muntz metal (C36500, C36800); Leaded nickel silver (C79600); Low brass, 80% (C24000); Low-leaded brass (C33500); Low-silicon bronze, B (C65100); Manganese bronze, A (C67500); Muntz metal, 60% (C28000); Nickel silver, 55-18 (C77000); Red brass, 85% (C23000); Yellow brass (C26800) Group 3 Aluminum bronze, D (C61400); Beryllium copper (C17000, C17200, C17500); Commercialbronze, 90% (C22000); Copper nickel, 10% (C70600); Copper nickel, 30% (C71500); Electrolytic tough pitch copper (C11000); Guilding, 95% (C21000); Nickel silver, 65-10 (C74500); Nickel silver, 65-12 (C75700); Nickel silver, 65-15 (C75400); Nickel silver, 65-18 (C75200); Oxygen-free copper (C10200) ; Phosphor bronze, 1.25% (C50200); Phosphor bronze, 10% D (C52400) Phosphor bronze, 5% A (C51000); Phosphor bronze, 8% C (C52100); Phosphorus deoxidized copper (C12200) Uncoated Carbide

HSS Wrought Alloys Description and UNS Alloy Numbers

Polycrystalline Diamond


Material Speed Condition (fpm)

Opt. Avg.

Group 1

A CD

300 350

f s

28 13 1170 1680

Group 2

A CD

200 250

f s

28 715

13 900

Group 3

A CD

100 110

f s

28 440

13 610

Opt.

Avg.

7 1780

13 2080

Abbreviations designate: A, annealed; CD, cold drawn. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide, 15; diamond, 9. See the footnote to Table 7.



SPEEDS AND FEEDS

Table 7. Cutting Feeds and Speeds for Turning Titanium and Titanium Alloys Tool Material HSS

Uncoated Carbide (Tough)

Material Brinell Hardness

f = feed (0.001 in./rev), s = speed (ft/min) Speed (fpm)

Opt.

Avg.

Commercially Pure and Low Alloyed 99.5Ti, 99.5Ti-0.15Pd

110–150

100–105

99.1Ti, 99.2Ti, 99.2Ti-0.15Pd, 98.9Ti-0.8Ni-0.3Mo

180–240

85–90

250–275

70

99.0 Ti

f s f s f s

28 55 28 50 20 75

13 190 13 170 10 210

f s

17 95

8 250

f s

17 55

8 150

Alpha Alloys and Alpha-Beta Alloys 5Al-2.5Sn, 8Mn, 2Al-11Sn-5Zr1Mo, 4Al-3Mo-1V, 5Al-6Sn-2Zr1Mo, 6Al-2Sn-4Zr-2Mo, 6Al-2Sn4Zr-6Mo, 6Al-2Sn-4Zr-2Mo-0.25Si

300–350

50

6Al-4V 6Al-6V-2Sn, Al-4Mo, 8V-5Fe-IAl

310–350 320–370 320–380

40 30 20

6Al-4V, 6Al-2Sn-4Zr-2Mo, 6Al-2Sn-4Zr-6Mo, 6Al-2Sn-4Zr-2Mo-0.25Si

320–380

40

4Al-3Mo-1V, 6Al-6V-2Sn, 7Al-4Mo

375–420

20

375–440

20

I Al-8V-5Fe

Beta Alloys 13V-11Cr-3Al, 8Mo-8V-2Fe-3Al, 3Al-8V-6Cr-4Mo-4Zr, 11.5Mo-6Zr-4.5Sn

{

275–350

25

375–440

20

The speed recommendations for turning with HSS (high-speed steel) tools may be used as starting speeds for milling titanium alloys, using Table 15a to estimate the feed required. Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide, 15.

Table 8. Cutting Feeds and Speeds for Turning Light Metals Tool Material Uncoated Carbide (Tough)

HSS Material Description All wrought and cast magnesium alloys All wrought aluminum alloys, including 6061T651, 5000, 6000, and 7000 series All aluminum sand and permanent mold casting alloys

Material Condition

Speed (fpm)

A, CD, ST, and A CD ST and A AC ST and A

800 600 500 750 600


f = feed (0.001 in./rev), s = speed (ft/min) Opt.

Avg.

Opt.

Avg.

f s

36 2820

17 4570

f s

36 865

17 1280

11 5890a

8 8270

f s

24 2010

11 2760

8 4765

4 5755

f s

32 430

15 720

10 5085

5 6570

f s

36 630

17 1060

11 7560

6 9930

Aluminum Die-Casting Alloys Alloys 308.0 and 319.0 Alloys 390.0 and 392.0 Alloy 413 All other aluminum die-casting alloys including alloys 360.0 and 380.0

—

—

AC ST and A — ST and A

80 60 — 100

AC

125



1039

a The feeds and speeds for turning Al alloys 308.0 and 319.0 with (polycrystalline) diamond tooling represent an expected tool life T = 960 minutes = 16 hours; corresponding feeds and speeds for 15minute tool life are 11⁄28600 and 6⁄37500. Abbreviations for material condition: A, annealed; AC, as cast; CD, cold drawn; and ST and A, solution treated and aged, respectively. Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the HSS speeds for other feeds and depths of cut. The combined feed/speed data are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. The data are based on tool grades (identified in Table 16) as follows: uncoated carbide, 15; diamond, 9.

Table 9. Cutting Feeds and Speeds for Turning Superalloys Tool Material Uncoated Carbide

HSS Turning Rough

Finish

Ceramic

Tough

Hard

Tough

CBN

f = feed (0.001 in./rev), s = speed (ft/min) Material Description T-D Nickel Discalloy 19-9DL, W-545 16-25-6, A-286, Incoloy 800, 801, { and 802, V-57 Refractaloy 26 J1300 Inconel 700 and 702, Nimonic 90 and { 95 S-816, V-36 S-590 Udimet 630 N-155 { Air Resist 213; Hastelloy B, C, G and X (wrought); Haynes 25 and 188; { J1570; M252 (wrought); MarM905 and M918; Nimonic 75 and 80 CW-12M; Hastelloy B and C (cast); { N-12M Rene 95 (Hot Isostatic Pressed) HS 6, 21, 2, 31 (X 40), 36, and 151; Haynes 36 and 151; Mar-M302, { M322, and M509, WI-52 Rene 41 Incoloy 901 Waspaloy Inconel 625, 702, 706, 718 (wrought), 721, 722, X750, 751, 901, 600, and { 604 AF2-1DA, Unitemp 1753 Colmonoy, Inconel 600, 718, K{ Monel, Stellite Air Resist 13 and 215, FSH-H14, Nasa CW-Re, X-45 Udimet 500, 700, and 710 Astroloy Mar-M200, M246, M421, and Rene 77, 80, and 95 (forged) B-1900, GMR-235 and 235D, IN 100 and 738, Inconel 713C and 718 { (cast), M252 (cast)

Speed (fpm) 70–80 15–35 25–35

80–100 35–40 30–40

30–35

35–40

15–20 15–25

20–25 20–30

10–12

12–15

10–15

15–20 15–30 20–25 15–25

10–20

15–20

20–25

8–12

10–15

—

—

10–12

10–15

10–15 10–20 10–30

12–20 20–35 25–35

15–20

20–35

8–10

10–15

—

—

10–12

10–15

10–15 5–10

12–20 5–15 10–12 10–15

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

f s

24 90

11 170

20 365

10 630

f s

20 75

10 135

20 245

10 420

f s

20 75

10 125

11 1170

6 2590

11 405

6 900

20 230

10 400

f s

28 20

13 40

11 895

6 2230

10 345

5 815

20 185

10 315

f s

28 15

13 15

11 615

6 1720

10 290

5 700

20 165

10 280

8–10 8–10

The speed recommendations for rough turning may be used as starting values for milling and drilling with HSS tools. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 15; ceramic, hard = 4, tough = 3; CBN = 1.



SPEEDS AND FEEDS

Speeds for HSS (high-speed steel) tools are based on a feed of 0.012 inch/rev and a depth of cut of 0.125 inch; use Table 5c to adjust the given speeds for other feeds and depths of cut. The combined feed/speed data in the remaining columns are based on a depth of cut of 0.1 inch, lead angle of 15 degrees, and nose radius of 3⁄64 inch. Use Table 5a to adjust given speeds for other feeds, depths of cut, and lead angles; use Table 5b to adjust given speeds for increased tool life up to 180 minutes. Examples are given in the text.

Speed and Feed Tables for Milling.—Tables 10 through 14 give feeds and speeds for milling. The data in the first speed column can be used with high-speed steel tools using the feeds given in Table 15a; these are the same speeds contained in previous editions of the Handbook. The remaining data in Tables 10 through 14 are combined feeds and speeds for end, face, and slit, slot, and side milling that use the speed adjustment factors given in Tables 15b, 15c, and 15d. Tool life for the combined feed/speed data can also be adjusted using the factors in Table 15e. Table 16 lists cutting tool grades and vendor equivalents. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters. Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄ ). These speeds are valid if the cutter axis is above or close to the center line of the work4 piece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inch, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut. Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. Using the Feed and Speed Tables for Milling: The basic feed for milling cutters is the feed per tooth (f), which is expressed in inches per tooth. There are many factors to consider in selecting the feed per tooth and no formula is available to resolve these factors. Among the factors to consider are the cutting tool material; the work material and its hardness; the width and the depth of the cut to be taken; the type of milling cutter to be used and its size; the surface finish to be produced; the power available on the milling machine; and the rigidity of the milling machine, the workpiece, the workpiece setup, the milling cutter, and the cutter mounting. The cardinal principle is to always use the maximum feed that conditions will permit. Avoid, if possible, using a feed that is less than 0.001 inch per tooth because such low feeds reduce the tool life of the cutter. When milling hard materials with small-diameter end mills, such small feeds may be necessary, but otherwise use as much feed as possible. Harder materials in general will require lower feeds than softer materials. The width and the depth of cut also affect the feeds. Wider and deeper cuts must be fed somewhat more slowly than narrow and shallow cuts. A slower feed rate will result in a better surface finish; however, always use the heaviest feed that will produce the surface finish desired. Fine chips produced by fine feeds are dangerous when milling magnesium because spontaneous combustion can occur. Thus, when milling magnesium, a fast feed that will produce a relatively thick chip should be used. Cutting stainless steel produces a work-hardened layer on the surface that has been cut. Thus, when milling this material, the feed should be large enough to allow each cutting edge on the cutter to penetrate below the work-hardened



1041

layer produced by the previous cutting edge. The heavy feeds recommended for face milling cutters are to be used primarily with larger cutters on milling machines having an adequate amount of power. For smaller face milling cutters, start with smaller feeds and increase as indicated by the performance of the cutter and the machine. When planning a milling operation that requires a high cutting speed and a fast feed, always check to determine if the power required to take the cut is within the capacity of the milling machine. Excessive power requirements are often encountered when milling with cemented carbide cutters. The large metal removal rates that can be attained require a high horsepower output. An example of this type of calculation is given in the section on Machining Power that follows this section. If the size of the cut must be reduced in order to stay within the power capacity of the machine, start by reducing the cutting speed rather than the feed in inches per tooth. The formula for calculating the table feed rate, when the feed in inches per tooth is known, is as follows: fm = ft nt N where fm =milling machine table feed rate in inches per minute (ipm) ft =feed in inch per tooth (ipt) nt =number of teeth in the milling cutter N =spindle speed of the milling machine in revolutions per minute (rpm) Example:Calculate the feed rate for milling a piece of AISI 1040 steel having a hardness of 180 Bhn. The cutter is a 3-inch diameter high-speed steel plain or slab milling cutter with 8 teeth. The width of the cut is 2 inches, the depth of cut is 0.062 inch, and the cutting speed from Table 11 is 85 fpm. From Table 15a, the feed rate selected is 0.008 inch per tooth. 12V 12 × 85 N = ---------- = ------------------- = 108 rpm πD 3.14 × 3 f m = f t n t N = 0.008 × 8 × 108 = 7 ipm (approximately) Example 1, Face Milling:Determine the cutting speed and machine operating speed for face milling an aluminum die casting (alloy 413) using a 4-inch polycrystalline diamond cutter, a 3-inch width of cut, a 0.10-inch depth of cut, and a feed of 0.006 inch/tooth. Table 10 gives the feeds and speeds for milling aluminum alloys. The feed/speed pairs for face milling die cast alloy 413 with polycrystalline diamond (PCD) are 8⁄2320 (0.008 in./tooth feed at 2320 fpm) and 4⁄4755 (0.004 in./tooth feed at 4755 fpm). These speeds are based on an axial depth of cut of 0.10 inch, an 8-inch cutter diameter D, a 6-inch radial depth (width) of cut ar, with the cutter approximately centered above the workpiece, i.e., eccentricity is low, as shown in Fig. 3. If the preceding conditions apply, the given feeds and speeds can be used without adjustment for a 45-minute tool life. The given speeds are valid for all cutter diameters if a radial depth of cut to cutter diameter ratio (ar/D) of 3⁄4 is maintained (i.e., 6⁄8 = 3⁄4). However, if a different feed or axial depth of cut is required, or if the ar/D ratio is not equal to 3⁄4, the cutting speed must be adjusted for the conditions. The adjusted cutting speed V is calculated from V = Vopt × Ff × Fd × Far, where Vopt is the lower of the two speeds given in the speed table, and Ff, Fd, and Far are adjustment factors for feed, axial depth of cut, and radial depth of cut, respectively, obtained from Table 15d (face milling); except, when cutting near the end or edge of the workpiece as in Fig. 4, Table 15c (side milling) is used to obtain Ff.



SPEEDS AND FEEDS

Work ar

Work Feed ar

Feed

D

Cutter

D Cutter e Fig. 3.

Fig. 4.

In this example, the cutting conditions match the standard conditions specified in the speed table for radial depth of cut to cutter diameter (3 in./4 in.), and depth of cut (0.01 in), but the desired feed of 0.006 in./tooth does not match either of the feeds given in the speed table (0.004 or 0.008). Therefore, the cutting speed must be adjusted for this feed. As with turning, the feed factor Ff is determined by calculating the ratio of the desired feed f to maximum feed fopt from the speed table, and from the ratio Vavg/Vopt of the two speeds given in the speed table. The feed factor is found at the intersection of the feed ratio row and the speed ratio column in Table 15d. The speed is then obtained using the following equation: Chosen feed - = ------f - = 0.006 ------------- = 0.75 -----------------------------------0.008 Optimum feed f opt

Average speed- = V avg ------------------------------------------------ = 4755 ------------ ≈ 2.0 Optimum speed V opt 2320

F f = ( 1.25 + 1.43 ) ⁄ 2 = 1.34

F d = 1.0

F ar = 1.0

V = 2320 × 1.34 × 1.0 × 1.0 = 3109 fpm, and 3.82 × 3109 ⁄ 4 = 2970 rpm Example 2, End Milling:What cutting speed should be used for cutting a full slot (i.e., a slot cut from the solid, in one pass, that is the same width as the cutter) in 5140 steel with hardness of 300 Bhn using a 1-inch diameter coated carbide (insert) 0° lead angle end mill, a feed of 0.003 in./tooth, and a 0.2-inch axial depth of cut? The feed and speed data for end milling 5140 steel, Brinell hardness = 275–325, with a coated carbide tool are given in Table 11 as 15⁄80 and 8⁄240 for optimum and average sets, respectively. The speed adjustment factors for feed and depth of cut for full slot (end milling) are obtained from Table 15b. The calculations are the same as in the previous examples: f/fopt = 3⁄15 = 0.2 and Vavg/Vopt = 240⁄80 = 3.0, therefore, Ff = 6.86 and Fd = 1.0. The cutting speed for a 45-minute tool life is V = 80 × 6.86 × 1.0 = 548.8, approximately 550 ft/min. Example 3, End Milling:What cutting speed should be used in Example 2 if the radial depth of cut ar is 0.02 inch and axial depth of cut is 1 inch? In end milling, when the radial depth of cut is less than the cutter diameter (as in Fig. 4), first obtain the feed factor Ff from Table 15c, then the axial depth of cut and lead angle factor Fd from Table 15b. The radial depth of cut to cutter diameter ratio ar/D is used in Table 15c to determine the maximum and minimum feeds that guard against tool failure at high feeds and against premature tool wear caused by the tool rubbing against the work at very low feeds. The feed used should be selected so that it falls within the minimum to maximum feed range, and then the feed factor Ff can be determined from the feed factors at minimum and maximum feeds, Ff1 and Ff2 as explained below.



1043

The maximum feed fmax is found in Table 15c by multiplying the optimum feed from the speed table by the maximum feed factor that corresponds to the ar/D ratio, which in this instance is 0.02⁄1 = 0.02; the minimum feed fmin is found by multiplying the optimum feed by the minimum feed factor. Thus, fmax = 4.5 × 0.015 = 0.0675 in./tooth and fmin = 3.1 × 0.015 = 0.0465 in./tooth. If a feed between these maximum and minimum values is selected, 0.050 in./tooth for example, then for ar/D = 0.02 and Vavg/Vopt = 3.0, the feed factors at maximum and minimum feeds are Ff1 = 7.90 and Ff2 = 7.01, respectively, and by interpolation, Ff = 7.01 + (0.050 − 0.0465)(0.0675 − 0.0465) × (7.90 − 7.01) = 7.16, approximately 7.2. The depth of cut factor Fd is obtained from Table 15b, using fmax from Table 15c instead of the optimum feed fopt for calculating the feed ratio (chosen feed/optimum feed). In this example, the feed ratio = chosen feed/fmax = 0.050⁄0.0675 = 0.74, so the feed factor is Fd = 0.93 for a depth of cut = 1.0 inch and 0° lead angle. Therefore, the final cutting speed is 80 × 7.2 × 0.93 = 587 ft/min. Notice that fmax obtained from Table 15c was used instead of the optimum feed from the speed table, in determining the feed ratio needed to find Fd. Slit Milling.—The tabular data for slit milling is based on an 8-tooth, 10-degree helix angle cutter with a width of 0.4 inch, a diameter D of 4.0 inch, and a depth of cut of 0.6 inch. The given feeds and speeds are valid for any diameters and tool widths, as long as sufficient machine power is available. Adjustments to cutting speeds for other feeds and depths of cut are made using Table 15c or 15d, depending on the orientation of the cutter to the work, as illustrated in Case 1 and Case 2 of Fig. 5. The situation illustrated in Case 1 is approximately equivalent to that illustrated in Fig. 3, and Case 2 is approximately equivalent to that shown in Fig. 4. Case 1: If the cutter is fed directly into the workpiece, i.e., the feed is perpendicular to the surface of the workpiece, as in cutting off, then Table 15d (face milling) is used to adjust speeds for other feeds. The depth of cut portion of Table 15d is not used in this case (Fd = 1.0), so the adjusted cutting speed V = Vopt × Ff × Far. In determining the factor Far from Table 15d, the radial depth of cut ar is the length of cut created by the portion of the cutter engaged in the work. Case 2: If the cutter feed is parallel to the surface of the workpiece, as in slotting or side milling, then Table 15c (side milling) is used to adjust the given speeds for other feeds. In Table 15c, the cutting depth (slot depth, for example) is the radial depth of cut ar that is used to determine maximum and minimum allowable feed/tooth and the feed factor Ff. These minimum and maximum feeds are determined in the manner described previously, however, the axial depth of cut factor Fd is not required. The adjusted cutting speed, valid for cutters of any thickness (width), is given by V = Vopt × Ff. Slit Mill

f Case 1 ar Chip Thickness

Work

ar Case 2 f feed/rev, f Fig. 5. Determination of Radial Depth of Cut or in Slit Milling



End Milling

HSS Material Condition*

Material All wrought aluminum alloys, 6061-T651, 5000, 6000, 7000 series All aluminum sand and permanent mold casting alloys

Alloys 360.0 and 380.0

—


—

Alloy 413 All other aluminum die-casting alloys

{

Slit Milling


Indexable Insert Uncoated Carbide

HSS

Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

f s

15 165

8 15 850 620

8 39 2020 755

20 8 1720 3750

4 16 8430 1600

8 39 4680 840

20 2390

f s f s f s

15 30 15 30

Aluminum Die-Casting Alloys 8 15 8 39 100 620 2020 755 8 15 8 39 90 485 1905 555 39 220

20 1720 20 8 1380 3105 20 370

16 160 4 16 7845 145

8 375 8 355

20 2390 20 2320

— ST and A

f s

AC

f s

15 30

8 90

15 355

8 39 1385 405

20 665

15 485

8 39 1905 555

20 8 1380 3105

8 2320

4 4755 4 16 7845 145

8 335

39 840 39 690

39 500

20 1680

39 690

20 2320

Abbreviations designate: A, annealed; AC, as cast; CD, cold drawn; and ST and A, solution treated and aged, respectively. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters. Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). These speeds are valid if the cutter axis is above or close to the center line of the workpiece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inch, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut. Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 15; diamond = 9.


SPEEDS AND FEEDS

—


f = feed (0.001 in./tooth), s = speed (ft/min)

CD ST and A CD ST and A


Face Milling


1044

Table 10. Cutting Feeds and Speeds for Milling Aluminum Alloys


Table 11. Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels End Milling HSS Brinell Hardness

Material

{

(Resulfurized): 1108, 1109, 1115, 1117, 1118, 1120, 1126, 1211

{

(Resulfurized): 1132, 1137, 1139, 1140, 1144, 1146, 1151

(Leaded): 11L17, 11L18, 12L13, 12L14


{

{

Uncoated Carbide

Opt.

Avg. Opt.

7 45

4 125 4 100

100–150

140

f s

150–200

130

f s

7 35

100–150

130

150–200

115

f s

7 30

175–225

115

f s

7 30

4 85

f s

7 25

4 70

f s

7 35

275–325

70 45

Slit Milling


Speed (fpm)

325–375

Face Milling

Coated Carbide Uncoated Carbide Coated Carbide Uncoated Carbide Coated Carbide

7 465

Avg. Opt. 4 735

7 800

Avg. Opt. 4 39 1050 225

Avg. Opt. 20 335

Avg. Opt.

39 415

20 685

39 215

20 405

Avg. Opt.

Avg.

39 265

20 495

39 525

20 830

4

7

4

7

4

39

20

39

20

39

20

39

20

85

325

565

465

720

140

220

195

365

170

350

245

495

39 185

20 350

39 90

20 235

39 135

20 325

39 265

20 495

39 525

20 830

39 175

20 330

4 100

39 215

20 405

39 185

20 350

39 415

20 685

7 210

4 435

7 300

4 560

39 90

20 170

35

100–150

140

150–200

130

200–250

110

f s

7 30

4 85

100–125

110

f s

7 45

4 125

125–175

110

f s

7 35

4 100

39 215

20 405

175–225

90

225–275

65

f s

7 30

4 85

39 185

20 350

7 465

4 735

7 800

4 39 1050 225

20 335


1045

375–425

SPEEDS AND FEEDS

Free-machining plain carbon steels (resulfurized): 1212, 1213, 1215

HSS


End Milling HSS

Material

Plain carbon steels: 1055, 1060, 1064, 1065, 1070, 1074, 1078, 1080, 1084, 1086, 1090, 1095, 1548, 1551, 1552, 1561, 1566

Free-machining alloy steels (Resulfurized): 4140, 4150

Brinell Hardness

Speed (fpm)

125–175

100

175–225

85

225–275

70

275–325

55

325–375

35

375–425

25

125–175

90

175–225

75

225–275

60

275–325

45

325–375

30

375–425

15

175–200

100

200–250

90

250–300

60

300–375

45

375–425

35

Uncoated Carbide

Face Milling

Slit Milling

Coated Carbide Uncoated Carbide Coated Carbide Uncoated Carbide Coated Carbide f = feed (0.001 in./tooth), s = speed (ft/min)

Opt.

Avg. Opt.

Avg. Opt.

f s

7 35

4 100

Avg. Opt.

39 215

20 405

f s

7 30

4 85

39 185

20 350

f s

7 25

4 70

7 210

4 435

7 300

4 560

39 90

20 170

39 175

20 330

39 90

20 235

39 135

20 325

f s

7 30

4 85

7 325

4 565

7 465

4 720

39 140

20 220

39 195

20 365

39 170

20 350

39 245

20 495

f s

7 30

4 85

39 185

20 350

f s

7 25

4 70

7 210

4 435

7 300

4 560

39 175

20 330

39 90

20 235

39 135

20 325

f s

15 7

8 30

15 105

8 270

15 270

8 450

39 295

20 475

39 135

20 305

7 25

4 70

f s

15 6

8 25

15 50

8 175

15 85

8 255

39 200

20 320

39 70

20 210

7 25

4 70

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

20 280

39 90

Avg. Opt.

20 170


Avg. Opt.

Avg. Opt.

Avg.

SPEEDS AND FEEDS

Plain carbon steels: 1027, 1030, 1033, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1045, 1046, 1048, 1049, 1050, 1052, 1524, 1526, 1527, 1541

HSS

1046

Table 11. (Continued) Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels


Table 11. (Continued) Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels End Milling HSS

Material

Free-machining alloy steels (Leaded): 41L30, 41L40, 41L47, 41L50, 43L47, 51L32, 52L100, 86L20, 86L40

Speed (fpm)

150–200

115

200–250

95

250–300

70

300–375

50

375–425

40

Face Milling

Slit Milling


Opt.

Avg. Opt.

f s

7 30

4 85

f s

7 30

4 85

f s

7 25

4 70

7 210

4 435

7 300

4 560

f s

15 7

8 30

15 105

8 270

15 220

7 325

Avg. Opt. 4 565

7 465

Avg. Opt. 4 720

39 140

Avg. Opt.

Avg. Opt.

39 195

20 365

39 185

20 350

39 175

8 450

39 90

20 220

20 170

Avg. Opt.

Avg.

39 170

20 350

39 245

20 495

20 330

39 90

20 235

39 135

20 325

39 295

20 475

39 135

20 305

39 265

20 495

39 70

20 210

39 115

20 290

125–175

100

175–225

90

225–275

60

f s

15 6

8 25

15 50

8 175

15 85

8 255

39 200

20 320

f s

15 5

8 20

15 45

8 170

15 80

8 240

39 190

20 305

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

20 280

15 5

8 30

15 105

8 270

15 220

8 450

39 295

20 475

39 135

20 305

39 265

20 495

39 70

20 210

39 115

20 290

275–325

50

325–375

40

375–425

25

175–225

75 (65)

f s

225–275

60

f s

15 5

8 25

15 50

8 175

15 85

8 255

39 200

20 320

f s

15 5

8 25

15 45

8 170

15 80

8 240

39 190

20 305

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

20 280

275–325

50 (40)

325–375

35 (30)

375–425

20

1047

Alloy steels: 1330, 1335, 1340, 1345, 4032, 4037, 4042, 4047, 4130, 4135, 4137, 4140, 4142, 4145, 4147, 4150, 4161, 4337, 4340, 50B44, 50B46, 50B50, 50B60, 5130, 5132, 5140, 5145, 5147, 5150, 5160, 51B60, 6150, 81B45, 8630, 8635, 8637, 8640, 8642, 8645, 8650, 8655, 8660, 8740, 9254, 9255, 9260, 9262, 94B30 E51100, E52100: use (HSS speeds)

Brinell Hardness

Uncoated Carbide

SPEEDS AND FEEDS

Alloy steels: 4012, 4023, 4024, 4028, 4118, 4320, 4419, 4422, 4427, 4615, 4620, 4621, 4626, 4718, 4720, 4815, 4817, 4820, 5015, 5117, 5120, 6118, 8115, 8615, 8617, 8620, 8622, 8625, 8627, 8720, 8822, 94B17

HSS



End Milling HSS

Material Ultra-high-strength steels (not AISI): AMS 6421 (98B37 Mod.), 6422 (98BV40), 6424, 6427, 6428, 6430, 6432, 6433, 6434, 6436, and 6442; 300M, D6ac

Nitriding steels (not AISI): Nitralloy 125, 135, 135 Mod., 225, and 230, Nitralloy N, Nitralloy EZ, Nitrex 1

Uncoated Carbide

Face Milling

Slit Milling


Brinell Hardness

Speed (fpm)

220–300

60

300–350

45

350–400

20

f s

43–52 Rc

—

f s

250–325

50

50–52 Rc

Opt.

Avg. Opt.

f s

Avg. Opt.

Avg. Opt.

4 355

8 150

4 320

5 20†

3 55

f s

8 165

4 355

—

f s

5 20†

3 55

200–250

60

f s

15 7

8 30

15 105

8 270

15 220

8 450

39 295

300–350

25

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

8 15

4 45

8 300

Avg. Opt.

8 165

39 130

8 300

Avg. Opt.

Avg. Opt.

Avg.

4 480 20 235

39 75

20 175

39 5

20 15

39 5

20 15

39 135

20 305

4 480

20 475

39 265

20 495

20 280

For HSS (high-speed steel) tools in the first speed column only, use Table 15a for recommended feed in inches per tooth and depth of cut. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters. Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). These speeds are valid if the cutter axis is above or close to the center line of the workpiece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inches, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut. Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: end and slit milling uncoated carbide = 20 except † = 15; face milling uncoated carbide = 19; end, face, and slit milling coated carbide = 10.


SPEEDS AND FEEDS

Maraging steels (not AISI): 18% Ni Grades 200, 250, 300, and 350

HSS

1048

Table 11. (Continued) Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels


Table 12. Cutting Feeds and Speeds for Milling Tool Steels End Milling HSS Material

Hot work, chromium type: H10, H11, H12, H13, H14, H19

Hot work, tungsten and molybdenum types: H21, H22, H23, H24, H25, H26, H41, H42, H43 Special-purpose, low alloy: L2, L3, L6 Mold: P2, P3, P4, P5, P6 P20, P21

{

150–200 175–225

85 55

175–225

50

200–250

40

200–250

50

200–250 225–275 150–200 200–250

45 40 60 50

325–375

30

48–50 Rc 50–52 Rc 52–56 Rc 150–200

— — — 55

200–250

45

150–200

65

100–150 150–200

75 60

200–250

50

225–275

40

225–275

30

Uncoated Carbide

Slit Milling Uncoated Carbide

CBN

Coated Carbide

f = feed (0.001 in./tooth), s = speed (ft/min) Opt.

f s

8 25

Avg.

4 70

Opt.

8 235

Avg.

Opt.

4 8 455 405

f s

f s

8 15

4 45

f s

8 150

4 320

5 20†

3 55

f s f s

f s

8 25

4 70

8 235

4 8 455 405

Avg.

Opt.

Avg.

4 39 635 235

20 385

39 255

20 385

39 130

20 235

Opt.

39 50 39 255

20 385

4 39 635 235

20 385

39 255

20 385


Avg.

Opt.

Avg.

Opt.

39 115

20 39 265 245

39 75

20 175

20 39 135 5†

39 115

Avg.

20 445

20 15

20 39 265 245

20 445

1049

High-speed steel: M1, M2, M6, M10, T1, T2, T6 M3-1, M4, M7, M30, M33, M34, M36, M41, M42, M43, M44, M46, M47, T5, T8 T15, M3-2

Speed (fpm)

Coated Carbide

SPEEDS AND FEEDS

Water hardening: W1, W2, W5 Shock resisting: S1, S2, S5, S6, S7 Cold work, oil hardening: O1, O2, O6, O7 Cold work, high carbon, high chromium: D2, D3, D4, D5, D7 Cold work, air hardening: A2, { A3, A8, A9, A10 A4, A6 A7

Brinell Hardness

Face Milling

Uncoated Carbide

HSS


End Milling HSS Material Free-machining stainless steels (Ferritic): 430F, 430FSe (Austenitic): 203EZ, 303, 303Se, 303MA, { 303Pb, 303Cu, 303 Plus X (Martensitic): 416, 416Se, 416 Plus X, 420F, 420FSe, 440F, 440FSe

{

Speed (fpm)

135–185

110

f s

135–185 225–275 135–185 185–240 275–325 375–425

100 80 110 100 60 30

f s

135–185

90

135–185 225–275

75 65

135–185

70

(Martensitic): 403, 410, 420, 501

135–175 175–225 275–325 375–425

95 85 55 35

{

Coated Carbide

Coated Carbide

Slit Milling Uncoated Carbide

Coated Carbide


Brinell Hardness

Stainless steels (Ferritic): 405, 409, 429, 430, 434, 436, 442, 446, 502 (Austenitic): 201, 202, 301, 302, 304, 304L, { 305, 308, 321, 347, 348 (Austenitic): 302B, 309, 309S, 310, 310S, 314, 316, 316L, 317, 330

Face Milling

Uncoated Carbide

HSS Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

7 30

4 80

7 305

4 780

7 420

4 1240

39 210

20 385

39 120

20 345

39 155

20 475

7 20

4 55

7 210

4 585

39 75

20 240

f s

7 30

4 80

7 305

4 780

39 120

20 345

39 155

20 475

f s

7 20

4 55

7 210

4 585

39 75

20 240

7 420

4 1240


39 210

20 385

SPEEDS AND FEEDS

Table 13. Cutting Feeds and Speeds for Milling Stainless Steels

1050

For HSS (high-speed steel) tools in the first speed column only, use Table 15a for recommended feed in inches per tooth and depth of cut. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters. Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). These speeds are valid if the cutter axis is above or close to the center line of the workpiece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inches, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut. Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 20, † = 15; coated carbide = 10; CBN = 1.


Table 13. (Continued) Cutting Feeds and Speeds for Milling Stainless Steels End Milling HSS Material

Stainless Steels (Martensitic): 414, 431, Greek Ascoloy, 440A, 440B, 440C

{

Speed (fpm)

225–275

55–60

275–325

45–50

375–425

30

150–200

60

275–325

50

325–375

40

375–450

25

Coated Carbide

Slit Milling

Coated Carbide

Uncoated Carbide

Coated Carbide

f = feed (0.001 in./tooth), s = speed (ft/min) Opt.

f s

7 20

Avg.

Opt.

Avg.

4 55

7 210

4 585

Opt.

Avg.

Opt.

Avg.

Opt.

39 75

Avg.

Opt.

Avg.

20 240

For HSS (high-speed steel) tools in the first speed column only, use Table 15a for recommended feed in inches per tooth and depth of cut. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters.

SPEEDS AND FEEDS

(Precipitation hardening): 15-5PH, 17-4PH, 177PH, AF-71, 17-14CuMo, AFC-77, AM-350, AM-355, AM-362, Custom 455, HNM, PH138, PH14-8Mo, PH15-7Mo, Stainless W

Brinell Hardness

Face Milling

Uncoated Carbide

HSS

Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). These speeds are valid if the cutter axis is above or close to the center line of the workpiece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inch, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut.


1051

Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 20; coated carbide = 10.


1052

Table 14. Cutting Feeds and Speeds for Milling Ferrous Cast Metals End Milling HSS Brinell Speed Hardness (fpm)

Material

Uncoated Carbide

HSS

Face Milling Coated Carbide

Uncoated Carbide

Coated Carbide

Slit Milling

Ceramic

CBN

Uncoated Carbide

Coated Carbide

f = feed (0.001 in./tooth), s = speed (ft/min) Opt. Avg. Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

39 140

20 225

39 285

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

39 1130

20 39 1630 200

20 39 530 205 20 39 400 145

Avg.

Opt.

Avg.

Gray Cast Iron 120–150

100

ASTM Class 25

160–200

80


190–220

70


220–260

50


250–320

30


100–215

50


120–175

40


150–250

30

(Ferritic): 32510, 35018

110–160

110

(Pearlitic): 40010, 43010, 45006, 45008, 48005, 50005

160–200

80

200–240

65

f 5 s 35

3 90

5 520

3 855

f 5 s 30

3 70

5 515

3 1100

f 5 s 30

3 70

5 180

f 5 s 25

3 65

5 150

f 7 s 15

4 35

7 125

f 7 s 10

4 30

7 90

20 535

20 420

39 95

20 39 160 185

20 395

39 845

20 39 1220 150

20 380

3 250

39 120

20 39 195 225

20 520

39 490

20 925

39 85

20 150

3 215

39 90

20 39 150 210

20 400

39 295

20 645

39 70

20 125

4 240

39 100

20 39 155 120

20 255

39 580

20 920

39 60

20 135

4 210

39 95

20 39 145 150

20 275

39 170

20 415

39 40

20 100

Malleable Iron

(Martensitic): 53004, 60003, 60004

200–255

55


220–260

50


240–280

45


250–320

25

(Ferritic): 60-40-18, 65-45-12

140–190

75

190–225

60

Nodular (Ductile) Iron

(Ferritic-Pearlitic): 80-55-06

{

225–260

50


240–300

40

(Martensitic): 120-90-02

270–330

25


SPEEDS AND FEEDS

ASTM Class 20


Table 14. (Continued) Cutting Feeds and Speeds for Milling Ferrous Cast Metals End Milling HSS

HSS

Face Milling Coated Carbide

Uncoated Carbide

Coated Carbide

Slit Milling

Ceramic

CBN

Uncoated Carbide

Coated Carbide


Brinell Speed Hardness (fpm)

Material

Uncoated Carbide

Opt. Avg. Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Opt.

Avg.

Cast Steels (Low carbon): 1010, 1020

100 95

175–225

80

225–300

60

150–200

85

200–250

75

250–300

50

175–225

70

(Medium-carbon alloy): 1330, 1340, 225–250 2325, 2330, 4125, 4130, 4140, 4330, { 250–300 4340, 8030, 80B30, 8040, 8430, 8440, 8630, 8640, 9525, 9530, 9535 300–350

65

(Medium carbon): 1030, 1040 1050

(Low-carbon alloy): 1320, 2315, 2320, 4110, 4120, 4320, 8020, 8620

{

{

50 30

f 7 s 25

4 7 70 245†

4 410

7 420

4 650

39 265‡

20 430

39 135†

20 39 260 245

20 450

f 7 s 20

4 7 55 160†

4 400

7 345

4 560

39 205‡

20 340

39 65†

20 39 180 180

20 370

f 7 s 15

4 7 45 120†

4 310

39 45†

20 135

f s

39 25

20 40


1053

For HSS (high-speed steel) tools in the first speed column only, use Table 15a for recommended feed in inches per tooth and depth of cut. End Milling: Table data for end milling are based on a 3-tooth, 20-degree helix angle tool with a diameter of 1.0 inch, an axial depth of cut of 0.2 inch, and a radial depth of cut of 1 inch (full slot). Use Table 15b to adjust speeds for other feeds and axial depths of cut, and Table 15c to adjust speeds if the radial depth of cut is less than the tool diameter. Speeds are valid for all tool diameters. Face Milling: Table data for face milling are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64-inch nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). These speeds are valid if the cutter axis is above or close to the center line of the workpiece (eccentricity is small). Under these conditions, use Table 15d to adjust speeds for other feeds and axial and radial depths of cut. For larger eccentricity (i.e., when the cutter axis to workpiece center line offset is one half the cutter diameter or more), use the end and side milling adjustment factors (Tables 15b and 15c) instead of the face milling factors. Slit and Slot Milling: Table data for slit milling are based on an 8-tooth, 10-degree helix angle tool with a cutter width of 0.4 inch, diameter D of 4.0 inches, and a depth of cut of 0.6 inch. Speeds are valid for all tool diameters and widths. See the examples in the text for adjustments to the given speeds for other feeds and depths of cut. Tool life for all tabulated values is approximately 45 minutes; use Table 15e to adjust tool life from 15 to 180 minutes. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 15 except † = 20; end and slit milling coated carbide = 10; face milling coated carbide = 11 except ‡ = 10. ceramic = 6; CBN = 1.

SPEEDS AND FEEDS

100–150 125–175


1054

Table 15a. Recommended Feed in Inches per Tooth (ft) for Milling with High Speed Steel Cutters End Mills Depth of Cut, .250 in

Depth of Cut, .050 in

Cutter Diam., in 1⁄ 2

Hardness, HB

Material

3⁄ 4

1 and up

Cutter Diam., in 1⁄ 4

1⁄ 2

3⁄ 4

1 and up

Plain or Slab Mills

Form Relieved Cutters

Face Mills and Shell End Mills

Slotting and Side Mills

Feed per Tooth, inch

Free-machining plain carbon steels

100–185

.001

.003

.004

.001

.002

.003

.004

.003–.008

.005

.004–.012

.002–.008

Plain carbon steels, AISI 1006 to 1030; 1513 to 1522

100–150

.001

.003

.003

.001

.002

.003

.004

.003–.008

.004

.004–.012

.002–.008

150–200

.001

.002

.003

.001

.002

.002

.003

.003–.008

.004

.003–.012

.002–.008

120–180

.001

.003

.003

.001

.002

.003

.004

.003–.008

.004

.004–.012

.002–.008

{ 180–220

.001

.002

.003

.001

.002

.002

.003

.003–.008

.004

.003–.012

.002–.008

220–300

.001

.002

.002

.001

.001

.002

.003

.002–.006

.003

.002–.008

.002–.006

Alloy steels having less than 3% carbon. Typical examples: AISI 4012, 4023, 4027, 4118, 4320 4422, 4427, 4615, 4620, 4626, 4720, 4820, 5015, 5120, 6118, 8115, 8620 8627, 8720, 8820, 8822, 9310, 93B17

125–175

.001

.003

.003

.001

.002

.003

.004

.003–.008

.004

.004–.012

.002–.008

175–225

.001

.002

.003

.001

.002

.003

.003

.003–.008

.004

.003–.012

.002–.008

225–275

.001

.002

.003

.001

.001

.002

.003

.002–.006

.003

.003–.008

.002–.006

275–325

.001

.002

.002

.001

.001

.002

.002

.002–.005

.003

.002–.008

.002–.005

Alloy steels having 3% carbon or more. Typical examples: AISI 1330, 1340, 4032, 4037, 4130, 4140, 4150, 4340, 50B40, 50B60, 5130, 51B60, 6150, 81B45, 8630, 8640, 86B45, 8660, 8740, 94B30

175–225

.001

.002

.003

.001

.002

.003

.004

.003–.008

.004

.003–.012

.002–.008

225–275

.001

.002

.003

.001

.001

.002

.003

.002–.006

.003

.003–.010

.002–.006

275–325

.001

.002

.002

.001

.001

.002

.003

.002–.005

.003

.002–.008

.002–.005

325–375

.001

.002

.002

.001

.001

.002

.002

.002–.004

.002

.002–.008

.002–.005

150–200

.001

.002

.002

.001

.002

.003

.003

.003–.008

.004

.003–.010

.002–.006

200–250

.001

.002

.002

.001

.002

.002

.003

.002–.006

.003

.003–.008

.002–.005

120–180

.001

.003

.004

.002

.003

.004

.004

.004–.012

.005

.005–.016

.002–.010

180–225

.001

.002

.003

.001

.002

.003

.003

.003–.010

.004

.004–.012

.002–.008

225–300

.001

.002

.002

.001

.001

.002

.002

.002–.006

.003

.002–.008

.002–.005

110–160

.001

.003

.004

.002

.003

.004

.004

.003–.010

.005

.005–.016

.002–.010

Tool steel

Gray cast iron

Free malleable iron


SPEEDS AND FEEDS

AISI 1033 to 1095; 1524 to 1566

{


Table 15a. (Continued) Recommended Feed in Inches per Tooth (ft) for Milling with High Speed Steel Cutters End Mills Depth of Cut, .250 in

Depth of Cut, .050 in

Cutter Diam., in

Material(Continued) Pearlitic-Martensitic malleable iron

Zinc alloys (die castings) Copper alloys (brasses & bronzes)

1⁄ 2

3⁄ 4

Plain or Slab Mills

Form Relieved Cutters

Face Mills and Shell End Mills

Slotting and Side Mills

Hardness, HB 160–200

.001

.003

.004

.001

.002

.003

.004

.003–.010

.004

.004–.012

.002–.018

200–240

.001

.002

.003

.001

.002

.003

.003

.003–.007

.004

.003–.010

.002–.006

240–300

.001

.002

.002

.001

.001

.002

.002

.002–.006

.003

.002–.008

.002–.005

100–180

.001

.003

.003

.001

.002

.003

.004

.003–.008

.004

.003–.012

.002–.008

180–240

.001

.002

.003

.001

.002

.003

.003

.003–.008

.004

.003–.010

.002–.006

240–300

.001

.002

.002

.005

.002

.002

.002

.002–.006

.003

.003–.008

.002–.005

…

.002

.003

.004

.001

.003

.004

.006

.003–.010

.005

.004–.015

.002–.012

100–150

.002

.004

.005

.002

.003

.005

.006

.003–.015

.004

.004–.020

.002–.010 .002–.008

1 and up

1⁄ 4

1 and up

Feed per Tooth, inch

150–250

.002

.003

.004

.001

.003

.004

.005

.003–.015

.004

.003–.012

Free cutting brasses & bronzes

80–100

.002

.004

.005

.002

.003

.005

.006

.003–.015

.004

.004–.015

.002–.010

Cast aluminum alloys—as cast

…

.003

.004

.005

.002

.004

.005

.006

.005–.016

.006

.005–.020

.004–.012

Cast aluminum alloys—hardened

…

.003

.004

.005

.002

.003

.004

.005

.004–.012

.005

.005–.020

.004–.012

Wrought aluminum alloys— cold drawn

…

.003

.004

.005

.002

.003

.004

.005

.004–.014

.005

.005–.020

.004–.012

Wrought aluminum alloys—hardened

…

.002

.003

.004

.001

.002

.003

.004

.003–.012

.004

.005–.020

.004–.012

Magnesium alloys

…

.003

.004

.005

.003

.004

.005

.007

.005–.016

.006

.008–.020

.005–.012

Ferritic stainless steel Austenitic stainless steel

Martensitic stainless steel

.001

.002

.003

.001

.002

.003

.003

.002–.006

.004

.004–.008

.002–.007

.001

.002

.003

.001

.002

.003

.003

.003–.007

.004

.005–.008

.002–.007

185–275

.001

.002

.003

.001

.002

.002

.002

.003–.006

.003

.004–.006

.002–.007

135–185

.001

.002

.002

.001

.002

.003

.003

.003–.006

.004

.004–.010

.002–.007

185–225

.001

.002

.002

.001

.002

.002

.003

.003–.006

.004

.003–.008

.002–.007

225–300

.0005

.002

.002

.0005

.001

.002

.002

.002–.005

.003

.002–.006

.002–.005

100–160

.001

.003

.004

.001

.002

.003

.004

.002–.006

.004

.002–.008

.002–.006


1055

Monel

135–185 135–185

SPEEDS AND FEEDS

Cast steel

3⁄ 4

Cutter Diam., in

1⁄ 2


1056

Table 15b. End Milling (Full Slot) Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle Cutting Speed, V = Vopt × Ff × Fd Ratio of the two cutting speeds Ratio of Chosen Feed to Optimum Feed

Depth of Cut and Lead Angle

(average/optimum) given in the tables Vavg/Vopt 1.00

1.25

1.50

2.00

2.50

3.00

4.00

1 in

(25.4 mm)

0.4 in

(10.2 mm)

0.2 in

(5.1 mm)

0.1 in

(2.4 mm)

0.04 in

(1.0 mm)

0°

45°

0°

45°

0°

45°

0°

45°

0°

45°

Feed Factor, Ff

Depth of Cut and Lead Angle Factor, Fd

1.0

1.0

1.0

1.0

1.0

1.0

1.0

0.91

1.36

0.94

1.38

1.00

0.71

1.29

1.48

1.44

1.00

1.06

1.09

1.14

1.18

1.21

1.27

0.91

1.33

0.94

1.35

1.00

0.72

1.26

1.43

1.40

1.66 1.59

0.80

1.00

1.12

1.19

1.31

1.40

1.49

1.63

0.92

1.30

0.95

1.32

1.00

0.74

1.24

1.39

1.35

1.53

0.70

1.00

1.18

1.30

1.50

1.69

1.85

2.15

0.93

1.26

0.95

1.27

1.00

0.76

1.21

1.35

1.31

1.44

0.60

1.00

1.20

1.40

1.73

2.04

2.34

2.89

0.94

1.22

0.96

1.25

1.00

0.79

1.18

1.28

1.26

1.26

0.50

1.00

1.25

1.50

2.00

2.50

3.00

4.00

0.95

1.17

0.97

1.18

1.00

0.82

1.14

1.21

1.20

1.21

0.40

1.00

1.23

1.57

2.29

3.08

3.92

5.70

0.96

1.11

0.97

1.12

1.00

0.86

1.09

1.14

1.13

1.16

0.30

1.00

1.14

1.56

2.57

3.78

5.19

8.56

0.98

1.04

0.99

1.04

1.00

0.91

1.04

1.07

1.05

1.09

0.20

1.00

0.90

1.37

2.68

4.49

6.86

17.60

1.00

0.85

1.00

0.95

1.00

0.99

0.97

0.93

0.94

0.88

0.10

1.00

0.44

0.80

2.08

4.26

8.00

20.80

1.05

0.82

1.00

0.81

1.00

1.50

0.85

0.76

0.78

0.67

For HSS (high-speed steel) tool speeds in the first speed column of Tables 10 through 14, use Table 15a to determine appropriate feeds and depths of cut. Cutting feeds and speeds for end milling given in Tables 11 through 14 (except those for high-speed steel in the first speed column) are based on milling a 0.20-inch deep full slot (i.e., radial depth of cut = end mill diameter) with a 1-inch diameter, 20-degree helix angle, 0-degree lead angle end mill. For other depths of cut (axial), lead angles, or feed, use the two feed/speed pairs from the tables and calculate the ratio of desired (new) feed to optimum feed (largest of the two feeds are given in the tables), and the ratio of the two cutting speeds (Vavg/Vopt). Find the feed factor Ff at the intersection of the feed ratio row and the speed ratio column in the left half of the Table. The depth of cut factor Fd is found in the same row as the feed factor, in the right half of the table under the column corresponding to the depth of cut and lead angle. The adjusted cutting speed can be calculated from V = Vopt × Ff × Fd, where Vopt is the smaller (optimum) of the two speeds from the speed table (from the left side of the column containing the two feed/speed pairs). See the text for examples. If the radial depth of cut is less than the cutter diameter (i.e., for cutting less than a full slot), the feed factor Ff in the previous equation and the maximum feed fmax must be obtained from Table 15c. The axial depth of cut factor Fd can then be obtained from this table using fmax in place of the optimum feed in the feed ratio. Also see the footnote to Table 15c.


SPEEDS AND FEEDS

1.00 0.90


Table 15c. End, Slit, and Side Milling Speed Adjustment Factors for Radial Depth of Cut Cutting Speed, V = Vopt × Ff × Fd Ratio of Radial Depth of Cut to Diameter

Vavg/Vopt Maximum Feed/Tooth Factor

1.25

1.50

2.00

2.50

Vavg/Vopt 3.00

4.00

Feed Factor Ff at Maximum Feed per Tooth, Ff1

Maximum Feed/Tooth Factor

1.25

1.50

2.00

2.50

3.00

4.00

Feed Factor Ff at Minimum Feed per Tooth, Ff2

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.70

1.18

1.30

1.50

1.69

1.85

2.15

0.75

1.00

1.15

1.24

1.46

1.54

1.66

1.87

0.70

1.24

1.48

1.93

2.38

2.81

3.68

0.60

1.00

1.23

1.40

1.73

2.04

2.34

2.89

0.70

1.24

1.56

2.23

2.95

3.71

5.32

0.50

1.00

1.25

1.50

2.00

2.50

3.00

4.00

0.70

1.20

1.58

2.44

3.42

4.51

6.96

1.10

1.25

1.55

2.17

2.83

3.51

4.94

0.77

1.25

1.55

2.55

3.72

5.08

8.30

1.35

1.20

1.57

2.28

3.05

3.86

5.62

0.88

1.23

1.57

2.64

4.06

5.76

10.00

0.20

1.50

1.14

1.56

2.57

3.78

5.19

8.56

1.05

1.40

1.56

2.68

4.43

6.37

11.80

0.10

2.05

0.92

1.39

2.68

4.46

6.77

13.10

1.44

0.92

1.29

2.50

4.66

7.76

17.40

0.05

2.90

0.68

1.12

2.50

4.66

7.75

17.30

2.00

0.68

1.12

2.08

4.36

8.00

20.80

0.02

4.50

0.38

0.71

1.93

4.19

7.90

21.50

3.10

0.38

0.70

1.38

3.37

7.01

22.20

This table is for side milling, end milling when the radial depth of cut (width of cut) is less than the tool diameter (i.e., less than full slot milling), and slit milling when the feed is parallel to the work surface (slotting). The radial depth of cut to diameter ratio is used to determine the recommended maximum and minimum values of feed/tooth, which are found by multiplying the feed/tooth factor from the appropriate column above (maximum or minimum) by feedopt from the speed tables. For example, given two feed/speed pairs 7⁄15 and 4⁄45 for end milling cast, medium-carbon, alloy steel, and a radial depth of cut to diameter ratio ar/D of 0.10 (a 0.05-inch width of cut for a 1⁄2-inch diameter end mill, for example), the maximum feed fmax = 2.05 × 0.007 = 0.014 in./tooth and the minimum feed fmin = 1.44 × 0.007 = 0.010 in./tooth. The feed selected should fall in the range between fmin and fmax. The feed factor Fd is determined by interpolating between the feed factors Ff1 and Ff2 corresponding to the maximum and minimum feed per tooth, at the appropriate ar/D and speed ratio. In the example given, ar/D = 0.10 and Vavg/Vopt = 45⁄15 = 3, so the feed factor Ff1 at the maximum feed per tooth is 6.77, and the feed factor Ff2 at the minimum feed per tooth is 7.76. If a working feed of 0.012 in./tooth is chosen, the feed factor Ff is half way between 6.77 and 7.76 or by formula, Ff = Ff1 + (feed − fmin)/(fmax − fmin) × (ff2 − ff1 ) = 6.77 + (0.012 − 0.010)/(0.014 − 0.010) × (7.76 − 6.77) = 7.27. The cutting speed is V = Vopt × Ff × Fd, where Fd is the depth of cut and lead angle factor from Table 15b that corresponds to the feed ratio (chosen feed)/fmax, not the ratio (chosen feed)/optimum feed. For a feed ratio = 0.012⁄0.014 = 0.86 (chosen feed/fmax), depth of cut = 0.2 inch and lead angle = 45°, the depth of cut factor Fd in Table 15b is between 0.72 and 0.74. Therefore, the final cutting speed for this example is V = Vopt × Ff × Fd = 15 × 7.27 × 0.73 = 80 ft/min.


1057

Slit and Side Milling: This table only applies when feed is parallel to the work surface, as in slotting. If feed is perpendicular to the work surface, as in cutting off, obtain the required speed-correction factor from Table 15d (face milling). The minimum and maximum feeds/tooth for slit and side milling are determined in the manner described above, however, the axial depth of cut factor Fd is not required. The adjusted cutting speed, valid for cutters of any thickness (width), is given by V = Vopt × Ff. Examples are given in the text.

SPEEDS AND FEEDS

0.40 0.30



1.00

2.00

1 in (25.4 mm) 15° 45°

1.0 1.10 1.20 1.32 1.50 1.75 2.03 2.42 2.96 3.74

1.0 1.12 1.25 1.43 1.66 2.00 2.43 3.05 4.03 5.84

0.78 0.78 0.80 0.81 0.81 0.81 0.82 0.84 0.86 0.90

Vavg/Vopt 1.10

1.0 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00 1.00

1.0 1.02 1.03 1.05 1.08 1.10 1.09 1.06 1.00 0.80

1.25 1.35 1.50 Feed Factor, Ff 1.0 1.0 1.0 1.05 1.07 1.09 1.09 1.10 1.15 1.13 1.22 1.22 1.20 1.25 1.35 1.25 1.35 1.50 1.28 1.44 1.66 1.32 1.52 1.85 1.34 1.60 2.07 1.20 1.55 2.24

1.11 1.10 1.10 1.09 1.09 1.09 1.08 1.07 1.06 1.04

0.4 in 0.2 in 0.1 in (10.2 mm) (5.1 mm) (2.4 mm) 15° 45° 15° 45° 15° 45° Depth of Cut Factor, Fd 0.94 1.16 0.90 1.10 1.00 1.29 0.94 1.16 0.90 1.09 1.00 1.27 0.94 1.14 0.91 1.08 1.00 1.25 0.95 1.14 0.91 1.08 1.00 1.24 0.95 1.13 0.92 1.08 1.00 1.23 0.95 1.13 0.92 1.08 1.00 1.23 0.95 1.12 0.92 1.07 1.00 1.21 0.96 1.11 0.93 1.06 1.00 1.18 0.96 1.09 0.94 1.05 1.00 1.15 0.97 1.06 0.96 1.04 1.00 1.10

0.04 in (1.0 mm) 15° 45° 1.47 1.45 1.40 1.39 1.38 1.37 1.34 1.30 1.24 1.15

1.66 1.58 1.52 1.50 1.48 1.47 1.43 1.37 1.29 1.18

Ratio of Radial Depth of Cut/Cutter Diameter, ar/D 1.00 0.72 0.73 0.75 0.75 0.76 0.76 0.78 0.80 0.82 0.87

0.75 0.50 0.40 0.30 0.20 Radial Depth of Cut Factor, Far 1.00 1.53 1.89 2.43 3.32 1.00 1.50 1.84 2.24 3.16 1.00 1.45 1.73 2.15 2.79 1.00 1.44 1.72 2.12 2.73 1.00 1.42 1.68 2.05 2.61 1.00 1.41 1.66 2.02 2.54 1.00 1.37 1.60 1.90 2.34 1.00 1.32 1.51 1.76 2.10 1.00 1.26 1.40 1.58 1.79 1.00 1.16 1.24 1.31 1.37

0.10 5.09 4.69 3.89 3.77 3.52 3.39 2.99 2.52 1.98 1.32

For HSS (high-speed steel) tool speeds in the first speed column, use Table 15a to determine appropriate feeds and depths of cut. Tabular feeds and speeds data for face milling in Tables 11 through 14 are based on a 10-tooth, 8-inch diameter face mill, operating with a 15-degree lead angle, 3⁄64inch cutter insert nose radius, axial depth of cut = 0.1 inch, and radial depth (width) of cut = 6 inches (i.e., width of cut to cutter diameter ratio = 3⁄4). For other depths of cut (radial or axial), lead angles, or feed, calculate the ratio of desired (new) feed to optimum feed (largest of the two feeds given in the speed table), and the ratio of the two cutting speeds (Vavg/Vopt). Use these ratios to find the feed factor Ff at the intersection of the feed ratio row and the speed ratio column in the left third of the table. The depth of cut factor Fd is found in the same row as the feed factor, in the center third of the table, in the column corresponding to the depth of cut and lead angle. The radial depth of cut factor Far is found in the same row as the feed factor, in the right third of the table, in the column corresponding to the radial depth of cut to cutter diameter ratio ar/D. The adjusted cutting speed can be calculated from V = Vopt × Ff × Fd × Far, where Vopt is the smaller (optimum) of the two speeds from the speed table (from the left side of the column containing the two feed/speed pairs). The cutting speeds as calculated above are valid if the cutter axis is centered above or close to the center line of the workpiece (eccentricity is small). For larger eccentricity (i.e., the cutter axis is offset from the center line of the workpiece by about one-half the cutter diameter or more), use the adjustment factors from Tables 15b and 15c (end and side milling) instead of the factors from this table. Use Table 15e to adjust end and face milling speeds for increased tool life up to 180 minutes. Slit and Slot Milling: Tabular speeds are valid for all tool diameters and widths. Adjustments to the given speeds for other feeds and depths of cut depend on the circumstances of the cut. Case 1: If the cutter is fed directly into the workpiece, i.e., the feed is perpendicular to the surface of the workpiece, as in cutting off, then this table (face milling) is used to adjust speeds for other feeds. The depth of cut factor is not used for slit milling (Fd = 1.0), so the adjusted cutting speed V = Vopt × Ff × Far. For determining the factor Far, the radial depth of cut ar is the length of cut created by the portion of the cutter engaged in the work. Case 2: If the cutter is fed parallel to the surface of the workpiece, as in slotting, then Tables 15b and 15c are used to adjust the given speeds for other feeds. See Fig. 5.


SPEEDS AND FEEDS

1.00 0.90 0.80 0.70 0.60 0.50 0.40 0.30 0.20 0.10

Cutting Speed V = Vopt × Ff × Fd × Far Depth of Cut, inch (mm), and Lead Angle

Ratio of the two cutting speeds (average/optimum) given in the tables

1.00

1058

Table 15d. Face Milling Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle


1059

Table 15e. Tool Life Adjustment Factors for Face Milling, End Milling, Drilling, and Reaming Tool Life, T (minutes) 15 45 90 180

Face Milling with Carbides and Mixed Ceramics fm fl fs 1.69 1.00 0.72 0.51

1.78 1.00 0.70 0.48

1.87 1.00 0.67 0.45

End Milling with Carbides and HSS fs fm fl 1.10 1.00 0.94 0.69

1.23 1.00 0.89 0.69

1.35 1.00 0.83 0.69

Twist Drilling and Reaming with HSS fs fm fl 1.11 1.00 0.93 0.87

1.21 1.00 0.89 0.80

1.30 1.00 0.85 0.72

The feeds and speeds given in Tables 11 through 14 and Tables 17 through 23 (except for HSS speeds in the first speed column) are based on a 45-minute tool life. To adjust the given speeds to obtain another tool life, multiply the adjusted cutting speed for the 45-minute tool life V45 by the tool life factor from this table according to the following rules: for small feeds, where feed ≤ 1⁄2 fopt, the cutting speed for the desired tool life T is VT = fs × V15; for medium feeds, where 1⁄2 fopt < feed < 3⁄4 fopt, VT = fm × V15; and for larger feeds, where 3⁄4 fopt ≤ feed ≤ fopt, VT = fl × V15. Here, fopt is the largest (optimum) feed of the two feed/speed values given in the speed tables or the maximum feed fmax obtained from Table 15c, if that table was used in calculating speed adjustment factors.

Table 16. Cutting Tool Grade Descriptions and Common Vendor Equivalents Grade Description Cubic boron nitride Ceramics

Cermets Polycrystalline Coated carbides

Uncoated carbides

Tool Identification Code 1 2 3 4 (Whiskers) 5 (Sialon) 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Approximate Vendor Equivalents Sandvik Coromant

Kennametal

CB50

KD050

CC620 CC650 CC670 CC680 CC690 CT515 CT525 CD10 GC-A GC3015 GC235 GC4025 GC415 H13A S10T S1P S30T S6 SM30

K060 K090 KYON2500 KYON2000 KYON3000 KT125 KT150 KD100 — KC910 KC9045 KC9025 KC950 K8, K4H K420, K28 K45 — K21, K25 KC710

Seco CBN2 0 480 480 — 480 — CM CR PAX20 — TP100 TP300 TP200 TP100 883 CP20 CP20 CP25 CP50 CP25

Valenite VC721 — Q32 — — Q6 VC605 VC610 VC727 — SV310 SV235 SV325 SV315 VC2 VC7 VC7 VC5 VC56 VC35M

See Table 2 on page 779 and the section Cemented Carbides and Other Hard Materials for more detailed information on cutting tool grades. The identification codes in column two correspond to the grade numbers given in the footnotes to Tables 1 to 4b, 6 to 14, and 17 to 23.



SPEEDS AND FEEDS

Using the Feed and Speed Tables for Drilling, Reaming, and Threading.—The first two speed columns in Tables 17 through 23 give traditional Handbook speeds for drilling and reaming. The following material can be used for selecting feeds for use with the traditional speeds. The remaining columns in Tables 17 through 23 contain combined feed/speed data for drilling, reaming, and threading, organized in the same manner as in the turning and milling tables. Operating at the given feeds and speeds is expected to result in a tool life of approximately 45 minutes, except for indexable insert drills, which have an expected tool life of approximately 15 minutes per edge. Examples of using this data follow. Adjustments to HSS drilling speeds for feed and diameter are made using Table 22; Table 5a is used for adjustments to indexable insert drilling speeds, where one-half the drill diameter D is used for the depth of cut. Tool life for HSS drills, reamers, and thread chasers and taps may be adjusted using Table 15e and for indexable insert drills using Table 5b. The feed for drilling is governed primarily by the size of the drill and by the material to be drilled. Other factors that also affect selection of the feed are the workpiece configuration, the rigidity of the machine tool and the workpiece setup, and the length of the chisel edge. A chisel edge that is too long will result in a very significant increase in the thrust force, which may cause large deflections to occur on the machine tool and drill breakage. For ordinary twist drills, the feed rate used is 0.001 to 0.003 in /rev for drills smaller than 1⁄ in, 0.002 to 0.006 in./rev for 1⁄ - to 1⁄ -in drills; 0.004 to 0.010 in./rev for 1⁄ - to 1⁄ -in drills; 8 8 4 4 2 0.007 to 0.015 in./rev for 1⁄2- to 1-in drills; and, 0.010 to 0.025 in./rev for drills larger than 1

inch. The lower values in the feed ranges should be used for hard materials such as tool steels, superalloys, and work-hardening stainless steels; the higher values in the feed ranges should be used to drill soft materials such as aluminum and brass. Example 1, Drilling:Determine the cutting speed and feed for use with HSS drills in drilling 1120 steel. Table 15a gives two sets of feed and speed parameters for drilling 1120 steel with HSS drills. These sets are 16⁄50 and 8⁄95, i.e., 0.016 in./rev feed at 50 ft/min and 0.008 in./rev at 95 fpm, respectively. These feed/speed sets are based on a 0.6-inch diameter drill. Tool life for either of the given feed/speed settings is expected to be approximately 45 minutes. For different feeds or drill diameters, the cutting speeds must be adjusted and can be determined from V = Vopt × Ff × Fd, where Vopt is the minimum speed for this material given in the speed table (50 fpm in this example) and Ff and Fd are the adjustment factors for feed and diameter, respectively, found in Table 22.



Table 17. Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Drilling

Reaming

Drilling

HSS Brinell Hardness

Material Free-machining plain carbon steels (Resulfurized): 1212, 1213, 1215

{

(Resulfurized): 1108, 1109, 1115, 1117, 1118, 1120, 1126, 1211

{

{

(Leaded): 11L17, 11L18, 12L13, 12L14

{


Plain carbon steels: 1027, 1030, 1033, 1035, 1036, 1037, 1038, 1039, 1040, 1041, 1042, 1043, 1045, 1046, 1048, 1049, 1050, 1052, 1524, 1526, 1527, 1541

{

{

Reaming

Threading

HSS

HSS


Speed (fpm)

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

f 21 s 55

Opt.

11 125

8 310

4 620

36 140

18 83 185 140

20 185

f 16 s 50

8 95

8 370

4 740

27 105

14 83 115 90

20 115

f s

8 365

4 735

60

f s

8 365

4 735

100

65

f 21 s 55

8 310

4 620

36 140

18 83 185 140

20 185

90 70 60 90 75 60 50 35 25

60 45 40 60 50 40 30 20 15

f s

8 365

4 735

f s

8 365

4 735

100–150

120

80

150–200 100–150 150–200

125 110 120

80 75 80

175–225

100

65

275–325 325–375 375–425 100–150 150–200

70 45 35 130 120

45 30 20 85 80

200–250

90

100–125 125–175 175–225 225–275 125–175 175–225 225–275 275–325 325–375 375–425

11 125

SPEEDS AND FEEDS

(Resulfurized): 1132, 1137, 1139, 1140, 1144, 1146, 1151

Indexable Insert Coated Carbide

HSS

1061



Drilling

Reaming

Drilling

HSS Material

Plain carbon steels (Continued): 1055, 1060, 1064, 1065, 1070, 1074, 1078, 1080, 1084, 1086, 1090, 1095, 1548, 1551, 1552, 1561, 1566

(Leaded): 41L30, 41L40, 41L47, 41L50, 43L47, 51L32, 52L100, 86L20, 86L40

Alloy steels: 4012, 4023, 4024, 4028, 4118, 4320, 4419, 4422, 4427, 4615, 4620, 4621, 4626, 4718, 4720, 4815, 4817, 4820, 5015, 5117, 5120, 6118, 8115, 8615, 8617, 8620, 8622, 8625, 8627, 8720, 8822, 94B17

{

{

Reaming

Threading

HSS

HSS


Brinell Hardness 125–175 175–225

Speed (fpm) 85 70

55 45

f 16 s 50

225–275

50

30

f s

275–325 325–375 375–425 175–200 200–250

40 30 15 90 80

25 20 10 60 50

Opt.

250–300

55

30

300–375 375–425

40 30

25 15

f 16 s 75

Avg. Opt.

Avg. Opt.

Avg.

8 370

4 740

27 105

14 83 115 90

20 115

8 365

4 735

8 410

4 685

26 150

13 83 160 125

20 160

8 355

4 600

8 140

f s f s f 16 s 50 f s

8 310

4 525

8 95

8 370 8 365

4 740 4 735

27 105

14 83 115 90

20 115

f 16 s 75

8 140

8 410

4 685

26 150

13 83 160 125

20 160

8 355

4 600

8 335

4 570

19 95

10 83 135 60

20 95

8 310

4 525

150–200

100

65

200–250

90

60

250–300 300–375 375–425 125–175 175–225

65 45 30 85 70

40 30 15 55 45

225–275

55

35

f s

275–325

50

30

f 11 s 50

325–375 375–425

35 25

25 15

f s

{

Avg. Opt. 8 95

6 85


SPEEDS AND FEEDS

Free-machining alloy steels (Resulfurized): 4140, 4150

{


HSS

1062

Table 17. (Continued) Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels


Table 17. (Continued) Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Drilling

Reaming

Drilling

HSS Material

Ultra-high-strength steels (not AISI): AMS 6421 (98B37 Mod.), 6422 (98BV40), 6424, 6427, 6428, 6430, 6432, 6433, 6434, 6436, and 6442; 300M, D6ac Maraging steels (not AISI): 18% Ni Grade 200, 250, 300, and 350 Nitriding steels (not AISI): Nitralloy 125, 135, 135 Mod., 225, and 230, Nitralloy N, Nitralloy EZ, Nitrex I

Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

8 410

4 685

26 150

13 83 160 125

20 160

8 355

4 600

8 335

4 570

19 95

10 83 135 60

20 95

f s

8 310

4 525

f s

8 325

4 545

26 150

13 83 160 125

20 160

50 (40)

f 16 s 75

225–275

60 (50)

40 (30)

f s f 11 s 50

6 85

275–325

45 (35)

30 (25)

325–375 375–425 220–300 300–350

30 (30) 20 (20) 50 35

15 (20) 15 (10) 30 20

350–400

20

10

f s

8 270

4 450

250–325

50

30

f s

8 325

4 545

40

f 16 s 75

8 410

4 685

20

f s

8 310

4 525

300–350

35

HSS

8 140

75 (60)

60

Threading

HSS


Speed (fpm)

175–225

200–250

Reaming

8 140

SPEEDS AND FEEDS

Alloy steels: 1330, 1335, 1340, 1345, 4032, 4037, 4042, 4047, 4130, 4135, 4137, 4140, 4142, 4145, 4147, 4150, 4161, 4337, 4340, 50B44, 50B46, 50B50, 50B60, 5130, 5132, 5140, 5145, 5147, 5150, { 5160, 51B60, 6150, 81B45, 8630, 8635, 8637, 8640, 8642, 8645, 8650, 8655, 8660, 8740, 9254, 9255, 9260, 9262, 94B30 E51100, E52100: use (HSS speeds)

Brinell Hardness


HSS

The two leftmost speed columns in this table contain traditional Handbook speeds for drilling and reaming with HSS steel tools. The section Feed Rates for Drilling and Reaming contains useful information concerning feeds to use in conjunction with these speeds.


1063

HSS Drilling and Reaming: The combined feed/speed data for drilling are based on a 0.60-inch diameter HSS drill with standard drill point geometry (2-flute with 118° tip angle). Speed adjustment factors in Table 22 are used to adjust drilling speeds for other feeds and drill diameters. Examples of using this data are given in the text. The given feeds and speeds for reaming are based on an 8-tooth, 25⁄32-inch diameter, 30° lead angle reamer, and a 0.008-inch radial depth of cut. For other feeds, the correct speed can be obtained by interpolation using the given speeds if the desired feed lies in the recommended range (between the given values of optimum and average feed). If a feed lower than the given average value is chosen, the speed should be maintained at the corresponding average speed (i.e., the highest of the two speed values given). The cutting speeds for reaming do not require adjustment for tool diameters for standard ratios of radical depth of cut to reamer diameter (i.e., fd = 1.00). Speed adjustment factors to modify tool life are found in Table 15e.


SPEEDS AND FEEDS

Indexable Insert Drilling: The feed/speed data for indexable insert drilling are based on a tool with two cutting edges, an insert nose radius of 3⁄64 inch, a 10-degree lead angle, and diameter D = 1 inch. Adjustments to cutting speed for feed and depth of cut are made using Table 5aAdjustment Factors) using a depth of cut of D/2, or one-half the drill diameter. Expected tool life at the given feeds and speeds is approximately 15 minutes for short hole drilling (i.e., where maximum hole depth is about 2D or less). Speed adjustment factors to increase tool life are found in Table 5b. Tapping and Threading: The data in this column are intended for use with thread chasers and for tapping. The feed used for tapping and threading must be equal to the lead (feed = lead = pitch) of the thread being cut. The two feed/speed pairs given for each material, therefore, are representative speeds for two thread pitches, 12 and 50 threads per inch (1⁄0.083 = 12, and 1⁄0.020 = 50). Tool life is expected to be approximately 45 minutes at the given feeds and speeds. When cutting fewer than 12 threads per inch (pitch ≥ 0.08 inch), use the lower (optimum) speed; for cutting more than 50 threads per inch (pitch ≤ 0.02 inch), use the larger (average) speed; and, in the intermediate range between 12 and 50 threads per inch, interpolate between the given average and optimum speeds. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: coated carbide = 10.

Example 2, Drilling:If the 1120 steel of Example 1 is to be drilled with a 0.60-inch drill at a feed of 0.012 in./rev, what is the cutting speed in ft/min? Also, what spindle rpm of the drilling machine is required to obtain this cutting speed? To find the feed factor Fd in Table 22, calculate the ratio of the desired feed to the optimum feed and the ratio of the two cutting speeds given in the speed tables. The desired feed is 0.012 in./rev and the optimum feed, as explained above is 0.016 in./rev, therefore, feed/fopt = 0.012⁄0.016 = 0.75 and Vavg/Vopt = 95⁄50 = 1.9, approximately 2. The feed factor Ff is found at the intersection of the feed ratio row and the speed ratio column. Ff = 1.40 corresponds to about halfway between 1.31 and 1.50, which are the feed factors that correspond to Vavg/Vopt = 2.0 and feed/fopt ratios of 0.7 and 0.8, respectively. Fd, the diameter factor, is found on the same row as the feed factor (halfway between the 0.7 and 0.8 rows, for this example) under the column for drill diameter = 0.60 inch. Because the speed table values are based on a 0.60-inch drill diameter, Fd = 1.0 for this example, and the cutting speed is V = Vopt × Ff × Fd = 50 × 1.4 × 1.0 = 70 ft/min. The spindle speed in rpm is N = 12 × V/(π × D) = 12 × 70/(3.14 × 0.6) = 445 rpm. Example 3, Drilling:Using the same material and feed as in the previous example, what cutting speeds are required for 0.079-inch and 4-inch diameter drills? What machine rpm is required for each? Because the feed is the same as in the previous example, the feed factor is Ff = 1.40 and does not need to be recalculated. The diameter factors are found in Table 22 on the same row as the feed factor for the previous example (about halfway between the diameter factors corresponding to feed/fopt values of 0.7 and 0.8) in the column corresponding to drill diameters 0.079 and 4.0 inches, respectively. Results of the calculations are summarized below. Drill diameter = 0.079 inch

Drill diameter = 4.0 inches

Ff = 1.40

Ff = 1.40

Fd = (0.34 + 0.38)/2 = 0.36

Fd = (1.95 + 1.73)/2 = 1.85

V = 50 × 1.4 × 0.36 = 25.2 fpm

V = 50 × 1.4 × 1.85 = 129.5 fpm

12 × 25.2/(3.14 × 0.079) = 1219 rpm

12 × 129.5/(3.14 × 4) = 124 rpm



1065

Drilling Difficulties: A drill split at the web is evidence of too much feed or insufficient lip clearance at the center due to improper grinding. Rapid wearing away of the extreme outer corners of the cutting edges indicates that the speed is too high. A drill chipping or breaking out at the cutting edges indicates that either the feed is too heavy or the drill has been ground with too much lip clearance. Nothing will “check” a high-speed steel drill quicker than to turn a stream of cold water on it after it has been heated while in use. It is equally bad to plunge it in cold water after the point has been heated in grinding. The small checks or cracks resulting from this practice will eventually chip out and cause rapid wear or breakage. Insufficient speed in drilling small holes with hand feed greatly increases the risk of breakage, especially at the moment the drill is breaking through the farther side of the work, due to the operator's inability to gage the feed when the drill is running too slowly. Small drills have heavier webs and smaller flutes in proportion to their size than do larger drills, so breakage due to clogging of chips in the flutes is more likely to occur. When drilling holes deeper than three times the diameter of the drill, it is advisable to withdraw the drill (peck feed) at intervals to remove the chips and permit coolant to reach the tip of the drill. Drilling Holes in Glass: The simplest method of drilling holes in glass is to use a standard, tungsten-carbide-tipped masonry drill of the appropriate diameter, in a gun-drill. The edges of the carbide in contact with the glass should be sharp. Kerosene or other liquid may be used as a lubricant, and a light force is maintained on the drill until just before the point breaks through. The hole should then be started from the other side if possible, or a very light force applied for the remainder of the operation, to prevent excessive breaking of material from the sides of the hole. As the hard particles of glass are abraded, they accumulate and act to abrade the hole, so it may be advisable to use a slightly smaller drill than the required diameter of the finished hole. Alternatively, for holes of medium and large size, use brass or copper tubing, having an outside diameter equal to the size of hole required. Revolve the tube at a peripheral speed of about 100 feet per minute, and use carborundum (80 to 100 grit) and light machine oil between the end of the pipe and the glass. Insert the abrasive under the drill with a thin piece of soft wood, to avoid scratching the glass. The glass should be supported by a felt or rubber cushion, not much larger than the hole to be drilled. If practicable, it is advisable to drill about halfway through, then turn the glass over, and drill down to meet the first cut. Any fin that may be left in the hole can be removed with a round second-cut file wetted with turpentine. Smaller-diameter holes may also be drilled with triangular-shaped cemented carbide drills that can be purchased in standard sizes. The end of the drill is shaped into a long tapering triangular point. The other end of the cemented carbide bit is brazed onto a steel shank. A glass drill can be made to the same shape from hardened drill rod or an old threecornered file. The location at which the hole is to be drilled is marked on the workpiece. A dam of putty or glazing compound is built up on the work surface to contain the cutting fluid, which can be either kerosene or turpentine mixed with camphor. Chipping on the back edge of the hole can be prevented by placing a scrap plate of glass behind the area to be drilled and drilling into the backup glass. This procedure also provides additional support to the workpiece and is essential for drilling very thin plates. The hole is usually drilled with an electric hand drill. When the hole is being produced, the drill should be given a small circular motion using the point as a fulcrum, thereby providing a clearance for the drill in the hole. Very small round or intricately shaped holes and narrow slots can be cut in glass by the ultrasonic machining process or by the abrasive jet cutting process.



Drilling

Reaming

Drilling


Material

HSS

Opt.

85

55

Shock resisting: S1, S2, S5, S6, S7

175–225

50

35

Cold work (oil hardening): O1, O2, O6, O7

175–225

45

30

200–250

30

20

(Air hardening): A2, A3, A8, A9, A10

200–250

50

35

A4, A6

200–250

45

30

A7

225–275

30

20

150–200

60

40

200–250

50

30

325–375

30

20

150–200

55

35

200–250

40

25

150–200

45

30

200–250

35

20

150–200

60

40

100–150

75

50

150–200

60

40

200–250

45

30

225–275

35

20

225–275

25

15

Hot work (chromium type): H10, H11, H12, H13, H14, H19

(Tungsten type): H21, H22, H23, H24, H25, H26 (Molybdenum type): H41, H42, H43

{

{ {

Special-purpose, low alloy: L2, L3, L6 Mold steel: P2, P3, P4, P5, P6P20, P21 High-speed steel: M1, M2, M6, M10, T1, T2, T6 M3-1, M4, M7, M30, M33, M34, M36, M41, M42, M43, M44, M46, M47, T5, T8 T15, M3-2

{

Threading

HSS

HSS

f 15 s 45

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

7 85

8 360

4 24 605 90

12 95

83 75

20 95

8 270

4 450

8 360

4 24 605 90

12 95

83 75

20 95

f s

f 15 s 45

7 85

See the footnote to Table 17 for instructions concerning the use of this table. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: coated carbide = 10.


SPEEDS AND FEEDS

150–200

{

Reaming


Speed (fpm)

Water hardening: W1, W2, W5

(High carbon, high chromium): D2, D3, D4, D5, D7


1066

Table 18. Feeds and Speeds for Drilling, Reaming, and Threading Tool Steels


Table 19. Feeds and Speeds for Drilling, Reaming, and Threading Stainless Steels Drilling

Reaming

Drilling


Material Free-machining stainless steels (Ferritic): 430F, 430FSe

HSS

Speed (fpm) 90

60

135–185 225–275 135–185 185–240 275–325 375–425

85 70 90 70 40 20

55 45 60 45 25 10

Stainless steels (Ferritic): 405, 409, 429, 430, 434

135–185

65

45

(Austenitic): 201, 202, 301, 302, 304, 304L, 305, 308, { 321, 347, 348 (Austenitic): 302B, 309, 309S, 310, 310S, 314, 316

135–185 225–275 135–185 135–175 175–225 275–325 375–425 225–275 275–325 375–425 225–275 275–325 375–425

55 50 50 75 65 40 25 50 40 25 45 40 20

35 30 30 50 45 25 15 30 25 15 30 25 10

150–200

50

30

275–325 325–375 375–450

45 35 20

25 20 10

(Austenitic): 203EZ, 303, 303Se, 303MA, 303Pb, 303Cu, 303 Plus X

{

(Martensitic): 416, 416Se, 416 Plus X, 420F, 420FSe, { 440F, 440FSe

(Martensitic): 403, 410, 420, 501

{

(Martensitic): 414, 431, Greek Ascoloy

{

(Martensitic): 440A, 440B, 440C

{

(Precipitation hardening): 15–5PH, 17–4PH, 17–7PH, AF–71, 17–14CuMo, AFC–77, AM–350, AM–355, { AM–362, Custom 455, HNM, PH13–8, PH14–8Mo, PH15–7Mo, Stainless W

Opt. f 15 s 25

7 45

8 320

4 24 540 50

12 50

83 40

20 51

f 15 s 20

7 40

8 250

4 24 425 40

12 40

83 35

20 45

f 15 s 25

7 45

8 320

4 24 540 50

12 50

83 40

20 51

f 15 s 20

7 40

8 250

4 24 425 40

12 40

83 35

20 45

f 15 s 20

7 40

8 250

4 24 425 40

12 40

83 35

20 45


1067

See the footnote to Table 17 for instructions concerning the use of this table. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: coated carbide = 10.

SPEEDS AND FEEDS

135–185

Reaming Threading Indexable Insert Coated Carbide HSS HSS f = feed (0.001 in./rev), s = speed (ft/min) Avg. Opt. Avg. Opt. Avg. Opt. Avg.


1068

Table 20. Feeds and Speeds for Drilling, Reaming, and Threading Ferrous Cast Metals Drilling

Reaming

Drilling

Reaming

Threading

HSS

HSS

Indexable Carbide Insert HSS

Material

Brinell Hardness

HSS

Uncoated

Coated


Speed (fpm)

Opt.

120–150

100

65

ASTM Class 25

160–200

90

60


190–220

80

55


220–260

60

40


250–320

30

20


100–215

50

30


120–175

40

25


150–250

30

20

(Ferritic): 32510, 35018

110–160

110

75

f s f s

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

6 26 485 85

13 83 65 90

20 80

21 50

10 83 30 55

20 45

30 95

16 83 80 100

20 85

22 65

11 83 45 70

20 60

28 80

14 83 60 80

20 70

16 80

8 90

11 85

6 180

11 235

13 50

6 50

11 70

6 150

11 195

6 405

Avg.

Malleable Iron

(Pearlitic): 40010, 43010, 45006, 45008, 48005, 50005

160–200

80

55

200–240

70

45

(Martensitic): 53004, 60003, 60004

200–255

55

35


220–260

50

30


240–280

45

30


250–320

25

15

(Ferritic): 60-40-18, 65-45-12

140–190

100

65

f s

19 80

10 100

f s

14 65

7 65

11 85

6 180

11 270 11 235

6 555 6 485

Nodular (Ductile) Iron f s

17 70

9 80

11 85

6 180

11 235


6 485

SPEEDS AND FEEDS

ASTM Class 20


Table 20. (Continued) Feeds and Speeds for Drilling, Reaming, and Threading Ferrous Cast Metals Drilling

Reaming

Drilling

Reaming

Threading

HSS

HSS

Indexable Carbide Insert HSS Brinell Hardness

Material (Martensitic): 120-90-02

{

(Ferritic-Pearlitic): 80-55-06

HSS

Uncoated

Coated


Speed (fpm)

Opt.

270–330

25

330–400

10

5

190–225

70

45

Avg. Opt.

Avg. Opt.

Avg. Opt.

6 150

6 405

Avg. Opt.

Avg.

15

50

30

240–300

40

25

(Low carbon): 1010, 1020

100–150

100

65

125–175

90

60

175–225

70

45

225–300

55

35

150–200

75

50

200–250

65

40

250–300

50

30

175–225

70

45

225–250

60

35

250–300

45

30

300–350

30

20

350–400

20

10

f s

13 60

6 60

f s

18 35

9 70

f s

15 35

7 60

11 70

11 195

21 55

11 83 40 60

20 55

29 75

15 83 85 65

20 85

24 65

12 83 70 55

20 70

Cast Steels

(Medium carbon): 1030, 1040, 1050

(Low-carbon alloy): 1320, 2315, 2320, 4110, 4120, 4320, 8020, 8620

{

{

(Medium-carbon alloy): 1330, 1340, 2325, 2330, 4125, 4130, 4140, 4330, 4340, { 8030, 80B30, 8040, 8430, 8440, 8630, 8640, 9525, 9530, 9535

f s

8 195†

4 475

8 130†

4 315


1069

See the footnote to Table 17 for instructions concerning the use of this table. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated = 15; coated carbide = 11, † = 10.

SPEEDS AND FEEDS

225–260



Drilling

Reaming

Drilling


Material

CD

All wrought aluminum alloys, 6061-T651, 5000, 6000, 7000 series All aluminum sand and permanent mold casting alloys

HSS

Reaming

Threading

HSS

HSS


Speed (fpm) 400


1070

Table 21. Feeds and Speeds for Drilling, Reaming, and Threading Light Metals

Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

400

ST and A

350

350

AC

500

500

ST and A

350

f 31 s 390

16 580

11 3235

6 11370

52 610

26 615

83 635

20 565

350


—

—

—

f 23 s 110

11 145

11 945

6 3325

38 145

19 130

83 145

20 130


—

—

—

f 27 s 90

14 125

11 855

6 3000

45 130

23 125

83 130

20 115

AC

300

300

ST and A

70

70

—

—

ST and A

45

40

f 24 s 65

12 85

11 555

6 1955

40 85

20 80

83 85

20 80

AC

125

100

f 27 s 90

14 125

11 855

6 3000

45 130

23 125

83 130

20 115

All wrought magnesium alloys

A,CD,ST and A

500

500

All cast magnesium alloys

A,AC, ST and A

450

450


{

Alloys 413 All other aluminum die-casting alloys

{

Magnesium Alloys

Abbreviations designate: A, annealed; AC, as cast; CD, cold drawn; and ST and A, solution treated and aged, respectively. See the footnote to Table 17 for instructions concerning the use of this table. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows; uncoated carbide = 15.


SPEEDS AND FEEDS

Aluminum Die-Casting Alloys


Table 22. Feed and Diameter Speed Adjustment Factors for HSS Twist Drills and Reamers Cutting Speed, V = Vopt × Ff × Fd Ratio of the two cutting speeds (average/optimum) given in the tables Vavg/Vopt

Tool Diameter


1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.30

0.44

0.56

0.78

1.00

0.90

1.00

1.06

1.09

1.14

1.18

1.21

1.27

0.32

0.46

0.59

0.79

1.00

0.80

1.00

1.12

1.19

1.31

1.40

1.49

1.63

0.34

0.48

0.61

0.80

0.70

1.00

1.15

1.30

1.50

1.69

1.85

2.15

0.38

0.52

0.64

0.60

1.00

1.23

1.40

1.73

2.04

2.34

2.89

0.42

0.55

0.50

1.00

1.25

1.50

2.00

2.50

3.00

5.00

0.47

0.40

1.00

1.23

1.57

2.29

3.08

3.92

5.70

0.30

1.00

1.14

1.56

2.57

3.78

5.19

0.20

1.00

0.90

1.37

2.68

4.49

0.10

1.00

1.44

0.80

2.08

4.36

1.25

1.50

2.00

2.50

0.60 in

1.00 in

2.00 in

3.00 in

4.00 in

(15 mm)

(25 mm)

(50 mm)

(75 mm)

(100 mm)

1.32

1.81

2.11

2.29

1.30

1.72

1.97

2.10

1.00

1.27

1.64

1.89

1.95

0.82

1.00

1.25

1.52

1.67

1.73

0.67

0.84

1.00

1.20

1.46

1.51

1.54

0.60

0.71

0.87

1.00

1.15

1.30

1.34

1.94

0.53

0.67

0.77

0.90

1.00

1.10

1.17

1.16

1.12

8.56

0.64

0.76

0.84

0.94

1.00

1.04

1.02

0.96

0.90

6.86

17.60

0.83

0.92

0.96

1.00

1.00

0.96

0.81

0.73

0.66

8.00

20.80

1.29

1.26

1.21

1.11

1.00

0.84

0.60

0.46

0.38

3.00

4.00

0.08 in

0.15 in

0.25 in

0.40 in

(2 mm)

(4 mm)

(6 mm)

(10 mm)

Diameter Factor, Fd

Feed Factor, Ff

1071


SPEEDS AND FEEDS

This table is specifically for use with the combined feed/speed data for HSS twist drills in Tables 17 through 23; use Tables 5a and 5b to adjust speed and tool life for indexable insert drilling with carbides. The combined feed/speed data for HSS twist drilling are based on a 0.60-inch diameter HSS drill with standard drill point geometry (2-flute with 118° tip angle). To adjust the given speeds for different feeds and drill diameters, use the two feed/speed pairs from the tables and calculate the ratio of desired (new) feed to optimum feed (largest of the two feeds from the speed table), and the ratio of the two cutting speeds Vavg/Vopt. Use the values of these ratios to find the feed factor Ff at the intersection of the feed ratio row and the speed ratio column in the left half of the table. The diameter factor Fd is found in the same row as the feed factor, in the right half of the table, under the column corresponding to the drill diameter. For diameters not given, interpolate between the nearest available sizes. The adjusted cutting speed can be calculated from V = Vopt × Ff × Fd, where Vopt is the smaller (optimum) of the two speeds from the speed table (from the left side of the column containing the two feed/speed pairs). Tool life using the selected feed and the adjusted speed should be approximately 45 minutes. Speed adjustment factors to modify tool life are found in Table 15e.


SPEEDS AND FEEDS Table 23. Feeds and Speeds for Drilling and Reaming Copper Alloys Group 1

Architectural bronze(C38500); Extra-high-leaded brass (C35600); Forging brass (C37700); Freecutting phosphor bronze (B-2) (C54400); Free-cutting brass (C36000); Free-cutting Muntz metal (C37000); High-leaded brass (C33200, C34200); High-leaded brass tube (C35300); Leaded commercial bronze (C31400); Leaded naval brass (C48500); Medium-leaded brass (C34000) Group 2 Aluminum brass, arsenical (C68700); Cartridge brass, 70% (C26000); High-silicon bronze, B (C65500); Admiralty brass (inhibited) (C44300, C44500); Jewelry bronze, 87.5% (C22600); Leaded Muntz metal (C36500, C36800); Leaded nickel silver (C79600); Low brass, 80% (C24000); Low-leaded brass (C33500); Low-silicon bronze, B (C65100); Manganese bronze, A (C67500); Muntz metal, 60% (C28000); Nickel silver, 55–18 (C77000); Red brass, 85% (C23000); Yellow brass (C26800) Group 3 Aluminum bronze, D (C61400); Beryllium copper (C17000, C17200, C17500); Commercial bronze, 90% (C22000); Copper nickel, 10% (C70600); Copper nickel, 30% (C71500);Electrolytic tough-pitch copper (C11000); Gilding, 95% (C21000); Nickel silver, 65–10 (C74500); Nickel silver, 65–12 (C75700); Nickel silver, 65–15 (C75400); Nickel silver, 65–18 (C75200); Oxygen-free copper (C10200); Phosphor bronze, 1.25% (C50200); Phosphor bronze, 10% D (C52400); Phosphor bronze, 5% A (C51000); Phosphor bronze, 8% C (C52100); Phosphorus deoxidized copper (C12200) Drilling Alloy Description and UNS Alloy Numbers

Group 1 Group 2 Group 3

Material Condition A CD A CD A CD

Reaming

HSS Speed (fpm) 160 175 120 140 60 65

160 175 110 120 50 60

Drilling Reaming Indexable Insert HSS Uncoated Carbide HSS f = feed (0.001 in./rev), s = speed (ft/min) Opt. Avg. Opt. Avg. Opt. Avg. Wrought Alloys f 21 11 11 6 36 18 s 210 265 405 915 265 230 f 24 12 11 6 40 20 s 100 130 205 455 130 120 f 23 11 11 6 38 19 s 155 195 150 340 100 175

Abbreviations designate: A, annealed; CD, cold drawn. The two leftmost speed columns in this table contain traditional Handbook speeds for HSS steel tools. The text contains information concerning feeds to use in conjunction with these speeds. HSS Drilling and Reaming: The combined feed/speed data for drilling and Table 22 are used to adjust drilling speeds for other feeds and drill diameters. Examples are given in the text. The given feeds and speeds for reaming are based on an 8-tooth, 25⁄32-inch diameter, 30° lead angle reamer, and a 0.008-inch radial depth of cut. For other feeds, the correct speed can be obtained by interpolation using the given speeds if the desired feed lies in the recommended range (between the given values of optimum and average feed). The cutting speeds for reaming do not require adjustment for tool diameter as long as the radial depth of cut does not become too large. Speed adjustment factors to modify tool life are found in Table 15e. Indexable Insert Drilling: The feed/speed data for indexable insert drilling are based on a tool with two cutting edges, an insert nose radius of 3⁄64 inch, a 10-degree lead angle, and diameter D of 1 inch. Adjustments for feed and depth of cut are made using Table 5a (Turning Speed Adjustment Factors) using a depth of cut of D/2, or one-half the drill diameter. Expected tool life at the given feeds and speeds is 15 minutes for short hole drilling (i.e., where hole depth is about 2D or less). Speed adjustment factors to increase tool life are found in Table 5b. The combined feed/speed data in this table are based on tool grades (identified in Table 16) as follows: uncoated carbide = 15.

Using the Feed and Speed Tables for Tapping and Threading.—The feed used in tapping and threading is always equal to the pitch of the screw thread being formed. The



1073

threading data contained in the tables for drilling, reaming, and threading (Tables 17 through 23) are primarily for tapping and thread chasing, and do not apply to thread cutting with single-point tools. The threading data in Tables 17 through 23 give two sets of feed (pitch) and speed values, for 12 and 50 threads/inch, but these values can be used to obtain the cutting speed for any other thread pitches. If the desired pitch falls between the values given in the tables, i.e., between 0.020 inch (50 tpi) and 0.083 inch (12 tpi), the required cutting speed is obtained by interpolation between the given speeds. If the pitch is less than 0.020 inch (more than 50 tpi), use the average speed, i.e., the largest of the two given speeds. For pitches greater than 0.083 inch (fewer than 12 tpi), the optimum speed should be used. Tool life using the given feed/speed data is intended to be approximately 45 minutes, and should be about the same for threads between 12 and 50 threads per inch. Example:Determine the cutting speed required for tapping 303 stainless steel with a 1⁄2– 20 coated HSS tap. The two feed/speed pairs for 303 stainless steel, in Table 19, are 83⁄35 (0.083 in./rev at 35 fpm) and 20⁄45 (0.020 in./rev at 45 fpm). The pitch of a 1⁄2–20 thread is 1⁄20 = 0.05 inch, so the required feed is 0.05 in./rev. Because 0.05 is between the two given feeds (Table 19), the cutting speed can be obtained by interpolation between the two given speeds as follows: 0.05 – 0.02- ( 45 – 35 ) = 40 fpm V = 35 + ----------------------------0.083 – 0.02 The cutting speed for coarse-pitch taps must be lower than for fine-pitch taps with the same diameter. Usually, the difference in pitch becomes more pronounced as the diameter of the tap becomes larger and slight differences in the pitch of smaller-diameter taps have little significant effect on the cutting speed. Unlike all other cutting tools, the feed per revolution of a tap cannot be independently adjusted—it is always equal to the lead of the thread and is always greater for coarse pitches than for fine pitches. Furthermore, the thread form of a coarse-pitch thread is larger than that of a fine-pitch thread; therefore, it is necessary to remove more metal when cutting a coarse-pitch thread. Taps with a long chamfer, such as starting or tapper taps, can cut faster in a short hole than short chamfer taps, such as plug taps. In deep holes, however, short chamfer or plug taps can run faster than long chamfer taps. Bottoming taps must be run more slowly than either starting or plug taps. The chamfer helps to start the tap in the hole. It also functions to involve more threads, or thread form cutting edges, on the tap in cutting the thread in the hole, thus reducing the cutting load on any one set of thread form cutting edges. In so doing, more chips and thinner chips are produced that are difficult to remove from deeper holes. Shortening the chamfer length causes fewer thread form cutting edges to cut, thereby producing fewer and thicker chips that can easily be disposed of. Only one or two sets of thread form cutting edges are cut on bottoming taps, causing these cutting edges to assume a heavy cutting load and produce very thick chips. Spiral-pointed taps can operate at a faster cutting speed than taps with normal flutes. These taps are made with supplementary angular flutes on the end that push the chips ahead of the tap and prevent the tapped hole from becoming clogged with chips. They are used primarily to tap open or through holes although some are made with shorter supplementary flutes for tapping blind holes. The tapping speed must be reduced as the percentage of full thread to be cut is increased. Experiments have shown that the torque required to cut a 100 per cent thread form is more than twice that required to cut a 50 per cent thread form. An increase in the percentage of full thread will also produce a greater volume of chips. The tapping speed must be lowered as the length of the hole to be tapped is increased. More friction must be overcome in turning the tap and more chips accumulate in the hole.



SPEEDS AND FEEDS

It will be more difficult to apply the cutting fluid at the cutting edges and to lubricate the tap to reduce friction. This problem becomes greater when the hole is being tapped in a horizontal position. Cutting fluids have a very great effect on the cutting speed for tapping. Although other operating conditions when tapping frequently cannot be changed, a free selection of the cutting fluid usually can be made. When planning the tapping operation, the selection of a cutting fluid warrants a very careful consideration and perhaps an investigation. Taper threaded taps, such as pipe taps, must be operated at a slower speed than straight thread taps with a comparable diameter. All the thread form cutting edges of a taper threaded tap that are engaged in the work cut and produce a chip, but only those cutting edges along the chamfer length cut on straight thread taps. Pipe taps often are required to cut the tapered thread from a straight hole, adding to the cutting burden. The machine tool used for the tapping operation must be considered in selecting the tapping speed. Tapping machines and other machines that are able to feed the tap at a rate of advance equal to the lead of the tap, and that have provisions for quickly reversing the spindle, can be operated at high cutting speeds. On machines where the feed of the tap is controlled manually—such as on drill presses and turret lathes—the tapping speed must be reduced to allow the operator to maintain safe control of the operation. There are other special considerations in selecting the tapping speed. Very accurate threads are usually tapped more slowly than threads with a commercial grade of accuracy. Thread forms that require deep threads for which a large amount of metal must be removed, producing a large volume of chips, require special techniques and slower cutting speeds. Acme, buttress, and square threads, therefore, are generally cut at lower speeds. Cutting Speed for Broaching.—Broaching offers many advantages in manufacturing metal parts, including high production rates, excellent surface finishes, and close dimensional tolerances. These advantages are not derived from the use of high cutting speeds; they are derived from the large number of cutting teeth that can be applied consecutively in a given period of time, from their configuration and precise dimensions, and from the width or diameter of the surface that can be machined in a single stroke. Most broaching cutters are expensive in their initial cost and are expensive to sharpen. For these reasons, a long tool life is desirable, and to obtain a long tool life, relatively slow cutting speeds are used. In many instances, slower cutting speeds are used because of the limitations of the machine in accelerating and stopping heavy broaching cutters. At other times, the available power on the machine places a limit on the cutting speed that can be used; i.e., the cubic inches of metal removed per minute must be within the power capacity of the machine. The cutting speeds for high-speed steel broaches range from 3 to 50 feet per minute, although faster speeds have been used. In general, the harder and more difficult to machine materials are cut at a slower cutting speed and those that are easier to machine are cut at a faster speed. Some typical recommendations for high-speed steel broaches are: AISI 1040, 10 to 30 fpm; AISI 1060, 10 to 25 fpm; AISI 4140, 10 to 25 fpm; AISI 41L40, 20 to 30 fpm; 201 austenitic stainless steel, 10 to 20 fpm; Class 20 gray cast iron, 20 to 30 fpm; Class 40 gray cast iron, 15 to 25 fpm; aluminum and magnesium alloys, 30 to 50 fpm; copper alloys, 20 to 30 fpm; commercially pure titanium, 20 to 25 fpm; alpha and beta titanium alloys, 5 fpm; and the superalloys, 3 to 10 fpm. Surface broaching operations on gray iron castings have been conducted at a cutting speed of 150 fpm, using indexable insert cemented carbide broaching cutters. In selecting the speed for broaching, the cardinal principle of the performance of all metal cutting tools should be kept in mind; i.e., increasing the cutting speed may result in a proportionately larger reduction in tool life, and reducing the cutting speed may result in a proportionately larger increase in the tool life. When broaching most materials, a suitable cutting fluid should be used to obtain a good surface finish and a better tool life. Gray cast iron can be broached without using a cutting fluid although some shops prefer to use a soluble oil.


Machinery's Handbook 27th Edition SPADE DRILLS

1075

Spade Drills Spade drills are used to produce holes ranging in size from about 1 inch to 6 inches diameter, and even larger. Very deep holes can be drilled and blades are available for core drilling, counterboring, and for bottoming to a flat or contoured shape. There are two principal parts to a spade drill, the blade and the holder. The holder has a slot into which the blade fits; a wide slot at the back of the blade engages with a tongue in the holder slot to locate the blade accurately. A retaining screw holds the two parts together. The blade is usually made from high-speed steel, although cast nonferrous metal and cemented carbide-tipped blades are also available. Spade drill holders are classified by a letter symbol designating the range of blade sizes that can be held and by their length. Standard stub, short, long, and extra long holders are available; for very deep holes, special holders having wear strips to support and guide the drill are often used. Long, extra long, and many short length holders have coolant holes to direct cutting fluid, under pressure, to the cutting edges. In addition to its function in cooling and lubricating the tool, the cutting fluid also flushes the chips out of the hole. The shank of the holder may be straight or tapered; special automotive shanks are also used. A holder and different shank designs are shown in Fig. 1; Figs. 2a through Fig. 2f show some typical blades. Milling machine taper shank

Body diameter Blade retaining screw

Coolant holes

Locating flats Body

Flute Blade slot

Seating surface Flute length

Morse taper shank

Straight shank

Coolant inductor

Automotive shank (special) Fig. 1. Spade Drill Blade Holder

Spade Drill Geometry.—Metal separation from the work is accomplished in a like manner by both twist drills and spade drills, and the same mechanisms are involved for each. The two cutting lips separate the metal by a shearing action that is identical to that of chip formation by a single-point cutting tool. At the chisel edge, a much more complex condition exists. Here the metal is extruded sideways and at the same time is sheared by the rotation of the blunt wedge-formed chisel edge. This combination accounts for the very high thrust force required to penetrate the work. The chisel edge of a twist drill is slightly rounded, but on spade drills, it is a straight edge. Thus, it is likely that it is more difficult for the extruded metal to escape from the region of the chisel edge with spade drills. However, the chisel edge is shorter in length than on twist drills and the thrust for spade drilling is less.



SPADE DRILLS Typical Spade Drill Blades

Fig. 2a. Standard blade

Fig. 2b. Standard blade with corner chamfer

Fig. 2d. Center cutting facing or Fig. 2e. Standard blade with split bottoming blade point or crankshaft point

Fig. 2c. Core drilling blade

Fig. 2f. Center cutting radius blade

Basic spade drill geometry is shown in Fig. 3. Normally, the point angle of a standard tool is 130 degrees and the lip clearance angle is 18 degrees, resulting in a chisel edge angle of 108 degrees. The web thickness is usually about 1⁄4 to 5⁄16 as thick as the blade thickness. Usually, the cutting edge angle is selected to provide this web thickness and to provide the necessary strength along the entire length of the cutting lip. A further reduction of the chisel edge length is sometimes desirable to reduce the thrust force in drilling. This reduction can be accomplished by grinding a secondary rake surface at the center or by grinding a split point, or crankshaft point, on the point of the drill. The larger point angle of a standard spade drill—130 degrees as compared with 118 degrees on a twist drill—causes the chips to flow more toward the periphery of the drill, thereby allowing the chips to enter the flutes of the holder more readily. The rake angle facilitates the formation of the chip along the cutting lips. For drilling materials of average hardness, the rake angle should be 10 to 12 degrees; for hard or tough steels, it should be 5 to 7 degrees; and for soft and ductile materials, it can be increased to 15 to 20 degrees. The rake surface may be flat or rounded, and the latter design is called radial rake. Radial rake is usually ground so that the rake angle is maximum at the periphery and decreases uniformly toward the center to provide greater cutting edge strength at the center. A flat rake surface is recommended for drilling hard and tough materials in order to reduce the tendency to chipping and to reduce heat damage. A most important feature of the cutting edge is the chip splitters, which are also called chip breaker grooves. Functionally, these grooves are chip dividers; instead of forming a single wide chip along the entire length of the cutting edge, these grooves cause formation of several chips that can be readily disposed of through the flutes of the holder. Chip splitters must be carefully ground to prevent the chips from packing in the grooves, which greatly reduces their effectiveness. Splitters should be ground perpendicular to the cutting lip and parallel to the surface formed by the clearance angle. The grooves on the two cut-


Machinery's Handbook 27th Edition SPADE DRILLING

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ting lips must not overlap when measured radially along the cutting lip. Fig. 4 and the accompanying table show the groove form and dimensions.

Rake angle

R Radial rake Front lip clearance angle Chip splitters

O.D. clearance angle Flat rake

O.D. land (circular)

Seating pad Locating ears

Blade diameter

Web

Chisel edge angle

Locating slot

Rake surface Cutting lip

Chisel edge Blade thickness

Cutting edge angle

0.031 Typ.

Back taper Point angle

Stepped O.D. clearance 0.031 R. Typ. O.D. clearance angle

Wedge angle (optional)

Fig. 3. Spade Drill Blade

On spade drills, the front lip clearance angle provides the relief. It may be ground on a drill grinding machine but usually it is ground flat. The normal front lip clearance angle is 8 degrees; in some instances, a secondary relief angle of about 14 degrees is ground below the primary clearance. The wedge angle on the blade is optional. It is generally ground on thicker blades having a larger diameter to prevent heel dragging below the cutting lip and to reduce the chisel edge length. The outside-diameter land is circular, serving to support and guide the blade in the hole. Usually it is ground to have a back taper of 0.001 to 0.002 inch per inch per side. The width of the land is approximately 20 to 25 per cent of the blade thickness. Normally, the outside-diameter clearance angle behind the land is 7 to 10 degrees. On many spade drill blades, the outside-diameter clearance surface is stepped about 0.030 inch below the land.

Fig. 4. Spade Drill Chip Splitter Dimensions

Spade Drilling.—Spade drills are used on drilling machines and other machine tools where the cutting tool rotates; they are also used on turning machines where the work



SPADE DRILLING

rotates and the tool is stationary. Although there are some slight operational differences, the methods of using spade drills are basically the same. An adequate supply of cutting fluid must be used, which serves to cool and lubricate the cutting edges; to cool the chips, thus making them brittle and more easily broken; and to flush chips out of the hole. Flood cooling from outside the hole can be used for drilling relatively shallow holes, of about one to two and one-half times the diameter in depth. For deeper holes, the cutting fluid should be injected through the holes in the drill. When drilling very deep holes, it is often helpful to blow compressed air through the drill in addition to the cutting fluid to facilitate ejection of the chips. Air at full shop pressure is throttled down to a pressure that provides the most efficient ejection. The cutting fluids used are light and medium cutting oils, water-soluble oils, and synthetics, and the type selected depends on the work material. Starting a spade drill in the workpiece needs special attention. The straight chisel edge on the spade drill has a tendency to wander as it starts to enter the work, especially if the feed is too light. This wander can result in a mispositioned hole and possible breakage of the drill point. The best method of starting the hole is to use a stub or short-length spade drill holder and a blade of full size that should penetrate at least 1⁄8 inch at full diameter. The holder is then changed for a longer one as required to complete the hole to depth. Difficulties can be encountered if spotting with a center drill or starting drill is employed because the angles on these drills do not match the 130-degree point angle of the spade drill. Longer spade drills can be started without this starting procedure if the drill is guided by a jig bushing and if the holder is provided with wear strips. Chip formation warrants the most careful attention as success in spade drilling is dependent on producing short, well-broken chips that can be easily ejected from the hole. Straight, stringy chips or chips that are wound like a clock spring cannot be ejected properly; they tend to pack around the blade, which may result in blade failure. The chip splitters must be functioning to produce a series of narrow chips along each cutting edge. Each chip must be broken, and for drilling ductile materials they should be formed into a “C” or “figure 9” shape. Such chips will readily enter the flutes on the holder and flow out of the hole. Proper chip formation is dependent on the work material, the spade drill geometry, and the cutting conditions. Brittle materials such as gray cast iron seldom pose a problem because they produce a discontinuous chip, but austenitic stainless steels and very soft and ductile materials require much attention to obtain satisfactory chip control. Thinning the web or grinding a split point on the blade will sometimes be helpful in obtaining better chip control, as these modifications allow use of a heavier feed. Reducing the rake angle to obtain a tighter curl on the chip and grinding a corner chamfer on the tool will sometimes help to produce more manageable chips. In most instances, it is not necessary to experiment with the spade drill blade geometry to obtain satisfactory chip control. Control usually can be accomplished by adjusting the cutting conditions; i.e., the cutting speed and the feed rate. Normally, the cutting speed for spade drilling should be 10 to 15 per cent lower than that for an equivalent twist drill, although the same speed can be used if a lower tool life is acceptable. The recommended cutting speeds for twist drills on Tables 17 through 23, starting on page 1061, can be used as a starting point; however, they should be decreased by the percentage just given. It is essential to use a heavy feed rate when spade drilling to produce a thick chip. and to force the chisel edge into the work. In ductile materials, a light feed will produce a thin chip that is very difficult to break. The thick chip on the other hand, which often contains many rupture planes, will curl and break readily. Table 1 gives suggested feed rates for different spade drill sizes and materials. These rates should be used as a starting point and some adjustments may be necessary as experience is gained.


Machinery's Handbook 27th Edition SPADE DRILLING

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Table 1. Feed Rates for Spade Drilling Feed—Inches per Revolution Spade Drill Diameter—Inches Material Free Machining Steel

Plain Carbon Steels

Free Machining Alloy Steels

Alloy Steels

Hardness, Bhn

1–11⁄4

11⁄4–2

2–3

3–4

4–5

5–8

100–240

0.014

0.016

0.018

0.022

0.025

0.030

240–325

0.010

0.014

0.016

0.020

0.022

0.025

100–225

0.012

0.015

0.018

0.022

0.025

0.030

225–275

0.010

0.013

0.015

0.018

0.020

0.025

275–325

0.008

0.010

0.013

0.015

0.018

0.020

150–250

0.014

0.016

0.018

0.022

0.025

0.030

250–325

0.012

0.014

0.016

0.018

0.020

0.025

325–375

0.010

0.010

0.014

0.016

0.018

0.020

125–180

0.012

0.015

0.018

0.022

0.025

0.030

180–225

0.010

0.012

0.016

0.018

0.022

0.025

225–325

0.009

0.010

0.013

0.015

0.018

0.020

325–400

0.006

0.008

0.010

0.012

0.014

0.016

Tool Steels Water Hardening

150–250

0.012

0.014

0.016

0.018

0.020

0.022

Shock Resisting

175–225

0.012

0.014

0.015

0.016

0.017

0.018

Cold Work

200–250

0.007

0.008

0.009

0.010

0.011

0.012

Hot Work

150–250

0.012

0.013

0.015

0.016

0.018

0.020

Mold

150–200

0.010

0.012

0.014

0.016

0.018

0.018

Special-Purpose

150–225

0.010

0.012

0.014

0.016

0.016

0.018

200–240

0.010

0.012

0.013

0.015

0.017

0.018

110–160

0.020

0.022

0.026

0.028

0.030

0.034

160–190

0.015

0.018

0.020

0.024

0.026

0.028

190–240

0.012

0.014

0.016

0.018

0.020

0.022

240–320

0.010

0.012

0.016

0.018

0.018

0.018

140–190

0.014

0.016

0.018

0.020

0.022

0.024

190–250

0.012

0.014

0.016

0.018

0.018

0.020

250–300

0.010

0.012

0.016

0.018

0.018

0.018

110–160

0.014

0.016

0.018

0.020

0.022

0.024

160–220

0.012

0.014

0.016

0.018

0.020

0.020

220–280

0.010

0.012

0.014

0.016

0.018

0.018

Ferritic

…

0.016

0.018

0.020

0.024

0.026

0.028

Austenitic

…

0.016

0.018

0.020

0.022

0.024

0.026

Martensitic

…

0.012

0.014

0.016

0.016

0.018

0.020

Ferritic

…

0.012

0.014

0.018

0.020

0.020

0.022

Austenitic

…

0.012

0.014

0.016

0.018

0.020

0.020

Martensitic

…

0.010

0.012

0.012

0.014

0.016

0.018

…

0.020

0.022

0.024

0.028

0.030

0.040

(Soft)

0.016

0.018

0.020

0.026

0.028

0.030

(Hard)

0.010

0.012

0.014

0.016

0.018

0.018

Titanium Alloys

…

0.008

0.010

0.012

0.014

0.014

0.016

High-Temperature Alloys

…

0.008

0.010

0.012

0.012

0.014

0.014

High-Speed

Gray Cast Iron

Ductile or Nodular Iron

Malleable Iron Ferritic Pearlitic Free Machining Stainless Steel

Stainless Steel

Aluminum Alloys Copper Alloys



SPADE DRILLING

Power Consumption and Thrust for Spade Drilling.—In each individual setup, there are factors and conditions influencing power consumption that cannot be accounted for in a simple equation; however, those given below will enable the user to estimate power consumption and thrust accurately enough for most practical purposes. They are based on experimentally derived values of unit horsepower, as given in Table 2. As a word of caution, these values are for sharp tools. In spade drilling, it is reasonable to estimate that a dull tool will increase the power consumption and the thrust by 25 to 50 per cent. The unit horsepower values in the table are for the power consumed at the cutting edge, to which must be added the power required to drive the machine tool itself, in order to obtain the horsepower required by the machine tool motor. An allowance for power to drive the machine is provided by dividing the horsepower at the cutter by a mechanical efficiency factor, em. This factor can be estimated to be 0.90 for a direct spindle drive with a belt, 0.75 for a back gear drive, and 0.70 to 0.80 for geared head drives. Thus, for spade drilling the formulas are πD -⎞ fN hp c = uhp ⎛ --------⎝ 4 ⎠ 2

B s = 148,500 uhp fD hp hp m = -------cem fm f = ---N where hpc = horsepower at the cutter hpm = horsepower at the motor Bs =thrust for spade drilling in pounds uhp = unit horsepower D =drill diameter in inches f =feed in inches per revolution fm =feed in inches per minute N =spindle speed in revolutions per minute em =mechanical efficiency factor Table 2. Unit Horsepower for Spade Drilling Material

Hardness

Plain Carbon and Alloy Steel

Cast Irons Stainless Steels

85–200 Bhn 200–275 275–375 375–425 45–52 Rc 110–200 Bhn 200–300 135–275 Bhn 30–45 Rc

uhp 0.79 0.94 1.00 1.15 1.44 0.5 1.08 0.94 1.08

Material Titanium Alloys High-Temp Alloys Aluminum Alloys Magnesium Alloys Copper Alloys

Hardness 250–375 Bhn 200–360 Bhn … … 20–80 Rb 80–100 Rb

uhp 0.72 1.44 0.22 0.16 0.43 0.72

Example:Estimate the horsepower and thrust required to drive a 2-inch diameter spade drill in AISI 1045 steel that is quenched and tempered to a hardness of 275 Bhn. From Table 17 on page 1061, the cutting speed, V, for drilling this material with a twist drill is 50 feet per minute. This value is reduced by 10 per cent for spade drilling and the speed selected is thus 0.9 × 50 = 45 feet per minute. The feed rate (from Table 1, page 1079) is 0.015 in/rev. and the unit horsepower from Table 2 above is 0.94. The machine efficiency factor is estimated to be 0.80 and it will be assumed that a 50 per cent increase in the unit horsepower must be allowed for dull tools.


Machinery's Handbook 27th Edition TREPANNING

1081

Step 1. Calculate the spindle speed from the following formula: N = 12V ---------πD where: N =spindle speed in revolutions per minute V =cutting speed in feet per minute D =drill diameter in inches 12 × 45 Thus, N = ------------------ = 86 revolutions per minute π×2 Step 2. Calculate the horsepower at the cutter: 2 × 2 2-⎞ 0.015 × 86 = 3.8 hp c = uhp ⎛ πD ----------⎞ fN = 0.94 ⎛ π -------------⎝ 4 ⎠ ⎝ 4 ⎠

Step 3. Calculate the horsepower at the motor and provide for a 50 per cent power increase for the dull tool: hp 3.8 hp m = -------c- = ---------- = 4.75 horsepower em 0.80 hp m (with dull tool) = 1.5 × 4.75 = 7.125 horsepower Step 4. Estimate the spade drill thrust: B s = 148,500 × uhp × fD = 148,500 × 0.94 × 0.015 × 2 = 4188 lb (for sharp tool) B s = 1.5 × 4188 = 6282 lb (for dull tool) Trepanning.—Cutting a groove in the form of a circle or boring or cutting a hole by removing the center or core in one piece is called trepanning. Shallow trepanning, also called face grooving, can be performed on a lathe using a single-point tool that is similar to a grooving tool but has a curved blade. Generally, the minimum outside diameter that can be cut by this method is about 3 inches and the maximum groove depth is about 2 inches. Trepanning is probably the most economical method of producing deep holes that are 2 inches, and larger, in diameter. Fast production rates can be achieved. The tool consists of a hollow bar, or stem, and a hollow cylindrical head to which a carbide or high-speed steel, single-point cutting tool is attached. Usually, only one cutting tool is used although for some applications a multiple cutter head must be used; e.g., heads used to start the hole have multiple tools. In operation, the cutting tool produces a circular groove and a residue core that enters the hollow stem after passing through the head. On outside-diameter exhaust trepanning tools, the cutting fluid is applied through the stem and the chips are flushed around the outside of the tool; inside-diameter exhaust tools flush the chips out through the stem with the cutting fluid applied from the outside. For starting the cut, a tool that cuts a starting groove in the work must be used, or the trepanning tool must be guided by a bushing. For holes less than about five diameters deep, a machine that rotates the trepanning tool can be used. Often, an ordinary drill press is satisfactory; deeper holes should be machined on a lathe with the work rotating. A hole diameter tolerance of ±0.010 inch can be obtained easily by trepanning and a tolerance of ±0.001 inch has sometimes been held. Hole runout can be held to ±0.003 inch per foot and, at times, to ±0.001 inch per foot. On heat-treated metal, a surface finish of 125 to 150 µm AA can be obtained and on annealed metals 100 to 250 µm AA is common.



SPEEDS AND FEEDS

ESTIMATING SPEEDS AND MACHINING POWER Estimating Planer Cutting Speeds.—Whereas most planers of modern design have a means of indicating the speed at which the table is traveling, or cutting, many older planers do not. Thus, the following formulas are useful for planers that do not have a means of indicating the table or cutting speed. It is not practicable to provide a formula for calculating the exact cutting speed at which a planer is operating because the time to stop and start the table when reversing varies greatly. The formulas below will, however, provide a reasonable estimate. Vc ≅ Sc L V S c ≅ -----c L where Vc =cutting speed; fpm or m/min Sc =number of cutting strokes per minute of planer table L =length of table cutting stroke; ft or m Cutting Speed for Planing and Shaping.—The traditional HSS cutting tool speeds in Tables 1 through 4b and Tables 6 through 9 can be used for planing and shaping. The feed and depth of cut factors in Tables 5c should also be used, as explained previously. Very often, other factors relating to the machine or the setup will require a reduction in the cutting speed used on a specific job. Cutting Time for Turning, Boring, and Facing.—The time required to turn a length of metal can be determined by the following formula in which T = time in minutes, L = length of cut in inches, f = feed in inches per revolution, and N = lathe spindle speed in revolutions per minute. L T = -----fN When making job estimates, the time required to load and to unload the workpiece on the machine, and the machine handling time, must be added to the cutting time for each length cut to obtain the floor-to-floor time. Planing Time.—The approximate time required to plane a surface can be determined from the following formula in which T = time in minutes, L = length of stroke in feet, Vc = cutting speed in feet per minute, Vr = return speed in feet per minute; W = width of surface to be planed in inches, F = feed in inches, and 0.025 = approximate reversal time factor per stroke in minutes for most planers: W 1 1 T = ----- L × ⎛⎝ ----- + -----⎞⎠ + 0.025 Vc Vr F Speeds for Metal-Cutting Saws.—The following speeds and feeds for solid-tooth, highspeed-steel, circular, metal-cutting saws are recommended by Saws International, Inc. (sfpm = surface feet per minute = 3.142 × blade diameter in inches × rpm of saw shaft ÷ 12). Speeds for Turning Unusual Materials.—Slate, on account of its peculiarly stratified formation, is rather difficult to turn, but if handled carefully, can be machined in an ordinary lathe. The cutting speed should be about the same as for cast iron. A sheet of fiber or pressed paper should be interposed between the chuck or steadyrest jaws and the slate, to protect the latter. Slate rolls must not be centered and run on the tailstock. A satisfactory method of supporting a slate roll having journals at the ends is to bore a piece of lignum vitae to receive the turned end of the roll, and center it for the tailstock spindle. Rubber can be turned at a peripheral speed of 200 feet per minute, although it is much easier to grind it with an abrasive wheel that is porous and soft. For cutting a rubber roll in


Machinery's Handbook 27th Edition MACHINING POWER

1083

Speeds, Feeds, and Tooth Angles for Sawing Various Materials ␤

α =Cutting angle β =Relief angle

␣

Materials

Front Rake Angle α (deg)

Back Rake Angle β (deg)

Aluminum

24

Light Alloys with Cu, Mg, and Zn

Stock Diameters (inches)

1⁄ –3⁄ 4 4

3⁄ –11⁄ 4 2

11⁄2–21⁄2

21⁄2–31⁄2

12

6500 sfpm 100 in/min

6200 sfpm 85 in/min

6000 sfpm 80 in/min

5000 sfpm 75 in/min

22

10

3600 sfpm 70 in/min

3300 sfpm 65 in/min

3000 sfpm 63 in/min

2600 sfpm 60 in/min

Light Alloys with High Si

20

8

650 sfpm 16 in/min

600 sfpm 16 in/min

550 sfpm 14 in/min

550 sfpm 12 in/min

Copper

20

10

1300 sfpm 24 in/min

1150 sfpm 24 in/min

1000 sfpm 22 in/min

800 sfpm 22 in/min

Bronze

15

8

1300 sfpm 24 in/min

1150 sfpm 24 in/min

1000 sfpm 22 in/min

800 sfpm 20 in/min

Hard Bronze

10

8

400 sfpm 6.3 in/min

360 sfpm 6 in/min

325 sfpm 5.5 in/min

300 sfpm 5.1 in/min

Cu-Zn Brass

16

8

2000 sfpm 43 in/min

2000 sfpm 43 in/min

1800 sfpm 39 in/min

1800 sfpm 35 in/min

Gray Cast Iron

12

8

82 sfpm 4 in/min

75 sfpm 4 in/min

72 sfpm 3.5 in/min

66 sfpm 3 in/min

Carbon Steel

20

8

160 sfpm 6.3 in/min

150 sfpm 5.9 in/min

150 sfpm 5.5 in/min

130 sfpm 5.1 in/min

Medium Hard Steel

18

8

100 sfpm 5.1 in/min

100 sfpm 4.7 in/min

80 sfpm 4.3 in/min

80 sfpm 4.3 in/min

Hard Steel

15

8

66 sfpm 4.3 in/min

66 sfpm 4.3 in/min

60 sfpm 4 in/min

57 sfpm 3.5 in/min

Stainless Steel

15

8

66 sfpm 2 in/min

63 sfpm 1.75 in/min

60 sfpm 1.75 in/min

57 sfpm 1.5 in/min

two, the ordinary parting tool should not be used, but a tool shaped like a knife; such a tool severs the rubber without removing any material. Gutta percha can be turned as easily as wood, but the tools must be sharp and a good soap-and-water lubricant used. Copper can be turned easily at 200 feet per minute. Limestone such as is used in the construction of pillars for balconies, etc., can be turned at 150 feet per minute, and the formation of ornamental contours is quite easy. Marble is a treacherous material to turn. It should be cut with a tool such as would be used for brass, but



MACHINING POWER

at a speed suitable for cast iron. It must be handled very carefully to prevent flaws in the surface. The foregoing speeds are for high-speed steel tools. Tools tipped with tungsten carbide are adapted for cutting various non-metallic products which cannot be machined readily with steel tools, such as slate, marble, synthetic plastic materials, etc. In drilling slate and marble, use flat drills; and for plastic materials, tungsten-carbide-tipped twist drills. Cutting speeds ranging from 75 to 150 feet per minute have been used for drilling slate (without coolant) and a feed of 0.025 inch per revolution for drills 3⁄4 and 1 inch in diameter. Estimating Machining Power.—Knowledge of the power required to perform machining operations is useful when planning new machining operations, for optimizing existing machining operations, and to develop specifications for new machine tools that are to be acquired. The available power on any machine tool places a limit on the size of the cut that it can take. When much metal must be removed from the workpiece it is advisable to estimate the cutting conditions that will utilize the maximum power on the machine. Many machining operations require only light cuts to be taken for which the machine obviously has ample power; in this event, estimating the power required is a wasteful effort. Conditions in different shops may vary and machine tools are not all designed alike, so some variations between the estimated results and those obtained on the job are to be expected. However, by using the methods provided in this section a reasonable estimate of the power required can be made, which will suffice in most practical situations. The measure of power in customary inch units is the horsepower; in SI metric units it is the kilowatt, which is used for both mechanical and electrical power. The power required to cut a material depends upon the rate at which the material is being cut and upon an experimentally determined power constant, Kp, which is also called the unit horsepower, unit power, or specific power consumption. The power constant is equal to the horsepower required to cut a material at a rate of one cubic inch per minute; in SI metric units the power constant is equal to the power in kilowatts required to cut a material at a rate of one cubic centimeter per second, or 1000 cubic millimeters per second (1 cm3 = 1000 mm3). Different values of the power constant are required for inch and for metric units, which are related as follows: to obtain the SI metric power constant, multiply the inch power constant by 2.73; to obtain the inch power constant, divide the SI metric power constant by 2.73. Values of the power constant in Tables 3a, and 3b can be used for all machining operations except drilling and grinding. Values given are for sharp tools. Table 3a. Power Constants, Kp, Using Sharp Cutting Tools Material

Kp Kp Brinell Inch Metric Hardness Units Units

Material

Brinell Hardness

Kp Kp Inch Metric Units Units

150–175

0.42

1.15

175–200 200–250 250–300

0.57 0.82 1.18

1.56 2.24 3.22

150–175 175–200 200–250 …

0.62 0.78 0.86 …

1.69 2.13 2.35 …

Ferrous Cast Metals

Gray Cast Iron

Alloy Cast Iron

100–120 120–140 140–160 { 160–180 180–200 200–220 220–240

0.28 0.35 0.38 0.52 0.60 0.71 0.91

0.76 0.96 1.04 1.42 1.64 1.94 2.48

Malleable Iron Ferritic

150–175 { 175–200 200–250

0.30 0.63 0.92

0.82 1.72 2.51

Cast Steel

Pearlitic

…

{

{



1085

Table 3a. (Continued) Power Constants, Kp, Using Sharp Cutting Tools Material

Kp Kp Brinell Inch Metric Hardness Units Units

Material

Brinell Hardness


High-Temperature Alloys, Tool Steel, Stainless Steel, and Nonferrous Metals High-Temperature Alloys A286 165 A286 285 Chromoloy 200 Chromoloy 310 Inco 700 330 Inco 702 230 Hastelloy-B 230 M-252 230 M-252 310 Ti-150A 340 U-500 375

0.82 0.93 0.78 1.18 1.12 1.10 1.10 1.10 1.20 0.65 1.10

2.24 2.54 3.22 3.00 3.06 3.00 3.00 3.00 3.28 1.77 3.00

…

1.00

2.73

0.75 0.88 0.98 1.20 1.30

2.05 2.40 2.68 3.28 3.55

Monel Metal

Tool Steel

175-200 200-250 { 250-300 300-350 350-400

150-175 175-200 200-250 … …

0.60 0.72 0.88 0.25 0.91

1.64 1.97 2.40 0.68 2.48

… … … …

0.83 0.50 0.25 0.30

2.27 1.36 0.68 0.82

Bronze Hard Medium

… …

0.91 0.50

2.48 1.36

Aluminum Cast Rolled (hard)

… …

0.25 0.33

0.68 0.90

Magnesium Alloys

…

0.10

0.27

Stainless Steel Zinc Die Cast Alloys Copper (pure) Brass Hard Medium Soft Leaded

{

The value of the power constant is essentially unaffected by the cutting speed, the depth of cut, and the cutting tool material. Factors that do affect the value of the power constant, and thereby the power required to cut a material, include the hardness and microstructure of the work material, the feed rate, the rake angle of the cutting tool, and whether the cutting edge of the tool is sharp or dull. Values are given in the power constant tables for different material hardness levels, whenever this information is available. Feed factors for the power constant are given in Table 4. All metal cutting tools wear but a worn cutting edge requires more power to cut than a sharp cutting edge. Factors to provide for tool wear are given in Table 5. In this table, the extra-heavy-duty category for milling and turning occurs only on operations where the tool is allowed to wear more than a normal amount before it is replaced, such as roll turning. The effect of the rake angle usually can be disregarded. The rake angle for which most of the data in the power constant tables are given is positive 14 degrees. Only when the deviation from this angle is large is it necessary to make an adjustment. Using a rake angle that is more positive reduces the power required approximately 1 per cent per degree; using a rake angle that is more negative increases the power required; again approximately 1 per cent per degree. Many indexable insert cutting tools are formed with an integral chip breaker or other cutting edge modifications, which have the effect of reducing the power required to cut a material. The extent of this effect cannot be predicted without a test of each design. Cutting fluids will also usually reduce the power required, when operating in the lower range of cutting speeds. Again, the extent of this effect cannot be predicted because each cutting fluid exhibits its own characteristics.



MACHINING POWER Table 3b. Power Constants, Kp, Using Sharp Cutting Tools

Material

Brinell Hardness


Material

Brinell Hardness

Kp Inch Units

Kp SI Metric Units

220–240 240–260 260–280 280–300 300–320 320–340 340–360

0.89 0.92 0.95 1.00 1.03 1.06 1.14

2.43 2.51 2.59 2.73 2.81 2.89 3.11

180–200 200–220 220–240 240–260 …

0.51 0.55 0.57 0.62 …

1.39 1.50 1.56 1.69 …

140–160 160–180 180–200 200–220 220–240 240–260 260–280 280–300 300–320 320–340 … … … …

0.56 0.59 0.62 0.65 0.70 0.74 0.77 0.80 0.83 0.89 … … … …

1.53 1.61 1.69 1.77 1.91 2.02 2.10 2.18 2.27 2.43 … … … …

Wrought Steels Plain Carbon Steels 80–100 100–120 120–140 140–160 160–180 180–200 200–220

All Plain Carbon Steels

0.63 0.66 0.69 0.74 0.78 0.82 0.85

1.72 1.80 1.88 2.02 2.13 2.24 2.32

All Plain Carbon Steels

Free Machining Steels AISI 1108, 1109, 1110, 1115, 1116, 1117, 1118, 1119, 1120, 1125, 1126, 1132

100–120 120–140 140–160 160–180 180–200

0.41 0.42 0.44 0.48 0.50

1.12 1.15 1.20 1.31 1.36

140–160 160–180 180–200 200–220 220–240 240–260 260–280 280–300 300–320 320–340 340–360 160–180 180–200 200–220

0.62 0.65 0.69 0.72 0.76 0.80 0.84 0.87 0.91 0.96 1.00 0.79 0.83 0.87

1.69 1.77 1.88 1.97 2.07 2.18 2.29 2.38 2.48 2.62 2.73 2.16 2.27 2.38

AISI 1137, 1138, 1139, 1140, 1141, 1144, 1145, 1146, 1148, 1151

Alloy Steels AISI 4023, 4024, 4027, 4028, 4032, 4037, 4042, 4047, 4137, 4140, 4142, 4145, 4147, 4150, 4340, 4640, 4815, 4817, 4820, 5130, 5132, 5135, 5140, 5145, 5150, 6118, 6150, 8637, 8640, 8642, 8645, 8650, 8740

AISI 1330, 1335, 1340, E52100

AISI 4130, 4320, 4615, 4620, 4626, 5120, 8615, 8617, 8620, 8622, 8625, 8630, 8720

The machine tool transmits the power from the driving motor to the workpiece, where it is used to cut the material. The effectiveness of this transmission is measured by the machine tool efficiency factor, E. Average values of this factor are given in Table 6. Formulas for calculating the metal removal rate, Q, for different machining operations are given in Table 7. These formulas are used together with others given below. The following formulas can be used with either customary inch or with SI metric units. Pc = K p CQW P K p CQW Pm = -----c = -------------------E E where Pc =power at the cutting tool; hp, or kW


(1) (2)


1087

Table 4. Feed Factors, C, for Power Constants Inch Units Feed in.a 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010 0.011 0.012 0.013

SI Metric Units

C

Feed in.a

1.60 1.40 1.30 1.25 1.19 1.15 1.11 1.08 1.06 1.04 1.02 1.00 0.98

0.014 0.015 0.016 0.018 0.020 0.022 0.025 0.028 0.030 0.032 0.035 0.040 0.060

a Turning, in/rev;

C

Feed mmb

C

Feed mmb

C

0.97 0.96 0.94 0.92 0.90 0.88 0.86 0.84 0.83 0.82 0.80 0.78 0.72

0.02 0.05 0.07 0.10 0.12 0.15 0.18 0.20 0.22 0.25 0.28 0.30 0.33

1.70 1.40 1.30 1.25 1.20 1.15 1.11 1.08 1.06 1.04 1.01 1.00 0.98

0.35 0.38 0.40 0.45 0.50 0.55 0.60 0.70 0.75 0.80 0.90 1.00 1.50

0.97 0.95 0.94 0.92 0.90 0.88 0.87 0.84 0.83 0.82 0.80 0.78 0.72

milling, in/tooth; planing and shaping, in/stroke; broaching, in/tooth. milling, mm/tooth; planing and shaping, mm/stroke; broaching, mm/tooth.

b Turning, mm/rev;

Table 5. Tool Wear Factors, W Type of Operation For all operations with sharp cutting tools Turning: Finish turning (light cuts) Normal rough and semifinish turning Extra-heavy-duty rough turning Milling: Slab milling End milling Light and medium face milling Extra-heavy-duty face milling Drilling: Normal drilling Drilling hard-to-machine materials and drilling with a very dull drill Broaching: Normal broaching Heavy-duty surface broaching Planing and Use values given for turning Shaping

Pm =power at the motor; hp, or kW Kp =power constant (see Tables 3a and 3b) Q =metal removal rate; in 3/min or cm3/s (see Table 7) C =feed factor for power constant (see Table 4) W =tool wear factor (see Table 5) E =machine tool efficiency factor (see Table 6) V =cutting speed, fpm, or m/min N =cutting speed, rpm f =feed rate for turning; in/rev or mm/rev


W 1.00 1.10 1.30 1.60–2.00 1.10 1.10 1.10–1.25 1.30–1.60 1.30 1.50 1.05–1.10 1.20–1.30


MACHINING POWER f =feed rate for planing and shaping; in/stroke, or mm/stroke ft =feed per tooth; in/tooth, or mm/tooth fm =feed rate; in/min or mm/min dt =maximum depth of cut per tooth: inch, or mm d =depth of cut; inch, or mm nt =number of teeth on milling cutter nc =number of teeth engaged in work w =width of cut; inch, or mm Table 6. Machine Tool Efficiency Factors, E Type of Drive

E

Type of Drive

E

Direct Belt Drive

0.90

Geared Head Drive

0.70–0.80

Back Gear Drive

0.75

Oil-Hydraulic Drive

0.60–0.90

Table 7. Formulas for Calculating the Metal Removal Rate, Q

Operation

Metal Removal Rate For Inch Units Only For SI Metric Units Only Q = in3/min Q = cm3/s

Single-Point Tools (Turning, Planing, and Shaping)

12Vfd

V- fd ----60

Milling

fmwd

f m wd ----------------60, 000

Surface Broaching

12Vwncdt

V- un d ----60 c t

Example:A 180–200 Bhn AISI 4130 shaft is to be turned on a geared head lathe using a cutting speed of 350 fpm (107 m/min), a feed rate of 0.016 in/rev (0.40 mm/rev), and a depth of cut of 0.100 inch (2.54 mm). Estimate the power at the cutting tool and at the motor, using both the inch and metric data. Inch units: Kp =0.62 (from Table 3b) C =0.94 (from Table 4) W =1.30 (from Table 5) E =0.80 (from Table 6) Q =12 Vfd = 12 × 350 × 0.016 × 0.100 (from Table 7) Q =6.72 in3/min Pc = K p CQW = 0.62 × 0.94 × 6.72 × 1.30 = 5.1 hp P 5 - = 6.4 hp Pm = -----c = --------E 0.80 SI metric units: Kp =1.69 (from Table 3b) C =0.94 (from Table 4) W =1.30 (from Table 5) E =0.80 (from Table 6)



1089

3 V- fd = 107 Q = ------------- × 0.40 × 2.54 = 1.81 cm /s (from Table 7) 60 60

Pc = K p CQW = 1.69 × 0.94 × 1.81 × 1.30 = 3.74 kW P Pm = -----c = 3.74 ---------- = 4.677 kW E 0.80 Whenever possible the maximum power available on a machine tool should be used when heavy cuts must be taken. The cutting conditions for utilizing the maximum power should be selected in the following order: 1) select the maximum depth of cut that can be used; 2) select the maximum feed rate that can be used; and 3) estimate the cutting speed that will utilize the maximum power available on the machine. This sequence is based on obtaining the longest tool life of the cutting tool and at the same time obtaining as much production as possible from the machine. The life of a cutting tool is most affected by the cutting speed, then by the feed rate, and least of all by the depth of cut. The maximum metal removal rate that a given machine is capable of machining from a given material is used as the basis for estimating the cutting speed that will utilize all the power available on the machine. Example:A 0.125 inch deep cut is to be taken on a 200–210 Bhn AISI 1050 steel part using a 10 hp geared head lathe. The feed rate selected for this job is 018 in./rev. Estimate the cutting speed that will utilize the maximum power available on the lathe. Kp =0.85 (From Table 3b) C =0.92 (From Table 4) W =1.30 (From Table 5) E =0.80 (From Table 6) Pm E 10 × 0.80 Q max = --------------- = ------------------------------------------0.85 × 0.92 × 1.30 K p CW

K p CQW⎞ ⎛ P = -------------------⎝ m E ⎠

3

= 7.87 in /min Q max 7.87 V = ------------ = -------------------------------------------12fd 12 × 0.018 × 0.125 = 291 fpm

( Q = 12Vfd )

Example:A 160-180 Bhn gray iron casting that is 6 inches wide is to have 1⁄8 inch stock removed on a 10 hp milling machine, using an 8 inch diameter, 10 tooth, indexable insert cemented carbide face milling cutter. The feed rate selected for this cutter is 0.012 in/tooth, and all the stock (0.125 inch) will be removed in one cut. Estimate the cutting speed that will utilize the maximum power available on the machine. Kp =0.52 (From Table 3a) C =1.00 (From Table 4) W =1.20 (From Table 5) E =0.80 (From Table 6)



MACHINING POWER

Pm E 3 10 × 0.80 Q max = --------------- = -------------------------------------------- = 12.82 in /min 0.52 × 1.00 × 1.20 K p CW Q max 12.82 = 17.1 in/min f m = ------------ = ---------------------wd 6 × 0.125 f max 17 - = ------------------------N = --------= 142.4 rpm ft nt 0.012 × 10 × 8 × 142 = 298.3 fpm V = πDN ------------ = π --------------------------12 12

p CQW⎞ ⎛P = K -------------------⎝ m E ⎠

( Q = f m wd ) ( fm = ft nt N ) ⎛ N = 12V ----------⎞ ⎝ πD ⎠

Estimating Drilling Thrust, Torque, and Power.—Although the lips of a drill cut metal and produce a chip in the same manner as the cutting edges of other metal cutting tools, the chisel edge removes the metal by means of a very complex combination of extrusion and cutting. For this reason a separate method must be used to estimate the power required for drilling. Also, it is often desirable to know the magnitude of the thrust and the torque required to drill a hole. The formulas and tabular data provided in this section are based on information supplied by the National Twist Drill Division of Regal-Beloit Corp. The values in Tables 8 through 11 are for sharp drills, and tool wear factors are given in Table 5. For most ordinary drilling operations 1.30 can be used as the tool wear factor. When drilling most difficult-to-machine materials and when the drill is allowed to become very dull, 1.50 should be used as the value of this factor. It is usually more convenient to measure the web thickness at the drill point than the length of the chisel edge; for this reason, the approximate w/d ratio corresponding to each c/d ratio for a correctly ground drill is provided in Table 9. For most standard twist drills the c/d ratio is 0.18, unless the drill has been ground short or the web has been thinned. The c/d ratio of split point drills is 0.03. The formulas given below can be used for spade drills, as well as for twist drills. Separate formulas are required for use with customary inch units and for SI metric units. Table 8. Work Material Factor, Kd, for Drilling with a Sharp Drill Work Material AISI 1117 (Resulfurized free machining mild steel) Steel, 200 Bhn Steel, 300 Bhn Steel, 400 Bhn Cast Iron, 150 Bhn Most Aluminum Alloys Most Magnesium Alloys Most Brasses Leaded Brass Austenitic Stainless Steel (Type 316) Titanium Alloy Ti6Al4V René 41

40Rc 40Rc

Hastelloy-C

Material Constant, Kd 12,000 24,000 31,000 34,000 14,000 7,000 4,000 14,000 7,000 24,000a for Torque 35,000a for Thrust 18,000a for Torque 29,000a for Thrust 40,000ab min. 30,000a for Torque 37,000a for Thrust

a Values based upon a limited number of tests. b Will increase with rapid wear.



1091

Table 9. Chisel Edge Factors for Torque and Thrust c/d

Approx. w/d

Torque Factor A

Thrust Factor B

Thrust Factor J

c/d

Approx. w/d

Torque Factor A

Thrust Factor B

Thrust Factor J

0.03 0.05 0.08 0.10 0.13 0.15

0.025 0.045 0.070 0.085 0.110 0.130

1.000 1.005 1.015 1.020 1.040 1.080

1.100 1.140 1.200 1.235 1.270 1.310

0.001 0.003 0.006 0.010 0.017 0.022

0.18 0.20 0.25 0.30 0.35 0.40

0.155 0.175 0.220 0.260 0.300 0.350

1.085 1.105 1.155 1.235 1.310 1.395

1.355 1.380 1.445 1.500 1.575 1.620

0.030 0.040 0.065 0.090 0.120 0.160

For drills of standard design, use c/d = 0.18; for split point drills, use c/d = 0.03 c/d = Length of Chisel Edge ÷ Drill Diameter. w/d = Web Thickness at Drill Point ÷ Drill Diameter.

For inch units only: T =2Kd Ff FT BW + KdD 2JW M =KdFf FM AW Pc =MN⁄ 63.025 For SI metric units only: T =0.05 Kd Ff FT BW + 0.007 Kd D2JW K d F f F M AW M = ----------------------------- = 0.000025 Kd Ff FM AW 40 ,000 Pc =MN⁄ 9550 Use with either inch or metric units: P P m = -----c E where Pc =Power at the cutter; hp, or kW Pm =Power at the motor; hp, or kW M =Torque; in. lb, or N.m T =Thrust; lb, or N Kd =Work material factor (See Table 8) Ff =Feed factor (See Table 10) FT =Thrust factor for drill diameter (See Table 11) FM =Torque factor for drill diameter (See Table 11) A =Chisel edge factor for torque (See Table 9) B =Chisel edge factor for thrust (See Table 9) J =Chisel edge factor for thrust (See Table 9) W =Tool wear factor (See Table 5) N =Spindle speed; rpm E =Machine tool efficiency factor (See Table 6) D =Drill diameter; in., or mm c =Chisel edge length; in., or mm (See Table 9) w =Web thickness at drill point; in., or mm (See Table 9)

(1) (2) (3) (4) (5) (6) (7)

Example:A standard 7⁄8 inch drill is to drill steel parts having a hardness of 200 Bhn on a drilling machine having an efficiency of 0.80. The spindle speed to be used is 350 rpm and the feed rate will be 0.008 in./rev. Calculate the thrust, torque, and power required to drill these holes: Kd =24,000 (From Table 8) Ff =0.021 (From Table 10) FT =0.899 (From Table 11) FM =0.786 (From Table 11) A =1.085 (From Table 9) B =1.355 (From Table 9) J =0.030 (From Table 9)



MACHINING POWER Table 10. Feed Factors Ff for Drilling Inch Units

SI Metric Units

Feed, in./rev

Ff

Feed, in./rev

Ff

Feed, mm/rev

Ff

Feed, mm/rev

0.0005 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

0.0023 0.004 0.007 0.010 0.012 0.014 0.017 0.019 0.021 0.023 0.025

0.012 0.013 0.015 0.018 0.020 0.022 0.025 0.030 0.035 0.040 0.050

0.029 0.031 0.035 0.040 0.044 0.047 0.052 0.060 0.068 0.076 0.091

0.01 0.03 0.05 0.08 0.10 0.12 0.15 0.18 0.20 0.22 0.25

0.025 0.060 0.091 0.133 0.158 0.183 0.219 0.254 0.276 0.298 0.330

0.30 0.35 0.40 0.45 0.50 0.55 0.65 0.75 0.90 1.00 1.25

Ff 0.382 0.432 0.480 0.528 0.574 0.620 0.708 0.794 0.919 1.000 1.195

Table 11. Drill Diameter Factors: FT for Thrust, FM for Torque Inch Units

SI Metric Units

Drill Dia., in.

FT

FM

Drill Dia., in.

FT

FM

Drill Dia., mm

FT

FM

Drill Dia., mm

FT

FM

0.063 0.094 0.125 0.156 0.188 0.219 0.250 0.281 0.313 0.344 0.375 0.438 0.500 0.563 0.625 0.688 0.750 0.813

0.110 0.151 0.189 0.226 0.263 0.297 0.330 0.362 0.395 0.426 0.456 0.517 0.574 0.632 0.687 0.741 0.794 0.847

0.007 0.014 0.024 0.035 0.049 0.065 0.082 0.102 0.124 0.146 0.171 0.226 0.287 0.355 0.429 0.510 0.596 0.689

0.875 0.938 1.000 1.063 1.125 1.250 1.375 1.500 1.625 1.750 1.875 2.000 2.250 2.500 2.750 3.000 3.500 4.000

0.899 0.950 1.000 1.050 1.099 1.195 1.290 1.383 1.475 1.565 1.653 1.741 1.913 2.081 2.246 2.408 2.724 3.031

0.786 0.891 1.000 1.116 1.236 1.494 1.774 2.075 2.396 2.738 3.100 3.482 4.305 5.203 6.177 7.225 9.535 12.13

1.60 2.40 3.20 4.00 4.80 5.60 6.40 7.20 8.00 8.80 9.50 11.00 12.50 14.50 16.00 17.50 19.00 20.00

1.46 2.02 2.54 3.03 3.51 3.97 4.42 4.85 5.28 5.96 6.06 6.81 7.54 8.49 9.19 9.87 10.54 10.98

2.33 4.84 8.12 12.12 16.84 22.22 28.26 34.93 42.22 50.13 57.53 74.90 94.28 123.1 147.0 172.8 200.3 219.7

22.00 24.00 25.50 27.00 28.50 32.00 35.00 38.00 42.00 45.00 48.00 50.00 58.00 64.00 70.00 76.00 90.00 100.00

11.86 12.71 13.34 13.97 14.58 16.00 17.19 18.36 19.89 21.02 22.13 22.86 25.75 27.86 29.93 31.96 36.53 39.81

260.8 305.1 340.2 377.1 415.6 512.0 601.6 697.6 835.3 945.8 1062 1143 1493 1783 2095 2429 3293 3981

W =1.30 (From Table 5) T =2KdFf FT BW + Kd d2JW = 2 × 24,000 × 0.21 × 0.899 × 1.355 × 1.30 + 24,000 × 0.8752 × 0.030 × 1.30 = 2313 lb M =Kd Ff FMAW = 24,000 × 0.021 × 0.786 × 1.085 × 1.30 = 559 in. lb MN 559 × 350 P c = ---------------- = ------------------------ = 3.1 hp 63 ,025 63 ,025

P 3.1 P m = -----c = ---------- = 3.9 hp E 0.80

Twist drills are generally the most highly stressed of all metal cutting tools. They must not only resist the cutting forces on the lips, but also the drill torque resulting from these forces and the very large thrust force required to push the drill through the hole. Therefore, often when drilling smaller holes, the twist drill places a limit on the power used and for very large holes, the machine may limit the power.


Machinery's Handbook 27th Edition MACHINING ECONOMETRICS

1093

MACHINING ECONOMETRICS Tool Wear And Tool Life Relationships Tool wear.—Tool-life is defined as the cutting time to reach a predetermined wear, called the tool wear criterion. The size of tool wear criterion depends on the grade used, usually a tougher grade can be used at bigger flank wear. For finishing operations, where close tolerances are required, the wear criterion is relatively small. Other alternative wear criteria are a predetermined value of the surface roughness, or a given depth of the crater which develops on the rake face of the tool. The most appropriate wear criteria depends on cutting geometry, grade, and materials. Tool-life is determined by assessing the time — the tool-life — at which a given predetermined flank wear is reached, 0.25, 0.4, 0.6, 0.8 mm etc. Fig. 1 depicts how flank wear varies with cutting time (approximately straight lines in a semi-logarithmic graph) for three combinations of cutting speeds and feeds. Alternatively, these curves may represent how variations of machinability impact on tool-life, when cutting speed and feed are constant. All tool wear curves will sooner or later bend upwards abruptly and the cutting edge will break, i.e., catastrophic failure as indicated by the white arrows in Fig. 1. LIVE GRAPH Click here to view

1

Wear, mm

Average

0.1

Low Average High

0.01 0

10

20

30

40

50

60

70

80

90

100 110 120 130 140 150

Cutting Time, minutes

Fig. 1. Flank Wear as a Function of Cutting Time

The maximum deviation from the average tool-life 60 minutes in Fig. 1 is assumed to range between 40 and 95 minutes, i.e. −33% and +58% variation. The positive deviation from the average (longer than expected tool-life) is not important, but the negative one (shorter life) is, as the edge may break before the scheduled tool change after 60 minutes, when the flank wear is 0.6 mm. It is therefore important to set the wear criterion at a safe level such that tool failures due to “normal” wear become negligible. This is the way machinability variations are mastered. Equivalent Chip Thickness (ECT).—ECT combines the four basic turning variables, depth of cut, lead angle, nose radius and feed per revolution into one basic parameter. For all other metal cutting operations such as drilling, milling and grinding, additional variables such as number of teeth, width of cut, and cutter diameter are included in the parameter ECT. In turning, milling, and drilling, according to the ECT principle, when the product of feed times depth of cut is constant the tool-life is constant no matter how the depth of cut or feed is selected, provided that the cutting speed and cutting edge length are maintained constant. By replacing the geometric parameters with ECT, the number of toollife tests to evaluate cutting parameters can be reduced considerably, by a factor of 4 in turning, and in milling by a factor of 7 because radial depth of cut, cutter diameter and number of teeth are additional parameters.



MACHINING ECONOMETRICS

The introduction of the ECT concept constitutes a major simplification when predicting tool-life and calculating cutting forces, torque, and power. ECT was first presented in 1931 by Professor R. Woxen, who both theoretically and experimentally proved that ECT is a basic metal cutting parameter for high-speed cutting tools. Dr. Colding later proved that the concept also holds for carbide tools, and extended the calculation of ECT to be valid for cutting conditions when the depth of cut is smaller than the tool nose radius, or for round inserts. Colding later extended the concept to all other metal cutting operations, including the grinding process. The definition of ECT is: ECT = Area ------------- (mm or inch) CEL A = cross sectional area of cut (approximately = feed × depth of cut), (mm2 or inch2) CEL = cutting edge length (tool contact rubbing length), (mm or inch), see Fig.9. An exact value of A is obtained by the product of ECT and CEL. In turning, milling, and drilling, ECT varies between 0.05 and 1 mm, and is always less than the feed/rev or feed/tooth; its value is usually about 0.7 to 0.9 times the feed.

where

Example 1:For a feed of 0.8 mm/rev, depth of cut a = 3 mm, and a cutting edge length CEL = 4 mm2, the value of ECT is approximately ECT = 0.8 × 3 ÷ 4 = 0.6 mm. The product of ECT, CEL, and cutting speed V (m/min or ft/min) is equal to the metal removal rate, MRR, which is measured in terms of the volume of chips removed per minute: MRR = 1000V × Area = 1000V × ECT × CEL mm 3 /min = V × Area cm 3 /min or inch 3 /min The specific metal removal rate SMRR is the metal removal rate per mm cutting edge length CEL, thus: SMMR = 1000V × ECT mm 3 /min/mm = V × ECT cm 3 /min/mm or inch 3 /min/inch Example 2:Using above data and a cutting speed of V = 250 m/min specific metal removal rate becomes SMRR = 0.6 × 250 = 150 (cm3/min/mm). ECT in Grinding: In grinding ECT is defined as in the other metal cutting processes, and is approximately equal to ECT = Vw × ar ÷ V, where Vw is the work speed, ar is the depth of cut, and A = Vw × ar. Wheel life is constant no matter how depth ar, or work speed Vw, is selected at V = constant (usually the influence of grinding contact width can be neglected). This translates into the same wheel life as long as the specific metal removal rate is constant, thus: SMMR = 1000Vw × ar mm 3 /min/mm In grinding, ECT is much smaller than in the other cutting processes, ranging from about 0.0001 to 0.001 mm (0.000004 to 0.00004 inch). The grinding process is described in a separate chapter GRINDING FEEDS AND SPEEDS starting on page 1158. Tool-life Relationships.—Plotting the cutting times to reach predetermined values of wear typically results in curves similar to those shown in Fig. 2 (cutting time versus cutting speed at constant feed per tooth) and Fig. 3 (cutting time versus feed per tooth at constant cutting speed). These tests were run in 1993 with mixed ceramics turn-milling hard steel, 82 RC, at the Technische Hochschule Darmstadt.


Machinery's Handbook 27th Edition MACHINING ECONOMETRICS LIVE GRAPH

1095

LIVE GRAPH

Click here to view

Click here to view

40

40

VB = 0.15 mm VB = 0.2 mm VB = 0.1 mm VB = 0.05 mm 30

LF (tool life travel ), mm

LF (tool life travel ), mm

30

20

20

10

10 VB 0.05 mm VB 0.1 mm VB 0.15 mm

0

0 0

0.05

0.1

0.15

0.2

Fz (feed per tooth), mm

Fig. 2. Influence of feed per tooth on cutting time

200

250

300

350

400

450

500

VC (cutting speed), m/min

Fig. 3. Influence of cutting speed on tool-life

Tool-life has a maximum value at a particular setting of feed and speed. Economic and productive cutting speeds always occur on the right side of the curves in Figs. 2 and 4, which are called Taylor curves, represented by the so called Taylor’s equation. The variation of tool-life with feed and speed constitute complicated relationships, illustrated in Figs. 6a, 6b, and 6c. Taylor’s Equation.—Taylor’s equation is the most commonly used relationship between tool-life T, and cutting speed V. It constitutes a straight line in a log-log plot, one line for each feed, nose radius, lead angle, or depth of cut, mathematically represented by: V × Tn = C (1a) where n = is the slope of the line C =is a constant equal to the cutting speed for T = 1 minute By transforming the equation to logarithmic axes, the Taylor lines become straight lines with slope = n. The constant C is the cutting speed on the horizontal (V) axis at tool-life T = 1 minute, expressed as follows lnV + n × lnT = lnC (1b) For different values of feed or ECT, log-log plots of Equation (1a) form approximately straight lines in which the slope decreases slightly with a larger value of feed or ECT. In practice, the Taylor lines are usually drawn parallel to each other, i.e., the slope n is assumed to be constant. Fig. 4 illustrates the Taylor equation, tool-life T versus cutting speed V, plotted in log-log coordinates, for four values of ECT = 0.1, 0.25, 0.5 and 0.7 mm. In Fig. 4, starting from the right, each T–V line forms a generally straight line that bends off and reaches its maximum tool-life, then drops off with decreasing speed (see also Figs. 2 and 3. When operating at short tool-lives, approximately when T is less than 5 minutes, each line bends a little so that the cutting speed for 1 minute life becomes less than the value calculated by constant C. The Taylor equation is a very good approximation of the right hand side of the real toollife curve (slightly bent). The portion of the curve to the left of the maximum tool-life gives shorter and shorter tool-lives when decreasing the cutting speed starting from the point of maximum tool-life. Operating at the maximum point of maximum tool-life, or to the left of it, causes poor surface finish, high cutting forces, and sometimes vibrations.



MACHINING ECONOMETRICS LIVE GRAPH Click here to view

100

Tmax

ECT = 0.1 ECT = 0.25 ECT = 0.5 ECT = 0.7

T minutes

T2,V2 b 10

n = a/b a

T1,V1

1 10

100

C

1000

V m/min

Fig. 4. Definition of slope n and constant C in Taylor’s equation

Evaluation of Slope n, and Constant C.—When evaluating the value of the Taylor slope based on wear tests, care must be taken in selecting the tool-life range over which the slope is measured, as the lines are slightly curved. The slope n can be found in three ways: • Calculate n from the formula n = (ln C - ln V)/ln T, reading the values of C and V for any value of T in the graph. • Alternatively, using two points on the line, (V1, T1) and (V2, T2), calculate n using the relationship V1 × T1n = V2 × T2n. Then, solving for n, ln ( V 1 ⁄ V 2 ) n = ------------------------ln ( T 2 ⁄ T 1 )

•

Graphically, n may be determined from the graph by measuring the distances “a” and “b” using a mm scale, and n is the ratio of a and b, thus, n = a/b

Example:Using Fig. 4, and a given value of ECT= 0.7 mm, calculate the slope and constant of the Taylor line. On the Taylor line for ECT= 0.7, locate points corresponding to tool-lives T1 = 15 minutes and T2 = 60 minutes. Read off the associated cutting speeds as, approximately, V1 = 110 m/min and V2 = 65 m/min. The slope n is then found to be n = ln (110/65)/ln (60/15) = 0.38 The constant C can be then determined using the Taylor equation and either point (T1, V1) or point (T2, V2), with equivalent results, as follows: C = V × Tn = 110 × 150.38 = 65 × 600.38 = 308 m/min (1027 fpm) The Generalized Taylor Equation.—The above calculated slope and constant C define tool-life at one particular value of feed f, depth of cut a, lead angle LA, nose radius r, and other relevant factors. The generalized Taylor equation includes these parameters and is written T n = A × f m × a p × LA q × r s

(2)

where A = area; and, n, m, p, q, and s = constants. There are two problems with the generalized equation: 1) a great number of tests have to be run in order to establish the constants n, m, p, q, s, etc.; and 2) the accuracy is not very good because Equation (2) yields straight lines when plotted versus f, a, LA, and r, when in reality, they are parabolic curves..



1097

The Generalized Taylor Equation using Equivalent Chip Thickness (ECT): Due to the compression of the aforementioned geometrical variables (f, a, LA, r, etc.) into ECT, Equation (2) can now be rewritten: V × T n = A × ECT m (3) Experimental data confirms that the Equation (3) holds, approximately, within the range of the test data, but as soon as the equation is extended beyond the test results, the error can become very great because the V–ECT curves are represented as straight lines by Equation (3)and the real curves have a parabolic shape. The Colding Tool-life Relationship.—This relationship contains 5 constants H, K, L, M, and N0, which attain different values depending on tool grade, work material, and the type of operation, such as longitudinal turning versus grooving, face milling versus end milling, etc. This tool-life relationship is proven to describe, with reasonable accuracy, how tool-life varies with ECT and cutting speed for any metal cutting and grinding operation. It is expressed mathematically as follows either as a generalized Taylor equation (4a), or, in logarithmic coordinates (4b): V×T

( N 0 – L × lnECT )

× ECT

H- + lnECT ⎛ – -----------------------⎞ ⎝ 2M 4M ⎠

= e

H-⎞ ⎛ K – ------⎝ 4M⎠

(4a)

– H- – z ( N – L ) y = K – x-----------(4b) 0 x 4M where x =ln ECT y =ln V z =ln T M = the vertical distance between the maximum point of cutting speed (ECTH, VH) for T = 1 minute and the speed VG at point (ECTG, VG), as shown in Fig. 5. 2M = the horizontal distance between point (ECTH, VG) and point (VG, ECTG) H and K = the logarithms of the coordinates of the maximum speed point (ECTH, VH) at tool-life T = 1 minute, thus H = ln(ECTH) and K = ln (VH) N0 and L = the variation of the Taylor slope n with ECT: n = N0 − L × ln (ECT) LIVE GRAPH Click here to view

1000 H-CURVE

VH

G-CURVE

K = ln(VH) M 2M

V, m/min

VG

100

Constants N0 and L define the change in the Taylor slope, n, with ECT

10 0.01

T=1 T = 100 T = 300

H = ln(ECTH)

ECTH 0.1

ECTG

1

ECT, mm

Fig. 5. Definitions of the constants H, K, L, M, and N0 for tool-life equation in the V-ECT plane with tool-life constant

The constants L and N0 are determined from the slopes n1 and n2 of two Taylor lines at ECT1 and ECT2, and the constant M from 3 V–ECT values at any constant tool-life. Constants H and K are then solved using the tool-life equation with the above-calculated values of L, N0 and M.




The G- and H-curves.—The G-curve defines the longest possible tool-life for any given metal removal rate, MRR, or specific metal removal rate, SMRR. It also defines the point where the total machining cost is minimum, after the economic tool-life TE, or optimal tool-life TO, has been calculated, see Optimization Models, Economic Tool-life when Feed is Constant starting on page 1110. The tool-life relationship is depicted in the 3 planes: T–V, where ECT is the plotted parameter (the Taylor plane); T–ECT, where V is plotted; and, V–ECT, where T is a parameter. The latter plane is the most useful because the optimal cutting conditions are more readily understood when viewing in the V–ECT plane. Figs. 6a, 6b, and 6c show how the tool-life curves look in these 3 planes in log-log coordinates. LIVE GRAPH Click here to view

T minutes

100

10

ECT = 0.1 ECT = 0.25 ECT = 0.5 ECT = 0.7

1 10

100

1000

V m/min

Fig. 6a. Tool-life vs. cutting sped T–V, ECT plotted

Fig. 6a shows the Taylor lines, and Fig. 6b illustrates how tool-life varies with ECT at different values of cutting speed, and shows the H-curve. Fig. 6c illustrates how cutting speed varies with ECT at different values of tool-life. The H- and G-curves are also drawn in Fig. 6c. LIVE GRAPH Click here to view

10000 V = 100 V = 150 V = 225 V = 250 V = 300

T minutes

1000

100

10

1 0.01

H-CURVE

0.1

1

ECT, mm

Fig. 6b. Tool-life vs. ECT, T–ECT, cutting speed plotted

A simple and practical method to ascertain that machining is not done to the left of the Hcurve is to examine the chips. When ECT is too small, about 0.03-0.05 mm, the chips tend to become irregular and show up more or less as dust.



1099


1000

H-CURVE

V, m/min

G-CURVE

100

T=1 T=5 T = 15 T = 30 T = 60 T = 100 T = 300 10 0.01

0.1

1

ECT, mm

Fig. 6c. Cutting speed vs. ECT, V–ECT, tool-life plotted

The V–ECT–T Graph and the Tool-life Envelope.— The tool-life envelope, in Fig. 7, is an area laid over the V–ECT–T graph, bounded by the points A, B, C, D, and E, within which successful cutting can be realized. The H- and G-curves represent two borders, lines AE and BC. The border curve, line AB, shows a lower limit of tool-life, TMIN = 5 minutes, and border curve, line DE, represents a maximum tool-life, TMAX = 300 minutes. TMIN is usually 5 minutes due to the fact that tool-life versus cutting speed does not follow a straight line for short tool-lives; it decreases sharply towards one minute tool-life. TMAX varies with tool grade, material, speed and ECT from 300 minutes for some carbide tools to 10000 minutes for diamond tools or diamond grinding wheels, although systematic studies of maximum tool-lives have not been conducted. Sometimes the metal cutting system cannot utilize the maximum values of the V–ECT–T envelope, that is, cutting at optimum V–ECT values along the G-curve, due to machine power or fixture constraints, or vibrations. Maximum ECT values, ECTMAX, are related to the strength of the tool material and the tool geometry, and depend on the tool grade and material selection, and require a relatively large nose radius. LIVE GRAPH Click here to view

V, m/min

1000

T=1 T=5 T = 15 T = 30 T = 60 T = 100 T = 300

H-curve

Big Radius To Avoid Breakage

A

A'

G-curve OF

Tool Breaks

B E' 100 0.01

E OR

Tmax

0.1

D

C

1

ECT, mm Fig. 7. Cutting speed vs. ECT, V–ECT, tool-life plotted

Minimum ECT values, ECTMIN, are defined by the conditions at which surface finish suddenly deteriorates and the cutting edge begins rubbing rather than cutting. These conditions begin left of the H-curve, and are often accompanied by vibrations and built-up edges on the tool. If feed or ECT is reduced still further, excessive tool wear with sparks and tool breakage, or melting of the edge occurs. For this reason, values of ECT lower than approx-




imately 0.03 mm should not be allowed. In Fig. 7, the ECTMIN boundary is indicated by contour line A′E′. In milling the minimum feed/tooth depends on the ratio ar/D, of radial depth of cut ar, and cutter diameter D. For small ar/D ratios, the chip thickness becomes so small that it is necessary to compensate by increasing the feed/tooth. See High-speed Machining Econometrics starting on page 1122 for more on this topic. Fig. 7 demonstrates, in principle, minimum cost conditions for roughing at point OR, and for finishing at point OF, where surface finish or tolerances have set a limit. Maintaining the speed at OR, 125 m/min, and decreasing feed reaches a maximum tool-life = 300 minutes at ECT = 0.2, and a further decrease of feed will result in shorter lives. Similarly, starting at point X (V = 150, ECT = 0.5, T = 15) and reducing feed, the H-curve will be reached at point E (ECT = 0.075, T = 300). Continuing to the left, tool-life will decrease and serious troubles occur at point E′ (ECT = 0.03). Starting at point OF (V = 300, ECT = 0.2, T = 15) and reducing feed the H-curve will be reached at point E (ECT = 0.08, T = 15). Continuing to the left, life will decrease and serious troubles occur at ECT = 0.03. Starting at point X (V = 400, ECT = 0.2, T = 5) and reducing feed the H-curve will be reached at point E (ECT = 0.09, T = 7). Continuing to the left, life will decrease and serious troubles occur at point A′ (ECT =0.03), where T = 1 minute. Cutting Forces and Chip Flow Angle.—There are three cutting forces, illustrated in Fig. 8, that are associated with the cutting edge with its nose radius r, depth of cut a, lead angle LA, and feed per revolution f, or in milling feed per tooth fz. There is one drawing for roughing and one for finishing operations.

