Machinery's Handbook

Machinery's Handbook 28th Edition A REFERENCE BOOK FOR THE MECHANICAL ENGINEER, DESIGNER, MANUFACTURING ENGINEER, DRA...

Author: Oberg | Jones | Horton | and Ryffel | Christopher McCauley | Riccardo Heald | and Mohammed Hussain

91 downloads 2501 Views 17MB Size Report

This content was uploaded by our users and we assume good faith they have the permission to share this book. If you own the copyright to this book and it is wrongfully on our website, we offer a simple DMCA procedure to remove your content from our site. Start by pressing the button below!
Report copyright / DMCA form

DOWNLOAD PDF

Machinery's Handbook 28th Edition

A REFERENCE BOOK FOR THE MECHANICAL ENGINEER, DESIGNER,

MANUFACTURING ENGINEER, DRAFTSMAN, TOOLMAKER, AND MACHINIST

Machinery’s Handbook 28th Edition BY ERIK OBERG, FRANKLIN D. JONES, HOLBROOK L. HORTON, AND HENRY H. RYFFEL

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

2008

INDUSTRIAL PRESS NEW YORK

Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com

Machinery's Handbook 28th 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, © 2008 by Industrial Press Inc., New York, NY. Library of Congress Cataloging-in-Publication Data Oberg, Erik, 1881—1951 Machinery's Handbook. 2704 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 2008 621.8'0212 72-622276 ISBN 978-0-8311-2800-5 (Toolbox Thumb Indexed 11.7 x 17.8 cm) ISBN 978-0-8311-2801-2 (Large Print Thumb Indexed 17.8 x 25.4 cm) ISBN 978-0-8311-2888-3 (CD-ROM) ISBN 978-0-8311-2828-9 (Toolbox Thumb Indexed / CD-ROM Combo 11.7 x 17.8 cm) ISBN 978-0-8311-2838-8 (Large Print Thumb Indexed / CD-ROM Combo 17.8 x 25.4 cm) LC card number 72-622276

INDUSTRIAL PRESS, INC. 989 Avenue of the Americas New York, New York 10018 MACHINERY'S HANDBOOK 28TH EDITION 䉭䉭䉭䉭

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 28th 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. “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. The 28th edition of the Handbook contains 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, Dimensioning, Gaging and Measuring, Machining Operations, Manufacturing Process, Fasteners, Threads and Threading, and Machine Elements. New material includes shaft alignment, taps and tapping, helical coil screw thread inserts, solid geometry, distinguishing between bolts and screws, statistics, calculating thread dimensions, keys and keyways, miniature screws, metric screw threads, and fluid mechanics. Other subjects in the Handbook that are new or have been revised, expanded, or updated are: plastics, punches, dies and presswork, lubrication, CNC programming and CNC thread cutting, metric wrench clearances, ANSI and ISO drafting practices, and ISO surface texture. 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. The Machinery's Handbook 28 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 thou-

v


Machinery's Handbook 28th Edition PREFACE sands 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 and standards 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 found 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 2706. 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 28th 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. 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 material on the mass moment of inertia of hollow circular rings, page 245, and on the effect of temperature on the radius of thin circular rings, page 379, 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 28th Edition TABLE OF CONTENTS

LICENSE AND LIMITED WARRANTY AGREEMENT COPYRIGHT PREFACE TABLE OF CONTENTS ACKNOWLEDGMENTS

ii iv v vii ix

MATHEMATICS

1

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

MECHANICS AND STRENGTH OF MATERIALS

154

• MECHANICS • VELOCITY, ACCELERATION, WORK, AND ENERGY • STRENGTH OF MATERIALS • PROPERTIES OF BODIES • BEAMS • COLUMNS • PLATES, SHELLS, AND CYLINDERS • SHAFTS • SPRINGS • DISC SPRINGS • FLUID MECHANICS

PROPERTIES, TREATMENT, AND TESTING OF MATERIALS 370 • THE ELEMENTS, HEAT, MASS, AND WEIGHT • PROPERTIES OF WOOD, CERAMICS, PLASTICS, METALS • STANDARD STEELS • TOOL STEELS • HARDENING, TEMPERING, AND ANNEALING • NONFERROUS ALLOYS • PLASTICS

DIMENSIONING, GAGING, AND MEASURING

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

TOOLING AND TOOLMAKING

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

MACHINING OPERATIONS

• 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 • CNC NUMERICAL CONTROL PROGRAMMING

MANUFACTURING PROCESSES

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

FASTENERS

607

730

975

1264

1422

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

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

vii


Machinery's Handbook 28th Edition TABLE OF CONTENTS

THREADS AND THREADING

1708

• SCREW THREAD SYSTEMS • UNIFIED SCREW THREADS • CALCULATING THREAD DIMENSIONS • 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

• 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

• PLAIN BEARINGS • BALL, ROLLER, AND NEEDLE BEARINGS • LUBRICATION • COUPLINGS, CLUTCHES, BRAKES • KEYS AND KEYSEATS • FLEXIBLE BELTS AND SHEAVES • TRANSMISSION CHAINS • BALL AND ACME LEADSCREWS • ELECTRIC MOTORS • ADHESIVES AND SEALANTS • O-RINGS • ROLLED STEEL, WIRE, AND SHEET-METAL • SHAFT ALIGNMENT

MEASURING UNITS

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

2027

2215

2555

INDEX

2605

INDEX OF STANDARDS

2693

INDEX OF INTERACTIVE EQUATIONS

2705

INDEX OF MATERIALS

2711

INDEX OF ADDITIONAL CONTENT ON THE CD

2757

ADDITIONAL ONLY ON THE CD

2765

• MATHEMATICS • MECHANICS AND STRENGTH OF MATERIALS • PROPERTIES, TREATMENT, AND TESTING OF MATERIALS • DIMENSIONING, GAGING, AND MEASURING • TOOLING AND TOOL MAKING • MACHINING OPERATIONS • MANUFACTURING PROCESS • FASTENERS • THREADS AND THREADING • GEARS, SPLINES, AND CAMS • MACHINE ELEMENTS

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

viii


Machinery's Handbook 28th Edition TABLE OF CONTENTS MATHEMATICS NUMBERS, FRACTIONS, AND DECIMALS 3 Fractional Inch, Decimal, Millimeter Conversion 4 Numbers 4 Positive and Negative Numbers 5 Sequence of 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 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

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

GEOMETRY 36 Arithmetical & Geometrical Progression 39 Analytical Geometry 39 Straight Line 42 Coordinate Systems 45 Circle

GEOMETRY (Continued)

47 50 53 53 65 65 65 66 66 67 67 69 75 76 79 80 81 87 92 93

Ellipse Spherical Areas and Volumes Parabola Hyperbola Areas and Volumes The Prismoidal Formula Pappus or Guldinus Rules Area of Revolution Surface Area of Irregular Plane Surface Areas of Cycloidal Curves Contents of Cylindrical Tanks Areas and Dimensions of Figures Formulas for Regular Polygons Circular Segments Circles and Squares of Equal Area Diagonals of Squares & Hexagons Volumes of Solids Circles in Circles and Rectangles Circles within Rectangles Rollers on a Shaft

SOLUTION OF TRIANGLES 94 95 95 97 100 102 104 105 109 109 110 114 114 116 118 120

Functions of Angles Laws of Sines and Cosines Trigonometric Identities Right-angled Triangles Obtuse-angled Triangles Degree-radian Conversion Functions of Angles, Graphic Trig Function Tables Versed Sine and Versed Cosine Sevolute and Involute Functions Involute Functions Tables Spherical Trigonometry Right Spherical Trigonometry Oblique Spherical Trigonometry Compound Angles Interpolation

LOGARITHMS 121 122 123 123 124 125

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

1 Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com

Machinery's Handbook 28th Edition TABLE OF CONTENTS MATHEMATICS MATRICES

ENGINEERING ECONOMICS (Continued)

129 Matrix Operations 129 Matrix Addition and Subtraction 129 Matrix Multiplication 130 Transpose of a Matrix 130 Determinant of a Square Matrix 131 Minors and Cofactors 131 Adjoint of a Matrix 132 Singularity and Rank of a Matrix 132 Inverse of a Matrix 132 Simultaneous Equations

ENGINEERING ECONOMICS 135 Interest 135 Simple and Compound Interest 136 Nominal vs. Effective Interest Rates 137 Cash Flow and Equivalence 138 Cash Flow Diagrams 140 Depreciation 140 Straight Line Depreciation 140 Sum of the Years Digits

140 140 141 141 142 143 144 144 144 144 147

Double Declining Balance Method Statutory Depreciation System Evaluating Alternatives Net Present Value Capitalized Cost Equivalent Uniform Annual Cost Rate of Return Benefit-cost Ratio Payback Period Break-even Analysis Overhead Expenses

MANUFACTURING DATA ANALYSIS 148 Statistics Theory 148 Statistical Distribution Curves 148 Normal Distribution Curve 148 Statistical Analysis 150 Applying Statistics 150 Minimum Number of Tests 150 Comparing Average Performance 152 Examples


Machinery's Handbook 28th Edition MATHEMATICS

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 indefinitely after the last figure, for example 0.0833 = 0.08333...


4

Machinery's Handbook 28th Edition 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 formulas. 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 28th 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


Machinery's Handbook 28th Edition RATIO AND PROPORTION

6

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

× 3.5 = 42 x = 12 ------------------------ = 2 21 21 1⁄ × 42 1 34 x = --------------- = --- × 3 = -4 14 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: × 14- = 63 days x = 18 ----------------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 28th 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- = ----40× 44- = 297 men -------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


8

Machinery's Handbook 28th Edition 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, 1 2×2+1 5 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



9

values cosecant, secant, and cotangent are often used for convenience and are the reciprocals of the sine, cosine, and tangent, respectively (see page 94). 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

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

1---  4--- 3 7---  2--- + ------ + = 4  4 16 8  2

1 16 1 8 15 2 ---  ------ + 4 ---  --- + 1 ------ = 2  16 4  8 32

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

16 8 15 39 7 2 ------ + 4 ------ + 1 ------ = 7 ------ = 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

3 1 2 --- – 1 ------ = 8 16

15-  --2- 7 ----– ------ = 16  2 32

3 2 1 2 ---  --- – 1 ------ = 8  2 16

30 723 ------ – ----= -----32 32 32

6 1 5 2 ------ – 1 ------ = 1 -----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 73×7 21 --- × ----= --------------- = -----4 16 4 × 16 64

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



10

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:

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

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

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 1.500

or

2.625 – 1.125 1.500

4.7505


Machinery's Handbook 28th 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. N1 --= ---------------------------------------------D 1 D 1 + -------------------------------1 D 2 + -----------------D3 + …

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

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- = -------------------1 - = -----------------1 ------------ = 2153 ----------------------------9277 9277 ÷ 2153 665D1 + R1 4 + ----------2153 1 665 1 R 1 = ------------ = ------------------ = ------------------- etc. D2 + R2 2153 158 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 1 1 1 1 1 1 1 1 1 2153 ------------ = --- + --- + --- + --- + --- + --- + --- + --- + --4 3 4 4 1 3 1 2 2 9277 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.


Machinery's Handbook 28th Edition CONJUGATE FRACTIONS

12

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

--10

--01

--14

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 28th 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.


14

Machinery's Handbook 28th Edition 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 28th 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.


Machinery's Handbook 28th Edition POWERS OF TEN NOTATION

16

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

2.3561945 = 3π -----4

5.2359878 = 5π -----3

π0.26179939 = ----12

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

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

7π5.4977871 = ----4

0.39269908 = π --8

1.2247449 =

2.6179939 = 5π -----6

5.7595865 = 11π --------6

0.52359878 = π --6

3--2 2

3.1415927 = π

6.2831853 = 2π

1.4142136 = π 1.5707963 = --2

9.8696044 = π 2

0.57735027 = ------33

3.6651914 = 7π -----6 3

3.9269908 = 5π -----4

12.566371 = 4π

2 2.4674011 = π ----4

4.1887902 = 4π -----3

0.62035049 =

3

π0.78539816 = -4

3----4π

1.7320508 =

9.424778 = 3π

57.29578 = 180 --------π 360114.59156 = -------π


Machinery's Handbook 28th 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 sin θ = e--------------------2i

iθ

– iθ

+e cos θ = e---------------------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,


18

Machinery's Handbook 28th Edition 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- + i  22 ------  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 magnitude = 8 + 6 = 10 direction = atan 6--- = 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 28th 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.



20

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


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



22


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



24


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



26


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


Machinery's Handbook 28th Edition PRIME NUMBERS

28

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 28th 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 arithmetic 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 = -------------

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


Machinery's Handbook 28th Edition ALGEBRA AND EQUATIONS

30

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. B+C = A–D then A = B+C+D Example: B = A–D–C C = A–D–B Principal Algebraic Expressions and Formulas a × a = aa = a 2

a 3 a3 ----- =  ---  3 b b

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

1- =  1--- 3 = 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

–

(a +

= (a + b)(a – b)

b2 b )2

=

a2

+ 2ab +

3

3

3

3

a =

2

3

3 4

3

a×3 b

3

ab =

3

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

3

1--- = -----1 - = a –1⁄3 a 3 a

2

a2 = ( 3 a ) = a2 / 3 4×3

2

3

a) = a

a =

3

a – b = ( a – b ) + 3ab ( a – b )

a×3 a×3 a = a

4 3

2

a 3 + b 3 = ( a + b ) – 3ab ( a + b )

a× a = a

3

3

2

3

a+b 2 a–b 2 ab =  ------------ –  ------------  2   2 

(3

3

( a – b ) = a – 3a b + 3ab – b

( a – b ) 2 = a 2 – 2ab + b 2

3

3

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

b2

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

3

a = x

then


Machinery's Handbook 28th 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 x = -------------------------------------------- = ---------------------- = --------- = 3 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 – 4ac x = --------------------------------------2a Example:Given the equation, 1x2 + 6x + 5 = 0, then a = 1, b = 6, and c = 5. 6 ± 6 2 – 4 × 1 × 5- = (------------------– 6 ) + 4- = – 1 x = –-------------------------------------------------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.


32

Machinery's Handbook 28th Edition 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 satisfy the requirements because 8 × 5 = 40 and 8 − 5 = 3. In the second line below, 5x is both added to and subtracted 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 28th Edition SOLUTION OF EQUATIONS

33

Cubic Equations.—If the given equation has the form: x3 + ax + b = 0 then b 2- a 3- + ---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


Machinery's Handbook 28th Edition SERIES

34

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) (17)

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.

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

x

d n (x ) dx

n–1

∫ x n dx

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

nx

n+1

d (g(u)) dx

du d g(u) dx du

∫ -------------ax + b

dx

1-ln ax + b a

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

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

∫ ( u ( x ) ± v ( x ) ) dx

∫ u ( x ) dx ± ∫ v ( x ) dx

∫ u ( x )v ( x ) dx

u ( x )v ( x ) – ∫ v ( x ) du ( x )

d (u(x) × v(x)) dx

u(x)

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


Machinery's Handbook 28th Edition DERIVATIVES AND INTEGRALS

35

Formulas for Differential and Integral Calculus (Continued) Derivative

Value

Integral

Value

d  ---------u ( x ) d x  v ( x )

d d v(x) u(x) – u(x) 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

∫ tan x dx

– log cos x log sin x

d ( tan x ) dx

sec x

d ( cot x ) dx

– cosec x

∫ cot x dx

d ( sec x ) dx

sec x tan x

∫ sin

d ( csc x ) dx

– csc x cot x

∫ cos

d x (e ) dx

e

x

∫ e dx

d ( log x ) dx

1 --x

∫ --x- dx

2

2

2

x dx

2

x dx

x

1

 – 1--- sin ( 2x ) + --1- x  4 2 1--1 sin ( 2x ) + --- x 4 2 e

x

log x x

d x (a ) dx

a log a

d ( asin x ) dx

1 ----------------2 1–x

d ( acos x ) dx

–1 -----------------2 1–x

d ( atan x ) dx

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

d ( acot x ) dx

–1 ------------2 1+x

d ( asec x ) dx

1 -------------------x x2 – 1

∫ x--------------2 2 –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

tan --x2

d ( log 10 x ) dx

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

∫ log x dx

x log x – x

x

∫ a dx

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

∫ -------------------2 2

dx

asin --xb

∫ -------------------2 2

dx

acosh --x- = log ( x + x – b ) b

∫ ---------------2 2 b +x

dx

1--atan --xb b

∫ --------------2 2 b –x

dx

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

dx

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

x

b –x

x –b

dx

∫e ∫e

2

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

sin bx dx

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

cos ( bx ) dx

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

ax

ax

2


36

Machinery's Handbook 28th Edition 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

a+l S = ----------- × n 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. a+l 5 + 40 S = ----------- ( l + d – a ) = --------------- ( 40 + 7 – 5 ) = 135 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. Ratio r =

n–1

--l- = a

17

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

17

11.25 = 1.153



37

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

2S – 2an d = ---------------------n(n – 1)

a

l

S

l

n

S

a

d

n

l = a + ( n – 1 )d

a

d

S

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

a

n

S

d

n

S

a

d

l

a

d

S

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

a

l

S

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

d

l

S

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

a

d

n

n S = --- [ 2a + ( n – 1 )d ] 2

a

d

l

a

l

n

d

l

n

a

d

l

n

S

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

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

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

2 – a2 a+l + -l + l--------------S = a---------= ----------- ( l + d – a ) 2d 2 2d n--S = (a + l) 2

n S = --- [ 2l – ( n – 1 )d ] 2



38

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

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


Machinery's Handbook 28th 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



40

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) y – y1 x – x1 - = ---------------. and P2(x2,y2) is --------------y1 – y2 x1 – x2 y1 – y2 The previous equation is frequently written in the form y – y 1 = ---------------- ( x – x 1 ) 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, ∆y = y--------------2 – y1 m = -----∆x x2 – x1



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 – 5x–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 ) .


42

Machinery's Handbook 28th Edition COORDINATE SYSTEMS

2 If the lines are parallel, their slopes are equal. Thus, y – 4 = --- ( 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 = -----m1 2--2 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 –  – --3- 2 + -- 4 m1 – m2 4 - = ----11- = 11 tan θ = --------------------------- = ------------------------ = -----------4- = ----------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- = --------17d = ------------------------------------- = -----------------------------------------2 2 2 2 4+9 13 2 +3 A +B 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).



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 its 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

θ = atan -yx

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

3.6 1

33.69

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.



44

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)

λ = π + atan y-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 ) λ = 360° + atan – 4--- = 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

x +y

P

2 O

z = z θ

x

r

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 28th 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 = Y

The center radius form of the circle equation is 2

2

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

circle reduces to x + y = r

2

2

g +f –c.

or

Center (h, k)

r

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

Additional Formulas: Listed below are additional formulas for determining the geometry of plane circles and arcs. Although trigonometry and circular measure are related, they both deal with angles in entirely different ways. L =perimeter of circle = πD = 2πR D

2

Tangent

D =diameter of circle = 2R = --L-

2

X= R – Y

2

2

Y= R – X

2

2

2

A

L N ea

R

I

M =area of complement section = πR = 0.2146R R – --------4

Mrea Tota l

N =total area of a circle = πR

π 2

Ar

2

X +Y

Tangent

N ---- = π

R =radius =

Y

X

2

Area T

I =distance from center to start of section T H =height of section T Q =chord length for segment S 2 –1 P T + S = area of segment = R × sin  ------- – IP -----2R

H

S Q P Fig. 1a.

2

Example 1:Find the area of a circular section with included angle of 30° and radius of 3 inches. 2 2 2 φ° 30 Solution: Referring to Fig. 1b, K =  --------- × π × R =  --------- × π × 3 = 2.35 in  360  360


Machinery's Handbook 28th Edition CIRCLE

46 Areas K and S

φ° L =perimeter of φ degrees =  --------- × 2πR 360

2 2 180 L E + 4F ------- = --------------------R =radius = --------- --- = 2K π φ L 8F

× L- – E ( R – F -) -------------------------------S =area of segment = R 2

2

φ

E =chord length = 2 × F × ( 2R – F ) = D × sin  --- 2 2

2

φ 2

4R – E = R ×  1 – cos  ---  F =chord height = R – ------------------------   2

180 L φ =angle at center of circle = --------- --π φ

φ° 2 × L-----------K =area of section =  --------- × π × R = R 360 2

Donut R1 =radius of outer circle of donut R2 =radius of inner circle of donut φ 2 2 U =area of segment of donut = --------- × π × ( R 1 – R 2 ) 360

W =total area of donut =

2 π ( R1

2

– R2 )

Fig. 1c.

Example 2:Find the chord length E of a circular segment (Fig. 1b), with a depth of 1 inch at the center, that is formed in a circle whose radius 5 inches. Solution: The chord length is E = 2 F ( 2R – F ) = 2 1 ( 2 × 5 – 1 ) = 2 9 = 6 in. Example 3:Find the area S of the circular segment from Example 2. Solution: First determine angle φ, then find the perimeter L of the segment, and then solve for area S, as follows: φ E ⁄ 2- = ----------6 ⁄ 2- = 3--tan  --- = ----------- 2 R–F 5–1 4

φ --- = 36.87° 2

φ = 73.74°

φ 73.74 L = --------- ( 2πR ) = ------------- × ( 10π ) = 6.43 inches 360 360 2 R × L E(R – F) 5 × 6.43 6 ( 5 – 1 ) Area S = ------------- – ---------------------- = ------------------- – -------------------- = 16.075 – 12 = 4.075 in 2 2 2 2 An alternate method for finding angle φ is to divide one half of the chord length by the φ chord radius to obtain sin(φ⁄2), thus sin --- = ------------- . 2 2R E- = ---------6 - = 0.6 sin φ --- = -----2R 2(5) 2

φ --- = 36.87° 2

φ = 73.74°


Machinery's Handbook 28th Edition ELLIPSE

47

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

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

2

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

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


Machinery's Handbook 28th Edition ELLIPSE

48

2

2

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

k = –3

a =

5

b =

3

c =

2

2--5

e =

Additional Formulas: An ellipse is the locus of points the sum of whose distances from two fixed points, called focus, is a constant. An ellipse can be represented parametrically by the equations x = acosθ and y = bsinθ, where x and y are the rectangular coordinates of any point on the ellipse, and the parameter θ is the angle at the center measured from the xaxis anticlockwise.

2

R1 =radius of director circle =

A +B

R2 =radius of equivalent circle = P =center to focus distance =

2

AB 2

A –B

2

2

2

2

A =major radius =

B +P

B =minor radius =

A –P

2

2B distance, origin to latus rectum = ---------

2

A

J =any point (X,Y) on curve where X = A sin θ = A cos φ and Y = B cos θ = B sin φ φ =angle with major axis = sin  --- = cos  --- B A –1

Y

–1

X

θ =angle with minor axis = 90° – φ


Machinery's Handbook 28th Edition ELLIPSE 2

49

L =total perimeter (approximate) = A 1.2  --- + 1.1  --- + 4 A A B

B

π L =perimeter (sections) =  --------- × 2φ AB 180

Area Calculations N =total surface area of ellipse = πAB W =sectional area between outer and inner ellipse = π ( A 1 B 1 – A 2 B 2 ) M =area of complement section = AB – πAB ----------4

– 1  X 1

S =area of section = AB × cos  ------ – X 1 Y 1 A –1 X T+S = combined area of sections T + S = AB × cos  -----2- – X 2 Y 2 A –1 X 2 V =area of section = R 2 × sin  --- – XY A –1 X K =area of section = AB × cos  --- A

Example 4:Find area of section K, and complement area M, given the major radius of ellipse is 4 inches, minor radius of ellipse is 3 inches, dimension X = 3.2388 inches. Solution: The sectional area K –1 X 1 – 1 3.2388 2 Area K = AB × cos  ------ = 4 × 3 × cos  ---------------- = 12 × 0.627 = 7.5253 in  A  4 

Solution: Complement area M 2 ×4×3 Area M = AB – πAB ----------- = 4 × 3 – π --------------------= 2.5752 in 4 4

Example 5:Find the area of elliptical section S, T + S, provided that major radius of ellipse is 4 inches, minor radius of ellipse is 3 inches, dimension X1 = 3.2388 inches, dimension Y1 = 1.7605 inches, and dimension X2 = 2.3638 inches. Solution: The sectional area S –1 X 1 – 1 3.2388 2 S = AB × cos  ------ – X 1 Y 1 = 4 × 3 × cos  ---------------- – ( 3.2388 × 1.7605 ) = 1.8233 in A 4

Solution: Sectional area T + S –1 X2 φ = cos  ------ = 53.77°  A

Y 2 = B sin φ = 3 sin ( 53.77° ) = 2.42

– 1  X 2

– 1 2.3638 T + S = AB × cos  ------ – X 2 Y 2 = 4 ⋅ 3 × cos  ---------------- – ( 2.3638 × 2.42 ) A 4

= 11.2432 – 5.7203 = 5.5229 in

2

Example 6:Find the area of elliptical section V, if the major radius of ellipse is 4 inches, minor radius of ellipse is 3 inches, dimension X = 2.3688 inches, dimension Y = 2.4231 inches.