Roughing: f -2

a ≥ r (1 – sin (LA)) feed x

Finishing: ECT

r(1 – sin(LA)) a O

a–x

CEL LA(U.S.)

O

b FR FH FA

CFA

–x⎞ CFA = 90 – atan ⎛⎝-a------FR b⎠ Axial Force = FA = FH cos(CFA) Radial Force = FR = FH sin(CFA)

s

x a–x

u r–a

r CFA

LA(U.S.) z = 90 – CFA f b = --- + r cos (LA) + 2 tan (LA)(a – r sin(LA))

z

f/

2

S r

a

c

a < r (1 – sin(LA))

FH FA

u= 90 – CFA

2 x = r – r2 – ---f4 f c = --- + r – (r – a)2 2 –x⎞ CFA = 90 – atan ⎛⎝-a---c---⎠

ISO LA = 90 – LA (U.S.)

Fig. 8. Definitions of equivalent chip thickness, ECT, and chip flow angle, CFA.

The cutting force FC, or tangential force, is perpendicular to the paper plane. The other two forces are the feed or axial force FA, and the radial force FR directed towards the work piece. The resultant of FA and FR is called FH. When finishing, FR is bigger than FA, while in roughing FA is usually bigger than FR. The direction of FH, measured by the chip flow angle CFA, is perpendicular to the rectangle formed by the cutting edge length CEL and ECT (the product of ECT and CEL constitutes the cross sectional area of cut, A). The important task of determining the direction of FH, and calculation of FA and FR, are shown in the formulas given in the Fig. 8. The method for calculating the magnitudes of FH, FA, and FR is described in the following. The first thing is to determine the value of the cutting force FC. Approximate formulas



1101

to calculate the tangential cutting force, torque and required machining power are found in the section ESTIMATING SPEEDS AND MACHINING POWER starting on page 1082. Specific Cutting Force, Kc: The specific cutting force, or the specific energy to cut, Kc, is defined as the ratio between the cutting force FC and the chip cross sectional area, A. thus, Kc = FC ÷ A N/mm2. The value of Kc decreases when ECT increases, and when the cutting speed V increases. Usually, Kc is written in terms of its value at ECT = 1, called Kc1, and neglecting the effect of cutting speed, thus Kc = Kc1 × ECT B, where B = slope in log-log coordinates LIVE GRAPH Click here to view

10000

V = 300 V = 250

Kc N/mm2

V = 200

1000 0.01

0.1

1

ECT, mm

Fig. 9. Kc vs. ECT, cutting speed plotted

A more accurate relationship is illustrated in Fig. 9, where Kc is plotted versus ECT at 3 different cutting speeds. In Fig. 9, the two dashed lines represent the aforementioned equation, which each have different slopes, B. For the middle value of cutting speed, Kc varies with ECT from about 1900 to 1300 N/mm2 when ECT increases from 0.1 to 0.7 mm. Generally the speed effect on the magnitude of Kc is approximately 5 to 15 percent when using economic speeds. LIVE GRAPH Click here to view

FH/FC

1

V=300

V=250 V=200

0.1 0.01

0.1

1

ECT, mm

Fig. 10. FH /FC vs. ECT, cutting speed plotted

Determination of Axial, FA, and Radial, FR, Forces: This is done by first determining the resultant force FH and then calculating FA and FR using the Fig. 8 formulas. FH is derived




from the ratio FH /FC, which varies with ECT and speed in a fashion similar to Kc. Fig. 10 shows how this relationship may vary. As seen in Fig. 10, FH/FC is in the range 0.3 to 0.6 when ECT varies from 0.1 to 1 mm, and speed varies from 200 to 250 m/min using modern insert designs and grades. Hence, using reasonable large feeds FH/FC is around 0.3 – 0.4 and when finishing about 0.5 – 0.6. Example:Determine FA and FR, based on the chip flow angle CFA and the cutting force FC, in turning. Using a value of Kc = 1500 N/mm2 for roughing, when ECT = 0.4, and the cutting edge length CEL = 5 mm, first calculate the area A = 0.4 × 5 = 2 mm2. Then, determine the cutting force FC = 2 × 1500 = 3000 Newton, and an approximate value of FH = 0.5 × 3000 = 1500 Newton. Using a value of Kc = 1700 N/mm2 for finishing, when ECT = 0.2, and the cutting edge length CEL = 2 mm, calculate the area A = 0.2 × 2 = 0.4 mm2. The cutting force FC = 0.4 × 1700 = 680 Newton and an approximate value of FH = 0.35 × 680 = 238 Newton. Fig. 8 can be used to estimate CFA for rough and finish turning. When the lead angle LA is 15 degrees and the nose radius is relatively large, an estimated value of the chip flow angle becomes about 30 degrees when roughing, and about 60 degrees in finishing. Using the formulas for FA and FR relative to FH gives: Roughing: FA = FH × cos (CFA) = 1500 × cos 30 = 1299 Newton FR = FH × sin (CFA) = 1500 × sin 30 = 750 Newton Finishing: FA = FH × cos (CFA) = 238 × cos 60 = 119 Newton FR = FH × sin (CFA) = 238 × sin 60 = 206 Newton The force ratio FH/FC also varies with the tool rake angle and increases with negative rakes. In grinding, FH is much larger than the grinding cutting force FC; generally FH/FC is approximately 2 to 4, because grinding grits have negative rakes of the order –35 to –45 degrees. Forces and Tool-life.—Forces and tool life are closely linked. The ratio FH/FC is of particular interest because of the unique relationship of FH/FC with tool-life. LIVE GRAPH Click here to view

1.8 1.6

H-CURVE

1.4

FH/FC

1.2 1 0.8 0.6 0.4 0.2 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ECT, mm

Fig. 11a. FH /FC vs. ECT

The results of extensive tests at Ford Motor Company are shown in Figs. 11a and 11b, where FH/FC and tool-life T are plotted versus ECT at different values of cutting speed V.



1103

For any constant speed, tool-life has a maximum at approximately the same values of ECT as has the function FH/FC. LIVE GRAPH Click here to view

1000

H-CURVE

T, min

100

10

1

0.1 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ECT, mm

Fig. 11b. Tool-life vs. ECT

The Force Relationship: Similar tests performed elsewhere confirm that the FH/FC function can be determined using the 5 tool-life constants (H, K, M, L, N0) introduced previously, and a new constant (LF/L). ( x – H )2 K – y – -------------------1- ⋅ F 4M H⎞ ln ⎛ ------- = -------------------------------------⎝a F ⎠ LF C ------ ( N 0 – Lx ) L

(5)

The constant a depends on the rake angle; in turning a is approximately 0.25 to 0.5 and LF/L is 10 to 20. FC attains it maximum values versus ECT along the H-curve, when the tool-life equation has maxima, and the relationships in the three force ratio planes look very similar to the tool-life functions shown in the tool-life planes in Figs. 6a, 6b, and 6c. LIVE GRAPH Click here to view

1000 LF/L = 5

LF/L = 10

T , minutes

LF/L = 20 100

10

1 0.1

1

FH/FC

Fig. 12. Tool-life vs. FH/FC

Tool-life varies with FH/FC with a simple formula according to Equation (5) as follows:



MACHINING ECONOMETRICS LF

F H ⎞ ----T = ⎛ --------- L ⎝ aF ⎠ C

where L is the constant in the tool-life equation, Equation (4a) or (4b), and LF is the corresponding constant in the force ratio equation, Equation (5). In Fig. 12 this function is plotted for a = 0.5 and for LF/L = 5, 10, and 20. Accurate calculations of aforementioned relationships require elaborate laboratory tests, or better, the design of a special test and follow-up program for parts running in the ordinary production. A software machining program, such as Colding International Corp. COMP program can be used to generate the values of all 3 forces, torque and power requirements both for sharp and worn tools Surface Finish Ra and Tool-life.—It is well known that the surface finish in turning decreases with a bigger tool nose radius and increases with feed; usually it is assumed that Ra increases with the square of the feed per revolution, and decreases inversely with increasing size of the nose radius. This formula, derived from simple geometry, gives rise to great errors. In reality, the relationship is more complicated because the tool geometry must taken into account, and the work material and the cutting conditions also have a significant influence. LIVE GRAPH Click here to view

Ra, mm

10

V = 475 V = 320 V = 234 V = 171 V = 168 V = 144 V = 120

1

0.1 0.001

0.01

0.1

1

ECT, mm

Fig. 13. Ra vs. ECT, nose radius r constant

Fig. 13 shows surface finish Ra versus ECT at various cutting speeds for turning cast iron with carbide tools and a nose radius r = 1.2 mm. Increasing the cutting speed leads to a smaller Ra value. Fig. 14 shows how the finish improves when the tool nose radius, r, increases at a constant cutting speed (168 m/min) in cutting nodular cast iron. In Fig. 15, Ra is plotted versus ECT with cutting speed V for turning a 4310 steel with carbide tools, for a nose radius r = 1.2 mm, illustrating that increasing the speed also leads to a smaller Ra value for steel machining. A simple rule of thumb for the effect of increasing nose radius r on decreasing surface finish Ra, regardless of the ranges of ECT or speeds used, albeit within common practical values, is as follows. In finishing, R a1 r 0.5 (6) -------- = ⎛ ----2⎞ ⎝r ⎠ R a2

1



1105

LIVE GRAPH

Click here to view

Click here to view

10

5 4.5 4 3.5

Ra

Ra

3 2.5

1 V = 260

2 1.5

V = 215

V = 170, r = 0.8 V = 170, r = 1.2 V = 170, r = 1.6

1

V = 175

0.5 0.1

0 0

0.05

0.1

0.15

0.2

0.01

0.25

0.1

1

ECT, mm

ECT

Fig. 14. Ra vs. ECT cutting speed constant, nose radius r varies

Fig. 15. Ra vs. ECT, cutting speed and nose radius r constant

In roughing, multiply the finishing values found using Equation (6) by 1.5, thus, Ra (Rough) = 1.5 × Ra (Finish) for each ECT and speed. Example 1:Find the decrease in surface roughness resulting from a tool nose radius change from r = 0.8 mm to r =1.6 mm in finishing. Also, find the comparable effect in roughing. For finishing, using r2 =1.6 and r1 = 0.8, Ra1/Ra2 = (1.6/0.8) 0.5 = 1.414, thus, the surface roughness using the larger tool radius is Ra2 = Ra1 ÷ 1.414 = 0.7Ra1 In roughing, at the same ECT and speed, Ra = 1.5 × Ra2 =1.5 × 0.7Ra1 = 1.05Ra1 Example 2:Find the decrease in surface roughness resulting from a tool nose radius change from r = 0.8 mm to r =1.2 mm For finishing, using r2 =1.2 and r1 = 0.8, Ra1/Ra2 = (1.2/0.8) 0.5 = 1.224, thus, the surface roughness using the larger tool radius is Ra2 = Ra1 ÷ 1.224 = 0.82Ra1 In roughing, at the same ECT and speed, Ra = 1.5 × Ra2 =1.5 × 0.82Ra1 = 1.23Ra1 It is interesting to note that, at a given ECT, the Ra curves have a minimum, see Figs. 13 and 15, while tool-life shows a maximum, see Figs. 6b and 6c. As illustrated in Fig. 16, Ra increases with tool-life T when ECT is constant, in principle in the same way as does the force ratio. LIVE GRAPH Click here to view

Ra

10

1

ECT = 0.03 ECT = 0.08 ECT = 0.12 ECT = 0.18 ECT = 0.30 0.1 1

10

100

1000

T, min.

Fig. 16. Ra vs. T, holding ECT constant

The Surface Finish Relationship: Ra is determined using the same type of mathematical relationship as for tool-life and force calculations: x – H Ra 2 y = K Ra – -------------------- – ( N 0Ra – L Ra )ln ( R a ) 4M Ra

where KRA, HRA, MRA, NORA, and LRA are the 5 surface finish constants.




Shape of Tool-life Relationships for Turning, Milling, Drilling and Grinding Operations—Overview.—A summary of the general shapes of tool-life curves (V–ECT–T graphs) for the most common machining processes, including grinding, is shown in double logarithmic coordinates in Fig. 17a through Fig. 17h. LIVE GRAPH

LIVE GRAPH

Click here to view

Click here to view

1000

V, m/min

V, m/min.

1000

100

100

Tool-life, T (minutes) T = 15

Tool-life (minutes)

T = 45

T = 15 T = 45

T =120

T = 120 10 0.01

0.1

10 0.01

1

0.1

1

ECT, mm

ECT, mm

Fig. 17a. Tool-life for turning cast iron using coated carbide

Fig. 17b. Tool-life for turning low-alloy steel using coated carbide

LIVE GRAPH

LIVE GRAPH

Click here to view

Click here to view

1000

1000

T = 15

Tool-life (minutes) T = 15

T = 45 T = 120

T = 45 T = 120

100

V, m/min

V, m/min.

100

10

10

1 1 0.01

0.1

ECT, mm

1

0.01

0.1

1

ECT, mm

Fig. 17c. Tool-life for end-milling AISI 4140 steel Fig. 17d. Tool-life for end-milling low-allow steel using high-speed steel using uncoated carbide



1107

LIVE GRAPH

Click here to view

Click here to view

1000

1000

V,m/min.

V, m/min

100

10

T = 45 T = 15

T = 120

T = 45

T = 15

T = 120 100

1 0.01

0.1

1

ECT, mm

Fig. 17e. Tool-life for end-milling low-alloy steel using coated carbide

0.1

0.01

1

Fig. 17f. Tool-life for face-milling SAE 1045 steel using coated carbide

LIVE GRAPH

LIVE GRAPH

Click here to view

Click here to view

1000

10000

T = 15 T = 45 T = 120

V, m/min.

V m/min

100

1000

10

T = 30 T = 10 T=1 100

1

0.00001 0.01

0.1

ECT, mm

Fig. 17g. Tool-life for solid carbide drill

1

0.0001

0.001

ECT, mm

Fig. 17h. Wheel-life in grinding M4 tool-steel

Calculation Of Optimized Values Of Tool-life, Feed And Cutting Speed Minimum Cost.—Global optimum is defined as the absolute minimum cost considering all alternative speeds, feeds and tool-lives, and refers to the determination of optimum tool-life TO, feed fO, and cutting speed VO, for either minimum cost or maximum production rate. When using the tool-life equation, T = f (V, ECT), determine the corresponding feed, for given values of depth of cut and operation geometry, from optimum equivalent chip thickness, ECTO. Mathematically the task is to determine minimum cost, employing the cost function CTOT = cost of machining time + tool changing cost + tooling cost. Minimum cost optima occur along the so-called G-curve, identified in Fig. 6c. Another important factor when optimizing cutting conditions involves choosing the proper cost values for cost per edge CE, replacement time per edge TRPL, and not least, the hourly rate HR that should be applied. HR is defined as the portion of the hourly shop rate that is applied to the operations and machines in question. If optimizing all operations in the portion of the shop for which HR is calculated, use the full rate; if only one machine is involved, apply a lower rate, as only a portion of the general overhead rate should be used, otherwise the optimum, and anticipated savings, are erroneous.




Production Rate.—The production rate is defined as the cutting time or the metal removal rate, corrected for the time required for tool changes, but neglecting the cost of tools. The result of optimizing production rate is a shorter tool-life, higher cutting speed, and a higher feed compared to minimum cost optimization, and the tooling cost is considerably higher. Production rates optima also occur along the G-curve. The Cost Function.—There are a number of ways the total machining cost CTOT can be plotted, for example, versus feed, ECT, tool-life, cutting speed or other parameter. In Fig. 18a, cost for a face milling operation is plotted versus cutting time, holding feed constant, and using a range of tool-lives, T, varying from 1 to 240 minutes. LIVE GRAPH Click here to view

CTOOL

CTOT

5.85 6.91 7.47 8.30 8.83

0.487 0.192 0.125 0.069 0.049

9.81 10.91 11.60 12.12 13.47

0.569 0.288 0.228 0.185 0.172

T 1 3 5 10 15

V 598 506 468 421 396

0.027

0.164

30

356

0.015 0.011 0.008 0.005

0.167 60 321 0.172 90 302 0.177 120 289 0.192 240 260

0.3 CTOT

T varies

CTOOL T varies 0.25

Total Cost

Cost of Face Milling Operation, $

Minimum cost

tc

0.2

Cost of Cutting Time

0.15

Hourly Rate = 60$/hour

0.1

0.05

Tooling Cost 0 5

7

9

11

13

15

Cutting Time, secsonds

Fig. 18a. Variation of tooling cost CTOOL, and total cost CC, with cutting time tc, including minimum cost cutting time

The tabulated values show the corresponding cutting speeds determined from the toollife equation, and the influence of tooling on total cost. Tooling cost, CTOOL = sum of tool cost + cost of replacing worn tools, decreases the longer the cutting time, while the total cost, CTOT, has a minimum at around 10 seconds of cutting time. The dashed line in the graph represents the cost of machining time: the product of hourly rate HR, and the cutting time tc divided by 60. The slope of the line defines the value of HR. 0.5 CTOT 1 Tool CTOT 2 Tools

0.45 0.4

CTOT 4 Tools

Cost, $

0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 5

6

7

8

9

10

11

12

13

14

15

Cutting time, seconds

Fig. 18b. Total cost vs. cutting time for simultaneously cutting with 1, 2, and 4 tools



1109

The cutting time for minimum cost varies with the ratio of tooling cost and HR. Minimum cost moves towards a longer cutting time (longer tool-life) when either the price of the tooling increases, or when several tools cut simultaneously on the same part. In Fig. 18b, this is exemplified by running 2 and 4 cutters simultaneously on the same work piece, at the same feed and depth of cut, and with a similar tool as in Fig. 18a. As the tooling cost goes up 2 and 4 times, respectively, and HR is the same, the total costs curves move up, but also moves to the right, as do the points of minimum cost and optimal cutting times. This means that going somewhat slower, with more simultaneously cutting tools, is advantageous. Global Optimum.—Usually, global optimum occurs for large values of feed, heavy roughing, and in many cases the cutting edge will break trying to apply the large feeds required. Therefore, true optima cannot generally be achieved when roughing, in particular when using coated and wear resistant grades; instead, use the maximum values of feed, ECTmax, along the tool-life envelope, see Fig. 7. As will be shown in the following, the first step is to determine the optimal tool-life TO, and then determine the optimum values of feeds and speeds. Optimum Tool-life TO = 22 minutes V22

tc, sec.

CTOOL

CTOT

0.03 0.08 0.10 0.17 0.20 0.40 0.60 0.70

416 397 374 301 276 171 119 91

28.067 11.017 9.357 6.831 6.334 5.117 4.903 4.924

0.1067 0.0419 0.0356 0.0260 0.0241 0.0194 0.0186 0.0187

0.4965 0.1949 0.1655 0.1208 0.1120 0.0905 0.0867 0.0871

Maximum Production Rate, T = 5 minutes V5 tc CTOOL CTOT fz 0.7

163

3.569

0.059

0.109

T Varies between 1 and 240 minutes fz = 0.10

Minimum Cost

ECT= 0.26

CTOOL T = 22 CTOT T = 22 CTOOL T varies CTOT T varies

0.5

0.45

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

tc secs. CTOOL

CTOT

T

V

0.487 0.192 0.125 0.069 0.049 0.027 0.015 0.011 0.008 0.005

0.569 0.288 0.228 0.185 0.172 0.164 0.167 0.172 0.177 0.192

1 3 5 10 15 30 60 90 120 240

598 506 468 421 396 357 321 302 289 260

5.850 6.914 7.473 8.304 8.832 9.815 10.906 11.600 12.119 13.467

0.6

0.55

Cost, $

Minimum Cost

fz

0 0

5

10

15

20

25

30

Cutting Time, seconds

Fig. 19. Variation of tooling and total cost with cutting time, comparing global optimum with minimum cost at fz = 0.1 mm

The example in Fig. 19 assumes that TO = 22 minutes and the feed and speed optima were calculated as fO = 0.6 mm/tooth, VO = 119 m/min, and cutting time tcO = 4.9 secs. The point of maximum production rate corresponds to fO = 0.7 mm/tooth, VO = 163 m/min, at tool-life TO =5 minutes, and cutting time tcO = 3.6 secs. The tooling cost is approximately 3 times higher than at minimum cost (0.059 versus 0.0186), while the piece cost is only slightly higher: $0.109 versus $0.087. When comparing the global optimum cost with the minimum at feed = 0.1 mm/tooth the graph shows it to be less than half (0.087 versus 0.164), but also the tooling cost is about 1/3 lower (0.0186 versus 0.027). The reason why tooling cost is lower depends on the tooling cost term tc × CE /T (see Calculation of Cost of Cutting and Grinding Operations on page




1115). In this example, cutting times tc= 4.9 and 9.81 seconds, at T = 22 and 30 minutes respectively, and the ratios are proportional to 4.9/22 = 0.222 and 9.81/30 = 0.327 respectively. The portions of the total cost curve for shorter cutting times than at minimum corresponds to using feeds and speeds right of the G-curve, and those on the other side are left of this curve. Optimization Models, Economic Tool-life when Feed is Constant.—Usually, optimization is performed versus the parameters tool-life and cutting speed, keeping feed at a constant value. The cost of cutting as function of cutting time is a straight line with the slope = HR = hourly rate. This cost is independent of the values of tool change and tooling. Adding the cost of tool change and tooling, gives the variation of total cutting cost which shows a minimum with cutting time that corresponds to an economic tool-life, TE. Economic tool-life represents a local optima (minimum cost) at a given constant value of feed, feed/tooth, or ECT. Using the Taylor Equation: V × T = C and differentiating CTOT with respect to T yields: Economic tool-life: TE = TV × (1/n − 1), minutes Economic cutting speed: VE = C/TEn, m/min, or sfm In these equations, n and C are constants in the Taylor equation for the given value of feed. Values of Taylor slopes, n, are estimated using the speed and feed Tables 1 through 23 starting on page 1027 and handbook Table 5b on page 1035 for turning, and Table 15e on page 1059 for milling and drilling; and TV is the equivalent tooling-cost time. TV = TRPL + 60 × CE ÷ HR, minutes, where TRPL = time for replacing a worn insert, or a set of inserts in a milling cutter or inserted drill, or a twist drill, reamer, thread chaser, or tap. TV is described in detail, later; CE = cost per edge, or set of edges, or cost per regrind including amortized price of tool; and HR = hourly shop rate, or that rate that is impacted by the changes of cutting conditions . In two dimensions, Fig. 20a shows how economic tool-life varies with feed per tooth. In this figure, the equivalent tooling-cost time TV is constant, however the Taylor constant n varies with the feed per tooth. LIVE GRAPH Click here to view

60

TE

TE , minutes

50

40

30

20

10

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fz , mm

Fig. 20a. Economic tool-life, TE vs. feed per tooth, fz



1111

Economic tool-life increases with greater values of TV, either when TRPL is longer, or when cost per edge CE is larger for constant HR, or when HR is smaller and TRPL and CE are unchanged. For example, when using an expensive machine (which makes HR bigger) the value of TV gets smaller, as does the economic tool-life, TE = TV × (1/n - 1). Reducing TE results in an increase in the economic cutting speed, VE. This means raising the cutting speed, and illustrates the importance, in an expensive system, of utilizing the equipment better by using more aggressive machining data. LIVE GRAPH Click here to view

T, minutes

1000

100

10 ECT = 1.54

ECT = 0.51

ECT = 0.8 1 10

100

1000

V, m/min

Fig. 20b. Tool-life vs. cutting speed, constant ECT

As shown in Fig. 20a for a face milling operation, economic tool-life TE varies considerably with feed/tooth fz, in spite of the fact that the Taylor lines have only slightly different slopes (ECT = 0.51, 0.6, 1.54), as shown in Fig. 20b. The calculation is based on the following cost data: TV = 6, hourly shop rate HR = $60/hour, cutter diameter D = 125 mm with number of teeth z = 10, and radial depth of cut ar = 40 mm. The conclusion relating to the determination of economic tool-life is that both hourly rate HR and slope n must be evaluated with reasonable accuracy in order to arrive at good values. However, the method shown will aid in setting the trend for general machining economics evaluations. Global Optimum, Graphical Method.—There are several ways to demonstrate in graphs how cost varies with the production parameters including optimal conditions. In all cases, tool-life is a crucial parameter. Cutting time tc is inversely proportional to the specific metal removal rate, SMRR = V × ECT, thus, 1/tc = V × ECT. Taking the log of both sides,

lnV = – lnECT – lnt c + C

(7)

where C is a constant. Equation (7) is a straight line with slope (– 1) in the V–ECT graph when plotted in a loglog graph. This means that a constant cutting time is a straight 45-degree line in the V–ECT graph, when plotted in log-log coordinates with the same scale on both axis (a square graph). The points at which the constant cutting time lines (at 45 degrees slope) are tangent to the tool-life curves define the G-curve, along which global optimum cutting occurs. Note: If the ratio a/CEL is not constant when ECT varies, the constant cutting time lines are not straight, but the cutting time deviation is quite small in most cases.




In the V–ECT graph, Fig. 21, 45-degree lines have been drawn tangent to each tool-life curve: T=1, 5, 15, 30, 60, 100 and 300 minutes. The tangential points define the G-curve, and the 45-degree lines represent different constant cutting times: 1, 2, 3, 10 minutes, etc. Following one of these lines and noting the intersection points with the tool-life curves T = 1, 5, etc., many different speed and feed combinations can be found that will give the same cutting time. As tool-life gets longer (tooling cost is reduced), ECT (feed) increases but the cutting speed has to be reduced. LIVE GRAPH Click here to view

1000

Constant cutting time increasing going down 45 Degrees

V, m/min

G-CURVE

T=1 T=5 T=15 T=30 T=60 100 0.1

ECT, mm

1

Fig. 21. Constant cutting time in the V-ECT plane, tool-life constant

Global Optimum, Mathematical Method.—Global optimization is the search for extremum of CTOT for the three parameters: T, ECT, and V. The results, in terms of the tool-life equation constants, are: Optimum tool-life: 1- – 1⎞ T O = T V × ⎛ ----⎝n ⎠ O n O = 2M × ( L × lnT O ) 2 + 1 – N 0 + L × ( 2M + H ) where nO = slope at optimum ECT. The same approach is used when searching for maximum production rate, but without the term containing tooling cost. Optimum cutting speed: VO = e

– M + K + ( H × L – N 0 ) × lnT O + M × L 2 × ( lnT O ) 2

Optimum ECT: ECT O = e

H + 2M × ( L × ln ( T O ) + 1 )

Global optimum is not reached when face milling for very large feeds, and CTOT decreases continually with increasing feed/tooth, but can be reached for a cutter with many teeth, say 20 to 30. In end milling, global optimum can often be achieved for big feeds and for 3 to 8 teeth.



1113

Determination Of Machine Settings And Calculation Of Costs Based on the rules and knowledge presented in Chapters 1 and 2, this chapter demonstrates, with examples, how machining times and costs are calculated. Additional formulas are given, and the speed and feed tables given in SPEED AND FEED TABLES starting on page 1022 should be used. Finally the selection of feeds, speeds and tool-lives for optimized conditions are described with examples related to turning, end milling, and face milling. There are an infinite number of machine settings available in the machine tool power train producing widely different results. In practice only a limited number of available settings are utilized. Often, feed is generally selected independently of the material being cut, however, the influence of material is critical in the choice of cutting speed. The tool-life is normally not known or directly determined, but the number of pieces produced before the change of worn tools is better known, and tool-life can be calculated using the formula for piece cutting time tc given in this chapter. It is well known that increasing feeds or speeds reduces the number of pieces cut between tool changes, but not how big are the changes in the basic parameter tool-life. Therefore, there is a tendency to select “safe” data in order to get a long tool-life. Another common practice is to search for a tool grade yielding a longer life using the current speeds and feeds, or a 10–20% increase in cutting speed while maintaining the current tool-life. The reason for this old-fashioned approach is the lack of knowledge about the opportunities the metal cutting process offers for increased productivity. For example, when somebody wants to calculate the cutting time, he/she can select a value of the feed rate (product of feed and rpm), and easily find the cutting time by dividing cutting distance by the feed rate. The number of pieces obtained out of a tool is a guesswork, however. This problem is very common and usually the engineers find desired toollives after a number of trial and error runs using a variety of feeds and speeds. If the user is not well familiar with the material cut, the tool-life obtained could be any number of seconds or minutes, or the cutting edge might break. There are an infinite number of feeds and speeds, giving the same feed rate, producing equal cutting time. The same cutting time per piece tc is obtained independent of the selection of feed/rev f and cutting speed V, (or rpm), as long as the feed rate FR remains the same: FR = f1 × rpm1 = f2 × rpm2 = f3 × rpm3 …, etc. However, the number of parts before tool change Nch will vary considerably including the tooling cost ctool and the total cutting cost ctot. The dilemma confronting the machining-tool engineer or the process planner is how to set feeds and speeds for either desired cycle time, or number of parts between tool changes, while balancing the process versus other operations or balancing the total times in one cell with another. These problems are addressed in this section. Nomenclature f = feed/rev or tooth, mm fE =economic feed fO =optimum feed T =tool-life, minutes TE =economic tool-life TO =optimum tool-life V =cutting speed, m/min VE =economic cutting speed VO =optimum cutting speed, m/min Similarly, economic and optimum values of: ctool = piece cost of tooling, $ CTOOL = cost of tooling per batch, $ ctot = piece total cost of cutting, $ CTOT =total cost of cutting per batch, $ FR =feed rate measured in the feeding direction, mm/rev N =batch size Nch = number of parts before tool change tc = piece cutting time, minutes TC =cutting time per batch, minutes tcyc = piece cycle time, minutes TCYC = cycle time before tool change, minutes




ti = idle time (tool “air” motions during cycle), minutes z = cutter number of teeth The following variables are used for calculating the per batch cost of cutting: CC =cost of cutting time per batch, $ CCH = cost of tool changes per batch, $ CE =cost per edge, for replacing or regrinding, $ HR =hourly rate, $ TV =equivalent tooling-cost time, minutes TRPL = time for replacing worn edge(s), or tool for regrinding, minutes Note: In the list above, when two variables use the same name, one in capital letters and one lower case, TC and tc for example, the variable name in capital letters refers to batch processing and lowercase letters to per piece processing, such as TC = Nch × tc, CTOT = Nch × ctot, etc. Formulas Valid For All Operation Types Including Grinding Calculation of Cutting Time and Feed Rate Feed Rate: FR = f × rpm (mm/min), where f is the feed in mm/rev along the feeding direction, rpm is defined in terms of work piece or cutter diameter D in mm, and cutting speed V in m/min, as follows: 1000V 318V rpm = ---------------- = ------------πD D Cutting time per piece: Note: Constant cutting time is a straight 45-degree line in the V–ECT graph, along which tool-life varies considerably, as is shown in Chapter 2. Dist - = Dist × πDt c = Dist ----------- = --------------------------------------f × rpm 1000V × f FR where the units of distance cut Dist, diameter D, and feed f are mm, and V is in m/min. In terms of ECT, cutting time per piece, tc, is as follows: × πD- × ----------------------------a t c = Dist -----------------------1000V CEL × ECT where a = depth of cut, because feed × cross sectional chip area = f × a = CEL × ECT. Example 3, Cutting Time:Given Dist =105 mm, D =100 mm, f = 0.3 mm, V = 300 m/min, rpm = 700, FR = 210 mm/min, find the cutting time. Cutting time = tc = 105 × 3.1416 × 100 ÷ (1000 × 300 × 0.3) = 0.366 minutes = 22 seconds Scheduling of Tool Changes Number of parts before tool change: Nch = T÷ tc Cycle time before tool change: TCYC = Nch × (tc + ti), where tcyc = tc + ti, where tc = cutting time per piece, ti = idle time per piece Tool-life: T = Nch × tc Example 4: Given tool-life T = 90 minutes, cutting time tc = 3 minutes, and idle time ti = 3 minutes, find the number of parts produced before a tool change is required and the time until a tool change is required.



1115

Number of parts before tool change = Nch = 90/3 = 30 parts. Cycle time before tool change = TCYC = 30 × (3 + 3) = 180 minutes Example 5: Given cutting time, tc = 1 minute, idle time ti = 1 minute, Nch = 100 parts, calculate the tool-life T required to complete the job without a tool change, and the cycle time before a tool change is required. Tool-life = T = Nch × tc = 100 × 1 = 100 minutes. Cycle time before tool change = TCYC = 100 × (1 + 1) = 200 minutes. Calculation of Cost of Cutting and Grinding Operations.—When machining data varies, the cost of cutting, tool changing, and tooling will change, but the costs of idle and slack time are considered constant. Cost of Cutting per Batch: CC = HR × TC/60 TC = cutting time per batch = (number of parts) × tc, minutes, or when determining time for tool change TCch = Nch × tc minutes = cutting time before tool change. tc = Cutting time/part, minutes HR = Hourly Rate Cost of Tool Changes per Batch: H T RPL $ ⋅ min = $ C CH = ------R- × T C × ------------------60 T min where T = tool-life, minutes, and TRPL = time for replacing a worn edge(s), or tool for regrinding, minutes Cost of Tooling per Batch: Including cutting tools and holders, but without tool changing costs, 60C E min --------------------- ⋅ $ ⋅ hr ----HR HR hr $- = $ $ ⋅ min ⋅ --------------------------C TOOL = ------- × T C × -------------------60 T min min Cost of Tooling + Tool Changes per Batch: Including cutting tools, holders, and tool changing costs, 60C T RPL + ------------EHR HR ( C TOOL + C CH ) = ------- × T C × ------------------------------T 60 Total Cost of Cutting per Batch: 60C ⎛ T RPL + ------------E-⎞ ⎜ HR HR ⎟ C TOT = ------- × T C ⎜ 1 + -------------------------------⎟ 60 T ⎜ ⎟ ⎝ ⎠ Equivalent Tooling-cost Time, TV: 60C The two previous expressions can be simplified by using T V = T RPL + ------------EHR thus: H T ( C TOOL + C CH ) = ------R- × T C × -----V60 T




T H C TOT = ------R- × T C ⎛ 1 + -----V-⎞ ⎝ T⎠ 60 CE = cost per edge(s) is determined using two alternate formulas, depending on whether tools are reground or inserts are replaced: Cost per Edge, Tools for Regrinding cost of tool + ( number of regrinds × cost/regrind ) C E = ----------------------------------------------------------------------------------------------------------------------1 + number of regrinds Cost per Edge, Tools with Inserts: cost of insert(s) cost of cutter body C E = --------------------------------------------------------------- + ----------------------------------------------------------------------------------number of edges per insert cutter body life in number of edges Note: In practice allow for insert failures by multiplying the insert cost by 4/3, that is, assuming only 3 out of 4 edges can be effectively used. Example 6, Cost per Edge–Tools for Regrinding:Use the data in the table below to calculate the cost per edge(s) CE, and the equivalent tooling-cost time TV, for a drill. Time for cutter replacement TRPL, minute

Cutter Price, $

Cost per regrind, $

Number of regrinds

Hourly shop rate, $

Batch size

Taylor slope, n

Economic cutting time, tcE minute

1

40

6

5

50

1000

0.25

1.5

Using the cost per edge formula for reground tools, CE = (40 + 5 × 6) ÷ (1 + 5) = $6.80 60C 60 ( 6.8 ) When the hourly rate is $50/hr, T V = T RPL + ------------E- = 1 + ------------------ = 9.16minutes HR 50 1 Calculate economic tool-life using T E = T V × ⎛ --- – 1⎞ thus, TE = 9.17 × (1/0.25 – 1) = ⎝n ⎠ 9.16 × 3 = 27.48 minutes. Having determined, elsewhere, the economic cutting time per piece to be tcE = 1.5 minutes, for a batch size = 1000 calculate: Cost of Tooling + Tool Change per Batch: H T 9.16- = $ 417 ( C TOOL + C CH ) = ------R- × T C × -----V- = 50 ------ × 1000 × 1.5 × -----------60 T 60 27.48 Total Cost of Cutting per Batch: H T 9.16 C TOT = ------R- × T C ⎛ 1 + -----V-⎞ = 50 ------ × 1000 × 1.5 × ⎛ 1 + -------------⎞ = $ 1617 ⎝ ⎝ T⎠ 27.48⎠ 60 60 Example 7, Cost per Edge–Tools with Inserts: Use data from the table below to calculate the cost of tooling and tool changes, and the total cost of cutting. For face milling, multiply insert price by safety factor 4/3 then calculate the cost per edge: CE =10 × (5/3) × (4/3) + 750/500 = 23.72 per set of edges When the hourly rate is $50, equivalent tooling-cost time is TV = 2 + 23.72 × 60/50 = 30.466 minutes (first line in table below). The economic tool-life for Taylor slope n = 0.333 would be TE = 30.466 × (1/0.333 –1) = 30.466 × 2 = 61 minutes. When the hourly rate is $25, equivalent tooling-cost time is TV = 2 + 23.72 × 60/25 = 58.928 minutes (second line in table below). The economic tool-life for Taylor slope n = 0.333 would be TE = 58.928 × (1/0.333 –1) =58.928 × 2 = 118 minutes.


Machinery's Handbook 27th Edition MACHINING ECONOMETRICS Time for replacement of inserts TRPL, minutes

Number of inserts

Price per insert

2 2

10 10

5 5

1

3

6

1

1

5

Edges per insert

Cutter Price

Face mill 750 750 End mill 2 75 Turning 3 50 3 3

1117

Edges per cutter

Cost per set of edges, CE

Hourly shop rate

TV minutes

500 500

23.72 23.72

50 25

30.466 58.928

200

4.375

50

6.25

100

2.72

30

6.44

With above data for the face mill, and after having determined the economic cutting time as tcE = 1.5 minutes, calculate for a batch size = 1000 and $50 per hour rate: Cost of Tooling + Tool Change per Batch: H T 50 30.466 ( C TOOL + C CH ) = ------R- × T C × -----V- = ------ × 1000 × 1.5 × ---------------- = $ 624 60 T 60 61 Total Cost of Cutting per Batch: H T 30.466 C TOT = ------R- × T C ⎛ 1 + -----V-⎞ = 50 ------ × 1000 × 1.5 × ⎛ 1 + ----------------⎞ = $ 1874 ⎝ ⎝ 60 T⎠ 60 61 ⎠ Similarly, at the $25/hour shop rate, (CTOOL + CCH) and CTOT are $312 and $937, respectively. Example 8, Turning: Production parts were run in the shop at feed/rev = 0.25 mm. One series was run with speed V1 = 200 m/min and tool-life was T1 = 45 minutes. Another was run with speed V2 = 263 m/min and tool-life was T2 = 15 minutes. Given idle time ti = 1 minute, cutting distance Dist =1000 mm, work diameter D = 50 mm. First, calculate Taylor slope, n, using Taylor’s equation V1 × T1n = V2 × T2n, as follows: V T 200- ÷ ln ----15- = 0.25 n = ln -----1- ÷ ln -----2 = ln -------V2 T1 263 45 Economic tool-life TE is next calculated using the equivalent tooling-cost time TV, as described previously. Assuming a calculated value of TV = 4 minutes, then TE can be calculated from 1 - – 1⎞ = 12 minutes T E = T V × ⎛ 1--- – 1⎞ = 4 × ⎛ --------⎝n ⎠ ⎝ 0.25 ⎠ Economic cutting speed, VE can be found using Taylor’s equation again, this time using the economic tool-life, as follows, V E1 × ( T E ) n = V 2 × ( T 2 ) n 0.25 T n V E1 = V 2 × ⎛ -----2-⎞ = 263 × ⎛ 15 ------⎞ = 278 m/min ⎝T ⎠ ⎝ 12⎠ E

Using the process data, the remaining economic parameters can be calculated as follows: Economic spindle rpm, rpmE = (1000VE)/(πD) = (1000 × 278)/(3.1416 × 50) = 1770 rpm Economic feed rate, FRE = f × rpmE = 0.25 × 1770 = 443 mm/min Economic cutting time, tcE = Dist/ FRE =1000/ 443 = 2.259 minutes Economic number of parts before tool change, NchE = TE ÷ tcE =12 ÷ 2.259 = 5.31 parts Economic cycle time before tool change, TCYCE = NchE × (tc + ti) = 5.31 × (2.259 + 1) = 17.3 minutes.




Variation Of Tooling And Total Cost With The Selection Of Feeds And Speeds It is a well-known fact that tool-life is reduced when either feed or cutting speed is increased. When a higher feed/rev is selected, the cutting speed must be decreased in order to maintain tool-life. However, a higher feed rate (feed rate = feed/rev × rpm, mm/min) can result in a longer tool-life if proper cutting data are applied. Optimized cutting data require accurate machinability databases and a computer program to analyze the options. Reasonably accurate optimized results can be obtained by selecting a large feed/rev or tooth, and then calculating the economic tool-life TE. Because the cost versus feed or ECT curve is shallow around the true minimum point, i.e., the global optimum, the error in applying a large feed is small compared with the exact solution. Once a feed has been determined, the economic cutting speed VE can be found by calculating the Taylor slope, and the time/cost calculations can be completed using the formulas described in last section. The remainder of this section contains examples useful for demonstrating the required procedures. Global optimum may or may not be reached, and tooling cost may or may not be reduced, compared to currently used data. However, the following examples prove that significant time and cost reductions are achievable in today’s industry. Note: Starting values of reasonable feeds in mm/rev can be found in the Handbook speed and feed tables, see Principal Speed andFeed Tables on page 1022, by using the favg values converted to mm as follows: feed (mm/rev) = feed (inch/rev) × 25.4 (mm/inch), thus 0.001 inch/rev = 0.001× 25.4 = 0.0254 mm/rev. When using speed and feed Tables 1 through 23, where feed values are given in thousandths of inch per revolution, simply multiply the given feed by 25.4/1000 = 0.0254, thus feed (mm/rev) = feed (0.001 inch/rev) × 0.0254 (mm/ 0.001inch). Example 9, Converting Handbook Feed Values From Inches to Millimeters: Handbook tables give feed values fopt and favg for 4140 steel as 17 and 8 × (0.001 inch/rev) = 0.017 and 0.009 inch/rev, respectively. Convert the given feeds to mm/rev. feed = 0.017 × 25.4 = 17 × 0.0254 = 0.4318 mm/rev feed = 0.008 × 25.4 = 8 × 0.0254 = 0.2032 mm/rev Example 10, Using Handbook Tables to Find the Taylor Slope and Constant:Calculate the Taylor slope and constant, using cutting speed data for 4140 steel in Table 1 starting on page 1027, and for ASTM Class 20 grey cast iron using data from Table 4a on page 1033, as follows: For the 175–250 Brinell hardness range, and the hard tool grade, ln ( V 1 ⁄ V 2 ) ( 525 ⁄ 705 )- = ln ------------------------------n = ------------------------= 0.27 C = V 1 × ( T 1 ) n = 1458 ln ( 15 ⁄ 45 ) ln ( T 2 ⁄ T 1 ) For the 175–250 Brinell hardness range, and the tough tool grade, ln ( V 1 ⁄ V 2 ) ( 235 ⁄ 320 )- = ln ------------------------------n = ------------------------= 0.28 C = V 1 × ( T 1 ) n = 685 ln ( T 2 ⁄ T 1 ) ln ( 15 ⁄ 45 ) For the 300–425 Brinell hardness range, and the hard tool grade, ln ( V 1 ⁄ V 2 ) ( 330 ⁄ 440 )- = 0.26 n = ------------------------- = ln ------------------------------C = V 1 × ( T 1 ) n = 894 ln ( T 2 ⁄ T 1 ) ln ( 15 ⁄ 45 ) For the 300–425 Brinell hardness range, and the tough tool grade, ln ( V 1 ⁄ V 2 ) ( 125 ⁄ 175 )- = 0.31 n = ------------------------- = ln ------------------------------C = V 1 × ( T 1 ) n = 401 ln ( T 2 ⁄ T 1 ) ln ( 15 ⁄ 45 ) For ASTM Class 20 grey cast iron, using hard ceramic,


Machinery's Handbook 27th Edition MACHINING ECONOMETRICS ln ( V 1 ⁄ V 2 ) ( 1490 ⁄ 2220 -) = 0.36 n = ------------------------- = ln ------------------------------------ln ( T 2 ⁄ T 1 ) ln ( 15 ⁄ 45 )

1119

C = V 1 × ( T 1 ) n = 5932

Selection of Optimized Data.—Fig. 22 illustrates cutting time, cycle time, number of parts before a tool change, tooling cost, and total cost, each plotted versus feed for a constant tool-life. Approximate minimum cost conditions can be determined using the formulas previously given in this section. First, select a large feed/rev or tooth, and then calculate economic tool-life TE, and the economic cutting speed VE, and do all calculations using the time/cost formulas as described previously. 1000 tc

100

tcyc # parts

10

CTOT

CTOOL

1

0.1

0.01

0.001 0.01

0.1

1

10

f, mm/rev

Fig. 22. Cutting time, cycle time, number of parts before tool change, tooling cost, and total cost vs. feed for tool-life = 15 minutes, idle time = 10 s, and batch size = 1000 parts

Example 11, Step by Step Procedure: Turning – Facing out:1) Select a big feed/rev, in this case f = 0.9 mm/rev (0.035 inch/rev). A Taylor slope n is first determined using the Handbook tables and the method described in Example 10. In this example, use n = 0.35 and C = 280. 2) Calculate TV from the tooling cost parameters: If cost of insert = $7.50; edges per insert = 2; cost of tool holder = $100; life of holder = 100 insert sets; and for tools with inserts, allowance for insert failures = cost per insert by 4/3, assuming only 3 out of 4 edges can be effectively used. Then, cost per edge = CE is calculated as follows: cost of insert(s) cost of cutter body C E = ---------------------------------------------------------------- + -----------------------------------------------------------------------------------number of edges per insert cutter body life in number of edges 7.50 × 4 ⁄ 3 100 = -------------------------- + --------- = $6.00 2 100 The time for replacing a worn edge of the facing insert =TRPL = 2.24 minutes. Assuming an hourly rate HR = $50/hour, calculate the equivalent tooling-cost time TV TV = TRPL + 60 × CE/HR =2.24 +60 × 6/50 = 9.44 minutes 3) Determine economic tool-life TE TE = TV × (1/n − 1) = 9.44 × (1/ 0.35 − 1) = 17.5 minutes 4) Determine economic cutting speed using the Handbook tables using the method shown in Example 10, V E = C ⁄ TEn m/min = 280 / 17.50.35 = 103 m/min




5) Determine cost of tooling per batch (cutting tools, holders and tool changing) then total cost of cutting per batch: CTOOL = HR × TC × (CE/T)/60 (CTOOL+CCH) = HR × TC × ((TRPL+CE/T)/60 CTOT = HR × TC (1 + (TRPL+CE)/T) Example 12, Face Milling – Minimum Cost : This example demonstrates how a modern firm, using the formulas previously described, can determine optimal data. It is here applied to a face mill with 10 teeth, milling a 1045 type steel, and the radial depth versus the cutter diameter is 0.8. The V–ECT–T curves for tool-lives 5, 22, and 120 minutes for this operation are shown in Fig. 23a. LIVE GRAPH Click here to view

1000

V, m/min

G-CURVE

100

T=5

T = 22

T = 120 10 0.1

1

10

ECT, mm

Fig. 23a. Cutting speed vs. ECT, tool-life constant

The global cost minimum occurs along the G-curve, see Fig. 6c and Fig. 23a, where the 45-degree lines defines this curve. Optimum ECT is in the range 1.5 to 2 mm. For face and end milling operations, ECT = z × fz × ar/D × aa/CEL ÷ π. The ratio aa/CEL = 0.95 for lead angle LA = 0, and for ar/D = 0.8 and 10 teeth, using the formula to calculate the feed/tooth range gives for ECT = 1.5, fz = 0.62 mm and for ECT = 2, fz = 0.83 mm. LIVE GRAPH Click here to view

0.6

T=5 T = 22 T = 120

0.5

0.4

tc

0.3

0.2 0.1

0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fz

Fig. 23b. Cutting time per part vs. feed per tooth

Using computer simulation, the minimum cost occurs approximately where Fig. 23a indicates it should be. Total cost has a global minimum at fz around 0.6 to 0.7 mm and a speed of around 110 m/min. ECT is about 1.9 mm and the optimal cutter life is TO = 22 minutes. Because it may be impossible to reach the optimum feed value due to tool breakage,



1121

the maximum practical feed fmax is used as the optimal value. The difference in costs between a global optimum and a practical minimum cost condition is negligible, as shown in Figs. 23c and 23e. A summary of the results are shown in Figs. 23a through 23e, and Table 1. 0.31 T = 120 T = 22

0.26

T=5

CTOT, $

0.21

0.16

0.11

0.06

0.01 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fz, mm

Fig. 23c. Total cost vs. feed/tooth

When plotting cutting time/part, tc, versus feed/tooth, fz, at T = 5, 22, 120 in Figs. 23b, tool-life T = 5 minutes yields the shortest cutting time, but total cost is the highest; the minimum occurs for fz about 0.75 mm, see Figs. 23c. The minimum for T = 120 minutes is about 0.6 mm and for TO = 22 minutes around 0.7 mm. 0.1 T=5

0.09 T = 22

0.08 T =120

Unit Tooling Cost, $

0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

fz, mm

Fig. 23d. Tooling cost versus feed/tooth

Fig. 23d shows that tooling cost drop off quickly when increasing feed from 0.1 to 0.3 to 0.4 mm, and then diminishes slowly and is almost constant up to 0.7 to 0.8 mm/tooth. It is generally very high at the short tool-life 5 minutes, while tooling cost of optimal tool-life 22 minutes is about 3 times higher than when going slow at T =120 minutes.



MACHINING ECONOMETRICS 0.3

CTOT, $

0.25

0.2

0.15

0.1

0.05

T = 120 T = 22 T=5

0 0

50

100

150

200

250

300

350

400

450

500

V, m/min

Fig. 23e. Total cost vs. cutting speed at 3 constant tool-lives, feed varies

The total cost curves in Fig. 23e. were obtained by varying feed and cutting speed in order to maintain constant tool-lives at 5, 22 and 120 minutes. Cost is plotted as a function of speed V instead of feed/tooth. Approximate optimum speeds are V = 150 m/min at T = 5 minutes, V = 180 m/min at T = 120 minutes, and the global optimum speed is VO = 110 m/min for TO = 22 minutes. Table 1 displays the exact numerical values of cutting speed, tooling cost and total cost for the selected tool-lives of 5, 22, and 120 minutes, obtained from the software program. Table 1. Face Milling, Total and Tooling Cost versus ECT, Feed/tooth fz, and Cutting Speed V, at Tool-lives 5, 22, and 120 minutes T = 5 minutes

T = 22 minutes

T = 120 minutes

fz

ECT

V

CTOT

CTOOL

V

CTOT

CTOOL

V

CTOT

CTOOL

0.03

0.08

489

0.72891

0.39759

416

0.49650

0.10667

344

0.49378

0.02351

0.08

0.21

492

0.27196

0.14834

397

0.19489

0.04187

311

0.20534

0.00978

0.10

0.26

469

0.22834

0.12455

374

0.16553

0.03556

289

0.17674

0.00842

0.17

0.44

388

0.16218

0.08846

301

0.12084

0.02596

225

0.13316

0.00634

0.20

0.51

359

0.14911

0.08133

276

0.11204

0.02407

205

0.12466

0.00594

0.40

1.03

230

0.11622

0.06339

171

0.09051

0.01945

122

0.10495

0.00500

0.60

1.54

164

0.10904

0.05948

119

0.08672

0.01863

83

0.10301

0.00491

0.70

1.80

141

0.10802

0.05892

102

0.08665

0.01862

70

0.10393

0.00495

0.80

2.06

124

0.10800

0.05891

89

0.08723

0.01874

60

0.10547

0.00502

1.00

2.57

98

0.10968

0.05982

69

0.08957

0.01924

47

0.10967

0.00522

High-speed Machining Econometrics High-speed Machining – No Mystery.—This section describes the theory and gives the basic formulas for any milling operation and high-speed milling in particular, followed by several examples on high-speed milling econometrics. These rules constitute the basis on which selection of milling feed factors is done. Selection of cutting speeds for general milling is done using the Handbook Table 10 through 14, starting on page 1044. High-speed machining is no mystery to those having a good knowledge of metal cutting. Machining materials with very good machinability, such as low-alloyed aluminum, have for ages been performed at cutting speeds well below the speed values at which these materials should be cut. Operating at these low speeds often results in built-up edges and poor surface finish, because the operating conditions selected are on the wrong side of the Taylor curve, i.e. to the left of the H-curve representing maximum tool-life values (see Fig. 4 on page 1096).



1123

In the 1950’s it was discovered that cutting speed could be raised by a factor of 5 to 10 when hobbing steel with HSS cutters. This is another example of being on the wrong side of the Taylor curve. One of the first reports on high-speed end milling using high-speed steel (HSS) and carbide cutters for milling 6061-T651 and A356-T6 aluminum was reported in a study funded by Defense Advanced Research Project Agency (DARPA). Cutting speeds of up to 4400 m/min (14140 fpm) were used. Maximum tool-lives of 20 through 40 minutes were obtained when the feed/tooth was 0.2 through 0.25 mm (0.008 to 0.01 inch), or measured in terms of ECT around 0.07 to 0.09 mm. Lower or higher feed/tooth resulted in shorter cutter lives. The same types of previously described curves, namely T–ECT curves with maximum tool-life along the H-curve, were produced. When examining the influence of ECT, or feed/rev, or feed/tooth, it is found that too small values cause chipping, vibrations, and poor surface finish. This is caused by inadequate (too small) chip thickness, and as a result the material is not cut but plowed away or scratched, due to the fact that operating conditions are on the wrong (left) side of the toollife versus ECT curve (T-ECT with constant speed plotted). There is a great difference in the thickness of chips produced by a tooth traveling through the cutting arc in the milling process, depending on how the center of the cutter is placed in relation to the workpiece centerline, in the feed direction. Although end and face milling cut in the same way, from a geometry and kinematics standpoint they are in practice distinguished by the cutter center placement away from, or close to, the work centerline, respectively, because of the effect of cutter placement on chip thickness. This is the criteria used to distinguishing between the end and face milling processes in the following. Depth of Cut/Cutter Diameter, ar/D is the ratio of the radial depth of cut ar and the cutter diameter D. In face milling when the cutter axis points approximately to the middle of the work piece axis, eccentricity is close to zero, as illustrated in Figs. 3 and 4, page 1042, and Fig. 5 on page 1043. In end milling, ar/D = 1 for full slot milling. Mean Chip Thickness, hm is a key parameter that is used to calculate forces and power requirements in high-speed milling. If the mean chip thickness hm is too small, which may occur when feed/tooth is too small (this holds for all milling operations), or when ar/D decreases (this holds for ball nose as well as for straight end mills), then cutting occurs on the left (wrong side) of the tool-life versus ECT curve, as illustrated in Figs. 6b and 6c. In order to maintain a given chip thickness in end milling, the feed/tooth has to be increased, up to 10 times for very small ar/D values in an extreme case with no run out and otherwise perfect conditions. A 10 times increase in feed/tooth results in 10 times bigger feed rates (FR) compared to data for full slot milling (valid for ar/D = 1), yet maintain a given chip thickness. The cutter life at any given cutting speed will not be the same, however. Increasing the number of teeth from say 2 to 6 increases equivalent chip thickness ECT by a factor of 3 while the mean chip thickness hm remains the same, but does not increase the feed rate to 30 (3 × 10) times bigger, because the cutting speed must be reduced. However, when the ar/D ratio matches the number of teeth, such that one tooth enters when the second tooth leaves the cutting arc, then ECT = hm. Hence, ECT is proportional to the number of teeth. Under ideal conditions, an increase in number of teeth z from 2 to 6 increases the feed rate by, say, 20 times, maintaining tool-life at a reduced speed. In practice about 5 times greater feed rates can be expected for small ar/D ratios (0.01 to 0.02), and up to 10 times with 3 times as many teeth. So, high-speed end milling is no mystery. Chip Geometry in End and Face Milling.—Fig. 24 illustrates how the chip forming process develops differently in face and end milling, and how mean chip thickness hm varies with the angle of engagement AE, which depends on the ar/D ratio. The pertinent chip geometry formulas are given in the text that follows.



MACHINING ECONOMETRICS Face Milling

End Milling

AE

hmax

ar hmax ar

hm

hm

AE

fz ar ---⎞⎠ cos AE = 1 – 2 × ⎛⎝---D

fz 2 ar ---⎞⎠ cos AE = 1 – 2 × ⎛⎝---D

Fig. 24.

Comparison of face milling and end milling geometry High-speed end milling refers to values of ar/D that are less than 0.5, in particular to ar/D ratios which are considerably smaller. When ar/D = 0.5 (AE = 90 degrees) and diminishing in end milling, the chip thickness gets so small that poor cutting action develops, including plowing or scratching. This situation is remedied by increasing the feed/tooth, as shown in Table 2a as an increasing fz/fz0 ratio with decreasing ar/D. For end milling, the fz/fz0 feed ratio is 1.0 for ar/D = 1 and also for ar/D = 0.5. In order to maintain the same hm as at ar/D = 1, the feed/tooth should be increased, by a factor of 6.38 when ar/D is 0.01 and by more than 10 when ar/D is less than 0.01. Hence high-speed end milling could be said to begin when ar/D is less than 0.5 In end milling, the ratio fz/fz0 = 1 is set at ar/D = 1.0 (full slot), a common value in vendor catalogs and handbooks, for hm = 0.108 mm. The face milling chip making process is exactly the same as end milling when face milling the side of a work piece and ar/D = 0.5 or less. However, when face milling close to and along the work centerline (eccentricity is close to zero) chip making is quite different, as shown in Fig. 24. When ar/D = 0.74 (AE = 95 degrees) in face milling, the fz/fz0 ratio = 1 and increases up to 1.4 when the work width is equal to the cutter diameter (ar/D = 1). The face milling fz/fz0 ratio continues to diminish when the ar/D ratio decreases below ar/D = 0.74, but very insignificantly, only about 11 percent when ar/D = 0.01. In face milling fz/fz0 = 1 is set at ar/D = 0.74, a common value recommended in vendor catalogs and handbooks, for hm = 0.151 mm. Fig. 25 shows the variation of the feed/tooth-ratio in a graph for end and face milling. LIVE GRAPH Click here to view

6.5 6

fz/fz0 , Face Milling

5.5

fz/fz0 , End Milling

5 4.5

fz/fz0

4 3.5 3 2.5 2 1.5 1 0.5 0 0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

ar/D

Fig. 25. Feed/tooth versus ar/D for face and end milling



1125

Table 2a. Variation of Chip Thickness and fz/fz0 with ar/D Face Milling

End Milling (straight)

ecentricitye = 0 z =8 fz0 = 0.017 cosAE = 1 − 2 × (ar/D)2

z =2 fz0 = 0.017 cosAE = 1 − 2 × (ar/D)

ar/D

AE

hm/fz

hm

ECT/hm

fz/fz0

AE

hm/fz

hm

ECT/hm

fz/fz0

1.0000 0.9000 0.8000 0.7355 0.6137 0.5000 0.3930 0.2170 0.1250 0.0625 0.0300 0.0100 0.0010

180.000 128.316 106.260 94.702 75.715 60.000 46.282 25.066 14.361 7.167 3.438 1.146 0.115

0.637 0.804 0.863 0.890 0.929 0.162 0.973 0.992 0.997 0.999 1.000 1.000 1.000

0.108 0.137 0.147 0.151 0.158 0.932 0.165 0.169 0.170 0.170 0.170 0.170 0.000

5.000 3.564 2.952 2.631 1.683 0.216 1.028 0.557 0.319 0.159 0.076 0.025 0.000

1.398 1.107 1.032 1.000 0.958 0.202 0.915 0.897 0.892 0.891 0.890 0.890 0.890

180.000 143.130 126.870 118.102 103.144 90.000 77.643 55.528 41.410 28.955 19.948 11.478 3.624

0.637 0.721 0.723 0.714 0.682 0.674 0.580 0.448 0.346 0.247 0.172 0.100 0.000

0.108 0.122 0.123 0.122 0.116 0.115 0.099 0.076 0.059 0.042 0.029 0.017 0.000

1.000 0.795 0.711 0.667 0.573 0.558 0.431 0.308 0.230 0.161 0.111 0.064 0.000

1.000 0.884 0.881 0.892 0.934 1.000 1.098 1.422 1.840 2.574 3.694 6.377 20.135

In Table 2a, a standard value fz0 = 0.17 mm/tooth (commonly recommended average feed) was used, but the fz/fz0 values are independent of the value of feed/tooth, and the previously mentioned relationships are valid whether fz0 = 0.17 or any other value. In both end and face milling, hm = 0.108 mm for fz0 = 0.17mm when ar/D =1. When the fz/fz0 ratio = 1, hm = 0.15 for face milling, and 0.108 in end milling both at ar/D = 1 and 0.5. The tabulated data hold for perfect milling conditions, such as, zero run-out and accurate sharpening of all teeth and edges. Mean Chip Thickness hm and Equivalent Chip Thickness ECT.—The basic formula for equivalent chip thickness ECT for any milling process is: ECT = fz × z/π × (ar/D) × aa/CEL, where fz = feed/tooth, z = number of teeth, D = cutter diameter, ar = radial depth of cut, aa = axial depth of cut, and CEL = cutting edge length. As a function of mean chip thickness hm: ECT = hm × (z/2) × (AE/180), where AE = angle of engagement. Both terms are exactly equal when one tooth engages as soon as the preceding tooth leaves the cutting section. Mathematically, hm = ECT when z = 360/AE; thus: for face milling, AE = arccos (1 – 2 × (ar/D)2) for end milling, AE = arccos (1 – 2 × (ar/D)) Calculation of Equivalent Chip Thickness (ECT) versus Feed/tooth and Number of teeth.: Table 2b is a continuation of Table 2a, showing the values of ECT for face and end milling for decreasing values ar/D, and the resulting ECT when multiplied by the fz/fz0 ratio fz0 = 0.17 (based on hm = 0.108). Small ar/D ratios produce too small mean chip thickness for cutting chips. In practice, minimum values of hm are approximately 0.02 through 0.04 mm for both end and face milling. Formulas.— Equivalent chip thickness can be calculated for other values of fz and z by means of the following formulas: Face milling: ECTF = ECT0F × (z/8) × (fz/0.17) × (aa/CEL) or, if ECTF is known calculate fz using: fz = 0.17 × (ECTF/ECT0F) × (8/z) × (CEL/aa)



MACHINING ECONOMETRICS Table 2b. Variation of ECT, Chip Thickness and fz/fz0 with ar/D Face Milling

ar/D 1.0000 0.9000 0.8080 0.7360 0.6137 0.5900 0.5000 0.2170 0.1250 0.0625 0.0300 0.0100 0.0010

hm 0.108 0.137 0.146 0.151 0.158 0.159 0.162 0.169 0.170 0.170 0.170 0.170 0.170

fz/fz0 1.398 1.107 1.036 1.000 0.958 0.952 0.932 0.897 0.892 0.891 0.890 0.890 0.890

ECT 0.411 0.370 0.332 0.303 0.252 0.243 0.206 0.089 0.051 0.026 0.012 0.004 0.002

End Milling (straight) ECT0 corrected for fz/fz0 0.575 0.410 0.344 0.303 0.242 0.231 0.192 0.080 0.046 0.023 0.011 0.004 0.002

hm 0.108 0.122 0.123 0.121 0.116 0.115 0.108 0.076 0.059 0.042 0.029 0.017 0.005

fz/fz0 1.000 0.884 0.880 0.892 0.934 0.945 1.000 1.422 1.840 2.574 3.694 6.377 20.135

ECT 0.103 0.093 0.083 0.076 0.063 0.061 0.051 0.022 0.013 0.006 0.003 0.001 0.001

ECT0 corrected for fz/fz0 0.103 0.082 0.073 0.067 0.059 0.057 0.051 0.032 0.024 0.017 0.011 0.007 0.005

In face milling, the approximate values of aa/CEL = 0.95 for lead angle LA = 0° (90° in the metric system); for other values of LA, aa/CEL = 0.95 × sin (LA), and 0.95 × cos (LA) in the metric system. Example, Face Milling: For a cutter with D = 250 mm and ar = 125 mm, calculate ECTF for fz = 0.1, z = 12, and LA = 30 degrees. First calculate ar/D = 0.5, and then use Table 2b and find ECT0F = 0.2. Calculate ECTF with above formula: ECTF = 0.2 × (12/8) × (0.1/0.17) × 0.95 × sin 30 = 0.084 mm. End milling: ECTE = ECT0E × (z/2) × (fz/0.17) × (aa/CEL), or if ECTE is known calculate fz from: fz = 0.17 × (ECTE/ECT0E) × (2/z)) × (CEL/aa) The approximate values of aa/CEL = 0.95 for lead angle LA = 0° (90° in the metric system). Example, High-speed End Milling:For a cutter with D = 25 mm and ar = 3.125 mm, calculate ECTE for fz = 0.1 and z = 6. First calculate ar/D = 0.125, and then use Table 2b and find ECT0E = 0.0249. Calculate ECTE with above formula: ECTE = 0.0249 × (6/2) × (0.1/0.17) × 0.95 × 1 = 0.042 mm. Example, High-speed End Milling: For a cutter with D = 25 mm and ar = 0.75 mm, calculate ECTE for fz = 0.17 and z = 2 and 6. First calculate ar/D = 0.03, and then use Table 2b and find fz/fz0 = 3.694 Then, fz = 3.694 × 0.17 = 0.58 mm/tooth and ECTE = 0.0119 × 0.95 = 0.0113 mm and 0.0357 × 0.95 = 0.0339 mm for 2 and 6 teeth respectively. These cutters are marked HS2 and HS6 in Figs. 26a, 26d, and 26e. Example, High-speed End Milling: For a cutter with D = 25 mm and ar = 0.25 mm, calculate ECTE for fz = 0.17 and z = 2 and 6. First calculate ar/D = 0.01, and then use Table 2b and find ECT0E = 0.0069 and 0.0207 for 2 and 6 teeth respectively. When obtaining such small values of ECT, there is a great danger to be far on the left side of the H-curve, at least when there are only 2 teeth. Doubling the feed would be the solution if cutter design and material permit. Example, Full Slot Milling:For a cutter with D = 25 mm and ar = 25 mm, calculate ECTE for fz = 0.17 and z = 2 and 6. First calculate ar/D =1, and then use Table 2b and find ECTE =



1127

0.108 × 0.95 = 0.103 and 3 × 0.108 × 0.95 = 0.308 for 2 and 6 teeth, respectively. These cutters are marked SL2 and SL6 in Figs. 26a, 26d, and 26e. Physics behind hm and ECT, Forces and Tool-life (T).—The ECT concept for all metal cutting and grinding operations says that the more energy put into the process, by increasing feed/rev, feed/tooth, or cutting speed, the life of the edge decreases. When increasing the number of teeth (keeping everything else constant) the work and the process are subjected to a higher energy input resulting in a higher rate of tool wear. In high-speed milling when the angle of engagement AE is small the contact time is shorter compared to slot milling (ar/D = 1) but the chip becomes shorter as well. Maintaining the same chip thickness as in slot milling has the effect that the energy consumption to remove the chip will be different. Hence, maintaining a constant chip thickness is a good measure when calculating cutting forces (keeping speed constant), but not when determining tool wear. Depending on cutting conditions the wear rate can either increase or decrease, this depends on whether cutting occurs on the left or right side of the H-curve. Fig. 26a shows an example of end milling of steel with coated carbide inserts, where cutting speed V is plotted versus ECT at 5, 15, 45 and 180 minutes tool-lives. Notice that the ECT values are independent of ar/D or number of teeth or feed/tooth, or whether fz or fz0 is used, as long as the corresponding fz/fz0-ratio is applied to determine ECTE. The result is one single curve per tool-life. Had cutting speed been plotted versus fz0, ar/D, or z values (number of teeth), several curves would be required at each constant tool-life, one for each of these parameters This illustrates the advantage of using the basic parameter ECT rather than fz, or hm, or ar/D on the horizontal axis. LIVE GRAPH Click here to view

1000

V, m/min

T=5 T=15 T=45 T=180

H-CURVE G-CURVE

HS 6

SL 2 HS 2 SL 6

100 0.001

0.01

0.1

1

ECT, mm

Fig. 26a. Cutting speed vs. ECT, tool-life plotted, for end milling

Example: The points (HS2, HS6) and (SL2, SL6) on the 45-minute curve in Fig. 26a relate to the previous high-speed and full slot milling examples for 2 and 6 teeth, respectively. Running a slot at fz0 = 0.17 mm/tooth (hm = 0.108, ECTE = 0.103 mm) with 2 teeth and for a tool-life 45 minutes, the cutting speed should be selected at V = 340 m/min at point SL2 and for six teeth (hm = 0.108 mm, ECTE = 0.308) at V = 240 m/min at point SL6. When high-speed milling for ar/D = 0.03 at fz = 3.394 × 0.17 = 0.58 mm/tooth = 0.58 mm/tooth, ECT is reduced to 0.011 mm (hm = 0.108) the cutting speed is 290 m/min to maintain T = 45 minutes, point HS2. This point is far to the left of the H-curve in Fig.26b, but if the number of teeth is increased to 6 (ECTE = 3 × 0.103 = 0.3090), the cutting speed is 360 m/min at T = 45 minutes and is close to the H-curve, point HS6. Slotting data using 6 teeth are on the right of this curve at point SL6, approaching the G-curve, but at a lower slotting speed of 240 m/min.




Depending on the starting fz value and on the combination of cutter grade - work material, the location of the H-curve plays an important role when selecting high-speed end milling data. Feed Rate and Tool-life in High-speed Milling, Effect of ECT and Number of Teeth.—Calculation of feed rate is done using the formulas in previously given: Feed Rate: FR = z × fz × rpm, where z × fz = f (feed/rev of cutter). Feed is measured along the feeding direction. rpm = 1000 × V/3.1416/D, where D is diameter of cutter. LIVE GRAPH

LIVE GRAPH

Click here to view

10000

Click here to view

10000

T=5 T = 15 T = 45 T = 180

FR, mm/min

FR, mm/min

T=5 T = 15 T = 45 T = 180

1000 1000

100

V, m/min

V, m/min

H-CURVE

T=5 T = 15 T = 45 T= 180 0.01

T=5 T = 15 T = 45 T = 180

100 0.01

0.1

ar/D

Fig. 26b. High speed feed rate and cutting speed versus ar/D at T = 5, 15, 45, and 180 minutes

0.1

ECT, mm

1

Fig. 26c. High speed feed rate and cutting speed versus ECT, ar/D plotted at T = 5, 15, 45, and 180 minutes

Fig. 26b shows the variation of feed rate FR plotted versus ar/D for tool-lives 5, 15, 45 and 180 minutes with a 25 mm diameter cutter and 2 teeth. Fig. 26c shows the variation of feed rate FR when plotted versus ECT. In both graphs the corresponding cutting speeds are also plotted. The values for ar/D = 0.03 in Fig. 26b correspond to ECT = 0.011 in Fig. 26c. Feed rates have minimum around values of ar/D = 0.8 and ECT=0.75 and not along the H-curve. This is due to the fact that the fz/fz0 ratio to maintain a mean chip thickness = 0.108 mm changes FR in a different proportion than the cutting speed. LIVE GRAPH Click here to view

100000 T = 45, SL

T = 45 T = 45, HS

H-CURVE

FR , mm/min.

HS6 HS4 10000 HS2 SL6 SL4 SL2 1000 0.01

0.1

1

ECT, mm

Fig. 26d. Feed rate versus ECT comparison of slot milling (ar/D = 1) and high-speed milling at (ar/D = 0.03) for 2, 4, and 6 teeth at T = 45 minutes



1129

A comparison of feed rates for full slot (ar/D = 1) and high-speed end milling (ar/D = 0.03 and fz = 3.69 × fz0 = 0.628 mm) for tool-life 45 minutes is shown in Fig. 26d. The points SL2, SL4, SL6 and HS2, HS4, HS6, refer to 2, 4, and 6 teeth (2 to 6 teeth are commonly used in practice). Feed rate is also plotted versus number of teeth z in Fig. 26e, for up to 16 teeth, still at fz = 0.628 mm. Comparing the effect of using 2 versus 6 teeth in high-speed milling shows that feed rates increase from 5250 mm/min (413 ipm) up to 18000 mm/min (1417ipm) at 45 minutes toollife. The effect of using 2 versus 6 teeth in full slot milling is that feed rate increases from 1480 mm/min (58 ipm) up to 3230 mm/min (127 ipm) at tool-life 45 minutes. If 16 teeth could be used at ar/D = 0.03, the feed rate increases to FR = 44700 mm/min (1760 ipm), and for full slot milling FR = 5350 mm/min (210 ipm). LIVE GRAPH Click here to view

FR , mm/min.

100000

HS6 HS4 10000 HS2

SL6 SL4

T = 45, SL

SL2

T = 45, HS

1000 0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15 16 17

Number teeth

Fig. 26e. Feed rate versus number of teeth comparison of slot milling (ar/D = 1) and high-speed milling at (ar/D = 0.03) for 2, 4, and 6 teeth at T = 45 minutes

Comparing the feed rates that can be obtained in steel cutting with the one achieved in the earlier referred DARPA investigation, using HSS and carbide cutters milling 6061-T651 and A356-T6 aluminum, it is obvious that aluminium end milling can be run at 3 to 6 times higher feed rates. This requires 3 to 6 times higher spindle speeds (cutter diameter 25 mm, radial depth of cut ar = 12.5 mm, 2 teeth). Had these tests been run with 6 teeth, the feed rates would increase up to 150000-300000 mm/min, when feed/tooth = 3.4 × 0.25 = 0.8 mm/tooth at ar/D = 0.03. Process Econometrics Comparison of High-speed and Slot End Milling .—W h e n making a process econometrics comparison of high-speed milling and slot end milling use the formulas for total cost ctot (Determination Of Machine Settings And Calculation Of Costs starting on page 1113). Total cost is the sum of the cost of cutting, tool changing, and tooling: ctot= HR × (Dist/FR) × (1 + TV/T)/60 where TV =TRPL + 60 × CE/HR = equivalent tooling-cost time, minutes TRPL = replacement time for a set of edges or tool for regrinding CE =cost per edge(s) HR =hourly rate, $




Fig. 27. compares total cost ctot, using the end milling cutters of the previous examples, for full slot milling with high-speed milling at ar/D =0.03, and versus ECT at T =45 minutes. 1 H-CURVE

minutes 2,4,6 teeth marked SL2 SL4 SL6

ctot , $

HS2 0.1 HS4 T = 45, z = 4, SL

HS6

T = 45, z = 6, SL T = 45, z = 2, HS T = 45, z = 4, H T = 45, z = 6, HS 0.01 0.01

0.1

1

ECT, mm

Fig. 27. Cost comparison of slot milling (ar/D = 1) and high-speed milling at (ar/D = 0.03) for 2, 4, and 6 teeth at T = 45 minutes

The feed/tooth for slot milling is fz0 = 0.17 and for high-speed milling at ar/D = 0.03 the feed is fz = 3.69 × fz0 = 0.628 mm. The calculations for total cost are done according to above formula using tooling cost at TV = 6, 10, and 14 minutes, for z = 2, 4, and 6 teeth respectively. The distance cut is Dist = 1000 mm. Full slot milling costs are, at feed rate FR = 3230 and z = 6 ctot = 50 × (1000/3230) × (1 + 14/45)/60 = $0.338 per part at feed rate FR =1480 and z = 2 ctot = 50 × (1000/1480) × (1 + 6/45)/60 = $0.638 per part High-speed milling costs, at FR=18000, z = 6 ctot = 50 × (1000/18000) × (1 + 14/45)/60 = $0.0606 per part at FR= 5250, z = 2 ctot = 50 × (1000/5250) × (1 + 6/45)/60 = $0.180 per part The cost reduction using high-speed milling compared to slotting is enormous. For highspeed milling with 2 teeth, the cost for high-speed milling with 2 teeth is 61 percent (0.208/0.338) of full slot milling with 6 teeth (z = 6). The cost for high-speed milling with 6 teeth is 19 percent (0.0638/0.338) of full slot for z = 6. Aluminium end milling can be run at 3 to 6 times lower costs than when cutting steel. Costs of idle (non-machining) and slack time (waste) are not considered in the example. These data hold for perfect milling conditions such as zero run-out and accurate sharpening of all teeth and edges.


Machinery's Handbook 27th Edition SCREW MACHINE SPEEDS AND FEEDS

1131

SCREW MACHINE FEEDS AND SPEEDS Feeds and Speeds for Automatic Screw Machine Tools.—Approximate feeds and speeds for standard screw machine tools are given in the accompanying table. Knurling in Automatic Screw Machines.—When knurling is done from the cross slide, it is good practice to feed the knurl gradually to the center of the work, starting to feed when the knurl touches the work and then passing off the center of the work with a quick rise of the cam. The knurl should also dwell for a certain number of revolutions, depending on the pitch of the knurl and the kind of material being knurled. See also KNURLS AND KNURLING starting on page 1240. When two knurls are employed for spiral and diamond knurling from the turret, the knurls can be operated at a higher rate of feed for producing a spiral than they can for producing a diamond pattern. The reason for this is that in the first case the knurls work in the same groove, whereas in the latter case they work independently of each other. Revolutions Required for Top Knurling.—The depth of the teeth and the feed per revolution govern the number of revolutions required for top knurling from the cross slide. If R is the radius of the stock, d is the depth of the teeth, c is the distance the knurl travels from the point of contact to the center of the work at the feed required for knurling, and r is the radius of the knurl; then c =

2

(R + r) – (R + r – d)

2

For example, if the stock radius R is 5⁄32 inch, depth of teeth d is 0.0156 inch, and radius of knurl r is 0.3125 inch, then 2

c = ( 0.1562 + 0.3125 ) – ( 0.1562 + 0.3125 – 0.0156 ) = 0.120 inch = cam rise required

2

Assume that it is required to find the number of revolutions to knurl a piece of brass 5⁄16 inch in diameter using a 32 pitch knurl. The included angle of the teeth for brass is 90 degrees, the circular pitch is 0.03125 inch, and the calculated tooth depth is 0.0156 inch. The distance c (as determined in the previous example) is 0.120 inch. Referring to the accompanying table of feeds and speeds, the feed for top knurling brass is 0.005 inch per revolution. The number of revolutions required for knurling is, therefore, 0.120 ÷ 0.005 = 24 revolutions. If conditions permit, the higher feed of 0.008 inch per revolution given in the table may be used, and 15 revolutions are then required for knurling. Cams for Threading.—The table Spindle Revolutions and Cam Rise for Threading on page 1134 gives the revolutions required for threading various lengths and pitches and the corresponding rise for the cam lobe. To illustrate the use of this table, suppose a set of cams is required for threading a screw to the length of 3⁄8 inch in a Brown & Sharpe machine. Assume that the spindle speed is 2400 revolutions per minute; the number of revolutions to complete one piece, 400; time required to make one piece, 10 seconds; pitch of the thread, 1⁄ inch or 32 threads per inch. By referring to the table, under 32 threads per inch, and 32 opposite 3⁄8 inch (length of threaded part), the number of revolutions required is found to be 15 and the rise required for the cam, 0.413 inch.



Cut

Tool Boring tools

Finishing Center drills Angular Circular Straight 1 Stock diameter under ⁄8 in. Button Dies { Chaser

Cutoff tools {

Drills, twist cut

Form tools, circular

{

Dia. of Hole, Inches … … … … … … … Under 1⁄8 Over 1⁄8 … … … … … … 0.02 0.04 1⁄ 16 3⁄ 32 1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ –5⁄ 8 8 … … … … … … …

Brassa Feed, Inches per Rev. … 0.012 0.010 0.008 0.008 0.006 0.010 0.003 0.006 0.0015 0.0035 0.0035 0.002 … … 0.0014 0.002 0.004 0.006 0.009 0.012 0.014 0.016 0.016 0.002 0.002 0.0015 0.0012 0.001 0.001 0.001

Feed, Inches per Rev. 0.008 0.010 0.008 0.007 0.006 0.005 0.010 0.0015 0.0035 0.0006 0.0015 0.0015 0.0008 … … 0.001 0.0014 0.002 0.0025 0.0035 0.004 0.005 0.005 0.006 0.0009 0.0008 0.0007 0.0006 0.0005 0.0005 0.0004

Material to be Machined Mild or Soft Steel Tool Steel, 0.80–1.00% C Surface Speed, Feet per Min. Surface Speed, Feet per Min. Feed, Carbon H.S.S. Carbon H.S.S. Inches Tools Tools Tools Tools per Rev. 50 110 0.004 30 60 70 150 0.005 40 75 70 150 0.004 40 75 70 150 0.003 40 75 70 150 0.002 40 75 70 150 0.0015 40 75 70 150 0.006 40 75 50 110 0.001 30 75 50 110 0.002 30 75 80 150 0.0004 50 85 80 150 0.001 50 85 80 150 0.001 50 85 80 150 0.0005 50 85 30 … … 14 … 30 40 … 16 20 40 60 0.0006 30 45 40 60 0.0008 30 45 40 60 0.0012 30 45 40 60 0.0016 30 45 40 75 0.002 30 60 40 75 0.003 30 60 40 75 0.003 30 60 40 75 0.0035 30 60 40 85 0.004 30 60 80 150 0.0006 50 85 80 150 0.0005 50 85 80 150 0.0004 50 85 80 150 0.0004 50 85 80 150 0.0003 50 85 80 150 0.0003 50 85 80 150 … … …


SCREW MACHINE SPEEDS AND FEEDS

Box tools, roller rest Single chip finishing

Width or Depth, Inches 0.005 1⁄ 32 1⁄ 16 1⁄ 8 3⁄ 16 1⁄ 4 0.005 … … … 3⁄ –1⁄ 64 8 1⁄ –1⁄ 16 8 … … … … … … … … … … … … 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 1

1132

Approximate Cutting Speeds and Feeds for Standard Automatic Screw Machine Tools—Brown and Sharpe


Approximate Cutting Speeds and Feeds for Standard Automatic Screw Machine Tools—Brown and Sharpe (Continued) Cut

Tool Turned diam. under 5⁄32 in. {

Turned diam. over 5⁄32 in.

{

Turret

{

Knee tools

Knurling tools {

Side or swing

{

Top

{

End cut

{

Pointing and facing tools Reamers and bits

Recessing tools { Inside cut

Swing tools, forming

Turning, straight and taperb Taps

1⁄ –1⁄ 16 8 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 1⁄ 32 1⁄ 16 1⁄ 8 3⁄ 16

…

Dia. of Hole, Inches … … … … … … … … … … … … … … … … 1⁄ or less 8 1⁄ or over 8 … … … … … … … … … … … … …

Brassa

{ {

Feed, Inches per Rev. 0.012 0.010 0.017 0.015 0.012 0.010 0.009 … 0.020 0.040 0.004 0.006 0.005 0.008 0.001 0.0025 0.010 – 0.007 0.010 0.001 0.005 0.0025 0.0008 0.002 0.0012 0.001 0.0008 0.008 0.006 0.005 0.004 …

Feed, Inches per Rev. 0.010 0.009 0.014 0.012 0.010 0.008 0.007 0.010 0.015 0.030 0.002 0.004 0.003 0.006 0.0008 0.002 0.008 – 0.006 0.010 0.0006 0.003 0.002 0.0006 0.0007 0.0005 0.0004 0.0003 0.006 0.004 0.003 0.0025 …

Material to be Machined Mild or Soft Steel Tool Steel, 0.80–1.00% C Surface Speed, Feet per Min. Surface Speed, Feet per Min. Feed, Carbon H.S.S. Carbon H.S.S. Inches Tools Tools Tools Tools per Rev. 70 150 0.008 40 85 70 150 0.006 40 85 70 150 0.010 40 85 70 150 0.008 40 85 70 150 0.008 40 85 70 150 0.006 40 85 70 150 0.0045 40 85 70 150 0.008 40 85 150 … 0.010 105 … 150 … 0.025 105 … 150 … 0.002 105 … 150 … 0.003 105 … 150 … 0.002 105 … 150 … 0.004 105 … 70 150 0.0005 40 80 70 150 0.0008 40 80 70 105 0.006 – 0.004 40 60 70 105 0.006 – 0.008 40 60 70 150 0.0004 40 75 70 150 0.002 40 75 70 105 0.0015 40 60 70 105 0.0004 40 60 70 150 0.0005 40 85 70 150 0.0003 40 85 70 150 0.0002 40 85 70 150 0.0002 40 85 70 150 0.0035 40 85 70 150 0.003 40 85 70 150 0.002 40 85 70 150 0.0015 40 85 25 30 … 12 15

b For taper turning use feed slow enough for greatest depth depth of cut.


1133

a Use maximum spindle speed on machine.

SCREW MACHINE SPEEDS AND FEEDS

Hollow mills and balance turning tools {

Width or Depth, Inches 1⁄ 32 1⁄ 16 1⁄ 32 1⁄ 16 1⁄ 8 3⁄ 16 1⁄ 4 1⁄ 32 On Off … … … … … … 0.003 – 0.004 0.004 – 0.008 … …


1134

Spindle Revolutions and Cam Rise for Threading Number of Threads per Inch Length of Threaded Portion, Inch

1⁄ 8

3⁄ 16

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

9⁄ 16

5⁄ 8

11⁄ 16

3⁄ 4

72

64

56

48

40

36

32

30

28

24

20

18

16

9.50

9.00

8.50

8.00

6.00

5.50

5.50

5.00

5.00

5.00

3.00

…

…

…

0.107

0.113

0.120

0.129

0.110

0.121

0.134

0.138

0.147

0.157

0.106

…

…

…

9.00

8.00

7.00

7.00

7.00

6.50

4.50

14

First Line: Revolutions of Spindle for Threading. Second Line: Rise on Cam for Threading, Inch

14.50 0.163 19.50 0.219 24.50 0.276 29.50 0.332 34.50 0.388 39.50 0.444 44.50 0.501 49.50 0.559 54.50 0.613 59.50 0.679 64.50 0.726

13.50 0.169 18.00 0.225 23.508 0.294 27.00 0.338 31.50 0.394 36.00 0.450 40.50 0.506 45.00 0.563 49.50 0.619 54.00 0.675 58.50 0.731

12.50 0.176 16.50 0.232 20.50 0.288 24.50 0.345 28.50 0.401 32.50 0.457 36.50 0.513 40.50 0.570 44.50 0.626 48.50 0.682 52.50 0.738

11.50 0.185 15.00 0.241 18.50 0.297 22.00 0.354 25.50 0.410 29.00 0.466 32.50 0.522 36.00 0.579 39.50 0.635 43.00 0.691 46.50 0.747

0.165 12.00 0.220 15.00 0.275 18.00 0.340 21.00 0.385 24.00 0.440 27.00 0.495 30.00 0.550 33.00 0.605 36.00 0.660 39.00 0.715

0.176 10.50 0.231 13.00 0.286 15.50 0.341 18.00 0.396 20.50 0.451 23.00 0.506 25.50 0.561 28.00 0.616 30.50 0.671 33.00 0.726

0.171 10.00 0.244 12.00 0.293 14.50 0.354 16.50 0.403 19.00 0.464 21.00 0.513 23.50 0.574 25.50 0.623 28.00 0.684 30.00 0.733

4.00

3.50

3.50

0.193

0.205

0.204

0.159

0.170

0.165

0.186

9.00

8.50

8.50

6.00

5.50

5.00

4.50

0.248 11.00 0.303 13.00 0.358 15.00 0.413 17.00 0.468 19.00 0.523 21.00 0.578 23.00 0.633 25.00 0.688 27.00 0.743

0.249 10.50 0.308 12.50 0.367 14.50 0.425 16.00 0.469 18.00 0.528 20.00 0.587 22.00 0.645 23.50 0.689 25.50 0.748

0.267 10.00 0.314 12.00 0.377 13.50 0.424 15.50 0.487 17.00 0.534 19.00 0.597 20.50 0.644 22.50 0.707 24.00 0.754


… … … … 4.00

0.213

0.234

0.236

0.239

0.243

7.50

6.50

6.00

5.50

5.00

0.266

0.276

0.283

0.292

0.304

9.00

8.00

7.00

6.50

6.00

0.319 10.50 0.372 12.00 0.425 13.50 0.478 15.00 0.531 16.50 0.584 18.00 0.638 19.50 0.691

0.340

0.330

0.345

0.364

9.00

8.50

7.50

7.00

0.383 10.50 0.446 11.50 0.489 13.00 0.553 14.00 0.595 15.50 0.659 16.50 0.701

0.401

0.398

0.425

9.50

8.50

7.50

0.448 10.50 0.496 11.50 0.543 13.00 0.614 14.00 0.661 15.00 0.708

0.451

0.455

9.50

8.50

0.504 10.50 0.558 11.50 0.611 12.50 0.664 13.50 0.717

0.516 9.50 0.577 10.50 0.637 11.00 0.668 12.00 0.728

CAMS THREADING ON SCREW MACHINES

1⁄ 16

80

Machinery's Handbook 27th Edition SCREW MACHINE CAM AND TOOL DESIGN

1135

Threading cams are often cut on a circular milling attachment. When this method is employed, the number of minutes the attachment should be revolved for each 0.001 inch rise, is first determined. As 15 spindle revolutions are required for threading and 400 for completing one piece, that part of the cam surface required for the actual threading operation equals 15 ÷ 400 = 0.0375, which is equivalent to 810 minutes of the circumference. The total rise, through an arc of 810 minutes is 0.413 inch, so the number of minutes for each 0.001 inch rise equals 810 ÷ 413 = 1.96 or, approximately, two minutes. If the attachment is graduated to read to five minutes, the cam will be fed laterally 0.0025 inch each time it is turned through five minutes of arc. Practical Points on Cam and Tool Design.—The following general rules are given to aid in designing cams and special tools for automatic screw machines, and apply particularly to Brown and Sharpe machines: 1) Use the highest speeds recommended for the material used that the various tools will stand. 2) Use the arrangement of circular tools best suited for the class of work. 3) Decide on the quickest and best method of arranging the operations before designing the cams. 4) Do not use turret tools for forming when the cross-slide tools can be used to better advantage. 5) Make the shoulder on the circular cutoff tool large enough so that the clamping screw will grip firmly. 6) Do not use too narrow a cutoff blade. 7) Allow 0.005 to 0.010 inch for the circular tools to approach the work and 0.003 to 0.005 inch for the cutoff tool to pass the center. 8) When cutting off work, the feed of the cutoff tool should be decreased near the end of the cut where the piece breaks off. 9) When a thread is cut up to a shoulder, the piece should be grooved or necked to make allowance for the lead on the die. An extra projection on the forming tool and an extra amount of rise on the cam will be needed. 10) Allow sufficient clearance for tools to pass one another. 11) Always make a diagram of the cross-slide tools in position on the work when difficult operations are to be performed; do the same for the tools held in the turret. 12) Do not drill a hole the depth of which is more than 3 times the diameter of the drill, but rather use two or more drills as required. If there are not enough turret positions for the extra drills needed, make provision for withdrawing the drill clear of the hole and then advancing it into the hole again. 13) Do not run drills at low speeds. Feeds and speeds recommended in the table starting on page 1132 should be followed as far as is practicable. 14) When the turret tools operate farther in than the face of the chuck, see that they will clear the chuck when the turret is revolved. 15) See that the bodies of all turret tools will clear the side of the chute when the turret is revolved. 16) Use a balance turning tool or a hollow mill for roughing cuts. 17) The rise on the thread lobe should be reduced so that the spindle will reverse when the tap or die holder is drawn out. 18) When bringing another tool into position after a threading operation, allow clearance before revolving the turret. 19) Make provision to revolve the turret rapidly, especially when pieces are being made in from three to five seconds and when only a few tools are used in the turret. It is sometimes desirable to use two sets of tools. 20) When using a belt-shifting attachment for threading, clearance should be allowed, as it requires extra time to shift the belt.



SCREW MACHINE

21) When laying out a set of cams for operating on a piece that requires to be slotted, cross-drilled or burred, allowance should be made on the lead cam so that the transferring arm can descend and ascend to and from the work without coming in contact with any of the turret tools. 22) Always provide a vacant hole in the turret when it is necessary to use the transferring arm. 23) When designing special tools allow as much clearance as possible. Do not make them so that they will just clear each other, as a slight inaccuracy in the dimensions will often cause trouble. 24) When designing special tools having intricate movements, avoid springs as much as possible, and use positive actions. Stock for Screw Machine Products.—The amount of stock required for the production of 1000 pieces on the automatic screw machine can be obtained directly from the table Stock Required for Screw Machine Products. To use this table, add to the length of the work the width of the cut-off tool blade; then the number of feet of material required for 1000 pieces can be found opposite the figure thus obtained, in the column headed “Feet per 1000 Parts.” Screw machine stock usually comes in bars 10 feet long, and in compiling this table an allowance was made for chucking on each bar. The table can be extended by using the following formula, in which F =number of feet required for 1000 pieces L =length of piece in inches W =width of cut-off tool blade in inches F = ( L + W ) × 84 The amount to add to the length of the work, or the width of the cut-off tool, is given in the following, which is standard in a number of machine shops: Diameter of Stock, Inches Width of Cut-off Tool Blade, Inches 0.000–0.250 0.045 0.251–0.375 0.062 0.376–0.625 0.093 0.626–1.000 0.125 1.001–1.500 0.156

It is sometimes convenient to know the weight of a certain number of pieces, when estimating the price. The weight of round bar stock can be found by means of the following formulas, in which W =weight in pounds D =diameter of stock in inches F =length in feet For brass stock: W = D2 × 2.86 × F For steel stock: W = D2 × 2.675 × F For iron stock: W = D2 × 2.65 × F


Machinery's Handbook 27th Edition STOCK FOR SCREW MACHINES

1137

Stock Required for Screw Machine Products The table gives the amount of stock, in feet, required for 1000 pieces, when the length of the finished part plus the thickness of the cut-off tool blade is known. Allowance has been made for chucking. To illustrate, if length of cut-off tool and work equals 0.140 inch, 11.8 feet of stock is required for the production of 1000 parts. Length of Piece and Cut-Off Tool

Feet per 1000 Parts

Length of Piece and Cut-Off Tool

Feet per 1000 Parts


0.050 0.060 0.070 0.080 0.090 0.100 0.110 0.120 0.130 0.140 0.150 0.160 0.170 0.180 0.190 0.200 0.210 0.220 0.230 0.240 0.250 0.260 0.270 0.280 0.290 0.300 0.310 0.320 0.330 0.340 0.350 0.360 0.370 0.380 0.390 0.400 0.410 0.420

4.2 5.0 5.9 6.7 7.6 8.4 9.2 10.1 10.9 11.8 12.6 13.4 14.3 15.1 16.0 16.8 17.6 18.5 19.3 20.2 21.0 21.8 22.7 23.5 24.4 25.2 26.1 26.9 27.7 28.6 29.4 30.3 31.1 31.9 32.8 33.6 34.5 35.3

0.430 0.440 0.450 0.460 0.470 0.480 0.490 0.500 0.510 0.520 0.530 0.540 0.550 0.560 0.570 0.580 0.590 0.600 0.610 0.620 0.630 0.640 0.650 0.660 0.670 0.680 0.690 0.700 0.710 0.720 0.730 0.740 0.750 0.760 0.770 0.780 0.790 0.800

36.1 37.0 37.8 38.7 39.5 40.3 41.2 42.0 42.9 43.7 44.5 45.4 46.2 47.1 47.9 48.7 49.6 50.4 51.3 52.1 52.9 53.8 54.6 55.5 56.3 57.1 58.0 58.8 59.7 60.5 61.3 62.2 63.0 63.9 64.7 65.5 66.4 67.2

0.810 0.820 0.830 0.840 0.850 0.860 0.870 0.880 0.890 0.900 0.910 0.920 0.930 0.940 0.950 0.960 0.970 0.980 0.990 1.000 1.020 1.040 1.060 1.080 1.100 1.120 1.140 1.160 1.180 1.200 1.220 1.240 1.260 1.280 1.300 1.320 1.340 1.360

Feet per 1000 Parts 68.1 68.9 69.7 70.6 71.4 72.3 73.1 73.9 74.8 75.6 76.5 77.3 78.2 79.0 79.8 80.7 81.5 82.4 83.2 84.0 85.7 87.4 89.1 90.8 92.4 94.1 95.8 97.5 99.2 100.8 102.5 104.2 105.9 107.6 109.2 110.9 112.6 114.3


Feet per 1000 Parts

1.380 1.400 1.420 1.440 1.460 1.480 1.500 1.520 1.540 1.560 1.580 1.600 1.620 1.640 1.660 1.680 1.700 1.720 1.740 1.760 1.780 1.800 1.820 1.840 1.860 1.880 1.900 1.920 1.940 1.960 1.980 2.000 2.100 2.200 2.300 2.400 2.500 2.600

116.0 117.6 119.3 121.0 122.7 124.4 126.1 127.7 129.4 131.1 132.8 134.5 136.1 137.8 139.5 141.2 142.9 144.5 146.2 147.9 149.6 151.3 152.9 154.6 156.3 158.0 159.7 161.3 163.0 164.7 166.4 168.1 176.5 184.9 193.3 201.7 210.1 218.5



BAND SAW BLADES

Band Saw Blade Selection.—The primary factors to consider in choosing a saw blade are: the pitch, or the number of teeth per inch of blade; the tooth form; and the blade type (material and construction). Tooth pitch selection depends on the size and shape of the work, whereas tooth form and blade type depend on material properties of the workpiece and on economic considerations of the job.

30

26 25 24 23 28 27 22

29

21

20 19

35

.75 1.5

18 17

40

16 15 14

.75 1.5

45 .75 1.5

50 800 900 1000 1250

55 Inch 0 .1

mm

14 18 14 18

14 18

.2 .3

5 10 15 20 25

10 14 8 12

10 14

10 14

6 10

4 6

.8

4 6

.9 1

11 4

1.5 2.5

9 2 3

75

8

2 3

5 8

1

1

2

11 10

1.5 2.5

3 4

5 8

.7

12

150 100

4 6 6 10

6 10

13

1.5 2.5

500 450 400 350 300 250 200

50

5 8

8 12

8 12

.4 .5 .6

700 600

7

2 3

3 4

6 5

3 4

13 4 2 1 4 1 23 4 3 31 4 3 2 2 2

1

2

33 4

4

Courtesy of American Saw and Manufacturing Company

The tooth selection chart above is a guide to help determine the best blade pitch for a particular job. The tooth specifications in the chart are standard variable-pitch blade sizes as specified by the Hack and Band Saw Association. The variable-pitch blades listed are designated by two numbers that refer to the approximate maximum and minimum tooth pitch. A 4⁄6 blade, for example, has a maximum tooth spacing of approximately 1⁄4 inch and a minimum tooth spacing of about 1⁄6 inch. Blades are available, from most manufacturers, in sizes within about ±10 per cent of the sizes listed. To use the chart, locate the length of cut in inches on the outside circle of the table (for millimeters use the inside circle) and then find the tooth specification that aligns with the length, on the ring corresponding to the material shape. The length of cut is the distance that any tooth of the blade is in contact with the work as it passes once through the cut. For cutting solid round stock, use the diameter as the length of cut and select a blade from the ring with the solid circle. When cutting angles, channels, I-beams, tubular pieces, pipe, and hollow or irregular shapes, the length of cut is found by dividing the cross-sectional area of the cut by the distance the blade needs to travel to finish the cut. Locate the length of cut on the outer ring (inner ring for mm) and select a blade from the ring marked with the angle, Ibeam, and pipe sections. Example:A 4-inch pipe with a 3-inch inside diameter is to be cut. Select a variable pitch blade for cutting this material.


Machinery's Handbook 27th Edition BAND SAW BLADES

1139

The area of the pipe is π/4 × (42 − 32) = 5.5 in.2 The blade has to travel 4 inches to cut through the pipe, so the average length of cut is 5.5⁄4 = 1.4 inches. On the tooth selection wheel, estimate the location of 1.4 inches on the outer ring, and read the tooth specification from the ring marked with the pipe, angle, and I-beam symbols. The chart indicates that a 4⁄6 variable-pitch blade is the preferred blade for this cut. Tooth Forms.—Band saw teeth are characterized by a tooth form that includes the shape, spacing (pitch), rake angle, and gullet capacity of the tooth. Tooth form affects the cutting efficiency, noise level, blade life, chip-carrying capacity, and the surface finish quality of the cut. The rake angle, which is the angle between the face of the tooth and a line perpendicular to the direction of blade travel, influences the cutting speed. In general, positive rake angles cut faster. The standard tooth form has conventional shape teeth, evenly spaced with deep gullets and a 0° rake angle. Standard tooth blades are used for generalpurpose cutting on a wide variety of materials. The skip tooth form has shallow, widely spaced teeth arranged in narrow bands and a 0° rake angle. Skip tooth blades are used for cutting soft metals, wood, plastics, and composite materials. The hook tooth form is similar to the skip tooth, but has a positive rake angle and is used for faster cutting of large sections of soft metal, wood, and plastics, as well as for cutting some metals, such as cast iron, that form a discontinuous chip. The variable-tooth (variable-pitch) form has a conventional tooth shape, but the tips of the teeth are spaced a variable distance (pitch) apart. The variable pitch reduces vibration of the blade and gives smoother cutting, better surface finish, and longer blade life. The variable positive tooth form is a variable-pitch tooth with a positive rake angle that causes the blade to penetrate the work faster. The variable positive tooth blade increases production and gives the longest blade life. Set is the angle that the teeth are offset from the straight line of a blade. The set affects the blade efficiency (i.e., cutting rate), chip-carrying ability, and quality of the surface finish. Alternate set blades have adjacent teeth set alternately one to each side. Alternate set blades, which cut faster but with a poorer finish than other blades, are especially useful for rapid rough cutting. A raker set is similar to the alternate set, but every few teeth, one of the teeth is set to the center, not to the side (typically every third tooth, but sometimes every fifth or seventh tooth). The raker set pattern cuts rapidly and produces a good surface finish. The vari-raker set, or variable raker, is a variable-tooth blade with a raker set. The variraker is quieter and produces a better surface finish than a raker set standard tooth blade. Wavy set teeth are set in groups, alternately to one side, then to the other. Both wavy set and vari-raker set blades are used for cutting tubing and other interrupted cuts, but the blade efficiency and surface finish produced are better with a vari-raker set blade. Types of Blades.—The most important band saw blade types are carbon steel, bimetal, carbide tooth, and grit blades made with embedded carbide or diamond. Carbon steel blades have the lowest initial cost, but they may wear out faster. Carbon steel blades are used for cutting a wide variety of materials, including mild steels, aluminum, brass, bronze, cast iron, copper, lead, and zinc, as well as some abrasive materials such as cork, fiberglass, graphite, and plastics. Bimetal blades are made with a high-speed steel cutting edge that is welded to a spring steel blade back. Bimetal blades are stronger and last longer, and they tend to produce straighter cuts because the blade can be tensioned higher than carbon steel blades. Because bimetal blades last longer, the cost per cut is frequently lower than when using carbon steel blades. Bimetal blades are used for cutting all ferrous and nonferrous metals, a wide range of shapes of easy to moderately machinable material, and solids and heavy wall tubing with moderate to difficult machinability. Tungsten carbide blades are similar to bimetal blades but have tungsten carbide teeth welded to the blade back. The welded teeth of carbide blades have greater wear and high-temperature resistance than either carbon steel or bimetal blades and produce less tooth vibration, while giving smoother, straighter, faster, and quieter cuts requiring less feed force. Carbide blades are used on tough alloys such as cobalt, nickel- and titanium-based alloys, and for nonferrous materials such as aluminum castings, fiberglass, and graphite. The carbide grit blade



BAND SAW BLADES

has tungsten carbide grit metallurgically bonded to either a gulleted (serrated) or toothless steel band. The blades are made in several styles and grit sizes. Both carbide grit and diamond grit blades are used to cut materials that conventional (carbon and bimetal) blades are unable to cut such as: fiberglass, reinforced plastics, composite materials, carbon and graphite, aramid fibers, plastics, cast iron, stellites, high-hardness tool steels, and superalloys. Band Saw Speed and Feed Rate.—The band speed necessary to cut a particular material is measured in feet per minute (fpm) or in meters per minute (m/min), and depends on material characteristics and size of the workpiece. Typical speeds for a bimetal blade cutting 4-inch material with coolant are given in the speed selection table that follows. For other size materials or when cutting without coolant, adjust speeds according to the instructions at the bottom of the table.

Cutting Rate (in.2/min)


30 28 26 24 22 20 18 16 14 12 10 8 6 4 2 0

0.75 1.5 1.5 2.5

23 34

46

58 8 12

0

50

100 150 200 250 300 350 400 450 500 550 600 Band Speed (ft/min)

Cutting Rates for Band Saws The feed or cutting rate, usually measured in square inches or square meters per minute, indicates how fast material is being removed and depends on the speed and pitch of the blade, not on the workpiece material. The graph above, based on material provided by American Saw and Mfg., gives approximate cutting rates (in.2/min) for various variablepitch blades and cutting speeds. Use the value from the graph as an initial starting value and then adjust the feed based on the performance of the saw. The size and character of the chips being produced are the best indicators of the correct feed force. Chips that are curly, silvery, and warm indicate the best feed rate and band speed. If the chips appear burned and heavy, the feed is too great, so reduce the feed rate, the band speed, or both. If the chips are thin or powdery, the feed rate is too low, so increase the feed rate or reduce the band speed. The actual cutting rate achieved during a cut is equal to the area of the cut divided by the time required to finish the cut. The time required to make a cut is equal to the area of the cut divided by the cutting rate in square inches per minute.


Machinery's Handbook 27th Edition BAND SAW BLADES

1141

Bimetal Band Saw Speeds for Cutting 4-Inch Material with Coolant Material Aluminum Alloys Cast Iron

Cobalt Copper

Iron Base Super Alloy Magnesium Nickel Nickel Alloy

Stainless Steel

Category (AISI/SAE) 1100, 2011, 2017, 2024, 3003, 5052, 5086, 6061, 6063, 6101, 6262, 7075 A536 (60-40-18) A47 A220 (50005), A536 (80-55-06) A48 (20 ksi) A536 (100-70-03) A48 (40 ksi) A220 (60004) A436 (1B) A220 (70003) A436 (2) A220 (80002), A436 (2B) A536 (120-90-02) A220 (90001), A48 (60 ksi) A439 (D-2) A439 (D-2B) WF-11 Astroloy M 356, 360 353 187, 1452 380, 544 173, 932, 934 330, 365 623, 624 230, 260, 272, 280, 464, 632, 655 101, 102, 110, 122, 172, 17510, 182, 220, 510, 625, 706, 715 630 811 Pyromet X-15 A286, Incoloy 800 and 801 AZ31B Nickel 200, 201, 205 Inconel 625 Incoloy 802, 804 Monel R405 20CB3 Monel 400, 401 Hastelloy B, B2, C, C4, C22, C276, F, G, G2, G3, G30, N, S, W, X, Incoloy 825, 926, Inconel 751, X750, Waspaloy Monel K500 Incoloy 901, 903, Inconel 600, 718, Ni-Span-C902, Nimonic 263, Rene 41, Udimet 500 Nimonic 75 416, 420 203EZ, 430, 430F, 4302 303, 303PB, 303SE, 410, 440F, 30323 304 414, 30403 347 316, 31603 Greek Ascoloy 18-18-2, 309, Ferralium 15-5PH, 17-4PH, 17-7PH, 2205, 310, AM350, AM355, Custom 450, Custom 455, PH13-8Mo, PH14-8Mo, PH15-7Mo 22-13-5, Nitronic 50, 60

Speed (fpm) 500

Speed (m/min) 152

360 300 240 230 185 180 170 150 145 140 125 120 100 80 60 65 60 450 400 375 350 315 285 265 245 235 230 215 120 90 900 85 100 90 85 80 75 70

110 91 73 70 56 55 52 46 44 43 38 37 30 24 18 20 18 137 122 114 107 96 87 81 75 72 70 66 37 27 274 26 30 27 26 24 23 21

65 60

20 18

50 190 150 140 120 115 110 100 95 90 80

15 58 46 43 37 35 34 30 29 27 24

60

18



BAND SAW BLADES

Bimetal Band Saw Speeds for Cutting 4-Inch Material with Coolant (Continued) Material Steel

Titanium

Category (AISI/SAE) 12L14 1213, 1215 1117 1030 1008, 1015, 1020, 1025 1035 1018, 1021, 1022, 1026, 1513, A242 Cor-Ten A 1137 1141, 1144, 1144 Hi Stress 41L40 1040, 4130, A242 Cor-Ten B, (A36 Shapes) 1042, 1541, 4140, 4142 8615, 8620, 8622 W-1 1044, 1045, 1330, 4340, E4340, 5160, 8630 1345, 4145, 6150 1060, 4150, 8640, A-6, O-1, S-1 H-11, H-12, H-13, L-6, O-6 1095 A-2 E9310 300M, A-10, E52100, HY-80, HY-100 S-5 S-7 M-1 HP 9-4-20, HP 9-4-25 M-2, M-42, T1 D-2 T-15 Pure, Ti-3Al-8V-6Cr-4Mo-4Z, Ti-8Mo-8V-2Fe-3Al Ti-2Al-11Sn-5Zr-1Mo, Ti-5Al-2.5Sn, Ti-6Al-2Sn-4Zr-2Mo Ti-6Al-4V Ti-7Al-4Mo, Ti-8Al-1Mo-1V

Speed (fpm) 425 400 340 330 320 310 300 290 280 275 270 250 240 225 220 210 200 190 185 180 175 160 140 125 110 105 100 90 70 80 75 70 65

Speed (m/min) 130 122 104 101 98 94 91 88 85 84 82 76 73 69 67 64 61 58 56 55 53 49 43 38 34 32 30 27 21 24 23 21 20

The speed figures given are for 4-in. material (length of cut) using a 3⁄4 variable-tooth bimetal blade and cutting fluid. For cutting dry, reduce speed 30–50%; for carbon steel band saw blades, reduce speed 50%. For other cutting lengths: increase speed 15% for 1⁄4-in. material (10⁄14 blade); increase speed 12% for 3⁄4-in. material (6⁄10 blade); increase speed 10% for 11⁄4-in. material (4⁄6 blade); decrease speed 12% for 8-in. material (2⁄3 blade). Table data are based on material provided by LENOX Blades, American Saw & Manufacturing Co.

Example:Find the band speed, the cutting rate, and the cutting time if the 4-inch pipe of the previous example is made of 304 stainless steel. The preceding blade speed table gives the band speed for 4-inch 304 stainless steel as 120 fpm (feet per minute). The average length of cut for this pipe (see the previous example) is 1.4 inches, so increase the band saw speed by about 10 per cent (see footnote on ) to 130 fpm to account for the size of the piece. On the cutting rate graph above, locate the point on the 4⁄6 blade line that corresponds to the band speed of 130 fpm and then read the cutting rate from the left axis of the graph. The cutting rate for this example is approximately 4 in. 2/min. The cutting time is equal to the area of the cut divided by the cutting rate, so cutting time = 5.5⁄4 = 1.375 minutes. Band Saw Blade Break-In.—A new band saw blade must be broken in gradually before it is allowed to operate at its full recommended feed rate. Break-in relieves the blade of residual stresses caused by the manufacturing process so that the blade retains its cutting ability longer. Break-in requires starting the cut at the material cutting speed with a low feed rate and then gradually increasing the feed rate over time until enough material has been cut. A blade should be broken in with the material to be cut.


Machinery's Handbook 27th Edition CUTTING FLUIDS

1143

To break in a new blade, first set the band saw speed at the recommended cutting speed for the material and start the first cut at the feed indicated on the starting feed rate graph below. After the saw has penetrated the work to a distance equal to the width of the blade, increase the feed slowly. When the blade is about halfway through the cut, increase the feed again slightly and finish the cut without increasing the feed again. Start the next and each successive cut with the same feed rate that ended the previous cut, and increase the feed rate slightly again before the blade reaches the center of the cut. Repeat this procedure until the area cut by the new blade is equal to the total area required as indicated on the graph below. At the end of the break-in period, the blade should be cutting at the recommended feed rate, otherwise adjusted to that rate.

% of Normal Feed

LIVE GRAPH

100 90 80 70 60 50 40 30 20 10 0 ft/min. 40 m/min. 12

Click here to view

80 24

120 37

Starting Feed Rate

160 49

200 61

240 73

280 85

320 98

360 110

Break-In Area

Band Speed (Machinability) LIVE GRAPH Total Break-In Area Required in.2 Click here to view 100 90 80 70 60 50 40 30 20 10 0 ft/min. 40 80 120 160 200 240 280 m/min. 12 24 37 49 61 73 85

cm2 645 580 515 450 385 320 260 195 130 65 0

320 98

360 110

Band Speed (Machinability) Cutting Fluids for Machining The goal in all conventional metal-removal operations is to raise productivity and reduce costs by machining at the highest practical speed consistent with long tool life, fewest rejects, and minimum downtime, and with the production of surfaces of satisfactory accuracy and finish. Many machining operations can be performed “dry,” but the proper application of a cutting fluid generally makes possible: higher cutting speeds, higher feed rates, greater depths of cut, lengthened tool life, decreased surface roughness, increased dimensional accuracy, and reduced power consumption. Selecting the proper cutting fluid for a specific machining situation requires knowledge of fluid functions, properties, and limitations. Cutting fluid selection deserves as much attention as the choice of machine tool, tooling, speeds, and feeds. To understand the action of a cutting fluid it is important to realize that almost all the energy expended in cutting metal is transformed into heat, primarily by the deformation of the metal into the chip and, to a lesser degree, by the friction of the chip sliding against the tool face. With these factors in mind it becomes clear that the primary functions of any cut-



CUTTING FLUIDS

ting fluid are: cooling of the tool, workpiece, and chip; reducing friction at the sliding contacts; and reducing or preventing welding or adhesion at the contact surfaces, which forms the “built-up edge” on the tool. Two other functions of cutting fluids are flushing away chips from the cutting zone and protecting the workpiece and tool from corrosion. The relative importance of the functions is dependent on the material being machined, the cutting tool and conditions, and the finish and accuracy required on the part. For example, cutting fluids with greater lubricity are generally used in low-speed machining and on most difficult-to-cut materials. Cutting fluids with greater cooling ability are generally used in high-speed machining on easier-to-cut materials. Types of Cutting and Grinding Fluids.—In recent years a wide range of cutting fluids has been developed to satisfy the requirements of new materials of construction and new tool materials and coatings. There are four basic types of cutting fluids; each has distinctive features, as well as advantages and limitations. Selection of the right fluid is made more complex because the dividing line between types is not always clear. Most machine shops try to use as few different fluids as possible and prefer fluids that have long life, do not require constant changing or modifying, have reasonably pleasant odors, do not smoke or fog in use, and, most important, are neither toxic nor cause irritation to the skin. Other issues in selection are the cost and ease of disposal. The major divisions and subdivisions used in classifying cutting fluids are: Cutting Oils, including straight and compounded mineral oils plus additives. Water-Miscible Fluids , including emulsifiable oils; chemical or synthetic fluids; and semichemical fluids. Gases. Paste and Solid Lubricants. Since the cutting oils and water-miscible types are the most commonly used cutting fluids in machine shops, discussion will be limited primarily to these types. It should be noted, however, that compressed air and inert gases, such as carbon dioxide, nitrogen, and Freon, are sometimes used in machining. Paste, waxes, soaps, graphite, and molybdenum disulfide may also be used, either applied directly to the workpiece or as an impregnant in the tool, such as in a grinding wheel. Cutting Oils.—Cutting oils are generally compounds of mineral oil with the addition of animal, vegetable, or marine oils to improve the wetting and lubricating properties. Sulfur, chlorine, and phosphorous compounds, sometimes called extreme pressure (EP) additives, provide for even greater lubricity. In general, these cutting oils do not cool as well as watermiscible fluids. Water-Miscible Fluids.—Emulsions or soluble oils are a suspension of oil droplets in water. These suspensions are made by blending the oil with emulsifying agents (soap and soaplike materials) and other materials. These fluids combine the lubricating and rust-prevention properties of oil with water's excellent cooling properties. Their properties are affected by the emulsion concentration, with “lean” concentrations providing better cooling but poorer lubrication, and with “rich” concentrations having the opposite effect. Additions of sulfur, chlorine, and phosphorus, as with cutting oils, yield “extreme pressure” (EP) grades. Chemical fluids are true solutions composed of organic and inorganic materials dissolved in water. Inactive types are usually clear fluids combining high rust inhibition, high cooling, and low lubricity characteristics with high surface tension. Surface-active types include wetting agents and possess moderate rust inhibition, high cooling, and moderate lubricating properties with low surface tension. They may also contain chlorine and/or sulfur compounds for extreme pressure properties. Semichemical fluids are combinations of chemical fluids and emulsions. These fluids have a lower oil content but a higher emulsifier and surface-active-agent content than



1145

emulsions, producing oil droplets of much smaller diameter. They possess low surface tension, moderate lubricity and cooling properties, and very good rust inhibition. Sulfur, chlorine, and phosphorus also are sometimes added. Selection of Cutting Fluids for Different Materials and Operations.—The choice of a cutting fluid depends on many complex interactions including the machinability of the metal; the severity of the operation; the cutting tool material; metallurgical, chemical, and human compatibility; fluid properties, reliability, and stability; and finally cost. Other factors affect results. Some shops standardize on a few cutting fluids which have to serve all purposes. In other shops, one cutting fluid must be used for all the operations performed on a machine. Sometimes, a very severe operating condition may be alleviated by applying the “right” cutting fluid manually while the machine supplies the cutting fluid for other operations through its coolant system. Several voluminous textbooks are available with specific recommendations for the use of particular cutting fluids for almost every combination of machining operation and workpiece and tool material. In general, when experience is lacking, it is wise to consult the material supplier and/or any of the many suppliers of different cutting fluids for advice and recommendations. Another excellent source is the Machinability Data Center, one of the many information centers supported by the U.S. Department of Defense. While the following recommendations represent good practice, they are to serve as a guide only, and it is not intended to say that other cutting fluids will not, in certain specific cases, also be effective. Steels: Caution should be used when using a cutting fluid on steel that is being turned at a high cutting speed with cemented carbide cutting tools. See Application of Cutting Fluids to Carbides later. Frequently this operation is performed dry. If a cutting fluid is used, it should be a soluble oil mixed to a consistency of about 1 part oil to 20 to 30 parts water. A sulfurized mineral oil is recommended for reaming with carbide tipped reamers although a heavy-duty soluble oil has also been used successfully. The cutting fluid recommended for machining steel with high speed cutting tools depends largely on the severity of the operation. For ordinary turning, boring, drilling, and milling on medium and low strength steels, use a soluble oil having a consistency of 1 part oil to 10 to 20 parts water. For tool steels and tough alloy steels, a heavy-duty soluble oil having a consistency of 1 part oil to 10 parts water is recommended for turning and milling. For drilling and reaming these materials, a light sulfurized mineral-fatty oil is used. For tough operations such as tapping, threading, and broaching, a sulfochlorinated mineralfatty oil is recommended for tool steels and high-strength steels, and a heavy sulfurized mineral-fatty oil or a sulfochlorinated mineral oil can be used for medium- and lowstrength steels. Straight sulfurized mineral oils are often recommended for machining tough, stringy low carbon steels to reduce tearing and produce smooth surface finishes. Stainless Steel: For ordinary turning and milling a heavy-duty soluble oil mixed to a consistency of 1 part oil to 5 parts water is recommended. Broaching, threading, drilling, and reaming produce best results using a sulfochlorinated mineral-fatty oil. Copper Alloys: Most brasses, bronzes, and copper are stained when exposed to cutting oils containing active sulfur and chlorine; thus, sulfurized and sulfochlorinated oils should not be used. For most operations a straight soluble oil, mixed to 1 part oil and 20 to 25 parts water is satisfactory. For very severe operations and for automatic screw machine work a mineral-fatty oil is used. A typical mineral-fatty oil might contain 5 to 10 per cent lard oil with the remainder mineral oil. Monel Metal: When turning this material, an emulsion gives a slightly longer tool life than a sulfurized mineral oil, but the latter aids in chip breakage, which is frequently desirable. Aluminum Alloys: Aluminum and aluminum alloys are frequently machined dry. When a cutting fluid is used it should be selected for its ability to act as a coolant. Soluble oils mixed to a consistency of 1 part oil to 20 to 30 parts water can be used. Mineral oil-base



CUTTING FLUIDS

cutting fluids, when used to machine aluminum alloys, are frequently cut back to increase their viscosity so as to obtain good cooling characteristics and to make them flow easily to cover the tool and the work. For example, a mineral-fatty oil or a mineral plus a sulfurized fatty oil can be cut back by the addition of as much as 50 per cent kerosene. Cast Iron: Ordinarily, cast iron is machined dry. Some increase in tool life can be obtained or a faster cutting speed can be used with a chemical cutting fluid or a soluble oil mixed to consistency of 1 part oil and 20 to 40 parts water. A soluble oil is sometimes used to reduce the amount of dust around the machine. Magnesium: Magnesium may be machined dry, or with an air blast for cooling. A light mineral oil of low acid content may be used on difficult cuts. Coolants containing water should not be used on magnesium because of the danger of releasing hydrogen caused by reaction of the chips with water. Proprietary water-soluble oil emulsions containing inhibitors that reduce the rate of hydrogen generation are available. Grinding: Soluble oil emulsions or emulsions made from paste compounds are used extensively in precision grinding operations. For cylindrical grinding, 1 part oil to 40 to 50 parts water is used. Solution type fluids and translucent grinding emulsions are particularly suited for many fine-finish grinding applications. Mineral oil-base grinding fluids are recommended for many applications where a fine surface finish is required on the ground surface. Mineral oils are used with vitrified wheels but are not recommended for wheels with rubber or shellac bonds. Under certain conditions the oil vapor mist caused by the action of the grinding wheel can be ignited by the grinding sparks and explode. To quench the grinding spark a secondary coolant line to direct a flow of grinding oil below the grinding wheel is recommended. Broaching: For steel, a heavy mineral oil such as sulfurized oil of 300 to 500 Saybolt viscosity at 100 degrees F can be used to provide both adequate lubricating effect and a dampening of the shock loads. Soluble oil emulsions may be used for the lighter broaching operations. Cutting Fluids for Turning, Milling, Drilling and Tapping.—The following table, Cutting Fluids Recommended for Machining Operations, gives specific cutting oil recommendations for common machining operations. Soluble Oils: Types of oils paste compounds that form emulsions when mixed with water: Soluble oils are used extensively in machining both ferrous and non-ferrous metals when the cooling quality is paramount and the chip-bearing pressure is not excessive. Care should be taken in selecting the proper soluble oil for precision grinding operations. Grinding coolants should be free from fatty materials that tend to load the wheel, thus affecting the finish on the machined part. Soluble coolants should contain rust preventive constituents to prevent corrosion. Base Oils: Various types of highly sulfurized and chlorinated oils containing inorganic, animal, or fatty materials. This “base stock” usually is “cut back” or blended with a lighter oil, unless the chip-bearing pressures are high, as when cutting alloy steel. Base oils usually have a viscosity range of from 300 to 900 seconds at 100 degrees F. Mineral Oils: This group includes all types of oils extracted from petroleum such as paraffin oil, mineral seal oil, and kerosene. Mineral oils are often blended with base stocks, but they are generally used in the original form for light machining operations on both freemachining steels and non-ferrous metals. The coolants in this class should be of a type that has a relatively high flash point. Care should be taken to see that they are nontoxic, so that they will not be injurious to the operator. The heavier mineral oils (paraffin oils) usually have a viscosity of about 100 seconds at 100 degrees F. Mineral seal oil and kerosene have a viscosity of 35 to 60 seconds at 100 degrees F.



1147

Cutting Fluids Recommended for Machining Operations Material to be Cut Aluminuma

Turning (or)

Mineral Oil with 10 Per cent Fat Soluble Oil

Milling (or) (or)

25 Per Cent Sulfur base Oilb with 75 Per Cent Mineral Oil Mineral Oil with 10 Per Cent Fat 25 Per Cent Lard Oil with 75 Per Cent Mineral Oil Soluble Oil Soluble Oil Dry Soluble Oil Soluble Oil 10 Per Cent Lard Oil with 90 Per Cent Mineral Oil

Alloy Steelsb Brass Tool Steels and Low-carbon Steels Copper Monel Metal Cast Ironc Malleable Iron Bronze Magnesiumd Material to be Cut

Soluble Oil Soluble Oil Soluble Oil Dry Soluble Oil Soluble Oil Mineral Seal Oil

Drilling Soluble Oil (75 to 90 Per Cent Water)

Aluminume (or)

10 Per Cent Lard Oil with 90 Per Cent Mineral Oil

Alloy Steelsb

Soluble Oil

Brass

Soluble Oil (75 to 90 Per Cent Water) 30 Per Cent Lard Oil with 70 Per Cent Mineral Oil

(or) Tool Steels and Low-carbon Steels

Soluble Oil

Copper

Soluble Oil

Monel Metal

Soluble Oil

Tapping (or) (or) (or)

(or) Dry

Malleable Iron

Soluble Oil

Bronze

Soluble Oil

Magnesiumd

60-second Mineral Oil

Lard Oil Sperm Oil Wool Grease 25 Per Cent Sulfur-base Oilb Mixed with Mineral Oil 30 Per Cent Lard Oil with 70 Per Cent Mineral Oil 10 to 20 Per Cent Lard Oil with Mineral Oil

(or)

Cast Ironc

Soluble Oil (96 Per Cent Water) Mineral Seal Oil Mineral Oil 10 Per Cent Lard Oil with 90 Per Cent Mineral Oil Soluble Oil (96 Per Cent Water)

(or)

25 to 40 Per Cent Lard Oil with Mineral Oil 25 Per Cent Sulfur-base Oilb with 75 Per Cent Mineral Oil Soluble Oil 25 to 40 Per Cent Lard Oil Mixed with Mineral Oil Sulfur-base Oilb Mixed with Mineral Oil Dry 25 Per Cent Lard Oil with 75 Per Cent Mineral Oil Soluble Oil 20 Per Cent Lard Oil with 80 Per Cent Mineral Oil 20 Per Cent Lard Oil with 80 Per Cent Mineral Oil

a In machining aluminum, several varieties of coolants may be used. For rough machining, where the

stock removal is sufficient to produce heat, water soluble mixtures can be used with good results to dissipate the heat. Other oils that may be recommended are straight mineral seal oil; a 50–50 mixture of mineral seal oil and kerosene; a mixture of 10 per cent lard oil with 90 per cent kerosene; and a 100second mineral oil cut back with mineral seal oil or kerosene. b The sulfur-base oil referred to contains 41⁄ per cent sulfur compound. Base oils are usually dark in 2 color. As a rule, they contain sulfur compounds resulting from a thermal or catalytic refinery process. When so processed, they are more suitable for industrial coolants than when they have had such compounds as flowers of sulfur added by hand. The adding of sulfur compounds by hand to the coolant reservoir is of temporary value only, and the non-uniformity of the solution may affect the machining operation. c A soluble oil or low-viscosity mineral oil may be used in machining cast iron to prevent excessive metal dust.



CUTTING FLUIDS

d When a cutting fluid is needed for machining magnesium, low or nonacid mineral seal or lard oils are recommended. Coolants containing water should not be used because of the fire danger when magnesium chips react with water, forming hydrogen gas. e Sulfurized oils ordinarily are not recommended for tapping aluminum; however, for some tapping operations they have proved very satisfactory, although the work should be rinsed in a solvent right after machining to prevent discoloration.

Application of Cutting Fluids to Carbides.—Turning, boring, and similar operations on lathes using carbides are performed dry or with the help of soluble oil or chemical cutting fluids. The effectiveness of cutting fluids in improving tool life or by permitting higher cutting speeds to be used, is less with carbides than with high-speed steel tools. Furthermore, the effectiveness of the cutting fluid is reduced as the cutting speed is increased. Cemented carbides are very sensitive to sudden changes in temperature and to temperature gradients within the carbide. Thermal shocks to the carbide will cause thermal cracks to form near the cutting edge, which are a prelude to tool failure. An unsteady or interrupted flow of the coolant reaching the cutting edge will generally cause these thermal cracks. The flow of the chip over the face of the tool can cause an interruption to the flow of the coolant reaching the cutting edge even though a steady stream of coolant is directed at the tool. When a cutting fluid is used and frequent tool breakage is encountered, it is often best to cut dry. When a cutting fluid must be used to keep the workpiece cool for size control or to allow it to be handled by the operator, special precautions must be used. Sometimes applying the coolant from the front and the side of the tool simultaneously is helpful. On lathes equipped with overhead shields, it is very effective to apply the coolant from below the tool into the space between the shoulder of the work and the tool flank, in addition to applying the coolant from the top. Another method is not to direct the coolant stream at the cutting tool at all but to direct it at the workpiece above or behind the cutting tool. The danger of thermal cracking is great when milling with carbide cutters. The nature of the milling operation itself tends to promote thermal cracking because the cutting edge is constantly heated to a high temperature and rapidly cooled as it enters and leaves the workpiece. For this reason, carbide milling operations should be performed dry. Lower cutting-edge temperatures diminish the danger of thermal cracking. The cuttingedge temperatures usually encountered when reaming with solid carbide or carbide-tipped reamers are generally such that thermal cracking is not apt to occur except when reaming certain difficult-to-machine metals. Therefore, cutting fluids are very effective when used on carbide reamers. Practically every kind of cutting fluid has been used, depending on the job material encountered. For difficult surface-finish problems in holes, heavy duty soluble oils, sulfurized mineral-fatty oils, and sulfochlorinated mineral-fatty oils have been used successfully. On some work, the grade and the hardness of the carbide also have an effect on the surface finish of the hole. Cutting fluids should be applied where the cutting action is taking place and at the highest possible velocity without causing splashing. As a general rule, it is preferable to supply from 3 to 5 gallons per minute for each single-point tool on a machine such as a turret lathe or automatic. The temperature of the cutting fluid should be kept below 110 degrees F. If the volume of fluid used is not sufficient to maintain the proper temperature, means of cooling the fluid should be provided. Cutting Fluids for Machining Magnesium.—In machining magnesium, it is the general but not invariable practice in the United States to use a cutting fluid. In other places, magnesium usually is machined dry except where heat generated by high cutting speeds would not be dissipated rapidly enough without a cutting fluid. This condition may exist when, for example, small tools without much heat-conducting capacity are employed on automatics. The cutting fluid for magnesium should be an anhydrous oil having, at most, a very low acid content. Various mineral-oil cutting fluids are used for magnesium.



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Occupational Exposure To Metal working Fluids The term metalworking fluids (MWFs) describes coolants and lubricants used during the fabrication of products from metals and metal substitutes. These fluids are used to prolong the life of machine tools, carry away debris, and protect or treat the surfaces of the material being processed. MWFs reduce friction between the cutting tool and work surfaces, reduce wear and galling, protect surface characteristics, reduce surface adhesion or welding, carry away generated heat, and flush away swarf, chips, fines, and residues. Table 1 describes the four different classes of metal working fluids: Table 1. Classes of Metalworking Fluids (MWFs) MWF

Straight oil (neat oil or cutting oil)

Description

Dilution factor

Highly refined petroleum oils (lubricant-base oils) or other animal, marine, vegetable, or synthetic oils used singly or in combination with or without additives. These are lubricants, none or function to improve the finish on the metal cut, and prevent corrosion.

Combinations of 30% to 85% highly refined, high-viscos1 part concentrate ity lubricant-base oils and emulsifiers that may include other to 5 to 40 parts Soluble oil performance additives. Soluble oils are diluted with water water (emulsifiable oil) before use at ratios of parts water. Semisynthetic

Contain smaller amounts of severely refined lubricant-base 1 part concentrate oil (5 to 30% in the concentrate), a higher proportion of to 10 to 40 parts emulsifiers that may include other performance additives, water and 30 to 50% water.

Synthetica

Contain no petroleum oils and may be water soluble or water dispersible. The simplest synthetics are made with 1 part concentrate organic and inorganic salts dissolved in water. Offer good to 10 to 40 parts rust protection and heat removal but usually have poor lubriwater cating ability. May be formulated with other performance additives. Stable, can be made bioresistant.

a Over the last several decades major changes in the U.S. machine tool industry have increased the consumption of MWFs. Specifically, the use of synthetic MWFs increased as tool and cutting speeds increased.

Occupational Exposures to Metal Working Fluids (MWFs).—W o r k e r s c a n b e exposed to MWFs by inhalation of aerosols (mists) or by skin contact resulting in an increased risk of respiratory (lung) and skin disease. Health effects vary based on the type of MWF, route of exposure, concentration, and length of exposure. Skin contact usually occurs when the worker dips his/her hands into the fluid, floods the machine tool, or handling parts, tools, equipment or workpieces coated with the fluid, without the use of personal protective equipment such as gloves and apron. Skin contact can also result from fluid splashing onto worker from the machine if guarding is absent or inadequate. Inhalation exposures result from breathing MWF mist or aerosol. The amount of mist generated (and the severity of the exposure) depends on a variety of factors: the type of MWF and its application process; the MWF temperature; the specific machining or grinding operation; the presence of splash guarding; and the effectiveness of the ventilation system. In general, the exposure will be higher if the worker is in close proximity to the machine, the operation involves high tool speeds and deep cuts, the machine is not enclosed, or if ventilation equipment was improperly selected or poorly maintained. In addition, high-pressure and/or excessive fluid application, contamination of the fluid with tramp oils, and improper fluid selection and maintenance will tend to result in higher exposure.



CUTTING FLUIDS

Each MWF class consists of a wide variety of chemicals used in different combinations and the risk these chemicals pose to workers may vary because of different manufacturing processes, various degrees of refining, recycling, improperly reclaimed chemicals, different degrees of chemical purity, and potential chemical reactions between components. Exposure to hazardous contaminants in MWFs may present health risks to workers. Contamination may occur from: process chemicals and ancillary lubricants inadvertently introduced; contaminants, metals, and alloys from parts being machined; water and cleaning agents used for routine housekeeping; and, contaminants from other environmental sources at the worksite. In addition, bacterial and fungal contaminants may metabolize and degrade the MWFs to hazardous end-products as well as produce endotoxins. The improper use of biocides to manage microbial growth may result in potential health risks. Attempts to manage microbial growth solely with biocides may result in the emergence of biocide-resistant strains from complex interactions that may occur among different member species or groups within the population. For example, the growth of one species, or the elimination of one group of organisms may permit the overgrowth of another. Studies also suggest that exposure to certain biocides can cause either allergic or contact dermatitis. Fluid Selection, Use, and Application.—The MWFs selected should be as nonirritating and nonsensitizing as possible while remaining consistent with operational requirements. Petroleum-containing MWFs should be evaluated for potential carcinogenicity using ASTM Standard E1687-98, “Determining Carcinogenic Potential of Virgin Base Oils in Metalworking Fluids”. If soluble oil or synthetic MWFs are used, ASTM Standard E149794, “Safe Use of Water-Miscible Metalworking Fluids” should be consulted for safe use guidelines, including those for product selection, storage, dispensing, and maintenance. To minimize the potential for nitrosamine formation, nitrate-containing materials should not be added to MWFs containing ethanolamines. Many factors influence the generation of MWF mists, which can be minimized through the proper design and operation of the MWF delivery system. ANSI Technical Report B11 TR2-1997, “Mist Control Considerations for the Design, Installation and Use of Machine Tools Using Metalworking Fluids” provides directives for minimizing mist and vapor generation. These include minimizing fluid delivery pressure, matching the fluid to the application, using MWF formulations with low oil concentrations, avoiding contamination with tramp oils, minimizing the MWF flow rate, covering fluid reservoirs and return systems where possible, and maintaining control of the MWF chemistry. Also, proper application of MWFs can minimize splashing and mist generation. Proper application includes: applying MWFs at the lowest possible pressure and flow volume consistent with provisions for adequate part cooling, chip removal, and lubrication; applying MWFs at the tool/workpiece interface to minimize contact with other rotating equipment; ceasing fluid delivery when not performing machining; not allowing MWFs to flow over the unprotected hands of workers loading or unloading parts; and using mist collectors engineered for the operation and specific machine enclosures. Properly maintained filtration and delivery systems provide cleaner MWFs, reduce mist, and minimize splashing and emissions. Proper maintenance of the filtration and delivery systems includes: the selection of appropriate filters; ancillary equipment such as chip handling operations, dissolved air-flotation devices, belt-skimmers, chillers or plate and frame heat exchangers, and decantation tanks; guard coolant return trenches to prevent dumping of floor wash water and other waste fluids; covering sumps or coolant tanks to prevent contamination with waste or garbage (e.g., cigarette butts, food, etc.); and, keeping the machine(s) clean of debris. Parts washing before machining can be an important part of maintaining cleaner MWFs. Since all additives will be depleted with time, the MWF and additives concentrations should be monitored frequently so that components and additives can be made up as needed. The MWF should be maintained within the pH and concentration ranges recom-



1151

mended by the formulator or supplier. MWF temperature should be maintained at the lowest practical level to slow the growth of microorganisms, reduce water losses and changes in viscosity, and–in the case of straight oils–reduce fire hazards. Fluid Maintenance.—Drums, tanks, or other containers of MWF concentrates should be stored appropriately to protect them from outdoor weather conditions and exposure to low or high temperatures. Extreme temperature changes may destabilize the fluid concentrates, especially in the case of concentrates mixed with water, and cause water to seep into unopened drums encouraging bacterial growth. MWFs should be maintained at as low a temperature as is practical. Low temperatures slow the growth of microorganisms, reduce water losses and change in viscosity, and in the case of straight oils, reduce the fire hazard risks. To maintain proper MWF concentrations, neither water nor concentrate should be used to top off the system. The MWF mixture should be prepared by first adding the concentrate to the clean water (in a clean container) and then adding the emulsion to that mixture in the coolant tank. MWFs should be mixed just before use; large amounts should not be stored, as they may deteriorate before use. Personal Protective Clothing: Personal protective clothing and equipment should always be worn when removing MWF concentrates from the original container, mixing and diluting concentrate, preparing additives (including biocides), and adding MWF emulsions, biocides, or other potentially hazardous ingredients to the coolant reservoir. Personal protective clothing includes eye protection or face shields, gloves, and aprons which do not react with but shed MWF ingredients and additives. System Service: Coolant systems should be regularly serviced, and the machines should be rigorously maintained to prevent contamination of the fluids by tramp oils (e.g., hydraulic oils, gear box oils, and machine lubricants leaking from the machines or total loss slideway lubrication). Tramp oils can destabilize emulsions, cause pumping problems, and clog filters. Tramp oils can also float to the top of MWFs, effectively sealing the fluids from the air, allowing metabolic products such as volatile fatty acids, mercaptols, scatols, ammonia, and hydrogen sulfide are produced by the anaerobic and facultative anaerobic species growing within the biofilm to accumulate in the reduced state. When replacing the fluids, thoroughly clean all parts of the system to inhibit the growth of microorganisms growing on surfaces. Some bacteria secrete layers of slime that may grow in stringy configurations that resemble fungal growth. Many bacteria secrete polymers of polysaccharide and/or protein, forming a glycocalyx which cements cells together much as mortar holds bricks. Fungi may grow as masses of hyphae forming mycelial mats. The attached community of microorganisms is called a biofilm and may be very difficult to remove by ordinary cleaning procedures. Biocide Treatment: Biocides are used to maintain the functionality and efficacy of MWFs by preventing microbial overgrowth. These compounds are often added to the stock fluids as they are formulated, but over time the biocides are consumed by chemical and biological demands Biocides with a wide spectrum of biocidal activity should be used to suppress the growth of the widely diverse contaminant population. Only the concentration of biocide needed to meet fluid specifications should be used since overdosing could lead to skin or respiratory irritation in workers, and under-dosing could lead to an inadequate level of microbial control. Ventilation Systems: The ventilation system should be designed and operated to prevent the accumulation or recirculation of airborne contaminants in the workplace. The ventilation system should include a positive means of bringing in at least an equal volume of air from the outside, conditioning it, and evenly distributing it throughout the exhausted area. Exhaust ventilation systems function through suction openings placed near a source of contamination. The suction opening or exhaust hood creates and air motion sufficient to overcome room air currents and any airflow generated by the process. This airflow cap-



CUTTING FLUIDS

tures the contaminants and conveys them to a point where they can either be discharged or removed from the airstream. Exhaust hoods are classified by their position relative to the process as canopy, side draft, down draft or enclosure. ANSI Technical Report B11 TR 21997 contains guidelines for exhaust ventilation of machining and grinding operations. Enclosures are the only type of exhaust hood recommended by the ANSI committee. They consist of physical barriers between the process and the worker's environment. Enclosures can be further classified by the extent of the enclosure: close capture (enclosure of the point of operation, total enclosure (enclosure of the entire machine), or tunnel enclosure (continuous enclosure over several machines). If no fresh make up air is introduced into the plant, air will enter the building through open doors and windows, potentially causing cross-contamination of all process areas. Ideally, all air exhausted from the building should be replaced by tempered air from an uncontaminated location. By providing a slight excess of make up air in relatively clean areas and s slight deficit of make up air in dirty areas, cross-contamination can be reduced. In addition, this air can be channeled directly to operator work areas, providing the cleanest possible work environment. Ideally, this fresh air should be supplied in the form of a lowvelocity air shower ( 30 N/µm). These data are then calibrated with the users own data in order to refine the estimate and optimize the grinding process, as discussed in User Calibration of Recommendations. The recommendations are valid for all grinding processes such as plunge grinding, cylindrical, and surface grinding with periphery or side of wheel, as well as for creep feed grinding. The grinding data machinability system is based on the basic parameters equivalent chip thickness ECT, and wheel speed V, and is used to determine specific metal removal rates SMRR and wheel-life T, including the work speed Vw after the grinding depths for roughing and finishing are specified. For each material group, the grinding data machinability system consists of T–V Taylor lines in log-log coordinates for 3 wheel speeds at wheel lives of 1, 10 and 100 minutes wheel-life with 4 different values of equivalent chip thickness ECT. The wheel speeds are designated V1, V10, and V100 respectively. In each table the corresponding specific metal removal rates SMRR are also tabulated and designated as SMRR1, SMRR10 and SMRR100 respectively. The user can select any value of ECT and interpolate between the Taylor lines. These curves look the same in grinding as in the other metal cutting processes and the slope is set at n = 0.26, so each Taylor line is formulated by V × T0.26 = C, where C is a constant tabulated at four ECT values, ECT = 17, 33, 50 and 75 × 10−5 mm, for each material group. Hence, for each value of ECT, V1 × 10.26 = V10 × 100.26 = V100 × 1000.26 = C. Side Feed, Roughing and Finishing.—In cylindrical grinding, the side feed, fs = C × Width, does not impact on the values in the tables, but on the feed rate FR, where the fraction of the wheel width C is usually selected for roughing and in finishing operations, as shown in the following table. Work Material Roughing, C Finishing, C Unhardened Steel 2 ⁄ 3–3⁄ 4 1⁄ 3–3⁄ 8 Stainless Steel 1⁄ 2 1⁄ 4 Cast Iron 3⁄ 4 3⁄ 8 Hardened Steel 1⁄ 2 1⁄ 4 Finishing: The depth of cut in rough grinding is determined by the allowance and usually set at ar = 0.01 to 0.025 mm. The depth of cut for finishing is usually set at ar = 0.0025 mm and accompanied by higher wheel speeds in order to improve surface finish. However, the most important criterion for critical parts is to increase the work speed in order to avoid thermal damage and surface cracks. In cylindrical grinding, a reduction of side feed fs


Machinery's Handbook 27th Edition GRINDING FEEDS AND SPEEDS

1167

improves Ra as well. Small grit sizes are very important when very small finishes are required. See Figs. 4, 5, and 6 for reference. Terms and Definitions aa =depth of cut ar =radial depth of cut, mm C =fraction of grinding wheel width CEL = cutting edge length, mm CU =Taylor constant D =wheel diameter, mm DIST = grinding distance, mm dw =work diameter, mm ECT = equivalent chip thickness = f(ar,V,Vw,fs), mm Vw fs ( ar + 1 ) = 1 ÷ (V ÷ Vw ÷ ar + 1 ÷ fs) = -----------------------------V = approximately Vw × ar ÷ V = SMRR ÷ V ÷ 1000 = z × fz × ar × aa ÷ CEL ÷ (πD) mm FR = feed rate, mm/min = fs × RPMw for cylindrical grinding = fi × RPMw for plunge (in-feed) grinding fi = in-feed in plunge grinding, mm/rev of work fs =side feed or engaged wheel width in cylindrical grinding = C × Width = aa approximately equal to the cutting edge length CEL Grinding ratio = MRR÷W* = SMRR × T÷W* = 1000 × ECT × V × T÷W* MRR = metal removal rate = SMRR × T = 1000 × fs × ar × Vw mm3/min SMRR = specific metal removal rate obtained by dividing MRR by the engaged wheel width (C × Width) = 1000 × ar × Vw mm3/mm width/min Note: 100 mm3/mm/min = 0.155 in3/in/min, and 1 in3/in/min = 645.16 mm3/mm/min T, TU = wheel-life = Grinding ratio × W ÷ (1000 × ECT × V) minutes tc = grinding time per pass = DIST÷FR min = DIST÷FR + tsp (min) when spark-out time is included = # Strokes × (DIST÷FR + tsp) (min) when spark-out time and strokes are included tsp = spark-out time, minutes V,VU = wheel speed, m/min Vw,VwU = work speed = SMRR ÷ 1000 ÷ ar m/min W* = volume wheel wear, mm3 Width = wheel width (mm) RPM = wheel speed = 1000 × V ÷ D ÷ π rpm RPMw = work speed = 1000 × Vw ÷ Dw ÷ π rpm Relative Grindability.—An overview of grindability of the data base, which must be based on a constant wheel wear rate, or wheel-life, is demonstrated using 10 minutes wheel-life shown in Table 2.



GRINDING FEEDS AND SPEEDS Table 2. Grindability Overview Vw

Material Group

ECT × 10−5

V10

SMRR10

Roughing Depth ar = 0.025

1 Unhardened 2 Stainless 3 Cast Iron 4 Tool Steel 5 Tool Steel 6 Tool Steel 7Tool Steel 8 Heat resistant 9 Carbide with Diamond Wheel 10 Ceramics with Diamond Wheel

33 33 33 33 33 33 33 33

3827 1080 4000 3190 2870 2580 1080 1045

1263 360 1320 1050 950 850 360 345

50 15 53 42 38 35 15 14

500 150 530 420 380 350 150 140

Finishing Depth ar = 0.0025

5

V600 = 1200 SMRR600 = 50

2

20

5

V600 = 411 SMRR600 = 21

0.84

84

Procedure to Determine Data.—The following wheel-life recommendations are designed for 4 values of ECT = 0.00017, 0.00033, 0.00050 and 0.00075 mm (shown as 17, 33, 50 and 75 in the tables). Lower values of ECT than 0.00010 mm (0.000004 in.) are not recommended as these may lie to the left of the H-curve. The user selects any one of the ECT values, or interpolates between these, and selects the wheel speed for 10 or 100 minutes life, denoted by V10 and V100, respectively. For other desired wheel lives the wheel speed can be calculated from the tabulated Taylor constants C and n = 0.26 as follows: (V × T(desired)) 0.26 = C, the value of which is tabulated for each ECT value. C is the value of cutting speed V at T = 1 minute, hence is the same as for the speed V1 (V1 ×1^0.26 =C) V10 C ÷ 100.26 = C ÷ 1.82 V100 C ÷ 1000.26 = C ÷ 3.31. Example 6: A tool steel in material group 6 with ECT = 0.00033, has constant C= 4690, V10 = 2578 m/min, and V100 = 1417 m/min. From this information, find the wheel speed for desired wheel-life of T = 15 minutes and T = 45 minutes For T = 15 minutes we get V15 = 4690 ÷ 150.26 = 2319 m/min (7730 fpm) and for T = 45 minutes V45 = 4690 ÷ 450.26 = 1743 m/min (5810 fpm). The Tables are arranged in 3 sections: 1. Speeds V10 and V1 = Constant CST(standard) for 4 ECT values 0.00017, 0.00033, 0.00050 and 0.00075 mm. Values CU and V10U refer to user calibration of the standard values in each material group, explained in the following. 2. Speeds V100 (first row of 3), V10 and V1 (last in row) corresponding to wheel lives 100, 10 and 1 minutes, for 4 ECT values 0.00017, 0.00033, 0.00050 and 0.00075 mm. 3. Specific metal removal rates SMRR100, SMRR10 and SMRR1 corresponding to wheel lives 100, 10 and 1 minutes, for the 4 ECT values 0.00017, 0.00033, 0.00050, and 0.00075 mm



1169

The 2 Graphs show: wheel life versus wheel speed in double logarithmic coordinates (Taylor lines); and, SMRR versus wheel speed in double logarithmic coordinates for 4 ECT values: 0.00017, 0.00033, 0.00050 and 0.00075 mm.

Tool Life T (min)

Table 1. Group 1—Unhardened Steels ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 8925

Constant C = 6965

Constant C = 5385

Constant C = 3885

VT

SMRR

VT

SMRR

VT

SMRR

VT

100

2695

460

2105

695

1625

815

1175

880

10

4905

835

3830

1265

2960

1480

2135

1600

1

8925

1520

6965

2300

5385

2695

3885

2915

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100

10000

SMRR, mm3/mm/min

ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

10

1 1000

Fig. 1a. T–V

1000

T=100 ECT = 17 ECT = 33 ECT = 50 ECT = 75 100 1000

10000

V, m/min

T=1 min. T=10 min.

10000

V, m/min

Fig. 1b. SMRR vs. V, T = 100, 10, 1 minutes

Tool Life T (min)

Table 2. Group 2—Stainless Steels SAE 30201 – 30347, SAE 51409 – 51501 ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 2270

Constant C = 1970

Constant C = 1505

Constant C = 1010

VT

SMRR

VT

SMRR

VT

SMRR

VT

100

685

115

595

195

455

225

305

230

10

1250

210

1080

355

825

415

555

415

1

2270

385

1970

650

1505

750

1010

760

LIVE GRAPH

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10000

100

SMRR, mm3/mm/min

ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

10

ECT = 17 ECT = 33 ECT = 50 ECT = 75

1000

100

1 100

1000

V, m/min

Fig. 2a. T–V

10000

100

1000

10000

V, m/min




GRINDING FEEDS AND SPEEDS

Tool Life T (min)

Table 3. Group 3—Cast Iron ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 10710

Constant C = 8360

Constant C = 6465

Constant C = 4665

VT

SMRR

VT

SMRR

VT

SMRR

VT

SMRR

100

3235

550

2525

835

1950

975

1410

1055

10

5885

1000

4595

1515

3550

1775

2565

1920

1

10710

1820

8360

2760

6465

3230

4665

3500

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10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

T = 1 min

SMRR, mm3/mm/min

T, minutes

100

1 1000

Fig. 3a. T–V

T = 10 min T = 100 min ECT = 17 ECT = 33 ECT = 50 ECT = 75 100

10000

V, m/min

1000

1000

10000

V, m/min


Tool Life T (min)

Table 4. Group 4—Tool Steels, M1, M8, T1, H, O, L, F, 52100

100

ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 7440

Constant C = 5805

Constant C = 4490

Constant C = 3240

VT

SMRR

VT

SMRR

VT

SMRR

VT

SMRR

2245

380

1755

580

1355

680

980

735

10

4090

695

3190

1055

2465

1235

1780

1335

1

7440

1265

5805

1915

4490

2245

3240

2430

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100

T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

1 1000

10000

V, m/min

Fig. 4a. T–V

SMRR, mm3/mm/min

10000

T = 1 min T = 10 min 1000

T = 100 min

100

ECT = 17 ECT = 33 ECT = 50 ECT = 75

1000

10000

V, m/min




1171

Tool Life T (min)

Table 5. Group 5—Tool Steels, M2, T2, T5, T6, D2, D5, H41, H42, H43, M50 ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 6695

Constant C = 5224

Constant C = 4040

Constant C = 2915

VT

SMRR

VT

SMRR

VT

SMRR

VT

100

2020

345

1580

520

1220

610

880

660

10

3680

625

2870

945

2220

1110

1600

1200

1

6695

1140

5225

1725

4040

2020

2915

2185

LIVE GRAPH

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100

10

SMRR, mm3/mm/min

10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

1000

ECT = 17 ECT = 33 ECT = 50 ECT = 75

1 1000

100

10000

V, m/min

Fig. 5a. T–V

1000

V, m/min

10000


Tool Life T (min)

Table 6. Group 6—Tool Steels, M3, M4, T3, D7 ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 5290

Constant C = 4690

Constant C = 3585

Constant C = 2395

VT

100

SMRR

VT

SMRR

VT

SMRR

VT

1600

270

SMRR

1415

465

1085

540

725

10

2910

540

495

2580

850

1970

985

1315

1

5290

985

900

4690

1550

3585

1795

2395

1795

LIVE GRAPH

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10000

T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75 10

SMRR, mm3/mm/min

100

1000

ECT = 17 ECT = 33 ECT = 50 ECT = 75 100

1 1000

V, m/min

Fig. 6a. Group 6 Tool Steels T–V

10000

1000

10000

V, m/min




GRINDING FEEDS AND SPEEDS

Tool Life T (min)

Table 7. Group 7—Tool Steels, T15, M15 ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 2270

Constant C = 1970

Constant C = 1505

Constant C = 1010

VT

SMRR

VT

SMRR

VT

SMRR

VT

100

685

115

595

195

455

225

305

230

10

1250

210

1080

355

825

415

555

415

1

2270

385

1970

650

1505

750

1010

760

LIVE GRAPH

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10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

ETC = 17 ETC = 33

SMRR, mm3/mm/min

100

T, minutes

SMRR

ETC = 50 ETC = 75

1000

100

1 100

1000

100

10000

1000

10000

V, m/min

V, m/min

Fig. 7a. T–V


Tool Life T (min)

Table 8. Group 8—Heat Resistant Alloys, Inconel, Rene, etc. ECT = 0.00017 mm

ECT = 0.00033 mm

ECT = 0.00050 mm

ECT = 0.00075 mm

Constant C = 2150

Constant C = 1900

Constant C = 1490

Constant C = 1035

VT

SMRR

VT

SMRR

VT

SMRR

VT

100

650

110

575

190

450

225

315

235

10

1185

200

1045

345

820

410

570

425

1

2150

365

1900

625

1490

745

1035

780

LIVE GRAPH

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100

10000

SMRR, mm3/mm/min

ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

10

1 100

1000

V, m/min

Fig. 8a. T–V

10000

ETC = 17 ETC = 33 ETC = 50 ETC = 75

1000

100 100

1000

10000

V, m/min




1173

Tool Life T (min)

Table 9. Group 9—Carbide Materials, Diamond Wheel ECT = 0.00002 mm

ECT = 0.00003 mm

ECT = 0.00005 mm

ECT = 0.00008 mm

Constant C = 9030

Constant C = 8030

Constant C = 5365

Constant C = 2880

VT

SMRR

VT

SMRR

VT

SMRR

VT

SMRR

4800

1395

30

1195

35

760

40

390

30

600

2140

45

1855

55

1200

60

625

50

10

4960

100

4415

130

2950

145

1580

125

LIVE GRAPH

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10000

T, minutes

1000

100

10

ECT = 2 ECT = 3 ECT = 5 ECT = 8

100

10

10000

1000

100

1000

SMRR, mm3/mm/min

ECT = 2 ECT = 3 ECT = 5 ECT = 8

100

1000

10000

V, m/min

V, m/min

Fig. 9a. T–V


Tool Life T (min)

Table 10. Group 10 — Ceramic Materials Al2O3, ZrO2, SiC, Si3N4, Diamond Wheel ECT = 0.00002 mm

ECT = 0.00003 mm

ECT = 0.00005 mm

ECT = 0.00008 mm

Constant C = 2460

Constant C = 2130

Constant C = 1740

Constant C = 1420

VT

SMRR

VT

SMRR

VT

SMRR

VT

4800

395

8

335

10

265

13

210

17

600

595

12

510

15

410

20

330

25

10

1355

25

1170

35

955

50

780

60

LIVE GRAPH

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10000

100 ECT = 2 ECT = 3 ECT = 5 ECT = 8

SMRR, mm3/mm/min

ECT = 2 ECT = 3 ECT = 5 ECT = 8

T, minutes

1000

100

10 100

SMRR

10 1000

V, m/min

Fig. 10a. T–V

10000

100

1000

10000

V, m/min




GRINDING FEEDS AND SPEEDS User Calibration of Recommendations

It is recommended to copy or redraw the standard graph for any of the material groups before applying the data calibration method described below. The method is based on the user’s own experience and data. The procedure is described in the following and illustrated in Table 11 and Fig. 12. Only one shop data set is needed to adjust all four Taylor lines as shown below. The required shop data is the user’s wheel-life TU obtained at the user’s wheel speed VU, the user’s work speed VwU, and depth of cut ar. 1) First the user finds out which wheel-life TU was obtained in the shop, and the corresponding wheel speed VU, depth of cut ar and work speed VwU. 2) Second, calculate: a) ECT = VwU × ar ÷ VU b) the user Taylor constant CU = VU × TU0.26 V10U = CU ÷ 100.26 V100U = CU ÷ 1000.26 3) Thirdly, the user Taylor line is drawn in the pertinent graph. If the user wheel-life TU is longer than that in the standard graph the speed values will be higher, or if the user wheellife is shorter the speeds CU, V10U, V100U will be lower than the standard values C, V10 and V100. The results are a series of lines moved to the right or to the left of the standard Taylor lines for ECT = 17, 33, 50 and 75 × 10−5 mm. Each standard table contains the values C = V1, V10, V100 and empty spaces for filling out the calculated user values: CU = VU × TU0.26, V10U = CU ÷ 100.26 and V100U = CU ÷ 1000.26. Example 7: Assume the following test results on a Group 6 material: user speed is VU = 1800 m/min, wheel-life TU = 7 minutes, and ECT = 0.00017 mm. The Group 6 data is repeated below for convenience. Standard Table Data, Group 6 Material Tool Life T (min)

ECT = 0.00017 mm Constant C = 5290 VT SMRR

100 10 1

1600 2910 5290

270 495 900

ECT = 0.00033 mm Constant C = 4690 VT SMRR 1415 2580 4690


465 850 1550

1085 1970 3585

540 985 1795

725 1315 2395

540 985 1795

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10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

SMRR, mm3/mm/min

100

T, minutes


1000

ECT = 17 ECT = 33 ECT = 50 ECT = 75 100

1 1000

V, m/min

Fig. 11a. Group 6 Tool Steels, T–V

10000

1000

10000

V, m/min




1175

Calculation Procedure 1) Calculate V1U, V10U, V100U and SMRR1U, SMRR10U, SMRR100U for ECT = 0.00017 mm a) V1U = the user Taylor constant CU = VU × TU0.26 = 1800 × 7 0.26 = 2985 m/min, and SMRR1U = 1000 × 2985 × 0.00017 = 507 mm3/mm width/min V10U = CU ÷ 100.26 = 2985 ÷ 10 0.26 = 1640 m/min, and SMRR10U = 1000 × 1640 × 0.00017 = 279 mm3/mm width/min V100U = CU ÷ 1000.26 = 2985 ÷ 100 0.26 = 900 m/min, and SMRR100U = 1000 × 900 × 0.00017 = 153 mm3/mm width/min 2) For ECT = 0.00017 mm, calculate the ratio of user Taylor constant to standard Taylor constant from the tables = CU ÷ CST = CU ÷ V1 = 2985 ÷ 5290 = 0.564 (see Table 6 for the value of CST = V1 at ECT = 0.00017 mm). 3) For ECT = 0.00033, 0.00050, and 0.00075 mm calculate the user Taylor constants from CU = CST × (the ratio calculated in step 2) = V1 × 0.564 = V1U. Then, calculate V10U and V100U and SMRR1U, SMRR10U, SMRR100U using the method in items 1b) and 1c) above. a) For ECT = 0.00033 mm V1U = CU = 4690 × 0.564 = 2645 m/min V10U = CU ÷ 100.26 = 2645 ÷ 10 0.26 = 1455 m/min V100U = CU ÷ 1000.26 = 2645 ÷ 100 0.26 = 800 m/min SMRR1U, SMRR10U, and SMRR100U = 876, 480, and 264 mm3/mm width/min b) For ECT = 0.00050 mm V1U = CU = 3590 × 0.564 = 2025 m/min V10U = CU ÷ 100.26 = 2025 ÷ 10 0.26 = 1110 m/min V100U = CU ÷ 1000.26 = 2025 ÷ 100 0.26 = 610 m/min SMRR1U, SMRR10U, and SMRR100U = 1013, 555, and 305 mm3/mm width/min c) For ECT = 0.00075 mm V1U = CU = 2395 × 0.564 = 1350 m/min V10U = CU ÷ 100.26 = 1350 ÷ 10 0.26 = 740 m/min V100U = CU ÷ 1000.26 = 1350 ÷ 100 0.26 = 405 m/min SMRR1U, SMRR10U, and SMRR100U = 1013, 555, and 305 mm3/mm width/min Thus, the wheel speed for any desired wheel-life at a given ECT can be calculated from V = CU ÷ T 0.26. For example, at ECT = 0.00050 mm and desired tool-life T = 9, V9 = 2025 ÷ 9 0.26 = 1144 m/min. The corresponding specific metal removal rate is SMRR = 1000 × 1144 × 0.0005 = 572 mm3/mm width/min (0.886 in3/inch width/min).

Tool Life T (min)

Table 11. User Calculated Data, Group 6 Material

100 10 1

ECT = 0.00017 mm User Constant CU = 2985 VT SMRR 900 1640 2985

153 279 507


264 480 876


305 555 1013



305 555 1013


GRINDING FEEDS AND SPEEDS LIVE GRAPH Click here to view

T minutes

100

Standard V10 = 2910 for T = 10 minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75 ECTU = 17 ECTU = 33 ECTU = 50 ECTU = 75

10 TU = 7

1 1000

VU = 1800

V m/min

10000

Fig. 12. Calibration of user grinding data to standard Taylor Lines User Input: VU = 1800 m/min, TU = 7 minutes, ECT = 0.00017 mm

Optimization.— As shown, a global optimum occurs along the G-curve, in selected cases for values of ECT around 0.00075, i.e. at high metal removal rates as in other machining operations. It is recommended to use the simple formula for economic life: TE = 3 × TV minutes. TV = TRPL + 60 × CE ÷ HR, minutes, where TRPL is the time required to replace wheel, CE = cost per wheel dressing = wheel cost + cost per dressing, and HR is the hourly rate. In grinding, values of TV range between 2 and 5 minutes in conventional grinders, which means that the economic wheel lives range between 6 and 15 minutes indicating higher metal removal rates than are commonly used. When wheels are sharpened automatically after each stroke as in internal grinding, or when grits are continually replaced as in abrasive grinding (machining), TV may be less than one minute. This translates into wheel lives around one minute in order to achieve minimum cost grinding. Grinding Cost, Optimization and Process Planning: More accurate results are obtained when the firm collects and systemizes the information on wheel lives, wheel and work speeds, and depths of cut from production runs. A computer program can be used to plan the grinding process and apply the rules and formulas presented in this chapter. A complete grinding process planning program, such as that developed by Colding International Corporation, can be used to optimize machine settings for various feed-speed preferences corresponding wheel-life requirements, minimum cost or maximum production rate grinding, required surface finish and sparkout time; machine and fixture requirements based on the grinding forces, torque and power for sharp and worn grinding wheels; and, detailed time and cost analysis per part and per batch including wheel dressing and wheel changing schedules. Table 12 summarizes the time and cost savings per batch as it relates to tool life. The sensitivity of how grinding parameters are selected is obvious. Minimum cost conditions yield a 51% reduction of time and 44% reduction of cost, while maximum production rate reduces total time by 65% but, at the expense of heavy wheel consumption (continuous dressing), cost by only 18%. Table 12. Wheel Life vs. Cost Preferences Long Life Economic Life Minimum Cost Max Production Rate

Time per Batch, minutes 2995 2433 1465 1041

Cost per Batch, $ Tooling Total Cost 39 2412 252 2211 199 1344 1244 1980

Reduction from Long Life,% Time Cost — — 19 8 51 44 65 18


Machinery's Handbook 27th Edition GRINDING WHEELS

1177

GRINDING AND OTHER ABRASIVE PROCESSES Processes and equipment discussed under this heading use abrasive grains for shaping workpieces by means of machining or related methods. Abrasive grains are hard crystals either found in nature or manufactured. The most commonly used materials are aluminum oxide, silicon carbide, cubic boron nitride and diamond. Other materials such as garnet, zirconia, glass and even walnut shells are used for some applications. Abrasive products are used in three basic forms by industry: a) Bonded to form a solid shaped tool such as disks (the basic shape of grinding wheels), cylinders, rings, cups, segments, or sticks to name a few. b) Coated on backings made of paper or cloth, in the form of sheets, strips, or belts. c) Loose, held in some liquid or solid carrier (for lapping, polishing, tumbling), or propelled by centrifugal force, air, or water pressure against the work surface (blast cleaning). The applications for abrasive processes are multiple and varied. They include: a) Cleaning of surfaces, also the coarse removal of excess material—such as rough offhand grinding in foundries to remove gates and risers. b) Shaping, such as in form grinding and tool sharpening. c) Sizing, a general objective, but of primary importance in precision grinding. d) Surface finish improvement, either primarily as in lapping, honing, and polishing or as a secondary objective in other types of abrasive processes. e) Separating, as in cut-off or slicing operations. The main field of application of abrasive processes is in metalworking, because of the capacity of abrasive grains to penetrate into even the hardest metals and alloys. However, the great hardness of the abrasive grains also makes the process preferred for working other hard materials, such as stones, glass, and certain types of plastics. Abrasive processes are also chosen for working relatively soft materials, such as wood, rubber, etc., for such reasons as high stock removal rates, long-lasting cutting ability, good form control, and fine finish of the worked surface. Grinding Wheels Abrasive Materials.—In earlier times, only natural abrasives were available. From about the beginning of this century, however, manufactured abrasives, primarily silicon carbide and aluminum oxide, have replaced the natural materials; even natural diamonds have been almost completely supplanted by synthetics. Superior and controllable properties, and dependable uniformity characterize the manufactured abrasives. Both silicon carbide and aluminum oxide abrasives are very hard and brittle. This brittleness, called friability, is controllable for different applications. Friable abrasives break easily, thus forming sharp edges. This decreases the force needed to penetrate into the work material and the heat generated during cutting. Friable abrasives are most commonly used for precision and finish grinding. Tough abrasives resist fracture and last longer. They are used for rough grinding, snagging, and off-hand grinding. As a general rule, although subject to variation: 1) Aluminum oxide abrasives are used for grinding plain and alloyed steel in a soft or hardened condition. 2) Silicon carbide abrasives are selected for cast iron, nonferrous metals, and nonmetallic materials. 3) Diamond is the best type of abrasive for grinding cemented carbides. It is also used for grinding glass, ceramics, and hardened tool steel.