Machinery's Handbook 28th Edition SPHERES

50

Solution: Sectional area V R2 =

AB

2

R 2 = AB = 3 × 4 = 12

–1 X – 1 2.3688 2 V = R 2 × sin  --- – XY = 12 × sin  ---------------- – ( 2.3688 × 2.4231 )  A  4 

= 7.6048 – 5.7398 = 1.865 in

2

Four-Arc Oval that Approximates an Ellipse*.—The method of constructing an approximate ellipse by circular arcs, described on page 63, 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. 2, 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 A 2- – Ar + Br – B ---------4 4 X = -------------------------------------------B – 2r

R = B --- + X 2

(2)

(3)

A

r

B R X

Fig. 2. Four Arc Oval Ellipse

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). Spheres.—The standard form for the equation of a sphere with radius R and centered at point (h, k, l) can be expressed by the equation: 2

2

2

2

(x – h) + (y – k) + (z – l) = R The general form for the equation of a sphere can be written as follows, where A cannot be zero. 2

2

2

Ax + Ay + Az + Bx + Cy + Dz + E = 0 The general and standard forms of the sphere equations are related as follows: * Four-Arc Oval material contributed by Manfred K. Brueckner


Machinery's Handbook 28th Edition SPHERES –B h = ------2A

–C k = ------2A

51

2

–D l = ------2A

R =

2

2

B +C +D E ------------------------------- – --2 A 4A

R =radius of sphere D =diameter of sphere Ns =total surface area of sphere Nv =total volume of sphere R1 =radius of outer sphere R2 =radius of inner sphere Ga, Ka, Sa, Ta, Ua, Wa, Za = sectional surface areas Gv, Kv, Sv, Tv, Uv, Wv, Zv = sectional volumes

Formulas for Spherical Areas and Volumes To Find Radius of sphere from volume Nv Section Entire Sphere

Formula RN =

3

3N ---------v 4π

To Find Radius of Section T

Area N a = 4πR

2

Formula 2

RT =

2

2 2

2

P – Q – 4H - P ---------------------------------+ ----  8H 4

Volume Volume

4π π 3 3 N v = --- × D = ------ × R 3 6


Machinery's Handbook 28th Edition SPHERES

52

Formulas for Spherical Areas and Volumes (Continued) To Find

Formula 2

To Find 2

Formula

Section G

G a = 4πR 1 + 4πR 2

Volume

4π 3 3 G v = ------ ( R 1 – R 2 ) 3

Section K

2 φ K a = 2πR  1 – cos ---  2

Volume

FK v = 2πR ---------------3

Section S

2 E S a = π ×  F + ------  4

Volume

F E S v = π × F ×  ------ + ------ 8 6

Volume

π 2 3Q 2 3P 2 T v = H × ---  H + ---------- + --------- 6 4 4 

Volume

3 3 U v = 2π ( R 1 – R 2 )  1 – cos φ ---  2

2

2

Section T

2

T a = 2πRH

2

Section U

2 2 U a = 2π ( R 1 + R 2 )  1 – cos φ ---  2

Section W

W a = 4π × R 1 × R 2

Volume

W v = 2π × R 1 × R 2

Section Z

φ 2 Z a = ( 4π × R 1 × R 2 ) --------360

Volume

2 φ 2 Z v = ( 2π × R 1 × R 2 ) --------360

2

2

2

Example 7:Find the inside and outside surface area Ga and volume Gv of wall G, provided that R1 is 5.0 inches, and R2 is 4.0 inches. Solution: Sectional area Ga and sectional volume Gv 2

2

2

2

G a = 4πR 1 + 4πR 2 = 4π5 + 4π4 = 515.22 in

2

4π 3 4π 3 3 3 3 G v = ------ ( R 1 – R 2 ) = ------ ( 5 – 4 ) = 255.52 in 3 3

Example 8:Find the surface area Ka and volume Kv of section K of a sphere of radius 5.9 inches, if included angle φ = 90° and depth F = 2 inches. Solution: Sectional area Ka and sectional volume Kv 2 2 2 K a = 2πR  1 – cos φ --- = 2π5  1 – cos 90° -------- = 46.00 in 2 2 2

2

F- = --------------2π5 2- = 104.72 in 3 K v = 2πR ---------------3 3

Example 9:Find the outside surface area Sa and sectional volume Sv of section S of a sphere if E = 7.071 inches and F= 2.0 inches. Solution: Sectional area Sa and sectional volume Sv 2

2

2 E  2 7.071  2 S a = π ×  F + ----- = π ×  2 + --------------= 51.85 in   4 4  2

2

2

2

3 Sv = π × F ×  E ------ + F ------ = π × 2 ×  7.071 --------------- + 2----- = 43.46 in 8  8 6 6

Example 10:Find the outside and inside surface area Ua and volume Uv of section U of a sphere, if R1 = 5.00 inches, R2 = 4.0 inches, and included angle φ = 30°. Solution: Sectional area Ua and sectional volume Uv


Machinery's Handbook 28th Edition PARABOLA

53

2 2 2 2 2 U a = 2π ( R 1 + R 2 )  1 – cos φ --- = 2π × ( 5 + 4 )  1 – cos 30° -------- = 8.78 in   2 2  3 3 3 3 3 φ 30° U v = 2π ( R 1 – R 2 )  1 – cos --- = 2π × ( 5 – 4 )  1 – cos -------- = 13.06 in   2 2 

Example 11:Find the total surface area Wa and volume Wv of ring W, if R1 = 5.00 inches and R2= 4.0 inches. Solution: Sectional area Wa and sectional volume Wv 2

2

W a = 4π × R 1 × R 2 = 4π × 5 × 4 = 789.56 in 2

W v = 2π × R 1 ×

2 R2

2

2

2

= 2π × 5 × 4 = 1579.13 in

3

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 Directrix x = h − p

Y

2

4y – 8x – 12y + 1 = 0 2

(y − k) = 4p(x − h)

2

4y – 12y = 8x – 1 2 1 y – 3y = 2x – --4

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

V F

3 3 2 y – 2y --- +  --- = 2x – 1--- + 9--2  2 4 4 2

2  y – 3--- = 2 ( x + 1 )  2

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. 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 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


Machinery's Handbook 28th Edition HYPERBOLA

54

2

2

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

Y

Asymptote

y − k = (b / a)(x − h)

V1 (h − a, k)

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

(x – 2) 4(y – 1) x – 2 ) - – (-----------------y – 1)- = 1 9 ------------------- – ---------------------- = (-----------------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 28th Edition GEOMETRICAL PROPOSITIONS

55

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.



56

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

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

a

c

a

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



57

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

D

1 /2

A

b

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

C

A B

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

B

A + B + C + D = 360 degrees

d

a

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

A1

h

h1

If a = a1 and h = h1, then Area A = area A 1

a1

a

The areas of triangles having equal base and equal height are equal.

h A

A1

c 1/ 2

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

If a = a1 and h = h1, then Area A = area A 1

a1

a

h1



58

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



59

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


Machinery's Handbook 28th Edition GEOMETRICAL CONSTRUCTIONS

60

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

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

A

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.



61

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:

A

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.

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

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 F FGH.

K

To lay out a 60-degree angle:

E

C

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



62

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



63

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.



64

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

3

1 D A

C

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.

B

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 28th Edition AREAS AND VOLUMES

65

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 h Then, volume V of the body is V = --- ( 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



66

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:



67

W A = ----- [ ( V 0 + V N ) + 4 ( V 1 + V 3 + … + V N – 1 ) + 2 ( V 2 + V 4 + … + V N – 2 ) ] 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’s 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 72). 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.

3.1416b 2 ( 3a + 2b ) A = ----------------------------------------------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 77, 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.


68

Machinery's Handbook 28th Edition 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 77 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 77 and 80 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 77, 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 77 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.



69

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 + b2

a =

d2 – b2 = A ÷ b

a =

d2 – a2 = A ÷ a

2

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



70

Right-Angled Triangle: Area = A = bc -----2 b2 + c2

a = 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 b 2 + c 2 = 6 2 + 8 2 = 36 + 64 = 100 = 10 inches b × c = 6----------× 8- = 48 A = ---------------- = 24 square inches 2 2 2 a =

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 bh- = b--- a 2 –  a--------------------------- Area = A = ----  2 2b 2

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 a2 + b2 – c2 2 9 10 2 + 9 2 – 8 2 2 117 2 A = --- a 2 –  ---------------------------- = --- 10 2 –  -------------------------------- = 4.5 100 –  ---------      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 bh- = b--- a 2 –  c--------------------------- Area = A = ----  2b 2 2

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 )h Area = 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



71

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 + cH- = -----------------------------------------------------------------( 12 + 8 )10 + 2 × 8 + 3 × 12A = (----------------------------------------------2 2 252- = 126 square inches 20 × 10 + 16 + 36- = -------= -----------------------------------------2 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

ns nsrs2 A = ------= ----- R 2 – ---2 2 4 R =

s2 r 2 + ---4

r =

s2 R 2 – ---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 ns 12 × 4.141 A = ----- R 2 – s---- = ------------------------- 8 2 – 4.141 ---------------- = 24.846 59.713 2 2 4 4

= 24.846 × 7.727 = 191.98 square centimeters



72 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: r × α × 3.1416- = 0.01745rα = -----2ALength of arc = l = ---------------------------------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 ) 2 + 4h 2 r = c------------------8h

h = r–

1⁄ 2

4r 2

α = angle, in degrees

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

–

c2

= r [ 1 – cos ( α ⁄ 2 ) ]

α = 57.296 --------------------l r

See also, Circular Segments starting on page 76. 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 + 4h 2 2 + 4 × 62 + 144- = 400 r = c------------------- = 16 ----------------------------= 256 ------------------------------- = 8 1⁄3 inches 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 67. 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



73

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 A = --------- ( R 2 – r 2 ) = 0.00873α ( R 2 – r 2 ) 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:

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

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



74 Parabola:

p l = length of arc = --2

2x 2x 2x 2x ------  1 + ----- + ln  ------ + 1 + ------ p p p p

When x is small in proportion to y, the following is a close approximation: 2 x 2 2 x 4 l = y 1 + ---  -- – ---  -- or , l= 5  y 3  y

4 y 2 + --- x 2 3

Example: If x = 2 and y = 24 feet, what is the approximate length l of the parabolic curve? 2 x 2 2 x 4 2 2 2 2 2 4 l = y 1 + ---  -- – ---  -- = 24 1 + ---  ------ – ---  ------ 5 y 5 24 3 y 3 24 1 2 1 - – 2--- × ---------------= 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: ab Area BCD = A = xy ----- – ------ ln  --x- + --y- 2  a b 2

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: 3 × 28 × 5- – ----------8- + --5- = 20 – 3 × ln 5.167 A = ----------× ln  -2 2 3 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 – b)A closer approximation is P = 3.1416 2 ( a 2 + b 2 ) – (------------------

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 28th Edition REGULAR POLYGONS

75

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 71. 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

--SR

S--r

--rR

--rS

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.


Machinery's Handbook 28th Edition REGULAR POLYGONS

76

Circular Segments.—The table that follows gives the principle formulas for dimensions of circular segments. The dimensions are illustrated in the figures on pages 72 and 77. 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 --2

α, h

h r = --------------------1 – cos --α2

α, l

180 l r = --------- --π α

r, c

2  c  α = acos  1 – -------- (13) 2  2r 

4r – c h = r – ---------------------2

r, h

α = 2 acos  1 – h---  r

(16)

r, l

180 l α = --------- π r

c, h

α = 4 atan 2h -----c

Given

c, l

(1)

(4)

(7)

(10)

h = r  1 – cos α ---  2

(2)

l = πrα ---------180

c α h = – --- tan --2 4

(5)

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

2h c = ----------αtan -4

(8)

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

(11)

πhα l = -----------------------------------α- 180  1 – cos -  2

(3)

(6)

(9)

α 180l  1 – cos --- 2 h = --------------------------------------- (12) πα π c l = ------ r asin  -----  2r 90

(15)

c = 2 h ( 2r – h ) (17)

π l = ------ r acos  1 – h---  90 r

(18)

(19)

c = 2r sin 90l -------πR

(20)

h = r  1 – cos 90l --------  πr 

(21)

(22)

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

(23)

c 2 + 4h 2 l = π  -------------------- atan 2h ----- 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 28th Edition SEGMENTS OF CIRCLES

77

Segments of Circles for Radius = 1.—Formulas for segments of circles are given on pages 72 and 76. 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 72 or 76. 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 72. 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


Machinery's Handbook 28th Edition SEGMENTS OF CIRCLES

78

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 28th Edition CIRCLES AND SQUARES

79

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.

Dia. of Circle, D

Side of Square, S

1⁄ 2

Area of Circle or Square

Dia. of Circle, D

Side of Square, S


Dia. of Circle, D

Side of Square, S


0.44

0.196

201⁄2

18.17

330.06

401⁄2

35.89

1288.25

1

0.89

0.785

21

18.61

346.36

41

36.34

1320.25

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

21⁄2

2.22

4.909

221⁄2

19.94

397.61

421⁄2

37.66

1418.63

3

2.66

7.069

23

20.38

415.48

43

38.11

1452.20

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

81⁄2

7.53

56.745

281⁄2

25.26

637.94

481⁄2

42.98

1847.45

9

7.98

63.617

29

25.70

660.52

49

43.43

1885.74

91⁄2

8.42

70.882

291⁄2

26.14

683.49

491⁄2

43.87

1924.42

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

10


Machinery's Handbook 28th Edition SQUARES AND HEXAGONS

80

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

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

E

d

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, for d = 2, D = 2.3094, and for d = 5⁄16, D = 0.3608. Therefore, D = 2.3094 + 0.3608 = 2.6702 inches. Example 2: Find E when d = 20.25 millimeters. From the table, for d = 20, E = 28.2843; for d = 0.2, E = 0.2828; and d = 0.05, E = 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 1⁄ 16 3⁄ 32

45.2548

67

77.3650

94.7523

0.0884

1.0464

1.2816

33

38.1051

46.6691

68

78.5197

96.1666

0.1083

0.1326

1.0825

1.3258

34

39.2598

48.0833

69

79.6744

97.5808

0.1

0.1155

0.1414

29⁄ 32 15⁄ 16 31⁄ 32

1.1186

1.3700

35

40.4145

49.4975

70

80.8291

98.9950

1⁄ 8 5⁄ 32 3⁄ 16

0.1443

0.1768

1.0

1.1547

1.4142

36

41.5692

50.9117

71

81.9838

100.409

0.1804

0.2210

2.0

2.3094

2.8284

37

42.7239

52.3259

72

83.1385

101.823

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

1⁄ 4 9⁄ 32

0.2887

0.3536

6.0

6.9282

8.4853

41

47.3427

57.9828

76

87.7573

107.480

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 3⁄ 8

0.3969

0.4861

10

11.5470

14.1421

45

51.9615

63.6396

80

92.3761

113.137

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

7⁄ 16 15⁄ 32

0.5052

0.6187

14

16.1658

19.7990

49

56.5803

69.2965

84

96.9949

118.794

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

9⁄ 16 19⁄ 32

0.6495

0.7955

18

20.7846

25.4559

53

61.1992

74.9533

88

101.614

124.451

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

0.0722

21⁄ 32 11⁄ 16

0.7578 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

3⁄ 4 25⁄ 32

0.8660

1.0607

26

30.0222

36.7696

61

70.4368

86.2671

96

110.851

135.765

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 7⁄ 8

0.9743

1.1932

30

34.6410

42.4264

65

75.0556

91.9239

100

115.470

141.421

1.0104

1.2374

31

35.7957

43.8406

66

76.2103

93.3381

…

…

…

0.9281

22

25.4034

31.1127

57

65.8180

80.6102

92

106.232

130.108


Machinery's Handbook 28th Edition VOLUMES OF SOLIDS

81

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, V- = ---------------25 = 25 b = depth = ---------- = 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: nsh s2 V = nsrh ------------ = --------- 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



82 Frustum of Pyramid:

h Volume = V = --- ( 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.

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



83

Portion of Cylinder: h Volume = 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 2 2 V =  --- × 2.5 3 + 0 × 9.82 ---------------- = --- × 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 =

d2 ----- + 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



84 Sphere:

3 3 ------------ = πd --------- = 4.1888r 3 = 0.5236d 3 Volume = V = 4πr 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: 2 V = 2πr --------------h- = 2.0944r 2 h = Volume 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

A = area of spherical surface

2 2 V = 3.1416h 2  r – h--- = 3.1416h  c----- + h-----  3 8 6

c 2- + h 2 A = 2πrh = 6.2832rh = 3.1416  --- 4 c = 2 h ( 2r – h ) ;

c 2 + 4h 2 r = -------------------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 ,625 + 2500 V = 3.1416 × 50 ×  125 ----------- + 50 -------- = 157.08 ×  15 --------------------------- = 372 ,247 mm 3 = 372 cm 3  8  8 6  6  2 + 4 × 50 2 15 ,625 + 10 ,000- = ---------------25 ,625 = 64 millimeters r = 125 ----------------------------------= --------------------------------------8 × 50 400 400

Ellipsoid: 4π Volume = V = ------ 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



85

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 α 4πr 3 V = --------- × ------------ = 0.0116αr 3 360 3 α A = --------- × 4πr 2 = 0.0349αr 2 360

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 V = ------ ( R 3 – r 3 ) = 4.1888 ( R 3 – r 3 ) 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 2π Area = A = -----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



86

Paraboloidal Segment: π Volume = V = --- 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 π2 = -----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 V = ------ πh ( 2D 2 + d 2 ) = 0.262h ( 2D 2 + d 2 ) 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 --------------------------------------------------------------------------------: --------------------------: ------------------------------------- = ⁄3 : ⁄2 : ⁄3 : 1 12 8 6 4


Machinery's Handbook 28th Edition CIRCLES IN A CIRCLE

87

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.



88

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



89

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



90

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



91

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

C A Fig. 25. N = 55

Fig. 26. N = 61

Fig. 27. N = 97

B Fig. 28.


Machinery's Handbook 28th Edition CIRCLES IN A RECTANGLE

92

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)

3

T

2

2

V, S

15

T

2

8

V, (S, H/D < 0.038)

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

2

V, (S, H/D < 0.732)

R

4

5

(S, H/D > 1.196)

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)

8 9 10

13

20

21 22 23 24 25

T

3

7

V, (S, H/D < 1.196)

R

3

7

(S, 0.165 < H/D < 0.479)

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 28th Edition ROLLERS ON A SHAFT

93

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 between two rollers, as indicated below. In the equations that follow, N is the number of rollers, and N ≥ 3. Equation (1a) applies when the clearance C = 0 d D = --------------------180 sin  ---------  N 

(1a)

Equation (1b) applies when clearance C > 0 then d C = D sin  180° – ( N – 1 ) asin  ----  – d   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. 180 180 d = D sin  --------- = D sin  --------- = 0.078459D  N   40  D = D S + d = 3 + 0.078459D 3 D = ------------------- = 3.2554 0.92154 d = D – D S = 0.2554 * Rollers on a Shaft contributed by Manfred K. Brueckner.


94

Machinery's Handbook 28th Edition 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 28th Edition TRIGONOMETRIC IDENTITIES

95

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: c ab ---------= ----------- = ------------ , sin C sin A sin B b sin A a = --------------or sin B a sin B b = --------------or sin A a sin C c = --------------or sin A

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 104, 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.


Machinery's Handbook 28th Edition TRIGONOMETRIC IDENTITIES

96 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 = tan 1⁄2 A =

1⁄ ( 1 2

– cos A )

cos 1⁄2 A =

1⁄ ( 1 2

+ cos A )

– cos Asin A 1 – cos A- = 1---------------------------------------= ---------------------1 + cos A sin A 1 + 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 28th Edition RIGHT-ANGLE TRIANGLES

97

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

sin B = 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

b c = ----------sin B

a = b × cot B

A = 90° − B

Side b; angle A

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

a = b × tan A

B = 90° − A

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

b = a × tan B

A = 90° − B

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

b = a × cot A

B = 90° − A

Side a; angle B Side a; angle A

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

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

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

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

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

= 0.57735027 = 1 = 1.7320508 = ∞


Machinery's Handbook 28th Edition RIGHT-ANGLE TRIANGLES

98

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°. a 12 12 c = ----------- = ---------------- = ------------------- = 13.2405 meters 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 28th Edition RIGHT- AND OBLIQUE-ANGLE TRIANGLES

99

Chart For The Rapid Solution of Right-Angle and Oblique-Angle Triangles C = A 2 B2

sin d =

A

e = 90 ° d

B A

-

A

A

B

B

e

B

90

90

B

90

90

d

C

C sin e = ---A

d

C B tan d = ---C

A = B2 C2

d = 90 ° e

A

e

A B

e

90 C

B 90

90

90

d

C C = A × sin e

B = A × cos e

A 90

e

90

90

d

d

C B =cot d

B 90

d

d

A

A × sin f B = ------------------sin d B

C C A = ---------sin e

A

e

90

A × sin e C = -------------------sin d

d

A × sin eC = ------------------sin d d

C e

e

A

B

e = 180° ( d + f ) d f

A

2 + C2 A2 cos d = B --------------------2×B×C

d

sin f = B ------×-----sin --------dA B

A

f

A Area = A × B × sin e 2

e

A

d

d

× sin d-------------------sin f = B A B

e

e =180° (d + f ) d

f

e A

tan d = A × sin e B A× cos e B

e e

f =180° (d + e)

B

d

C

d f

d

d C

C

e =180°(d + f )

A

f

B = C × cot e e B

90

f

d

90

90

C

C

C = B × tan e

e B

B

C

C A = -----------cos d

d

B A = ---------cos ee

90

B

A

C

C = B × cot d B

A

90

C

BA = ---------sin d 90

A

B

d

d

A

e

A B

d

C

C = A × cos d

B = A × sin d

90

A2 C2

B=

f C

A

e


100

Machinery's Handbook 28th Edition 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 a × sin C- = ------------------------5 × sin 38 °- = ---------------------------5 × 0.61566 c = -------------------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′ a × sin C 9 × 0.57358 c = --------------------- = ---------------------------- = 5.2 inches sin A 0.99269


Machinery's Handbook 28th Edition OBLIQUE-ANGLE TRIANGLES

101

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 × sin C× b × sin Cc = a-------------------Area = a----------------------------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

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

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

If a > 0.5858l, maximum deflection is

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

BEAM STRESS AND DEFLECTION TABLES

W s = --------- ( 3l – 11x ) 16Z

Deflections at Critical Pointsa

between load and point of fixture, at

x = 2n -----m

263



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

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

Maximum stress at point

Wl-----8Z

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

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

Deflections at Critical Pointsa 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

x 2 Wl  s = -------  1⁄3 – x-- + 1⁄2  --   l Z  l 

Maximum stress, at support,

Wl-----3Z

Wx 2 y = -------------- ( 2l – x ) 2 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 y = ------------ ( 3l – 2x ) 12EI

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


Maximum deflection, at free end,

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


of fixture,

264

Table 1. (Continued) Stresses and Deflections in Beams

Machinery's Handbook 28th Edition 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 18. — Fixed at Both Ends, Load at Center Between each end and load,

Wx 2 y = ------------ ( 3l – 4x ) 48EI

Stress at ends

Wl ------8Z

Stress at load

Wl– -----8Z

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

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

Stress at end next to segment of length a,

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

Wv 2 a 2

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

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

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

Deflection at load,

3 b3 Wa ---------------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 )


W s = ------ ( 1⁄4 l – x ) 2Z


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

load,

2Wa b – ------------------Zl 3

265



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 y = -------------- ( l – x ) 2 24EIl

Deflections at Critical Pointsa 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 = ------------  ------------------------ – R1  Z  2l 1  Between R2 and R,

l 2 – u  ( l 2 – u )W 2  s = -------------  ------------------------– R2  Z  2l 2 

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 1 – R 1 ) W1 2

R1 l1 and is – -------------2ZW 1 Greatest stress in the second span is at

l2 u = ------- ( W 2 – R 2 ) W2 and is,

Between R1 and R,

x ( l1 – x )  y = --------------------  ( 2l 1 – x ) ( 4R 1 – W 1 ) 24EI  W1 ( l1 – x )2  – --------------------------- l1  Between R2 and R,

u ( l2 – u )  y = ---------------------  ( 2l 2 – u ) ( 4R 2 – W 2 ) 24EI  W2 ( l2 – u ) 2  – --------------------------- l2 

R 22 l 2 – ------------2ZW 2


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


x 2 Wl  s = -------  1⁄6 – x-- +  --  2Z  l  l

266


Machinery's Handbook 28th Edition 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 22. — Continuous Beam, with Two Equal Spans, Uniform Load

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

Maximum stress at

Wl-----8Z

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

Stress is zero at x = 1⁄4l Greatest negative stress is at x = 5⁄8l and is,

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 s = --------- ( 3l – 11x ) 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 x = ------ l 11

Between point A and load,

Wx 2 y = ------------ ( 9l – 11x ) 96EI

Maximum deflection is at v = 0.4472l, and is

Wl 3 ---------------------107.33EI

Between point B and load,

Wv y = ------------ ( 3l 2 – 5v 2 ) 96EI

Greatest negative stress at center of span,

Deflection at load,

7 - Wl 3 ---------------768 EI


point A,


5 Wl – ------ ------32 Z

267



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

l1

a2

v

R2

1 ------[ m ( l1 – u ) – W1 a1 u ] l1 Z Between R and W2, s =

1 ------[ m ( l2 – x ) – W2 a2 x ] l2 Z Between R2 and W2,

l2

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  y = ---------  ( l 1 – w ) ( l 1 + w )r 1 – ------------ 6EI  l1  Between R and W1,

u y = -------------- [ W 1 a 1 b 1 ( l 1 + a 1 ) 6EIl 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 y = -------------- [ W 2 a 2 b 2 ( l 2 + a 2 ) 6EIl 2 – W 2 a 2 x 2 – m ( 2l 2 – x ) ( l 2 – x ) ]

Deflections at Critical Pointsa 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

W 2 b 23  v  y = ---------  ( l 2 – v ) ( l 2 + v )r 2 – ------------ 6EI  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. 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

268


Machinery's Handbook 28th Edition RECTANGULAR AND ROUND SOLID BEAMS

269

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 Length, l Beam Height, h inch (mm) inch (mm) lb/in2 (N/mm2) Beam fixed at one end, loaded at the other

6lW ---------- = h bf

6lW ---------- = f bh 2

Total Load, W lb (N)

2 bfh ----------- = 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

bfh 2- = W ---------3l

Beam supported at both ends, single load in middle

3lW- = b ---------2fh 2

3lW ---------- = h 2bf

3lW- = f ----------2bh 2

2 2bfh -------------- = 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

3Wa ----------- = b fh 2

3Wa = h ----------bf

3Wa ----------- = f bh 2

l, any length 2 bh -----------f = a 3W

bh 2-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 28th Edition UNIFORMLY LOADED BEAMS

270

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

3

5.092Wa ---------------------- = d f

5.092Wa ---------------------- = f d3

l, any length

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.


Machinery's Handbook 28th Edition BEAMS OF UNIFORM STRENGTH

271

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 x The computed bending stress fb is then found from f b = M  ---- sin φ + ---- cos φ where M  Ix  Iy 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.



272

Table 3a. Beams of Uniform Strength Throughout Their Length Type of Beam

Description

Formulaa

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.



273

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.

2Sbh 2P = --------------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.

4Sbh 2P = --------------3l

a For details of English and metric SI units used in the formulas, see footnote on page

272.


274

Machinery's Handbook 28th Edition DEFLECTION IN BEAM DESIGN

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 258 (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 2510, 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 258): 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 258 (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 258 (Case 2):


Machinery's Handbook 28th Edition CURVED BEAMS

275

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 276 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 276, 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 276 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. I 1 1 K = 1.00 + 0.5 -------2- ------------ + --bc 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



276

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

y0a .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.



277

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 236, the moment of inertia of the section is 2 × (4)3 ÷ 12 = 10.667 inches4. Using the straight-beam formula, page 275, 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 276 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 236, 50 × (100)3 /12 = 4,170,000 mm4. Using the straight-beam formula, page 275, 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


278

Machinery's Handbook 28th Edition SIZE OF RAIL TO CARRY LOAD

effect. From the table on page 276, 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


Machinery's Handbook 28th Edition STRESSES PRODUCED BY SHOCKS

279

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.