GRINDING WHEELS

4) Cubic Boron Nitride (CBN) is known by several trade names including Borazon (General Electric Co.), ABN (De Beers), Sho-bon (Showa-Denko), and Elbor (USSR). CBN is a synthetic superabrasive used for grinding hardened steels and wear-resistant superalloys. (See Cubic Boron Nitride (CBN) starting on page 1013.) CBN grinding wheels have long lives and can maintain close tolerances with superior surface finishes. Bond Properties and Grinding Wheel Grades.—The four main types of bonds used for grinding wheels are the vitrified, resinoid, rubber, and metal. Vitrified bonds are used for more than half of all grinding wheels made, and are preferred because of their strength and other desirable qualities. Being inert, glass-like materials, vitrified bonds are not affected by water or by the chemical composition of different grinding fluids. Vitrified bonds also withstand the high temperatures generated during normal grinding operations. The structure of vitrified wheels can be controlled over a wide range of strength and porosity. Vitrified wheels, however, are more sensitive to impact than those made with organic bonds. Resinoid bonds are selected for wheels subjected to impact, or sudden loads, or very high operating speeds. They are preferred for snagging, portable grinder uses, or roughing operations. The higher flexibility of this type of bond—essentially a filled thermosetting plastic—helps it withstand rough treatment. Rubber bonds are even more flexible than the resinoid type, and for that reason are used for producing a high finish and for resisting sudden rises in load. Rubber bonded wheels are commonly used for wet cut-off wheels because of the nearly burr-free cuts they produce, and for centerless grinder regulating wheels to provide a stronger grip and more reliable workpiece control. Metal bonds are used in CBN and diamond wheels. In metal bonds produced by electrodeposition, a single layer of superabrasive material (diamond or CBN) is bonded to a metal core by a matrix of metal, usually nickel. The process is so controlled that about 30– 40 per cent of each abrasive particle projects above the deposited surface, giving the wheel a very aggressive and free-cutting action. With proper use, such wheels have remarkably long lives. When dulled, or worn down, the abrasive can be stripped off and the wheel renewed by a further deposit process. These wheels are also used in electrical discharge grinding and electrochemical grinding where an electrically conductive wheel is needed. In addition to the basic properties of the various bond materials, each can also be applied in different proportions, thereby controlling the grade of the grinding wheel. Grinding wheel grades commonly associated with hardness, express the amount of bond material in a grinding wheel, and hence the strength by which the bond retains the individual grains. During grinding, the forces generated when cutting the work material tend to dislodge the abrasive grains. As the grains get dull and if they don't fracture to resharpen themselves, the cutting forces will eventually tear the grains from their supporting bond. For a “soft” wheel the cutting forces will dislodge the abrasive grains before they have an opportunity to fracture. When a “hard” wheel is used, the situation is reversed. Because of the extra bond in the wheel the grains are so firmly held that they never break loose and the wheel becomes glazed. During most grinding operations it is desirable to have an intermediate wheel where there is a continual slow wearing process composed of both grain fracture and dislodgement. The grades of the grinding wheels are designated by capital letters used in alphabetical order to express increasing “hardness” from A to Z. Grinding Wheel Structure.—The individual grains, which are encased and held together by the bond material, do not fill the entire volume of the grinding wheel; the intermediate open space is needed for several functional purposes such as heat dissipation, coolant application, and particularly, for the temporary storage of chips. It follows that the



1179

spacing of the grains must be greater for coarse grains which cut thicker chips and for large contact areas within which the chips have to be retained on the surface of the wheel before being disposed of. On the other hand, a wide spacing reduces the number of grains that contact the work surface within a given advance distance, thereby producing a coarser finish. In general, denser structures are specified for grinding hard materials, for high-speed grinding operations, when the contact area is narrow, and for producing fine finishes and/or accurate forms. Wheels with open structure are used for tough materials, high stock removal rates, and extended contact areas, such as grinding with the face of the wheel. There are, however, several exceptions to these basic rules, an important one being the grinding of parts made by powder metallurgy, such as cemented carbides; although they represent one of the hardest industrial materials, grinding carbides requires wheels with an open structure. Most kinds of general grinding operations, when carried out with the periphery of the wheel, call for medium spacing of the grains. The structure of the grinding wheels is expressed by numerals from 1 to 16, ranging from dense to open. Sometimes, “induced porosity” is used with open structure wheels. This term means that the grinding wheel manufacturer has placed filler material (which later burns out when the wheel is fired to vitrify the bond) in the grinding wheel mix. These fillers create large “pores” between grain clusters without changing the total volume of the “pores” in the grinding wheel. Thus, an A46-H12V wheel and an A46H12VP wheel will contain the same amounts of bond, abrasive, and air space. In the former, a large number of relatively small pores will be distributed throughout the wheel. The latter will have a smaller number of larger pores. American National Standard Grinding Wheel Markings.—ANSI Standard B74.131990“ Markings for Identifying Grinding Wheels and Other Bonded Abrasives,” applies to grinding wheels and other bonded abrasives, segments, bricks, sticks, hones, rubs, and other shapes that are for removing material, or producing a desired surface or dimension. It does not apply to specialities such as sharpening stones and provides only a standard system of markings. Wheels having the same standard markings but made by different wheel manufacturers may not—and probably will not—produce exactly the same grinding action. This desirable result cannot be obtained because of the impossibility of closely correlating any measurable physical properties of bonded abrasive products in terms of their grinding action. Symbols for designating diamond and cubic boron wheel compositions are given on page 1204. Sequence of Markings.—The accompanying illustration taken from ANSI B74.13-1990 shows the makeup of a typical wheel or bonded abrasive marking.

The meaning of each letter and number in this or other markings is indicated by the following complete list. 1) Abrasive Letters: The letter (A) is used for aluminum oxide, (C) for silicon carbide, and (Z) for aluminum zirconium. The manufacturer may designate some particular type in any one of these broad classes, by using his own symbol as a prefix (example, 51). 2) Grain Size: The grain sizes commonly used and varying from coarse to very fine are indicated by the following numbers: 8, 10, 12, 14, 16, 20, 24, 30, 36, 46, 54, 60,70, 80, 90, 100, 120, 150, 180, and 220. The following additional sizes are used occasionally: 240, 280, 320, 400, 500, and 600. The wheel manufacturer may add to the regular grain number an additional symbol to indicate a special grain combination.



GRINDING WHEELS

3) Grade: Grades are indicated by letters of the alphabet from A to Z in all bonds or processes. Wheel grades from A to Z range from soft to hard. 4) Structure: The use of a structure symbol is optional. The structure is indicated by Nos. 1 to 16 (or higher, if necessary) with progressively higher numbers indicating a progressively wider grain spacing (more open structure). 5) Bond or Process: Bonds are indicated by the following letters: V, vitrified; S, silicate; E, shellac or elastic; R, rubber; RF, rubber reinforced; B, resinoid (synthetic resins); BF, resinoid reinforced; O, oxychloride. 6) Manufacturer's Record: The sixth position may be used for manufacturer's private factory records; this is optional. American National Standard Shapes and Sizes of Grinding Wheels.—T h e A N S I Standard B74.2-1982 which includes shapes and sizes of grinding wheels, gives a wide variety of grinding wheel shape and size combinations. These are suitable for the majority of applications. Although grinding wheels can be manufactured to shapes and dimensions different from those listed, it is advisable, for reasons of cost and inventory control, to avoid using special shapes and sizes, unless technically warranted. Standard shapes and size ranges as given in this Standard together with typical applications are shown in Table 1a for inch dimensions and in Table 1b for metric dimensions. The operating surface of the grinding wheel is often referred to as the wheel face. In the majority of cases it is the periphery of the grinding wheel which, when not specified otherwise, has a straight profile. However, other face shapes can also be supplied by the grinding wheel manufacturers, and also reproduced during usage by appropriate truing. ANSI B74.2-1982 standard offers 13 different shapes for grinding wheel faces, which are shown in Table 2. The Selection of Grinding Wheels.—In selecting a grinding wheel, the determining factors are the composition of the work material, the type of grinding machine, the size range of the wheels used, and the expected grinding results, in this approximate order. The Norton Company has developed, as the result of extensive test series, a method of grinding wheel recommendation that is more flexible and also better adapted to taking into consideration pertinent factors of the job, than are listings based solely on workpiece categories. This approach is the basis for Tables 3 through 6, inclusive. Tool steels and constructional steels are considered in the detailed recommendations presented in these tables. Table 3 assigns most of the standardized tool steels to five different grindability groups. The AISI-SAE tool steel designations are used. After having defined the grindability group of the tool steel to be ground, the operation to be carried out is found in the first column of Table 4. The second column in this table distinguishes between different grinding wheel size ranges, because wheel size is a factor in determining the contact area between wheel and work, thus affecting the apparent hardness of the grinding wheel. Distinction is also made between wet and dry grinding. Finally, the last two columns define the essential characteristics of the recommended types of grinding wheels under the headings of first and second choice, respectively. Where letters are used preceding A, the standard designation for aluminum oxide, they indicate a degree of friability different from the regular, thus: SF = semi friable (Norton equivalent 16A) and F = friable (Norton equivalent 33A and 38A). The suffix P, where applied, expresses a degree of porosity that is more open than the regular.



1181

Table 1a. Standard Shapes and Inch Size Ranges of Grinding Wheels ANSI B74.2-1982 Size Ranges of Principal Dimensions, Inches Applications

D = Dia.

T = Thick.

H = Hole

Type 1. Straight Wheel For peripheral grinding.

1⁄ to 3⁄ 64 8

1⁄ to 16

12 to 48

1⁄ to 2

6

5 to 20

14 to 30

1 to 20

5 or 12

8 to 14

1 to 12

1⁄ to 4

4

1⁄ to 4

2

3⁄ to 7⁄ 32 8

General purpose

6 to 36

1⁄ to 2

4

1⁄ to 2

For wet tool grinding only

30 or 36

3 or 4

20

CUTTING OFF (Organic bonds only) CYLINDRICAL GRINDING Between centers CYLINDRICAL GRINDING Centerless grinding wheels CYLINDRICAL GRINDING Centerless regulating wheels INTERNAL GRINDING

1 to 48

6

3 to 6

OFFHAND GRINDING Grinding on the periphery

1⁄ to 4

11⁄2

1⁄ to 2

3

11⁄4

SAW GUMMING (F-type face)

6 to 12

SNAGGING Floor stand machines

12 to 24

1 to 3

11⁄4 to 21⁄2

SNAGGING Floor stand machines (Organic bond, wheel speed over 6500 sfpm)

20 to 36

2 to 4

6 or 12

SNAGGING Mechanical grinders (Organic bond, wheel speed up to 16,500 sfpm)

24

SNAGGING Portable machines SNAGGING Portable machines (Reinforced organic bond, 17,000 sfpm) SNAGGING Swing frame machines SURFACE GRINDING Horizontal spindle machines TOOL GRINDING Broaches, cutters, mills, reamers, taps, etc.

2 to 3

12

3 to 8

1⁄ to 4

1

6 or 8

3⁄ or 4

1

1

2 to 3

31⁄2 to

6 to 24

1⁄ to 2

6

11⁄4 to

6 to 10

1⁄ to 1⁄ 4 2

5⁄ to 8

12 to 24

3⁄ to 5⁄ 8 8

12 12 5

Type 2. Cylindrical Wheel Side grinding wheel — mounted on the diameter; may also be mounted in a chuck or on a plate.

W = Wall SURFACE GRINDING Vertical spindle machines

8 to 20

4 or 5


1 to 4


GRINDING WHEELS

Table 1a. (Continued) Standard Shapes and Inch Size Ranges of Grinding Wheels ANSI B74.2-1982 Size Ranges of Principal Dimensions, Inches Applications

D = Dia.

T = Thick.

H = Hole

Type 5. Wheel, recessed one side For peripheral grinding. Allows wider faced wheels than the available mounting thickness, also grinding clearance for the nut and flange.

CYLINDRICAL GRINDING Between centers

12 to 36

11⁄2 to 4

5 or 12

CYLINDRICAL GRINDING Centerless regulating wheel

8 to 14

3 to 6

3 or 5

INTERNAL GRINDING

3⁄ to 8

4

3⁄ to 8

2

1⁄ to 7⁄ 8 8

SURFACE GRINDING Horizontal spindle machines

7 to 24

3⁄ to 4

6

11⁄4 to 12

Type 6. Straight-Cup Wheel Side grinding wheel, in whose dimensioning the wall thickness (W) takes precedence over the diameter of the recess. Hole is 5⁄ -11UNC-2B threaded for the snagging wheels and 8 1⁄ or 11⁄ ″ for the tool grinding wheels. 2 4

W = Wall SNAGGING Portable machines, organic bond only.

4 to 6

2

TOOL GRINDING Broaches, cutters, mills, reamers, taps, etc.

2 to 6

1 1⁄4 to 2

3⁄ to 4

11⁄2

5⁄ or 3⁄ 16 8

Type 7. Wheel, recessed two sides Peripheral grinding. Recesses allow grinding clearance for both flanges and also narrower mounting thickness than overall thickness.


12 to 36

11⁄2 to 4

5 or 12

CYLINDRICAL GRINDING Centerless regulating wheel

8 to 14

4 to 20

3 to 6


12 to 24

2 to 6

5 to 12



1183


D = Dia.

T = Thick.

H = Hole

Type 11. Flaring-Cup Wheel Side grinding wheel with wall tapered outward from the back; wall generally thicker in the back.

SNAGGING Portable machines, organic bonds only, threaded hole

4 to 6

2


2 to 5

1 1⁄4 to 2

5⁄ -11 8

UNC-2B

1⁄ to 2

1 1⁄4

Type 12. Dish Wheel Grinding on the side or on the Uface of the wheel, the U-face being always present in this type.


3 to 8

1⁄ or 3⁄ 2 4

1⁄ to 2

1 1⁄4

Type 13. Saucer Wheel Peripheral grinding wheel, resembling the shape of a saucer, with cross section equal throughout.

1⁄ to 2

SAW GUMMING Saw tooth shaping and sharpening

8 to 12

1 3⁄4 U&E 11⁄2

1⁄ to 4

3⁄ to 4

1 1⁄4

Type 16. Cone, Curved Side Type 17. Cone, Straight Side, Square Tip Type 17R. Cone, Straight Side, Round Tip (Tip Radius R = J/2)

SNAGGING Portable machine, threaded holes

11⁄4 to 3

2 to 31⁄2


3⁄ -24UNF-2B 8

to 5⁄ -11UNC-2B 8


GRINDING WHEELS


D = Dia.

T = Thick.

H = Hole

Type 18. Plug, Square End Type 18R. Plug, Round End R = D/2

Type 19. Plugs, Conical End, Square Tip Type 19R. Plugs, Conical End, Round Tip (Tip Radius R = J/2)

SNAGGING Portable machine, threaded holes

11⁄4 to 3

2 to 31⁄2

3⁄ -24UNF-2B 8

to 5⁄ -11UNC-2B 8

Type 20. Wheel, Relieved One Side Peripheral grinding wheel, one side flat, the other side relieved to a flat.


12 to 36

3⁄ to 4

4

5 to 20

Type 21. Wheel, Relieved Two Sides Both sides relieved to a flat.

Type 22. Wheel, Relieved One Side, Recessed Other Side One side relieved to a flat.

Type 23. Wheel, Relieved and Recessed Same Side The other side is straight.

CYLINDRICAL GRINDING Between centers, with wheel periphery

20 to 36

2 to 4


12 or 20


1185


D = Dia.

T = Thick.

H = Hole

Type 24. Wheel, Relieved and Recessed One Side, Recessed Other Side One side recessed, the other side is relieved to a recess.

Type 25. Wheel, Relieved and Recessed One Side, Relieved Other Side One side relieved to a flat, the other side relieved to a recess.

Type 26. Wheel, Relieved and Recessed Both Sides

CYLINDRICAL GRINDING Between centers, with the periphery of the wheel

20 to 36

2 to 4

12 or 20

TYPES 27 & 27A. Wheel, Depressed Center 27. Portable Grinding: Grinding normally done by contact with work at approx. a 15° angle with face of the wheel. 27A. Cutting-off: Using the periphery as grinding face. CUTTING OFF Reinforced organic bonds only SNAGGING Portable machine

16 to 30

U = E = 5⁄32 to 1⁄4

1 or 1 1⁄2

3 to 9

U = Uniform thick. 1⁄8 to 3⁄8

3⁄ or 7⁄ 8 8

Type 28. Wheel, Depressed Center (Saucer Shaped Grinding Face) Grinding at approx. 15° angle with wheel face.

SNAGGING Portable machine

7 or 9

U = Uniform thickness 1⁄4

Throughout table large open-head arrows indicate grinding surfaces.


7⁄ 8


GRINDING WHEELS Table 1b. Standard Shapes and Metric Size Ranges of Grinding Wheels ANSI B74.2-1982 Size Ranges of Principal Dimensions, Millimeters Applications

D = Diam.

T = Thick.

H = Hole

Type 1. Straight Wheela CUTTING OFF (nonreinforced and reinforced organic bonds only)

150 to 1250

0.8 to 10

16 to 152.4


300 to 1250

20 to 160

127 to 508

CYLINDRICAL GRINDING Centerless grinding wheels

350 to 750

25 to 500

127 or 304.8

CYLINDRICAL GRINDING Centerless regulating wheels

200 to 350

25 to 315

76.2 to 152.4

6 to 100

6 to 50

2.5 to 25

General purpose

150 to 900

13 to 100

20 to 76.2

For wet tool grinding only

750 or 900

80 or 100

508

SAW GUMMING (F-type face)

150 to 300

6 to 40

32

SNAGGING Floor stand machines

300 to 600

25 to 80

32 to 76.2

SNAGGING Floor stand machines(organic bond, wheel speed over 33 meters per second)

500 to 900

50 to 100

152.4 or 304.8

SNAGGING Mechanical grinders (organic bond, wheel speed up to 84 meters per second)

600

50 to 80

304.8

SNAGGING Portable machines

80 to 200

6 to 25

10 to 16

SNAGGING Swing frame machines (organic bond)

300 to 600

50 to 80

88.9 to 304.8


150 to 600

13 to 160

32 to 304.8


150 to 250

6 to 20

32 to 127

INTERNAL GRINDING OFFHAND GRINDING Grinding on the periphery

Type 2. Cylindrical Wheela

W = Wall SURFACE GRINDING Vertical spindle machines

200 to 500

100 or 125


25 to 100


1187

Table 1b. (Continued) Standard Shapes and Metric Size Ranges of Grinding Wheels ANSI B74.2-1982 Size Ranges of Principal Dimensions, Millimeters Applications

D = Diam.

T = Thick.

H = Hole

Type 5. Wheel, recessed one sidea CYLINDRICAL GRINDING Between centers

300 to 900

40 to 100

127 or 304.8


200 to 350

80 to 160

76.2 or 127

INTERNAL GRINDING

10 to 100

10 to 50

3.18 to 25

Type 6. Straight-Cup Wheela

W = Wall SNAGGING Portable machines, organic bond only (hole is 5⁄8-11 UNC-2B)

100 to 150

50

20 to 40

TOOL GRINDING Broaches, cutters, mills, reamers, taps, etc. (Hole is 13 to 32 mm)

50 to 150

32 to 50

8 or 10

Type 7. Wheel, recessed two sidesa CYLINDRICAL GRINDING Between centers

300 to 900

40 to 100

127 or 304.8


200 to 350

100 to 500

76.2 to 152.4

Type 11. Flaring-Cup Wheela SNAGGING Portable machines, organic bonds only, threaded hole

100 to 150

50


50 to 125

32 to 50

13 to 32

13 or 20

13 to 32

5⁄ -11 8

UNC-2B

Type 12. Dish Wheela TOOL GRINDING Broaches, cutters, mills, reamers, taps, etc.

80 to 200

Type 27 and 27A. Wheel, depressed centera CUTTING OFF Reinforced organic bonds only

400 to 750

U=E=6

25.4 or 38.1

SNAGGING Portable machines

80 to 230

U = E = 3.2 to 10

9.53 or 22.23

a See Table 1a for diagrams and descriptions of each wheel type.

All dimensions in millimeters.



GRINDING WHEELS Table 2. Standard Shapes of Grinding Wheel Faces ANSI B74.2-1982

Recommendations, similar in principle, yet somewhat less discriminating have been developed by the Norton Company for constructional steels. These materials can be ground either in their original state (soft) or in their after-hardened state (directly or following carburization). Constructional steels must be distinguished from structural steels which are used primarily by the building industry in mill shapes, without or with a minimum of machining. Constructional steels are either plain carbon or alloy type steels assigned in the AISISAE specifications to different groups, according to the predominant types of alloying elements. In the following recommendations no distinction is made because of different compositions since that factor generally, has a minor effect on grinding wheel choice in constructional steels. However, separate recommendations are made for soft (Table 5) and



1189

hardened (Table 6) constructional steels. For the relatively rare instance where the use of a single type of wheel for both soft and hardened steel materials is considered more important than the selection of the best suited types for each condition of the work materials, Table 5 lists “All Around” wheels in its last column. For applications where cool cutting properties of the wheel are particularly important, Table 6 lists, as a second alternative, porous-type wheels. The sequence of choices as presented in these tables does not necessarily represent a second, or third best; it can also apply to conditions where the first choice did not provide optimum results and by varying slightly the composition of the grinding wheel, as indicated in the subsequent choices, the performance experience of the first choice might be improved. Table 3. Classification of Tool Steels by their Relative Grindability Relative Grindability Group

AISI-SAE Designation of Tool Steels

GROUP 1—Any area of work surface

W1, W2, W5

High grindability tool and die steels

O1, O2, O6, O7

(Grindability index greater than 12)

H10, H11, H12, H13, H14

S1, S2, S4, S5, S6, S7

L2, L6 GROUP 2—Small area of work surface

H19, H20, H21, H22, H23, H24, H26

(as found in tools)

P6, P20, P21 T1, T7, T8

Medium grindability tool and die steels

M1, M2, M8, M10, M33, M50

(Grindability index 3 to 12)

D1, D2, D3, D4, D5, D6 A2, A4, A6, A8, A9, A10

GROUP 3—Small area of work surface

T4, T5, T6, T8

(as found in tools)

M3, M6, M7, M34, M36, M41, M42, M46, M48, M52, M62

Low grindability tool and die steels

D2, D5

(Grindability index between 1.0 and 3)

A11

GROUP 4—Large area of work surface (as found in dies)

All steels found in Groups 2 and 3

Medium and low grindability tool and die steels (Grindability index between 1.0 and 12) GROUP 5—Any area of work surface

D3, D4, D7 M4

Very low grindability tool and die steels

A7

(Grindability index less than 1.0)

T15



GRINDING WHEELS Table 4. Grinding Wheel Recommendations for Hardened Tool Steels According to their Grindability Operation

Surfacing Surfacing wheels

Segments or Cylinders Cups

Wheel or Rim First-Choice Diameter, Specifications Inches Group 1 Steels 14 and smaller 14 and smaller Over 14 11⁄2 rim or less 3⁄ rim or less 4

Second-Choice Specifications

Wet FA46-I8V Dry FA46-H8V Wet FA36-I8V Wet FA30-H8V

SFA46-G12VP FA46-F12VP SFA36-I8V FA30-F12VP

Wet FA36-H8V

FA46-F12VP

(for rims wider than 11⁄2 inches, go one grade softer in available specifications) Cutter sharpening Straight wheel Dish shape Cup shape Form tool grinding

Cylindrical Centerless Internal Production grinding

Tool room grinding

… … … … … 8 and smaller 8 and smaller 10 and larger 14 and smaller 16 and larger …

Wet FA46-K8V FA60-K8V Dry FA46-J8V FA46-H12VP Dry FA60-J8V FA60-H12VP Dry FA46-L8V FA60-H12VP Wet SFA46-L5V SFA60-L5V Wet FA60-L8V to FA100-M7V Dry FA60-K8V to FA100-L8V Wet FA60-L8V to FA80-M6V Wet SFA60-L5V … Wet SFA60-M5V … Wet SFA60-M5V …

Under 1⁄2

Wet SPA80-N6V

SFA80-N7V

1⁄ to 2

Wet SFA60-M5V

SFA60-M6V

Wet SFA54-L5V Wet SFA46-L5V Dry FA80-L6V

SFA54-L6V SFA46-K5V SFA80-L7V

1 Over 1 to 3 Over 3 Under 1⁄2

1⁄ to 1 Dry FA70-K7V 2 Over 1 to 3 Dry FA60-J8V Over 3 Dry FA46-J8V Group 2 Steels

Surfacing Straight wheels


14 and smaller 14 and smaller Over 14 11⁄2 rim or less 3⁄ rim or less 4

SFA70-K7V FA60-H12VP FA54-H12VP

Wet FA46-I8V Dry FA46-H8V Wet FA46-H8V Wet FA30-G8V

FA46-G12VP FA46-F12VP SFA46-I8V FA36-E12VP

Wet FA36-H8V

FA46-F12VP

(for rims wider than 11⁄2 inches, go one grade softer in available specifications)



1191

Table 4. (Continued) Grinding Wheel Recommendations for Hardened Tool Steels According to their Grindability Operation Cutter sharpening Straight wheel Dish shape Cup shape Form tool grinding

Cylindrical Centerless Internal Production grinding

Tool room grinding

Wheel or Rim Diameter, Inches … … … … … 8 and smaller 8 and smaller 10 and larger 14 and less 16 and larger …

First-Choice Specifications

Wet FA46-L5V FA60-K8V Dry FA46-J8V FA60-H12VP Dry FA60-J5V FA60-G12VP Dry FA46-K5V FA60-G12VP Wet FA46-L5V FA60-J8V Wet FA60-K8V to FA120-L8V Dry FA80-K8V to FA150-K8V Wet FA60-K8V to FA120-L8V Wet FA60-L5V SFA60-L5V Wet FA60-K5V SFA60-K5V Wet FA60-M5V SFA60-M5V

Under 1⁄2

Wet FA80-L6V

1⁄ to 2

Wet FA70-K5V

SFA70-K5V

Wet FA60-J8V Wet FA54-J8V

SFA60-J7V SFA54-J8V

Under 1⁄2

Dry FA80-I8V

Dry FA70-J8V 1 Over 1 to 3 Dry FA60-I8V Over 3 Dry FA54-I8V Group 3 Steels


SFA80-L6V

1 Over 1 to 3 Over 3

1⁄ to 2



14 and smaller 14 and smaller Over 14 11⁄2 rim or less 3⁄ rim or less 4

SFA80-K7V SFA70-J7V FA60-G12VP FA54-G12VP

Wet FA60-I8V Dry FA60-H8V Wet FA60-H8V Wet FA46-G8V

FA60-G12VP FA60-F12VP SFA60-I8V FA46-E12VP

Wet FA46-G8V

FA46-E12VP

(for rims wider than 11⁄2 inches, go one grade softer in available specifications) Cutter grinding Straight wheel Dish shape Cup shape Form tool grinding

… … … … … 8 and smaller 8 and smaller 10 and larger

Wet FA46-J8V FA60-J8V Dry FA46-I8V FA46-G12VP Dry FA60-H8V FA60-F12VP Dry FA46-I8V FA60-F12VP Wet FA46-J8V FA60-J8V Wet FA80-K8V to FA150-L9V Dry FA100-J8V to FA150-K8V Wet FA80-J8V to FA150-J8V



GRINDING WHEELS

Table 4. (Continued) Grinding Wheel Recommendations for Hardened Tool Steels According to their Grindability Operation Cylindrical Centerless Internal Production grinding

Tool room grinding

Wheel or Rim Diameter, Inches 14 and less 16 and larger …

First-Choice Specifications Wet FA80-L5V Wet FA60-L6V Wet FA60-L5V

Segments Cylinders Cups

Form tool grinding

Cylindrical Internal Production grinding

Tool room grinding

SFA80-L6V SFA60-K5V SFA60-L5V

Under 1⁄2

Wet FA90-L6V

SFA90-L6V

1⁄ to 2

Wet FA80-L6V

SFA80-L6V

Wet FA70-K5V Wet FA60-J5V Dry FA90-K8V

SFA70-K5V SFA60-J5V SFA90-K7V


1⁄ to 1 Dry FA80-J8V 2 Over 1 to 3 Dry FA70-I8V Over 3 Dry FA60-I8V Group 4 Steels



14 and smaller 14 and smaller Over 14 1 1⁄2 rim or less 1 1⁄2 rim or less 3⁄ rim or less 4

SFA80-J7V SFA70-G12VP SFA60-G12VP

Wet FA60-I8V Wet FA60-H8V Wet FA46-H8V Wet FA46-G8V

C60-JV C60-IV C60-HV C46-HV

Wet FA46-G8V

C60-HV

Wet FA46-G6V

C60-IV

(for rims wider than 1 1⁄2 inches, go one grade softer in available specifications) 8 and smaller Wet FA60-J8V to FA150-K8V 8 and smaller Dry FA80-I8V to FA180-J8V 10 and larger Wet FA60-J8V to FA150-K8V 14 and less Wet FA80-K8V C60-KV 16 and larger Wet FA60-J8V C60-KV Under 1⁄2

Wet FA90-L8V

1⁄ to 2

C90-LV


Wet FA80-K5V

C80-KV

Wet FA70-J8V Wet FA60-I8V Dry FA90-K8V

C70-JV C60-IV C90-KV

1⁄ to 1 2 Over 1 to 3 Over 3

Dry FA80-J8V

C80-JV

Dry FA70-I8V Dry FA60-H8V

C70-IV C60-HV



1193

Table 4. (Continued) Grinding Wheel Recommendations for Hardened Tool Steels According to their Grindability Wheel or Rim Diameter, Inches

Operation

FirstChoice Specifications

SecondChoice Specifications

ThirdChoice Specifications

Group 5 Steels Surfacing Straight wheels


14 and smaller

Wet SFA60-H8V

FA60-E12VP

C60-IV

14 and smaller

Dry SFA80-H8V

FA80-E12VP

C80-HV

Over 14

Wet SFA60-H8V

FA60-E12VP

C60-HV

1 1⁄2 rim or less

Wet SFA46-G8V

FA46-E12VP

C46-GV

3⁄ rim 4

Wet SFA60-G8V

FA60-E12VP

C60-GV

or less

(for rims wider than 1 1⁄2 inches, go one grade softer in available specifications) Cutter grinding …

Wet SFA60-I8V

SFA60-G12VP

…

…

Dry SFA60-H8V

SFA80-F12VP

…

Dish shape

…

Dry SFA80-H8V

SFA80-F12VP

…

Cup shape

…

Dry SFA60-I8V

SFA60-G12VP

…

…

Wet SFA60-J8V

SFA60-H12VP

…

Straight wheels

Form tool grinding

Cylindrical

…

8 and smaller

Wet FA80-J8V to FA180-J9V

8 and smaller

Dry FA100-I8V to FA220-J9V

…

10 and larger

Wet FA80-J8V to FA180-J9V

…

14 and less

Wet FA80-J8V

C80-KV

FA80-H12VP

16 and larger

Wet FA80-I8V

C80-KV

FA80-G12VP

Wet FA80-J5V

C80-LV

…

…

Centerless Internal

Wet FA100-L8V

C90-MV

…

Wet FA90-K8V

C80-LV

…

Over 1 to 3

Wet FA80-J8V

C70-KV

FA80-H12VP

Over 3

Wet FA70-I8V

C60-JV

FA70-G12VP

Dry FA100-K8V

C90-KV

…

Dry FA90-J8V

C80-JV

…

Production grind- Under 1⁄2 ing 1⁄ to 1 2

Tool room grinding

Under 1⁄ to 2

1⁄ 2

1

Over 1 to 3

Dry FA80-I8V

C70-IV

FA80-G12VP

Over 3

Dry FA70-I8V

C60-IV

FA70-G12VP



GRINDING WHEELS

Table 5. Grinding Wheel Recommendations for Constructional Steels (Soft) Grinding Operation Surfacing Straight wheels

Wheel or Rim Diameter, Inches

First Choice

Alternate Choice (Porous type)

All-Around Wheel

14 and smaller 14 and smaller Over 14

Wet FA46-J8V Dry FA46-I8V Wet FA36-J8V

FA46-H12VP FA46-H12VP FA36-H12VP

FA46-J8V FA46-I8V FA36-J8V

Wet FA24-H8V

FA30-F12VP

FA24-H8V

FA30-G12VP

FA24-H8V

FA30-F12VP

FA30-H8V

11⁄2 rim or

Segments

less Cylinders

11⁄2 rim or

Cups

3⁄ rim 4

less

Cylindrical

Wet FA24-I8V Wet FA24-H8V

or less

(for wider rims, go one grade softer) Wet SFA60-M5V … Wet SFA54-M5V … Wet SFA54-N5V … Wet SFA60-M5V …

14 and smaller 16 and larger …

Centerless Internal

Under 1⁄2

SFA60-L5V SFA54-L5V SFA60-M5V SFA80-L6V

1

Wet SFA60-L5V

…

SFA60-K5V

Over 1 to 3 Over 3

Wet SFA54-K5V Wet SFA46-K5V

… …

SFA54-J5V SFA46-J5V

1⁄ to 2

Table 6. Grinding Wheel Recommendations for Constructional Steels (Hardened or Carburized) Grinding Operation Surfacing Straight wheels

Wheel or Rim Diameter, Inches 14 and smaller 14 and smaller Over 14

Segments or Cylinders

11⁄2 rim or less

Cups

3⁄ rim 4

Forms and Radius Grinding

or less

8 and smaller 8 and smaller 10 and larger

Cylindrical Work diameter 1 inch and smaller Over 1 inch 1 inch and smaller Over 1 inch Centerless Internal

First Choice

Alternate Choice (Porous Type)

Wet FA46-I8V Dry FA46-H8V Wet FA36-I8V Wet FA30-H8V

FA46-G12VP FA46-F12VP FA36-G12VP FA36-F12VP

Wet FA36-H8V

FA46-F12VP

(for wider rims, go one grade softer) Wet FA60-L7V to FA100-M8V Dry FA60-K8V to FA100-L8V Wet FA60-L7V to FA80-M7V

Under 1⁄2

Wet SFA80-L6V Wet SFA80-K5V Wet SFA60-L5V Wet SFA60-L5V Wet SFA80-M6V Wet SFA80-N6V

… … … … … …

1⁄ to 2

1

Wet SFA60-M5V

…

Over 1 to 3 Over 3 Under 1⁄2

Wet SFA54-L5V Wet SFA46-K5V Dry FA80-L6V

… … …

1⁄ to 2

1

Dry FA70-K8V

…

Over 1 to 3 Over 3

Dry FA60-J8V Dry FA46-J8V

FA60-H12VP FA54-H12VP

14 and smaller 14 and smaller 16 and larger 16 and larger …



1195

Cubic Boron Nitride (CBN) Grinding Wheels.—Although CBN is not quite as hard, strong, and wear-resistant as a diamond, it is far harder, stronger, and more resistant to wear than aluminum oxide and silicon carbide. As with diamond, CBN materials are available in different types for grinding workpieces of 50 Rc and above, and for superalloys of 35 Rc and harder. Microcrystalline CBN grinding wheels are suitable for grinding mild steels, medium-hard alloy steels, stainless steels, cast irons, and forged steels. Wheels with larger mesh size grains (up to 20⁄30), now available, provide for higher rates of metal removal. Special types of CBN are produced for resin, vitrified, and electrodeposited bonds. Wheel standards and nomenclature generally conform to those used for diamond wheels (page 1201), except that the letter B instead of D is used to denote the type of abrasive. Grinding machines for CBN wheels are generally designed to take full advantage of the ability of CBN to operate at high surface speeds of 9,000–25,000 sfm. CBM is very responsive to changes in grinding conditions, and an increase in wheel speed from 5,000 to 10,000 sfm can increase wheel life by a factor of 6 or more. A change from a water-based coolant to a coolant such as a sulfochlorinated or sulfurized straight grinding oil can increase wheel life by a factor of 10 or more. Machines designed specifically for use with CBN grinding wheels generally use either electrodeposited wheels or have special trueing systems for other CBN bond wheels, and are totally enclosed so they can use oil as a coolant. Numerical control systems are used, often running fully automatically, including loading and unloading. Machines designed for CBN grinding with electrodeposited wheels are extensively used for form and gear grinding, special systems being used to ensure rapid mounting to exact concentricity and truth in running, no trueing or dressing being required. CBN wheels can produce workpieces having excellent accuracy and finish, with no trueing or dressing for the life of the wheel, even over many hours or days of production grinding of hardened steel components. Resin-, metal-, and vitrified-bond wheels are used extensively in production grinding, in standard and special machines. Resin-bonded wheels are used widely for dry tool and cutter resharpening on conventional hand-operated tool and cutter grinders. A typical wheel for such work would be designated 11V9 cup type, 100⁄120 mesh, 75 concentration, with a 1⁄16 or 1⁄8 in. rim section. Special shapes of resin-bonded wheels are used on dedicated machines for cutting tool manufacture. These types of wheels are usually self-dressing, and allow full machine control of the operation without the need for an operator to see, hear, or feel the action. Metal-bonded CBN wheels are usually somewhat cheaper than those using other types of bond because only a thin layer of abrasive is present. Metal bonding is also used in manufacture of CBN honing stones. Vitrified-bond CBN wheels are a recent innovation, and high-performance bonds are still being developed. These wheels are used for grinding cams, internal diameters, and bearing components, and can be easily redressed. An important aspect of grinding with CBN and diamond wheels is reduced heating of the workpiece, thought to result from their superior thermal conductivity compared with aluminum oxide, for instance. CBN and diamond grains also are harder, which means that they stay sharp longer than aluminum oxide grains. The superior ability to absorb heat from the workpiece during the grinding process reduces formation of untempered martensite in the ground surface, caused by overheating followed by rapid quenching. At the same time, a higher compressive residual stress is induced in the surface, giving increased fatigue resistance, compared with the tensile stresses found in surfaces ground with aluminum oxide abrasives. Increased fatigue resistance is of particular importance for gear grinding, especially in the root area. Variations from General Grinding Wheel Recommendations.—Recommendations for the selection of grinding wheels are usually based on average values with regard to both operational conditions and process objectives. With variations from such average values,



GRINDING WHEELS

the composition of the grinding wheels must be adjusted to obtain optimum results. Although it is impossible to list and to appraise all possible variations and to define their effects on the selection of the best suited grinding wheels, some guidance is obtained from experience. The following tabulation indicates the general directions in which the characteristics of the initially selected grinding wheel may have to be altered in order to approach optimum performance. Variations in a sense opposite to those shown will call for wheel characteristic changes in reverse. Conditions or Objectives To increase cutting rate To retain wheel size and/or form For small or narrow work surface For larger wheel diameter To improve finish on work For increased work speed or feed rate For increased wheel speed

For interrupted or coarse work surface For thin walled parts To reduce load on the machine drive motor

Direction of Change Coarser grain, softer bond, higher porosity Finer grain, harder bond Finer grain, harder bond Coarser grain Finer grain, harder bond, or resilient bond Harder bond Generally, softer bond, except for highspeed grinding, which requires a harder bond for added wheel strength Harder bond Softer bond Softer bond

Dressing and Truing Grinding Wheels.—The perfect grinding wheel operating under ideal conditions will be self sharpening, i.e., as the abrasive grains become dull, they will tend to fracture and be dislodged from the wheel by the grinding forces, thereby exposing new, sharp abrasive grains. Although in precision machine grinding this ideal sometimes may be partially attained, it is almost never attained completely. Usually, the grinding wheel must be dressed and trued after mounting on the precision grinding machine spindle and periodically thereafter. Dressing may be defined as any operation performed on the face of a grinding wheel that improves its cutting action. Truing is a dressing operation but is more precise, i.e., the face of the wheel may be made parallel to the spindle or made into a radius or special shape. Regularly applied truing is also needed for accurate size control of the work, particularly in automatic grinding. The tools and processes generally used in grinding wheel dressing and truing are listed and described in Table 1. Table 1. Tools and Methods for Grinding Wheel Dressing and Truing Designation

Description

Rotating Hand Dressers

Freely rotating discs, either star-shaped with protruding points or discs with corrugated or twisted perimeter, supported in a fork-type handle, the lugs of which can lean on the tool rest of the grinding machine.

Abrasive Sticks

Made of silicon carbide grains with a hard bond. Applied directly or supported in a handle. Less frequently abrasive sticks are also made of boron carbide.

Application Preferred for bench- or floor-type grinding machines; also for use on heavy portable grinders (snagging grinders) where free-cutting proper ties of the grinding wheel are primarily sought and the accuracy of the trued profile is not critical. Usually hand held and use limited to smaller-size wheels. Because it also shears the grains of the grinding wheel, or preshaping, prior to final dressing with, e.g., a diamond.



1197

Table 1. (Continued) Tools and Methods for Grinding Wheel Dressing and Truing Designation

Description

Abrasive Wheels (Rolls)

Silicon carbide grains in a hard vitrified bond are cemented on ball-bearing mounted spindles. Use either as hand tools with handles or rigidly held in a supporting member of the grinding machine. Generally freely rotating; also available with adjustable brake for diamond wheel dressing.

Single-Point Diamonds

A diamond stone of selected size is mounted in a steel nib of cylindrical shape with or without head, dimensioned to fit the truing spindle of specific grinding machines. Proper orientation and retainment of the diamond point in the setting is an important requirement.

Single-Point Form Truing Diamonds

Selected diamonds having symmetrically located natural edges with precisely lapped diamond points, controlled cone angles and vertex radius, and the axis coinciding with that of the nib.

Cluster-Type Diamond Dresser

Several, usually seven, smaller diamond stones are mounted in spaced relationship across the working surface of the nib. In some tools, more than a single layer of such clusters is set at parallel levels in the matrix, the deeper positioned layer becoming active after the preceding layer has worn away.

Impregnated Matrix-Type Diamond Dressers

The operating surface consists of a layer of small, randomly distributed, yet rather uniformly spaced diamonds that are retained in a bond holding the points in an essentially common plane. Supplied either with straight or canted shaft, the latter being used to cancel the tilt of angular truing posts.

Form- Generating Truing Devices

Swiveling diamond holder post with adjustable pivot location, arm length, and swivel arc, mounted on angularly adjustable cross slides with controlled traverse movement, permits the generation of various straight and circular profile elements, kept in specific mutual locations.

Application Preferred for large grinding wheels as a diamond saver, but also for improved control of the dressed surface characteristics. By skewing the abrasive dresser wheel by a few degrees out of parallel with the grinding wheel axis, the basic crushing action is supplemented with wiping and shearing, thus producing the desired degree of wheel surface smoothness. The most widely used tool for dressing and truing grinding wheels in precision grinding. Permits precisely controlled dressing action by regulating infeed and cross feed rate of the truing spindle when the latter is guided by cams or templates for accurate form truing. Used for truing operations requiring very accurately controlled, and often steeply inclined wheel profiles, such as are needed for thread and gear grinding, where one or more diamond points participate in generating the resulting wheel periphery form. Dependent on specially designed and made truing diamonds and nibs. Intended for straight-face dressing and permits the utilization of smaller, less expensive diamond stones. In use, the holder is canted at a 3° to 10° angle, bringing two to five points into contact with the wheel. The multiplepoint contact permits faster cross feed rates during truing than may be used with single-point diamonds for generating a specific degree of wheel-face finish. For the truing of wheel surfaces consisting of a single or several flat elements. The nib face should be held tangent to the grinding wheel periphery or parallel with a flat working surface. Offers economic advantages where technically applicable because of using less expensive diamond splinters presented in a manner permitting efficient utilization. Such devices are made in various degrees of complexity for the positionally controlled interrelation of several different profile elements. Limited to regular straight and circular sections, yet offers great flexibility of setup, very accurate adjustment, and unique versatility for handling a large variety of frequently changing profiles.



GRINDING WHEELS

Table 1. (Continued) Tools and Methods for Grinding Wheel Dressing and Truing Designation

Description

ContourDuplicating Truing Devices

The form of a master, called cam or template, shaped to match the profile to be produced on the wheel, or its magnified version, is translated into the path of the diamond point by means of mechanical linkage, a fluid actuator, or a pantograph device.

Grinding Wheel Contouring by Crush Truing

A hardened steel or carbide roll, which is free to rotate and has the desired form of the workpiece, is fed gradually into the grinding wheel, which runs at slow speed. The roll will, by crushing action, produce its reverse form in the wheel. Crushing produces a free-cutting wheel face with sharp grains.

Rotating Diamond RollType Grinding Wheel Truing

Special rolls made to agree with specific profile specifications have their periphery coated with a large number of uniformly distributed diamonds, held in a matrix into which the individual stones are set by hand (for larger diamonds) or bonded by a plating process (for smaller elements).

Diamond Dressing Blocks

Made as flat blocks for straight wheel surfaces, are also available for radius dressing and profile truing. The working surface consists of a layer of electroplated diamond grains, uniformly distributed and capable of truing even closely toleranced profiles.

Application Preferred single-point truing method for profiles to be produced in quantities warranting the making of special profile bars or templates. Used also in small- and medium-volume production when the complexity of the profile to be produced excludes alternate methods of form generation. Requires grinding machines designed for crush truing, having stiff spindle bearings, rigid construction, slow wheel speed for truing, etc. Due to the cost of crush rolls and equipment, the process is used for repetitive work only. It is one of the most efficient methods for precisely duplicating complex wheel profiles that are capable of grinding in the 8-microinch AA range. Applicable for both surface and cylindrical grinding. The diamond rolls must be rotated by an air, hydraulic, or electric motor at about one-fourth of the grinding wheel surface speed and in opposite direction to the wheel rotation. Whereas the initial costs are substantially higher than for single-point diamond truing the savings in truing time warrants the method's application in large-volume production of profile-ground components. For straight wheels, dressing blocks can reduce dressing time and offer easy installation on surface grinders, where the blocks mount on the magnetic plate. Recommended for smalland medium-volume production for truing intricate profiles on regular surface grinders, because the higher pressure developed in crush dressing is avoided.

Guidelines for Truing and Dressing with Single-Point Diamonds.—The diamond nib should be canted at an angle of 10 to 15 degrees in the direction of the wheel rotation and also, if possible, by the same amount in the direction of the cross feed traverse during the truing (see diagram). The dragging effect resulting from this “angling,” combined with the occasional rotation of the diamond nib in its holder, will prolong the diamond life by limiting the extent of wear facets and will also tend to produce a pyramid shape of the diamond tip. The diamond may also be set to contact the wheel at about 1⁄8 to 1⁄4 inch below its centerline. Depth of Cut: This amount should not exceed 0.001 inch per pass for general work, and will have to be reduced to 0.0002 to 0.0004 inch per pass for wheels with fine grains used for precise finishing work. Diamond crossfeed rate: This value may be varied to some extent depending on the required wheel surface: faster crossfeed for free cutting, and slower crossfeed for produc-



1199

ing fine finishes. Such variations, however, must always stay within the limits set by the grain size of the wheel. Thus, the advance rate of the truing diamond per wheel revolution should not exceed the diameter of a grain or be less than half of that rate. Consequently, the diamond crossfeed must be slower for a large wheel than for a smaller wheel having the same grain size number. Typical crossfeed values for frequently used grain sizes are given in Table 2.

10 – 15 C L 10 – 15 1

CROSSFEED

8"

– 1 4"

Table 2. Typical Diamond Truing and Crossfeeds Grain Size Crossfeed per Wheel Rev., in. Grain Size Crossfeed per Wheel Rev., in.

30

36

46

50

0.014–0.024

0.012–0.019

0.008–0.014

0.007–0.012

60

80

120

…

0.006–0.010

0.004–0.007

0.0025–0.004

…

These values can be easily converted into the more conveniently used inch-per-minute units, simply by multiplying them by the rpm of the grinding wheel. Example:For a 20-inch diameter wheel, Grain No. 46, running at 1200 rpm: Crossfeed rate for roughing-cut truing—approximately 17 ipm, for finishing-cut truing—approximately 10 ipm Coolant should be applied before the diamond comes into contact with the wheel and must be continued in generous supply while truing. The speed of the grinding wheel should be at the regular grinding rate, or not much lower. For that reason, the feed wheels of centerless grinding machines usually have an additional speed rate higher than functionally needed, that speed being provided for wheel truing only. The initial approach of the diamond to the wheel surface must be carried out carefully to prevent sudden contact with the diamond, resulting in penetration in excess of the selected depth of cut. It should be noted that the highest point of a worn wheel is often in its center portion and not at the edge from which the crossfeed of the diamond starts. The general conditions of the truing device are important for best truing results and for assuring extended diamond life. A rigid truing spindle, well-seated diamond nib, and firmly set diamond point are mandatory. Sensitive infeed and smooth traverse movement at uniform speed also must be maintained. Resetting of the diamond point.: Never let the diamond point wear to a degree where the grinding wheel is in contact with the steel nib. Such contact can damage the setting of the diamond point and result in its loss. Expert resetting of a worn diamond can repeatedly add to its useful life, even when applied to lighter work because of reduced size.



GRINDING WHEELS

Size Selection Guide for Single-Point Truing Diamonds.—There are no rigid rules for determining the proper size of the diamond for any particular truing application because of the very large number of factors affecting that choice. Several of these factors are related to the condition, particularly the rigidity, of the grinding machine and truing device, as well as to such characteristics of the diamond itself as purity, crystalline structure, etc. Although these factors are difficult to evaluate in a generally applicable manner, the expected effects of several other conditions can be appraised and should be considered in the selection of the proper diamond size. The recommended sizes in Table 3 must be considered as informative only and as representing minimum values for generally favorable conditions. Factors calling for larger diamond sizes than listed are the following: Silicon carbide wheels (Table 3 refers to aluminum oxide wheels) Dry truing Grain sizes coarser than No. 46 Bonds harder than M Wheel speed substantially higher than 6500 sfm. It is advisable to consider any single or pair of these factors as justifying the selection of one size larger diamond. As an example: for truing an SiC wheel, with grain size No. 36 and hardness P, select a diamond that is two sizes larger than that shown in Table 3 for the wheel size in use. Table 3. Recommended Minimum Sizes for Single-Point Truing Diamonds Diamond Size in Caratsa 0.25 0.35 0.50 0.60 0.75 1.00 1.25 1.50 1.75 2.00 2.50 3.00 3.50 4.00

Index Number (Wheel Dia. × Width in Inches) 3 6 10 15 21 30 48 65 80 100 150 200 260 350

Examples of Max. Grinding Wheel Dimensions Diameter 4 6 8 10 12 12 14 16 20 20 24 24 30 36

Width 0.75 1 1.25 1.50 1.75 2.50 3.50 4.00 4.00 5.00 6.00 8.00 8.00 10.00

a One carat equals 0.2 gram.

Single-point diamonds are available as loose stones, but are preferably procured from specialized manufacturers supplying the diamonds set into steel nibs. Expert setting, comprising both the optimum orientation of the stone and its firm retainment, is mandatory for assuring adequate diamond life and satisfactory truing. Because the holding devices for truing diamonds are not yet standardized, the required nib dimensions vary depending on the make and type of different grinding machines. Some nibs are made with angular heads, usually hexagonal, to permit occasional rotation of the nib either manually, with a wrench, or automatically.


Machinery's Handbook 27th Edition DIAMOND WHEELS

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Diamond Wheels Diamond Wheels.—A diamond wheel is a special type of grinding wheel in which the abrasive elements are diamond grains held in a bond and applied to form a layer on the operating face of a non-abrasive core. Diamond wheels are used for grinding very hard or highly abrasive materials. Primary applications are the grinding of cemented carbides, such as the sharpening of carbide cutting tools; the grinding of glass, ceramics, asbestos, and cement products; and the cutting and slicing of germanium and silicon. Shapes of Diamond Wheels.—The industry-wide accepted Standard (ANSI B74.31974) specifies ten basic diamond wheel core shapes which are shown in Table 1 with the applicable designation symbols. The applied diamond abrasive layer may have different cross-sectional shapes. Those standardized are shown in Table 2. The third aspect which is standardized is the location of the diamond section on the wheel as shown by the diagrams in Table 3. Finally, modifications of the general core shape together with pertinent designation letters are given in Table 4. The characteristics of the wheel shape listed in these four tables make up the components of the standard designation symbol for diamond wheel shapes. An example of that symbol with arbitrarily selected components is shown in Fig. 1.

Fig. 1. A Typical Diamond Wheel Shape Designation Symbol

An explanation of these components is as follows: Basic Core Shape: This portion of the symbol indicates the basic shape of the core on which the diamond abrasive section is mounted. The shape is actually designated by a number. The various core shapes and their designations are given in Table 1. Diamond Cross-Section Shape: This, the second component, consisting of one or two letters, denotes the cross-sectional shape of the diamond abrasive section. The various shapes and their corresponding letter designations are given in Table 2. Diamond Section Location: The third component of the symbol consists of a number which gives the location of the diamond section, i.e., periphery, side, corner, etc. An explanation of these numbers is shown in Table 3. Modification: The fourth component of the symbol is a letter designating some modification, such as drilled and counterbored holes for mounting or special relieving of diamond section or core. This modification position of the symbol is used only when required. The modifications and their designations are given in Table 4.



DIAMOND WHEELS Table 1. Diamond Wheel Core Shapes and Designations ANSI B74.3-1974 1

9

2

11

3

12

4

14

6

15

Table 2. Diamond Cross-sections and Designations ANSI B74.3-1974



1203

Table 3. Designations for Location of Diamond Section on Diamond Wheel ANSI B74.3-1974 Designation No. and Location

Description

1 — Periphery

The diamond section shall be placed on the periphery of the core and shall extend the full thickness of the wheel. The axial length of this section may be greater than, equal to, or less than the depth of diamond, measured radially. A hub or hubs shall not be considered as part of the wheel thickness for this definition.

2 — Side

The diamond section shall be placed on the side of the wheel and the length of the diamond section shall extend from the periphery toward the center. It may or may not include the entire side and shall be greater than the diamond depth measured axially. It shall be on that side of the wheel which is commonly used for grinding purposes.

3 — Both Sides

The diamond sections shall be placed on both sides of the wheel and shall extend from the periphery toward the center. They may or may not include the entire sides, and the radial length of the diamond section shall exceed the axial diamond depth.

4 — Inside Bevel or Arc

This designation shall apply to the general wheel types 2, 6, 11, 12, and 15 and shall locate the diamond section on the side wall. This wall shall have an angle or arc extending from a higher point at the wheel periphery to a lower point toward the wheel center.

5 — Outside Bevel or Arc

This designation shall apply to the general wheel types, 2, 6, 11, and 15 and shall locate the diamond section on the side wall. This wall shall have an angle or arc extending from a lower point at the wheel periphery to a higher point toward the wheel center.

6 — Part of Periphery

The diamond section shall be placed on the periphery of the core but shall not extend the full thickness of the wheel and shall not reach to either side.

Illustration

7 — Part of Side The diamond section shall be placed on the side of the core and shall not extend to the wheel periphery. It may or may not extend to the center.



DIAMOND WHEELS Table 3. (Continued) Designations for Location of Diamond Section on Diamond Wheel ANSI B74.3-1974

Designation No. and Location

Description

Illustration

8 — Throughout Designates wheels of solid diamond abrasive section without cores. 9 — Corner

Designates a location which would commonly be considered to be on the periphery except that the diamond section shall be on the corner but shall not extend to the other corner.

10 — Annular

Designates a location of the diamond abrasive section on the inner annular surface of the wheel.

Composition of Diamond and Cubic Boron Nitride Wheels.—According to American National Standard ANSI B74.13-1990, a series of symbols is used to designate the composition of these wheels. An example is shown below.

Fig. 2. Designation Symbols for Composition of Diamond and Cubic Boron Nitride Wheels

The meaning of each symbol is indicated by the following list: 1) Prefix: The prefix is a manufacturer's symbol indicating the exact kind of abrasive. Its use is optional. 2) Abrasive Type: The letter (B) is used for cubic boron nitride and (D) for diamond. 3) Grain Size: The grain sizes commonly used and varying from coarse to very fine are indicated by the following numbers: 8, 10, 12, 14, 16, 20, 24, 30, 36, 46, 54, 60, 70, 80, 90, 100, 120, 150, 180, and 220. The following additional sizes are used occasionally: 240, 280, 320, 400, 500, and 600. The wheel manufacturer may add to the regular grain number an additional symbol to indicate a special grain combination. 4) Grade: Grades are indicated by letters of the alphabet from A to Z in all bonds or processes. Wheel grades from A to Z range from soft to hard. 5) Concentration: The concentration symbol is a manufacturer's designation. It may be a number or a symbol. 6) Bond: Bonds are indicated by the following letters: B, resinoid; V, vitrified; M, metal. 7) Bond Modification: Within each bond type a manufacturer may have modifications to tailor the bond to a specific application. These modifications may be identified by either letters or numbers. 8) Abrasive Depth: Abrasive section depth, in inches or millimeters (inches illustrated), is indicated by a number or letter which is the amount of total dimensional wear a user may expect from the abrasive portion of the product. Most diamond and CBN wheels are made with a depth of coating on the order of 1⁄16 in., 1⁄8 in., or more as specified. In some cases the diamond is applied in thinner layers, as thin as one thickness of diamond grains. The L is included in the marking system to identify a layered type product. 9) Manufacturer's Identification Symbol: The use of this symbol is optional.



1205

Table 4. Designation Letters for Modifications of Diamond Wheels ANSI B74.3-1974 Designation Lettera

Description

B — Drilled and Counterbored

Holes drilled and counterbored in core.

C — Drilled and Countersunk

Holes drilled and countersunk in core.

H — Plain Hole

Straight hole drilled in core.

M — Holes Plain and Threaded

Mixed holes, some plain, some threaded, are in core.

P — Relieved One Core relieved on one side of wheel. Thickness of core Side is less than wheel thickness.

R — Relieved Two Sides

Core relieved on both sides of wheel. Thickness of core is less than wheel thickness.

S — SegmentedDiamond Section

Wheel has segmental diamond section mounted on core. (Clearance between segments has no bearing on definition.)

SS — Segmental and Slotted

Wheel has separated segments mounted on a slotted core.

T — Threaded Holes

Threaded holes are in core.

Q — Diamond Inserted

Three surfaces of the diamond section are partially or completely enclosed by the core.

V — Diamond Inverted

Any diamond cross section, which is mounted on the core so that the interior point of any angle, or the concave side of any arc, is exposed shall be considered inverted. Exception: Diamond cross section AH shall be placed on the core with the concave side of the arc exposed.

a Y — Diamond Inserted and Inverted. See definitions for Q and V.


Illustration


DIAMOND WHEELS

The Selection of Diamond Wheels.—Two general aspects must be defined: (a) The shape of the wheel, also referred to as the basic wheel type and (b) The specification of the abrasive portion. Table 5. General Diamond Wheel Recommendations for Wheel Type and Abrasive Specification Typical Applications or Operation

Basic Wheel Type

Single Point Tools (offhand grinding)

D6A2C

Single Point Tools (machine ground)

D6A2H

Chip Breakers

D1A1

Abrasive Specification Rough: MD100-N100-B1⁄8 Finish: MD220-P75-B1⁄8 Rough: MD180-J100-B1⁄8 Finish: MD320-L75-B1⁄8 MD150-R100-B1⁄8

Multitooth Tools and Cutters (face mills, end mills, reamers, broaches, etc.) Rough: MD100-R100-B1⁄8 Combination: MD150-R100-B1⁄8

Sharpening and Backing off

D11V9

Fluting

D12A2

MD180-N100-B1⁄8

Saw Sharpening

D12A2

MD180-R100-B1⁄8

Surface Grinding (horizontal spindle)

D1A1

Finish: MD220-R100-B1⁄8

Rough: MD120-N100-B1⁄8 Finish: MD240-P100-B1⁄8 MD80-R75-B1⁄8

Surface Grinding (vertical spindle)

D2A2T

Cylindrical or Centertype Grinding

D1A1

MD120-P100-B1⁄8

Internal Grinding

D1A1

MD150-N100-B1⁄8

D1A1R

MD150-R100-B1⁄4

Disc

MD400-L50-B1⁄16

Slotting and Cutoff Lapping Hand Honing

DH1, DH2

Rough: MD220-B1⁄16 Finish: MD320-B1⁄6

General recommendations for the dry grinding, with resin bond diamond wheels, of most grades of cemented carbides of average surface to ordinary finishes at normal rates of metal removal with average size wheels, as published by Cincinnati Milacron, are listed in Table 5. A further set of variables are the dimensions of the wheel, which must be adapted to the available grinding machine and, in some cases, to the configuration of the work. The general abrasive specifications in Table 5 may be modified to suit operating conditions by the following suggestions: Use softer wheel grades for harder grades of carbides, for grinding larger areas or larger or wider wheel faces. Use harder wheel grades for softer grades of carbides, for grinding smaller areas, for using smaller and narrower face wheels and for light cuts.


Machinery's Handbook 27th Edition GRINDING WHEEL SAFETY

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Use fine grit sizes for harder grades of carbides and to obtain better finishes. Use coarser grit sizes for softer grades of carbides and for roughing cuts. Use higher diamond concentration for harder grades of carbides, for larger diameter or wider face wheels, for heavier cuts, and for obtaining better finish. Guidelines for the Handling and Operation of Diamond Wheels.—G r i n d i n g machines used for grinding with diamond wheels should be of the precision type, in good service condition, with true running spindles and smooth slide movements. Mounting of Diamond Wheels: Wheel mounts should be used which permit the precise centering of the wheel, resulting in a runout of less than 0.001 inch axially and 0.0005 inch radially. These conditions should be checked with a 0.0001-inch type dial indicator. Once mounted and centered, the diamond wheel should be retained on its mount and stored in that condition when temporarily removed from the machine. Truing and Dressing: Resinoid bonded diamond wheels seldom require dressing, but when necessary a soft silicon carbide stick may be hand-held against the wheel. Peripheral and cup type wheels may be sharpened by grinding the cutting face with a 60 to 80 grit silicon carbide wheel. This can be done with the diamond wheel mounted on the spindle of the machine, and with the silicon carbide wheel driven at a relatively slow speed by a specially designed table-mounted grinder or by a small table-mounted tool post grinder. The diamond wheel can be mounted on a special arbor and ground on a lathe with a tool post grinder; peripheral wheels can be ground on a cylindrical grinder or with a special brakecontrolled truing device with the wheel mounted on the machine on which it is used. Cup and face type wheels are often lapped on a cast iron or glass plate using a 100 grit silicon carbide abrasive. Care must be used to lap the face parallel to the back, otherwise they must be ground to restore parallelism. Peripheral diamond wheels can be trued and dressed by grinding a silicon carbide block or a special diamond impregnated bronze block in a manner similar to surface grinding. Conventional diamonds must not be used for truing and dressing diamond wheels. Speeds and Feeds in Diamond Grinding.—General recommendations are as follows: Wheel Speeds: The generally recommended wheel speeds for diamond grinding are in the range of 5000 to 6000 surface feet per minute, with this upper limit as a maximum to avoid harmful “overspeeding.” Exceptions from that general rule are diamond wheels with coarse grains and high concentration (100 per cent) where the wheel wear in dry surface grinding can be reduced by lowering the speed to 2500–3000 sfpm. However, this lower speed range can cause rapid wheel breakdown in finer grit wheels or in those with reduced diamond concentration. Work Speeds: In diamond grinding, work rotation and table traverse are usually established by experience, adjusting these values to the selected infeed so as to avoid excessive wheel wear. Infeed per Pass: Often referred to as downfeed and usually a function of the grit size of the wheel. The following are general values which may be increased for raising the productivity, or lowered to improve finish or to reduce wheel wear. Wheel Grit Size Range 100 to 120 150 to 220 250 and finer

Infeed per Pass 0.001 inch 0.0005 inch 0.00025 inch

Grinding Wheel Safety Safety in Operating Grinding Wheels.—Grinding wheels, although capable of exceptional cutting performance due to hardness and wear resistance, are prone to damage caused by improper handling and operation. Vitrified wheels, comprising the major part of grinding wheels used in industry, are held together by an inorganic bond which is actually



GRINDING WHEEL SAFETY

a type of pottery product and therefore brittle and breakable. Although most of the organic bond types are somewhat more resistant to shocks, it must be realized that all grinding wheels are conglomerates of individual grains joined by a bond material whose strength is limited by the need of releasing the dull, abrasive grains during use. It must also be understood that during the grinding process very substantial forces act on the grinding wheel, including the centrifugal force due to rotation, the grinding forces resulting from the resistance of the work material, and shocks caused by sudden contact with the work. To be able to resist these forces, the grinding wheel must have a substantial minimum strength throughout that is well beyond that needed to hold the wheel together under static conditions. Finally, a damaged grinding wheel can disintegrate during grinding, liberating dormant forces which normally are constrained by the resistance of the bond, thus presenting great hazards to both operator and equipment. To avoid breakage of the operating wheel and, should such a mishap occur, to prevent damage or injury, specific precautions must be applied. These safeguards have been formulated into rules and regulations and are set forth in the American National Standard ANSI B7.1-1988, entitled the American National Standard Safety Requirements for the Use, Care, and Protection of Abrasive Wheels. Handling, Storage and Inspection.—Grinding wheels should be hand carried, or transported, with proper support, by truck or conveyor. A grinding wheel must not be rolled around on its periphery. The storage area, positioned not far from the location of the grinding machines, should be free from excessive temperature variations and humidity. Specially built racks are recommended on which the smaller or thin wheels are stacked lying on their sides and the larger wheels in an upright position on two-point cradle supports consisting of appropriately spaced wooden bars. Partitions should separate either the individual wheels, or a small group of identical wheels. Good accessibility to the stored wheels reduces the need of undesirable handling. Inspection will primarily be directed at detecting visible damage, mostly originating from handling and shipping. Cracks which are not obvious can usually be detected by “ring testing,” which consists of suspending the wheel from its hole and tapping it with a nonmetallic implement. Heavy wheels may be allowed to rest vertically on a clean, hard floor while performing this test. A clear metallic tone, a “ring”, should be heard; a dead sound being indicative of a possible crack or cracks in the wheel. Machine Conditions.—The general design of the grinding machines must ensure safe operation under normal conditions. The bearings and grinding wheel spindle must be dimensioned to withstand the expected forces and ample driving power should be provided to ensure maintenance of the rated spindle speed. For the protection of the operator, stationary machines used for dry grinding should have a provision made for connection to an exhaust system and when used for off-hand grinding, a work support must be available. Wheel guards are particularly important protection elements and their material specifications, wall thicknesses and construction principles should agree with the Standard’s specifications. The exposure of the wheel should be just enough to avoid interference with the grinding operation. The need for access of the work to the grinding wheel will define the boundary of guard opening, particularly in the direction of the operator. Grinding Wheel Mounting.—The mass and speed of the operating grinding wheel makes it particularly sensitive to imbalance. Vibrations that result from such conditions are harmful to the machine, particularly the spindle bearings, and they also affect the ground surface, i.e., wheel imbalance causes chatter marks and interferes with size control. Grinding wheels are shipped from the manufacturer’s plant in a balanced condition, but retaining the balanced state after mounting the wheel is quite uncertain. Balancing of the mounted wheel is thus required, and is particularly important for medium and large size


Machinery's Handbook 27th Edition GRINDING WHEEL SAFETY

1209

wheels, as well as for producing acccurate and smooth surfaces. The most common way of balancing mounted wheels is by using balancing flanges with adjustable weights. The wheel and balancing flanges are mounted on a short balancing arbor, the two concentric and round stub ends of which are supported in a balancing stand. Such stands are of two types: 1) the parallel straight-edged, which must be set up precisely level; and 2) the disk type having two pairs of ball bearing mounted overlapping disks, which form a V for containing the arbor ends without hindering the free rotation of the wheel mounted on that arbor. The wheel will then rotate only when it is out of balance and its heavy spot is not in the lowest position. Rotating the wheel by hand to different positions will move the heavy spot, should such exist, from the bottom to a higher location where it can reveal its presence by causing the wheel to turn. Having detected the presence and location of the heavy spot, its effect can be cancelled by displacing the weights in the circular groove of the flange until a balanced condition is accomplished. Flanges are commonly used means for holding grinding wheels on the machine spindle. For that purpose, the wheel can either be mounted directly through its hole or by means of a sleeve which slips over a tapered section of the machine spindle. Either way, the flanges must be of equal diameter, usually not less than one-third of the new wheel’s diameter. The purpose is to securely hold the wheel between the flanges without interfering with the grinding operation even when the wheel becomes worn down to the point where it is ready to be discarded. Blotters or flange facings of compressible material should cover the entire contact area of the flanges. One of the flanges is usually fixed while the other is loose and can be removed and adjusted along the machine spindle. The movable flange is held against the mounted grinding wheel by means of a nut engaging a threaded section of the machine spindle. The sense of that thread should be such that the nut will tend to tighten as the spindle revolves. In other words, to remove the nut, it must be turned in the direction that the spindle revolves when the wheel is in operation. Safe Operating Speeds.—Safe grinding processes are predicated on the proper use of the previously discussed equipment and procedures, and are greatly dependent on the application of adequate operating speeds. The Standard establishes maximum speeds at which grinding wheels can be operated, assigning the various types of wheels to several classification groups. Different values are listed according to bond type and to wheel strength, distinguishing between low, medium and high strength wheels. For the purpose of general information, the accompanying table shows an abbreviated version of the Standard’s specification. However, for the governing limits, the authoritative source is the manufacturer’s tag on the wheel which, particularly for wheels of lower strength, might specify speeds below those of the table. All grinding wheels of 6 inches or greater diameter must be test run in the wheel manufacturer’s plant at a speed that for all wheels having operating speeds in excess of 5000 sfpm is 1.5 times the maximum speed marked on the tag of the wheel. The table shows the permissible wheel speeds in surface feet per minute (sfpm) units, whereas the tags on the grinding wheels state, for the convenience of the user, the maximum operating speed in revolutions per minute (rpm). The sfpm unit has the advantage of remaining valid for worn wheels whose rotational speed may be increased to the applicable sfpm value. The conversion from either one to the other of these two kinds of units is a matter of simple calculation using the formulas: D- × π sfpm = rpm × ----12

or

sfpm × 12 rpm = -----------------------D×π



GRINDING WHEEL SAFETY

where D = maximum diameter of the grinding wheel, in inches. Table 2, showing the conversion values from surface speed into rotational speed, can be used for the direct reading of the rpm values corresponding to several different wheel diameters and surface speeds. Special Speeds: Continuing progress in grinding methods has led to the recognition of certain advantages that can result from operating grinding wheels above, sometimes even higher than twice, the speeds considered earlier as the safe limits of grinding wheel operations. Advantages from the application of high speed grinding are limited to specific processes, but the Standard admits, and offers code regulations for the use of wheels at special high speeds. These regulations define the structural requirements of the grinding machine and the responsibilities of the grinding wheel manufacturers, as well as of the users. High speed grinding should not be applied unless the machines, particularly guards, spindle assemblies, and drive motors, are suitable for such methods. Also, appropriate grinding wheels expressly made for special high speeds must be used and, of course, the maximum operating speeds indicated on the wheel’s tag must never be exceeded. Portable Grinders.—The above discussed rules and regulations, devised primarily for stationary grinding machines apply also to portable grinders. In addition, the details of various other regulations, specially applicable to different types of portable grinders are discussed in the Standard, which should be consulted, particularly for safe applications of portable grinding machines. Table 1. Maximum Peripheral Speeds for Grinding Wheels Based on ANSI B7.1–1988 Classification No.

1

2 3 4 5 6 7 8 9 10 11 12

Maximum Operating Speeds, sfpm, Depending on Strength of Bond Types of Wheelsa Straight wheels — Type 1, except classifications 6, 7, 9, 10, 11, and 12 below Taper Side Wheels — Type 4b Types 5, 7, 20, 21, 22, 23, 24, 25, 26 Dish wheels — Type 12 Saucer wheels — Type 13 Cones and plugs — Types 16, 17, 18, 19 Cylinder wheels — Type 2 Segments Cup shape tool grinding wheels — Types 6 and 11 (for fixed base machines) Cup shape snagging wheels — Types 6 and 11 (for portable machines) Abrasive disks Reinforced wheels — except cutting-off wheels (depending on diameter and thickness) Type 1 wheels for bench and pedestal grinders, Types 1 and 5 also in certain sizes for surface grinders Diamond and cubic boron nitride wheels Metal bond Steel centered cutting off Cutting-off wheels — Larger than 16-inch diameter (incl. reinforced organic) Cutting-off wheels — 16-inch diameter and smaller (incl. reinforced organic) Thread and flute grinding wheels Crankshaft and camshaft grinding wheels

Inorganic Bonds

Organic Bonds

5,500 to 6,500

6,500 to 9,500

5,000 to 6,000

5,000 to 7,000

4,500 to 6,000

6,000 to 8,500

4,500 to 6,500

6,000 to 9,500

5,500 to 6,500

5,500 to 8,500

…

9,500 to 16,000

5,500 to 7,550

6,500 to 9,500

to 6,500 to 12,000 to 16,000

to 9,500 … to 16,000

…

9,500 to 14,200

…

9,500 to 16,000

8,000 to 12,000 5,500 to 8,500

8,000 to 12,000 6,500 to 9,500

a See Tables 1a and 1b starting on page

1181. Non-standard shape. For snagging wheels, 16 inches and larger — Type 1, internal wheels — Types 1 and 5, and mounted wheels, see ANSI B7.1–1988. Under no conditions should a wheel be operated faster than the maximum operating speed established by the manufacturer. b

Values in this table are for general information only.



Table 2. Revolutions per Minute for Various Grinding Speeds and Wheel Diameters (Based on ANSI B7.1–1988) Peripheral (Surface) Speed, Feet per Minute Wheel Diameter, Inch

4,500

5,000

5,500

6,000

6,500

7,000

7,500

8,000

9,000

9,500

10,000

12,000

14,000

16,000

15,279 7,639 5,093 3,820 3,056 2,546 2,183 1,910 1,698 1,528 1,273 1,091 955 849 764 694 637 588 546 509 477 449 424 402 382 364 347 332 318 288 255 212

17,189 8,594 5,730 4,297 3,438 2,865 2,456 2,149 1,910 1,719 1,432 1,228 1,074 955 859 781 716 661 614 573 537 506 477 452 430 409 391 374 358 324 286 239

19,099 9,549 6,366 4,775 3,820 3,183 2,728 2,387 2,122 1,910 1,592 1,364 1,194 1,061 955 868 796 735 682 637 597 562 531 503 477 455 434 415 398 360 318 265

21,008 10,504 7,003 5,252 4,202 3,501 3,001 2,626 2,334 2,101 1,751 1,501 1,313 1,167 1,050 955 875 808 750 700 657 618 584 553 525 500 477 457 438 396 350 292

22,918 11,459 7,639 5,730 4,584 3,820 3,274 2,865 2,546 2,292 1,910 1,637 1,432 1,273 1,146 1,042 955 881 819 764 716 674 637 603 573 546 521 498 477 432 382 318

24,828 12,414 8,276 6,207 4,966 4,138 3,547 3,104 2,759 2,483 2,069 1,773 1,552 1,379 1,241 1,129 1,035 955 887 828 776 730 690 653 621 591 564 540 517 468 414 345

26,738 13,369 8,913 6,685 5,348 4,456 3,820 3,342 2,971 2,674 2,228 1,910 1,671 1,485 1,337 1,215 1,114 1,028 955 891 836 786 743 704 668 637 608 581 557 504 446 371

28,648 14,324 9,549 7,162 5,730 4,775 4,093 3,581 3,183 2,865 2,387 2,046 1,790 1,592 1,432 1,302 1,194 1,102 1,023 955 895 843 796 754 716 682 651 623 597 541 477 398

30,558 15,279 10,186 7,639 6,112 5,093 4,365 3,820 3,395 3,056 2,546 2,183 1,910 1,698 1,528 1,389 1,273 1,175 1,091 1,019 955 899 849 804 764 728 694 664 637 577 509 424

32,468 16,234 10,823 8,117 6,494 5,411 4,638 4,058 3,608 3,247 2,706 2,319 2,029 1,804 1,623 1,476 1,353 1,249 1,160 1,082 1,015 955 902 854 812 773 738 706 676 613 541 451

34,377 17,189 11,459 8,594 6,875 5,730 4,911 4,297 3,820 3,438 2,865 2,456 2,149 1,910 1,719 1,563 1,432 1,322 1,228 1,146 1,074 1,011 955 905 859 819 781 747 716 649 573 477

36,287 18,144 12,096 9,072 7,257 6,048 5,184 4,536 4,032 3,629 3,024 2,592 2,268 2,016 1,814 1,649 1,512 1,396 1,296 1,210 1,134 1,067 1,008 955 907 864 825 789 756 685 605 504

38,197 19,099 12,732 9,549 7,639 6,366 5,457 4,775 4,244 3,820 3,183 2,728 2,387 2,122 1,910 1,736 1,592 1,469 1,364 1,273 1,194 1,123 1,061 1,005 955 909 868 830 796 721 637 531

45,837 22,918 15,279 11,459 9,167 7,639 6,548 5,730 5,093 4,584 3,820 3,274 2,865 2,546 2,292 2,083 1,910 1,763 1,637 1,528 1,432 1,348 1,273 1,206 1,146 1,091 1,042 996 955 865 764 637

53,476 26,738 17,825 13,369 10,695 8,913 7,639 6,685 5,942 5,348 4,456 3,820 3,342 2,971 2,674 2,431 2,228 2,057 1,910 1,783 1,671 1,573 1,485 1,407 1,337 1,273 1,215 1,163 1,114 1,009 891 743

61,115 30,558 20,372 15,279 12,223 10,186 8,731 7,639 6,791 6,112 5,093 4,365 3,820 3,395 3,056 2,778 2,546 2,351 2,183 2,037 1,910 1,798 1,698 1,608 1,528 1,455 1,389 1,329 1,273 1,153 1,019 849


Wheel Diameter, Inch 1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 53 60 72

1211

8,500

Revolutions per Minute

GRINDING WHEEL SPEEDS

1 2 3 4 5 6 7 8 9 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 53 60 72

4,000


CYLINDRICAL GRINDING Cylindrical Grinding

Cylindrical grinding designates a general category of various grinding methods that have the common characteristic of rotating the workpiece around a fixed axis while grinding outside surface sections in controlled relation to that axis of rotation. The form of the part or section being ground in this process is frequently cylindrical, hence the designation of the general category. However, the shape of the part may be tapered or of curvilinear profile; the position of the ground surface may also be perpendicular to the axis; and it is possible to grind concurrently several surface sections, adjacent or separated, of equal or different diameters, located in parallel or mutually inclined planes, etc., as long as the condition of a common axis of rotation is satisfied. Size Range of Workpieces and Machines: Cylindrical grinding is applied in the manufacture of miniature parts, such as instrument components and, at the opposite extreme, for grinding rolling mill rolls weighing several tons. Accordingly, there are cylindrical grinding machines of many different types, each adapted to a specific work-size range. Machine capacities are usually expressed by such factors as maximum work diameter, work length and weight, complemented, of course, by many other significant data. Plain, Universal, and Limited-Purpose Cylindrical Grinding Machines.—The plain cylindrical grinding machine is considered the basic type of this general category, and is used for grinding parts with cylindrical or slightly tapered form. The universal cylindrical grinder can be used, in addition to grinding the basic cylindrical forms, for the grinding of parts with steep tapers, of surfaces normal to the part axis, including the entire face of the workpiece, and for internal grinding independently or in conjunction with the grinding of the part’s outer surfaces. Such variety of part configurations requiring grinding is typical of work in the tool room, which constitutes the major area of application for universal cylindrical grinding machines. Limited-purpose cylindrical grinders are needed for special work configurations and for high-volume production, where productivity is more important than flexibility of adaptation. Examples of limited-purpose cylindrical grinding machines are crankshaft and camshaft grinders, polygonal grinding machines, roll grinders, etc. Traverse or Plunge Grinding.—In traverse grinding, the machine table carrying the work performs a reciprocating movement of specific travel length for transporting the rotating workpiece along the face of the grinding wheel. At each or at alternate stroke ends, the wheel slide advances for the gradual feeding of the wheel into the work. The length of the surface that can be ground by this method is generally limited only by the stroke length of the machine table. In large roll grinders, the relative movement between work and wheel is accomplished by the traverse of the wheel slide along a stationary machine table. In plunge grinding, the machine table, after having been set, is locked and, while the part is rotating, the wheel slide continually advances at a preset rate, until the finish size of the part is reached. The width of the grinding wheel is a limiting factor of the section length that can be ground in this process. Plunge grinding is required for profiled surfaces and for the simultaneous grinding of multiple surfaces of different diameters or located in different planes. When the configuration of the part does not make use of either method mandatory, the choice may be made on the basis of the following general considerations: traverse grinding usually produces a better finish, and the productivity of plunge grinding is generally higher. Work Holding on Cylindrical Grinding Machines.—The manner in which the work is located and held in the machine during the grinding process determines the configuration of the part that can be adapted for cylindrical grinding and affects the resulting accuracy of the ground surface. The method of work holding also affects the attainable production rate, because the mounting and dismounting of the part can represent a substantial portion of the total operating time.


Machinery's Handbook 27th Edition CYLINDRICAL GRINDING

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Whatever method is used for holding the part on cylindrical types of grinding machines, two basic conditions must be satisfied: 1) the part should be located with respect to its correct axis of rotation; and 2) the work drive must cause the part to rotate, at a specific speed, around the established axis. The lengthwise location of the part, although controlled, is not too critical in traverse grinding; however, in plunge grinding, particularly when shoulder sections are also involved, it must be assured with great accuracy. Table 1 presents a listing, with brief discussions, of work-holding methods and devices that are most frequently used in cylindrical grinding. Table 1. Work-Holding Methods and Devices for Cylindrical Grinding Designation

Description

Discussion

Centers, nonrotating (“dead”), with drive plate

Headstock with nonrotating spindle holds The simplest method of holding the work the center. Around the spindle, an indebetween two opposite centers is also the pendently supported sleeve carries the potentially most accurate, as long as cordrive plate for rotating the work. Tailstock rectly prepared and located center holes for opposite center. are used in the work.

Centers, driving type

Word held between two centers obtains its rotation from the concurrently applied drive by the live headstock spindle and live tailstock spindle.

Eliminates the drawback of the common center-type grinding with driver plate, which requires a dog attached to the workpiece. Driven spindles permit the grinding of the work up to both ends.

Chuck, geared, or camactuated

Two, three, or four jaws moved radially through mechanical elements, hand-, or power-operated, exert concentrically acting clamping force on the workpiece.

Adaptable to workpieces of different configurations and within a generally wide capacity of the chuck. Flexible in uses that, however, do not include high-precision work.

Chuck, diaphragm

Force applied by hand or power of a flexible Rapid action and flexible adaptation to difdiaphragm causes the attached jaws to ferent work configurations by means of deflect temporarily for accepting the special jaws offer varied uses for the work, which is held when force is grinding of disk-shaped and similar parts. released.

Collets

Holding devices with externally or internally acting clamping force, easily adaptable to power actuation, assuring high centering accuracy.

Limited to parts with previously machined or ground holding surfaces, because of the small range of clamping movement of the collet jaws.

Face plate

Has four independently actuated jaws, any or several of which may be used, or entirely removed, using the base plate for supporting special clamps.

Used for holding bulky parts, or those of awkward shape, which are ground in small quantities not warranting special fixtures.

Magnetic plate

Flat plates, with pole distribution adapted to Applicable for light cuts such as are frethe work, are mounted on the spindle like quent in tool making, where the rapid chucks and may be used for work with the clamping action and easy access to both locating face normal to the axis. the O.D. and the exposed face are sometimes of advantage.

Steady rests

Two basic types are used: (a) the two-jaw type supporting the work from the back (back rest), leaving access by the wheel; (b) the three-jaw type (center rest).

Special fixtures

Single-purpose devices, designed for a par- Typical workpieces requiring special fixturticular workpiece, primarily for providing are, as examples, crankshafts where ing special locating elements. the holding is combined with balancing functions; or internal gears located on the pitch circle of the teeth for O.D. grinding.

A complementary work-holding device, used in conjunction with primary work holders, to provide additional support, particularly to long and/or slender parts.

Selection of Grinding Wheels for Cylindrical Grinding.—For cylindrical grinding, as for grinding in general, the primary factor to be considered in wheel selection is the work material. Other factors are the amount of excess stock and its rate of removal (speeds and feeds), the desired accuracy and surface finish, the ratio of wheel and work diameter, wet or dry grinding, etc. In view of these many variables, it is not practical to set up a complete



CYLINDRICAL GRINDING

list of grinding wheel recommendations with general validity. Instead, examples of recommendations embracing a wide range of typical applications and assuming common practices are presented in Table 2. This is intended as a guide for the starting selection of grinding-wheel specifications which, in case of a not entirely satisfactory performance, can be refined subsequently. The content of the table is a version of the grinding-wheel recommendations for cylindrical grinding by the Norton Company using, however, non-proprietary designations for the abrasive types and bonds. Table 2. Wheel Recommendations for Cylindrical Grinding Material Aluminum Armatures (laminated) Axles (auto & railway) Brass Bronze Soft Hard Bushings (hardened steel) Bushings (cast iron) Cam lobes (cast alloy) Roughing Finishing Cam lobes (hardened steel) Roughing Finishing Cast iron Chromium plating Commercial finish High finish Reflective finish Commutators (copper) Crankshafts (airplane) Pins Bearings Crankshafts (automotive pins and bearings) Finishing Roughing & finishing Regrinding Regrinding, sprayed metal Drills

Wheel Marking SFA46-18V SFA100-18V A54-M5V C36-KV C36-KV A46-M5V BFA60-L5V C36-JV BFA54-N5V A70-P6B BFA54-L5V BFA80-T8B C36-JV SFA60-J8V A150-K5E C500-I9E C60-M4E BFA46-K5V A46-L5V

A54-N5V A54-O5V A54-M5V C60-JV BFA54-N5V

Material Forgings Gages (plug) General-purpose grinding Glass Gun barrels Spotting and O.D. Nitralloy Before nitriding After nitriding Commercial finish High finish Reflective finish Pistons (aluminum) (cast iron) Plastics Rubber Soft Hard Spline shafts Sprayed metal Steel Soft 1 in. dia. and smaller over 1 in dia. Hardened 1 in. dia. and smaller over 1 in. dia. 300 series stainless Stellite Titanium Valve stems (automative) Valve tappets

Wheel Marking A46-M5V SFA80-K8V SFA54-L5V BFA220-011V BFA60-M5V A60-K5V SFA60-18V C100-1V C500-19E SFA46-18V C36-KV C46-JV SFA20-K5B C36-KB SFA60-N5V C60-JV

SFA60-M5V SFA46-L5V SFA80-L8V SFA60-K5V SFA46-K8V BFA46-M5V C60-JV BFA54-N5V BFA54-M5V

Note: Prefixes to the standard designation “A” of aluminum oxide indicate modified abrasives as follows: BFA = Blended friable (a blend of regular and friable), SFA = Semifriable.

Operational Data for Cylindrical Grinding.—In cylindrical grinding, similarly to other metalcutting processes, the applied speed and feed rates must be adjusted to the operational conditions as well as to the objectives of the process. Grinding differs, however, from other types of metalcutting methods in regard to the cutting speed of the tool which, in grinding, is generally not a variable; it should be maintained at, or close to the optimum rate, commonly 6500 feet per minute peripheral speed. In establishing the proper process values for grinding, of prime consideration are the work material, its condition (hardened or soft), and the type of operation (roughing or finishing). Other influencing factors are the characteristics of the grinding machine (stability, power), the specifications of the grinding wheel, the material allowance, the rigidity and



1215

balance of the workpiece, as well as several grinding process conditions, such as wet or dry grinding, the manner of wheel truing, etc. Variables of the cylindrical grinding process, often referred to as grinding data, comprise the speed of work rotation (measured as the surface speed of the work); the infeed (in inches per pass for traverse grinding, or in inches per minute for plunge grinding); and, in the case of traverse grinding, the speed of the reciprocating table movement (expressed either in feet per minute, or as a fraction of the wheel width for each revolution of the work). For the purpose of starting values in setting up a cylindrical grinding process, a brief listing of basic data for common cylindrical grinding conditions and involving frequently used materials, is presented in Table 3. Table 3. Basic Process Data for Cylindrical Grinding Traverse Grinding Work Material Plain Carbon Steel Alloy Steel Tool Steel Copper Alloys

Aluminum Alloys

Material Condition

Work Surface Speed, fpm

Infeed, Inch/Pass

Traverse for Each Work Revolution, In Fractions of the Wheel Width

Roughing

Roughing

Finishing

Annealed

100

0.002

0.0005

1⁄ 2

1⁄ 6

Hardened

70

0.002

0.0003–0.0005

1⁄ 4

1⁄ 8

Annealed

100

0.002

0.0005

1⁄ 2

1⁄ 6

Hardened

70

0.002

0.0002–0.0005

1⁄ 4

1⁄ 8

Annealed

60

0.002

0.0005 max.

1⁄ 2

1⁄ 6

Hardened Annealed or Cold Drawn Cold Drawn or Solution Treated

50

0.002

0.0001–0.0005

1⁄ 4

1⁄ 8 1⁄ 6

1⁄ 6

Finishing

100

0.002

0.0005 max.

1⁄ 3

150

0.002

0.0005 max.

1⁄ 3

Plunge Grinding Work Material Steel, soft Plain carbon steel, hardened Alloy and tool steel, hardened

Infeed per Revolution of the Work, Inch Roughing

Finishing

0.0005 0.0002 0.0001

0.0002 0.000050 0.000025

These data, which are, in general, considered conservative, are based on average operating conditions and may be modified subsequently by: a) reducing the values in case of unsatisfactory quality of the grinding or the occurrence of failures; and b) increasing the rates for raising the productivity of the process, particularly for rigid workpieces, substantial stock allowance, etc.

High-Speed Cylindrical Grinding.—The maximum peripheral speed of the wheels in regular cylindrical grinding is generally 6500 feet per minute; the commonly used grinding wheels and machines are designed to operate efficiently at this speed. Recently, efforts were made to raise the productivity of different grinding methods, including cylindrical grinding, by increasing the peripheral speed of the grinding wheel to a substantially higher than traditional level, such as 12,000 feet per minute or more. Such methods are designated by the distinguishing term of high-speed grinding. For high-speed grinding, special grinding machines have been built with high dynamic stiffness and static rigidity, equipped with powerful drive motors, extra-strong spindles and bearings, reinforced wheel guards, etc., and using grinding wheels expressly made and tested for operating at high peripheral speeds. The higher stock-removal rate accomplished by high-speed grinding represents an advantage when the work configuration and material permit, and the removable stock allowance warrants its application.




CAUTION: High-speed grinding must not be applied on standard types of equipment, such as general types of grinding machines and regular grinding wheels. Operating grinding wheels, even temporarily, at higher than approved speed constitutes a grave safety hazard. Areas and Degrees of Automation in Cylindrical Grinding.—Power drive for the work rotation and for the reciprocating table traverse are fundamental machine movements that, once set for a certain rate, will function without requiring additional attention. Loading and removing the work, starting and stopping the main movements, and applying infeed by hand wheel are carried out by the operator on cylindrical grinding machines in their basic degree of mechanization. Such equipment is still frequently used in tool room and jobbing-type work. More advanced levels of automation have been developed for cylindrical grinders and are being applied in different degrees, particularly in the following principal respects: a) Infeed, in which different rates are provided for rapid approach, roughing and finishing, followed by a spark-out period, with presetting of the advance rates, the cutoff points, and the duration of time-related functions. b) Automatic cycling actuated by a single lever to start work rotation, table reciprocation, grinding-fluid supply, and infeed, followed at the end of the operation by wheel slide retraction, the successive stopping of the table movement, the work rotation, and the fluid supply. c) Table traverse dwells (tarry) in the extreme positions of the travel, over preset periods, to assure uniform exposure to the wheel contact of the entire work section. d) Mechanized work loading, clamping, and, after termination of the operation, unloading, combined with appropriate work-feeding devices such as indexing-type drums. e) Size control by in-process or post-process measurements. Signals originated by the gage will control the advance movement or cause automatic compensation of size variations by adjusting the cutoff points of the infeed. f) Automatic wheel dressing at preset frequency, combined with appropriate compensation in the infeed movement. g) Numerical control obviates the time-consuming setups for repetitive work performed on small- or medium-size lots. As an application example: shafts with several sections of different lengths and diameters can be ground automatically in a single operation, grinding the sections in consecutive order to close dimensional limits, controlled by an in-process gage, which is also automatically set by means of the program. The choice of the grinding machine functions to be automated and the extent of automation will generally be guided by economic considerations, after a thorough review of the available standard and optional equipment. Numerical control of partial or complete cycles is being applied to modern cylindrical and other grinding machines. Cylindrical Grinding Troubles and Their Correction.—Troubles that may be encountered in cylindrical grinding may be classified as work defects (chatter, checking, burning, scratching, and inaccuracies), improperly operating machines (jumpy infeed or traverse), and wheel defects (too hard or soft action, loading, glazing, and breakage). The Landis Tool Company has listed some of these troubles, their causes, and corrections as follows: Chatter: Sources of chatter include: 1) faulty coolant; 2) wheel out of balance; 3) wheel out of round; 4) wheel too hard; 5) improper dressing; 6) faulty work support or rotation; 7) improper operation; 8) faulty traverse; 9) work vibration; 10) outside vibration transmitted to machine; 11) interference; 12) wheel base; and 13) headstock. Suggested procedures for correction of these troubles are: 1) Faulty coolant: Clean tanks and lines. Replace dirty or heavy coolant with correct mixture. 2) Wheel out of balance: Rebalance on mounting before and after dressing. Run wheel without coolant to remove excess water. Store a removed wheel on its side to keep retained



1217

water from causing a false heavy side. Tighten wheel mounting flanges. Make sure wheel center fits spindle. 3) Wheel out of round: True before and after balancing. True sides to face. 4) Wheel too hard: Use coarser grit, softer grade, more open bond. See Wheel Defects on page 1219. 5) Improper dressing: Use sharp diamond and hold rigidly close to wheel. It must not overhang excessively. Check diamond in mounting. 6) Faulty work support or rotation: Use sufficient number of work rests and adjust them more carefully. Use proper angles in centers of work. Clean dirt from footstock spindle and be sure spindle is tight. Make certain that work centers fit properly in spindles. 7) Improper operation: Reduce rate of wheel feed. 8) Faulty traverse: See Uneven Traverse or Infeed of Wheel Head on page 1219. 9) Work vibration: Reduce work speed. Check workpiece for balance. 10) Outside vibration transmitted to machine: Check and make sure that machine is level and sitting solidly on foundation. Isolate machine or foundation. 11) Interference: Check all guards for clearance. 12) Wheel base: Check spindle bearing clearance. Use belts of equal lengths or uniform cross-section on motor drive. Check drive motor for unbalance. Check balance and fit of pulleys. Check wheel feed mechanism to see that all parts are tight. 13) Headstock: Put belts of same length and cross-section on motor drive; check for correct work speeds. Check drive motor for unbalance. Make certain that headstock spindle is not loose. Check work center fit in spindle. Check wear of face plate and jackshaft bearings. Spirals on Work (traverse lines with same lead on work as rate of traverse): Sources of spirals include: 1) machine parts out of line; and 2) truing. Suggested procedures for correction of these troubles are: 1) Machine parts out of line: Check wheel base, headstock, and footstock for proper alignment. 2) Truing: Point truing tool down 3 degrees at the workwheel contact line. Round off wheel edges. Check Marks on Work: Sources of check marks include: 1 ) i m p r o p e r o p e r a t i o n ; 2) improper heat treatment; 3) improper size control; 4) improper wheel; a n d 5) improper dressing. Suggested procedures for correction of these troubles are: 1) Improper operation: Make wheel act softer. See Wheel Defects. Do not force wheel into work. Use greater volume of coolant and a more even flow. Check the correct positioning of coolant nozzles to direct a copious flow of clean coolant at the proper location. 2) Improper heat treatment: Take corrective measures in heat-treating operations. 3) Improper size control: Make sure that engineering establishes reasonable size limits. See that they are maintained. 4) Improper wheel: Make wheel act softer. Use softer-grade wheel. Review the grain size and type of abrasive. A finer grit or more friable abrasive or both may be called for. 5) Improper dressing: Check that the diamond is sharp, of good quality, and well set. Increase speed of the dressing cycle. Make sure diamond is not cracked. Burning and Discoloration of Work: Sources of burning and discoloration are:improper operationand improper wheel. Suggested procedures for correction of these troubles are: 1) Improper operation: Decrease rate of infeed. Don’t stop work while in contact with wheel. 2) Improper wheel: Use softer wheel or obtain softer effect. See Wheel Defects. Use greater volume of coolant.




Isolated Deep Marks on Work: Source of trouble is an unsuitable wheel. Use a finer wheel and consider a change in abrasive type. Fine Spiral or Thread on Work: Sources of this trouble are: 1) improper operation; a n d 2) faulty wheel dressing. Suggested procedures for corrections of these troubles are: 1) Improper operation: Reduce wheel pressure. Use more work rests. Reduce traverse with respect to work rotation. Use different traverse rates to break up pattern when making numerous passes. Prevent edge of wheel from penetrating by dressing wheel face parallel to work. 2) Faulty wheel dressing: Use slower or more even dressing traverse. Set dressing tool at least 3 degrees down and 30 degrees to the side from time to time. Tighten holder. Don’t take too deep a cut. Round off wheel edges. Start dressing cut from wheel edge. Narrow and Deep Regular Marks on Work: Source of trouble is that the wheel is too coarse. Use finer grain size. Wide, Irregular Marks of Varying Depth on Work: Source of trouble is too soft a wheel. Use a harder grade wheel. See Wheel Defects. Widely Spaced Spots on Work: Sources of trouble are oil spots or glazed areas on wheel face. Balance and true wheel. Keep oil from wheel face. Irregular “Fish-tail” Marks of Various Lengths and Widths on Work: Source of trouble is dirty coolant. Clean tank frequently. Use filter for fine finish grinding. Flush wheel guards after dressing or when changing to finer wheel. Wavy Traverse Lines on Work: Source of trouble is wheel edges. Round off. Check for loose thrust on spindle and correct if necessary. Irregular Marks on Work: Cause is loose dirt. Keep machine clean. Deep, Irregular Marks on Work: Source of trouble is loose wheel flanges. Tighten and make sure blotters are used. Isolated Deep Marks on Work: Sources of trouble are: 1) grains pull out; coolant too strong; 2) coarse grains or foreign matter in wheel face; and 3) improper dressing. Respective suggested procedures for corrections of these troubles are: 1) decrease soda content in coolant mixture; 2) dress wheel; and 3) use sharper dressing tool. Brush wheel after dressing with stiff bristle brush. Grain Marks on Work: Sources of trouble are: 1) improper finishing cut; 2) grain sizes of roughing and finishing wheels differ too much; 3) dressing too coarse; and 4) wh eel too coarse or too soft. Respective suggested procedures for corrections of these troubles are: start with high work and traverse speeds; finish with high work speed and slow traverse, letting wheel “spark-out” completely; finish out better with roughing wheel or use finer roughing wheel; use shallower and slower cut; and use finer grain size or harder-grade wheel. Inaccuracies in Work: Work out-of-round, out-of-parallel, or tapered. Sources of trouble are: 1) misalignment of machine parts; 2) work centers; 3) improper operation; 4) coolant; 5) wheel; 6) improper dressing; 7) spindle bearings; and 8) work. Suggested procedures for corrections of these troubles are: 1) Misalignment of machine parts: Check headstock and tailstock for alignment and proper clamping. 2) Work centers: Centers in work must be deep enough to clear center point. Keep work centers clean and lubricated. Check play of footstock spindle and see that footstock spindle is clean and tightly seated. Regrind work centers if worn. Work centers must fit taper of work-center holes. Footstock must be checked for proper tension. 3) Improper operation: Don’t let wheel traverse beyond end of work. Decrease wheel pressure so work won’t spring. Use harder wheel or change feeds and speeds to make



1219

wheel act harder. Allow work to “spark-out.” Decrease feed rate. Use proper number of work rests. Allow proper amount of tarry. Workpiece must be balanced if it is an odd shape. 4) Coolant: Use greater volume of coolant. 5) Wheel: Rebalance wheel on mounting before and after truing. 6) Improper dressing: Use same positions and machine conditions for dressing as in grinding. 7) Spindle bearings: Check clearance. 8) Work: Work must come to machine in reasonably accurate form. Inaccurate Work Sizing (when wheel is fed to same position, it grinds one piece to correct size, another oversize, and still another undersize): Sources of trouble are: 1) improper work support or rotation; 2) wheel out of balance; 3) loaded wheel; 4) improper infeed; 5) improper traverse; 6) coolant; 7) misalignment; and 8) work. Suggested procedures for corrections of these troubles are: 1) Improper work support or rotation: Keep work centers clean and lubricated. Regrind work-center tips to proper angle. Be sure footstock spindle is tight. Use sufficient work rests, properly spaced. 2) Wheel out of balance: Balance wheel on mounting before and after truing. 3) Loaded wheel: See Wheel Defects. 4) Improper infeed: Check forward stops of rapid feed and slow feed. When readjusting position of wheel base by means of the fine feed, move the wheel base back after making the adjustment and then bring it forward again to take up backlash and relieve strain in feed-up parts. Check wheel spindle bearings. Don’t let excessive lubrication of wheel base slide cause “floating.” Check and tighten wheel feed mechanism. Check parts for wear. Check pressure in hydraulic system. Set infeed cushion properly. Check to see that pistons are not sticking. 5) Improper traverse: Check traverse hydraulic system and the operating pressure. Prevent excessive lubrication of carriage ways with resultant “floating” condition. Check to see if carriage traverse piston rods are binding. Carriage rack and driving gear must not bind. Change length of tarry period. 6) Coolant: Use greater volume of clean coolant. 7) Misalignment: Check level and alignment of machine. 8) Work: Workpieces may vary too much in length, permitting uneven center pressure. Uneven Traverse or Infeed of Wheel Head: Sources of uneven traverse or infeed of wheel head are: carriage and wheel head, hydraulic system, interference, unbalanced conditions, and wheel out of balance. Suggested procedures for correction of these troubles are: 1) Carriage and wheel head: Ways may be scored. Be sure to use recommended oil for both lubrication and hydraulic system. Make sure ways are not so smooth that they press out oil film. Check lubrication of ways. Check wheel feed mechanism, traverse gear, and carriage rack clearance. Prevent binding of carriage traverse cylinder rods. 2) Hydraulic systems: Remove air and check pressure of hydraulic oil. Check pistons and valves for oil leakage and for gumminess caused by incorrect oil. Check worn valves or pistons that permit leakage. 3) Interference: Make sure guard strips do not interfere. 4) Unbalanced conditions: Eliminate loose pulleys, unbalanced wheel drive motor, uneven belts, or high spindle keys. 5) Wheel out of balance: Balance wheel on mounting before and after truing. Wheel Defects: When wheel is acting too hard, such defects as glazing, some loading, lack of cut, chatter, and burning of work result.




Suggested procedures for correction of these faults are: 1) Increase work and traverse speeds as well as rate of in-feed; 2) decrease wheel speed, diameter, or width; 3 ) d r e s s more sharply; 4) use thinner coolant; 5) don’t tarry at end of traverse; 6) select softer wheel grade and coarser grain size; 7) avoid gummy coolant; and 8) on hardened work select finer grit, more fragile abrasive or both to get penetration. Use softer grade. When wheel is acting too soft, such defects as wheel marks, tapered work, short wheel life, and not-holding-cut result. Suggested procedures for correction of these faults are: 1) Decrease work and traverse speeds as well as rate of in-feed; 2) increase wheel speed, diameter, or width; 3 ) d r e s s with little in-feed and slow traverse; 4) use heavier coolants; 5) don’t let wheel run off work at end of traverse; and 6) select harder wheel or less fragile grain or both. Wheel Loading and Glazing: Sources of the trouble of wheel loading or glazing are: 1) Incorrect wheel; 2) improper dress; 3) faulty operation; 4) faulty coolant; a n d 5) gummy coolant. Suggested procedures for correction of these faults are: 1) Incorrect wheel: Use coarser grain size, more open bond, or softer grade. 2) Improper dressing: Keep wheel sharp with sharp dresser, clean wheel after dressing, use faster dressing traverse, and deeper dressing cut. 3) Faulty operation: Control speeds and feeds to soften action of wheel. Use less in-feed to prevent loading; more in-feed to stop glazing. 4) Faulty coolant: Use more, cleaner and thinner coolant, and less oily coolant. 5) Gummy coolant: To stop wheel glazing, increase soda content and avoid the use of soluble oils if water is hard. In using soluble oil coolant with hard water a suitable conditioner or “softener” should be added. Wheel Breakage: Suggested procedures for the correction of a radial break with three or more pieces are: 1) Reduce wheel speed to or below rated speed; 2) mount wheel properly, use blotters, tight arbors, even flange pressure and be sure to keep out dirt between flange and wheel; 3) use plenty of coolant to prevent over-heating; 4) use less in-feed; and 5) don’t allow wheel to become jammed on work. A radial break with two pieces may be caused by excessive side strain. To prevent an irregular wheel break, don’t let wheel become jammed on work; don’t allow striking of wheel; and never use wheels that have been damaged in handling. In general, do not use a wheel that is too tight on the arbor since the wheel is apt to break when started. Prevent excessive hammering action of wheel. Follow rules of the American National Standard Safety Requirements for the Use, Care, and Protection of Abrasive Wheels (ANSI B7.11988). Centerless Grinding In centerless grinding the work is supported on a work rest blade and is between the grinding wheel and a regulating wheel. The regulating wheel generally is a rubber bonded abrasive wheel. In the normal grinding position the grinding wheel forces the work downward against the work rest blade and also against the regulating wheel. The latter imparts a uniform rotation to the work giving it its same peripheral speed which is adjustable. The higher the work center is placed above the line joining the centers of the grinding and regulating wheels the quicker the rounding action. Rounding action is also increased by a high work speed and a slow rate of traverse (if a through-feed operation). It is possible to have a higher work center when using softer wheels, as their use gives decreased contact pressures and the tendency of the workpiece to lift off the work rest blade is lessened. Long rods or bars are sometimes ground with their centers below the line-of-centers of the wheels to eliminate the whipping and chattering due to slight bends or kinks in the rods or bars, as they are held more firmly down on the blade by the wheels.


Machinery's Handbook 27th Edition CENTERLESS GRINDING

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There are three general methods of centerless grinding which may be described as through-feed, in-feed, and end-feed methods. Through-feed Method of Grinding.—The through-feed method is applied to straight cylindrical parts. The work is given an axial movement by the regulating wheel and passes between the grinding and regulating wheels from one side to the other. The rate of feed depends upon the diameter and speed of the regulating wheel and its inclination which is adjustable. It may be necessary to pass the work between the wheels more than once, the number of passes depending upon such factors as the amount of stock to be removed, the roundness and straightness of the unground work, and the limits of accuracy required. The work rest fixture also contains adjustable guides on either side of the wheels that directs the work to and from the wheels in a straight line. In-feed Method of Centerless Grinding.—When parts have shoulders, heads or some part larger than the ground diameter, the in-feed method usually is employed. This method is similar to “plungecut” form grinding on a center type of grinder. The length or sections to be ground in any one operation are limited by the width of the wheel. As there is no axial feeding movement, the regulating wheel is set with its axis approximately parallel to that of the grinding wheel, there being a slight inclination to keep the work tight against the end stop. End-feed Method of Grinding.—The end-feed method is applied only to taper work. The grinding wheel, regulating wheel, and the work rest blade are set in a fixed relation to each other and the work is fed in from the front mechanically or manually to a fixed end stop. Either the grinding or regulating wheel, or both, are dressed to the proper taper. Automatic Centerless Grinding.—The grinding of relatively small parts may be done automatically by equipping the machine with a magazine, gravity chute, or hopper feed, provided the shape of the part will permit using these feed mechanisms. Internal Centerless Grinding.—Internal grinding machines based upon the centerless principle utilize the outside diameter of the work as a guide for grinding the bore which is concentric with the outer surface. In addition to straight and tapered bores, interrupted and “blind” holes can be ground by the centerless method. When two or more grinding operations such as roughing and finishing must be performed on the same part, the work can be rechucked in the same location as often as required. Centerless Grinding Troubles.—A number of troubles and some corrective measures compiled by a manufacturer are listed here for the through-feed and in-feed methods of centerless grinding. Chattermarks are caused by having the work center too high above the line joining the centers of the grinding and regulating wheels; using too hard or too fine a grinding wheel; using too steep an angle on the work support blade; using too thin a work support blade; “play” in the set-up due to loosely clamped members; having the grinding wheel fit loosely on the spindle; having vibration either transmitted to the machine or caused by a defective drive in the machine; having the grinding wheel out-of-balance; using too heavy a stock removal; and having the grinding wheel or the regulating wheel spindles not properly adjusted. Feed lines or spiral marks in through-feed grinding are caused by too sharp a corner on the exit side of the grinding wheel which may be alleviated by dressing the grinding wheel to a slight taper about 1⁄2 inch from the edge, dressing the edge to a slight radius, or swiveling the regulating wheel a bit. Scored work is caused by burrs, abrasive grains, or removed material being imbedded in or fused to the work support blade. This condition may be alleviated by using a coolant with increased lubricating properties and if this does not help a softer grade wheel should be used.



SURFACE GRINDING

Work not ground round may be due to the work center not being high enough above the line joining the centers of the grinding and regulating wheels. Placing the work center higher and using a softer grade wheel should help to alleviate this condition. Work not ground straight in through-feed grinding may be due to an incorrect setting of the guides used in introducing and removing the work from the wheels, and the existence of convex or concave faces on the regulating wheel. For example, if the work is tapered on the front end, the work guide on the entering side is deflected toward the regulating wheel. If tapered on the back end, then the work guide on the exit side is deflected toward the regulating wheel. If both ends are tapered, then both work guides are deflected toward the regulating wheel. The same barrel-shaped pieces are also obtained if the face of the regulating wheel is convex at the line of contact with the work. Conversely, the work would be ground with hollow shapes if the work guides were deflected toward the grinding wheel or if the face of the regulating wheel were concave at the line of contact with the work. The use of a warped work rest blade may also result in the work not being ground straight and the blade should be removed and checked with a straight edge. In in-feed grinding, in order to keep the wheel faces straight which will insure straightness of the cylindrical pieces being ground, the first item to be checked is the straightness and the angle of inclination of the work rest blade. If this is satisfactory then one of three corrective measures may be taken: the first might be to swivel the regulating wheel to compensate for the taper, the second might be to true the grinding wheel to that angle that will give a perfectly straight workpiece, and the third might be to change the inclination of the regulating wheel (this is true only for correcting very slight tapers up to 0.0005 inch). Difficulties in sizing the work in in-feed grinding are generally due to a worn in-feed mechanism and may be overcome by adjusting the in-feed nut. Flat spots on the workpiece in in-feed grinding usually occur when grinding heavy work and generally when the stock removal is light. This condition is due to insufficient driving power between the work and the regulating wheel which may be alleviated by equipping the work rest with a roller that exerts a force against the workpiece; and by feeding the workpiece to the end stop using the upper slide. Surface Grinding The term surface grinding implies, in current technical usage, the grinding of surfaces which are essentially flat. Several methods of surface grinding, however, are adapted and used to produce surfaces characterized by parallel straight line elements in one direction, while normal to that direction the contour of the surface may consist of several straight line sections at different angles to each other (e.g., the guideways of a lathe bed); in other cases the contour may be curved or profiled (e.g., a thread cutting chaser). Advantages of Surface Grinding.—Alternate methods for machining work surfaces similar to those produced by surface grinding are milling and, to a much more limited degree, planing. Surface grinding, however, has several advantages over alternate methods that are carried out with metal-cutting tools. Examples of such potential advantages are as follows: 1) Grinding is applicable to very hard and/or abrasive work materials, without significant effect on the efficiency of the stock removal. 2) The desired form and dimensional accuracy of the work surface can be obtained to a much higher degree and in a more consistent manner. 3) Surface textures of very high finish and—when the appropriate system is utilized— with the required lay, are generally produced. 4) Tooling for surface grinding as a rule is substantially less expensive, particularly for producing profiled surfaces, the shapes of which may be dressed into the wheel, often with simple devices, in processes that are much more economical than the making and the maintenance of form cutters.


Machinery's Handbook 27th Edition SURFACE GRINDING

1223

5) Fixturing for work holding is generally very simple in surface grinding, particularly when magnetic chucks are applicable, although the mechanical holding fixture can also be simpler, because of the smaller clamping force required than in milling or planing. 6) Parallel surfaces on opposite sides of the work are produced accurately, either in consecutive operations using the first ground surface as a dependable reference plane or, simultaneously, in double face grinding, which usually operates without the need for holding the parts by clamping. 7) Surface grinding is well adapted to process automation, particularly for size control, but also for mechanized work handling in the large volume production of a wide range of component parts. Principal Systems of Surface Grinding.—Flat surfaces can be ground with different surface portions of the wheel, by different arrangements of the work and wheel, as well as by different interrelated movements. The various systems of surface grinding, with their respective capabilities, can best be reviewed by considering two major distinguishing characteristics: 1) The operating surface of the grinding wheel, which may be the periphery or the face (the side); 2) The movement of the work during the process, which may be traverse (generally reciprocating) or rotary (continuous), depending on the design of a particular category of surface grinders. The accompanying Table 1and the text that follows provides a concise review of the principal surface grinding systems, defined by the preceding characteristics. It should be noted that many surface grinders are built for specific applications, and do not fit exactly into any one of these major categories. Operating Surface, Periphery of Wheel: Movement of Work, Reciprocating: W o r k i s mounted on the horizontal machine table that is traversed in a reciprocating movement at a speed generally selected from a steplessly variable range. The transverse movement, called cross feed of the table or of the wheel slide, operates at the end of the reciprocating stroke and assures the gradual exposure of the entire work surface, which commonly exceeds the width of the wheel. The depth of the cut is controlled by the downfeed of the wheel, applied in increments at the reversal of the transverse movement. Operating Surface, Periphery of Wheel: Movement of Work, Rotary: Work is mounted, usually on the full-diameter magnetic chuck of the circular machine table that rotates at a preset constant or automatically varying speed, the latter maintaining an approximately equal peripheral speed of the work surface area being ground. The wheelhead, installed on a cross slide, traverses over the table along a radial path, moving in alternating directions, toward and away from the center of the table. Infeed is by vertical movement of the saddle along the guideways of the vertical column, at the end of the radial wheelhead stroke. The saddle contains the guideways along which the wheelhead slide reciprocates. Operating Surface, Face of Wheel: Movement of Work,Reciprocating: O p e r a t i o n i s similar to the reciprocating table-type peripheral surface grinder, but grinding is with the face, usually with the rim of a cup-shaped wheel, or a segmental wheel for large machines. Capable of covering a much wider area of the work surface than the peripheral grinder, thus frequently no need for cross feed. Provides efficient stock removal, but is less adaptable than the reciprocating table-type peripheral grinder. Operating Surface, Face of Wheel: Movement of Work, Rotary: The grinding wheel, usually of segmental type, is set in a position to cover either an annular area near the periphery of the table or, more commonly, to reach beyond the table center. A large circular magnetic chuck generally covers the entire table surface and facilitates the mounting of workpieces, even of fixtures, when needed. The uninterrupted passage of the work in contact with the large wheel face permits a very high rate of stock removal and the machine,



SURFACE GRINDING Table 1. Principal Systems of Surface Grinding — Diagrams

Reciprocating — Periphery of Wheel

Rotary — Periphery of Wheel

Reciprocating — Face (Side) of Wheel

Traverse Along Straight Line or Arcuate Path — Face (Side) of Wheel

Rotary — Face (Side) of Wheel



1225

with single or double wheelhead, can be adapted also to automatic operation with continuous part feed by mechanized work handling. Operating Surface, Face of Wheel: Movement of Work, Traverse Along Straight or Arcuate Path: The grinding wheel, usually of segmental type, is set in a position to cover either an annular area near the periphery of the table or, more commonly, to reach beyond the table center. A large circular magnetic chuck generally covers the entire table surface and facilitates the mounting of workpieces, even of fixtures, when needed. The uninterrupted passage of the work in contact with the large wheel face permits a very high rate of stock removal and the machine, with single or double wheelhead, can be adapted also to automatic operation with continuous part feed by mechanized work handling. Selection of Grinding Wheels for Surface Grinding.—The most practical way to select a grinding wheel for surface grinding is to base the selection on the work material. Table 2a gives the grinding wheel recommendations for Types 1, 5, and 7 straight wheels used on reciprocating and rotary table surface grinders with horizontal spindles. Table 2b gives the grinding wheel recommendations for Type 2 cylinder wheels, Type 6 cup wheels, and wheel segments used on vertical spindle surface grinders. The last letters (two or three) that may follow the bond designation V (vitrified) or B (resinoid) refer to: 1) bond modification, “BE” being especially suitable for surface grinding; 2) special structure, “P” type being distinctively porous; and 3) for segments made of 23A type abrasives, the term 12VSM implies porous structure, and the letter “P” is not needed. The wheel markings in Tables 2a and 2b are those used by the Norton Co., complementing the basic standard markings with Norton symbols. The complementary symbols used in these tables, that is, those preceding the letter designating A (aluminum oxide) or C (silicon carbide), indicate the special type of basic abrasive that has the friability best suited for particular work materials. Those preceding A (aluminum oxide) are 57—a versatile abrasive suitable for grinding steel in either a hard or soft state. 38—the most friable abrasive. 32—the abrasive suited for tool steel grinding. 23—an abrasive with intermediate grinding action, and 19—the abrasive produced for less heat-sensitive steels. Those preceding C (silicon carbide) are 37—a general application abrasive, and 39—an abrasive for grinding hard cemented carbide. Table 2a. Grinding Wheel Recommendations for Surface Grinding— Using Straight Wheel Types 1, 5, and 7 Horizontal-spindle, reciprocating-table surface grinders Wheels less than 16 inches diameter

Material Cast iron Nonferrous metal Soft steel Hardened steel, broad contact Hardened steel, narrow contact or interrupted cut General-purpose wheel Cemented carbides

Wheels 16 inches diameter and over

Horizontal-spindle, rotary-table surface grinders Wheels of any diameter

37C36-K8V or 23A46-I8VBE 37C36-K8V 23A46-J8VBE 32A46-H8VBE or 32A60-F12VBEP

37C36-K8V 23A36-J8VBE 32A36-H8VBE or 32A36-F12VBEP

32A46-I8VBE

32A36-J8VBE

32A46-J8VBE

23A46-H8VBE Diamond wheelsa

23A36-I8VBE Diamond wheelsa

23A46-I8VBE Diamond wheelsa

23A36-I8VBE

37C36-K8V or 23A46-I8VBE 37C36-K8V 23A46-J8VBE 32A46-I8VBE

a General diamond wheel recommendations are listed in Table 5 on page 1206.



SURFACE GRINDING

Table 2b. Grinding Wheel Recommendations for Surface Grinding—Using Type 2 Cylinder Wheels, Type 6 Cup Wheels, and Wheel Segments Type 2 Cylinder Wheels

Material High tensile cast iron and nonferrous metals Soft steel, malleable cast iron, steel castings, boiler plate Hardened steel—broad contact

37C24-HKV 23A24-I8VBE or 23A30-G12VBEP 32A46-G8VBE or 32A36-E12VBEP

Hardened steel—narrow contact or interrupt cut

32A46-H8VBE

General-purpose use

23A30-H8VBE or 23A30-E12VBEP

Type 6 Cup Wheels

Wheel Segments

37C24-HVK

37C24-HVK 23A24-I8VSM or 23A30-H12VSM 32A36-G8VBE or 32A46-E12VBEP 32A46-G8VBE or 32A60-G12VBEP 23A30-H8VSM or 23A30-G12VSM

23A24-I8VBE 32A46-G8VBE or 32A60-E12VBEP 32A60-H8VBE …

Process Data for Surface Grinding.—In surface grinding, similarly to other metal-cutting processes, the speed and feed rates that are applied must be adjusted to the operational conditions as well as to the objectives of the process. Grinding differs, however, from other types of metal cutting methods in regard to the cutting speed of the tool; the peripheral speed of the grinding wheel is maintained within a narrow range, generally 5500 to 6500 surface feet per minute. Speed ranges different from the common one are used in particular processes which require special wheels and equipment. Table 3. Basic Process Data for Peripheral Surface Grinding on Reciprocating Table Surface Grinders

Work Material

Hardness

Table Speed, fpm

Downfeed, in. per pass Finish, Rough max.

Annealed, cold drawn

5500–6500 50–100

0.003

0.0005

1⁄ 4

52–65 Rc

5500–6500 50–100

0.003

0.0005

1⁄ 10

52 Rc max.

Annealed or quenched and tempered

5500–6500 50–100

0.003

0.001

1⁄ 4

52–65 Rc

Carburized and/or quenched and tempered

5500–6500 50–100

0.003

0.0005

1⁄ 10

5500–6500 50–100

0.002

0.0005

1⁄ 5

5500–6500 50–100

0.002

0.0005

1⁄ 10

Alloy steels

150–275 Bhn Annealed Tool steels 56–65 Rc Nitriding steels

Gray irons Ductile irons Stainless steels, martensitic Aluminum alloys

Quenched and tempered

200–350 Bhn Normalized, annealed 60–65 Rc

Cast steels

Crossfeed per pass, fraction of wheel width


52 Rc max. Plain carbon steel

Material Condition

Wheel Speed, fpm

Nitrided

5500–6500 50–100

0.003

0.001

1⁄ 4

5500–6500 50–100

0.003

0.0005

1⁄ 10

52 Rc max.

Normalized, annealed

5500–6500 50–100

0.003

0.001

1⁄ 4

Over 52 Rc


5500–6500 50–100

0.003

0.0005

1⁄ 10

52 Rc max.

As cast, annealed, and/or quenched and tempered

5000–6500 50–100

0.003

0.001

1⁄ 3

52 Rc max.

As cast, annealed or quenched and tempered

5500–6500 50–100

0.003

0.001

1⁄ 5

135–235 Bhn Annealed or cold drawn

5500–6500 50–100

0.002

0.0005

1⁄ 4

Over 275 Bhn Quenched and tempered

5500–6500 50–100

0.001

0.0005

1⁄ 8

5500–6500 50–100

0.003

0.001

1⁄ 3

30–150 Bhn

As cast, cold drawn or treated

In establishing the proper process values for grinding, of prime consideration are the work material, its condition, and the type of operation (roughing or finishing). Table 3 gives basic process data for peripheral surface grinding on reciprocating table surface



1227

grinders. For different work materials and hardness ranges data are given regarding table speeds, downfeed (infeed) rates and cross feed, the latter as a function of the wheel width. Common Faults and Possible Causes in Surface Grinding.—Approaching the ideal performance with regard to both the quality of the ground surface and the efficiency of surface grinding, requires the monitoring of the process and the correction of conditions adverse to the attainment of that goal. Defective, or just not entirely satisfactory surface grinding may have any one or more of several causes. Exploring and determining the cause for eliminating its harmful effects is facilitated by knowing the possible sources of the experienced undesirable performance. Table 4, associating the common faults with their possible causes, is intended to aid in determining the actual cause, the correction of which should restore the desired performance level. While the table lists the more common faults in surface grinding, and points out their frequent causes, other types of improper performance and/or other causes, in addition to those indicated, are not excluded. Vitrified Grinding Wheels.—The term “vitrified” denotes the type of bond used in these grinding wheels. The bond in a grinding wheel is the material which holds the abrasive grains together and supports them while they cut. With a given type of bond, it is the amount of bond that determines the “hardness” or softness” of wheels. The abrasive itself is extremely hard in all wheels, and the terms “hard” and “soft” refer to the strength of bonding; the greater the percentage of bond with respect to the abrasive, the heavier the coating of bond around the abrasive grains and the stronger the bond posts, the “harder” the wheel. Most wheels are made with a vitrified bond composed of clays and feldspar selected for their fusibility. During the “burning” process in grinding wheel manufacture, the clays are fused into a molten glass condition. Upon cooling, a span or post of this glass connects each abrasive grain to its neighbors to make a rigid, strong, grinding wheel. These wheels are porous, free cutting and unaffected by water, acids, oils, heat, or cold. Vitrified wheels are extensively used for cylindrical grinding, surface grinding, internal grinding and cutter grinding. Silicate Bonding Process.—Silicate grinding wheels derive their name from the fact that silicate of soda or water glass is the principal ingredient used in the bond. These wheels are also sometimes referred to as semi-vitrified wheels. Ordinarily, they cut smoothly and with comparatively little heat, and for grinding operations requiring the lowest wheel wear, compatible with cool cutting, silicate wheels are often used. Their grade is also dependable and much larger wheels can be made by this bonding process than by the vitrified process. Some of the grinding operations for which silicate wheels have been found to be especially adapted are as follows: for grinding high-speed steel machine shop tools, such as reamers, milling cutters, etc.; for hand-grinding lathe and planer tools; for surface grinding with machines of the vertical ring-wheel type; and for operations requiring dish-shaped wheels and cool cutting. These wheels are unequaled for wet grinding on hardened steel and for wet tool grinding. They are easily recognized by their light gray color. Oilstones.—The natural oilstones commonly used are the Washita and Arkansas. The Washita is a coarser and more rapidly cutting stone, and is generally considered the most satisfactory for sharpening woodworkers’ tools. There are various grades of Washita rock, varying from the perfect crystallized and porous whetstone grit, to vitreous flint and hard sandstone. The best whetstones are porous and uniform in texture and are composed entirely of silica crystals. The poorer grades are less porous, making them vitreous or “glassy.” They may also have hard spots or sand holes, or contain grains of sand among the crystals. For general work, a soft, free-grit, quick-cutting stone is required, although a finegrit medium-hard stone is sometimes preferable. These are commonly furnished in three grits: fine, medium, and coarse, and in all required shapes.



Wheel loading

Wheel glazing

Rapid wheel wear

Not firmly seated

Work sliding on chuck

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Poor size holding

.. .. ..

Work not parallel

Poor finish

.. 䊉 .. 䊉 .. .. 䊉䊉 .. 䊉 .. 䊉 .. ..

Scratches on surface

.. .. ..

Chatter marks

.. .. 䊉

Feed lines

.. .. ..

Burning or checking

.. .. ..

.. .. ..

䊉䊉䊉

.. 䊉 ..

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Abrupt section changes

䊉

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Grit too fine Grit too coarse Grade too hard Grade too soft Wheel not balanced Dense structure Improper coolant Insufficient coolant Dirty coolant Diamond loose or chipped Diamond dull No or poor magnetic force Chuck surface worn or burred

.. .. 䊉 .. .. .. .. 䊉 .. 䊉 .. .. 䊉

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Chuck not aligned

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Vibrations in machine

..

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Plane of movement out of parallel

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Too low work speed Too light feed Too heavy cut Chuck retained swarf Chuck loading improper Insufficient blocking of parts Wheel runs off the work Wheel dressing too fine Wheel edge not chamfered Loose dirt under guard

.. .. 䊉䊉䊉 .. .. 䊉 .. ..

.. .. .. 䊉䊉 .. 䊉 .. .. ..


WORK RETAINMENT

.. .. ..

.. .. ..

Work not flat

TOOLING AND COOLANT MACHINE AND SETUP OPERATIONAL CONDITIONS

WHEEL CONDITION

.. .. ..

Heat treat stresses Work too thin Work warped

FAULTS

SURFACE QUALITY

SURFACE GRINDING

GRINDING WHEEL

WORK CONDITION

CAUSES

METALLURGICAL DEFECTS Burnishing of work

WORK DIMENSION

1228

Table 4. Common Faults and Possible Causes in Surface Grinding

Machinery's Handbook 27th Edition OFFHAND GRINDING

1229

Offhand Grinding Offhand grinding consists of holding the wheel to the work or the work to the wheel and grinding to broad tolerances and includes such operations as certain types of tool sharpening, weld grinding, snagging castings and other rough grinding. Types of machines that are used for rough grinding in foundries are floor- and bench-stand machines. Wheels for these machines vary from 6 to 30 inches in diameter. Portable grinding machines (electric, flexible shaft, or air-driven) are used for cleaning and smoothing castings. Many rough grinding operations on castings can be best done with shaped wheels, such as cup wheels (including plate mounted) or cone wheels, and it is advisable to have a good assortment of such wheels on hand to do the odd jobs the best way. Floor- and Bench-Stand Grinding.—The most common method of rough grinding is on double-end floor and bench stands. In machine shops, welding shops, and automotive repair shops, these grinders are usually provided with a fairly coarse grit wheel on one end for miscellaneous rough grinding and a finer grit wheel on the other end for sharpening tools. The pressure exerted is a very important factor in selecting the proper grinding wheel. If grinding is to be done mostly on hard sharp fins, then durable, coarse and hard wheels are required, but if grinding is mostly on large gate and riser pads, then finer and softer wheels should be used for best cutting action. Portable Grinding.—Portable grinding machines are usually classified as air grinders, flexible shaft grinders, and electric grinders. The electric grinders are of two types; namely, those driven by standard 60 cycle current and so-called high-cycle grinders. Portable grinders are used for grinding down and smoothing weld seams; cleaning metal before welding; grinding out imperfections, fins and parting lines in castings and smoothing castings; grinding punch press dies and patterns to proper size and shape; and grinding manganese steel castings. Wheels used on portable grinders are of three bond types; namely, resinoid, rubber, and vitrified. By far the largest percentage is resinoid. Rubber bond is used for relatively thin wheels and where a good finish is required. Some of the smaller wheels such as cone and plug wheels are vitrified bonded. Grit sizes most generally used in wheels from 4 to 8 inches in diameter are 16, 20, and 24. In the still smaller diameters, finer sizes are used, such as 30, 36, and 46. The particular grit size to use depends chiefly on the kind of grinding to be done. If the work consists of sharp fins and the machine has ample power, a coarse grain size combined with a fairly hard grade should be used. If the job is more in the nature of smoothing or surfacing and a fairly good finish is required, then finer and softer wheels are called for. Swing-Frame Grinding.—This type of grinding is employed where a considerable amount of material is to be removed as on snagging large castings. It may be possible to remove 10 times as much material from steel castings using swing-frame grinders as with portable grinders; and 3 times as much material as with high-speed floor-stand grinders. The largest field of application for swing-frame machines is on castings which are too heavy to handle on a floor stand; but often it is found that comparatively large gates and risers on smaller castings can be ground more quickly with swing-frame grinders, even if fins and parting lines have to be ground on floor stands as a second operation. In foundries, the swing-frame machines are usually suspended from a trolley on a jib that can be swung out of the way when placing the work on the floor with the help of an overhead crane. In steel mills when grinding billets, a number of swing-frame machines are usually suspended from trolleys on a line of beams which facilitate their use as required. The grinding wheels used on swing-frame machines are made with coarser grit sizes and harder grades than wheels used on floor stands for the same work. The reason is that greater grinding pressures can be obtained on the swing-frame machines.



ABRASIVE CUTTING Abrasive Belt Grinding

Abrasive belts are used in the metalworking industry for removing stock, light cleaning up of metal surfaces, grinding welds, deburring, breaking and polishing hole edges, and finish grinding of sheet steel. The types of belts that are used may be coated with aluminum oxide (the most common coating) for stock removal and finishing of all alloy steels, highcarbon steel, and tough bronzes; and silicon carbide for use on hard, brittle, and low-tensile strength metals which would include aluminum and cast irons. Table 1 is a guide to the selection of the proper abrasive belt, lubricant, and contact wheel. This table is entered on the basis of the material used and type of operation to be done and gives the abrasive belt specifications (type of bonding andabrasive grain size and material), the range of speeds at which the belt may best be operated, the type of lubricant to use, and the type and hardness of the contact wheel to use. Table 2 serves as a guide in the selection of contact wheels. This table is entered on the basis of the type of contact wheel surface and the contact wheel material. The table gives the hardness and/or density, the type of abrasive belt grinding for which the contact wheel is intended, the character of the wheel action and such comments as the uses, and hints for best use. Both tables are intended only as guides for general shop practice; selections may be altered to suit individual requirements. There are three types of abrasive belt grinding machines. One type employs a contact wheel behind the belt at the point of contact of the workpiece to the belt and facilitates a high rate of stock removal. Another type uses an accurate parallel ground platen over which the abrasive belt passes and facilitates the finishing of precision parts. A third type which has no platens or contact wheel is used for finishing parts having uneven surfaces or contours. In this type there is no support behind the belt at the point of contact of the belt with the workpiece. Some machines are so constructed that besides grinding against a platen or a contact wheel the workpiece may be moved and ground against an unsupported portion of the belt, thereby in effect making it a dual machine. Although abrasive belts at the time of their introduction were used dry, since the advent of the improved waterproof abrasive belts, they have been used with coolants, oil-mists, and greases to aid the cutting action. The application of a coolant to the area of contact retards loading, resulting in a cool, free cutting action, a good finish and a long belt life. Abrasive Cutting Abrasive cut-off wheels are used for cutting steel, brass and aluminum bars and tubes of all shapes and hardnesses, ceramics, plastics, insulating materials, glass and cemented carbides. Originally a tool or stock room procedure, this method has developed into a highspeed production operation. While the abrasive cut-off machine and cut-off wheel can be said to have revolutionized the practice of cutting-off materials, the metal saw continues to be the more economical method for cutting-off large cross-sections of certain materials. However, there are innumerable materials and shapes that can be cut with much greater speed and economy by the abrasive wheel method. On conventional chop-stroke abrasive cutting machines using 16-inch diameter wheels, 2-inch diameter bar stock is the maximum size that can be cut with satisfactory wheel efficiency, but bar stock up to 6 inches in diameter can be cut efficiently on oscillating-stroke machines. Tubing up to 31⁄2 inches in diameter can also be cut efficiently. Abrasive wheels are commonly available in four types of bonds: Resinoid, rubber, shellac and fiber or fabric reinforced. In general, resinoid bonded cut-off wheels are used for dry cutting where burrs and some burn are not objectionable and rubber bonded wheels are used for wet cutting where cuts are to be smooth, clean and free from burrs. Shellac bonded wheels have a soft, free cutting quality which makes them particularly useful in the tool room where tool steels are to be cut without discoloration. Fiber reinforced bonded wheels are able to withstand severe flexing and side pressures and fabric reinforced bonded



Table 1. Guide to the Selection and Application of Abrasive Belts

Material Hot-and Cold-Rolled Steel

Belt Speed, fpm

Roughing

R/R Al2O3

24–60

4000–65000

Light-body or none

Cog-tooth, serrated rubber

70–90

Polishing

R/G or R/R Al2O3

80–150

4500–7000

Light-body or none

Plain or serrated rubber, sectional or finger-type cloth wheel, free belt

20–60

R/G or electro-coated Al2O3 cloth

180–500

4500–7000

Heavy or with abrasive compound

Smooth-faced rubber or cloth

20–40

Fine Polishing Stainless Steel

Titanium

Durometer Hardness

50–80

3500–5000

Light-body or none


70–90

Polishing

R/G or R/R Al2O3

80–120

4000–5500

Light-body or none


30–60

Closed-coat SiC

150–280

4500–5500

Heavy or oil mist


20–40

Roughing

R/R SiC or Al2O3

24–80

5000–6500

Light


70–90

Polishing

R/G SiC or Al2O3

100–180

4500–6500

Light


30–50

Closed-coat SiC or electro-coated Al2O3

220–320

4500–6500


Plain faced rubber, finger-type cloth or free belt

20–50

36–80

2200–4500

Light-body


70–90

Roughing

R/R SiC or Al2O3

Polishing

Closed-coat SiC or electro-coated Al2O3 or R/G SiC or Al2O3

100–150

4000–6500

Light-body


30–50

Fine Polishing

Closed-coat SiC or electro-coated Al2O3

180–320

4000–6500

Light or with abrasive compound

Same as for polishing

20–30

Roughing

R/R SiC or Al2O3

24–80

4500–6500

Light-body

Hard wheel depending on application

50–70

Polishing

R/G SiC or Al2O3

100–180

4500–6500

Light-body

Plain rubber, cloth or free belt

30–50

Electro-coated Al2O3 or closed-coat SiC

220–320

4500–6500


Plain or finger-type cloth wheel, or free belt

20–30

Fine Polishing Cast Iron

Type

Roughing

R/R Al2O3

24–60

2000–4000

None


70–90

Polishing

R/R Al2O3

80–150

4000–5500

None

Serrated rubber

30–70

Fine Polishing

R/R Al2O3

120–240

4000–5500

Light-body

Smooth-faced rubber

30–40 70–80

Roughing

R/R SiC or Al2O3

36–50

700–1500

Sulfur-chlorinated

Small-diameter, cog-tooth serrated rubber

Polishing

R/R SiC

60–120

1200–2000

Light-body

Standard serrated rubber

Fine Polishing

R/R SiC

120–240

1200–2000

Light-body


50 20–40

1231

a R/R indicates that both the making and sizing bond coats are resin. R/G indicates that the making coat is glue and the sizing coat is resin. The abbreviations Al O for 2 3 aluminum oxide and SiC for silicon carbide are used. Almost all R/R and R/G Al2O3 and SiC belts have a heavy-drill weight cloth backing. Most electro-coated Al2O3 and closed-coat SiC belts have a jeans weight cloth backing.


ABRASIVE CUTTING

Non-ferrous Die-castings

Type of Grease Lubricant

R/R Al2O3

Fine Polishing Copper Alloys or Brass

Abrasive Belta

Roughing

Fine Polishing Aluminum, Cast or Fabricated

Contact Wheel

Grit

Type of Operation


ABRASIVE CUTTING Table 2. Guide to the Selection and Application of Contact Wheels Hardness and Density

Surface

Material

Cog-tooth

Rubber

Standard serrated

Rubber

X-shaped serrations

Rubber

20 to 50 durometer

Plain face

Rubber

20 to 70 durometer

Flat flexible

Compressed canvas

About nine densities from very hard to very soft

Flat flexible

Solid sectional canvas

Soft, medium, and hard

Flat flexible

Buff section canvas

Soft

Contour polishing

Flat flexible

Sponge rubber inserts

5 to 10 durometer, soft

Polishing

Flexible

Fingers of canvas attached to hub

Soft

Polishing

Flat flexible

Rubber segments

Varies in hardness

Flat flexible

Inflated rubber

Air pressure controls hardness

70 to 90 durometer 40 to 50 durometer, medium density

Purposes

Wheel Action

Comments

Roughing

Fast cutting, allows long belt life.

For cutting down projections on castings and weld beads.

Roughing

Leaves rough- to mediumground surface.

For smoothing projections and face defects.

Flexibility of rubber allows entry into contours. Medium polishing, light removal. Plain wheel face allows conRoughing trolled penetration of abraand sive grain. Softer wheels polishing give better finishes. Hard wheels can remove Roughing metal, but not as quickly as and cog-tooth rubber wheels. polishing Softer wheels polish well. Uniform polishing. Avoids abrasive pattern on work. Polishing Adjusts to contours. Can be performed for contours. Roughing and polishing

Same as for standard serrated wheels but preferred for soft non-ferrous metals.

For large or small flat faces.

Good for medium-range grinding and polishing.

A low-cost wheel with uniform density at the face. Handles all types of polishing. Can be widened or narrowed For fine polishing and finishby adding or removing secing. tions. Low cost. Has replaceable segments. Uniform polishing and finPolishes and blends conishing. Polishes and blends tours. Segments allow dencontours. sity changes. Uniform polishing and finishing.

For polishing and finishing.

Roughing Grinds or polishes dependand ing on density and hardness polishing of inserts.

For portable machines. Uses replaceable segments that save on wheel costs and allow density changes.

Roughing and Uniform finishing. polishing

Adjusts to contours.

wheels which are highly resistant to breakage caused by extreme side pressures, are fast cutting and have a low rate of wear. The types of abrasives available in cut-off wheels are: Aluminum oxide, for cutting steel and most other metals; silicon carbide, for cutting non-metallic materials such as carbon, tile, slate, ceramics, etc.; and diamond, for cutting cemented carbides. The method of denoting abrasive type, grain size, grade, structure and bond type by using a system of markings is the same as for grinding wheels (see page 1179). Maximum wheel speeds given in the American National Standard “Safety Requirements for The Use, Care, and Protection of Abrasive Wheels” (ANSI B7.1-1988) range from 9500 to 14,200 surface feet per minute for organic bonded cut-off wheels larger than 16 inches in diameter and from 9500 to 16,000 surface feet per minute for organic bonded cut-off wheels 16 inches in diameter and smaller. Maximum wheel speeds specified by the manufacturer should never be exceeded even though they may be lower than those given in the B7.1 Standard. There are four basic types of abrasive cutting machines: Chop-stroke, oscillating stroke, horizontal stroke and work rotating. Each of these four types may be designed for dry cutting or for wet cutting (includes submerged cutting).


Machinery's Handbook 27th Edition HONING PROCESS

1233

The accompanying table based upon information made available by The Carborundum Co. gives some of the probable causes of cutting off difficulties that might be experienced when using abrasive cut-off wheels. Probable Causes of Cutting-Off Difficulties Difficulty Angular Cuts and Wheel Breakage Burning of Stock

Excessive Wheel Wear

Excessive Burring

Probable Cause (1) Inadequate clamping which allows movement of work while the wheel is in the cut. The work should be clamped on both sides of the cut. (2) Work vise higher on one side than the other causing wheel to be pinched. (3) Wheel vibration resulting from worn spindle bearings. (4) Too fast feeding into the cut when cutting wet. (1) Insufficient power or drive allowing wheel to stall. (2) Cuts too heavy for grade of wheel being used. (3) Wheel fed through the work too slowly. This causes a heating up of the material being cut. This difficulty encountered chiefly in dry cutting. (1) Too rapid cutting when cutting wet. (2) Grade of wheel too hard for work, resulting in excessive heating and burning out of bond. (3) Inadequate coolant supply in wet cutting. (4) Grade of wheel too soft for work. (5) Worn spindle bearings allowing wheel vibration. (1) Feeding too slowly when cutting dry. (2) Grit size in wheel too coarse. (3) Grade of wheel too hard. (4) Wheel too thick for job.

Honing Process The hone-abrading process for obtaining cylindrical forms with precise dimensions and surfaces can be applied to internal cylindrical surfaces with a wide range of diameters such as engine cylinders, bearing bores, pin holes, etc. and also to some external cylindrical surfaces. The process is used to: 1) eliminate inaccuracies resulting from previous operations by generating a true cylindrical form with respect to roundness and straightness within minimum dimensional limits; 2) generate final dimensional size accuracy within low tolerances, as may be required for interchangeability of parts; 3) provide rapid and economical stock removal consistent with accomplishment of the other results; and 4) generate surface finishes of a specified degree of surface smoothness with high surface quality. Amount and Rate of Stock Removal.—Honing may be employed to increase bore diameters by as much as 0.100 inch or as little as 0.001 inch. The amount of stock removed by the honing process is entirely a question of processing economy. If other operations are performed before honing then the bulk of the stock should be taken off by the operation that can do it most economically. In large diameter bores that have been distorted in heat treating, it may be necessary to remove as much as 0.030 to 0.040 inch from the diameter to make the bore round and straight. For out-of-round or tapered bores, a good “rule of thumb” is to leave twice as much stock (on the diameter) for honing as there is error in the bore. Another general rule is: For bores over one inch in diameter, leave 0.001 to 0.0015 inch stock per inch of diameter. For example, 0.002 to 0.003 inch of stock is left in twoinch bores and 0.010 to 0.015 inch in ten-inch bores. Where parts are to be honed for finish only, the amount of metal to be left for removing tool marks may be as little as 0.0002 to 0.015 inch on the diameter. In general, the honing process can be employed to remove stock from bore diameters at the rate of 0.009 to 0.012 inch per minute on cast-iron parts and from 0.005 to 0.008 inch per minute on steel parts having a hardness of 60 to 65 Rockwell C. These rates are based on parts having a length equal to three or four times the diameter. Stock has been removed



HONING PROCESS

from long parts such as gun barrels, at the rate of 65 cubic inches per hour. Recommended honing speeds for cast iron range from 110 to 200 surface feet per minute of rotation and from 50 to 110 lineal feet per minute of reciprocation. For steel, rotating surface speeds range from 50 to 110 feet per minute and reciprocation speeds from 20 to 90 lineal feet per minute. The exact rotation and reciprocation speeds to be used depend upon the size of the work, the amount and characteristics of the material to be removed and the quality of the finish desired. In general, the harder the material to be honed, the lower the speed. Interrupted bores are usually honed at faster speeds than plain bores. Formula for Rotative Speeds.—Empirical formulas for determining rotative speeds for honing have been developed by the Micromatic Hone Corp. These formulas take into consideration the type of material being honed, its hardness and its surface characteristics; the abrasive area; and the type of surface pattern and degree of surface roughness desired. Because of the wide variations in material characteristics, abrasives available, and types of finishes specified, these formulas should be considered as a guide only in determining which of the available speeds (pulley or gear combinations) should be used for any particular application. K×D The formula for rotative speed, S, in surface feet per minute is: S = --------------W×N R The formula for rotative speed in revolutions per minute is: R.P.M = --------------W×N where, K and R are factors taken from the table on the following page, D is the diameter of the bore in inches, W is the width of the abrasive stone or stock in inches, and N is the number of stones. Although the actual speed of the abrasive is the resultant of both the rotative speed and the reciprocation speed, this latter quantity is seldom solved for or used. The reciprocation speed is not determined empirically but by testing under operating conditions. Changing the reciprocation speed affects the dressing action of the abrasive stones, therefore, the reciprocation speed is adjusted to provide for a desired surface finish which is usually a well lubricated bearing surface that will not scuff. Table of Factors for Use in Rotative Speed Formulas Hardnessb Soft Character of Surfacea Base Metal Dressing Surface Severe Dressing

Medium

Hard

Factors Material

K

R

K

R

K

R

Cast Iron Steel Cast Iron Steel Cast Iron Steel

110 80 150 110 200 150

420 300 570 420 760 570

80 60 110 80 150 110

300 230 420 300 570 420

60 50 80 60 110 80

230 190 300 230 420 300

a The character of the surface is classified according to its effect on the abrasive; Base Metal being a honed, ground or fine bored section that has little dressing action on the grit; Dressing Surface being a rough bored, reamed or broached surface or any surface broken by cross holes or ports; Severe Dressing being a surface interrupted by keyways, undercuts or burrs that dress the stones severely. If over half of the stock is to be removed after the surface is cleaned up, the speed should be computed using the Base Metal factors for K and R. b Hardness designations of soft, medium and hard cover the following ranges on the Rockwell “ C” hardness scale, respectively: 15 to 45, 45 to 60 and 60 to 70.


Machinery's Handbook 27th Edition LAPS AND LAPPING

1235

Possible Adjustments for Eliminating Undesirable Honing Conditions Adjustment Required to Correct Conditiona Abrasiveb Grain Size

Hardness

Structure

Feed Pressure

Reciprocation

R.P.M.

Runout Time

Stroke Length

Abrasive Glazing Abrasive Loading Too Rough Surface Finish Too Smooth Surface Finish Poor Stone Life Slow Stock Removal Taper — Large at Ends Taper — Small at Ends

Friability

Undesirable Condition

Other

+ 0 0 0 − + 0 0

−− −− ++ −− + −− 0 0

−− − ++ −− ++ − 0 0

+ − − + − + 0 0

++ ++ − + − ++ 0 0

++ + − + − ++ 0 0

−− −− ++ −− + −− 0 0

− 0 + − 0 0 0 0

0 0 0 0 0 0 − +

a The + and + + symbols generally indicate that there should be an increase or addition while the − and − − symbols indicate that there should be a reduction or elimination. In each case, the double symbol indicates that the contemplated change would have the greatest effect. The 0 symbol means that a change would have no effect. b For the abrasive adjustments the + and + + symbols indicate a more friable grain, a finer grain, a harder grade or a more open structure and the − and − − symbols just the reverse. Compiled by Micromatic Hone Corp.

Abrasive Stones for Honing.—Honing stones consist of aluminum oxide, silicon carbide, CBN or diamond abrasive grits, held together in stick form by a vitrified clay, resinoid or metal bond. CBN metal-bond stones are particularly suitable and widely used for honing. The grain and grade of abrasive to be used in any particular honing operation depend upon the quality of finish desired, the amount of stock to be removed, the material being honed and other factors. The following general rules may be followed in the application of abrasive for honing: 1) Silicon-carbide abrasive is commonly used for honing cast iron, while aluminum-oxide abrasive is generally used on steel; 2) The harder the material being honed, the softer the abrasive stick used; 3) A rapid reciprocating speed will tend to make the abrasive cut fast because the dressing action on the grits will be severe; and 4) To improve the finish, use a finer abrasive grit, incorporate more multi-direction action, allow more “run-out” time after honing to size, or increase the speed of rotation. Surface roughnesses ranging from less than 1 micro-inch r.m.s. to a relatively coarse roughness can be obtained by judicious choice of abrasive and honing time but the most common range is from 3 to 50 micro-inches r.m.s. Adjustments for Eliminating Undesirable Honing Conditions.—The accompanying table indicates adjustments that may be made to correct certain undesirable conditions encountered in honing. Only one change should be made at a time and its effect noted before making other adjustments. Tolerances.—For bore diameters above 4 inches the tolerance of honed surfaces with respect to roundness and straightness ranges from 0.0005 to 0.001 inch; for bore diameters from 1 to 4 inches, 0.0003 to 0.0005 inch; and for bore diameters below 1 inch, 0.00005 to 0.0003 inch. Laps and Lapping Material for Laps.—Laps are usually made of soft cast iron, copper, brass or lead. In general, the best material for laps to be used on very accurate work is soft, close-grained cast iron. If the grinding, prior to lapping, is of inferior quality, or an excessive allowance has been left for lapping, copper laps may be preferable. They can be charged more easily and cut more rapidly than cast iron, but do not produce as good a finish. Whatever material is



LAPS AND LAPPING

used, the lap should be softer than the work, as, otherwise, the latter will become charged with the abrasive and cut the lap, the order of the operation being reversed. A common and inexpensive form of lap for holes is made of lead which is cast around a tapering steel arbor. The arbor usually has a groove or keyway extending lengthwise, into which the lead flows, thus forming a key that prevents the lap from turning. When the lap has worn slightly smaller than the hole and ceases to cut, the lead is expanded or stretched a little by the driving in of the arbor. When this expanding operation has been repeated two or three times, the lap usually must be trued or replaced with a new one, owing to distortion. The tendency of lead laps to lose their form is an objectionable feature. They are, however, easily molded, inexpensive, and quickly charged with the cutting abrasive. A more elaborate form for holes is composed of a steel arbor and a split cast-iron or copper shell which is sometimes prevented from turning by a small dowel pin. The lap is split so that it can be expanded to accurately fit the hole being operated upon. For hardened work, some toolmakers prefer copper to either cast iron or lead. For holes varying from 1⁄4 to 1⁄2 inch in diameter, copper or brass is sometimes used; cast iron is used for holes larger than 1⁄2 inch in diameter. The arbors for these laps should have a taper of about 1⁄4 or 3⁄8 inch per foot. The length of the lap should be somewhat greater than the length of the hole, and the thickness of the shell or lap proper should be from 1⁄8 to 1⁄6 its diameter. External laps are commonly made in the form of a ring, there being an outer ring or holder and an inner shell which forms the lap proper. This inner shell is made of cast iron, copper, brass or lead. Ordinarily the lap is split and screws are provided in the holder for adjustment. The length of an external lap should at least equal the diameter of the work, and might well be longer. Large ring laps usually have a handle for moving them across the work. Laps for Flat Surfaces.—Laps for producing plane surfaces are made of cast iron. In order to secure accurate results, the lapping surface must be a true plane. A flat lap that is used for roughing or “blocking down” will cut better if the surface is scored by narrow grooves. These are usually located about 1⁄2 inch apart and extend both lengthwise and crosswise, thus forming a series of squares similar to those on a checker-board. An abrasive of No. 100 or 120 emery and lard oil can be used for charging the roughing lap. For finer work, a lap having an unscored surface is used, and the lap is charged with a finer abrasive. After a lap is charged, all loose abrasive should be washed off with gasoline, for fine work, and when lapping, the surface should be kept moist, preferably with kerosene. Gasoline will cause the lap to cut a little faster, but it evaporates so rapidly that the lap soon becomes dry and the surface caked and glossy in spots. Loose emery should not be applied while lapping, for if the lap is well charged with abrasive in the beginning, is kept well moistened and not crowded too hard, it will cut for a considerable time. The pressure upon the work should be just enough to insure constant contact. The lap can be made to cut only so fast, and if excessive pressure is applied it will become “stripped” in places. The causes of scratches are: Loose abrasive on the lap; too much pressure on the work, and poorly graded abrasive. To produce a perfectly smooth surface free from scratches, the lap should be charged with a very fine abrasive. Grading Abrasives for Lapping.—For high-grade lapping, abrasives can be evenly graded as follows: A quantity of flour-emery or other abrasive is placed in a heavy cloth bag, which is gently tapped, causing very fine particles to be sifted through. When a sufficient quantity has been obtained in this way, it is placed in a dish of lard or sperm oil. The largest particles will then sink to the bottom and in about one hour the oil should be poured into another dish, care being taken not to disturb the sediment at the bottom. The oil is then allowed to stand for several hours, after which it is poured again, and so on, until the desired grade is obtained.



1237

Charging Laps.—To charge a flat cast-iron lap, spread a very thin coating of the prepared abrasive over the surface and press the small cutting particles into the lap with a hard steel block. There should be as little rubbing as possible. When the entire surface is apparently charged, clean and examine for bright spots; if any are visible, continue charging until the entire surface has a uniform gray appearance. When the lap is once charged, it should be used without applying more abrasive until it ceases to cut. If a lap is over-charged and an excessive amount of abrasive is used, there is a rolling action between the work and lap which results in inaccuracy. The surface of a flat lap is usually finished true, prior to charging, by scraping and testing with a standard surface-plate, or by the well-known method of scraping-in three plates together, in order to secure a plane surface. In any case, the bearing marks or spots should be uniform and close together. These spots can be blended by covering the plates evenly with a fine abrasive and rubbing them together. While the plates are being ground in, they should be carefully tested and any high spots which may form should be reduced by rubbing them down with a smaller block. To charge cylindrical laps for internal work, spread a thin coating of prepared abrasive over the surface of a hard steel block, preferably by rubbing lightly with a cast-iron or copper block; then insert an arbor through the lap and roll the latter over the steel block, pressing it down firmly to embed the abrasive into the surface of the lap. For external cylindrical laps, the inner surface can be charged by rolling-in the abrasive with a hard steel roller that is somewhat smaller in diameter than the lap. The taper cast-iron blocks which are sometimes used for lapping taper holes can also be charged by rolling-in the abrasive, as previously described; there is usually one roughing and one finishing lap, and when charging the former, it may be necessary to vary the charge in accordance with any error which might exist in the taper. Rotary Diamond Lap.—This style of lap is used for accurately finishing very small holes, which, because of their size, cannot be ground. While the operation is referred to as lapping, it is, in reality, a grinding process, the lap being used the same as a grinding wheel. Laps employed for this work are made of mild steel, soft material being desirable because it can be charged readily. Charging is usually done by rolling the lap between two hardened steel plates. The diamond dust and a little oil is placed on the lower plate, and as the lap revolves, the diamond is forced into its surface. After charging, the lap should be washed in benzine. The rolling plates should also be cleaned before charging with dust of a finer grade. It is very important not to force the lap when in use, especially if it is a small size. The lap should just make contact with the high spots and gradually grind them off. If a diamond lap is lubricated with kerosene, it will cut freer and faster. These small laps are run at very high speeds, the rate depending upon the lap diameter. Soft work should never be ground with diamond dust because the dust will leave the lap and charge the work. When using a diamond lap, it should be remembered that such a lap will not produce sparks like a regular grinding wheel; hence, it is easy to crowd the lap and “strip” some of the diamond dust. To prevent this, a sound intensifier or “harker” should be used. This is placed against some stationary part of the grinder spindle, and indicates when the lap touches the work, the sound produced by the slightest contact being intensified. Grading Diamond Dust.—The grades of diamond dust used for charging laps are designated by numbers, the fineness of the dust increasing as the numbers increase. The diamond, after being crushed to powder in a mortar, is thoroughly mixed with high-grade olive oil. This mixture is allowed to stand five minutes and then the oil is poured into another receptacle. The coarse sediment which is left is removed and labeled No. 0, according to one system. The oil poured from No. 0 is again stirred and allowed to stand ten minutes, after which it is poured into another receptacle and the sediment remaining is labeled No. 1. This operation is repeated until practically all of the dust has been recovered from the oil, the time that the oil is allowed to stand being increased as shown by the following table. This is done in order to obtain the smaller particles that require a longer time for precipitation:



LAPS AND LAPPING To obtain No. 1 — 10 minutes

To obtain No. 4 — 2 hours

To obtain No. 2 — 30 minutes

To obtain No. 5 — 10 hours

To obtain No. 3 — 1 hour To obtain No. 6 — until oil is clear The No. 0 or coarse diamond which is obtained from the first settling is usually washed in benzine, and re-crushed unless very coarse dust is required. This No. 0 grade is sometimes known as “ungraded” dust. In some places the time for settling, in order to obtain the various numbers, is greater than that given in the table. Cutting Properties of Laps and Abrasives.—In order to determine the cutting properties of abrasives when used with different lapping materials and lubricants, a series of tests was conducted, the results of which were given in a paper by W. A. Knight and A. A. Case, presented before the American Society of Mechanical Engineers. In connection with these tests, a special machine was used, the construction being such that quantitative results could be obtained with various combinations of abrasive, lubricant, and lap material. These tests were confined to surface lapping. It was not the intention to test a large variety of abrasives, three being selected as representative; namely, Naxos emery, carborundum, and alundum. Abrasive No. 150 was used in each case, and seven different lubricants, five different pressures, and three different lap materials were employed. The lubricants were lard oil, machine oil, kerosene, gasoline, turpentine, alcohol, and soda water. These tests indicated throughout that there is, for each different combination of lap and lubricant, a definite size of grain that will give the maximum amount of cutting. With all the tests, except when using the two heavier lubricants, some reduction in the size of the grain below that used in the tests (No. 150) seemed necessary before the maximum rate of cutting was reached. This reduction, however, was continuous and soon passed below that which gave the maximum cutting rate. Cutting Qualities with Different Laps.—The surfaces of the steel and cast-iron laps were finished by grinding. The hardness of the different laps, as determined by the scleroscope was, for cast-iron, 28; steel, 18; copper, 5. The total amount ground from the testpieces with each of the three laps showed that, taking the whole number of tests as a standard, there is scarcely any difference between the steel and cast iron, but that copper has somewhat better cutting qualities, although, when comparing the laps on the basis of the highest and lowest values obtained with each lap, steel and cast iron are as good for all practical purposes as copper, when the proper abrasive and lubricant are used. Wear of Laps.—The wear of laps depends upon the material from which they are made and the abrasive used. The wear on all laps was about twice as fast with carborundum as with emery, while with alundum the wear was about one and one-fourth times that with emery. On an average, the wear of the copper lap was about three times that of the cast-iron lap. This is not absolute wear, but wear in proportion to the amount ground from the testpieces. Lapping Abrasives.—As to the qualities of the three abrasives tested, it was found that carborundum usually began at a lower rate than the other abrasives, but, when once started, its rate was better maintained. The performance gave a curve that was more nearly a straight line. The charge or residue as the grinding proceeded remained cleaner and sharper and did not tend to become pasty or mucklike, as is so frequently the case with emery. When using a copper lap, carborundum shows but little gain over the cast-iron and steel laps, whereas, with emery and alundum, the gain is considerable. Effect of Different Lapping Lubricants.—The action of the different lubricants, when tested, was found to depend upon the kind of abrasive and the lap material. Lard and Machine Oil: The test showed that lard oil, without exception, gave the higher rate of cutting, and that, in general, the initial rate of cutting is higher with the lighter lubri-



1239

cants, but falls off more rapidly as the test continues. The lowest results were obtained with machine oil, when using an emery-charged, cast-iron lap. When using lard oil and a carborundum-charged steel lap, the highest results were obtained. Gasoline and Kerosene: On the cast-iron lap, gasoline was superior to any of the lubricants tested. Considering all three abrasives, the relative value of gasoline, when applied to the different laps, is as follows: Cast iron, 127; copper, 115; steel, 106. Kerosene, like gasoline, gives the best results on cast iron and the poorest on steel. The values obtained by carborundum were invariably higher than those obtained with emery, except when using gasoline and kerosene on a copper lap. Turpentine and Alcohol: Turpentine was found to do good work with carborundum on any lap. With emery, turpentine did fair work on the copper lap, but, with the emery on cast-iron and steel laps, it was distinctly inferior. Alcohol gives the lowest results with emery on the cast-iron and steel laps. Soda Water: Soda water gives medium results with almost any combination of lap and abrasives, the best work being on the copper lap and the poorest on the steel lap. On the cast-iron lap, soda water is better than machine or lard oil, but not so good as gasoline or kerosene. Soda water when used with alundum on the copper lap, gave the highest results of any of the lubricants used with that particular combination. Lapping Pressures.—Within the limits of the pressures used, that is, up to 25 pounds per square inch, the rate of cutting was found to be practically proportional to the pressure. The higher pressures of 20 and 25 pounds per square inch are not so effective on the copper lap as on the other materials. Wet and Dry Lapping.—With the “wet method” of using a surface lap, there is a surplus of oil and abrasive on the surface of the lap. As the specimen being lapped is moved over it, there is more or less movement or shifting of the abrasive particles. With the “dry method,” the lap is first charged by rubbing or rolling the abrasive into its surface. All surplus oil and abrasive are then washed off, leaving a clean surface, but one that has embedded uniformly over it small particles of the abrasive. It is then like the surface of a very fine oilstone and will cut away hardened steel that is rubbed over it. While this has been termed the dry method, in practice, the lap surface is kept moistened with kerosene or gasoline. Experiments on dry lapping were carried out on the cast-iron, steel, and copper laps used in the previous tests, and also on one of tin made expressly for the purpose. Carborundum alone was used as the abrasive and a uniform pressure of 15 pounds per square inch was applied to the specimen throughout the tests. In dry lapping, much depends upon the manner of charging the lap. The rate of cutting decreased much more rapidly after the first 100 revolutions than with the wet method. Considering the amounts ground off during the first 100 revolutions, and the best result obtained with each lap taken as the basis of comparison, it was found that with a tin lap, charged by rolling No. 150 carborundum into the surface, the rate of cutting, when dry, approached that obtained with the wet method. With the other lap materials, the rate with the dry method was about one-half that of the wet method. Summary of Lapping Tests.—The initial rate of cutting does not greatly differ for different abrasives. There is no advantage in using an abrasive coarser than No. 150. The rate of cutting is practically proportional to the pressure. The wear of the laps is in the following proportions: cast iron, 1.00; steel, 1.27; copper, 2.62. In general, copper and steel cut faster than cast iron, but, where permanence of form is a consideration, cast iron is the superior metal. Gasoline and kerosene are the best lubricants to use with a cast-iron lap. Machine and lard oil are the best lubricants to use with copper or steel laps. They are, however, least effective on a cast-iron lap. In general, wet lapping is from 1.2 to 6 times as fast as dry lapping, depending upon the material of the lap and the manner of charging.



KNURLS AND KNURLING

KNURLS AND KNURLING ANSI Standard Knurls and Knurling.—The ANSI/ASME Standard B94.6-1984 covers knurling tools with standardized diametral pitches and their dimensional relations with respect to the work in the production of straight, diagonal, and diamond knurling on cylindrical surfaces having teeth of uniform pitch parallel to the cylinder axis or at a helix angle not exceeding 45 degrees with the work axis. These knurling tools and the recommendations for their use are equally applicable to general purpose and precision knurling. The advantage of this ANSI Standard system is the provision by which good tracking (the ability of teeth to mesh as the tool penetrates the work blank in successive revolutions) is obtained by tools designed on the basis of diametral pitch instead of TPI (teeth per inch) when used with work blank diameters that are multiples of 1⁄64 inch for 64 and 128 diametral pitch or 1⁄32 inch for 96 and 160 diametral pitch. The use of knurls and work blank diameters which will permit good tracking should improve the uniformity and appearance of knurling, eliminate the costly trial and error methods, reduce the failure of knurling tools and production of defective work, and decrease the number of tools required. Preferred sizes for cylindrical knurls are given in Table 1 and detailed specifications appear in Table 2. Table 1. ANSI Standard Preferred Sizes for Cylindrical Type Knurls ANSI/ASME B94.6-1984 Nominal Outside Diameter Dnt

Width of Face F

Diameter of Hole A

64

1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

3⁄ 16 1⁄ 4 3⁄ 8 3⁄ 8

3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4

32 40 48 56

5⁄ 8

5⁄ 16

7⁄ 32

40

3⁄ 4

5⁄ 8 3⁄ 8

1⁄ 4 5⁄ 16

48 64

Standard Diametral Pitches, P 96 128 160 Number of Teeth, Nt, for Standard Pitches 48 60 72 84

64 80 96 112

80 100 120 140

60

80

100

72 96

96 128

120 160

Additional Sizes for Bench and Engine Lathe Tool Holders

1

The 96 diametral pitch knurl should be given preference in the interest of tool simplification. Dimensions Dnt, F, and A are in inches.

Table 2. ANSI Standard Specifications for Cylindrical Knurls with Straight or Diagonal Teeth ANSI/ASME B94.6-1984 Diametral Pitch P

Nominal Diameter, Dnt 1⁄ 2

5⁄ 8

3⁄ 4

7⁄ 8

1

Tracking Correction Factor Q

0.9864

0.0006676

Major Diameter of Knurl, Dot, +0.0000, −0.0015

64

0.4932

0.6165

0.7398

0.8631

Tooth Depth, h, + 0.0015, − 0.0000 Straight

Diagonal

0.024

0.021

96

0.4960

0.6200

0.7440

0.8680

0.9920

0.0002618

0.016

0.014

128

0.4972

0.6215

0.7458

0.8701

0.9944

0.0001374

0.012

0.010

160

0.4976

0.6220

0.7464

0.8708

0.9952

0.00009425

0.009

0.008

Radius at Root R 0.0070 0.0050 0.0060 0.0040 0.0045 0.0030 0.0040 0.0025

All dimensions except diametral pitch are in inches. Approximate angle of space between sides of adjacent teeth for both straight and diagonal teeth is 80 degrees. The permissible eccentricity of teeth for all knurls is 0.002 inch maximum (total indicator reading). Number of teeth in a knurl equals diametral pitch multiplied by nominal diameter. Diagonal teeth have 30-degree helix angle, ψ.


Machinery's Handbook 27th Edition KNURLS AND KNURLING

1241

The term Diametral Pitch applies to the quotient obtained by dividing the total number of teeth in the circumference of the work by the basic blank diameter; in the case of the knurling tool it would be the total number of teeth in the circumference divided by the nominal diameter. In the Standard the diametral pitch and number of teeth are always measured in a transverse plane which is perpendicular to the axis of rotation for diagonal as well as straight knurls and knurling. Cylindrical Knurling Tools.—The cylindrical type of knurling tool comprises a tool holder and one or more knurls. The knurl has a centrally located mounting hole and is provided with straight or diagonal teeth on its periphery. The knurl is used to reproduce this tooth pattern on the work blank as the knurl and work blank rotate together. *Formulas for Cylindrical Knurls

P =diametral pitch of knurl = Nt ÷ Dnt

(1)

Dnt = nominal diameter of knurl = Nt ÷ P

(2)

Nt =no. of teeth on knurl = P × Dnt *P nt *P ot

=circular pitch on nominal diameter = π ÷ P =circular pitch on major diameter = πDot ÷ Nt

Dot = major diameter of knurl = Dnt − (NtQ ÷ π) Q =Pnt − Pot = tracking correction factor in Formula

(3) (4) (5) (6) (7)

Tracking Correction Factor Q: Use of the preferred pitches for cylindrical knurls, Table 2, results in good tracking on all fractional work-blank diameters which are multiples of 1⁄64 inch for 64 and 128 diametral pitch, and 1⁄32 inch for 96 and 160 diametral pitch; an indication of good tracking is evenness of marking on the work surface during the first revolution of the work. The many variables involved in knurling practice require that an empirical correction method be used to determine what actual circular pitch is needed at the major diameter of the knurl to produce good tracking and the required circular pitch on the workpiece. The empirical tracking correcton factor, Q, in Table 2 is used in the calculation of the major diameter of the knurl, Formula (6).

Cylindrical Knurl * Note:

For diagonal knurls, Pnt and Pot are the transverse circular pitches which are measured in the plane perpendicular to the axis of rotation.



KNURLS AND KNURLING

Flat Knurling Tools.—The flat type of tool is a knurling die, commonly used in reciprocating types of rolling machines. Dies may be made with either single or duplex faces having either straight or diagonal teeth. No preferred sizes are established for flat dies. Flat Knurling Die with Straight Teeth:

R =radius at root P =diametral pitch = Nw ÷ Dw Dw =work blank (pitch) diameter = Nw ÷ P Nw =number of teeth on work = P × Dw h =tooth depth Q =tracking correction factor (see Table 2) Pl =linear pitch on die =circular pitch on work pitch diameter = P − Q

(8) (9) (10)

(11)

Table 3. ANSI Standard Specifications for Flat Knurling Dies ANSI/ASME B94.6-1984 Diametral Pitch, P

Linear Pitch,a Pl

Tooth Depth, h Straight

Diagonal

Tooth Depth, h

Radius at Root, R

Diametral Pitch, P

Linear Pitch,a Pl

Straight

Diagonal

128

0.0244

0.012

0.010

0.0045 0.0030

160

0.0195

0.009

0.008

0.0040 0.0025

64

0.0484

0.024

0.021

0.0070 0.0050

96

0.0325

0.016

0.014

0.0060 0.0040

Radius at Root, R

a The linear pitches are theoretical. The exact linear pitch produced by a flat knurling die may vary slightly from those shown depending upon the rolling condition and the material being rolled.