280

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.

QaL 96hEI p = -----------  1 + 1 + ---------------- 4I  QL 3 

p = a 6QhE --------------LI

Fixed at one end; struck at the other.

QaL p = -----------  1 + 1 + 6hEI ------------- I  QL 3 

p = a 6QhE --------------LI

Fixed at both ends; struck in center.

QaL p = -----------  1 + 1 + 384hEI ------------------- 8I  QL 3 

6QhEp = a -------------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 258 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), Wl Wl 2h 96hEI p = -------  1 + 1 + ---------------------------- = -------  1 + 1 + ---------------- 4Z  4Z  Wl 3 ÷ 48EI Wl 3 

(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



281

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

8QD-  Ghd 4 - f = ----------1 + 1 + ----------------πd 3  4QD 3 n

QhG f = 1.27 ------------Dd 2 n

Square

9QD  Ghd 4  - 1 + 1 + -------------------------f = ----------4d 3  0.9πQD 3 n

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: 1 Wv 2 E K = --- × ---------- foot-pounds 2 g

or

6Wv 2------------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 202 for more on this topic.


282

Machinery's Handbook 28th Edition STRENGTH OF COLUMNS

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 284. S p = ------------------------ = ultimate load, lbs. per sq. in. l 2 1 + K  -  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 284, 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 – --- ----2 4r 1 l2 Allowable unit stress, pin ends = 15 ,000 – --- ----2 3r


Machinery's Handbook 28th Edition STRENGTH OF COLUMNS

283

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. Cπ 2 IE = total ultimate load, in pounds P = ---------------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 284. 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 l2 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 28th Edition RANKINE AND EULER FORMULAS

284

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 + ----------------2 5000r

S p = -------------------------l2 1 + ----------------2 2500r

S p = -------------------------l2 1 + ----------------2 1250r

Wrought Iron

S p = ------------------------------l2 1 + --------------------2 35 ,000r

S p = ------------------------------l2 1 + --------------------2 17 ,500r

S p = -------------------------l2 1 + ---------------2 8750r

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 + ---------------------- + ----2 2 25 ,000r r

S p = ------------------------------------------l2 cz 1 + ---------------------- + ----2 2 12 ,500r r

S p = -------------------------------------l2 cz 1 + ----------------- + ----2 2 r 6250r

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

4π 2 IE P = --------------l2

Euler's Formulas for Slender Columns One End Fixed and Both Ends One End Rounded Rounded

2π 2 IE P = --------------l2

2 IE P = π ----------l2

One End Fixed and One End Free

π 2 IEP = ----------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.


Machinery's Handbook 28th Edition COLUMNS

285

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 432.) The radius of gyration r for a rectangular section (page 236) 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 = ------------- = ----------------------------------Q 3.70 = 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


286

Machinery's Handbook 28th Edition COLUMNS

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  = 2d 2 × 40 ,000  1 – 0.01945 -------------------  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, r 2 5400 ------------------------=  -------------  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), r 2 40 ,000 × 2 ×  ------------- r 2 2 × r2 0.289 × 40 , 000 2d 5400 = ------------------------------------------- = ----------------------------------------------------------Q 0.0778 5400 × 0.0778 × 0.289 × 0.289 r 4 = -------------------------------------------------------------------------- = 0.0004386 40 ,000 × 2 d = 0.145 ------------- = 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 1 + l 2 ⁄ 18 ,000r 2 18 ,000 l ⁄ r- - ×  1.6 – -------main members, safe unit stress, psi = --------------------------------------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 287.


Machinery's Handbook 28th Edition ALLOWABLE LOADS FOR STEEL PIPE COLUMNS

287

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.


288

Machinery's Handbook 28th Edition ALLOWABLE LOADS FOR STEEL PIPE COLUMNS 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

7

424

299

209

140

91 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.


Machinery's Handbook 28th Edition PLATES, SHELLS, AND CYLINDERS

289

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: × t2 ------------P = C 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 432 and 512). 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


290


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 .

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 Item d), above, for definition of r0). L 0.62W S = --------------log e --------  2r 0 t2

(7)

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.

0.62W L S = --------------log e -------- + 0.577  2r 0 t2

0.75W S = -----------------------------------l2 L  2 t  --- + 1.61 -----2 l L

(9)

0.1422W (12) d = ----------------------------------L 2.21 3 Et  ---- + ---------- l3 L2 g) Rectangular plate with all edges fixed and a uniformly distributed load over the surface of the plate. 0.5W S = -------------------------------------5 L  2 t --- + 0.623l ------------------ l L5 

(11)

(13)

0.0284W d = ------------------------------------------2 L- + 1.056l  3 Et --------------------  l3 L4 

(14)



291

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. 2 S = 0.39W --------------(15) (16) d = 0.221WR ------------------------t2 Et 3 b) Edge fixed around circumference and a uniformly distributed load over the surface of the plate. 2 (17) S = 0.24W --------------(18) d = 0.0543WR ---------------------------t2 Et 3 c) Edge supported around the circumference and a concentrated load at the center.

0.55WR 2 t 20.48W R - – 0.0185 ----d = ---------------------(19) 1 + 1.3 loge -------------S = --------------0.325t Et 3 R2 t2 d) Edge fixed around circumference and a concentrated load at the center. 0.62W t 2R - + 0.0264 ----S = --------------loge -------------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)


292


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. D + p- – 1 t = ----  S---------- 2 S–p

(25)

The table Ratio of Outside Radius to Inside Radius, Thick Cylinders on page 293 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: D t = ---2

S + ( 1 – µ )p- – 1 ----------------------------S – ( 1 + µ )p

(27)

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.



293

Ratio of Outside Radius to Inside Radius, Thick Cylinders Working Pressure in Cylinder, Pounds per Square Inch

Allowable Stress per Sq. In. of Section

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

2000

1.732

…

…

…

…

…

…

…

…

…

…

…

…

2500

1.528

2.000

…

…

…

…

…

…

…

…

…

…

…

3000

1.414

1.732

2.236

…

…

…

…

…

…

…

…

…

…

3500

1.342

1.581

1.915

2.449

…

…

…

…

…

…

…

…

…

4000

1.291

1.483

1.732

2.082

2.646

…

…

…

…

…

…

…

…

4500

1.254

1.414

1.612

1.871

2.236

2.828

…

…

…

…

…

…

…

5000

1.225

1.363

1.528

1.732

2.000

2.380

3.000

…

…

…

…

…

…

5500

1.202

1.323

1.464

1.633

1.844

2.121

2.517

3.162

…

…

…

…

…

6000

1.183

1.291

1.414

1.558

1.732

1.949

2.236

2.646

3.317

…

…

…

…

6500

…

1.265

1.374

1.500

1.648

1.826

2.049

2.345

2.769

3.464

…

…

…

7000

…

1.243

1.342

1.453

1.581

1.732

1.915

2.145

2.449

2.887

3.606

…

…

7500

…

1.225

1.314

1.414

1.528

1.658

1.813

2.000

2.236

2.550

3.000

3.742

…

8000

…

1.209

1.291

1.382

1.483

1.599

1.732

1.890

2.082

2.324

2.646

3.109

3.873

8500

…

1.195

1.271

1.354

1.446

1.549

1.667

1.803

1.964

2.160

2.408

2.739

3.215

9000

…

1.183

1.254

1.330

1.414

1.508

1.612

1.732

1.871

2.035

2.236

2.490

2.828

9500

…

…

1.238

1.309

1.387

1.472

1.567

1.673

1.795

1.936

2.104

2.309

2.569

10,000

…

…

1.225

1.291

1.363

1.441

1.528

1.624

1.732

1.856

2.000

2.171

2.380

10,500

…

…

1.213

1.275

1.342

1.414

1.494

1.581

1.679

1.789

1.915

2.062

2.236

11,000

…

…

1.202

1.260

1.323

1.390

1.464

1.544

1.633

1.732

1.844

1.972

2.121

11,500

…

…

1.192

1.247

1.306

1.369

1.438

1.512

1.593

1.683

1.784

1.897

2.028

12,000

…

…

1.183

1.235

1.291

1.350

1.414

1.483

1.558

1.641

1.732

1.834

1.949

12,500

…

…

…

1.225

1.277

1.333

1.393

1.458

1.528

1.604

1.687

1.780

1.883

13,000

…

…

…

1.215

1.265

1.318

1.374

1.435

1.500

1.571

1.648

1.732

1.826

13,500

…

…

…

1.206

1.254

1.304

1.357

1.414

1.475

1.541

1.612

1.690

1.776

14,000

…

…

…

1.198

1.243

1.291

1.342

1.395

1.453

1.515

1.581

1.653

1.732

14,500

…

…

…

1.190

1.234

1.279

1.327

1.378

1.433

1.491

1.553

1.620

1.693

15,000

…

…

…

1.183

1.225

1.268

1.314

1.363

1.414

1.469

1.528

1.590

1.658

16,000

…

…

…

1.171

1.209

1.249

1.291

1.335

1.382

1.431

1.483

1.539

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.


294


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: t P = 86 ,670 ---- – 1386 (28) D t P = 50 ,210 ,000  ----  D

3

(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: t P = 597.6 ---- – 9.556 (30) D t 3 P = 346 ,200  ----  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:



295

( 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 Working Pressure in Pounds per Square Inch

Outside Diameter of Tube, Inches

100

7

0.152

0.160

0.168

0.177

0.185

0.193

0.201

8

0.174

0.183

0.193

0.202

0.211

0.220

0.229

9

0.196

0.206

0.217

0.227

0.237

0.248

0.258

10

0.218

0.229

0.241

0.252

0.264

0.275

0.287

11

0.239

0.252

0.265

0.277

0.290

0.303

0.316

12

0.261

0.275

0.289

0.303

0.317

0.330

0.344

13

0.283

0.298

0.313

0.328

0.343

0.358

0.373

14

0.301

0.320

0.337

0.353

0.369

0.385

0.402

15

0.323

0.343

0.361

0.378

0.396

0.413

0.430

16

0.344

0.366

0.385

0.404

0.422

0.440

0.459

16

0.366

0.389

0.409

0.429

0.448

0.468

0.488

18

0.387

0.412

0.433

0.454

0.475

0.496

0.516

120

140

160

180

200

220

Thickness of Tube in Inches. Safety Factor, 5

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

303 238

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


Machinery's Handbook 28th Edition SHAFTS

296

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 246) 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



297

For small, short shafts: 3 D ND = 3 38P ---------(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

× 300 = 63 horsepower P = 2-------------------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

9.55 × 10 P 10 P or T = ----------------------------T = -----------(8) (8a) 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:



298

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 0.83 × 10 P P = ------------------------(11a) or D = 3 ---------------------------(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- = 0.23 degree α = ------------------------------------------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-



299

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

PD = 4.6 × 4 --(14b) 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

PD = 4.0 × 3 --(15b) 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 its own weight 2

L = 5.2 3 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 inches.



300

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

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

37⁄16

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 298 and Linear Deflection of Shafting on page 299 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



301

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

or

(16a)

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, 5.1 2 2 D = B 3 ------- ( K m M ) + ( K t T ) pt

(17)

(18a)

or D = B×

3

63 ,000K t P 2 5.1 ------- ( K m M ) 2 +  -------------------------  pt N

(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 9.55K t P 2 5.1 2 D = B 3 ------- ( K m M ) +  --------------------  N  pt 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 per millimeter squared; and V = maximum transverse shearing load in kilograms.



302

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 Km Kt

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 D1 K = ------ = 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 2373. 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: 5.1 2 2 D = B 3 ------- [ ( K m M ) + ( K m M ) + ( K t T ) ] St



303

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 199 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 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 suffi-



304

cient 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.


Machinery's Handbook 28th Edition SPRINGS

305

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 351 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°


306

Machinery's Handbook 28th Edition SPRING MATERIALS 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


Machinery's Handbook 28th Edition SPRING MATERIALS

307

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.


308


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 heattreatment. 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) This alloy can be formed in the annealed condition and then precipitation hardened after forming at



309

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.


310

Machinery's Handbook 28th Edition STRESSES IN SPRINGS

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.



311

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 318). 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


Machinery's Handbook 28th Edition STRESSES IN SPRINGS LIVE GRAPH

220 210 200 190 180 170 160 150 140 130 120 110 100 90 80

Click here to view

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)

312


Fig. 2. Allowable Working Stresses for Compression Springs — Music Wirea

LIVE GRAPH 160

Click here to view Torsional Stress (corrected) Pounds per Square Inch (thousands)

150 140 130

Oil-tempered Steel Wire QQ-W-428, Type I; ASTM A229, Class II

Light Service 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 Torsional Stress (corrected) Pounds per Square Inch (thousands)

Click here to view

180 170

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


Machinery's Handbook 28th Edition STRESSES IN SPRINGS LIVE GRAPH Click here to view

160

Corrosion-resisting Steel Wire QQ-W-423, ASTM A313

150 Torsional Stress (corrected) Pounds per Square Inch (thousands)

313

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 Click here to view 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

Torsional Stress (corrected) Pounds per Square Inch (thousands)

LIVE GRAPH

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


Machinery's Handbook 28th Edition STRESSES IN SPRINGS LIVE GRAPH 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


314


220 210 200 190 180 170 160 150 140 130 120 110 100 90 80 70

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


Fig. 8. Recommended Design Stresses in Bending for Helical Torsion Springs — LIVE GRAPH Oil-Tempered MB Round Wire Click here to view


290 280 270 260 250 240 230 220 210 200 190 180 170 160 150 140

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


Fig. 9. Recommended Design Stresses in Bending for Helical Torsion Springs — LIVE GRAPH Stainless Steel Round Wire Click here to view


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.