All dimensions except diametral pitch are in inches.

Teeth on Knurled Work

Formulas Applicable to Knurled Work.—The following formulas are applicable to knurled work with straight, diagonal, and diamond knurling.


Machinery's Handbook 27th Edition KNURLS AND KNURLING

1243

Formulas for Straight or Diagonal Knurling with Straight or Diagonal Tooth Cylindrical Knurling Tools Set with Knurl Axis Parallel with Work Axis: P =diametral pitch = Nw ÷ Dw Dw =work blank diameter = Nw ÷ P Nw =no. of teeth on work = P × Dw a =“addendum” of tooth on work = (Dow − Dw) ÷ 2 h =tooth depth (see Table 2) Dow = knurled diameter (outside diameter after knurling) = Dw + 2a

(12) (13) (14) (15) (16)

Formulas for Diagonal and Diamond Knurling with Straight Tooth Knurling Tools Set at an Angle to the Work Axis: ψ =angle between tool axis and work axis P =diametral pitch on tool Pψ =diametral pitch produced on work blank (as measured in the transverse plane) by setting tool axis at an angle ψ with respect to work blank axis Dw =diameter of work blank; and Nw =number of teeth produced on work blank (as measured in the transverse plane) (17) then, Pψ =P cos ψ and, N =DwP cos ψ (18) For example, if 30 degree diagonal knurling were to be produced on 1-inch diameter stock with a 160 pitch straight knurl:

If,

N w = D w P cos 30 ° = 1.000 × 160 × 0.86603 = 138.56 teeth Good tracking is theoretically possible by changing the helix angle as follows to correspond to a whole number of teeth (138): cos ψ = N w ÷ D w P = 138 ÷ ( 1 × 160 ) = 0.8625 ψ = 30 1⁄2 degrees, approximately Whenever it is more practical to machine the stock, good tracking can be obtained by reducing the work blank diameter as follows to correspond to a whole number of teeth (138): Nw 138 - = ---------------------------= 0.996 inch D w = ---------------P cos ψ 160 × 0.866 Table 4. ANSI Standard Recommended Tolerances on Knurled Diameters ANSI/ASME B94.6-1984 Tolerance Class I II III

64

+ 0.005 − 0.012 + 0.000 − 0.010 + 0.000 − 0.006

96 128 Tolerance on Knurled Outside Diameter + 0.004 + 0.003 − 0.010 − 0.008 + 0.000 + 0.000 − 0.009 − 0.008 + 0.000 + 0.000 − 0.005 − 0.004

Diametral Pitch 160 64

+ 0.002 − 0.006 + 0.000 − 0.006 + 0.000 − 0.003

± 0.0015

96 128 Tolerance on Work-Blank Diameter Before Knurling ± 0.0010

± 0.0007

160

± 0.0005

± 0.0015

± 0.0010

± 0.0007

± 0.0005

+ 0.000 − 0.0015

+ 0.0000 − 0.0010

+ 0.000 − 0.0007

+ 0.0000 − 0.0005



KNURLS AND KNURLING

Recommended Tolerances on Knurled Outside Diameters.—T h e r e c o m m e n d e d applications of the tolerance classes shown in Table 4 are as follows: Class I: Tolerances in this classification may be applied to straight, diagonal and raised diamond knurling where the knurled outside diameter of the work need not be held to close dimensional tolerances. Such applications include knurling for decorative effect, grip on thumb screws, and inserts for moldings and castings. Class II: Tolerances in this classification may be applied to straight knurling only and are recommended for applications requiring closer dimensional control of the knurled outside diameter than provided for by Class I tolerances. Class III: Tolerances in this classification may be applied to straight knurling only and are recommended for applications requiring closest possible dimensional control of the knurled outside diameter. Such applications include knurling for close fits. Note: The width of the knurling should not exceed the diameter of the blank, and knurling wider than the knurling tool cannot be produced unless the knurl starts at the end of the work. Marking on Knurls and Dies.—Each knurl and die should be marked as follows: a. when straight to indicate its diametral pitch; b. when diagonal, to indicate its diametral pitch, helix angle, and hand of angle. Concave Knurls.—The radius of a concave knurl should not be the same as the radius of the piece to be knurled. If the knurl and the work are of the same radius, the material compressed by the knurl will be forced down on the shoulder D and spoil the appearance of the work. A design of concave knurl is shown in the accompanying illustration, and all the important dimensions are designated by letters. To find these dimensions, the pitch of the knurl required must be known, and also, approximately, the throat diameter B. This diameter must suit the knurl holder used, and be such that the circumference contains an even number of teeth with the required pitch. When these dimensions have been decided upon, all the other unknown factors can be found by the following formulas: Let R = radius of piece to be knurled; r = radius of concave part of knurl; C = radius of cutter or hob for cutting the teeth in the knurl; B = diameter over concave part of knurl (throat diameter); A = outside diameter of knurl; d = depth of tooth in knurl; P = pitch of knurl (number of teeth per inch circumference); p = circular pitch of knurl; then r = R + 1⁄2d; C = r + d; A = B + 2r − (3d + 0.010 inch); and d = 0.5 × p × cot α/2, where α is the included angle of the teeth. As the depth of the tooth is usually very slight, the throat diameter B will be accurate enough for all practical purposes for calculating the pitch, and it is not necessary to take into consideration the pitch circle. For example, assume that the pitch of a knurl is 32, that the throat diameter B is 0.5561 inch, that the radius R of the piece to be knurled is 1⁄16 inch, and that the angle of the teeth is 90 degrees; find the dimensions of the knurl. Using the notation given: 1- = 0.03125 inch p = --1- = ----d = 0.5 × 0.03125 × cot 45° = 0.0156 inch P 32 1- + 0.0156 r = -------------------- = 0.0703 inch C = 0.0703 + 0.0156 = 0.0859 inch 16 2 A = 0.5561 + 0.1406 – ( 0.0468 + 0.010 ) = 0.6399 inch


Machinery's Handbook 27th Edition ACCURACY

1245

MACHINE TOOL ACCURACY Accuracy, Repeatability, and Resolution: In machine tools, accuracy is the maximum spread in measurements made of slide movements during successive runs at a number of target points, as discussed below. Repeatability is the spread of the normal curve at the target point that has the largest spread. A rule of thumb says that repeatability is approximately half the accuracy value, or twice as good as the accuracy, but this rule is somewhat nullified due to the introduction of error-compensation features on NC machines. Resolution refers to the smallest units of measurement that the system (controller plus servo) can recognize. Resolution is an electronic/electrical term and the unit is usually smaller than either the accuracy or the repeatability. Low values for resolution are usually, though not necessarily, applied to machines of high accuracy. In addition to high cost, a low-resolution-value design usually has a low maximum feed rate and the use of such designs is usually restricted to applications requiring high accuracy. Positioning Accuracy:The positioning accuracy of a numerically controlled machine tool refers to the ability of an NC machine to place the tip of a tool at a preprogrammed target. Although no metal cutting is involved, this test is very significant for a machine tool and the cost of an NC machine will rise almost geometrically with respect to its positioning accuracy. Care, therefore, should be taken when deciding on the purchase of such a machine, to avoid paying the premium for unneeded accuracy but instead to obtain a machine that will meet the tolerance requirements for the parts to be produced. Accuracy can be measured in many ways. A tool tip on an NC machine could be moved, for example, to a target point whose X-coordinate is 10.0000 inches. If the move is along the X-axis, and the tool tip arrives at a point that measures 10.0001 inches, does this mean that the machine has an accuracy of 0.0001 inch? What if a repetition of this move brought the tool tip to a point measuring 10.0003 inches, and another repetition moved the tool to a point that measured 9.9998 inches? In practice, it is expected that there would be a scattering or distribution of measurements and some kind of averaging is normally used. Mean Positional Deviation = 0.0003 = xj

Positional Deviation xij

Readings Normal Curve

x-Axis

Target 10.0000

Mean (Avg.) 10.0003

Distance Between Increments = 0.001"

Fig. 1. In a Normal Distribution, Plotted Points Cluster Around the Mean.

Although averaging the results of several runs is an improvement over a single run, the main problem with averaging is that it does not consider the extent or width of the spread of readings. For example, if one measurement to the 10.0000-inch target is 9.9000 inches and another is 10.1000 inches, the difference of the two readings is 0.2000 inch, and the accuracy is poor. However, the readings average a perfect 10 inches. Therefore, the average and the spread of several readings must both be considered in determining the accuracy. Plotting the results of a large number of runs generates a normal distribution curve, as shown in Fig. 1. In this example, the readings are plotted along the X-axis in increments of



ACCURACY

0.0001 inch (0.0025 mm). Usually, five to ten such readings are sufficient. The distance of any one reading from the target is called the positional deviation of the point. The distance of the mean, or average, for the normal distribution from the target is called the mean positional deviation. The spread for the normal curve is determined by a mathematical formula that calculates the distance from the mean that a certain percentage of the readings fall into. The mathematical formula used calculates one standard deviation, which represents approximately 32 per cent of the points that will fall within the normal curve, as shown in Fig. 2. One standard deviation is also called one sigma, or 1σ. Plus or minus one sigma (±1σ) represents 64 per cent of all the points under the normal curve. A wider range on the curve, ±2σ, means that 95.44 per cent of the points are within the normal curve, and ±3σ means that 99.74 per cent of the points are within the normal curve. If an infinite number of runs were made, almost all the measurements would fall within the ±3σ range.

64% of Readings 95.44% of Readings 99.74% of Readings –1␴ ␴ +1␴ ␴ –2␴ ␴

+2␴ ␴

–3␴ ␴

+3␴ ␴ Mean (Avg.)

Fig. 2. Percentages of Points Falling in the ±1σ (64%), ±2σ (95.44%), and ±3σ (99.74%) Ranges

The formula for calculating one standard deviation is 1σ =

1 ----------n–1

n

∑ ( Xij – Xj )

2

i=1

where n = number of runs to the target; i = identification for any one run; Xij = positional deviation for any one run (see Fig. 1); and, Xj = mean positional deviation (see Fig. 1). The bar over the X in the formula indicates that the value is the mean or average for the normal distribution. Example:From Fig. 3, five runs were made at a target point that is 10.0000 inches along the X-axis and the positional deviations for each run were: x1j = −0.0002, x2j = +0.0002, x3j = +0.0005, x4j = +0.0007, and x5j = +0.0008 inch. The algebraic total of these five runs is +0.0020, and the mean positional deviation = Xj = 0.0020⁄5 = 0.0004. The calculations for one standard deviation are: 1σ =

1 - [ ( X – X )2 + ( X – X )2 + ( X – X )2 + ( X – X ) 2 + ( X – X )2 ] ----------j j j j j 1j 2j 3j 4j 5j n–1

1σ =

1 - ( – 0.0002 – 0.0004 ) 2 ----------[ + ( 0.0002 – 0.0004 ) 2 + 5–1 ( 0.0005 – 0.0004 ) 2 + ( 0.0007 – 0.0004 ) 2 + ( 0.0008 – 0.0004 ) 2 ]

=

--1- ( 0.00000066 ) = 4

-6

0.17 ×10 = 0.0004

Three sigma variations or 3σ, is 3 times sigma, equal to 0.0012 for the example.



1247

If an infinite number of trials were made to the target position of 10.0000 inches for the ongoing example, 99.74 per cent of the points would fall between 9.9992 and 10.0016 inches, giving a spread of ± 3σ, or 0.0024 inch. This spread alone is not considered as the accuracy but rather the repeatability for the target point 10.0000.

Fig. 3. Readings for Five Runs to Target Points P1, P2, P3, P4, and P5 Result in a Mean Positional Deviation of 0.0004

To calculate the accuracy, it is not sufficient to make a number of runs to one target point along a particular axis, but rather to a number of points along the axis, the number depending on the length of axis travel provided. For example, a travel of about 3 ft requires 5, and a travel of 6 ft requires 10 target points. The standard deviation and spread for the normal curve must be determined at each target point, as shown in Fig. 4. The accuracy for the axis would then be the spread between the normal curve with the most negative position and the normal curve with the most positive position. Technically, the accuracy is a spread rather than a ± figure, but it is often referred to as a ± figure and it may be assumed that a ±0.003, for expediency, is equal to a spread of 0.006. The above description for measuring accuracy considers unidirectional approaches to target points. Bidirectional movements (additional movements to the same target point from either direction) will give different results, mostly due to backlash in the lead-screw, though backlash is small with ballnut leadscrews. Measurements made with bidirectional movements will show greater spreads and somewhat less accuracy than will unidirectional movements.

x–Axis TP1

TP2

TP3

TP4

TP5

(a)

Spread = Accuracy = 0.004⬙ (b) Fig. 4. Two Ways of Plotting Five Target Point Spreads

Rules for determining accuracy were standardized in guidelines last revised by the Association for Manufacturing Technology (AMT) in 1972. Some European machine tool builders use the VDI/DGQ 3441 (German) guidelines, which are similar to those of the



ACCURACY

AMT in that normal distributions are used and a number of target points are selected along an axis. Japanese standards JIS B6201, JIS B6336, and JIS B6338 are somewhat simpler and consider only the spread of the readings, so that the final accuracy figure may be almost double that given by the AMT or VDI methods. The International Standards Organization (ISO), in 1988, issued ISO 230-2, which follows the procedures discussed above, but is somewhat less strict than the AMT recommendations. Table 1 lists some types of NC machines and the degree of accuracy that they normally provide. Table 1. Degrees of Accuracy Expected with NC Machine Tools Accuracy Type of NC Machine Large boring machines or boring mills Small milling machines Large machining centers Small and medium-sized machining centers Lathes, slant bed, small and medium sizes Lathes, small precision Horizontal jigmill Vertical jig boring machines Vertical jig grinding machines Cylindrical grinding machines, small to medium sizes Diamond turning lathes

inches 0.0010–0.0020 0.0006–0.0010 0.0005–0.0008 0.0003–0.0006 0.0002–0.0005 0.0002–0.0003 0.0002–0.0004 0.0001–0.0002 0.0001–0.0002

mm 0.025–0.050 0.015–0.025 0.012–0.020 0.008–0.015 0.006–0.012 0.004–0.008 0.004–0.010 0.002–0.005 0.002–0.005

0.00004–0.0003

0.001–0.007

0.00002–0.0001

0.0005–0.003

Significance of Accuracy:Numerically controlled machines are generally considered to be more accurate and more consistent in their movements than their conventional counterparts. CNC controllers have improved the accuracy by providing the ability to compensate for mechanical inaccuracies. Thus, compensation for errors in the lead-screw, parallelism and squareness of the machine ways, and for the effects of heating can be made automatically on NC machines. Some machine tool types are expected to be more accurate than others; for instance, grinding machines are more accurate than milling machines, and lathes for diamond turning are more accurate than normal slant-bed lathes. Accuracy of machine tools depends on temperature, air pressure, local vibrations, and humidity. ISO standard 230-2 requires that, where possible, the ambient temperature for conducting such tests be held between 67.1 and 68.9 degrees F (19.5 and 20.5 degrees C). Autocollimation:Checks on movements of slides and spindles, and alignment and other characteristics of machine tools are performed with great accuracy by means of an autocollimator, which is an optical, noncontact, angle-measuring instrument. Flatness, straightness, perpendicularity, and runout can also be checked by autocollimation. The instrument is designed to project a beam of light from a laser or an incandescent bulb onto an optically flat mirror. When the light beam is reflected back to the instrument, the distance traveled by the beam, also deviations from a straight line, can be detected by the projector and calculated electronically or measured by the scale. Autocollimators have a small angular measuring range and are usually calibrated in arcseconds. One arc-second is an angle of 4.85 millionths of an inch (0.00000485 in.) per inch of distance from the vertex, and is often rounded to 5 millionths of an inch per inch. Angles can also be described in terms of radians and 1 arc-second is equal to 4.85 microradians, or 0.0000573 deg. In practice, the interferometer or autocollimator is fixed to a rigid structure and the optical mirror, which should have a flatness of one-quarter wavelength of the light used (see page 723), is fixed to the workpiece to be measured. The initial reading is taken, and then



1249

the workpiece is moved to another position. Readings of movement can be made to within a few millionths of an inch. Angular displacements, corresponding to successive positions, of about 1 arc-second can be taken from most autocollimators, in azimuth or elevation or a combination of the two. Generally, the line width of the reticle limits the accuracy of reading such instruments. Laser interferometers are designed to allow autocollimation readings to be taken by a photodetector instead of the eye, and some designs can measure angles to 0.001 arc-second, closer than is required for most machine shop applications. Output from an electronic autocollimator is usually transferred to a computer for recording or analysis if required. The computer calculates, lists, and plots the readings for the target points automatically, under control of the inspection program. A typical plot from such a setup is seen in Fig. 5, where the central line connects the averages for the normal distributions at each target point. The upper line connects the positive outer limits and the lower line the negative outer limits for the normal distributions. The normal spread, indicating the accuracy of positioning, is 0.00065 inch (0.016 mm), for the Y-axis along which the measurements were taken.

Date Humidity Air Press. Air Temp. Mach. Temp.

1984 / 6 / 11 Percent 41.00 In. Hg 27.36 Deg. F 77.50 Deg. F 76.50

Machining Center Axis Travel From –0.30 to –15.30

Axis - Y Runs - 8 Points - 16 In Increments of 1.0000

+ 0.0010 + 0.0005

– 0.0005 – 15.30 – 0.0010 – 0.30 – 1.80

– 3.30

– 4.80

– 6.30

– 7.80

– 9.30

– 10.80

– 12.30

– 13.80

Fig. 5. Laser Interferometer Plots of Movements of Slides on a Large Horizontal Machining Center Showing an Accuracy of 0.00065 inch (0.016 mm) for the y Axis

Effect of Machine Accuracy on Part Tolerances Part tolerances are usually shown on prints, usually in a control block to ANSI Standard 14.5M-1994 (see Geometric Dimensioning and Tolerancing starting on page 630.) Table 2 shows some part tolerance symbols that relate to machine tool positioning accuracy. The accuracy of a part is affected by machine and cutting tool dynamics, alignment, fixture accuracy, operator settings, and accuracies of the cutting tools, holders, and collets, but the positioning accuracy of the machine probably has the greatest influence. Spindle rotation accuracy, or runout, also has a large influence on part accuracy. The ratio of the attainable part accuracy to the no-load positioning accuracy can vary from 1.7:1 to 8.31:1, depending on the type of cutting operation. For instance, making a hole by drilling, followed by a light boring or reaming operation, produces a quite accurate result in about the 1.7:1 range, whereas contour milling on hard material could be at the higher end of the range. A good average for part accuracy versus machine positioning accuracy is 3.3:1, which means that the part accuracy is 3.3 times the positioning accuracy.



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Table 2. Symbols and Feature Control Frames ANSI Y14.5M-1994 Symbol

Characteristic

Meaning of Characteristic

The allowable true position tolerance of a feature from a datum (assume feature to be a drilled hole). Feature control block might appear as: Position

Relationship to the Machine Tool Assume tolerance is 0.005 mm. Machine positioning accuracy would be at least 0.005 × 0.707 = 0.0035 mm even if it is assumed that the hole accuracy is the same as the positioning accuracy. Machine could be milling, drilling, or machining center.

y – axis

⭋ 0.005 A A is the datum, which can be another surface, another hole, or other feature

True Position Tolerance Zone

ACCURACY

x – axis 45

Position

Assume feature to be a turned circumference, the axis of which has to be within a tolerance to another feature. Feature control block would appear as follows if feature A were the axis of hole 1:

Center (axis) for Hole 2

⭋ 0.005 A

Center (axis) for Hole 1


True Position Tolerance Zone 2 (0.005 mm) Hole 2



Characteristic


Relationship to the Machine Tool

The roundness tolerance establishes a band. Roundness

This tolerance would apply to turning and would be the result of radial spindle runout.

Diametral accuracy of the part would depend on the positioning accuracy of the cross-slide of lathe or grinder. PosiUsually expressed as a ± tolerance attached to the dimension. tioning accuracy would be from 1⁄2 to 1⁄4 of part accuracy, depending chiefly on the rigidity of the tool, depth of cut, and material being cut.

ACCURACY

Diameter

Tolerance band

Specifies a uniform boundary, along a true profile.

Tolerance 0.005

Profile of a surface

Datum A

Affected by positioning accuracy of machine. There would be side and/or end forces on the tool so expect part to machine positioning accuracy to be high, say, 5:1

Feature control block might appear as:


1251

⭋ 0.005 A


Characteristic



1252


A feature (surface) parallel to a datum plane or datum axis.

Tolerance 0.010 Affected by positioning accuracy, machine alignment, and fixturing.

Parallelism

Datum A Feature control block might appear as:

ACCURACY

⭋ 0.010 A

Applies to turning. The axis of the feature must lie within the tolerance zone of another axis.

Tolerance 0.010

A

Concentricity

Affected by positioning accuracy, most likely along Z axis.

Datum A Feature control block might appear as follows:

⭋ 0.005 A




Characteristic



Applies to the runout (both radial and axial) of a circular feature at any one position around the circumference or flat, perpendicular to the axis.

Runout

Runout at a Point (Radial)

Radial runout on part is not affected by spindle radial runout unless whole machine is untrue. Axial runout on part is affected by axial runout on machine. Feature would normally be perpendicular to datum. Feature control block might appear as:

⭋ 0.005 A

Runout at a Point (Axial)

Would be affected by either radial or axial runout, or both, machine misalignment, or setup.

Total runout

ACCURACY

Runout at a Point (Radial)

Similar to runout but applies to total surface and therefore consider both radial and axial runout.

A feature is perpendicular to a datum plane or axis. Perpendicularity

Tolerance Zone

Affected principally by misalignment of machine or fixturing.

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NUMERICAL CONTROL

NUMERICAL CONTROL Introduction.—The Electronic Industries Association (EIA) defines numerical control as “a system in which actions are controlled by the direct insertion of numerical data at some point.” More specifically, numerical control, or NC as it will be called here, involves machines controlled by electronic systems designed to accept numerical data and other instructions, usually in a coded form. These instructions may come directly from some source such as a punched tape, a floppy disk, directly from a computer, or from an operator. The key to the success of numerical control lies in its flexibility. To machine a different part, it is only necessary to “play” a different tape. NC machines are more productive than conventional equipment and consequently produce parts at less cost even when the higher investment is considered. NC machines also are more accurate and produce far less scrap than their conventional counterparts. By 1985, over 110,000 NC machine tools were operating in the United States. Over 80 per cent of the dollars being spent on the most common types of machine tools, namely, drilling, milling, boring, and turning machines, are going into NC equipment. NC is a generic term for the whole field of numerical control and encompasses a complete field of endeavor. Sometimes CNC, which stands for Computer Numerical Control and applies only to the control system, is used erroneously as a replacement term for NC. Albeit a monumental development, use of the term CNC should be confined to installations where the older hardware control systems have been replaced. Metal cutting is the most popular application, but NC is being applied successfully to other equipment, including punch presses, EDM wire cutting machines, inspection machines, laser and other cutting and torching machines, tube bending machines, and sheet metal cutting and forming machines. State of the CNC Technology Today.—Early numerical control machines were ordinary machines retrofitted with controls and motors to drive tools and tables. The operations performed were the same as the operations were on the machines replaced. Over the years, NC machines began to combine additional operations such as automatically changing tools and workpieces. The structure of the machines has been strengthened to provide more rigid platforms. These changes have resulted in a class of machine that can outperform its predecessors in both speed and accuracy. Typical capabilities of a modern machining center are accuracy better than ±0.00035 inch; spindle speeds in the range up to 25,000 rpm or more, and increasing; feed rates up to 400 inches per minute and increasing; tool change times hovering between 2 and 4 seconds and decreasing. Specialized machines have been built that can achieve accuracy better than one millionth (0.000001) of an inch. Computer numerical control of machines has undergone a great deal of change in the last decade, largely as a result of rapid increases in computer capability. Development of new and improved materials for tooling and bearings, improvements in tool geometry, and the added structural stiffness of the new machines have made it possible to perform cutting operations at speeds and feeds that were formerly impossible to attain. Numerical Control vs. Manual Operations.—The initial cost of a CNC machine is generally much higher than a manual machine of the same nominal capacity, and the higher initial cost leads to a higher overall cost of the machine per hour of its useful life. However, the additional cost of a CNC machine has to be considered against potential savings that the machine may make possible. Some of the individual factors that make NC and CNC machining attractive are considered below. Labor is usually one of the highest costs in the production of a part, but the labor rate paid to a CNC machine operator may be lower than the rate paid to the operator of conventional machines. This statement is particularly true when there is a shortage of operators with specialized skills necessary for setting up and operating a manual machine. However, it should not be assumed that skilled CNC machine operators are not needed because most CNCs have manual overrides that allow the operator to adjust feeds and speeds and to manually edit or enter programs as necessary. Also, skilled setup personnel and operators are


Machinery's Handbook 27th Edition NUMERICAL CONTROL

1255

likely to promote better production rates and higher efficiency in the shop. In addition, the labor rate for setting up and operating a CNC machine can sometimes be divided between two or more machines, further reducing the labor costs and cost per part produced. The quantity and quality requirements for an order of parts often determines what manufacturing process will be used to produce them. CNC machines are probably most effective when the jobs call for a small to medium number of components that require a wide range of operations to be performed. For example, if a large number of parts are to be machined and the allowable tolerances are large, then manual or automatic fixed-cycle machines may be the most viable process. But, if a large quantity of high quality parts with strict tolerances are required, then a CNC machine will probably be able to produce the parts for the lowest cost per piece because of the speed and accuracy of CNC machines. Moreover, if the production run requires designing and making a lot of specialized form tools, cams, fixtures, or jigs, then the economics of CNC machining improves even more because much of the preproduction work is not required by the nature of the CNC process. CNC machines can be effective for producing one-of-a-kind jobs if the part is complicated and requires a lot of different operations that, if done manually, would require specialized setups, jigs, fixtures, etc. On the other hand, a single component requiring only one or two setups might be more practical to produce on a manual machine, depending on the tolerances required. When a job calls for a small to medium number of components that require a wide range of operations, CNC is usually preferable. CNC machines are also especially well suited for batch jobs where small numbers of components are produced from an existing part program, as inventory is needed. Once the part program has been tested, a batch of the parts can be run whenever necessary. Design changes can be incorporated by changing the part program as required. The ability to process batches also has an additional benefit of eliminating large inventories of finished components. CNC machining can help reduce machine idle time. Surveys have indicated that when machining on manual machines, the average time spent on material removal is only about 40 per cent of the time required to complete a part. On particularly complicated pieces, this ratio can drop to as low as 10 per cent or even less. The balance of the time is spent on positioning the tool or work, changing tools, and similar activities. On numerically controlled machines, the metal removal time frequently has been found to be in excess of 70 per cent of the total time spent on the part. CNC nonmachining time is lower because CNC machines perform quicker tool changes and tool or work positioning than manual machines. CNC part programs require a skilled programmer and cost additional preproduction time, but specialized jigs and fixtures that are frequently required with manual machines are not usually required with CNC machines, thereby reducing setup time and cost considerably. Additional advantages of CNC machining are reduced lead time; improved cutting efficiency and longer tool life, as a result of better control over the feeds and speeds; improved quality and consistently accurate parts, reduced scrap, and less rework; lower inspection costs after the first part is produced and proven correct; reduced handling of parts because more operations can be performed per setup; and faster response to design changes because most part changes can be made by editing the CNC program. Numerical Control Standards.—Standards for NC hardware and software have been developed by many organizations, and copies of the latest standards may be obtained from the following: Electronic Industries Association (EIA), 2001 Pennsylvania Avenue NW, Washington, DC 20006 (EIA and ANSI/EIA); American Society of Mechanical Engineers (ASME), 345 East 47th Street, New York, NY 10017 (ANSI/ASME); American National Standards Institute (ANSI), 25 West 43rd Street, New York, NY 10036 (ANSI, ANSI/EIA, ANSI/ASME, and ISO); National Standards Association, Inc. (NSA), 1200 Quince Orchard Boulevard, Gaithersburg, MD 20878; NMTBA The Association for Manufacturing Technology, 7901 Westpark Drive, McLean, VA 22102. Some of the standards and their contents are listed briefly in the accompanying table.



NUMERICAL CONTROL Numerical Control Standards

Standard Title ANSI/CAM-I 101-1990

Description Dimensional Measuring Interface Specification

ANSI/ASME B5.50 V-Flange Tool Shanks for Machining Centers with Automatic Tool Changers ANSI/ASME B5.54-1992

Methods for Performance Evaluation of Computer Numerically Controlled Machining Centers

ANSI/ASME B89.1.12M

Methods for Performance Evaluation of Coordinate Measuring Machines

ANSI/EIA 227-A

1-inch Perforated Tape

ANSI/EIA 232-D

Interface Between Data Terminal Equipment and Data Circuit-Terminating Equipment Employing Serial Binary Data Interchange

ANSI/EIA 267-B

Axis and Motion Nomenclature for Numerically Controlled Machines

ANSI/EIA 274-D

Interchangeable Variable Block Data Format for Positioning, Contouring and Contouring/Positioning Numerically Controlled Machines

ANSI/EIA 358-B

Subset of American National Standarde Code for Information Interchange for Numerical Machine Control Perforated Tape

ANSI/EIA 408

Interface Between NC Equipment and Data Terminal Equipment Employing Parallel Binary Data Interchange

ANSI/EIA 423-A

Electrical Characteristics of Unbalanced Voltage Digital Interface Circuits

ANSI/EIA 431

Electrical Interface Between Numerical Control and Machine Tools

ANSI/EIA 441

Operator Interface Function of Numerical Controls

ANSI/EIA 449

General Purpose 37-position and 9-position Interface for Data Terminal Equipment and Data Circuit-Terminating Equipment Employing Serial Binary Data Interchange

ANSI/EIA 484

Electrical and Mechanical Interface Characteristics and Line Control Protocol Using Communication Control Characters for Serial Data Link between a Direct Numerical Control System and Numerical Control Equipment Employing Asynchronous Full Duplex Transmission

ANSI/EIA 491-A -1990

Interface between a Numerical Control Unit and Peripheral Equipment Employing Asynchronous Binary Data Interchange over Circuits having EIA-423-A Electrical Characteristics

ANSI/EIA 494

32-bit Binary CL Interchange (BCL) Input Format for Numerically Controlled Machines

EIA AB3-D

Glossary of Terms for Numerically Controlled Machines

EIA Bulletin 12

Application Notes on Interconnection between Interface Circuits Using RS449 and RS-232-C

ANSI X 3.94

Programming Aid for Numerically Controlled Manufacturing

ANSI X 3.37

Programming Language APT

ANSI X 3.20

1-inch Perforated Tape Take-up Reels for Information Interchange

ANSI X 3.82

One-sided Single Density Unformatted 5.25 inch Flexible Disc Cartridges



1257

Numerical Control Standards (Continued) Standard Title

Description

ISO 841

Numerical Control of Machines—Axis and Motion Nomenclature

ISO 2806

Numerical Control of Machines—Bilingual Vocabulary

ISO 2972

Numerical Control of Machines—Symbols

ISO 3592

Numerical Control of Machines—Numerical Control Processor Output, Logical Structure and Major Words

ISO 4336

Numerical Control of Machines—Specification of Interface Signals between the Numerical Control Unit and the Electrical Equipment of a Numerically Controlled Machine

ISO 4343

Numerical Control of Machines—NC Processor Output— Minor Elements of 2000-type Records (Post Processor Commands)

ISO TR 6132

Numerical Control of Machines—Program Format and Definition of Address Words—Part 1: Data Format for Positioning, Line Motion and Contouring Control Systems

ISO 230-1

Geometric Accuracy of Machines Operating Under No-Load or Finishing Conditions

ISO 230-2

Determination of Accuracy and Repeatability of Positioning of Numerically Controlled Machine Tools

NAS 911

Numerically Controlled Skin/Profile Milling Machines

NAS 912

Numerically Controlled Spar Milling Machines

NAS 913

Numerically Controlled Profiling and Contouring Milling Machines

NAS 914

Numerically Controlled Horizontal Boring, Drilling and Milling Machines

NAS 960

Numerically Controlled Drilling Machines

NAS 963

Computer Numerically Controlled Vertical and Horizontal Jig Boring Machines

NAS 970

Basic Tool Holders for Numerically Controlled Machine Tools

NAS 971

Precision Numerically Controlled Measuring/Inspection Machines

NAS 978

Numerically Controlled Machining Centers

NAS 990

Numerically Controlled Composite Filament Tape Laying Machines

NAS 993

Direct Numerical Control System

NAS 994

Adaptive Control System for Numerically Controlled Milling Machines

NAS 995

Specification for Computerized Numerical Control (CNC)

NMTBA

Common Words as They Relate to Numerical Control Software

NMTBA

Definition and Evaluation of Accuracy and Repeatability of Numerically Controlled Machine Tools

NMTBA

Numerical Control Character Code Cross Reference Chart

NMTBA

Selecting an Appropriate Numerical Control Programming Method

NEMA 1A1

Industrial Cell Controller Classification Concepts and Selection Guide



NUMERICAL CONTROL

Programmable Controller.—Frequently referred to as a PC or PLC (the latter term meaning Programmable Logic Controller), a programmable controller is an electronic unit or small computer. PLCs are used to control machinery, equipment, and complete processes, and to assist CNC systems in the control of complex NC machine tools and flexible manufacturing modules and cells. In effect, PLCs are the technological replacements for electrical relay systems.

Fig. 1. Programmable Controllers' Four Basic Elements

As shown in Fig. 1, a PLC is composed of four basic elements: the equipment for handling input and output (I/O) signals, the central processing unit (CPU), the power supply, and the memory. Generally, the CPU is a microprocessor and the brain of the PLC. Early PLCs used hardwired special-purpose electronic logic circuits, but most PLCs now being offered are based on microprocessors and have far more logic and control capabilities than was possible with hardwired systems. The CPU scans the status of the input devices continuously, correlates these inputs with the control logic in the memory, and produces the appropriate output responses needed to control the machine or equipment. Input to a PLC is either discrete or continuous. Discrete inputs may come from push buttons, micro switches, limit switches, photocells, proximity switches or pressure switches, for instance. Continuous inputs may come from sources such as thermocouples, potentiometers, or voltmeters. Outputs from a PLC normally are directed to actuating hardware such as solenoids, solenoid valves, and motor starters. The function of a PLC is to examine the status of an input or set of inputs and, based on this status, actuate or regulate an output or set of outputs. Digital control logic and sensor input signals are stored in the memory as a series of binary numbers (zeros and ones). Each memory location holds only one “bit” (either 0 or 1) of binary information; however, most of the data in a PLC are used in groups of 8 bits, or bytes. A word is a group of bytes that is operated on at one time by the PLC. The word size in modern PLCs ranges from 8 to 32 bits (1 to 4 bytes), depending on the design of the PLC. In general, the larger the word size that a system is able to operate on (that is, to work on at one time), the faster the system is going to perform. New systems are now beginning to appear that can operate on 64 bits of information at a time. There are two basic categories of memory: volatile and nonvolatile. Volatile memory loses the stored information when the power is turned off, but nonvolatile memory retains its logic even when power is cut off. A backup battery must be used if the information stored in volatile memory is to be retained. There are six commonly used types of memory. Of these six, random-access memory (RAM) is the most common type because it is the easiest to program and edit. RAM is also the only one of the six common types that is vola-



1259

tile memory. The five nonvolatile memory types are: core memory, read-only memory (ROM), programmable read-only memory (PROM), electronically alterable programmable read-only memory (EAPROM), and electronically erasable programmable read-only memory (EEPROM). EEPROMs are becoming more popular due to their relative ease of programming and their nonvolatile characteristic. ROM is often used as a generic term to refer to the general class of read-only memory types and to indicate that this type of memory is not usually reprogrammed. More than 90 per cent of the microprocessor PLCs now in the field use RAM memory. RAM is primarily used to store data, which are collected or generated by a process, and to store programs that are likely to change frequently. For example, a part program for machining a workpiece on a CNC machining center is loaded into and stored in RAM. When a different part is to be made, a different program can be loaded in its place. The nonvolatile memory types are usually used to store programs and data that are not expected to be changed. Programs that directly control a specific piece of equipment and contain specific instructions that allow other programs (such as a part program stored in RAM) to access and operate the hardware are usually stored in nonvolatile memory or ROM. The benefit of ROM is that stored programs and data do not have to be reloaded into the memory after the power has been turned off. PLCs are used primarily with handling systems such as conveyors, automatic retrieval and storage systems, robots, and automatic guided vehicles (AGV), such as are used in flexible manufacturing cells, modules, and systems (see Flexible Manufacturing Systems (FMS), Flexible Manufacturing Cell, and Flexible Manufacturing Module). PLCs are also to be found in applications as diverse as combustion chamber control, chemical process control, and printed-circuit-board manufacturing. Types of Programmable Controllers Type

No. of I/Os

General Applications

Math Capability

Mini

32

Replaces relays, timers, and counters.

Yes

Micro

32–64

Replaces relays, timers, and counters.

Yes

Small

64–128

Replaces relays, timers, and counters. Used for materials handling, and some process control.

Yes

Medium

128–512

Replaces relays, timers, and counters. Used for materials handling, process control, and data collection.

Yes

512+

Replaces relays, timers, and counters. Master control for other PLCs and cells and for generation of reports. High-level network capability

Yes

Large

Types of PLCs may be divided into five groups consisting of micro, mini, small, medium, and large according to the number of I/Os, functional capabilities, and memory capacity. The smaller the number of I/Os and memory capacity, and the fewer the functions, the simpler the PLC. Micro and mini PLCs are usually little more than replacements for relay systems, but larger units may have the functional capabilities of a small computer and be able to handle mathematical functions, generate reports, and maintain high-level communications.



NUMERICAL CONTROL

The preceding guidelines have some gray areas because mini, micro, and small PLCs are now available with large memory sizes and functional capacities normally reserved for medium and large PLCs. The accompanying table compares the various types of PLCs and their applications. Instructions that are input to a PLC are called programs. Four major programming languages are used with PLCs, comprising ladder diagrams, Boolean mnemonics, functional blocks, and English statements. Some PLC systems even support high-level programming languages such as BASIC and PASCAL. Ladder diagrams and Boolean mnemonics are the basic control-level languages. Functional blocks and English statements are considered high-level languages. Ladder diagrams were used with electrical relay systems before these systems were replaced by PLCs and are still the most popular programming method, so they will be discussed further.

Fig. 2. One Rung on a Ladder Diagram

A ladder diagram consists of symbols, or ladder logic elements, that represent relay contacts or switches and other elements in the control system. One of the more basic symbols represents a normally open switch and is described by the symbol ü ą. Another symbol is the normally closed switch, described by the symbol ü\ą. When the normally open switch is activated, it will close, and when the normally closed switch is activated, it will open. Fig. 2 shows one rung (line) on a ladder diagram. Switch 1001 is normally open and switch 1002 is closed. A symbol for a coil (0001) is shown at the right. If switch 1001 is actuated, it will close. If switch 1002 is not activated, it will stay closed. With the two switches closed, current will flow through the line and energize coil 0001. The coil will activate some mechanism such as an electric motor, a robot, or an NC machine tool, for instance. As an example, Fig. 3 shows a flexible manufacturing module (FMM), consisting of a turning center (NC lathe), an infeed conveyor, an outfeed conveyor, a robot that moves workpieces between the infeed conveyor, the turning center, and the outfeed conveyor, and a PLC. The arrowed lines show the signals going to and coming from the PLC. Fig. 4 shows a ladder diagram for a PLC that would control the operations of the FMM by: 1) Activating the infeed conveyor to move the workpiece to a position where the robot can pick it up 2) Activating the robot to pick up the workpiece and load it into the chuck on the NC lathe 3) Activating the robot to remove the finished workpiece and place it on the outfeed conveyor 4) Activating the outfeed conveyor to move the workpiece to the next operation



1261

Fig. 3. Layout of a Flexible Manufacturing Module

Fig. 4. Portion of a Typical Ladder Diagram for Control of a Flexible Manufacturing Module Including a Turning Center, Conveyors, a Robot, and a Programmable Controller

In Rung 1 of Fig. 4, a request signal for a workpiece from the NC lathe closes the normally open switch 1001. Switch 1002 will remain closed if photocell 1 is not activated, i.e., if it does not detect a workpiece. The signal therefore closes the circuit, energizes the coil, and starts the conveyor motor to bring the next workpiece into position for the robot to grasp.



NUMERICAL CONTROL

In Rung 2, switch 1002 (which has been changed in the program of the PLC from a normally closed to a normally open switch) closes when it is activated as photocell 1 detects the workpiece. The signal thus produced, together with the closing of the now normally open switch 1001, energizes the coil, causing the robot to pick up the workpiece from the infeed conveyor. In Rung 3, switch 1004 on the lathe closes when processing of the part is completed and it is ready to be removed by the robot. Photocell 2 checks to see if there is a space on the conveyor to accept the completed part. If no part is seen by photocell 2, switch 1003 will remain closed, and with switch 1004 closed, the coil will be energized, activating the robot to transfer the completed part to the outfeed conveyor. Rung 4 shows activation of the output conveyor when a part is to be transferred. Normally open switch 1004 was closed when processing of the part was completed. Switch 1003 (which also was changed from a normally closed to a normally open switch by the program) closes if photocell 2 detects a workpiece. The circuit is then closed and the coil is energized, starting the conveyor motor to move the workpiece clear to make way for the succeeding workpiece. Closed-Loop System.—Also referred to as a servo or feedback system, a closed-loop system is a control system that issues commands to the drive motors of an NC machine. The system then compares the results of these commands as measured by the movement or location of the machine component, such as the table or spindlehead. The feedback devices normally used for measuring movement or location of the component are called resolvers, encoders, Inductosyns, or optical scales. The resolver, which is a rotary analog mechanism, is the least expensive, and has been the most popular since the first NC machines were developed. Resolvers are normally connected to the lead-screws of NC machines. Linear measurement is derived from monitoring the angle of rotation of the leadscrew and is quite accurate. Encoders also are normally connected to the leadscrew of the NC machine, and measurements are in digital form. Pulses, or a binary code in digital form, are generated by rotation of the encoder, and represent turns or partial turns of the leadscrew. These pulses are well suited to the digital NC system, and encoders have therefore become very popular with such systems. Encoders generally are somewhat more expensive than resolvers. The Inductosyn (a trade name of Farrand Controls, Inc.) also produces analog signals, but is attached to the slide or fixed part of a machine to measure the position of the table, spindlehead, or other component. The Inductosyn provides almost twice the measurement accuracy of the resolver, but is considerably more expensive, depending on the length of travel to be measured. Optical scales generally produce information in digital form and, like the Inductosyn, are attached to the slide or fixed part of the machine. Optical scale measurements are more accurate than either resolvers or encoders and, because of their digital nature, are well suited to the digital computer in a CNC system. Like the Inductosyn, optical scales are more costly than either resolvers or encoders. Open-Loop System.—A control system that issues commands to the drive motors of an NC machine and has no means of assessing the results of these commands is known as an open-loop system. In such a system, no provision is made for feedback of information concerning movement of the slide(s), or rotation of the leadscrew(s). Stepping motors are popular as drives for open-loop systems. Adaptive Control.—Measuring performance of a process and then adjusting the process to obtain optimum performance is called adaptive control. In the machine tool field, adaptive control is a means of adjusting the feed and/or speed of the cutting tool, based on sensor feedback information, to maintain optimum cutting conditions. A typical arrangement is seen in Fig. 5. Adaptive control is used primarily for cutting higher-strength materials



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such as titanium, although the concept is applicable to the cutting of any material. The costs of the sensors and software have restricted wider use of the feature.

Fig. 5.

The sensors used for adaptive control are generally mounted on the machine drive shafts, tools, or even built into the drive motor. Typically, sensors are used to provide information such as the temperature at the tip of the cutting tool and the cutting force exerted by the tool. The information measured by the sensors is used by the control system computer to analyze the cutting process and adjust the feeds and speeds of the machine to maximize the material removal rate or to optimize another process variable such as surface finish. For the computer to effectively evaluate the process in real time (i.e., while cutting is in progress), details such as maximum allowable tool temperature, maximum allowable cutting force, and information about the drive system need to be integrated into the computer program monitoring the cutting process. Adaptive control can be used to detect worn, broken, or dull tooling. Ordinarily, the adaptive control system monitors the cutting process to keep the process variables (cutting speed and feed rate, for example) within the proper range. Because the force required to machine a workpiece is lowest when the tool is new or recently resharpened, a steady increase in cutting force during a machining operation, assuming that the feed remains the same, is an indication that the tool is becoming dull (temperature may increase as well). Upon detecting cutting forces that are greater than a predetermined maximum allowable force, the control system causes the feed rate, the cutting speed, or both to be adjusted to maintain the cutting force within allowable limits. If the cutting force cannot be maintained without causing the speed and/or feed rate to be adjusted outside its allowable limits, the machine will be stopped, indicating that the tool is too dull and must be resharpened or replaced. On some systems, the process monitoring equipment can interface directly with the machine control system, as discussed above. On other systems, the adaptive control is implemented by a separate monitoring system that is independent of the machine control system. These systems include instrumentation to monitor the operations of the machine tool, but do not have the capability to directly change operating parameters, such as feeds and speeds. In addition, this type of control does not require any modification of the existing part programs for control of the machine. Flexible Manufacturing Systems (FMS).—A flexible manufacturing system (FMS) is a computer-controlled machining arrangement that can perform a variety of continuous metal-cutting operations on a range of components without manual intervention. The objective of such a system is to produce components at the lowest possible cost, especially components of which only small quantities are required. Flexibility, or the ability to switch from manufacture of one type of component to another, or from one type of machining to another, without interrupting production, is the prime requirement of such a system. In general, FMS are used for production of numbers of similar parts between 200 and 2000,



NUMERICAL CONTROL

although larger quantities are not uncommon. An FMS involves almost all the departments in a company, including engineering, methods, tooling and part programming, planning and scheduling, purchasing, sales and customer service, accounting, maintenance, and quality control. Initial costs of an FMS are estimated as being borne (percentages in parentheses) by machine tools (46.2), materials handling systems (7.7), tooling and fixtures (5.9), pallets (1.9), computer hardware (3.7), computer software (2.2), wash stations (2.8), automatic storage and retrieval systems (6.8), coolant and chip systems (2.4), spares (2), and others (18.4). FMS are claimed to bring reductions in direct labor (80–90), production planning and control (65), and inspection (70). Materials handling and shop supervision are reduced, and individual productivity is raised. In the materials field, savings are made in tooling (35), scrap and rework (65), and floor space (50). Inventory is reduced and many other costs are avoided. Intangible savings claimed to result from FMS include reduced tooling changeover time, ability to produce complex parts, to incorporate engineering changes more quickly and efficiently than with other approaches, and to make special designs, so that a company can adapt quickly to changing market conditions. Requirements for spare parts with good fit are easily met, and the lower costs combine with higher quality to improve market share. FMS also are claimed to improve morale among workers, leading to higher productivity, with less paper work and more orderly shop operations. Better control of costs and improved cost data help to produce more accurate forecasts of sales and manpower requirements. Response to surges in demand and more economical materials ordering are other advantages claimed with FMS. Completion of an FMS project is said to average 57 months, including 20 months from the time of starting investigations to the placing of the purchase order. A further 13 months are needed for delivery and a similar period for installation. Debugging and building of production takes about another 11 months before production is running smoothly. FMS are expensive, requiring large capital outlays and investments in management time, software, engineering, and shop support. Efficient operation of FMS also require constant workflow because gaps in the production cycle are very costly. Flexible Manufacturing Cell.—A flexible manufacturing cell usually consists of two or three NC machines with some form of pallet-changing equipment or an industrial robot. Prismatic-type parts, such as would be processed on a machining center, are usually handled on pallets. Cylindrical parts, such as would be machined on an NC lathe, usually are handled with an overhead type of robot. The cell may be controlled by a computer, but is often run by programmable controllers. The systems can be operated without attendants, but the mixture of parts usually must be less than with a flexible manufacturing system (FMS). Flexible Manufacturing Module.—A flexible manufacturing module is defined as a single machining center (or turning center) with some type of automatic materials handling equipment such as multiple pallets for machining centers, or robots for manipulating cylindrical parts and chucks for turning centers. The entire module is usually controlled by one or more programmable logic controllers. Axis Nomenclature.—To distinguish among the different motions, or axes, of a machine tool, a system of letter addresses has been developed. A letter is assigned, for example, to the table of the machine, another to the saddle, and still another to the spindle head. These letter addresses, or axis designations, are necessary for the electronic control system to assign movement instructions to the proper machine element. The assignment of these letter addresses has been standardized on a worldwide basis and is contained in three standards, all of which are in agreement. These standards are EIA RS-267-B, issued by the Electronics Industries Association; AIA NAS-938, issued by the Aerospace Industries Association; and ISO/R 841, issued by the International Organization for Standardization.



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The standards are based on a “right-hand rule,” which describes the orientation of the motions as well as whether the motions are positive or negative. If a right hand is laid palm up on the table of a vertical milling machine, as shown in Fig. 1, for example, the thumb will point in the positive X-direction, the forefinger in the positive Y-direction, and the erect middle finger in the positive Z-direction, or up. The direction signs are based on the motion of the cutter relative to the workpiece. The movement of the table shown in Fig. 2 is therefore positive, even though the table is moving to the left, because the motion of the cutter relative to the workpiece is to the right, or in the positive direction. The motions are considered from the part programmer's viewpoint, which assumes that the cutter always moves around the part, regardless of whether the cutter or the part moves. The right-hand rule also holds with a horizontal-spindle machine and a vertical table, or angle plate, as shown in Fig. 3. Here, spindle movement back and away from the angle plate, or workpiece, is a positive Z-motion, and movement toward the angle plate is a negative Z-motion. Rotary motions also are governed by a right-hand rule, but the fingers are joined and the thumb is pointed in the positive direction of the axis. Fig. 4 shows the designations of the rotary motions about the three linear axes, X, Y, and Z. Rotary motion about the X-axis is designated as A; rotary motion about the Y-axis is B; and rotary motion about the Z-axis is C. The fingers point in the positive rotary directions. Movement of the rotary table around the Y-axis shown in Fig. 4 is a B motion and is common with horizontal machining centers. Here, the view is from the spindle face looking toward the rotary table. Referring, again, to linear motions, if the spindle is withdrawn axially from the work, the motion is a positive Z. A move toward the work is a negative Z. When a second linear motion is parallel to another linear motion, as with the horizontal boring mill seen in Fig. 5, the horizontal motion of the spindle, or quill, is designated as Z and a parallel motion of the angle plate is W. A movement parallel to the X-axis is U and a movement parallel to the Y-axis is V. Corresponding motions are summarized as follows: Linear

Rotary

Linear and Parallel

X

A

U

Y

B

V

Z

C

W

Fig. 1.

Fig. 2.



NUMERICAL CONTROL

Fig. 3.

Fig. 4.

Axis designations for a lathe are shown in Fig. 6. Movement of the cross-slide away from the workpiece, or the centerline of the spindle, is noted as a plus X. Movement toward the workpiece is a minus X. The middle finger points in the positive Z-direction; therefore, movement away from the headstock is positive and movement toward the headstock is negative. Generally, there is no Y-movement. The machine shown in Fig. 6 is of conventional design, but most NC lathes look more like that shown in Fig. 7. The same right-hand rule applies to this four-axis lathe, on which each turret moves along its own two independent axes. Movement of the outside-diameter or upper turret, up and away from the workpiece, or spindle centerline, is a positive Xmotion, and movement toward the workpiece is a negative X-motion. The same rules apply to the U-movement of the inside-diameter, or boring, turret. Movement of the lower turret parallel to the Z-motion of the outside-diameter turret is called the W-motion. A popular lathe configuration is to have both turrets on one slide, giving a two-axis system rather than the four-axis system shown. X-and Z-motions may be addressed for either of the two heads. Upward movement of the boring head therefore is a positive X-motion.

Fig. 5.

Fig. 6.



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Fig. 7.

Axis nomenclature for other machine configurations is shown in Fig. 9. The letters with the prime notation (e.g., X′, Y′, Z′, W′, A′, and B′) mean that the motion shown is positive, because the movement of the cutter with respect to the work is in a positive direction. In these instances, the workpiece is moving rather than the cutter. Total Indicator Reading (TIR).—Total indicator reading is used as a measure of the range of machine tool error. TIR is particularly useful for describing the error in a machine tool spindle, referred to as runout. As shown in Fig. 8, there are two types of runout: axial and radial, which can be measured with a dial indicator. Axial runout refers to the wobble of a spindle and is measured at the spindle face. Radial runout is the range of movement of the spindle centerline and is measured on the side of the spindle or quill.

Fig. 8.



NUMERICAL CONTROL

Fig. 9.



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NUMERICAL CONTROL PROGRAMMING Programming.—A numerical control (NC) program is a list of instructions (commands) that completely describes, in sequence, every operation to be carried out by a machine. When a program is run, each instruction is interpreted by the machine controller, which causes an action such as starting or stopping of a spindle or coolant, changing of spindle speed or rotation, or moving a table or slide a specified direction, distance, or speed. The form that program instructions can take, and how programs are stored and/or loaded into the machine, depends on the individual machine/control system. However, program instructions must be in a form (language) that the machine controller can understand. A programming language is a system of symbols, codes, and rules that describes the manner in which program instructions can be written. One of the earliest and most widely recognized numerical control programming languages is based on the Standard ANSI/EIA RS-274-D-1980. The standard defines a recommended data format and codes for sending instructions to machine controllers. Although adherence to the standard is not mandatory, most controller manufacturers support it and most NC machine controllers (especially controllers on older NC machines using tape input) can accept data in a format that conforms, at least in part, with the recommended codes described in the RS-274-D standard. Most newer controllers also accept instructions written in proprietary formats offered (specified) by the controller's manufacturer. One of the primary benefits of a standardized programming format is easy transfer of programs from one machine to another, but even standardized code formats such as RS274-D are implemented differently on different machines. Consequently, a program written for one machine may not operate correctly on another machine without some modification of the program. On the other hand, proprietary formats are attractive because of features that are not available using the standardized code formats. For example, a proprietary format may make available certain codes that allow a programmer, with only a few lines of code, to program complex motions that would be difficult or even impossible to do in the standard language. The disadvantage of proprietary formats is that transferring programs to another machine may require a great deal of program modification or even complete rewriting. Generally, with programs written in a standardized format, the modifications required to get a program written for one machine to work on another machine are not extensive. In programming, before describing the movement of any machine part, it is necessary to establish a coordinate system(s) as a reference frame for identifying the type and direction of the motion. A description of accepted terminology used worldwide to indicate the types of motion and the orientation of machine axes is contained in a separate section (Axis Nomenclature). Part geometry is programmed with reference to the same axes as are used to describe motion. Manual data input (MDI) permits the machine operator to insert machining instructions directly into the NC machine control system via push buttons, pressure pads, knobs, or other arrangements. MDI has been available since the earliest NC machines were designed, but the method was less efficient than tape for machining operations and was used primarily for setting up the NC machine. Computer numerical control (CNC) systems, with their canned cycles and other computing capabilities, have now made the MDI concept more feasible and for some work MDI may be more practical than preparing a program. The choice depends very much on the complexity of the machining work to be done and, to a lesser degree, on the skill of the person who prepares the program. Conversational part programming is a form of MDI that requires the operator or programmer to answer a series of questions displayed on the control panel of the CNC. The operator replies to questions that describe the part, material, tool and machine settings, and machining operations by entering numbers that identify the material, blank size and thickness or diameter, tool definitions, and other required data. Depending on capability, some



NUMERICAL CONTROL

controls can select the required spindle speed and feed rate automatically by using a materials look-up table; other systems request the appropriate feed and speed data. Tool motions needed to machine a part are described by selecting a linear or circular motion programming mode and entering endpoint and intersection coordinates of lines and radius, diameter, tangent points, and directions of arcs and circles (with some controllers, intersection and tangent points are calculated automatically). Machined elements such as holes, slots, and bolt circles are entered by selecting the appropriate tool and describing its action, or with “canned routines” built into the CNC to perform specific machining operations. On some systems, if a feature is once described, it can be copied and/or moved by: translation (copy and/or move), rotation about a point, mirror image (copy and rotate about an axis), and scaling (copy and change size). On many systems, as each command is entered, a graphic image of the part or operation gives a visual check that the program is producing the intended results. When all the necessary data have been entered, the program is constructed and can be run immediately or saved on tape, floppy disk, or other storage media for later use. Conversational programming gives complete control of machine operations to the shop personnel, taking advantage of the experience and practical skills of the machine operator/programmer. Control systems that provide conversational programming usually include many built-in routines (fixed or canned cycles) for commonly used machining operations and may also have routines for specialized operations. Built-in routines speed programming because one command may replace many lines of program code that would take considerable time to write. Some built-in cycles allow complex machining operations to be programmed simply by specifying the final component profile and the starting stock size, handling such details as developing tool paths, depth of cut, number of roughing passes, and cutter speed automatically. On turning machines, built-in cycles for reducing diameters, chamfer and radius turning, and cutting threads automatically are common. Although many CNC machines have a conversational programming mode, the programming methods used and the features available are not standardized. Some control systems cannot be programmed from the control panel while another program is running (i.e., while a part is being machined), but those systems that can be thus programmed are more productive because programming does not require the machine to be idle. Conversational programming is especially beneficial In reducing programming time in shops that do most of their part programming from the control panel of the machine. Manual part programming describes the preparation of a part program by manually writing the part program in word addressed format. In the past, this method implied programming without using a computer to determine tool paths, speeds and feeds, or any of the calculations normally required to describe the geometry of a part. Today, however, computers are frequently used for writing and storing the program on disk, as well as for calculations required to program the part. Manual part programming consists of writing codes, in a format appropriate to the machine controller, that instruct the controller to perform a specific action. The most widely accepted form of coding the instructions for numerically controlled machines uses the codes and formats suggested in the ANSI/EIA RS-274-D-1980, standard. This type of programming is sometimes called G-code programming, referring to a commonly used word address used in the RS-274-D standard. Basic details of programming in this format, using the various codes available, are discussed in the next section (G-Code Programming). Computer-assisted part programming (CAPP) uses a computer to help in the preparation of the detailed instructions for operating an NC machine. In the past, defining a curve or complicated surface profile required a series of complex calculationsto describe the features in intimate detail. However, with the introduction of the microprocessor as an integral part of the CNC machine, the process of defining many complex shapes has been reduced to the simple task of calling up a canned cycle to calculate the path of the cutter. Most new CNC systems have some graphic programming capability, and many use



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graphic images of the part “drawn” on a computer screen. The part programmer moves a cutter about the part to generate the part program or the detailed block format instructions required by the control system. Machining instructions, such as the speed and feed rate, are entered via the keyboard. Using the computer as an assistant is faster and far more accurate than the manual part programming method. Computer-assisted part programming methods generally can be characterized as either language-based or graphics-based, the distinction between the two methods being primarily in the manner by which the tool paths are developed. Some modern-language-based programming systems, such as Compact II, use interactive alphanumeric input so that programming errors are detected as soon as they are entered. Many of these programming systems are completely integrated with computer graphics and display an image of the part or operation as soon as an instruction is entered. The language-based programming systems are usually based on, or are a variation of, the APT programming language, which is discussed separately within this section (APT Programming). The choice between computer-assisted part programming and manual part programming depends on the complexity of the part (particularly its geometry) and how many parts need to be programmed. The more complicated the part, the more benefit to be gained by CAPP, and if many parts are to be programmed, even if they are simple ones, the benefits of a computer-aided system are substantial. If the parts are not difficult to program but involve much repetition, computer-assisted part programming may also be preferred. If parts are to be programmed for several different control systems, a high-level part programming language such as APT will make writing the part programs easier. Because almost all machines have some deviations from standard practices, and few control systems use exactly the same programming format, a higher-level language allows the programmer to concentrate primarily on part geometry and machining considerations. The postprocessors (see Postprocessors below) for the individual control systems accommodate most of the variations in the programming required. The programmer only needs to write the program; the postprocessor deals with the machine specifics. Graphical programming involves building a two- or three-dimensional model of a part on a computer screen by graphically defining the geometric shapes and surfaces of the part using the facilities of a CAD program. In many cases, depending on features of the CAD software package, the same computer drawing used in the design and drafting stage of a project can also be used to generate the program to produce the part. The graphical entities, such as holes, slots, and surfaces, are linked with additional information required for the specific machining operations needed. Most of the cutter movements (path of the cutter), such as those needed for the generation of pockets and lathe roughing cuts, are handled automatically by the computer. The program may then sort the various machining operations into an efficient sequence so that all operations that can be performed with a particular tool are done together, if possible. The output of graphical part programming is generally an alphanumeric part programming language output file, in a format such as an APT or Compact II file. The part programming language file can be manually checked, and modified, as necessary before being run, and to help detect errors, many graphics programming systems also include some form of part verification software that simulates machining the part on the computer screen. Nongraphic data, such as feed rates, spindle speeds and coolant on/off, must be typed in by the part programmer or entered from acomputer data base at the appropriate points in the program, although some programs prompt for this information when needed. When the part program language file is run or compiled, the result is a center line data (CL data) file describing the part. With most computer-aided part programming output files, the CL data file needs to be processed through a postprocessor (see Postprocessors below) to tailor the final code produced to the actual machine being used. Postprocessor output is in a form that can be sent directly to the control system, or can be saved on tape or magnetic media and transferred to the machine tool when necessary. The



NUMERICAL CONTROL

graphic image of the part and the alphanumeric output files are saved in separate files so that either can be edited in the future if changes in the part become necessary. Revised files must be run and processed again for the part modifications to be included in the part program. Software for producing part programs is discussed further in the CAD/CAM section. Postprocessors.—A postprocessor is computer software that contains a set of computer instructions designed to tailor the cutter center line location data (CL data), developed by a computerized part programming language, to meet the requirements of a particular machine tool/system combination. Generally, when a machine tool is programmed in a graphical programming environment or any high-level language such as APT, a file is created that describes all movements required of a cutting tool to make the part. The file thus created is run, or compiled, and the result is a list of coordinates (CL data) that describes the successive positions of the cutter relative to the origin of the machine's coordinate system. The output of the program must be customized to fit the input requirements of the machine controller that will receive the instructions. Cutter location data must be converted into a format recognized by the control system, such as G codes and M codes, or into another language or proprietary format recognized by the controller. Generally, some instructions are also added or changed by the programmer at this point. The lack of standardization among machine tool control systems means that almost all computerized part programming languages require a postprocessor to translate the computer-generated language instructions into a form that the machine controller recognizes. Postprocessors are software and are generally prepared for a fee by the machine tool builder, the control system builder, a third party vendor, or by the user. G-Code Programming Programs written to operate numerical control (NC) machines with control systems that comply with the ANSI/EIA RS-274-D-1980, Standard consist of a series of data blocks, each of which is treated as a unit by the controller and contains enough information for a complete command to be carried out by the machine. Each block is made up of one or more words that indicate to the control system how its corresponding action is to be performed. A word is an ordered set of characters, consisting of a letter plus some numerical digits, that triggers a specific action of a machine tool. The first letter of the word is called the letter address of the word, and is used to identify the word to the control system. For example, X is the letter address of a dimension word that requires a move in the direction of the X-axis, Y is the letter address of another dimension word; and F is the letter address of the feed rate. The assigned letter addresses and their meanings, as listed in ANSI/EIA RS-274-D, are shown in Table 1. Format Classification.—The format classification sheet completely describes the format requirements of a control system and gives other important information required to program a particular control including: the type of machine, the format classification shorthand and format detail, a listing of specific letter address codes recognized by the system (for example, G-codes: G01, G02, G17, etc.) and the range of values the available codes may take (S range: 10 to 1800 rpm, for example), an explanation of any codes not specifically assigned by the Standard, and any other unique features of the system. The format classification shorthand is a nine- or ten-digit code that gives the type of system, the number of motion and other words available, the type and format of dimensional data required by the system, the number of motion control channels, and the number of numerically controlled axes of the system. The format detail verysuccinctly summarizes details of the machine and control system. This NC shorthand gives the letter address words and word lengths that can be used to make up a block. The format detail defines the basic features of the control system and the type of machine tool to which it refers. For example, the format detail



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Table 1. Letter Addresses Used in Numerical Control Letter Address

Description

Refers to

A

Angular dimension about the X-axis. Measured in decimal parts of a degree

Axis nomenclature

B

Angular dimension about the Y-axis. Measured in decimal parts of a degree

Axis nomenclature

C

Angular dimension about the Z-axis. Measured in decimal parts of a degree

Axis nomenclature

D

Angular dimension about a special axis, or third feed function, or tool function for selection of tool compensation

Axis nomenclature

E

Angular dimension about a special axis or second feed function

Axis nomenclature

F

Feed word (code)

Feed words

G

Preparatory word (code)

Preparatory words

H

Unassigned

I

Interpolation parameter or thread lead parallel to the X-axis

Circular interpolation and threading

J

Interpolation parameter or thread lead parallel to the Yaxis


K

Interpolation parameter or thread lead parallel to the Zaxis


L

Unassigned

M

Miscellaneous or auxilliary function

N

Sequence number

Sequence number

O

Sequence number for secondary head only

Sequence number

P

Third rapid-traverse dimension or tertiary-motion dimension parallel to X

Axis nomenclature

Q

Second rapid-traverse dimension or tertiary-motion dimension parallel to Y

Axis nomenclature

R

First rapid-traverse dimension or tertiary-motion dimension parallel to Z or radius for constant surface-speed calculation

Axis nomenclature Spindle speed

Miscellaneous functions

S

Spindle-speed function

T

Tool function

Tool function

U

Secondary-motion dimension parallel to X

Axis nomenclature

V

Secondary-motion dimension parallel to Y

Axis nomenclature

W

Secondary-motion dimension parallel to Z

Axis nomenclature Axis nomenclature

X

Primary X-motion dimension

Y

Primary Y-motion dimension

Axis nomenclature

Z

Primary Z-motion dimension

Axis nomenclature

N4G2X + 24Y + 24Z + 24B24I24J24F31T4M2 specifies that the NC machine is a machining center (has X-, Y-, and Z-axes) and a tool changer with a four-digit tool selection code (T4); the three linear axes are programmed with two digits before the decimal point and four after the decimal point (X + 24Y + 24Z + 24) and can be positive or negative; probably has a horizontal spindle and rotary table (B24



NUMERICAL CONTROL

= rotary motion about the Y-axis); has circular interpolation (I24J24); has a feed rate range in which there are three digits before and one after the decimal point (F31); and can handle a four-digit sequence number (N4), two-digit G-words (G2), and two-digit miscellaneous words (M2). The sequence of letter addresses in the format detail is also the sequence in which words with those addresses should appear when used in a block. The information given in the format shorthand and format detail is especially useful when programs written for one machine are to be used on different machines. Programs that use the variable block data format described in RS-274-D can be used interchangeably on systems that have the same format classification, but for complete program compatibility between machines, other features of the machine and control system must also be compatible, such as the relationships of the axes and the availability of features and control functions. Control systems differ in the way that the numbers may be written. Most newer CNC machines accept numbers written in a decimal-point format, however, some systems require numbers to be in a fixed-length format that does not use an explicit decimal point. In the latter case, the control system evaluates a number based on the number of digits it has, including zeros. Zero suppression in a control system is an arrangement that allows zeros before the first significant figure to be dropped (leading zero suppression) or allows zeros after the last significant figure to be dropped (trailing zero suppression). An X-axis movement of 05.3400, for example, could be expressed as 053400 if represented in the full field format, 53400 (leading zero suppression), or 0534 (trailing zero suppression). With decimal-point programming, the above number is expressed simply as 5.34. To ensure program compatibility between machines, all leading and trailing zeros should be included in numbers unless decimal-point programming is used. Sequence Number (N-Word).—A block normally starts with a sequence number that identifies the block within the part program. Most control systems use a four-digit sequence number allowing step numbers up to N9999. The numbers are usually advanced by fives or tens in order to leave spaces for additional blocks to be inserted later if required. For example, the first block in a program would be N0000, the next block N0005; the next N0010; and so on. The slash character, /, placed in a block, before the sequence number, is called an optional stop and causes the block to be skipped over when actuated by the operator. The block that is being worked on by the machine is often displayed on a digital readout so that the operator may know the precise operation being performed. Preparatory Word (G-Word).—A preparatory word (also referred to as a preparatory function or G-code) consists of the letter address G and usually two digits. The preparatory word is placed at the beginning of a block, normally following the sequence number. Most newer CNC machines allow more than one G-code to be used in a single block, although many of the older systems do not. To ensure compatability with older machines and with the RS-274-D Standard, only one G-code per block should be used. The G-word indicates to the control system how to interpret the remainder of theblock. For example, G01 refers to linear interpolation and indicates that the words following in the block will move the cutter in a straight line. The G02 code indicates that the words following in the block will move the cutter in a clockwise circular path. A G-word can completely change the normal meaning of other words in a block. For example, X is normally a dimension word that describes a distance or position in the X-direction. However, if a block contains the G04 word, which is the code for a dwell, the X word represents the time, in seconds, that the machine is to dwell. The majority of G-codes are designated as modal, which means that once used, the code remains in effect for succeeding blocks unless it is specifically changed or canceled. Therefore, it is not necessary to include modal G-codes in succeeding blocks except to change or cancel them. Unless a G-code is modal, it is only effective within its designated block for the operation it defines. Table 2, G-Code Addresses, lists standardized G-code addresses and modality.



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Table 2. G-Code Addresses Code G00 G01

Description ab * Rapid traverse, point to point (M,L) abc Linear interpolation (M,L)

G02

abc

G03

abc

G04

ab

G05

ab

G06

abc

G07

c

G08

ab

G09

ab

G10–G12

ab

G13–G16 G13–G16

Circular interpolation — clockwise movement (M,L)

Code G34

ab*

G35

abc

G36-G39 G36

ab c

Circular interpolation—counterclockwise movement (M,L) Dwell—a programmed time delay (M,L) Unassigned

G37, G37.1, G37.2, G37.3 G37.4

Parabolic interpolation (M,L)

G38

Used for programming with cylindrical diameter values (L) Programmed acceleration (M,L). d Also for lathe programming with cylindrical diameter values Programmed deceleration (M,L). d Used to stop the axis movement at a precise location (M,L)

G38.1

Description Thread cutting, increasing lead (L) Thread cutting, decreasing lead (L) Permanently unassigned Used for automatic acceleration and deceleration when the blocks are short (M,L) Used for tool gaging (M,L)

Used for probing to measure the diameter and center of a hole (M) Used with a probe to measure the parallelness of a part with respect to an axis (M)

G39, G39.1

Generates a nonprogrammed block to improve cycle time and corner cutting quality when used with cutter compensation (M) Tool tip radius compensation used with linear generated block (L) Tool tip radius compensation used used with circular generated block (L)

G39 G39.1

ac

Unassigned. dSometimes used for machine lock and unlock devices Axis selection (M,L)

G40

abc

b

Unassigned

G41

abc

Cancel cutter compensation/ offset (M) Cutter compensation, left (M)

abc

Cutter compensation, right (M)

G14, G14.1

Used for computing lines and circle intersections (M,L) Used for scaling (M,L)

G42

c

G43

abc

Cutter offset, inside corner (M,L)

G15–G16

c

G44

abc

G15, G16.1

c

Cutter offset, outside corner (M,L) Unassigned

G13

G16.2 G17–G19

c abc

G20 G22–G32

ab

G22–G23

c

G22.1, G233.1

c

G24

c

G27–G29

G30 G31, G31.1, G31.2, G31.3, G31.4 G33

abc

Polar coordinate programming (M) Cylindrical interpolation—C axis (L) End face milling—C axis (L)

G45–G49 G50–G59

ab a

Reserved for adaptive control (M,L) Unassigned

X-Y, X-Z, Y-Z plane selection, respectively (M,L) Unassigned

G50 G50.1

c

Cancel mirror image (M,L)

Unassigned

G51.1

c

Program mirror image (M,L)

Defines safety zones in which the machine axis may not enter (M,L) Defines safety zones in which the cutting tool may not exit (M,L) Single-pass rough-facing cycle (L) Used for automatically moving to and returning from home position (M,L)

G52

b

Unassigned

Return to an alternate home position (M,L) External skip function, moves an axis on a linear path until an external signal aborts the move (M,L) Thread cutting, constant lead (L)

bb

G52 G53 G53 G54–G59 G54–G59.3 G60–G62

bc c bc c abc

Used to offset the axes with respect to the coordinate zero point (see G92) (M,L) Datum shift cancel Call for motion in the machine coordinate system (M,L) Datum shifts (M,L) Allows for presetting of work coordinate systems (M,L) Unassigned



NUMERICAL CONTROL Table 2. (Continued) G-Code Addresses

Code G61

G62 G63 G63 G64–G69 G64

c

c

a bc abc c

G65

c

G66

c

G66.1

c

G67

c

G68

c

G69

c

G70 G71 G72

abc

G72 G72

b

G73 G73

abc ac

c

b c

G74

ac

G74

bc

G74

c

G74 G75

ac

G75 G75

b

G76–G79

ab

Description Modal equivalent of G09 except that rapid moves are not taken to a complete stop before the next motion block is executed (M,L) Automatic corner override, reduces the feed rate on an inside corner cut (M,L) Unassigned

Code

Description Cancel fixed cycles

G80

abc

G81

abc

Drill cycle, no dwell and rapid out (M,L)

G82

abc

Drill cycle, dwell and rapid out (M,L)

G83

abc

Tapping mode (M,L) Unassigned Cutting mode, usually set by the system installer (M,L) Calls for a parametric macro (M,L) Calls for a parametric macro. Applies to motion blocks only (M,L)

G84 G84.1 G85

abc

G86

abc

G87

abc

Deep hole peck drilling cycle (M,L) Right-hand tapping cycle (M,L) Left-hand tapping cycle (M,L) Boring cycle, no dwell, feed out (M,L) Boring cycle, spindle stop, rapid out (M,L) Boring cycle, manual retraction (M,L)

G88

abc

Same as G66 but applies to all blocks (M,L) Stop the modal parametric macro (see G65, G66, G66.1) (M,L) Rotates the coordinate system (i.e., the axes) (M)

G88.1

Cancel axes rotation (M)

G88.4

c abc

G88.2 G88.3

Boring cycle, spindle stop, manual retraction (M,L) Pocket milling (rectangular and circular), roughing cycle (M) Pocket milling (rectangular and circular), finish cycle (M) Post milling, roughs out material around a specified area (M) Post milling, finish cuts material around a post (M) Hemisphere milling, roughing cycle (M) Hemisphere milling, finishing cycle (M)

Inch programming (M,L) Metric programming (M,L) Circular interpolation CW (three-dimensional) (M) Unassigned Used to perform the finish cut on a turned part along the Z-axis after the roughing cuts initiated under G73, G74, or G75 codes (L) Unassigned Deep hole peck drilling cycle (M); OD and ID roughing cycle, running parallel to the Z-axis (L) Cancel multiquadrant circular interpolation (M,L) Move to home position (M,L)

G88.5

G90

abc

Absolute dimension input (M,L)

G91

abc

Left-hand tapping cycle (M)

G92

abc

Rough facing cycle (L)

G93

abc

Multiquadrant circular interpolation (M,L) Unassigned Roughing routine for castings or forgings (L) Unassigned

G94

c

G95

abc

G96

abc

G97

abc

Incremental dimension input (M,L) Preload registers, used to shift the coordinate axes relative to the current tool position (M,L) Inverse time feed rate (velocity/distance) (M,L) Feed rate in inches or millimeters per minute (ipm or mpm) (M,L) Feed rate given directly in inches or millimeters per revolution (ipr or mpr) (M,L) Maintains a constant surface speed, feet (meters) per minute (L) Spindle speed programmed in rpm (M,L) Unassigned

G88.6

G89

abc

G89.1

G89.2

G98–99

Boring cycle, dwell and feed out (M,L) Irregular pocket milling, roughing cycle (M)

Irregular pocket milling, finishing cycle (M)

ab



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a Adheres to ANSI/EIA RS-274-D; b Adheres to ISO 6983/1,2,3 Standards; where both symbols appear together, the ANSI/EIA and ISO standard codes are comparable; c This code is modal. All codes that are not identified as modal are nonmodal, when used according to the corresponding definition. d Indicates a use of the code that does not conform with the Standard. Symbols following a description: (M) indicates that the code applies to a mill or machining center; (L) indicates that the code applies to turning machines; (M,L) indicates that the code applies to both milling and turning machines. Codes that appear more than once in the table are codes that are in common use, but are not defined by the Standard or are used in a manner that is different than that designated by the Standard (e.g., see G61).

Most systems that support the RS-274-D Standard codes do not use all the codes available in the Standard. Unassigned G-words in the Standard are often used by builders of machine tool control systems for a variety of special purposes, sometimes leading to confusion as to the meanings of unassigned codes. Even more confusing, some builders of systems and machine tools use the less popular standardized codes for other than the meaning listed in the Standard. For these reasons, machine code written specifically for one machine/controller will not necessarily work correctly on another machine controller without modification. Dimension words contain numerical data that indicate either a distance or a position. The dimension units are selected by using G70 (inch programming) or G71 (metric programming) code. G71 is canceled by a G70 command, by miscellaneous functions M02 (end of program), or by M30 (end of data). The dimension words immediately follow the G-word in a block and on multiaxis machines should be placed in the following order: X, Y, Z, U, V, W, P, Q, R, A, B, C, D, and E. Absolute programming (G90) is a method of defining the coordinate locations of points to which the cutter (or workpiece) is to move based on the fixed machine zero point. In Fig. 1, the X − Y coordinates of P1 are X = 1.0, Y = 0.5 and the coordinates of P2 are X = 2.0, Y = 1.1. To indicate the movement of the cutter from one point to another when using the absolute coordinate system, only the coordinates of the destination point P2 are needed. Incremental programming (G91) is a method of identifying the coordinates of a particular location in terms of the distance of the new location from the current location. In the example shown in Fig. 2, a move from P1 to P2 is written as X + 1.0, Y + 0.6. If there is no movement along the Z-axis, Z is zero and normally is not noted. An X − Y incremental move from P2 to P3 in Fig. 2 is written as X + 1.0, Y − 0.7.

Fig. 1.

Fig. 2.

Most CNC systems offer both absolute and incremental part programming. The choice is handled by G-code G90 for absolute programming and G91 for incremental programming. G90 and G91 are both modal, so they remain in effect until canceled.



NUMERICAL CONTROL

The G92 word is used to preload the registers in the control system with desired values. A common example is the loading of the axis-position registers in the control system for a lathe. Fig. 3 shows a typical home position of the tool tip with respect to the zero point on the machine. The tool tip here is registered as being 15.0000 inches in the Z-direction and 4.5000 inches in the X-direction from machine zero. No movement of the tool is required. Although it will vary with different control system manufacturers, the block to accomplish the registration shown in Fig. 3 will be approximately: N0050 G92 X4.5 Z15.0 Miscellaneous Functions (M-Words).—Miscellaneous functions, or M-codes, also referred to as auxiliary functions, constitute on-off type commands. M functions are used to control actions such as starting and stopping of motors, turning coolant on and off, changing tools, and clamping and unclamping parts. M functions are made up of the letter M followed by a two-digit code. Table 3 lists the standardized M-codes, however, the functions available will vary from one control system to another. Most systems provide fewer M functions than the complete list and may use some of the unassigned codes to provide additional functions that are not covered by the Standard. If an M-code is used in a block, it follows the T-word and is normally the last word in the block. Table 3. Miscellaneous Function Words from ANSI/EIA RS-274-D Code

Description

M00

Automatically stops the machine. The operator must push a button to continue with the remainder of the program. An optional stop acted upon only when the operator has previously signaled for this command by pushing a button. The machine will automatically stop when the control system senses the M01 code. This end-of-program code stops the machine when all commands in the block are completed. May include rewinding of tape. Start spindle rotation in a clockwise direction—looking out from the spindle face. Start spindle rotation in a counterclockwise direction—looking out from the spindle face. Stop the spindle in a normal and efficient manner. Command to change a tool (or tools) manually or automatically. Does not cover tool selection, as is possible with the T-words. M07 (coolant 2) and M08 (coolant 1) are codes to turn on coolant. M07 may control flood coolant and M08 mist coolant. Shuts off the coolant. M10 applies to automatic clamping of the machine slides, workpiece, fixture spindle, etc. M11 is an unclamping code. An inhibiting code used to synchronize multiple sets of axes, such as a four-axis lathe having two independently operated heads (turrets). Starts CW spindle motion and coolant on in the same command. Starts CCW spindle motion and coolant on in the same command. Rapid traverse of feed motion in either the +(M15) or −(M16) direction. Unassigned. Oriented spindle stop. Causes the spindle to stop at a predetermined angular position. Permanently unassigned. An end-of-tape code similar to M02, but M30 will also rewind the tape; also may switch automatically to a second tape reader. A command known as interlock bypass for temporarily circumventing a normally provided interlock.

M01

M02 M03 M04 M05 M06 M07 to M08 M09 M10 to M11 M12 M13 M14 M15 to M16 M17 to M18 M19 M20 to M29 M30 M31



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Table 3. (Continued) Miscellaneous Function Words from ANSI/EIA RS-274-D Code M32 to M35 M36 to M39 M40 to M46 M47 M48 to M49 M50 to M57 M58 to M59 M60 to M89 M90 to M99

Description Unassigned. Permanently unassigned. Used to signal gear changes if required at the machine; otherwise, unassigned. Continues program execution from the start of the program unless inhibited by an interlock signal. M49 deactivates a manual spindle or feed override and returns the parameter to the programmed value; M48 cancels M49. Unassigned. Holds the rpm constant at the value in use when M59 is initiated; M58 cancels M59. Unassigned. Reserved for use by the machine user.

Feed Function (F-Word).—F-word stands for feed-rate word or feed rate. The meaning of the feed word depends on the system of units in use and the feed mode. For example, F15 could indicate a feed rate of 0.15 inch (or millimeter) per revolution or 15 inches (or millimeters) per minute, depending on whether G70 or G71 is used to indicate inch or metric programming and whether G94 or G95 is used to specify feed rate expressed as inches (or mm) per minute or revolution. The G94 word is used to indicate inches/minute (ipm) or millimeters/minute (mmpm) and G95 is used for inches/revolution (ipr) or millimeters/revolution (mmpr). The default system of units is selected by G70 (inch programming) or G71 (metric programming) prior to using the feed function. The feed function is modal, so it stays in effect until it is changed by setting a new feed rate. In a block, the feed function is placed immediately following the dimension word of the axis to which it applies or immediately following the last dimension word to which it applies if it is used for more than one axis.

Fig. 3.

In turning operations, when G95 is used to set a constant feed rate per revolution, the spindle speed is varied to compensate for the changing diameter of the work — the spindle speed increases as the working diameter decreases. To prevent the spindle speed from increasing beyond a maximum value, the S-word, see Spindle Function (S-Word), is used to specify the maximum allowable spindle speed before issuing the G95 command. If the spindle speed is changed after the G95 is used, the feed rate is also changed accordingly. If G94 is used to set a constant feed per unit of time (inches or millimeters per minute), changes in the spindle speed do not affect the feed rate. Feed rates expressed in inches or millimeters per revolution can be converted to feed rates in inches or millimeters per minute by multiplying the feed rate by the spindle speed in revolutions per minute: feed/minute = feed/revolution × spindle speed in rpm. Feed rates for milling cutters are sometimes given in inches or millimeters per tooth. To convert feed



NUMERICAL CONTROL

per tooth to feed per revolution, multiply the feed rate per tooth by the number of cutter teeth: feed/revolution = feed/tooth × number of teeth. For certain types of cuts, some systems require an inverse-time feed command that is the reciprocal of the time in minutes required to complete the block of instructions. The feed command is indicated by a G93 code followed by an F-word value found by dividing the feed rate, in inches (millimeters) or degrees per minute, by the distance moved in the block: feed command = feed rate/distance = (distance/time)/distance = 1/time. Feed-rate override refers to a control, usually a rotary dial on the control system panel, that allows the programmer or operator to override the programmed feed rate. Feed-rate override does not change the program; permanent changes can only be made by modifying the program. The range of override typically extends from 0 to 150 per cent of the programmed feed rate on CNC machines; older hardwired systems are more restrictive and most cannot be set to exceed 100 per cent of the preset rate. Spindle Function (S-Word).—An S-word specifies the speed of rotation of the spindle. The spindle function is programmed by the address S followed by the number of digits specified in the format detail (usually a four-digit number). Two G-codes control the selection of spindle speed input: G96 selects a constant cutting speed in surface feet per minute (sfm) or meters per minute (mpm) and G97 selects a constant spindle speed in revolutions per minute (rpm). In turning, a constant spindle speed (G97) is applied for threading cycles and for machining parts in which the diameter remains constant. Feed rate can be programmed with either G94 (inches or millimeters per minute) or G95 (inches or millimeters per revolution) because each will result in a constant cutting speed to feed relationship. G96 is used to select a constant cutting speed (i.e., a constant surface speed) for facing and other cutting operations in which the diameter of the workpiece changes. The spindle speed is set to an initial value specified by the S-word and then automatically adjusted as the diameter changes so that a constant surface speed is maintained. The control system adjusts spindle speed automatically, as the working diameter of the cutting tool changes, decreasing spindle speed as the working diameter increasesor increasing spindle speed as the working diameter decreases. When G96 is used for a constant cutting speed, G95 in a succeeding block maintains a constant feed rate per revolution. Speeds given in surface feet or meters per minute can be converted to speeds in revolutions per minute (rpm) by the formulas: sfm × 12rpm = -------------------π×d

× 1000rpm = mpm ----------------------------π×d

where d is the diameter, in inches or millimeters, of the part on a lathe or of the cutter on a milling machine; and π is equal to 3.14159. Tool Function (T-Word).—The T-word calls out the tool that is to be selected on a machining center or lathe having an automatic tool changer or indexing turret. On machines without a tool changer, this word causes the machine to stop and request a tool change. This word also specifies the proper turret face on a lathe. The word usually is accompanied by several numbers, as in T0101, where the first pair of numbers refers to the tool number (and carrier or turret if more than one) and the second pair of numbers refers to the tool offset number. Therefore, T0101 refers to tool 1, offset 1. Information about the tools and the tool setups is input to the CNC system in the form of a tool data table. Details of specific tools are transferred from the table to the part program via the T-word. The tool nose radius of a lathe tool, for example, is recorded in the tool data table so that the necessary tool path calculations can be made by the CNC system. The miscellaneous code M06 can also be used to signal a tool change, either manually or automatically.



1281

Compensation for variations in the tool nose radius, particularly on turning machines, allows the programmer to program the part geometry from the drawing and have the tool follow the correct path in spite of variations in the tool nose shape. Typical of the data required, as shown in Fig. 4, are the nose radius of the cutter, the X and Z distances from the gage point to some fixed reference point on the turret, and the orientation of the cutter (tool tip orientation code), as shown in Fig. 5. Details of nose radius compensation for numerical control is given in a separate section (Indexable Insert Holders for NC).

Fig. 4.

Fig. 5.

Tool offset, also called cutter offset, is the amount of cutter adjustment in a direction parallel to the axis of a tool. Tool offset allows the programmer to accommodate the varying dimensions of different tooling by assuming (for the sake of the programming) that all the tools are identical. The actual size of the tool is totally ignored by the programmer who programs the movement of the tools to exactly follow the profile of theworkpiece shape. Once tool geometry is loaded into the tool data table and the cutter compensation controls of the machine activated, the machine automatically compensates for the size of the tools in the programmed movements of the slide. In gage length programming, the tool length and tool radius or diameter are included in the program calculations. Compensation is then used only to account for minor variations in the setup dimensions and tool size.

Fig. 6.

Customarily, the tool offset is used in the beginning of a program to initialize each individual tool. Tool offset also allows the machinist to correct for conditions, such as tool wear, that would cause the location of the cutting edge to be different from the programmed location. For example, owing to wear, the tool tip in Fig. 6 is positioned a distance of 0.0065 inch from the location required for the work to be done. To compensate for this wear, the operator (or part programmer), by means of the CNC control panel, adjusts the tool tip with reference to the X- and Z-axes, moving the tool closer to the work by



NUMERICAL CONTROL

0.0065 inch throughout its traverse. The tool offset number causes the position of the cutter to be displaced by the value assigned to that offset number.

Fig. 7.

Fig. 8.

Changes to the programmed positions of cutting tool tip(s) can be made by tool length offset programs included in the control system. A dial or other means is generally provided on milling, drilling, and boring machines, and machining centers, allowing the operator or part programmer to override the programmed axial, or Z-axis, position. This feature is particularly helpful when setting the lengths of tools in their holders or setting a tool in a turret, as shown in Fig. 7, because an exact setting is not necessary. The tool can be set to an approximate length and the discrepancy eliminated by the control system. The amount of offset may be determined by noting the amount by which the cutter is moved manually to a fixed point on the fixture or on the part, from the programmed Z-axis location. For example, in Fig. 7, the programmed Z-axis motion results in the cutter being moved to position A, whereas the required location for the tool is at B. Rather than resetting the tool or changing the part program, the tool length offset amount of 0.0500 inch is keyed into the control system. The 0.0500-inch amount is measured by moving the cutter tip manually to position B and reading the distance moved on the readout panel. Thereafter, every time that cutter is brought into the machining position, the programmed Z-axis location will be overridden by 0.0500 inch. Manual adjustment of the cutter center path to correct for any variance between nominal and actual cutter radius is called cutter compensation. The net effect is to move the path of the center of the cutter closer to, or away from, the edge of the workpiece, as shown in Fig. 8. The compensation may also be handled via a tool data table. When cutter compensation is used, it is necessary to include in the program a G41 code if the cutter is to be to the left of the part and a G42 code if to the right of the part, as shown in Fig. 8. A G40 code cancels cutter compensation. Cutter compensation with earlier hardwire systems was expensive, very limited, and usually held to ±0.0999 inch. The range for cutter compensation with CNC control systems can go as high as ±999.9999 inches, although adjustments of this magnitude are unlikely to be required.

Fig. 9.

Linear Interpolation.—The ability of the control system to guide the workpiece along a straight-line path at an angle to the slide movements is called linear interpolation. Move-



1283

ments of the slides are controlled through simultaneous monitoring of pulses by the control system. For example, if monitoring of the pulses for the X-axis of a milling machine is at the same rate as for the Y-axis, the cutting tool will move at a 45-degree angle relative to the X-axis. However, if the pulses are monitored at twice the rate for the X-axis as for the Yaxis, the angle that the line of travel will make with the X-axis will be 26.57 degrees (tangent of 26.57 degrees = 1⁄2), as shown in Fig. 9. The data required are the distances traveled in the X- and Y-directions, and from these data, the control system will generate the straight line automatically. This monitoring concept also holds for linear motions along three axes. The required G-code for linear interpolation blocks is G01. The code is modal, which means that it will hold for succeeding blocks until it is changed. Circular Interpolation.—A simplified means of programming circular arcs in one plane, using one block of data, is called circular interpolation. This procedure eliminates the need to break the arc into straight-line segments. Circular interpolation is usually handled in one plane, or two dimensions, although three-dimensional circular interpolation is described in the Standards. The plane to be used is selected by a G or preparatory code. In Fig. 10, G17 is used if the circle is to be formed in the X−Y plane,

Fig. 10.

Fig. 11.

G18 if in the X−Z plane, and G19 if in the Y−Z plane. Often the control system is preset for the circular interpolation feature to operate in only one plane (e.g., the X−Y plane for milling machines or machining centers or the X−Z plane for lathes), and for these machines, the G-codes are not necessary. A circular arc may be described in several ways. Originally, the RS-274 Standard specified that, with incremental programming, the block should contain: 1) A G-code describing the direction of the arc, G02 for clockwise (CW), and G03 for counterclockwise (CCW). 2) Directions for the component movements around the arc parallel to the axes. In the example shown in Fig. 11, the directions are X = +1.1 inches and Y = +1.0 inch. The signs are determined by the direction in which the arc is being generated. Here, both X and Y are positive. 3) The I dimension, which is parallel to the X-axis with a value of 1.3 inches, and the J dimension, which is parallel to the Y-axis with a value of 0.3 inch. These values, which locate point A with reference to the center of the arc, are called offset dimensions. The block for this work would appear as follows: N0025 G02 X011000 Y010000 I013000 J003000 (The sequence number, N0025, is arbitrary.) The block would also contain the plane selection (i.e., G17, G18, or G19), if this selection is not preset in the system. Most of the newer control systems allow duplicate words in the



NUMERICAL CONTROL

same block, but most of the older systems do not. In these older systems, it is necessary to insert the plane selection code in a separate and prior block, for example, N0020 G17. Another stipulation in the Standard is that the arc is limited to one quadrant. Therefore, four blocks would be required to complete a circle. Four blocks would also be required to complete the arc shown in Fig. 12, which extends into all four quadrants. When utilizing absolute programming, the coordinates of the end point are described. Again from Fig. 11, the block, expressed in absolute coordinates, appears as: N0055 G02 X01800 Y019000 I013000 J003000 where the arc is continued from a previous block; the starting point for the arc in this block would be the end point of the previous block.

Fig. 12.

Fig. 13.

The Standard still contains the format discussed, but simpler alternatives have been developed. The latest version of the Standard (RS-274-D) allows multiple quadrant programming in one block, by inclusion of a G75 word. In the absolute-dimension mode (G90), the coordinates of the arc center are specified. In the incremental-dimension mode (G91), the signed (plus or minus) incremental distances from the beginning point of the arc to the arc center are given. Most system builders have introduced some variations on this format. One system builder utilizes the center and the end point of the arc when in an absolute mode, and might describe the block for going from A to B in Fig. 13 as: N0065 G75 G02 X2.5 Y0.7 I2.2 J1.6 The I and the J words are used to describe the coordinates of the arc center. Decimal-point programming is also used here. A block for the same motion when programmed incrementally might appear as: N0075 G75 G02 X1.1 Y − 1.6 I0.7 J0.7 This approach is more in conformance with the RS-274-D Standard in that the X and Y values describe the displacement between the starting and ending points (points A and B), and the I and J indicate the offsets of the starting point from the center. Another and even more convenient way of formulating a circular motion block is to note the coordinates of the ending point and the radius of the arc. Using absolute programming, the block for the motion in Fig. 13 might appear as: N0085 G75 G02 X2.5 Y0.7 R10.0 The starting point is derived from the previous motion block. Multiquadrant circular interpolation is canceled by a G74 code. Helical and Parabolic Interpolation.—Helical interpolation is used primarily for milling large threads and lubrication grooves, as shown in Fig. 14. Generally, helical interpolation involves motion in all three axes (X, Y, Z) and is accomplished by using circular



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interpolation (G02 or G03) while changing the third dimension. Parabolic interpolation (G06) is simultaneous and coordinated control of motion-such that the resulting cutter path describes part of a parabola. The RS-274-D Standard provides further details. Subroutine.—A subroutine is a set of instructions or blocks that can be inserted into a program and repeated whenever required. Parametric subroutines permit letters or symbols to be inserted into the program in place of numerical values (see Parametric Expressions and Macros). Parametric subroutines can be called during part programming and values assigned to the letters or symbols. This facility is particularly helpful when dealing with families of parts. A subprogram is similar to a subroutine except that a subprogram is not wholly contained within another program, as is a subroutine. Subprograms are used when it is necessary to perform the same task frequently, in different programs. The advantage of subprograms over subroutines is that subprograms may be called by any other program, whereas the subroutine can only be called by the program that contains the subroutine. There is no standard subroutine format; however, the example below is typical of a program that might be used for milling the three pockets shown in Fig. 15. In the example, the beginning and end of the subroutine are indicated by the codes M92 and M93, respectively, and M94 is the code that is used to call the subroutine. The codes M92, M93, and M94 are not standardized (M-codes M90 through M99 are reserved for the user) and may be different from control system to control system. The subroutine functions may use different codes or may not be available at all on other systems. N0010 G00 X.6 Y.85

Cutter is moved at a rapid traverse rate to a position over the corner of the first pocket to be cut.

N0020 M92

Tells the system that the subroutine is to start in the next block.

N0030 G01 Z−.25 F2.0

Cutter is moved axially into the workpiece 0.25 inch at 2.0 ipm.

N0040 X.8

Cutter is moved to the right 0.8 inch.

N0050 Y.2

Cutter is moved laterally up 0.2 inch.

N0060 X−.8

Cutter is moved to the left 0.8 inch.

N0070 Y.2

Cutter is moved laterally up 0.2 inch.

Fig. 14.

Fig. 15.



NUMERICAL CONTROL

N0080 X.8

Cutter is moved to the right 0.8 inch.

N0090 G00 Z.25 M93

Cutter is moved axially out of pocket at rapid traverse rate. Last block of subroutine is signaled by word M93.

N0100 X.75 Y.5

Cutter is moved to bottom left-hand corner of second pocket at rapid traverse rate.

N0110 M94 N0030

Word M94 calls for repetition of the subroutine that starts at sequence number N0030 and ends at sequence number N0090.

N0120 G00 X.2 Y−I.3

After the second pocket is cut by repetition of sequence numbers N0030 through N0090, the cutter is moved to start the third pocket.

N0130 M94 N0030

Repetition of subroutine is called for by word M94 and the third pocket is cut.

Parametric Expressions and Macros.—Parametric programming is a method whereby a variable or replaceable parameter representing a value is placed in the machining code instead of using the actual value. In this manner, a section of code can be used several or many times with different numerical values, thereby simplifying the programming and reducing the size of the program. For example, if the values of X and Y in lines N0040 to N0080 of the previous example are replaced as follows: N0040 X#1 N0050 Y#2 N0060 X#3 N0070 Y#4 then the subroutine starting at line N0030 is a parametric subroutine. That is, the numbers following the # signs are the variables or parameters that will be replaced with actual values when the program is run. In this example, the effect of the program changes is to allow the same group of code to be used for milling pockets of different sizes. If on the other hand, lines N0010, N0100, and N0120 of the original example were changed in a similar manner, the effect would be to move the starting location of each of the slots to the location specified by the replaceable parameters. Before the program is run, the values that are to be assigned to each of the parameters or variables are entered as a list at the start of the part program in this manner: #1 = .8 #2 = .2 #3 = .8 #4 = .2 All that is required to repeat the same milling process again, but this time creating a different size pocket, is to change the values assigned to each of the parameters #1, #2, #3, and #4 as necessary. Techniques for using parametric programming are not standardized and are not recognized by all control systems. For this reason, consult the programming manual of the particular system for specific details.



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As with a parametric subroutine, macro describes a type of program that can be recalled to allow insertion of finite values for letter variables. The difference between a macro and a parametric subroutine is minor. The term macro normally applies toa source program that is used with computer-assisted part programming; the parametric subroutine is a feature of the CNC system and can be input directly into that system. Conditional Expressions.—It is often useful for a program to make a choice between two or more options, depending on whether or not a certain condition exists. A program can contain one or more blocks of code that are not needed every time the program is run, but are needed some of the time. For example, refer to the previous program for milling three slots. An occasion arises that requires that the first and third slots be milled, but not the second one. If the program contained the following block of code, the machine could be easily instructed to skip the milling of the second slot: N0095 IF [#5 EQ 0] GO TO N0120 In this block, #5 is the name of a variable; EQ is a conditional expression meaning equals; and GO TO is a branch statement meaning resume execution of the program at the following line number. The block causes steps N0100 and N0110 of the program to be skipped if the value of #5 (a dummy variable) is set equal to zero. If the value assigned to #5 is any number other than zero, the expression (#5 EQ 0) is not true and the remaining instructions in block N0095 are not executed. Program execution continues with the next step, N0100, and the second pocket is milled. For the second pocket to be milled, parameter #5 is initialized at the beginning of the program with a statement such as #5 = 1 or #5 = 2. Initializing #5 = 0 guarantees that the pocket is not machined. On control systems that automatically initialize all variables to zero whenever the system is reset or a program is loaded, the second slot will not be machined unless the #5 is assigned a nonzero value each time the program is run. Other conditional expressions are: NE = not equal to; GT = greater than; LT = less than; GE = greater than or equal to; and LE = less than or equal to. As with parametric expressions, conditional expressions may not be featured on all machines and techniques and implementation will vary. Therefore, consult the control system programming manual for the specific command syntax. Fixed (Canned) Cycles.—Fixed (canned) cycles comprise sets of instructions providing for a preset sequence of events initiated by a single command or a block of data. Fixed cycles generally are offered by the builder of the control system or machine tool as part of the software package that accompanies the CNC system. Limited numbers of canned cycles began to appear on hardwire control systems shortly before their demise. The canned cycles offered generally consist of the standard G-codes covering driling, boring, and tapping operations, plus options that have been developed by the system builder such as thread cutting and turning cycles. (See Thread Cutting and Turning Cycles.) Some standard canned cycles included in RS-274-D are shown herewith. A block of data that might be used to generate the cycle functions is also shown above each illustration. Although the G-codes for the functions are standardized, the other words in the block and the block format are not, and different control system builders have different arrangements. The blocks shown are reasonable examples of fixed cycles and do not represent those of any particular system builder.



NUMERICAL CONTROL

The G81 block for a simple drilling cycle is: N_____ G81 X_____Y_____C_____D_____F_____EOB N_____X_____Y_____EOB

This G81 drilling cycle will move the drill point from position A to position B and then down to C at a rapid traverse rate; the drill point will next be fed from C to D at the programmed feed rate, then returned to C at the rapid traverse rate. If the cycle is to be repeated at a subsequent point, such as point E in the illustration, it is necessary Only to give the required X and Y coordinates. This repetition capability is typical of canned cycles. The G82 block for a spotfacing or drilling cycle with a dwell is: N_____G82 X_____Y_____C_____D_____T_____F_____EOB

This G82 code produces a cycle that is very similar to the cycle of the G81 code except for the dwell period at point D. The dwell period allows the tool to smooth out the bottom of the counterbore or spotface. The time for the dwell, in seconds, is noted as a T-word. The G83 block for a peck-drilling cyle is: N_____G83 X_____Y_____C_____D_____K_____F_____EOB

In the G83 peck-drilling cycle, the drill is moved from point A to point B and then to point C at the rapid traverse rate; the drill is then fed the incremental distance K, followed by



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rapid return to C. Down feed again at the rapid traverse rate through the distance K is next, after which the drill is fed another distance K. The drill is thenrapid traversed back to C, followed by rapid traverse for a distance of K + K; down feed to D follows before the drill is rapid traversed back to C, to end the cycle. The G84 block for a tapping cycle is: N_____G84 X_____Y_____C_____D_____F_____EOB

The G84 canned tapping cycle starts with the end of the tap being moved from point A to point B and then to point C at the rapid traverse rate. The tap is then fed to point D, reversed, and moved back to point C. The G85 block for a boring cycle with tool retraction at the feed rate is: N_____G85 X_____Y_____C_____D_____F_____EOB

In the G85 boring cycle, the tool is moved from point A to point B and then to point C at the rapid traverse rate. The tool is next fed to point D and then, while still rotating, is moved back to point C at the same feed rate. The G86 block for a boring cycle with rapid traverse retraction is: N_____G86 X_____Y_____C_____D_____F_____EOB

The G86 boring cycle is similar to the G85 cycle except that the tool is withdrawn at the rapid traverse rate.



NUMERICAL CONTROL

The G87 block for a boring cycle with manual withdrawal of the tool is: N_____G87 X_____Y_____C_____D_____F_____EOB

In the G87 canned boring cycle, the cutting tool is moved from A to B and then to C at the rapid traverse rate. The tool is then fed to D. The cycle is identical to the other boring cycles except that the tool is withdrawn manually. The G88 block for a boring cycle with dwell and manual withdrawal is: N_____G88 X_____Y_____C_____D_____T_____F_____EOB

In the G88 dwell cycle, the tool is moved from A to B to C at the rapid traverse rate and then fed at the prescribed feed rate to D. The tool dwells at D, then stops rotating and is withdrawn manually. The G89 block for a boring cycle with dwell and withdrawal at the feed rate is: N_____G89 X_____Y_____C_____D_____T_____F_____EOB



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Fig. 16.

Turning Cycles.—Canned turning cycles are available from most system builders and are designed to allow the programmer to describe a complete turning operation in one or a few blocks. There is no standard for this type of operation, so a wide variety of programs have developed. Fig. 16 shows a hypothetical sequence in which the cutter is moved from the start point to depth for the first pass. If incremental programming is in effect, this distance is specified as D1. The depths of the other cuts will also be programmed as D2, D3, and so on. The length of the cut will be set by the W-word, and will remain the same with each pass. The preparatory word that calls for the roughing cycle is G77. The roughing feed rate is 0.03 ipr (inch per revolution), and the finishing feed rate (last pass) is 0.005 ipr. The block appears as follows: N0054 G77 W = 3.1 D1 = .4 D2 = .3 D3 = .3 D4 = .1 F1 = .03 F2 = .005 Thread Cutting.—Most NC lathes can produce a variety of thread types including constant-lead threads, variable-lead threads (increasing), variable-lead threads (decreasing), multiple threads, taper threads, threads running parallel to the spindle axis, threads (spiral groove) perpendicular to the spindle axis, and threads containing a combination of the preceding. Instead of the feed rate, the lead is specified in the threading instruction block, so that the feed rate is made consistent with, and dependent upon, the selected speed (rpm) of the spindle. The thread lead is generally noted by either an I- or a K-word. The I-word is used if the thread is parallel to the X-axis and the K-word if the thread is parallel to the Z-axis, the latter being by far the most common. The G-word for a constant-lead thread is G33, for an increasing variable-lead thread is G34, and for a decreasing variable-lead thread is G35. Taper threads are obtained by noting the X- and Z-coordinates of the beginning and end points of the thread if the G90 code is in effect (absolute programming), or the incremental movement from the beginning point to the end point of the thread if the G91 code (incremental programming) is in effect. N0001 G91 (Incremental programming) N0002 G00 X−.1000 (Rapid traverse to depth) N0003 G33 Z−1.0000 K.0625 (Produce a thread with a constant lead of 0.625 inch) N0004 G00 X.1000 (Withdraw at rapid traverse) N0005 Z1.0000 (Move back to start point)



NUMERICAL CONTROL

Fig. 17.

Fig. 18.

Multiple threads are specified by a code in the block that spaces the start of the threads equally around the cylinder being threaded. For example, if a triple thread is to be cut, the threads will start 120 degrees apart. Typical single-block thread cutting utilizing a plunge cut is illustrated in Fig. 17 and shows two passes. The passes areidentical except for the distance of the plunge cut. Builders of control systems and machine tools use different codewords for threading, but those shown below can be considered typical. For clarity, both zeros and decimal points are shown. The only changes in the second pass are the depth of the plunge cut and the withdrawal. The blocks will appear as follows: N0006 X − .1050 N0007 G33 Z − 1.0000 K.0625 N0008 G00 X.1050 N0009 Z1.000 Compound thread cutting, rather than straight plunge thread cutting, is possible also, and is usually used on harder materials. As illustrated in Fig. 18, the starting point for the thread is moved laterally in the -Z direction by an amount equal to the depth of the cut times the tangent of an angle that is slightly less than 30 degrees. The program for the second pass of the example shown in Fig. 18 is as follows: N0006 X − .1050 Z − .0028 N0007 G33 Z − 1.0000 K.0625 N0008 G00 X.1050 N0009 Z1.0000 Fixed (canned), one-block cycles also have been developed for CNC systems to produce the passes needed to complete a thread. These cycles may be offered by the builder of the control system or machine tool as standard or optional features. Subroutines also can generally be prepared by the user to accomplish the same purpose (see Subroutine). A oneblock fixed threading cycle might look something like: N0048 G98 X − .2000 Z − 1.0000 D.0050 F.0010 where G98 = preparatory code for the threading cycle X − .2000 = total distance from the starting point to the bottom of the thread Z − 1.0000 = length of the thread D.0050 = depths of successive cuts F.0010 = depth(s) of the finish cut(s) APT Programming APT.—APT stands for Automatically Programmed Tool and is one of many computer languages designed for use with NC machine tools. The selection of a computer-assisted part-programming language depends on the type and complexity of the parts being machined more than on any other factor. Although some of the other languages may be easier to use, APT has been chosen to be covered in this book because it is a nonproprietary



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language in the public domain, has the broadest range of capability, and is one of the most advanced and universally accepted NC programming languages available. APT (or a variation thereof) is also one of the languages that is output by many computer programs that produce CNC part programs directly from drawings produced with CAD systems. APT is suitable for use in programming part geometry from simple to exceptionally complex shapes. APT was originally designed and used on mainframe computers, however, it is now available, in many forms, on mini- and microcomputers as well. APT has also been adopted as ANSI Standard X3.37and by the International Organization for Standardization (ISO) as a standardized language for NC programming. APT is a very dynamic program and is continually being updated. APT is being used as a processor for partprogramming graphic systems, some of which have the capability of producing an APT program from a graphic screen display or CAD drawing and of producing a graphic display on the CAD system from an APT program. APT is a high-level programming language. One difference between APT and the ANSI/EIA RS-274-D (G-codes) programming format discussed in the last section is that APT uses English like words and expressions to describe the motion of the tool or workpiece. APT has the capability of programming the machining of parts in up to five axes, and also allows computations and variables to be included in the programming statements so that a whole family of similar parts can be programmed easily. This section describes the general capabilities of the APT language and includes a ready reference guide to the basic geometry and motion statements of APT, which is suitable for use in programming the machining of the majority of cubic type parts involving two-dimensional movements. Some of the three-dimensional geometry capability of APT and a description of its fivedimensional capability are also included. Section 0 Controls the information flow PARTNO XXXX MACHIN/XXXX CUTTER/ .25 FROM/P1 (( )) )) (( FINI

Section 1 Converts English-like part program into computer language. Also checks for syntax errors in the part program.

Section 2 Heart of APT system. Performs geometry calculations. Output is center-line path of cutter or cutter location (CLC), described as coordinate points.

Section 3 Handles redundant operations and axis shifts.

Section 4 Converts to the block data and format required by the machine tool/system combination. Referred to as a postprocessor.

Tape output or direct to machine control system via DNC

As shown above, the APT system can be thought of comprising the input program, the five sections 0 through IV, and the output program. The input program shown on the left progresses through the first four sections and all four are controlled by the fifth, section 0. Section IV, the postprocessor, is the software package that is added to sections II and III to customize the output and produce the necessary program format (including the G-words, M-words, etc.) so that the coded instructions will be recognizable by the control system. The postprocessor is software that is separate from the main body of the APT program, but for purposes of discussion, it may be easier to consider it as a unit within the APT program.



NUMERICAL CONTROL

APT Computational Statements.—Algebraic and trigonometric functions and computations can be performed with the APT system as follows: Arithmetic Form 25 × 25 25 ÷ 25 25 + 25 25 − 25

APT Form 25*25 25⁄25 25 + 25 25 − 25

Arithmetic Form APT Form Arithmetic Form 25**2 cos θ 252 25**n tan θ 25n √25 SQRTF (25) arctan .5000 sin θ SINF(θ)

APT Form COSF(θ) TANF(θ) ATANF(.5)

Computations may be used in the APT system in two ways. One way is to let a factor equal the computation and then substitute the factor in a statement; the other is to put the computation directly into the statement. The following is a series of APT statements illustrating the first approach. P1 = POINT/0,0,1 T =(25*2⁄3 + (3**2 − 1)) P2 = POINT/T,0,0 The second way would be as follows; P1 = POINT/0,0,1 P2 = POINT/(25*2⁄3 + (3**2 − 1)),0,0 Note: The parentheses have been used as they would be in an algebraic formula so that the calculations will be carried out in proper sequence. The operations within the inner parentheses would be carried out first. It is important for the total number of left-hand parentheses to equal the total number of right-hand parentheses; otherwise, the program will fail. APT Geometry Statements.—Before movements around the geometry of a part can be described, the geometry must be defined. For example, in the statement GOTO/P1, the computer must know where P1 is located before the statement can be effective. P1 therefore must be described in a geometry statement, prior to its use in the motion statement GOTO/P1. The simplest and most direct geometry statement for a point is P1 = POINT/X ordinate, Y ordinate, Z ordinate If the Z ordinate is zero and the point lies on the X−Y plane, the Z location need not be noted. There are other ways of defining the position of a point, such as at the intersection of two lines or where a line is tangent to a circular arc. These alternatives are described below, together with ways to define lines and circles. Referring to the preceding statement, P1 is known as a symbol. Any combination of letters and numbers may be used as a symbol providing the total does not exceed six characters and at least one of them is a letter. MOUSE2 would be an acceptable symbol, as would CAT3 or FRISBE. However, it is sensible to use symbols that help define the geometry. For example, C1 or CIR3 would be good symbols for a circle. A good symbol for a vertical line would be VL5. Next, and after the equal sign, the particular geometry is noted. Here, it is a POINT. This word is a vocabulary word and must be spelled exactly as prescribed. Throughout, the designers of APT have tried to use words that are as close to English as possible. A slash follows the vocabulary word and is followed by a specific description of the particular geometry, such as the coordinates of the point P1. A usable statement for P1 might appear as P1 = POINT/1,5,4. The 1 would be the X ordinate; the 5, the Y ordinate; and the 4, the Z ordinate. Lines as calculated by the computer are infinitely long, and circles consist of 360 degrees. As the cutter is moved about the geometry under control of the motion statements, the lengths of the lines and the amounts of the arcs are “cut” to their proper size. (Some of the geometry statements shown in the accompanying illustrations for defining POINTS, LINES, CIRCLES, TABULATED CYLINDERS, CYLINDERS, CONES, and SPHERES, in the APT language, may not be included in some two-dimensional [ADAPT] systems.)


Machinery's Handbook 27th Edition NUMERICAL CONTROL Points


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NUMERICAL CONTROL Lines


Machinery's Handbook 27th Edition NUMERICAL CONTROL Lines (Continued)

P2 and P3 are points close to the tangent points of L1 and the intersection point of L2, therefore cannot be end points of the tabulated cylinder


1297


NUMERICAL CONTROL Circles



1299

Circles

APT Motion Statements.—APT is based on the concept that a milling cutter is guided by two surfaces when in a contouring mode. Examples of these surfaces are shown in Fig. 1, and they are called the “part” and the “drive” surfaces. Usually, the partsurface guides the bottom of the cutter and the drive surface guides the side of the cutter. These surfaces may or may not be actual surfaces on the part, and although they may be imaginary to the part programmer, they are very real to the computer. The cutter is either stopped or redirected by a third surface called a check surface. If one were to look directly down on these surfaces, they would appear as lines, as shown in Figs. 2a through 2c.

Fig. 1. Contouring Mode Surfaces

When the cutter is moving toward the check surface, it may move to it, onto it, or past it, as illustrated in Fig. 2a. When the cutter meets the check surface, it may go right, denoted by the APT command GORGT, or go left, denoted by the command GOLFT, in Fig. 2b.



NUMERICAL CONTROL

Alternatively, the cutter may go forward, instructed by the command GOFWD, as in Fig. 2c. The command GOFWD is used when the cutter is moving either onto or off a tangent circular arc. These code instructions are part of what are called motion commands. Fig. 3 shows a cutter moving along a drive surface, L1, toward a check surface, L2. When it arrives at L2, the cutter will make a right turn and move along L2 and past the new check surface L3. Note that L2 changes from a check surface to a drive surface the moment the cutter begins to move along it. The APT motion statement for this move is: GORGT/L2,PAST,L3 Contouring Cutter Movements

Fig. 2a.

Fig. 2b.

Fig. 2c.

Fig. 3. Motion Statements for Movements Around a Workpiece

Still referring to Fig. 3, the cutter moves along L3 until it comes to L4. L3 now becomes the drive surface and L4 the check surface. The APT statement is: GORGT/L3,TO,L4 The next statement is: GOLFT/L4,TANTO,C1 Even though the cutter is moving to the right, it makes a left turn if one is looking in the direction of travel of the cutter. In writing the motion statements, the part programmers must imagine they are steering the cutter. The drive surface now becomes L4 and the check surface, C1. The next statement will therefore be: GOFWD/C1,TANTO,L5 This movement could continue indefinitely, with the cutter being guided by the drive, part, and check surfaces. Start-Up Statements: For the cutter to move along them, it must first be brought into contact with the three guiding surfaces by means of a start-up statement. There are three different start-up statements, depending on how many surfaces are involved. A three-surface start-up statement is one in which the cutter is moved to the drive, part, and check surfaces, as seen in Fig. 4a. A two-surface start-up is one in which the cutter is



1301

moved to the drive and part surfaces, as in Fig. 4b. A one-surface start-up is one in which the cutter is moved to the drive surface and the X−Y plane, where Z = 0, as in Fig. 4c. With the two- and one-surface start-up statements, the cutter moves in the most direct path, or perpendicular to the surfaces. Referring to Fig. 4a(three-surface start-up), the move is initiated from a point P1. The two statements that will move the cutter from P1 to the three surfaces are: FROM/P1 GO/TO,DS,TO,PS,TO,CS Circles



NUMERICAL CONTROL

DS is used as the symbol for the Drive Surface; PS as the symbol for the Part Surface; and CS as the symbol for the Check Surface. The surfaces must be denoted in this sequence. The drive surface is the surface that the cutter will move along after coming in contact with the three surfaces. The two statements applicable to the two-surface start-up (Fig. 4b) are: FROM/P1 GO/TO,DS,TO,PS The one-surface start-up (Fig. 4c) is: FROM/P1 GO/TO,DS Planes

Cutter Movement Surfaces

Fig. 4a.

Fig. 4b.

Fig. 4c.



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Tabulated Cylinder

3-D Geometry

A cone is defined by its vertex, its axis as a unit vector, and the half angle (refer to cylinder for an example of a vector statement) CON1 = CONE/P1,V1,45

A sphere is defined by the center and the radius SP1 = SPHERE/P1, RADIUS, 2.5 or SP1 = SPHERE/5, 5, 3, 2.5 (where 5, 5, and 3 are the X, Y, and Z coordinates or P1, and 2.5 is the radius)



NUMERICAL CONTROL

Fig. 5. A Completed Two-Surface Start-Up

Note that, in all three motion statements, the slash mark (/) lies between the GO and the TO. When the cutter is moving to a point rather than to surfaces, such as in a start-up, the statement is GOTO/ rather than GO/TO. A two-surface start-up, Fig. 3, when completed, might appear as shown in Fig. 5, which includes the motion statements needed. The motion statements, as they would appear in a part program, are shown at the left, below: FROM/P1 FROM/P1 GO/TO,L1,TO,PS GOTO/P2 GORGT/L1,TO,L2 GOTO/P3 GORGT/L2,PAST,L3 GOTO/P4 GORGT/L3,TO,L4 GOTO/P5 GOLFT/L4,TANTO,C1 GOTO/P6 GOFWD/C1,TANTO,L5 GOTO/P7 GOFWD/L5,PAST,L1 GOTO/P2 GOTO statements can move the cutter throughout the range of the machine, as shown in Fig. 6. APT statements for such movements are shown at the right in the preceding example. The cutter may also be moved incrementally, as shown in Fig. 7. Here, the cutter is to move 2 inches in the + X direction, 1 inch in the + Y direction, and 1.5 inches in the + Z direction. The incremental move statement (indicated by DLTA) is: GODLTA/2,1,1.5 The first position after the slash is the X movement; the second the Y movement, and the third, the Z movement. Five-Axis Machining: Machining on five axes is achieved by causing the APT program to generate automatically a unit vector that is normal to the surface being machined, as shown in Fig. 8. The vector would be described by its X, Y, and Z components. These components, along with the X, Y, and Z coordinate positions of the tool tip, are fed into the postprocessor, which determines the locations and angles for the machine tool head and/or table. APT Postprocessor Statements.—Statements that refer to the operation of the machine rather than to the geometry of the part or the motion of the cutter about the part are called postprocessor statements. APT postprocessor statements have been standardized internationally. Some common statements and an explanation of their meaning follow:



1305

MACHIN/ Specifies the postprocessor that is to be used. Every postprocessor has an identity code, and this code must follow the slash mark (/). For example: MACHIN/LATH,82 FEDRATE/ Denotes the feed rate. If in inches per minute (ipm), only the number

Fig. 6. A Series of GOTO Statements

Fig. 7. Incremental Cutter Movements

Fig. 8. Five-Axis Machining

need be shown. If in inches per revolution (ipr), IPR must be shown, for example: FEDRAT/.005,IPR RAPID Means rapid traverse and applies only to the statement that immediately follows it SPINDL/ Refers to spindle speed. If in revolutions per minute (rpm), only the number need be shown. If in surface feet per minute (sfm), the letters SFM need to be shown, for example: SPINDL/ 100SFM COOLNT/ Means cutting fluid and can be subdivided into: COOLNT/ON, COOLNT/MIST, COOLNT/FLOOD, COOLNT/OFF TURRET/ Used to call for a selected tool or turret position CYCLE/ Specifies a cycle operation such as a drilling or boring cycle. An example of a drilling cycle is: CYCLE/DRILL,RAPTO,.45,FEDTO,0,IPR,.004. The next statement might be GOTO/PI and the drill will then move to P1 and perform the cycle operation. The cycle will repeat until the CYCLE/OFF statement is read



NUMERICAL CONTROL

END Stops the machine but does not turn off the control system

Fig. 9. Symbols for Geometrical Elements

APT Example Program.—A dimensioned drawing of a part and a drawing with the symbols for the geometry elements are shown in Fig. 9. A complete APT program for this part, starting with the statement PARTNO 47F36542 and ending with FINI, is shown at the left below. The numbers at the left of the statements are for reference purposes only, and are not part of the program. The cutter is set initially at a point represented by the symbol SP, having coordinates X = −0.5, Y = −0.5, Z = 0.75, and moves to L1 (extended) with a one-surface start-up so that the bottom of the cutter rests on the X−Y plane. The cutter then moves counterclockwise around the part, past L1 (extended), and returns to SP. The coordinates of P1 are X = 0, Y = 0, and Z = 1. (1) (2) (3) (4) (5) (6) (7)

(10) (11) (12)

PARTNO CUTTER/.25 FEDRAT/5 SP = POINT/−.5, −.5, .75 P1 = POINT/0, 0, 1 L1 = LINE/P1, ATANGL, 0 C1 = CIRCLE/(1.700 + 1.250), .250, .250 C2 = CIRCLE/1.700, 1.950, .5 L2 = LINE/RIGHT, TANTO, C1, RIGHT, TANTO, C2 L3 = LINE/P1, LEFT, TANTO, C2 FROM/SP GO/TO, L1

(13) (14) (15) (16) (17) (18)

GORGT/L1, TANTO, C1 GOFWD/C1, TANTO, L2 GOFWD/L2, TANTO, C2 GOFWD/C2, TANTO, L3 GOFWD/L3, PAST, L1 GOTO/SP

(8) (9)

(1) (2) (3) (4) (5) (6) (7)

PARTNO CUTTER/.25 FEDRAT/5 SP = POINT/−.5, −.5, .75 P1 = POINT/0, 0, 1 L1 = LINE/P1, ATANGL, 0 C1 = CIRCLE/(1.700 + 1.250), .250, .250

(8) C2 = CIRCLE/1.700, 1.950, .5 (9) L2 = LINE/RIGHT, TANTO, C1, RIGHT, TANTO, C2 (10) L3 = LINE/P1, LEFT, TANTO, C2 (11) FROM/SP (12) FRO −.500 −.5000 .7500 M (13) GO/TO/, L1 (14) GT −.5000 −.1250 .0000 (15) GORGT/L1, TANTO, C1 (16) GT 2.9500 −.1250 .0000 (17) GOFWD/C1, TANTO, L2 (18) CIR 2.9500 .2500 .3750 CCLW


Machinery's Handbook 27th Edition NUMERICAL CONTROL (19) FINI

(19) (20) (21) (22) (23) (24) (25) (26) (27) (28) (29)

3.2763 .4348 GOFWD/L2, TANTO, C2 GT 2.2439 2.2580 GOFWD/C2, TANTO, L3 CIR 1.700 1.9500 1.1584 2.2619 GOFWD/L3, PAST, L1 GT −.2162 −.1250 GOTO/SP GT −.5000 −.5000 FINI

1307 .0000 .0000 .6250 CCLW .0000 .0000 .7500

Referring to the numbers at the left of the program: (1) PARTNO must begin every program. Any identification can follow. (2) The diameter of the cutter is specified. Here it is 0.25 inch. (3) The feed rate is given as 5 inches per minute, which is contained in a postprocessor statement. (4)–(10) Geometry statements. (11)–(18) Motion statements. (19) All APT programs end with FINI. A computer printout from section II of the APT program is shown at the right, above. This program was run on a desktop personal computer. Lines (1) through (10) repeat the geometry statements from the original program. The motion statements are also repeated, and below each motion statement are shown the X, Y, and Z coordinates of the end points of the center-line (CL) movements for the cutter. Two lines of data follow those for the circular movements. For example, Line (18), which follows Line (17), GOFWD/C1,TANTO,L2, describes the X coordinate of the center of the arc, 2.9500, the Y coordinate of the center of the arc, 0.2500, and the radius of the arc required to be traversed by the cutter. This radius is that of the arc shown on the part print, plus the radius of the cutter (0.2500 + 0.1250 = 0.3750). Line (18) also shows that the cutter is traveling in a counterclockwise (CCLW) motion. A circular motion is described in Lines (22), (23), and (24). Finally, the cutter is directed to return to the starting point, SP, and this command is noted in Line (27). The X, Y, and Z coordinates of SP are shown in Line (28). APT for Turning.—In its basic form, APT is not a good program for turning. Although APT is probably the most suitable program for three-, four-, and five-axis machining, it is awkward for the simple two-axis geometry required for lathe operations. To overcome this problem, preprocessors have been developed especially for lathe part programming. The statements in the lathe program are automatically converted to basic APT statements in the computer and processed by the regular APT processor. An example of a lathe program, based on the APT processor and made available by the McDonnell Douglas Automation Co., is shown below. The numbers in parentheses are not part of the program, but are used only for reference. Fig. 10 shows the general set-up for the part, and Fig. 11 shows an enlarged view of the part profile with dimensions expressed along what would be the Xand Y-axes on the part print.



NUMERICAL CONTROL

Fig. 10. Setup for APT Turning

Fig. 11.

(1) (2) (3) (4) (5)

PARTNO LATHE EXAMPLE MACHIN/MODEL LATHE T1 = TOOL/FACE, 1, XOFF, −1, YOFF, −6, RADIUS, .031 BLANK1 = SHAPE/FACE, 3.5, TURN, 2 PART1 = SHAPE/FACE, 3.5, TAPER, 3.5, .5, ATANGL, − 45, TURN, 1,$ FILLET, .25 FACE, 1.5 TURN, 2 (6) FROM/(20–1), (15–6) (7) LATHE/ROUGH, BLANK1, PART1, STEP, .1, STOCK, .05,$ SFM, 300, IPR, .01, T1 (8) LATHE/FINISH, PART1, SFM, 400, IPR, .005, T1 (9) END (10) FINI



1309

Line (3) describes the tool. Here, the tool is located on face 1 of the turret and its tip is −1 inch “off” (offset) in the X direction and −6 inches “off” in the Y direction, when considering X−Y rather than X−Z axes. The cutting tool tip radius is also noted in this statement. Line (4) describes the dimensions of the rough material, or blank. Lines parallel to the Xaxis are noted as FACE lines, and lines parallel to the Z-axis are noted as TURN lines. The FACE line (LN1) is located 3.5 inches along the Z-axis and parallel to the X-axis. The TURN line (LN2) is located 2 inches above the Z-axis and parallel to it. Note that in Figs. 10 and 11, the X-axis is shown in a vertical position and the Z-axis in a horizontal position. Line (5) describes the shape of the finished part. The term FILLET is used in this statement to describe a circle that is tangent to the line described by TURN, 1 and the line that is described by FACE, 1.5. The $ sign means that the statement is continued on the next line. These geometry elements must be contiguous and must be described in sequence. Line (6) specifies the position of the tool tip at the start of the operation, relative to the point of origin. Line (7) describes the roughing operation and notes that the material to be roughed out lies between BLANK1 and PART1; that the STEP, or depth of roughing cuts, is to be 0.1 inch; that 0.05 inch is to be left for the finish cut; that the speed is to be 300 sfm and the feed rate is to be 0.01 ipr; and that the tool to be used is identified by the symbol T1. Line (8) describes the finish cut, which is to be along the contour described by PART1. Indexable Insert Holders for NC.—Indexable insert holders for numerical control lathes are usually made to more precise standards than ordinary holders. Where applicable, reference should be made to American National Standard B212.3-1986, Precision Holders for Indexable Inserts. This standard covers the dimensional specifications, styles, and designations of precision holders for indexable inserts, which are defined as tool holders that locate the gage insert (a combination of shim and insert thicknesses) from the back or front and end surfaces to a specified dimension with a ± 0.003 inch (± 0.08 mm) tolerance. In NC programming, the programmed path is that followed by the center of the tool tip, which is the center of the point, or nose radius, of the insert. The surfaces produced are the result of the path of the nose and the major cutting edge, so it is necessary to compensate for the nose or point radius and the lead angle when writing the program. Table 1, from B212.3, gives the compensating dimensions for different holder styles. The reference point is determined by the intersection of extensions from the major and minor cutting edges, which would be the location of the point of a sharp pointed tool. The distances from this point to the nose radius are L1 and D1; L2 and D2 are the distances from the sharp point to the center of the nose radius. Threading tools have sharp corners and do not require a radius compensation. Other dimensions of importance in programming threading tools are also given in Table 2; the data were developed by Kennametal, Inc. The C and F characters are tool holder dimensions other than the shank size. In all instances, the C dimension is parallel to the length of the shank and the F dimension is parallel to the side dimension; actual dimensions must be obtained from the manufacturer. For all K style holders, the C dimension is the distance from the end of the shank to the tangent point of the nose radius and the end cutting edge of the insert. For all other holders, the C dimension is from the end of the shank to a tangent to the nose radius of the insert. The F dimension on all B, D, E, M, P, and V style holders is measured from the back side of the shank to the tangent point of the nose radius and the side cutting edge of the insert. For all A, F, G, J, K, and L style holders, the F dimension is the distance from the back side of the shank to the tangent of the nose radius of the insert. In all these designs, the nose radius is the standard radius corresponding to those given in the paragraph Cutting Point Configuration on page 758.



NUMERICAL CONTROL Table 1. Insert Radius Compensation ANSI B212.3-1986 Square Profile Turning 15° Lead Angle

B Stylea Also applies to R Style

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64 1⁄ 16

.0035

.0191

.0009

.0110

.0070

.0383

.0019

.0221

.0105

.0574

.0028

.0331

.0140

.0765

.0038

.0442

Turning 45° Lead Angle D Stylea Also applies to S Style

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0065

.0221

.0065

0

.0129

.0442

.0129

0

.0194

.0663

.0194

0

1⁄ 16

.0259

.0884

.0259

0

Facing 15° Lead Angle

K Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0009

.0110

.0035

.0191

.0019

.0221

.0070

.0383

.0028

.0331

.0105

.0574

1⁄ 16

.0038

.0442

.0140

.0765

Triangle Profile Turning 0° Lead Angle

G

Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64 1⁄ 16

.0114

.0271

0

.0156

.0229

.0541

0

.0312

.0343

.0812

0

.0469

.0458

.1082

0

.0625

Turning and Facing 15° Lead Angle B Stylea Also applies to R Style

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64 1⁄ 16

.0146

.0302

.0039

.0081

.0291

.0604

.0078

.0162

.0437

.0906

.0117

.0243

.0582

.1207

.0156

.0324


F Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

0

.0156

.0114

.0271

0

.0312

.0229

.0541

0

.0469

.0343

.0812

1⁄ 16

0

.0625

.0458

.1082



1311

Table 1. (Continued) Insert Radius Compensation ANSI B212.3-1986 Triangle Profile (continued) Turning & Facing 3° Lead Angle

J

Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64 1⁄ 16

.0106

.0262

.0014

.0170

.0212

.0524

.0028

.0340

.0318

.0786

.0042

.0511

.0423

.1048

.0056

.0681

80° Diamond Profile Turning & Facing 0° Lead Angle

G Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0030

.0186

0

.0156

.0060

.0312

0

.0312

.0090

.0559

0

.0469

1⁄ 16

.0120

.0745

0

.0625

Turning & Facing 5° Reverse Lead Angle

L Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0016

.0172

.0016

.0172

.0031

.0344

.0031

.0344

.0047

.0516

.0047

.0516

1⁄ 16

.0062

.0688

.0062

.0688

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

0

.0156

.0030

.0186

0

.0312

.0060

.0372

0

.0469

.0090

.0559

1⁄ 16

0

.0625

.0120

.0745


F Stylea

Turning 15° Lead Angle

R Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0011

.0167

.0003

.0117

.0022

.0384

.0006

.0234

.0032

.0501

.0009

.0351

1⁄ 16

.0043

.0668

.0012

.0468


K Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0003

.0117

.0011

.0167

.0006

.0234

.0022

.0334

.0009

.0351

.0032

.0501

1⁄ 16

.0012

.0468

.0043

.0668



NUMERICAL CONTROL Table 1. (Continued) Insert Radius Compensation ANSI B212.3-1986 55° Profile Profiling 3° Reverse Lead Angle

J Stylea

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0135

.0292

.0015

.0172

.0271

.0583

.0031

.0343

.0406

.0875

.0046

.0519

1⁄ 16

.0541

.1166

.0062

.0687

35° Profile Profiling 3° Reverse Lead Angle J Stylea Negative rake holders have 6° back rake and 6° side rake

Rad.

L-1

L-2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64

.0330

.0487

.0026

.0182

.0661

.0973

.0051

.0364

.0991

.1460

.0077

.0546

1⁄ 16

.1322

.1947

.0103

.0728

Profiling 5° Lead Angle

L Stylea

Rad.

L-1

L -2

D-1

D-2

1⁄ 64 1⁄ 32 3⁄ 64 1⁄ 16

.0324

.0480

.0042

.0198

.0648

.0360

.0086

.0398

.0971

.1440

.0128

.0597

.1205

.1920

.0170

.0795

a L-1

and D-1 over sharp point to nose radius; and L-2 and D-2 over sharp point to center of nose radius. The D-1 dimension for the B, E, D, M, P, S, T, and V style tools are over the sharp point of insert to a sharp point at the intersection of a line on the lead angle on the cutting edge of the insert and the C dimension. The L-1 dimensions on K style tools are over the sharp point of insert to sharp point intersection of lead angle and F dimensions. All dimensions are in inches.

Table 2. Threading Tool Insert Radius Compensation for NC Programming Threading Insert Size 2 3 4 5

T 5⁄ Wide 32 3⁄ Wide 16 1⁄ Wide 4 3⁄ Wide 8

R .040 .046 .053 .099

U .075 .098 .128 .190

Y .040 .054 .054 …

X .024 .031 .049 …

All dimensions are given in inches. Courtesy of Kennametal, Inc.


Z .140 .183 .239 …


1313

V-Flange Tool Shanks and Retention Knobs.—Dimensions of ANSI B5.18-1972 (R1998) standard tool shanks and corresponding spindle noses are detailed on pages 940 through 944, and are suitable for spindles used in milling and associated machines. Corresponding equipment for higher-precision numerically controlled machines, using retention knobs instead of drawbars, is usually made to the ANSI/ASME B5.50-1985 standard. Essential Dimensions of V-Flange Tool Shanks ANSI/ASME B5.50-1985

A

Size 30 40 45 50 60

B

C

D

E

F

G

H

J

K

Tolerance

±0.005

±0.010

Min.

+ 0.015 −0.000

UNC 2B

±0.010

±0.002

+0.000 −0.015

+0.000 −0.015

Gage Dia. 1.250 1.750 2.250 2.750 4.250

1.875 2.687 3.250 4.000 6.375

0.188 0.188 0.188 0.250 0.312

1.00 1.12 1.50 1.75 2.25

0.516 0.641 0.766 1.031 1.281

0.500-13 0.625-11 0.750-10 1.000-8 1.250-7

1.531 2.219 2.969 3.594 5.219

1.812 2.500 3.250 3.875 5.500

0.735 0.985 1.235 1.485 2.235

0.640 0.890 1.140 1.390 2.140

A

L

M

N

P

R

S

T

Z

Tolerance

±0.001

±0.005

+0.000 −0.015

Min.

±0.002

±0.010

Min. Flat

+0.000 −0.005

Size 30 40 45 50

Gage Dia. 1.250 1.750 2.250 2.750

0.645 0.645 0.770 1.020

1.250 1.750 2.250 2.750

1.38 1.38 1.38 1.38

2.176 2.863 3.613 4.238

0.590 0.720 0.850 1.125

0.650 0.860 1.090 1.380

1.250 1.750 2.250 2.750

60

4.250

1.020

4.250

1.500

5.683

1.375

2.04

4.250

0.030 0.060 0.090 0.090 0.120 0.200

Notes: Taper tolerance to be 0.001 in. in 12 in. applied in direction that increases rate of taper. Geometric dimensions symbols are to ANSI Y14.5M-1982. Dimensions are in inches. Deburr all sharp edges. Unspecified fillets and radii to be 0.03 ± 0.010R, or 0.03 ± 0.010 × 45 degrees. Data for size 60 are not part of Standard. For all sizes, the values for dimensions U (tol. ± 0.005) are 0.579: for V (tol. ± 0.010), 0.440; for W (tol. ± 0.002), 0.625; for X (tol. ± 0.005), 0.151; and for Y (tol. ± 0.002), 0.750.



NUMERICAL CONTROL Essential Dimensions of V-Flange Tool Shank Retention Knobs ANSI/ASME B5.50-1985

Size

A

B

C

D

E

F

30

0.500-13

0.520

0.385

1.10

0.460

0.320

40

0.625-11

0.740

0.490

1.50

0.640

0.440

45

0.750-10

0.940

0.605

1.80

0.820

0.580

50

1.000-8

1.140

0.820

2.30

1.000

0.700

60

1.250-7

1.460

1.045

3.20

1.500

1.080

UNC- 2A

±0.005

±0.005

±0.040

±0.005

±0.005

Tolerances Size

G

H

J

K

L

M

R

30

0.04

0.10

0.187

0.65 0.64

0.53

0.19

0.094

40

0.06

0.12

0.281

0.94 0.92

0.75

0.22

0.094

0.375

1.20 1.18

1.00

0.22

0.094

0.468

1.44 1.42

1.25

0.25

0.125

2.14 2.06

45 50 60 Tolerances

0.08 0.10

0.16 0.20

0.14

0.30

0.500

±0.010

±0.010

±0.010

1.50

0.31

0.125

+0.000 −0.010

±0.040

+0.010 −0.005

Notes: Dimensions are in inches. Material: low-carbon steel. Heat treatment: carburize and harden to 0.016 to 0.028 in. effective case depth. Hardness of noted surfaces to be Rockwell 56-60; core hardness Rockwell C35-45. Hole J shall not be carburized. Surfaces C and R to be free from tool marks. Deburr all sharp edges. Geometric dimension symbols are to ANSI Y14.5M-1982. Data for size 60 are not part of Standard.


Machinery's Handbook 27th Edition CAD/CAM

1315

CAD/CAM CAD/CAM.—CAD in engineering means computer-aided design using a computer graphics system to develop mechanical, electrical/electronic, and architectural designs. A second D (CADD) is sometimes added (computer-aided drafting and design) and simply indicates a mechanical drafting or drawing program. CAD technology is the foundation for a wide variety of engineering, design, drafting, analysis, and manufacturing activities. Often a set of drawings initially developed in the design phase of a project is also used for analyzing and optimizing the design, creating mechanical drawings of parts and assemblies and for generating NC/CNC part programs that control machining operations. Formerly, after a component had been designed with CAD, the design was passed to a part programmer who developed a program for machining the components, either manually or directly on the computer (graphic) screen, but the process often required redefining and reentering part geometry. This procedure is often regarded as the CAM part of CAD/CAM, although CAM (for computer-aided manufacturing) has a much broader meaning and involves the computer in many other manufacturing activities such as factory simulation and planning analyses. Improvements in the speed and capability of computers, operating systems, and programs (including, but not limited to CAD) have simplified the process of integrating the manufacturing process and passing drawings (revised, modified, and translated, as necessary) through the design, analysis, simulation, and manufacturing stages. A CAD drawing is a graphic representation of part geometry data stored in a drawing database file. The drawing database generally contains the complete list of entity (line, arc, etc.) and coordinate information required to build the CAD drawing, and additional information that may be required to define solid surfaces and other model characteristics. The format of data in a drawing file depends on the CAD program used to create the file. Generally, drawings are not directly interchangeable between drawing programs, however, drawings created in one system can usually be translated into an intermediate format or file type, such as DXF, that allows some of the drawing information to be exchanged between different programs. Translation frequently results in some loss of detail or loss of other drawing information because the various drawing programs do not all have the same features. The section Drawing Exchange Standards covers some of the available methods of transferring drawing data between different CAD programs.

Fig. 1. Simple Wireframe Cube with Hidden Lines Automatically Removed

The simplest CAD drawings are two-dimensional and conform to normal engineering drafting practice showing orthographic (front, top, and side views, for example), exploded, isometric, or other views of a component. Depending on the complexity of the part and machining requirements, two-dimensional drawings are often sufficient for use in developing NC/CNC part programs. If a part can be programmed within a two-dimensional



CAD/CAM

CAD framework, a significant cost saving may be realized because 3-D drawings require considerably more time, drawing skill, and experience to produce than 2-D drawings. Wireframes are the simplest two- and three-dimensional forms of drawing images and are created by defining all edges of a part and, where required, lines defining surfaces. Wireframe drawing elements consist primarily of lines and arcs that can be used in practically any combination. A wireframe drawing of a cube, as in Fig. 1, consists of 12 lines of equal length (some are hidden and thus not shown), each perpendicular to the others. Information about the interior of the cube and the character of the surfaces is not included in the drawing. With such a system, if a 1-inch cube is drawn and a 0.5-inch cylinder is required to intersect the cube's surface at the center of one of its faces, the intersection points cannot be determined because nothing is known about the area between the edges. A wireframe model of this type is ambiguous if the edges overlap or do not meet where they should. Hidden-line removal can be used to indicate the relative elevations of the drawing elements, but normally a drawing cannot be edited when hidden lines have been removed. Hidden lines can be shown dashed or can be omitted from the view. Two-dimensional drawing elements, such as lines, arcs, and circles, are constructed by directly or indirectly specifying point coordinates, usually x and y, that identify the location, size, and orientation of the entities. Three-dimensional drawings are also made up of a collection of lines, arcs, circles, and other drawing elements and are stored in a similar manner. A third point coordinate, z, indicates the elevation of a point in 3-D drawings. On the drawing screen, working in the x-y plane, the elevation is commonly thought of as the distance of a point or object into the screen (away from the observer) or out of the viewing screen (toward the observer). Coordinate axes are oriented according to the right-hand rule: If the fingers of the right hand point in the direction from the positive x-axis to the positive y-axis, the thumb of the right hand points in the direction of the positive z-axis. Assigning a thickness (or extruding) to objects drawn in two dimensions quickly gives some 3-D characteristics to an object and can be used to create simple prismatic 3-D shapes, such as cubes and cylinders. Usually, the greatest difficulty in creating 3-D drawings is in picking and visualizing the three-dimensional points in a two-dimensional workspace (the computer display screen). To assist in the selection of 3-D points, many CAD programs use a split or windowed screen drawing area that can simultaneously show different views of a drawing. Changes made in the current or active window are reflected in each of the other windows. A typical window setup might show three orthogonal (mutually perpendicular) views of the drawing and a perspective or 3-D view. Usually, the views shown can be changed as required to suit the needs of the operator. If carefully constructed, wireframe images may contain enough information to completely define the external geometry of simple plane figures. Wireframe images are especially useful for visualization of 3-D objects and are effectively used during the design process to check fits, clearances, and dimensional accuracy. Parts designed to be used together can be checked for accuracy of fit by bringing them together in a drawing, superimposing the images, and graphically measuring clearances. If the parts have been designed or drawn incorrectly, the errors will frequently be obvious and appropriate corrections can be made. A more complicated level of 3-D drawing involves solids, with sections of the part being depicted on the screen as solid geometrical structures called primitives, such as cylinders, spheres, and cubes. Primitives can be assembled on a drawing to show more complex parts. Three distinct forms of image may be generated by 3-D systems, although not all systems make use of all three. Surface Images: A surface image defines not only the edges of the part, but also the “skin” of each face or surface. For the example mentioned previously, the intersection for the 0.5-inch cylinder would be calculated and drawn in position. Surface models are necessary for designing free-form objects such as automotive body panels and plastics injection moldings used in consumer goods. For a surface model, the computer must be provided



1317

with much more information about the part in addition to the x, y, z coordinates defining each point, as in a wireframe. This information may include tangent vectors, surface normals, and weighting that determines how much influence one point has on another, twists, and other mathematical data that define abstract curves, for instance. Fig. 2 shows a typical 3-D surface patch. Shaded images may be constructed using simulated light sources, reflections, colors, and textures to make renderings more lifelike. Surface images are sometimes ambiguous, with surfaces that overlap or miss each other entirely. Information about the interior of the part, such as the center of gravity or the volume, also may not be available, depending on the CAD package.

z x

90˚ y 30˚ Fig. 2. A 3-D Surface Patch

30˚

Fig. 3. Isometric Drawing Showing Orientation of Principle Drawing Axes

Solid Images: A solid image is the ultimate electronic representation of a part, containing all the necessary information about edges, surfaces, and the interior. Most solid-imaging programs can calculate volume, center of mass, centroid, and moment of inertia. Several methods are available for building a solid model. One method is to perform Boolean operations on simple shapes such as cylinders, cones, cubes, and blocks. Boolean operations are used to union (join), difference (subtract one from another), and intersect (find the common volume between two objects). Thus, making a hole in a part requires subtracting a cylinder from a rectangular block. This type of program is called constructive solid geometry (CSG). The boundary representation type of imaging program uses profiles of 2-D shapes that it extrudes, rotates, and otherwise translates in 3-D space to create the required solid. Sometimes combinations of the above two programs are used to attain a blend of flexibility, accuracy, and performance. For more precision, greatly increased time is needed for calculations, so compromises sometimes are needed to maintain reasonable productivity. Solid images may be sliced or sectioned on the screen to provide a view of the interior. This type of image is also useful for checking fit and assembly of one part with another. Solid images provide complete, unambiguous representation of a part, but the programs require large amounts of computer memory. Each time a Boolean operation is performed, the list of calculations that must be done to define the model becomes longer, so that computation time increases. Drawing Projections.—Several different techniques are used to display objects on paper or a computer screen to give an accurate three-dimensional appearance. Several of these methods are commonly used in CAD drawings. Isometric drawings, as in Fig. 3, can be used to good effect for visualizing a part because they give the impression of a 3-D view and are often much faster to create. Isometric drawings are created in 2-D space, with the x- and y-axes being inclined at 30 degrees to the horizontal, as shown in Fig. 3, and the z-axis as vertical. Holes and cylinders in isometric drawings become elliptical. Because of the orientation of the x-, y-, and z-axes, the true length of lines may not be accurately represented in isometric drawings and dimensions



CAD/CAM

should not be taken directly from a print. Some CAD programs have a special set of predefined drawing axes to facilitate creating isometric drawings. In parallel projections, lines that are parallel in an object, assembly, or part being portrayed remain parallel in the drawing. Parallel projections show 3-D objects in a dimensionally correct manner, so that relative and scaled dimensions may be taken directly from a drawing. However, drawings may not appear as realistic as isometric or perspective drawings. A characteristic of perspective drawings is that parallel lines converge (see Fig. 4) so that objects that are farther away from the observer appear smaller. Perspective drawing techniques are used in some three-dimensional drawings to convey the true look of an object, or group of objects. Because objects in perspective drawings are not drawn to scale, dimensional information cannot be extracted from the drawings of a part. Some 3-D drawing packages have a true perspective drawing capability, and others use a simulation technique to portray a 3-D perspective. An axonometric projection is a 3-D perpendicular projection of an object onto a surface, such that the object is tilted relative to its normal orientation. An axonometric projection of a cube, as in Fig. 1, shows three faces of the cube. CAD systems are adept at using this type of view, making it easy to see an object from any angle.

0.01

Fig. 4. Perspective Drawing of Three EqualSize Cubes and Construction Lines

Fig. 5. A Common Positioning Error

Drawing Tips and Traps.—Images sometimes appear correct on the screen but contain errors that show up when the drawing is printed or used to produce NC/CNC part programs. In Fig. 5, the two lines within the smaller circle appear to intersect at a corner, but when the view of the intersection is magnified, as in the larger circle, it is clear that the lines actually do not touch. Although an error of this type may not be easily visible, other parts placed in the drawing relative to this part will be out of position. A common problem that shows up in plotting, but is difficult to detect on the screen, comes from placing lines in the same spot. When two or more lines occupy exactly the same location on the screen, there is usually no noticeable effect on the display. However, when the drawing is plotted, each line is plotted separately, causing the single line visible to become thicker and darker. Likewise, if a line that appears continuous on the screen is actually made up of several segments, plotting the line will frequently result in a broken, marred, or blotted appearance to the line because the individual segments are plotted separately, and at different times. To avoid these problems and to get cleaner looking plots, replace segmented lines with single lines and avoid constructions that place one line directly on top of another. Exact decimal values should be used when entering point coordinates from the keyboard, if possible; fractional sizes should be entered as fractions, not truncated decimals. For example, 5⁄16 should be entered as 0.3125 or 5⁄16, not 0.313. Accumulated rounding errors and surprises later on when parts do not fit are thus reduced. Drawing dimensions, on the



1319

other hand, should not have more significant digits or be more precise than necessary. Unnecessary precision in dimensioning leads to increased difficulty in the production stage because the part has to be made according to the accuracy indicated on the drawing. Snap and object snap commands make selecting lines, arcs, circles, or other drawing entities faster, easier, and more accurate when picking and placing objects on the screen. Snap permits only points that are even multiples of the snap increment to be selected by the pointer. A 1⁄8-inch snap setting, for example, will allow points to be picked at exactly 1⁄8-inch intervals. Set the snap increment to the smallest distance increment (1 in., 1⁄4 in., 1 ft., etc.) being used in the area of the drawing under construction and reset the snap increment frequently, if necessary. The snap feature can be turned off during a command to override the setting or to select points at a smaller interval than the snap increment allows. Some systems permit setting a different snap value for each coordinate axis. The object snap selection mode is designed to select points on a drawing entity according to predefined characteristics of the entity. For example, if end-point snap is in effect, picking a point anywhere along a line will select the end point of the line nearest the point picked. Object snap modes include point, intersection, midpoint, center and quadrants of circles, tangency point (allows picking a point on an arc or circle that creates a tangent to a line), and perpendicular point (picks a point that makes a perpendicular from the base point to the object selected). When two or more object snap modes are used together, the nearest point that meets the selection criteria will be chosen. Using object snap will greatly reduce the frequency of the type of problem shown in Fig. 5. Copy: Once drawn, avoid redrawing the same object. It is almost always faster to copy and modify a drawing than to draw it again. The basic copy commands are: copy, array, offset, and mirror. Use these, along with move and rotate and the basic editing commands, to modify existing objects. Copy and move should be the most frequently used commands. If possible, create just one instance of a drawing object and then copy and move it to create others. To create multiple copies of an object, use the copy, multiple feature to copy selected objects as many times as required simply by indicating the destination points. The array command makes multiple copies of an object according to a regular pattern. The rectangular array produces rows and columns, and the polar array puts the objects into a circular pattern, such as in a bolt circle. Offset copies an entity and places the new entity a specified distance from the original and is particularly effective at placing parallel lines and curves, and for creating concentric copies of closed shapes. Mirror creates a mirror image copy of an object, and is useful for making right- and left-hand variations of an object as well as for copying objects from one side of an assembly to the other. In some CAD programs, a system variable controls whether text is mirrored along with other objects. Many manufacturers distribute drawings of their product lines in libraries of CAD drawings, usually as DXF files, that can be incorporated into existing drawings. The suitability of such drawings depends on the CAD program and drawing format being used, the skill of the technician who created the drawings, and the accuracy of the drawings. A typical example, Fig. 6, shows a magnetically coupled actuator drawing distributed by Tol-OMatic, Inc. Libraries of frequently used drawing symbols and blocks are also available from commercial sources. Create Blocks of Frequently Used Objects: Once created, complete drawings or parts of drawings can be saved and later recalled, as needed, into another drawing. Such objects can be scaled, copied, stretched, mirrored, rotated, or otherwise modified without changing the original. When shapes are initially drawn in unit size (i.e., fitting within a 1 × 1 square) and saved, they can be inserted into any drawing and scaled very easily. One or more individual drawing elements can be saved as a group element, or block, that can be manipulated in a drawing as a single element. Block properties vary, depending on the drawing program, but are among the most powerful features of CAD. Typically, blocks are uniquely named



CAD/CAM

and, as with simple objects, may be saved in a file on the disk. Blocks are ideal for creating libraries of frequently used drawing symbols. Blocks can be copied, moved, scaled very easily, rotated, arrayed, and inserted as many times as is required in a drawing and manipulated as one object. When scaled, each object within the block is also scaled to the same degree.

Fig. 6. Manufacturer's Drawing of a Magnetically Coupled Actuator (Courtesy of Tol-O-Matic, Inc.)

When a family of parts is to be drawn, create and block a single drawing of the part that fits within a unit cube of convenient size, such as 1 × 1 × 1. When the block is inserted in a drawing, it is scaled appropriately in the x-, y-, and z-directions. For example, 3⁄8-inch bolts can be drawn 1 inch long in the x-direction and 3⁄8-inch in diameter in the y-z plane. If a 5inch bolt is needed, insert the “bolt” block with a scale of 5 in the x-direction and a scale of 1 in the y- and z-directions. Once blocked, the individual components of a block (lines, arcs, circles, surfaces, and text, for example) cannot be individually changed or edited. To edit a block, a copy (instance) of the block must be exploded (unblocked) to divide it into its original components. Once exploded, all the individual elements of the block (except other blocks) can be edited. When the required changes have been made, the block must be redefined (redeclared as a block by giving it a name and identifying its components). If the block is redefined using the same name, any previous references to the block in the drawing will be updated to match the redefined block. For example, an assembly drawing is needed that shows a mechanical frame with 24 similar control panels attached to it. Once one of the panels is drawn and defined as a block (using the name PANEL, for instance), the block can be inserted (or copied) into the drawing 24 times. Later, if changes need to be made to the panel design, one instance of the block PANEL can be exploded, modified, and redefined with the name PANEL. When PANEL is redefined, every other copy of the PANEL block in the drawing is also redefined, so every copy of PANEL in the drawing is updated. On the other hand, if the block was redefined with a different name, say, PANEL1, existing copies of PANEL remain unchanged. When redefining a block that already exists in the drawing, be sure to use the same insertion point that was used for the original definition of the block; otherwise, the positions of existing blocks with the same name will be changed. Use of Text Attributes to Request Drawing Information Automatically: Text attributes are a useful method for attaching textual information to a particular part or feature of a drawing. An attribute is basically a text variable that has a name and can be assigned a value. Attributes are created by defining attribute characteristics such as a name, location in the drawing, text size and style, and default value. The attribute value is assigned when the attribute is inserted into a drawing as part of a block. Fig. 7 shows two views of a title block for size A to C drawing sheets. The upper figure includes the title block dimensions (included only for reference) and the names and locations of the attributes (COMPANY, TITLE1, TITLE2, etc.). When a block containing text



1321

attributes is inserted in a drawing, the operator is asked to enter the value of each attribute. To create this title block, first draw the frame of the title block and define the attributes (name, location and default value for: company name and address, drawing titles [2 lines], drawing size, drawing number, revision number, scale, and sheet number). Finally, create and name a block containing the title frame and all the attribute definitions (do not include the dimensions).

0.62

1.75

0.38 0.25

0.38

1.00 1.75

0.38 1.75

4.25 6.25

Fig. 7. Title Block for A to C Size Drawing Sheets Showing the Placement of Text Attributes. The Lower Figure Shows the Completed Block

When the block is inserted into a drawing, the operator is asked to enter the attribute values (such as company name, drawing title, etc.), which are placed into the title block at the predetermined location. The lower part of Fig. 7 shows a completed title block as it might appear inserted in a drawing. A complete drawing sheet could include several additional blocks, such as a sheet frame, a revision block, a parts list block, and any other supplementary blocks needed. Some of these blocks, such as the sheet frame, title, and parts list blocks, might be combined into a single block that could be inserted into a drawing at one time. Define a Default Drawing Configuration: Drawing features that are commonly used in a particular type of drawing can be set up in a template file so that frequently used settings, such as text and dimension styles, text size, drawing limits, initial view, and other default settings, are automatically set up when a new drawing is started. Different configurations can be defined for each frequently used drawing type, such as assembly, parts, or printed circuit drawings. When creating a new drawing, use one of the template files as a pattern or open a template file and use it to create the new drawing, saving it with a new name. Scaling Drawings: Normally, for fast and accurate drawing, it is easiest to draw most objects full scale, or with a 1:1 scale. This procedure greatly simplifies creation of the initial drawing, and ensures accuracy, because scale factors do not need to be calculated. If it becomes necessary to fit a large drawing onto a small drawing sheet (for example, to fit a 15 × 30 inch assembly onto a 11 × 17 inch, B-sized, drawing sheet), the drawing sheet can be scaled larger to fit the assembly size. Likewise, large drawing sheets can be scaled down to fit small drawings. The technique takes some practice, but it permits the drawing assembly to be treated full scale. If editing is required at a later date (to move something or add a hole in a particular location, for example), changes can be made without rescaling and dimensions can be taken directly from the unscaled drawing on the computer. Scaling Text on Drawing Sheets: It is usually desirable that text, dimensions, and a few other features on drawings stay a consistent size on each sheet, even when the drawing size is very different. The following procedure ensures that text and dimensions (other features



CAD/CAM

as well, if desired) will be the same size, from drawing to drawing without resorting to scaling the drawing to fit onto the drawing sheet. Create a drawing sheet having the exact dimensions of the actual sheet to be output (A, B, C, D, or E size, for example). Use text attributes, such as the title block illustrated in Fig. 7, to include any text that needs to be entered each time the drawing sheet is used. Create a block of the drawing sheet, including the text attributes, and save the block to disk. Repeat for each size drawing sheet required. Establish the nominal text and dimension size requirements for the drawing sheet when it is plotted full size (1:1 scale). This is the size text that will appear on a completed drawing. Use Table 1 as a guide to recommended text sizes of various drawing features. Table 1. Standard Sizes of Mechanical Drawing Lettering ANSI Y14.2M–1992 Inch Use For

Min. Letter Heights, (in)

Drawing title, drawing size, CAGE Code, drawing number, and revision lettera Section and view letters Zone letters and numerals in borders Drawing block headings All other characters

0.24 0.12 0.24 0.24 0.10 0.12

Metric Drawing Size

Min. Letter Heights, (mm)

Drawing Size

D, E, F, H, J, K A, B, C, G All All All All

6 3 6 6 2.5 3

A0, A1 A2, A3, A4 All All All All

a When used within the title block.

Test the sheet by setting the text size and dimension scale variables to their nominal values (established above) and place some text and dimensions onto the drawing sheet. Plot a copy of the drawing sheet and check that text and dimensions are the expected size. To use the drawing sheet, open a drawing to be placed on the sheet and insert the sheet block into the drawing. Scale and move the sheet block to locate the sheet relative to the drawing contents. When scaling the sheet, try to use whole-number scale factors (3:1, 4:1, etc.), if possible; this will make setting text size and dimension scale easier later on. Set the text-size variable equal to the nominal text size multiplied by the drawing sheet insertion scale (for example, for 0.24 text height on a drawing sheet scaled 3:1, the text-size variable will be set to 3 × 0.24 = 0.72). Likewise, set the dimension-scale variable equal to the nominal dimension size multiplied by the drawing sheet insertion scale. Once the text size and dimensions scale variables have been set, enter all the text and dimensions into the drawing. If text of another size is needed, multiply the new nominal text size by the sheet scale to get the actual size of the text to use in the drawing. Use Appropriate Detail: Excessive detail may reduce the effectiveness of the drawing, increase the drawing time on individual commands and the overall time spent on a drawing, and reduce performance and speed of the CAD program. Whenever possible, symbolic drawing elements should be used to represent more complicated parts of a drawing unless the appearance of that particular component is essential to the drawing. Drawing everything to scale often serves no purpose but to complicate a drawing and increase drawing time. The importance of detail depends on the purpose of a drawing, but detail in one drawing is unnecessary in another. For example, the slot size of a screw head (length and width) varies with almost every size of screw. If the purpose of a drawing is to show the type and location of the hardware, a symbolic representation of a screw is usually all that is required. The same is generally true of other screw heads, bolt threads, bolt head diameters and width across the flats, wire diameters, and many other hardware features. Drawing Exchange Standards.—The ability to transfer working data between different CAD, CAD/CAM, design analysis, and NC/CNC programs is one of the most important requirements of engineering drawing programs. Once an engineer, designer, draftsman, or machinist enters relevant product data into his or her machine (computer or machine tool), the information defining the characteristics of the product should be available to the others



1323

involved in the project without recreating or reentering it. In view of manufacturing goals of reducing lead time and increasing productivity, concurrent engineering, and improved product performance, interchangeable data are a critical component in a CAD/CAM program. Depending on the requirements of a project, it may be entirely possible to transfer most if not all of the necessary product drawings from one drawing system to another. IGES stands for Initial Graphics Exchange Specification and is a means of exchanging or converting drawings and CAD files for use in a different computer graphics system. The concept is shown diagrammatically in Fig. 8. Normally, a drawing prepared on the computer graphics system supplied by company A would have to be redrawn before it would operate on the computer graphics system supplied by company B. However, with IGES, the drawing can be passed through a software package called a preprocessor that converts it into a standardized IGES format that can be stored on a magnetic disk. A postprocessor at company B is then used to convert the standard IGES format to that required for their graphics system. Both firms would be responsible for purchasing or developing their own preprocessors and postprocessors, to suit their own machines and control systems. Almost all the major graphics systems manufacturing companies today either have or are developing IGES preprocessor and postprocessor programs to convert software from one system to another.

Fig. 8.

DXF stands for Drawing Exchange Format and is a pseudo-standard file format used for exchanging drawings and associated information between different CAD and design analysis programs. Nearly all two- and three-dimensional CAD programs support some sort of drawing exchange through the use of DXF files, and most can read and export DXF files. There are, however, differences in the drawing features supported and the manner in which the DXF files are handled by each program. For example, if a 3-D drawing is exported in the DXF format and imported into a 2-D CAD program, some loss of information results because all the 3-D features are not supported by the 2-D program, so that most attempts to make a transfer between such programs fail completely. Most common drawing entities (lines, arcs, etc.) will transfer successfully, although other problems may occur. For example, drawing entities that are treated as a single object in an original drawing (such as blocks, hatch patterns, and symbols) may be divided into hundreds of individual components when converted into a DXF file. Consequently, such a drawing may become much more difficult to edit after it is transferred to another drawing program. ASCII stands for American Standard Code for Information Interchange. ASCII is a code system that describes the manner in which character-based information is stored in a computer system. Files stored in the ASCII format can be transferred easily between computers, even those using different operating systems. Although ASCII is not a drawing file format, many CAD drawing formats (DXF and IGES, for example) are ASCII files. In these files, the drawing information is stored according to a specific format using ASCII characters. ASCII files are often referred to as pure text files because they can be read and edited by simple text editors. HPGL, for Hewlett-Packard Graphics Language, is a format that was first developed for sending vector- (line-) based drawing information to pen plotters. The format is commonly used for sending drawing files to printers and plotters for printing. Because HPGL is a character-based format (ASCII), it can be transferred between computers easily. Normally, devices that recognize the HPGL format can print the files without using the program on which the file (a drawing, for example) was created.



CAD/CAM

STL is a CAD drawing format that is primarily used to send CAD drawings to rapid automated prototyping machines. STL is a mnemonic abbreviation for stereo-lithography, the technique that is used to create three-dimensional solid models directly from computergenerated drawings and for which the drawing format was originally developed. Most prototyping machines use 3-D CAD drawing files in STL format to create a solid model of the part represented by a drawing. STEP stands for Standard for Exchange of Product Model Data and is a series of existing and proposed ISO standards written to allow access to all the data that surround a product. It extends the IGES idea of providing a geometric data transfer to include all the other data that would need to be communicated about a product over its lifetime, and facilitates the use and accessibility of the product data. Although STEP is a new standard, software tools have been developed for converting data from the IGES to STEP format and from STEP to IGES. Rapid Automated Prototyping.—Rapid automated prototyping is a method of quickly creating an accurate three-dimensional physical model directly from a computerized conception of the part. The process is accomplished without machining or the removal of any material, but rather is a method of building up the model in three-dimensional space. The process makes it possible to easily and automatically create shapes that would be difficult or impossible to produce by any other method. Currently, production methods are able to produce models with an accuracy tolerance of ± 0.005 inch. Models are typically constructed of photoreactive polymer resins, nylon, polycarbonate or other thermoplastics, and investment casting wax. The model size is limited by the capability of the modeling machines to about 1 cubic foot at the present, however, large models can be built in sections and glued or otherwise fastened together. Much of the work and a large part of the cost associated with creating a physical model by rapid prototyping are in the initial creation of the CAD model. The model needs to be a 3D design model, built using wireframe, surface, or solid CAD modeling techniques. Many full-featured CAD systems support translation of drawing files into the STL format, which is the preferred file format for downloading CAD models to rapid prototyping machines. CAD programs without STL file format capability can use the IGES or DXF file format. This process can be time-consuming and expensive because additional steps may have to be taken by the service bureau to recreate features lost in converting the IGES or DXF file into STL format. If the design file has to be edited by a service bureau to recreate surfaces lost in the translation, unwanted changes to the model may occur, unnoticed. The safest route is to create a CAD model and export it directly into the STL format, leaving little chance for unexpected errors. Reverse STL generators are also available that will display a file saved in STL format or convert it into a form that can be imported into a CAD program. DNC.—DNC stands for Direct Numerical Control and refers to a method of controlling numerical control machines from a remote location by means of a link to a computer or computer network. In its simplest form, DNC consists of one NC or CNC machine linked by its serial port to a computer. The computer may be used to develop and store CNC part programs and to transfer part programs to the machine as required. DNC links are normally two-directional, meaning that the NC/CNC can be operated from a computer terminal and the computer can be operated or ordered to supply data to the NC/CNC from the machine's control panel. The number of machines that can be connected to a DNC network depends on the network's capability; in theory, any number of machines can be attached, and controlled. The type of network depends on the individual DNC system, but most industry standard network protocols are supported, so DNC nodes can be connected to existing networks very easily. Individual NC/CNC machines on a network can be controlled locally, from a network terminal in another building, or even from a remote location miles away through phone or leased lines.


Machinery's Handbook 27th Edition CAM/CAD

1325

Machinery Noise.—Noise from machinery or mechanical systems can be controlled to some degree in the design or development stage if quantified noise criteria are provided the designer. Manufacturers and consumers may also use the same information in deciding whether the noise generated by a machine will be acceptable for a specific purpose. Noise criteria for may be classified as follows: 1) relating to the degree of interference with speech communications; 2) relating to physiological damage to humans, especially hearing; and 3) those relating to psychological disturbances in people exposed to noise. Sound Level Specifications: Noise criteria generally are specified in some system of units representing sound levels. One commonly used system specifies sound levels in units called decibels on the “A” scale, written dBA. The dBA scale designates a sound level system weighted to match human hearing responses to various frequencies and loudness. For example, to permit effective speech communication, typical criteria for indoor maximum noise levels are: meeting and conference rooms, 42 dBA; private offices and small meeting rooms, 38 to 47 dBA; supervisors' offices and reception rooms, 38 to 52 dBA; large offices and cafeterias, 42 to 52 dBA; laboratories, drafting rooms, and general office areas, 47 to 56 dBA; maintenance shops, computer rooms, and washrooms, 52 to 61 dBA; control and electrical equipment rooms, 56 to 66 dBA; and manufacturing areas and foremen’s offices, 66 dBA. Similarly, there are standards and recommendations for daily permissible times of exposure at various steady sound levels to avoid hearing damage. For a working shift of 8 hours, a steady sound level of 90 dBA is the maximum generally permitted, with marked reduction in allowable exposure times for higher sound levels.* Measuring Machinery Noise.—The noise level produced by a single machine can be measured by using a standard sound level meter of the handheld type set to the dBA scale. However, when other machines are running at the same time, or when there are other background noises, the noise of the machine cannot be measured directly. In such cases, two measurements, taken as follows, can be used to calculate the noise level of the individual machine. The meter should be held at arm's length and well away from any bystanders to avoid possible significant error up to 5 dBA. Step 1. At the point of interest, measure the total noise, T, in decibels; that is, measure the noise of the shop and the machine in question when all machines are running; Step 2. Turn off the machine in question and measure B, the remaining background noise level; Step 3. Calculate M, the noise of the machine alone, M = 10log10[10(T/10) − 10(B/10)]. T-----

B-----

M = 10 log ⎛ 10 10 – 10 10⎞ ⎝ ⎠

Example 1:With a machine running, the sound level meter reads 51 decibels as the total shop noise T; and with the machine shut off the meter reads 49 decibels as the remaining background noise B. What is the noise level M of the machine alone? 51-----

49-----

M = 10 log ⎛⎝ 10 10 – 10 10⎞⎠ = 46.7 decibels dBA

Example 2:If in Example 1 the remaining background noise level B was 41 decibels instead of 49, what is the noise level of the machine alone? 51 ------

41 ------

M = 10 log ⎛ 10 10 – 10 10⎞ = 50.5 decibels dBA ⎝ ⎠

Note: From this example it is evident that when the background noise level B is approximately 10 or more decibels lower than the total noise level T measured at the machine in question, then the background noise does not contribute significantly to the sound level at the machine and, for practical purposes, M = T and no calculation is required. *

After April 1983, if employee noise exposures equal or exceed an 8-hour, time-weighted average sound level of 85 dB, OSHA requires employers to administer an effective hearing conservation program.


Machinery's Handbook 27th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES PUNCHES, DIES, AND PRESS WORK 1329 Punches and Dies 1329 Clearance 1330 Lubricants for Press Work 1330 Annealing Drawn Shells 1330 Drawing Rectangular Shapes 1330 Speeds and Pressures for Presses 1331 Pressure Required for Punching 1331 Shut Height of Press 1331 Drawn Shells 1331 Diameters of Shell Blanks 1333 Drawn Cylindrical Shells 1334 Depth and Diameter Reductions 1335 Sheet Metal 1335 Lengths of Straight Stock 1339 Other Bending Allowance Formulas 1339 Joining and Edging 1344 Fine Blanking 1346 Steel Rule Dies 1347 Making Steel Rule Dies

ELECTRICAL DISCHARGE MACHINING 1349 EDM Terms 1351 EDM Process 1354 Electrical Control Adjustments 1355 Workpiece Materials 1355 Characteristics of Materials 1355 Electrode Materials 1356 Types of Electrodes 1357 Making Electrodes 1359 Wire EDM

IRON AND STEEL CASTINGS 1360 Material Properties 1360 Gray Cast Iron 1360 White Cast Iron 1360 Chilled Cast Iron 1360 Alloy Cast Iron 1361 Malleable-iron Castings 1361 Ductile Cast Iron 1362 Steel Castings 1362 Carbon Steel Castings 1363 Mechanical Properties 1363 Alloy Steel Castings 1364 Heat-Resistant Steel Castings

IRON AND STEEL CASTINGS (Continued)

1364 1365 1367 1368 1368 1368 1368 1369 1369 1369 1369 1370 1370 1371 1371 1371 1372 1372 1372 1372 1373 1373 1373 1373 1374 1374 1374 1375 1375 1375 1375 1376 1376 1376 1376 1376 1377 1377 1377 1379 1379 1379 1379

Corrosion-Resistant Steel Castings Casting of Metals Removal of Gates and Risers Blast Cleaning of Castings Heat Treatment of Steel Castings Estimating Casting Weight Woods for Patterns Selection of Wood Pattern Varnish Shrinkage Allowances Metal Patterns Weight of Casting Die Casting Porosity Designing Die Castings Alloys Used for Die Casting Aluminum-Base Alloys Zinc-Base Alloys Copper-Base Alloys Magnesium-Base Alloys Tin-Base Alloys Lead-Base Alloys Dies for Die-Casting Machines Die-Casting Bearing Metal Injection Molding of Metal Precision Investment Casting Casting Materials Master Mold Shrinkage Allowances Casting Dimensions Investment Materials Casting Operations Investment Removal Investment Castings Casting Weights and Sizes Design for Investment Casting Casting Milling Cutters Extrusion of Metals Basic Process Powder Metallurgy Advantages of Powder Metallurgy Limiting Factors Design of Briquetting Tools

1326


Machinery's Handbook 27th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES SOLDERING AND BRAZING

WELDING (Continued)

1380 Soldering 1380 Forms Available 1380 Fluxes for Soldering 1380 Methods of Application 1382 Ultrasonic Fluxless Soldering 1382 Brazing 1382 Filler Metals 1382 Brazing Filler Metals 1382 Brazing Filler Metals 1382 Selection of Filler Metals 1386 Fluxes for Brazing 1387 Steadying Work 1387 Supplying Heat 1387 Symbol Application

WELDING 1389 Welding Electrodes and Fluxes 1389 Processes 1390 Gas Metal Arc Welding (GMAW) 1390 Electrode Diameters 1391 Maximum Deposition Rates 1391 GMAW Welding of Sheet Steel 1391 Application of Shielding Gases 1393 Welding Controls 1395 GMAW Spray Transfer 1395 Deposition Rates of Electrodes 1397 Optimum Settings for GMAW 1397 Spray Transfer Voltage 1398 Flux-Cored Arc Welding 1398 Flux-Cored Welding Electrodes 1398 Gas-Shielded Electrodes 1399 Settings for FCAW Electrodes 1399 Weld Requirements 1399 Selecting an FCAW Electrode 1400 FCAW Electrodes 1401 Contact Tip Recess 1401 Porosity and Worm Tracks 1401 Welding with Various Diameter 1402 High-Deposition Electrodes 1403 Deposition Rates for Vertical Up Welding 1403 Deposition Rates of Flat and Horizontal Welds 1403 Electrode Diameters and Deposition Rates 1404 Shielding Gases and FCAW Electrodes

1405 Shielded Metal Arc Welding 1406 ANSI/AWS Standard 1406 AWS E60XX Electrodes 1408 AWS E70XX Electrodes 1409 Gas Tungsten Arc Welding 1409 GTAW Welding Current 1411 Tungsten Electrode Type 1412 Selection of GTAW 1412 Tungsten Electrode Compositions 1412 Electrode and Current Selection 1413 Current Ranges for GTAW Electrodes 1413 Current Ranges for EWP and EWZ and GTAW Electrodes 1414 Filler Metals 1414 Shielding Gases 1414 Plasma Arc Welding (PAW) 1414 Gases for Plasma Arc Welding 1415 Shielding Gases 1415 PAW Welding Equipment 1416 Applications 1416 Welding Aluminum 1417 Plasma Arc Surface Coating 1418 Plasma Arc Cutting of Metals 1418 Precision Plasma Arc Cutting 1418 Flame Cutting of Metals 1418 Arc Cutting 1419 The Cutting Torch 1419 Adjustment of Cutting Torch 1419 Metals That Can Be Cut 1419 Cutting Stainless Steel 1419 Cutting Cast Iron 1419 Mechanically Guided Torches 1419 Cutting Steel Castings 1420 Thickness of Metal 1420 Hard Facing 1420 Hard-Facing Materials 1420 High-Speed Steels 1421 Austenitic Manganese Steels 1421 Austenitic High-Chromium Irons 1421 Cobalt-Base Alloys 1422 Copper-Base Alloys 1423 Nickel-Chromium-Boron Alloys 1424 Chromium Plating 1424 Electron-Beam (EB) Welding 1425 Pipe Welding 1428 Use of Flux-cored Electrodes 1428 Complete Weld Fusion 1429 Other Methods

1327


Machinery's Handbook 27th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES WELDING

LASERS

(Continued)

(Continued)

1429 Pipe Welding Procedure 1429 Thick-Walled, Carbon-Steel Pipes, Root Welding 1430 Thick-Walled, Carbon-Steel Pipes, Fill and Cover Welds 1431 Thin-Walled Carbon Steel Pipes, Root, Fill and Cover Pass 1432 Weld and Welding Symbols 1432 ANSI Weld and Welding Symbols 1433 Basic Weld Symbols 1434 Supplementary Weld Symbols 1434 Welding Codes, Rules, Regulations, and Specifications 1435 Letter Designations for Welding 1436 ANSI Welding Symbols 1441 Nondestructive Testing 1441 Symbols

1454 Heat Treatment with Lasers 1454 Materials Applicability 1454 Hardening Rates 1454 Cladding with Lasers 1455 Marking with Lasers 1455 Mask Marking 1455 Scanned-Beam Marking

LASERS 1443 1443 1443 1444 1445 1445 1446 1446 1447 1447 1448 1448 1449 1450 1451 1451 1452 1452 1452 1453 1453 1453 1453 1454 1454

Introduction Laser Light Laser Beams Beam Focusing Types of Industrial Lasers Industrial Laser Systems Safety Laser Beam/Material Interaction Thermal Properties of Workpieces Cutting Metal with Lasers Beam Assistance Techniques Cut Edge Roughness Heat-Affected Zones Cutting of Nonmetals Welding with Lasers Laser Welding Theory Welded Joint Design Welding Rates Processing Gas Drilling with Lasers Laser Drilling Theory Direct Drilling Percussive Drilling Trepanning Drilling Rates

FINISHING OPERATIONS 1456 Power Brush Finishing 1456 Description of Brushes 1456 Use of Brushes 1456 Deburring and Producing a Radius 1457 Eliminating Undesirable Conditions 1457 Characteristics in Power Brush 1457 Polishing and Buffing 1457 Polishing Wheels 1460 Polishing Operations and Abrasives 1460 Buffing Wheels 1460 Speed of Polishing Wheels 1461 Grain Numbers of Emery 1461 Grades of Emery Cloth 1461 Etching and Etching Fluids 1461 Etching Fluids 1462 Conversion Coatings and the Coloring of Metals 1462 Passivation of Copper 1462 Coloring of Copper Alloys 1463 Coloring of Iron and Steel 1463 Anodizing Aluminum Alloys 1464 Magnesium Alloys 1464 Titanium Alloys 1464 Plating 1464 Surface Coatings 1472 Flame Spraying Process

1328


Machinery's Handbook 27th Edition MANUFACTURING PROCESSES

1329

PUNCHES, DIES, AND PRESS WORK Clearance between Punches and Dies.—The amount of clearance between a punch and die for blanking and perforating is governed by the thickness and kind of stock to be operated upon. For thin material, the punch should be a close sliding fit to prevent ragged edges, but for heavier stock, there should be some clearance. The clearance between the punch and die in cutting heavy material reduces the pressure required for the punching operation and the danger of breaking the punch. Meaning of the Term “Clearance”.—There is a difference of opinion among diemakers as to the method of designating clearance. The prevailing practice of fifteen firms specializing in die work is as follows: Ten of these firms define clearance as the space between the punch and die on one side, or one-half the difference between the punch and die sizes. The remaining five firms consider clearance as the total difference between the punch and die sizes; for example, if the die is round, clearance equals die diameter minus punch diameter. The advantage of designating clearance as the space on each side is particularly evident with dies of irregular form or of angular shape. Although the practice of designating clearance as the difference between the punch and die diameters may be satisfactory for round dies, it leads to confusion when the dies are of unsymmetrical forms. The term “clearance” should not be used in specifications without indicating clearly just what it means. According to one die manufacturer, the term “cutting clearance” is used to indicate the space between the punch and die on each side, and the term “die clearance” refers to the angular clearance provided below the cutting edge so that the parts will fall easily through the die. The term “clearance” as here used means the space on one side only; hence, for round dies, clearance equals die radius minus punch radius. Clearances Generally Allowed.—For brass and soft steel, most dies are given a clearance on one side equal to the stock thickness multiplied by 0.05 or 0.06; but one-half of this clearance is preferred for some classes of work, and a clearance equal to the stock thickness multiplied by 0.10 may give the cleanest fracture for certain other operations such as punching holes in ductile steel boiler plate. Where Clearance Is Applied.—Whether clearance is deducted from the diameter of the punch or added to the diameter of the die depends upon the nature of the work. If a blank of given size is required, the die is made to that size and the punch is made smaller. Inversely, when holes of a given size are required, the punch is made to the diameter wanted and the die is made larger. Therefore, for blanking to a given size, the clearance is deducted from the size of the punch, and for perforating, the clearance is added to the size of the die. Effect of Clearance on Working Pressure.—Clearance affects not only the smoothness of the fracture, but also the pressure required for punching or blanking. This pressure is greatest when the punch diameter is small compared to the thickness of the stock. In one test, for example, a punching pressure of about 32,000 pounds was required to punch 3⁄4inch holes into 5⁄16-inch mild steel plate when the clearance was about 10 per cent. With a clearance of about 4.5 per cent, the pressure increased to 33,000 pounds and a clearance of 2.75 per cent resulted in a pressure of 34,500 pounds. Soft ductile metal requires more clearance than hard metal, although it has been common practice to increase the clearance for harder metals. In punching holes in fairly hard steel, a clean fracture was obtained with a clearance of only 0.03 times stock thickness. Angular Clearance for Dies.—The angular clearance ordinarily used in a blanking die varies from 1 to 2 degrees, although dies intended for producing a comparatively small number of blanks are sometimes given a clearance angle of 4 or 5 degrees to facilitate making the die quickly. When large numbers of blanks are required, a clearance of about 1 degree is used.



PUNCHES, DIES, AND PRESS WORK

There are two methods of giving clearance to dies: In one method, the clearance extends to the top face of the die; and in the other, there is a space about 1⁄8 inch below the cutting edge that is left practically straight, or having a very small amount of clearance. For very soft metal, such as soft, thin brass, the first method is employed, but for harder material, such as hard brass, steel, etc., it is better to have a very small clearance for a short distance below the cutting edge. When a die is made in this way, thousands of blanks can be cut with little variation in their size, as grinding the die face will not enlarge the hole to any appreciable extent. Lubricants for Press Work.—Blanking dies used for carbon and low-alloy steels are often run with only residual mill lubricant, but will last longer if lightly oiled. Higher alloy and stainless steels require thicker lubricants. Kerosene is usually used with aluminum. Lubricant thickness needs to be about 0.0001 in. and can be obtained with about 1 pint of fluid to cover 500 sq. ft of material. During successive strokes, metal debris adheres to the punch and may accelerate wear, but damage may be reduced by application of the lubricant to the sheet or strip by means of rollers or spray. High-speed blanking may require heavier applications or a continuous airless spraying of oil. For sheet thicker than 1⁄8 in. and for stainless steel, high-pressure lubricants containing sulfurs and chlorines are often used. Shallow drawing and forming of steel can be done with low-viscosity oils and soap solutions, but deeper draws require light- to medium-viscosity oils containing fats and such active elements as sulfur or phosphorus, and mineral fillers such as chalk or mica. Deep drawing often involves ironing or thinning of the walls by up to 35 per cent, and thick oils containing high proportions of chemically active compounds are used. Additives used in drawing compounds are selected for their ability to maintain a physical barrier between the tool surfaces and the metal being shaped. Dry soaps and polymer films are frequently used for these purposes. Aluminum can be shallow drawn with oils of low to medium viscosity, and for deep drawing, tallow may be added, also wax or soap suspensions for very large reductions. Annealing Drawn Shells.—When drawing steel, iron, brass, or copper, annealing is necessary after two or three draws have been made, because the metal is hardened by the drawing process. For steel and brass, anneal between alternate reductions, at least. Tin plate or stock that cannot be annealed without spoiling the finish must ordinarily be drawn to size in one or two operations. Aluminum can be drawn deeper and with less annealing than the other commercial metals, provided the proper grade is used. If it is necessary to anneal aluminum, it should be heated in a muffle furnace, care being taken to see that the temperature does not exceed 700 degrees F. Drawing Brass.—When drawing brass shells or cup-shaped articles, it is usually possible to make the depth of the first draw equal to the diameter of the shell. By heating brass to a temperature just below what would show a dull red in a dark room, it is possible to draw difficult shapes, otherwise almost impossible, and to produce shapes with square corners. Drawing Rectangular Shapes.—When square or rectangular shapes are to be drawn, the radius of the corners should be as large as possible, because defects usually occur in the corners when drawing. Moreover, the smaller the radius, the less the depth that can be obtained in the first draw. The maximum depths that can be drawn with corners of a given radii are approximately as follows: With a radius of 3⁄32 to 3⁄16 inch, depth of draw, 1 inch; radius3⁄16 to 3⁄8 inch, depth 11⁄2 inches; radius3⁄8 to 1⁄2 inch, depth 2 inches; and radius1⁄2 to 3⁄4 inch, depth 3 inches. These figures are taken from actual practice and can doubtless be exceeded slightly when using metal prepared for the process. If the box needs to be quite deep and the radius is quite small, two or more drawing operations will be necessary. Speeds and Pressures for Presses.—The speeds for presses equipped with cutting dies depend largely upon the kind of material being worked, and its thickness. For punching


Machinery's Handbook 27th Edition PUNCHES, DIES, AND PRESS WORK

1331

and shearing ordinary metals not over 1⁄4 inch thick, the speeds usually range between 50 and 200 strokes per minute, 100 strokes per minute being a fair average. For punching metal over 1⁄4 inch thick, geared presses with speeds ranging from 25 to 75 strokes per minute are commonly employed. The cutting pressures required depend upon the shearing strength of the material, and the actual area of the surface being severed. For round holes, the pressure required equals the circumference of the hole × the thickness of the stock × the shearing strength. To allow for some excess pressure, the tensile strength may be substituted for the shearing strength; the tensile strength for these calculations may be roughly assumed as follows: Mild steel, 60,000; wrought iron, 50,000; bronze, 40,000; copper, 30,000; aluminum, 20,000; zinc, 10,000; and tin and lead, 5,000 pounds per square inch. Pressure Required for Punching.—The formula for the force in tons required to punch a circular hole in sheet steel is πDST/2000, where S = the shearing strength of the material in lb/in.2, T = thickness of the steel in inches, and 2000 is the number of lb in 1 ton. An approximate formula is DT × 80, where D and T are the diameter of the hole and the thickness of the steel, respectively, both in inches, and 80 is a factor for steel. The result is the force in tons. Example:Find the pressure required to punch a hole, 2 inches in diameter, through 1⁄4-in. thick steel. By applying the approximate formula, 2 × 1⁄4 × 80 = 40 tons. If the hole is not circular, replace the hole diameter with the value of one-third of the perimeter of the hole to be punched. Example:Find the pressure required to punch a 1-inch square hole in 1⁄4-in. thick steel. The total length of the hole perimeter is 4 in. and one-third of 4 in. is 11⁄3 in., so the force is 11⁄3 × 1⁄4 × 80 = 26 2⁄3 tons. The corresponding factor for punching holes in brass is 65 instead of 80. So, to punch a hole measuring 1 by 2 inches in 1⁄4-in. thick brass sheet, the factor for hole size is the perimeter length 6 ÷ 3 = 2, and the formula is 2 × 1⁄4 × 65 = 32 1⁄2 tons. Shut Height of Press.—The term “shut height,” as applied to power presses, indicates the die space when the slide is at the bottom of its stroke and the slide connection has been adjusted upward as far as possible. The “shut height” is the distance from the lower face of the slide, either to the top of the bed or to the top of the bolster plate, there being two methods of determining it; hence, this term should always be accompanied by a definition explaining its meaning. According to one press manufacturer, the safest plan is to define “shut height” as the distance from the top of the bolster to the bottom of the slide, with the stroke down and the adjustment up, because most dies are mounted on bolster plates of standard thickness, and a misunderstanding that results in providing too much die space is less serious than having insufficient die space. It is believed that the expression “shut height” was applied first to dies rather than to presses, the shut height of a die being the distance from the bottom of the lower section to the top of the upper section or punch, excluding the shank, and measured when the punch is in the lowest working position. Diameters of Shell Blanks.—The diameters of blanks for drawing plain cylindrical shells can be obtained from Table 1 on the following pages, which gives a very close approximation for thin stock. The blank diameters given in this table are for sharp-cornered shells and are found by the following formula in which D = diameter of flat blank; d = diameter of finished shell; and h = height of finished shell. D =

2

d + 4dh

(1)

Example:If the diameter of the finished shell is to be 1.5 inches, and the height, 2 inches, the trial diameter of the blank would be found as follows:



PUNCHES, DIES, AND PRESS WORK D =

2

1.5 + 4 × 1.5 × 2 =

14.25 = 3.78 inches

For a round-cornered cup, the following formula, in which r equals the radius of the corner, will give fairly accurate diameters, provided the radius does not exceed, say, 1⁄4 the height of the shell: D =

2

d + 4dh – r

(2)

These formulas are based on the assumption that the thickness of the drawn shell is the same as the original thickness of the stock, and that the blank is so proportioned that its area will equal the area of the drawn shell. This method of calculating the blank diameter is quite accurate for thin material, when there is only a slight reduction in the thickness of the metal incident to drawing; but when heavy stock is drawn and the thickness of the finished shell is much less than the original thickness of the stock, the blank diameter obtained from Formula (1) or (2) will be too large, because when the stock is drawn thinner, there is an increase in area. When an appreciable reduction in thickness is to be made, the blank diameter can be obtained by first determining the “mean height” of the drawn shell by the following formula. This formula is only approximately correct, but will give results sufficiently accurate for most work: htM = ---T

(3)

where M = approximate mean height of drawn shell; h = height of drawn shell; t = thickness of shell; and T = thickness of metal before drawing. After determining the mean height, the blank diameter for the required shell diameter is obtained from the table previously referred to, the mean height being used instead of the actual height. Example:Suppose a shell 2 inches in diameter and 3 3⁄4 inches high is to be drawn, and that the original thickness of the stock is 0.050 inch, and the thickness of drawn shell, 0.040 inch. To what diameter should the blank be cut? Obtain the mean height from Formula (3) : × 0.040- = 3 inches M = ht ----- = 3.75 ----------------------------T 0.050 According to the table, the blank diameter for a shell 2 inches in diameter and 3 inches high is 5.29 inches. Formula (3) is accurate enough for all practical purposes, unless the reduction in the thickness of the metal is greater than about one-fifth the original thickness. When there is considerable reduction, a blank calculated by this formula produces a shell that is too long. However, the error is in the right direction, as the edges of drawn shells are ordinarily trimmed. If the shell has a rounded corner, the radius of the corner should be deducted from the figures given in the table. For example, if the shell referred to in the foregoing example had a corner of 1⁄4-inch radius, the blank diameter would equal 5.29 − 0.25 = 5.04 inches. Another formula that is sometimes used for obtaining blank diameters for shells, when there is a reduction in the thickness of the stock, is as follows: D =

2 2 2 a + ( a – b ) h--t


(4)


Table 1. Diameters of Blanks for Drawn Cylindrical Shells Height of Shell

Diam. of Shell

1⁄ 4

1⁄ 2

3⁄ 4

1

1 1⁄4

1 1⁄2

1 3⁄4

2

2 1⁄4

2 1⁄2

2 3⁄4

3 1⁄4

3 1⁄2

3 3⁄4

1⁄ 4

0.56

0.75

0.90

1.03

1.14

1.25

1.35

1.44

1.52

1.60

1.68

1.75

1.82

1.89

1.95

2.01

2.14

2.25

2.36

2.46

1⁄ 2

0.87

1.12

1.32

1.50

1.66

1.80

1.94

2.06

2.18

2.29

2.40

2.50

2.60

2.69

2.78

2.87

3.04

3.21

3.36

3.50

3⁄ 4

1.14

1.44

1.68

1.89

2.08

2.25

2.41

2.56

2.70

2.84

2.97

3.09

3.21

3.33

3.44

3.54

3.75

3.95

4.13

4.31

1

1.41

1.73

2.00

2.24

2.45

2.65

2.83

3.00

3.16

3.32

3.46

3.61

3.74

3.87

4.00

4.12

4.36

4.58

4.80

5.00

1 1⁄4

1.68

2.01

2.30

2.56

2.79

3.01

3.21

3.40

3.58

3.75

3.91

4.07

4.22

4.37

4.51

4.64

4.91

5.15

5.39

5.62

1 1⁄2

1.94

2.29

2.60

2.87

3.12

3.36

3.57

3.78

3.97

4.15

4.33

4.50

4.66

4.82

4.98

5.12

5.41

5.68

5.94

6.18

1 3⁄4

2.19

2.56

2.88

3.17

3.44

3.68

3.91

4.13

4.34

4.53

4.72

4.91

5.08

5.26

5.41

5.58

5.88

6.17

6.45

6.71

2

2.45

2.83

3.16

3.46

3.74

4.00

4.24

4.47

4.69

4.90

5.10

5.29

5.48

5.66

5.83

6.00

6.32

6.63

6.93

7.21

2 1⁄4

2.70

3.09

3.44

3.75

4.04

4.31

4.56

4.80

5.03

5.25

5.46

5.66

5.86

6.05

6.23

6.41

6.75

7.07

7.39

7.69

2 1⁄2

2.96

3.36

3.71

4.03

4.33

4.61

4.87

5.12

5.36

5.59

5.81

6.02

6.22

6.42

6.61

6.80

7.16

7.50

7.82

8.14

2 3⁄4

3.21

3.61

3.98

4.31

4.62

4.91

5.18

5.44

5.68

5.92

6.15

6.37

6.58

6.79

6.99

7.18

7.55

7.91

8.25

8.58

3

3.46

3.87

4.24

4.58

4.90

5.20

5.48

5.74

6.00

6.25

6.48

6.71

6.93

7.14

7.35

7.55

7.94

8.31

8.66

9.00

3 1⁄4

3.71

4.13

4.51

4.85

5.18

5.48

5.77

6.04

6.31

6.56

6.80

7.04

7.27

7.49

7.70

7.91

8.31

8.69

9.06

9.41

3 1⁄2

3.97

4.39

4.77

5.12

5.45

5.77

6.06

6.34

6.61

6.87

7.12

7.36

7.60

7.83

8.05

8.26

8.67

9.07

9.45

9.81

3 3⁄4

4.22

4.64

5.03

5.39

5.73

6.05

6.35

6.64

6.91

7.18

7.44

7.69

7.92

8.16

8.38

8.61

9.03

9.44

9.83

10.20

3

4

4 1⁄2

5

5 1⁄2

6

4.47

4.90

5.29

5.66

6.00

6.32

6.63

6.93

7.21

7.48

7.75

8.00

8.25

8.49

8.72

8.94

9.38

9.80

10.20

10.58

4 1⁄4

4.72

5.15

5.55

5.92

6.27

6.60

6.91

7.22

7.50

7.78

8.05

8.31

8.56

8.81

9.04

9.28

9.72

10.15

10.56

10.96 11.32

4.98

5.41

5.81

6.19

6.54

6.87

7.19

7.50

7.79

8.08

8.35

8.62

8.87

9.12

9.37

9.60

10.06

10.50

10.92

5.22

5.66

6.07

6.45

6.80

7.15

7.47

7.78

8.08

8.37

8.65

8.92

9.18

9.44

9.69

9.93

10.40

10.84

11.27

11.69

5

5.48

5.92

6.32

6.71

7.07

7.42

7.75

8.06

8.37

8.66

8.94

9.22

9.49

9.75

10.00

10.25

10.72

11.18

11.62

12.04

5 1⁄4

5.73

6.17

6.58

6.97

7.33

7.68

8.02

8.34

8.65

8.95

9.24

9.52

9.79

10.05

10.31

10.56

11.05

11.51

11.96

12.39

5 1⁄2

5.98

6.42

6.84

7.23

7.60

7.95

8.29

8.62

8.93

9.23

9.53

9.81

10.08

10.36

10.62

10.87

11.37

11.84

12.30

12.74

5 3⁄4

6.23

6.68

7.09

7.49

7.86

8.22

8.56

8.89

9.21

9.52

9.81

10.10

10.38

10.66

10.92

11.18

11.69

12.17

12.63

13.08

6

6.48

6.93

7.35

7.75

8.12

8.49

8.83

9.17

9.49

9.80

10.10

10.39

10.68

10.95

11.23

11.49

12.00

12.49

12.96

13.42


1333

4 1⁄2 4 3⁄4


4



In this formula, D = blank diameter; a = outside diameter; b = inside diameter; t = thickness of shell at bottom; and h = depth of shell. This formula is based on the volume of the metal in the drawn shell. It is assumed that the shells are cylindrical, and no allowance is made for a rounded corner at the bottom, or for trimming the shell after drawing. To allow for trimming, add the required amount to depth h. When a shell is of irregular cross-section, if its weight is known, the blank diameter can be determined by the following formula: WD = 1.1284 ----(5) wt where D = blank diameter in inches; W = weight of shell; w = weight of metal per cubic inch; and t = thickness of the shell. In the construction of dies for producing shells, especially of irregular form, a common method to be used is to make the drawing tool first. The actual blank diameter then can be determined by trial. One method is to cut a trial blank as near to size and shape as can be estimated. The outline of this blank is then scribed on a flat sheet, after which the blank is drawn. If the finished shell shows that the blank is not of the right diameter or shape, a new trial blank is cut either larger or smaller than the size indicated by the line previously scribed, this line acting as a guide. If a model shell is available, the blank diameter can also be determined as follows: First, cut a blank somewhat large, and from the same material used for making the model; then, reduce the size of the blank until its weight equals the weight of the model. Depth and Diameter Reductions of Drawn Cylindrical Shells.—The depth to which metal can be drawn in one operation depends upon the quality and kind of material, its thickness, the slant or angle of the dies, and the amount that the stock is thinned or “ironed” in drawing. A general rule for determining the depth to which cylindrical shells can be drawn in one operation is as follows: The depth or length of the first draw should never be greater than the diameter of the shell. If the shell is to have a flange at the top, it may not be practicable to draw as deeply as is indicated by this rule, unless the metal is extra good, because the stock is subjected to a higher tensile stress, owing to the larger blank needed to form the flange. According to another rule, the depth given the shell on the first draw should equal one-third the diameter of the blank. Ordinarily, it is possible to draw sheet steel of any thickness up to 1⁄4 inch, so that the diameter of the first shell equals about sixtenths of the blank diameter. When drawing plain shells, the amount that the diameter is reduced for each draw must be governed by the quality of the metal and its susceptibility to drawing. The reduction for various thicknesses of metal is about as follows: Approximate thickness of sheet steel

1⁄ 16

1⁄ 8

3⁄ 16

1⁄ 4

5⁄ 16

Possible reduction in diameter for each succeeding step, per cent

20

15

12

10

8

For example, if a shell made of 1⁄16-inch stock is 3 inches in diameter after the first draw, it can be reduced 20 per cent on the next draw, and so on until the required diameter is obtained. These figures are based upon the assumption that the shell is annealed after the first drawing operation, and at least between every two of the following operations. Necking operations—that is, the drawing out of a short portion of the lower part of the cup into a long neck—may be done without such frequent annealings. In double-action presses, where the inside of the cup is supported by a bushing during drawing, the reductions possible may be increased to 30, 24, 18, 15, and 12 per cent, respectively. (The latter figures may also be used for brass in single-action presses.) When a hole is to be pierced at the bottom of a cup and the remaining metal is to be drawn after the hole has been pierced or punched, always pierce from the opposite direction to



1335

that in which the stock is to be drawn after piercing. It may be necessary to machine the metal around the pierced hole to prevent the starting of cracks or flaws in the subsequent drawing operations. The foregoing figures represent conservative practice and it is often possible to make greater reductions than are indicated by these figures, especially when using a good drawing metal. Taper shells require smaller reductions than cylindrical shells, because the metal tends to wrinkle if the shell to be drawn is much larger than the punch. The amount that the stock is “ironed” or thinned out while being drawn must also be considered, because a reduction in gage or thickness means greater force will be exerted by the punch against the bottom of the shell; hence the amount that the shell diameter is reduced for each drawing operation must be smaller when much ironing is necessary. The extent to which a shell can be ironed in one drawing operation ranges between 0.002 and 0.004 inch per side, and should not exceed 0.001 inch on the final draw, if a good finish is required. Allowances for Bending Sheet Metal.—In bending steel, brass, bronze, or other metals, the problem is to find the length of straight stock required for each bend; these lengths are added to the lengths of the straight sections to obtain the total length of the material before bending. If L = length in inches, of straight stock required before bending; T = thickness in inches; and R = inside radius of bend in inches: For 90° bends in soft brass and soft copper see Table 2 or: L = ( 0.55 × T ) + ( 1.57 × R ) (1) For 90° bends in half-hard copper and brass, soft steel, and aluminum see Table 3 or: L = ( 0.64 × T ) + ( 1.57 × R ) (2) For 90° bends in bronze, hard copper, cold-rolled steel, and spring steel see Table 4 or: L = ( 0.71 × T ) + ( 1.57 × R ) (3) Angle of Bend Other Than 90 Degrees: For angles other than 90 degrees, find length L, using tables or formulas, and multiply L by angle of bend, in degrees, divided by 90 to find length of stock before bending. In using this rule, note that angle of bend is the angle through which the material has actually been bent; hence, it is not always the angle as given on a drawing. To illustrate, in Fig. 1, the angle on the drawing is 60 degrees, but the angle of bend A is 120 degrees (180 − 60 = 120); in Fig. 2, the angle of bend A is 60 degrees; in Fig. 3, angle A is 90 − 30 = 60 degrees. Formulas (1), (2), and (3) are based on extensive experiments of the Westinghouse Electric Co. They apply to parts bent with simple tools or on the bench, where limits of ± 1⁄64 inch are specified. If a part has two or more bends of the same radius, it is, of course, only necessary to obtain the length required for one of the bends and then multiply by the number of bends, to obtain the total allowance for the bent sections.

Fig. 1.

Fig. 2.

Fig. 3.

Example, Showing Application of Formulas:Find the length before bending of the part illustrated by Fig. 4. Soft steel is to be used. For bend at left-hand end (180-degree bend) L = [ ( 0.64 × 0.125 ) + ( 1.57 × 0.375 ) ] × 180 --------- = 1.338 90



1336

Table 2. Lengths of Straight Stock Required for 90-Degree Bends in Soft Copper and Soft Brass Radius R of Bend, Inches

Thickness T of Material, Inch 1⁄ 32

3⁄ 64

1⁄ 16

5⁄ 64

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

1⁄ 32

0.058

0.066

0.075

0.083

0.092

0.101

0.118

0.135

0.152

0.169

0.187

0.204

0.221

3⁄ 64

0.083

0.091

0.100

0.108

0.117

0.126

0.143

0.160

0.177

0.194

0.212

0.229

0.246

1⁄ 16

0.107

0.115

0.124

0.132

0.141

0.150

0.167

0.184

0.201

0.218

0.236

0.253

0.270

3⁄ 32

0.156

0.164

0.173

0.181

0.190

0.199

0.216

0.233

0.250

0.267

0.285

0.302

0.319

1⁄ 8

0.205

0.213

0.222

0.230

0.239

0.248

0.265

0.282

0.299

0.316

0.334

0.351

0.368

5⁄ 32

0.254

0.262

0.271

0.279

0.288

0.297

0.314

0.331

0.348

0.365

0.383

0.400

0.417

3⁄ 16

0.303

0.311

0.320

0.328

0.337

0.346

0.363

0.380

0.397

0.414

0.432

0.449

0.466

7⁄ 32

0.353

0.361

0.370

0.378

0.387

0.396

0.413

0.430

0.447

0.464

0.482

0.499

0.516

1⁄ 4

0.401

0.409

0.418

0.426

0.435

0.444

0.461

0.478

0.495

0.512

0.530

0.547

0.564

9⁄ 32

0.450

0.458

0.467

0.475

0.484

0.493

0.510

0.527

0.544

0.561

0.579

0.596

0.613

5⁄ 16

0.499

0.507

0.516

0.524

0.533

0.542

0.559

0.576

0.593

0.610

0.628

0.645

0.662

11⁄ 32

0.549

0.557

0.566

0.574

0.583

0.592

0.609

0.626

0.643

0.660

0.678

0.695

0.712

3⁄ 8

0.598

0.606

0.615

0.623

0.632

0.641

0.658

0.675

0.692

0.709

0.727

0.744

0.761

13⁄ 32

0.646

0.654

0.663

0.671

0.680

0.689

0.706

0.723

0.740

0.757

0.775

0.792

0.809

7⁄ 16

0.695

0.703

0.712

0.720

0.729

0.738

0.755

0.772

0.789

0.806

0.824

0.841

0.858

15⁄ 32

0.734

0.742

0.751

0.759

0.768

0.777

0.794

0.811

0.828

0.845

0.863

0.880

0.897

1⁄ 2

0.794

0.802

0.811

0.819

0.828

0.837

0.854

0.871

0.888

0.905

0.923

0.940

0.957

9⁄ 16

0.892

0.900

0.909

0.917

0.926

0.935

0.952

0.969

0.986

1.003

1.021

1.038

1.055

5⁄ 8

0.990

0.998

1.007

1.015

1.024

1.033

1.050

1.067

1.084

1.101

1.119

1.136

1.153

11⁄ 16

1.089

1.097

1.106

1.114

1.123

1.132

1.149

1.166

1.183

1.200

1.218

1.235

1.252

3⁄ 4

1.187

1.195

1.204

1.212

1.221

1.230

1.247

1.264

1.281

1.298

1.316

1.333

1.350

13⁄ 16

1.286

1.294

1.303

1.311

1.320

1.329

1.346

1.363

1.380

1.397

1.415

1.432

1.449

7⁄ 8

1.384

1.392

1.401

1.409

1.418

1.427

1.444

1.461

1.478

1.495

1.513

1.530

1.547

15⁄ 16

1.481

1.489

1.498

1.506

1.515

1.524

1.541

1.558

1.575

1.592

1.610

1.627

1.644

1.580 1.678

1.588 1.686

1.597 1.695

1.605 1.703

1.614 1.712

1.623 1.721

1.640 1.738

1.657 1.755

1.674 1.772

1.691 1.789

1.709 1.807

1.726 1.824

1.743 1.841

1.777

1.785

1.794

1.802

1.811

1.820

1.837

1.854

1.871

1.888

1.906

1.923

1.940

1 3⁄16

1.875

1.883

1.892

1.900

1.909

1.918

1.935

1.952

1.969

1.986

2.004

2.021

2.038

1 1⁄4

1.972

1.980

1.989

1.997

2.006

2.015

2.032

2.049

2.066

2.083

2.101

2.118

2.135

1 1 1⁄16 1

1⁄ 8



1⁄ 64


Table 3. Lengths of Straight Stock Required for 90-Degree Bends in Half-Hard Brass and Sheet Copper, Soft Steel, and Aluminum Radius R of Bend, Inches


1⁄ 16

5⁄ 64

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

0.059

0.069

0.079

0.089

0.099

0.109

0.129

0.149

0.169

0.189

0.209

0.229

0.249

0.084

0.094

0.104

0.114

0.124

0.134

0.154

0.174

0.194

0.214

0.234

0.254

0.274

0.108

0.118

0.128

0.138

0.148

0.158

0.178

0.198

0.218

0.238

0.258

0.278

0.298

0.157

0.167

0.177

0.187

0.197

0.207

0.227

0.247

0.267

0.287

0.307

0.327

0.347

0.206

0.216

0.226

0.236

0.246

0.256

0.276

0.296

0.316

0.336

0.356

0.376

0.396

0.255

0.265

0.275

0.285

0.295

0.305

0.325

0.345

0.365

0.385

0.405

0.425

0.445

0.305

0.315

0.325

0.335

0.345

0.355

0.375

0.395

0.415

0.435

0.455

0.475

0.495

0.354

0.364

0.374

0.384

0.394

0.404

0.424

0.444

0.464

0.484

0.504

0.524

0.544

0.403

0.413

0.423

0.433

0.443

0.453

0.473

0.493

0.513

0.533

0.553

0.573

0.593

0.452

0.462

0.472

0.482

0.492

0.502

0.522

0.542

0.562

0.582

0.602

0.622

0.642

0.501

0.511

0.521

0.531

0.541

0.551

0.571

0.591

0.611

0.631

0.651

0.671

0.691

0.550

0.560

0.570

0.580

0.590

0.600

0.620

0.640

0.660

0.680

0.700

0.720

0.740

0.599

0.609

0.619

0.629

0.639

0.649

0.669

0.689

0.709

0.729

0.749

0.769

0.789

0.648

0.658

0.668

0.678

0.688

0.698

0.718

0.738

0.758

0.778

0.798

0.818

0.838

0.697

0.707

0.717

0.727

0.737

0.747

0.767

0.787

0.807

0.827

0.847

0.867

0.887

0.746

0.756

0.766

0.776

0.786

0.796

0.816

0.836

0.856

0.876

0.896

0.916

0.936

0.795

0.805

0.815

0.825

0.835

0.845

0.865

0.885

0.905

0.925

0.945

0.965

0.985

0.844

0.854

0.864

0.874

0.884

0.894

0.914

0.934

0.954

0.974

0.994

1.014

1.034

0.894

0.904

0.914

0.924

0.934

0.944

0.964

0.984

1.004

1.024

1.044

1.064

1.084

0.992

1.002

1.012

1.022

1.032

1.042

1.062

1.082

1.102

1.122

1.42

1.162

1.182

1.090

1.100

1.110

1.120

1.130

1.140

1.160

1.180

1.200

1.220

1.240

1.260

1.280

1.188

1.198

1.208

1.218

1.228

1.238

1.258

1.278

1.298

1.318

1.338

1.358

1.378

1.286

1.296

1.306

1.316

1.326

1.336

1.356

1.376

1.396

1.416

1.436

1.456

1.476

1.384

1.394

1.404

1.414

1.424

1.434

1.454

1.474

1.494

1.514

1.534

1.554

1.574

1.483

1.493

1.503

1.513

1.523

1.553

1.553

1.573

1.693

1.613

1.633

1.653

1.673

1 1 1⁄16

1.581 1.697

1.591 1.689

1.601 1.699

1.611 1.709

1.621 1.719

1.631 1.729

1.651 1.749

1.671 1.769

1.691 1.789

1.711 1.809

1.731 1.829

1.751 1.849

1.771 1.869

1 1⁄8

1.777

1.787

1.797

1.807

1.817

1.827

1.847

1.867

1.887

1.907

1.927

1.947

1.967

1 3⁄16

1.875

1.885

1.895

1.905

1.915

1.925

1.945

1.965

1.985

1.005

2.025

2.045

2.065

1 1⁄4

1.973

1.983

1.993

1.003

2.013

2.023

2.043

2.063

2.083

2.103

2.123

2.143

2.163

1⁄ 32 3⁄ 64 1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 17⁄ 32 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16


1337

1⁄ 32


1⁄ 64



3⁄ 64

1⁄ 16

5⁄ 64

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

1⁄ 32

0.060

0.071

0.082

0.093

0.104

0.116

0.138

0.160

0.182

0.204

0.227

0.249

0.271

3⁄ 64

0.085

0.096

0.107

0.118

0.129

0.141

0.163

0.185

0.207

0.229

0.252

0.274

0.296

1⁄ 16

0.109

0.120

0.131

0.142

0.153

0.165

0.187

0.209

0.231

0.253

0.276

0.298

0.320

3⁄ 32

0.158

0.169

0.180

0.191

0.202

0.214

0.236

0.258

0.280

0.302

0.325

0.347

0.369

1⁄ 8

0.207

0.218

0.229

0.240

0.251

0.263

0.285

0.307

0.329

0.351

0.374

0.396

0.418

5⁄ 32

0.256

0.267

0.278

0.289

0.300

0.312

0.334

0.356

0.378

0.400

0.423

0.445

0.467

3⁄ 16

0.305

0.316

0.327

0.338

0.349

0.361

0.383

0.405

0.427

0.449

0.472

0.494

0.516

7⁄ 32

0.355

0.366

0.377

0.388

0.399

0.411

0.433

0.455

0.477

0.499

0.522

0.544

0.566

1⁄ 4

0.403

0.414

0.425

0.436

0.447

0.459

0.481

0.503

0.525

0.547

0.570

0.592

0.614

9⁄ 32

0.452

0.463

0.474

0.485

0.496

0.508

0.530

0.552

0.574

0.596

0.619

0.641

0.663

5⁄ 16

0.501

0.512

0.523

0.534

0.545

0.557

0.579

0.601

0.623

0.645

0.668

0.690

0.712

11⁄ 32

0.551

0.562

0.573

0.584

0.595

0.607

0.629

0.651

0.673

0.695

0.718

0.740

0.762

3⁄ 8

0.600

0.611

0.622

0.633

0.644

0.656

0.678

0.700

0.722

0.744

0.767

0.789

0.811

13⁄ 32

0.648

0.659

0.670

0.681

0.692

0.704

0.726

0.748

0.770

0.792

0.815

0.837

0.859

7⁄ 16

0.697

0.708

0.719

0.730

0.741

0.753

0.775

0.797

0.819

0.841

0.864

0.886

0.908

15⁄ 32

0.736

0.747

0.758

0.769

0.780

0.792

0.814

0.836

0.858

0.880

0.903

0.925

0.947

1⁄ 2

0.796

0.807

0.818

0.829

0.840

0.852

0.874

0.896

0.918

0.940

0.963

0.985

1.007

9⁄ 16

0.894

0.905

0.916

0.927

0.938

0.950

0.972

0.994

1.016

1.038

1.061

1.083

1.105

5⁄ 8

0.992

1.003

1.014

1.025

1.036

1.048

1.070

1.092

1.114

1.136

1.159

1.181

1.203

11⁄ 16

1.091

1.102

1.113

1.124

1.135

1.147

1.169

1.191

1.213

1.235

1.258

1.280

1.302

3⁄ 4

1.189

1.200

1.211

1.222

1.233

1.245

1.267

1.289

1.311

1.333

1.356

1.378

1.400

13⁄ 16

1.288

1.299

1.310

1.321

1.332

1.344

1.366

1.388

1.410

1.432

1.455

1.477

1.499

7⁄ 8

1.386

1.397

1.408

1.419

1.430

1.442

1.464

1.486

1.508

1.530

1.553

1.575

1.597

15⁄ 16

1.483

1.494

1.505

1.516

1.527

1.539

1.561

1.583

1.605

1.627

1.650

1.672

1.694

1.582 1.680

1.593 1.691

1.604 1.702

1.615 1.713

1.626 1.724

1.638 1.736

1.660 1.758

1.682 1.780

1.704 1.802

1.726 1.824

1.749 1.847

1.771 1.869

1.793 1.891

1.779

1.790

1.801

1.812

1.823

1.835

1.857

1.879

1.901

1.923

1.946

1.968

1.990

1 3⁄16

1.877

1.888

1.899

1.910

1.921

1.933

1.955

1.977

1.999

2.021

2.044

2.066

2.088

1 1⁄4

1.974

1.985

1.996

2.007

2.018

2.030

2.052

2.074

2.096

2.118

2.141

2.163

2.185

1 1 1⁄16 1

1⁄ 8



1⁄ 64

1338

Table 4. Lengths of Straight Stock Required for 90-Degree Bends in Hard Copper, Bronze, Cold-Rolled Steel, and Spring Steel Radius R of Bend, Inches


1339

For bend at right-hand end (60-degree bend) L = [ ( 0.64 × 0.125 ) + ( 1.57 × 0.625 ) ] × 60 ------ = 0.707 90 Total length before bending = 3.5 + 1.338 + 0.707 = 5.545 inches

Fig. 4.

Fig. 5.

Other Bending Allowance Formulas.—When bending sheet steel or brass, add from 1⁄3 to 1⁄2 of the thickness of the stock, for each bend, to the sum of the inside dimensions of the finished piece, to get the length of the straight blank. The harder the material the greater the allowance (1⁄3 of the thickness is added for soft stock and 1⁄2 of the thickness for hard material). The data given in the table, Allowances for Bends in Sheet Metal on page 1340, refer more particularly to the bending of sheet metal for counters, bank fittings and general office fixtures, for which purpose it is not absolutely essential to have the sections of the bends within very close limits. Absolutely accurate data for this work cannot be deduced, as the stock varies considerably as to hardness, etc. The figures given apply to sheet steel, aluminum, brass and bronze. Experience has demonstrated that for the semisquare corners, such as are formed in a V-die, the amount to be deducted from the sum of the outside bend dimensions, as shown in Fig. 5 by the sum of the letters from a to e, is as follows: X = 1.67 BG, where X = the amount to be deducted; B = the number of bends; and G = the decimal equivalent of the gage. The values of X for different gages and numbers of bends are given in the table. Its application may be illustrated by an example: A strip having two bends is to have outside dimensions of 2, 11⁄2 and 2 inches, and is made of stock 0.125 inch thick. The sum of the outside dimensions is thus 51⁄2 inches, and from the table the amount to be deducted is found to be 0.416; hence the blank will be 5.5 − 0.416 = 5.084 inches long. The lower part of the table applies to square bends which are either drawn through a block of steel made to the required shape, or else drawn through rollers in a drawbench. The pressure applied not only gives a much sharper corner, but it also elongates the material more than in the V-die process. In this case, the deduction is X = 1.33 BG. Joining and Edging A duct system is an assembly whose main function is to convey air. Elements of the duct system are sheets, transverse joints, longitudinal seams, and reinforcements.The sheets must be able to withstand deflection caused by both internal pressure and vibration due to turbulent air flow. Transverse joints must be able to withstand 1.5 times the maximum operating pressure without failure. Transverse joint designs should be consistent with the static pressure class, sealing requirements, materials involved, and support interval distances. Notching, bending, folding, and fit up tolerances shall be appropriate for the proper class. Longitudinial seams also must be able to withstand 1.5 times the operating pressure without deformation. Seams shall be formed and assembled with proper dimension and proportion for tight and secure fit up. Seams may be a butt, corner, plug, or spot weld design. Seams shall be selected based on material and pressure. A duct section between adjacent hangers must be able to carry its own weight and to resist external loads for which



PUNCHES, DIES, AND PRESS WORK Allowances for Bends in Sheet Metal

Formed in a Press by a V-die

Rolled or Drawn in a Draw-bench

Amount to be Deducted from the Sum of the Outside Bend Dimensions, Inches

Gage

Thick ness Inches

Square Bends

1 Bend

18 16 14 13 12 11 10 18 16 14 13 12 11 10

0.0500 0.0625 0.0781 0.0937 0.1093 0.1250 0.1406 0.0500 0.0625 0.0781 0.0937 0.1093 0.1250 0.1406

0.083 0.104 0.130 0.156 0.182 0.208 0.234 0.066 0.083 0.104 0.125 0.145 0.166 0.187

2 Bends

3 Bends

4 Bends

5 Bends

6 Bends

7 Bends

0.166 0.208 0.260 0.312 0.364 0.416 0.468 0.133 0.166 0.208 0.250 0.291 0.333 0.375

0.250 0.312 0.390 0.468 0.546 0.625 0.703 0.200 0.250 0.312 0.375 0.437 0.500 0.562

0.333 0.416 0.520 0.625 0.729 0.833 0.937 0.266 0.333 0.416 0.500 0.583 0.666 0.750

0.416 0.520 0.651 0.781 0.911 1.041 1.171 0.333 0.416 0.521 0.625 0.729 0.833 0.937

0.500 0.625 0.781 0.937 1.093 1.250 1.406 0.400 0.500 0.625 0.750 0.875 1.000 1.125

0.583 0.729 0.911 1.093 1.276 1.458 1.643 0.466 0.583 0.729 0.875 1.020 1.166 1.312

it is constructed. The reinforcing members must be able to resist the deflection of the sheet, and its own deflection. There is a relationship between duct width, reinforcement spacing, reinforcement size, pressure, and sheet thickness. For constant pressure and constant duct size, the thicker sheet allows more distance between reinforcements. The higher the pressure the shorter the spacing between reinforcements. Joints and intermediate reinforcements are labor intensive and may be more costly than the savings gained by a reduction in wall thickness. Thicker duct wall and stronger joints are more cost effective than using more reinforcement. The following material illustrates various joint designs, used both in duct work and other sheet metal asseblies. Sheet Metal Joints Plain Lap and Flush Lap:

Fig. 6. Plain Lap

The plain lap (Fig. 6 ) and flush lap (Fig. 7 ) are both used for various materials such as galvanized or black iron, copper, stainless steel, aluminum, or other metals, and may be soldered, and/or riveted, as well as spot, tack, or solid-welded. Lap dimensions vary with the particular application, and since it is the duty of the draftsman to specify straight joints in lengths that use full-sheet sizes, transverse lap dimensions must be known.

Fig. 7. Flush Lap

Raw and Flange Corner: The raw and flange corner (Fig. 8) is generally spot-welded, but may be riveted or soldered. For heavy gages it is tack-welded or solid-welded. Fig. 8. Raw and Flange Corner



1341

Flange and Flange Corner: The flange and flange corner (Fig. 9) is a refinement of the raw and flange corner. It is particularly useful for heavy-gage duct sections which require flush outside corners and must be fielderected. Fig. 9. Flange and Flange Corner

Standing Seam:

Fig. 10. Standing Seam

The standing seam (Fig. 10) is often used for large plenums, or casings. Before the draftsman is able to lay out a casing drawing, one of the items of information needed is seam allowance measurements, so that panel sizes can be detailed for economical use of standard sheets. Considering velocity levels, standing seams are considered for duct interiors: 1″ seam is normally applied for duct widths up to 42″, and 11⁄2″ for bigger ducts.

Groove Seam:

Fig. 11. Groove Seam

The groove seam (Fig. 11) is often used for rectangular or round duct straight joints, or to join some sheets for fittings that are too large to be cut out from standard sheets. It is also known as the pipelock, or flat lock seam.

Corner Standing Seam: The corner standing seam (Fig. 12) has similar usage to the standing seam, and also can be used for straight-duct sections. This type of seams are mostly applied at the ends at 8″ intervals. Fig. 12. Corner Standing Seam

Double Seam:

Fig. 13. Double Corner Seam

The double corner seam (Fig. 13) at one time was the most commonly used method for duct fitting fabrication. However, although it is seldom used because of the hand operations required for assembly, the double seam can be used advantageously for duct fittings with compound curves. It is called the slide lock seam. Machines are available to automatically close this seam.

Slide-Corner:

Fig. 14. Slide Corner

The slide-corner (Fig. 14) is a large version of the double seam. It is often used for field assembly of straight joints, such as in an existing ceiling space, or other restricted working area where ducts must be built in place. To assemble the duct segments, opposite ends of each seam are merely “entered” and then pushed into position. Ducts are sent to job sites “knocked-down” for more efficient use of shipping space.

Button Punch Snap Lock:

Fig. 15. Button Punch Snap Lock

The button punch snap lock (Fig. 15) is a flush-type seam which may be soldered or caulked. This seam can be modified slightly for use as a “snap lock”. This types of seam is not applicable for aluminum or other soft metals. This seam may be used up to 4″ w.g. by using screws at the ends. The pocket depth should not be smaller than 5⁄8″ for 20, 22 and 26 gage.




Pittsburg:

The Pittsburg (Fig. 16) is the most commonly used seam for standard gage duct construction. The common pocket depths are 5⁄16″ and 5⁄8″ depending on the thickness of sheet. Fig. 16. Pittsburgh

Flange: The flange (Fig. 17) is an end edge stiffener. The draftsman must indicate size of the flange, direction of bend, degree of bend (if other than 90°) and when full corners are desired. Full corners are generally advisable for collar connections to concrete or masonry wall openings at louvers. Fig. 17. Flange

Hem: The hem edge (Fig. 18) is a flat, finished edge. As with the flange, this must be designated by the draftsman. For example, drawing should show: 3⁄4″ hem out.

Fig. 18. Hem

Flat Drive Slip:

Fig. 19. Drive Slip

This is one of the simplest transverse joints. It is applicable where pressure is less than 2″ w.g. This is a slide type connection generally used on small ducts in combination of “S” slips. Service above 2″ inches w.g. is not applicable.

Standing Drive Slip: H

This is also a slide type connection. It is made by elongating flat drive slip, fasten standing portions 2″ from each end. It is applicable for any length in 2″ w.g, 36″ for 3″ inch w.g., and 30″ inches at 4″ w.g. service.

Fig. 20. Standing Drive Slip

Flat Drive Slip Reinforced: This is the reinforcement on flat drive slip by adding a transverse angle section after a fixed interval. Fig. 21. Drive Slip Reinforced

Double “S” Slip Reinforced:

Fig. 22. Double “S” Slip

The double “S” slip is applied, to eliminate the problem of notching and bending, especially for large ducts. Apply 24 gage sheet for 30″ width or less, 22 gage sheet over 30″ width.

Flat “S” Slip:

Fig. 23. Plain “S” Slip

Normally the “S” slip is used for small ducts. However, it is also useful if the connection of a large duct is tight to a beam, column or other object, and an “S” slip is substituted for the shop standard slip. Service above 2″ inches w.g. is not applicable. Gage shall not be less than 24, and shall not 2 gage less than the duct gage. When it is applied on all four edges, fasten within 2″ of the corners and at 12″ maximum interval.



1343

Hemmed “S” Slip:

Fig. 24. Hemmed “S” Slip

This is the modified “S” slip, by adding hem and an angle for reinforcing. The hem edge is a flat, and finished edge. Hemmed “S” slip is mostly applied with angle. The drive is generally 16 gage, formed a 1 inch height slip pocket and screws at the end. Notching and bending operations on an “S” slip joints can be cumbersome and costly, especially for large sizes. Tied each section of the duct within 2″ from the corner at maximum 6-inch interval.

Other Types of Duct Connections Clinch-bar Slip and Flange:

Fig. 25. Clinch-bar Slip and Flange

The clinch-bar slip and flange (Fig. 25), uses the principle of the standing seam, but with a duct lap in the direction of airflow. These slips are generally assembled as a framed unit with full corners either riveted or spot-welded, which adds to the duct cross-section rigidity. Reinforcement may be accomplished by spot welding the flat-bar to the flange of the large end. Accessibility to all four sides of the duct is required because the flange of the slip must be folded over the flange on the large end after the ducts are connected.

Clinch-bar Slip and Angle :

Fig. 26. Clinch-bar Slip and Angle

The clinch bar slip and angle (Fig. 26), is similar to clinch bar slip (Fig. 25), but it has a riveted or spot-welded angle on the large end. This connection can also have a raw large end which is inserted into the space between the angle and the shop-fabricated slip. Matched angles (minimum of 16 ga) are riveted or spot welded to the smaller sides of the ducts, to pull the connection “home.”

Flanged Duct Connections Angle Frame, or Ring:

Fig. 27. Raw Ends and Matched ∠s

Any of the following flanged connections may have gaskets. The draftsman should not allow for gasket thicknesses in calculations for running length dimensions, nor should he indicate angle sizes, bolt centers, etc., as these items are established in job specifications and approved shop standards. Generally, angles are fastened to the duct sections in the shop. If conditions at the job site require consideration for length contingencies, the draftsman should specify “loose angles” such as at a connection to equipment which may be located later. The most common matched angle connection is the angle frame, or ring (Fig. 27). The angles are fastened flush to the end of the duct.

Flanged End and Angle:

Fig. 28. Flanged Ends and Matched ∠s

The flanged end and angle (Fig. 28), is often used for ducts 16 ga or lighter, as the flange provides a metal-to-metal gasket and holds the angle frame or ring on the duct without additional fastening. The draftsman may indicate in a field note that a round-duct fitting is to be ″rotated as required″.This type of angle-ring-connection is convenient for such a condition.

Formed Flanges:

Fig. 29. Formed Flanges

Double flanges (Fig. 29), are similar to Fig. 21, except that the connecting flange has a series of matched bolt holes. This connection, caulked airtight, is ideal for single-wall apparatus casings or plenums. The flanges are formed at the ends of the duct, after assembly they will form a T shape. Mating flanges shall be locked together by long clips. In order to form effective seal, gasket is used with suitable density and resiliency. At the corners 16 gage thickness steel corner are used with 3⁄8″ diameter bolts.



FINE BLANKING

Double Flanges and Cleat:

Double Flanges and Cleat (Fig. 30) is identical to (Fig. 29), but has an air seal cleat. The reinforcements is attached to the duct wall on both sides of the joint. Fig. 30. Double Flanges and Cleat

Clinch-type Flanged Connections:

Fig. 31. Bead Clinch and Z Rings

Clinch-type flanged connections for round ducts, 16 ga or lighter, are shown in Fig. 31. The angles or rings can be loose, as explained in Flanged End and Angle, (Fig. 28). The draftsman should indicate flange sizes, bend direction, and type of assembly. An example such as the flange lap for a field assembly of a 10-gage casing corner would be written: 1 1⁄2″ flange out square on side with 9⁄32″∅ bolt holes 12″ CC. At the beginning and ending angles are connected by rivets or welding. The bolt will be 5⁄16″ ∅ at 6″ maximum spacing 4″ w.g..

Fine Blanking The process called fine blanking uses special presses and tooling to produce flat components from sheet metal or plate, with high dimensional accuracy. According to Hydrel A. G., Romanshorn, Switzerland, fine-blanking presses can be powered hydraulically or mechanically, or by a combination of these methods, but they must have three separate and distinct movements. These movements serve to clamp the work material, to perform the blanking operation, and to eject the finished part from the tool. Forces of 1.5–2.5 times those used in conventional stamping are needed for fine blanking, so machines and tools must be designed and constructed accordingly. In mechanical fine-blanking presses the clamping and ejection forces are exerted hydraulically. Such presses generally are of toggle-type design and are limited to total forces of up to about 280 tons. Higher forces generally require all-hydraulic designs. These presses are also suited to embossing, coining, and impact extrusion work. Cutting elements of tooling for fine blanking generally are made from 12 per cent chromium steel, although high speed steel and tungsten carbide also are used for long runs or improved quality. Cutting clearances between the intermediate punch and die are usually held between 0.0001 and 0.0003 in. The clamping elements are sharp projections of 90degree V-section that follow the outline of the workpiece and that are incorporated into each tool as part of the stripper plate with thin material and also as part of the die plate when material thicker than 0.15 in. is to be blanked. Pressure applied to the elements containing the V-projections prior to the blanking operation causes the sharp edges to enter the material surface, preventing sideways movement of the blank. The pressure applied as the projections bite into the work surface near the contour edges also squeezes the material, causing it to flow toward the cutting edges, reducing the usual rounding effect at the cut edge. When small details such as gear teeth are to be produced, V-projections are often used on both sides of the work, even with thin materials, to enhance the flow effect. With suitable tooling, workpieces can be produced with edges that are perpendicular to top and bottom surfaces within 0.004 in. on thicknesses of 0.2 in., for instance. V-projection dimensions for various material thicknesses are shown in the table Dimensions for V-projections Used in Fine-Blanking Tools. Fine-blanked edges are free from the fractures that result from conventional tooling, and can have surface finishes down to 80 µin. Ra with suitable tooling. Close tolerances can be


Machinery's Handbook 27th Edition FINE BLANKING

1345

Dimensions for V-projections Used in Fine-Blanking Tools

V-Projections On Stripper Plate Only Material Thickness 0.040-0.063 0.063-0.098 0.098-0.125 0.125-0.157 0.157-0.197 0.157–0.197 0.197–0.248 0.248–0.315 0.315–0.394 0.394–0.492 0.492–0.630 All units are in inches.

V-Projections On Both Stripper and Die Plate

A h r V-Projections On Stripper Plate Only 0.040 0.012 0.008 0.055 0.015 0.008 0.083 0.024 0.012 0.098 0.028 0.012 0.110 0.032 0.012 V-Projections On Both Stripper and Die Plate 0.098 0.020 0.008 0.118 0.028 0.008 0.138 0.032 0.008 0.177 0.040 0.020 0.217 0.047 0.020 0.276 0.063 0.020

H

R

… … … … …

… … … … …

0.032 0.040 0.047 0.060 0.070 0.087

0.032 0.040 0.047 0.060 0.080 0.118

held on inner and outer forms, and on hole center distances. Flatness of fine-blanked components is better than that of parts made by conventional methods, but distortion may occur with thin materials due to release of internal stresses. Widths must be slightly greater than are required for conventional press working. Generally, the strip width must be 2–3 times the thickness, plus the width of the part measured transverse to the feed direction. Other factors to be considered are shape, material quality, size and shape of the V-projection in relation to the die outline, and spacing between adjacent blanked parts. Holes and slots can be produced with ratios of width to material thickness down to 0.7, compared with the 1:1 ratio normally specified for conventional tooling. Operations such as countersinking, coining, and bending up to 60 degrees can be incorporated in fine-blanking tooling. The cutting force in lb exerted in fine blanking is 0.9 times the length of the cut in inches times the material thickness in inches, times the tensile strength in lbf/in.2. Pressure in lb exerted by the clamping element(s) carrying the V-projections is calculated by multiplying the length of the V-projection, which depends on its shape, in inches by its height (h), times the material tensile strength in lbf/in.2, times an empirical factor f. Factor f has been determined to be 2.4–4.4 for a tensile strength of 28,000–113,000 lbf/in.2. The clamping pressure is approximately 30 per cent of the cutting force, calculated as above. Dimensions and positioning of the V-projection(s) are related to the material thickness, quality, and tensile strength. A small V-projection close to the line of cut has about the same effect as a large V-projection spaced away from the cut. However, if the V-projection is too close to the cut, it may move out of the material at the start of the cutting process, reducing its effectiveness.



STEEL RULE DIES

Positioning the V-projection at a distance from the line of cut increases both material and blanking force requirements. Location of the V-projection relative to the line of cut also affects tool life. Steel Rule Dies Steel rule dies (or knife dies) were patented by Robert Gair in 1879, and, as the name implies, have cutting edges made from steel strips of about the same proportions as the steel strips used in making graduated rules for measuring purposes. According to J. A. Richards, Sr., of the J. A. Richards Co., Kalamazoo, MI, a pioneer in the field, these dies were first used in the printing and shoemaking industries for cutting out shapes in paper, cardboard, leather, rubber, cork, felt, and similar soft materials. Steel rule dies were later adopted for cutting upholstery material for the automotive and other industries, and for cutting out simple to intricate shapes in sheet metal, including copper, brass, and aluminum. A typical steel rule die, partially cut away to show the construction, is shown in Fig. 1, and is designed for cutting a simple circular shape. Such dies generally cost 25 to 35 per cent of the cost of conventional blanking dies, and can be produced in much less time. The die shown also cuts a rectangular opening in the workpiece, and pierces four holes, all in one press stroke. Upper die shoe

Fool proofing pin locations

Male punch

Lignostone die block Steel rule with land for shearing Piercing punch

Fool proofing pin locations

Die strippers may be neoprene, spring ejector, or positive knock out

Parallels for slug clearance

Lower die plate

Lower die shoe

Subdie plate

Fig. 1. Steel Rule Die for Cutting a Circular Shape, Sectioned to Show the Construction

The die blocks that hold the steel strips on edge on the press platen or in the die set may be made from plaster, hot lead or type metal, or epoxy resin, all of which can be poured to shape. However, the material most widely used for light work is 3⁄4-in. thick, five- or sevenply maple or birch wood. Narrow slots are cut in this wood with a jig saw to hold the strips vertically. Where greater forces are involved, as with operations on metal sheets, the blocks usually are made from Lignostone densified wood or from metal. In the 3⁄4-in. thickness mostly used, medium- and high-density grades of Lignostone are available. The 3⁄4-in. thickness is made from about 35 plies of highly compressed lignite wood, bonded with


Machinery's Handbook 27th Edition STEEL RULE DIES

1347

phenolformaldehyde resin, which imparts great density and strength. The material is made in thicknesses up to 6 in., and in various widths and lengths. Steel rule die blocks can carry punches of various shapes to pierce holes in the stock, also projections designed to form strengthening ribs and other shapes in material such as aluminum, at the same time as the die cuts the component to shape. Several dies can be combined or nested, and operated together in a large press, to produce various shapes simultaneously from one sheet of material. As shown in Fig. 1, the die steel is held in the die block slot on its edge, usually against the flat platen of a die set attached to the moving slide of the press. The sharp, free end of the rule faces toward the workpiece, which is supported by the face of the other die half. This other die half may be flat or may have a punch attached to it, as shown, and it withstands the pressure exerted in the cutting or forming action when the press is operated. The closed height of the die is adjusted to permit the cutting edge to penetrate into the material to the extent needed, or, if there is a punch, to carry the cutting edges just past the punch edges for the cutting operation. After the sharp edge has penetrated it, the material often clings to the sides of the knife. Ejector inserts made from rubber, combinations of cork and rubber, and specially compounded plastics material, or purpose-made ejectors, either spring- or positively actuated, are installed in various positions alongside the steel rules and the punch. These ejectors are compressed as the dies close, and when the dies open, they expand, pushing the material clear of the knives or the punch. The cutting edges of the steel rules can be of several shapes, as shown in profile in Fig. 2, to suit the material to be cut, or the type of cutting operation. Shape A is used for shearing in the punch in making tools for blanking and piercing operations, the sharp edge later being modified to a flat, producing a 90° cutting edge, B. The other shapes in Fig. 2 are used for cutting various soft materials that are pressed against a flat surface for cutting. The shape at C is used for thin, and the shape at D for thicker materials.

;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;; ;;;;;;;; ;; A

B

C

D

Fig. 2. Cutting Edges for Steel Rule Dies

Steel rule die steel is supplied in lengths of 30 and 50 in., or in coils of any length, with the edges ground to the desired shape, and heat treated, ready for use. The rule material width is usually referred to as the height, and material can be obtained in heights of 0.95, 1, 11⁄8, 11⁄4, and 11⁄2 in. Rules are available in thicknesses of 0.055, 0.083, 0.11, 0.138, 0.166, and 0.25 in. (4 to 18 points in printers' measure of 72 points = 1 in.). Generally, stock thicknesses of 0.138 or 0.166 in. (10 and 12 points) are preferred, the thinner rules being used mainly for dies requiring intricate outlines. The stock can be obtained in soft or hard temper. The standard edge bevel is 46°, but bevels of 40 to 50° can be used. Thinner rule stock is easiest to form to shape and is often used for short runs of 50 pieces or thereabouts. The thickness and hardness of the material to be blanked also must be considered when choosing rule thickness. Making of Steel Rule Dies.—Die making begins with a drawing of the shape required. Saw cutting lines may be marked directly on the face of the die block in a conventional layout procedure using a height gage, or a paper drawing may be pasted to or drawn on the die



STEEL RULE DIES

board. Because paper stretches and shrinks, Mylar or other nonshrink plastics sheets may be preferred for the drawing. A hole is drilled off the line to allow a jig saw to be inserted, and jig saw or circular saw cuts are then made under manual control along the drawing lines to produce the slots for the rules. Jig saw blades are available in a range of sizes to suit various thicknesses of rule and for sawing medium-density Lignostone, a speed of 300 strokes/min is recommended, the saw having a stroke of about 2 in. To make sure the rule thickness to be used will be a tight fit in the slot, trials are usually carried out on scrap pieces of die block before cuts are made on a new block. During slot cutting, the saw blade must always be maintained vertical to the board being cut, and magnifying lenses are often used to keep the blade close to the line. Carbide or carbide-tipped saw blades are recommended for clean cuts as well as for long life. To keep any “islands” (such as the center of a circle) in position, various places in the sawn line are cut to less than full depth for lengths of 1⁄4 to 1⁄2 in., and to heights of 5⁄8 to 3⁄4 in. to bridge the gaps. Slots of suitable proportions must be provided in the steel rules, on the sides away from the cutting edges, to accommodate these die block bridges. Rules for steel rule dies are bent to shape to fit the contours called for on the drawing by means of small, purpose-built bending machines, fitted with suitable tooling. For bends of small radius, the tooling on these machines is arranged to perform a peening or hammering action to force the steel rule into close contact with the radius-forming component of the machine so that quite small radii, as required for jig saw puzzles, for instance, can be produced with good accuracy. Some forms are best made in two or more pieces, then joined by welding or brazing. The edges to be joined are mitered for a perfect fit, and are clamped securely in place for joining. Electrical resistance or a gas heating torch is used to heat the joint. Wet rags are applied to the steel at each side of the joint to keep the material cool and the hardness at the preset level, as long as possible. When shapes are to be blanked from sheet metal, the steel rule die is arranged with flat, 90° edges (B, in Fig. 2), which cut by pushing the work past a close-fitting counter-punch. This counterpunch, shown in Fig. 1, may be simply a pad of steel or other material, and has an outline corresponding to the shape of the part to be cut. Sometimes the pad may be given a gradual, slight reduction in height to provide a shearing action as the moving tool pushes the work material past the pad edges. As shown in Fig. 1, punches can be incorporated in the die to pierce holes, cut slots, or form ribs and other details during the blanking operation. These punches are preferably made from high-carbon, high-vanadium, alloy steel, heat treated to Rc 61 to 63, with the head end tempered to Rc 45 to 50. Heat treatment of the high-carbon-steel rules is designed to produce a hardness suited to the application. Rules in dies for cutting cartons and similar purposes, with mostly straight cuts, are hardened to Rc 51 to 58. For dies requiring many intricate bends, lower-carbon material is used, and is hardened to Rc 38 to 45. And for dies to cut very intricate shapes, a steel in dead-soft condition with hardness of about Rb 95 is recommended. After the intricate bends are made, this steel must be carburized before it is hardened and tempered. For this material, heat treatment uses an automatic cycle furnace, and consists of carburizing in a liquid compound heated to 1500°F and quenching in oil, followed by “tough” tempering at 550°F and cooling in the furnace. After the hardened rule has been reinstalled in the die block, the tool is loaded into the press and the sharp die is used with care to shear the sides of the pad to match the die contours exactly. A close fit, with clearances of about half those used in conventional blanking dies, is thus ensured between the steel rule and the punch. Adjustments to the clearances can be made at this point by grinding the die steel or the punch. After the adjustment work is done, the sharp edges of the rule steel are ground flat to produce a land of about 1⁄64 in. wide (A in Fig. 2), for the working edges of the die. Clearances for piercing punches should be similar to those used on conventional piercing dies.


Machinery's Handbook 27th Edition ELECTRICAL DISCHARGE MACHINING

1349

ELECTRICAL DISCHARGE MACHINING Generally called EDM, electrical discharge machining uses an electrode to remove metal from a workpiece by generating electric sparks between conducting surfaces. The two main types of EDM are termed sinker or plunge, used for making mold or die cavities, and wire, used to cut shapes such as are needed for stamping dies. For die sinking, the electrode usually is made from copper or graphite and is shaped as a positive replica of the shape to be formed on or in the workpiece. A typical EDM sinker machine, shown diagrammatically in Fig. 1, resembles a vertical milling machine, with the electrode attached to the vertical slide. The slide is moved down and up by an electronic, servo-controlled drive unit that controls the spacing between the electrode and the workpiece on the table. The table can be adjusted in three directions, often under numerical control, to positions that bring a workpiece surface to within 0.0005 to 0.030 in. from the electrode surface, where a spark is generated.

Fig. 1. Sinker or Plunge Type EDM Machines Are Used to Sink Cavities in Molds and Dies

Fig. 2. Wire Type EDM Machines Are Used to Cut Stamping Die Profiles.

Wire EDM, shown diagrammatically in Fig. 2, are numerically controlled and somewhat resemble a bandsaw with the saw blade replaced by a fine brass or copper wire, which forms the electrode. This wire is wound off one reel, passed through tensioning and guide rollers, then through the workpiece and through lower guide rollers before being wound onto another reel for storage and eventual recycling. One set of guide rollers, usually the lower, can be moved on two axes at 90 degrees apart under numerical control to adjust the angle of the wire when profiles of varying angles are to be produced. The table also is movable in two directions under numerical control to adjust the position of the workpiece relative to the wire. Provision must be made for the cut-out part to be supported when it is freed from the workpiece so that it does not pinch and break the wire. EDM applied to grinding machines is termed EDG. The process uses a graphite wheel as an electrode, and wheels can be up to 12 in. in diameter by 6 in. wide. The wheel periphery is dressed to the profile required on the workpiece and the wheel profile can then be transferred to the workpiece as it is traversed past the wheel, which rotates but does not touch the work. EDG machines are highly specialized and are mainly used for producing complex profiles on polycrystaline diamond cutting tools and for shaping carbide tooling such as form tools, thread chasers, dies, and crushing rolls. EDM Terms*.— Anode: The positive terminal of an electrolytic cell or battery. In EDM, incorrectly applied to the tool or electrode. * Source: Hansvedt Industries



ELECTRICAL DISCHARGE MACHINING

Barrel effect: In wire EDM, a condition where the center of the cut is wider than the entry and exit points of the wire, due to secondary discharges caused by particles being pushed to the center by flushing pressure from above and beneath the workpiece. Capacitor: An electrical component that stores an electric charge. In some EDM power supplies, several capacitors are connected across the machining gap and the current for the spark comes directly from the capacitors when they are discharged. Cathode: The negative terminal in an electrolytic cell or battery. In EDM incorrectly applied to the workpiece. Colloidal suspension: Particles suspended in a liquid that are too fine to settle out. In EDM, the tiny particles produced in the sparking action form a colloidal suspension in the dielectric fluid. Craters: Small cavities left on an EDM surface by the sparking action, also known as pits. Dielectric filter : A filter that removes particles from 5 µm (0.00020 in.) down to as fine as 1 µm (0.00004 in) in size, from dielectric fluid. Dielectric fluid : The non-conductive fluid that circulates between the electrode and the workpiece to provide the dielectric strength across which an arc can occur, to act as a coolant to solidify particles melted by the arc, and to flush away the solidified particles. Dielectric strength: In EDM, the electrical potential (voltage) needed to break down (ionize) the dielectric fluid in the gap between the electrode and the workpiece. Discharge channel: The conductive pathway formed by ionized dielectric and vapor between the electrode and the workpiece. Dither: A slight up and down movement of the machine ram and attached electrode, used to improve cutting stability. Duty cycle: The percentage of a pulse cycle during which the current is turned on (on time), relative to the total duration of the cycle. EDG: Electrical discharge grinding using a machine that resembles a surface grinder but has a wheel made from electrode material. Metal is removed by an EDM process rather than by grinding. Electrode growth: A plating action that occurs at certain low-power settings, whereby workpiece material builds up on the electrode, causing an increase in size. Electrode wear: Amount of material removed from the electrode during the EDM process. This removal can be end wear or corner wear, and is measured linearly or volumetrically but is most often expressed as end wear per cent, measured linearly. Electro-forming: An electro-plating process used to make metal EDM electrodes. Energy: Measured in joules, is the equivalent of volt-coulombs or volt-ampere- seconds. Farad: Unit of electrical capacitance, or the energy-storing capacity of a capacitor. Gap: The closest point between the electrode and the workpiece where an electrical discharge will occur. (See Overcut) Gap current: The average amperage flowing across the machining gap. Gap voltage: The voltage across the gap while current is flowing. The voltage across the electrode/workpiece before current flows is called the open gap voltage. Heat-affected zone. The layer below the recast layer, which has been subjected to elevated temperatures that have altered the properties of the workpiece metal. Ion: An atom or group of atoms that has lost or gained one or more electrons and is therefore carrying a positive or negative electrical charge, and is described as being ionized. Ionization: The change in the dielectric fluid that is subjected to a voltage potential whereby it becomes electrically conductive, allowing it to conduct the arc. Low-wear: An EDM process in which the volume of electrode wear is between 2 and 15 per cent of the volume of workpiece wear. Normal negative polarity wear ratios are 15 to 40 per cent. Negative electrode: The electrode voltage potential is negative relative to the workpiece. No-wear: An EDM process in which electrode wear is virtually eliminated and the wear ratio is usually less than 2 per cent by volume.



1351

Orbit: A programmable motion between the electrode and the workpiece, produced by a feature built in to the machine, or an accessory, that produces a cavity or hole larger than the electrode. The path can be planetary (circular), vectorial, or polygonal (trace). These motions can often be performed in sequence, and combined with x-axis movement of the electrode. Overcut: The distance between one side of an electrode and the adjacent wall of the workpiece cavity. Overcut taper: The difference between the overcut dimensions at the top (entrance) and at the bottom of the cavity. Plasma: A superheated, highly ionized gas that forms in the discharge channel due to the applied voltage. Positive electrode: The electrode voltage potential is positive with respect to the workpiece. is the opposite of this condition. Power parameters: A set of power supply, servo, electrode material, workpiece material, and flushing settings that are selected to produce a desired metal removal rate and surface finish. Quench: The rapid cooling of the EDM surface by the dielectric fluid, which is partially responsible for metallurgical changes in the recast layer and in the heat- affected zone. Recast layer: A layer created by the solidification of molten metal on the workpiece surface after it has been melted by the EDM process. Secondary discharge: A discharge that occurs as conductive particles are carried out along the side of the electrode by the dielectric fluid. Spark in: A method of locating an electrode with respect to the workpiece, using high frequency, low amperage settings so that there is no cutting action. The electrode is advanced toward the workpiece until contact is indicated and this point is used as the basis for setting up the job. Spark out: A technique used in orbiting, which moves the electrode in the same path until sparking ceases. Square wave: An electrical wave shape generated by a solid state power supply. Stroke: The distance the ram travels under servo control. UV axis: A mechanism that provides for movement of the upper head of a wire EDM machine to allow inclined surfaces to be generated. White layer: The surface layer of an EDM cut that is affected by the heat generated during the process. The characteristics of the layer depend on the material, and may be extremely hard martensite or an annealed layer. Wire EDM: An EDM machine or process in which the electrode is a continuously unspooling, conducting wire that moves in preset patterns in relation to the workpiece. Wire guide: A replaceable precision round diamond insert, sized to match the wire, that guides the wire at the entrance and exit points of a wire cut. Wire speed: The rate at which the wire is fed axially through the workpiece (not the rate at which cutting takes place), adjusted so that clean wire is maintained in the cut but slow enough to minimize waste. The EDM Process.—During the EDM process, energy from the sparks created between the electrode and the workpiece is dissipated by the melting and vaporizing of the workpiece material preferentially, only small amounts of material being lost from the electrode. When current starts to flow between the electrode and the work, the dielectric fluid in the small area in which the gap is smallest, and in which the spark will occur, is transformed into a plasma of hydrogen, carbon, and various oxides. This plasma forms a conducting passageway, consisting of ionized or electrically charged particles, through which the spark can form between the electrode and the workpiece. After current starts to flow, to heat and vaporize a tiny area, the striking voltage is reached, the voltage drops, and the field of ionized particles loses its energy, so that the spark can no longer be sustained. As the voltage then begins to rise again with the increase in resistance, the electrical supply is




cut off by the control, causing the plasma to implode and creating a low-pressure pulse that draws in dielectric fluid to flush away metallic debris and cool the impinged area. Such a cycle typically lasts a few microseconds (millionths of a second, or µs), and is repeated continuously in various places on the workpiece as the electrode is moved into the work by the control system. Flushing: An insulating dielectric fluid is made to flow in the space between the workpiece and the electrode to prevent premature spark discharge, cool the workpiece and the electrode, and flush away the debris. For sinker machines, this fluid is paraffin, kerosene, or a silicon-based dielectric fluid, and for wire machines, the dielectric fluid is usually deionized water. The dielectric fluid can be cooled in a heat exchanger to prevent it from rising above about 100°F, at which cooling efficiency may be reduced. The fluid must also be filtered to remove workpiece particles that would prevent efficient flushing of the spark gaps. Care must be taken to avoid the possibility of entrapment of gases generated by sparking. These gases may explode, causing danger to life, breaking a valuable electrode or workpiece, or causing a fire. Flushing away of particles generated during the process is vital to successful EDM operations. A secondary consideration is the heat transferred to the side walls of a cavity, which may cause the workpiece material to expand and close in around the electrode, leading to formation of dc arcs where conductive particles are trapped. Flushing can be done by forcing the fluid to pass through the spark gap under pressure, by sucking it through the gap, or by directing a side nozzle to move the fluid in the tank surrounding the workpiece. In pressure flushing, fluid is usually pumped through strategically placed holes in the electrode or in the workpiece. Vacuum flushing is used when side walls must be accurately formed and straight, and is seldom needed on numerically controlled machines because the table can be programmed to move the workpiece sideways. Flushing needs careful consideration because of the forces involved, especially where fluid is pumped or sucked through narrow passageways, and large hydraulic forces can easily be generated. Excessively high pressures can lead to displacement of the electrode, the workpiece, or both, causing inaccuracy in the finished product. Many low-pressure flushing holes are preferable to a few high-pressure holes. Pressure-relief valves in the system are recommended. Electronic Controls: The electrical circuit that produces the sparks between the electrode and the workpiece is controlled electronically, the length of the extremely short on and off periods being matched by the operator or the programmer to the materials of the electrode and the workpiece, the dielectric, the rate of flushing, the speed of metal removal, and the quality of surface finish required. The average current flowing between the electrode and the workpiece is shown on an ammeter on the power source, and is the determining factor in machining time for a specific operation. The average spark gap voltage is shown on a voltmeter. EDM machines can incorporate provision for orbiting the electrode so that flushing is easier, and cutting is faster and increased on one side. Numerical control can also be used to move the workpiece in relation to the electrode with the same results. Numerical control can also be used for checking dimensions and changing electrodes when necessary. The clearance on all sides between the electrode and the workpiece, after the machining operation, is called the overcut or overburn. The overcut becomes greater with increases in the on time, the spark energy, or the amperage applied, but its size is little affected by voltage changes. Allowances must be made for overcut in the dimensioning of electrodes. Sidewall encroachment and secondary discharge can take up parts of these allowances, and electrodes must always be made smaller to avoid making a cavity or hole too large. Polarity: Polarity can affect processing speed, finish, wear, and stability of the EDM operation. On sinker machines, the electrode is generally, made positive to protect the electrode from excessive wear and preserve its dimensional accuracy. This arrangement



1353

removes metal at a slower rate than electrode negative, which is mostly used for highspeed metal removal with graphite electrodes. Negative polarity is also used for machining carbides, titanium, and refractory alloys using metallic electrodes. Metal removal with graphite electrodes can be as much as 50 per cent faster with electrode negative polarity than with electrode positive, but negative polarity results in much faster electrode wear, so it is generally restricted to electrode shapes that can be redressed easily. Newer generators can provide less than 1 per cent wear with either copper or graphite electrodes during roughing operations. Roughing is typically done with a positive-polarity electrode using elevated on times. Some electrodes, particularly micrograin graphites, have a high resistance to wear. Fine-grain, high-density graphites provide better wear characteristics than coarser, less dense grades, and copper-tungsten resists wear better than pure copper electrodes. Machine Settings: For vertical machines, a rule of thumb for power selection on graphite and copper electrodes is 50 to 65 amps per square inch of electrode engagement. For example, an electrode that is 1⁄2 in. square might use 0.5 × 0.5 × 50 = 12.5 amps. Although each square inch of electrode surface may be able to withstand higher currents, lower settings should be used with very large jobs or the workpiece may become overheated and it may be difficult to clean up the recast layer. Lower amperage settings are required for electrodes that are thin or have sharp details. The voltage applied across the arc gap between the electrode and the workpiece is ideally about 35 volts, but should be as small as possible to maintain stability of the process. Spark Frequency: Spark frequency is the number of times per second that the current is switched on and off. Higher frequencies are used for finishing operations and for work on cemented carbide, titanium, and copper alloys. The frequency of sparking affects the surface finish produced, low frequencies being used with large spark gaps for rapid metal removal with a rough finish, and higher frequencies with small gaps for finer finishes. High frequency usually increases, and low frequency reduces electrode wear. The Duty Cycle: Electronic units on modern EDM machines provide extremely close control of each stage in the sparking cycle, down to millionths of a second (µs). A typical EDM cycle might last 100 µs. Of this time, the current might be on for 40 µs and off for 60 µs. The relationship between the lengths of the on and off times is called the duty cycle and it indicates the degree of efficiency of the operation. The duty cycle states the on time as a percentage of the total cycle time and in the previous example it is 40 per cent. Although reducing the off time will increase the duty cycle, factors such as flushing efficiency, electrode and workpiece material, and dielectric condition control the minimum off time. Some EDM units incorporate sensors and fuzzy logic circuits that provide for adaptive control of cutting conditions for unattended operation. Efficiency is also reported as the amount of metal removed, expressed as in.3/hr. In the EDM process, work is done only during the on time, and the longer the on time, the more material is removed in each sparking cycle. Roughing operations use extended on time for high metal-removal rates, resulting in fewer cycles per second, or lower frequency. The resulting craters are broader and deeper so that the surface is rougher and the heat-affected zone (HAZ) on the workpiece is deeper. With positively charged electrodes, the spark moves from the electrode toward the workpiece and the maximum material is removed from the workpiece. However, every spark takes a minute particle from the electrode so that the electrode also is worn away. Finishing electrodes tend to wear much faster than roughing electrodes because more sparks are generated in unit time. The part of the cycle needed for reionizing the dielectric (the off time) greatly affects the operating speed. Although increasing the off time slows the process, longer off times can increase stability by providing more time for the ejected material to be swept away by the flow of the dielectric fluid, and for deionization of the fluid, so that erratic cycling of the servo-mechanisms that advance and retract the electrode is avoided. In any vertical EDM




operation, if the overcut, wear, and finish are satisfactory, machining speed can best be adjusted by slowly decreasing the off time setting in small increments of 1 to 5 µs until machining becomes erratic, then returning to the previous stable setting. As the off time is decreased, the machining gap or gap voltage will slowly fall and the working current will rise. The gap voltage should not be allowed to drop below 35 to 40 volts. Metal Removal Rates (MRR): Amounts of metal removed in any EDM process depend largely on the length of the on time, the energy/spark, and the number of sparks/second. The following data were provided by Poco Graphite, Inc., in their EDM Technical Manual. For a typical roughing operation using electrode positive polarity on high-carbon steel, a 67 per cent duty cycle removed 0.28 in.3/hr. For the same material, a 50 per cent duty cycle removed 0.15 in.3/hr, and a 33 per cent duty cycle for finishing removed 0.075 in.3/hr. In another example, shown in the top data row in Table 1, a 40 per cent duty cycle with a frequency of 10 kHz and peak current of 50 amps was run for 5 minutes of cutting time. Metal was removed at the rate of 0.8 in.3/hr with electrode wear of 2.5 per cent and a surface finish of 400 µin. Ra. When the on and off times in this cycle were halved, as shown in the second data row in Table 1, the duty cycle remained at 40 per cent, but the frequency doubled to 20 kHz. The result was that the peak current remained unaltered, but with only half the on time the MRR was reduced to 0.7 in.3/hr, the electrode wear increased to 6.3 per cent, and the surface finish improved to 300 µin. Ra. The third and fourth rows in Table 1 show other variations in the basic cycle and the results. Table 1. Effect of Electrical Control Adjustments on EDM Operations

On Time (µs) 40 20 40 40

Off Time (µs) 60 30 10 60

Frequency (kHz) 10 20 20 10

Peak Current (Amps) 50 50 50 25

Metal Removal Rate (in.3/hr) 0.08 0.7 1.2 0.28

Electrode Wear (%) 2.5 6.3 1.4 2.5

Surface Finish (µ in. Ra) 400 300 430 350

The Recast Layer: One drawback of the EDM process when used for steel is the recast layer, which is created wherever sparking occurs. The oil used as a dielectric fluid causes the EDM operation to become a random heat-treatment process in which the metal surface is heated to a very high temperature, then quenched in oil. The heat breaks down the oil into hydrocarbons, tars, and resins, and the molten metal draws out the carbon atoms and traps them in the resolidified metal to form the very thin, hard, brittle surface called the recast layer that covers the heat-affected zone (HAZ). This recast layer has a white appearance and consists of particles of material that have been melted by the sparks, enriched with carbon, and drawn back to the surface or retained by surface tension. The recast layer is harder than the parent metal and can be as hard as glass, and must be reduced or removed by vapor blasting with glass beads, polishing, electrochemical or abrasive flow machining, after the shaping process is completed, to avoid cracking or flaking of surface layers that may cause failure of the part in service. Beneath the thin recast layer, the HAZ, in steel, consists of martensite that usually has been hardened by the heating and cooling sequences coupled with the heat-sink cooling effect of a thick steel workpiece. This martensite is hard and its rates of expansion and contraction are different from those of the parent metal. If the workpiece is subjected to heating and cooling cycles in use, the two layers are constantly stressed and these stresses may cause formation of surface cracks. The HAZ is usually much deeper in a workpiece cut on a sinker than on a wire machine, especially after roughing, because of the increased heating effect caused by the higher amounts of energy applied.



1355

The depth of the HAZ depends on the amperage and the length of the on time, increasing as these values increase, to about 0.012 to 0.015 in. deep. Residual stress in the HAZ can range up to 650 N/mm2. The HAZ cannot be removed easily, so it is best avoided by programming the series of cuts taken on the machine so that most of the HAZ produced by one cut is removed by the following cut. If time is available, cut depth can be reduced gradually until the finishing cuts produce an HAZ having a thickness of less than 0.0001 in. Workpiece Materials.—Most homogeneous materials used in metalworking can be shaped by the EDM process. Some data on typical workpiece materials are given in Table 2. Sintered materials present some difficulties caused by the use of a cobalt or other binder used to hold the carbide or other particles in the matrix. The binder usually melts at a lower temperature than the tungsten, molybdenum, titanium, or other carbides, so it is preferentially removed by the sparking sequence and the carbide particles are thus loosened and freed from the matrix. The structures of sintered materials based on tungsten, cobalt, and molybdenum require higher EDM frequencies with very short on times, so that there is less danger of excessive heat buildup, leading to melting. Copper-tungsten electrodes are recommended for EDM of tungsten carbides. When used with high frequencies for powdered metals, graphite electrodes often suffer from excessive wear. Workpieces of aluminum, brass, and copper should be processed with metallic electrodes of low melting points such as copper or copper-tungsten. Workpieces of carbon and stainless steel that have high melting points should be processed with graphite electrodes. The melting points and specific gravities of the electrode material and of the workpiece should preferably be similar. Table 2. Characteristics of Common Workpiece Materials for EDM

Material Aluminum Brass Cobalt Copper Graphite Inconel Magnesium Manganese Molybdenum Nickel Carbon Steel Tool Steel Stainless Steel Titanium Tungsten Zinc

Specific Gravity 2.70 8.40 8.71 8.89 2.07 … 1.83 7.30 10.20 8.80 7.80 … … 4.50 18.85 6.40

Melting Point

Vaporization Temperature

°F

°C

°F

°C

1220 1710 2696 1980

660 930 1480 1082

4442

2450

N/A 2350 1202 2300 4748 2651 2500 2730 2750 3200 6098 790

1285 650 1260 2620 1455 1371 1500 1510 1700 3370 420

… 5520 4710 6330

2900 2595 3500 …

2025 3870 10,040 4900

1110 2150 5560 2730 … … …

5900 10,670 1663

3260 5930 906

Conductivity (Silver = 100) 63.00 … 16.93 97.61 70.00 … 39.40 15.75 17.60 12.89 12.00 … … 13.73 14.00 26.00

Electrode Materials.—Most EDM electrodes are made from graphite, which provides a much superior rate of metal removal than copper because of the ability of graphite to resist thermal damage. Graphite has a density of 1.55 to 1.85 g/cm3, lower than most metals. Instead of melting when heated, graphite sublimates, that is, it changes directly from a solid to a gas without passing through the liquid stage. Sublimation of graphite occurs at a temperature of 3350°C (6062°F). EDM graphite is made by sintering a compressed mixture of fine graphite powder (1 to 100 micron particle size) and coal tar pitch in a furnace. The open structure of graphite means that it is eroded more rapidly than metal in the EDM process. The electrode surface is also reproduced on the surface of the workpiece. The sizes of individual surface recesses may be reduced during sparking when the work is moved under numerical control of workpiece table movements.




The fine grain sizes and high densities of graphite materials that are specially made for high-quality EDM finishing provide high wear resistance, better finish, and good reproduction of fine details, but these fine grades cost more than graphite of larger grain sizes and lower densities. Premium grades of graphite cost up to five times as much as the least expensive and about three times as much as copper, but the extra cost often can be justified by savings during machining or shaping of the electrode. Graphite has a high resistance to heat and wear at lower frequencies, but will wear more rapidly when used with high frequencies or with negative polarity. Infiltrated graphites for EDM electrodes are also available as a mixture of copper particles in a graphite matrix, for applications where good machinability of the electrode is required. This material presents a trade-off between lower arcing and greater wear with a slower metal-removal rate, but costs more than plain graphite. EDM electrodes are also made from copper, tungsten, silver-tungsten, brass, and zinc, which all have good electrical and thermal conductivity. However, all these metals have melting points below those encountered in the spark gap, so they wear rapidly. Copper with 5 per cent tellurium, added for better machining properties, is the most commonly used metal alloy. Tungsten resists wear better than brass or copper and is more rigid when used for thin electrodes but is expensive and difficult to machine. Metal electrodes, with their more even surfaces and slower wear rates, are often preferred for finishing operations on work that requires a smooth finish. In fine-finishing operations, the arc gap between the surfaces of the electrode and the workpiece is very small and there is a danger of dc arcs being struck, causing pitting of the surface. This pitting is caused when particles dislodged from a graphite electrode during fine-finishing cuts are not flushed from the gap. If struck by a spark, such a particle may provide a path for a continuous discharge of current that will mar the almost completed work surface. Some combinations of electrode and workpiece material, electrode polarity, and likely amounts of corner wear are listed in Table 3. Corner wear rates indicate the ability of the electrode to maintain its shape and reproduce fine detail. The column headed Capacitance refers to the use of capacitors in the control circuits to increase the impact of the spark without increasing the amperage. Such circuits can accomplish more work in a given time, at the expense of surface-finish quality and increased electrode wear. Table 3. Types of Electrodes Used for Various Workpiece Materials Electrode Copper Copper Copper Copper Copper Copper Copper Copper-tungsten Copper-tungsten Copper-tungsten Copper-tungsten Copper-tungsten Graphite Graphite Graphite Graphite Graphite Graphite Graphite Graphite

Electrode Polarity + + + − − − − + − − − − + − + − + − − −

Workpiece Material Steel Inconel Aluminum Titanium Carbide Copper Copper-tungsten Steel Copper Copper-tungsten Titanium Carbide Steel Steel Inconel Inconel Aluminum Aluminum Titanium Copper

Corner Wear (%) 2–10 2–10 200 mm

Width Across Flats, S

> 125 and < 200 mm

Body Diameter, Ds

< 125 mm

Nominal Bolt Dia., D and Thread Pitch M5 × 0.8 M6 × 1 M8 × 1.25

Wrenching Height, K1

For Bolt Lengths

Basic Thread Min Length,a B 2.4 16 22 35 2.8 18 24 37 3.7 22 28 41 4.5 26 32 45 4.5 26 32 45 5.2 30 36 49 6.2 34 40 53 7.0 38 44 57 8.8 46 52 65 10.5 54 60 73 13.1 66 72 85 15.8 78 84 97 18.2 90 96 109 21.0 102 108 121 24.5 … 124 137 28.0 … 140 153 31.5 … 156 169 35.0 … 172 185 39.2 … 192 205 43.4 … 212 225

a Basic thread length, B, is a reference dimension. b This size with width across flats of 15 mm is not standard. Unless specifically ordered, M10 hex bolts with 16 mm width across flats will be furnished. All dimensions are in millimeters. For additional manufacturing and acceptance specifications, reference should be made to the ANSI B18.2.3.5M-1979 (R1995) standard.

Materials and Mechanical Properties.—Unless otherwise specified, steel metric screws and bolts, with the exception of heavy hex structural bolts, hex lag screws, and socket head cap screws, conform to the requirements specified in SAE J1199 or ASTM F568. Steel heavy hex structural bolts conform to ASTM A325M or ASTM A490M. Alloy steel socket head cap screws conform to ASTM A574M, property class 12.9, where the numeral 12 represents approximately one-hundredth of the minimum tensile strength in megapascals and the decimal .9 approximates the ratio of the minimum yield stress to the minimum tensile stress. This is in accord with ISO designation practice. Screws and bolts


Machinery's Handbook 27th Edition METRIC SCREWS AND BOLTS

1551

of other materials, and all materials for hex lag bolts, have properties as agreed upon by the purchaser and the manufacturer. Except for socket head cap screws, metric screws and bolts are furnished with a natural (as processed) finish, unplated or uncoated unless otherwise specified. Alloy steel socket head cap screws are furnished with an oiled black oxide coating (thermal or chemical) unless a protective plating or coating is specified by the purchaser. Metric Screw and Bolt Identification Symbols.—Screws and bolts are identified on the top of the head by property class symbols and manufacturer's identification symbol. Metric Screw and Bolt Designation.—Metric screws and bolts with the exception of socket head cap screws are designated by the following data, preferably in the sequence shown: product name, nominal diameter and thread pitch (except for hex lag screws), nominal length, steel property class or material identification, and protective coating, if required. Example:Hex cap screw, M10 × 1.5 × 50, class 9.8, zinc plated Heavy hex structural bolt, M24 × 3 × 80, ASTM A490M Hex lag screw, 6 × 35, silicon bronze. Socket head cap screws (metric series) are designated by the following data in the order shown: ANSI Standard number, nominal size, thread pitch, nominal screw length, name of product (may be abbreviated SHCS), material and property class (alloy steel screws are supplied to property class 12.9 as specified in ASTM A574M: corrosion-resistant steel screws are specified to the property class and material requirements in ASTM F837M), and protective finish, if required. Example:B18.3.1M—6 × 1 × 20 Hexagon Socket Head Cap Screw, Alloy Steel B18.3.1M—10 × 1.5 × 40 SHCS, Alloy Steel Zinc Plated. Metric Screw and Bolt Thread Lengths.—The length of thread on metric screws and bolts (except for metric lag screws) is controlled by the grip gaging length, Lg max. This is the distance measured parallel to the axis of the screw or bolt, from under the head bearing surface to the face of a noncounterbored or noncountersunk standard GO thread ring gage assembled by hand as far as the thread will permit. The maximum grip gaging length, as calculated and rounded to one decimal place, is equal to the nominal screw length, L, minus the basic thread length, B, or in the case of socket head cap screws, minus the minimum thread length LT. B and LT are reference dimensions intended for calculation purposes only and will be found in Tables 12 and 14, respectively. Table 13. Basic Thread Lengths for Metric Round Head Square Neck Bolts ANSI/ASME B18.5.2.2M-1982, R1993 Nom. Bolt Dia., D and Thread Pitch M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

Bolt Length, L ≤ 125

> 125 and ≤ 200

> 200

Basic Thread Length, B 16 18 22 26 30

22 24 28 32 36

35 37 41 45 49

Bolt Length, L

Nom. Bolt Dia., D and Thread Pitch

≤ 125

M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 …

34 38 46 54 …

> 125 and ≤ 200

> 200

Basic Thread length, B 40 44 52 60 …

All dimensions are in millimeters Basic thread length B is a reference dimension intended for calculation purposes only.


53 57 65 73 …


METRIC SCREWS AND BOLTS

Table 14. Socket Head Cap Screws (Metric Series)—Length of Complete Thread ANSI/ASME B18.3.1M-1986 Length of Complete Thread, LT

Nominal Size

Nominal Size

Length of Complete Thread, LT

Nominal Size

Length of Complete Thread, LT

M20

52.0

M1.6

15.2

M6

24.0

M2

16.0

M8

28.0

M24

60.0

M2.5

17.0

M10

32.0

M30

72.0

M3

18.0

M12

36.0

M36

84.0

M4

20.0

M14

40.0

M42

96.0

M5

22.0

M16

44.0

M48

108.0

Grip length, LG equals screw length, L, minus LT. Total length of thread LTT equals LT plus 5 times the pitch of the coarse thread for the respective screw size. Body length LB equals L minus LTT.

The minimum thread length for hex lag screws is equal to one-half the nominal screw length plus 12 mm, or 150 mm, whichever is shorter. Screws too short for this formula to apply are threaded as close to the head as practicable. Metric Screw and Bolt Diameter-Length Combinations.—For a given diameter, the recommended range of lengths of metric cap screws, formed hex screws, heavy hex screws, hex flange screws, and heavy hex flange screws can be found in Table 16, for heavy hex structural bolts in Table 17, for hex lag screws in Table 15, for round head square neck bolts in Table 18, and for socket head cap screws in Table 19. No recommendations for diameter-length combinations are given in the Standards for hex bolts and heavy hex bolts. Hex bolts in sizes M5 through M24 and heavy hex bolts in sizes M12 through M24 are standard only in lengths longer than 150 mm or 10D, whichever is shorter. When shorter lengths of these sizes are ordered, hex cap screws are normally supplied in place of hex bolts and heavy hex screws in place of heavy hex bolts. Hex bolts in sizes M30 and larger and heavy hex bolts in sizes M30 and M36 are standard in all lengths; however, at manufacturer's option, hex cap screws may be substituted for hex bolts and heavy hex screws for heavy hex bolts for any diameter-length combination. Table 15. Recommended Diameter-Length Combinations for Metric Hex Lag Screws ANSI B18.2.3.8M-1981 (R1999) Nominal Screw Diameter

Nominal Screw Diameter

Nominal Length, L

5

6

8

10

12

16

20

24

Nominal Length, L

10

12

16

20

24

8

d

…

…

…

…

…

…

…

90

d

d

d

d

d

10

d

d

…

…

…

…

…

…

100

d

d

d

d

d

12

d

d

d

…

…

…

…

…

110

…

d

d

d

d

14

d

d

d

…

…

…

…

…

120

…

d

d

d

d

16

d

d

d

d

…

…

…

…

130

…

…

d

d

d

20

d

d

d

d

d

…

…

…

140

…

…

d

d

d

25

d

d

d

d

d

d

…

…

150

…

…

d

d

d

30

d

d

d

d

d

d

d

…

160

…

…

d

d

d

35

d

d

d

d

d

d

d

d

180

…

…

…

d

d

40

d

d

d

d

d

d

d

d

200

…

…

…

d

d

45

d

d

d

d

d

d

d

d

220

…

…

…

…

d

50

d

d

d

d

d

d

d

d

240

…

…

…

…

d

60

…

d

d

d

d

d

d

d

260

…

…

…

…

d

70

…

…

d

d

d

d

d

d

280

…

…

…

…

d

80

…

…

d

d

d

d

d

d

300

…

…

…

…

d

All dimensions are in millimeters. Recommended diameter-length combinations are indicated by the symbol d.



1553

Table 16. Rec’d Diameter-Length Combinations for Metric Hex Cap Screws, Formed Hex and Heavy Hex Screws, Hex Flange and Heavy Hex Flange Screws Diameter—Pitch Nominal Lengtha

M5 ×0.8

M6 ×1

M8 ×1.25

M10 ×1.5

M12 ×1.75

M14 ×2

M16 ×2

M20 ×2.5

M24 ×3

M30 ×3.5

M36 ×4

8

d

…

…

…

…

…

…

…

…

…

…

10

d

d

…

…

…

…

…

…

…

…

…

12

d

d

d

…

…

…

…

…

…

…

…

14

d

d

d

db

…

…

…

…

…

…

…

16

d

d

d

d

db

db

…

…

…

…

…

20

d

d

d

d

d

d

…

…

…

…

…

25

d

d

d

d

d

d

d

…

…

…

…

30

d

d

d

d

d

d

d

d

…

…

…

35

d

d

d

d

d

d

d

d

d

…

…

40

d

d

d

d

d

d

d

d

d

d

…

45

d

d

d

d

d

d

d

d

d

d

…

50

d

d

d

d

d

d

d

d

d

d

d

(55)

…

d

d

d

d

d

d

d

d

d

d

60

…

d

d

d

d

d

d

d

d

d

d

(65)

…

…

d

d

d

d

d

d

d

d

d

70

…

…

d

d

d

d

d

d

d

d

d

(75)

…

…

d

d

d

d

d

d

d

d

d

80

…

…

d

d

d

d

d

d

d

d

d

(85)

…

…

…

d

d

d

d

d

d

d

d

90

…

…

…

d

d

d

d

d

d

d

d

100

…

…

…

d

d

d

d

d

d

d

d

110

…

…

…

…

d

d

d

d

d

d

d

120

…

…

…

…

d

d

d

d

d

d

d

130

…

…

…

…

…

d

d

d

d

d

d

140

…

…

…

…

…

d

d

d

d

d

d

150

…

…

…

…

…

…

d

d

d

d

d

160

…

…

…

…

…

…

d

d

d

d

d

(170)

…

…

…

…

…

…

…

d

d

d

d

180

…

…

…

…

…

…

…

d

d

d

d

(190)

…

…

…

…

…

…

…

d

d

d

d

200

…

…

…

…

…

…

…

d

d

d

d

220

…

…

…

…

…

…

…

…

d

d

d

240

…

…

…

…

…

…

…

…

d

d

d

260

…

…

…

…

…

…

…

…

…

d

d

280

…

…

…

…

…

…

…

…

…

d

d

300

…

…

…

…

…

…

…

…

…

d

d

a Lengths

in parentheses are not recommended. Recommended lengths of formed hex screws, hex flange screws, and heavy hex flange screws do not extend above 150 mm. Recommended lengths of heavy hex screws do not extend below 20 mm. Standard sizes for government use. Recommended diameter-length combinations are indicated by the symbol d. Screws with lengths above heavy cross lines are threaded full length. b Does not apply to hex flange screws and heavy hex flange screws.

All dimensions are in millimeters. For available diameters of each type of screw, see respective dimensional table.



METRIC SCREWS AND BOLTS Table 17. Recommended Diameter-Length Combinations for Metric Heavy Hex Structural Bolts Nominal Diameter and Thread Pitch

Nominal Length, L

M16 × 2

M20 × 2.5

M22 × 2.5

M24 × 3

M27 × 3

M30 × 3.5

M36 × 4

d

…

d

d

… …

d

d

d

… … …

d

d

d

d

… … … …

d

d

d

d

d

… … … … …

d

d

d

d

d

d

d

d

d

d

d

d

… … … … … … …

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

45 50 55 60 65 70 75 80 85 90 95 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300

All dimensions are in millimeters. Recommended diameter-length combinations are indicated by the symbol d. Bolts with lengths above the heavy cross lines are threaded full length.

Table 18. Recommended Diameter-Length Combinations for Metric Round Head Square Neck Bolts Nominal Length,a L 10 12 (14) 16 20 25 30 35 40 45 50 (55) 60 (65) 70 (75) 80

Nominal Diameter and Thread Pitch M5 × 0.8

M6 ×1

M8 × 1.25

M10 × 1.5

M12 × 1.75

M14 ×2

M16 ×2

M20 × 2.5

M24 ×3

d

…

d

d

d

d

… … …

d

d

d

… … … …

d

d

d

d

… … … … …

d

d

d

d

d

… … … … … …

… … … … … …

d

d

d

d

d

d

d

d

d

d

d

d

d

d

… … … … … … … …

d

d

d

d

d

d

d

d

… … … … … … … … …

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

… … … … … …

… … … …


d


1555

Table 18. (Continued) Recommended Diameter-Length Combinations for Metric Round Head Square Neck Bolts Nominal Diameter and Thread Pitch

Nominal Length,a L

M5 × 0.8 … … … … … … … … … … … … … … …

(85) 90 100 110 120 130 140 150 160 (170) 180 (190) 200 220 240

M6 ×1 … … … … … … … … … … … … … … …

M8 × 1.25 … … … … … … … … … … … … … … …

M10 × 1.5

M12 × 1.75

M14 ×2

M16 ×2

M20 × 2.5

M24 ×3

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

… … … … … … … … … … … …

… … … … … … … … … …

… … … … … … … …

… … … … … …

… …

d d

a Bolts with lengths above the heavy cross lines are threaded full length. Lengths in ( ) are not recom-

mended. All dimensions are in millimeters. Recommended diameter-length combinations are indicated by the symbol d. Standard sizes for government use.

Table 19. Diameter-Length Combinations for Socket Head Cap Screws (Metric Series) Nominal Length, L 20 25 30 35 40 45 50 55 60 65 70 80 90 100 110 120 130 140 150 160 180 200 220 240 260 300

Nominal Size M1.6

M2

d

d

d d

… … … … … … … … … … … … … … … … … … … … … … …

d

M2.5 d

M3

M4

M5

M6

d

M8

M10

M12

M14

M16

M20

M24

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

…

d

d

d

… … … … … … … … … … … … … … … … … … … … …

… … … … … … … … … … … … … … … … … … …

… … … … … … … … … … … … … … … …

… … … … … … … … … … … … … …

… … … … … … … … … … … …

… … … … … … … … … …

… … … … … …

… … … …

d

… …

d

d

d

d

All dimensions are in millimeters. Screws with lengths above heavy cross lines are threaded full length. Diameter-length combinations are indicated by the symbol d. Standard sizes for government use. In addition to the lengths shown, the following lengths are standard: 3, 4, 5, 6, 8, 10, 12, and 16 mm. No diameter-length combinations are given in the Standard for these lengths. Screws larger than M24 with lengths equal to or shorter than LTT (see Table 14 footnote) are threaded full length.




Metric Screw and Bolt Thread Series.—Unless otherwise specified, metric screws and bolts, except for hex lag screws, are furnished with metric coarse threads conforming to the dimensions for general purpose threads given in ANSI B1.13M (see American National Standard Metric Screw Threads M Profile on page 1783). Except for socket head cap screws, the tolerance class is 6g, which applies to plain finish (unplated or uncoated) screws or bolts and to plated or coated screws or bolts before plating or coating. For screws with additive finish, the 6g diameters may be exceeded by the amount of the allowance, i.e. the basic diameters apply to the screws or bolts after plating or coating. For socket head cap screws, the tolerance class is 4g6g, but for plated screws, the allowance g may be consumed by the thickness of plating so that the maximum limit of size after plating is tolerance class 4h6h. Thread limits are in accordance with ANSI B1.13M. Metric hex lag screws have a special thread which is covered in Table 5. Metric Screw and Bolt Clearance Holes.—Clearance holes for screws and bolts with the exception of hex lag screws, socket head cap screws, and round head square neck bolts are given in Table 20. Clearance holes for round head square neck bolts are given in Table 8 and drill and counterbore sizes for socket head cap screws are given in Table 21. Table 20. Recommended Clearance Holes for Metric Hex Screws and Bolts Nominal Dia., D and Thread Pitch M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M22 × 2.5a M24 × 3 M27 × 3a

Clearance Hole Dia., Basic, Dh

Clearance Hole Dia., Basic,Dh

Close

Normal, Preferred

Loose

Nominal Dia., D and Thread Pitch

Close

Normal, Preferred

Loose

5.3 6.4 8.4 10.5 13.0 15.0 17.0 21.0 23.0

5.5 6.6 9.0 11.0 13.5 15.5 17.5 22.0 24.0

5.8 7.0 10.0 12.0 14.5 16.5 18.5 24.0 26.0

M30 × 3.5 M36 × 4 M42 × 4.5 M48 × 5 M56 × 5.5 M64 × 6 M72 × 6 M80 × 6 M90 × 6

31.0 37.0 43.0 50.0 58.0 66.0 74.0 82.0 93.0

33.0 39.0 45.0 52.0 62.0 70.0 78.0 86.0 96.0

35.0 42.0 48.0 56.0 66.0 74.0 82.0 91.0 101.0

25.0 28.0

26.0 30.0

28.0 32.0

M100 × 6 …

104.0 …

107.0 …

112.0 …

a Applies only to heavy hex structural bolts.

All dimensions are in millimeters. Does not apply to hex lag screws, hex socket head cap screws, or round head square neck bolts. Normal Clearance: This is preferred for general purpose applications and should be specified unless special design considerations dictate the need for either a close or loose clearance hole. Close Clearance: This should be specified only where conditions such as critical alignment of assembled parts, wall thickness or other limitations necessitate use of a minimum hole. When close clearance holes are specified, special provision (e.g. countersinking) must be made at the screw or bolt entry side to permit proper seating of the screw or bolt head. Loose Clearance: This should be specified only for applications where maximum adjustment capability between components being assembled is necessary. Recommended Tolerances: The clearance hole diameters given in this table are minimum size. Recommended tolerances are: for screw or bolt diameter M5, +0.2 mm; for M6 through M16, +0.3 mm; for M20 through M42, +0.4 mm; for M48 through M72, +0.5 mm; and for M80 through M100, +0.6 mm.



1557

Table 21. Drill and Counterbore Sizes for Metric Socket Head Cap Screws

Nominal Size or Basic Screw Diameter

Nominal Drill Size, A Close Fitb

Normal Fitc

Counterbore Diameter, X

Countersink Diameter,a Y

M1.6

1.80

1.95

3.50

2.0

M2

2.20

2.40

4.40

2.6

M2.5

2.70

3.00

5.40

3.1

M3

3.40

3.70

6.50

3.6

M4

4.40

4.80

8.25

4.7

M5

5.40

5.80

9.75

5.7

M6

6.40

6.80

11.25

6.8

M8

8.40

8.80

14.25

9.2

M10

10.50

10.80

17.25

11.2

M12

12.50

12.80

19.25

14.2

M14

14.50

14.75

22.25

16.2

M16

16.50

16.75

25.50

18.2

M20

20.50

20.75

31.50

22.4

M24

24.50

24.75

37.50

26.4

M30

30.75

31.75

47.50

33.4

M36

37.00

37.50

56.50

39.4

M42

43.00

44.00

66.00

45.6

M48

49.00

50.00

75.00

52.6

a Countersink:

It is considered good practice to countersink or break the edges of holes which are smaller than B Max. (see Table 24) in parts having a hardness which approaches, equals, or exceeds the screw hardness. If such holes are not countersunk, the heads of screws may not seat properly or the sharp edges on holes may deform the fillets on screws, thereby making them susceptible to fatigue in applications involving dynamic loading. The countersink or corner relief, however, should not be larger than is necessary to ensure that the fillet on the screw is cleared. Normally, the diameter of countersink does not have to exceed B Max. Countersinks or corner reliefs in excess of this diameter reduce the effective bearing area and introduce the possibility of embedment where the parts to be fastened are softer than the screws or of brinnelling or flaring the heads of the screws where the parts to be fastened are harder than the screws. b Close Fit: The close fit is normally limited to holes for those lengths of screws which are threaded to the head in assemblies where only one screw is to be used or where two or more screws are to be used and the mating holes are to be produced either at assembly or by matched and coordinated tooling. c Normal Fit: The normal fit is intended for screws of relatively long length or for assemblies involving two or more screws where the mating holes are to be produced by conventional tolerancing methods. It provides for the maximum allowable eccentricity of the longest standard screws and for certain variations in the parts to be fastened, such as: deviations in hole straightness, angularity between the axis of the tapped hole and that of the hole for shank, differences in center distances of the mating holes, etc. All dimensions are in millimeters.




Table 22. Recommended Clearance Holes for Metric Round Head Square Neck Bolts

Clearance Nom. Bolt Dia., D and Thd. Pitch M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

Closea

Normalb

Clearance Loosec

Minimum Hole Diameter or Square Width, H

Corner Radius Rh

… … 9.0 11.0 13.5

0.2 0.3 0.4 0.4 0.6

5.5 6.6 … … 13.0

5.8 7.0 10.0 12.0 14.5

Nom. Bolt Dia., D and Thd. Pitch M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 …

Closea

Normalb

Loosec

Minimum Hole Diameter or Square Width, H 15.0 17.0 21.0 25.0 …

15.5 17.5 22.0 26.0 …

16.5 18.5 24.0 28.0 …

Corner Radius Rh 0.6 0.6 0.8 1.0 …

a Close Clearance: Close clearance should be specified only for square holes in very thin and/or soft material, or for slots, or where conditions such as critical alignment of assembled parts, wall thickness, or other limitations necessitate use of a minimal hole. Allowable swell or fins on the bolt body and/or fins on the corners of the square neck may interfere with close clearance round or square holes. b Normal Clearance: Normal clearance hole sizes are preferred for general purpose applications and should be specified unless special design considerations dictate the need for either a close or loose clearance hole. c Loose Clearance: Loose clearance hole sizes should be specified only for applications where maximum adjustment capability between components being assembled is necessary. Loose clearance square hole or slots may not prevent bolt turning during wrenching.


Table 23. Drilled Head Dimensions for Metric Hex Socket Head Cap Screws

Two holes Nominal Size or Basic Screw Diameter M3 M4 M5 M6 M8 M10 M12 M16 M20 M24 M30 M36

Six holes Hole Center Location, W Max Min

Drilled Hole Diameter, X Max Min

1.20 1.60 2.00 2.30 2.70 3.30 4.00 5.00 6.30 7.30 9.00 10.50

0.95 1.35 1.35 1.35 1.35 1.65 1.65 1.65 2.15 2.15 2.15 2.15

0.80 1.20 1.50 1.80 2.20 2.80 3.50 4.50 5.80 6.80 8.50 10.00

0.80 1.20 1.20 1.20 1.20 1.50 1.50 1.50 2.00 2.00 2.00 2.00


Hole Alignment Check Plug Diameter Basic 0.75 0.90 0.90 0.90 0.90 1.40 1.40 1.40 1.80 1.80 1.80 1.80


1559

All dimensions are in millimeters. Drilled head metric hexagon socket head cap screws normally are not available in screw sizes smaller than M3 nor larger than M36. The M3 and M4 nominal screw sizes have two drilled holes spaced 180 degrees apart. Nominal screw sizes M5 and larger have six drilled holes spaced 60 degrees apart unless the purchaser specifies two drilled holes. The positioning of holes on opposite sides of the socket should be such that the hole alignment check plug will pass completely through the head without any deflection. When so specified by the purchaser, the edges of holes on the outside surface of the head will be chamfered 45 degrees to a depth of 0.30 to 0.50 mm.

Table 24. American National Standard Socket Head Cap Screws— Metric Series ANSI/ASME B18.3.1M-1986

Body Diameter, D

Head Diameter A

Chamfer or Radius S

Hexagon Socket Sizea J

Spline TransiKey Socket Engage tion Dia. Sizea ment M T Ba

Min

Max

Nom.

Nom.

Min

Max

1.52 1.91 2.40 2.89 3.88 4.86 5.85 7.83 9.81 11.79 13.77 15.76 19.73 23.70 29.67 35.64 41.61 47.58

0.16 0.20 0.25 0.30 0.40 0.50 0.60 0.80 1.00 1.20 1.40 1.60 2.00 2.40 3.00 3.60 4.20 4.80

1.5 1.5 2.0 2.5 3.0 4.0 5.0 6.0 8.0 10.0 12.0 14.0 17.0 19.0 22.0 27.0 32.0 36.0

1.829 1.829 2.438 2.819 3.378 4.648 5.486 7.391 … … … … … … … … … …

0.80 1.00 1.25 1.50 2.00 2.50 3.00 4.00 5.00 6.00 7.00 8.00 10.00 12.00 15.00 18.00 21.00 24.00

2.0 2.6 3.1 3.6 4.7 5.7 6.8 9.2 11.2 14.2 16.2 18.2 22.4 26.4 33.4 39.4 45.6 52.6

Head Height H

Nom. Size and Thread Pitch

Max

Min

Max

Min

Max

M1.6 × 0.35 M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75 M14 × 2b M16 × 2 M20 × 2.5 M24 × 3 M30 × 3.5 M36 × 4 M42 × 4.5 M48 × 5

1.60 2.00 2.50 3.00 4.00 5.00 6.00 8.00 10.00 12.00 14.00 16.00 20.00 24.00 30.00 36.00 42.00 48.00

1.46 1.86 2.36 2.86 3.82 4.82 5.82 7.78 9.78 11.73 13.73 15.73 19.67 23.67 29.67 35.61 41.61 47.61

3.00 3.80 4.50 5.50 7.00 8.50 10.00 13.00 16.00 18.00 21.00 24.00 30.00 36.00 45.00 54.00 63.00 72.00

2.87 3.65 4.33 5.32 6.80 8.27 9.74 12.70 15.67 17.63 20.60 23.58 29.53 35.48 44.42 53.37 62.31 71.27

1.60 2.00 2.50 3.00 4.00 5.00 6.00 8.00 10.00 12.00 14.00 16.00 20.00 24.00 30.00 36.00 42.00 48.00



METRIC NUTS

a See also Table 25. b The M14 × 2 size is not recommended for use in new designs.

All dimensions are in millimeters LG is grip length and LB is body length (see Table 14). For length of complete thread, see Table 14. For additional manufacturing and acceptance specifications, see ANSI/ASME B18.3.1M-1986.

Table 25. American National Standard Hexagon and Spline Sockets for Socket Head Cap Screws—Metric Series ANSI/ASME B18.3.1M-1986

METRIC HEXAGON SOCKETS

METRIC SPLINE SOCKET

See Table 24 Nominal Hexagon Socket Size

1.5 2 2.5 3 4 5 6 8 10

Socket Width Across Flats, J Max

Min

1.545 2.045 2.560 3.071 4.084 5.084 6.095 8.115 10.127

1.520 2.020 2.520 3.020 4.020 5.020 6.020 8.025 10.025

See Table 24 Nominal Socket Width Hexagon Across Corners, Socket C Size Metric Hexagon Sockets Min 1.73 2.30 2.87 3.44 4.58 5.72 6.86 9.15 11.50

Socket Major Diameter, M

Nominal Spline Socket Size

Max

Min

1.829 2.438 2.819 3.378 4.648 5.486 7.391

1.8796 2.4892 2.9210 3.4798 4.7752 5.6134 7.5692

1.8542 2.4638 2.8702 3.4290 4.7244 5.5626 7.5184

12 14 17 19 22 24 27 32 36

Socket Width Across Flats, J Max

Min

Min

12.146 14.159 17.216 19.243 22.319 24.319 27.319 32.461 36.461

12.032 14.032 17.050 19.065 22.065 24.065 27.065 32.080 36.080

13.80 16.09 19.56 21.87 25.31 27.60 31.04 36.80 41.38

Metric Spline Socketsa Socket Minor Diameter, N Max Min 1.6256 2.0828 2.4892 2.9972 4.1402 4.8260 6.4516

Socket Width Across Corners, C

1.6002 2.0320 2.4384 2.9464 4.0894 4.7752 6.4008

Width of Tooth, P Max

Min

0.4064 0.5588 0.6350 0.7620 0.9906 1.2700 1.7272

0.3810 0.5334 0.5842 0.7112 0.9398 1.2192 2.6764

a The tabulated dimensions represent direct metric conversions of the equivalent inch size spline sockets shown in American National Standard Socket Cap, Shoulder and Set Screws — Inch Series ANSI B18.3. Therefore, the spline keys and bits shown therein are applicable for wrenching the corresponding size metric spline sockets.

Metric Nuts The American National Standards covering metric nuts have been established in cooperation with the Department of Defense in such a way that they could be used by the Government for procurement purposes. Extensive information concerning these nuts is given in the following text and tables, but for more complete manufacturing and acceptance specifications, reference should be made to the respective Standards, which may be obtained by


Machinery's Handbook 27th Edition METRIC NUTS

1561

non-governmental agencies from the American National Standards Institute, 25 West 43rd Street, New York, N.Y. 10036. Manufacturers should be consulted concerning items and sizes which are in stock production. Comparison with ISO Standards.—American National Standards for metric nuts have been coordinated to the extent possible with comparable ISO Standards or proposed Standards, thus: ANSI B18.2.4.1M Metric Hex Nuts, Style 1 with ISO 4032; B18.2.4.2M Metric Hex Nuts, Style 2 with ISO 4033; B18.2.4.4M Metric Hex Flange Nuts with ISO 4161; B18.2.4.5M Metric Hex Jam Nuts with ISO 4035; and B18.2.4.3M Metric Slotted Hex Nuts, B18.2.4.6M Metric Heavy Hex Nuts in sizes M12 through M36, and B18.16.3M Prevailing-Torque Type Steel Metric Hex Nuts and Hex Flange Nuts with comparable draft ISO Standards. The dimensional differences between each ANSI Standard and the comparable ISO Standard or draft Standard are very few, relatively minor, and none will affect the interchangeability of nuts manufactured to the requirements of either. At its meeting in Varna, May 1977, ISO/TC2 studied several technical reports analyzing design considerations influencing determination of the best series of widths across flats for hex bolts, screws, and nuts. A primary technical objective was to achieve a logical ratio between under head (nut) bearing surface area (which determines the magnitude of compressive stress on the bolted members) and the tensile stress area of the screw thread (which governs the clamping force that can be developed by tightening the fastener). The series of widths across flats in the ANSI Standards agree with those which were selected by ISO/TC2 to be ISO Standards. One exception for width across flats of metric hex nuts, styles 1 and 2, metric slotted hex nuts, metric hex jam nuts, and prevailing-torque metric hex nuts is the M10 size. These nuts in M10 size are currently being produced in the United States with a width across flats of 15 mm. This width, however, is not an ISO Standard. Unless these M10 nuts with width across flats of 15 mm are specifically ordered, the M10 size with 16 mm width across flats will be furnished. In ANSI Standards for metric nuts, letter symbols designating dimensional characteristics are in accord with those used in ISO Standards, except capitals have been used for data processing convenience instead of lower case letters used in ISO Standards. Metric Nut Tops and Bearing Surfaces.—Metric hex nuts, styles 1 and 2, slotted hex nuts, and hex jam nuts are double chamfered in sizes M16 and smaller and in sizes M20 and larger may either be double chamfered or have a washer-faced bearing surface and a chamfered top at the option of the manufacturer. Metric heavy hex nuts are optional either way in all sizes. Metric hex flange nuts have a flange bearing surface and a chamfered top and prevailing-torque type metric hex nuts have a chamfered bearing surface. Prevailingtorque type metrix hex flange nuts have a flange bearing surface. All types of metric nuts have the tapped hole countersunk on the bearing face and metric slotted hex nuts, hex flange nuts, and prevailing-torque type hex nuts and hex flange nuts may be countersunk on the top face. Materials and Mechanical Properties.—Nonheat-treated carbon steel metric hex nuts, style 1 and slotted hex nuts conform to material and property class requirements specified for property class 5 nuts; hex nuts, style 2 and hex flange nuts to property class 9 nuts; hex jam nuts to property class 04 nuts, and nonheat-treated carbon and alloy steel heavy hex nuts to property classes 5, 9, 8S, or 8S3 nuts; all as covered in ASTM A563M. Carbon steel metric hex nuts, style 1 and slotted hex nuts that have specified heat treatment conform to material and property class requirements specified for property class 10 nuts; hex nuts, style 2 to property class 12 nuts; hex jam nuts to property class 05 nuts; hex flange nuts to property classes 10 and 12 nuts; and carbon or alloy steel heavy hex nuts to property classes 10S, 10S3, or 12 nuts, all as covered in ASTM A563M. Carbon steel prevailing-torque type hex nuts and hex flange nuts conform to mechanical and property class requirements as given in ANSI B18.16.1M.



METRIC NUTS Table 26. American National Standard Metric Hex Nuts, Styles 1 and 2 ANSI/ASME B18.2.4.1M and B18.2.4.2M-1979 (R1995)

Nominal Nut Dia. and Thread Pitch

Width Across Flats, S Max

Width Across Corners, E Min

Max

Min

Thickness, M Max

Bearing Face Dia., Dw

Washer Face Thickness, C

Min

Min

Max

Min

1.05 1.35 1.75 2.15 2.55 2.90 4.40 4.90 6.44 8.7 8.04 10.37 12.10 14.10 16.90 20.20 24.30 29.40

2.3 3.1 4.1 4.6 5.1 6.0 7.0 8.9 11.6 13.6 14.6 16.6 19.4 22.4 27.9 32.5 42.5 50.8

… … … … … … … … … 0.6 … … … … 0.8 0.8 0.8 0.8

… … … … … … … … … 0.3 … … … … 0.4 0.4 0.4 0.4

2.65 3.00 3.50 4.80 5.40 7.14 9.6 8.94 11.57 13.40 15.70 19.00 22.60 27.30 33.10

4.6 5.1 5.9 6.9 8.9 11.6 13.6 14.6 16.6 19.6 22.5 27.7 33.2 42.7 51.1

… … … … … … 0.6 … … … … 0.8 0.8 0.8 0.8

… … … … … … 0.3 … … … … 0.4 0.4 0.4 0.4

Metric Hex Nuts — Style 1 M1.6 × 0.35 M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 aM10 × 1.5 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 M30 × 3.5 M36 × 4

3.20 4.00 5.00 5.50 6.00 7.00 8.00 10.00 13.00 15.00 16.00 18.00 21.00 24.00 30.00 36.00 46.00 55.00

3.02 3.82 4.82 5.32 5.82 6.78 7.78 9.78 12.73 14.73 15.73 17.73 20.67 23.67 29.16 35.00 45.00 53.80

3.70 4.62 5.77 6.35 6.93 8.08 9.24 11.55 15.01 17.32 18.48 20.78 24.25 27.71 34.64 41.57 53.12 63.51

M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 aM10 × 1.5 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 M30 × 3.5 M36 × 4

5.50 6.00 7.00 8.00 10.00 13.00 15.00 16.00 18.00 21.00 24.00 30.00 36.00 46.00 55.00

5.32 5.82 6.78 7.78 9.78 12.73 14.73 15.73 17.73 20.67 23.67 29.16 35.00 45.00 53.80

6.35 6.93 8.08 9.24 11.55 15.01 17.32 18.48 20.78 24.25 27.71 34.64 41.57 53.12 63.51

3.41 4.32 5.45 6.01 6.58 7.66 8.79 11.05 14.38 16.64 17.77 20.03 23.36 26.75 32.95 39.55 50.85 60.79

1.30 1.60 2.00 2.40 2.80 3.20 4.70 5.20 6.80 9.1 8.40 10.80 12.80 14.80 18.00 21.50 25.60 31.00

Metric Hex Nuts — Style 2 6.01 6.58 7.66 8.79 11.05 14.38 16.64 17.77 20.03 23.35 26.75 32.95 39.55 50.85 60.79

2.90 3.30 3.80 5.10 5.70 7.50 10.0 9.30 12.00 14.10 16.40 20.30 23.90 28.60 34.70

a This size with width across flats of 15 mm is not standard. Unless specifically ordered, M10 hex nuts with 16 mm width across flats will be furnished.




1563

Table 27. American National Standard Metric Slotted Hex Nuts ANSI B18.2.4.4M-1982 (R1999)



Width Across Corners, E

Thickness, M


Unslotted Thickness, F

Width of Slot, N

Washer Face Thickness C

Max

Min

Max

Min

Max

Min

Min

Max

Min

Max

Min

Max

Min

M5 × 0.8

8.00

7.78

9.24

8.79

5.10

4.80

6.9

3.2

2.9

2.0

1.4

…

…

M6 × 1

10.00

9.78

11.55 11.05

5.70

5.40

8.9

3.5

3.2

2.4

1.8

…

…

M8 × 1.25

13.00 12.73 15.01 14.38

7.50

7.14

11.6

4.4

4.1

2.9

2.3

…

…

× 1.5

15.00 14.73 17.32 16.64

10.0

9.6

13.6

5.7

5.4

3.4

2.8

0.6

0.3

M10 × 1.5

16.00 15.73 18.48 17.77

9.30

8.94

14.6

5.2

4.9

3.4

2.8

…

…

M12 × 1.75

18.00 17.73 20.78 20.03 12.00 11.57

16.6

7.3

6.9

4.0

3.2

…

…

M14 × 2

21.00 20.67 24.25 23.35 14.10 13.40

19.6

8.6

8.0

4.3

3.5

…

…

M16 × 2

24.00 23.67 27.71 26.75 16.40 15.70

22.5

9.9

9.3

5.3

4.5

…

…

M20 × 2.5

30.00 29.16 34.64 32.95 20.30 19.00

27.7

13.3

12.2

5.7

4.5

0.8

0.4

M24 × 3

36.00 35.00 41.57 39.55 23.90 22.60

33.2

15.4

14.3

6.7

5.5

0.8

0.4

M30 × 3.5

46.00 45.00 53.12 50.85 28.60 27.30

42.7

18.1

16.8

8.5

7.0

0.8

0.4

M36 × 4

55.00 53.80 63.51 60.79 34.70 33.10

51.1

23.7

22.4

8.5

7.0

0.8

0.4

aM10

a This size with width across flats of 15 mm is not standard. Unless specifically ordered, M10 slotted

hex nuts with 16 mm width across flats will be furnished. All dimensions are in millimeters.

Metric nuts of other materials, such as stainless steel, brass, bronze, and aluminum alloys, have properties as agreed upon by the manufacturer and purchaser. Properties of nuts of several grades of non-ferrous materials are covered in ASTM F467M. Unless otherwise specified, metric nuts are furnished with a natural (unprocessed) finish, unplated or uncoated. Metric Nut Thread Series.—Metric nuts have metric coarse threads with class 6H tolerances in accordance with ANSI B1.13M (see Metric Screw and Bolt Diameter-Length CombinationsMetric Screw Threads in index). For prevailing-torque type metric nuts this condition applies before introduction of the prevailing torque feature. Nuts intended for use with externally threaded fasteners which are plated or coated with a plating or coating thickness (e.g., hot dip galvanized) requiring overtapping of the nut thread to permit assembly, have over-tapped threads in conformance with requirements specified in ASTM A563M.



METRIC NUTS Table 28. American National Standard Metric Hex Flange Nuts ANSI B18.2.4.4M-1982 (R1999)

DETAIL X

Nominal Nut Dia. and Thread Pitch M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5



Flange Dia., Dc

Bearing Circle Dia., Dw

Flange Edge Thickness, C

Thickness, M

Flange Top Fillet Radius, R

Max

Min

Max

Min

Max

Min

Min

Max

Min

Max

8.00 10.00 13.00 15.00 18.00 21.00 24.00 30.00

7.78 9.78 12.73 14.73 17.73 20.67 23.67 29.16

9.24 11.55 15.01 17.32 20.78 24.25 27.71 34.64

8.79 11.05 14.38 16.64 20.03 23.35 26.75 32.95

11.8 14.2 17.9 21.8 26.0 29.9 34.5 42.8

9.8 12.2 15.8 19.6 23.8 27.6 31.9 39.9

1.0 1.1 1.2 1.5 1.8 2.1 2.4 3.0

5.00 6.00 8.00 10.00 12.00 14.00 16.00 20.00

4.70 5.70 7.60 9.60 11.60 13.30 15.30 18.90

0.3 0.4 0.5 0.6 0.7 0.9 1.0 1.2


Types of Metric Prevailing-Torque Type Nuts.—There are three basic designs for prevailing-torque type nuts: 1) All-metal, one-piece construction nuts which derive their prevailing-torque characteristics from controlled distortion of the nut thread and/or body. 2) Metal nuts which derive their prevailing-torque characteristics from addition or fusion of a nonmetallic insert, plug. or patch in their threads. 3) Top insert, two-piece construction nuts which derive their prevailing-torque characteristics from an insert, usually a full ring of non-metallic material, located and retained in the nut at its top surface. The first two designs are designated in Tables 29 and 30 as “all-metal” type and the third design as “top-insert” type.



Table 29. American National Standard Prevailing-Torque Metric Hex Nuts — Property Classes 5, 9, and 10 ANSI/ASME B18.16.3M-1998

Property Classes 5 and 10 Nuts All Metala Type

Property Class 9 Nuts

Top Insert Type

All Metal Type

Top Insert Type

Property Class 5 and 10 9 Nuts Nuts Wrenching Height, M1



Max

Min

Max

Min

Min

Max

Thickness, M Min Max

Min

Max

Min

Min

Min

Min

M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 bM10 × 1.5

5.50 6.00 7.00 8.00 10.00 13.00 15.00

5.32 5.82 6.78 7.78 9.78 12.73 14.73

6.35 6.93 8.08 9.24 11.55 15.01 17.32

6.01 6.58 7.66 8.79 11.05 14.38 16.64

3.10 3.50 4.00 5.30 5.90 7.10 9.70

2.65 3.00 3.50 4.80 5.40 6.44 8.70

4.50 5.00 6.00 6.80 8.00 9.50 12.50

3.90 4.30 5.30 6.00 7.20 8.50 11.50

3.10 3.50 4.00 5.30 6.70 8.00 11.20

2.65 3.00 3.50 4.80 5.40 7.14 9.60

4.50 5.00 6.00 7.20 8.50 10.20 13.50

3.90 4.30 5.30 6.40 7.70 9.20 12.50

1.4 1.7 1.9 2.7 3.0 3.7 5.6

1.4 1.7 1.9 2.7 3.0 4.3 6.2

M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 M30 × 3.5 M36 × 4

16.00 18.00 21.00 24.00 30.00 36.00 46.00 55.00

15.73 17.73 20.67 23.67 29.16 35.00 45.00 53.80

18.48 20.78 24.25 27.71 34.64 41.57 53.12 63.51

17.77 20.03 23.35 26.75 32.95 39.55 50.85 60.79

9.00 11.60 13.20 15.20 19.00 23.00 26.90 32.50

8.04 10.37 12.10 14.10 16.90 20.20 24.30 29.40

11.90 14.90 17.00 19.10 22.80 27.10 32.60 38.90

10.90 13.90 15.80 17.90 21.50 25.60 30.60 36.90

10.50 13.30 15.40 17.90 21.80 26.40 31.80 38.50

8.94 11.57 13.40 15.70 19.00 22.60 27.30 33.10

12.80 16.10 18.30 20.70 25.10 29.50 35.60 42.60

11.80 15.10 17.10 19.50 23.80 28.00 33.60 40.60

4.8 6.7 7.8 9.1 10.9 13.0 15.7 19.0

5.6 7.7 8.9 10.5 12.7 15.1 18.2 22.1

4.6 5.1 5.9 6.9 8.9 11.6 13.6 14.6 16.6 19.6 22.5 27.7 33.2 42.7 51.1

Max

METRIC NUTS



a Also includes metal nuts with non-metallic inserts, plugs, or patches in their threads.



1565

b This size with width across flats of 15 mm is not standard. Unless specifically ordered, M10 slotted hex nuts with 16 mm width across flats will be furnished.


METRIC NUTS

Bearing Circle Dia., Dw

Flange Edge Thickness, C

Flange Top Fillet Radius, R

Table 30. American National Standard Prevailing-Torque Metric Hex Flange Nuts ANSI B18.16.3M-1998

Max

Min

Max

Min

Max

Min

Min

Max

M6 × 1

10.00

9.78

11.55

11.05

7.30

5.70

8.80

8.00

14.2

12.2

1.1

0.4

M8 × 1.25

13.00

12.73

15.01

14.38

9.40

7.60

10.70

9.70

17.9

15.8

1.2

0.5

Nominal Dia. and Thread Pitch



Flange Dia., Dc

Top Insert Type

All Metal Typea

Thickness, M (All Nut Property Classes) Max

Min

Max

Min

M10 × 1.5

15.00

14.73

17.32

16.64

11.40

9.60

13.50

12.50

21.8

19.6

1.5

0.6

M12 × 1.75

18.00

17.73

20.78

20.03

13.80

11.60

16.10

15.10

26.0

23.8

1.8

0.7

M14 × 2

21.00

20.67

24.25

23.35

15.90

13.30

18.20

17.00

29.9

27.6

2.1

0.9

M16 × 2

24.00

23.67

27.71

26.75

18.30

15.30

20.30

19.10

34.5

31.9

2.4

1.0

M20 × 2.5

30.00

29.16

34.64

32.95

22.40

18.90

24.80

23.50

42.8

39.9

3.0

1.2

a Also includes metal nuts with nonmetallic inserts, plugs, or patches in their threads.


Metric Nut Identification Symbols.—Carbon steel hex nuts, styles 1 and 2, hex flange nuts, and carbon and alloy steel heavy hex nuts are marked to identify the property class and manufacturer in accordance with requirements specified in ASTM A563M. The aforementioned nuts when made of other materials, as well as slotted hex nuts and hex jam nuts, are marked to identify the property class and manufacturer as agreed upon by manufacturer and purchaser. Carbon steel prevailing-torque type hex nuts and hex flange nuts are marked to identify property class and manufacturer as specified in ANSI B18.16.1M. Prevailing-torque type nuts of other materials are identified as agreed upon by the manufacturer and purchaser. Metric Nut Designation.—Metric nuts are designated by the following data, preferably in the sequence shown: product name, nominal diameter and thread pitch, steel property class or material identification, and protective coating, if required. (Note: It is common practice in ISO Standards to omit thread pitch from the product designation when the nut threads are the metric coarse thread series, e.g., M10 stands for M10 × 1.5). Example:Hex nut, style 1, M10 × 1.5, ASTM A563M class 10, zinc plated Heavy hex nut, M20 × 2.5, silicon bronze, ASTM F467, grade 651 Slotted hex nut, M20, ASTM A563M class 10.



1567

Table 31. American National Standard Metric Hex Jam Nuts and Heavy Hex Nuts ANSI B18.2.4.5M and B18.2.4.6M-1979 (R1998)

HEX JAM NUTS Nominal Nut Dia. and Thread Pitch

Width Across Flats, S Max

HEAVY HEX NUTS

Width Across Corners, E Min

Max

Min

Thickness, M Max


Washer Face Thickness, C

Min

Min

Max

Min

Metric Hex Jam Nuts M5 × 0.8 M6 × 1 M8 × 1.25 × 1.5 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 M30 × 3.5 M36 × 4

8.00 10.00 13.00 15.00

7.78 9.78 12.73 14.73

9.24 11.55 15.01 17.32

8.79 11.05 14.38 16.64

2.70 3.20 4.00 5.00

2.45 2.90 3.70 4.70

6.9 8.9 11.6 13.6

… … … …

… … … …

16.00 18.00 21.00 24.00 30.00 36.00 46.00 55.00

15.73 17.73 20.67 23.67 29.16 35.00 45.00 53.80

18.48 20.78 24.25 27.71 34.64 41.57 53.12 63.51

17.77 20.03 23.35 26.75 32.95 39.55 50.85 60.79

5.00 6.00 7.00 8.00 10.00 12.00 15.00 18.00

4.70 5.70 6.42 7.42 9.10 10.90 13.90 16.90

14.6 16.6 19.6 22.5 27.7 33.2 42.7 51.1

… … … … 0.8 0.8 0.8 0.8

… … … … 0.4 0.4 0.4 0.4

M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5 M22 × 2.5 M24 × 3 M27 × 3 M30 × 3.5 M36 × 4 M42 × 4.5 M48 × 5 M56 × 5.5 M64 × 6 M72 × 6 M80 × 6 M90 × 6 M100 × 6

21.00 24.00 27.00 34.00 36.00 41.00 46.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 135.00 150.00

20.16 23.16 26.16 33.00 35.00 40.00 45.00 49.00 58.80 67.90 77.60 87.20 96.80 106.40 116.00 130.50 145.00

24.25 27.71 31.18 39.26 41.57 47.34 53.12 57.74 69.28 80.83 92.38 103.92 115.47 127.02 138.56 155.88 173.21

11.9 13.6 16.4 19.4 22.3 22.9 26.3 29.1 35.0 40.4 46.4 54.1 62.1 70.1 78.1 87.8 97.8

19.2 22.0 24.9 31.4 33.3 38.0 42.8 46.6 55.9 64.5 73.7 82.8 92.0 101.1 110.2 124.0 137.8

0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2

0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6

aM10

Metric Heavy Hex Nuts 22.78 26.17 29.56 37.29 39.55 45.20 50.85 55.37 66.44 77.41 88.46 99.41 110.35 121.30 132.24 148.77 165.30

12.3 14.3 17.1 20.7 23.6 24.2 27.6 30.7 36.6 42.0 48.0 56.0 64.0 72.0 80.0 90.0 100.0

a This size with width across flats of 15 mm is not standard. Unless specifically ordered, M10 hex jam nuts with 16 mm width across flats will be furnished.




METRIC WASHERS Metric Washers

Metric Plain Washers.—American National Standard ANSI B18.22M-1981 (R1990) covers general specifications and dimensions for flat, round-hole washers, both soft (as fabricated) and hardened, intended for use in general-purpose applications. Dimensions are given in the following table. Manufacturers should be consulted for current information on stock sizes. Comparison with ISO Standards.—The washers covered by this ANSI Standard are nominally similar to those covered in various ISO documents. Outside diameters were selected, where possible, from ISO/TC2/WG6/N47 “General Plan for Plain Washers for Metric Bolts, Screws, and Nuts.” The thicknesses given in the ANSI Standard are similar to the nominal ISO thicknesses, however the tolerances differ. Inside diameters also differ. ISO metric washers are currently covered in ISO 887, “Plain Washers for Metric Bolts, Screws, and Nuts – General Plan.” Types of Metric Plain Washers.—Soft (as fabricated) washers are generally available in nominal sizes 1.6 mm through 36 mm in a variety of materials. They are normally used in low-strength applications to distribute bearing load, to provide a uniform bearing surface, and to prevent marring of the work surface. Hardened steel washers are normally available in sizes 6 mm through 36 mm in the narrow and regular series. They are intended primarily for use in high-strength joints to minimize embedment, to provide a uniform bearing surface, and to bridge large clearance holes and slots. Metric Plain Washer Materials and Finish.—Soft (as fabricated) washers are made of nonhardened steel unless otherwise specified by the purchaser. Hardened washers are made of through-hardened steel tempered to a hardness of 38 to 45 Rockwell C. Unless otherwise specified, washers are furnished with a natural (as fabricated) finish, unplated or uncoated with a light film of oil or rust inhibitor. Metric Plain Washer Designation.—When specifying metric plain washers, the designation should include the following data in the sequence shown: description, nominal size, series, material type, and finish, if required. Example:Plain washer, 6 mm, narrow, soft, steel, zinc plated Plain washer, 10 mm, regular, hardened steel.


Machinery's Handbook 27th Edition METRIC WASHERS

1569

Table 32. American National Standard Metric Plain Washers ANSI B18.22M-1981, R1990 Nominal Washer Sizea 1.6

2

2.5

3

3.5

4

5

6

8

10

12

14

16

20

24

30

36

Washer Series Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide Narrow Regular Wide

Inside Diameter, A

Outside Diameter, B

Max 2.09 2.09 2.09 2.64 2.64 2.64 3.14 3.14 3.14 3.68 3.68 3.68 4.18 4.18 4.18 4.88 4.88 4.88 5.78 5.78 5.78 6.87 6.87 6.87 9.12 9.12 9.12 11.12 11.12 11.12 13.57 13.57 13.57 15.52 15.52 15.52 17.52 17.52 17.52 22.32 22.32 22.32 26.12 26.12 26.12 33.02 33.02 33.02 38.92 38.92 38.92

Max 4.00 5.00 6.00 5.00 6.00 8.00 6.00 8.00 10.00 7.00 10.00 12.00 9.00 10.00 15.00 10.00 12.00 16.00 11.00 15.00 20.00 13.00 18.80 25.40 18.80b 25.40b 32.00 20.00 28.00 39.00 25.40 34.00 44.00 28.00 39.00 50.00 32.00 44.00 56.00 39.00 50.00 66.00 44.00 56.00 72.00 56.00 72.00 90.00 66.00 90.00 110.00

Min 1.95 1.95 1.95 2.50 2.50 2.50 3.00 3.00 3.00 3.50 3.50 3.50 4.00 4.00 4.00 4.70 4.70 4.70 5.50 5.50 5.50 6.65 6.65 6.65 8.90 8.90 8.90 10.85 10.85 10.85 13.30 13.30 13.30 15.25 15.25 15.25 17.25 17.25 17.25 21.80 21.80 21.80 25.60 25.60 25.60 32.40 32.40 32.40 38.30 38.30 38.30

Min 3.70 4.70 5.70 4.70 5.70 7.64 5.70 7.64 9.64 6.64 9.64 11.57 8.64 9.64 14.57 9.64 11.57 15.57 10.57 14.57 19.48 12.57 18.37 24.88 18.37b 24.48b 31.38 19.48 27.48 38.38 24.88 33.38 43.38 27.48 38.38 49.38 31.38 43.38 54.80 38.38 49.38 64.80 43.38 54.80 70.80 54.80 70.80 88.60 64.80 88.60 108.60

Thickness, C Max 0.70 0.70 0.90 0.90 0.90 0.90 0.90 0.90 1.20 0.90 1.20 1.40 1.20 1.40 1.75 1.20 1.40 2.30 1.40 1.75 2.30 1.75 1.75 2.30 2.30 2.30 2.80 2.30 2.80 3.50 2.80 3.50 3.50 2.80 3.50 4.00 3.50 4.00 4.60 4.00 4.60 5.10 4.60 5.10 5.60 5.10 5.60 6.40 5.60 6.40 8.50

Min 0.50 0.50 0.60 0.60 0.60 0.60 0.60 0.60 0.80 0.60 0.80 1.00 0.80 1.00 1.20 0.80 1.00 1.60 1.00 1.20 1.60 1.20 1.20 1.60 1.60 1.60 2.00 1.60 2.00 2.50 2.00 2.50 2.50 2.00 2.50 3.00 2.50 3.00 3.50 3.00 3.50 4.00 3.50 4.00 4.50 4.00 4.50 5.00 4.50 5.00 7.00

a Nominal washer sizes are intended for use with comparable screw and bolt sizes. b The 18.80⁄18.37 and 25.40⁄24.48 mm outside diameters avoid washers which could be used in coin-operated devices. All dimensions are in millimeters.



BOLTS, SCREWS, AND NUTS

BRITISH FASTENERS British Standard Square and Hexagon Bolts, Screws and Nuts.—Important dimensions of precision hexagon bolts, screws and nuts (BSW and BSF threads) as covered by British Standard 1083:1965 are given in Tables 1 and 2. The use of fasteners in this standard will decrease as fasteners having Unified inch and ISO metric threads come into increasing use. Dimensions of Unified precision hexagon bolts, screws and nuts (UNC and UNF threads) are given in BS 1768:1963 (obsolescent); of Unified black hexagon bolts, screws and nuts (UNC and UNF threads) in BS 1769:1951 (obsolescent); and of Unified black square and hexagon bolts, screws and nuts (UNC and UNF threads) in BS 2708:1956 (withdrawn). Unified nominal and basic dimensions in these British Standards are the same as the comparable dimensions in the American Standards, but the tolerances applied to these basic dimensions may differ because of rounding-off practices and other factors. For Unified dimensions of square and hexagon bolts and nuts as given in ANSI/ASME B18.2.1-1996 and ANSI/ASME B18.2.2-1987 (R1999) see Tables 1 through 4 starting on page 1514, and 7 to 10 starting on page 1519. ISO metric precision hexagon bolts, screws and nuts are specified in the British Standard BS 3692:1967 (obsolescent) (see British Standard ISO Metric Precision Hexagon Bolts, Screws and Nuts starting on page 1578), and ISO metric black hexagon bolts, screws and nuts are covered by British Standard BS 4190:1967 (obsolescent). See the section MACHINE SCREWS AND NUTS starting on page 1587 for information on British Standard metric, Unified, Whitworth, and BSF machine screws and nuts. British Standard Screwed Studs.—General purpose screwed studs are covered in British Standard 2693: Part 1:1956. The aim in this standard is to provide for a stud having tolerances which would not render it expensive to manufacture and which could be used in association with standard tapped holes for most purposes. Provision has been made for the use of both Unified Fine threads, Unified Coarse threads, British Standard Fine threads, and British Standard Whitworth threads as shown in the table on page 1573. Designations: The metal end of the stud is the end which is screwed into the component. The nut end is the end of the screw of the stud which is not screwed into the component. The plain portion of the stud is the unthreaded length. Recommended Fitting Practices for Metal End of Stud: It is recommended that holes tapped to Class 3B limits (see Table 3 starting on page 1736) in accordance with B.S. 1580 “Unified Screw Threads“ or to Close Class limits in accordance with B.S. 84 “Screw Threads of Whitworth Form” as appropriate, be used in association with the metal end of the stud specified in this standard. Where fits are not critical, however, holes may be tapped to Class 2B limits (see table on page 1736) in accordance with B.S. 1580 or Normal Class limits in accordance with B.S. 84. It is recommended that the B.A. stud specified in this standard be associated with holes tapped to the limits specified for nuts in B.S. 93, 1919 edition. Where fits for these studs are not critical, holes may be tapped to limits specified for nuts in the current edition of B.S. 93. In general, it will be found that the amount of oversize specified for the studs will produce a satisfactory fit in conjunction with the standard tapping as above. Even when interference is not present, locking will take place on the thread runout which has been carefully controlled for this purpose. Where it is considered essential to assure a true interference fit, higher grade studs should be used. It is recommended that standard studs be used even under special conditions where selective assembly may be necessary.


; ; ;; ;;


British Standard Whitworth (BSW) and Fine (BSF) Precision Hexagon Bolts, Screws, and Nuts A

R

F

C

B

G

D

R

F

45

B

G

F

R

Alternative Ends

D

D

0.015 30 Hexagon Head Bolt, Washer Faced

0.015 30 Hexagon Head Screw, Washer Faced

11/4" D Rad. Approx.

30

Alternative Full-Bearing Head

A C

E E

0.015

A

E

C

G

D

D

Rolled Thread End

H

Chamfer

Hexagon Nut, Full

30 Ordinary Bearing

30 30 Double Chamfered

30 30 Hexagon Lock-Nut

30 Washer Faced

Alternative Hexagon Slotted Nuts

A C

D

P H

A 0.015

P

C

M

G

30

30

Double Chamfered

30 Washer Faced

D

J

N

Sharp Edge Removed

J

J

K

M

L 30

Hexagon Castle Nut, Full Bearing

For dimensions, see Tables 1 and 2.


0.015

G

L 30

30

Double Chamfered

30 Washer Faced

1571

30 Hexagon Slotted Nut, Full Bearing

Enlarged View of Nut Countersink

Alternate Hexagon Castle Nuts

P

N

120–+ 10


Alternative Hexagon Ordinary Nuts

Rounded End


Bolts, Screws, and Nuts

Bolts and Screws

Width Number of Threads per Inch

Across Flats A

BSW

BSF

1⁄ 4

20

26

5⁄ 16

18

3⁄ 8

16

7⁄ 16

Diameter of Washer Face G

Radius Under Head R

Nuts Thickness Head F

Thickness Ordinary E

Lock H

Max.

Min.a

Max.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

0.445

0.438

0.51

0.428

0.418

0.025

0.015

0.2500

0.2465

0.176

0.166

0.200

0.190

0.185

0.180

22

0.525

0.518

0.61

0.508

0.498

0.025

0.015

0.3125

0.3090

0.218

0.208

0.250

0.240

0.210

0.200

20

0.600

0.592

0.69

0.582

0.572

0.025

0.015

0.3750

0.3715

0.260

0.250

0.312

0.302

0.260

0.250

14

18

0.710

0.702

0.82

0.690

0.680

0.025

0.015

0.4375

0.4335

0.302

0.292

0.375

0.365

0.275

0.265

1⁄ 2

12

16

0.820

0.812

0.95

0.800

0.790

0.025

0.015

0.5000

0.4960

0.343

0.333

0.437

0.427

0.300

0.290

9⁄ 16

12

16

0.920

0.912

1.06

0.900

0.890

0.045

0.020

0.5625

0.5585

0.375

0.365

0.500

0.490

0.333

0.323

5⁄ 8

11

14

1.010

1.000

1.17

0.985

0.975

0.045

0.020

0.6250

0.6190

0.417

0.407

0.562

0.552

0.375

0.365

3⁄ 4

10

12

1.200

1.190

1.39

1.175

1.165

0.045

0.020

0.7500

0.7440

0.500

0.480

0.687

0.677

0.458

0.448

7⁄ 8

9

11

1.300

1.288

1.50

1.273

1.263

0.065

0.040

0.8750

0.8670

0.583

0.563

0.750

0.740

0.500

0.490

1

8

10

1.480

1.468

1.71

1.453

1.443

0.095

0.060

1.0000

0.9920

0.666

0.636

0.875

0.865

0.583

0.573

11⁄8

7

9

1.670

1.640

1.93

1.620

1.610

0.095

0.060

1.1250

1.1170

0.750

0.710

1.000

0.990

0.666

0.656

11⁄4

7

9

1.860

1.815

2.15

1.795

1.785

0.095

0.060

1.2500

1.2420

0.830

0.790

1.125

1.105

0.750

0.730

13⁄8b

…

8

2.050

2.005

2.37

1.985

1.975

0.095

0.060

1.3750

1.3650

0.920

0.880

1.250

1.230

0.833

0.813

11⁄2

6

8

2.220

2.175

2.56

2.155

2.145

0.095

0.060

1.5000

1.4900

1.000

0.960

1.375

1.355

0.916

0.896

13⁄4

5

7

2.580

2.520

2.98

2.495

2.485

0.095

0.060

1.7500

1.7400

1.170

1.110

1.625

1.605

1.083

1.063

2

4.5

7

2.760

2.700

3.19

2.675

2.665

0.095

0.060

2.0000

1.9900

1.330

1.270

1.750

1.730

1.166

1.146

a When bolts from 1⁄ to 1 inch are hot forged, the tolerance on the width across flats shall be two and a half times the tolerance shown in the table and shall be unilaterally 4

minus from maximum size. For dimensional notation, see diagram on page 1571. b Noted standard with BSW thread. All dimensions in inches except where otherwise noted.



Nominal Size D

Across Corners C

Diameter of Unthreaded Portion of Shank B

1572

Table 1. British Standard Whitworth (BSW) and Fine (BSF) Precision Hexagon Slotted and Castle Nuts BS 1083:1965 (obsolescent)


Table 2. British Standard Whitworth (BSW) and Fine (BSF) Precision Hexagon Slotted and Castle Nuts BS 1083:1965 (obsolescent) Slotted Nuts Number of Threads per Inch

Castle Nuts

Lower Face to Bottom of Slot H

Thickness P

Total Thickness J

Slotted and Castle Nuts

Lower Face to Bottom of Slot K

Castellated Portion Diameter L

Slots Width M

Depth N

BSW

BSF

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Approx.

1⁄ 4

20

26

0.200

0.190

0.170

0.160

0.290

0.280

0.200

0.190

0.430

0.425

0.100

0.090

0.090

5⁄ 16

18

22

0.250

0.240

0.190

0.180

0.340

0.330

0.250

0.240

0.510

0.500

0.100

0.090

0.090

3⁄ 8

16

20

0.312

0.302

0.222

0.212

0.402

0.392

0.312

0.302

0.585

0.575

0.100

0.090

0.090

7⁄ 16

14

18

0.375

0.365

0.235

0.225

0.515

0.505

0.375

0.365

0.695

0.685

0.135

0.125

0.140

1⁄ 2

12

16

0.437

0.427

0.297

0.287

0.577

0.567

0.437

0.427

0.805

0.795

0.135

0.125

0.140

9⁄ 16

12

16

0.500

0.490

0.313

0.303

0.687

0.677

0.500

0.490

0.905

0.895

0.175

0.165

0.187

5⁄ 8

11

14

0.562

0.552

0.375

0.365

0.749

0.739

0.562

0.552

0.995

0.985

0.175

0.165

0.187

3⁄ 4

10

12

0.687

0.677

0.453

0.443

0.921

0.911

0.687

0.677

1.185

1.165

0.218

0.208

0.234

7⁄ 8

9

11

0.750

0.740

0.516

0.506

0.984

0.974

0.750

0.740

1.285

1.265

0.218

0.208

0.234

1 11⁄8

8 7

10 9

0.875 1.000

0.865 0.990

0.595 0.720

0.585 0.710

1.155 1.280

1.145 1.270

0.875 1.000

0.865 0.990

1.465 1.655

1.445 1.635

0.260 0.260

0.250 0.250

0.280 0.280

11⁄4

7

9

1.125

1.105

0.797

0.777

1.453

1.433

1.125

1.105

1.845

1.825

0.300

0.290

0.328

13⁄8a

…

8

1.250

1.230

0.922

0.902

1.578

1.558

1.250

1.230

2.035

2.015

0.300

0.290

0.328

11⁄2

6

8

1.375

1.355

1.047

1.027

1.703

1.683

1.375

1.355

2.200

2.180

0.300

0.290

0.328

13⁄4

5

7

1.625

1.605

1.250

1.230

2.000

1.980

1.625

1.605

2.555

2.535

0.343

0.333

0.375

2

4.5

7

1.750

1.730

1.282

1.262

2.218

2.198

1.750

1.730

2.735

2.715

0.426

0.416

0.468

standard with BSW thread. For widths across flats, widths across corners, and diameter of washer face see Table 1. For dimensional notation, see diagram on page 1571.


Nominal Size D

a Not


1573

All dimensions in inches except where otherwise noted.



Table 3. British Standard ISO Metric Precision Hexagon Bolts, Screws and Nuts BS 3692:1967 (obsolescent)

Washer-Faced Hexagon Head Bolt

Washer-Faced Hexagon Head Screw

Full Bearing Head (Alternative Permissible on Bolts and Screws)

Alternative Types of End Permissible on Bolts and Screws

Normal Thickness Nut

Thin Nut

Enlarged View of Nut Countersink

Slotted Nut (Six Slots) Sizes M4 to M39 Only

Castle Nut (Six Slots) Sizes M12 to M39 Only

Castle Nut (Eight Slots) Sizes M42 to M68 Only



Table 4. British Standard ISO Metric Precision Hexagon Bolts and Screws BS 3692:1967 (obsolescent) Nom.Size and Thread Dia.a d

0.35 0.4 0.45 0.5 0.7 0.8 1 1.25 1.5 1.75 2 2 2.5 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5.5 5.5 6 6

Thread Runout a Max. 0.8 1.0 1.0 1.2 1.6 2.0 2.5 3.0 3.5 4.0 5.0 5.0 6.0 6.0 6.0 7.0 7.0 8.0 8.0 10.0 10.0 11.0 11.0 12.0 12.0 19.0 19.0 21.0 21.0

Dia. of Washer Face dt

Dia. of Unthreaded Shank d Max. Min.

Width Across Flats s Max. Min.

Width Across Corners e Max. Min.

Max.

1.6 2.0 2.5 3.0 4.0 5.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 27.0 30.0 33.0 36.0 39.0 42.0 45.0 48.0 52.0 56.0 60.0 64.0 68.0

3.2 4.0 5.0 5.5 7.0 8.0 10.0 13.0 17.0 19.0 22.0 24.0 27.0 30.0 32.0 36.0 41.0 46.0 50.0 55.0 60.0 65.0 70.0 75.0 80.0 85.0 90.0 95.0 100.0

3.7 4.6 5.8 6.4 8.1 9.2 11.5 15.0 19.6 21.9 25.4 27.7 31.2 34.6 36.9 41.6 47.3 53.1 57.7 63.5 69.3 75.1 80.8 86.6 92.4 98.1 103.9 109.7 115.5

… … … 5.08 6.55 7.55 9.48 12.43 16.43 18.37 21.37 23.27 26.27 29.27 31.21 34.98 39.98 44.98 48.98 53.86 58.86 63.76 68.76 73.76 … … … … …

1.46 1.86 2.36 2.86 3.82 4.82 5.82 7.78 9.78 11.73 13.73 15.73 17.73 19.67 21.67 23.67 26.67 29.67 32.61 35.61 38.61 41.61 44.61 47.61 51.54 55.54 59.54 63.54 67.54

3.08 3.88 4.88 5.38 6.85 7.85 9.78 12.73 16.73 18.67 21.67 23.67 26.67 29.67 31.61 35.38 40.38 45.38 49.38 54.26 59.26 64.26 69.26 74.26 79.26 84.13 89.13 94.13 99.13

3.48 4.38 5.51 6.08 7.74 8.87 11.05 14.38 18.90 21.10 24.49 26.75 30.14 33.53 35.72 39.98 45.63 51.28 55.80 61.31 66.96 72.61 78.26 83.91 89.56 95.07 100.72 106.37 112.02

Transition Dia.b da

Min.

Depth of Washer Face c

Max.

Radius Under Headb r Max. Min.

… … … 4.83 6.30 7.30 9.23 12.18 16.18 18.12 21.12 23.02 26.02 28.80 30.74 34.51 39.36 44.36 48.36 53.24 58.24 63.04 68.04 73.04 … … … … …

… … … 0.1 0.1 0.2 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.5 0.5 0.5 0.6 0.6 0.6 0.6 … … … … …

2.0 2.6 3.1 3.6 4.7 5.7 6.8 9.2 11.2 14.2 16.2 18.2 20.2 22.4 24.4 26.4 30.4 33.4 36.4 39.4 42.4 45.6 48.6 52.6 56.6 63.0 67.0 71.0 75.0

0.2 0.3 0.3 0.3 0.35 0.35 0.4 0.6 0.6 1.1 1.1 1.1 1.1 1.2 1.2 1.2 1.7 1.7 1.7 1.7 1.7 1.8 1.8 2.3 2.3 3.5 3.5 3.5 3.5

0.1 0.1 0.1 0.1 0.2 0.2 0.25 0.4 0.4 0.6 0.6 0.6 0.6 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.6 1.6 2.0 2.0 2.0 2.0

Height of Head k Max. Min. 1.225 1.525 2.125 2.125 2.925 3.650 4.15 5.65 7.18 8.18 9.18 10.18 12.215 13.215 14.215 15.215 17.215 19.26 21.26 23.26 25.26 26.26 28.26 30.26 33.31 35.31 38.31 40.31 43.31

0.975 1.275 1.875 1.875 2.675 3.35 3.85 5.35 6.82 7.82 8.82 9.82 11.785 12.785 13.785 14.785 16.785 18.74 20.74 22.74 24.74 25.74 27.74 29.74 32.69 34.69 37.69 39.69 42.69

Eccentricity of Head Max.