315

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 Factora

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


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.


Machinery's Handbook 28th Edition STRESSES IN SPRINGS LIVE GRAPH

316 120

Click here to view

Final Stress, Including Curvature Correction, 1000 psi

110 0′′ 0.03 nder 5′′ ire u 0.12 o W t ic 31′′ Mus e 0.0 ir ic W adium Mus Van 0%C ome el 0.8 ade Chr g Ste gr in B r p lM OT S Stee .08%c ring 0 p l e S e e OT g St grad Sprin teel mb *HD gS in r p S 302 *HD ype 8-8 t eel 1 t S s H.T. inles ard *Sta ull h f r e opp ard mC ng h ylliu spri *Ber 5% e z ron ur B osph *Ph ss a r B ring *Sp d Lan irst to F e Du ess

100 90 80 70 60 50 40 30 20 10 0 0

tial

Ini

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


Machinery's Handbook 28th Edition SPRING DESIGN

317

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 2518, and gages in decimals of an inch are given in the table on page 2519. 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.


318


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 322, 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 322. 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.



319

Table 3. Formulas for Compression Springs Type of End Open or Plain (not ground)

Open or Plain (with ends ground)

Squared or Closed (not ground)

Closed and Ground

Formulaa

Feature 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 FL – 3d = ------------------p

N = TC – 2 FL – 2d = ------------------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

a The symbol notation is given on page

305.

Table 4. Formulas for Compression and Extension Springs Formulaa, b Feature

Springs made from round wire

Springs made from square wire

Gd 4 F 0.393Sd 3 = -------------P = ---------------------D 8ND 3

3 Gd 4 F ---------------------- = --------------------P = 0.416Sd D 5.58ND 3

Stress, Torsional, S Pounds per square inch

PD GdF- = -----------------S = -------------0.393d 3 πND 2

D GdF - = P -----------------S = --------------------0.416d 3 2.32ND 2

Deflection, F Inch

8PND 3 πSND 2 F = ------------------ = -----------------Gd Gd 4

2.32SND 2 5.58PND 3 F = -------------------------- = ------------------------Gd Gd 4

4F GdF------------- = ------------N = Gd 8PD 3 πSD 2

Gd 4 F = -------------------GdF N = --------------------5.58PD 3 2.32SD 2

Wire Diameter, d Inch

πSND 2- = d = ----------------GF

2.32SND 2- = d = -----------------------GF

Stress due to Initial Tension, Sit

S S it = --- × IT P

Load, P Pounds

Number of Active Coils, N

a The symbol notation is given on page

3

2.55PD-----------------S

3

PD ---------------0.416S

S S it = --- × IT P

305.

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.

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 --- = --------------0.1375 f


Machinery's Handbook 28th Edition SPRING DESIGN LIVE GRAPH

320

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



321

86 ,300 Step 6: Stress Solid = ---------------- × 1.5 = 103 ,500 pounds per square inch 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. 3 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 2519, 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.



322

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

.010

.012

.014

.016

.018

.020

.022

.024

.026

.028

.030

Deflection f (inch) per coil, at Load P .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

.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

(pounds) c … … .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

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 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.


SPRING DESIGN

5⁄ 32 11⁄ 64

Wire Size or Washburn and Moen Gauge, and Decimal Equivalent b

Machinery's Handbook 28th Edition 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

SPRING DESIGN

1⁄ 2

.026

a This


323

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 322.


324

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

a This



SPRING DESIGN

1

Deflection f (inch) per coil, at Load P (pounds)

Machinery's Handbook 28th Edition 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

SPRING DESIGN

Nom.

11

a This


325



326

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


Machinery's Handbook 28th Edition 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 38 Torsional Stress, Pounds per Square Inch (thousands)

327

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 highly stressed than the coils in the body and are subjected to a bending stress at section B



328

(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 2S 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. 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.



329

Fig. 17. Extension Spring Design Example

Step 3: The number of active coils. (say 6) F 0.625 AC = --- = ---------------- = 5.86 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 procedure. 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 7 P 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.



330

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: 5PD 2- = -------------------------------------5 × 9 × 0.6875 2 = 139 ,200 pounds per square inch 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


Machinery's Handbook 28th Edition SPRING DESIGN .05 inch × Outside diameter

331

± .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



332

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 developed 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 338. 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



333

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.



334

Fig. 19. The Most Commonly Used Types of Ends for Torsion Springs

1.3

LIVE GRAPH

Correction Factor, K

Click here to view

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 produce the same torque; i.e., 20 × 0.5 = 10 pound-inches; 10 × 1 = 10 pound-inches; and 5 × 2



335

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 305.

= 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. 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.


336


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



337

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 340, 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). 0.500 + 0.085- = 6.88 and thus the curvature correction factor The spring index D ---- = -------------------------------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. F90N + -------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. 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:



338

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 335 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 348, 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: 10.18 × 10 = 165 ,764 pounds per square inch S b = 10.18T ----------------- = ------------------------d3 0.085 3 Step 5: Calculate the number of coils from the equation, Table 13: EdF ° 28 ,500 ,000 × 0.085 × 90- = 5.73 (say 5 3⁄ ) N = ------------------= ----------------------------------------------------------4 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 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.



339

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.



340

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



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

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 gauge, the values are for oil-tempered MB

with a modulus of 28,500,000 psi.


SPRING DESIGN

1⁄ 16

Machinery's Handbook 28th Edition Table 14. (Continued) Torsion Spring Deflections AMW Wire Gauge Decimal Equivalenta

8 .020

9 .022

10 .024

11 .026

12 .029

13 .031

14 .033

15 .035

16 .037

17 .039

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

SPRING DESIGN

9⁄ 32


341

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 gauge, the values are for oil-tempered MB with a modulus of 28,500,000 psi.


342

Table 14. (Continued) Torsion Spring Deflections AMW Wire Gauge Decimal Equivalenta

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


17⁄ 32

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

5⁄ 8

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

3⁄ 4

Wire Gaugeab or Size and Decimal Equivalent

31 .085

32 .090

33 .095

34 .100

35 .106

36 .112

37 .118

1⁄ 8 .125

10 .135

9 .1483

5⁄ 32 .1563

8 .162

7 .177

3⁄ 16 .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. a For


SPRING DESIGN

21⁄ 32

Machinery's Handbook 28th Edition Table 14. (Continued) Torsion Spring Deflections AMW Wire Gauge Decimal Equivalenta

24 .055

25 .059

26 .063

27 .067

28 .071

29 .075

30 .080

7⁄ 8 15⁄ 16

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

Inside Diameter, inch 13⁄ 16

31 .085


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

1.000

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

Washburn and Moen Gauge or Size and Decimal Equivalent a

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 .250

9⁄ 32 .2813

5⁄ 16 .3125

11⁄ 32 .3438

3⁄ 8 .375

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 335. Note: Intermediate values may be interpolated within reasonable accuracy.

SPRING DESIGN

0.9375

1

a For

343



344

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

Factor

Stainless 316 Up to 1⁄8 inch diameter

0.75

Over 1⁄8 to 1⁄4 inch diameter

0.65

Over 1⁄4 inch diameter

0.65


0.85


0.75



0.65


1.07

Stainless 431

0.80


1.12

Stainless 420

0.85

Stainless 17–7 PH 1.00

…

…

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

up to 5

±5°

over 10 to 20

Tolerance ±15°

over 5 to 10

±10°

over 20 to 40

±30°



345

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 L 2 = ----------6Et 2S b bt 2 P = ---------------3L 3F = 4Ebt -----------------L3

4PL 3f = -----------Ebt 3 2S b L 2 = -------------3Et S b bt 2 P = -----------6L Ebt 3 F = --------------4L 3

3 f = 6PL ------------Ebt 3

Sb L 2 = ----------Et S b bt 2 P = -----------6L Ebt 3 F = --------------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



346

Table 19. (Continued) Formulas for Flat Springs

Feature

Stress, Sb Bending psi

Thickness, t Inches

3PLS b = ---------2bt 2 6EtF = ------------L2

6PL S b = ---------bt 2 3EtF = ------------2L 2

6PL S b = ---------bt 2 EtF = --------L2

6PL S b = ---------bt 2 EtF = ---------------0.87L 2

Sb L 2 t = ----------6EF

2S b L 2 t = -------------3EF

Sb L 2 t = ----------EF

0.87S b L 2 t = ---------------------EF

=

3

PL 3 -------------4EbF

=

3

4PL 3 ------------EbF

=

3

6PL 3 ------------EbF

=

3

5.22PL 3 -------------------EbF

Based on standard beam formulas where the deflection is small. See page 305 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 351. 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.



347

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 11,700,000 11,600,000 11,500,000 11,400,000

In Tension, E 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.



348

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



349

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.



350

Table 23. Arbor Diameters for Springs Made from Music Wire Wire Dia. (inch)

Spring Outside Diameter (inch) 1⁄ 16

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

11⁄ 32

3⁄ 8

7⁄ 16

1⁄ 2

Arbor Diameter (inch)

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

0.154

0.164

…

…

…

…

0.012

0.034

0.059

0.081

0.101

0.119

0.135

0.150

0.163

0.177

0.189

0.200

…

…

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

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)

9⁄ 16

5⁄ 8

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

…

…

…

Spring Outside Diameter (inches) 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)

0.054

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


Machinery's Handbook 28th Edition DISC SPRINGS

351

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 group are 8–4.2–0.2 and 40–20.4–1 respectively. Group 2 has 45 standard disc spring


Machinery's Handbook 28th Edition DISC SPRING MATERIALS

352

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 1.7701 (Germany) and BS 735 A50 (Great Britain) are used in foreign countries. Some


Machinery's Handbook 28th Edition DISC SPRING STACKING

353

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 28th Edition DISC SPRING STACKING

354

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.


Machinery's Handbook 28th Edition DISC SPRING FORCES AND STRESSES

355

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: 4⋅E⋅s -  h – --s- ⋅ ( h – s ) ⋅ t + t 3 F = ----------------------------------------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 28th Edition DISC SPRING FORCES AND STRESSES LIVE GRAPH

356

Click here to view

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



357

From Fig. 8, Da ------ = D ---- – ( a + b ) (5) 2 2 where a = t × sinα and b = r × cosα. Substitution of a and b values into Equation (5) gives: D ------a = D ---- – ( t sin α + r cos α ) (6) 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: Da   2h 1 2h ------ = D ---- – t  sin atan  ------------- + --- cos atan  -------------   D – d  D – d 6 2 2  

(8)

  2h 1 2h D a = D – 2t  sin atan  ------------- + --- cos 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 -  h – --s- ⋅ ( h – s ) ⋅ t + t 3 F = ----------------------------------------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  δ---------- δ  K 1 = ---------------------------------------δ+1 2 π ⋅  ------------ – -------- δ – 1 ln δ 2

(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)



358

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 - K 24 ⋅  h′ – --s- ⋅ ( h′ – s ) ⋅ t′ + ( t′ ) 3 F = ----------------------------------------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 – 4ac K 4 = --------------------------------------(13) 2a 3 2 2 where a = t′(H − 4t′ + 3t) (5H − 8 t′ + 3t); b = 32(t′) ; and, c = −t [5(H – t) + 32t ]. 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-


Machinery's Handbook 28th Edition DISC SPRING FATIGUE LIFE

359

late stresses. The minus sign “−” indicates that compressive stresses are acting in a direction opposite to the tensile stresses. Point 0:

4E ⋅ t ⋅ s ⋅ K 4 3 σ 0 = – --- ⋅ ----------------------------------------π ( 1 – µ2 ) ⋅ K ⋅ D2 1

(14)

a

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: – 1 – 1 6  δ---------- ln δ  K 2 = -----------------------------π ⋅ ln δ

(18)

3 ⋅ (δ – 1) K 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 28th Edition DISC SPRING FATIGUE LIFE LIVE GRAPH

360


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) 1400

LIVE GRAPH

A

Click here to view

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) 1400

LIVE GRAPH

Click here to view

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)


Machinery's Handbook 28th Edition DISC SPRING FATIGUE LIFE

361

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: – log N σ max – 0.5σ min = 10.29085532 ------------------------------------------------0.00542096 For disc springs in Group 2:

(23)

– log N σ max – 0.5σ min = 10.10734911 ------------------------------------------------0.00537616 For disc springs in Group 3:

(24)

13.23985664 – log N σ max – 0.5σ min = ------------------------------------------------(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.


362

Machinery's Handbook 28th Edition DISC SPRING RECOMMENDED DIMENSION RATIOS

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 )- = 10.10734911 – 5.69897- = 820 1250 – 0.5σ min = -------------------------------------------------------------------------------------------------------------------------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.