Eccentricity of Shank and Split Pin Hole to the Thread Max.

0.18 0.18 0.18 0.18 0.22 0.22 0.22 0.27 0.27 0.33 0.33 0.33 0.33 0.33 0.39 0.39 0.39 0.39 0.39 0.46 0.46 0.46 0.46 0.46 0.46 0.54 0.54 0.54 0.54

0.14 0.14 0.14 0.14 0.18 0.18 0.18 0.22 0.22 0.27 0.27 0.27 0.27 0.33 0.33 0.33 0.33 0.33 0.39 0.39 0.39 0.39 0.39 0.39 0.46 0.46 0.46 0.46 0.46


M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33) M36 (M39) M42 (M45) M48 (M52) M56 (M60) M64 (M68)

Pitch of Thread (Coarse PitchSeries)

a Sizes shown in parentheses are non-preferred.

All dimensions are in millimeters. For illustration of bolts and screws see Table 3.


1575

b A true radius is not essential provided that the curve is smooth and lies wholly within the maximum radius, determined from the maximum transitional diameter, and the minimum radius specified.


Nominal Size and Thread Diametera d

0.35 0.4 0.45 0.5 0.7 0.8 1 1.25 1.5 1.75 2 2 2.5 2.5 2.5 3 3 3.5 3.5 4 4 4.5 4.5 5 5 5.5 5.5 6 6

Width Across Flats s

Width Across Corners e

Thickness of Normal Nut m

Tolerance on Squareness of Thread to Face of Nutb

Eccentricity of Hexagon

Thickness of Thin Nut t

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Max.

Max.

Min.

3.20 4.00 5.00 5.50 7.00 8.00 10.00 13.00 17.00 19.00 22.00 24.00 27.00 30.00 32.00 36.00 41.00 46.00 50.00 55.00 60.00 65.00 70.00 75.00 80.00 85.00 90.00 95.00 100.00

3.08 3.88 4.88 5.38 6.85 7.85 9.78 12.73 16.73 18.67 21.67 23.67 26.67 29.67 31.61 35.38 40.38 45.38 49.38 54.26 59.26 64.26 69.26 74.26 79.26 84.13 89.13 94.13 99.13

3.70 4.60 5.80 6.40 8.10 9.20 11.50 15.00 19.60 21.90 25.4 27.7 31.20 34.60 36.90 41.60 47.3 53.1 57.70 63.50 69.30 75.10 80.80 86.60 92.40 98.10 103.90 109.70 115.50

3.48 4.38 5.51 6.08 7.74 8.87 11.05 14.38 18.90 21.10 24.49 6.75 30.14 33.53 35.72 39.98 45.63 51.28 55.80 61.31 66.96 72.61 78.26 83.91 89.56 95.07 100.72 106.37 112.02

1.30 1.60 2.00 2.40 3.20 4.00 5.00 6.50 8.00 10.00 11.00 13.00 15.00 16.00 18.00 19.00 22.00 24.00 26.00 29.00 31.00 34.00 36.00 38.00 42.00 45.00 48.00 51.00 54.00

1.05 1.35 1.75 2.15 2.90 3.70 4.70 6.14 7.64 9.64 10.57 12.57 14.57 15.57 17.57 18.48 21.48 23.48 25.48 28.48 30.38 33.38 35.38 37.38 41.38 44.38 47.38 50.26 53.26

0.05 0.06 0.08 0.09 0.11 0.13 0.17 0.22 0.29 0.32 0.37 0.41 0.46 0.51 0.54 0.61 0.70 0.78 0.85 0.94 1.03 1.11 1.20 1.29 1.37 1.46 1.55 1.63 1.72

0.14 0.14 0.14 0.14 0.18 0.18 0.18 0.22 0.22 0.27 0.27 0.27 0.27 0.33 0.33 0.33 0.33 0.33 0.39 0.39 0.39 0.39 0.39 0.39 0.46 0.46 0.46 0.46 0.46

… … … … … … … 5.0 6.0 7.0 8.0 8.0 9.0 9.0 10.0 10.0 12.0 12.0 14.0 14.0 16.0 16.0 18.0 18.0 20.0 … … … …

… … … … … … … 4.70 5.70 6.64 7.64 7.64 8.64 8.64 9.64 9.64 11.57 11.57 13.57 13.57 15.57 15.57 17.57 17.57 19.48 … … … …

a Sizes shown in parentheses are non-preferred. b As measured with the nut squareness gage described in the text and illustrated in Appendix A of the Standard and a feeler gage.

All dimensions are in millimeters. For illustration of hexagon nuts and thin nuts see Table 3.



M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33) M36 (M39) M42 (M45) M48 (M52) M56 (M60) M64 (M68)

Pitch of Thread (Coarse Pitch Series)

1576

Table 5. British Standard ISO Metric Precision Hexagon Nuts and Thin Nuts BS 3692:1967 (obsolescent)


Table 6. British Standard ISO Metric Precision Hexagon Slotted Nuts and Castle Nuts BS 3692:1967 (obsolescent) Nominal Size and Thread Diametera d

Width Across Flats s

Width Across Corners e

Diameter d2

Lower Face of Nut to Bottom of Slot m

Thickness h Max.

Min.

Radius (0.25 n) r

Width of Slot n

Min.

Eccentricity of the Slots

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

7.00

6.85

8.10

7.74

…

…

5

4.70

3.2

2.90

1.45

1.2

0.3

Max. 0.18

M5

8.00

7.85

9.20

8.87

…

…

6

5.70

4.0

3.70

1.65

1.4

0.35

0.18

M6

10.00

9.78

11.50

11.05

…

…

7.5

7.14

5

4.70

2.25

2

0.5

0.18

M8

13.00

12.73

15.00

14.38

…

…

9.5

9.14

6.5

6.14

2.75

2.5

0.625

0.22

M10

17.00

16.73

19.60

18.90

…

…

12

11.57

8

7.64

3.05

2.8

0.70

0.22

M12

19.00

18.67

21.90

21.10

17

16.57

15

14.57

10

9.64

3.80

3.5

0.875

(M14)

22.00

21.67

25.4

24.49

19

18.48

16

15.57

11

10.57

3.80

3.5

0.875

0.27

M16

24.00

23.67

27.7

26.75

22

21.48

19

18.48

13

12.57

4.80

4.5

1.125

0.27

(M18)

27.00

26.67

31.20

30.14

25

24.48

21

20.48

15

14.57

4.80

4.5

1.125

0.27

M20

30.00

29.67

34.60

33.53

28

27.48

22

21.48

16

15.57

4.80

4.5

1.125

0.33

(M22)

32.00

31.61

36.90

35.72

30

29.48

26

25.48

18

17.57

5.80

5.5

1.375

0.33 0.33

0.27

M24

36.00

35.38

41.60

39.98

34

33.38

27

26.48

19

18.48

5.80

5.5

1.375

(M27)

41.00

40.38

47.3

45.63

38

37.38

30

29.48

22

21.48

5.80

5.5

1.375

0.33

M30

46.00

45.38

53.1

51.28

42

41.38

33

32.38

24

23.48

7.36

7

1.75

0.33

(M33)

50.00

49.38

57.70

55.80

46

45.38

35

34.38

26

25.48

7.36

7

1.75

0.39

M36

55.00

54.26

63.50

61.31

50

49.38

38

37.38

29

28.48

7.36

7

1.75

0.39

(M39)

60.00

59.26

69.30

66.96

55

54.26

40

39.38

31

30.38

7.36

7

1.75

0.39

M42

65.00

64.26

75.10

72.61

58

57.26

46

45.38

34

33.38

9.36

9

2.25

0.39

(M45)

70.00

69.26

80.80

78.26

62

61.26

48

47.38

36

35.38

9.36

9

2.25

0.39

M48

75.00

74.26

86.60

83.91

65

64.26

50

49.38

38

37.38

9.36

9

2.25

0.39

(M52)

80.00

79.26

92.40

89.56

70

69.26

54

53.26

42

41.38

9.36

9

2.25

0.46

M56

85.00

84.13

98.10

95.07

75

74.26

57

56.26

45

44.38

9.36

9

2.25

0.46

(M60)

90.00

89.13

103.90

100.72

80

79.26

63

62.26

48

47.38

11.43

11

2.75

0.46

M64

95.00

94.13

109.70

106.37

85

84.13

66

65.26

51

50.26

11.43

11

2.75

0.46

(M68)

100.00

99.13

115.50

112.02

90

89.13

69

68.26

54

53.26

11.43

11

2.75

0.46


Max.

M4



1577

All dimensions are in millimeters. For illustration of hexagon slotted nuts and castle nuts see Table 3.



After several years of use of BS 2693:Part 1:1956 (obsolescent), it was recognized that it would not meet the requirements of all stud users. The thread tolerances specified could result in clearance of interference fits because locking depended on the run-out threads. Thus, some users felt that true interference fits were essential for their needs. As a result, the British Standards Committee has incorporated the Class 5 interference fit threads specified in American Standard ASA B1.12 into the BS 2693:Part 2:1964, “Recommendations for High Grade Studs.” British Standard ISO Metric Precision Hexagon Bolts, Screws and Nuts.—This British Standard BS 3692:1967 (obsolescent) gives the general dimensions and tolerances of precision hexagon bolts, screws and nuts with ISO metric threads in diameters from 1.6 to 68 mm. It is based on the following ISO recommendations and draft recommendations: R 272, R 288, DR 911, DR 947, DR 950, DR 952 and DR 987. Mechanical properties are given only with respect to carbon or alloy steel bolts, screws and nuts, which are not to be used for special applications such as those requiring weldability, corrosion resistance or ability to withstand temperatures above 300°C or below − 50°C. The dimensional requirements of this standard also apply to non-ferrous and stainless steel bolts, screws and nuts. Finish: Finishes may be dull black which results from the heat-treating operation or may be bright finish, the result of bright drawing. Other finishes are possible by mutual agreement between purchaser and producer. It is recommended that reference be made to BS 3382 “Electroplated Coatings on Threaded Components” in this respect. General Dimensions: The bolts, screws and nuts conform to the general dimensions given in Tables 3, 4, 5 and 6. Nominal Lengths of Bolts and Screws: The nominal length of a bolt or screw is the distance from the underside of the head to the extreme end of the shank including any chamfer or radius. Standard nominal lengths and tolerances thereon are given in Table 7. Table 7. British Standard ISO Metric Bolt and Screw Nominal Lengths BS 3692:1967 (obsolescent) Nominal Lengtha l 5 6 (7) 8 (9) 10 (11) 12 14 16 (18) 20 (22) 25 (28)

Tolerance ± 0.24 ± 0.24 ± 0.29 ± 0.29 ± 0.29 ± 0.29 ± 0.35 ± 0.35 ± 0.35 ± 0.35 ± 0.35 ± 0.42 ± 0.42 ± 0.42 ± 0.42

Nominal Lengtha l 30 (32) 35 (38) 40 45 50 55 60 65 70 75 80 85 …

Tolerance ± 0.42 ± 0.50 ± 0.50 ± 0.50 ± 0.50 ± 0.50 ± 0.50 ± 0.60 ± 0.60 ± 0.60 ± 0.60 ± 0.60 ± 0.60 ± 0.70 …

Nominal Lengtha l 90 (95) 100 (105) 110 (115) 120 (125) 130 140 150 160 170 180 190

Tolerance ± 0.70 ± 0.70 ± 0.70 ± 0.70 ± 0.70 ± 0.70 ± 0.70 ± 0.80 ± 0.80 ± 0.80 ± 0.80 ± 0.80 ± 0.80 ± 0.80 ± 0.925

Nominal Lengtha l 200 220 240 260 280 300 325 350 375 400 425 450 475 500 …

Tolerance ± 0.925 ± 0.925 ± 0.925 ± 1.05 ± 1.05 ± 1.05 ± 1.15 ± 1.15 ± 1.15 ± 1.15 ± 1.25 ± 1.25 ± 1.25 ± 1.25 …

a Nominal lengths shown in parentheses are non-preferred.


Bolt and Screw Ends: The ends of bolts and screws may be finished with either a 45degree chamfer to a depth slightly exceeding the depth of thread or a radius approximately


Machinery's Handbook 27th Edition BOLTS, SCREWS, AND NUTS

1579

equal to 11⁄4 times the nominal diameter of the shank. With rolled threads, the lead formed at the end of the bolt by the thread rolling operation may be regarded as providing the necesssary chamfer to the end; the end being reasonably square with the center line of the shank. Screw Thread Form: The form of thread and diameters and associated pitches of standard ISO metric bolts, screws, and nuts are in accordance with BS 3643:Part 1:1981 (1998), “Principles and Basic Data” The screw threads are made to the tolerances for the medium class of fit (6H/6g) as specified in BS 3643:Part 2:1981 (1998), “Specification for Selected Limits of Size.” Length of Thread on Bolts: The length of thread on bolts is the distance from the end of the bolt (including any chamfer or radius) to the leading face of a screw ring gage which has been screwed as far as possible onto the bolt by hand. Standard thread lengths of bolts are 2d + 6 mm for a nominal length of bolt up to and including 125 mm, 2d + 12 mm for a nominal bolt length over 125 mm up to and including 200 mm, and 2d + 25 mm for a nominal bolt length over 200 mm. Bolts that are too short for minimum thread lengths are threaded as screws and designated as screws. The tolerance on bolt thread lengths are plus two pitches for all diameters. Length of Thread on Screws: Screws are threaded to permit a screw ring gage being screwed by hand to within a distance from the underside of the head not exceeding two and a half times the pitch for diameters up to and including 52 mm and three and a half times the pitch for diameters over 52 mm. Angularity and Eccentricity of Bolts, Screws and Nuts: The axis of the thread of the nut is square to the face of the nut subject to the “squareness tolerance” given in Table 5. In gaging, the nut is screwed by hand onto a gage, having a truncated taper thread, until the thread of the nut is tight on the thread of the gage. A sleeve sliding on a parallel extension of the gage, which has a face of diameter equal to the minimum distance across the flats of the nut and exactly at 90 degrees to the axis of the gage, is brought into contact with the leading face of the nut. With the sleeve in this position, it should not be possible for a feeler gage of thickness equal to the “squareness tolerance” to enter anywhere between the leading nut face and sleeve face. The hexagon flats of bolts, screws and nuts are square to the bearing face, and the angularity of the head is within the limits of 90 degrees, plus or minus 1 degree. The eccentricity of the hexagon flats of nuts relative to the thread diameter should not exceed the values given in Table 5 and the eccentricity of the head relative to the width across flats and eccentricity between the shank and thread of bolts and screws should not exceed the values given in Table 4. Chamfering, Washer Facing and Countersinking: Bolt and screw heads have a chamfer of approximately 30 degrees on their upper faces and, at the option of the manufacturer, a washer face or full bearing face on the underside. Nuts are countersunk at an included angle of 120 degrees plus or minus 10 degrees at both ends of the thread. The diameter of the countersink should not exceed the nominal major diameter of the thread plus 0.13 mm up to and including 12 mm diameter, and plus 0.25 mm above 12 mm diameter. This stipulation does not apply to slotted, castle or thin nuts. Strength Grade Designation System for Steel Bolts and Screws: This Standard includes a strength grade designation system consisting of two figures. The first figure is one tenth of the minimum tensile strength in kgf/mm2, and the second figure is one tenth of the ratio between the minimum yield stress (or stress at permanent set limit, R0.2) and the minimum tensile strength, expressed as a percentage. For example with the strength designation grade 8.8, the first figure 8 represents 1⁄10 the minimum tensile strength of 80 kgf/mm2 and the second figure 8 represents 1⁄10 the ratio



STUDS stress at permanent set limit R 0.2 % 1 × 64 × 100 ------------------------------------------------------------------------------------ = ----- ------ --------minimum tensile strength 10 80 1

the numerical values of stress and strength being obtained from the accompanying table. Strength Grade Designations of Steel Bolts and Screws Strength Grade Designation Tensile Strength (Rm), Min.

4.6 40

4.8 40

5.6 50

5.8 50

6.6 60

6.8 60

8.8 80

10.9 12.9 14.9 100 120 140

Yield Stress (Re), Min.

24

32

30

40

36

48

…

…

…

…

Stress at Permanent Set Limit (R0.2), Min.

…

…

…

…

…

…

64

90

108

126

All stress and strength values are in kgf/mm2 units.

Strength Grade Designation System for Steel Nuts: The strength grade designation system for steel nuts is a number which is one-tenth of the specified proof load stress in kgf/mm2. The proof load stress corresponds to the minimum tensile strength of the highest grade of bolt or screw with which the nut can be used. Strength Grade Designations of Steel Nuts Strength Grade Designation Proof Load Stress (kgf/mm2)

4 40

5 50

6 60

8 80

12 120

14 140

Recommended Bolt and Nut Combinations Grade of Bolt 4.6 4.8 5.6 5.8 6.6 6.8 8.8 10.9 12.9 14.9 Recommended Grade of Nut 4 4 5 5 6 6 8 12 12 14 Note: Nuts of a higher strength grade may be substituted for nuts of a lower strength grade.

Marking: The marking and identification requirements of this Standard are only mandatory for steel bolts, screws and nuts of 6 mm diameter and larger; manufactured to strength grade designations 8.8 (for bolts or screws) and 8 (for nuts) or higher. Bolts and screws are identified as ISO metric by either of the symbols “ISO M” or “M”, embossed or indented on top of the head. Nuts may be indented or embossed by alternative methods depending on their method of manufacture. Designation: Bolts 10 mm diameter, 50 mm long manufactured from steel of strength grade 8.8, would be designated: “Bolts M10 × 50 to BS 3692 — 8.8.” Brass screws 8 mm diameter, 20 mm long would be designated: “Brass screws M8 × 20 to BS 3692.” Nuts 12 mm diameter, manufactured from steel of strength grade 6, cadmium plated could be designated: “Nuts M12 to BS 3692 — 6, plated to BS 3382: Part 1.” Miscellaneous Information: The Standard also gives mechanical properties of steel bolts, screws and nuts [i.e., tensile strengths; hardnesses (Brinell, Rockwell, Vickers); stresses (yield, proof load); etc.], material and manufacture of steel bolts, screws and nuts; and information on inspection and testing. Appendices to the Standard give information on gaging; chemical composition; testing of mechanical properties; examples of marking of bolts, screws and nuts; and a table of preferred standard sizes of bolts and screws, to name some.


Machinery's Handbook 27th Edition STUDS

1581

British Standard General Purpose Studs BS 2693:Part 1:1956 (obsolescent)

Min.

UN THREADS 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500 0.8750 1 1.0000 11⁄8 1.1250 11⁄4 1.2500 13⁄8 1.3750 11⁄2 1.5000 BS THREADS 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000

Designation No. 2 4

Max.

Minor Diameter

Min.

Max.

Min.

Major Dia.

Effective Diameter

Thds. per In.

Max.

Major Dia.

Thds. per In.

Major Dia.

Nom. Dia. D

Limits for End Screwed into Component (All threads except BA)

Min.

Effective Diameter Max.

UNF THREADS

Minor Dia.

Min.

Max.

Min.

UNC THREADS

28 24 24 20 20 18 18 16 14 12 12 12 12 12

0.2435 0.3053 0.3678 0.4294 0.4919 0.5538 0.6163 0.7406 0.8647 0.9886 1.1136 1.2386 1.3636 1.4886

0.2294 0.2265 0.2883 0.2852 0.3510 0.3478 0.4084 0.4050 0.4712 0.4675 0.5302 0.5264 0.5929 0.5889 0.7137 0.7094 0.8332 0.8286 0.9510 0.9459 1.0762 1.0709 1.2014 1.1959 1.3265 1.3209 1.4517 1.4459 BSF THREADS

0.2088 0.2643 0.3270 0.3796 0.4424 0.4981 0.5608 0.6776 0.7920 0.9029 1.0281 1.1533 1.2784 1.4036

0.2037 0.2586 0.3211 0.3729 0.4356 0.4907 0.5533 0.6693 0.7828 0.8925 1.0176 1.1427 1.2677 1.3928

20 18 16 14 13 12 11 10 9 8 7 7 6 6

0.2419 0.3038 0.3656 0.4272 0.4891 0.5511 0.6129 0.7371 0.8611 0.9850 1.1086 1.2336 1.3568 1.4818

0.2201 0.2172 0.2793 0.2762 0.3375 0.3343 0.3945 0.3911 0.4537 0.4500 0.5122 0.5084 0.5700 0.5660 0.6893 0.6850 0.8074 0.8028 0.9239 0.9188 1.0375 1.0322 1.1627 1.1572 1.2723 1.2667 1.3975 1.3917 BSW THREADS

0.1913 0.2472 0.3014 0.3533 0.4093 0.4641 0.5175 0.6316 0.7433 0.8517 0.9550 1.0802 1.1761 1.3013

0.1849 0.2402 0.2936 0.3447 0.4000 0.4542 0.5069 0.6200 0.7306 0.8376 0.9393 1.0644 1.1581 1.2832

26 22 20 18 16 16 14 12 11 10 9 9 8 8

0.2455 0.3077 0.3699 0.4320 0.4942 0.5566 0.6187 0.7432 0.8678 0.9924 1.1171 1.2419 1.3665 1.4913

0.2280 0.2863 0.3461 0.4053 0.4637 0.5263 0.5833 0.7009 0.8214 0.9411 1.0592 1.1844 1.3006 1.4258

0.2034 0.2572 0.3141 0.3697 0.4237 0.4863 0.5376 0.6475 0.7632 0.8771 0.9881 1.1133 1.2206 1.3458

0.1984 0.2517 0.3083 0.3635 0.4172 0.4797 0.5305 0.6398 0.7551 0.8686 0.9792 1.1042 1.2110 1.3360

20 18 16 14 12 12 11 10 9 8 7 7 6 …

0.2452 0.3073 0.3695 0.4316 0.4937 0.5560 0.6183 0.7428 0.8674 0.9920 1.1164 1.2413 1.4906 …

0.2206 0.2798 0.3381 0.3952 0.4503 0.5129 0.5708 0.6903 0.8085 0.9251 1.0388 1.1640 1.3991 …

0.1886 0.2442 0.0981 0.3495 0.3969 0.4595 0.5126 0.6263 0.7374 0.8451 0.9473 1.0725 1.2924 …

0.1831 0.2383 0.2919 0.3428 0.3897 0.4521 0.5050 0.6182 0.7288 0.8360 0.9376 1.0627 1.2818 …

0.2251 0.2832 0.3429 0.4019 0.4600 0.5225 0.5793 0.6966 0.8168 0.9360 1.0539 1.1789 1.2950 1.4200

0.2177 0.2767 0.3349 0.3918 0.4466 0.5091 0.5668 0.6860 0.8039 0.9200 1.0335 1.1585 1.3933 …

Limits for End Screwed into Component (BA Threads)a Major Diameter Effective Diameter Pitch 0.8100 mm 0.03189 in. 0.6600 mm 0.2598 in.

Max. 4.700 mm 0.1850 in. 3.600 mm 0.1417 in.

Min. 4.580 mm 0.1803 in. 3.500 mm 0.1378 in.

Max. 4.275 mm 0.1683 in. 3.260 mm 0.1283 in.

Min. 4.200 mm 0.1654 in. 3.190 mm 0.1256 in.

Minor Diameter Max. 3.790 mm 0.1492 in. 2.865 mm 0.1128 in.

Min. 3.620 mm 0.1425 in. 2.720 mm 0.1071 in.

a Approximate inch equivalents are shown below the dimensions given in mm.

Nom. Stud. Dia. 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

For Thread Length (Component End) of 1D 1.5D 7⁄ 1 8 11⁄8 13⁄8 13⁄8 15⁄8 15⁄8 17⁄8 2 13⁄4

Minimum Nominal Lengths of Studsa For Thread Length Nom. (Component End) of Stud. 1D 1.5D Dia. 9⁄ 2 23⁄8 16 1⁄ 5⁄ 2 25⁄8 8 4 3⁄ 3 25⁄8 4 7⁄ 31⁄8 35⁄8 8 1 1 4 3 ⁄2

Nom. Stud Dia. 11⁄8 11⁄4 13⁄8 11⁄2 …

For Thread Length (Component End) of 1D 1.5D 4 45⁄8 43⁄4 51⁄2 5 53⁄4 6 51⁄4 … …

a The standard also gives preferred and standard lengths of studs: Preferred lengths of studs: 7⁄ , 1, 8 11⁄8, 11⁄4, 13⁄8, 11⁄2, 13⁄4, 2, 21⁄4,21⁄2, 23⁄4, 3, 31⁄4, 31⁄2 and for lengths above 31⁄2 the preferred increment is 1⁄2. 7 1 1 3 1 5 3 7 1 1 3 1 5 3 7 1 Standard lengths of studs: ⁄8, 1, 1 ⁄8, 1 ⁄4, 1 ⁄8, 1 ⁄2, 1 ⁄8, 1 ⁄4, 1 ⁄8, 2, 2 ⁄8, 2 ⁄4, 2 ⁄8, 2 ⁄2, 2 ⁄8, 2 ⁄4, 2 ⁄8, 3, 3 ⁄8, 31⁄4, 33⁄8, 31⁄2 and for lengths above 31⁄2 the standard increment is 1⁄4.

All dimensions are in inches except where otherwise noted. See page 1877 for interference-fit threads.



WASHERS British Standard Single Coil Rectangular Section Spring Washers Metric Series — Types B and BP BS 4464:1969 (1998)

Nom. Size &Thread Dia., d

Max

Min

Width, b

Thickness, s

Outside Dia., d2 Max

Radius, r Max

k (Type BP Only)

M1.6 M2 (M2.2) M2.5 M3 (M3.5) M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33) M36 (M39) M42 (M45) M48 (M52) M56 (M60) M64 (M68)

1.9 2.3 2.5 2.8 3.3 3.8 4.35 5.35 6.4 8.55 10.6 12.6 14.7 16.9 19.0 21.1 23.3 25.3 28.5 31.5 34.6 37.6 40.8 43.8 46.8 50.0 54.1 58.1 62.3 66.3 70.5

1.7 2.1 2.3 2.6 3.1 3.6 4.1 5.1 6.1 8.2 10.2 12.2 14.2 16.3 18.3 20.3 22.4 24.4 27.5 30.5 33.5 36.5 39.6 42.6 45.6 48.8 52.8 56.8 60.9 64.9 69.0

0.7 ± 0.1 0.9 ± 0.1 1.0 ± 0.1 1.0 ± 0.1 1.3 ± 0.1 1.3 ± 0.1 1.5 ± 0.1 1.8 ± 0.1 2.5 ± 0.15 3 ± 0.15 3.5 ± 0.2 4 ± 0.2 4.5 ± 0.2 5 ± 0.2 5 ± 0.2 6 ± 0.2 6 ± 0.2 7 ± 0.25 7 ± 0.25 8 ± 0.25 10 ± 0.25 10 ± 0.25 10 ± 0.25 12 ± 0.25 12 ± 0.25 12 ± 0.25 14 ± 0.25 14 ± 0.25 14 ± 0.25 14 ± 0.25 14 ± 0.25

0.4 ± 0.1 0.5 ± 0.1 0.6 ± 0.1 0.6 ± 0.1 0.8 ± 0.1 0.8 ± 0.1 0.9 ± 0.1 1.2 ± 0.1 1.6 ± 0.1 2 ± 0.1 2.2 ± 0.15 2.5 ± 0.15 3 ± 0.15 3.5 ± 0.2 3.5 ± 0.2 4 ± 0.2 4 ± 0.2 5 ± 0.2 5 ± 0.2 6 ± 0.25 6 ± 0.25 6 ± 0.25 6 ± 0.25 7 ± 0.25 7 ± 0.25 7 ± 0.25 8 ± 0.25 8 ± 0.25 8 ± 0.25 8 ± 0.25 8 ± 0.25

3.5 4.3 4.7 5.0 6.1 6.6 7.55 9.15 11.7 14.85 18.0 21.0 24.1 27.3 29.4 33.5 35.7 39.8 43.0 48.0 55.1 58.1 61.3 68.3 71.3 74.5 82.6 86.6 90.8 93.8 99.0

0.15 0.15 0.2 0.2 0.25 0.25 0.3 0.4 0.5 0.65 0.7 0.8 1.0 1.15 1.15 1.3 1.3 1.65 1.65 2.0 2.0 2.0 2.0 2.3 2.3 2.3 2.65 2.65 2.65 2.65 2.65

… … … … … 0.15 0.15 0.15 0.2 0.3 0.3 0.4 0.4 0.4 0.4 0.4 0.4 0.5 0.5 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0

Inside Dia.,d1

All dimensions are given in millimeters. Sizes shown in parentheses are non-preferred, and are not usually stock sizes.


Machinery's Handbook 27th Edition WASHERS

1583

British Standard Double Coil Rectangular Section Spring Washers; Metric Series — Type D BS 4464:1969 (1998)

Inside Dia., d1

Nom. Size, d

Max

Min

Width, b

Thickness, s

O.D., d2 Max

Radius, r Max

M2 (M2.2) M2.5 M3.0 (M3.5) M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33)

2.4 2.6 2.9 3.6 4.1 4.6 5.6 6.6 8.8 10.8 12.8 15.0 17.0 19.0 21.5 23.5 26.0 29.5 33.0 36.0

2.1 2.3 2.6 3.3 3.8 4.3 5.3 6.3 8.4 10.4 12.4 14.5 16.5 18.5 20.8 22.8 25.0 28.0 31.5 34.5

0.9 ± 0.1 1.0 ± 0.1 1.2 ± 0.1 1.2 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 2 ± 0.1 3 ± 0.15 3 ± 0.15 3.5 ± 0.20 3.5 ± 0.2 5 ± 0.2 5 ± 0.2 5 ± 0.2 5 ± 0.2 6 ± 0.2 6.5 ± 0.2 7 ± 0.25 8 ± 0.25 8 ± 0.25

0.5 ± 0.05 0.6 ± 0.05 0.7 ± 0.1 0.8 ± 0.1 0.8 ± 0.1 0.8 ± 0.1 0.9 ± 0.1 1 ± 0.1 1.2 ± 0.1 1.2 ± 0.1 1.6 ± 0.1 1.6 ± 0.1 2 ± 0.1 2 ± 0.1 2 ± 0.1 2.5 ± 0.15 3.25 ± 0.15 3.25 ± 0.15 3.25 ± 0.15

4.4 4.8 5.5 6.2 7.5 8.0 9.8 12.9 15.1 18.2 20.2 25.4 27.4 29.4 31.9 35.9 39.4 44.0 49.5

0.15 0.2 0.23 0.25 0.25 0.25 0.3 0.33 0.4 0.4 0.5 0.5 0.65 0.65 0.65 0.8 1.1 1.1 1.1

M36 (M39) M42 M48 M56 M64

40.0 43.0 46.0 52.0 60.0 70.0

38.0 41.0 44.0 50.0 58.0 67.0

10 ± 0.25 10 ± 0.25 10 ± 0.25 10 ± 0.25 12 ± 0.25 12 ± 0.25

3.25 ± 0.15 3.25 ± 0.15 3.25 ± 0.15 4.5 ± 0.2 4.5 ± 0.2 4.5 ± 0.2 4.5 ± 0.2

52.5 60.5 63.5 66.5 72.5 84.5 94.5

1.1 1.1 1.1 1.5 1.5 1.5 1.5

All dimensions are given in millimeters. Sizes shown in parentheses are non-preferred, and are not usually stock sizes. The free height of double coil washers before compression is normally approximately five times the thickness but, if required, washers with other free heights may be obtained by arrangement with manufacturer.



WASHERS

British Standard Single Coil Square Section Spring Washers; Metric Series — Type A-1 BS 4464:1969 (1998)

British Standard Single Coil Square Section Spring Washers; Metric Series — Type A-2 BS 4464:1969 (1998) Inside Dia., d1

Nom. Size, d

Max

Min

Thickness & Width, s

O.D., d2 Max

Radius, r Max

M3 (M3.5) M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33) M36 (M39) M42 (M45) M48

3.3 3.8 4.35 5.35 6.4 8.55 10.6 12.6 14.7 16.9 19.0 21.1 23.3 25.3 28.5 31.5 34.6 37.6 40.8 43.8 46.8 50.0

3.1 3.6 4.1 5.1 6.1 8.2 10.2 12.2 14.2 16.3 18.3 20.3 22.4 24.4 27.5 30.5 33.5 36.5 39.6 42.6 45.6 48.8

1 ± 0.1 1 ± 0.1 1.2 ± 0.1 1.5 ± 0.1 1.5 ± 0.1 2 ± 0.1 2.5 ± 0.15 2.5 ± 0.15 3 ± 0.2 3.5 ± 0.2 3.5 ± 0.2 4.5 ± 0.2 4.5 ± 0.2 5 ± 0.2 5 ± 0.2 6 ± 0.2 6 ± 0.2 7 ± 0.25 7 ± 0.25 8 ± 0.25 8 ± 0.25 8 ± 0.25

5.5 6.0 6.95 8.55 9.6 12.75 15.9 17.9 21.1 24.3 26.4 30.5 32.7 35.7 38.9 43.9 47.0 52.1 55.3 60.3 63.3 66.5

0.3 0.3 0.4 0.5 0.5 0.65 0.8 0.8 1.0 1.15 1.15 1.5 1.5 1.65 1.65 2.0 2.0 2.3 2.3 2.65 2.65 2.65

All dimensions are in millimeters. Sizes shown in parentheses are nonpreferred and are not usually stock sizes.

British Standard for Metric Series Metal Washers.—BS 4320:1968 (1998) specifies bright and black metal washers for general engineering purposes. Bright Metal Washers: These washers are made from either CS4 cold-rolled strip steel BS 1449:Part 3B or from CZ 108 brass strip B.S. 2870: 1980, both in the hard condition. However, by mutual agreement between purchaser and supplier, washers may be made available with the material in any other condition, or they may be made from another material, or may be coated with a protective or decorative finish to some appropriate British Standard. Washers are reasonably flat and free from burrs and are normally supplied unchamfered. They may, however, have a 30-degree chamfer on one edge of the external diameter. These washers are made available in two size categories, normal and large diameter, and in two thicknesses, normal (Form A or C) and light (Form B or D). The thickness of a light-range washer is from 1⁄2 to 2⁄3 the thickness of a normal range washer. Black Metal Washers: These washers are made from mild steel, and can be supplied in three size categories designated normal, large, and extra large diameters. The normaldiameter series is intended for bolts ranging from M5 to M68 (Form E washers), the largediameter series for bolts ranging from M8 to M39 (Form F washers), and the extra large series for bolts from M5 to M39 (Form G washers). A protective finish can be specified by the purchaser in accordance with any appropriate British Standard.


Machinery's Handbook 27th Edition WASHERS

1585

Washer Designations: The Standard specifies the details that should be given when ordering or placing an inquiry for washers. These details are the general description, namely, bright or black washers; the nominal size of the bolt or screw involved, for example, M5; the designated form, for example, Form A or Form E; the dimensions of any chamfer required on bright washers; the number of the Standard BS 4320:1968 (1998), and coating information if required, with the number of the appropriate British Standard and the coating thickness needed. As an example, in the use of this information, the designation for a chamfered, normal-diameter series washer of normal-range thickness to suit a 12-mm diameter bolt would be: Bright washers M12 (Form A) chamfered to B.S. 4320. British Standard Bright Metal Washers — Metric Series BS 4320:1968 (1998) NORMAL DIAMETER SIZES Nominal Size of Bolt or Screw M 1.0 M 1.2 (M 1.4) M 1.6 M 2.0 (M 2.2) M 2.5 M3 (M 3.5) M4 (M 4.5) M5 M6 (M 7) M8 M 10 M 12 (M 14) M 16 (M 18) M 20 (M 22) M24 (M 27) M30 (M 33) M 36 (M 39) Nominal Size of Bolt or Screw M4 M5 M6 M8 M 10 M 12 (M 14) M 16 (M 18) M 20 (M 22) M 24 (M 27) M 30 (M 33) M 36 (M 39)

Thickness Inside Diameter Nom 1.1 1.3 1.5 1.7 2.2 2.4 2.7 3.2 3.7 4.3 4.8 5.3 6.4 7.4 8.4 10.5 13.0 15.0 17.0 19.0 21 23 25 28 31 34 37 40

Max 1.25 1.45 1.65 1.85 2.35 2.55 2.85 3.4 3.9 4.5 5.0 5.5 6.7 7.7 8.7 10.9 13.4 15.4 17.4 19.5 21.5 23.5 25.5 28.5 31.6 34.6 37.6 40.6

Outside Diameter

Min 1.1 1.3 1.5 1.7 2.2 2.4 2.7 3.2 3.7 4.3 4.8 5.3 6.4 7.4 8.4 10.5 13.0 15.0 17.0 19.0 21 23 25 28 31 34 37 40

Form A (Normal Range) Nom Max Min Nom Max Min 2.5 2.5 2.3 0.3 0.4 0.2 3.0 3.0 2.8 0.3 0.4 0.2 3.0 3.0 2.8 0.3 0.4 0.2 4.0 4.0 3.7 0.3 0.4 0.2 5.0 5.0 4.7 0.3 0.4 0.2 5.0 5.0 4.7 0.5 0.6 0.4 6.5 6.5 6.2 0.5 0.6 0.4 7 7 6.7 0.5 0.6 0.4 7 7 6.7 0.5 0.6 0.4 9 9 8.7 0.8 0.9 0.7 9 9 8.7 0.8 0.9 0.7 10 10 9.7 1.0 1.1 0.9 12.5 12.5 12.1 1.6 1.8 1.4 14 14 13.6 1.6 1.8 1.4 17 17 16.6 1.6 1.8 1.4 21 21 20.5 2.0 2.2 1.8 24 24 23.5 2.5 2.7 2.3 28 28 27.5 2.5 2.7 2.3 30 30 29.5 3.0 3.3 2.7 34 34 33.2 3.0 3.3 2.7 37 37 36.2 3.0 3.3 2.7 39 39 38.2 3.0 3.3 2.7 44 44 43.2 4.0 4.3 3.7 50 50 49.2 4.0 4.3 3.7 56 56 55.0 4.0 4.3 3.7 60 60 59.0 5.0 5.6 4.4 66 66 65.0 5.0 5.6 4.4 72 72 71.0 6.0 6.6 5.4 LARGE DIAMETER SIZES

Nom … … … … … … … … … … … … 0.8 0.8 1.0 1.25 1.6 1.6 2.0 2.0 2.0 2.0 2.5 2.5 2.5 3.0 3.0 3.0

Form B (Light Range) Max … … … … … … … … … … … … 0.9 0.9 1.1 1.45 1.80 1.8 2.2 2.2 2.2 2.2 2.7 2.7 2.7 3.3 3.3 3.3

Min … … … … … … … … … … … … 0.7 0.7 0.9 1.05 1.40 1.4 1.8 1.8 1.8 1.8 2.3 2.3 2.3 2.7 2.7 2.7

Thickness Inside Diameter Nom 4.3 5.3 6.4 8.4 10.5 13.0 15.0 17.0 19.0 21 23 25 28 31 34 37 40

Max 4.5 5.5 6.7 8.7 10.9 13.4 15.4 17.4 19.5 21.5 23.5 25.5 28.5 31.6 34.6 37.6 40.6

Outside Diameter Min 4.3 5.3 6.4 8.4 10.5 13.0 15 17 19 21 23 25 28 31 34 37 40

Nom 10.0 12.5 14 21 24 28 30 34 37 39 44 50 56 60 66 72 77

Max 10.0 12.5 14 21 24 28 30 34 37 39 44 50 56 60 66 72 77

Min 9.7 12.1 13.6 20.5 23.5 27.5 29.5 33.2 36.2 38.2 43.2 49.2 55 59 65 71 76

Form C (Normal Range) Nom Max Min 0.8 0.9 0.7 1.0 1.1 0.9 1.6 1.8 1.4 1.6 1.8 1.4 2.0 2.2 1.8 2.5 2.7 2.3 2.5 2.7 2.3 3.0 3.3 2.7 3.0 3.3 2.7 3.0 3.3 2.7 3.0 3.3 2.7 4.0 4.3 3.7 4.0 4.3 3.7 4.0 4.3 3.7 5.0 5.6 4.4 5.0 5.6 4.4 6.0 6.6 5.4

Nom … … 0.8 1.0 1.25 1.6 1.6 2.0 2.0 2.0 2.0 2.5 2.5 2.5 3.0 3.0 3.0

All dimensions are in millimeters. Nominal bolt or screw sizes shown in parentheses are nonpreferred.


Form D (Light Range) Max … … 0.9 1.1 1.45 1.8 1.8 2.2 2.2 2.2 2.2 2.7 2.7 2.7 3.3 3.3 3.3

Min … … 0.7 0.9 1.05 1.4 1.4 1.8 1.8 1.8 1.8 2.3 2.3 2.3 2.7 2.7 2.7


Next page

WASHERS

British Standard Black Metal Washers — Metric Series BS 4320:1968 (1998) Inside Diameter

NORMAL DIAMETER SIZES (Form E) Outside Diameter

Nom Bolt or Screw Size

Nom

Max

Min

M5 M6 (M 7) M8 M 10 M 12 (M 14) M 16 (M 18) M 20 (M 22) M 24 (M 27) M 30 (M 33) M 36 (M 39) M 42 (M 45) M 48 (M 52) M 56 (M 60) M 64 (M 68)

5.5 6.6 7.6 9.0 11.0 14 16 18 20 22 24 26 30 33 36 39 42 45 48 52 56 62 66 70 74

5.8 7.0 8.0 9.4 11.5 14.5 16.5 18.5 20.6 22.6 24.6 26.6 30.6 33.8 36.8 39.8 42.8 45.8 48.8 53 57 63 67 71 75

5.5 6.6 7.6 9.0 11.0 14 16 18 20 22 24 26 30 33 36 39 42 45 48 52 56 62 66 70 74

M8 M 10 M 12 (M 14) M 16 (M 18) M 20 (M 22) M 24 (M 27) M 30 (M 33) M 36 (M 39)

9 11 14 16 18 20 22 24 26 30 33 36 39 42

9.4 11.5 14.5 16.5 18.5 20.6 22.6 24.6 26.6 30.6 33.8 36.8 39.8 42.8

M5 M6 (M 7) M8 M 10 M 12 (M 14) M 16 (M 18) M 20 (M 22) M 24 (M 27) M 30 (M 33) M 36 (M39)

5.5 6.6 7.6 9 11 14 16 18 20 22 24 26 30 33 36 39 42

5.8 7.0 8.0 9.4 11.5 14.5 16.5 18.5 20.6 22.6 24.6 26.6 30.6 33.8 36.8 39.8 42.8

Nom

Max

Min

10.0 10.0 9.2 12.5 12.5 11.7 14.0 14.0 13.2 17 17 16.2 21 21 20.2 24 24 23.2 28 28 27.2 30 30 29.2 34 34 32.8 37 37 35.8 39 39 37.8 44 44 42.8 50 50 48.8 56 56 54.5 60 60 58.5 66 66 64.5 72 72 70.5 78 78 76.5 85 85 83 92 92 90 98 98 96 105 105 103 110 110 108 115 115 113 120 120 118 LARGE DIAMETER SIZES (Form F) 9.0 21 21 20.2 11 24 24 23.2 14 28 28 27.2 16 30 30 29.2 18 34 34 32.8 20 37 37 35.8 22 39 39 37.8 24 44 44 42.8 26 50 50 48.8 30 56 56 54.5 33 60 60 58.5 36 66 66 64.5 39 72 72 70.5 42 77 77 75.5 EXTRA LARGE DIAMETER SIZES (Form G) 5.5 15 15 14.2 6.6 18 18 17.2 7.6 21 21 20.2 9.0 24 24 23.2 11.0 30 30 29.2 14.0 36 36 34.8 16.0 42 42 40.8 18 48 48 46.8 20 54 54 52.5 22 60 60 58.5 24 66 66 64.5 26 72 72 70.5 30 81 81 79 33 90 90 88 36 99 99 97 39 108 108 106 42 117 117 115

Thickness Nom

Max

Min

1.0 1.6 1.6 1.6 2.0 2.5 2.5 3.0 3.0 3.0 3.0 4 4 4 5 5 6 7 7 8 8 9 9 9 10

1.2 1.9 1.9 1.9 2.3 2.8 2.8 3.6 3.6 3.6 3.6 4.6 4.6 4.6 6.0 6.0 7.0 8.2 8.2 9.2 9.2 10.2 10.2 10.2 11.2

0.8 1.3 1.3 1.3 1.7 2.2 2.2 2.4 2.4 2.4 2.4 3.4 3.4 3.4 4.0 4.0 5.0 5.8 5.8 6.8 6.8 7.8 7.8 7.8 8.8

1.6 2 2.5 2.5 3 3 3 3 4 4 4 5 5 6

1.9 2.3 2.8 2.8 3.6 3.6 3.6 3.6 4.6 4.6 4.6 6.0 6.0 7

1.3 1.7 2.2 2.2 2.4 2.4 2.4 2.4 3.4 3.4 3.4 4 4 5

1.6 2 2 2 2.5 3 3 4 4 5 5 6 6 8 8 10 10

1.9 2.3 2.3 2.3 2.8 3.6 3.6 4.6 4.6 6.0 6.0 7 7 9.2 9.2 11.2 11.2

1.3 1.7 1.7 1.7 2.2 2.4 2.4 3.4 3.4 4 4 5 5 6.8 6.8 8.8 8.8

All dimensions are in millimeters. Nominal bolt or screw sizes shown in parentheses are nonpreferred.



Previous page

MACHINE SCREWS

1587

MACHINE SCREWS AND NUTS American National Standard Machine Screws and Machine Screw Nuts.—T h i s Standard ANSI B18.6.3 covers both slotted and recessed head machine screws. Dimensions of various types of slotted machine screws, machine screw nuts, and header points are given in Tables 1 through 12. The Standard also covers flat trim head, oval trim head and drilled fillister head machine screws and gives cross recess dimensions and gaging dimensions for all types of machine screw heads. Information on metric machine screws B18.6.7M is given beginning on page 1596. Threads: Except for sizes 0000, 000, and 00, machine screw threads may be either Unified Coarse (UNC) and Fine thread (UNF) Class 2A (see American Standard for Unified Screw Threads starting on page 1732) or UNRC and UNRF Series, at option of manufacturer. Thread dimensions for sizes 0000, 000, and 00 are given in Table 7 on page 1592. Threads for hexagon machine screw nuts may be either UNC or UNF, Class 2B, and for square machine screw nuts are UNC Class 2B. Length of thread: Machine screws of sizes No. 5 and smaller with nominal lengths equal to 3 diameters and shorter have full form threads extending to within 1 pitch (thread) of the bearing surface of the head, or closer, if practicable. Nominal lengths greater than 3 diameters, up to and including 11⁄8 inch, have full form threads extending to within two pitches (threads) of the bearing surface of the head, or closer, if practicable. Unless otherwise specified, screws of longer nominal length have a minimum length of full form thread of 1.00 inch.Machine screws of sizes No. 6 and larger with nominal length equal to 3 diameters and shorter have full form threads extending to within 1 pitch (thread) of the bearing surface of the head, or closer, if practicable. Nominal lengths greater than 3 diameters, up to and including 2 inches, have full form threads extending to within 2 pitches (threads) of the bearing surface of the head, or closer, if practicable. Screws of longer nominal length, unless otherwise specified, have a minimum length of full form thread of 1.50 inches. Table 1. Square and Hexagon Machine Screw Nuts ANSI B18.6.3-1972 (R1991) F

H

F

H

Optional; See Note G1

G 30

30 Nom. Size 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8

Basic Dia. 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750

Basic F 5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 5⁄ 16 11⁄ 32 3⁄ 8 7⁄ 16 7⁄ 16 9⁄ 16 5⁄ 8

Max. F 0.156 0.156 0.188 0.188 0.250 0.312 0.312 0.344 0.375 0.438 0.438 0.562 0.625

Min. F 0.150 0.150 0.180 0.180 0.241 0.302 0.302 0.332 0.362 0.423 0.423 0.545 0.607

Max. G 0.221 0.221 0.265 0.265 0.354 0.442 0.442 0.486 0.530 0.619 0.619 0.795 0.884

Min. G 0.206 0.206 0.247 0.247 0.331 0.415 0.415 0.456 0.497 0.581 0.581 0.748 0.833

Max. G1

Min. G1

0.180 0.180 0.217 0.217 0.289 0.361 0.361 0.397 0.433 0.505 0.505 0.650 0.722

0.171 0.171 0.205 0.205 0.275 0.344 0.344 0.378 0.413 0.482 0.482 0.621 0.692

Max. H 0.050 0.050 0.066 0.066 0.098 0.114 0.114 0.130 0.130 0.161 0.193 0.225 0.257

Min. H 0.043 0.043 0.057 0.057 0.087 0.102 0.102 0.117 0.117 0.148 0.178 0.208 0.239

All dimensions in inches. Hexagon machine screw nuts have tops flat and chamfered. Diameter of top circle should be the maximum width across flats within a tolerance of minus 15 per cent. Bottoms are flat but may be chamfered if so specified. Square machine screw nuts have tops and bottoms flat without chamfer.



MACHINE SCREWS

Diameter of body: The diameter of machine screw bodies is not less than Class 2A thread minimum pitch diameter nor greater than the basic major diameter of the thread. Crossrecessed trim head machine screws not threaded to the head have an 0.062 in. minimum length shoulder under the head with diameter limits as specified in the dimensional tables in the standard. Designation: Machine screws are designated by the following data in the sequence shown: Nominal size (number, fraction, or decimal equivalent); threads per inch; nominal length (fraction or decimal equivalent); product name, including head type and driving provision; header point, if desired; material; and protective finish, if required. For example: 1⁄ − 20 × 11⁄ Slotted Pan Head Machine Screw, Steel, Zinc Plated 4 4 6 − 32 × 3⁄4 Type IA Cross Recessed Fillister Head Machine Screw, Brass Machine screw nuts are designated by the following data in the sequence shown: Nominal size (number, fraction, or decimal equivalent); threads per inch; product name; material; and protective finish, if required. For example: 10 − 24 Hexagon Machine Screw Nut, Steel, Zinc Plated 0.138 − 32 Square Machine Screw Nut, Brass Table 2. American National Standard Slotted 100-Degree Flat Countersunk Head Machine Screws ANSI B18.6.3-1972 (R1977) T J 99 101

A

H L Nominal Sizea or Basic Screw Dia. 0000 000 00 0 1 2 3 4 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8

0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1380 0.1640 0.1900 0.2500 0.3125 0.3750

Head Dia., A Min., Max., Edge Edge Rounded Sharp or Flat 0.043 0.037 0.064 0.058 0.093 0.085 0.119 0.096 0.146 0.120 0.172 0.143 0.199 0.167 0.225 0.191 0.279 0.238 0.332 0.285 0.385 0.333 0.507 0.442 0.635 0.556 0.762 0.670

Head Height, H Ref. 0.009 0.014 0.020 0.026 0.031 0.037 0.043 0.049 0.060 0.072 0.083 0.110 0.138 0.165

Slot Width, J Max. 0.008 0.012 0.017 0.023 0.026 0.031 0.035 0.039 0.048 0.054 0.060 0.075 0.084 0.094

Min. 0.005 0.008 0.010 0.016 0.019 0.023 0.027 0.031 0.039 0.045 0.050 0.064 0.072 0.081

Slot Depth, T Max. 0.008 0.011 0.013 0.013 0.016 0.019 0.022 0.024 0.030 0.036 0.042 0.055 0.069 0.083

Min. 0.004 0.007 0.008 0.008 0.010 0.012 0.014 0.017 0.022 0.027 0.031 0.042 0.053 0.065

a When specifying nominal size in decimals, zeros preceding the decimal point and in the fourth decimal place are omitted. All dimensions are in inches.


Machinery's Handbook 27th Edition MACHINE SCREWS

1589

Table 3. American National Standard Slotted Flat Countersunk Head and Close Tolerance 100-Degree Flat Countersunk Head Machine Screws ANSI B18.6.3-1972 (R1991)

Nominal Sizea or Basic Screw Dia. 0000 000 00 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Max., Lb

0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

SLOTTED FLAT COUNTERSUNK HEAD TYPE Head Dia., A Head Slot Height, H Width, J Min., Max., Edge c Sharp Edge Ref. Max. Min.

.... .... .... 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 … … …

0.043 0.064 0.093 0.119 0.146 0.172 0.199 0.225 0.252 0.279 0.332 0.385 0.438 0.507 0.635 0.762 0.812 0.875 1.000 1.125 1.375

0.037 0.058 0.085 0.099 0.123 0.147 0.171 0.195 0.220 0.244 0.292 0.340 0.389 0.452 0.568 0.685 0.723 0.775 0.889 1.002 1.230

0.011 0.016 0.028 0.035 0.043 0.051 0.059 0.067 0.075 0.083 0.100 0.116 0.132 0.153 0.191 0.230 0.223 0.223 0.260 0.298 0.372

0.008 0.011 0.017 0.023 0.026 0.031 0.035 0.039 0.043 0.048 0.054 0.060 0.067 0.075 0.084 0.094 0.094 0.106 0.118 0.133 0.149

0.004 0.007 0.010 0.016 0.019 0.023 0.027 0.031 0.035 0.039 0.045 0.050 0.056 0.064 0.072 0.081 0.081 0.091 0.102 0.116 0.131

Slot Depth, T Max.

Min.

0.007 0.009 0.014 0.015 0.019 0.023 0.027 0.030 0.034 0.038 0.045 0.053 0.060 0.070 0.088 0.106 0.103 0.103 0.120 0.137 0.171

0.003 0.005 0.009 0.010 0.012 0.015 0.017 0.020 0.022 0.024 0.029 0.034 0.039 0.046 0.058 0.070 0.066 0.065 0.077 0.088 0.111

a When specifying nominal size in decimals, zeros preceding the decimal point and in the fourth decimal place are omitted. b These lengths or shorter are undercut. c May be rounded or flat.

CLOSE TOLERANCE 100-DEGREE FLAT COUNTERSUNK HEAD TYPE Slot Head Diameter, A Head Width, Height, Max., Min., J H Edge Edgec Sharp Ref. Max. Min.

Nominal Sizea or Basic Screw Dia. 4 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8

Slot Depth, T Max.

Min.

0.1120 0.1380 0.1640 0.1900 0.2500

0.225 0.279 0.332 0.385 0.507

0.191 0.238 0.285 0.333 0.442

0.049 0.060 0.072 0.083 0.110

0.039 0.048 0.054 0.060 0.075

0.031 0.039 0.045 0.050 0.064

0.024 0.030 0.036 0.042 0.055

0.017 0.022 0.027 0.031 0.042

0.3125

0.635

0.556

0.138

0.084

0.072

0.069

0.053

0.3750

0.762

0.670

0.165

0.094

0.081

0.083

0.065

0.4375

0.890

0.783

0.193

0.094

0.081

0.097

0.076

0.5000

1.017

0.897

0.221

0.106

0.091

0.111

0.088

0.5625

1.145

1.011

0.249

0.118

0.102

0.125

0.099

0.6250

1.272

1.124

0.276

0.133

0.116

0.139

0.111




MACHINE SCREWS

Table 4. American National Standard Slotted Undercut Flat Countersunk Head and Plain and Slotted Hex Washer Head Machine Screws ANSI B18.6.3-1972 (R1991) SLOTTED UNDERCUT FLAT COUNTERSUNK HEAD TYPE

Nominal Sizea or Basic Screw Dia. 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000

Max., Lb 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Head Dia., A Min., Edge Max., Rnded. Edge or Flat Sharp

Head Height, H Max. Min.

Slot Width, J Max. Min.

Slot Depth, T Max. Min.

0.119 0.146 0.172 0.199 0.225 0.252 0.279 0.332 0.385 0.438 0.507 0.635 0.762 0.812 0.875

0.025 0.031 0.036 0.042 0.047 0.053 0.059 0.070 0.081 0.092 0.107 0.134 0.161 0.156 0.156

0.023 0.026 0.031 0.035 0.039 0.043 0.048 0.054 0.060 0.067 0.075 0.084 0.094 0.094 0.106

0.011 0.014 0.016 0.019 0.022 0.024 0.027 0.032 0.037 0.043 0.050 0.062 0.075 0.072 0.072

0.099 0.123 0.147 0.171 0.195 0.220 0.244 0.292 0.340 0.389 0.452 0.568 0.685 0.723 0.775

0.018 0.023 0.028 0.033 0.038 0.043 0.048 0.058 0.068 0.078 0.092 0.116 0.140 0.133 0.130

0.016 0.019 0.023 0.027 0.031 0.035 0.039 0.045 0.050 0.056 0.064 0.072 0.081 0.081 0.091

0.007 0.009 0.011 0.012 0.014 0.016 0.017 0.021 0.024 0.028 0.032 0.041 0.049 0.045 0.046

a When specifying nominal size in decimals, zeros preceding the decimal point and in the fourth decimal place are omitted. b These lengths or shorter are undercut.

PLAIN AND SLOTTED HEX WASHER HEAD TYPES

Nominal Sizea or Basic Screw Dia. 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8

Width Across Flats, A Max. Min.

Width AcrossCorn., W Min.

Head Height, H

Washer Dia., B

Washer Thick., U

Slota Width, J

Slota Depth, T

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500

0.125 0.125 0.188 0.188 0.250 0.250 0.312 0.312 0.375

0.120 0.120 0.181 0.181 0.244 0.244 0.305 0.305 0.367

0.134 0.134 0.202 0.202 0.272 0.272 0.340 0.340 0.409

0.050 0.055 0.060 0.070 0.093 0.110 0.120 0.155 0.190

0.040 0.044 0.049 0.058 0.080 0.096 0.105 0.139 0.172

0.166 0.177 0.243 0.260 0.328 0.348 0.414 0.432 0.520

0.154 0.163 0.225 0.240 0.302 0.322 0.384 0.398 0.480

0.016 0.016 0.019 0.025 0.025 0.031 0.031 0.039 0.050

0.010 0.010 0.011 0.015 0.015 0.019 0.019 0.022 0.030

…. …. 0.039 0.043 0.048 0.054 0.060 0.067 0.075

…. …. 0.031 0.035 0.039 0.045 0.050 0.056 0.064

…. …. 0.042 0.049 0.053 0.074 0.080 0.103 0.111

…. …. 0.025 0.030 0.033 0.052 0.057 0.077 0.083

0.3125

0.500 0.489

0.545

0.230 0.208 0.676 0.624 0.055 0.035 0.084 0.072 0.134 0.100

0.3750

0.562 0.551

0.614

0.295 0.270 0.780 0.720 0.063 0.037 0.094 0.081 0.168 0.131

a Unless otherwise specified, hexagon washer head machine screws are not slotted.




1591

Table 5. American National Standard Slotted Truss Head and Plain and Slotted Hexagon Head Machine Screws ANSI B18.6.3-1972 (R1991) SLOTTED TRUSS HEAD TYPE

Head Dia., A Min.


Max.

0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

0.049 0.077 0.106 0.131 0.164 0.194 0.226 0.257 0.289 0.321 0.384 0.448 0.511 0.573 0.698 0.823 0.948 1.073 1.198 1.323 1.573

0.043 0.071 0.098 0.119 0.149 0.180 0.211 0.241 0.272 0.303 0.364 0.425 0.487 0.546 0.666 0.787 0.907 1.028 1.149 1.269 1.511

Head Height, H Min.

Max.

0.014 0.022 0.030 0.037 0.045 0.053 0.061 0.069 0.078 0.086 0.102 0.118 0.134 0.150 0.183 0.215 0.248 0.280 0.312 0.345 0.410

0.010 0.018 0.024 0.029 0.037 0.044 0.051 0.059 0.066 0.074 0.088 0.103 0.118 0.133 0.162 0.191 0.221 0.250 0.279 0.309 0.368

Head Radius, R Max.

Max.

Slot Width, J Min.

0.032 0.051 0.070 0.087 0.107 0.129 0.151 0.169 0.191 0.211 0.254 0.283 0.336 0.375 0.457 0.538 0.619 0.701 0.783 0.863 1.024

0.009 0.013 0.017 0.023 0.026 0.031 0.035 0.039 0.043 0.048 0.054 0.060 0.067 0.075 0.084 0.094 0.094 0.106 0.118 0.133 0.149

Slot Depth, T Min.

Max.

0.005 0.009 0.010 0.016 0.019 0.023 0.027 0.031 0.035 0.039 0.045 0.050 0.056 0.064 0.072 0.081 0.081 0.091 0.102 0.116 0.131

0.009 0.013 0.018 0.022 0.027 0.031 0.036 0.040 0.045 0.050 0.058 0.068 0.077 0.087 0.106 0.124 0.142 0.161 0.179 0.196 0.234

0.005 0.009 0.012 0.014 0.018 0.022 0.026 0.030 0.034 0.037 0.045 0.053 0.061 0.070 0.085 0.100 0.116 0.131 0.146 0.162 0.182

a Where specifying nominal size in decimals, zeros preceding decimal points and in the fourth decimal place are omitted.

PLAIN AND SLOTTED HEXAGON HEAD TYPES

Regular Head Width Across Across Corn., W Flats, A Max. Min. Min.

Large Head Width Across Across Corn., W Flats, A Max. Min. Min.

Max.

Min.

Max.

Min.

Max.

Min.

.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500

.125 .125 .188 .188 .188 .250 .250 .312 .312 .375

.120 .120 .181 .181 .181 .244 .244 .305 .305 .367

.134 .134 .202 .202 .202 .272 .272 .340 .340 .409

.... .... .... .219 .250 .... .312 .... .375 .438

.... .... .... .213 .244 .... .305 .... .367 .428

.... .... .... .238 .272 .... .340 .... .409 .477

.044 .050 .055 .060 .070 .093 .110 .120 .155 .190

.036 .040 .044 .049 .058 .080 .096 .105 .139 .172

.... .... .... .039 .043 .048 .054 .060 .067 .075

.... .... .... .031 .035 .039 .045 .050 .056 .064

.... .... .... .036 .042 .046 .066 .072 .093 .101

… … … .02 .03 .03 .05 .057 .07 .08

0.3125

.500

.489

.545

....

....

....

.230

.208

.084

.072

.122

.10

0.3750

.562

.551

.614

....

....

....

.295

.270

.094

.081

.156

.13

Nominal Sizea or Basic Screw Dia. 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8

Head Height, H

Slota Width, J

a Unless otherwise specified, hexagon head machine screws are not slotted.



Slota Depth, T


MACHINE SCREWS Table 6. American National Standard Slotted Pan Head Machine Screws ANSI B18.6.3-1972 (R1991)

0000 000 00 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Max.

Min.


.042 .066 .090 .116 .142 .167 .193 .219 .245 .270 .322 .373 .425 .492 .615 .740 .863 .987 1.041 1.172 1.435

.036 .060 .082 .104 .130 .155 .180 .205 .231 .256 .306 .357 .407 .473 .594 .716 .837 .958 1.000 1.125 1.375

.016 .023 .032 .039 .046 .053 .060 .068 .075 .082 .096 .110 .125 .144 .178 .212 .247 .281 .315 .350 .419

Head Dia., A

Nominal Sizea or Basic Screw Dia. 0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

.010 .017 .025 .031 .038 .045 .051 .058 .065 .072 .085 .099 .112 .130 .162 .195 .228 .260 .293 .325 .390

Head Radius, R Max. .007 .010 .015 .020 .025 .035 .037 .042 .044 .046 .052 .061 .078 .087 .099 .143 .153 .175 .197 .219 .263



.008 .012 .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075 .084 .094 .094 .106 .118 .133 .149

.008 .012 .016 .022 .027 .031 .036 .040 .045 .050 .058 .068 .077 .087 .106 .124 .142 .161 .179 .197 .234

.004 .008 .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064 .072 .081 .081 .091 .102 .116 .131

.004 .008 .010 .014 .018 .022 .026 .030 .034 .037 .045 .053 .061 .070 .085 .100 .116 .131 .146 .162 .192

a Where specifying nominal size in decimals, zeros preceding decimal and in the fourth decimal place are omitted.


Table 7. Nos. 0000, 000 and 00 Threads ANSI B18.6.3-1972 (R1991) Appendix

0000-160 or 0.0210-160

NS

2

.0210 .0195 .0169 .0158

000-120 or 0.0340-120

NS

2

00-90 or 0.0470-90

NS

00-96 or 0.0470-96

NS

Major Diameter

Internalc

Pitch Diameter

Minor Dia.

Class

Class

Series Designat.

Externalb

Nominal Sizea and Threads Per Inch

.0011

.0128

.0340 .0325 .0286 0.272

.0014

2

.0470 .0450 .0398 .0382

2

.0470 .0450 .0402 .0386

Max.

Min.

Max.

Min.

Tol.

Pitch Diameter

Major Dia.

Min.

Max.

Tol.

Min.

2

.0169

.0181

.0012

.0210

.0232

2

.0286

.0300

.0014

.034

.0016

.0326

2

.0398

.0414

.0016

.047

.0016

.0334

2

.0402

.0418

.0016

.047

a Where

specifying nominal size in decimals, zeros preceding decimal and in the fourth decimal place are omitted. b There is no allowance provided on the external threads. c The minor diameter limits for internal threads are not specified, they being determined by the amount of thread engagement necessary to satisfy the strength requirements and tapping performance in the intended application. All dimensions are in inches.



1593

Table 8. American National Standard Slotted Fillister and Slotted Drilled Fillister Head Machine Screws ANSI B18.6.3-1972 (R1991)

SLOTTED FILLISTER HEAD TYPE

0000 000 00 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Total Head Height, O

Head Side Height, H

Head Dia., A

Nominal Size1 or Basic Screw Dia.

Slot Width, J

Slot Depth, T

Max.

Min.

Max.

Min.

Max.

Min.

Max

Min.

Max.

Min.

0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500

.038 .059 .082 .096 .118 .140 .161 .183 .205 .226 .270 .313 .357 .414

.032 .053 .072 .083 .104 .124 .145 .166 .187 .208 .250 .292 .334 .389

.019 .029 .037 .043 .053 .062 .070 .079 .088 .096 .113 .130 .148 .170

.011 .021 .028 .038 .045 .053 .061 .069 .078 .086 .102 .118 .134 .155

.025 .035 .047 .055 .066 .083 .095 .107 .120 .132 .156 .180 .205 .237

.15 .027 .039 .047 .058 .066 .077 .088 .100 .111 .133 .156 .178 .207

.008 .012 .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075

.004 .006 .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064

.012 .017 .022 .025 .031 .037 .043 .048 .054 .060 .071 .083 .094 .109

.006 .011 .015 .015 .020 .025 .030 .035 .040 .045 .054 .064 .074 .087

0.3125

.518

.490

.211

.194

.295

.262

.084

.072

.137

.110

0.3750

.622

.590

.253

.233

.355

.315

.094

.081

.164

.133

0.4375

.625

.589

.265

.242

.368

.321

.094

.081

.170

.135

0.5000

.750

.710

.297

.273

.412

.362

.106

.091

.190

.151

0.5625

.812

.768

.336

.308

.466

.410

.118

.102

.214

.172

0.6250

.875

.827

.375

.345

.521

.461

.133

.116

.240

.193

0.7500

1.000

.945

.441

.406

.612

.542

.149

.131

.281

.226

Drilled Hole Locat., E

Drilled Hole. Dia., F

SLOTTED DRILLED FILLISTER HEAD TYPE Nominal Size1 or Basic Screw Dia. 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8

Head Dia., A

Head Side Height, H


Slot Width, J

Slot Depth, T

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Basic

Basic

0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500

.140 .161 .183 .205 .226 .270 .313 .357 .414

.124 .145 .166 .187 .208 .250 .292 .334 .389

.062 .070 .079 .088 .096 .113 .130 .148 .170

.055 .064 .072 .081 .089 .106 .123 .139 .161

.083 .095 .107 .120 .132 .156 .180 .205 .237

.070 .082 .094 .106 .118 .141 .165 .188 .219

.031 .035 .039 .043 .048 .054 .060 .067 .075

.023 .027 .031 .035 .039 .045 .050 .056 .064

.030 .034 .038 .042 .045 .065 .075 .087 .102

.022 .026 .030 .033 .035 .054 .064 .074 .087

.026 .030 .035 .038 .043 .043 .043 .053 .062

.031 .037 .037 .046 .046 .046 .046 .046 .062

0.3125

.518

.490

.211

.201

.295

.276

.084

.072

.130

.110

.078

.070

0.3750

.622

.590

.253

.242

.355

.333

.094

.081

.154

.134

.094

.070

All dimensions are in inches. 1Where specifying nominal size in decimals, zeros preceding decimal points and in the fourth decimal place are omitted. 2Drilled hole shall be approximately perpendicular to the axis of slot and may be permitted to break through bottom of the slot. Edges of the hole shall be free from burrs. 3A slight rounding of the edges at periphery of head is permissible provided the diameter of the bearing circle is equal to no less than 90 per cent of the specified minimum head diameter.



MACHINE SCREWS Table 9. American National Standard Slotted Oval Countersunk Head Machine Screws ANSI B18.6.3-1972 (R1991)

Max Lb

Nominal Sizea or Basic Screw Dia. 00 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

… 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 … … …

Head Dia., A Min., Edge Rnded. or Flat

Head Side Height, H,

Max., Edge Sharp .093 .119 .146 .172 .199 .225 .252 .279 .332 .385 .438 .507 .635 .762 .812 .875 1.000 1.125 1.375

.085 .099 .123 .147 .171 .195 .220 .244 .292 .340 .389 .452 .568 .685 .723 .775 .889 1.002 1.230


Slot Depth, T

Slot Width, J

Ref.

Max.

Min.

Max.

Min.

Max.

Min.

.028 .035 .043 .051 .059 .067 .075 .083 .100 .116 .132 .153 .191 .230 .223 .223 .260 .298 .372

.042 .056 .068 .080 .092 .104 .116 .128 .152 .176 .200 .232 .290 .347 .345 .354 .410 .467 .578

.034 .041 .052 .063 .073 .084 .095 .105 .126 .148 .169 .197 .249 .300 .295 .299 .350 .399 .497

.017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075 .084 .094 .094 .106 .118 .133 .149

.010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064 .072 .081 .081 .091 .102 .116 .131

.023 .030 .038 .045 .052 .059 .067 .074 .088 .103 .117 .136 .171 .206 .210 .216 .250 .285 .353

.016 .025 .031 .037 .043 .049 .055 .060 .072 .084 .096 .112 .141 .170 .174 .176 .207 .235 .293

a When specifying nominal size in decimals, zeros preceding decimal points and in the fourth decimal place are omitted. b These lengths or shorter are undercut. All dimensions are in inches.

Table 10. American National Standard Header Points for Machine Screws before Threading ANSI B18.6.3-1972 (R1991) Nom. Size

Threads per Inch

Max. P

Min. P

24

0.125

0.112

32

0.138

0.124

24 28 20 28 18 24 16 24 14 20 13 20

0.149 0.156 0.170 0.187 0.221 0.237 0.270 0.295 0.316 0.342 0.367 0.399

0.134 0.141 0.153 0.169 0.200 0.215 0.244 0.267 0.287 0.310 0.333 0.362

11⁄4

10 Nom. Size. 2 4 5 6 8

Threads per Inch 56 64 40 48 40 44 32 40 32 36

Max. P 0.057 0.060 0.074 0.079 0.086 0.088 0.090 0.098 0.114 0.118

Min. P 0.050 0.053 0.065 0.070 0.076 0.079 0.080 0.087 0.102 0.106

Max. L

12

1⁄ 2

1⁄ 4

1⁄ 2

5⁄ 16

1⁄ 2

3⁄ 8

3⁄ 4

7⁄ 16

1

1⁄ 2

Max. L

13⁄8 11⁄2 11⁄2 11⁄2 11⁄2 11⁄2

All dimensions in inches. Edges of point may be rounded and end of point need not be flat nor perpendicular to shank. Machine screws normally have plain sheared ends but when specified may have header points, as shown above.



1595

Table 11. American National Standard Slotted Binding Head and Slotted Undercut Oval Countersunk Head Machine Screws ANSI B18.6.3-1972 (R1991)

Nominal Sizea or Basic Screw Dia. 0000 000 00 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8

0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750

SLOTTED BINDING HEAD TYPE Slot Head Oval Width, Height, J F Max. Min. Max. Min.


Undercutb Dia., U Max. Min.

Undercutb Depth, X Max. Min.

.009 .015 .023 .026 .035 .043 .052 .061 .069 .078 .095 .112 .130 .152 .194 .235

.009 .013 .018 .018 .024 .030 .036 .042 .048 .053 .065 .077 .089 .105 .134 .163

… … … .098 .120 .141 .162 .184 .205 .226 .269 .312 .354 .410 .513 .615

… … … .007 .008 .010 .011 .012 .014 .015 .017 .020 .023 .026 .032 .039

Head Dia., A Max. Min.

Total Head Height, O Max. Min.

.046 .073 .098 .126 .153 .181 .208 .235 .263 .290 .344 .399 .454 .525 .656 .788

.014 .021 .028 .032 .041 .050 .059 .068 .078 .087 .105 .123 .141 .165 .209 .253

.040 .067 .090 .119 .145 .171 .197 .223 .249 .275 .326 .378 .430 .498 .622 .746

.006 .008 .011 .012 .015 .018 .022 .025 .029 .032 .039 .045 .052 .061 .077 .094

.003 .005 .007 .008 .011 .013 .016 .018 .021 .024 .029 .034 .039 .046 .059 .071

.008 .012 .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075 .084 .094

.004 .006 .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064 .072 .081

.005 .009 .012 .009 .014 .020 .025 .030 .035 .040 .050 .060 .070 .084 .108 .132

… … … .086 .105 .124 .143 .161 .180 .199 .236 .274 .311 .360 .450 .540

… … … .002 .003 .005 .006 .007 .009 .010 .012 .015 .018 .021 .027 .034

a Where specifying nominal size in decimals, zeros preceding decimal points and in the fourth decimal place are omitted. b Unless otherwise specified, slotted binding head machine screws are not undercut.

Nominal Sizea or Basic Screw Dia. 0

0.0600

1

0.0730

2

0.0860

3

0.0990

4

0.1120

5

0.1250

6

0.1380

8

0.1640

10

0.1900

12

0.2160

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

0.2500 0.3125 0.3750 0.4375 0.5000

SLOTTED UNDERCUT OVAL COUNTERSUNK HEAD TYPES Total Head Dia., Head Slot Head A Side Width, Height, Height, Min., J O H Edge Max., Max. Rnded. Edge or Flat Ref. Max. Min. Max. Min. Sharp La 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 8 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

Slot Depth, T Max.

Min.

.119

.099

.025

.046

.033

.023

.016

.028

.022

.146

.123

.031

.056

.042

.026

.019

.034

.027

.172

.147

.036

.065

.050

.031

.023

.040

.033

.199

.171

.042

.075

.059

.035

.027

.047

.038

.225

.195

.047

.084

.067

.039

.031

.053

.043

.252

.220

.053

.094

.076

.043

.035

.059

.048

.279

.244

.059

.104

.084

.048

.039

.065

.053

.332

.292

.070

.123

.101

.054

.045

.078

.064

.385

.340

.081

.142

.118

.060

.050

.090

.074

.438

.389

.092

.161

.135

.067

.056

.103

.085

.507

.452

.107

.186

.158

.075

.064

.119

.098

.635

.568

.134

.232

.198

.084

.072

.149

.124

.762

.685

.161

.278

.239

.094

.081

.179

.149

.812

.723

.156

.279

.239

.094

.081

.184

.154

.875

.775

.156

.288

.244

.106

.091

.204

.169

a These lengths or shorter are undercut.




MACHINE SCREWS Table 12. Slotted Round Head Machine Screws ANSI B18.6.3-1972 (R1991) Appendix


0.0210 0.0340 0.0470 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

Head Diameter, A Min. .035 .056 .080 .099 .122 .146 .169 .193 .217 .240 .287 .334 .382 .443 .557 .670 .707 .766 .887 .944 1.185

Max. .041 .062 .089 .113 .138 .162 .187 .211 .236 .260 .309 .359 .408 .472 .590 .708 .750 .813 .938 1.000 1.250

Head Height, H Min. .016 .025 .036 .043 .051 .059 .067 .075 .083 .091 .107 .123 .139 .160 .198 .237 .307 .332 .385 .411 .516

Max. .022 .031 .045 .053 .061 .069 .078 .086 .095 .103 .120 .137 .153 .175 .216 .256 .328 .355 .410 .438 .547

Slot Width, J Min. .004 .008 .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064 .072 .081 .081 .091 .102 .116 .131

Max. .008 .012 .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075 .084 .094 .094 .106 .118 .133 .149

Slot Depth, T Min. .013 .012 .018 .029 .033 .037 .040 .044 .047 .051 .058 .065 .073 .082 .099 .117 .148 .159 .183 .195 .242

Max. .017 .018 .026 .039 .044 .048 .053 .058 .063 .068 .077 .087 .096 .109 .132 .155 .196 .211 .242 .258 .320

a When specifying nominal size in decimals, zeros preceding decimal point and in the fourth decimal place are omitted.

All dimensions are in inches. Not recommended, use Pan Head machine screws.

ANSI Cross References for Machine Screws and Metric Machine Screw

Type I Cross Recess

Type IA Cross Recess

Type II Cross Recess

Type III Square Center

Machine Screw Cross Recesses.—Four cross recesses, Types I, IA, II, and III, may be used in lieu of slots in machine screw heads. Dimensions for recess diameter M, width N, and depth T (not shown above) together with recess penetration gaging depths are given in American National Standard ANSI B18.6.3-1972 (R1991) for machine screws, and in ANSI/ASME B18.6.7M-1985 for metric machine screws. American National Standard Metric Machine Screws.—This Standard B18.6.7M covers metric flat and oval countersunk and slotted and recessed pan head machine screws and metric hex head and hex flange head machine screws. Dimensions are given in Tables 1 through 4 and 6.



1597

Table 1. American National Standard Thread Lengths for Metric Machine Screws ANSI/ASME B18.6.7M-1985

Pan, Hex, and Hex Flange Head Screws L

LUS

Flat and Oval Countersunk Head Screws LU

LUS

L Nominal Screw Lengtha

Heat-Treated Recessed Flat Countersunk Head Screws LU L

L

Nominal Screw Size and Thread Pitch

Nominal Screw Length Equal to or Shorter thana

Maxd

Maxe

Over

To and Including

Maxd

Maxe

Nominal Screw Length Longer thana

M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

6 8 9 10 12 15 18 24 30 36

1.0 1.1 1.2 1.5 1.8 2.0 2.5 3.1 3.8 4.4

0.4 0.5 0.5 0.6 0.7 0.8 1.0 1.2 1.5 1.8

6 8 9 10 12 15 18 24 30 36

30 30 30 50 50 50 50 50 50 50

1.0 1.1 1.2 1.5 1.8 2.0 2.5 3.1 3.8 4.4

0.8 0.9 1.0 1.2 1.4 1.6 2.0 2.5 3.0 3.5

30 30 30 50 50 50 50 50 50 50

Unthreaded Lengthb

Unthreaded Lengthb

B Full Form Thread Lengthc

Min 25.0 25.0 25.0 38.0 38.0 38.0 38.0 38.0 38.0 38.0

a The length tolerances for metric machine screws are: up to 3 mm, incl., ± 0.2 mm; over 3 to 10 mm, incl., ± 0.3 mm; over 10 to 16 mm, incl., ± 0.4 mm; over 16 to 50 mm, incl., ± 0.5 mm; over 50 mm, ± 1.0 mm. b Unthreaded lengths L and L U US represent the distance, measured parallel to the axis of screw, from the underside of the head to the face of a nonchamfered or noncounterbored standard GO thread ring gage assembled by hand as far as the thread will permit. c Refer to the illustrations for respective screw head styles. d The L US values apply only to heat treated recessed flat countersunk head screws. e The L values apply to all screws except heat treated recessed flat countersunk head screws. U All dimensions in millimeters.



Slotted and Style A

Body Diameter

Body and Shoulder Diameter

LSHa

DS Shoulder Diameter

Body Diameter

DK

K

Head Diameter Shoulder Length

Theoretical Sharp

Actual

Head Height

Max

Min

Max

Min

Min

Max

Min

Max

Min

Min

Max Ref

M2 × 0.4b

2.00

1.65

2.00

1.86

1.65

0.50

0.30

4.4

4.1

3.5

1.2

M2.5 × 0.45

2.50

2.12

2.50

2.36

2.12

0.55

0.35

5.5

5.1

4.4

1.5

R

N

Underhead Fillet Radius

T

Slot Width

Slot Depth

Max

Min

Max

Min

Max

0.8

0.4

0.7

0.5

0.6

Min 0.4

1.0

0.5

0.8

0.6

0.7

0.5

M3 × 0.5

3.00

2.58

3.00

2.86

2.58

0.60

0.40

6.3

5.9

5.2

1.7

1.2

0.6

1.0

0.8

0.9

0.6

M3.5 × 0.6

3.50

3.00

3.50

3.32

3.00

0.70

0.50

8.2

7.7

6.9

2.3

1.4

0.7

1.2

1.0

1.2

0.9

M4 × 0.7

4.00

3.43

4.00

3.82

3.43

0.80

0.60

9.4

8.9

8.0

2.7

1.6

0.8

1.5

1.2

1.3

1.0

M5 × 0.8

5.00

4.36

5.00

4.82

4.36

0.90

0.70

10.4

9.8

8.9

2.7

2.0

1.0

1.5

1.2

1.4

1.1

M6 × 1

6.00

5.21

6.00

5.82

5.21

1.10

0.90

12.6

11.9

10.9

3.3

2.4

1.2

1.9

1.6

1.6

1.2

M8 × 1.25

8.00

7.04

8.00

7.78

7.04

1.40

1.10

17.3

16.5

15.4

4.6

3.2

1.6

2.3

2.0

2.3

1.8

M10 × 1.5

10.00

8.86

10.00

9.78

8.86

1.70

1.30

20.0

19.2

17.8

5.0

4.0

2.0

2.8

2.5

2.6

2.0

a All

recessed head heat-treated steel screws of property class 9.8 or higher strength have the Style B head form. Recessed head screws other than those specifically designated to be Style B have the Style A head form. The underhead shoulder on the Style B head form is mandatory and all other head dimensions are common to both the Style A and Style B head forms. b This size is not specified for Type III square recessed flat countersunk heads; Type II cross recess is not specified for any size. All dimensions in millimeters. For dimension B, see Table 1. For dimension L, see Table 7.


MACHINE SCREWS


Style B DSHa

DS

1598

Table 2. American National Standard Slotted, Cross and Square Recessed Flat Countersunk Head Metric Machine Screws ANSI/ASME B18.6.7M-1985


Table 3. American National Standard Slotted, Cross and Square Recessed Oval Countersunk Head Metric Machine Screws ANSI/ASME B18.6.7M-1985

K

F

RF

R

N

T

Actual

Head Side Height

Raised Head Height

Head Top Radius

Underhead Fillet Radius

Slot Width

Slot Depth

DK Head Diameter Theoretical Sharp

Body Diameter Min

Max

Min

Min

Max Ref

Max

Approx

Max

Min

Max

Min

Max

M2 × 0.4a

2.00

1.65

4.4

4.1

3.5

1.2

0.5

5.0

0.8

0.4

0.7

0.5

1.0

0.8

M2.5 × 0.45

2.50

2.12

5.5

4.4

1.5

0.6

6.6

1.0

0.5

0.8

0.6

1.2

1.0

Max

5.1

Min

M3 × 0.5

3.00

2.58

6.3

5.9

5.2

1.7

0.7

7.4

1.2

0.6

1.0

0.8

1.5

1.2

M3.5 × 0.6

3.50

3.00

8.2

7.7

6.9

2.3

0.8

10.9

1.4

0.7

1.2

1.0

1.7

1.4

M4 × 0.7

4.00

3.43

9.4

8.9

8.0

2.7

1.0

11.6

1.6

0.8

1.5

1.2

1.9

1.6

M5 × 0.8

5.00

4.36

10.4

9.8

8.9

2.7

1.2

11.9

2.0

1.0

1.5

1.2

2.4

2.0

M6 × 1

6.00

5.21

12.6

11.9

10.9

3.3

1.4

14.9

2.4

1.2

1.9

1.6

2.8

2.4

M8 × 1.25

8.00

7.04

17.3

16.5

15.4

4.6

2.0

19.7

3.2

1.6

2.3

2.0

3.7

3.2

M10 × 1.5

10.00

8.86

20.0

19.2

17.8

5.0

2.3

22.9

4.0

2.0

2.8

2.5

4.4

3.8

MACHINE SCREWS

DS Nominal Screw Size and Thread Pitch

a This size is not specified for Type III square recessed oval countersunk heads; Type II cross recess is not specified for any size.

1599

All dimensions in millimeters. For dimension B, see Table 1. For dimension L, see Table 7.



M2 × 0.4a M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5

Ds

DK

R1

K

Body Diameter Max Min

Head Diameter Max Min

Head Height Max Min

2.00 2.50 3.00 3.50 4.00 5.00 6.00 8.00 10.00

4.0 5.0 5.6 7.0 8.0 9.5 12.0 16.0 20.0

1.3 1.5 1.8 2.1 2.4 3.0 3.6 4.8 6.0

1.65 2.12 2.58 3.00 3.43 4.36 5.21 7.04 8.86

3.7 4.7 5.3 6.6 7.6 9.1 11.5 15.5 19.4

1.1 1.3 1.6 1.9 2.2 2.7 3.3 4.5 5.7

Head Radius Max 0.8 1.0 1.2 1.4 1.6 2.0 2.5 3.2 4.0

R1

K Head Height Max Min 1.6 2.1 2.4 2.6 3.1 3.7 4.6 6.0 7.5

1.4 1.9 2.2 2.3 2.8 3.4 4.3 5.6 7.1

Head Radius Ref 3.2 4.0 5.0 6.0 6.5 8.0 10.0 13.0 16.0

DA

R Underhead Fillet Transition Dia Radius Max Min 2.6 3.1 3.6 4.1 4.7 5.7 6.8 9.2 11.2

a This size not specified for Type III square recessed pan heads; Type II cross recess is not specified for any size.

All dimensions in millimeters. For dimension B, see Table 1. For dimension L, see Table 7.


0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.4 0.4

N Slot Width Max Min 0.7 0.8 1.0 1.2 1.5 1.5 1.9 2.3 2.8

0.5 0.6 0.8 1.0 1.2 1.2 1.6 2.0 2.5

T

W

Slot Depth Min

Unslotted Head Thickness Min

0.5 0.6 0.7 0.8 1.0 1.2 1.4 1.9 2.4

0.4 0.5 0.7 0.8 0.9 1.2 1.4 1.9 2.4

MACHINE SCREWS

Cross and Square Recess

Slotted Nominal Screw Size and Thread Pitch

1600

Table 4. American National Standard Slotted and Cross and Square Recessed Pan Head Metric Machine Screws ANSI/ASME B18.6.7M-1985

Machinery's Handbook 27th Edition METRIC MACHINE SCREWS

1601

Table 5. American National Standard Header Points for Metric Machine Screws Before Threading ANSI/ASME B18.6.7M-1985

Nominal Screw Size and Thread Pitch M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

DP Point Diameter Max 1.33 1.73 2.12 2.46 2.80 3.60 4.25 5.82 7.36 8.90

Min 1.21 1.57 1.93 2.24 2.55 3.28 3.85 5.30 6.71 8.11

La Nominal Screw Length Max 13 13 16 20 25 30 40 40 40 45

a Header points apply to these nominal lengths or shorter. The pointing of longer lengths may require machining to the dimensions specified.

All dimensions in millimeters. The edge of the point may be rounded and the end of point need not be flat nor perpendicular to the axis of screw shank.

Threads: Threads for metric machine screws are coarse M profile threads, as given in ANSI B1.13M (see page 1783), unless otherwise specified. Length of Thread: The lengths of threads on metric machine screws are given in Table 1 for the applicable screw type, size, and length. Diameter of Body: The body diameters of metric machine screws are within the limits specified in the dimensional tables (Tables 3 through 4 and 6). Designation: Metric machine screws are designated by the following data in the sequence shown: Nominal size and thread pitch; nominal length; product name, including head type and driving provision; header point if desired; material (including property class, if steel); and protective finish, if required. For example: M8 × 1.25 × 30 Slotted Pan Head Machine Screw, Class 4.8 Steel, Zinc Plated M3.5 × 0.6 × 20 Type IA Cross Recessed Oval Countersunk Head Machine Screw, Header Point, Brass It is common ISO practice to omit the thread pitch from the product size designation when screw threads are the metric coarse thread series, e.g., M10 stands for M10 × 1.5.



1602

Table 6. American National Standard Hex and Hex Flange Head Metric Machine Screws ANSI/ASME B18.6.7M-1985 Hex Head

M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75 M10 × 1.5b

Sa

Ea

Hex Width Across Flats

Body Diameter

DA

K

R Underhead Fillet

Hex Width Across Corners

Head Height

Transition Dia

Radius

Max

Min

Max

Min

Min

Max

Min

Max

Min

2.00 2.50 3.00 3.50 4.00 5.00 6.00 8.00 10.00 12.00 10.00

1.65 2.12 2.58 3.00 3.43 4.36 5.21 7.04 8.86 10.68 8.86

3.20 4.00 5.00 5.50 7.00 8.00 10.00 13.00 16.00 18.00 15.00

3.02 3.82 4.82 5.32 6.78 7.78 9.78 12.73 15.73 17.73 14.73

3.38 4.28 5.40 5.96 7.59 8.71 10.95 14.26 17.62 19.86 16.50

1.6 2.1 2.3 2.6 3.0 3.8 4.7 6.0 7.5 9.0 7.5

1.3 1.8 2.0 2.3 2.6 3.3 4.1 5.2 6.5 7.8 6.5

2.6 3.1 3.6 4.1 4.7 5.7 6.8 9.2 11.2 13.2 11.2

0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.4 0.4

a Dimensions across flats and across corners of the head are measured at the point of maximum metal. Taper of sides of head (angle between one side and the axis) shall

not exceed 2° or 0.10 mm, whichever is greater, the specified width across flats being the large dimension. b The M10 size screws having heads with 15 mm width across flats are not ISO Standard. Unless M10 size screws with 15 mm width across flats are specifically ordered, M10 size screws with 16 mm width across flats shall be furnished.


METRIC MACHINE SCREWS

DS Nominal Screw Size and Thread Pitch


Table 6. (Continued) American National Standard Hex and Hex Flange Head Metric Machine Screws ANSI/ASME B18.6.7M-1985 Hex Flange Head

Max

Min

Max

Min

Hex Width Across Corners, Ea Min

M2 × 0.4 M2.5 × 0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

2.00 2.50 3.00 3.50 4.00 5.00 6.00 8.00 10.00 12.00

1.65 2.12 2.58 3.00 3.43 4.36 5.21 7.04 8.86 10.68

3.00 3.20 4.00 5.00 5.50 7.00 8.00 10.00 13.00 15.00

2.84 3.04 3.84 4.82 5.32 6.78 7.78 9.78 12.72 14.72

3.16 3.39 4.27 5.36 5.92 7.55 8.66 10.89 14.16 16.38

Hex Width Across Flats, Sa

Hex Height, K1 Min,

Flange Edge Thickness, Cb Min

Flange Top Fillet Radius, R1 Max

Max Transition Dia, DA

Min Radius, R

1.3 1.6 1.9 2.4 2.8 3.5 4.2 5.6 7.0 8.4

0.3 0.3 0.4 0.5 0.6 0.7 1.0 1.2 1.4 1.8

0.1 0.2 0.2 0.2 0.2 0.3 0.4 0.5 0.6 0.7

2.6 3.1 3.6 4.1 4.7 5.7 6.8 9.2 11.2 13.2

0.1 0.1 0.1 0.1 0.2 0.2 0.3 0.4 0.4 0.4

Flange Diameter, DC

Max

Min

Overall Head Height, K

4.5 5.4 6.4 7.5 8.5 10.6 12.8 16.8 21.0 24.8

4.1 5.0 5.9 6.9 7.8 9.8 11.8 15.5 19.3 23.3

2.2 2.7 3.2 3.8 4.3 5.4 6.7 8.6 10.7 13.7

Underhead Fillet


1603

a Dimensions across flats and across corners of the head are measured at the point of maximum metal. Taper of sides of head (angle between one side and the axis) shall not exceed 2° or 0.10 mm, whichever is greater, the specified width across flats being the large dimension. b The contour of the edge at periphery of flange is optional provided the minimum flange thickness is maintained at the minimum flange diameter. The top surface of flange may be straight or slightly rounded (convex) upward. All dimensions in millimeters. A slight rounding of all edges of the hexagon surfaces of indented hex heads is permissible provided the diameter of the bearing circle is not less than the equivalent of 90 per cent of the specified minimum width across flats dimension. Heads may be indented, trimmed, or fully upset at the option of the manufacturer. For dimension B, see Table 1. For dimension L, see Table 7.

METRIC MACHINE SCREWS

Body Diameter, DS



MACHINE SCREWS

Table 7. Recommended Nominal Screw Lengths for Metric Machine Screws Nominal Screw Length 2.5 3 4 5 6 8 10 13 16 20 25 30 35 40 45 50 55 60 65 70 80 90

Nominal Screw Size M2 PH A A A A A A A A A

M2.5

M3

PH A A A A A A A A A


M3.5

M4


PH A A A A A A A A A A

M5

PH A A A A A A A A A A A

M6

A A A A A A A A A A A A A

M8

A A A A A A A A A A A A A A A

M10

M12

A A A A A A A A A A A A A A A

H H H H H H H H H H H H H H

All dimensions in millimeters. 1The nominal screw lengths included between the heavy lines are recommended for the respective screw sizes and screw head styles as designated by the symbols. A — Signifies screws of all head styles covered in this standard. P — Signifies pan head screws. H — Signifies hex and hex flange head screws.

Table 8. Clearance Holes for Metric Machine Screws ANSI/ASME B18.6.7M-1985 Appendix Nominal Screw Size M2 M2.5 M3 M3.5 M4 M5 M6 M8 M10 M12

Close Clearanceb 2.20 2.70 3.20 3.70 4.30 5.30 6.40 8.40 10.50 13.00

Basic Clearance Hole Diametera Normal Clearance (Preferred)b 2.40 2.90 3.40 3.90 4.50 5.50 6.60 9.00 11.00 13.50

Loose Clearanceb 2.60 3.10 3.60 4.20 4.80 5.80 7.00 10.00 12.00 14.50

a The values given in this table are minimum limits. The recommended plus tolerances are as follows: for clearance hole diameters over 1.70 to and including 5.80 mm, plus 0.12, 0.20, and 0.30 mm for close, normal, and loose clearances, respectively; for clearance hole diameters over 5.80 to 14.50 mm, plus 0.18, 0.30, and 0.45 mm for close, normal, and loose clearances, respectively. b Normal clearance hole sizes are preferred. Close clearance hole sizes are for situations such as critical alignment of assembled components, wall thickness, or other limitations which necessitate the use of a minimal hole. Countersinking or counterboring at the fastener entry side may be necessary for the proper seating of the head. Loose clearance hole sizes are for applications where maximum adjustment capability between the components being assembled is necessary.

All dimensions in millimeters.



1605

British Machine Screws.—Many of these classifications of fasteners are covered in British Standards B.S. 57:1951, “B.A. Screws, Bolts and Nuts”; BS 450:1958 (obsolescent), “Machine Screws and Machine Screw Nuts (BSW and BSF Threads)”; B.S. 1981:1953, “Unified Machine Screws and Machine Screw Nuts”; BS 2827:1957 (obsolescent):1957, “Machine Screw Nuts, Pressed Type (B.A. and Whitworth Form Threads)”; B.S. 3155:1960, “American Machine Screws and Nuts in Sizes Below 1⁄4 inch Diameter”; and BS 4183:1967 (obsolescent), “Machine Screws and Machine Screw Nuts, Metric Series.” At a conference organized by the British Standards Institution in 1965 at which the major sectors of British industry were represented, a policy statement was approved that urged British firms to regard the traditional screw thread systems—Whitworth, B.A. and BSF— as obsolescent, and to make the internationally-agreed ISO metric thread their first choice (with ISO Unified thread as second choice) for all future designs. It is recognized that some sections of British industry already using ISO inch (Unified) screw threads may find it necessary, for various reasons, to continue with their use for some time: Whitworth and B.A. threads should, however, be superseded by ISO metric threads in preference to an intermediate change to ISO inch threads. Fasteners covered by B.S. 57, B.S. 450 and BS 2827:1957 (obsolescent) eventually would be superseded and replaced by fasteners specified by B.S. 4183. British Standard Whitworth (BSW) and Fine (BSF) Machine Screws.—British Standard BS 450:1958 (obsolescent) covers machine screws and nuts with British Standard Whit-worth and British Standard Fine threads. All the various heads in common use in both slotted and recessed forms are covered. Head shapes are shown on page 1614 and dimensions on page 1617. It is intended that this standard will eventually be superseded by B.S. 4183, “Machine Screws and Machine Screw Nuts, Metric Series.” British Standard Machine Screws and Machine Screw Nuts, Metric Series.—British Standard BS 4183:1967 (obsolescent) gives dimensions and tolerances for: countersunk head, raised countersunk head, and cheese head slotted head screws in a diameter range from M1 (1 mm) to M20 (20 mm); pan head slotted head screws in a diameter range from M2.5 (2.5 mm) to M10 (10 mm); countersunk head and raised countersunk head recessed head screws in a diameter range from M2.5 (2.5 mm) to M12 (12 mm); pan head recessed head screws in a diameter range from M2.5 (2.5 mm) to M10 (10 mm); and square and hexagon machine screw nuts in a diameter range from M1.6 (1.6 mm) to M10 (10 mm). Mechanical properties are also specified for steel, brass and aluminum alloy machine screws and machine screw nuts in this standard. Material: The materials from which the screws and nuts are manufactured have a tensile strength not less than the following: steel, 40 kgf/mm2 (392 N/mm2); brass, 32 kgf/mm2 (314 N/mm2); and aluminum alloy, 32 kgf/mm2 (314 N/mm2). The unit, kgf/mm2 is in accordance with ISO DR 911 and the unit in parentheses has the relationship, 1 kgf = 9.80665 Newtons. These minimum strengths are applicable to the finished products. Steel machine screws conform to the requirements for strength grade designation 4.8. The strength grade designation system for machine screws consists of two figures, the first is 1⁄10 of the minimum tensile strength in kgf/mm2, the second is 1⁄10 of the ratio between the yield stress and the minimum tensile strength expressed as a percentage: 1⁄10 minimum tensile yield stress strength of 40 kgf/mm2 gives the symbol “4”; 1⁄10 ratio ------------------------------------------------------------ % = 1⁄10 × minimum tensile strength 32⁄ × 100⁄1 = “8”; giving the strength grade designation “4.8.” Multiplication of these two 40 figures gives the minimum yield stress in kgf/mm2. Coating of Screws and Nuts: It is recommended that the coating comply with the appropriate part of BS 3382. “Electroplated Coatings on Threaded Components.”



MACHINE SCREWS

Screw Threads: Screw threads are ISO metric coarse pitch series threads in accordance with B.S. 3643. “ISO Metric Screw Threads,” Part 1, “Thread Data and Standard Thread Series.” The external threads used for screws conform to tolerance Class 6g limits (medium fit) as given in B.S. 3643, “ISO Metric Screw Threads,” Part 2, “Limits and Tolerances for Coarse Pitch Series Threads.” The internal threads used for nuts conform to tolerance Class 6H limits (medium fit) as given in B.S. 3643: Part 2. Nominal Lengths of Screws: For countersunk head screws the nominal length is the distance from the upper surface of the head to the extreme end of the shank, including any chamfer, radius, or cone point. For raised countersunk head screws the nominal length is the distance from the upper surface of the head (excluding the raised portion) to the extreme end of the shank, including any chamfer, radius, or cone point. For pan and cheese head screws the nominal length is the distance from the underside of the head to the extreme end of the shank, including any chamfer, radius, or cone point. Standard nominal lengths and tolerances are given in Table 5. Lengths of Thread on Screws: The length of thread is the distance from the end of the screw (including any chamfer, radius, or cone point) to the leading face of a nut without countersink which has been screwed as far as possible onto the screw by hand. The minimum thread length is shown in the following table: Nominal Thread Dia., da

M1

M1.2

(M1.4)

M1.6

M2

(M2.2)

M2.5

M3

(M3.5)

M4

Thread Length b (Min.)

b

b

b

15

16

17

18

19

20

22

Nominal Thread Dia., da

(M4.5)

M5

M6

M8

M10

M12

(M14)

M16

(M18)

M20

Thread Length b (Min.)

24

25

28

34

40

46

52

58

64

70

a Items shown in parentheses are non-preferred. b Threaded up to the head.


Screws of nominal thread diameter M1, M1.2 and M1.4 and screws of larger diameters that are too short for the above thread lengths are threaded as far as possible up to the head. In these screws the length of unthreaded shank under the head does not exceed 11⁄2 pitches for lengths up to twice the diameter and 2 pitches for longer lengths, and is defined as the distance from the leading face of a nut that has been screwed as far as possible onto the screw by hand to: 1) the junction of the basic major diameter and the countersunk portion of the head on countersunk and raised countersunk heads; and 2) the underside of the head on other types of heads. Diameter of Unthreaded Shank on Screws: The diameter of the unthreaded portion of the shank on screws is not greater than the basic major diameter of the screw thread and not less than the minimum effective diameter of the screw thread. The diameter of the unthreaded portion of shank is closely associated with the method of manufacture; it will generally be nearer the major diameter of the thread for turned screws and nearer the effective diameter for those produced by cold heading. Radius Under the Head of Screws: The radius under the head of pan and cheese head screws runs smoothly into the face of the head and shank without any step or discontinuity. A true radius is not essential providing that the curve is smooth and lies wholly within the maximum radius. Any radius under the head of countersunk head screws runs smoothly into the conical bearing surface of the head and the shank without any step or discontinuity. The radius values given in Tables 1 and 2 are regarded as the maximum where the shank diameter is equal to the major diameter of the thread and minimum where the shank diameter is approximately equal to the effective diameter of the thread.



Table 1. British Standard Slotted Countersunk Head Machine Screws—Metric Series BS 4183:1967 (obsolescent) Nominal Size da

Head Diameter D

Thread Length b

Thread Run-out a

Flushness Tolerancec

Min.

Max. 2pd

Max.

Max.

Min.

Max. 0.3d

Min. 0.2d

e

0.50

....

0.45

0.31

0.30

0.20

0.1

e

0.50

....

0.50

0.36

0.36

0.24

0.63

0.1

e

0.60

....

0.50

0.36

0.42

0.28

0.72 0.90 0.99 1.12 1.35 1.57 1.80 2.03 2.25 2.70 3.60 4.50 5.40 6.30 7.20 8.10 9.00

0.1 0.1 0.1 0.1 0.1 0.2 0.2 0.2 0.2 0.25 0.4 0.4 0.6 0.6 0.6 0.6 0.8

15.0 16.0 17.0 18.0 19.0 20.0 22.0 24.0 25.0 28.0 34.0 40.0 46.0 52.0 58.0 64.0 70.0

0.70 0.80 0.90 0.90 1.00 1.20 1.40 1.50 1.60 2.00 2.50 3.00 3.50 4.00 4.00 5.00 5.00

.... .... .... 0.10 0.12 0.13 0.15 0.17 0.19 0.23 0.29 0.37 0.44 0.52 0.60 0.67 0.75

0.60 0.70 0.80 0.80 1.00 1.00 1.20 1.20 1.51 1.91 2.31 2.81 3.31 3.31 4.37 4.37 5.37

0.46 0.56 0.66 0.66 0.86 0.86 1.06 1.06 1.26 1.66 2.06 2.56 3.06 3.06 4.07 4.07 5.07

0.48 0.60 0.66 0.75 0.90 1.05 1.20 1.35 1.50 1.80 2.40 3.00 3.60 4.20 4.80 5.40 6.00

0.32 0.40 0.44 0.50 0.60 0.70 0.80 0.90 1.00 1.20 1.60 2.00 2.40 2.80 3.20 3.60 4.00

Head Height k Radius rb

Min. 1.75d

Max. 0.5d

Min. 0.45d

M1

2.00

1.75

0.50

0.45

0.1

M1.2

2.40

2.10

0.60

0.54

(M1.4)

2.80

2.45

0.70

M1.6 M2.0 (M2.2) M2.5 M3 (M3.5) M4 (M4.5) M5 M6 M8 M10 M12 (M14) M16 (M18) M20

3.20 4.00 4.40 5.00 6.00 7.00 8.00 9.00 10.00 12.00 16.00 20.00 24.00 28.00 32.00 36.00 40.00

2.80 3.50 3.85 4.38 5.25 6.10 7.00 7.85 8.75 10.50 14.00 17.50 21.00 24.50 28.00 31.50 35.00

0.80 1.00 1.10 1.25 1.50 1.75 2.00 2.25 2.50 3.00 4.00 5.00 6.00 7.00 8.00 9.00 10.00

Slot Width n

Slot Depth t

MACHINE SCREWS

Max. (Theor. Sharp) 2d

a Nominal sizes shown in parentheses are non-preferred. b See Radius Under the Head of Screws description in text. c See Dimensions of 90-Degree Countersunk Head Screws description in text. d See text following table in Lengths of Thread on Screws description in text. e Threaded up to head.


1607

All dimensions are given in millimeters. For dimensional notation, see diagram on page 1610. Recessed head screws are also standard and are available. For dimensions see British Standard.


Head Diameter D Nominal Size da

Head Height k

Radius Under Head rb

Thread Length b

Thread Runout a

Height of Raised Portion f

Head Radius R

Min.

Max. 2pc

Slot Width n

1608

Table 2. British Standard Slotted Raised Countersunk Head Machine Screws—Metric Series BS 4183:1967 (obsolescent) Slot Depth t

Min. 1.75d

Nom. 0.25d

Nom.

Max.

Min.

Max. 0.5d

Min. 0.4d

M1

2.00

1.75

0.50

0.45

0.1

d

0.50

0.25

2.0

0.45

0.31

0.50

0.40

M1.2

2.40

2.10

0.60

0.54

0.1

d

0.50

0.30

2.5

0.50

0.36

0.60

0.48

(M1.4)

2.80

2.45

0.70

0.63

0.1

d

0.60

0.35

2.5

0.50

0.36

0.70

0.56

M1.6

3.20

2.80

0.80

0.72

0.1

15.0

0.70

0.40

3.0

0.60

0.46

0.80

0.64

M2.0

4.00

3.50

1.00

0.90

0.1

16.0

0.80

0.50

4.0

0.70

0.56

1.00

0.80

(M2.2)

4.40

3.85

1.10

0.99

0.1

17.0

0.90

0.55

4.0

0.80

0.66

1.10

0.88

Max. 0.5d

Min. 0.45d

M2.5

5.00

4.38

1.25

1.12

0.1

18.0

0.90

0.60

5.0

0.80

0.66

1.25

1.00

M3

6.00

5.25

1.50

1.35

0.1

19.0

1.00

0.75

6.0

1.00

0.86

1.50

1.20

(M3.5)

7.00

6.10

1.75

1.57

0.2

20.0

1.20

0.90

6.0

1.00

0.86

1.75

1.40

M4

8.00

7.00

2.00

1.80

0.2

22.0

1.40

1.00

8.0

1.20

1.06

2.00

1.60

(M4.5) M5

9.00

7.85

2.25

2.03

0.2

24.0

1.50

1.10

8.0

1.20

1.06

2.25

1.80

10.00

8.75

2.50

2.25

0.2

25.0

1.60

1.25

10.0

1.51

1.26

2.50

2.00

M6

12.00

10.50

3.00

2.70

0.25

28.0

2.00

1.50

12.0

1.91

1.66

3.00

2.40

M8

16.00

14.00

4.00

3.60

0.4

34.0

2.50

2.00

16.0

2.31

2.06

4.00

3.20

M10

20.00

17.50

5.00

4.50

0.4

40.0

3.00

2.50

20.0

2.81

2.56

5.00

4.00

M12

24.00

21.00

6.00

5.40

0.6

46.0

3.50

3.00

25.0

3.31

3.06

6.00

4.80

(M14)

28.00

24.50

7.00

6.30

0.6

52.0

4.00

3.50

25.0

3.31

3.06

7.00

5.60

M16

32.00

28.00

8.00

7.20

0.6

58.0

4.00

4.00

32.0

4.37

4.07

8.00

6.40

(M18)

36.00

31.50

9.00

8.10

0.6

64.0

5.00

4.50

32.0

4.37

4.07

9.00

7.20

M20

40.00

35.00

10.00

9.00

0.8

70.0

5.00

5.00

40.0

5.37

5.07

10.00

8.00

a Nominal sizes shown in parentheses are non-preferred. b See Radius Under the Head of Screws description in text. c See text following table in Lengths of Thread on Screws description in text. d Threaded up to head.

All dimensions are given in millimeters. For dimensional notation see diagram on page 1610. Recessed head screws are also standard and available. For dimensions see British Standard.


MACHINE SCREWS

Max. (Theor. Sharp) 2d


1609

Ends of Screws: When screws are made with rolled threads, the “lead” formed by the thread rolling operation is normally regarded as providing the necessary chamfer and no other machining is necessary. The ends of screws with cut threads are normally finished with a chamfer conforming to the dimension in Fig. 1a through Fig. 1d. At the option of the manufacturer, the ends of screws smaller than M6 (6-mm diameter) may be finished with a radius approximately equal to 11⁄4 times the nominal diameter of the shank. When cone point ends are required, they should have the dimensions given in Fig. 1a through Fig. 1d. Nominal Length Nominal Length d

90

d

Cut Thread Chamfered End Fig. 1a. Rolled Thread End (Approximate Form as Rolled)

d

Radius Approx. 1 1/ 4 d

Nominal Length Fig. 1c. Cut Thread Radiused End (Permissible on Sizes Below M6 Dia.)

Fig. 1b. Chamfer to Extend to Slightly Below the Minor Dia.

90

d

Nominal Length Fig. 1d. Cone Pointed End (Permissible on Cut or Rolled Thread Screws, but Regarded as "Special")

Dimensions of 90-Degree Countersunk Head Screws: One of the appendices to this British Standard states that countersunk head screws should fit into the countersunk hole with as great a degree of flushness as possible. To achieve this condition, it is necessary for the dimensions of both the head of the screw and the countersunk hole to be controlled within prescribed limits. The maximum or design size of the head is controlled by a theoretical diameter to a sharp corner and the minimum head angle of 90 degrees. The minimum head size is controlled by a minimum head diameter, the maximum head angle of 92 degrees and a flushness tolerance (see Fig. 2). The edge of the head may be flat or rounded, as shown in Fig. 3.

Fig. 2. Head Configuration

Fig. 3. Edge Configuration



MACHINE SCREWS

British Standard Machine Screws and Machine Screw Nuts—Metric Series l l

k a r

b

90 +2 D D n

d Edge May Be Rounded or Flat, But Not Sharp Edges

t

Shank Dia. ≈ Effective Dia.

Shank Dia. ≈ Major Dia.

Slotted Countersunk Head Machine Screws

l

f

l

k a r 90 +2 D D n

b d

R

Edge May Be Shank Dia. ≈ Rounded or Shank Dia. ≈ Effective Major Dia. Flat, But Not Dia. Sharp Edges Slotted Raised Countersunk Head Machine Screws

t

k

l

R

l

a r

b

D n

d t

0 TO 5

da

k

Shank Dia. ≈ Effective Dia. Slotted Pan Head Machine Screws

l

R

l

a r

b

D n 0 TO 5


d t

da

Shank Dia. ≈ Effective Dia. Slotted Cheese Head Machine Screws

; d

s d

;


e

m s e Square Nut Hexagon Nut Machine Screw Nuts, Pressed Type, Square and Hexagon

m

For dimensions, see Tables 1 through 5.



1611

Table 3. British Standard Slotted Pan Head Machine Screws— Metric Series BS 4183:1967 (obsolescent) Nominal Size da M2.5 M3 (M3.5) M4 (M4.5) M5 M6 M8 M10

Head Diameter D

Head Height k

Head Radius R

Radius Under Head r

Transition Diameter da

Max. 2d

Min.

Max. 0.6d

Min.

Max 0.4d

Min.

Max.

5.00 6.00 7.00 8.00 9.00 10.00 12.00 16.00 20.00

4.70 5.70 6.64 7.64 8.64 9.64 11.57 15.57 19.48

1.50 1.80 2.10 2.40 2.70 3.00 3.60 4.80 6.00

1.36 1.66 1.96 2.26 2.56 2.86 3.42 4.62 5.82

1.00 1.20 1.40 1.60 1.80 2.00 2.50 3.20 4.00

0.10 0.10 0.20 0.20 0.20 0.20 0.25 0.40 0.40

3.10 3.60 4.30 4.70 5.20 5.70 6.80 9.20 11.20

a Nominal sizes shown in parentheses are non-preferred.

Nominal Size da M2.5 M3 (M3.5) M4 (M4.5) M5 M6 M8 M10

Thread Length b

Thread Run-out a

Min.

Max. 2pb

Max.

Min.

Max. 0.6k

Min. 0.4k

18.00 19.00 20.00 22.00 24.00 25.00 28.00 34.00 40.00

0.90 1.00 1.20 1.40 1.50 1.60 2.00 2.50 3.00

0.80 1.00 1.00 1.20 1.20 1.51 1.91 2.31 2.81

0.66 0.86 0.86 1.06 1.06 1.26 1.66 2.06 2.56

0.90 1.08 1.26 1.44 1.62 1.80 2.16 2.88 3.60

0.60 0.72 0.84 0.96 1.08 1.20 1.44 1.92 2.40

Slot Width n

Slot Depth t

a Nominal sizes shown in parentheses are non-preferred. b See Lengths of Thread on Screws on page 1606. All dimensions are in millimeters. For dimensional notation, see diagram on page 1610. Recessed head screws are also standard and available. For dimensions, see British Standard.



Head Height k

Head Diameter D

Nominal Size da

Radius rb

Transition Diameter da

Thread Length b

Thread Run-out a

1612

Table 4. British Standard Slotted Cheese Head Machine Screws—Metric Series BS 4183:1967 (obsolescent) Slot Depth t

Slot Width n

Max.

Min.

Max.

Min.

Min.

Max.

Min.

Max. c

Max.

Min.

Max.

Min.

M1

2.00

1.75

0.70

0.56

0.10

1.30

b

0.50

0.45

0.31

0.44

0.30

M1.2

2.30

2.05

0.80

0.66

0.10

1.50

b

0.50

0.50

0.36

0.49

0.35

(M1.4)

2.60

2.35

0.90

0.76

0.10

1.70

b

0.60

0.50

0.36

0.60

0.40

M1.6

3.00

2.75

1.00

0.86

0.10

2.00

15.00

0.70

0.60

0.46

0.65

0.45 0.60

3.80

3.50

1.30

1.16

0.10

2.60

16.00

0.80

0.70

0.56

0.85

4.00

3.70

1.50

1.36

0.10

2.80

17.00

0.90

0.80

0.66

1.00

0.70

M2.5

4.50

4.20

1.60

1.46

0.10

3.10

18.00

0.90

0.80

0.66

1.00

0.70 0.90

M3

5.50

5.20

2.00

1.86

0.10

3.60

19.00

1.00

1.00

0.86

1.30

(M3.5)

6.00

5.70

2.40

2.26

0.10

4.10

20.00

1.20

1.00

0.86

1.40

1.00

M4

7.00

6.64

2.60

2.46

0.20

4.70

22.00

1.40

1.20

1.06

1.60

1.20

(M4.5)

8.00

7.64

3.10

2.92

0.20

5.20

24.00

1.50

1.20

1.06

1.80

1.40

M5

8.50

8.14

3.30

3.12

0.20

5.70

25.00

1.60

1.51

1.26

2.00

1.50

M6

10.00

9.64

3.90

3.72

0.25

6.80

28.00

2.00

1.91

1.66

2.30

1.80

M8

13.00

12.57

5.00

4.82

0.40

9.20

34.00

2.50

2.31

2.06

2.80

2.30

M10

16.00

15.57

6.00

5.82

0.40

11.20

40.00

3.00

2.81

2.56

3.20

2.70

M12

18.00

17.57

7.00

6.78

0.60

14.20

46.00

3.50

3.31

3.06

3.80

3.20

(M14)

21.00

20.48

8.00

7.78

0.60

16.20

52.00

4.00

3.31

3.06

4.20

3.60

M16

24.00

23.48

9.00

8.78

0.60

18.20

58.00

4.00

4.37

4.07

4.60

4.00

(M18)

27.00

26.48

10.00

9.78

0.60

20.20

64.00

5.00

4.37

4.07

5.10

4.50

M20

30.00

29.48

11.00

10.73

0.80

22.40

70.00

5.00

5.27

5.07

5.60

5.00

a Nominal sizes shown in parentheses are non-preferred. b Threaded up to head. c See text following table in Lengths of Thread on Screws description in text.

All dimensions are given in millimeters. For dimensional notation, see diagram on page 1610.

General Dimensions: The general dimensions and tolerances for screws and nuts are given in the accompanying tables. Although slotted screw dimensions are given, recessed head screws are also standard and available. Dimensions of recessed head screws are given in BS 4183:1967 (obsolescent).


MACHINE SCREWS

M2 (M2.2)


Table 5. British Standard Machine Screws and Nuts — Metric Series BS 4183:1967 (obsolescent) Concentricity Tolerances

IT 13

IT 13

Countersunk & Raised Countersunk Heads Pan & Cheese Heads

Nominal Size da M1, M1.2, (M1.4) M1.6 M2, (M2.2), M2.5, M3 (M3.5) M4, (M4.5), M5 M6 M8 M10, M12 (M14) M16, (M18), M20

Head to Shank

Head to Shank and Slot to Head (IT 13) Countersunk, Raised Csk., and Pan Heads

Cheese Heads

0.14 0.18 0.18 0.22 0.22 0.27 0.27 0.33 0.33 0.39

0.14 0.14 0.18 0.18 0.22 0.22 0.27 0.27 0.33 0.33

All dimensions are given in millimeters. For dimensional notation, see diagram on page 1610.


Width Across Flats s Corners e Min. Square 3.02 4.5 3.82 5.7 4.32 6.4 4.82 7.1 5.32 7.8 5.82 8.5 6.78 9.9 7.78 11.3 9.78 14.1 12.73 18.4 16.73 24.0

Nominal Size da M1.6 M2 (M2.2) (M2.5) M3 (M3.5) M4 M5 M6 M8 M10

Max. 3.2 4.0 4.5 5.0 5.5 6.0 7.0 8.0 10.0 13.0 17.0

Nominal Size da M1.6 M2 (M2.2) M2.5 M3 (M3.5) M4 M5 M6 M8 M10 M8 M10

Width Across Corners e Hexagon 3.7 4.6 5.2 5.8 6.4 6.9 8.1 9.2 11.5 15.0 19.6 13.0 17.0

Thickness m Min 0.75 0.95 0.95 1.35 1.35 1.75 1.75 2.25 2.75 3.70 4.70 18.4 24.0

Max. 1.0 1.2 1.2 1.6 1.6 2.0 2.0 2.5 3.0 4.0 5.0 12.73 16.73

1613

a Nominal sizes and lengths shown in parentheses are non-preferred.

Dimensions of Machine Screw Nuts, Pressed Type, Square and Hexagon

MACHINE SCREWS

Slot to Head

Nominal Lengths and Tolerances on Length for Machine Screws Tolerance Nominal Lengtha Tolerance ±0.12 45 ±0.50 ±0.12 50 ±0.060 ±0.20 55 ±0.60 ±0.20 60 ±0.60 ±0.24 65 ±0.60 ±0.24 70 ±0.60 ±0.24 75 ±0.60 ±0.29 80 ±0.60 ±0.29 85 ±0.70 ±0.29 90 ±0.70 ±0.29 (95) ±0.70 ±0.35 100 ±0.70 ±0.35 (105) ±0.70 ±0.35 110 ±0.70 ±0.35 (115) ±0.70 ±0.35 120 ±0.70 ±0.42 (125) ±0.70 ±0.42 130 ±0.80 ±0.42 140 ±0.80 ±0.42 150 ±0.80 ±0.42 160 ±0.80 ±0.50 190 ±0.925 ±0.50 200 ±0.925

Nominal Lengtha 1.5 2 2.5 3 4 5 6 (7) 8 (9) 10 (11) 12 14 16 (18) 20 (22) 25 (28) 30 (38) 40


MACHINE SCREWS

British Unified Machine Screws and Nuts.—British Standard B.S. 1981:1953 covers certain types of machine screws and machine screw nuts for which agreement has been reached with the United States and Canada as to general dimensions for interchangeability. These types are: countersunk, raised-countersunk, pan, and raised-cheese head screws with slotted or recessed heads; small hexagon head screws; and precision and pressed nuts. All have Unified threads. Head shapes are shown on page 1614 and dimensions are given on page 1616. Identification: As revised by Amendment No. 1 in February 1955, this standard now requires that the above-mentioned screws and nuts that conform to this standard should have a distinguishing feature applied to identify them as Unified. All recessed head screws are to be identified as Unified by a groove in the form of four arcs of a circle in the upper surface of the head. All hexagon head screws are to be identified as Unified by: 1) a circular recess in the upper surface of the head; 2) a continuous line of circles indented on one or more of the flats of the hexagon and parallel to the screw axis; and 3) at least two contiguous circles indented on the upper surface of the head. All machine screw nuts of the pressed type shall be identified as Unified by means of the application of a groove indented in one face of the nut approximately midway between the major diameter of the thread and flats of the square or hexagon. Slotted head screws shall be identified as Unified either by a circular recess or by a circular platform or raised portion on the upper surface of the head. Machine screw nuts of the precision type shall be identified as Unified by either a groove indented on one face of the front approximately midway between the major diameter of the thread and the flats of the hexagon or a continuous line of circles indented on one or more of the flats of the hexagon and parallel to the nut axis.

;; ;;;;;;;; ; ;;;; ;; ; ;;;;;;;;;; Recessed and Hexagon Head Screws

Precision Type

Pressed Type

Hexagon Machine Screw Nuts

Slotted Head Screws Identification Markings for British Standard Unified Machine Screws

British Standard Machine Screws and Nuts ricc:1958 (obsolescent) and B.S. 1981:1953

80° Countersunk head screw (Unified) 90° Countersink head screw (BSW & BSF)

Round head screw (BSW & BSF)



1615

British Standard Machine Screws and Nuts (Continued) ricc:1958 (obsolescent) and B.S. 1981:1953

80° Raised countersunk head screw (Unified) 90° Raised countersunk head screw (BSW & BSF)

Mushroom head screw (BSW & BSF)

Pan head screw (Unified, BSW & BSF)

Hexagon head screw (Unified)

Cheese head screw (BSW & BSF)

Hexagon head screw (Unified) alternate design

Raised cheese head screw (Unified)

Hexagon machine screw nut (Unified)

*Countersinks to suit the screws should have a maximum angle of 80° (Unified) or 90° (BSF and BSW) with a negative tolerance. †Unified countersunk and raised countersunk head screws 2 inches long and under are threaded right up to the head. Other Unified, BSW and BSF machine screws 2 inches long and under have an unthread shank equal to twice the pitch. All Unified, BSW and BSF machine screws longer than 2 inches have a minimum thread length of 13⁄4 inches.



MACHINE SCREWS British Standard Unified Machine Screws and Nuts B.S. 1981:1953 Threads per Inch UNC UNF

Nom.Size of Screw

Basic Dia. D

4 6 8 10

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

0.112 0.138 0.164 0.190 0.250 0.3125 0.375 0.4375 0.500 0.625 0.750

40 32 32 24c 20 18 16 14 13 11 10

… … … 32 28 24 24 20 20 18 16

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

0.112 0.138 0.164 0.190 0.250 0.3125 0.375 0.4375 0.500 0.625 0.750

40 32 32 24c 20 18 16 14 13 11 10

… … … 32 28 24 24 20 20 18 16

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

0.112 0.138 0.164 0.190 0.250 0.3125 0.375 0.4375 0.500 0.625 0.750

40 32 32 24c 20 18 16 14 13 11 10

… … … 32 28 24 24 20 20 18 16

4 6 8 10

4 6 8 10

Dia. of Head A Depth of Head B Max. Min. Max. Min. 80° Countersunk Head Screwsa,b 0.211 0.194 0.067 … 0.260 0.242 0.083 … 0.310 0.291 0.100 … 0.359 0.339 0.116 … 0.473 0.450 0.153 … 0.593 0.565 0.191 … 0.712 0.681 0.230 … 0.753 0.719 0.223 … 0.808 0.770 0.223 … 1.041 0.996 0.298 … 1.275 1.223 0.372 … Pan Head Screwsb 0.219 0.205 0.068 0.058 0.270 0.256 0.082 0.072 0.322 0.306 0.096 0.085 0.373 0.357 0.110 0.099 0.492 0.473d 0.144 0.130 0.615 0.594 0.178 0.162 0.740 0.716 0.212 0.195 0.863 0.838 0.247 0.227 0.987 0.958 0.281 0.260 1.125 1.090 0.350 0.325 1.250 1.209 0.419 0.390 Raised Cheese-Head Screwsb 0.183 0.166 0.107 0.088 0.226 0.208 0.132 0.111 0.270 0.250 0.156 0.133 0.313 0.292 0.180 0.156 0.414 0.389 0.237 0.207 0.518 0.490 0.295 0.262 0.622 0.590 0.355 0.315 0.625 0.589 0.368 0.321 0.750 0.710 0.412 0.362 0.875 0.827 0.521 0.461 1.000 0.945 0.612 0.542

Width of Slot H Max. Min.

Depth of Slot J

0.039 0.048 0.054 0.060 0.075 0.084 0.094 0.094 0.106 0.133 0.149

0.031 0.039 0.045 0.050 0.064 0.072 0.081 0.081 0.091 0.116 0.131

0.025 0.031 0.037 0.044 0.058 0.073 0.086 0.086 0.086 0.113 0.141

0.039 0.048 0.054 0.060 0.075 0.084 0.094 0.094 0.106 0.133 0.149

0.031 0.039 0.045 0.050 0.064 0.072 0.081 0.081 0.091 0.116 0.131

0.036 0.044 0.051 0.059 0.079 0.101 0.122 0.133 0.152 0.189 0.226

0.039 0.048 0.054 0.060 0.075 0.084 0.094 0.094 0.106 0.133 0.149

0.031 0.039 0.045 0.050 0.064 0.072 0.081 0.081 0.091 0.116 0.131

0.042 0.053 0.063 0.074 0.098 0.124 0.149 0.153 0.171 0.217 0.254

a All dimensions, except J, given for the No. 4 to 3⁄ -inch sizes, incl., also apply to all the 80° Raised 8 Countersunk Head Screws given in the Standard. b Also available with recessed heads. c Non-preferred. d By arrangement may also be 0.468.

Nom. Size

Basic Dia. D

Threads per Inch UNC UNF

4 6 8 10

0.112 0.138 0.164 0.190

40 32 32 24c

4 6 8 10

0.112 0.138 0.164 0.190

40 32 32 24c

4 6 8 10

0.112 0.138 0.164 0.190 0.250 0.3125 0.375

40 32 32 24c 20 18 16

Width Across Flats A Corners C Max. Min. Max.

H'd Depth B Nut Thick. E Max. Min.

Wash. Face Dia. F Min.

Max.

Hexagon Head Screws

1⁄ 4 5⁄ 16 3⁄ 8

… 0.1875 0.1835 0.216 0.060 … 0.2500 0.2450 0.289 0.080 … 0.2500 0.2450 0.289 0.110 32 0.3125 0.3075 0.361 0.120 Hexagon Machine Screw Nuts—Precision Type … 0.1875 0.1835 0.216 0.098 … 0.2500 0.2450 0.269 0.114 … 0.3125 0.3075 0.361 0.130 … 0.3125 0.3075 0.361 0.130 Hexagon Machine Screw Nuts—Pressed Type … 0.2500 0.2410 0.289 0.087 … 0.3125 0.3020 0.361 0.114 … 0.3438 0.3320 0.397 0.130 32 0.3750 0.3620 0.433 0.130 28 0.4375 0.4230 0.505 0.193 24 0.5625 0.5450 0.649 0.225 24 0.6250 0.6070 0.722 0.257

0.055 0.074 0.104 0.113

0.183 0.245 0.245 0.307

0.173 0.235 0.235 0.297

0.087 0.102 0.117 0.117

… … … …

… … … …

0.077 0.102 0.117 0.117 0.178 0.208 0.239

… … … … … … …

… … … … … … …

All dimensions in inches. See page 1614 for a pictorial representation and letter dimensions.



1617

Depth of Head B Max. Min.

… 32c 28c 26 22 20 18 16 16c 14 12

0.219 0.328 0.383 0.438 0.547 0.656 0.766 0.875 0.984 1.094 1.312

0.201 0.307 0.360 0.412 0.518 0.624 0.729 0.835 0.941 1.046 1.257

0.056 0.084 0.098 0.113 0.141 0.169 0.197 0.225 0.253 0.281 0.338

… … … … … … … … … … …

0.039 0.050 0.055 0.061 0.071 0.082 0.093 0.104 0.115 0.126 0.148

0.032 0.042 0.046 0.051 0.061 0.072 0.082 0.092 0.103 0.113 0.134

0.027 0.041 0.048 0.055 0.069 0.083 0.097 0.111 0.125 0.138 0.166

40 24 … 20 18 16 14 12 12c 11 10

… 32c 28c 26 22 20 18 16 16c 14 12

0.219 0.328 0.383 0.438 0.547 0.656 0.766 0.875 0.984 1.094 1.312

0.206 0.312d 0.365 0.417 0.524 0.629 0.735 0.840 0.946 1.051 1.262

0.087 0.131 0.153 0.175 0.219 0.262 0.306 0.350 0.394 0.437 0.525

0.082 0.124 0.145 0.165 0.207 0.249 0.291 0.333 0.375 0.417 0.500

0.039 0.050 0.055 0.061 0.071 0.082 0.093 0.104 0.115 0.126 0.148

0.032 0.042 0.046 0.051 0.061 0.072 0.082 0.092 0.103 0.113 0.134

0.048 0.072 0.084 0.096 0.120 0.144 0.168 0.192 0.217 0.240 0.288

0.1250 0.1875 0.2188 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

40 24 … 20 18 16 14 12 12c 11 10

… 32c 28c 26 22 20 18 16 16c 14 12

0.245 0.373 0.425 0.492 0.615 0.740 0.863 0.987 1.031 1.125 1.250

0.231 0.375 0.407 0.473e 0.594 0.716 0.838 0.958 0.999 1.090 1.209

0.075 0.110 0.125 0.144 0.178 0.212 0.247 0.281 0.315 0.350 0.419

0.065 0.099 0.112 0.130 0.162 0.195 0.227 0.260 0.293 0.325 0.390

0.039 0.050 0.055 0.061 0.071 0.082 0.093 0.104 0.115 0.126 0.148

0.032 0.042 0.046 0.051 0.061 0.072 0.082 0.092 0.103 0.113 0.134

0.040 0.061 0.069 0.078 0.095 0.112 0.129 0.145 0.162 0.179 0.213

Cheese Head Screwsb

1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

0.1250 0.1875 0.2188 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

40 24 … 20 18 16 14 12 12c 11 10

… 32c 28c 26 22 20 18 16 16c 14 12

0.188 0.281 0.328 0.375 0.469 0.562 0.656 0.750 0.844 0.938 1.125

0.180 0.270 0.315 0.360 0.450 0.540 0.630 0.720 0.810 0.900 1.080

0.087 0.131 0.153 0.175 0.219 0.262 0.306 0.350 0.394 0.437 0.525

0.082 0.124 0.145 0.165 0.207 0.249 0.291 0.333 0.375 0.417 0.500

0.039 0.050 0.055 0.061 0.071 0.082 0.093 0.104 0.115 0.126 0.148

0.032 0.042 0.046 0.051 0.061 0.072 0.082 0.092 0.103 0.113 0.134

0.039 0.059 0.069 0.079 0.098 0.118 0.138 0.157 0.177 0.197 0.236

1⁄ 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8

0.1250 0.1875 0.2500 0.3125 0.3750

40 24 20 18 16

… 32c 26 22 20

0.289 0.448 0.573 0.698 0.823

0.272 0.425 0.546 0.666 0.787

0.078 0.118 0.150 0.183 0.215

0.066 0.103 0.133 0.162 0.191

0.043 0.060 0.075 0.084 0.094

0.035 0.050 0.064 0.072 0.081

0.040 0.061 0.079 0.096 0.112

Pan Head Screwsb

Round Head Screwsb

90° Countersunk Head Screwsab

Dia. of Head A Max. Min.

Mushroom Head Screwsb

British Standard Whitworth (BSW) and Fine (BSF) Machine Screws BS 450:1958 (obsolescent) Threads per Inch BSW BSF

Nom. Size of Screw

Basic Dia. D

1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 1⁄ 8 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

0.1250 0.1875 0.2188 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

40 24 … 20 18 16 14 12 12c 11 10

0.1250 0.1875 0.2188 0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

Width of Slot H Max. Min.

Depth of Slot J

a All dimensions, except J, given for the 1⁄ -through 3⁄ -inch sizes also apply to all the 90° Raised 8 8 Countersunk Head Screw dimensions given in the Standard. b These screws are also available with recessed heads; dimensions of recess are not given here but may be found in the Standard. c Non-preferred size; avoid use whenever possible. d By arrangement may also be 0.309. e By arrangement may also be 0.468. All dimensions in inches. See diagram on page 1614 for a pictorial representation of screws and letter dimensions.



CAP SCREWS

CAP AND SET SCREWS Slotted Head Cap Screws.—American National Standard ANSI/ASME B18.6.2-1998 is intended to cover the complete general and dimensional data for the various styles of slotted head cap screws as well as square head and slotted headless set screws (see page 1625). Reference should be made to this Standard for information or data not found in the following text or tables. Length of Thread: The length of complete (full form) thread on cap screws is equal to twice the basic screw diameter plus 0.250 in. with a plus tolerance of 0.188 in. or an amount equal to 21⁄2 times the pitch of the thread, whichever is greater. Cap screws of lengths too short to accommodate the minimum thread length have full form threads extending to within a distance equal to 21⁄2 pitches (threads) of the head. Designation: Slotted head cap screws are designated by the following data in the sequence shown: Nominal size (fraction or decimal equivalent); threads per inch; screw length (fraction or decimal equivalent); product name; material; and protective finish, if required. Examples: 1⁄2-13 × 3 Slotted Round Head Cap Screw, SAE Grade 2 Steel, Zinc Plated. .750-16 × 2.25 Slotted Flat Countersunk Head Cap Screw, Corrosion Resistant Steel. Table 1. American National Standard Slotted Flat Countersunk Head Cap Screws ANSI/ASME B18.6.2-1998

Head Dia., A Nominal Sizea or Basic Screw Dia.

Body Dia., E

Edge Sharp

Edge Rnd'd. or Flat

Head Hgt., H

Slot Width, J

Slot Depth, T

Filet Rad., U

Max.

Min.

Max.

Min.

Ref.

Max.

Min.

Max.

Min.

Max.

1⁄ 4

0.2500

.2500

.2450

.500

.452

.140

.075

.064

.068

.045

.100

5⁄ 16

0.3125

.3125

.3070

.625

.567

.177

.084

.072

.086

.057

.125

3⁄ 8

0.3750

.3750

.3690

.750

.682

.210

.094

.081

.103

.068

.150

7⁄ 16

0.4375

.4375

.4310

.812

.736

.210

.094

.081

.103

.068

.175

1⁄ 2

0.5000

.5000

.4930

.875

.791

.210

.106

.091

.103

.068

.200

9⁄ 16

0.5625

.5625

.5550

1.000

.906

.244

.118

.102

.120

.080

.225

5⁄ 8

0.6250

.6250

.6170

1.125

1.020

.281

.133

.116

.137

.091

.250

3⁄ 4

0.7500

.7500

.7420

1.375

1.251

.352

.149

.131

.171

.115

.300

7⁄ 8

0.8750

.8750

.8660

1.625

1.480

.423

.167

.147

.206

.138

.350

1

1.0000

1.0000

.9900

1.875

1.711

.494

.188

.166

.240

.162

.400

11⁄8

1.1250

1.1250

1.1140

2.062

1.880

.529

.196

.178

.257

.173

.450

11⁄4

1.2500

1.2500

1.2390

2.312

2.110

.600

.211

.193

.291

.197

.500

13⁄8

1.3750

1.3750

1.3630

2.562

2.340

.665

.226

.208

.326

.220

.550

11⁄2

1.5000

1.5000

1.4880

2.812

2.570

.742

.258

.240

.360

.244

.600

a When

specifying a nominal size in decimals, the zero preceding the decimal point is omitted as is any zero in the fourth decimal place. All dimensions are in inches. Threads: Threads are Unified Standard Class 2A; UNC, UNF and 8 UN Series or UNRC, UNRF, and 8 UNR Series.


Machinery's Handbook 27th Edition CAP SCREWS

1619

Table 2. American National Standard Slotted Round Head Cap Screws ANSI/ASME B18.6.2-1998

Nom. Sizea or Basic Screw Diameter 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

0.2500 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.7500

Body Diameter, E Max. Min.

Head Diameter, A Max. Min.




.2500 .3125 .3750 .4375 .5000 .5625 .6250 .7500

.437 .562 .625 .750 .812 .937 1.000 1.250

.191 .245 .273 .328 .354 .409 .437 .546

.075 .084 .094 .094 .106 .118 .133 .149

.117 .151 .168 .202 .218 .252 .270 .338

.2450 .3070 .3690 .4310 .4930 .5550 .6170 .7420

.418 .540 .603 .725 .786 .909 .970 1.215

.175 .226 .252 .302 .327 .378 .405 .507

.064 .072 .081 .081 .091 .102 .116 .131

.097 .126 .138 .167 .178 .207 .220 .278

a When specifying a nominal size in decimals, the zero preceding the decimal point is omitted as is any zero in the fourth decimal place.

All dimensions are in inches. Fillet Radius, U: For fillet radius see foonote to table below. Threads: Threads are Unified Standard Class 2A; UNC, UNF and 8 UN Series or UNRC, UNRF and 8 UNR Series.

Table 3. American National Standard Slotted Fillister Head Cap Screws ANSI/ASME B18.6.2-1998

Body Dia.., E Max. Min.

Head Dia.., A Max. Min.

Head Side Height, H Max. Min.

Total Head Height, O Max. Min.



0.2500 0.3125 0.3750 0.4375 0.5000 0.5625

.2500 .3125 .3750 .4375 .5000 .5625

.2450 .3070 .3690 .4310 .4930 .5550

.375 .437 .562 .625 .750 .812

.363 .424 .547 .608 .731 .792

.172 .203 .250 .297 .328 .375

.157 .186 .229 .274 .301 .346

.216 .253 .314 .368 .413 .467

.194 .230 .284 .336 .376 .427

.075 .084 .094 .094 .106 .118

.064 .072 .081 .081 .091 .102

.097 .115 .142 .168 .193 .213

.077 .090 .112 .133 .153 .168

0.6250 0.7500 0.8750 1.0000

.6250 .7500 .8750 1.0000

.6170 .7420 .8660 .9900

.875 1.000 1.125 1.312

.853 .976 1.098 1.282

.422 .500 .594 .656

.391 .466 .556 .612

.521 .612 .720 .803

.478 .566 .668 .743

.133 .149 .167 .188

.116 .131 .147 .166

.239 .283 .334 .371

.189 .223 .264 .291

Nom. Sizea or Basic Screw Dia. 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

1

a When specifying nominal size in decimals, the zero preceding the decimal point is omitted as is any zero in the fourth decimal place.

All dimensions are in inches. Fillet Radius, U: The fillet radius is as follows: For screw sizes 1⁄4 to 3⁄8 incl., .031 max. and .016 min.; 7⁄16 to 9⁄16, incl., .047 max., .016 min.; and for 5⁄8 to 1, incl., .062 max., .031 min. Threads: Threads are Unified Standard Class 2A; UNC, UNF and 8 UN Series or UNRC, UNRF and 8 UNR Series.



CAP SCREWS Table 4. American National Standard Hexagon and Spline Socket Head Cap Screws ANSI/ASME B18.3-1998

Nominal Size 0 1 2 3 4 5 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8 1 11⁄8 11⁄4 13⁄8 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4 4

Body Diameter, D Max Min 0.0600 0.0568 0.0730 0.0695 0.0860 0.0822 0.0990 0.0949 0.1120 0.1075 0.1250 0.1202 0.1380 0.1329 0.1640 0.1585 0.1900 0.1840 0.2500 0.2435 0.3125 0.3053 0.3750 0.3678 0.4375 0.4294 0.5000 0.4919 0.6250 0.6163 0.7500 0.7406 0.8750 0.8647 1.0000 0.9886 1.1250 1.1086 1.2500 1.2336 1.3750 1.3568 1.5000 1.4818 1.7500 1.7295 2.0000 1.9780 2.2500 2.2280 2.5000 2.4762 2.7500 2.7262 3.0000 2.9762 3.2500 3.2262 3.5000 3.4762 3.7500 3.7262 4.0000 3.9762

Head Diameter, A Max Min 0.096 0.091 0.118 0.112 0.140 0.134 0.161 0.154 0.183 0.176 0.205 0.198 0.226 0.218 0.270 0.262 0.312 0.303 0.375 0.365 0.469 0.457 0.562 0.550 0.656 0.642 0.750 0.735 0.938 0.921 1.125 1.107 1.312 1.293 1.500 1.479 1.688 1.665 1.875 1.852 2.062 2.038 2.250 2.224 2.625 2.597 3.000 2.970 3.375 3.344 3.750 3.717 4.125 4.090 4.500 4.464 4.875 4.837 5.250 5.211 5.625 5.584 6.000 5.958

Head Height, H Max Min 0.060 0.057 0.073 0.070 0.086 0.083 0.099 0.095 0.112 0.108 0.125 0.121 0.138 0.134 0.164 0.159 0.190 0.185 0.250 0.244 0.312 0.306 0.375 0.368 0.438 0.430 0.500 0.492 0.625 0.616 0.750 0.740 0.875 0.864 1.000 0.988 1.125 1.111 1.250 1.236 1.375 1.360 1.500 1.485 1.750 1.734 2.000 1.983 2.250 2.232 2.500 2.481 2.750 2.730 3.000 2.979 3.250 3.228 3.500 3.478 3.750 3.727 4.000 3.976

Spline Socketa Size, M 0.060 0.072 0.096 0.096 0.111 0.111 0.133 0.168 0.183 0.216 0.291 0.372 0.454 0.454 0.595 0.620 0.698 0.790 … … … … … … … … … … … … … …

Nom. Hex. Socket Size, J 0.050 1⁄ 0.062 16 5⁄ 0.078 64 5⁄ 0.078 64 3⁄ 0.094 32 3⁄ 0.094 32 7⁄ 0.109 64 9⁄ 0.141 64 5⁄ 0.156 32 3⁄ 0.188 16 1⁄ 0.250 4 5⁄ 0.312 16 3⁄ 0.375 8 3⁄ 0.375 8 1⁄ 0.500 2 5⁄ 0.625 8 3⁄ 0.750 4 3⁄ 0.750 4 7⁄ 0.875 8 7⁄ 0.875 8 1 1.000 1 1.000 11⁄4 1.250 11⁄2 1.500 13⁄4 1.750 13⁄4 1.750 2 2.000 21⁄4 2.250 1 2 ⁄4 2.250 23⁄4 2.750 23⁄4 2.750 3 3.000

Fillet Ext., F Max 0.007 0.007 0.008 0.008 0.009 0.010 0.010 0.012 0.014 0.014 0.017 0.020 0.023 0.026 0.032 0.039 0.044 0.050 0.055 0.060 0.065 0.070 0.080 0.090 0.100 0.110 0.120 0.130 0.140 0.150 0.160 0.170

Key Engagementa, T 0.025 0.031 0.038 0.044 0.051 0.057 0.064 0.077 0.090 0.120 0.151 0.182 0.213 0.245 0.307 0.370 0.432 0.495 0.557 0.620 0.682 0.745 0.870 0.995 1.120 1.245 1.370 1.495 1.620 1.745 1.870 1.995

a Key engagement depths are minimum. Spline socket sizes are nominal.

All dimensions in inches. The body length LB of the screw is the length of the unthreaded cylindrical portion of the shank. The length of thread, LT, is the distance from the extreme point to the last complete (full form) thread. Standard length increments for screw diameters up to 1 inch are 1⁄16 inch for lengths 1⁄8 through 1⁄4 inch, 1⁄8 inch for lengths 1⁄4 through 1 inch, 1⁄4 inch for lengths 1 through 3 1⁄2 inches, 1⁄2 inch for lengths 3 1⁄2 through 7 inches, 1 inch for lengths 7 through 10 inches and for diameters over 1 inch are 1⁄2 inch for lengths 1 through 7 inches, 1 inch for lengths 7 through 10 inches, and 2 inches for lengths over 10 inches. Heads may be plain or knurled, and chamfered to an angle E of 30 to 45 degrees with the surface of the flat. The thread conforms to the Unified Standard with radius root, Class 3A UNRC and UNRF for screw sizes No. 0 through 1 inch inclusive, Class 2A UNRC and UNRF for over 1 inch through 1 1⁄ inches inclusive, and Class 2A UNRC for larger sizes. Socket dimensions are given in Table 11. 2 For details not shown, including materials, see ANSI/ASME B18.3-1998.



1621

Table 5. Drill and Counterbore Sizes For Socket Head Cap Screws (1960 Series)

Nominal Drill Size Nominal Size or Basic Screw Diameter 0 1 2 3 4 5 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄4 11⁄2 13⁄4 2

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2500 0.3125 0.3750 0.4375 0.5000 0.6250 0.7500 0.8750 1.0000 1.2500 1.5000 1.7500 2.0000

Close Fitb Number or Fractional Decimal Size Size

Normal Fitc Number or Fractional Decimal Size Size A

51 46 3⁄ 32

36 1⁄ 8 9⁄ 64

23 15 5 17⁄ 64 21⁄ 64 25⁄ 64 29⁄ 64 33⁄ 64 41⁄ 64 49⁄ 64 57⁄ 64 1 1 ⁄64 9 1 ⁄32 117⁄32 125⁄32 21⁄32

0.067 0.081 0.094 0.106 0.125 0.141 0.154 0.180 0.206 0.266 0.328 0.391 0.453 0.516 0.641 0.766 0.891 1.016 1.281 1.531 1.781 2.031

49 43 36 31 29 23 18 10 2 9⁄ 32 11⁄ 32 13⁄ 32 15⁄ 32 17⁄ 32 21⁄ 32 25⁄ 32 29⁄ 32 1 1 ⁄32 5 1 ⁄16 19⁄16 113⁄16 21⁄16

0.073 0.089 0.106 0.120 0.136 0.154 0.170 0.194 0.221 0.281 0.344 0.406 0.469 0.531 0.656 0.781 0.906 1.031 1.312 1.562 1.812 2.062

Counterbore Diameter B 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 3⁄ 8 7⁄ 16 17⁄ 32 5⁄ 8 23⁄ 32 13⁄ 16

1 13⁄16 13⁄8 15⁄8 2 23⁄8 23⁄4 31⁄8

Countersink Diametera C 0.074 0.087 0.102 0.115 0.130 0.145 0.158 0.188 0.218 0.278 0.346 0.415 0.483 0.552 0.689 0.828 0.963 1.100 1.370 1.640 1.910 2.180

a Countersink: It is considered good practice to countersink or break the edges of holes which are smaller than (D Max + 2F Max) in parts having a hardness which approaches, equals or exceeds the screw hardness. If such holes are not countersunk, the heads of screws may not seat properly or the sharp edges on holes may deform the fillets on screws thereby making them susceptible to fatigue in applications involving dynamic loading. The countersink or corner relief, however, should not be larger than is necessary to insure that the fillet on the screw is cleared. b Close Fit: The close fit is normally limited to holes for those lengths of screws which are threaded to the head in assemblies where only one screw is to be used or where two or more screws are to be used and the mating holes are to be produced either at assembly or by matched and coordinated tooling. c Normal Fit: The normal fit is intended for screws of relatively long length or for assemblies involving two or more screws where the mating holes are to be produced by conventional tolerancing methods. It provides for the maximum allowable eccentricity of the longest standard screws and for certain variations in the parts to be fastened, such as: deviations in hole straightness, angularity between the axis of the tapped hole and that of the hole for the shank, differences in center distances of the mating holes, etc.

All dimensions in inches. Source: Appendix to American National Standard ANSI/ASME B18.3-1998.



CAP SCREWS

Table 6. American National Standard Hexagon and Spline Socket Flat Countersunk Head Cap Screws ANSI/ASME B18.3-1998

Nominal Size 0 1 2 3 4 5 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

Body Diameter Max. Min. D 0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2500 0.3125 0.3750 0.4375 0.5000 0.6250 0.7500 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000

0.0568 0.0695 0.0822 0.0949 0.1075 0.1202 0.1329 0.1585 0.1840 0.2435 0.3053 0.3678 0.4294 0.4919 0.6163 0.7406 0.8647 0.9886 1.1086 1.2336 1.3568 1.4818

Head Diameter Theoretical Sharp Abs. Max. Min. A 0.138 0.168 0.197 0.226 0.255 0.281 0.307 0.359 0.411 0.531 0.656 0.781 0.844 0.938 1.188 1.438 1.688 1.938 2.188 2.438 2.688 2.938

0.117 0.143 0.168 0.193 0.218 0.240 0.263 0.311 0.359 0.480 0.600 0.720 0.781 0.872 1.112 1.355 1.604 1.841 2.079 2.316 2.553 2.791

HeadHeight

Reference H

Spline Socket Size M

Hexagon Socket Size Nom. J

Key Engagement Min. T

0.044 0.054 0.064 0.073 0.083 0.090 0.097 0.112 0.127 0.161 0.198 0.234 0.234 0.251 0.324 0.396 0.468 0.540 0.611 0.683 0.755 0.827

0.048 0.060 0.060 0.072 0.072 0.096 0.096 0.111 0.145 0.183 0.216 0.251 0.291 0.372 0.454 0.454 … … … … … …

0.035 0.050 0.050 1⁄ 16 1⁄ 16 5⁄ 64 5⁄ 64 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8 7⁄ 8 1

0.025 0.031 0.038 0.044 0.055 0.061 0.066 0.076 0.087 0.111 0.135 0.159 0.159 0.172 0.220 0.220 0.248 0.297 0.325 0.358 0.402 0.435

All dimensions in inches. The body of the screw is the unthreaded cylindrical portion of the shank where not threaded to the head; the shank being the portion of the screw from the point of juncture of the conical bearing surface and the body to the flat of the point. The length of thread LT is the distance measured from the extreme point to the last complete (full form) thread. Standard length increments of No. 0 through 1-inch sizes are as follows: 1⁄16 inch for nominal screw lengths of 1⁄8 through 1⁄4 inch; 1⁄8 inch for lengths of 1⁄4 through 1 inch; 1⁄4 inch for lengths of 1 inch through 3 1⁄2 inches; 1⁄2 inch for lengths of 3 1⁄2 through 7 inches; and 1 inch for lengths of 7 through 10 inches, incl. For screw sizes over 1 inch, length increments are: 1⁄2 inch for nominal screw lengths of 1 inch through 7 inches; 1 inch for lengths of 7 through 10 inches; and 2 inches for lengths over 10 inches. Threads shall be Unified external threads with radius root; Class 3A UNRC and UNRF series for sizes No. 0 through 1 inch and Class 2A UNRC and UNRF series for sizes over 1 inch to 1 1⁄2 inches, incl. For manufacturing details not shown, including materials, see American National Standard ANSI/ASME B18.3-1998 Socket dimensions are given in Table 11.



1623

Table 7. American National Standard Hexagon Socket and Spline Socket Button Head Cap Screws ANSI/ASME B18.3-1998

Screw Diameter Nominal Size

Basic

Head Diameter Max.

D

Min.

Head Height Max.

A

Min. H

Head Side Height

Spline Socket Sizea

Hexagon Socket Sizea

Standard Length

Ref.

Nom.

Nom.

Max.

S

M

J

L

0

0.0600

0.114

0.104

0.032

0.026

0.010

0.048

0.035

1⁄ 2

1

0.0730

0.139

0.129

0.039

0.033

0.010

0.060

0.050

1⁄ 2

2

0.0860

0.164

0.154

0.046

0.038

0.010

0.060

0.050

1⁄ 2

3

0.0990

0.188

0.176

0.052

0.044

0.010

0.072

1⁄ 16

1⁄ 2

4

0.1120

0.213

0.201

0.059

0.051

0.015

0.072

1⁄ 16

1⁄ 2

5

0.1250

0.238

0.226

0.066

0.058

0.015

0.096

5⁄ 64

1⁄ 2

6

0.1380

0.262

0.250

0.073

0.063

0.015

0.096

5⁄ 64

5⁄ 8

8

0.1640

0.312

0.298

0.087

0.077

0.015

0.111

3⁄ 32

10

0.1900

0.361

0.347

0.101

0.091

0.020

0.145

1⁄ 8

1

3⁄ 4

1⁄ 4

0.2500

0.437

0.419

0.132

0.122

0.031

0.183

5⁄ 32

1

5⁄ 16

0.3125

0.547

0.527

0.166

0.152

0.031

0.216

3⁄ 16

1

3⁄ 8

0.3750

0.656

0.636

0.199

0.185

0.031

0.251

7⁄ 32

11⁄4

1⁄ 2

0.5000

0.875

0.851

0.265

0.245

0.046

0.372

5⁄ 16

2

5⁄ 8

0.6250

1.000

0.970

0.331

0.311

0.062

0.454

3⁄ 8

2

a Socket dimensions are given in Table 11.

All dimensions in inches. These cap screws have been designed and recommended for light fastening applications. They are not suggested for use in critical high-strength applications where socket head cap screws should normally be used. Standard length increments for socket button head cap screws are as follows: 1⁄16 inch for nominal screw lengths of 1⁄8 through 1⁄4 inch, 1⁄8 inch for nominal screw lengths of 1⁄4 through 1 inch, and 1⁄4 inch for nominal screw lengths of 1 inch through 2 inches. Tolerances on lengths are −0.03 inch for lengths up to 1 inch inclusive. For lengths from 1 through 2 inches, inclusive, length tolerances are − 0.04 inch. The thread conforms to the Unified standard, Class 3A, with radius root, UNRC and UNRF. To prevent interference, American National Standard ANSI/ASME B18.3.4M-1986 gives metric dimensional and general requirements for a lower head profile hexagon socket button head cap screw. Because of its design, wrenchability and other design factors are reduced; therefore, B18.3.4M should be reviewed carefully. Available only in metric sizes and with metric threads. For manufacturing details, including materials, not shown, see American National Standard ANSI/ASME B18.3-1998



CAP SCREWS

Table 8. American National Standard Hexagon Socket Head Shoulder Screws ANSI/ASME B18.3-1998

Nominal Size 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1 11⁄4 11⁄2 13⁄4 2

Shoulder Diameter Max. Min. D 0.2480 0.3105 0.3730 0.4980 0.6230 0.7480 0.9980 1.2480 1.4980 1.7480 1.9980

0.2460 0.3085 0.3710 0.4960 0.6210 0.7460 0.9960 1.2460 1.4960 1.7460 1.9960

Thread Neck Diameter Nominal Size

Max.

Min. G

Head Diameter Max. Min. A

Head Height Max. Min. H

Head Side Height Min. S

Nominal Thread Size D1

Thread Length E

0.375 0.438 0.562 0.750 0.875 1.000 1.312 1.750 2.125 2.375 2.750

0.357 0.419 0.543 0.729 0.853 0.977 1.287 1.723 2.095 2.345 2.720

0.188 0.219 0.250 0.312 0.375 0.500 0.625 0.750 1.000 1.125 1.250

0.157 0.183 0.209 0.262 0.315 0.421 0.527 0.633 0.842 0.948 1.054

10–24 1⁄ -20 4 5⁄ -18 16 3⁄ -16 8 1⁄ -13 2 5⁄ -11 8 3⁄ -10 4 7⁄ -9 8 11⁄8-7 11⁄4-7 11⁄2-6

0.375 0.438 0.500 0.625 0.750 0.875 1.000 1.125 1.500 1.750 2.000

Thread Neck Width

Shoulder Neck Dia.

Shoulder Neck Width

Max.

Min.

Max.

I

K

F

0.177 0.209 0.240 0.302 0.365 0.490 0.610 0.735 0.980 1.105 1.230

Thread Neck Fillet Max.

Min. N

Head Fillet Extension Above D

Hexagon Socket Size

Max.

Nom.

M

J

1⁄ 4

0.142

0.133

0.083

0.227

0.093

0.023

0.017

0.014

1⁄ 8

5⁄ 16

0.193

0.182

0.100

0.289

0.093

0.028

0.022

0.017

5⁄ 32

3⁄ 8

0.249

0.237

0.111

0.352

0.093

0.031

0.025

0.020

3⁄ 16

1⁄ 2

0.304

0.291

0.125

0.477

0.093

0.035

0.029

0.026

1⁄ 4

5⁄ 8

0.414

0.397

0.154

0.602

0.093

0.042

0.036

0.032

5⁄ 16

3⁄ 4

0.521

0.502

0.182

0.727

0.093

0.051

0.045

0.039

3⁄ 8

1

0.638

0.616

0.200

0.977

0.125

0.055

0.049

0.050

1⁄ 2

11⁄4

0.750

0.726

0.222

1.227

0.125

0.062

0.056

0.060

5⁄ 8

11⁄2

0.964

0.934

0.286

1.478

0.125

0.072

0.066

0.070

13⁄4

1.089

1.059

0.286

1.728

0.125

0.072

0.066

0.080

1

2

1.307

1.277

0.333

1.978

0.125

0.102

0.096

0.090

11⁄4

7⁄ 8

All dimensions are in inches. The shoulder is the enlarged, unthreaded portion of the screw. Standard length increments for shoulder screws are: 1⁄8 inch for nominal screw lengths of 1⁄4 through 3⁄4 inch; 1⁄4 inch for lengths above 3⁄4 through 5 inches; and 1⁄2 inch for lengths over 5 inches. The thread conforms to the Unified Standard Class 3A, UNC. Hexagon socket sizes for the respective shoulder screw sizes are the same as for set screws of the same nominal size (see Table 7) except for shoulder screw size 1 inch, socket size is 1⁄2 inch, for screw size 1 1⁄2 inches, socket size is 7⁄8 inch, and for screw size 2 inches, socket size is 1 1⁄4 inches. For details not shown, including materials, see ANSI/ASME B18.3-1998.


Machinery's Handbook 27th Edition SET SCREWS

1625

Table 9. American National Standard Slotted Headless Set Screws ANSI/ASME B18.6.2-1998

FLAT POINT

DOG POINT HALF DOG POINT

CUP POINT Nominal Sizea or Basic Screw Diameter 0 1 2 3 4 5 6 8 10 12 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

OVAL POINT

Slot Width, J

Slot Depth, T

Cup and Flat Point Dia., C

CONE POINT Dog Point Dia., P

Point Length Dog, Q

Half Dog, Q1

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2160 0.2500

.014 .016 .018 .020 .024 .026 .028 .032 .035 .042 .049

.010 .012 .014 .016 .018 .020 .022 .026 .029 .035 .041

.020 .020 .025 .028 .031 .036 .040 .046 .053 .061 .068

.016 .016 .019 .022 .025 .026 .030 .036 .043 .051 .058

.033 .040 .047 .054 .061 .067 .074 .087 .102 .115 .132

.027 .033 .039 .045 .051 .057 .064 .076 .088 .101 .118

.040 .049 .057 .066 .075 .083 .092 .109 .127 .144 .156

.037 .045 .053 .062 .070 .078 .087 .103 .120 .137 .149

.032 .040 .046 .052 .058 .063 .073 .083 .095 .115 .130

.028 .036 .042 .048 .054 .057 .067 .077 .085 .105 .120

.017 .021 .024 .027 .030 .033 .038 .043 .050 .060 .068

.013 .017 .020 .023 .026 .027 .032 .037 .040 .050 .058

0.3125

.055

.047

.083

.073

.172

.156

.203

.195

.161

.151

.083

.073

0.3750

.068

.060

.099

.089

.212

.194

.250

.241

.193

.183

.099

.089

0.4375

.076

.068

.114

.104

.252

.232

.297

.287

.224

.214

.114

.104

0.5000

.086

.076

.130

.120

.291

.270

.344

.334

.255

.245

.130

.120

0.5625

.096

.086

.146

.136

.332

.309

.391

.379

.287

.275

.146

.134

0.6250

.107

.097

.161

.151

.371

.347

.469

.456

.321

.305

.164

.148

0.7500

.134

.124

.193

.183

.450

.425

.562

.549

.383

.367

.196

.180

a When

specifying a nominal size in decimals a zero preceding the decimal point or any zero in the fourth decimal place is omitted. All dimensions are in inches. Crown Radius, I: The crown radius has the same value as the basic screw diameter to three decimal places. Oval Point Radius, R: Values of the oval point radius according to nominal screw size are: For a screw size of 0, a radius of .045; 1, .055; 2, .064; 3, .074; 4, .084; 5, .094; 6, .104; 8, .123; 10, .142; 12, .162; 1⁄4, .188; 5⁄16, .234; 3⁄8, .281; 7⁄16, .328; 1⁄2, .375; 9⁄16, .422; 5⁄8, .469; and for 3⁄4, .562. Cone Point Angle, Y: The cone point angle is 90° ± 2° for the following nominal lengths, or longer, shown according to screw size: For nominal size 0, a length of 5⁄64; 1, 3⁄32; 2, 7⁄64; 3, 1⁄8; 4, 5⁄32; 5, 3⁄16; 6, 3⁄16; 8, 1⁄4; 10, 1⁄4; 12, 5⁄16; 1⁄4, 5⁄16; 5⁄16, 3⁄8; 3⁄8, 7⁄16; 7⁄16, 1⁄2; 1⁄2, 9⁄16; 9⁄16, 5⁄8; 5⁄8, 3⁄4; and for 3⁄4, 7⁄8. For shorter screws, the cone point angle is 118° ± 2°. Point Angle X: The point angle is 45°, + 5°, − 0°, for screws of nominal lengths, or longer, as given just above for cone point angle, and 30°, min. for shorter screws. Threads: are Unified Standard Class 2A; UNC and UNF Series or UNRC and UNRF Series.



SET SCREWS

Table 10. American National Standard Hexagon and Spline Socket Set Screw Optional Cup Points ANSI/ASME B18.3-1998

TYPE A

TYPE B

TYPE C

TYPE D

* This diameter may be counterbored.

TYPE E

TYPE F

Point Dia. Nom. Size

Max.

Min.

Max.

C 0 1 2 3 4 5 6 8 10

TYPE G

Point Dia. Min.

Point Dia. Max.

C1

Point Length

Min.

Max.

C2

Min. S

1⁄ 4

0.033 0.040 0.047 0.054 0.061 0.067 0.074 0.087 0.102 0.132

0.027 0.033 0.039 0.045 0.051 0.057 0.064 0.076 0.088 0.118

0.032 0.038 0.043 0.050 0.056 0.062 0.069 0.082 0.095 0.125

0.027 0.033 0.038 0.045 0.051 0.056 0.062 0.074 0.086 0.114

0.027 0.035 0.043 0.051 0.059 0.068 0.074 0.090 0.101 0.156

0.022 0.030 0.038 0.046 0.054 0.063 0.068 0.084 0.095 0.150

0.007 0.008 0.010 0.011 0.013 0.014 0.017 0.021 0.024 0.027

0.004 0.005 0.007 0.007 0.008 0.009 0.012 0.016 0.019 0.022

5⁄ 16

0.172

0.156

0.156

0.144

0.190

0.185

0.038

0.033

3⁄ 8

0.212

0.194

0.187

0.174

0.241

0.236

0.041

0.036

7⁄ 16

0.252

0.232

0.218

0.204

0.286

0.281

0.047

0.042

1⁄ 2

0.291

0.270

0.250

0.235

0.333

0.328

0.054

0.049

5⁄ 8

0.371

0.347

0.312

0.295

0.425

0.420

0.067

0.062

3⁄ 4

0.450

0.425

0.375

0.357

0.523

0.518

0.081

0.076

7⁄ 8

1 11⁄8

0.530 0.609 0.689

0.502 0.579 0.655

0.437 0.500 0.562

0.418 0.480 0.542

… … …

… … …

… … …

… … …

11⁄4

0.767

0.733

0.625

0.605

…

…

…

…

13⁄8

0.848

0.808

0.687

0.667

…

…

…

…

11⁄2

0.926

0.886

0.750

0.730

…

…

…

…

13⁄4

1.086 1.244

1.039 1.193

0.875 1.000

0.855 0.980

… …

… …

… …

… …

2

All dimensions are in inches. The cup point types shown are those available from various manufacturers.



1627

Table 11. American National Standard Hexagon and Spline Sockets ANSI/ASME B18.3-1998

BROACHED SOCKET

Nominal Socket Size 0.028 0.035 0.050 1⁄ 16 5⁄ 64 3⁄ 32 7⁄ 64 1⁄ 8

Socket Width Across Flats Max. Min. J 0.0285 0.0355 0.0510 0.0635 0.0791 0.0952 0.1111 0.1270

0.0280 0.0350 0.0500 0.0625 0.0781 0.0937 0.1094 0.1250

Nominal Socket Size 9⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8

…

HEXAGON SOCKETS Socket Socket Width Width Across Flats Across Flats Nominal Max. Min. Max. Min. Socket J J Size 0.1426 0.1587 0.1900 0.2217 0.2530 0.3160 0.3790 …

0.1406 0.1562 0.1875 0.2187 0.2500 0.3125 0.3750 …

7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8

0.4420 0.5050 0.5680 0.6310 0.7570 0.8850 1.0200 …

1 …

0.4375 0.5000 0.5625 0.6250 0.7500 0.8750 1.0000 …

Nominal Socket Size 11⁄4 11⁄2 13⁄4 2 21⁄4 23⁄4 3 …

Socket Width Across Flats Max. Min. J 1.2750 1.5300 1.7850 2.0400 2.2950 2.8050 3.0600 …

1.2500 1.5000 1.7500 2.0000 2.2500 2.7500 3.0000 …

SPLINE SOCKETS Nominal Socket Size

Number of Teeth

0.033 0.048 0.060 0.072 0.096 0.111 0.133 0.145 0.168 0.183 0.216 0.251 0.291 0.372 0.454 0.595 0.620 0.698 0.790

4 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6

Socket Major Diameter Max. Min. M 0.0350 0.050 0.062 0.074 0.098 0.115 0.137 0.149 0.173 0.188 0.221 0.256 0.298 0.380 0.463 0.604 0.631 0.709 0.801

0.0340 0.049 0.061 0.073 0.097 0.113 0.135 0.147 0.171 0.186 0.219 0.254 0.296 0.377 0.460 0.601 0.627 0.705 0.797

Socket Minor Diameter Min. N

Max.

0.0260 0.041 0.051 0.064 0.082 0.098 0.118 0.128 0.150 0.163 0.190 0.221 0.254 0.319 0.386 0.509 0.535 0.604 0.685

0.0255 0.040 0.050 0.063 0.080 0.096 0.116 0.126 0.147 0.161 0.188 0.219 0.252 0.316 0.383 0.506 0.531 0.600 0.681

Width of Tooth Max.

Min. P

0.0120 0.011 0.014 0.016 0.022 0.025 0.030 0.032 0.036 0.039 0.050 0.060 0.068 0.092 0.112 0.138 0.149 0.168 0.189

0.0115 0.010 0.013 0.015 0.021 0.023 0.028 0.030 0.033 0.037 0.048 0.058 0.066 0.089 0.109 0.134 0.145 0.164 0.185

All dimensions are in inches. * Socket depths, T, for various screw types are given in the standard but are not shown here. Where sockets are chamfered, the depth of chamfer shall not exceed 10 per cent of the nominal socket size for sizes up to and including 1⁄16 inch for hexagon sockets and 0.060 for spline sockets, and 7.5 per cent for larger sizes.



SET SCREWS Table 12. American National Standard Square Head Set Screws ANSI/ASME B18.6.2-1998

FLAT POINT

DOG POINT HALF DOG POINT

CUP POINT Nominal Size* or Basic Screw Diameter

OVAL POINT

Cup and Flat Point Diams., C

CONE POINT Point Length

Dog and Half Dog Point Diams., P

Dog, Q

Oval Point Rad., R +.031 −.000

Max.

Min

Max.

Max.

Min.

Max.

Min.

0.1900

.102

.088

.127

.120

.095

.085

.050

.040

.142

1⁄ 4

0.2500

.132

.118

.156

.149

.130

.120

.068

.058

.188

5⁄ 16

0.3125

.172

.156

.203

.195

.161

.151

.083

.073

.234

3⁄ 8

0.3750

.212

.194

.250

.241

.193

.183

.099

.089

.281

7⁄ 16

0.4375

.252

.232

.297

.287

.224

.214

.114

.104

.328

1⁄ 2

0.500

.291

.270

.344

.334

.255

.245

.130

.120

.375

9⁄ 16

0.5625

.332

.309

.391

.379

.287

.275

.146

.134

.422

5⁄ 8

0.6250

.371

.347

.469

.456

.321

.305

.164

.148

.469

3⁄ 4

0.7500

.450

.425

.562

.549

.383

.367

.196

.180

.562

7⁄ 8

0.8750

.530

.502

.656

.642

.446

.430

.227

.211

.656

1

1.0000

.609

.579

.750

.734

.510

.490

.260

.240

.750

11⁄8

1.1250

.689

.655

.844

.826

.572

.552

.291

.271

.844

11⁄4

1.2500

.767

.733

.938

.920

.635

.615

.323

.303

.938

13⁄8

1.3750

.848

.808

1.031

1.011

.698

.678

.354

.334

1.031

11⁄2

1.5000

.926

.886

1.125

1.105

.760

.740

.385

.365

1.125

10

Min.

Half Dog, Q1

All dimensions are in inches. *Threads: Threads are Unified Standard Class 2A; UNC, UNF and 8 UN Series or UNRC, UNRF and 8 UNR Series. Length of Thread: Square head set screws have complete (full form) threads extending over that portion of the screw length which is not affected by the point. For the respective constructions, threads extend into the neck relief, to the conical underside of head, or to within one thread (as measured with a thread ring gage) from the flat underside of the head. Threads through angular or crowned portions of points have fully formed roots with partial crests. * When specifying a nominal size in decimals, the zero preceding the decimal point is omitted as is any

zero in the fourth decimal place.



1629

Table 13. American National Standard Square Head Set Screws ANSI/ASME B18.6.2-1998

OPTIONAL HEAD CONSTRUCTIONS Nominal Size or Basic Screw Diameter

Width Across Width Across Head Height, Flats,F Corners,G H

Neck Relief Diameter, K

Neck Relief Fillet Rad.,S

Neck Relief Width, U

Head Rad.,,W Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

10

0.1900

.188

.180

.265

.247

.148

.134

.145

.140

.027

.083

0.48

1⁄ 4

0.2500

.250

.241

.354

.331

.196

.178

.185

.170

.032

.100

0.62

5⁄ 16

0.3125

.312

.302

.442

.415

.245

.224

.240

.225

.036

.111

0.78

3⁄ 8

0.3750

.375

.362

.530

.497

.293

.270

.294

.279

.041

.125

0.94

7⁄ 16

0.4375

.438

.423

.619

.581

.341

.315

.345

.330

.046

.143

1.09

1⁄ 2

0.5000

.500

.484

.707

.665

.389

.361

.400

.385

.050

.154

1.25

9⁄ 16

0.5625

.562

.545

.795

.748

.437

.407

.454

.439

.054

.167

1.41

5⁄ 8

0.6250

.625

.606

.884

.833

.485

.452

.507

.492

.059

.182

1.56

3⁄ 4

0.7500

.750

.729 1.060 1.001

.582

.544

.620

.605

.065

.200

1.88

7⁄ 8

0.8750

.875

.852 1.237 1.170

.678

.635

.731

.716

.072

.222

2.19

1

1.0000

1.000

.974 1.414 1.337

.774

.726

.838

.823

.081

.250

2.50

11⁄8

1.1250

1.125 1.096 1.591 1.505

.870

.817

.939

.914

.092

.283

2.81

11⁄4

1.2500

1.250 1.219 1.768 1.674

.966

.908 1.064 1.039

.092

.283

3.12

13⁄8

1.3750

1.375 1.342 1.945 1.843 1.063 1.000 1.159 1.134

.109

.333

3.44

11⁄2

1.5000

1.500 1.464 2.121 2.010 1.159 1.091 1.284 1.259

.109

.333

3.75

Designation: Square head set screws are designated by the following data in the sequence shown: Nominal size (number, fraction or decimal equivalent); threads per inch; screw length (fraction or decimal equivalent); product name; point style; material; and protective finish, if required. Examples: 1⁄4 - 20 × 3⁄4 Square Head Set Screw, Flat Point, Steel, Cadmium Plated. .500 − 13 × 1.25 Square Head Set Screw, Cone Point, Corrosion Resistant Steel. Cone Point Angle, Y: For the following nominal lengths, or longer, shown according to nominal size, the cone point angle is 90° ± 2°: For size No. 10, 1⁄4; 1⁄4, 5⁄16; 5⁄16, 3⁄8; 3⁄8, 7⁄16; 7⁄16, 1⁄2; 1⁄2, 9⁄16; 9⁄16, 5⁄8; 5⁄8, 3⁄4; 3⁄ , 7⁄ ; 7⁄ , 1; 1, 11⁄ ; 11⁄ , 11⁄ ; 11⁄ , 11⁄ ; 13⁄ , 15⁄ ; and for 11⁄ , 13⁄ . For shorter screws the cone point angle is 4 8 8 8 8 4 4 2 8 8 2 4 118° ± 2°. Point Types: Unless otherwise specified, square head set screws are supplied with cup points. Cup points as furnished by some manufacturers may be externally or internally knurled. Where so specified by the purchaser, screws have cone, dog, half-dog, flat or oval points as given on the following page. Point Angle, X: The point angle is 45°, + 5°, − 0° for screws of the nominal lengths, or longer, given just above for cone point angle, and 30° min. for shorter lengths.



SCREW SOCKET KEYS AND BITS Table 14. Applicability of Hexagon and Spline Keys and Bits

Nominal Key or Bit Size

Cap Screws 1960 Series

Flat Countersunk Head Cap Screws

Button Head Cap Screws

Shoulder Screws

Set Screws

0 1&2 3&4 5&6

Nominal Screw Sizes HEXAGON KEYS AND BITS

1⁄ 16

0.062

… … 0 1

5⁄ 64

0.078

2&3

5&6

5&6

…

8

3⁄ 32

0.094

4&5

8

8

…

10

7⁄ 64

…

0.028 0.035 0.050

… 0 1&2 3&4

… 0 1&2 3&4

… … … …

0.109

6

…

…

…

1⁄ 8

0.125

…

10

10

1⁄ 4

1⁄ 4

9⁄ 64

0.141

8

…

…

…

…

5⁄ 32

0.156

10

1⁄ 4

1⁄ 4

5⁄ 16

5⁄ 16

3⁄ 16

0.188

1⁄ 4

5⁄ 16

5⁄ 16

3⁄ 8

3⁄ 8

7⁄ 32

0.219

…

3⁄ 8

3⁄ 8

…

7⁄ 16

1⁄ 4

0.250

5⁄ 16

7⁄ 16

…

1⁄ 2

1⁄ 2

5⁄ 16

0.312

3⁄ 8

1⁄ 2

1⁄ 2

5⁄ 8

5⁄ 8

3⁄ 8

0.375

7⁄ & 1⁄ 16 2

5⁄ 8

5⁄ 8

3⁄ 4

3⁄ 4

7⁄ 16

0.438

…

…

…

…

…

1⁄ 2

0.500

5⁄ 8

3⁄ 4

…

1

7⁄ 8

9⁄ 16

0.562

…

7⁄ 8

…

…

1 & 11⁄8

5⁄ 8

0.625

3⁄ 4

3⁄ 4

0.750

7⁄ & 8

7⁄ 8

0.875

1

…

11⁄4

11⁄4 & 13⁄8

11⁄8

…

…

11⁄2

11⁄8 & 11⁄4

11⁄4 & 13⁄8

…

11⁄2

…

13⁄4

13⁄4 & 2

1

1.000

13⁄8 & 11⁄2

11⁄2

…

11⁄4

1.250

13⁄4

…

…

2

…

11⁄2

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

… …

… …

… …

… … 0&1 2&3 4 5&6 8 10 … 1⁄ 4

1

1.500

2

13⁄4

1.750

21⁄4 &

2

2.000

23⁄4

21⁄4 23⁄4 3

21⁄2

31⁄4

2.250

3&

2.750 3.000

31⁄2 &

33⁄4

4

SPLINE KEYS AND BITS … … 0 1 2&3 4&5 6 … 8 10

… 0 1&2 3&4 5&6 8 … 10 … 1⁄ 4

… 0 1&2 3&4 5&6 8 … 10 … 1⁄ 4

… … … … … … … … … …

0.216

1⁄ 4

5⁄ 16

5⁄ 16

…

3⁄ 8

0.251

…

3⁄ 8

3⁄ 8

…

7⁄ 16

0.291

5⁄ 16

7⁄ 16

…

…

1⁄ 2

0.372

3⁄ 8

1⁄ 2

1⁄ 2

…

5⁄ 8

0.454

7⁄ & 1⁄ 16 2

5⁄ & 3⁄ 8 4

5⁄ 8

…

3⁄ 4

0.595

5⁄ 8

…

…

…

7⁄ 8

0.620

3⁄ 4

…

…

…

…

0.698 0.790

7⁄ 8

… …

… …

… …

… …

0.033 0.048 0.060 0.072 0.096 0.111 0.133 0.145 0.168 0.183

1

Source: Appendix to American National Standard ANSI/ASME B18.3-1998.


… 5⁄ 16

Machinery's Handbook 27th Edition SCREW SOCKET KEYS AND BITS

1631

Table 15. ANSI Hexagon and Spline Socket Set Screws ANSI/ASME B18.3-1998

Flat Point

Oval Point Cone Point

0 1 2 3 4 5 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2 13⁄4 2

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1640 0.1900 0.2500 0.3125 0.3750 0.4375 0.5000 0.6250 0.7500 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000 1.7500 2.0000

Dia. Max. P

Lgth. Max. Q

Oval Point Radius Basic R

0.040 0.049 0.057 0.066 0.075 0.083 0.092 0.109 0.127 0.156 0.203 0.250 0.297 0.344 0.469 0.562 0.656 0.750 0.844 0.938 1.031 1.125 1.312 1.500

0.017 0.021 0.024 0.027 0.030 0.033 0.038 0.043 0.049 0.067 0.082 0.099 0.114 0.130 0.164 0.196 0.227 0.260 0.291 0.323 0.354 0.385 0.448 0.510

0.045 0.055 0.064 0.074 0.084 0.094 0.104 0.123 0.142 0.188 0.234 0.281 0.328 0.375 0.469 0.562 0.656 0.750 0.844 0.938 1.031 1.125 1.321 1.500

0.050 0.060 0.060 0.070 0.070 0.080 0.080 0.090 0.100 0.125 0.156 0.188 0.219 0.250 0.312 0.375 0.500 0.562 0.562 0.625 0.625 0.750 1.000 1.000

Half Dog

Cup Point Half Dog Point

Socket Size Nominal Size or Basic Screw Diameter

For optional cup points and their dimensions see Table 10. Min. Key Engagement Lgth. Depth Limit for Hex. Spl. Angle THa TSa Yb

Hex. Nom. J

Spl. Nom. M

0.028 0.035 0.035 0.050 0.050 1⁄ 16 1⁄ 16 5⁄ 64 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 3⁄ 4 1 1

0.033 0.033 0.048 0.048 0.060 0.072 0.072 0.096 0.111 0.145 0.183 0.216 0.251 0.291 0.372 0.454 0.595 … … … … … … …

Cup and Flat Point Diameters Max. Min. C 0.033 0.040 0.047 0.054 0.061 0.067 0.074 0.087 0.102 0.132 0.172 0.212 0.252 0.291 0.371 0.450 0.530 0.609 0.689 0.767 0.848 0.926 1.086 1.244

0.027 0.033 0.039 0.045 0.051 0.057 0.064 0.076 0.088 0.118 0.156 0.194 0.232 0.270 0.347 0.425 0.502 0.579 0.655 0.733 0.808 0.886 1.039 1.193

0.026 0.035 0.040 0.040 0.045 0.055 0.055 0.080 0.080 0.125 0.156 0.188 0.219 0.250 0.312 0.375 0.500 … … … … … … …

0.09 0.09 0.13 0.13 0.19 0.19 0.19 0.25 0.25 0.31 0.38 0.44 0.50 0.57 0.75 0.88 1.00 1.13 1.25 1.50 1.63 1.75 2.00 2.25

a Reference should be made to the Standard for shortest optimum nominal lengths to which the minimum key engagement depths TH and TS apply. b Cone point angle Y is 90 degrees plus or minus 2 degrees for these nominal lengths or longer and 118 degrees plus or minus 2 degrees for shorter nominal lengths. All dimensions are in inches. The thread conforms to the Unified Standard, Class 3A, UNC and UNF series. The socket depth T is included in the Standard and some are shown here. The nominal length L of all socket type set screws is the total or overall length. For nominal screw lengths of 1⁄16 through 3⁄16 inch (0 through 3 sizes incl.) the standard length increment is 0.06 inch; for lengths 1⁄8 through 1 inch the increment is 1⁄8 inch; for lengths 1 through 2 inches the increment is 1⁄4 inch; for lengths 2 through 6 inches the increment is 1⁄2 inch; for lengths 6 inches and longer the increment is 1 inch. Socket dimensions are given in Table 11. Length Tolerance: The allowable tolerance on length L for all set screws of the socket type is ± 0.01 inch for set screws up to 5⁄8 inch long; ± 0.02 inch for screws over 5⁄8 to 2 inches long; ± 0.03 inch for screws over 2 to 6 inches long and ± 0.06 inch for screws over 6 inches long. Socket dimensions are given in Table 11. For manufacturing details, including materials, not shown, see American National Standard ANSI/ASME B18.3-1998.



HEXAGON SOCKET SCREWS

British Standard Hexagon Socket Screws — Metric Series.—The first five parts of British Standard BS 4168: 1981 provide specifications for hexagon socket head cap screws and hexagon socket set screws. Hexagon Socket Head Cap Screws: The dimensional data in Table 1 are based upon BS 4168: Part 1: 1981. These screws are available in stainless steel and alloy steel, the latter having class 12.9 properties as specified in BS 6104:Part 1. When ordering these screws, the designation “Hexagon socket head cap screw BS 4168 M5 × 20-12.9” would mean, as an example, a cap screw having a thread size of d = M5, nominal length l = 20 mm, and property class 12.9. Alloy steel cap screws are furnished with a black oxide finish (thermal or chemical); stainless steel cap screws with a plain finish. Combinations of thread size, nominal length, and length of thread are shown in Table 2; the screw threads in these combinations are in the ISO metric coarse pitch series specified in BS 3643 with tolerances in the 5g6g class. (See Metric Screw Threads in Index.) Hexagon Socket Set Screws: Part 2 of B.S. 4168:1981 specifies requirements for hexagon socket set screws with fiat point having ISO metric threads, and diameters from 1.6 mm up to and including 24 mm. The dimensions of these set screws along with those of cone-point, dog-point, and cup-point set screws in accord, respectively, with Parts 3, 4, and 5 of the Standard are given in Table 3 and the accompanying illustration. All of these set screws are available in either steel processed to mechanical properties class 45H B.S. 6104:Part 3; or stainless steel processed to mechanical properties described in B.S. 6105. Steel set screws are furnished with black oxide (thermal or chemical) finish; stainless steel set screws are furnished plain. The tolerances applied to the threads of these set screws are for ISO product grade A, based on ISO 4759⁄1-1978 “Tolerances for fasteners — Part 1: Bolts, screws, and nuts with thread diameters greater than or equal to 1.6 mm and less than or equal to 150 mm and product grades A, B, and C.” Hexagon socket set screws are designated by the type, the thread size, nominal length, and property class. As an example, for a flat-point set screw of thread size d = M6, nominal length l = 12 mm, and property class 45H: Hexagon socket set screw flat point BS 4168 M6 × 12-45H British Standard Hexagon Socket Countersunk and Button Head Screws — Metric Series: British Standard BS 4168:1967 provides a metric series of hexagon socket countersunk and button head screws. The dimensions of these screws are given in Table 4. The revision of this Standard will constitute Parts 6 and 8 of BS 4168. British Standards for Mechanical Properties of Fasteners: B.S. 6104: Part 1:1981 specifies mechanical properties for bolts, screws, and studs with nominal diameters up to and including 39 mm of any triangular ISO thread and made of carbon or alloy steel. It does not apply to set screws and similar threaded fasteners. Part 2 of this Standard specifies the mechanical properties of set screws and similar fasteners, not under tensile stress, in the range from M1.6 up to and including M39 and made of carbon or alloy steel. B.S. 6105:1981 provides specifications for bolts, screws, studs, and nuts made from austenitic, ferritic, and martensitic grades of corrosion-resistant steels. This Standard applies only to fastener components after completion of manufacture with nominal diameters from M1.6 up to and including M39. These Standards are not described further here. Copies may be obtained from the British Standards Institution, 2 Park Street, London W1A 2BS and also from the American National Standards Institute, 25 West 43rd Street, New York, N.Y. 10036.



Table 1. British Standard Hexagon Socket Head Cap Screws—Metric Series BS 4168:Part 1:1981 (obsolescent)

Body Diameter, D Max 1.6 2 2.5 3 4 5 6 8 10 12 14 16 20 24 30 36

Min 1.46 1.86 2.36 2.86 3.82 4.82 5.82 7.78 9.78 11.73 13.73 15.73 19.67 23.67 29.67 35.61

Maxc 3 3.8 4.5 5.5 7 8.5 10 13 16 18 21 24 30 36 45 54

Head Diameter, A Maxd 3.14 3.98 4.68 5.68 7.22 8.72 10.22 13.27 16.27 18.27 21.33 24.33 30.33 36.39 45.39 54.46

Head Height, H Min 2.86 3.62 4.32 5.32 6.78 8.28 9.78 12.73 15.73 17.73 20.67 23.67 29.67 35.61 44.61 53.54

Max 1.6 2 2.5 3 4 5 6 8 10 12 14 16 20 24 30 36

Min 1.46 1.86 2.36 2.86 3.82 4.82 5.70 7.64 9.64 11.57 13.57 15.57 19.48 23.48 29.48 35.38

Hexagon Socket Size, Jb Nom 1.5 1.5 2 2.5 3 4 5 6 8 10 12 14 17. 19 22 27

Key Engagement, K Min 0.7 1 1.1 1.3 2 2.5 3 4 5 6 7 8 10 12 15.5 19

Wall Thickness, W Min 0.55 0.55 0.85 1.15 1.4 1.9 2.3 3.3 4 4.8 5.8 6.8 8.6 10.4 13.1 15.3

Fillet Dia., Rad., da F Min Max 0.1 2 0.1 2.6 0.1 3.1 0.1 3.6 0.2 4.7 0.2 5.7 0.25 6.8 0.4 9.2 0.4 11.2 0.6 14.2 0.6 16.2 0.6 18.2 0.8 22.4 0.8 26.4 1 33.4 1 39.4

CAP SCREWS

Nominal Size,a d M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 (M14) M16 M20 M24 M30 M36

a The size shown in ( ) is non-preferred. b See Table 2 for min/max. c For plain heads.

1633

d For knurled heads.




SCREW SOCKETS Table 2. British Standard Hexagon Socket Screws — Metric Series BS 4168:Part 1:1981 (obsolescent) Dimensions of Hexagon Sockets

Socket Width Across Flats, J

Nominal Socket Size

Socket Width Across Flats, J

Max.

Min.

Nominal Socket Size

1.5

1.545

1.52

6

6.095

2.0

2.045

2.02

8

8.115

8.025

2.5

2.56

2.52

10

10.115

10.025

3

3.08

3.02

12

12.142

12.032

4

4.095

4.02

14

14.142

14.032

5

5.095

5.02

17

17.23

17.05

…

…

19

19.275

19.065

…

Max.

Min. 6.02

15

16

17

18

20

22

24

28

M36

… …

M30

… …

M24

… …

M20

… …

M16

… …

(M14)

… …

M12

… …

Nominal Length, L

M8

M6

M5

M4

M3

M2.5

M2

… …

16 20 25 30 35 40 45 50 55 60 65 70 80 90 100 110 120 130 140 150 160 180 200 b (ref)

Nominal Thread Size, D M10

2.5 3 4 5 6 8 10 12 16 20 25 30 35 40 45 50 55 60 65 70 80 … … b (ref)

Nominal Thread Size, D M1.6

Nominal Length, L

Association of Nominal and Thread Lengths for Each Thread Size

32

36

40

44

52

60

72

84

All dimensions are in millimeters. The popular lengths are those between the stepped solid lines. Lengths above the shaded areas are threaded to the head within 3 pitch lengths (3P). Lengths within and below the shaded areas have values of Lg and Ls (see Table 1) given by the formulas: Lgmax = L nom − b ref, and Lsmin = Lgmax − 5P.



Table 3. British Standard Hexagon Socket Set Screws — Metric Series BS 4168:Parts 2, 3, 4, and 5:1994

Socket Size, s

Depth of Key Engagement, ta

Length of Dog on Dog Point Screwsb

Range of Popular Lengths Flat Point

Cone Point

Dog Point

Cup Point

Short Dog, z

End Diameters Cone Point dt

Dog Point, dp

Cup Point, dz

b

max

max

max

max

2.5

0.8

0

0.8

0.8

3.0

1.0

0

1.0

1.0

1.5

4

1.5

0

1.5

1.2

1.75

5

2.0

0

2.0

1.4

Pitch, P

nom

min

min

l

l

l

l

min

M1.6

0.35

0.7

0.7

1.5

2–8

2–8

2–8

2–8

0.4

0.65

0.8

1.05

M2

0.4

0.9

0.8

1.7

2–10

2–10

2.5–10

2–10

0.5

0.75

1.0

1.25

M2.5

0.45

1.3

1.2

2.0

2–12

2.5–12

3–12

2–12

0.63

0.88

1.25

M3

0.5

1.5

1.2

2.0

2–16

2.5–16

4–16

2.5–16

0.75

1.0

1.5

M4

0.7

2.0

1.5

2.5

2.5–20

3–20

5–20

3–20

1.0

1.25

2.0

2.25

6

2.5

0

2.5

2.0

M5

0.8

2.5

2.0

3.0

3–25

4–25

6–25

4–25

1.25

1.5

2.5

2.75

6

3.5

0

3.5

2.5

M6

1.0

3.0

2.0

3.5

4–30

5–30

8–30

5–30

1.5

1.75

3.0

3.25

8

4.0

1.5

4.0

3.0

M8

1.25

4.0

3.0

5.0

5–40

6–40

8–40

6–40

2.0

2.25

4.0

4.3

10

5.5

2.0

5.5

5.0

M10

1.5

5.0

4.0

6.0

6–50

8–50

10–50

8–50

2.5

2.75

5.0

5.3

12

7.0

2.5

7.0

6.0

M12

1.75

6.0

4.8

8.0

8–60

10–60

12–60

10–60

3.0

3.25

6.0

6.3

16

8.5

3.0

8.5

8.0

M16

2.0

8.0

6.4

10.0

10–60

12–60

16–60

12–60

4.0

4.3

8.0

8.36

20

12.0

4.0

12.0

10.0

M20

2.5

10.0

8.0

12.0

12–60

16–60

20–60

16–60

5.0

5.3

10.0

10.36

25

15.0

5.0

15.0

14.0

M24

3.0

12.0

10.0

15.0

16–60

20–60

25–60

20–60

6.0

6.3

12.0

12.43

30

18.0

6.0

18.0

16.0

max

min

max

SCREW SOCKETS

Flat Point, dz

Long Dog, z

Nom. Size, d

a The smaller of the two t min. values applies to certain short-length set screws. These short-length screws are those whose length is approximately equal to the diameter

All dimensions are in millimeters. For dimensional notation, see diagram, page 1637.


1635

of the screw. The larger t min. values apply to longer-length screws. b A dog point set screw having a nominal length equal to or less than the length shown in the (*) column of the table is supplied with length z shown in the short dog column. For set screws of lengths greater than shown in the (*) column, z for long dogs applies.


SCREW SOCKETS Table 4. British Standard Hexagon Socket Countersunk and Button Head Screws — Metric Series BS 4168:1967

COUNTERSUNK HEADSCREWS Head Height, H

Head Diameter, A

Body Diameter, D

Hexagon Socket Size, J

Key Engagement, K

Fillet Radius, F

Max.

Min.

Theor. Sharp Max.

Nom.

Min.

Max.

M3

3.00

2.86

6.72

5.82

1.86

0.20

2.00

1.05

0.40

M4

4.00

3.82

8.96

7.78

2.48

0.20

2.50

1.49

0.40

M5

5.00

4.82

11.20

9.78

3.10

0.20

3.00

1.86

0.40

Nom. Sizea

M6

Absolute Min.

Ref.

Flushness Tolerance

6.00

5.82

13.44

11.73

3.72

0.20

4.00

2.16

0.60

M8

8.00

7.78

17.92

15.73

4.96

0.24

5.00

2.85

0.70

M10

10.00

9.78

22.40

19.67

6.20

0.30

6.00

3.60

0.80

M12

12.00

11.73

26.88

23.67

7.44

0.36

8.00

4.35

1.10

(M14)

14.00

13.73

30.24

26.67

8.12

0.40

10.00

4.65

1.10

M16

16.00

15.73

33.60

29.67

8.80

0.45

10.00

4.89

1.10

(M18)

18.00

17.73

36.96

32.61

9.48

0.50

12.00

5.25

1.10

M20

20.00

19.67

40.32

35.61

10.16

0.54

12.00

5.45

1.10


BUTTON HEADSCREWS

Nom. Size, D

Head Diameter,

Head Height,

Head Side Height,

Hexagon Socket Size,

Key Engagement,

A

H

S

J

K

F

da

Fillet Radius

Max.

Min.

Max.

Min.

Ref.

Nom.

Min.

Min.

Max.

M3

5.50

5.32

1.60

1.40

0.38

2.00

1.04

0.10

3.60

M4

7.50

7.28

2.10

1.85

0.38

2.50

1.30

0.20

4.70

M5

9.50

9.28

2.70

2.45

0.50

3.00

1.56

0.20

5.70

M6

10.50

10.23

3.20

2.95

0.80

4.00

2.08

0.25

6.80

M8

14.00

13.73

4.30

3.95

0.80

5.00

2.60

0.40

9.20

M10

18.00

17.73

5.30

4.95

0.80

6.00

3.12

0.40

11.20

M12

21.00

20.67

6.40

5.90

0.80

8.00

4.16

0.60

14.20




1637

British Standard Hexagon Socket Set Screws — Metric Series BS 4168:Parts 2, 3, 4, and 5:1994

FLAT POINT

CUP POINT

DOG POINT

CONE POINT

ALTERNATE CONE POINT (M6 AND LARGER)

*The 120° angle is mandatory for short-length screws shown in the Standard. Short-length screws are those whose length is, approximately, equal to the diameter of the screw. **The 45° angle applies only to that portion of the point below the root diameter, df, of the thread. ***The cone angle applies only to the portion of the point below the root diameter, df, of the thread and shall be 120° for certain short lengths listed in the Standard. All other lengths have a 90° cone angle. †The popular length ranges of these set screws are listed in Table 3. These lengths have been selected from the following nominal lengths: 2, 2.5, 3, 4, 6, 8, 10, 12, 16, 20, 25,30, 35, 40, 45, 50, 55, and 60 millimeters.

Holding Power of Set-screws.—While the amount of power a set-screw of given size will transmit without slipping (when used for holding a pulley, gear, or other part from turning relative to a shaft) varies somewhat according to the physical properties of both set-screw and shaft and other variable factors, experiments have shown that the safe holding force in pounds for different diameters of set-screws should be approximately as follows: For 1⁄4-inch diameter set-screws the safe holding force is 100 pounds, for 3⁄8-inch



COUNTERSUNK AND BUTTON HEAD SCREWS

diameter set-screws the safe holding force is 250 pounds, for 1⁄2-inch diameter set-screws the safe holding force is 500 pounds, for 3⁄4-inch diameter set-screws the safe holding force is 1300 pounds, and for 1-inch diameter set-screws the safe holding force is 2500 pounds. The power or torque that can be safely transmitted by a set-screw may be determined from the formulas, P = (DNd2.3) ÷ 50; or T = 1250Dd2.3 in which P is the horsepower transmitted; T is the torque in inch-pounds transmitted; D is the shaft diameter in inches; N is the speed of the shaft in revolutions per minute; and d is the diameter of the set-screw in inches. Example:How many 1⁄2-inch diameter set-screws would be required to transmit 3 horsepower at a shaft speed of 1000 rpm if the shaft diameter is 1 inch? Using the first formula given above, the power transmitted by a single 1⁄2-inch diameter set-screw is determined: P = [1 × 1000 × (1⁄2)2.3] ÷ 50 = 4.1 hp. Therefore a single 1⁄2-inch diameter set-screw is sufficient. Example:In the previous example, how many 3⁄8-inch diameter set-screws would be required? P = [1 × 1000 × (3⁄8)2.3] ÷ 50 = 2.1 hp. Therefore two 3⁄8-inch diameter set-screws are required. Table 5. British Standard Whitworth (BSW) and British Standard Fine (BSF) Bright Square Head Set-Screws (With Flat Chamfered Ends)

No. 1 Standard Nominal Size and Max. Dia., Inches

1

Number of Threads per Inch

No. 2 Standard

No. 3 Standard

Depth of Head B

Width Across Flats C

Depth of Head D

Width Across Flats E

Depth of Head F

BSF

Width Across Flats A

1⁄ 4

20

26

0.250

0.250

0.313

0.250

0.375

0.250

5⁄ 16

18

22

0.313

0.313

0.375

0.313

0.438

0.313

3⁄ 8

16

20

0.375

0.375

0.438

0.375

0.500

0.375

7⁄ 16

14

18

0.438

0.438

0.500

0.438

0.625

0.438

1⁄ 2

12

16

0.500

0.500

0.563

0.500

0.750

0.500

5⁄ 8

11

14

0.625

0.625

0.750

0.625

0.875

0.625

3⁄ 4

10

12

0.750

0.750

0.875

0.750

1.000

0.750

7⁄ 8

9

11

0.875

0.875

1.000

0.875

1.125

0.875

8

10

1.000

1.000

1.125

1.000

1.250

1.000

BSW

* Depth of Head B, D and F same as for Width Across Flats, No. 1 Standard. Dimensions A, B, C, D, E, and F are in inches.


Machinery's Handbook 27th Edition SELF-THREADING SCREWS

1639

SELF-THREADING SCREWS ANSI Standard Sheet Metal, Self-Tapping, and Metallic Drive Screws.—T a b l e 1 shows the various types of “self-tapping” screw threads covered by the ANSI B18.6.41981 (R1991) standard. (Metric thread forming and thread cutting tapping screws are discussed beginning on page 1654). ANSI designations are also shown. Types A, AB, B, BP and C when turned into a hole of proper size form a thread by a displacing action. Types D, F, G, T, BF and BT when turned into a hole of proper size form a thread by a cutting action. Type U when driven into a hole of proper size forms a series of multiple threads by a displacing action. These screws have the following descriptions and applications: Type A: Spaced-thread screw with gimlet point primarily for use in light sheet metal, resin-impregnated plywood, and asbestos compositions. This type is no longer recommended. Use Type AB in new designs and whenever possible substitute for Type A in existing designs. Type AB: Spaced-thread screw with same pitches as Type B but with gimlet point, primarily for similar uses as for Type A. Type B: Spaced-thread screw with a blunt point with pitches generally somewhat finer than Type A. Used for thin metal, non-ferrous castings, plastics, resin-impregnated plywood, and asbestos compositions. Type BP: Spaced-thread screw, the same as Type B but having a conical point extending beyond incomplete entering threads. Used for piercing fabrics or in assemblies where holes are misaligned. Type C: Screws having machine screw diameter-pitch combinations with threads approximately Unified Form and with blunt tapered points. Used where a machine screw thread is preferable to the spaced-thread types of thread forming screws. Also useful when chips from machine screw thread-cutting screws are objectionable. In view of the declining use of Type C screws, which in general require high driving torques, in favor of more efficient designs of thread tapping screws, they are not recommended for new designs. Types D, F, G, and T: Thread-cutting screws with threads approximating machine screw threads, with blunt point, and with tapered entering threads having one or more cutting edges and chip cavities. The tapered threads of the Type F may be complete or incomplete at the producer's option; all other types have incomplete tapered threads. These screws can be used in materials such as aluminum, zinc, and lead die-castings; steel sheets and shapes; cast iron; brass; and plastics. Types BF and BT: Thread-cutting screws with spaced threads as in Type B, with blunt points, and one or more cutting grooves. Used in plastics, asbestos, and other similar compositions. Type U: Multiple-threaded drive screw with large helix angle, having a pilot point, for use in metal and plastics. This screw is forced into the work by pressure and is intended for making permanent fastenings. ANSI Standard Head Types for Tapping and Metallic Drive Screws: Many of the head types used with “self-tapping” screw threads are similar to the head types of American National Standard machine screws shown in the section with that heading. Round Head: The round head has a semi-elliptical top surface and a flat bearing surface. Because of the superior slot driving characteristics of pan head screws over round head screws, and the overlap in dimensions of cross recessed pan heads and round heads, it is recommended that pan head screws be used in new designs and wherever possible substituted in existing designs. Undercut Flat and Oval Countersunk Heads: For short lengths, 82-degree and oval countersunk head tapping screws have heads undercut to 70 per cent of normal side height to afford greater length of thread on the screws.



SELF-THREADING SCREWS

Flat Countersunk Head: The flat countersunk head has a flat top surface and a conical bearing surface with a head angle for one design of approximately 82 degrees and for another design of approximately 100 degrees. Because of its limited usage and in the interest of curtailing product varieties, the 100-degree flat countersunk head is considered nonpreferred. Oval Countersunk Head: The oval countersunk head has a rounded top surface and a conical bearing surface with a head angle of approximately 82 degrees. Flat and Oval Countersunk Trim Heads: Flat and oval countersunk trim heads are similar to the 82-degree flat and oval countersunk heads except that the size of head for a given size screw is one (large trim head) or two (small trim head) sizes smaller than the regular flat and oval countersunk head size. Oval countersunk trim heads have a definite radius where the curved top surface meets the conical bearing surface. Trim heads are furnished only in cross recessed types. Pan Head: The slotted pan head has a flat top surface rounded into cylindrical sides and a flat bearing surface. The recessed pan head has a rounded top and a flat bearing surface. This head type is now preferred to the round head. Fillister Head: The fillister head has a rounded top surface, cylindrical sides, and a flat bearing surface. Hex Head: The hex head has a flat or indented top surface, six flat sides, and a flat bearing surface. Because the slotted hex head requires a secondary operation in manufacture which often results in burrs at the extremity of the slot that interfere with socket wrench engagement and the wrenching capability of the hex far exceeds that of the slot, it is not recommended for new designs. Hex Washer Head: The hex washer head has an indented top surface and six flat sides formed integrally with a flat washer that projects beyond the sides and provides a flat bearing surface. Because the slotted hex washer head requires a secondary operation in manufacture which often results in burrs at the extremity of the slot that often interferes with socket wrench engagement and because the wrenching capability of the hex far exceeds that of the slot in the indented head, it is not recommended for new designs. Truss Head: The truss head has a low rounded top surface with a flat bearing surface, the diameter of which for a given screw size is larger than the diameter of the corresponding round head. In the interest of product simplification and recognizing that the truss head is an inherently weak design, it is not recommended for new designs. Method of Designation.—Tapping screws are designated by the following data in the sequence shown: Nominal size (number, fraction or decimal equivalent); threads per inch; nominal length (fraction or decimal equivalent); point type; product name, including head type and driving provision; material; and protective finish, if required. Examples: 1⁄ –14 × 11⁄ Type AB Slotted Pan Head Tapping Screw, Steel, Nickel Plated 4 2

6–32 × 3⁄4 Type T, Type 1A Cross Recessed Pan Head Tapping Screw, Corrosion Resistant Steel 0.375–16 × 1.50 Type D, Washer Head Tapping Screw, Steel Metallic Drive Screws: Type U metallic drive screws are designated by the following data in the sequence shown: Nominal size (number, fraction, or decimal equivalent); nominal length (fraction or decimal equivalent); product name, including head type; material; and protective finish, if required. Examples: 10 × 5⁄16 Round Head Metallic Drive Screw, Steel 0.312 × 0.50 Round Head Metallic Drive Screw, Steel, Zinc Plated



1641

Table 1. ANSI Standard Threads and Points for Thread Forming Self-Tapping Screws ANSI B18.6.4-1981 (R1991)

See Tables 3, 5, and 6 for thread data.



SELF-THREADING SCREWS Table 2. ANSI Standard Threads and Points for Thread Cutting Self-Tapping Screws ANSI B18.6.4-1981 (R1991)

See Tables 5 and 7 for thread data.

Cross Recesses.—Type I cross recess has a large center opening, tapered wings, and blunt bottom, with all edges relieved or rounded. Type IA cross recess has a large center opening, wide straight wings, and blunt bottom, with all edges relieved or rounded. Type II consists of two intersecting slots with parallel sides converging to a slightly truncated apex at the bottom of the recess. Type III has a square center opening, slightly tapered side walls, and a conical bottom, with top edges relieved or rounded. Table 3. ANSI Standard Cross Recesses for Self-Tapping Screws ANSI B18.6.4-1981 (R1991) and Metric Thread Forming and Thread Cutting Tapping Screws ANSI/ASME B18.6.5M-1986

TYPE I

TYPE IA

TYPE II


TYPE III


1643

Table 4. ANSI Standard Thread and Point Dimensions for Types AB, A and U Thread Forming Tapping Screws ANSI B18.6.4-1981 (R1991) Nominal Size or Basic Screw Diameter 0 1 2 3 4 5 6 7 8 10 12

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1510 0.1640 0.1900 0.2160

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

0.2500 0.3125 0.3750 0.4375 0.5000

Type AB (Formerly BA) D d Major Minor Diameter Diameter Max. Min. Max. Min.

Threads per inch 48 42 32 28 24 20 20 19 18 16 14 14 12 12 10 10

0.060 0.075 0.088 0.101 0.114 0.130 0.139 0.154 0.166 0.189 0.215 0.246 0.315 0.380 0.440 0.504

0.054 0.069 0.082 0.095 0.108 0.123 0.132 0.147 0.159 0.182 0.208 0.237 0.306 0.371 0.429 0.493

0.036 0.049 0.064 0.075 0.086 0.094 0.104 0.115 0.122 0.141 0.164 0.192 0.244 0.309 0.359 0.423

L Minimum Practical Screw Lengths 90° Heads Csk. Heads 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

0.033 0.046 0.060 0.071 0.082 0.090 0.099 0.109 0.116 0.135 0.157 0.185 0.236 0.299 0.349 0.413

5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 3⁄ 8 7⁄ 16 21⁄ 32 19⁄ 32 3⁄ 4 29⁄ 32 11⁄32 15⁄32

1

Type A Nominal Sizea Basic Screw Diameter 0 1 2 3 4 5 6 7 8 10 12 14 16 18 20 24

Threads per inch

0.0600 0.0730 0.0860 0.0990 0.1120 0.1250 0.1380 0.1510 0.1640 0.1900 0.2160 0.2420 0.2680 0.2940 0.3200 0.3720

40 32 32 28 24 20 18 16 15 12 11 10 10 9 9 9

D

d

Major Diameter Max. Min.

Minor Diameter Max. Min.

0.060 0.075 0.088 0.101 0.114 0.130 0.141 0.158 0.168 0.194 0.221 0.254 0.280 0.306 0.333 0.390

0.042 0.051 0.061 0.076 0.083 0.095 0.102 0.114 0.123 0.133 0.162 0.185 0.197 0.217 0.234 0.291

0.057 0.072 0.084 0.097 0.110 0.126 0.136 0.152 0.162 0.188 0.215 0.248 0.274 0.300 0.327 0.383

L These Lengths or Shorter —Use Type AB 90° Heads Csk. Heads 1⁄ 8 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4

0.039 0.048 0.056 0.071 0.078 0.090 0.096 0.108 0.116 0.126 0.155 0.178 0.189 0.209 0.226 0.282

3⁄ 16 3⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 13⁄ 16 13⁄ 16

1

a Where specifying nominal size in decimals, zeros preceding decimal and in fourth place are omit-

ted. Type U Metallic Drive Screws Out. Dia.

Pilot Dia.

Out. Dia.

Pilot Dia.

Nom. Size

No. of Starts

Max.

Min.

Max.

Min.

Nom. Size

No. of Starts

Max.

Min.

Max.

Min.

00 0 2 4 6

6 6 8 7 7

0.060 0.075 0.100 0.116 0.140

0.057 0.072 0.097 0.112 0.136

0.049 0.063 0.083 0.096 0.116

0.046 0.060 0.080 0.092 0.112

8 10 12 14 5⁄ 16

8 8 8 9 11

0.167 0.182 0.212 0.242 0.315

0.162 0.177 0.206 0.236 0.309

0.136 0.150 0.177 0.202 0.272

0.132 0.146 0.173 0.198 0.267

7

8

0.154

0.150

0.126

0.122

3⁄ 8

12

0.378

0.371

0.334

0.329

All dimensions are in inches. See Table 1 for thread diagrams. Sizes shown in bold face type are preferred. Type A screws are no longer recommended.




Table 5. ANSI Standard Thread and Point Dimensions for B and BP Thread Forming and BF and BT Thread Cutting Tapping Screws ANSI B18.6.4-1981 (R1991) THREAD FORMING TYPES B AND BP d P S

D Nominal Sizea or Basic Screw Diameter 0 0.0600 1 0.0730 2 0.0860 3 0.0990 4 0.1120 5 0.1250 6 0.1380 7 0.1510 8 0.1640 10 0.1900 12 0.2160 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

0.2500 0.3125 0.3750 0.4375 0.5000

Major Diameter

Thds per Inchb 48 42 32 28 24 20 20 19 18 16 14 14 12 12 10 10

Max 0.060 0.075 0.088 0.101 0.114 0.130 0.139 0.154 0.166 0.189 0.215 0.246 0.315 0.380 0.440 0.504

Min 0.054 0.069 0.082 0.095 0.108 0.123 0.132 0.147 0.159 0.182 0.208 0.237 0.306 0.371 0.429 0.493

Max 0.036 0.049 0.064 0.075 0.086 0.094 0.104 0.115 0.122 0.141 0.164 0.192 0.244 0.309 0.359 0.423

Min 0.033 0.046 0.060 0.071 0.082 0.090 0.099 0.109 0.116 0.135 0.157 0.185 0.236 0.299 0.349 0.413

Point Taper Lengthd

Point Diameterc

Minor Diameter

Max 0.031 0.044 0.058 0.068 0.079 0.087 0.095 0.105 0.112 0.130 0.152 0.179 0.230 0.293 0.343 0.407

Min 0.027 0.040 0.054 0.063 0.074 0.082 0.089 0.099 0.106 0.123 0.145 0.171 0.222 0.285 0.335 0.399

Max 0.042 0.048 0.062 0.071 0.083 0.100 0.100 0.105 0.111 0.125 0.143 0.143 0.167 0.167 0.200 0.200

Min 0.031 0.036 0.047 0.054 0.063 0.075 0.075 0.079 0.083 0.094 0.107 0.107 0.125 0.125 0.150 0.150

L Minimum Practical Nominal Screw Lengths Type B Type BP 90° Csk 90° Csk Heads Heads Heads Heads 1⁄ 8 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 15⁄ 32 17⁄ 32 5⁄ 8 11⁄ 16

1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 7⁄ 16 1⁄ 2 19⁄ 32 11⁄ 16 25⁄ 32 27⁄ 32

5⁄ 32 3⁄ 16 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 13⁄ 32 7⁄ 16 1⁄ 2 9⁄ 16 21⁄ 32 27⁄ 32 15⁄ 16 1 1 ⁄8 11⁄4

3⁄ 16 7⁄ 32 9⁄ 32 5⁄ 16 11⁄ 32 13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 19⁄ 32 21⁄ 32 3⁄ 4 31⁄ 32 11⁄8 1 1 ⁄4 113⁄32

a Where specifying nominal size in decimals, zeros preceding decimal and in the fourth decimal place shall be omitted. b The width of flat at crest of thread shall not exceed 0.004 inch for sizes up to No. 8, inclusive, and 0.006 inch for larger sizes. c Point diameters specified apply to screw threads before roll threading. d Points of screws are tapered and fluted or slotted. The flute on Type BT screws has an included angle of 90 to 95 degrees and the thread cutting edge is located above the axis of the screw. Flutes and slots extend through first full form thread beyond taper except for Type BF screw on which tapered threads may be complete at manufacturer's option and flutes may be one pitch short of first full form thread.

THREAD CUTTING TYPES BF AND BTd d P

D Nominal Sizea or Basic Screw Diameter 0 0.0600 1 0.0730 2 0.0860 3 0.0990 4 0.1120 5 0.1250 6 0.1380 7 0.1510 8 0.1640 10 0.1900 12 0.2160 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

0.2500 0.3125 0.3750 0.4375 0.5000

Thds per Inchb 48 42 32 28 24 20 20 19 18 16 14 14 12 12 10 10

Major Diameter Max 0.060 0.075 0.088 0.101 0.114 0.130 0.139 0.154 0.166 0.189 0.215 0.246 0.315 0.380 0.440 0.504

Min 0.054 0.069 0.082 0.095 0.108 0.123 0.132 0.147 0.159 0.182 0.208 0.237 0.306 0.371 0.429 0.493

Minor Diameter Max 0.036 0.049 0.064 0.075 0.086 0.094 0.104 0.115 0.122 0.141 0.164 0.192 0.244 0.309 0.359 0.423

Min 0.033 0.046 0.060 0.071 0.082 0.090 0.099 0.109 0.116 0.135 0.157 0.185 0.236 0.299 0.349 0.413

S Point Taper Lengthd

Point Diameterc Max 0.031 0.044 0.058 0.068 0.079 0.087 0.095 0.105 0.112 0.130 0.152 0.179 0.230 0.293 0.343 0.407

Min 0.027 0.040 0.054 0.063 0.074 0.082 0.089 0.099 0.106 0.123 0.145 0.171 0.222 0.285 0.335 0.399

Max 0.042 0.048 0.062 0.071 0.083 0.100 0.100 0.105 0.111 0.125 0.143 0.143 0.167 0.167 0.200 0.200

Min 0.031 0.036 0.047 0.054 0.063 0.075 0.075 0.079 0.083 0.094 0.107 0.107 0.125 0.125 0.150 0.150

All dimensions are in inches. See Tables 1 and 2 for thread diagrams.


L Minimum Practical Nominal Screw Lengths 90° Csk Heads Heads 1⁄ 8 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 15⁄ 32 17⁄ 32 5⁄ 8 11⁄ 16

1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 9⁄ 32 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8 7⁄ 16 1⁄ 2 19⁄ 32 11⁄ 16 25⁄ 32 27⁄ 32


Table 6. Thread and Point Dimensions for Type C Thread Forming Tapping Screws (ANSI B18.6.4–1981, R1991 Appendix) Threads per inch 56 64 48 56 40 48 40 44 32 40 32 36 24 32 24 28 20 28 18 24 16 24 14 20 13 20

D

P

Major Diameter Max Min 0.0860 0.0813 0.0860 0.0816 0.0990 0.0938 0.0990 0.0942 0.1120 0.1061 0.1120 0.1068 0.1250 0.1191 0.1250 0.1195 0.1380 0.1312 0.1380 0.1321 0.1640 0.1571 0.1640 0.1577 0.1900 0.1818 0.1900 0.1831 0.2160 0.2078 0.2160 0.2085 0.2500 0.2408 0.2500 0.2425 0.3125 0.3026 0.3125 0.3042 0.3750 0.3643 0.3750 0.3667 0.4375 0.4258 0.4375 0.4281 0.5000 0.4876 0.5000 0.4906

Point Diameterb Max Min 0.068 0.061 0.070 0.064 0.078 0.070 0.081 0.074 0.087 0.078 0.091 0.083 0.100 0.091 0.102 0.094 0.107 0.096 0.113 0.104 0.132 0.122 0.136 0.126 0.148 0.135 0.158 0.148 0.174 0.161 0.180 0.168 0.200 0.184 0.214 0.202 0.257 0.239 0.271 0.257 0.312 0.293 0.333 0.319 0.366 0.344 0.387 0.371 0.423 0.399 0.450 0.433

a Where specifying nominal size in decimals, zeros

S Point Taper Lengthc For Short Screws For Long Screws Max Min Max Min 0.062 0.045 0.080 0.062 0.055 0.039 0.070 0.055 0.073 0.052 0.094 0.073 0.062 0.045 0.080 0.062 0.088 0.062 0.112 0.088 0.073 0.052 0.094 0.073 0.088 0.062 0.112 0.088 0.080 0.057 0.102 0.080 0.109 0.078 0.141 0.109 0.088 0.062 0.112 0.088 0.109 0.078 0.141 0.109 0.097 0.069 0.125 0.097 0.146 0.104 0.188 0.146 0.109 0.078 0.141 0.109 0.146 0.104 0.188 0.146 0.125 0.089 0.161 0.125 0.175 0.125 0.225 0.175 0.125 0.089 0.161 0.125 0.194 0.139 0.250 0.194 0.146 0.104 0.188 0.146 0.219 0.156 0.281 0.219 0.146 0.104 0.188 0.146 0.250 0.179 0.321 0.250 0.175 0.125 0.225 0.175 0.269 0.192 0.346 0.269 0.175 0.125 0.225 0.175

L Determinant Lengths for Point Taperc 90° Heads Csk Heads 5⁄ 32 1⁄ 8 3⁄ 16 5⁄ 32 7⁄ 32 3⁄ 16 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 1⁄ 4 7⁄ 32 11⁄ 32 1⁄ 4 11⁄ 32 5⁄ 16 13⁄ 32 5⁄ 16 15⁄ 32 11⁄ 32 1⁄ 2 11⁄ 32 19⁄ 32 13⁄ 32 5⁄ 8 13⁄ 32

3⁄ 16 3⁄ 16 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 9⁄ 32 1⁄ 4 5⁄ 16 9⁄ 32 11⁄ 32 5⁄ 16 7⁄ 16 11⁄ 32 7⁄ 16 13⁄ 32 17⁄ 32 13⁄ 32 19⁄ 32 15⁄ 32 11⁄ 16 1⁄ 2 3⁄ 4 9⁄ 16 25⁄ 32 9⁄ 16

Minimum Practical Nominal Screw Lengths 90° Heads Csk Heads 5⁄ 32 1⁄ 8 5⁄ 32 5⁄ 32 3⁄ 16 5⁄ 32 3⁄ 16 3⁄ 16 1⁄ 4 3⁄ 16 1⁄ 4 7⁄ 32 5⁄ 16 1⁄ 4 5⁄ 16 9⁄ 32 3⁄ 8 9⁄ 32 7⁄ 16 5⁄ 16 15⁄ 32 5⁄ 16 9⁄ 16 3⁄ 8 19⁄ 32 3⁄ 8

3⁄ 16 5⁄ 32 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 1⁄ 4 1⁄ 4 5⁄ 16 1⁄ 4 5⁄ 16 9⁄ 32 13⁄ 32 5⁄ 16 13⁄ 32 3⁄ 8 1⁄ 2 3⁄ 8 9⁄ 16 15⁄ 32 5⁄ 8 1⁄ 2 23⁄ 32 17⁄ 32 3⁄ 4 17⁄ 32


Nominal Sizeaor Basic Screw Diameter 2 0.0860 2 0.0860 3 0.0990 3 0.0990 4 0.1120 4 0.1120 5 0.1250 5 0.1250 6 0.1380 6 0.1380 8 0.1640 8 0.1640 10 0.1900 10 0.1900 12 0.2160 12 0.2160 1⁄ 4 0.2500 1⁄ 4 0.2500 5⁄ 16 0.3125 5⁄ 16 0.3125 3⁄ 8 0.3750 3⁄ 8 0.3750 7⁄ 16 0.4375 7⁄ 16 0.4375 1⁄ 2 0.5000 1⁄ 2 0.5000

preceding decimal and in the fourth decimal place shall be omitted.

b The tabulated values apply to screw blanks before roll threading. c Screws of these nominal lengths and shorter shall have point taper length specified above for short screws. Longer lengths shall have point taper length specified for long screws.


1645

All dimensions are in inches. See Table 1 for thread diagrams. Type C is not recommended for new designs. Tapered threads shall have unfinished crests.


1646

Table 7. ANSI Standard Thread and Point Dimensions for Types D, F, G, and T Thread Cutting Tapping Screws ANSI B18.6.4-1981 (R1991) Threads per inch 56 64 48 56 40 48 40 44 32 40 32 36 24 32 24 28 20 28 18 24 16 24 14 20 13 20

D Major Diameter Max 0.0860 0.0860 0.0990 0.0990 0.1120 0.1120 0.1250 0.1250 0.1380 0.1380 0.1640 0.1640 0.1900 0.1900 0.2160 0.2160 0.2500 0.2500 0.3125 0.3125 0.3750 0.3750 0.4375 0.4375 0.5000 0.5000

Min 0.0813 0.0816 0.0938 0.0942 0.1061 0.1068 0.1191 0.1195 0.1312 0.1321 0.1571 0.1577 0.1818 0.1831 0.2078 0.2085 0.2408 0.2425 0.3026 0.3042 0.3643 0.3667 0.4258 0.4281 0.4876 0.4906

P Point Diameterb Max 0.068 0.070 0.078 0.081 0.087 0.091 0.100 0.102 0.107 0.113 0.132 0.136 0.148 0.158 0.174 0.180 0.200 0.214 0.257 0.271 0.312 0.333 0.366 0.387 0.423 0.450

Min 0.061 0.064 0.070 0.074 0.078 0.083 0.091 0.094 0.096 0.104 0.122 0.126 0.135 0.148 0.161 0.168 0.184 0.202 0.239 0.257 0.293 0.319 0.344 0.371 0.399 0.433

S Point Taper Lengthc For Short Screws For Long Screws Max Min Max Min 0.062 0.045 0.080 0.062 0.055 0.039 0.070 0.055 0.073 0.052 0.094 0.073 0.062 0.045 0.080 0.062 0.088 0.062 0.112 0.088 0.073 0.052 0.094 0.073 0.088 0.062 0.112 0.088 0.080 0.057 0.102 0.080 0.109 0.078 0.141 0.109 0.088 0.062 0.112 0.088 0.109 0.078 0.141 0.109 0.097 0.069 0.125 0.097 0.146 0.104 0.188 0.146 0.109 0.078 0.141 0.109 0.146 0.104 0.188 0.146 0.125 0.089 0.161 0.125 0.175 0.125 0.225 0.175 0.125 0.089 0.161 0.125 0.194 0.139 0.250 0.194 0.146 0.104 0.188 0.146 0.219 0.156 0.281 0.219 0.146 0.104 0.188 0.146 0.250 0.179 0.321 0.250 0.175 0.125 0.225 0.175 0.269 0.192 0.346 0.269 0.175 0.125 0.225 0.175

L Determinant Lengths for Point Taperc 90° Heads Csk Heads 5⁄ 32 1⁄ 8 3⁄ 16 5⁄ 32 7⁄ 32 3⁄ 16 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 1⁄ 4 7⁄ 32 11⁄ 32 1⁄ 4 11⁄ 32 5⁄ 16 13⁄ 32 5⁄ 16 15⁄ 32 11⁄ 32 1⁄ 2 11⁄ 32 19⁄ 32 13⁄ 32 5⁄ 8 13⁄ 32

3⁄ 16 3⁄ 16 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 9⁄ 32 1⁄ 4 5⁄ 16 9⁄ 32 11⁄ 32 5⁄ 16 7⁄ 16 11⁄ 32 7⁄ 16 13⁄ 32 17⁄ 32 13⁄ 32 19⁄ 32 15⁄ 32 11⁄ 16 1⁄ 2 3⁄ 4 9⁄ 16 25⁄ 32 9⁄ 16

Minimum Practical Nominal Screw Lengths 90° Heads Csk Heads 5⁄ 32 1⁄ 8 5⁄ 32 5⁄ 32 3⁄ 16 5⁄ 32 3⁄ 16 3⁄ 16 1⁄ 4 3⁄ 16 1⁄ 4 7⁄ 32 5⁄ 16 1⁄ 4 5⁄ 16 9⁄ 32 3⁄ 8 9⁄ 32 7⁄ 16 5⁄ 16 15⁄ 32 5⁄ 16 9⁄ 16 3⁄ 8 19⁄ 32 3⁄ 8

3⁄ 16 5⁄ 32 7⁄ 32 3⁄ 16 1⁄ 4 7⁄ 32 1⁄ 4 1⁄ 4 5⁄ 16 1⁄ 4 5⁄ 16 9⁄ 32 13⁄ 32 5⁄ 16 13⁄ 32 3⁄ 8 1⁄ 2 3⁄ 8 9⁄ 16 15⁄ 32 5⁄ 8 1⁄ 2 23⁄ 32 17⁄ 32 3⁄ 4 17⁄ 32

a Where specifying nominal size in decimals, zeros preceding decimal and in the fourth decimal place shall be omitted. b The tabulated values apply to screw blanks before roll threading. c Screws of these nominal lengths and shorter shall have point taper length specified above for short screws. Longer lengths shall have point taper length specified for long screws. All dimensions are in inches. See Table 2 for thread diagrams. Type “Type D“ otherwise designated “Type 1.“ Type “Type T“ otherwise designated “Type 23.”



Nominal Sizea or Basic Screw Diameter 2 0.0860 2 0.0860 3 0.0990 3 0.0990 4 0.1120 4 0.1120 5 0.1250 5 0.1250 6 0.1380 6 0.1380 8 0.1640 8 0.1640 10 0.1900 10 0.1900 12 0.2160 12 0.2160 1⁄ 4 0.2500 1⁄ 4 0.2500 5⁄ 16 0.3125 5⁄ 16 0.3125 3⁄ 8 0.3750 3⁄ 8 0.3750 7⁄ 16 0.4375 7⁄ 16 0.4375 1⁄ 2 0.5000 1⁄ 2 0.5000


1647

Table 8. Approximate Hole Sizes for Type A Steel Thread Forming Screws

Screw Size

4

6

7

8

Metal Thickness

In Steel, Stainless Steel, Monel Metal, Brass, and Aluminum Sheet Metal Hole Size Hole Size Drilled Pierced Drilled Pierced Metal or Clean or or Clean or ThickDrill Screw Punched Extruded Punched Extruded ness Size Size

0.015

…

0.086

44

0.018 0.024 0.030 0.036 0.015 0.018 0.024 0.030 0.036 0.015 0.018 0.024 0.030 0.036 0.048 0.018

… 0.098 0.098 0.098 … … 0.111 0.111 0.111 … … 0.120 0.120 0.120 0.120 …

0.086 0.094 0.094 0.098 0.104 0.104 0.104 0.104 0.106 0.116 0.116 0.116 0.116 0.116 0.120 0.125

44 42 42 40 37 37 37 37 36 32 32 32 32 32 31 1⁄ 8

8

10

12

14

0.024

0.136

0.125

0.030 0.036 0.048 0.018 0.024 0.030 0.036 0.048 0.024 0.030 0.036 0.048 0.024 0.030 0.036 0.048

0.136 0.136 0.136 … 0.157 0.157 0.157 0.157 … 0.185 0.185 0.185 … 0.209 0.209 0.209

0.125 0.125 0.128 0.136 0.136 0.136 0.136 0.149 0.161 0.161 0.161 0.161 0.185 0.189 0.191 0.196

In Plywood (Resin Impregnated) Screw Size

Hole Size

Drill Size

Min. Mat'l Thickness

4 6 7 8 10 12 14

0.098 0.110 0.128 0.140 0.170 0.189 0.228

40 35 30 28 18 12 1

0.188 0.188 0.250 0.250 0.312 0.312 0.438

Drill Size 1⁄ 8 1⁄ 8 1⁄ 8

30 29 29 29 29 25 20 20 20 20 13 12 11 9

In Asbestos Compositions Penetration in Blind Holes Min. Max. 0.250 0.250 0.312 0.312 0.375 0.375 0.500

0.750 0.750 0.750 0.750 1.000 1.000 1.000

Screw Size

Hole Size

Drill Size


4 6 7 8 10 12 14

0.094 0.106 0.125 0.136 0.161 0.185 0.213

42 36 1⁄ 8 29 20 13 3

0.188 0.188 0.250 0.250 0.312 0.312 0.438

Penetration in Blind Holes Min. Max. 0.250 0.250 0.312 0.312 0.375 0.375 0.500

0.750 0.750 0.750 0.750 1.000 1.000 1.000

Type A is not recommended, use Type AB. See footnote at bottom of Table 9.

Table 9. Approximate Hole Sizes for Type C Steel Thread Forming Screws Screw Size

4–40

6–32

8–32

Metal Thickness

Hole Size

Drill Size

0.037 0.048 0.062 0.075 0.105 0.134 0.037 0.048 0.062 0.075 0.105

0.094 0.094 0.096 0.100 0.102 0.102 0.113 0.116 0.116 0.122 0.125

42 42 41 39 38 38 33 32 32 3.1mm 1⁄ 8

0.134

0.125

0.037 0.048 0.062 0.075 0.105 0.134

0.136 0.144 0.144 0.147 0.150 0.150

1⁄ 8 29 27 27 26 25 25

Screw Size

10-24

10–32

12–24

In Sheet Steel Metal Hole Thickness Size

Drill Size

Screw Size

Metal Thickness

Hole Size

Drill Size

0.037 0.048 0.062 0.075 0.105 0.134 0.037 0.048 0.062 0.075 0.105

0.221 0.221 0.228 0.234 0.234 0.236 0.224 0.228 0.232 0.234 0.238

2 2 1 A A 6mm 5.7mm 1 5.9mm A B

0.037 0.048 0.062 0.075 0.105 0.134 0.037 0.048 0.062 0.075 0.105

0.154 0.161 0.166 0.170 0.173 0.177 0.170 0.170 0.170 0.173 0.177

23 20 19 18 17 16 18 18 18 17 16

0.134

0.177

16

0.134

0.238

B

0.037 0.048 0.062 0.075 0.105 0.134

0.189 0.194 0.194 0.199 0.199 0.199

12 10 10 8 8 8

0.037 0.048 0.062 0.075 0.105 0.134

0.290 0.290 0.290 0.295 0.295 0.295

L L L M M M

1⁄ –20 4

1⁄ –28 4

5⁄ –18 16

All dimensions are in inches except drill sizes. It may be necessary to vary the hole size to suit a particular application. Type C is not recommended for new designs.



SELF-THREADING SCREWS Table 10. Approximate Pierced or Extruded Hole Sizes for Types AB, B, and BP Steel Thread Forming Screws

Screw Size

Metal Thickness

Pierced or Extruded Hole Size

0.015 0.018 0.024 0.030 0.036 0.015 0.018 0.024 0.030 0.036 0.018

0.086 0.086 0.098 0.098 0.098 0.111 0.111 0.111 0.111 0.111 0.120

0.024 0.030 0.036 0.048 0.024 0.030 0.036

0.086 0.086 0.086 0.086 0.111 0.111 0.111

Screw Size


Metal Thickness

Screw Size

Metal Thickness


0.030 0.036 0.048 0.024 0.030 0.036 0.048 0.030 0.036 0.048 …

0.157 0.157 0.157 0.185 0.185 0.185 0.185 0.209 0.209 0.209 …

0.036 0.048 0.024 0.030 0.036 0.048 …

0.136 0.136 0.157 0.157 0.157 0.157 …

In Steel, Stainless Steel, Monel Metal, and Brass Sheet Metal

4

6

7

0.024 0.030 0.036 0.048 0.018 0.024 0.030 0.036 0.048 0.018 0.024

7

8

10

0.120 0.120 0.120 0.120 0.136 0.136 0.136 0.136 0.136 0.157 0.157

10

12

1⁄ 4

…

In Aluminum Alloy Sheet Metal

4

6

6

0.048 0.024 0.030 0.036 0.048 0.024 0.030

7

8

0.111 0.120 0.120 0.120 0.120 0.136 0.136

8

10 …

All dimensions are in inches except whole number screw and drill sizes. Since conditions differ widely, it may be necessary to vary the hole size to suit a particular application.

Table 11. Drilled Hole Sizes for Types AB, B, and BP Steel Thread Forming Screws Screw Size

Hole Size

Drill Size


Penetration in Blind Holes Min.

Max.

Screw Size

Hole Size

In Plywood (Resin Impregnated) 2 4 6

0.073 0.100 0.125

7 8 10 12 1⁄ 4

0.136 0.144 0.173 0.194 0.228

2 4 6 7 8 10 12 1⁄ 4 2 4 6 7

49 39 1⁄ 8 29 27 17 10 1

47 42 31 30


Penetration in Blind Holes Min.

Max.

In Asbestos Compositions

0.125 0.188 0.188

0.188 0.250 0.250

0.500 0.625 0.625

2 4 6

0.076 0.101 0.120

48 38 31

0.125 0.188 0.188

0.188 0.250 0.250

0.500 0.625 0.625

0.188 0.188 0.250 0.312 0.312

0.250 0.250 0.312 0.375 0.375

0.750 0.750 1.000 1.000 1.000

7 8 10 12 1⁄ 4

0.136 0.147 0.166 0.196 0.228

29 26 19 9 1

0.250 0.312 0.312 0.312 0.438

0.312 0.375 0.375 0.375 0.500

0.750 0.750 1.000 1.000 1.000

… … … … … … … …

2 4 6 7 8 10 12 1⁄ 4

0.078 0.100 0.128 0.136 0.150 0.177 0.199 0.234

In Aluminum, Magnesium, Zinc, Brass, and Bronze Castingsa 0.078 47 … 0.125 0.104 37 … 0.188 0.128 30 … 0.250 0.144 27 … 0.250 0.152 24 … 0.250 0.177 16 … 0.250 0.199 8 … 0.281 15⁄ 0.234 … 0.312 64 0.078 0.094 0.120 0.128

Drill Size

In Phenol Formaldehyde Plasticsa 47 39 30 29 25 16 8 15⁄ 64

… … … … … … … …

0.188 0.250 0.250 0.250 0.312 0.312 0.375 0.375

… … … … … … … …

In Cellulose Acetate and Nitrate, and Acrylic and Styrene Resinsa … 0.188 … 8 0.144 27 … 0.250 … 10 0.170 18 … 0.250 … 12 0.191 11 1⁄ … 0.250 … 0.221 2 4

… … … …

0.312 0.312 0.375 0.375

… … … …

a Data below apply to Types B and BP only.

All dimensions are in inches except whole number screw and drill sizes. Since conditions differ widely, it may be necessary to vary the hole size to suit a particular application.



1649

Table 12a. Approximate Drilled or Clean-Punched Hole Sizes for Types AB, B, and BP Steel Thread Forming Screws Screw Size

Metal Thickness

Hole Size

0.015 0.018 0.024 0.030 0.036 0.048 0.060 0.015 0.018 0.024 0.030 0.036 0.048 0.060 0.075 0.015 0.018 0.024 0.030 0.036 0.048 0.060 0.075 0.105

0.064 0.064 0.067 0.070 0.073 0.073 0.076 0.086 0.086 0.089 0.094 0.094 0.096 0.100 0.102 0.104 0.104 0.106 0.106 0.110 0.111 0.116 0.120 0.128

52 52 51 50 49 49 48 44 44 43 42 42 41 39 38 37 37 36 36 35 34 32 31 30

0.024 0.030 0.036 0.048 0.060 0.030 0.036 0.048 0.060 0.075 0.105 0.030 0.036 0.048 0.060 0.75 0.105 0.128 to 250 0.030 0.036 0.048

0.064 0.064 0.064 0.067 0.070 0.086 0.086 0.086 0.089 0.089 0.094 0.104 0.104 0.104 0.106 0.110 0.111

52 52 52 51 50 44 44 44 43 43 42 37 37 37 36 35 34

120

31

0.113 0.113 0.116

33 33 32

Drill Size

Screw Size

Metal Thickness

Hole Size

Drill Size

Screw Size

Metal Thickness

Hole Size

Drill Size

0.125 0.135 0.164 0.024 0.030 0.036 0.048 0.060 0.075 0.105 0.125 0.135 0.164 0.030 0.036 0.048 0.060 0.075 0.105 0.125 0.135 0.164 0.187 0.194

0.170 0.170 0.173 0.166 0.166 0.166 0.170 0.177 0.182 0.185 0.196 0.196 0.201 0.194a 0.194a 0.194a 0.199a 0.204a 0.209 0.228 0.228 0.234 0.234 0.234

18 18 17 19 19 19 18 16 14 13 9 9 7 10a 10a 10a 8a 6a 4 1 1 15⁄ 64 15⁄ 64 15⁄ 64

0.164 0.200 to 0.375 0.048 0.060 0.075 0.105 0.125 0.135 0.164 0.200 to 0.375 0.060 0.075 0.105 0.125 0.135 0.164 0.187 0.194 0.200 to 0.375

0.159

21

0.166

19

0.161 0.166 0.173 0.180 0.182 0.182 0.189

20 19 17 15 14 14 12

0.196

9

0.199 0.201 0.204 0.209 0.209 0.213 0.213 0.221

8 7 6 4 4 3 3 2

228

1

In Steel, Stainless Steel, Monel Metal, and Brass Sheet Metal

2

4

6

2

4

6

7

7

8

10

0.018 0.024 0.030 0.036 0.048 0.060 0.075 0.105 0.024 0.030 0.036 0.048 0.060 0.075 0.105 0.125 0.135 0.024 0.030 0.036 0.048 0.060 0.075 0.105

0.116 0.116 0.116 0.116 0.120 0.128 0.136 0.140 0.125 0.125 0.125 0.128 0.136 0.140 0.150 0.150 0.152 0.144 0.144 0.147 0.152a 0.152a 0.157 0.161

32 32 32 32 31 30 29 28 1⁄ 8 1⁄ 8 1⁄ 8 30 29 28 25 25 24 27 27 26 24a 24a 22 20

In Aluminum Alloy Sheet Metal 0.060 0.120 31 0.075 0.128 30 0.105 0.136 29 7 0.128 to 0.136 29 0.250 0.030 0.116 32 0.036 0.120 31 0.048 0.128 30 0.060 0.136 29 0.075 0.140 28 8 0.105 0.147 26 0.125 0.147 26 0.135 0.149 25 0.162 to 0.152 24 0.375 0.036 0.144 27 0.048 0.144 27 0.060 0.144 27 0.075 0.147 26 10 0.105 0.147 26 0.125 0.154 23 0.135 0.154 23

10

12

1⁄ 4

10

12

1⁄ 4

a For Types B and BP only; for Type AB see concluded Table 12b following.

Since conditions differ widely, it may be necessary to vary the hole size to suit a particular application. Hole sizes for metal thicknesses above 0.075 inch are for Types B and BP only.




Table 12b. Supplementary Data for Types AB Thread Forming Screws in Steel, Stainless Steel, Monel Metal, and Brass Sheet Metal Screw Size

Metal Thickness

Hole Size

10

0.018

0.144

27

10

0.048

0.149

25

10

0.060

0.154

23

…

…

…

…

Drill Size

Screw Size

Metal Thickness

Hole Size

Drill Size

Screw Size

Metal Thickness

Hole Size

Drill Size

0.048

0.205

5

0.060

0.228

1

0.075

0.232

5.9 mm

…

…

…

In Steel, Stainless Steel, Monel Metal, and Brass Sheet Metal 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4

0.018

0.196

9

0.024

0.196

9

0.030

0.196

9

1⁄ 4 1⁄ 4 1⁄ 4

0.036

0.196

9

…

All dimensions are in inches except numbered screw and drill sizes.

Table 13. Approximate Hole Sizes for Types D, F, G, and T Steel Thread Cutting Screws in Sheet Metals Steel Screw Size

2–56

3–48

4–40

5–40

6–32

8–32

Thickness 0.050 0.060 0.083 0.109 0.125 0.140 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.050 0.060 0.083 0.109 0.125 0.140

Hole Size 0.073 0.073 0.073 0.073 0.076 0.076 0.081 0.081 0.082 0.086 0.086 0.086 0.089 0.089 0.089 0.094 0.096 0.098 0.098 0.102 0.106 0.106 0.106 0.106 0.109 0.110 0.116 0.116 0.110 0.113 0.116 0.116 0.116 0.120 0.125 0.125 0.136 0.140 0.140 0.144 0.144 0.147

Drill Size 49 49 49 49 48 48 46 46 45 44 44 44 43 43 43 42 41 40 40 38 36 36 36 36 7⁄ 64 35 32 32 35 33 32 32 32 31 1⁄ 8 1⁄ 8 29 28 28 27 27 26

Aluminum Alloy Hole Drill Size Size 0.070 50 0.073 49 0.073 49 0.073 49 0.073 49 0.073 49 5⁄ 0.078 64 0.081 46 0.082 45 0.082 45 0.082 45 0.086 44 0.086 44 0.089 43 0.089 43 0.089 43 0.094 42 0.094 42 3⁄ 0.094 32 0.098 40 0.102 38 0.102 38 0.104 37 0.104 37 0.106 36 0.106 36 0.110 35 0.113 33 7⁄ 0.109 64 7⁄ 0.109 64 0.111 34 0.113 33 0.116 32 0.116 32 0.120 31 1⁄ 0.125 8 0.136 29 0.136 29 0.136 29 0.140 28 0.140 28 0.144 27

Steel Screw Size 8–32

10–24

10–32

12–24

1⁄ –20 4

Thickness 0.187 0.250 0.312 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500

Hole Size 0.150 0.150 0.150 0.152 0.154 0.161 0.161 0.166 0.170 0.173 0.173 0.173 0.173 0.159 0.166 0.166 0.170 0.170 0.170 0.177 0.177 0.177 0.177 0.180 0.182 0.188 0.191 0.191 0.199 0.199 0.199 0.199 0.199 0.213 0.219 0.221 0.221 0.228 0.228 0.228 0.228 0.228

Drill Size 25 25 25 24 23 20 20 19 18 17 17 17 17 21 19 19 18 18 18 16 16 16 16 15 14 3⁄ 16 11 11 8 8 8 8 8 3 7⁄ 32 2 2 1 1 1 1 1


Aluminum Alloy Hole Drill Size Size 0.147 26 0.150 25 0.150 25 0.150 25 0.152 24 0.154 23 0.157 22 0.159 21 0.161 20 0.166 19 11⁄ 0.172 64 0.173 17 0.173 17 0.161 20 0.161 20 0.161 20 0.166 19 0.166 19 0.166 19 11⁄ 0.172 64 0.177 16 0.177 16 0.177 16 0.177 16 0.180 15 0.182 14 0.185 13 3⁄ 0.188 16 0.191 11 0.199 8 0.199 8 0.199 8 0.199 8 0.206 5 0.209 4 0.213 3 0.213 3 0.221 2 0.228 1 0.228 1 0.228 1 0.228 1


1651

Table 13. (Continued) Approximate Hole Sizes for Types D, F, G, and T Steel Thread Cutting Screws in Sheet Metals Steel Screw Size

1⁄ –28 4

5⁄ –18 16

5⁄ –24 16

Thickness 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500 0.109 0.125 0.140

Hole Size 0.221 0.228 0.228 0.234 0.234 0.234 0.234 0.234 0.234 0.277 0.277 0.281 0.290 0.290 0.290 0.290 0.290 0.290 0.290 0.290

Drill Size 2 1 1 A 15⁄ 64 15⁄ 64 15⁄ 64 15⁄ 64 15⁄ 64 J J 9⁄ 32 L L L L L L L L

Aluminum Alloy Hole Drill Size Size 7⁄ 0.219 32 0.221 2 0.221 2 0.221 2 0.228 1 15⁄ 0.234 64 15⁄ 0.234 64 15 ⁄64 0.234 15⁄ 0.234 64 0.266 H 0.272 I 0.272 I 0.281 K 0.290 L 0.290 L 0.290 L 0.290 L 0.281 K 9 ⁄32 0.281 9⁄ 0.281 32

Steel Screw Size

5⁄ –24 16

3⁄ –16 8

3⁄ –24 8

Thickness 0.187 0.250 0.312 0.375 0.500

Hole Size 0.295 0.295 0.295 0.295 0.295

Drill Size M M M M M

0.125 0.140 0.187 0.250 0.312 0.375 0.500 0.125 0.140 0.187 0.250 0.312 0.375 0.500 …

0.339 0.339 0.348 0.358 0.358 0.358 0.358 0.348 0.348 0.358 0.358 0.358 0.358 0.358 …

R R S T T T T S S T T T T T …

Aluminum Alloy Hole Drill Size Size 0.290 L 0.295 M 0.295 M 0.295 M 0.295 M 0.328 0.332 0.339 0.348 0.348 0.348 0.348 0.344 0.344 0.348 0.358 0.358 0.358 0.358 …

21⁄ 64

Q R S S S S 11⁄ 32 11⁄ 32 S T T T T …

All dimensions are in inches except numbered drill and screw sizes. It may be necessary to vary the hole size to suit a particular application.

Table 14. Approximate Hole Sizes for Types D, F, G, and T Steel Thread Cutting Screws in Cast Metals and Plastics Screw Size

2–56

3–48

4–40

5–40

Thickness

Cast Iron Hole Drill Size Size

Zinc and Aluminuma Hole Drill Size Size

0.050

0.076

48

0.073

49

0.083

0.113

33

0.106

36

0.060

0.076

48

0.073

49

0.109

0.113

33

0.110

35

0.083

0.076

48

0.076

48

0.125

0.116

32

0.110

35

0.109

0.078

5⁄ 64

0.076

48

0.140

0.116

32

0.110

35

0.125

0.078

5⁄ 64

0.076

48

0.187

0.116

32

0.111

34

0.140

0.078

5⁄ 64

0.076

48

0.250

0.116

32

0.113

33

0.050

0.089

43

0.082

45

0.050

0.120

31

0.116

32

0.060

0.089

43

0.082

45

0.060

0.120

31

0.120

31

0.083

0.089

43

0.082

45

0.109

0.089

43

0.086

44

0.125

0.089

43

0.089

43

0.140

0.094

42

0.089

0.187

0.094

42

0.050

0.100

0.060

0.100

0.083

Screw Size

5–40

Thickness

Cast Iron Hole Drill Size Size

Zinc and Aluminuma Hole Drill Size Size

0.083

0.125

1⁄ 8

0.120

31

0.109

0.125

1⁄ 8

0.120

31

0.125

0.125

1⁄ 8

0.120

31

43

0.140

0.125

1⁄ 8

0.120

31

0.089

43

0.187

0.128

30

0.120

31

39

0.090

41

0.250

0.128

30

0.120

31

39

0.096

41

0.050

0.147

26

0.144

27

0.102

38

0.096

41

0.060

0.150

25

0.144

27

0.109

0.102

38

0.096

41

0.083

0.150

25

0.144

27

0.125

0.102

38

0.100

39

0.109

0.150

25

0.144

27

0.140

0.102

38

0.100

39

0.125

0.150

25

0.147

26

0.187

0.104

37

0.100

39

0.140

0.150

25

0.147

26

0.050

0.111

34

0.106

36

0.187

0.154

23

0.147

26

0.060

0.111

34

0.106

36

0.250

0.154

23

0.150

25

0.312

0.154

23

0.150

25

6–32

8–32



SELF-THREADING SCREWS Table 14. (Continued) Approximate Hole Sizes for Types D, F, G, and T Steel Thread Cutting Screws in Cast Metals and Plastics

Screw Size

10–24

10–32

12–24

1⁄ –20 4

Thickness 0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375

Cast Iron Hole Drill Size Size 0.170 18 0.170 18 11⁄ 0.172 64 0.173 17 0.173 17 0.173 17 0.177 16 0.177 16 0.177 16 0.177 16

Zinc and Aluminuma Hole Drill Size Size 0.161 20 0.166 19 0.166 19 0.166 19 0.166 19 0.166 19 0.170 18 0.170 18 11⁄ 0.172 64 11⁄ 0.172 64

0.050 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.060 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500

0.173 0.173 0.177 0.177 0.177 0.177 0.180 0.180 0.180 0.180 0.196 0.199 0.199 0.199 0.199 0.203 0.204 0.204 0.204 0.204

17 17 16 16 16 16 15 15 15 15 9 8 8 8 8 13⁄ 64 6 6 6 6

0.170 0.170 0.172 0.172 0.172 0.172 0.172 0.173 0.173 0.177 0.189 0.191 0.191 0.191 0.194 0.194 0.196 0.196 0.199 0.199

18 18 11⁄ 64 11⁄ 64 11⁄ 64 11⁄ 64 11⁄ 64 17 17 16 12 11 11 11 10 10 9 9 8 8

0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500

0.228 0.228 0.228 0.228 0.234 0.234 0.234 0.234 0.234

1 1 1 1 15⁄ 64 15⁄ 64 15⁄ 64 15⁄ 64 15⁄ 64

0.219 0.219 0.221 0.221 0.221 0.228 0.228 0.228 0.228

7⁄ 32 7⁄ 32

Screw Size

1⁄ –28 4

5⁄ –18 16

5⁄ –24 16

3⁄ –16 8

2 2 2 1 1 1 1

3⁄ –24 8

Thickness 0.083 0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500

Cast Iron Hole Drill Size Size 0.234 A 15⁄ 0.234 64 15⁄ 0.234 64 15⁄ 0.234 64 0.238 B 0.238 B 0.238 B 0.238 B 0.238 B

0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500

0.290 0.290 0.290 0.295 0.295 0.295 0.295 0.295

L L L M M M M M

Zinc and Aluminuma Hole Drill Size Size 0.228 1 0.228 1 0.228 1 0.228 1 0.228 1 0.234 A 0.234 A 15⁄ 0.234 64 15⁄ 0.234 64 0.277 J 0.281 K 0.281 K 9⁄ 0.281 32 9⁄ 0.281 32 0.290 L 0.290 L 0.290 L

0.109 0.125 0.140 0.187 0.250 0.312 0.375 0.500 0.125 0.140 0.187 0.250 0.312 0.375

0.295 0.295 0.295 0.302 0.302 0.302 0.302 0.302 0.348 0.348 0.348 0.348 0.348 0.348

M M M N N N N N S S S S S S

0.290 0.290 0.290 0.290 0.290 0.295 0.295 0.295 0.339 0.339 0.339 0.344 0.344 0.348

L L L L L M M M R R R 11⁄ 32 11⁄ 32 S

0.500

0.348

S

0.348

S

0.125 0.140 0.187 0.250 0.312 0.375 0.500

0.358 0.358 0.358 0.358 0.358 0.358 0.358

T T T T T T T

0.348 0.348 0.348 0.358 0.358 0.358 0.358

S S S T T T T

a Die Castings

Phenol Formaldehydea Depth of Penetration Min Max

Screw Size

Hole Size

Drill Size

2–56 3–48 4–40 5–40 6–32 8–32 10–24 10–32 1⁄ –20 4

0.078 0.089 0.098 0.113 0.116 0.144 0.161 0.166 0.228

5⁄ 64 43 40 33 32 27 20 19 1

0.219 0.219 0.250 0.250 0.250 0.312 0.375 0.375 0.375

0.375 0.375 0.312 0.438 0.312 0.500 0.500 0.500 0.625

Hole Size 0.076 0.086 0.093 0.110 0.116 0.144 0.161 0.166 0.228

Cellulose Acetate, Cellulose Nitrate, Acrylic Resin, and Styrene Resina Depth of Penetration Drill Size Min Max 48 44 42 35 32 27 20 19 1

0.219 0.219 0.250 0.250 0.250 0.312 0.375 0.375 0.375

a Plastics

For footnotes see Table 13.


0.375 0.375 0.312 0.438 0.312 0.500 0.500 0.500 1.000


1653

Table 15. Approximate Hole Sizes for Types BF and BT Steel Thread Cutting Screws in Cast Metals In Die Cast Zinc and Aluminum Screw Size

2

3

4

5

6

8

Thickness

Hole Size

Drill Size

0.060 0.083 0.109 0.125 0.140

0.073 0.073 0.076 0.076 0.076

49 49 48 48 48

0.060

0.086

0.083 0.109 0.125 0.140 0.188 0.109 0.125 0.140 0.188 0.250 0.109 0.125 0.140 0.188 0.250 0.125 0.140 0.188 0.250

Screw Size

Thickness

Hole Size

Drill Size

0.125 0.140 0.188 0.250 0.312

0.166 0.166 0.166 0.170 0.172

19 19 19 18 11⁄ 64

44

0.375

0.172

11⁄ 64

0.086 0.086 0.086 0.089 0.089 0.098 0.100 0.100 0.100 0.102 0.111 0.111 0.113 0.113 0.116 0.120 0.120 0.120 0.125

44 44 44 43 43 40 39 39 39 38 34 34 33 33 32 31 31 31

0.191 0.191 0.191 0.196 0.196 0.196 0.221 0.221 0.221 0.228 0.228 0.228 0.281 0.281 0.281 0.281 0.290 0.290 0.344

11 11 11 9 9 9 2 2 2 1 1 1 K K K K L L

1⁄ 8

0.125 0.140 0.188 0.250 0.312 0.375 0.125 0.140 0.188 0.250 0.312 0.375 0.125 0.140 0.188 0.250 0.312 0.375 0.125

11⁄ 32

0.312

0.125

1⁄ 8

0.140

0.344

11⁄ 32

0.125

0.149

25

0.188

0.344

11⁄ 32

0.140

0.149

25

0.250

0.344

11⁄ 32

0.188 0.250 0.312

0.149 0.152 0.152

25 24 24

0.312 0.375 …

0.348 0.348 …

S S …

10

12

1⁄ 4

5⁄ 16

3⁄ 8

All dimensions are in inches except numbered drill and screw sizes. It may be necessary to vary the hole size to suit a particular application.

Table 16. Approximate Hole Size for Types BF and BT Steel Thread Cutting Screws in Plastics Phenol Formaldehyde

Cellulose Acetate, Cellulose Nitrate, Acrylic Resin and Styrene Resin

Depth of Penetration

Depth of Penetration

Min

Max

Hole Size

Drill Size

Min

Max

5⁄ 64

0.094

0.250

0.076

48

0.094

0.250

0.089

43

0.125

0.312

0.089

43

0.125

0.312

0.104

37

0.125

0.312

0.100

39

0.125

0.312

5

0.116

32

0.188

0.375

0.113

33

0.188

0.375

6

0.125

1⁄ 8

0.188

0.375

0.120

31

0.188

0.375

Hole Size

Drill Size

2

0.078

3 4

Screw Size

8

0.147

26

0.250

0.500

0.144

27

0.250

0.500

10

0.170

18

0.312

0.625

0.166

19

0.312

0.625

12

0.194

10

0.375

0.625

0.189

12

0.375

0.625

1⁄ 4

0.228

1

0.375

0.750

0.221

2

0.375

0.750

For footnotes see above table.



THREAD INSERTS

Table 17. Approximate Hole Sizes for Type U Hardened Steel Metallic Drive Screws Screw Size

Hole Size

Drill Size

In Ferrous and Non-Ferrous Castings, Sheet Metals, Plastics, Plywood (Resin-Impregnated) and Fiber Screw Hole Drill Screw Size Size Size Size

Hole Size

Drill Size

00 0 2 4

.052 .067 .086 .104

55 51 44 37

.191 .221 .295 .358

11 2 M T

6 7 8 10

.120 .136 .144 .161

31 29 27 20

12 14 5⁄ 16 3⁄ 8

All dimensions are in inches except whole number screw and drill sizes and letter drill sizes.

Table 18. ANSI Standard Torsional Strength Requirements for Tapping Screws ANSI B18.6.4-1981 (R1991) Nom. Screw Size 2 3 4 5 6 7 8 10 12 14

Type A 4 9 12 18 24 30 39 48 83 125

Types AB,B,BF, BP,andBT 4 9 13 18 24 30 39 56 88 …

Types C, D, F, G, and T Coarse Fine Thread Thread 5 6 9 10 13 15 18 20 23 27 … … 42 47 56 74 93 108 … …

NomScrew Size 1⁄ 4

16 18 5⁄ 16 20 24 3⁄ 8 7⁄ 16 1⁄ 2 …

Type A … 152 196 … 250 492 … … … …

Types AB, B, BF, BP, and BT 142 … … 290 … … 590 620 1020 …

Types C, D, F, G, and T Coarse Fine Thread Thread 140 179 … … … … 306 370 … … … … 560 710 700 820 1075 1285 … …

Torsional strength data are in pound-inches.

Self-tapping Thread Inserts.—Self-tapping screw thread inserts are essentially hard bushings with internal and external threads. The internal threads conform to Unified and American standard classes 2B and 3B, depending on the type of insert used. The external thread has cutting edges on the end that provide the self-tapping feature. These inserts may be used in magnesium, aluminum, cast iron, zinc, plastics, and other materials. Self-tapping inserts are made of case-hardened carbon steel, stainless steel, and brass, the brass type being designed specifically for installation in wood. Screw Thread Inserts.—Screw thread inserts are helically formed coils of diamondshaped stainless steel or phosphor bronze wire that screw into a threaded hole to form a mating internal thread for a screw or stud. These inserts provide a convenient means of repairing stripped-out threads and are also used to provide stronger threads in soft materials such as aluminum, zinc die castings, wood, magnesium, etc. than can be obtained by direct tapping of the base metal involved. According to the Heli-Coil Corp., conventional design practice in specifying boss diameters or edge distances can usually be applied since the major diameter of a hole tapped to receive a thread insert is not much larger than the major diameter of thread the insert provides. Screw thread inserts are available in thread sizes from 4–40 to 11⁄2–6 inch National and Unified Coarse Thread Series and in 6–40 to 11⁄2–12 sizes in the fine-thread series. When used in conjunction with appropriate taps and gages, screw thread inserts will meet requirements of 2, 2B, 3, and 3B thread classes. ANSI Standard Metric Thread Forming and Thread Cutting Tapping Screws.— Table 1 shows the various types of metric thread forming and thread cutting screw threads covered by the standard ANSI/ASME B18.6.5M-1986. The designations of the American National Standards Institute are shown.


Machinery's Handbook 27th Edition METRIC SELF-THREADING SCREWS

1655

Table 1. ANSI Standard Threads and Points for Metric Thread Forming and Thread Cutting Tapping Screws ANSI/ASME B18.6.5M-1986

DETAIL OF THREAD FORM

TYPE BF

DETAIL OF THREAD FORM

TYPE BT

TYPE F

TYPE D

TYPE T See Tables 3 and 4 for thread data.

Thread Forming Tapping Screws: These types are generally for application in materials where large internal stresses are permissible or desirable, to increase resistance to loosening. These screws have the following descriptions and applications:



METRIC SELF-THREADING SCREWS

Type AB: Spaced thread screw with gimlet point primarily intended for use in thin metal, resin impregnated plywood, and asbestos compositions. Type B: Spaced thread screw with a blunt point that has tapered entering threads with unfinished crests and same pitches as Type AB. Used for thin metal, nonferrous castings, resin impregnated plywood, certain resilient plastics, and asbestos compositions. Thread Cutting Tapping Screws: These screws are generally for application in materials where disruptive internal stresses are undesirable or where excessive driving torques are encountered with thread forming tapping screws. These screws have the following descriptions and applications: Types BF and BT: Spaced threads with blunt point and tapered entering threads having unfinished crests, as on Type B, with one or more cutting edges or chip cavities, intended for use in plastics, asbestos compositions, and other similar materials. Types D, F, and T: Tapping screws with threads of machine screw diameter-pitch combinations (metric coarse thread series) approximating a 60 degree basic thread form (not necessarily conforming to any standard thread profile) with a blunt point and tapered entering threads with unfinished crests and having one or more cutting edges and chip cavities, intended for use in materials such as aluminum, zinc, and lead die castings; steel sheets and shapes; cast iron; brass; and plastics. ANSI Standard Head Types for Metric Thread Forming and Cutting Tapping Screws.—The head types covered by ANSI/ASME B18.6.5M-1986 include those commonly applicable to metric tapping screws and are described as follows: Flat Countersunk Head: The flat countersunk head has a flat top surface and a conical bearing surface with a head angle of 90 to 92 degrees. Oval Countersunk Head: The oval countersunk head has a rounded top surface and a conical bearing surface with a head angle of 90 to 92 degrees. Pan Head: The slotted pan head has a flat top surface rounding into cylindrical sides and a flat bearing surface. The recessed pan head has a rounded top surface blending into cylindrical sides and a flat bearing surface. Hex Head: The hex head has a flat or indented top surface, six flat sides, and a flat bearing surface. Hex Flange Head: The hex flange head has a flat or indented top surface and six flat sides formed integrally with a frustroconical or slightly rounded (convex) flange that projects beyond the sides and provides a flat bearing surface. Method of Designation.—Metric tapping screws are designated with the following data, preferably in the sequence shown: Nominal size; thread pitch; nominal length; thread and point type; product name, including head style and driving provision; material; and protective finish, if required. Examples: 6.3 × 1.8 × 30 Type AB, Slotted Pan Head Tapping Screw, Steel, Zinc Plated 6 × 1 × 20 Type T, Type 1A Cross Recessed Pan Head Tapping Screw, Corrosion Resistant Steel 4.2 × 1.4 × 13 Type BF, Type 1 Cross Recessed Oval Countersunk Head Tapping Screw, Steel, Chromium Plated 10 × 1.5 × 40 Type D, Hex Flange Head Tapping Screw, Steel



1657

Table 2. Recommended Nominal Screw Lengths for Metric Tapping Screws ANSI/ASME B18.6.5M-1986 Nominal Screw Size for Types AB, B, BF, and BT 2.2

-

2.9

Nominal Screw Length

2

2.5

4

PH

PH PH

3.5

4.2

4.8

5.5

6.3

8

9.5

-

6

8

10

Nominal Screw Size for Types D, F, and T

5

PH

6

A

3

3.5

4

5

A

PH

8

A

A

A

PH

PH

10

A

A

A

A

A

PH

13

A

A

A

A

A

A

A

PH

A

A

A

A

A

A

A

PH

20

A

A

A

A

A

A

25

A

A

A

A

A

A

A

30

A

A

A

A

A

35

A

16

40

PH

A

A

A

A

A

A

A

A

A

A

45 50

A

A

55

A

60

A

Table 3. ANSI Standard Thread and Point Dimensions for Types AB and B Metric Thread Forming Tapping Screws ANSI/ASME B18.6.5M-1986 D1

D2

D3

Y

L

Z

Point Taper Length Type Bc

Min. Practical Nominal Screw Lengthd

Basic Screw Diameter

Basic Thread Pitch

Refe

Refe

Max

Min

Max

Min

Max

Min

Max

2.2 × 0.8

2.184

0.79

2.24

2.10

1.63

1.52

1.47

1.37

1.6

1.2

2.0

4

6

4

5

2.9 × 1

2.845

1.06

2.90

2.76

2.18

2.08

2.01

1.88

2.1

1.6

2.6

6

7

5

7

3.5 × 1.3

3.505

1.27

3.53

3.35

2.64

2.51

2.41

2.26

2.5

1.9

3.2

7

9

6

8

4.2 × 1.4

4.166

1.41

4.22

4.04

3.10

2.95

2.84

2.69

2.8

2.1

3.7

8

10

7

10

4.8 × 1.6

4.826

1.59

4.80

4.62

3.58

3.43

3.30

3.12

3.2

2.4

4.3

9

12

8

11

5.5 × 1.8

5.486

1.81

5.46

5.28

4.17

3.99

3.86

3.68

3.6

2.7

5.0

11

14

9

12

6.3 × 1.8

6.350

1.81

6.25

6.03

4.88

4.70

4.55

4.34

3.6

2.7

6.0

12

16

10

13

8 × 2.1

7.938

2.12

8.00

7.78

6.20

5.99

5.84

5.64

4.2

3.2

7.5

16

20

12

17

9.5 × 2.1

9.525

2.12

9.65

9.43

7.85

7.59

7.44

7.24

4.2

3.2

8.0

19

24

14

19

Thread Major Diameter

Thread Minor Diameter

Point Diameterb

Min

Point Length Factor TypeAB Reff

Type AB

Type B

Note 7 Note 8 Note 7 Note 8

Nominal Screw Size and Thread Pitcha

a The

body diameter (unthreaded portion) is not less than the minimum minor diameter nor greater than the maximum major diameter of the thread. b The tabulated values shall apply to screw blanks prior to roll threading. c The tabulated maximum limits are equal to approximately two times the thread pitch. d Lengths shown are theoretical minimums and are intended to assist the user in the selection of appropriate short screw lengths. Refer to Table 2 for recommended diameter-length combinations. e Basic screw diameter and basic thread pitch shall be used for calculation purposes wherever these factors appear in formulations for dimensions. f The minimum effective grip length on Type AB tapping screws shall be determined by subtracting the point length factor from the minimum screw length. All dimensions are in millimeters. See Table 1 for thread diagrams. 7 Pan, hex, and hex flange heads. 8 Flat and oval countersunk heads.




Table 4. ANSI Standard Thread and Point Dimensions for Types BF, BT, D, F, and T Metric Thread Cutting Tapping Screws ANSI/ASME B18.6.5M-1986 Types BF and BT D1

D2

D3

Y

L Minimal Practical Nominal Screw Lengthc

Point Diametera

Point Taper Length Type Bb

Basic Screw Diameter

Basic Thread Pitch

Refd

Refd

Max

Min

Max

Min

Max

Min

Max

2.2 × 0.8

2.184

0.79

2.24

2.10

1.63

1.52

1.47

1.37

1.6

2.9 × 1

2.845

1.06

2.90

2.76

2.18

2.08

2.01

1.88

2.1

3.5 × 1.3

3.505

1.27

3.53

3.35

2.64

2.51

2.41

2.26

4.2 × 1.4

4.166

1.41

4.22

4.04

3.10

2.95

2.84

4.8 × 1.6

4.826

1.59

4.80

4.62

3.58

3.43

3.30

5.5 × 1.8

5.486

1.81

5.46

5.28

4.17

3.99

3.86

6.3 × 1.8

6.350

1.81

6.25

6.03

4.88

4.70

8 × 2.1

7.938

2.12

8.00

7.78

6.20

9.5 × 2.1

9.525

2.12

9.65

9.43

7.85



Thread Minor Diameter

Min

Pan, Hex and Hex Flange Heads

Flat and Oval Csunk Heads

1.2

4

5

1.6

5

7

2.5

1.9

6

8

2.69

2.8

2.1

7

10

3.12

3.2

2.4

8

11

3.68

3.6

2.7

9

12

4.55

4.34

3.6

2.7

10

13

5.99

5.84

5.64

4.2

3.2

12

17

7.59

7.44

7.24

4.2

3.2

14

19

a The tabulated values apply to screw blanks prior to roll threading. b The tabulated maximum limits are equal to approximately two times the thread pitch. c Lengths shown are theoretical minimums and are intended to assist in the selection of appropriate short screw lengths. See Table 2 for recommended length-diameter combinations. For Types D, F, and T, shorter screws are available with the point length reduced to the limits tabulated for short screws. d Basic screw diameter and basic thread pitch are used for calculation purposes whenever these factors appear in formulations for dimensions.

Types D, F, T D1 Nominal Screw Size and Thread Pitch

D3


DS

Y

L

Point Taper Length

Minimum Practical Nominal Screw Lengthc

For Short Screws

For Long Screwsb

Flat and Oval Csunk Heads 5

Max

Min

Max

Min

Min

Max

Min

Max

Min

Pan, Hex and Hex Flange Heads

2 × 0.4

2.00

1.88

1.45

1.39

1.65

1.4

1.0

1.8

1.4

4

2.5 × 0.45

2.50

2.37

1.88

1.82

2.12

1.6

1.1

2.0

1.6

4

6

3 × 0.5

3.00

2.87

2.32

2.26

2.58

1.8

1.3

2.3

1.8

5

6

3.5 × 0.6

3.50

3.35

2.68

2.60

3.00

2.1

1.5

2.7

2.1

5

8

4 × 0.7

4.00

3.83

3.07

2.97

3.43

2.5

1.8

3.2

2.5

6

9

5 × 0.8

5.00

4.82

3.94

3.84

4.36

2.8

2.0

3.6

2.8

7

10

Point Diametera

Body Diametera

6×1

6.00

5.79

4.69

4.55

5.21

3.5

2.5

4.5

3.5

9

12

8 × 1.25

8.00

7.76

6.40

6.24

7.04

4.4

3.1

5.6

4.4

11

16

10 × 1.5

10.00

9.73

8.08

7.88

8.86

5.3

3.8

6.8

5.3

13

18

a Minimum

limits for body diameter (unthreaded portion) are tabulated for convenient reference. For Types BF and BT, the body diameter is not less than the minimum minor diameter nor greater than the maximum major diameter of the thread. b Long screws are screws of nominal lengths equal to or longer than those listed under L. All dimensions are in millimeters. See Table 1 for thread diagrams.

Material and Heat Treatment.—Tapping screws are normally fabricated from carbon steel and are suitably processed to meet the performance and test requirements outlined in the standard, B18.6.5M. Tapping screws may also be made from corrosion resistant steel, Monel, brass, and aluminum alloys. The materials, properties, and performance characteristics applicable to such screws should be mutually agreed upon between the manufacturer and the purchaser.



1659

Table 5. Clearance Holes for Metric Tapping Screws ANSI/ASME B18.6.5M-1986 Appendix Nominal Screw Size and Thread Pitch 2.2 ×0.8 2.9 ×1 3.5 ×1.3 4.2 ×1.4 4.8 ×1.6 5.5 ×1.8 6.3×1.8 8 ×2.1 9.5 ×2.1

Basic Clearance Hole Diametera Normal Clearance Close Loose (Preferred)b Clearanceb Clearanceb Types AB, B, BF, and BT 2.40 2.60 2.80 3.10 3.30 3.50 3.70 3.90 4.20 4.50 4.70 5.00 5.10 5.30 5.60 5.90 6.10 6.50 6.70 6.90 7.30 8.40 9.00 10.00 10.00 10.50 11.50

Nominal Screw Size and Thread Pitch 2 ×0.4 2.5 ×0.45 3 ×0.5 3.5 ×0.6 4 ×0.7 5 ×0.8 6 ×1 8 ×1.25 10 ×1.5

Basic Clearance Hole Diametera Normal Clearance Close Loose (Preferred)b Clearanceb Clearanceb Types D, F, and T 2.20 2.40 2.60 2.70 2.90 3.10 3.20 3.40 3.60 3.70 3.90 4.20 4.30 4.50 4.80 5.30 5.50 5.80 6.40 6.60 7.00 8.40 9.00 10.00 10.50 11.00 12.00

a The values given in this table are minimum limits. The recommended plus tolerances are as follows: for clearance hole diameters over 1.70 to and including 5.80 mm, plus 0.12, 0.20, and 0.30 mm for close, normal, and loose clearances, respectively; over 5.80 to and including 14.50 mm, plus 0.18, 0.30, and 0.45 mm for close, normal, and loose clearances, respectively. b Normal clearance hole sizes are preferred. Close clearance hole sizes are for situations such as critical alignment of assembled components, wall thickness, or other limitations that necessitate the use of a minimal hole. Countersinking or counterboring at the fastener entry side may be necessary for the proper seating of the head. Loose clearance hole sizes are for applications where maximum adjustment capability between the components being assembled is necessary.


Approximate Installation Hole Sizes for Metric Tapping Screws.—The approximate hole sizes given in Tables 7 through 9 provide general guidance in selecting holes for installing the respective types of metric thread forming and thread cutting tapping screws in various commonly used materials. Types AB, B, BF, and BT metric tapping screws are covered in these tables; hole sizes for Types D, F, and T metric thread cutting tapping screws are still under development. Table 6. Approximate Pierced or Extruded Hole Sizes for Steel Types AB and B Metric Thread Forming Tapping Screws Nominal Screw Size andThread Pitch

2.9 × 1

3.5 × 1.3

2.9 × 1 3.5 × 1.3

Metal Thickness

Nominal Nominal Screw Size Screw Size andThread andThread Metal Hole Hole Pitch Pitch Thickness Size Size In Steel, Stainless Steel, Monel, and Brass Sheet Metal

0.38 0.46 0.61 0.76 0.91 0.38 0.46 0.61 0.76 0.91

2.18 2.18 2.49 2.49 2.49 2.82 2.82 2.82 2.82 2.82

0.61 0.76 0.91 1.22 0.61 0.76

2.18 2.18 2.18 2.18 2.82 2.82

0.46 0.61 0.76 0.91 1.22 0.46 0.61 4.8 × 1.6 0.76 0.91 1.22 In Aluminum Alloy 0.91 3.5 × 1.3 1.22 0.61 0.76 4.2 × 1.4 0.91 1.22 4.2 × 1.4

3.45 3.45 3.45 3.45 3.45 3.99 3.99 3.99 3.99 3.99 2.82 2.82 3.45 3.45 3.45 3.45

Metal Thickness

Hole Size

0.61 0.76 0.91 1.22 … 0.76 0.91 1.22 … …

4.70 4.70 4.70 4.70 … 5.31 5.31 5.31 … …

0.61 0.76 0.91 1.22 … …

3.99 3.99 3.99 3.99 … …

5.5 × 1.8

6.3 × 1.8

4.8 × 1.6





Table 7. Approximate Drilled or Clean-Punched Hole Sizes for Steel Type AB Metric Thread Forming Tapping Screws in Sheet Metal Nominal Screw Size and Thread Pitch


Metal Thickness

Hole Size

0.38

1.63

52

0.61

2.69

36

0.46

1.63

52

0.76

2.69

36

0.61

1.70

51

0.91

2.79

0.76

1.78

50

1.22

0.91

1.85

49

1.22

1.85

49

1.52

1.93

0.38 0.46


Metal Thickness

Hole Size

Drill Sizea

1.22

3.78

25

1.52

3.91

23

35

1.90

3.99

22

2.82

34

0.46

…

…

1.52

2.95

32

0.61

4.22

19

1.90

3.05

31

0.76

4.22

19

48

0.46

…

…

0.91

4.22

19

2.18

44

0.61

3.18

…

1.22

4.32

18

2.18

44

0.76

3.18

…

1.52

4.50

16

0.61

2.26

43

0.91

3.18

…

1.90

4.62

14

0.76

2.39

42

1.22

3.25

30

0.46

4.98

9

0.91

2.39

42

1.52

3.45

29

0.61

4.98

9

1.22

2.44

41

1.90

3.56

28

0.76

4.98

9

1.52

2.54

39

0.46

3.66

27

0.91

4.98

9

1.90

2.59

38

0.61

3.66

27

1.22

5.21

W

0.38

2.64

37

0.76

3.66

27

1.52

5.79

1

0.46

2.64

37

0.91

3.73

26

1.90

5.89

…

0.38

…

…

0.61

…

…

1.22

3.66

27

0.46

…

…

0.76

2.64

37

1.52

3.66

27

0.61

1.63

52

0.91

2.64

37

1.90

3.73

26

Drill Sizea

Metal Thickness

Hole Size

Drill Sizea

In Steel, Stainless Steel, Monel, and Brass Sheet Metal

2.2 × 0.8

2.9 × 1

3.5 × 1.3

3.5 × 1.3

4.2 × 1.4

4.8 × 1.6

4.8 × 1.6

5.5 × 1.8

6.3 × 1.8

In Aluminum Alloy Sheet Metal

2.2 × 0.8

2.9 × 1

3.5 × 1.3

3.5 × 1.3

4.8 × 1.6

0.76

1.63

52

1.22

2.64

37

0.46

…

…

0.91

1.63

52

1.52

2.69

36

0.61

…

…

1.22

1.70

51

1.90

2.79

35

0.76

…

…

1.52

1.78

50

0.46

…

…

0.91

…

…

0.38

…

…

0.61

…

…

1.22

4.09

20

0.46

…

…

0.76

2.95

32

1.52

4.22

19

0.61

…

…

0.91

3.05

31

1.90

4.39

17

0.76

2.18

44

1.22

3.25

30

0.46

…

…

0.91

2.18

44

1.52

3.45

29

0.61

…

…

1.22

2.18

44

1.90

3.56

28

0.76

…

…

1.52

2.26

43

0.46

…

…

0.91

…

…

1.90

2.26

43

0.61

…

…

1.22

…

…

0.38

…

…

0.76

…

…

1.52

5.05

8

0.46

…

…

0.91

3.66

27

1.90

5.11

7

4.2 × 1.4

4.8 × 1.6

5.5 × 1.8

6.3 × 1.8

a Customary drill size references have been retained where the metric hole diameters are direct con-

versions of their decimal inch equivalents. All dimensions are in millimeters except drill sizes.



1661

Table 8. Approximate Hole Sizes for Steel Type AB Metric Thread Forming Tapping Screws in Plywoods and Asbestos Nominal Screw Size and Thread Pitch

Drill Sizea

Hole Size

Penetration in Blind Holes

Min Mat'l Thickness

Min

Penetration in Blind Holes Drill Sizea

Hole Size

Max

In Plywood (Resin Impregnated)

Min Mat'l Thickness

Min

Max

In Asbestors Compositions

2.2 ×0.8

1.85

49

3.18

4.78

12.70

1.93

48

3.18

4.78

2.9 ×1

2.54

39

4.78

6.35

15.88

2.57

38

4.78

6.35

15.88

3.5 ×1.3

3.18

…

4.78

6.35

15.88

3.05

31

4.78

6.35

15.88

4.2 ×1.4

3.66

27

4.78

6.35

19.05

3.73

26

7.92

9.52

19.05

4.8 ×1.6

4.39

17

6.35

7.92

25.40

4.22

19

7.92

9.52

25.40

5.5 ×1.8

4.93

10

7.92

9.52

25.40

4.98

9

7.92

9.52

25.40

6.3 ×1.8

5.79

1

7.92

9.52

25.40

5.79

1

11.13

12.70

25.40

12.70

a Customary drill size references have been retained where the metric hole diameters are direct conversions of their decimal inch equivalents.

All dimensions are in millimeters except drill sizes.

Table 9. Approximate Hole Sizes for Steel Type B Metric Thread Forming Tapping Screws in Plywoods, Asbestos, and Plastics Nominal Screw Size and Thread Pitch

Drill Sizea

Hole Size


Min Mat'l Thickness

Min

Max


Hole Size

Drill Sizea

Min Mat'l Thickness

Penetration in Blind Holes Min

Max 25.40

In Plywood (Resin Impregnated) 2.2 × 0.8

1.85

49

3.18

4.78

12.70

4.8 × 1.6

4.39

17

6.35

7.92

2.9 × 1

2.54

39

4.78

6.35

15.88

5.5 × 1.8

4.93

10

7.92

9.52

25.40

3.5 × 1.3

3.18

…

4.78

6.35

15.88

6.3 × 1.8

5.79

1

7.92

9.52

25.40

4.2 × 1.4

3.66

27

4.78

6.35

19.05

…

…

…

…

…

…

a Customary drill size references have been retained where the metric hole diameters are direct con-

versions of their decimal inch equivalents. Nominal Screw Size and Thread Pitch

Hole Size

Drill Sizea


Min Mat'l Thickness

Min

Max

4.78 6.35 6.35 9.52 9.52 9.52 12.70

12.70 15.88 15.88 19.05 25.40 25.40 25.40

In Asbestos Compositions 2.2 × 0.8 2.9 × 1 3.5 × 1.3 4.2 × 1.4 4.8 × 1.6 5.5 × 1.8 6.3 × 1.8 Nominal Screw Size and Thread Pitch

1.93 2.57 3.05 3.73 4.22 4.98 5.79 Hole Size

Drill Sizea

48 38 31 26 19 9 1 Min Penetration in Blind Holes

3.18 4.78 4.78 7.92 7.92 7.92 11.13 Hole Size

In Phenol Formaldehyde 2.2 × 0.8 2.9 × 1 3.5 × 1.3 4.2 × 1.4 4.8 × 1.6 5.5 × 1.8 6.3 × 1.8

1.98 2.54 3.25 3.81 4.50 5.05 5.94

47 39 30 25 16 8 …

Drill Sizea

Min Penetration in Blind Holes

In Cellulose Acetate & Nitrate, Acrylic and Styrene Resins 4.78 6.35 6.35 7.92 7.92 9.52 9.52

1.98 2.39 3.05 3.66 4.32 4.85 5.61

47 42 32 27 18 11 2



4.78 6.35 6.35 7.92 7.92 9.52 9.52



Table 10. Approximate Drilled or Clean-Punched Hole Sizes for Steel Type B Metric Thread Forming Tapping Screws in Sheet Metal and Cast Metals Nominal Screw Size and Thread Pitch

2.2 × 0.8

2.9 × 1

3.5 × 1.3

2.2 × 0.8

2.9 × 1

3.5 × 1.3

Nominal Nominal Screw Screw Metal Size and Size and Drill Drill ThickHole Thread Thread Sizea ness Size Sizea Pitch Pitch In Steel, Stainless Steel, Monel, and Brass Sheet Metal

Metal Thickness

Hole Size

0.38 0.46 0.61 0.76 0.91 1.22 1.52 0.38 0.46 0.61 0.76 0.91 1.22 1.52 1.90 0.38 0.46 0.61 0.76 0.91 1.22 1.52

1.63 1.63 1.70 1.78 1.85 1.85 1.93 2.18 2.18 2.26 2.39 2.39 2.44 2.54 2.59 2.64 2.64 2.69 2.69 2.79 2.82 2.95

52 52 51 50 49 49 48 44 44 43 42 42 41 39 38 37 37 36 36 35 34 32

0.61 0.76 0.91 1.22 1.52 0.76 0.91 1.22 1.52 1.90 2.67 0.76 0.91 1.22 1.52 1.90 2.67 3.25 to 6.25

1.63 1.63 1.63 1.70 1.78 2.18 2.18 2.18 2.26 2.26 2.39 2.64 2.64 2.64 2.69 2.79 2.82

52 52 52 51 50 44 44 44 43 43 42 37 37 37 36 35 34

3.05

31

1.90 2.67 0.61 0.76 0.91 1.22 1.52 1.90 2.67 3.18 3.43 0.61 0.76 0.91 1.22 1.52 1.90 2.67 3.18 3.43 4.17

3.5 × 1.3

4.2 × 1.4

4.8 × 1.6

3.05 3.25 3.18 3.18 3.18 3.25 3.45 3.56 3.81 3.81 3.86 3.66 3.66 3.73 3.86 3.86 3.99 4.09 4.32 4.32 4.39

31 30 … … … 30 29 28 25 25 24 27 27 26 24 24 22 20 18 18 17

In Aluminum Alloy Sheet Metal 0.76 2.95 32 0.91 3.05 31 1.22 3.25 30 1.52 3.45 29 1.90 3.56 28 2.67 3.73 26 4.2 × 1.4 3.18 3.73 26 3.43 3.78 25 4.11 to 9.52 3.86 24 0.91 3.66 27 1.22 3.66 27 1.52 3.66 27 1.90 3.73 26 2.67 3.73 26 3.18 3.91 23 4.8 × 1.6 3.43 3.91 23 4.17 4.04 21 5.08 to 9.52 4.22 19

5.5 × 1.8

6.3 × 1.8

5.5 × 1.8

6.3 × 1.8

Metal Thickness

Hole Size

Drill Sizea

0.61 0.76 0.91 1.22 1.52 1.90 2.67 3.18 3.43 4.17 0.76 0.91 1.22 1.52 1.90 2.67 3.18 3.43 4.17 4.75 4.93

4.22 4.22 4.22 4.32 4.50 4.62 4.70 4.98 4.98 5.11 4.93 4.93 4.93 5.05 5.18 5.31 5.79 5.79 5.94 5.94 5.94

19 19 19 18 16 14 13 9 9 7 10 10 10 8 6 4 1 1 … … …

1.22 1.52 1.90 2.67 3.18 3.43 4.17 5.08 to 9.52 1.52 1.90 2.67 3.18 3.43 4.17 4.75 4.93 5.08 to 9.52

4.09 4.22 4.39 4.57 4.62 4.62 4.80

20 19 17 15 14 14 12

4.98 5.05 5.11 5.18 5.31 5.31 5.41 5.41 5.61

9 8 7 6 4 4 3 3 2

5.79

1

a Customary drill size references have been retained where the metric hole diameters are direct conversions of their decimal inch equivalents.


Hole Size

2.2 × 0.8 2.9 × 1 3.5 × 1.3 4.2 × 1.4

1.98 2.64 3.25 3.86

In Aluminum, Magnesium, Zinc, Brass, and Bronze Cast Metals Nominal Screw Size Min Drill and Thread Hole Penetration a Pitch Size Size in Blind Holes 47 37 30 24

3.18 4.78 6.35 6.35

4.8 × 1.6 5.5 × 1.8 6.3 × 1.8 …

4.50 5.05 5.94 …

Drill Sizea

Min Penetration in Blind Holes

16 8 4 …

6.35 7.14 7.92 …

All dimensions are in millimeters, except drill sizes.



1663

Table 11. Approximate Hole Sizes for Steel Types BF and BT Metric Thread Cutting Tapping Screws for Cast Metals and Plastics Nominal Screw Size and Thread Pitch

2.2 × 0.8

2.9 × 1

4.8 × 1.6

5.5 × 1.8

6.3 × 1.8

Material Thickness

Hole Size

1.52 2.11 2.77 3.18 3.56 2.77 3.18 3.56 4.78 6.35 3.18 3.56 4.78 6.35 7.92 9.52 3.18 3.56 4.78 6.35 7.92 9.52 3.18 3.56 4.78

1.85 1.85 1.93 1.93 1.93 2.49 2.54 2.54 2.54 2.59 4.22 4.22 4.22 4.32 4.37 4.37 4.85 4.85 4.85 4.98 4.98 4.98 5.61 5.61 5.61

Nominal Screw Size and Thread Pitch 2.2 × 0.8 2.9 × 1.0 3.5 × 1.3 4.2 × 1.4 4.8 × 1.6 5.5 × 1.8 6.3 × 1.8 2.2 × 0.8 2.9 × 1.0 3.5 × 1.3 4.2 × 1.4 4.8 × 1.6 5.5 × 1.8 6.3 × 1.8

Nominal Drill Screw Size and Sizea Thread Pitch In Die Cast Zinc and Aluminum

Hole Size

49 49 48 48 48 40 39 39 39 38 19 19 19 18 … … 11 11 11 9 9 9 2 2 2

3.5 × 1.3

4.2 × 1.4

6.3 × 1.8

8 × 2.1

9.5 × 2.1

Drill Sizea In Phenol Formaldehyde

Material Thickness

Drill Sizea

Hole Size

3.18 3.05 3.56 3.05 4.78 3.05 6.35 3.18 7.92 3.18 3.18 3.78 3.56 3.78 4.78 3.78 6.35 3.86 7.92 3.86 6.35 5.79 7.92 5.79 9.52 5.79 3.18 7.14 3.56 7.14 4.78 7.14 6.35 7.14 7.92 7.37 9.52 7.37 3.18 8.74 3.56 8.74 4.78 8.74 6.35 8.74 7.92 8.84 9.52 8.84 Depth of Penetration Min Max

1.98 … 2.39 2.64 37 3.18 3.18 … 4.78 3.73 26 6.35 4.32 18 7.92 4.93 10 9.52 5.79 1 9.52 In Cellulose Acetate and Nitrate, Acrylic and Styrene Resins 1.93 48 2.39 2.54 39 3.18 3.05 31 4.78 3.66 27 6.35 4.22 19 7.92 4.80 12 9.52 5.61 2 9.52

31 31 31 … … 25 25 25 24 24 1 1 1 K K K K L L … … … … S S

6.35 7.92 9.52 12.70 15.88 15.88 19.05 6.35 7.92 9.52 12.70 15.88 15.88 19.05

a Customary drill size references have been retained where the metric hole sizes are direct conversions of their decimal inch equivalents.


The finish (plating or coating) on metric tapping screws and the material composition and hardness of the mating component are factors that affect assembly torques in individual applications. Although the recommended installation hole sizes given in Tables 7 through 9 were based on the use of plain unfinished carbon steel metric tapping screws, experience has shown that the specified holes are also suitable for screws having most types of commercial finishes. However, owing to various finishes providing different degrees of lubricity, some adjustment of installation torques may be necessary to suit individual applications. Also, where exceptionally heavy finishes are involved or screws are to be assembled into materials of higher hardness, some deviation from the specified hole sizes may be required to provide optimum assembly. The necessity and extent of such deviations can best be determined by experiment in the particular assembly environment.



1664

T-SLOTS, BOLTS, AND NUTS Table 1. American National Standard T-Slots ANSI/ASME B5.1M-1985 (R1998) T-SLOTS

Nominal T-Bolt Sizea inch

mm

0.250 0.312 0.375 0.500 0.625 0.750 1.000 1.250 1.500

4 5 6 8 10 12 16 20 24 30 36 42 48

Width of Throat A1b inch

mm

0.282 0.344 0.438 0.562 0.688 0.812 1.062 1.312 1.562

5 6 8 10 12 14 18 22 28 36 42 48 54

Width of Headspace B1

Depth of Headspace C1

inch

inch

min

0.500 0.594 0.719 0.906 1.188 1.375 1.750 2.125 2.562

mm max

min

max

0.562 0.656 0.781 0.969 1.250 1.469 1.844 2.219 2.656

10 11 14.5 16 19 23 30 37 46 56 68 80 90

11 12.5 16 18 21 25 32 40 50 60 72 85 95

min

0.203 0.234 0.297 0.359 0.453 0.594 0.781 1.031 1.281

Depth of Throat D1

mm

inch

max

min

max

0.234 0.266 0.328 0.391 0.484 0.625 0.828 1.094 1.344

3 5 7 7 8 9 12 16 20 25 32 36 40

3.5 6 8 8 9 11 14 18 22 28 35 40 44

min

0.125 0.156 0.219 0.312 0.438 0.562 0.750 1.000 1.250

Rounding or Breaking of Cornersc

mm

inch

max

min

max

0.375 0.438 0.562 0.688 0.875 1.062 1.250 1.562 1.938

4.5 5 7 9 11 12 16 20 26 33 39 44 50

7 8 11 14 17 19 24 29 36 46 53 59 66

R1 max

0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03

W1 max

0.02 0.03 0.03 0.03 0.03 0.03 0.06 0.06 0.06

mm U1 max

R1 max

W1 max

U1 max

0.03 0.03 0.03 0.03 0.05 0.05 0.05 0.05 0.05

0.5 0.5 0.5 0.5 0.5 0.5 0.8 0.8 0.8 0.8 0.8 1.5 1.5

0.8 0.8 0.8 0.8 0.8 0.8 0.8 0.8 1.5 1.5 1.5 2.5 2.5

0.8 0.8 0.8 0.8 0.8 0.8 1.3 1.3 1.3 1.3 1.3 2 2

a Width of tongue (tenon) to be used with the above T-Slots will be found in the complete standard, B5.1M. b Throat dimensions are basic. When slots are intended to be used for holding only, tolerances can be 0.0 + 0.010 inch or H12 Metric (ISO/R286); when intended for location, tolerance can be 0.0 + 0.001 inch or H8 Metric (see page 670). c Corners of T-Slots may be square or may be rounded or broken to the indicated maximum dimensions at the manufacturer's option.

For the dimensions of tongue seats, inserted tongues, and solid tongues refer to the complete standard, B5.1M.


T-BOLTS, SLOTS, NUTS, AND TONGUES

Suggested Approximate Dimensions For Rounding Or Breaking Of Corners

Basic Dimensions


Table 2. American National Standard T-Bolts ANSI/ASME B5.1M-1985 (R1998) T-BOLTS

Width Across Flats B2

inch

metric

inch

UNC-2A

ISOd

max

min

max

0.250–20 0.312–18 0.375–16 0.500–13 0.625–11 0.750–10 1.000–8 1.250–7 1.500–6

M4 M5 M6 M8 M10 M12 M16 M20 M24 M30 M36 M42 M48

0.469 0.562 0.688 0.875 1.125 1.312 1.688 2.062 2.500

0.438 0.531 0.656 0.844 1.094 1.281 1.656 2.031 2.469

9 10 13 15 18 22 28 34 43 53 64 75 85

Width Across Corners mm

mm

min

max

max

max

min

max

8.5 9.5 12 14 17 21 27 33 42 52 63 74 84

0.663 0.796 0.972 1.238 1.591 1.856 2.387 2.917 3.536

12.7 14.1 18.4 21.2 25.5 31.1 39.6 48.1 60.8 75 90.5 106.1 120.2

0.156 0.188 0.250 0.312 0.406 0.531 0.688 0.938 1.188

0.141 0.172 0.234 0.297 0.391 0.500 0.656 0.906 1.156

2.5 4 6 6 7 8 10 14 18 23 28 32 36

a For inch tolerances for thread diameters of bolts or studs and for threads see page

R2

Height C2

inch

inch

mm

W2

inch

mm

inch

mm

min

max

max

max

max

2.1 3.6 5.6 5.6 6.6 7.6 9.6 13.2 17.2 22.2 27.2 30.5 34.5

0.02 0.02 0.02 0.02 0.03 0.03 0.03 0.03 0.03

0.3 0.3 0.5 0.5 0.5 0.5 0.8 0.8 0.8 0.8 0.8 1 1

0.03 0.03 0.03 0.06 0.06 0.06 0.06 0.06 0.06

0.5 0.5 0.8 0.8 0.8 1.5 1.5 1.5 1.5 1.5 1.5 2 2


Rounding of Cornersc

Bolt Head Dimensions

Nominal T-Bolt Size and Thread A2ab

1736.

b T-slots to be used with these bolts will be found in Table 1. d Metric thread grade and tolerance position is 5g 6g (see page

1790).


1665

c Corners of T-bolts may be square or may be rounded or broken to the indicated maximum dimensions at the manufacturer's option.


1666

Table 3. American National Standard T-Nuts ANSI/ASME B5.1M-1985 (R1998) T-NUTS

0.250

inch

mm

max

mm min

max

min

inch

mm

UNC-3B

ISOd

Width of Nut B3 inch max

mm min

Rounding of Corners

Height of Nut C3

max min

inch max

mm min

max

min

Total Thickness Including Tonguec K3 inch

mm

Length of Nutc L3 inch

W3

R3

mm

inch

mm

inch

mm

max

max

max

max

4

…

…

…

…

…

…

…

…

…

…

…

5

…

…

…

…

…

…

…

…

…

…

…

…

…

6

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

…

… … …

…

0.312

8

0.330

0.320

8.7

8.5

0.250–20

M6

0.562

0.531

15

14

0.188

0.172

6

5.6

0.281

9

0.562

18

0.02

0.5

0.03

0.8

0.375

10

0.418

0.408

11

10.75

0.312–18

M8

0.688

0.656

18

17

0.250

0.234

7

6.6

0.375

10.5

0.688

20

0.02

0.5

0.03

0.8

0.500

12

0.543

0.533

13.5

13.25

0.375–1

6M10

0.875

0.844

22

21

0.312

0.297

8

7.6

0.531

12

0.875

23

0.02

0.5

0.06

1.5

0.625

16

0.668

0.658

17.25

17

0.500–13

M12

1.125

1.094

28

27

0.406

0.391

10

9.6

0.625

15

1.125

27

0.03

0.8

0.06

1.5

0.750

20

0.783

0.773

20.5

20.25

0.625–11

M16

1.312

1.281

34

33

0.531

0.500

14

13.2

0.781

21

1.312

35

0.03

0.8

0.06

1.5

1.000

24

1.033

1.018

26.5

26

0.750–10

M20

1.688

1.656

43

42

0.688

0.656

18

17.2

1.000

27

1.688

46

0.03

0.8

0.06

1.5

1.250

30

1.273

1.258

33

32.5

1.000–8

M24

2.062

2.031

53

52

0.938

0.906

23

22.2

1.312

34

2.062

53

0.03

0.8

0.06

1.5

1.500

36

1.523

1.508

39.25

38.75

1.250–7

M30

2.500

2.469

64

63

1.188

1.156

28

27.2

1.625

42

2.500

65

0.03

0.8

0.06

1.5

42

46.75

46.25

M36

75

74

32

30.5

48

75

1

2

48

52.5

51.75

M42

85

84

36

34.5

54

85

1

2

a T-slot dimensions to fit the above nuts will be found in Table 1. b For tolerances of inch threads see page

1736.

c No tolerances are given for “Total Thickness” or “Nut Length” as they need not be held to close limits. d Metric tapped thread grade and tolerance position is 5H (see page

1790).



inch

Tap for Studb E3

Width of Tongue A3

Nominal T-Bolt Sizea

Machinery's Handbook 27th Edition COTTER AND CLEVIS PINS

1667

PINS AND STUDS Dowel-Pins.—Dowel-pins are used either to retain parts in a fixed position or to preserve alignment. Under normal conditions a properly fitted dowel-pin is subjected solely to shearing strain, and this strain occurs only at the junction of the surfaces of the two parts which are being held by the dowel-pin. It is seldom necessary to use more than two dowelpins for holding two pieces together and frequently one is sufficient. For parts that have to be taken apart frequently, and where driving out of the dowel-pins would tend to wear the holes, and also for very accurately constructed tools and gages that have to be taken apart, or that require to be kept in absolute alignment, the taper dowel-pin is preferable. The taper dowel-pin is most commonly used for average machine work, but the straight type is given the preference on tool and gage work, except where extreme accuracy is required, or where the tool or gage is to be subjected to rough handling. The size of the dowel-pin is governed by its application. For locating nests, gage plates, etc., pins from 1⁄8 to 3⁄16 inch in diameter are satisfactory. For locating dies, the diameter of the dowel-pin should never be less than 1⁄4 inch; the general rule is to use dowel-pins of the same size as the screws used in fastening the work. The length of the dowel-pin should be about one and one-half to two times its diameter in each plate or part to be doweled. When hardened cylindrical dowel-pins are inserted in soft parts, ream the hole about 0.001 inch smaller than the dowel-pin. If the doweled parts are hardened, grind (or lap) the hole 0.0002 to 0.0003 inch under size. The hole should be ground or lapped straight, that is, without taper or “bell-mouth.” American National Standard Cotter Pins ANSI B18.8.1-1972 (R1994) L

C

D

C

A

B

L

A

B

Plane of Contact with Gage Dia. Aa & Width B Max.

Wire Width B Min.

Head Dia. C Min.

Prong Length D Min.

Hole Size

3⁄ 16

0.176

0.137

0.38

0.09

0.203

7⁄ 32

0.207

0.161

0.44

0.10

0.234

0.078

1⁄ 4

0.225

0.176

0.50

0.11

0.266

0.04

0.094

5⁄ 16

0.280

0.220

0.62

0.14

0.312

0.19

0.04

0.109

3⁄ 8

0.335

0.263

0.75

0.16

0.375

0.080

0.22

0.05

0.125

7⁄ 16

0.406

0.320

0.88

0.20

0.438

0.120

0.093

0.25

0.06

0.141

1⁄ 2

0.473

0.373

1.00

0.23

0.500

9⁄ 64

0.134

0.104

0.28

0.06

0.156

5⁄ 8

0.598

0.472

1.25

0.30

0.625

5⁄ 32

0.150

0.116

0.31

0.07

0.172

3⁄ 4

0.723

0.572

1.50

0.36

0.750

Nom. Size

Dia. Aa & Width B Max.

Wire Width B Min.

Head Dia. C Min.

Prong Length D Min.

Hole Size

1⁄ 32

0.032

0.022

0.06

0.01

0.047

3⁄ 64

0.048

0.035

0.09

0.02

0.062

1⁄ 16

0.060

0.044

0.12

0.03

5⁄ 64

0.076

0.057

0.16

3⁄ 32

0.090

0.069

7⁄ 64

0.104

1⁄ 8

Nom. Size

are: −0.004 inch for the 1⁄32- to 3⁄16-inch sizes, incl.; −0.005 inch for the 7⁄32- to 5⁄16-inch sizes, incl.; −0.006 inch for the 3⁄8- to 1⁄2-inch sizes, incl.; and −0.008 inch for the 5⁄8- and 3⁄4-inch sizes. Note: Tolerances for length are: up to 1 inch ± 0.030 inch, over 1 inch ±0.060 inch. All dimensions are in inches. a Tolerances


; ;


1668

DOWEL PINS

American National Standard Clevis Pins ANSI B18.8.1-1972 (R1994)

Radius

1

G

+ 0.02 – 0.00

B A

H D F

45

L 0.005 0.015

Optional Nom.Size (Basic Pin Dia.)

C

R

E Dia. (Break Corners)

Shank Dia.A Max

Head Dia.B Max.a

Head Hgt.C Max.b

Head Chamfer D Nom.c

Hole Dia.E Max.d

Point Dia.F Max.e

Pin Lgth.G Basicf

Head to HoleCenter H Max.g

Max.

Min.

Cotter Pin Size for Hole

Point Length L

3⁄ 16

0.186

0.32

0.07

0.02

0.088

0.15

0.58

0.504

0.055

0.035

1⁄ 16

1⁄ 4

0.248

0.38

0.10

0.03

0.088

0.21

0.77

0.692

0.055

0.035

1⁄ 16

5⁄ 16

0.311

0.44

0.10

0.03

0.119

0.26

0.94

0.832

0.071

0.049

3⁄ 32

3⁄ 8

0.373

0.51

0.13

0.03

0.119

0.33

1.06

0.958

0.071

0.049

3⁄ 32

7⁄ 16

0.436

0.57

0.16

0.04

0.119

0.39

1.19

1.082

0.071

0.049

3⁄ 32

1⁄ 2

0.496

0.63

0.16

0.04

0.151

0.44

1.36

1.223

0.089

0.063

1⁄ 8

5⁄ 8

0.621

0.82

0.21

0.06

0.151

0.56

1.61

1.473

0.089

0.063

1⁄ 8

3⁄ 4

0.746

0.94

0.26

0.07

0.182

0.68

1.91

1.739

0.110

0.076

5⁄ 32

7⁄ 8

0.871

1.04

0.32

0.09

0.182

0.80

2.16

1.989

0.110

0.076

5⁄ 32

0.996

1.19

0.35

0.10

0.182

0.93

2.41

2.239

0.110

0.076

5⁄ 32

a Tolerance is −0.05 inch.

b Tolerance is −0.02 inch. c Tolerance is ±0.01 inch.

d Tolerance is −0.015 inch. e Tolerance is −0.01 inch.

f Lengths tabulated are intended for use with standard clevises, without spacers. When other lengths are required, it is recommended that they be limited wherever possible to nominal lengths in 0.06-inch increments. g Tolerance is −0.020 inch. All dimensions are in inches.

British Standard for Metric Series Dowel Pins.—Steel parallel dowel pins specified in British Standard 1804:Part 2:1968 are divided into three grades which provide different degrees of pin accuracy. Grade 1 is a precision ground pin made from En 32A or En 32B low carbon steel (BS 970) or from high carbon steel to BS 1407 or BS 1423. Pins below 4 mm diameter are unhardened. Those of 4 mm diameter and above are hardened to a minimum of 750 HV 30 in accordance with BS 427, but if they are made from steels to BS 1407 or BS 1423 then the hardness shall be within the range 600 to 700 HV 30, in accordance with BS 427. The values of other hardness scales may be used in accordance with BS 860. Grade 2 is a ground pin made from any of the steels used for Grade 1. The pins are normally supplied unhardened, unless a different condition is agreed on between the purchaser and supplier. Grade 3 pins are made from En 1A free cutting steel (BS 970) and are supplied with a machined, bright rolled or drawn finish. They are normally supplied unhardened unless a different condition is agreed on between the purchaser and supplier. Pins of any grade may be made from different steels in accordance with BS 970, by mutual agreement between the purchaser and manufacturer. If steels other than those in the


Machinery's Handbook 27th Edition DOWEL PINS

1669

standard range are used, the hardness of the pins shall also be decided on by mutual agreement between purchaser and supplier. As shown in the illustration at the head of the accompanying table, one end of each pin is chamfered to provide a lead. The other end may be similarly chamfered, or domed. British Standard Parallel Steel Dowel Pins — Metric Series BS 1804: Part 2: 1968

Nom. Length L, mm 4 6 8 10 12 16 20 25 30 35 40 45 50 60 70 80 90 100 110 120

Nominal Diameter D, mm 4 5 6 8 Chamfer a max, mm 0.6 0.75 0.9 1.2 Standard Sizes

1

1.5

2

2.5

3

0.3

0.3

0.3

0.4

0.45

10

12

16

20

25

1.5

1.8

2.5

3

4

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d

d d

d

Limits of Tolerance on Diameter Gradea Tolerance Zone Nom. Dia., mm Over To & Incl. 3 3 6 10 14 18 24

6 10 14 18 24 30

1

2

3

m5

h7

h11

+7

+2

+9 +12 +15 +15 +17 +17

+4 +6 +7 +7 +8 +8

Limits of Tolerance, 0.001 mm 0 −12b 0 0 0 0 0 0

−12 −15 −18 −18 −21 −21

0

−60

0 0 0 0 0 0

−75 −90 −110 −110 −130 −130

a The limits of tolerance for grades 1 and 2 dowel pins have been chosen to provide satisfactory assembly when used in standard reamed holes (H7 and H8 tolerance zones). If the assembly is not satisfactory, refer to B.S. 1916: Part 1, Limits and Fits for Engineering, and select a different class of fit. b This tolerance is larger than that given in BS 1916, and has been included because the use of a closer tolerance would involve precision grinding by the manufacturer, which is uneconomic for a grade 2 dowel pin. The tolerance limits on the overall length of all grades of dowel pin up to and including 50 mm long are +0.5, −0.0 mm, and for pins over 50 mm long are +0.8, −0.0 mm. The Standard specifies that the roughness of the cylindrical surface of grades 1 and 2 dowel pins, when assessed in accordance with BS 1134, shall not be greater than 0.4 µm CLA (16 CLA).



1670

Table 1. American National Standard Hardened Ground Machine Dowel Pins ANSI/ASME B18.8.2-1995

Pin Diameter, A

3⁄ 32 1⁄ 8 5⁄ d 32 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1

Standard Series Pins

Point Diameter, B

Oversize Series Pins

Crown Height, C

Crown Radius, R

Range of Preferred Lengths,b L 3⁄ –3⁄ 16 4 …

Single Shear Load, for Carbon or Alloy Steel, Calculated lb

Suggested Hole Diameterc

Basic

Max

Min

Basic

Max

Min

Max

Min

Max

Min

0.0627 0.0783

0.0628 0.0784

0.0626 0.0782

0.0635 0.0791

0.0636 0.0792

0.0634 0.0790

0.058 0.074

0.048 0.064

0.020 0.026

0.008 0.010

Max

Min

400 620

0.0625 0.0781

0.0620 0.0776

0.0938

0.0940

0.0941

0.0939

0.0948

0.0949

0.0947

0.089

0.079

0.031

0.012

0.1250

0.1252

0.1253

0.1251

0.1260

0.1261

0.1259

0.120

0.110

0.041

0.016

5⁄ –1 16 3⁄ –2 8

1,600

0.1250

0.1245

0.1562

0.1564

0.1565

0.1563

0.1572

0.1573

0.1571

0.150

0.140

0.052

0.020

…

2,500

900

0.0937 0.1562

0.0932 0.1557

0.1875

0.1877

0.1878

0.1876

0.1885

0.1886

0.1884

0.180

0.170

0.062

0.023

0.2500

0.2502

0.2503

0.2501

0.2510

0.2511

0.2509

0.240

0.230

0.083

0.031

0.3125

0.3127

0.3128

0.3126

0.3135

0.3136

0.3134

0.302

0.290

0.104

0.039

0.3750

0.3752

0.3753

0.3751

0.3760

0.3761

0.3759

0.365

0.350

0.125

0.047

0.4375

0.4377

0.4378

0.4376

0.4385

0.4386

0.4384

0.424

0.409

0.146

0.055

0.5000

0.5002

0.5003

0.5001

0.5010

0.5011

0.5009

0.486

0.471

0.167

0.063

0.6250

0.6252

0.6253

0.6251

0.6260

0.6261

0.6259

0.611

0.595

0.208

0.078

0.7500

0.7502

0.7503

0.7501

0.7510

0.7511

0.7509

0.735

0.715

0.250

0.094

0.8750

0.8752

0.8753

0.8751

0.8760

0.8761

0.8759

0.860

0.840

0.293

0.109

1.0000

1.0002

1.0003

1.0001

1.0010

1.0011

1.0009

0.980

0.960

0.333

0.125

1⁄ –2 2 1⁄ –21⁄ 2 2 1⁄ –21⁄ 2 2 1⁄ –3 2 7⁄ –3 8 3⁄ , 1–4 4 1 1 ⁄4–5 11⁄2–6 2,21⁄2–6 2,21⁄2–5,6

3,600

0.1875

0.1870

6,400

0.2500

0.2495

10,000

0.3125

0.3120

14,350

0.3750

0.3745

19,550

0.4375

0.4370

25,500

0.5000

0.4995

39,900

0.6250

0.6245

57,000

0.7500

0.7495

78,000

0.8750

0.8745

102,000

1.0000

0.9995

a Where specifying nominal size as basic diameter, zeros preceding decimal and in the fourth decimal place are omitted. b Lengths increase in 1⁄ -inch steps up to 3⁄ inch, in 1⁄ -inch steps from 3⁄ inch to 1 inch, in 1⁄ -inch steps from 1 inch to 21⁄ inches, and in 1⁄ -inch steps above 21⁄ inches. 16 8 8 8 4 2 2 2 Tolerance on length is ±0.010 inch. c These hole sizes have been commonly used for press fitting Standard Series machine dowel pins into materials such as mild steels and cast iron. In soft materials such as aluminum or zinc die castings, hole size limits are usually decreased by 0.0005 inch to increase the press fit. d Nonpreferred sizes, not recommended for use in new designs. All dimensions are in inches.


DOWEL PINS

Nominal Sizea or Nominal Pin Diameter 1⁄ 0.0625 16 5⁄ d 0.0781 64


1671

If a dowel pin is driven into a blind hole where no provision is made for releasing air, the worker assembling the pin may be endangered, and damage may be caused to the associated component, or stresses may be set up. The appendix of the Standard describes one method of overcoming this problem by providing a small flat surface along the length of a pin to permit the release of air. For purposes of marking, the Standard states that each package or lot of dowel pins shall bear the manufacturer's name or trademark, the BS number, and the grade of pin. American National Standard Hardened Ground Machine Dowel Pins.—H a r d e n e d ground machine dowel pins are furnished in two diameter series: Standard Series having basic diameters 0.0002 inch over the nominal diameter, intended for initial installations; and Oversize Series having basic diameters 0.001 inch over the nominal diameter, intended for replacement use. Preferred Lengths and Sizes: The preferred lengths and sizes in which these pins are normally available are given in Table 1. Other sizes and lengths are produced as required by the purchaser. Effective Length: The effective length, Le, must not be less than 75 per cent of the overall length of the pin. Shear Strength: Single shear strength values are listed in Table 1. Prior versions of ANSI/ASME B18.8.2-1995 had listed double shear load minimum values and had specified a minimum single shear strength of 130,000 psi. See ANSI/ASME B18.8.2-1995, Appendix B for a description of the double shear test. Designation: These pins are designated by the following data in the sequence shown: Product name (noun first), including pin series, nominal pin diameter (fraction or decimal equivalent), length (fraction or decimal equivalent), material, and protective finish, if required. Examples: Pins, Hardened Ground Machine Dowel — Standard Series, 3⁄8 × 11⁄2, Steel, Phosphate Coated. Pins, Hardened Ground Machine Dowel — Oversize Series, 0.625 × 2.500, Steel Installation Precaution: Pins should not be installed by striking or hammering and when installing with a press, a shield should be used and safety glasses worn. American National Standard Hardened Ground Production Dowel Pins.—H a r d ened ground production dowel pins have basic diameters that are 0.0002 inch over the nominal pin diameter. Preferred Lengths and Sizes: The preferred lengths and sizes in which these pins are available are given in Table 2. Other sizes and lengths are produced as required by the purchaser. Shear Strength: Single shear strength values are listed in Table 2. Prior versions of ANSI/ASME B18.8.2-1995 had listed double shear load minimum values and had specified a minimum single shear strength of 102,000 psi. See ANSI/ASME B18.8.2-1995, Appendix B for a description of the double shear test. Ductility: These standard pins are sufficiently ductile to withstand being pressed into holes 0.0005 inch smaller than the nominal pin diameter in hardened steel without cracking or shattering. Designation: These pins are designated by the following data in the sequence shown: Product name (noun first), nominal pin diameter (fraction or decimal equivalent), length (fraction or decimal equivalent), material, and protective finish, if required. Examples: Pins, Hardened Ground Production Dowel, 1⁄8 × 3⁄4, Steel, Phosphate Coated Pins, Hardened Ground Production Dowel, 0.375 × 1.500, Steel



DOWEL PINS

Table 2. American National Standard Hardened Ground Production Dowel Pins ANSI/ASME B18.8.2-1995

Nominal Sizea or Nominal Pin Diameter

Corner Radius, R


Basic

Max

Min

Max

Min

Range of Preferred Lengths,b L

Max

Min

1⁄ 16

0.0625

0.0627

0.0628

0.0626

0.020

0.010

3⁄ – 16 1

395

0.0625

0.0620

3⁄ 32

0.0938

0.0939

0.0940

0.0938

0.020

0.010

3⁄ –2 16

700

0.0937

0.0932

7⁄ 64

0.1094

0.1095

0.1096

0.1094

0.020

0.010

3⁄ –2 16

950

0.1094

0.1089

1⁄ 8

0.1250

0.1252

0.1253

0.1251

0.020

0.010

3⁄ –2 16

1,300

0.1250

0.1245

5⁄ 32

0.1562

0.1564

0.1565

0.1563

0.020

0.010

3⁄ –2 16

2,050

0.1562

0.1557

3⁄ 16

0.1875

0.1877

0.1878

0.1876

0.020

0.010

3⁄ –2 16

2,950

0.1875

0.1870

7⁄ 32

0.2188

0.2189

0.2190

0.2188

0.020

0.010

1⁄ –2 4

3,800

0.2188

0.2183

Pin Diameter, A

Single Shear Load, Calculated,lb

1⁄ 4

0.2500

0.2502

0.2503

0.2501

0.020

0.010

1⁄ –11⁄ , 4 2

13⁄4, 2–21⁄2

5,000

0.2500

0.2495

5⁄ 16

0.3125

0.3127

0.3128

0.3126

0.020

0.010

5⁄ –11⁄ , 16 2

13⁄4, 2–21⁄2

8,000

0.3125

0.3120

3⁄ 8

0.3750

0.3752

0.3753

0.3751

0.020

0.010

3⁄ –11⁄ , 8 2

13⁄4, 2–3

11,500

0.3750

0.3745

a Where specifying nominal pin size in decimals, zeros preceding decimal and in the fourth decimal

place are omitted. b Lengths increase in 1⁄ -inch steps up to 1 inch, in 1⁄ -inch steps from 1 inch to 2 inches and then are 16 8 21⁄4, 21⁄2, and 3 inches. c These hole sizes have been commonly used for press fitting production dowel pins into materials such as mild steels and cast iron. In soft materials such as aluminum or zinc die castings, hole size limits are usually decreased by 0.0005 inch to increase the press fit. All dimensions are in inches.

American National Standard Unhardened Ground Dowel Pins.—U n h a r d e n e d ground dowel pins are normally produced by grinding the outside diameter of commercial wire or rod material to size. Consequently, the maximum diameters of the pins, as specified in Table 3, are below the minimum commercial stock sizes by graduated amounts from 0.0005 inch on the 1⁄16-inch nominal pin size to 0.0028 inch on the 1-inch nominal pin size. Preferred Lengths and Sizes: The preferred lengths and sizes in which unhardened ground pins are normally available are given in Table 3. Other sizes and lengths are produced as required by the purchaser. Shear Strength: These pins must have a single shear strength of 64,000 psi minimum for pins made from steel and 40,000 psi minimum for pins made from brass and must be capable of withstanding the minimum double shear loads given in Table 3 when tested in accordance with the procedure outlined in ANSI/ASME B18.8.2-1995, Appendix B. Designation: These pins are designated by the following data in the order shown: Product name (noun first), nominal pin diameter (fraction or decimal equivalent), length (fraction or decimal equivalent), material, and protective finish, if required. Examples: Pins, Unhardened Ground Dowel, 1⁄8 × 3⁄4, Steel Pins, Unhardened Ground Dowel, 0.250 × 2.500, Steel, Zinc Plated



1673

Table 3. American National Standard Unhardened Ground Dowel Pins ANSI/ASME B18.8.2-1995

Nominal Sizea or Basic Pin Diameter

1

Pin Diameter, A

Chamfer Length,C

Range of Preferred Lengths,b L


Double Shear Load Min, lb. CarbonSteel

Brass

0.0580

350

220

0.0907

0.0892

820

510

0.1062

0.1047

1,130

710

1⁄ –2 4

0.1217

0.1202

1,490

930

0.005

1⁄ –2 4

0.1528

0.1513

2,350

1,470

0.005

1⁄ –2 4

0.1840

0.1825

3,410

2,130

0.025

0.005

1⁄ –2 4

0.2151

0.2136

4,660

2,910

0.2465

0.025

0.005

1⁄ –11⁄ , 4 2

0.2462

0.2447

6,120

3,810

0.3094

0.3089

0.040

0.020

5⁄ –11⁄ , 16 2

13⁄4, 2–21⁄2

0.3085

0.3070

9,590

5,990

0.3750

0.3717

0.3712

0.040

0.020

3⁄ –11⁄ , 8 2

13⁄4, 2–21⁄2

0.3708

0.3693

13,850

8,650

7⁄ 16

0.4375

0.4341

0.4336

0.040

0.020

7⁄ –5⁄ , 3⁄ , 7⁄ –11⁄ , 16 8 4 8 2 13⁄4, 2–21⁄2

0.4331

0.4316

18,900

11,810

1⁄ 2

0.5000

0.4964

0.4959

0.040

0.020

1⁄ , 5⁄ , 3⁄ , 7⁄ , 1–11⁄ , 2 8 4 8 2 13⁄4, 2–3

0.4954

0.4939

24,720

15,450

5⁄ 8

0.6250

0.6211

0.6206

0.055

0.035

5⁄ , 3⁄ , 7⁄ , 8 4 8 2, 21⁄2–4

0.6200

0.6185

38,710

24,190

3⁄ 4

0.7500

0.7458

0.7453

0.055

0.035

3⁄ , 7⁄ , 1, 11⁄ , 11⁄ , 4 8 4 2 13⁄4, 2, 21⁄2–4

0.7446

0.7431

55,840

34,900

7⁄ 8

0.8750

0.8705

0.8700

0.070

0.050

7⁄ , 8

1, 11⁄4, 11⁄2, 13⁄4, 2, 21⁄2–4

0.8692

0.8677

76,090

47,550

1.0000

0.9952

0.9947

0.070

0.050

1, 11⁄4, 11⁄2, 13⁄4, 2, 21⁄2–4

0.9938

0.9923

99,460

62,160

Max

Min

Max

Max

Min

0.005

1⁄ –1 4

0.0595

0.025

0.005

1⁄ –11⁄ 4 2

0.1063

0.025

0.005

0.1223

0.1218

0.025

0.005

0.1562

0.1535

0.1530

0.025

0.1875

0.1847

0.1842

0.025

7⁄ 32

0.2188

0.2159

0.2154

1⁄ 4

0.2500

0.2470

5⁄ 16

0.3125

3⁄ 8

1⁄ 16

0.0625

0.0600

0.0595

0.025

3⁄ 32

0.0938

0.0912

0.0907

d7⁄ 64

0.1094

0.1068

1⁄ 8

0.1250

5⁄ 32 3⁄ 16

Min

…

13⁄4, 2–21⁄2

1–11⁄2, 13⁄4,

a Where specifying pin size in decimals, zeros preceding decimal and in the fourth decimal place are omitted. b Lengths increase in 1⁄ -inch increments from 1⁄ to 1 inch, in 1⁄ -inch increments from 1 inch to 2 16 4 8 inches, and in 1⁄4-inch increments from 2 to 21⁄2 inches, and in 1⁄2-inch increments from 21⁄2 to 4 inches. c These hole sizes have been found to be satisfactory for press fitting pins into mild steel and cast and malleable irons. In soft materials such as aluminum alloys or zinc die castings, hole size limits are usually decreased by 0.0005 inch to increase the press fit. d Nonpreferred size, not recommended for use in new designs.


American National Standard Straight Pins.—The diameter of both chamfered and square end straight pins is that of the commercial wire or rod from which the pins are made. The tolerances shown in Table 4 are applicable to carbon steel and some deviations in the diameter limits may be necessary for pins made from other materials.



STRAIGHT PINS

Table 4. American National Standard Chamfered and Square End Straight Pins ANSI/ASME B18.8.2-1995

CHAMFERED STRAIGHT PIN Nominal Sizea or Basic Pin Diameter 1⁄ 16 3⁄ 32 7⁄ 64 1⁄ 8 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4

Pin Diameter, A

SQUARE END STRAIGHT PIN

Chamfer Length, C

Max

Min

Max

Min

0.062 0.094 0.109 0.125 0.156

0.0625 0.0937 0.1094 0.1250 0.1562

0.0605 0.0917 0.1074 0.1230 0.1542

0.025 0.025 0.025 0.025 0.025

0.005 0.00 0.005 0.005 0.005

0.188 0.219 0.250

0.1875 0.2187 0.2500

0.1855 0.2167 0.2480

0.025 0.025 0.025

0.005 0.005 0.005

Nominal Sizeb or Basic Pin Diameter 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1

Pin Diameter, A

Chamfer Length, C

Max

Min

Max

Min

0.312 0.375 0.438 0.500 0.625

0.3125 0.3750 0.4375 0.5000 0.6250

0.3105 0.3730 0.4355 0.4980 0.6230

0.040 0.040 0.040 0.040 0.055

0.020 0.020 0.020 0.020 0.035

0.750 0.875 1.000

0.7500 0.8750 1.0000

0.7480 0.8730 0.9980

0.055 0.055 0.055

0.035 0.035 0.035

a Where specifying nominal size in decimals, zeros preceding decimal point are omitted. b Where specifying nominal size in decimals, zeros preceding decimal point are omitted.


Length Increments: Lengths are as specified by the purchaser; however, it is recommended that nominal pin lengths be limited to increments of not less than 0.062 inch. Material: Straight pins are normally made from cold drawn steel wire or rod having a maximum carbon content of 0.28 per cent. Where required, pins may also be made from corrosion resistant steel, brass, or other metals. Designation: Straight pins are designated by the following data, in the sequence shown: Product name (noun first), nominal size (fraction or decimal equivalent), material, and protective finish, if required. Examples: Pin, Chamfered Straight, 1⁄8 × 1.500, Steel Pin, Square End Straight, 0.250 × 2.250, Steel, Zinc Plated American National Standard Taper Pins.—Taper pins have a uniform taper over the pin length with both ends crowned. Most sizes are supplied in commercial and precision classes, the latter having generally tighter tolerances and being more closely controlled in manufacture. Diameters: The major diameter of both commercial and precision classes of pins is the diameter of the large end and is the basis for pin size. The diameter at the small end is computed by multiplying the nominal length of the pin by the factor 0.02083 and subtracting the result from the basic pin diameter. See also Table 5. Taper: The taper on commercial class pins is 0.250 ± 0.006 inch per foot and on the precision class pins is 0.250 ± 0.004 inch per foot of length. Materials: Unless otherwise specified, taper pins are made from SAE 1211 steel or cold drawn SAE 1212 or 1213 steel or equivalents, and no mechanical property requirements apply. Hole Sizes: Under most circumstances, holes for taper pins require taper reaming. Sizes and lengths of taper pins for which standard reamers are available are given in Table 6. Drilling specifications for taper pins are given below.


Machinery's Handbook 27th Edition TAPER PINS

1675

Designation: Taper pins are designated by the following data in the sequence shown: Product name (noun first), class, size number (or decimal equivalent), length (fraction or three-place decimal equivalent), material, and protective finish, if required. Examples: Pin, Taper (Commercial Class) No. 0 × 3⁄4, Steel Pin, Taper (Precision Class) 0.219 × 1.750, Steel, Zinc Plated Table 5. Nominal Diameter at Small Ends of Standard Taper Pins Pin Number and Small End Diameter for Given Length

Pin Length in inches

0

1

2

3

4

5

6

7

8

9

10

3⁄ 4

0.140

0.156

0.177

0.203

0.235

0.273

0.325

0.393

0.476

0.575

0.690

11⁄4

0.135 0.130

0.151 0.146

0.172 0.167

0.198 0.192

0.230 0.224

0.268 0.263

0.320 0.315

0.388 0.382

0.471 0.466

0.570 0.565

0.685 0.680

11⁄2

0.125

0.141

0.162

0.187

0.219

0.258

0.310

0.377

0.460

0.560

0.675

13⁄4

0.120

0.136

0.157

0.182

0.214

0.252

0.305

0.372

0.455

0.554

0.669

2 21⁄4

0.114 0.109

0.130 0.125

0.151 0.146

0.177 0.172

0.209 0.204

0.247 0.242

0.299 0.294

0.367 0.362

0.450 0.445

0.549 0.544

0.664 0.659

21⁄2

0.104

0.120

0.141

0.166

0.198

0.237

0.289

0.356

0.440

0.539

0.654

23⁄4

0.099

0.115

0.136

0.161

0.193

0.232

0.284

0.351

0.434

0.534

0.649

3 31⁄4

0.094 …

0.110 …

0.131 …

0.156 0.151

0.188 0.182

0.227 0.221

0.279 0.273

0.346 0.340

0.429 0.424

0.528 0.523

0.643 0.638

31⁄2

…

…

…

0.146

0.177

0.216

0.268

0.335

0.419

0.518

0.633

33⁄4

…

…

…

0.141

0.172

0.211

0.263

0.330

0.414

0.513

0.628

4 41⁄4

… …

… …

… …

0.136 0.131

0.167 0.162

0.206 0.201

0.258 0.253

0.326 0.321

0.409 0.403

0.508 0.502

0.623 0.617

41⁄2

…

…

…

0.125

0.156

0.195

0.247

0.315

0.398

0.497

0.612

5 51⁄2

… …

… …

… …

… …

0.146 …

0.185 …

0.237 …

0.305 0.294

0.389 0.377

0.487 0.476

0.602 0.591

6

…

…

…

…

…

…

…

0.284

0.367

0.466

0.581

1

Drilling Specifications for Taper Pins.—When helically fluted taper pin reamers are used, the diameter of the through hole drilled prior to reaming is equal to the diameter at the small end of the taper pin. (See Table 5.) However, when straight fluted taper reamers are to be used, it may be necessary, for long pins, to step drill the hole before reaming, the number and sizes of the drills to be used depending on the depth of the hole (pin length). To determine the number and sizes of step drills required: Find the length of pin to be used at the top of the chart on page 1676 and follow this length down to the intersection with that heavy line which represents the size of taper pin (see taper pin numbers at the right-hand end of each heavy line). If the length of pin falls between the first and second dots, counting from the left, only one drill is required. Its size is indicated by following the nearest horizontal line from the point of intersection (of the pin length) on the heavy line over to the drill diameter values at the left. If the intersection of pin length comes between the second and third dots, then two drills are required. The size of the smaller drill then corresponds to the intersection of the pin length and the heavy line and the larger is the corresponding drill diameter for the intersection of one-half this length with the heavy line. Should the pin length fall between the third and fourth dots, three drills are required. The smallest drill will have a diameter corresponding to the intersection of the total pin length with the heavy line, the next in size will have a diameter corresponding to the intersection of two-thirds of this length with the heavy line and the largest will have a diameter corresponding to the intersection of one-third of this length with the heavy line. Where the intersection falls between two drill sizes, use the smaller.



TAPER-PIN REAMER DRILLS Chart to Facilitate Selection of Number and Sizes of Drills for Step-Drilling Prior to Taper Reaming

Drill dia 0.0156 0.0312 0.0469 0.0625 0.0781 0.0938 0.1094 0.1250 0.1406 0.1562 0.1719 0.1875 0.2031 0.2188 0.2344 0.2500 0.2656 0.2812 0.2969 0.3125 0.3281 0.3438 0.3594 0.3750 0.3906 0.4062 0.4219 0.4375 0.4531 0.4688 0.4844 0.5000 0.5156 0.5312 0.5469 0.5625 0.5781 0.5938 0.6094 0.6250 0.6406 0.6562 0.6719 0.6875 0.7031

Pin dia

Length of Pin in Inches 2 3 4

1

5

6

7/0

0.0625 0.0780 0.0940 0.1090 0.1250 0.1410 0.1560

6/0 5/0 4/0 3/0

2/0

0 1 2 3 4

0.1720 0.1930 0.2190

5 6

0.2500 0.2890 7

0.3410 8

0.4090 9

0.4920

10

0.5910

0.7060


Machinery's Handbook 27th Edition TAPER AND GROOVED PINS

1677

Examples:For a No. 10 taper pin 6inches long, three drills would be used, of the sizes and for the depths shown in the accompanying diagram. For a No. 10 taper pin 3-inches long, two drills would be used because the 3inch length falls between the second and third dots. The first or through drill will be 0.6406 inch and the second drill, 0.6719 inch for a depth of 11⁄2 inches. Table 6. American National Standard Taper Pins ANSI/ASME B18.8.2-1995

Pin Size Number and Basic Pin Dia.a

Major Diameter (Large End), A Commercial Class Precision Class Max Min Max Min

End Crown Radius, R Max Min

Range of Lengths,b L Other Stand. Reamer Avail.c

7⁄ 0 6⁄ 0 5⁄ 0 4⁄ 0 3⁄ 0 2⁄ 0

0.0625

0.0638

0.0618

0.0635

0.0625

0.072

0.052

…

0.0780

0.0793

0.0773

0.0790

0.0780

0.088

0.068

…

0.0940

0.0953

0.0933

0.0950

0.0940

0.104

0.084

0.1090

0.1103

0.1083

0.1100

0.1090

0.119

0.099

0.1250

0.1263

0.1243

0.1260

0.1250

0.135

0.115

0.1410

0.1423

0.1403

0.1420

0.1410

0.151

0.131

0

0.1560

0.1573

0.1553

0.1570

0.1560

0.166

0.146

1

0.1720

0.1733

0.1713

0.1730

0.1720

0.182

0.162

2

0.1930

0.1943

0.1923

0.1940

0.1930

0.203

0.183

3

0.2190

0.2203

0.2183

0.2200

0.2190

0.229

0.209

4

0.2500

0.2513

0.2493

0.2510

0.2500

0.260

0.240

5

0.2890

0.2903

0.2883

0.2900

0.2890

0.299

0.279

6

0.3410

0.3423

0.3403

0.3420

0.3410

0.351

0.331

7

0.4090

0.4103

0.4083

0.4100

0.4090

0.419

0.399

8

0.4920

0.4933

0.4913

0.4930

0.4920

0.502

0.482

9

0.5910

0.5923

0.5903

0.5920

0.5910

0.601

0.581

10

0.7060

0.7073

0.7053

0.7070

0.7060

0.716

0.696

11 12 13 14

0.8600 1.0320 1.2410 1.5210

0.8613 1.0333 1.2423 1.5223

0.8593 1.0313 1.2403 1.5203

… … … …

… … … …

0.870 1.042 1.251 1.531

0.850 1.022 1.231 1.511

1⁄ –1 4 1⁄ –1 4 1⁄ –1 4 1⁄ –11⁄ 2 4 1⁄ –11⁄ 2 4 3⁄ –11⁄ 4 4 3⁄ –11⁄ 4 2 3⁄ –13⁄ 4 4 3⁄ –2 4 1 1–2 ⁄2 11⁄4–3 11⁄4–33⁄4 11⁄4–41⁄2 11⁄4–51⁄4 11⁄2–6

… … … …

1⁄ –1 4 1⁄ –1⁄ 4 2 11⁄4, 11⁄2 11⁄4–2 11⁄4–2 11⁄2–21⁄2 11⁄2–3 11⁄2–3 13⁄4–3

2–4 21⁄4–4 23⁄4–6 31⁄4–6 4–8 43⁄4–8 51⁄2–8 61⁄4–8 2–8 2–9 3–11 3–13

a When specifying nominal pin size in decimals, zeros preceding the decimal and in the fourth decimal place are omitted. b Lengths increase in 1⁄ -inch steps up to 1 inch and in 1⁄ -inch steps above 1 inch. 8 4 c Standard reamers are available for pin lengths in this column. All dimensions are in inches. For nominal diameters, B, see Table 5.

American National Standard Grooved Pins.—These pins have three equally spaced longitudinal grooves and an expanded diameter over the crests of the ridges formed by the material displaced when the grooves are produced. The grooves are aligned with the axes of the pins. There are seven types of grooved pins as shown in the illustration on page 1679. Standard Sizes and Lengths: The standard sizes and lengths in which grooved pins are normally available are given in Table 7.



PINS AND STUDS

Materials: Grooved pins are normally made from cold drawn low carbon steel wire or rod. Where additional performance is required, carbon steel pins may be supplied surface hardened and heat treated to a hardness consistent with the performance requirements. Pins may also be made from alloy steel, corrosion resistant steel, brass, Monel and other non-ferrous metals having chemical properties as agreed upon between manufacturer and purchaser. Performance Requirements: Grooved pins are required to withstand the minimum double shear loads given in Table 7 for the respective materials shown, when tested in accordance with the Double Shear Testing of Pins as set forth in ANSI/ASME B18.8.2-1995, Appendix B. Hole Sizes: To obtain maximum product retention under average conditions, it is recommended that holes for the installation of grooved pins be held as close as possible to the limits shown in Table 7. The minimum limits correspond to the drill size, which is the same as the basic pin diameter. The maximum limits are generally suitable for length-diameter ratios of not less than 4 to 1 nor greater than 10 to 1. For smaller length-to-diameter ratios, the hole should be held closer to the minimum limits where retention is critical. Conversely for larger ratios where retention requirements are less important, it may be desirable to increase the hole diameters beyond the maximum limits shown. Designation: Grooved pins are designated by the following data in the sequence shown: Product name (noun first) including type designation, nominal size (number, fraction or decimal equivalent), length (fraction or decimal equivalent), material, including specification or heat treatment where necessary, protective finish, if required. Examples: Pin, Type A Grooved, 3⁄32 × 3⁄4, Steel, Zinc Plated Pin, Type F Grooved, 0.250 × 1.500, Corrosion Resistant Steel American National Standard Grooved T-Head Cotter Pins and Round Head Grooved Drive Studs.—The cotter pins have a T-head and the studs a round head. Both pins and studs have three equally spaced longitudinal grooves and an expanded diameter over the crests of the raised ridges formed by the material displaced when the grooves are formed. Standard Sizes and Lengths: The standard sizes and range of standard lengths are given in Tables 8 and 9. Material: Unless otherwise specified these pins are made from low carbon steel. Where so indicated by the purchaser they may be made from corrosion resistant steel, brass or other non-ferrous alloys. Hole Sizes: To obtain optimum product retention under average conditions, it is recommended that holes for the installation of grooved T-head cotter pins and grooved drive studs be held as close as possible to the limits tabulated. The minimum limits given correspond to the drill size, which is equivalent to the basic shank diameter. The maximum limits shown are generally suitable for length-diameter ratios of not less than 4 to 1 and not greater than 10 to 1. For smaller length-to-diameter ratios, the holes should be held closer to minimum limits where retention is critical. Conversely, for larger length-to-diameter ratios or where retention requirements are not essential, it may be desirable to increase the hole diameter beyond the maximum limits shown. Designation: Grooved T-head cotter pins and round head grooved drive studs are designated by the following data, in the order shown: Product name (noun first), nominal size (number, fraction or decimal equivalent), length (fraction or decimal equivalent), material including specification or heat treatment where necessary, and protective finish, if required. Examples: Pin, Grooved T-Head Cotter, 1⁄4 × 11⁄4, Steel, Zinc Plated Drive Stud, Round Head Grooved, No. 10 × 1⁄2, Corrosion Resistant Steel



L

L

See Note 3 B

E

A

F See Note 2 Type A B

See Note 3

D

D

C

C

C

A

A

F See Note 2 Type C E

L 2

E

B

L

E

30° – 45° Both Ends Type F

E E

L

L 2

L L 4

E

L 2

PINS

A

F See Note 2 Type B

A

F

See Note 2 Type D

E See Note 3

J

A

F

See Note 2 Type E

F

E

L H

B

F

L 2 C

K A

G Type G

F Both Ends – See Note 2


1679

Types of American National Standard Grooved Pins, ANSI/ASME B18.8.2-1995 (For notes see bottom of Table 7.)