Machinery's Handbook 28th Edition DISC SPRING EXAMPLE

363

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 α = atan  ------------------ = atan ( 0.11282 ) = 6.4°  80 – 41 1 D a = 80 – 2 × 4  sin [ atan ( 0.11282 ) ] + --- cos [ atan ( 0.11282 ) ]   6 D a = 77.78 mm (3.062 in) 5) Calculating constant K1 from Equation (11): δ = D ---- = 1.95122 d 2

– 1-  1.95122 -------------------------- 1.95122  K 1 = ------------------------------------------------------------------------------ = 0.6841 1.95122 + 1 2 π ⋅ ---------------------------- – -----------------------------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 -  2.2 – 0.9 F min = ------------------------------------------------------------------------ ⋅ ( 2.2 – 0.9 ) ⋅ 4 + 4 3 0.9 2 ( 1 – 0.3 2 ) ( 0.6841 ) ( 77.78 ) 2  F min = 14390N (3235 lbf) 4 ⋅ 206000 -  2.2 – 1.32 F max = --------------------------------------------------------------------------- ⋅ ( 2.2 – 1.32 ) ⋅ 4 + 4 3 1.32 2  ( 1 – 0.3 2 ) ( 0.6841 ) ( 77.78 ) 2  F max = 20050N (4510 lbf) 7) Calculating constant K2, Equation (18): δ = D ---- = 80 ------ = 1.95122 d 41 – 1 – 1 1.95122 – 1- – 1 6  δ----------6  ---------------------------- ln ( 1.95122 )   ln δ  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 )


364


9) Compressive stress σ0 at point 0 due to maximum deflection, Equation (14): 4E ⋅ t ⋅ s ⋅ K 4 4 ⋅ 206000 ⋅ 4 ⋅ 1.32 ⋅ 1 - = – --3- ⋅ ---------------------------------------------------------------σ 0 = – --3- ⋅ ----------------------------------------π ( 1 – 0.3 2 ) ⋅ 0.6841 ⋅ 77.78 2 π ( 1 – µ2 ) ⋅ K ⋅ D2 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): 4E ⋅ K 4 ⋅ s ⋅ K 3 ⋅ t – K 2 ⋅ K 4 ⋅  h – --s-  2 σ 2min = --------------------------------------------------------------------------------------------- = 2 2 ( 1 – µ ) ⋅ K1 ⋅ Da 0.9 4 ⋅ 206000 ⋅ 1 ⋅ 0.9 ⋅ 1.3589 ⋅ 4 – 1.2086 ⋅ 1 ⋅  2.2 – -------  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): 4E ⋅ K 4 ⋅ s ⋅ K 3 ⋅ t – K 2 ⋅ K 4 ⋅  h – --s-  2 σ 2max = --------------------------------------------------------------------------------------------- = 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 0.9- + 1.3589 ⋅ 4 4 ⋅ 206000 ⋅ 1 ⋅ 0.9 ⋅ 1 ⋅ ( 2 ⋅ 1.3589 – 1.2086 ) ⋅  2.2 – -----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 4 ⋅ 206000 ⋅ 1 ⋅ 1.32 ⋅ 1 ⋅ ( 2 ⋅ 1.3589 – 1.2086 ) ⋅  2.2 – ---------- + 1.3589 ⋅ 4 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.



365

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 s min = ---- = ---------- = 1.54mm 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.


366

Machinery's Handbook 28th Edition FLUID PROPERTIES

FLUID MECHANICS Properties of Fluids Fluids.—A fluid is a substance, which deforms continuously when subjected to a shear stress. A small amount of shear force can cause fluids to move, but a solid needs a certain amount of shear stress to yield. The difference in behavior between solid and liquids is due to their molecular structure. In solids, the position of molecules is fixed in space; the molecules are close to each other and have strong molecular attraction. However, in fluids the molecules can move and change their position instantly and only relatively weak molecular forces exist between them. Every flowing fluid has a shear stress, but a stagnant fluid does not have a shear force. Compressibility is another distinguishing factor that separates fluids from gases. Liquids are relatively incompressible, but gases are strongly compressible and expand indefinitely when all external forces are removed. The pressure at a point in a fluid is the same in all directions. Pressure exerted by a fluid on a solid surface is always normal (perpendicular) to the surface. Viscosity.—Viscosity is a property of fluids that determines the resistance of the fluid to shearing stresses. Viscosity of a fluids is due to cohesion and interaction between fluids. An ideal fluid has no viscosity. Viscosity is dependent on temperature, but independent of pressure. A Saybolt viscositimeter is used to measure the viscosity of a fluid. µτ = F --- = ----A du dy The effect of viscosity on a fluid is usually expressed in terms of a non-dimensional parameter called the Reynolds Number Re. It is a dimensionless number that represents the ratio of inertia force to viscous force. R e = ρvD ----------µg ρvD R e = ----------µ vD R e = ------ν

( For U.S. units ) ( For SI units ) ( applying kinematic viscosity )

Ren = Reynolds number v =velocity; ft/s, m/s D =diameter; ft, m ρ =density; lb/ft3, kg/m3 (for water 62.4 lb/ft3, 1000 kg/m3) g =gravity acceleration; ft/s2, m/s2 (g= 32.2 ft/s2 or g= 9.81 m/s2) µ =absolute viscosity; lbf-sec/ft2, N-s/m2 (1 lbf-sec/ft2= 47.88 N-s/m2 = 47.88 Pa) ν =kinematic viscosity; ft2/s, m2/s (1 ft2/s = 0.0929 m2/s) Kinematic Viscosity: It is the ratio of absolute viscosity to mass density. It is usually expressed by nu. The unit is ft2/sec or m2/ sec. (SI) ν = µ --ρ

(US) µg ν = --------cρ


Machinery's Handbook 28th Edition FLUID STATICS

367

Statics Pressure.— Pressure is defined as the average force per unit area. Mathematically if dF represents infinitesimal force applied over an infinitisimal area, dA, the pressure is p =

dF dA

Considering an incompressible fluid, p1 is the pressure and z1 is the elevation at point 1, and p2 is the pressure and z2 is the elevation at point 2. At the datum the pressure is equal. Pressure increases as elevation decreases, and pressure reduces as elevation increases. At point 1 the pressure will be pressure will be

p2 ----- + Z 2 γ

p1 ----- + Z 1 γ

P2/γ

P1/γ

2 1

and at point 2 the

Z2

.

Z1 DATUM

Because the pressure is equal at the datum, p p1 ----- + Z 1 = ----2- + Z 2 γ γ p1 p2 ----- – ----- = Z 2 – Z 1 γ γ p1 – p2 = γ ( Z2 – Z1 ) If p2 is the pressure of the open liquid surface, then p2 is the pressure of the atmosphere. In order to determine the gauge pressure, we can treat p2 = 0. If the elevation change from point 1 to point 2 is h, then p 1 – p 2 = γh p 1 = γh The pressure at any point is equal to the height times density of the fluid. p psi × 144 h ( in ft of H 2 0 ) = --- = ---------------------- = 2.308 × psi γ 62.4 kN ------2 p m - = 0.102 × kN ------h ( in m of H 2 0 ) = --- = --------2 9.81 γ m If the pressure is measured relative to the absolute zero pressure, it is called the absolute pressure; when pressure is measured relative to the atmospheric pressure as a base, it is called gage pressure. When measuring gage pressure, atmospheric pressure is not included. Pressure gages show zero at atmosphere pressure. If the gage pressure is below atmospheric pressure, the pressure is called vacuum. A perfect vacuum indicates absolute zero pressure. P absolute = P gage + P atmosphere P absolute = P atmosphere – P vacuum


368

Machinery's Handbook 28th Edition FLUID STATICS A

P (Gage) A

LOCAL ATMOSPHERIC PRESSURE

P (Vacuum) B

P (Absolute)

B

A

P (Absolute) B

ABSOLUTE ZERO

Hydrostatic Pressure on Surfaces The hydrostatic force on a surface is the resultant force of a horizontal component of force and a vertical component of force. Pressure on Horizontal Plane Surfaces.—The pressure on a horizontal plane surface is uniform over the surface and acts through the center of the surface.The horizontal component of the total pressure on a curved surface is equal to the total pressure on the projection of the surface on the vertical plane.The point of application of the horizontal component is at the center of the projected area. The total horizontal force on a vertical surface is the pressure times the surface area. P = ρgh P = γh F h = PA v = γhA v Pressure on Vertical Plane Surfaces.—The pressure on a vertical plane surface increases linearly with depth. The pressure distribution will be triangular. The vertical component of the total pressure on a curved surface is equal to the weight of the liquid extending from the curved surface to the free surface of the liquid. The center of pressure will pass through the center of gravity of the curved surface. The center of pressure is located at 2⁄3 of the depth. 1 1 1 1 F v = P avg A = --- ( P 1 + P 2 )A = --- ( 0 + ρgh )A = --- ρghA = --- γhA 2 2 2 2 Pressure on Inclined Plane Surfaces.—The average pressure on an inclined plate is 1 P avg = --- ρg ( h 1 + h 2 ) 2 F = P avg × A The resultant center of pressure Ic h r = h c + -------Ah c where hr =the distance (slant distance) measured on the plane area from the free surface to the center of pressure hc =the distance (straight distance) measured on the plane area from the free surface to the center of pressure


Machinery's Handbook 28th Edition FLUID STATICS

369

Ic =second moment of the area about a horizontal axis through the centroid and in the plane of the area A =the total surface area Example:The tank shown is filled with diesel fuel (ρ = 49.92 lbm/ft3); What is the force on a 1 ft long section of the wall. C

10 ‘

21

.21

‘

B

A

15 ‘ D

15 ‘

Solution: The average depth is (0+25)/2 = 12.5 ft. The average horizontal force on a 1 ft section of a wall ABC is equal to the horizontal force on section CBD P h = γAh c = 49.92 ( 25 × 1 ) × ( 12.5 ) = 15600 lbf The vertical component of force on the inclined surface is equal to the weight of the liquid above it. P v = weight of the diesel above AB 1 =  ( 15 × 10 ) + --- × ( 15 × 15 ) × 1 × 49.92   2 = 13104 lb Forces on Curved and Compound Surfaces.— The horizontal force on a curved surface is equal to the horizontal force on a vertical projection plane from the inclined plane. The vertical force on a curved surface is equal to the weight of the fluid column above it. The resultant of horizontal and vertical component of force will give the resultant force and the direction in which the force is acting. F =

2

2

Fh + Fv

F tan θ = -----vFh


Machinery's Handbook 28th Edition TABLE OF CONTENTS PROPERTIES, TREATMENT, AND TESTING OF MATERIALS THE ELEMENTS, HEAT, MASS, AND WEIGHT 372 373 373 376 377 377 379 381 383 383 384 384 384

The Elements Latent Heat Specific Heat Coefficient of Thermal Expansion Ignition Temperatures Thermal Properties of Metals Adjusting Length for 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 385 Properties of Wood 385 Mechanical Properties 386 Weight of Wood 387 Density of Wood 387 Machinability of Wood 389 Properties of 389 Ceramics 390 Plastics 391 Investment Casting Alloys 393 Powdered Metals 394 Elastic Properties of Materials 395 Tensile Strength of Spring Wire 395 Temperature Effects on Strength

STANDARD STEELS 396 Property, Composition, Application 396 Standard Steel Classification 398 Numbering Systems 398 Unified Numbering System 399 Standard Steel Numbering System 399 Binary, Ternary and Quarternary 399 Damascus Steel 400 AISI-SAE Numbers for Steels 401 AISI-SAE Designation System 402 Composition of Carbon Steels 404 Composition of Alloy Steels 406 Composition of Stainless Steels 407 Thermal Treatments of Steel 408 Applications of Steels 410 Carbon Steels 413 Carburizing Grade Alloy Steels

STANDARD STEELS (Continued)

414 415 418 420 422

Hardenable Grade Alloy Steels Characteristics of Stainless Steels Chromium-Nickel Austenitic Steels High-Strength, Low-Alloy Steels Mechanical Properties of Steels

TOOL STEELS 433 433 436 437 439 439 446 446 448 449 451 451 452 452 453 455 455 457 457 459 460 460 460

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

HARDENING, TEMPERING, AND ANNEALING 461 Heat Treatment Of Standard Steels 461 Heat-Treating Definitions 465 Hardness and Hardenability 467 Case Hardening 469 Slow Cooling 469 Rapid Cooling or Quenching 470 Heat-Treating Furnaces 471 Physical Properties 471 Hardening 473 Hardening Temperatures 474 Heating Steel in Liquid Baths 474 Salt Baths 475 Quenching Baths 475 Hardening or Quenching Baths


Machinery's Handbook 28th Edition TABLE OF CONTENTS PROPERTIES, TREATMENT, AND TESTING OF MATERIALS HARDENING, TEMPERING, AND ANNEALING (Continued)

476 476 477 479 480 484 484 485 485 485 487 487 490 490 491 492 494 495 496 496 499 501 502 505 505 506 506 506 507 507 507 508

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 Typical Heat Treatments 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

NONFERROUS ALLOYS 512 513 513 518 527 529 530 533 533 536 542 542 543

NONFERROUS ALLOYS (Continued)

544 Magnesium Alloys 547 Nickel and Nickel Alloys 547 Titanium and Titanium Alloys 549 Mechanical Properties Table

PLASTICS 550 Properties of Plastics 550 Characteristics of Plastics 551 Plastics Materials 553 Application Properties 558 Stress and Strain in Plastics 565 Strength and Modulus 569 Thermal Properties 571 Electrical Properties 574 Chemical Resistance 574 Mechanical Properties 574 Design Analysis 574 Structural Analysis 576 Design Stresses 577 Thermal Stresses 578 Designing for Stiffness 578 Manufacture of Plastics Products 580 Sheet Thermoforming 580 Blow Molding 580 Processing of Thermosets 582 Polyurethanes 582 Reinforced Plastics 583 Injection Molding 587 Load-Bearing Parts 591 Melt Flow in the Mold 592 Design for Assembly 596 Assembly with Fasteners 597 Machining Plastics 603 Plastics Gearing 606 Bakelite

Strength of Nonferrous Metals Copper and Copper Alloys Cast Copper Alloys Wrought Copper Alloys Cu –Silicon, –Beryllium Alloys Aluminum and Aluminum Alloys Temper Designations Alloy Designation Systems Casting Alloys Wrought Alloys Clad Aluminum Alloys Principal Alloy Groups Type Metal


372

Machinery's Handbook 28th Edition 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 28th Edition HEAT

373

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 metric system, heat is measured 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.