Chamfer Pilot Length, C Length,b D Ref Min 0.015 … 0.031 … 0.031 0.016 0.031 0.016 0.031 0.016 0.031 0.016 0.031 0.016 0.062 0.031 0.062 0.031 0.062 0.031 0.062 0.031 0.094 0.047 0.094 0.047 0.094 0.047 0.094 0.047

Crown Height,b E Max Min … … … … 0.0115 0.0015 0.0137 0.0037 0.0141 0.0041 0.0160 0.0060 0.0180 0.0080 0.0220 0.0120 0.0230 0.0130 0.0270 0.0170 0.0310 0.0210 0.0390 0.0290 0.0440 0.0340 0.0520 0.0420 0.0570 0.0470

Crown Radius,b F Max Min … … … … 0.088 0.068 0.104 0.084 0.135 0.115 0.150 0.130 0.166 0.146 0.198 0.178 0.260 0.240 0.291 0.271 0.322 0.302 0.385 0.365 0.479 0.459 0.541 0.521 0.635 0.615

Neck Width, G Max Min … … … … … … … … 0.038 0.028 0.038 0.028 0.069 0.059 0.069 0.059 0.069 0.059 0.101 0.091 0.101 0.091 0.132 0.122 0.132 0.122 0.195 0.185 0.195 0.185

Shoulder Length, H Max Min … … … … … … … … 0.041 0.031 0.041 0.031 0.041 0.031 0.057 0.047 0.057 0.047 0.072 0.062 0.072 0.062 0.104 0.094 0.135 0.125 0.135 0.125 0.135 0.125

Neck Radius, J Ref … … … … 0.016 0.016 0.031 0.031 0.031 0.047 0.047 0.062 0.062 0.094 0.094

Neck Diameter, K Max Min … … … … … … … … 0.067 0.057 0.082 0.072 0.088 0.078 0.109 0.099 0.130 0.120 0.151 0.141 0.172 0.162 0.214 0.204 0.255 0.245 0.298 0.288 0.317 0.307

Range of Standard Lengthsc 1⁄ –1⁄ 8 2 1⁄ –5⁄ 8 8 1⁄ –1 8 1⁄ –1 4 1⁄ –11⁄ 4 4 1⁄ –11⁄ 4 4 1⁄ –11⁄ 4 2 3⁄ –2 8 3⁄ –21⁄ 8 4 1⁄ –3 2 1⁄ –31⁄ 2 4 5⁄ –31⁄ 8 2 3⁄ –41⁄ 4 4 7⁄ –41⁄ 8 2 1–41⁄2

a For expanded diameters, B, see ANSI/ASME B18.8.2-1995. b Pins in 1⁄ - and 3⁄ -inch sizes of any length and all sizes of 1⁄ -inch nominal length or shorter are not crowned or chamfered. 32 64 4 c Standard lengths increase in 1⁄ -inch steps from 1⁄ to 1 inch, and in 1⁄ -inch steps above 1 inch. Standard lengths for the 1⁄ -, 3⁄ -, 1⁄ -, 8 8 4 32 64 16 3 7 1 length for the ⁄32-, ⁄64-, and ⁄8-inch sizes do not apply to Type G grooved pins. d Non-stock items, not recommended for new designs.

and 5⁄64-inch sizes and the 1⁄4-inch

Nominal Pin Size Pin Material

1⁄ 32

3⁄ 64

Steels

1⁄ 16

5⁄ 64

3⁄ 32

7⁄ 64

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

15,000 35,200 24,800 12,100

19,600 46,000 32,400 15,800

0.4428 0.4375

0.5060 0.5000

Double Shear Load, Min, lb

Low Carbon Alloy (Rc 40 – 48 hardness) Corrosion Resistant Brass Maximum Diameter Minimum Diameter

100 180 140 60

220 400 300 140

0.0324 0.0312

0.0482 0.0469

410 620 890 1,220 1,600 2,300 3,310 4,510 5,880 7,660 11,000 720 1,120 1,600 2,180 2,820 4,520 6,440 8,770 11,500 17,900 26,000 540 860 1,240 1,680 2,200 3,310 4,760 6,480 8,460 12,700 18,200 250 390 560 760 990 1,540 2,220 3,020 3,950 6,170 9,050 Recommended Hole Sizes for Unplated Pins (The minimum drill size is the same as the pin size. See also text on page 1678.) 0.0640 0.0798 0.0956 0.1113 0.1271 0.1587 0.1903 0.2219 0.2534 0.3166 0.3797 0.0625 0.0781 0.0938 0.1094 0.1250 0.1563 0.1875 0.2188 0.2500 0.3125 0.3750



PINS AND STUDS

Pin Diameter,a A Max Min 0.0312 0.0302 0.0469 0.0459 0.0625 0.0615 0.0781 0.0771 0.0938 0.0928 0.1094 0.1074 0.1250 0.1230 0.1563 0.1543 0.1875 0.1855 0.2188 0.2168 0.2500 0.2480 0.3125 0.3105 0.3750 0.3730 0.4375 0.4355 0.5000 0.4980

1680

Table 7. American National Standard Grooved Pins ANSI/ASME B18.8.2-1995 Nominal Size or Basic Pin Diameter 1⁄ d 0.0312 32 3⁄ d 0.0469 64 1⁄ 0.0625 16 5⁄ d 0.0781 64 3⁄ 0.0938 32 7⁄ d 0.1094 64 1⁄ 0.1250 8 5⁄ 0.1563 32 3⁄ 0.1875 16 7⁄ 0.2188 32 1⁄ 0.2500 4 5⁄ 0.3125 16 3⁄ 0.3750 8 7⁄ 0.4375 16 1⁄ 0.5000 2

Machinery's Handbook 27th Edition PINS AND STUDS

1681

Table 8. American National Standard Grooved T-Head Cotter Pins ANSI/ASME B18.8.2-1995

Nominal Sizea or Basic Shank Dia. 5⁄ 0.156 32 3⁄ 0.187 16 1⁄ 0.250 4 5⁄ 0.312 16 23⁄ 0.359 64 1⁄ 0.500 2

Shank Diameter, A Max 0.154 0.186 0.248 0.310 0.358 0.498

Length, N

Min 0.150 0.182 0.244 0.305 0.353 0.493

Max 0.08 0.09 0.12 0.16 0.18 0.25

Head Dia., O Max 0.26 0.30 0.40 0.51 0.57 0.79

Min 0.24 0.28 0.38 0.48 0.54 0.76

Head Height, P

Head Width, Q

Max 0.11 0.13 0.17 0.21 0.24 0.32

Max 0.18 0.22 0.28 0.34 0.38 0.54

Min 0.09 0.11 0.15 0.19 0.22 0.30

Min 0.15 0.18 0.24 0.30 0.35 0.49

Range of Standard Lengths,b L 3⁄ –11⁄ 4 8 3⁄ –11⁄ 4 4 1–11⁄2 1 1 ⁄8–2 11⁄4–2

2–3

Recommended Hole Size Max 0.161 0.193 0.257 0.319 0.366 0.508

Min 0.156 0.187 0.250 0.312 0.359 0.500

a When specifying nominal size in decimals, zeros preceding decimal point and in the fourth decimal

place are omitted. b Lengths increase in 1⁄ -inch steps from 3⁄ to 11⁄ inch and in 1⁄ -inch steps above 11⁄ inches. For groove 8 4 4 4 4 length, M, dimensions see ANSI/ASME B18.8.2-1995. All dimensions are in inches.

For expanded diameter, B, dimensions, see ANSI/ASME B18.8.2-1995.

Table 9. American National Standard Round Head Grooved Drive Studs ANSI/ASME B18.8.2-1995

Stud Size Number and Basic Shank Diametera 0 0.067 2 0.086 4 0.104 6 0.120 7 0.136 8 0.144 10 0.161 12 0.196 14 0.221 16 0.250

Shank Diameter, A Head Diameter, O Max 0.067 0.086 0.104 0.120 0.136 0.144 0.161 0.196 0.221 0.250

Min 0.065 0.084 0.102 0.118 0.134 0.142 0.159 0.194 0.219 0.248

Max 0.130 0.162 0.211 0.260 0.309 0.309 0.359 0.408 0.457 0.472

Min 0.120 0.146 0.193 0.240 0.287 0.287 0.334 0.382 0.429 0.443

Head Height, P Max 0.050 0.070 0.086 0.103 0.119 0.119 0.136 0.152 0.169 0.174

Min 0.040 0.059 0.075 0.091 0.107 0.107 0.124 0.140 0.156 0.161

Range of Standard Lengths,b L 1⁄ –1⁄ 8 4 1⁄ –1⁄ 8 4 3⁄ –5⁄ 16 16 1⁄ –3⁄ 4 8 5⁄ –1⁄ 16 2 3⁄ –5⁄ 8 8 3⁄ –5⁄ 8 8 1⁄ 3⁄ 24 1⁄ –3⁄ 2 4 1⁄ 2

Recommended Hole Size Max 0.0686 0.0877 0.1059 0.1220 0.1382 0.1463 0.1636 0.1990 0.2240 0.2534

Min 0.0670 0.0860 0.1040 0.1200 0.1360 0.1440 0.1610 0.1960 0.2210 0.2500

a Where

Drill Size 51 44 37 31 29 27 20 9 2 1⁄ 4

specifying nominal size in decimals, zeros preceding decimal point and in the fourth decimal place are omitted. b Lengths increase in 1⁄ -inch steps from 1⁄ to 3⁄ inch and in 1⁄ -inch steps above 3⁄ inch. 16 8 8 8 8 All dimensions are in inches. For pilot length, M, and expanded diameter, B, dimensions see ANSI/ASME B18.8.2-1995.



PINS Table 10. American National Standard Slotted Type Spring Pins ANSI/ASME B18.8.2-1995

Nominal Sizea or Basic Pin Diameter

Average Pin Diameter, A Max Min

Cham fer Dia., B Max

Chamfer Length, C Max Min

Material Stock SAE Thick Recommended SAE 1070 – 30302 BerylHole ness, lium and 1095 and Size F SAE 51420 30304 Copper Basic Max Min Double Shear Load, Min, lb

Range of Practical Lengthsb

1⁄ 16

0.062

0.069

0.066

0.059

0.028

0.007

0.012

0.065

0.062

430

250

270

3⁄ –1 16

5⁄ 64

0.078

0.086

0.083

0.075

0.032

0.008

0.018

0.081

0.078

800

460

500

3⁄ –11⁄ 16 2

3⁄ 32

0.094

0.103

0.099

0.091

0.038

0.008

0.022

0.097

0.094

1,150

670

710

3⁄ –11⁄ 16 2

1⁄ 8

0.125

0.135

0.131

0.122

0.044

0.008

0.028

0.129

0.125

1,875

1,090

1,170

5⁄ –2 16

9⁄ 64

0.141

0.149

0.145

0.137

0.044

0.008

0.028

0.144

0.140

2,175

1,260

1,350

3⁄ –2 8

5⁄ 32

0.156

0.167

0.162

0.151

0.048

0.010

0.032

0.160

0.156

2,750

1,600

1,725

7⁄ –21⁄ 16 2

3⁄ 16

0.188

0.199

0.194

0.182

0.055

0.011

0.040

0.192

0.187

4,150

2,425

2,600

1⁄ –21⁄ 2 2

7⁄ 32

0.219

0.232

0.226

0.214

0.065

0.011

0.048

0.224

0.219

5,850

3,400

3,650

1⁄ –3 2

1⁄ 4

0.250

0.264

0.258

0.245

0.065

0.012

0.048

0.256

0.250

7,050

4,100

4,400

1⁄ –31⁄ 2 2

5⁄ 16

0.312

0.330

0.321

0.306

0.080

0.014

0.062

0.318

0.312

10,800

6,300

6,750

3⁄ –4 4

3⁄ 8

0.375

0.395

0.385

0.368

0.095

0.016

0.077

0.382

0.375

16,300

9,500

10,200

3⁄ , 7⁄ , 1,11⁄ , 4 8 4 11⁄2,13⁄4, 2–4

7⁄ 16

0.438

0.459

0.448

0.430

0.095

0.017

0.077

0.445

0.437

19,800

11,500

12,300

1, 11⁄4,11⁄2, 13⁄4, 2–4

1⁄ 2

0.500

0.524

0.513

0.485

0.110

0.025

0.094

0.510

0.500

27,100

15,800

17,000

11⁄4, 11⁄2, 13⁄4, 2–4

5⁄ 8

0.625

0.653

0.640

0.608

0.125

0.030

0.125

0.636

0.625

46,000

18,800

…

2–6

3⁄ 4

0.750

0.784

0.769

0.730

0.150

0.030

0.150

0.764

0.750

66,000

23,200

…

2–6

a Where specifying nominal size in decimals, zeros preceding decimal point are omitted. b Length increments are 1⁄ inch from 1⁄ to 1 inch; 1⁄ from 1 inch to 2 inches; and 1⁄ inch from 2 inches 16 8 8 4 to 6 inches.


American National Standard Spring Pins.—These pins are made in two types: one type has a slot throughout its length; the other is shaped into a coil. Preferred Lengths and Sizes: The preferred lengths and sizes in which these pins are normally available are given in Tables 10 and 11. Materials: Spring pins are normally made from SAE 1070–1095 carbon steel, SAE 6150H alloy steel, SAE types 51410 through 51420, 30302 and 30304 corrosion resistant steels, and beryllium copper alloy, heat treated or cold worked to attain the hardness and performance characteristics set forth in ANSI/ASME B18.8.2-1995. Designation: Spring pins are designated by the following data in the sequence shown: Examples: Pin, Coiled Spring, 1⁄4 × 11⁄4, Standard Duty, Steel, Zinc Plated Pin, Slotted Spring, 1⁄2 × 3, Steel, Phosphate Coated



Table 11. American National Standard Coiled Type Spring Pins ANSI/ASME B18.8.2-1995

Pin Diameter, A Heavy Duty Max Min … … … … … … … … 0.070 0.066 0.086 0.082 0.103 0.098 0.118 0.113 0.136 0.130 0.168 0.161 0.202 0.194 0.235 0.226 0.268 0.258 0.334 0.322 0.400 0.386 0.466 0.450 0.532 0.514 0.658 0.640 0.784 0.766

Chamfer Light Duty Max … … … … 0.073 0.089 0.106 0.121 0.139 0.172 0.207 0.240 0.273 0.339 0.405 0.471 0.537 … …

Min … … … … 0.067 0.083 0.099 0.114 0.131 0.163 0.196 0.228 0.260 0.324 0.388 0.452 0.516 … …

Dia., B Max 0.029 0.037 0.045 0.050 0.059 0.075 0.091 0.106 0.121 0.152 0.182 0.214 0.243 0.304 0.366 0.427 0.488 0.613 0.738

Length, C Ref 0.024 0.024 0.024 0.024 0.028 0.032 0.038 0.038 0.044 0.048 0.055 0.065 0.065 0.080 0.095 0.095 0.110 0.125 0.150

Recommended Hole Size Max Min 0.032 0.031 0.040 0.039 0.048 0.046 0.053 0.051 0.065 0.061 0.081 0.077 0.097 0.093 0.112 0.108 0.129 0.124 0.160 0.155 0.192 0.185 0.224 0.217 0.256 0.247 0.319 0.308 0.383 0.370 0.446 0.431 0.510 0.493 0.635 0.618 0.760 0.743

1070–1095 and 51420

30302 and 30304

Standard Duty 90a 65 100 135a 145 190a 190 250a 330 265 550 425 775 600 1,050 825 1,400 1,100 2,200 1,700 3,150 2,400 4,200 3,300 5,500 4,300 8,700 6,700 12,600 9,600 17,000 13,300 22,500 17,500 … 35,000b … 50,000b

SAE Material Number 1070–1095 30302 and and 51420 30304 Double Shear Load, Min, lb Heavy Duty … … … … … … … … 475 360 800 575 1,150 825 1,500 1,150 2,000 1,700 3,100 2,400 4,500 3,500 5,900 4,600 7,800 6,200 12,000 9,300 18,000 14,000 23,500 18,000 32,000 25,000 … 48,000b … 70,000b

1070–1095 and 51420

30302 and 30304

Light Duty … … … … … … … … 205 160 325 250 475 360 650 500 825 650 1,300 1,000 1,900 1,450 2,600 2,000 3,300 2,600 5,200 4,000 … … … … … … … … … …



1683

a Sizes 1⁄ inch through 0.052 inch are not available in SAE 1070–1095 carbon steel. 32 b Sizes 5⁄ inch and larger are produced from SAE 6150H alloy steel, not SAE 1070–1095 carbon steel. Practical lengths, L, for sizes 1⁄ through 0.052 inch are 1⁄ through 8 32 8 5⁄ inch and for the 7⁄ -inch size, 1⁄ through 13⁄ inches. For lengths of other sizes see Table 10. 8 64 4 4

PINS

Nominal Size or Basic Pin Diameter 1⁄ 0.031 32 0.039 3⁄ 0.047 64 0.052 1⁄ 0.062 16 5⁄ 0.078 64 3⁄ 0.094 32 7⁄ 0.109 64 1⁄ 0.125 8 5⁄ 0.156 32 3⁄ 0.188 16 7⁄ 0.219 32 1⁄ 0.250 4 5⁄ 0.312 16 3⁄ 0.375 8 7⁄ 0.438 16 1⁄ 0.500 2 5⁄ 0.625 8 3⁄ 0.750 4

Standard Duty Max Min 0.035 0.033 0.044 0.041 0.052 0.049 0.057 0.054 0.072 0.067 0.088 0.083 0.105 0.099 0.120 0.114 0.138 0.131 0.171 0.163 0.205 0.196 0.238 0.228 0.271 0.260 0.337 0.324 0.403 0.388 0.469 0.452 0.535 0.516 0.661 0.642 0.787 0.768


RETAINING RINGS

RETAINING RINGS Retaining Rings.—The purpose of a retaining ring is to act as an artificial shoulder that will retain an object in a housing (internal ring), as shown in Fig. 1, or on a shaft (external ring). Two types of retaining ring are common, the stamped ring and the spiral-wound ring. The stamped type of retaining ring, or snap ring, is stamped from tempered sheet metal and has a nonuniform cross-section. The typical spiral-wound retaining ring has a uniform cross-section and is made up of two or more turns of coiled, spring-tempered steel, although one-turn spiral-wound rings are common. Spiral-wound retaining rings provide a continuous gapless shoulder to a housing or shaft. Most stamped rings can only be installed at or near the end of a shaft or housing. The spiral-wound design generally requires installation from the end of a shaft or housing. Both types, stamped and spiral, are usually installed into grooves on the shaft or housing.

Housing

Retained Part

Max. Groove Chamfer or Radius + Max. Side Clearance + Max. Retained Part Chamfer or Radius = Maximum Total Radius or Chamfer

Fig. 1. Typical Retaining Ring Installation Showing Maximum Total Radius or Chamfer (Courtesy Spirolox Retaining Rings)

In the section that follows, Tables 1 through 6 give dimensions and data on general-purpose tapered and reduced cross-section metric retaining rings (stamped type) covered by ANSI B27.7-1977, R1993. Tables 1 and 4 cover Type 3AM1 tapered external retaining rings, Tables 2 and 5 cover Type 3BM1 tapered internal rings, and Tables 3 and 6 cover Type 3CM1 reduced cross-section external rings. Tables 7 through 10 cover inch sizes of internal and external spiral retaining rings corresponding to MIL-R-27426 Types A (external) and B (internal), Class 1 (medium duty) and Class 2 (heavy duty). Tables 11 through 17 cover stamped retaining rings in inch sizes. Table 1. American National Standard Metric Tapered Retaining Rings — Basic External Series — 3AM1 ANSI B27.7-1977, R1993


Machinery's Handbook 27th Edition RETAINING RINGS

1685

Shaft Dia.

Table 1. (Continued) American National Standard Metric Tapered Retaining Rings — Basic External Series — 3AM1 ANSI B27.7-1977, R1993 Ring Free Dia.

Groove Thick ness

Dia.

Width Depth d ref

Ring Edge Margin Z min

Shaft Diam S

Free Dia. D

Groove Thick ness

Dia.

Width Depth W

d ref

Edge Margin

S

D

t

G

W

t

G

4

3.60

0.25

3.80

0.32

0.1

0.3

36

33.25

1.3

33.85

1.4

1.06

3.2

5

4.55

0.4

4.75

0.5

0.13

0.4

38

35.20

1.3

35.8

1.4

1.10

Z min 3.3

6

5.45

0.4

5.70

0.5

0.15

0.5

40

36.75

1.6

37.7

1.75

1.15

3.4

7

6.35

0.6

6.60

0.7

0.20

0.6

42

38.80

1.6

39.6

1.75

1.20

3.6

8

7.15

0.6

7.50

0.7

0.25

0.8

43

39.65

1.6

40.5

1.75

1.25

3.8

9

8.15

0.6

8.45

0.7

0.28

0.8

45

41.60

1.6

42.4

1.75

1.30

3.9

10

9.00

0.6

9.40

0.7

0.30

0.9

46

42.55

1.6

43.3

1.75

1.35

4.0

11

10.00

0.6

10.35

0.7

0.33

1.0

48

44.40

1.6

45.2

1.75

1.40

4.2

12

10.85

0.6

11.35

0.7

0.33

1.0

50

46.20

1.6

47.2

1.75

1.40

4.2

13

11.90

0.9

12.30

1.0

0.35

1.0

52

48.40

2.0

49.1

2.15

1.45

4.3

14

12.90

0.9

13.25

1.0

0.38

1.2

54

49.9

2.0

51.0

2.15

1.50

4.5

15

13.80

0.9

14.15

1.0

0.43

1.3

55

50.6

2.0

51.8

2.15

1.60

4.8

16

14.70

0.9

15.10

1.0

0.45

1.4

57

52.9

2.0

53.8

2.15

1.60

4.8

17

15.75

0.9

16.10

1.0

0.45

1.4

58

53.6

2.0

54.7

2.15

1.65

4.9

18

16.65

1.1

17.00

1.2

0.50

1.5

60

55.8

2.0

56.7

2.15

1.65

4.9

19

17.60

1.1

17.95

1.2

0.53

1.6

62

57.3

2.0

58.6

2.15

1.70

5.1

20

18.35

1.1

18.85

1.2

0.58

1.7

65

60.4

2.0

61.6

2.15

1.70

5.1

21

19.40

1.1

19.80

1.2

0.60

1.8

68

63.1

2.0

64.5

2.15

1.75

5.3

22

20.30

1.1

20.70

1.2

0.65

1.9

70

64.6

2.4

66.4

2.55

1.80

5.4

23

21.25

1.1

21.65

1.2

0.67

2.0

72

66.6

2.4

68.3

2.55

1.85

5.5

24

22.20

1.1

22.60

1.2

0.70

2.1

75

69.0

2.4

71.2

2.55

1.90

5.7

25

23.10

1.1

23.50

1.2

0.75

2.3

78

72.0

2.4

74.0

2.55

2.00

6.0

26

24.05

1.1

24.50

1.2

0.75

2.3

80

74.2

2.4

75.9

2.55

2.05

6.1

27

24.95

1.3

25.45

1.4

0.78

2.3

82

76.4

2.4

77.8

2.55

2.10

6.3

28

25.80

1.3

26.40

1.4

0.80

2.4

85

78.6

2.4

80.6

2.55

2.20

6.6

30

27.90

1.3

28.35

1.4

0.83

2.5

88

81.4

2.8

83.5

2.95

2.25

6.7

32

29.60

1.3

30.20

1.4

0.90

2.7

90

83.2

2.8

85.4

2.95

2.30

6.9

34

31.40

1.3

32.00

1.4

1.00

3.0

95

88.1

2.8

90.2

2.95

2.40

7.2

35

32.30

1.3

32.90

1.4

1.05

3.1

100

92.5

2.8

95.0

2.95

2.50

7.5

All dimensions are in millimeters. Sizes −4, −5, and −6 are available in beryllium copper only. These rings are designated by series symbol and shaft diameter, thus: for a 4 mm diameter shaft, 3AM1-4; for a 20 mm diameter shaft, 3AM1-20; etc. Ring Free Diameter Tolerances: For ring sizes −4 through −6, +0.05, −0.10 mm; for sizes −7 through −12, +0.05, −0.15 mm; for sizes −13 through − 26, +0.15, −0.25 mm; for sizes −27 through −38, +0.25, −0.40 mm; for sizes −40 through −50, +0.35, −0.50 mm; for sizes −52 through −62, +0.35, −0.65 mm; and for sizes −65 through −100, +0.50, −0.75 mm. Groove Diameter Tolerances: For ring sizes −4 through −6, −0.08 mm; for sizes −7 through −10, − 0.10 mm; for sizes −11 through −15, −0.12 mm; for sizes −16 through −26, −0.15 mm; for sizes −27 through − 36, −0.20 mm; for sizes −38 through −55, −0.30 mm; and for sizes −57 through −100, − 0.40 mm. Groove Diameter F.I.M. (full indicator movement) or maximum allowable deviation of concentricity between groove and shaft: For ring sizes −4 through −6, 0.03 mm; for ring sizes −7 through − 12, 0.05 mm; for sizes −13 through −28, 0.10 mm; for sizes −30 through −55, 0.15 mm; and for sizes −57 through − 00, 0.20 mm. Groove Width Tolerances: For ring size −4, +0.05 mm; for sizes −5 and −6, +0.10 mm, for sizes − 7 through −38, +0.15 mm; and for sizes −40 through − 100, +0.20 mm. Groove Maximum Bottom Radii,R: For ring sizes −4 through −6, none; for sizes −7 through −18, 0.1 mm; for sizes −19 through −30, 0.2 mm; for sizes −32 through −50, 0.3 mm; and for sizes −52 through −100, 0.4 mm. For manufacturing details not shown, including materials, see ANSI B27.71977, R1993.



RETAINING RINGS

Table 2. American National Standard Metric Tapered Retaining Rings — Basic Internal Series — 3BM1 ANSI B27.7-1977, R1993

Dia.

Width

Depth

Edge Margin

Shaft Dia.

Free Dia.

Thickness

Dia.

Width

Depth

Edge Margin

Groove

Thickness

Ring

Free Dia.

Groove

Shaft Dia.

Ring

S 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 30 32 34 35 36 37 38 40 42 45 46 47 48 50 52 55 57 58 60 62 63

D 8.80 10.00 11.10 12.20 13.30 14.25 15.45 16.60 17.70 18.90 20.05 21.10 22.25 23.30 24.40 25.45 26.55 27.75 28.85 29.95 31.10 33.40 35.35 37.75 38.75 40.00 41.05 42.15 44.25 46.60 49.95 51.05 52.15 53.30 55.35 57.90 61.10 63.25 64.4 66.8 68.6 69.9

t 0.4 0.6 0.6 0.6 0.6 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 0.9 1.1 1.1 1.1 1.1 1.1 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.6 1.6 1.6 1.6 1.6 1.6 1.6 2.0 2.0 2.0 2.0 2.0 2.0 2.0

G 8.40 9.45 10.50 11.60 12.65 13.70 14.80 15.85 16.90 18.00 19.05 20.10 21.15 22.20 23.30 24.35 25.4 26.6 27.7 28.8 29.8 31.9 33.9 36.1 37.2 38.3 39.3 40.4 42.4 44.5 47.6 48.7 49.8 50.9 53.1 55.3 58.4 60.5 61.6 63.8 65.8 66.9

W 0.5 0.7 0.7 0.7 0.7 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.2 1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.4 1.75 1.75 1.75 1.75 1.75 1.75 1.75 2.15 2.15 2.15 2.15 2.15 2.15 2.15

d ref 0.2 0.23 0.25 0.3 0.33 0.35 0.40 0.43 0.45 0.50 0.53 0.55 0.57 0.60 0.65 0.67 0.70 0.80 0.85 0.90 0.90 0.95 0.95 1.05 1.10 1.15 1.15 1.20 1.20 1.25 1.30 1.35 1.40 1.45 1.55 1.65 1.70 1.75 1.80 1.90 1.90 1.95

Z min 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.7 1.8 1.9 2.0 2.1 2.4 2.6 2.7 2.7 2.9 2.9 3.2 3.3 3.5 3.5 3.6 3.6 3.7 3.9 4.0 4.2 4.3 4.6 5.0 5.1 5.3 5.4 5.7 5.7 5.9

S 65 68 70 72 75 78 80 82 85 88 90 92 95 98 100 102 105 108 110 115 120 125 130 135 140 145 150 155 160 165 170 175 180 185 190 200 210 220 230 240 250 …

D 72.2 75.7 77.5 79.6 83.3 86.8 89.1 91.1 94.4 97.9 100.0 102.2 105.6 109.0 110.7 112.4 115.8 119.2 120.8 126.0 132.4 137.1 142.5 148.5 154.1 159.5 164.5 168.8 175.1 180.3 185.6 191.3 196.6 202.7 207.7 217.8 230.3 240.5 251.4 262.3 273.3 …

t 2.4 2.4 2.4 2.4 2.4 2.8 2.8 2.8 2.8 2.8 2.80 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 2.8 3.2 3.2 3.2 3.2 3.2 4.0 4.0 4.0 4.0 4.0 4.8 4.8 4.8 4.8 4.8 4.8 4.8 4.8 …

G 69.0 72.2 74.4 76.5 79.7 82.8 85.0 87.2 90.4 93.6 95.7 97.8 101.0 104.2 106.3 108.4 111.5 114.6 116.7 121.9 127.0 132.1 137.2 142.3 147.4 152.5 157.6 162.7 167.8 172.9 178.0 183.2 188.4 193.6 198.8 209.0 219.4 230.0 240.6 251.0 261.4 …

W 2.55 2.55 2.55 2.55 2.55 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 2.95 3.40 3.40 3.40 3.40 3.40 4.25 4.25 4.25 4.25 4.25 5.10 5.10 5.10 5.10 5.10 5.10 5.10 5.10 …

d ref 2.00 2.10 2.20 2.25 2.35 2.40 2.50 2.60 2.70 2.80 2.85 2.90 3.00 3.10 3.15 3.20 3.25 3.30 3.35 3.45 3.50 3.55 3.60 3.65 3.70 3.75 3.80 3.85 3.90 3.95 4.00 4.10 4.20 4.30 4.40 4.50 4.70 5.00 5.30 5.50 5.70 …

Z min 6.0 6.3 6.6 6.7 7.1 7.2 7.5 7.8 8.1 8.4 8.6 8.7 9.0 9.3 9.5 9.6 9.8 9.9 10.1 10.4 10.5 10.7 10.8 11.0 11.1 11.3 11.4 11.6 11.7 11.9 12.0 12.3 12.6 12.9 13.2 13.5 14.1 15.0 15.9 16.5 17.1 …

All dimensions are in millimeters. These rings are designated by series symbol and shaft diameter, thus: for a 9 mm diameter shaft, 3BM1-9; for a 22 mm diameter shaft, 3BM1-22; etc. Ring Free Diameter Tolerances: For ring sizes −8 through −20, +0.25, −0.13 mm; for sizes −21 through −26, +0.40, −0.25 mm; for sizes −27 through −38, +0.65, −0.50 mm; for sizes −40 through − 50, +0.90, −0.65 mm; for sizes −52 through −75, +1.00, −0.75 mm; for sizes −78 through −92, +1.40,



1687

−1.40 mm; for sizes −95 through −155, +1.65, −1.65 mm; for sizes −160 through −180, +2.05, −2.05 mm; and for sizes −185 through −250, +2.30, −2.30 mm. Groove Diameter Tolerances: For ring sizes −8 and −9, +0.06 mm; for sizes −10 through −18, +0.10 mm; for sizes −19 through − 28, +0.15 mm; for sizes −30 through −50, +0.20 mm; for sizes − 52 through −98, +0.30; for sizes −100 through −160, +0.40 mm; and for sizes −165 through −250, +0.50 mm. Groove Diameter F.I.M. (full indicator movement) or maximum allowable deviation of concentricity between groove and shaft: For ring sizes −8 through −10, 0.03 mm; for sizes −11 through −15, 0.05 mm; for sizes −16 through −25, 0.10 mm; for sizes −26 through −45, 0.15 mm; for sizes −46 through −80, 0.20 mm; for sizes −82 through −150, 0.25 mm; and for sizes −155 through −250, 0.30 mm. Groove Width Tolerances: For ring size −8, +0.10 mm; for sizes −9 through −38, +0.15 mm; for sizes −40 through −130, +0.20 mm; and for sizes −135 through −250, +0.25 mm. Groove Maximum Bottom Radii: For ring sizes −8 through −17, 0.1 mm; for sizes −18 through − 30, 0.2 mm; for sizes −32 through −55, 0.3 mm; and for sizes −56 through −250, 0.4 mm. For manufacturing details not shown, including materials, see ANSI B27.7-1977, R1993.

Table 3. American National Standard Metric Reduced Cross Section Retaining Rings — E Ring External Series —3CM1 ANSI B27.7-1977, R1993

S

D

t

Y nom

G

W

d ref

Z min

S

D

t

Y nom

1 2 3 4 5 6 7 8 9 10

0.64 1.30 2.10 2.90 3.70 4.70 5.25 6.15 6.80 7.60

0.25 0.25 0.4 0.6 0.6 0.6 0.6 0.6 0.9 0.9

2.0 4.0 5.6 7.2 8.5 11.1 13.4 14.6 15.8 16.8

0.72 1.45 2.30 3.10 3.90 4.85 5.55 6.40 7.20 8.00

0.32 0.32 0.5 0.7 0.7 0.7 0.7 0.7 1.0 1.0

0.14 0.28 0.35 0.45 0.55 0.58 0.73 0.80 0.90 1.00

0.3 0.6 0.7 0.9 1.1 1.2 1.5 1.6 1.8 2.0

11 12 13 15 16 18 20 22 25 …

8.55 9.20 9.95 11.40 12.15 13.90 15.60 17.00 19.50 …

0.9 1.1 1.1 1.1 1.1 1.3 1.3 1.3 1.3 …

17.4 18.6 20.3 22.8 23.8 27.2 30.0 33.0 37.1 …

8.90 9.60 10.30 11.80 12.50 14.30 16.00 17.40 20.00 …

Edge Margin

Depth

Dia. G

Width

Groove Outer Dia.

Thickness

Free Dia.

Shaft Dia.

Edge Margin

Ring Depth

Dia.

Width

Groove Outer Dia.

Thickness

Free Dia.

Shaft Dia.

Ring

W

d ref

Z min

1.0 1.2 1.2 1.2 1.2 1.4 1.4 1.4 1.4 …

1.05 1.20 1.35 1.60 1.75 1.85 2.00 2.30 2.50 …

2.1 2.4 2.7 3.2 3.5 3.7 4.0 4.6 5.0 …

All dimensions are in millimeters. Size −1 is available in beryllium copper only. These rings are designated by series symbol and shaft diameter, thus: for a 2 mm diameter shaft, 3CM1-2; for a 13 mm shaft, 3CMI -13; etc. Ring Free Diameter Tolerances: For ring sizes − 1 through −7, +0.03, −0.08 mm; for sizes −8 through −13, +0.05, −0.10 mm; and for sizes −15 through −25, +0.10, −0.15 mm. Groove Diameter Tolerances: For ring sizes −1 and −2, −0.05 mm; for sizes −3 through −6, −0.08; for sizes −7 through −11, −0.10 mm; for sizes −12 through −18, − 0.15 mm; and for sizes −20 through −25, − 0.20 mm. Groove Diameter F.I.M. (Full Indicator Movement) or maximum allowable deviation of concentricity between groove and shaft: For ring sizes −1 through −3, 0.04 mm; for −4 through −6, 0.05 mm; for −7 through −10, 0.08 mm; for −11 through −25, 0.10 mm. Groove Width Tolerances: For ring sizes − 1 and −2, +0.05 mm; for size −3, +0.10 mm; and for sizes −4 through − 25, +0.15 mm. Groove Maximum Bottom Radii: For ring sizes −1 and −2, 0.05 mm; for −3 through −7, 0.15 mm; for −8 through −13, 0.25 mm; and for −15 through −25, 0.4 mm. For manufacturing details not shown, including materials, see ANSI B27.7-1977, R1993.



RETAINING RINGS

Ring Seated in Groove

Ring Expanded over Shaft

Table 4. American National Standard Metric Basic External Series 3AM1 Retaining Rings, Checking and Performance Data ANSI B27.7-1977, R1993 Ring Series and Size No.

Clearance Dia. Ring Over Shaft

Ring in Groove

Gaging Diametera

Allowable Thrust Loads Sharp Corner Abutment

Maximum Allowable Corner Radii and Chamfers

Allowable Assembly Speedb

3AM1

C1

C2

K max

Pr c

Pgd

R max

Ch max

…

No.

mm

mm

mm

kN

kN

mm

mm

rpm

−4a

7.0

6.8

4.90

0.6

0.2

0.35

0.25

70 000

−5a

8.2

7.9

5.85

1.1

0.3

0.35

0.25

70 000

−6a

9.1

8.8

6.95

1.4

0.4

0.35

0.25

70 000

−7

12.3

11.8

8.05

2.6

0.7

0.45

0.3

60 000

−8

13.6

13.0

9.15

3.1

1.0

0.5

0.35

55 000

−9

14.5

13.8

10.35

3.5

1.2

0.6

0.35

48 000

−10

15.5

14.7

11.50

3.9

1.5

0.7

0.4

42 000

−11

16.4

15.6

12.60

4.3

1.8

0.75

0.45

38 000

−12

17.4

16.6

13.80

4.7

2.0

0.8

0.45

34 000

−13

19.7

18.8

15.05

7.5

2.2

0.8

0.5

31 000

−14

20.7

19.7

15.60

8.1

2.6

0.9

0.5

28 000

−15

21.7

20.6

17.20

8.7

3.2

1.0

0.6

27 000

−16

22.7

21.6

18.35

9.3

3.5

1.1

0.6

25 000

−17

23.7

22.6

19.35

9.9

4.0

1.1

0.6

24 000

−18

26.2

25.0

20.60

16.0

4.4

1.2

0.7

23 000

−19

27.2

25.9

21.70

16.9

4.9

1.2

0.7

21 500

−20

28.2

26.8

22.65

17.8

5.7

1.2

0.7

20 000

−21

29.2

27.7

23.80

18.6

6.2

1.3

0.7

19 000

−22

30.3

28.7

24.90

19.6

7.0

1.3

0.8

18 500

−23

31.3

29.6

26.00

20.5

7.6

1.3

0.8

18 000

−24

34.1

32.4

27.15

21.4

8.2

1.4

0.8

17 500

−25

35.1

33.3

28.10

22.3

9.2

1.4

0.8

17 000

−26

36.0

34.2

29.25

23.2

9.6

1.5

0.9

16 500

−27

37.8

35.9

30.35

28.4

10.3

1.5

0.9

16 300

−28

38.8

36.9

31.45

28.4

11.0

1.6

1.0

15 800

−30

40.8

38.8

33.6

31.6

12.3

1.6

1.0

15 000

−32

42.8

40.7

35.9

33.6

14.1

1.7

1.0

14 800

−34

44.9

42.5

37.9

36

16.7

1.7

1.1

14 000



1689

Table 4. (Continued) American National Standard Metric Basic External Series 3AM1 Retaining Rings, Checking and Performance Data ANSI B27.7-1977, R1993 Ring Series and Size No.

Clearance Dia. Ring Over Shaft

Ring in Groove

Gaging Diametera

Allowable Thrust Loads Sharp Corner Abutment

Maximum Allowable Corner Radii and Chamfers

Allowable Assembly Speedb

3AM1

C1

C2

K max

Pr c

Pgd

R max

Ch max

…

No.

mm

mm

mm

kN

kN

mm

mm

rpm

−35

45.9

43.4

39.0

37

18.1

1.8

1.1

13 500

−36

48.6

46.1

40.2

38

18.9

1.9

1.2

13 300

−38

50.6

48.0

42.5

40

20.5

2.0

1.2

12 700

−40

54.0

51.3

44.5

52

22.6

2.1

1.2

12 000

−42

56.0

53.2

46.9

54

24.8

2.2

1.3

11 000

−43

57.0

54.0

47.9

55

26.4

2.3

1.4

10 800

−45

59.0

55.9

50.0

58

28.8

2.3

1.4

10 000

−46

60.0

56.8

50.9

59

30.4

2.4

1.4

9 500

−48

62.4

59.1

53.0

62

33

2.4

1.4

8 800

−50

64.4

61.1

55.2

64

35

2.4

1.4

8 000

−52

67.6

64.1

57.4

84

37

2.5

1.5

7 700

−54

69.6

66.1

59.5

87

40

2.5

1.5

7 500

−55

70.6

66.9

60.4

89

44

2.5

1.5

7 400

−57

72.6

68.9

62.7

91

45

2.6

1.5

7 200

−58

73.6

69.8

63.6

93

46

2.6

1.6

7 100

−60

75.6

71.8

65.8

97

49

2.6

1.6

7 000

−62

77.6

73.6

67.9

100

52

2.7

1.6

6 900

−65

80.6

76.6

71.2

105

54

2.8

1.7

6 700

−68

83.6

79.5

74.5

110

58

2.9

1.7

6 500

−70

88.1

83.9

76.4

136

62

2.9

1.7

6 400

−72

90.1

85.8

78.5

140

65

2.9

1.7

6 200

−75

93.1

88.7

81.7

147

69

3.0

1.8

5 900

−78

95.4

92.1

84.6

151

76

3.0

1.8

5 600

−80

97.9

93.1

87.0

155

80

3.1

1.9

5 400

−82

100.0

95.1

89.0

159

84

3.2

1.9

5 200

−85

103.0

97.9

92.1

165

91

3.2

1.9

5 000

−88

107.0

100.8

95.1

199

97

3.2

1.9

4 800

−90

109.0

103.6

97.1

204

101

3.2

1.9

4 500

−95

114.0

108.6

102.7

215

112

3.4

2.1

4 350

−100

119.5

113.7

108.0

227

123

3.5

2.1

4 150

a For checking when ring is seated in groove. b These values have been calculated for steel rings. c These values apply to rings made from SAE 1060–1090 steels and PH 15-7 Mo stainless steel used on shafts hardened to Rc 50 minimum, with the exception of sizes −4, −5, and −6 which are supplied in beryllium copper only. Values for other sizes made from beryllium copper can be calculated by multiplying the listed values by 0.75. The values listed include a safety factor of 4. d These values are for all standard rings used on low carbon steel shafts. They include a safety factor of 2. Maximum allowable assembly loads with R max or Ch max are: For rings sizes −4, 0.2 kN; for sizes −5 and −6, 0.5 kN; for sizes −7 through −12, 2.1 kN; for sizes −13 through −17, 4.0 kN; for sizes −18 through −26, 6.0 kN; for sizes −27 through −38, 8.6 kN; for sizes −40 through − 50, 13.2 kN; for sizes −52 through −68, 22.0 kN; for sizes −70 through −85, 32 kN; and for sizes −88 through −100, 47 kN.

Source: Appendix to American National Standard ANSI B27.7-1977, R1993.



RETAINING RINGS

Table 5. American National Standard Metric Basic Internal Series 3BMI Retaining Rings — Checking and Performance Data ANSI B27.7-1977, R1993

Max Allowable Radius of Retained Part

Ring Compressed in Bore Ring Series and Size No. 3BMI No. −8 −9 −10 −11 −12 −13 −14 −15 −16 −17 −18 −19 −20 −21 −22 −23 −24 −25 −26 −27 −28 −30 −32 −34 −35 −36 −37 −38 −40 −42 −45 −46 −47 −48 −50 −52 −55 −57

Clearance Dia. Ring Ring in in Bore Groove C1

C2

mm 4.4 4.6 5.5 5.7 6.7 6.8 6.9 7.9 8.8 9.8 10.3 11.4 11.6 12.6 13.5 14.5 15.5 16.5 17.5 17.4 18.2 20.0 22.0 24.0 25.0 26.0 27.0 28.0 29.2 29.7 32.3 33.3 34.3 35.0 36.9 38.6 40.8 42.2

mm 4.8 5.0 6.0 6.3 7.3 7.5 7.7 8.7 9.7 10.8 11.3 12.5 12.7 13.8 14.8 15.9 16.9 18.1 19.2 19.2 20.0 21.9 23.9 26.1 27.2 28.3 29.3 30.4 31.6 32.2 34.9 36.0 37.1 37.9 40.0 41.9 44.2 45.7

Max Allowable Chamfer of Retained Part

Ring Seated in Groove Gaging Diametera A min mm 1.40 1.50 1.85 1.95 2.25 2.35 2.65 2.80 2.80 3.35 3.40 3.40 3.8 4.2 4.3 4.9 5.2 6.0 5.7 5.9 6.0 6.0 7.3 7.6 8.0 8.3 8.4 8.6 9.7 9.0 9.6 9.7 10.0 10.5 12.1 11.7 11.9 12.5

Allowable Thrust Loads Sharp Corner Abutment Prb

Pgc

kN 2.4 4.4 4.9 5.4 5.8 8.9 9.7 10.4 11.0 11.7 12.3 13.1 13.7 14.5 22.5 23.5 24.8 25.7 26.8 33 34 37 39 42 43 44 45 46 62 65 69 71 72 74 77 99 105 109

kN 1.0 1.2 1.5 2.0 2.4 2.6 3.2 3.7 4.2 4.9 5.5 6.0 6.6 7.3 8.3 8.9 9.7 11.6 12.7 14.0 14.6 16.5 17.6 20.6 22.3 23.9 24.6 26.4 27.7 30.2 33.8 36 38 40 45 50 54 58

Maximum Allowable Corner Radii and Chamfers R max mm 0.4 0.5 0.5 0.6 0.6 0.7 0.7 0.7 0.7 0.75 0.75 0.8 0.9 0.9 0.9 1.0 1.0 1.0 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.2 1.7 1.7 1.7 1.7 1.7 1.7 1.7 2.0 2.0 2.0


Ch max mm 0.3 0.35 0.35 0.4 0.4 0.5 0.5 0.5 0.5 0.6 0.6 0.65 0.7 0.7 0.7 0.8 0.8 0.8 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.3 1.3 1.3 1.3 1.3 1.3 1.3 1.6 1.6 1.6


1691

Table 5. (Continued) American National Standard Metric Basic Internal Series 3BMI −58 −60 −62 −63 −65 −68 −70 −72 −75 −78 −80 −82 −85 −88 −90 −92 −95 −98 −100 −102 −105 −108 −110 −115 −120 −125 −130 −135 −140 −145 −150 −155 −160 −165 −170 −175 −180 −185 −190 −200 −210 −220 −230 −240 −250

43.2 45.5 47.0 47.8 49.4 52.0 53.8 55.9 58.2 61.2 63.0 63.5 66.8 69.6 71.6 73.6 76.7 78.3 80.3 82.2 85.1 88.1 88.4 93.2 98.2 103.1 108.0 110.4 115.3 120.4 125.3 130.4 133.8 138.7 143.6 146.0 151.4 154.7 159.5 169.2 177.5 184.1 194.0 200.4 210.0

46.8 49.3 50.8 51.7 53.4 56.2 58.2 60.4 62.9 66.0 68.0 68.7 72.2 75.2 77.3 79.4 82.7 84.5 86.6 88.6 91.6 94.7 95.1 100.1 105.2 110.2 115.2 117.7 122.7 127.9 132.9 138.1 141.6 146.6 151.6 154.2 159.8 163.3 168.3 178.2 186.9 194.1 204.6 211.4 221.4

13.0 12.7 14.0 14.2 14.2 14.4 16.1 17.4 16.8 17.6 17.2 18.8 19.1 20.4 21.4 22.2 22.6 22.6 24.1 25.5 26.0 26.4 27.5 29.4 27.2 30.3 31.0 30.4 30.4 31.6 33.5 37.0 35.0 33.1 38.2 37.7 39.0 37.3 35.0 43.9 40.6 38.3 49.0 45.4 53.0

111 115 119 120 149 156 161 166 172 209 215 220 228 236 241 247 255 263 269 273 281 290 295 309 321 335 349 415 429 444 460 475 613 632 651 670 690 851 873 919 965 1000 1060 1090 1150

60 66 68 71 75 82 88 93 101 108 115 122 131 141 147 153 164 174 181 187 196 205 212 227 241 255 269 283 298 313 327 343 359 374 390 403 434 457 480 517 566 608 686 725 808

2.0 2.0 2.0 2.0 2.0 2.3 2.3 2.3 2.3 2.5 2.5 2.6 2.6 2.8 2.8 2.9 3.0 3.0 3.1 3.2 3.3 3.5 3.6 3.7 3.9 4.0 4.0 4.3 4.3 4.3 4.3 4.3 4.5 4.6 4.6 4.8 5.0 5.1 5.3 5.4 5.8 6.1 6.3 6.6 6.7

1.6 1.6 1.6 1.6 1.6 1.8 1.8 1.8 1.8 2.0 2.0 2.1 2.1 2.2 2.2 2.4 2.5 2.5 2.5 2.6 2.6 2.7 2.8 2.9 3.1 3.2 3.2 3.4 3.4 3.4 3.4 3.4 3.6 3.7 3.7 3.8 4.0 4.1 4.3 4.3 4.6 4.9 5.1 5.3 5.4

a For checking when ring is seated in groove. b These values apply to rings made from SAE 1060-1090 steels and PH 15-7 Mo stainless steel used in bores hardened to Rc 50 minimum. Values for rings made from beryllium copper can be calculated by multiplying the listed values by 0.75. The values listed include a safety factor of 4. c These values are for standard rings used in low carbon steel bores. They include a safety factor of 2. Maximum allowable assembly loads for R max or Ch max are: For ring size −8, 0.8 kN; for sizes − 9 through −12, 2.0 kN; for sizes −13 through −21, 4.0 kN; for sizes −22 through −26, 7.4 kN; for sizes −27 through −38, 10.8 kN; for sizes −40 through −50, 17.4 kN; for sizes −52 through −63, 27.4 kN; for size −65, 42.0 kN; for sizes −68 through −72, 39 kN; for sizes −75 through −130, 54 kN; for sizes −135 through −155, 67 kN; for sizes −160 through −180, 102 kN; and for sizes −185 through −250, 151 kN. Source: Appendix to American National Standard ANSI B27.7-1977, R1993.



RETAINING RINGS

Table 6. American National Standard Metric E-Type External Series 3CM1 Retaining Rings — Checking and Performance Data ANSI B27.7-1977, R1993

Max. Allowable Radius of Retained Part

Ring Seated in Groove Ring Series and Size No. 3CM1 No. −1 −2 −3 −4 −5 −6 −7 −8 −9 −10 −11 −12 −13 −15 −16 −18 −20 −22 −25

Clearance Diameter Ring in Groove C2 mm 2.2 4.3 6.0 7.6 8.9 11.5 14.0 15.1 16.5 17.5 18.0 19.3 21.0 23.5 24.5 27.9 30.7 33.7 37.9

Max. Allowable Chamfer of Retained Part Maximum Allowable Corner Radii and Chamfers

Allowable Thrust Loads Sharp Corner Abutment Pr b Pgc kN 0.06 0.13 0.3 0.7 0.9 1.1 1.2 1.4 3.0 3.4 3.7 4.9 5.4 6.2 6.6 8.7 9.8 10.8 12.2

R max mm 0.4 0.8 1.1 1.6 1.6 1.6 1.6 1.7 1.7 1.7 1.7 1.9 2.0 2.0 2.0 2.1 2.2 2.2 2.4

kN 0.02 0.09 0.17 0.3 0.4 0.6 0.8 1.0 1.3 1.6 1.9 2.3 2.9 4.0 4.5 5.4 6.5 8.1 10.1

Allowable Assembly Speeda … rpm 40 000 40 000 34 000 31 000 27 000 25 000 23 000 21 500 19 500 18 000 16 500 15 000 13 000 11 500 10 000 9 000 8 000 7 000 5 000

Ch max mm 0.25 0.5 0.7 1.2 1.2 1.2 1.2 1.3 1.3 1.3 1.3 1.4 1.5 1.5 1.5 1.6 1.7 1.7 1.9

a These values have been calculated for steel rings. b These values apply to rings made from SAE 1060-1090 steels and PH 15-7 Mo stainless steel used on shafts hardened to Rc 50 minimum, with the exception of size −1 which is supplied in beryllium copper only. Values for other sizes made from beryllium copper can be calculated by multiplying the listed values by 0.75. The values listed include a safety factor of 4. c These values apply to all standard rings used on low carbon steel shafts. They include a safety factor of 2. Maximum allowable assembly loads with R max or Ch max are as follows:

Ring Size No.

Maximum Allowable Load,kN

Ring Size No.

Maximum AllowableLoad, kN

Ring Size No.

Maximum AllowableLoad, kN

−1 −2 −3 −4 −5 −6 −7

0.06 0.13 0.3 0.7 0.9 1.1 1.2

−8 −9 −10 −11 −12 −13 −15

1.4 3.0 3.4 3.7 4.9 5.4 6.2

−16 −18 −20 −22 −25 … …

6.6 8.7 9.8 10.8 12.2 … …

Source: Appendix to American National Standard ANSI B27.7-1977, R1993.



;;; ;; ;;; ;; ;;; ;; ;;; ;; ;;; ;; ;;; ;;

1693

SIZE 0.500 to 1.500

G

SIZE 1.562 and UP

A

C F

E

D

Table 7. Medium Duty Internal Spiral Retaining Rings MIL-R-27426 Ring

Groove

Static Thrust Load (lb)

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

0.500 0.512 0.531 0.562 0.594 0.625 0.656 0.687 0.718 0.750 0.777 0.781 0.812 0.843 0.866 0.875 0.906 0.938 0.968 0.987 1.000 1.023 1.031 1.062 1.093 1.125 1.156 1.188 1.218 1.250 1.281 1.312 1.343 1.375 1.406 1.437 1.456 1.468 1.500 1.562 1.574 1.625 1.653 1.687 1.750 1.813

0.532 0.544 0.564 0.594 0.626 0.658 0.689 0.720 0.751 0.790 0.817 0.821 0.853 0.889 0.913 0.922 0.949 0.986 1.025 1.041 1.054 1.078 1.084 1.117 1.147 1.180 1.210 1.249 1.278 1.312 1.342 1.374 1.408 1.442 1.472 1.504 1.523 1.535 1.567 1.634 1.649 1.701 1.730 1.768 1.834 1.894

0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.045 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.065 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.075 0.085 0.085 0.085 0.085 0.085 0.085 0.095 0.095 0.095 0.095 0.095 0.095 0.108 0.108 0.108 0.108 0.118 0.118 0.118

0.526 0.538 0.557 0.588 0.619 0.651 0.682 0.713 0.744 0.782 0.808 0.812 0.843 0.880 0.903 0.912 0.939 0.975 1.015 1.030 1.043 1.066 1.074 1.104 1.135 1.167 1.198 1.236 1.266 1.298 1.329 1.360 1.395 1.427 1.458 1.489 1.508 1.520 1.552 1.617 1.633 1.684 1.712 1.750 1.813 1.875

0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.030 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.036 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.042 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.048 0.056 0.056 0.056 0.056 0.056 0.056 0.056

2000 2050 2130 2250 2380 2500 2630 2750 2870 3360 3480 3500 3640 3780 3880 3920 4060 4200 4340 4420 4480 5470 5510 5680 5840 6010 6180 7380 7570 7770 7960 8150 8340 8540 8740 8930 9050 9120 9320 10100 10180 10510 10690 10910 11310 11720

Ring

Groove


Groove

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

Groove

405 420 455 495 535 610 670 725 790 800 835 840 915 1155 1250 1250 1335 1430 1950 1865 1910 1660 1650 1745 1820 1935 2020 2115 2195 2510 2425 2532 2875 3070 3180 3330 3410 3460 3605 3590 3640 3875 4020 4510 4895 5080

3.437 3.500 3.543 3.562 3.625 3.687 3.740 3.750 3.812 4.437 4.500 4.527 4.562 4.625 4.687 4.724 4.750 4.812 4.875 4.921 4.937 5.000 5.118 5.125 5.250 5.375 5.500 5.511 5.625 5.708 5.750 5.875 5.905 6.000 6.125 6.250 6.299 6.375 6.500 6.625 6.692 6.750 6.875 7.000 7.086 7.125

3.574 3.636 3.684 3.703 3.769 3.832 3.885 3.894 3.963 4.611 4.674 4.701 4.737 4.803 4.867 4.903 4.930 4.993 5.055 5.102 5.122 5.185 5.304 5.311 5.436 5.566 5.693 5.703 5.818 5.909 5.950 6.077 6.106 6.202 6.349 6.474 6.524 6.601 6.726 6.863 6.931 6.987 7.114 7.239 7.337 7.376

0.188 0.188 0.198 0.198 0.198 0.198 0.198 0.198 0.208 0.238 0.238 0.238 0.238 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312

3.543 3.606 3.653 3.672 3.737 3.799 3.852 3.862 3.930 4.573 4.636 4.663 4.698 4.765 4.827 4.864 4.890 4.952 5.015 5.061 5.081 5.144 5.262 5.269 5.393 5.522 5.647 5.658 5.772 5.861 5.903 6.028 6.058 6.153 6.297 6.422 6.471 6.547 6.672 6.807 6.874 6.932 7.057 7.182 7.278 7.317

0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.079 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094

27660 28170 28520 28670 29180 29680 30100 30180 30680 35710 36220 36440 36720 43940 44530 44880 45130 45710 46310 46750 46900 47500 48620 48690 49880 51050 52250 52350 53440 54230 54630 55810 56100 57000 69500 70920 71480 72340 73760 75180 75940 76590 78010 79430 80410 80850

18240 18575 19515 19620 20330 20675 20975 21030 22525 30215 30645 30830 31065 32420 32855 33115 33300 33735 34175 34495 35595 36050 36905 36955 37590 39565 40485 40565 41405 43730 44050 45010 45240 45965 52750 53825 54250 54905 55980 60375 60985 61515 62655 63790 68125 68500



RETAINING RINGS

Table 7. (Continued) Medium Duty Internal Spiral Retaining Rings MIL-R-27426 Bore Dia. A 1.850 1.875 1.938 2.000 2.047 2.062 2.125 2.165 2.188 2.250 2.312 2.375 2.437 2.440 2.500 2.531 2.562 2.625 2.677 2.688 2.750 2.813 2.834 2.875 2.937 2.952 3.000 3.062 3.125 3.149 3.187 3.250 3.312 3.346 3.375

Ring Dia. G 1.937 1.960 2.025 2.091 2.138 2.154 2.217 2.260 2.284 2.347 2.413 2.476 2.543 2.546 2.606 2.641 2.673 2.736 2.789 2.803 2.865 2.929 2.954 2.995 3.058 3.073 3.122 3.186 3.251 3.276 3.311 3.379 3.446 3.479 3.509

Groove

Wall E 0.118 0.118 0.118 0.128 0.128 0.128 0.128 0.138 0.138 0.138 0.138 0.138 0.148 0.148 0.148 0.148 0.148 0.148 0.158 0.158 0.158 0.158 0.168 0.168 0.168 0.168 0.168 0.168 0.178 0.178 0.178 0.178 0.188 0.188 0.188

Dia. C 1.917 1.942 2.005 2.071 2.118 2.132 2.195 2.239 2.262 2.324 2.390 2.453 2.519 2.522 2.582 2.617 2.648 2.711 2.767 2.778 2.841 2.903 2.928 2.969 3.031 3.046 3.096 3.158 3.223 3.247 3.283 3.350 3.416 3.450 3.479

Width D 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068

Static Thrust Load (lb) Ring 11960 12120 12530 12930 13230 13330 13740 14000 14150 14550 14950 15350 15760 15780 16160 16360 16560 16970 17310 17380 17780 18190 18320 18590 18990 19090 24150 24640 25150 25340 25650 26160 26660 26930 27160

Groove 5735 5825 6250 7090 7275 7225 7450 8020 8105 8335 9030 9275 10005 10015 10625 10900 11030 11305 12065 12115 12530 12675 13340 13530 13825 13890 14420 14720 15335 15450 15640 16270 17245 17425 17575

Bore Dia. A 7.250 7.375 7.480 7.500 7.625 7.750 7.875 8.000 8.250 8.267 8.464 8.500 8.750 8.858 9.000 9.055 9.250 9.448 9.500 9.750 10.000 10.250 10.500 10.750 11.000 3.875 3.938 4.000 4.063 4.125 4.188 4.250 4.312 4.330 4.375

Ring Dia. G 7.501 7.628 7.734 7.754 7.890 8.014 8.131 8.266 8.528 8.546 8.744 8.780 9.041 9.151 9.293 9.359 9.555 9.755 9.806 10.068 10.320 10.582 10.834 11.095 11.347 4.025 4.089 4.157 4.222 4.284 4.347 4.416 4.479 4.497 4.543

Wall E 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.312 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.375 0.208 0.208 0.218 0.218 0.218 0.218 0.228 0.228 0.228 0.228

Groove Dia. C 7.442 7.567 7.672 7.692 7.827 7.952 8.077 8.202 8.462 8.479 8.676 8.712 8.972 9.080 9.222 9.287 9.482 9.680 9.732 9.992 10.242 10.502 10.752 11.012 11.262 3.993 4.056 5.124 4.187 4.249 4.311 4.380 4.442 4.460 4.505

Width D 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.094 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068

Static Thrust Load (lb) Ring 82270 83690 84880 85110 86520 87940 89360 90780 93620 93810 96040 96450 99290 100520 102130 102750 104960 107210 107800 110640 113470 116310 119150 121980 124820 30680 31700 32190 32700 33200 33710 34210 34710 34850 32210

Groove 69700 70900 71910 72105 77125 78390 79655 80920 87575 87755 89850 90230 97265 98465 100045 105190 107455 109755 110360 118145 121175 129340 132490 141030 144310 22525 23265 24835 25225 25610 25795 27665 28065 28185 28475

Source: Spirolox Retaining Rings, RR Series. All dimensions are in inches. Depth of groove d = (C − A)/2. Standard material: carbon spring steel (SAE 1070-1090). Ring Thickness, F: For shaft sizes 0.500 through 0.718, 0.025; for sizes 0.750 through 0.938, 0.031; for sizes 0.968 through 1.156, 0.037; for sizes 1.188 through 1.500, 0.043; for sizes 1.562 through 2.952, 0.049; for sizes 3.000 through 4.562, 0.061; for sizes 4.625 through 6.000, 0.072; for sizes 6.125 through 11.000, 0.086. Ring Free Diameter Tolerances: For housing sizes 0.500 through 1.031, +0.013, −0.000; for sizes 1.062 through 1.500, +0.015, −0.000; for sizes 1.562 through 2.047, +0.020, −0.000; for sizes 2.062 through 3.000, +0.025, −0.000; for sizes 3.062 through 4.063, +0.030, −0.000; for sizes 4.125 through 5.125, +0.035, −0.000; for sizes 5.250 through 6.125, +0.045, −0.000; for sizes 6.250 through 7.125, +0.055, −0.000; for sizes 7.250 through 11.000, +0.065, −0.000. Ring Thickness Tolerances: Thickness indicated is for unplated rings; add 0.002 to upper thickness tolerance for plated rings. For housing sizes 0.500 through 1.500, ±0.002; for sizes 1.562 through 4.562, ±0.003; for sizes 4.625 through 11.000, ±0.004. Groove Diameter Tolerances: For housing sizes 0.500 through 0.750, ±0.002; for sizes 0.777 through 1.031, ±0.003; for sizes 1.062 through 1.500, ±0.004; for sizes 1.562 through 2.047, ±0.005; for sizes 2.062 through 5.125, ±0.006; for sizes 5.250 through 6.000, ±0.007; for sizes 6.125 through 11.000, ±0.008. Groove Width Tolerances: For housing sizes 0.500 through 1.156, +0.003, −0.000; for sizes 1.188 through 2.952, +0.004, −0.000; for sizes 3.000 through 6.000, +0.005, −0.000; for sizes 6.125 through 11.000, +0.006, −0.000.



1695

Table 8. Medium Duty External Spiral Retaining Rings MIL-R-27426

; ; ; ; ; ;

SIZE 0.500 to 1.500

G

SIZE 1.562 and UP

C A F

E

D

Ring

Groove


Ring

Groove


Groove

Shaft Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

Groove

550

3.343

3.210

0.188

3.239

0.068

26910

17410

640

3.375

3.242

0.188

3.271

0.068

27160

17570

2210

700

3.437

3.301

0.188

3.331

0.068

27660

18240

0.030

2250

730

3.500

3.363

0.188

3.394

0.068

28170

18580

0.569

0.030

2380

740

3.543

3.402

0.198

3.433

0.068

28520

19510

0.055

0.594

0.030

2500

970

3.562

3.422

0.198

3.452

0.068

28670

19620

0.617

0.055

0.625

0.030

2630

1020

3.625

3.483

0.198

3.515

0.068

29180

19970

0.669

0.629

0.055

0.638

0.030

2680

1040

3.687

3.543

0.198

3.575

0.068

29680

20680

0.687

0.647

0.055

0.656

0.030

2750

1060

3.740

3.597

0.198

3.628

0.068

30100

20970

0.718

0.679

0.055

0.687

0.030

2870

1110

3.750

3.606

0.198

3.638

0.068

30180

21030

0.750

0.710

0.065

0.719

0.036

3360

1100

3.812

3.668

0.198

3.700

0.068

30680

21380

0.781

0.741

0.065

0.750

0.036

3500

1210

3.875

3.724

0.208

3.757

0.068

31190

22890

0.812

0.771

0.065

0.781

0.036

3640

1260

3.938

3.784

0.208

3.820

0.068

31700

23270

0.843

0.803

0.065

0.812

0.036

3780

1310

4.000

3.842

0.218

3.876

0.068

32190

24840

0.875

0.828

0.065

0.838

0.036

3920

1620

4.063

3.906

0.218

3.939

0.068

32700

25230

0.906

0.860

0.065

0.869

0.036

4060

1680

4.125

3.967

0.218

4.000

0.068

33200

25820

0.937

0.889

0.065

0.900

0.036

4200

1740

4.134

3.975

0.218

4.010

0.068

33270

25670

0.968

0.916

0.075

0.925

0.042

5180

2080

4.188

4.030

0.218

4.058

0.068

33710

27260

0.984

0.930

0.075

0.941

0.042

5260

2120

4.250

4.084

0.228

4.120

0.068

34210

27660

1.000

0.946

0.075

0.957

0.042

5350

2150

4.312

4.147

0.218

4.182

0.068

34710

28070

1.023

0.968

0.075

0.980

0.042

5470

2200

4.331

4.164

0.218

4.200

0.068

34860

28410

1.031

0.978

0.075

0.988

0.042

5510

2220

4.375

4.208

0.218

4.245

0.068

35210

28480

1.062

1.007

0.075

1.020

0.042

5680

2230

4.437

4.271

0.218

4.307

0.068

35710

28880

1.093

1.040

0.075

1.051

0.042

5840

2300

4.500

4.326

0.238

4.364

0.068

36220

30640

1.125

1.070

0.075

1.083

0.042

6010

2370

4.562

4.384

0.250

4.422

0.079

43340

31980

1.156

1.102

0.075

1.114

0.042

6180

2430

4.625

4.447

0.250

4.485

0.079

43940

32420

1.188

1.127

0.085

1.140

0.048

7380

2850

4.687

4.508

0.250

4.457

0.079

44530

32860

1.218

1.159

0.085

1.170

0.048

7570

2930

4.724

4.546

0.250

4.584

0.079

44880

33120

1.250

1.188

0.085

1.202

0.048

7770

3000

4.750

4.571

0.250

4.610

0.079

45130

33300

1.281

1.221

0.085

1.233

0.048

7960

3080

4.812

4.633

0.250

4.672

0.079

45710

33730

1.312

1.251

0.095

1.264

0.048

8150

3150

4.875

4.695

0.250

4.735

0.079

46310

34170

1.343

1.282

0.095

1.295

0.048

8340

3230

4.937

4.757

0.250

4.797

0.079

46900

34610

1.375

1.308

0.095

1.323

0.048

8540

3580

5.000

4.820

0.250

4.856

0.079

47500

36050

1.406

1.340

0.095

1.354

0.048

8740

3660

5.118

4.934

0.250

4.974

0.079

48620

36900

1.437

1.370

0.095

1.385

0.048

8930

3740

5.125

4.939

0.250

4.981

0.079

48690

36950

1.468

1.402

0.095

1.416

0.048

9120

3820

5.250

5.064

0.250

5.107

0.079

49880

37590

1.500

1.433

0.095

1.448

0.048

9320

3910

5.375

5.187

0.250

5.228

0.079

51060

39560

1.562

1.490

0.108

1.507

0.056

10100

4300

5.500

5.308

0.250

5.353

0.079

52250

40480

1.575

1.503

0.108

1.520

0.056

10190

4340

5.511

5.320

0.250

5.364

0.079

52350

40560

1.625

1.549

0.108

1.566

0.056

10510

4800

5.625

5.433

0.250

5.478

0.079

53440

41400

Shaft Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

0.500

0.467

0.045

0.474

0.030

2000

0.531

0.498

0.045

0.505

0.030

2130

0.551

0.518

0.045

0.525

0.030

0.562

0.529

0.045

0.536

0.594

0.561

0.045

0.625

0.585

0.656



RETAINING RINGS

Table 8. (Continued) Medium Duty External Spiral Retaining Rings MIL-R-27426 1.687

1.610

0.118

1.628

0.056

10910

4980

5.750

5.550

0.250

5.597

0.079

54630

44050

1.750

1.673

0.118

1.691

0.056

11310

5170

5.875

5.674

0.250

5.722

0.079

55810

45010

1.771

1.690

0.118

1.708

0.056

11450

5590

5.905

5.705

0.250

5.752

0.079

56100

45240

1.813

1.730

0.118

1.749

0.056

11720

5810

6.000

5.798

0.250

5.847

0.079

57000

45970

1.875

1.789

0.128

1.808

0.056

12120

6290

6.125

5.903

0.312

5.953

0.094

69500

52750

1.938

1.844

0.128

1.861

0.056

12530

7470

6.250

6.026

0.312

6.078

0.094

70920

53830

1.969

1.882

0.128

1.902

0.056

12730

6610

6.299

6.076

0.312

6.127

0.094

71480

54250

2.000

1.909

0.128

1.992

0.056

12930

7110

6.375

6.152

0.312

6.203

0.094

72340

54900

2.062

1.971

0.128

2.051

0.056

13330

7870

6.500

6.274

0.312

6.328

0.094

73760

55980

2.125

2.029

0.128

2.082

0.056

13740

7990

6.625

6.390

0.312

6.443

0.094

75180

60380

2.156

2.060

0.138

2.091

0.056

13940

8020

6.750

6.513

0.312

6.568

0.094

76590

61515

2.188

2.070

0.138

2.113

0.056

14150

8220

6.875

6.638

0.312

6.693

0.094

78010

62650

2.250

2.092

0.138

2.176

0.056

14550

8340

7.000

6.761

0.312

6.818

0.094

79430

63790

2.312

2.153

0.138

2.234

0.056

14950

9030

7.125

6.877

0.312

6.933

0.094

80850

68500

2.362

2.211

0.138

2.284

0.056

15270

9230

7.250

6.999

0.312

7.058

0.094

82270

69700

2.375

2.273

0.138

2.297

0.056

15350

9280

7.375

7.125

0.312

7.183

0.094

83690

70900

2.437

2.331

0.148

2.355

0.056

15760

10000

7.500

7.250

0.312

7.308

0.094

85110

72100

2.500

2.394

0.148

2.418

0.056

16160

10260

7.625

7.363

0.312

7.423

0.094

86520

77120

2.559

2.449

0.148

2.473

0.056

16540

11020

7.750

7.486

0.312

7.548

0.094

87940

78390

2.562

2.452

0.148

2.476

0.056

16560

11030

7.875

7.611

0.312

7.673

0.094

89360

79650

2.625

2.514

0.148

2.539

0.056

16970

11300

8.000

7.734

0.312

7.798

0.094

90780

80920

2.688

2.572

0.158

2.597

0.056

17380

12250

8.250

7.972

0.375

8.038

0.094

93620

87580

2.750

2.635

0.158

2.660

0.056

17780

12390

8.500

8.220

0.375

8.288

0.094

96450

90230

2.813

2.696

0.168

2.722

0.056

18190

12820

8.750

8.459

0.375

8.528

0.094

99290

97270

2.875

2.755

0.168

2.781

0.056

18590

13530

9.000

8.707

0.375

8.778

0.094

102130

100050

2.937

2.817

0.168

2.843

0.056

18990

13820

9.250

8.945

0.375

9.018

0.094

104960

107560

2.952

2.831

0.168

2.858

0.056

19090

13890

9.500

9.194

0.375

9.268

0.094

107800

110360

3.000

2.877

0.168

2.904

0.068

24150

14420

9.750

9.432

0.375

9.508

0.094

110640

118150

3.062

2.938

0.168

2.966

0.068

24640

14720

10.000

9.680

0.375

9.758

0.094

113470

121180

3.125

3.000

0.178

3.027

0.068

25150

15335

10.250

9.918

0.375

9.998

0.094

116310

129340

3.149

3.023

0.178

3.051

0.068

25340

15450

10.500

10.166

0.375

10.248

0.094

119150

132490

3.187

3.061

0.178

3.089

0.068

25650

15640

10.750

10.405

0.375

10.488

0.094

121980

141030

3.250

3.121

0.178

3.150

0.068

26160

16270

11.000

10.653

0.375

10.738

0.094

124820

144310

3.312

3.180

0.188

3.208

0.068

26660

17250

Source: Spirolox Retaining Rings, RS Series. All dimensions are in inches. Depth of groove d = (A − C)/2. Standard material: carbon spring steel (SAE 1070–1090). Ring Thickness, F: For shaft sizes 0.500 through 0.718, 0.025; for sizes 0.750 through 0.937, 0.031; for sizes 0.968 through 1.156, 0.037; for sizes 1.188 through 1.500, 0.043; for sizes 1.562 through 2.952, 0.049; for sizes 3.000 through 4.500, 0.061; for sizes 4.562 through 6.000, 0.072; for sizes 6.125 through 11.000, 0.086. Ring Free Diameter Tolerances: For shaft sizes 0.500 through 1.031, +0.000, + 0.000, −0.013; for sizes 1.062 through 1.500, +0.000, −0.015; for sizes 1.562 through 2.125, +0.000, −0.020; for sizes 2.156 through 2.688, +0.000, −0.025; for sizes 2.750 through 3.437, +0.000, −0.030; for sizes 3.500 through 5.125, +0.000, −0.040; for sizes 5.250 through 6.125, +0.000, −0.050; for sizes 6.250 through 7.375, +0.000, −0.060; for sizes 7.500 through 11.000, +0.000, −0.070. Ring Thickness Tolerances: Thickness indicated is for unplated rings; add 0.002 to upper tolerance for plated rings. For shaft sizes 0.500 through 1.500, ± 0.002; for sizes 1.562 through 4.500, ± 0.003; for sizes 4.562 through 11.000, ± 0.004. Groove Diameter Tolerances: For shaft sizes 0.500 through 0.562, ±0.002; for sizes 0.594 through 1.031, ± 0.003; for sizes 1.062 through 1.500, ± 0.004; for sizes 1.562 through 2.000, ± 0.005; for sizes 2.062 through 5.125, ±0.006; for sizes 5.250 through 6.000, ± 0.007; for sizes 6.125 through 11.000, ± 0.008. Groove Width Tolerances: For shaft sizes 0.500 through 1.156, +0.003, −0.000; for sizes 1.188 through 2.952, +0.004, −0.000; for sizes 3.000 through 6.000, +0.005, −0.000; for sizes 6.125 through 11.000, +0.006, −0.000.



;; ;; ;; ;; ;; ;;

1697

SIZE 0.500 to 0.750

G

SIZE 0.777 and UP

A

C F

E

D

Table 9. Heavy Duty Internal Spiral Retaining Rings MIL-R-27426 Ring

Groove


Ring

Groove


Groove

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

Groove

310

3.543

3.781

0.281

3.755

0.120

49420

28250

2590

325

3.562

3.802

0.281

3.776

0.120

49680

28815

0.039

2840

455

3.625

3.868

0.281

3.841

0.120

50560

30160

0.655

0.039

3160

655

3.750

4.002

0.312

3.974

0.120

52310

33720

0.065

0.732

0.039

3480

965

3.875

4.136

0.312

4.107

0.120

54050

37250

0.807

0.065

0.796

0.039

3790

1065

3.938

4.203

0.312

4.174

0.120

54930

39045

0.777

0.836

0.075

0.825

0.046

4720

1026

4.000

4.270

0.312

4.240

0.120

55790

41025

0.812

0.873

0.075

0.862

0.046

4930

1150

4.125

4.369

0.312

4.339

0.120

57540

38495

0.866

0.931

0.075

0.920

0.046

5260

1395

4.250

4.501

0.312

4.470

0.120

59280

41955

0.875

0.943

0.085

0.931

0.046

5310

1520

4.330

4.588

0.312

4.556

0.120

60400

44815

0.901

0.972

0.085

0.959

0.046

5470

1675

4.500

4.768

0.312

4.735

0.120

62770

50290

0.938

1.013

0.085

1.000

0.046

5690

1925

4.625

4.899

0.312

4.865

0.120

64510

54155

1.000

1.080

0.085

1.066

0.046

6070

2310

4.750

5.030

0.312

4.995

0.120

66260

58270

1.023

1.105

0.085

1.091

0.046

6210

2480

5.000

5.297

0.312

5.260

0.120

69740

65095

1.062

1.138

0.103

1.130

0.056

7010

1940

5.250

5.559

0.350

5.520

0.139

83790

68315

1.125

1.205

0.103

1.197

0.056

7420

2280

5.375

5.690

0.350

5.650

0.139

85780

72840

1.188

1.271

0.103

1.262

0.056

7840

2615

5.500

5.810

0.350

5.770

0.139

87780

74355

1.250

1.339

0.103

1.330

0.056

8250

3110

5.750

6.062

0.350

6.020

0.139

91770

77735

1.312

1.406

0.118

1.396

0.056

8650

3650

6.000

6.314

0.350

6.270

0.139

95760

81120

1.375

1.471

0.118

1.461

0.056

9070

4075

6.250

6.576

0.380

6.530

0.174

122520

80655

1.439

1.539

0.118

1.528

0.056

9490

4670

6.500

6.838

0.380

6.790

0.174

127420

90295

1.456

1.559

0.118

1.548

0.056

9600

4890

6.625

6.974

0.380

6.925

0.174

129870

92060

1.500

1.605

0.118

1.594

0.056

9900

5275

6.750

7.105

0.380

7.055

0.174

132320

102475

1.562

1.675

0.128

1.658

0.068

12780

4840

7.000

7.366

0.380

7.315

0.174

137220

110410

1.625

1.742

0.128

1.725

0.068

13290

5415

7.250

7.628

0.418

7.575

0.209

170370

103440

1.653

1.772

0.128

1.755

0.068

13520

5695

7.500

7.895

0.418

7.840

0.209

176240

115780

1.688

1.810

0.128

1.792

0.068

13810

6070

7.750

8.157

0.418

8.100

0.209

182120

127270

1.750

1.876

0.128

1.858

0.068

14320

7635

8.000

8.419

0.418

8.360

0.209

187990

139370

1.812

1.940

0.128

1.922

0.068

14820

7305

8.250

8.680

0.437

8.620

0.209

193870

152695

1.850

1.981

0.158

1.962

0.068

15130

7960

8.500

8.942

0.437

8.880

0.209

199740

161735

1.875

2.008

0.158

1.989

0.068

15340

8305

8.750

9.209

0.437

9.145

0.209

205620

173065

1.938

2.075

0.158

2.056

0.068

15850

9125

9.000

9.471

0.437

9.405

0.209

211490

182515

2.000

2.142

0.158

2.122

0.068

16360

10040

9.250

9.737

0.437

9.669

0.209

217370

194070

2.062

2.201

0.168

2.186

0.086

21220

8280

9.500

10.000

0.500

9.930

0.209

223240

204550

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

0.500

0.538

0.045

0.530

0.039

2530

0.512

0.550

0.045

0.542

0.039

0.562

0.605

0.055

0.596

0.625

0.675

0.055

0.688

0.743

0.750



RETAINING RINGS

Table 9. (Continued) Heavy Duty Internal Spiral Retaining Rings MIL-R-27426 Ring

Groove


Ring

Groove


Groove

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

Groove

8935

9.750

10.260

0.500

10.189

0.209

229120

214325

22520

9745

10.000

10.523

0.500

10.450

0.209

234990

225330

23160

10455

10.250

10.786

0.500

10.711

0.209

240870

236605

0.086

23790

11700

10.500

11.047

0.500

10.970

0.209

246740

247110

2.517

0.086

24440

12715

10.750

11.313

0.500

11.234

0.209

252620

260530

0.200

2.584

0.086

25110

13550

11.000

11.575

0.500

11.495

0.209

258490

272645

2.667

0.200

2.648

0.086

25730

14640

11.250

11.838

0.500

11.756

0.209

264360

285040

2.531

2.700

0.200

2.681

0.086

26050

15185

11.500

12.102

0.562

12.018

0.209

270240

298285

2.562

2.733

0.225

2.714

0.103

29940

12775

11.750

12.365

0.562

12.279

0.209

276120

311240

2.625

2.801

0.225

2.781

0.103

30680

13780

12.000

12.628

0.562

12.540

0.209

281990

324475

2.688

2.868

0.225

2.848

0.103

31410

14775

12.250

12.891

0.562

12.801

0.209

287860

337980

2.750

2.934

0.225

2.914

0.103

32140

15790

12.500

13.154

0.562

13.063

0.209

293740

352390

2.813

3.001

0.225

2.980

0.103

32870

16845

12.750

13.417

0.562

13.324

0.209

299610

366460

2.834

3.027

0.225

3.006

0.103

33120

17595

13.000

13.680

0.662

13.585

0.209

305490

380805

2.875

3.072

0.225

3.051

0.103

33600

18505

13.250

13.943

0.662

13.846

0.209

311360

395430

3.000

3.204

0.225

3.182

0.103

35060

20795

13.500

14.207

0.662

14.108

0.209

317240

411000

3.062

3.271

0.281

3.248

0.120

42710

18735

13.750

14.470

0.662

14.369

0.209

323110

426185

3.125

3.338

0.281

3.315

0.120

43590

19865

14.000

14.732

0.662

14.630

0.209

328990

441645

3.157

3.371

0.281

3.348

0.120

44020

20345

14.250

14.995

0.662

14.891

0.209

334860

457380

3.250

3.470

0.281

3.446

0.120

45330

22120

14.500

15.259

0.750

15.153

0.209

340740

474120

3.346

3.571

0.281

3.546

0.120

46670

23905

14.750

15.522

0.750

15.414

0.209

346610

490415

3.469

3.701

0.281

3.675

0.120

48390

26405

15.000

15.785

0.750

15.675

0.209

352490

506990

3.500

3.736

0.281

3.710

0.120

48820

27370

Bore Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

2.125

2.267

0.168

2.251

0.086

21870

2.188

2.334

0.168

2.318

0.086

2.250

2.399

0.168

2.382

0.086

2.312

2.467

0.200

2.450

2.357

2.535

0.200

2.440

2.602

2.500

Source: Spirolox Retaining Rings, RRN Series. All dimensions are in inches. Depth of groove d = (C − A)/2. Thickness indicated is for unplated rings; add 0.002 to upper thickness tolerance for plated rings. Standard material: carbon spring steel (SAE 1070–1090). Ring Thickness, F: For housing sizes 0.500 through 0.750, 0.035; for sizes 0.777 through 1.023, 0.042; for sizes 1.062 through 1.500, 0.050; for sizes 1.562 through 2.000, 0.062; for sizes 2.062 through 2.531, 0.078; for sizes 2.562 through 3.000, 0.093; for sizes 3.062 through 5.000, 0.111; for sizes 5.250 through 7.000, 0.156; for sizes 7.250 through 15.000, 0.187. Ring Free Diameter Tolerances: For housing sizes 0.500 through 1.500, +0.013, −0.000; for sizes 1.562 through 2.000, +0.020, −0.000; for sizes 2.062 through 2.531, + 0.025, −0.000; for sizes 2.562 through 3.000, +0.030, −0.000; for sizes 3.062 through 5.000, +0.035, −0.000; for sizes 5.250 through 6.000, +0.050, −0.000; for sizes 6.250 through 7.000, +0.055. −0.000; for sizes 7.250 through 10.500, +0.070, −0.000; for sizes 10.750 through 12.750, +0.120, −0.000; for sizes 13.000 through 15.000, +0.140, −0.000. Ring Thickness Tolerances: For housing sizes 0.500 through 1.500, ± 0.002; for sizes 1.562 through 5.000, ± 0.003; for sizes 5.250 through 6.000, ± 0.004; for sizes 6.250 through 15.000, ± 0.005. Groove Diameter Tolerances: For housing sizes 0.500 through 0.750, ± 0.002; for sizes 0.777 through 1.023, ± 0.003; for sizes 1.062 through 1.500, ± 0.004; for sizes 1.562 through 2.000, ± 0.005; for sizes 2.062 through 5.000, ± 0.006; for sizes 5.250 through 6.000, ± 0.007; for sizes 6.250 through 10.500, ± 0.008; for sizes 10.750 through 12.500, ± 0.010; for sizes 12.750 through 15.000, ± 0.012. Groove Width Tolerances: For housing sizes 0.500 through 1.023, +0.003, −0.000; for sizes 1.062 through 2.000, +0.004, −0.000; for sizes 2.062 through 5.000, +0.005, −0.000; for sizes 5.250 through 6.000, +0.006, −0.000; for sizes 6.250 through 7.000, +0.008, −0.000; for sizes 7.250 through 15.000, +0.008, −0.000.



;; ;; ;; ;; ;; ;;

1699

SIZE 0.469 to 0.669

G

SIZE 0.688 and UP

C A F

E

D

Table 10. Heavy Duty External Spiral Retaining Rings MIL-R-27426 Ring

Groove


Shaft Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

0.469 0.500 0.551 0.562 0.594 0.625 0.669 0.688 0.750 0.781 0.812 0.875 0.938 0.984 1.000 1.023 1.062 1.125 1.188 1.250 1.312 1.375 1.438 1.500 1.562 1.625 1.687 1.750 1.771 1.812 1.875 1.969 2.000 2.062 2.125 2.156 2.250 2.312 2.375 2.437 2.500 2.559 2.625 2.687

0.439 0.464 0.514 0.525 0.554 0.583 0.623 0.641 0.698 0.727 0.756 0.814 0.875 0.919 0.932 0.953 0.986 1.047 1.105 1.163 1.218 1.277 1.336 1.385 1.453 1.513 1.573 1.633 1.651 1.690 1.751 1.838 1.867 1.932 1.989 2.018 2.105 2.163 2.223 2.283 2.343 2.402 2.464 2.523

0.045 0.050 0.050 0.050 0.050 0.055 0.055 0.065 0.065 0.065 0.065 0.075 0.075 0.085 0.085 0.085 0.103 0.103 0.103 0.103 0.118 0.118 0.118 0.118 0.128 0.128 0.128 0.128 0.128 0.128 0.158 0.158 0.158 0.168 0.168 0.168 0.168 0.168 0.200 0.200 0.200 0.200 0.200 0.200

0.443 0.468 0.519 0.530 0.559 0.588 0.629 0.646 0.704 0.733 0.762 0.821 0.882 0.926 0.940 0.961 0.998 1.059 1.118 1.176 1.232 1.291 1.350 1.406 1.468 1.529 1.589 1.650 1.669 1.708 1.769 1.857 1.886 1.946 2.003 2.032 2.120 2.178 2.239 2.299 2.360 2.419 2.481 2.541

0.029 0.039 0.039 0.039 0.039 0.039 0.039 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.068 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086

1880 2530 2790 2840 3000 3160 3380 4170 4550 4740 4930 5310 5690 5970 6070 6210 7010 7420 7840 8250 8650 9070 9490 9900 12780 13290 13800 14320 14490 14820 15340 16110 16360 21220 21870 22190 23160 23790 24440 25080 25730 26340 27020 27650

Ring

Groove


Groove

Shaft Dia. A

Dia. G

Wall E

Dia. C

Width D

Ring

Groove

510 440 540 560 700 820 1070 960 1250 1430 1620 2000 2440 2790 2950 3170 2810 2890 3450 4110 4810 5650 6340 7060 6600 7330 8190 8760 9040 9440 9950 11040 11420 11820 12980 13390 14650 15510 16170 16840 17530 17940 18930 19640

3.500 3.543 3.625 3.687 3.750 3.875 3.938 4.000 4.250 4.375 4.500 4.750 5.000 5.250 5.500 5.750 6.000 6.250 6.500 6.750 7.000 7.250 7.500 7.750 8.000 8.250 8.500 8.750 9.000 9.250 9.500 9.750 10.000 10.250 10.500 10.750 11.000 11.250 11.500 11.750 12.000 12.250 12.500 12.750

3.293 3.333 3.411 3.469 3.527 3.647 3.708 3.765 4.037 4.161 4.280 4.518 4.756 4.995 5.228 5.466 5.705 5.938 6.181 6.410 6.648 6.891 7.130 7.368 7.606 7.845 8.083 8.324 8.560 8.798 9.036 9.275 9.508 9.745 9.984 10.221 10.459 10.692 10.934 11.171 11.410 11.647 11.885 12.124

0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.270 0.350 0.350 0.350 0.350 0.418 0.418 0.418 0.418 0.418 0.437 0.437 0.437 0.437 0.437 0.437 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.500 0.562 0.562 0.562 0.562 0.562 0.562

3.316 3.357 3.435 3.493 3.552 3.673 3.734 3.792 4.065 4.190 4.310 4.550 4.790 5.030 5.265 5.505 5.745 5.985 6.225 6.465 6.705 6.942 7.180 7.420 7.660 7.900 8.140 8.383 8.620 8.860 9.100 9.338 9.575 9.814 10.054 10.293 10.533 10.772 11.011 11.250 11.490 11.729 11.969 12.208

0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.139 0.139 0.139 0.139 0.174 0.174 0.174 0.174 0.174 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209 0.209

48820 49420 50560 51430 52310 54050 54930 55790 59280 61020 62770 66260 69740 83790 87780 91770 95760 122520 127420 132320 137220 142130 176240 182120 187990 193870 199740 205620 211490 217370 223240 229120 234990 240870 246740 252620 258490 264360 270240 276120 281990 287860 293740 299610

32250 33000 34490 35820 37180 39190 40230 41660 39370 40530 42810 47570 52580 57830 64720 70540 76610 82930 89510 96330 103400 111810 120170 128060 136200 144590 153220 160800 171250 180640 190280 201140 212810 223780 234490 246000 257230 269270 281590 294180 306450 319580 332360 346030



RETAINING RINGS

Table 10. (Continued) Heavy Duty External Spiral Retaining Rings MIL-R-27426 Shaft Dia. A 2.750 2.875 2.937 3.000 3.062 3.125 3.156 3.250 3.344 3.437

Ring Dia. G 2.584 2.702 2.760 2.818 2.878 2.936 2.965 3.054 3.144 3.234

Groove

Wall E 0.225 0.225 0.225 0.225 0.225 0.225 0.225 0.225 0.225 0.225

Dia. C 2.602 2.721 2.779 2.838 2.898 2.957 2.986 3.076 3.166 3.257

Width D 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103

Static Thrust Load (lb) Ring 32140 33600 34320 35060 35780 36520 36880 37980 39080 40170

Groove 20380 22170 23240 24340 25140 26290 26860 28320 29800 30980

Shaft Dia. A 13.000 13.250 13.500 13.750 14.000 14.250 14.500 14.750 15.000

Ring Dia. G 12.361 12.598 12.837 13.074 13.311 13.548 13.787 14.024 14.262

Wall E 0.662 0.662 0.662 0.662 0.662 0.662 0.750 0.750 0.750

Groove Static Thrust Load (lb) Dia. Width C D Ring Groove 12.448 0.209 305490 359330 12.687 0.209 311360 373530 12.927 0.209 317240 387340 13.166 0.209 323110 402090 13.405 0.209 328990 417110 13.644 0.209 334860 432410 13.884 0.209 340740 447250 14.123 0.209 346610 463090 14.363 0.209 352490 478450

Source: Spirolox Retaining Rings, RSN Series. All dimensions are in inches. Depth of groove d = (A − C)/2. Thickness indicated is for unplated rings; add 0.002 to upper tolerance for plated rings. Standard material: carbon spring steel (SAE 1070-1090). Ring Thickness, F: For shaft size 0.469, 0.025; for sizes 0.500 through 0.669, 0.035; for sizes 0.688 through 1.023, 0.042; for sizes 1.062 through 1.500, 0.050; for sizes 1.562 through 2.000, 0.062; for sizes 2.062 through 2.687, 0.078; for sizes 2.750 through 3.437, 0.093; for sizes 3.500 through 5.000, 0.111; for sizes 5.250 through 6.000, 0.127; for sizes 6.250 through 7.250, 0.156; for sizes 7.500 through 15.000, 0.187. Ring Free Diameter Tolerances: For shaft sizes 0.469 through 1.500, +0.000, −0.013; for sizes 1.562 through 2.000, +0.000, −0.020; for sizes 2.062 through 2.687, + 0.000, −0.025; for sizes 2.750 through 3.437, +0.000, −0.030; for sizes 3.500 through 5.000, +0.000, −0.035; for sizes 5.250 through 6.000, +0.000, −0.050; for sizes 6.250 through 7.000, +0.000, −0.060; for sizes 7.250 through 10.000, +0.000, −0.070; for sizes 10.250 through 12.500, +0.000, −0.090; for sizes 12.750 through 15.000, +0.000, −0.110. Ring Thickness Tolerances: For shaft sizes 0.469 through 1.500, ±0.002; for sizes 1.562 through 5.000, ±0.003; for sizes 5.250 through 6.000, ±0.004; for sizes 6.250 through 15.000, ±0.005. Groove Diameter Tolerances: For shaft sizes 0.469 through 0.562, ±0.002; for sizes 0.594 through 1.023, ±0.003; for sizes 1.062 through 1.500, ±0.004; for sizes 1.562 through 2.000, ±0.005; for sizes 2.062 through 5.000, ±0.006; for sizes 5.250 through 6.000, ±0.007; for sizes 6.250 through 10.000, ±0.008; for sizes 10.250 through 12.500, ±0.010; for sizes 12.750 through 15.000, ±0.012. Groove Width Tolerances: For shaft sizes 0.469 through 1.023, +0.003, −0.000; for sizes 1.062 through 2.000, +0.004, −0.000; for sizes 2.062 through 5.000, +0.005, −0.000; for sizes 5.250 through 6.000, +0.006; −0.000; for sizes 6.250 through 7.250, + 0.008, −0.000; for sizes 7.500 through 15.000, +0.008, −0.000.

Thrust Load Capacity: The most important criterion in determining which ring is best suited for a specific application is thrust load capacity. The strength of the retaining ring and groove must both be considered when analyzing the thrust load capacity of an application to determine whether the groove or the retaining ring is likely to fail first. When a retaining ring application fails, the fault will usually be with the groove, unless the groove material is of very high strength. Ring Material: The standard materials for spiral-wound retaining rings are SAE 1070 to 1090 carbon spring steels and 18-8 type 302 stainless steels. The 1070 to 1090 carbon spring steels provide high-strength retaining rings at low cost. Type 302 stainless steel withstands ordinary rusting. Other materials are used for specialized applications, such as the type 316 stainless frequently used in the food industry. For high-temperature use, superalloy A286 rings can be used at up to 900°F and Inconel X-750 at up to 1200°F. Other materials, such as 316 stainless steel, 17-7PH and Inconel stainless steels are sometimes used for special-purpose and custom-made rings. Standard ring are typically supplied uncoated, however, special finishes such as cadmium, phosphate, zinc, or black oxide coatings for carbon spring steel rings and passivation of stainless steel rings are available.



1701

Table 11. Important Dimensions of Inch Series External Retaining Rings MS 16624 A

;; ;; ;; L

GD

S

U

H Shaft Dia. D 0.125 0.156 0.188 0.197 0.219 0.236 0.250 0.276 0.281 0.312 0.344 0.354 0.375 0.394 0.406 0.438 0.469 0.500 0.551 0.562 0.594 0.625 0.669 0.672 0.688 0.750 0.781 0.812 0.844 0.875 0.938 0.984 1.000 1.023 1.062 1.125 1.188 1.250 1.312 1.375 1.438 1.500 1.562 1.625 1.687 1.750 1.772

Ring Dia. Thick. A T 0.112 0.010 0.142 0.010 0.168 0.015 0.179 0.015 0.196 0.015 0.215 0.015 0.225 0.025 0.250 0.025 0.256 0.025 0.281 0.025 0.309 0.025 0.320 0.025 0.338 0.025 0.354 0.025 0.366 0.025 0.395 0.025 0.428 0.025 0.461 0.035 0.509 0.035 0.521 0.035 0.550 0.035 0.579 0.035 0.621 0.035 0.621 0.035 0.635 0.042 0.693 0.042 0.722 0.042 0.751 0.042 0.780 0.042 0.810 0.042 0.867 0.042 0.910 0.042 0.925 0.042 0.946 0.042 0.982 0.050 1.041 0.050 1.098 0.050 1.156 0.050 1.214 0.050 1.272 0.050 1.333 0.050 1.387 0.050 1.446 0.062 1.503 0.062 1.560 0.062 1.618 0.062 1.637 0.062

Lugs: D = 0.125 to 0.236

Dia. G 0.117 0.146 0.175 0.185 0.205 0.222 0.230 0.255 0.261 0.290 0.321 0.330 0.352 0.369 0.382 0.412 0.443 0.468 0.519 0.530 0.559 0.588 0.629 0.631 0.646 0.704 0.733 0.762 0.791 0.821 0.882 0.926 0.940 0.961 0.998 1.059 1.118 1.176 1.232 1.291 1.350 1.406 1.468 1.529 1.589 1.650 1.669

Groove Width W 0.012 0.012 0.018 0.018 0.018 0.018 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.039 0.039 0.039 0.039 0.039 0.039 0.039 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.046 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.056 0.068 0.068 0.068 0.068 0.068

;;; ;;; ;;; ;;; ;;;

W

T

Margin E 0.012 0.015 0.018 0.018 0.021 0.021 0.030 0.030 0.030 0.033 0.033 0.036 0.036 0.036 0.036 0.039 0.039 0.048 0.048 0.048 0.051 0.054 0.060 0.060 0.063 0.069 0.072 0.075 0.080 0.081 0.084 0.087 0.090 0.093 0.096 0.099 0.105 0.111 0.120 0.126 0.132 0.141 0.141 0.144 0.147 0.150 0.153

Shaft Dia. D 1.812 1.875 1.969 2.000 2.062 2.125 2.156 2.250 2.312 2.375 2.438 2.500 2.559 2.625 2.688 2.750 2.875 2.938 3.000 3.062 3.125 3.156 3.250 3.346 3.438 3.500 3.543 3.625 3.688 3.750 3.875 3.938 4.000 4.250 4.375 4.500 4.750 5.000 5.250 5.500 5.750 6.000 6.250 6.500 6.750 7.000 7.500

E

Lugs: D = 4.25 to 8.00 Ring Dia. Thick. A T 1.675 0.062 1.735 0.062 1.819 0.062 1.850 0.062 1.906 0.078 1.964 0.078 1.993 0.078 2.081 0.078 2.139 0.078 2.197 0.078 2.255 0.078 2.313 0.078 2.377 0.078 2.428 0.078 2.485 0.078 2.543 0.093 2.659 0.093 2.717 0.093 2.775 0.093 2.832 0.093 2.892 0.093 2.920 0.093 3.006 0.093 3.092 0.093 3.179 0.093 3.237 0.109 3.277 0.109 3.352 0.109 3.410 0.109 3.468 0.109 3.584 0.109 3.642 0.109 3.700 0.109 3.989 0.109 4.106 0.109 4.223 0.109 4.458 0.109 4.692 0.109 4.927 0.125 5.162 0.125 5.396 0.125 5.631 0.125 5.866 0.156 6.100 0.156 6.335 0.156 6.570 0.156 7.009 0.187

Dia. G 1.708 1.769 1.857 1.886 1.946 2.003 2.032 2.120 2.178 2.239 2.299 2.360 2.419 2.481 2.541 2.602 2.721 2.779 2.838 2.898 2.957 2.986 3.076 3.166 3.257 3.316 3.357 3.435 3.493 3.552 3.673 3.734 3.792 4.065 4.190 4.310 4.550 4.790 5.030 5.265 5.505 5.745 5.985 6.225 6.465 6.705 7.180


Groove Width W 0.068 0.068 0.068 0.068 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.086 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.103 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.120 0.139 0.139 0.139 0.139 0.174 0.174 0.174 0.174 0.209

Margin E 0.156 0.159 0.168 0.171 0.174 0.183 0.186 0.195 0.201 0.204 0.207 0.210 0.210 0.216 0.219 0.222 0.231 0.237 0.243 0.246 0.252 0.255 0.261 0.270 0.270 0.276 0.279 0.285 0.291 0.297 0.303 0.306 0.312 0.276 0.276 0.285 0.300 0.315 0.330 0.351 0.366 0.381 0.396 0.411 0.426 0.441 0.480


RETAINING RINGS

Source: Industrial Retaining Rings, 3100 Series. All dimensions are in inches. Depth of groove d = (D − G)/2. Thickness indicated is for unplated rings; for most plated rings, the maximum ring thickness will not exceed the minimum groove width (W) minus 0.0002 inch. Standard material: carbon spring steel (SAE 1060-1090). Ring Free Diameter Tolerances: For shaft sizes 0.125 through 0.250, +0.002, −0.004; for sizes 0.276 through 0.500, +0.002, −0.005; for sizes 0.551 through 1.023, +0.005, −0.010; for sizes 1.062 through 1.500, +0.010, −0.015; for sizes 1.562 through 2.000, +0.013, −0.020; for sizes 2.062 through 2.500, +0.015, −0.025; for sizes 2.559 through 5.000, +0.020, −0.030; for sizes 5.250 through 6.000, +0.020, −0.040; for sizes 6.250 through 6.750, +0.020, −0.050; for sizes 7.000 and 7.500, +0.050, −0.130. Ring Thickness Tolerances: For shaft sizes 0.125 and 0.156, ±0.001; for sizes 0.188 through 1.500, ±0.002; for sizes 1.562 through 5.000, ±0.003; for sizes 5.250 through 6.000, ±0.004; for sizes 6.250 through 7.500, ±0.005. Groove Diameter Tolerances: For shaft sizes 0.125 through 0.250, ±0.0015; for sizes 0.276 through 0.562, ±0.002; for sizes 0.594 through 1.023, ±0.003; for sizes 1.062 though 1.500, ±0.004; for sizes 1.562 through 2.000, ±0.005; for sizes 2.062 through 5.000, ±0.006; for sizes 5.250 through 6.000, ±0.007; for sizes 6.250 through 7.500, ±0.008. Groove Width Tolerances: For shaft sizes 0.125 through 0.236, +0.002, −0.000; for sizes 0.250 through 1.023, +0.003, −0.000; for sizes 1.062 through 2.000, +0.004, −0.000; for sizes 2.062 through 5.000, +0.005, −0.000; for sizes 5.250 through 6.000, +0.006, −0.000; for sizes 6.250 through 7.500, +0.008, −0.000.

A

T L

S

U

H

;;; ;;; ;;; ;;; ;;; ;;; ;;;

;; ;

W

Lugs: D = 2.062 to 2.750 D = 3.000 to 4.625

DG

E

Table 12. Important Dimensions of Inch Series Internal Retaining Rings Ring

Groove

Ring

Groove

Housing Dia. D

Dia. A

Thick. T

Dia. G

Width W

Margin E

Housing Dia. D

Dia. A

Thick. T

Dia. G

Width W

Margin E

0.250

0.280

0.015

0.268

0.018

0.027

2.500

2.775

0.078

2.648

0.086

0.222

0.312

0.346

0.015

0.330

0.018

0.027

2.531

2.775

0.078

2.681

0.086

0.225

0.375

0.415

0.025

0.397

0.029

0.033

2.562

2.844

0.093

2.714

0.103

0.228

0.438

0.482

0.025

0.461

0.029

0.036

2.625

2.910

0.093

2.781

0.103

0.234

0.453

0.498

0.025

0.477

0.029

0.036

2.677

2.980

0.093

2.837

0.103

0.240

0.500

0.548

0.035

0.530

0.039

0.045

2.688

2.980

0.093

2.848

0.103

0.240

0.512

0.560

0.035

0.542

0.039

0.045

2.750

3.050

0.093

2.914

0.103

0.246

0.562

0.620

0.035

0.596

0.039

0.051

2.812

3.121

0.093

2.980

0.103

0.252

0.625

0.694

0.035

0.665

0.039

0.060

2.835

3.121

0.093

3.006

0.103

0.255

0.688

0.763

0.035

0.732

0.039

0.066

2.875

3.191

0.093

3.051

0.103

0.264

0.750

0.831

0.035

0.796

0.039

0.069

2.953

3.325

0.093

3.135

0.103

0.273

0.777

0.859

0.042

0.825

0.046

0.072

3.000

3.325

0.093

3.182

0.103

0.273

0.812

0.901

0.042

0.862

0.046

0.075

3.062

3.418

0.109

3.248

0.120

0.279

0.866

0.961

0.042

0.920

0.046

0.081

3.125

3.488

0.109

3.315

0.120

0.285

0.875

0.971

0.042

0.931

0.046

0.084

3.149

3.523

0.109

3.341

0.120

0.288

0.901

1.000

0.042

0.959

0.046

0.087

3.156

3.523

0.109

3.348

0.120

0.288

0.938

1.041

0.042

1.000

0.046

0.093

3.250

3.623

0.109

3.446

0.120

0.294

1.000

1.111

0.042

1.066

0.046

0.099

3.346

3.734

0.109

3.546

0.120

0.300

1.023

1.136

0.042

1.091

0.046

0.102

3.469

3.857

0.109

3.675

0.120

0.309

1.062

1.180

0.050

1.130

0.056

0.102

3.500

3.890

0.109

3.710

0.120

0.315



1703

Table 12. (Continued) Important Dimensions of Inch Series Internal Retaining Rings Ring

Groove

Ring

Groove

Housing Dia. D

Dia. A

Thick. T

Dia. G

Width W

Margin E

Housing Dia. D

Dia. A

Thick. T

Dia. G

Width W

Margin E

1.125

1.249

0.050

1.197

0.056

0.108

3.543

3.936

0.109

3.755

0.120

0.318

1.181

1.319

0.050

1.255

0.056

0.111

3.562

3.936

0.109

3.776

0.120

0.321

1.188

1.319

0.050

1.262

0.056

0.111

3.625

4.024

0.109

3.841

0.120

0.324

1.250

1.388

0.050

1.330

0.056

0.120

3.740

4.157

0.109

3.964

0.120

0.336

1.259

1.388

0.050

1.339

0.056

0.120

3.750

4.157

0.109

3.974

0.120

0.336

1.312

1.456

0.050

1.396

0.056

0.126

3.875

4.291

0.109

4.107

0.120

0.348

1.375

1.526

0.050

1.461

0.056

0.129

3.938

4.358

0.109

4.174

0.120

0.354

1.378

1.526

0.050

1.464

0.056

0.129

4.000

4.424

0.109

4.240

0.120

0.360

1.438

1.596

0.050

1.528

0.056

0.135

4.125

4.558

0.109

4.365

0.120

0.360

1.456

1.616

0.050

1.548

0.056

0.138

4.250

4.691

0.109

4.490

0.120

0.360

1.500

1.660

0.050

1.594

0.056

0.141

4.331

4.756

0.109

4.571

0.120

0.360

1.562

1.734

0.062

1.658

0.068

0.144

4.500

4.940

0.109

4.740

0.120

0.360

1.575

1.734

0.062

1.671

0.068

0.144

4.625

5.076

0.109

4.865

0.120

0.360

1.625

1.804

0.062

1.725

0.068

0.150

4.724

5.213

0.109

4.969

0.120

0.366

1.653

1.835

0.062

1.755

0.068

0.153

4.750

5.213

0.109

4.995

0.120

0.366

1.688

1.874

0.062

1.792

0.068

0.156

5.000

5.485

0.109

5.260

0.120

0.390

1.750

1.942

0.062

1.858

0.068

0.162

5.250

5.770

0.125

5.520

0.139

0.405

1.812

2.012

0.062

1.922

0.068

0.165

5.375

5.910

0.125

5.650

0.139

0.405

1.850

2.054

0.062

1.962

0.068

0.168

5.500

6.066

0.125

5.770

0.139

0.405

1.875

2.054

0.062

1.989

0.068

0.171

5.750

6.336

0.125

6.020

0.139

0.405

1.938

2.141

0.062

2.056

0.068

0.177

6.000

6.620

0.125

6.270

0.139

0.405

2.000

2.210

0.062

2.122

0.068

0.183

6.250

6.895

0.156

6.530

0.174

0.420

2.047

2.280

0.078

2.171

0.086

0.186

6.500

7.170

0.156

6.790

0.174

0.435

2.062

2.280

0.078

2.186

0.086

0.186

6.625

7.308

0.156

6.925

0.174

0.450

2.125

2.350

0.078

2.251

0.086

0.189

6.750

7.445

0.156

7.055

0.174

0.456

2.165

2.415

0.078

2.295

0.086

0.195

7.000

7.720

0.156

7.315

0.174

0.471

2.188

2.415

0.078

2.318

0.086

0.195

7.250

7.995

0.187

7.575

0.209

0.486

2.250

2.490

0.078

2.382

0.086

0.198

7.500

8.270

0.187

7.840

0.209

0.510

2.312

2.560

0.078

2.450

0.086

0.207

7.750

8.545

0.187

8.100

0.209

0.525

2.375

2.630

0.078

2.517

0.086

0.213

8.000

8.820

0.187

8.360

0.209

0.540

2.440

2.702

0.078

2.584

0.086

0.216

8.250

9.095

0.187

8.620

0.209

0.555

Source: Industrial Retaining Rings, 3000 Series. All dimensions are in inches. Depth of groove d = (G − D)/2. Thickness indicated is for unplated rings. Standard material: carbon spring steel (SAE 1060-1090). Ring Free Diameter Tolerances: For housing sizes 0.250 through 0.777, +0.010, −0.005; for sizes 0.812 through 1.023, +0.015, − 0.010; for sizes 1.062 through 1.500, + 0.025, − 0.020; for sizes 1.562 through 2.000, +0.035, −0.025; for sizes 2.047 through 3.000, +0.040, −0.030; for sizes 3.062 through 3.625, ±0.055; for sizes 3.740 through 6.000, ±0.065; for sizes 6.250 through 7.000, ±0.080; for sizes 7.250 through 8.250, ±0.090. Ring Thickness Tolerances: For housing sizes 0.250 through 1.500, ±0.002; for sizes 1.562 through 5.000, ±0.003; for sizes 5.250 through 6.000, ±0.004; for sizes 6.250 through 8.250, ±0.005. Groove Diameter Tolerances: For housing sizes 0.250 and 0.312, ±0.001; for sizes 0.375 through 0.750, ±0.002; for sizes 0.777 through 1.023 ±0.003; for sizes 1.062 through 1.500, ±0.004; for sizes 1.562 through 2.000, ±0.005; for sizes 2.047 through 5.000 ±0.006; for sizes 5.250 through 6.000, ±0.007; for sizes 6.250 through 8.250, ±0.008. Groove Width Tolerances: For housing sizes 0.250 and 0.312, +0.002, − 0.000; for sizes 0.375 through 1.023, +0.003, −0.000; for sizes 1.062 through 2.000, +0.004, −0.000; for sizes 2.047 through 5.000, +0.005; −0.000; for sizes 5.250 through 6.000, +0.006, −0.000; for sizes 6.250 through 8.250, +0.008, −0.000.



RETAINING RINGS

;; ;;

Table 13. Important Dimensions of Inch Series External Retaining Rings MS16632 L

AB

T

Shaft Diameter D 0.125 0.156 0.188 0.219 0.236 0.250 0.281 0.312 0.375 0.406 0.437 0.500 0.562 0.625 0.687 0.750 0.812 0.875 0.937 1.000 1.125 1.188 1.250 1.375 1.500 1.750 2.000

Free Dia. A 0.102 0.131 0.161 0.187 0.203 0.211 0.242 0.270 0.328 0.359 0.386 0.441 0.497 0.553 0.608 0.665 0.721 0.777 0.830 0.887 0.997 1.031 1.110 1.220 1.331 1.555 1.777

Ring Thickness T 0.015 0.015 0.015 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.035 0.035 0.035 0.042 0.042 0.042 0.042 0.042 0.042 0.050 0.050 0.050 0.050 0.050 0.062 0.062

Diameter B 0.164 0.205 0.245 0.275 0.295 0.311 0.344 0.376 0.448 0.485 0.516 0.581 0.653 0.715 0.780 0.845 0.915 0.987 1.054 1.127 1.267 1.321 1.410 1.550 1.691 1.975 2.257

Diameter G 0.106 0.135 0.165 0.193 0.208 0.220 0.247 0.276 0.335 0.364 0.393 0.450 0.507 0.563 0.619 0.676 0.732 0.789 0.843 0.900 1.013 1.047 1.126 1.237 1.350 1.576 1.800

;;; ;;; ;;; ;;; ;;;

W

GD

E

Groove Width W 0.018 0.018 0.018 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.039 0.039 0.039 0.046 0.046 0.046 0.046 0.046 0.046 0.056 0.056 0.056 0.056 0.056 0.068 0.068

aStatic

Margin E 0.020 0.020 0.022 0.026 0.028 0.030 0.034 0.036 0.040 0.042 0.044 0.050 0.056 0.062 0.068 0.074 0.080 0.086 0.094 0.100 0.112 0.140 0.124 0.138 0.150 0.174 0.200

Thrust Load (lb) Ring Groove 85 40 110 55 130 70 260 100 280 115 295 130 330 170 370 200 440 265 480 300 515 340 825 440 930 550 1030 690 1700 820 1850 985 2010 1150 2165 1320 2320 1550 2480 1770 3300 2200 3500 2900 3600 2700 4000 3300 4400 4000 6400 5300 7300 7000

a Thrust Load Safety Factors: Ring, 4; groove, 2. Groove wall thrust loads are for grooves machined in cold-rolled steel with a tensile yield strength of 45,000 psi; for other shaft materials, the thrust load varies proportionally with the yield strength. Source: Industrial Retaining Rings, 2000 Series. All dimensions are in inches. Depth of groove d = (D − G)/2. Standard material: carbon spring steel (SAE 1060-1090). Thickness indicated is for unplated rings; for most plated rings with shaft sizes less than 1.000 inch, the maximum thickness will not exceed the minimum groove width (W) minus 0.0002 inch; for larger rings, the ring thickness may increase by 0.002 inch. Groove Maximum Bottom Radii: For shaft diameters less than 0.500 inch, 0.005 inch; for shaft sizes 0.500 through 1.000 inch, 0.010 inch; all larger sizes, 0.015 inch. Ring Free Diameter Tolerances: For shaft sizes 0.125 through 0.188, +0.002, −0.004; for sizes 0.219 through 0.437, +0.003, −0.005; for sizes 0.500 through 0.625, ±0.006; for sizes 0.687 through 1.000, ±0.007; for sizes 1.125 through 1.500, ±0.008; for sizes 1.750 and 2.000, ±0.010. Ring Thickness Tolerances: For shaft sizes 0.125 through 1.500, ±0.002; for sizes 1.750 and 2.000, ±0.003. Groove Diameter Tolerances: For shaft sizes 0.125 through 0.188, ±0.0015; for sizes 0.219 through 0.437, ±0.002; for sizes 0.500 through 1.000, ±0.003; for sizes 1.125 through 1.500, ±0.004; for sizes 1.750 and 2.000, ±0.005. Groove Width Tolerances: For shaft sizes 0.125 through 0.188, +0.002, −0.000; for sizes 0.219 through 1.000, +0.003, −0.000; for sizes 1.125 through 2.000, +0.004, −0.000.



1705

;;; ;;; ;;; ;;;

Table 14. Important Dimensions of Inch Series External Retaining Rings MS16633 W

A B

GD

E

T Shaft Diameter D 0.040 0.062 0.062a 0.062b 0.094 0.094 0.110 0.125 0.140 0.140c 0.140d 0.156 0.172 0.188 0.188 0.218 0.250 0.312 0.375 0.437 0.437 0.500 0.625 0.744 0.750 0.750 0.875 0.985 1.000 1.188 1.375

Free Dia. A 0.025 0.051 0.051 0.051 0.073 0.069 0.076 0.094 0.100 0.108 0.102 0.114 0.125 0.145 0.122 0.185 0.207 0.243 0.300 0.337 0.375 0.392 0.480 0.616 0.616 0.574 0.668 0.822 0.822 1.066 1.213

Ring Thickness T 0.010 0.010 0.010 0.020 0.015 0.015 0.015 0.015 0.015 0.015 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.025 0.035 0.035 0.035 0.042 0.042 0.050 0.050 0.050 0.050 0.050 0.050 0.062 0.062

Diameter B 0.079 0.140 0.156 0.187 0.187 0.230 0.375 0.230 0.203 0.250 0.270 0.282 0.312 0.335 0.375 0.437 0.527 0.500 0.660 0.687 0.600 0.800 0.940 1.000 1.000 1.120 1.300 1.500 1.500 1.626 1.875

Diameter G 0.026 0.052 0.052 0.052 0.074 0.074 0.079 0.095 0.102 0.110 0.105 0.116 0.127 0.147 0.125 0.188 0.210 0.250 0.303 0.343 0.380 0.396 0.485 0.625 0.625 0.580 0.675 0.835 0.835 1.079 1.230

Groove Width W 0.012 0.012 0.012 0.023 0.018 0.018 0.018 0.018 0.018 0.018 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.029 0.039 0.039 0.039 0.046 0.046 0.056 0.056 0.056 0.056 0.056 0.056 0.068 0.068

Margin E 0.014 0.010 0.010 0.010 0.020 0.020 0.030 0.030 0.038 0.030 0.034 0.040 0.044 0.040 0.062 0.030 0.040 0.062 0.072 0.094 0.058 0.104 0.140 0.118 0.124 0.170 0.200 0.148 0.164 0.108 0.144

aStatic Thrust Load (lb) Ring Groove 13 7 20 7 20 7 40 7 45 20 45 20 55 40 65 45 70 60 70 45 150 55 165 70 180 90 195 90 195 135 225 75 260 115 325 225 685 315 800 485 800 290 1100 600 1370 1040 1940 1050 1960 1100 1960 1500 2200 2050 2570 1710 2620 1900 3400 1500 4100 2300

a Thrust Load Safety Factors: Ring 3; groove, 2.

Source: Industrial Retaining Rings, 1000 Series. All dimensions are in inches. Depth of groove d = (D − G)/2. Standard material: carbon spring steel (SAE 1060 –1090). Thickness indicated is for unplated rings; for most plated rings with shaft sizes less than 0.625, the maximum ring thickness will not exceed the minimum groove width (W) minus 0.0002 inch; for larger rings, the thickness may increase by 0.002 inch. Groove Maximum Bottom Radii: For shaft sizes 0.040 and 0.062, 0.003 inch; for sizes 0.094 through 0.250, 0.005 inch; for sizes 0.312 through 0.437, 0.010 inch; for sizes 0.500 through 1.375, 0.015 inch. Ring Free Diameter Tolerances: For shaft sizes 0.040 through 0.250, +0.001, −0.003; for sizes 0.312 through 0.500, +0.002, −0.004; for sizes 0.625 through 1.000, +0.003, −0.005; for sizes 1.188 and 1.375, +0.006, −0.010. Ring Thickness Tolerances: For shaft sizes 0.040 and 0.062a, ±0.001; for sizes 0.062b through 1.000, ±0.002; for sizes 1.188 and 1.375, ±0.003. Groove Diameter Tolerances: For shaft sizes 0.040 through 0.218, +0.002, −0.000; for sizes 0.250 through 1.000, +0.003, −0.000; for sizes 1.188 and 1.375, +0.005, −0.000. Grove Width Tolerances: For shaft sizes 0.040 through 0.140c, +0.002, −0.000; for sizes 0.140d through 1.000, +0.003, −0.000; for sizes 1.188 and 1.375, +0.004, −0.000.



RETAINING RINGS

;;; ;;; ;;; ;;;

Table 15. Dimensions of Inch Series External Retaining Rings MS3215 W

A B

GD

E

T Ring

Groove

a Static

Shaft Diameter D

Free Dia. A

Thickness T

Diameter B

Diameter G

Width W

Margin E

0.094 0.125 0.156 0.188 0.219 0.250 0.312 0.312 0.375 0.438 0.500 0.562

0.072 0.093 0.113 0.143 0.182 0.204 0.242 0.242 0.292 0.332 0.385 0.430

0.015 0.015 0.025 0.025 0.025 0.025 0.025 0.035 0.035 0.035 0.042 0.042

0.206 0.270 0.335 0.375 0.446 0.516 0.588 0.588 0.660 0.746 0.810 0.870

0.074 0.095 0.116 0.147 0.188 0.210 0.250 0.250 0.303 0.343 0.396 0.437

0.018 0.018 0.029 0.029 0.029 0.029 0.029 0.039 0.039 0.039 0.046 0.046

0.020 0.030 0.040 0.040 0.031 0.040 0.062 0.062 0.072 0.096 0.104 0.124

Thrust Load (lb)

Ring 55 75 150 180 215 250 300 420 520 600 820 930

Groove 13 25 40 50 50 75 135 135 190 285 360 480

a Thrust Load Safety Factors: Ring, 3; groove, 2.

Source: Industrial Retaining Rings, 1200 Series. All dimensions are in inches. Depth of groove d = (D − G)/2. Standard material: carbon spring steel (SAE 1060-1090). Thickness indicated is for unplated rings; for most plated rings the maximum thickness will not exceed the minimum groove width (W) minus 0.0002 inch. Groove Maximum Bottom Radii: For shaft sizes 0.250 and smaller, 0.005 inch; for sizes 0.312 through 0.438, 0.010 inch; for sizes 0.500 and 0.562, 0.015 inch. Ring Free Diameter Tolerances: For shaft sizes 0.094 through 0.156, +0.001, −0.003; for sizes 0.188 through 0.312, ±0.003; for sizes 0.375 through 0.562, ±0.004. Ring Thickness Tolerances: For all shaft sizes, ±0.002. Groove Diameter Tolerances: For shaft sizes 0.094 through 0.188, +0.002, −0.000; for sizes 0.219 and 0.250, ±0.002; for sizes 0.312 through 0.562, ±0.003. Groove Width Tolerances: For shaft sizes 0.094 and 0.125, +0.002, − 0.000; for sizes 0.156 through 0.562, +0.003, −0.000.

The thrust load capacities shown in the tables of this section include safety factors. Usually, a safety factor of 2 is used for groove thrust load calculations when the load is applied through a retained part and groove with both having sharp corners and where the minimum side clearance exists between the retained part and the shaft or bore. Groove thrust load values in the tables of this section are based on these conditions. A safety factor of 3 is usual for calculations of thrust load capacity based on ring shear. Ideally, the corner of a retained part in contact with a retaining ring should have square corners and contact the ring as closely as possible to the shaft or housing. The tabulated thrust capacities assume that minimum clearances exist between the retained part and shaft or housing, that the groove and retained part have square corners, and that contact between the retained part and the ring occurs close to the shaft or housing. If these conditions apply, the tabulated thrust loads apply. If the application does not meet the previous conditions but the side clearances, radii, and chamfers are less than the maximum total radius or chamfer of Fig. 1, then the thrust load capacity must be reduced by dividing the tabulated value by 2. The maximum total radius is given by 0.5(b − d) and the maximum total chamfer by 0.375(b − d), where b is the radial wall thickness, and d is the groove depth. The recommended maximum total radius or chamfer specifications are intended to be used as guidelines by the designer, and to ensure the ring application will withstand published and calculated values of static thrust loads.



1707

In analyzing the retaining ring loading conditions, a static, uniformly applied load is usually assumed. Dynamic and eccentric loads, however, are frequently encountered. Eccentric loading occurs when the load is concentrated on a small portion of the ring, such as may be caused by incorrectly machined surfaces, cocking of the retained part, and axial misalignment of parts. Conditions leading to eccentric loading on the ring should be avoided. In addition to the factors that affect the static thrust capacity, applications in which shock or impact loading occurs must be evaluated very carefully and tested in service to assess the effect of the mass and velocity of the retained part striking the ring. Vibration caused by impact loading can also cause the ring to fail if the resonant frequency of the system (retaining ring application) coincides with the resonant frequency of the retaining ring.

;;;;; ; ; ; ; ;;; ; ; ;;; ; ; ;;; ; ;;;; ;;;;;

Table 16. Dimensions of Inch Series Self-Locking External Retaining Rings A

T L

S

U

H Shaft Diameter Min. D 0.078 0.092 0.123 0.134 0.154 0.185 0.248 0.310 0.373 0.434 0.497 0.622 0.745

Max. D 0.080 0.096 0.127 0.138 0.158 0.189 0.252 0.316 0.379 0.440 0.503 0.628 0.755

Ring

Free Dia. A 0.074 0.089 0.120 0.130 0.150 0.181 0.238 0.298 0.354 0.412 0.470 0.593 0.706

Thickness T 0.025 0.025 0.025 0.025 0.025 0.035 0.035 0.042 0.042 0.050 0.050 0.062 0.062

D

;;; ;;; ;;; ;;; ;;;

Optical Groove

Diameter G

Width W

0.041 0.048 0.048 0.056 0.056 0.069 0.069

GD

E

aStatic

Margin E

The use of grooves with these shaft sizes is not suggested.

0.240 0.303 0.361 0.419 0.478 0.599 0.718

W

0.030 0.030 0.030 0.030 0.040 0.045 0.050

Thrust Load (lb) Ring Groove 10 0 10 0 20 0 20 0 22 0 25 0 35 90 50 110 55 185 60 280 65 390 85 570 90 845

a Thrust Load Safety Factors: Ring, 1; groove, 2.

Source: Industrial Retaining Rings, 7100 Series. All dimensions are in inches. Depth of groove d = (D − G)/2. Standard material: carbon spring steel (SAE 1060-1090). Thickness indicated is for unplated rings; for plated, phosphate coated, and stainless steel rings, the maximum ring thickness may be exceeded by 0.002 inch. Ring Free Diameter Tolerances: For shaft sizes 0.078 through 0.138, +0.002, −0.003; for sizes 0.154 through 0.252, +0.002, −0.004; for sizes 0.310 through 0.440, +0.003, −0.005; for sizes 0.497 through 0.755, +0.004, −0.006. Ring Thickness Tolerances: For shaft sizes 0.078 through 0.158, ±0.002; for sizes 0.185 through 0.503, ±0.003; for sizes 0.622 through 0.755, ±0.004. Groove Diameter Tolerances: For shaft sizes less than 0.248, grooves are not recommended; for other sizes, grooves are optional. For shaft sizes 0.248 through 0.316, +0.005, −0.0015; for sizes 0.373 through 0.628, +0.001, −0.002; for sizes 0.745 and 0.755, +0.002, −0.003. Groove Width Tolerances: For shaft sizes 0.248 through 0.379, +0.003, −0.000; for sizes 0.434 through 0.755, +0.004, −0.000.



RETAINING RINGS

;;; ;;;;; ; ;;; ;;;;; ; ;;; ;;;; ;;; ;;;; ;;; ;;;;; ; ;;; ;;;;; ; ;;; ;;;

; ; ; ;;; ; ; ;;; ;;; ;;; ;;; ; ; ;;; ; ; ;

Table 17. Inch Series Internal and External Self-Locking Retaining Rings

Internal C

T

C

D

E

Housing

Ring Dimensions

Min. D

Max. D

Thick. T

Dia. D

Margin E

Static Thrust Load

0.311 0.374 0.437 0.498 0.560 0.623 0.748 0.873 0.936 0.998 1.248 1.436 1.498

0.313 0.376 0.439 0.502 0.564 0.627 0.752 0.877 0.940 1.002 1.252 1.440 1.502

0.010 0.010 0.010 0.010 0.010 0.010 0.015 0.015 0.015 0.015 0.015 0.015 0.015

0.136 0.175 0.237 0.258 0.312 0.390 0.500 0.625 0.687 0.750 0.938 1.117 1.188

0.040 0.040 0.040 0.040 0.040 0.040 0.060 0.060 0.060 0.060 0.060 0.060 0.060

80 75 70 60 50 45 75 70 70 70 60 60 60

External T

D

E

Shaft

Ring Dimensions

Min. D

Max. D

Thick. T

Dia. D

Margin E

Static Thrust Load

0.093 0.124 0.155 0.187 0.218 0.239 0.249 0.311 0.374 0.437 0.498 0.560 0.623 0.748 0.873 0.998

0.095 0.126 0.157 0.189 0.220 0.241 0.251 0.313 0.376 0.440 0.502 0.564 0.627 0.752 0.877 1.002

0.010 0.010 0.010 0.010 0.010 0.015 0.010 0.010 0.010 0.015 0.015 0.015 0.015 0.015 0.015 0.015

0.250 0.325 0.356 0.387 0.418 0.460 0.450 0.512 0.575 0.638 0.750 0.812 0.875 1.000 1.125 1.250

0.040 0.040 0.040 0.040 0.040 0.060 0.040 0.040 0.040 0.060 0.060 0.060 0.060 0.060 0.060 0.060

15 20 25 35 35 35 40 40 40 50 50 50 50 50 55 60

Source: Industrial Retaining Rings, 6000 Series (internal) and 6100 Series (external). All dimensions are in inches, thrust loads are in pounds. Thickness indicated is for unplated rings. Standard material: carbon spring steel (SAE 1060-1090). Internal Rings: Thrust loads are for rings made of standard material inserted into cold-rolled, lowcarbon housing. Ring Thickness Tolerances: For housing sizes 0.311 through 0.627, ±0.001; for sizes 0.748 through 1.502, ±0.002. Ring Diameter Tolerances: For housing sizes 0.311 through 0.439, ±0.005; for sizes 0.498 through 1.502, ±0.010. External Rings: Thrust loads are for rings made of standard material installed onto cold-rolled, low-carbon shafts. Ring Thickness Tolerances: For shaft sizes 0.093 through 0.220, ±0.001; for size 0.239, ±0.002; for sizes 0.249 through 0.376, ±0.001; for sizes 0.437 through 1.002, ±0.002. Ring Diameter Tolerances: For shaft sizes 0.093 through 0.502, ±0.005; for sizes 0.560 through 1.002, ±0.010.

Centrifugal Capacity: Proper functioning of a retaining ring depends on the ring remaining seated on the groove bottom. External rings “cling” to the groove bottom because the ring ID is slightly smaller than the diameter at the bottom of the groove. Ring speed should be kept below the allowable steady-state speed of the ring, or self-locking rings specially designed for high-speed applications should be used, otherwise an external ring can lose its grip on the groove. Applications of large retaining rings that tend to spin in their grooves when subjected to sudden acceleration or deceleration of the retained part can benefit from a ring with more “cling” (i.e., a smaller interior diameter) as long as the stress of installation is within permissible limits. Special rings are also available that lock into a hole in the bottom of the groove, thereby preventing rotation. The following equation can be used to determine the allowable steady-state speed N of an external spiral retaining ring:



N =

1709

0.466C 1 E 3 × 10 12 --------------------------------------------------R n3 ( 1 + C 1 ) ( R o3 – R i3 )

(1)

where the speed N is in revolutions per minute, C1 is the minimum ring cling to groove bottom, E is the ring radial wall, Rn is the free neutral ring radius, Ro is the free outside ring radius, and Ri is the free inside ring radius, all in inches. For external spiral rings, the minimum ring cling is given by: C1 = (C − G)/G, where C is the mean groove diameter in inches, and G is the maximum ring free ID in inches.

; ; ;; ;; ; ; ;; ;; ; ; ;; ;; ; ; ;; ;; ; ; ;; ;; ; ; ;; ;; ; ; ;; ;; ;; ;; ;;

(a)

(b)

(c)

Fig. 2. Localized Groove Yielding under Load. (a) Groove Profile before Loading; (b) Localized Yielding of Retained Part and Groove under Load; (c) Groove Profile after Loading beyond Thrust Capacity (Courtesy Spirolox Retaining Rings)

Rotation between Parts: The use of spiral-wound rings to retain a rotating part should be limited to applications with rotation in only one direction. The ring should be matched so that the rotation tends to wind the spring into the groove. External rings should be wound in the direction of rotation of the retained part but internal rings should be wound against the direction of rotation of the rotating part. Failure to observe these precautions will cause the ring to wind out of the groove. Spiral-wound rings can be obtained with either righthand (normal rotation) or left-hand (reverse rotation) wound configurations. Stamped retaining rings do not have these limitations, and may be used for applications that require rotation of the retained part, regardless of the direction of rotation. Retaining Ring Failure.—Failure of a retaining ring application can result from failure of the ring itself, failure of the groove, or both. If a ring fails, the cause is likely to be from shearing of the ring. Shear failure occurs when a ring is installed in a groove and loaded by a retained part with both the groove and the retained part having a compressive yield strength greater than 45,000 psi; or when the load is applied through a retained part and groove, both having sharp corners and line-to-line contact; or when the ring is too thin in section compared with its diameter. To examine the possibility of ring shear, the allowable thrust Ps, based on the shear strength of the ring material, is given by πDtS P s = ---------------s (2) K where Ps is in lbf, D is the shaft or housing diameter in inches, t is the ring thickness in inches, Ss is the shear strength of the ring material in lb/in.2, and K is the factor of safety. Groove Failure: The most common type of groove failure is yielding of the groove material that occurs when the thrust load, applied through the retaining ring against the corner of the groove, exceeds the compressive yield strength of the groove. This yielding of the groove results from a low compressive yield strength of the groove material, and allows the ring to tilt and come out of the groove, as illustrated in Fig. 2(b). When dishing of a ring occurs as a result of yielding in the groove material, a bending moment across the cross-section of the ring generates a tensile stress that is highest at the



RETAINING RINGS

interior diameter of the ring. If the maximum stress is greater than the yield strength of the ring material, the ring ID will grow and the ring will become permanently dished in shape. To determine the thrust load capacity of a ring based on groove deformation, the allowable angle of ring deflection must be calculated, then the thrust load based on groove yield can be determined. However, for spiral-wound rings, the thrust load PG that initiates the onset of groove deformation can be estimated from the following: πDdS P G = ----------------yK

(3)

where PG is given in lbf, D is the shaft or housing diameter in inches, d is the groove depth in inches, Sy is the yield strength of the groove material, and K is the safety factor. For stamped rings, estimate PG by multiplying Equation (3) by the fraction of the groove circumference that contacts the ring. The thrust load capacity of a particular retaining ring application can be increased by changing the workpiece material that houses the groove. Increasing the yield strength of the groove material increases the thrust load capacity of the retaining ring application. However, increasing the strength of the groove material may cause the failure mechanism to shift from groove deformation to ring shear. Therefore, use the lower of the values obtained from Equations (2) and (3) for the allowable thrust load. Groove Design and Machining: In most applications, grooves are located near the end of a shaft or housing bore to facilitate installation and removal of the rings. The groove is normally located a distance at least two to three times the groove depth from the end of the shaft or bore. If the groove is too close to the end of the shaft or bore, the groove may shear or yield. The following equation can be used to determine the minimum safe distance Y of a groove from the end of a shaft or housing: KP t Y = ------------πDS c

(4)

where K is the factor of safety, Pt is the thrust load on the groove in pounds, Sc is the shear strength of the groove material in psi, and D is the shaft or housing diameter in inches. A properly designed and machined groove is just as important in a retaining ring application as the ring itself. The walls of grooves should be perpendicular to the shaft or bore diameter; the grooves should have square corners on the top edges, and radii at the bottom, within the tolerances specified by the manufacturers, as shown in Fig. 1 (page 1684). Test data indicate that the ultimate thrust capacity for both static and dynamic loading conditions is greatly affected if these groove requirements are not met. For spiral-wound rings, the maximum bottom groove radius is 0.005 inch for rings up to 1.000 inch free diameter and 0.010 inch for larger rings, internal or external. For stamped rings, the maximum bottom groove radius varies with ring size and style. Table 18. Retaining Ring Standards MIL-R-21248B

Military MS-16633 Open-type external uniform cross-section MS-16634 Open-type external uniform cross-section cylindrically MS-3215 Open-type external tapered cross-section MS-16632 Crescent-type external MS-16625 Internal MS-16629 Internal cylindrically bowed MS-16624 Closed-type external tapered cross-section



1711

Table 18. Retaining Ring Standards (Continued) Military MS-16628 Closed-type external tapered cross-section cylindrically bowed

MIL-R-21248B

MS-16627 Internal inverted MS-16626 Closed-type external tapered cross-section MS-90707 Self-locking external tapered cross-section MIL-R-27426

AS 3215 AS 3216 AS 3217 AS 3218 AS 3219

B27.6-1972, R1983 B27.7-1977, R1983 B27.8M-1977, R1983

MA4016 MA4017 MA4020 MA4021 MA4029 MA4030 MA4035 MA4036

DIN 471, 472, 6799, 984, 5417, 7993 LN 471, 472, 6799

MS-3217 External heavy-duty tapered cross-section Uniform cross-section spiral retaining rings, Type 1-External, Type 2-Internal Acrospace Standard Ring, Retaining—Spiral, Internal, Heavy Duty, Stainless Steel Ring, Retaining—Spiral, External, Heavy Duty, Stainless Steel Ring, Retaining—Spiral, Internal, Light Duty, Stainless Steel Ring, Retaining—Spiral, External, Light Duty, Stainless Steel Ring, Wound, Dimensional and Acceptance Standard for Spiral Wound Retaining Rings ANSI General Purpose Uniform Cross-Section Spiral Retaining Rings General Purpose Tapered and Reduced Cross-Section Retaining Rings (Metric) General Purpose Metric Tapered and Reduced CrossSection Retaining Rings Type 3DM1—Heavy Duty External Rings Type 3EM1—Reinforced “E” Rings Type 3FM1—“C” Type Rings ANSI/SAE Ring, Retaining—External Spiral Wound, Heavy and Medium Duty, Crescent, Metric Ring, Retaining—External Spiral Wound, Heavy and Medium Duty, Crescent, Metric Ring, Retaining—External Tapered, Type 1, Class 2, AMS 5520, Metric Ring, Retaining—Internal Tapered, Type 1, Class 1, AMS 5520, Metric Ring, Retaining—Internal, Beveled, Tapered, Type 2, Class 1, AMS 5520, Metric Ring, Retaining—External, Reinforced E-Ring, Type 1, Class 3, AMS 5520, Metric Rings, Retaining—Spiral Wound, Uniform Section, Corrosion Resistant, Procurement Specification for, Metric Ring, Retaining—Tapered Width, Uniform Thickness, Corrosion Resistant, Procurement Specification for, Metric DIN Standards for normal and heavy type, internal and external retaining rings and retaining washers Aerospace standards for internal and external retaining rings



WING NUTS, WING SCREWS AND THUMB SCREWS

WING NUTS, WING SCREWS, AND THUMB SCREWS Wing Nuts.—A wing nut is a nut having wings designed for manual turning without driver or wrench. As covered by ANSI B18.17-1968 (R1983) wing nuts are classified first, by type on the basis of the method of manufacture; and second, by style on the basis of design characteristics. They consist of: Type A: Type A wing nuts are cold forged or cold formed solid nuts having wings of moderate height. In some sizes they are produced in regular, light, and heavy series to best suit the requirements of specific applications. Dimensions are given in Table 1. Table 1. American National Standard Type A Wing Nuts ANSI B18.17-1968, R1983

Nominal Size or Basic Major Diameter of Threada

Thds. per Inch

3 4

(0.0990) (0.1120)

48, 56 40, 38

5

(0.1250)

40, 44

6

(0.1380)

32, 40

8

(0.1640)

32, 36

10

(0.1900)

24, 32

12

(0.2160)

24, 28

1⁄ 4

(0.2500)

20, 28

5⁄ 16

(0.3125)

18, 24

Seriesb

Nut Blank Size (Ref) AA AA AA A AA A A B A B B C B C D C D E D E E F E F F

A

B

C

D

E

G

Wing Spread

Wing Height

Wing Thick.

Between Wings

Boss Dia.

Boss Height

Max Min Max Min Max Min Max Min Max Min Max Min

3⁄ 8

(0.3750)

16, 24

7⁄ 16

(0.4375)

14, 20

1⁄ 2

(0.5000)

13, 20

9⁄ 16 5⁄ 8 3⁄ 4

(0.5625)

12, 18

Hvy. Hvy. Lgt. Hvy. Lgt. Hvy. Lgt. Hvy. Lgt. Hvy. Lgt. Hvy. Lgt. Reg. Hvy. Lgt. Reg. Hvy. Lgt. Reg. Lgt. Hvy. Lgt. Hvy. Hvy.

0.72 0.72 0.72 0.91 0.72 0.91 0.91 1.10 0.91 1.10 1.10 1.25 1.10 1.25 1.44 1.25 1.44 1.94 1.44 1.94 1.94 2.76 1.94 2.76 2.76

0.59 0.59 0.59 0.78 0.59 0.78 0.78 0.97 0.78 0.97 0.97 1.12 0.97 1.12 1.31 1.12 1.31 1.81 1.31 1.81 1.81 2.62 1.81 2.62 2.62

0.41 0.41 0.41 0.47 0.41 0.47 0.47 0.57 0.47 0.57 0.57 0.66 0.57 0.66 0.79 0.66 0.79 1.00 0.79 1.00 1.00 1.44 1.00 1.44 1.44

0.28 0.28 0.28 0.34 0.28 0.34 0.34 0.43 0.34 0.43 0.43 0.53 0.43 0.53 0.65 0.53 0.65 0.87 0.65 0.87 0.87 1.31 0.87 1.31 1.31

0.11 0.11 0.11 0.14 0.11 0.14 0.14 0.18 0.14 0.18 0.18 0.21 0.18 0.21 0.24 0.21 0.24 0.33 0.24 0.33 0.33 0.40 0.33 0.40 0.40

0.07 0.07 0.07 0.10 0.07 0.10 0.10 0.14 0.10 0.14 0.14 0.17 0.14 0.17 0.20 0.17 0.20 0.26 0.20 0.26 0.26 0.34 0.26 0.34 0.34

0.21 0.21 0.21 0.27 0.21 0.27 0.27 0.33 0.27 0.33 0.33 0.39 0.39 0.39 0.48 0.39 0.48 0.65 0.48 0.65 0.65 0.90 0.65 0.90 0.90

0.17 0.17 0.17 0.22 0.17 0.22 0.22 0.26 0.22 0.26 0.26 0.32 0.26 0.32 0.42 0.32 0.42 0.54 0.42 0.54 0.54 0.80 0.54 0.80 0.80

0.33 0.33 0.33 0.43 0.33 0.43 0.43 0.50 0.43 0.50 0.50 0.58 0.50 0.58 0.70 0.58 0.70 0.93 0.70 0.93 0.93 1.19 0.93 1.19 1.19

0.29 0.29 0.29 0.39 0.29 0.39 0.39 0.45 0.39 0.45 0.45 0.51 0.45 0.51 0.64 0.51 0.64 0.86 0.64 0.86 0.86 1.13 0.86 1.13 1.13

0.14 0.14 0.14 0.18 0.14 0.18 0.18 0.22 0.18 0.22 0.22 0.25 0.22 0.25 0.30 0.25 0.30 0.39 0.30 0.39 0.39 0.55 0.39 0.55 0.55

(0.6250)

11, 18

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 0.90 0.80 1.19 1.13 0.55 0.51

(0.7500)

10, 16

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 0.90 0.80 1.19 1.13 0.55 0.51

a Where specifying nominal size in decimals, zeros in the fourth decimal place are omitted. b Lgt. = Light; Hvy. = Heavy; Reg. = Regular. Sizes shown in bold face are preferred.

All dimensions in inches.


0.10 0.10 0.10 0.14 0.10 0.14 0.14 0.17 0.14 0.17 0.17 0.20 0.17 0.20 0.26 0.20 0.26 0.35 0.26 0.35 0.35 0.51 0.35 0.51 0.51

Machinery's Handbook 27th Edition WING NUTS, WING SCREWS AND THUMB SCREWS

1713

Type B: Type B wing nuts are hot forged solid nuts available in two wing styles: Style 1, having wings of moderate height; and Style 2, having high wings. Dimensions are given in Table 2. Table 2. American National Standard Type B Wing Nuts ANSI B18.17-1968, R1983

STYLE 1 Nominal Size or Basic Major Diameter of Threada

Thds. per Inch

STYLE 2

A

B

C

D

E

G

Wing Spread

Wing Height

Wing Thick.

Between Wings

Boss Dia.

Boss Height

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Type B, Style 1 5 (0.1250)

40

0.78

0.72

0.36

0.30

0.13

0.10

0.28

0.22

0.31

0.28

0.22

0.16

10 (0.1900)

24

0.97

0.91

0.45

0.39

0.15

0.12

0.34

0.28

0.39

0.36

0.28

0.22

1⁄ (0.2500) 4

20

1.16

1.09

0.56

0.50

0.17

0.14

0.41

0.34

0.47

0.44

0.34

0.28

5⁄ (0.3125) 16

18

1.44

1.38

0.67

0.61

0.18

0.15

0.50

0.44

0.55

0.52

0.41

0.34

3⁄ (0.3750) 8

16

1.72

1.66

0.80

0.73

0.20

0.17

0.59

0.53

0.63

0.60

0.47

0.41

7⁄ (0.4375) 16

14

2.00

1.94

0.91

0.84

0.21

0.18

0.69

0.62

0.71

0.68

0.53

0.47

1⁄ (0.5000) 2

13

2.31

2.22

1.06

0.94

0.23

0.20

0.78

0.69

0.79

0.76

0.62

0.50

9⁄ (0.5625) 16

12

2.59

2.47

1.17

1.05

0.25

0.21

0.88

0.78

0.88

0.84

0.69

0.56

5⁄ (0.6250) 8

11

2.84

2.72

1.31

1.19

0.27

0.23

0.94

0.84

0.96

0.92

0.75

0.62

3⁄ (0.7500) 4

10

3.31

3.19

1.52

1.39

0.29

0.25

1.10

1.00

1.12

1.08

0.88

0.75

Type B, Style 2 5 (0.1250)

40

0.81

0.75

0.62

0.56

0.12

0.09

0.28

0.22

0.31

0.28

0.22

0.16

10 (0.1900)

24

1.01

0.95

0.78

0.72

0.14

0.11

0.35

0.29

0.39

0.36

0.28

0.22

1⁄ (0.2500) 4

20

1.22

1.16

0.94

0.88

0.16

0.13

0.41

0.35

0.47

0.44

0.34

0.28

5⁄ (0.3125) 16

18

1.43

1.37

1.09

1.03

0.17

0.14

0.48

0.42

0.55

0.52

0.41

0.34 0.41

3⁄ (0.3750) 8

16

1.63

1.57

1.25

1.19

0.18

0.15

0.55

0.49

0.63

0.60

0.47

7⁄ (0.4375) 16

14

1.90

1.84

1.42.

1.36

0.19

0.16

0.62

0.56

0.71

0.68

0.53

0.47

1⁄ (0.5000) 2

13

2.13

2.04

1.58

1.45

0.20

0.17

0.69

0.60

0.79

0.76

0.62

0.50

9⁄ (0.5625) 16

12

2.40

2.28

1.75

1.62

0.22

0.18

0.76

0.67

0.88

0.84

0.69

0.56

5⁄ (0.6250) 8

11

2.60

2.48

1.91

1.78

0.23

0.19

0.83

0.74

0.96

0.92

0.75

0.62

3⁄ (0.7500) 4

10

3.02

2.90

2.22

2.09

0.24

0.20

0.97

0.88

1.12

1.08

0.88

0.75

a Where specifying nominal size in decimals, zeros in the fourth decimal place are omitted.





Table 3. American National Standard Type C Wing Nuts ANSI B18.17-1968, R1983

STYLE 1 Nominal Size or Basic Major Diameter of Threada

Thds. per Inch

4 (0.1120) 5 (0.1250)

40 40

6 (0.1380)

32

Serie s

STYLE 2

STYLE 3

A B C D E F G Nut Blan Wing Wing Wing Between Boss Boss Boss k Spread Height Thick. Wings Dia. Dia. Height Size (Ref) Max Min Max Min Max Min Max Min Max Min Max Min Max Min Type C, Style 1

8 (0.1640) 32 10 (0.1900) 24, 32

Reg. Reg. Reg. Hvy. Reg. Reg. Reg. Hvy.

AA AA AA A A A A B

0.66 0.66 0.66 0.85 0.85 0.85 0.85 1.08

0.64 0.64 0.64 0.83 0.83 0.83 0.83 1.05

0.36 0.36 0.36 0.43 0.43 0.43 0.43 0.57

0.35 0.35 0.35 0.42 0.42 0.42 0.42 0.53

0.11 0.11 0.11 0.14 0.14 0.14 0.14 0.16

0.09 0.09 0.09 0.12 0.12 0.12 0.12 0.14

0.18 0.18 0.18 0.29 0.29 0.29 0.29 0.32

0.16 0.16 0.16 0.27 0.27 0.27 0.27 0.30

0.27 0.27 0.27 0.38 0.38 0.38 0.38 0.44

0.25 0.25 0.25 0.36 0.36 0.36 0.36 0.42

0.32 0.32 0.32 0.41 0.41 0.41 0.41 0.48

0.30 0.30 0.30 0.40 0.40 0.40 0.40 0.46

0.16 0.16 0.16 0.20 0.20 0.20 0.20 0.23

0.14 0.14 0.14 0.18 0.18 0.18 0.18 0.21

12 (0.2160)

24

1⁄ (0.2500) 4

20, 28

Reg.

B

5⁄ (0.3125) 16

18, 24

Reg.

C

1.23 1.20 0.64 0.62 0.20 0.18 0.39 0.35 0.50 0.49 0.57 0.55 0.26 0.24

3⁄ (0.3750) 8

16, 24

Reg.

D

1.45 1.42 0.74 0.72 0.23 0.21 0.46 0.42 0.62 0.60 0.69 0.67 0.29 0.27

7⁄ (0.4375) 16

14, 20

1⁄ (0.5000) 2

13, 20

Reg. Hvy. Reg. Hvy.

E EH E EH

1.89 1.89 1.89 1.89

1.86 1.86 1.86 1.86

5 (0.1250) 40 6 (0.1380) 32 8 (0.1640) 32 10 (0.1900) 24, 32 12 (0.2160) 24

… … … … …

… … … … …

0.82 0.82 1.01 1.01 1.20

0.80 0.80 0.99 0.99 1.18

1.08 1.05 0.57 0.53 0.16 0.14 0.32 0.30 0.44 0.42 0.48 0.46 0.23 0.21

0.91 0.93 0.91 0.93

0.90 0.29 0.28 0.91 0.34 0.33 0.90 0.29 0.28 0.91 0.34 0.33 Type C, Style 2 0.25 0.23 0.09 0.08 0.25 0.23 0.09 0.08 0.28 0.27 0.11 0.09 0.28 0.27 0.11 0.09 0.32 0.31 0.12 0.11

0.67 0.63 0.67 0.63

0.65 0.62 0.65 0.62

0.75 0.81 0.75 0.81

0.73 0.79 0.73 0.79

0.83 0.89 0.83 0.89

0.82 0.87 0.82 0.87

0.38 0.42 0.38 0.42

0.37 0.40 0.37 0.40

0.21 0.21 0.29 0.29 0.38

0.19 0.19 0.28 0.28 0.37

0.26 0.26 0.36 0.36 0.44

0.24 0.24 0.34 0.34 0.43

… … … … …

… … … … …

0.17 0.17 0.19 0.19 0.22

0.15 0.15 0.18 0.18 0.20

0.22 0.20

1⁄ (0.2500) 4

20

…

…

1.20 1.18 0.32 0.31 0.12 0.11 0.38 0.37 0.44 0.43

…

…

5⁄ (0.3125) 16

18

…

…

1.51 1.49 0.36 0.35 0.14 0.12 0.44 0.43 0.51 0.49

…

…

0.24 0.23

3⁄ (0.3750) 8

16

…

…

1.89 1.86 0.58 0.55 0.20 0.17 0.44 0.43 0.63 0.62

…

…

0.37 0.35

5 (0.1250) 40 6 (0.1380) 32 8 (0.1640) 32 10 (0.1900) 24, 32 12 (0.2160) 24

… … … … …

… … … … …

0.92 0.92 0.92 1.14 1.14

0.36 0.36 0.36 0.42 0.42

… … … … …

… … … … …

0.25 0.25 0.25 0.29 0.29

0.29 0.27

0.89 0.89 0.89 1.12 1.12

0.70 0.70 0.70 0.85 0.85

Type C, Style 3 0.67 0.16 0.15 0.67 0.16 0.15 0.67 0.16 0.15 0.83 0.19 0.17 0.83 0.19 0.17

0.26 0.26 0.26 0.32 0.32

0.24 0.24 0.24 0.30 0.30

0.38 0.38 0.38 0.44 0.44

0.24 0.24 0.24 0.27 0.27

1⁄ (0.2500) 4

20

…

…

1.14 1.12 0.85 0.83 0.19 0.17 0.32 0.30 0.44 0.42

…

…

5⁄ (0.3125) 16

18

…

…

1.29 1.27 1.04 1.02 0.23 0.22 0.39 0.36 0.50 0.49

…

…

0.35 0.34

3⁄ (0.3750) 8

16

…

…

1.51 1.49 1.20 1.18 0.27 0.25 0.45 0.42 0.62 0.60

…

…

0.43 0.42

a Where specifying nominal size in decimals, zeros in the fourth decimal place are omitted.

All dimensions in inches. Sizes shown in bold face are preferred.

Type C: Type C wing nuts are die cast solid nuts and are available in three wing styles: Style 1, having wings of moderate height; Style 2, having low wings; and Style 3, having high wings. In some sizes, the Style 1 nuts are produced in regular, light, and heavy series to best suit the requirements of specific applications. Dimensions are given in Table 3.



1715

Table 4. American National Standard Type D Wing Nuts ANSI B18.17-1968, R1983

STYLE 1

STYLE 2 (LOW WING) A Wing Spread

D Between Wings

Thds. per Inch

E Boss Dia.

Seriesb

8 (0.1640) 10 (0.1900) 12 (0.2160) 1⁄ (0.2500) 4

32, 36 24, 32 24, 28 20, 28

… … … …

Max Min Max Min Max Min Type D, Style 1

Min

Max Min

0.78 0.91 1.09 1.11

0.25 0.34 0.34 0.34

0.41 0.53 0.53 0.62

5⁄ (0.3125) 16 3⁄ (0.3750) 8

18, 24

…

1.30 1.24 0.59 0.53 0.30 0.26

0.46

0.73 0.67

0.14

0.18

0.06 0.05

16, 24

…

1.41 1.34 0.67 0.61 0.34 0.30

0.69

0.83 0.77

0.16

0.18

0.06 0.05

5 (0.1250) 6 (0.1380) 8 (0.1640)

40 32 32

10 (0.1900)

24, 32

12 (0.2160) 1⁄ (0.2500) 4

24 20

Reg. Reg. Reg. Reg. Hvy. Reg. Reg.

1.03 1.03 1.03 1.40 1.21 1.21 1.21

0.97 0.97 0.97 1.34 1.16 1.16 1.16

Type D, Style 2 0.25 0.19 0.19 0.13 0.25 0.19 0.19 0.13 0.25 0.19 0.19 0.13 0.34 0.28 0.25 0.18 0.28 0.26 0.31 0.25 0.28 0.26 0.31 0.25 0.28 0.26 0.31 0.25

0.30 0.30 0.30 0.32 0.60 0.60 0.60

0.40 0.40 0.40 0.53 0.61 0.61 0.61

0.34 0.34 0.34 0.47 0.55 0.55 0.55

0.07 0.08 0.08 0.09 0.09 0.11 0.11

0.09 0.09 0.09 0.16 0.13 0.13 0.13

0.04 0.04 0.04 0.05 0.05 0.05 0.05

0.03 0.03 0.03 0.04 0.04 0.04 0.04

10 (0.1900)

24, 32

12 (0.2160)

24

1⁄ (0.2500) 4

20

5⁄ (0.3125) 16

18

Lgt. Reg. Reg. Lgt. Reg. Hvy. Reg. Hvy.

1.31 1.40 1.28 1.28 1.78 1.47 1.78 1.47

1.25 1.34 1.22 1.22 1.72 1.40 1.72 1.40

Type D, Style 3 0.48 0.42 0.29 0.23 0.53 0.47 0.25 0.19 0.40 0.34 0.23 0.17 0.40 0.34 0.23 0.17 0.66 0.60 0.31 0.25 0.50 0.44 0.37 0.31 0.66 0.60 0.31 0.25 0.50 0.44 0.37 0.31

0.47 0.50 0.59 0.59 0.70 0.66 0.70 0.66

0.65 0.75 0.73 0.73 1.03 1.03 1.03 1.03

0.59 0.69 0.67 0.67 0.97 0.97 0.97 0.97

0.08 0.08 0.11 0.11 0.14 0.14 0.14 0.14

0.12 0.14 0.12 0.12 0.17 0.14 0.17 0.14

0.04 0.04 0.04 0.04 0.06 0.08 0.06 0.08

0.03 0.03 0.03 0.03 0.04 0.06 0.04 0.06

0.72 0.85 1.03 1.05

B Wing Height

0.40 0.47 0.47 0.50

0.34 0.41 0.41 0.44

C Wing Thick.

STYLE 3 (LARGE BASE)

Nominal Size or Basic Major Diameter of Threada

0.18 0.21 0.21 0.25

0.14 0.17 0.17 0.21

0.35 0.47 0.47 0.56

G Boss Hgt.

H Wall Hgt.

T Stock Thick.

Min

Min

Max Min

0.08 0.10 0.10 0.11

0.12 0.12 0.12 0.12

0.04 0.04 0.05 0.05

0.03 0.03 0.04 0.04

a Where specifying nominal size in decimals, zeros in the fourth decimal place are omitted. b Lgt. = Light; Hvy. = Heavy; Reg. = Regular.


Type D: Type D wing nuts are stamped sheet metal nuts and are available in three styles: Style 1, having wings of moderate height; Style 2, having low wings; and Style 3, having wings of moderate height and a larger bearing surface. In some sizes, Styles 2 and 3 are produced in regular, light, and heavy series to best suit the requirements of specific applications. Dimensions are given in Table 4. Specification of Wing Nuts.—When specifying wing nuts, the following data should be included in the designation and should appear in the following sequence: nominal size (number, fraction or decimal equivalent), threads per inch, type, style and/or series, material, and finish. Examples: 10—32 Type A Wing Nut, Regular Series, Steel, Zinc Plated. 0.250—20 Type C Wing Nut, Style 1, Zinc Alloy, Plain. Threads for Wing Nuts.—Threads are in conformance with the ANSI Standard Unified Thread, Class 2B for all types of wing nuts except type D which have a modified Class 2B thread. Because of the method of manufacture, the minor diameter of the thread in type D




nuts may be somewhat larger than the Unified Thread Class 2B maximum but shall in no case exceed the minimum pitch diameter. Materials and Finish for Wing Nuts.—Types A, B, and D wing nuts are normally supplied as specified by the user in carbon steel, brass or corrosion resistant steel of good quality and adaptable to the manufacturing process. Type C wing nuts are made from die cast zinc alloy. Unless otherwise specified, wing nuts are supplied with a plain (unplated or uncoated) finish. Wing Screws.—A wing screw is a screw having a wing-shaped head designed for manual turning without a driver or wrench. As covered by ANSI B18.17-1968 (R1983) wing screws are classified first, by type on the basis of the method of manufacture, and second, by style on the basis of design characteristics. They consist of the following: Type A: Type A wing screws are of two-piece construction having cold formed or cold forged wing portions of moderate height. In some sizes they are produced in regular, light, and heavy series to best suit the requirements of specific applications. Dimensions are given in Table 5. Type B: Type B wing screws are of hot forged one-piece construction available in two wing styles: Style 1, having wings of moderate height; and Style 2, having high wings. Dimensions are given in Table 5. Type C: Type C wing screws are available in two styles: Style 1, of a one-piece die cast construction having wings of moderate height; and Style 2, of a two-piece construction having a die cast wing portion of moderate height. Dimensions are given in Table 6. Type D: Type D wing screws are of two-piece welded construction having stamped sheet metal wing portions of moderate height. Dimensions are given in Table 6. Materials for Wing Screws and Thumb Screws: Type A wing screws are normally supplied in carbon steel with the shank portion case hardened. When so specified, they also may be made from corrosion resistant steel, brass or other materials as agreed upon by the manufacturer and user. Type B wing screws are normally made from carbon steel but also may be made from corrosion resistant steel, brass or other materials. Type C, Style 1, wing screws are supplied only in die cast zinc alloy. Type C, Style 2, wing screws have the wing portion made from die cast zinc alloy with the shank portion normally made from carbon steel. Where so specified, the shank portion may be made from corrosion resistant steel, brass or other materials as agreed upon by the manufacturer and user. Type D wing screws are normally supplied in carbon steel but also may be made from corrosion resistant steel, brass or other materials. Thumb screws of all types are normally made from a good commercial quality of carbon steel having a maximum ultimate tensile strength of 48,000 psi. Where so specified, carbon steel thumb screws are case hardened. They are also made from corrosion resistant steel, brass, and other materials as agreed upon by the manufacturer and user. Unless otherwise specified, wing screws and thumb screws are supplied with a plain (unplated or uncoated) finish. Thumb Screws.—A thumb screw is a screw having a flattened head designed for manual turning without a driver or wrench. As covered by ANSI B18.17-1968 (R1983) thumb screws are classified by type on the basis of design characteristics. They consist of the following: Type A: Type A thumb screws are forged one-piece screws having a shoulder under the head and are available in two series: regular and heavy. Dimensions are given in Table 7. Type B: Type B thumb screws are forged one-piece screws without a shoulder and are available in two series: regular and heavy. Dimensions are given in Table 7.



1717

Table 5. American National Standard Types A and B Wing Screws ANSI B18.17-1968, R1983

TYPE A Nominal Size or Basic Major Diametera

Thds. per Inch

Seriesb

TYPE B Head Blank size (Ref)

A

B

C

E

G

L

Wing Spread

Wing Height

Wing Thick.

Boss Dia.

Boss Height.

Practical Screw Lengths

Max Min Max Min Max Min Max Min Max Min

Max

Min

Type A 4 (0.1120)

40

6 (0.1380)

32

8 (0.1640)

32

10 (0.1900) 12 (0.2160)

1⁄ (0.2500) 4

5⁄ (0.3125) 16

3⁄ (0.3750) 8

7⁄ (0.4375) 16

24, 32 24

20

18

16

14

1⁄ (0.5000) 2

13

5⁄ (0.6250) 8

11

Hvy.

AA

0.72 0.59 0.41 0.28 0.11 0.07 0.33 0.29 0.14 0.10

Lgt.

AA

0.72 0.59 0.41 0.28 0.11 0.07 0.33 0.29 0.14 0.10

Hvy.

A

0.91 0.78 0.47 0.34 0.14 0.10 0.43 0.39 0.18 0.14

Lgt.

A

0.91 0.78 0.47 0.34 0.14 0.10 0.43 0.39 0.18 0.14

Hvy.

B

1.10 0.97 0.57 0.43 0.18 0.14 0.50 0.45 0.22 0.17

Lgt.

A

0.91 0.78 0.47 0.34 0.14 0.10 0.43 0.39 0.18 0.14

Hvy.

B

1.10 0.97 0.57 0.43 0.18 0.14 0.50 0.45 0.22 0.17

Lgt.

B

1.10 0.97 0.57 0.43 0.18 0.14 0.50 0.45 0.22 0.17

0.75 0.25 } 0.75 0.25 } 0.75 0.38 } 1.00 0.38 } 1.00 0.38

Hvy.

C

1.25 1.12 0.66 0.53 0.21 0.17 0.58 0.51 0.25 0.20

Lgt.

B

1.10 0.97 0.57 0.43 0.18 0.14 0.50 0.45 0.22 0.17

C

1.25 1.12 0.66 0.53 0.21 0.17 0.58 0.51 0.25 0.20 } 1.50 0.50

Reg. Hvy.

D

1.44 1.31 0.79 0.65 0.24 0.20 0.70 0.64 0.30 0.26

Lgt.

C

1.25 1.12 0.66 0.53 0.21 0.17 0.58 0.51 0.25 0.20 1.44 1.31 0.79 0.65 0.24 0.20 0.70 0.64 0.30 0.26 } 1.50 0.50

Reg.

D

Hvy.

E

1.94 1.81 1.00 0.87 0.33 0.26 0.93 0.86 0.39 0.35

Lgt.

D

1.44 1.31 0.79 0.65 0.24 0.20 0.70 0.64 0.30 0.26

Reg.

E

1.94 1.81 1.00 0.87 0.33 0.26 0.93 0.86 0.39 0.35 } 2.00 0.75

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 1.19 1.13 0.55 0.51

Lgt.

E

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 1.19 1.13 0.55 0.51

Lgt.

E

1.94 1.81 1.00 0.87 0.33 0.26 0.93 0.86 0.39 0.35

1.94 1.81 1.00 0.87 0.33 0.26 0.93 0.86 0.39 0.35

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 1.19 1.13 0.55 0.51

Hvy.

F

2.76 2.62 1.44 1.31 0.40 0.34 1.19 1.13 0.55 0.51

} 4.00 1.00 } 4.00 1.00 4.00 1.25

Type B, Style 1 10 (0.1900)

24

…

…

0.97 0.91 0.45 0.39 0.15 0.12 0.39 0.36 0.28 0.22

2.00 0.50

1⁄ (0.2500) 4

20

…

…

1.16 1.09 0.56 0.50 0.17 0.14 0.47 0.44 0.34 0.28

3.00 0.50

5⁄ (0.3125) 16

18

…

…

1.44 1.38 0.67 0.61 0.18 0.15 0.55 0.52 0.41 0.34

3.00 0.50

3⁄ (0.3750) 8

16

…

…

1.72 1.66 0.80 0.73 0.20 0.17 0.63 0.60 0.47 0.41

4.00 0.50

7⁄ (0.4375) 16

14

…

…

2.00 1.94 0.91 0.84 0.21 0.18 0.71 0.68 0.53 0.47

3.00 1.00

1⁄ (0.5000) 2

13

…

…

2.31 2.22 1.06 0.94 0.23 0.20 0.79 0.76 0.62 0.50

3.00 1.00

5⁄ (0.6250) 8

11

…

…

2.84 2.72 1.31 1.19 0.27 0.23 0.96 0.92 0.75 0.62

2.50 1.00

Type B, Style 2 10 (0.1900)

24

…

…

1.01 0.95 0.78 0.72 0.14 0.11 0.39 0.36 0.28 0.22

1.25 0.50

1⁄ (0.2500) 4

20

…

…

1.22 1.16 0.94 0.88 0.16 0.13 0.47 0.44 0.34 0.28

2.00 0.50

5⁄ (0.3125) 16

18

…

…

1.43 1.37 1.09 1.03 0.17 0.14 0.55 0.52 0.41 0.34

2.00 0.50

3⁄ (0.3750) 8

16

…

…

1.63 1.57 1.25 1.19 0.18 0.15 0.63 0.60 0.47 0.41

2.00 0.50

All dimensions in inches. Sizes shown in bold face are preferred. 1Plain point, unless alternate point from styles shown in Table 8 is specified by user. a Where specifyin nominal size in decimals, zeros in the fourth decimal place are omitted. b Hvy. = Heavy; Lgt. = Light; Reg. = Regular.



WING NUTS, WING SCREWS AND THUMB SCREWS Table 6. American National Standard Types C and D Wing Screws ANSI B18.17-1968, R1983

TYPE C

TYPE D A

B

Thds. per Inch

Wing Spread Max Min

Wing Height Max Min

6 (0.1380) 8 (0.1640) 10 (0.1900) 1⁄ (0.2500) 4

32 32 24, 32 20

0.85 0.85 0.85 1.08

0.83 0.83 0.83 1.05

0.45 0.45 0.45 0.56

0.43 0.43 0.43 0.53

0.15 0.15 0.15 0.17

0.12 0.12 0.12 0.14

… … … …

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