Machinery's Handbook 28th Edition HEAT

374

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 28th Edition THERMAL PROPERTIES OF MATERIALS

375

Table 7. Values of Thermal Conductivity (k) and of Conductance (C) of Common Building and Insulating Materials Type of Material BUILDING Batt: Mineral Fiber Mineral Fiber Mineral Fiber Mineral Fiber Mineral Fiber Block: Cinder Cinder Cinder Block: Concrete Concrete Concrete Board: Asbestos Cement Plaster Plywood Brick: Common Face Concrete (poured) Floor: Wood Subfloor Hardwood Finish Tile Glass: Architectural Mortar: Cement Plaster: Sand Sand and Gypsum Stucco Roofing: Asphalt Roll Shingle, asb. cem. Shingle, asphalt Shingle, wood

Thickness, in. … 2–23⁄4

k or Ca … 0.14

0.09 3–31⁄2 31⁄2–61⁄2 0.05 6–7 0.04 0.03 81⁄2 … … 4 0.90 8 0.58 12 0.53 … … 4 1.40 8 0.90 12 0.78 … … 1⁄ 16.5 4 1⁄ 2.22 2 3⁄ 4

… 1 1 1 … 3⁄ 4 3⁄ 4

1.07 … 5.0 9.0 12.0 … 1.06

Thickness, in.

k or Ca

Max. Temp.,° F

Density, lb per cu. ft.

ka

… Avg.

… 1.61

… …

… …

… …

7⁄ 16 …

1.49

…

…

…

Stone:

…

…

…

…

Lime or Sand Wall Tile:

1 …

12.50 …

… …

… …

… …

4 8 12 Avg.

0.9 0.54 0.40 0.7

… … … …

… … … …

… … … …

… … … … …

… … … … …

… 400 1200 350 350

… 3 to 8 6 to 12 0.65 0.65

… 0.26 0.26c 0.33 0.31

Blanket, Hairfelt

…

…

180

10

0.29

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 0.35c 0.29 0.28 0.25 0.22 0.31 … 0.27

Type of Material BUILDING (Continued) Siding: Metalb Wood, Med. Density

Hollow Clay, 1-Cell Hollow Clay, 2-Cell Hollow Clay, 3-Cell Hollow Gypsum INSULATING Blanket, Mineral Fiber: Felt Rock or Slag Glass Textile

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

1⁄ 2

11.10

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

…

…

…

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

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.


Machinery's Handbook 28th Edition THERMAL PROPERTIES OF MATERIALS

376

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 28th Edition PROPERTIES OF MATERIALS

377

Table 12. Freezing Mixtures Temperature Change,°F Mixture Common salt (NaCl), 1 part; snow, 3 parts Common salt (NaCl), 1 part; snow, 1 part Calcium chloride (CaCl2), 3 parts; snow, 2 parts

From

To

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 −11

Sal ammoniac (NH4Cl), 1 part; saltpeter (KNO3), 1 part; water,1 part

46

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


Machinery's Handbook 28th Edition PROPERTIES OF MATERIALS

378

Table 13. Typical Thermal Properties of Various Metals (Continued) 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

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

29.5

0.12

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

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

0.265 0.25 0.25 0.25 0.25 0.25 0.25 0.25

liquidus approximately, 2100 to 2200, depending on composition

liquidus, 2640

20.0 18.0 20.8

7.5 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 28th Edition LENGTH/TEMPERATURE CHANGES

379

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 376, 377, 389, 390, 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


Machinery's Handbook 28th Edition LENGTH/TEMPERATURE CHANGES

380

Table 14. Differences in Length in Microinches/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 28th Edition SPECIFIC GRAVITY

381

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


Machinery's Handbook 28th Edition SPECIFIC GRAVITY

382

Table 16. Specific Gravity of Gases At 32°F Gas Aira Acetylene Alcohol vapor Ammonia Carbon dioxide Carbon monoxide Chlorine

Sp. Gr. 1.000 0.920 1.601 0.592 1.520 0.967 2.423

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.

with a weight at the bottom so as to float in an upright position in the liquid, the density of 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 28th Edition WEIGHT OF PILES

383

Average Weights and Volumes of Solid Fuels.—Anthracite coal, 55–65 lb/ft3; 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 … …


Machinery's Handbook 28th Edition WEIGHT OF PILES

384

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 28th Edition WOOD

385

PROPERTIES OF WOOD, CERAMICS, PLASTICS, METALS 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.


386


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

Tensile Strength Perp. to Grain (psi)

990 280 850 240 990 230 1,130 300 1,290 290 1,400 340 1,510 250 944 180 1,060 230 1,540 330 1,290 290 1,170 250 1,350 400 1,040 260 940 260 1,110 300 1,200 240 1,290 220 970 220

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



387

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. G M ρ = 62.4  --------------------------------------------  1 + ---------  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



388

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 9 1 ⁄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.


Machinery's Handbook 28th Edition 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) MgO·SiO2 (Steatite) 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

16

7.5

1825

0.11

2MgO·SiO2 (Forsterite)

Al2O3

Coeff. of Expansionb (10−6 in./in.-°F)

94% 96% 99.5% 99.9%

220

1.94

10

90

…

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 …


389

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)

390

Typical Properties of Plastics Materials Dielectric Strength (V/mil)

Machinery's Handbook 28th Edition PROPERTIES OF INVESTMENT CASTING ALLOYS

391

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


Machinery's Handbook 28th Edition PROPERTIES OF INVESTMENT CASTING ALLOYS

392

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 28th Edition PROPERTIES OF POWDER METAL ALLOYS

393

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

F-0000

100Fe

6.5

FN-0005

0.45C, 0.50 MnS

6.4–6.8

F-0000

0.02C, 0.45P

6.6–7.2

35–50 Rb

F-0008

0.6–0.9C

6.2–7

50–70 Rb

61–100

35–57

30–40

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

BRITISH STANDARD METRIC ISO LIMITS AND FITS

Over

a Not applicable to sizes up to 1 mm.


667

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.


668

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

24

30

+8

+15

+22

+28

+35

+41

+48

+55

+64

+75

+88

+118

+160

+218

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

Machinery's Handbook 28th Edition 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

+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

Md

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

+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

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.


669

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 P 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


670

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 28th Edition PREFERRED NUMBERS

671

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


Machinery's Handbook 28th Edition PREFERRED METRIC SIZES

672

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 671). 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 (R2004) 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 671). 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 28th Edition BRITISH STANDARD PREFERRED SIZES

673

products, the preferred number series R5 to R40 (see page 671) 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

6.2 6.5

1.7

7

1.6 1.8

9

2.6

12

11

2.8 3 3.5 3.8

17

4.2

95

105

56

110

21

162 165

172

112

275 280

178

285

180

290

118 120

265 270

175 115

64

255 260

168 170

58 62

245 250

108

60 22

158

98

54

235 240

160

102

55

19 20

4.8

155

100

18 4.5

230 152

90

52

225

150 88

48

215 220

148

92

16

4

142 145

85

50 15

205 210

82

42

13

198 200

138

45

14

192

140

80

46

3.2

135

78

44

188

132

76

3rd

195

75

40

2nd

190

130

38

9.5

2.5

70

35

1st

128

74 32

Choice 3rd

125

72

36

2.2

2nd

122

34 7.5

1st

66

28

8.5

10

65

Choice 3rd

68

8

2

2.4

23 24

2nd

30 6.8

2.1

1st

26

1.5

1.9

Choice 3rd

25

6

1.4

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.

Preferred Sizes for Flat Metal Products.—See Metric Sizes for Flat Metal Products starting on page 2523.


674

Machinery's Handbook 28th Edition 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



675

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


676


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 28th Edition SINE-BAR

677

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-


678


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 102). 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



679

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 696 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 681 gives constants for a 5-inch sine-bar, and starting on page 688 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 685) 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 formulas 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.


680

Machinery's Handbook 28th Edition 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 678; 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- + cos B ′ csc --2 The taper per foot corresponding to certain half-angles of taper may be found in the table on page 696. 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 28th Edition 5-INCH SINE-BAR CONSTANTS

681

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



682

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



683


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



684


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



685


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



686


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



687


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


Machinery's Handbook 28th Edition 100-MILLIMETER SINE-BAR CONSTANTS

688

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



689

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



690


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



691


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



692


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



693


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



694


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 28th Edition ANGLES AND TAPERS

695

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 )



696

Tapers per Foot and Corresponding Angles Taper per Foot

Included Angle

Angle with Center Line

Taper per Foot

Included Angle

Angle with Center Line

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

0.074604°

0°

4′

29″ 0°

2′

14″

17⁄8

8.934318°

8°

56′

0.149208°

0

8

57

4

29

9.230863°

9

13 51

4″

4°

28′

4

36

2″

0.298415

0

17

54

0

8

57

115⁄16 2

9.527283

9

31 38

4

45

49

0.447621

0

26

51

0

13

26

21⁄8

10.119738

10

7 11

5

3

36

0.596826

0

35

49

0

17

54

21⁄4

10.711650

10

42 42

5

21

21

0.746028

0

44

46

0

22

23

23⁄8

11.302990

11

18 11

5

39

5

51

11.893726

11

53 37

5

56

49

12.483829

12

29

13.073267

13

0

0.895228

0

1.044425

1

2

40

0

31

20

1.193619

1

11

37

0

35

49

1.342808

1

20

34

0

40

17

21⁄2 25⁄8 23⁄4 27⁄8

13.662012

13

1.491993

1

29

31

0

44

46

3

14.250033

14

1.641173

1

38

28

0

49

14

31⁄8

14.837300

1.790347

1

47

25

0

53

43

31⁄4

15.423785

1.939516

1

56

22

0

58

11

33⁄8

16.009458

2.088677

2

5

19

1

2

40

31⁄2

16.594290

2.237832

2

14

16

1

7

8

35⁄8

17.178253

33⁄4 37⁄8

53

43

0

26

2.386979

2

23

13

1

11

37

2.536118

2

32

10

1

16

5

2.685248

2

41

7

1

20

33

56

2

6

14

31

4 24

6

32

12

39 43

6

49

52

15

0

7

7

30

14

50 14

7

25

7

15

25 26

7

42

43

16

0 34

8

0

17

16

35 39

8

17

50

17

10 42

8

35

21

17.761318

17

45 41

8

52

50

18.343458

18

20 36

9

10

18

4

18.924644

18

55 29

9

27

44

30 17

2.834369

2

50

4

1

25

2

41⁄8

19.504850

19

2.983481

2

59

1

1

29

30

41⁄4

20.084047

20

3.132582

3

7

57

1

33

59

43⁄8

20.662210

3.281673

3

16

54

1

38

27

41⁄2

21.239311

3.430753

3

25

51

1

42

55

45⁄8

3.579821

3

34

47

1

47

24

3.728877

3

43

44

1

51

52

3.877921

3

52

41

1

56

20

9

45

9

3

10

2

31

20

39 44

10

19

52

21

14 22

10

37

11

21.815324

21

48 55

10

54

28

43⁄4

22.390223

22

23 25

11

11

42

47⁄8 5

22.963983

22

57 50

11

28

55

5

23.536578

23

32 12

11

46

6

24.107983

24

6 29

12

3

14

24.678175

24

40 41

12

20

21

25.247127

25

14 50

12

37

25

25.814817

25

48 53

12

54

27

26.381221

26

22 52

13

11

26

26.946316

26

56 47

13

28

23

27.510079

27

30 36

13

45

18

4 21

14

2

10

4.026951

4

1

37

2

0

49

4.175968

4

10

33

2

5

17

4.324970

4

19

30

2

9

45

4.473958

4

28

26

2

14

13

4.622931

4

37

23

2

18

41

1

4.771888

4

46

19

2

23

9

11⁄16

5.069753

5

4

11

2

32

6

51⁄8 51⁄4 53⁄8 51⁄2 55⁄8 53⁄4 57⁄8

11⁄8

5.367550

5

22

3

2

41

2

6

28.072487

28

13⁄16

5.665275

5

39

55

2

49

57

61⁄8

28.633518

28

38

1

14

19

0

11⁄4

5.962922

5

57

47

2

58

53

61⁄4

29.193151

29

11 35

14

35

48

29.751364

29

45

5

14

52

32

30.308136

30

18 29

15

9

15

30.863447

30

51 48

15

25

54

31.417276

31

25

2

15

42

31

31.969603

31

58 11

15

59

5

32

31 13

16

15

37

15⁄16 13⁄8 17⁄16 11⁄2 19⁄16 15⁄8 111⁄16 13⁄4 113⁄16

6.260490

6

15

38

3

7

49

6.557973

6

33

29

3

16

44

6.855367

6

51

19

3

25

40

7.152669

7

9

10

3

34

35

7.449874

7

27

0

3

43

30

63⁄8 61⁄2 65⁄8 63⁄4 67⁄8

7.746979

7

44

49

3

52

25

7

32.520409

8.043980

8

2

38

4

1

19

71⁄8

33.069676

33

8.340873

8

20

27

4

10

14

71⁄4

33.617383

33

8.637654

8

38

16

4

19

8

73⁄8

34.163514

34

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 102.



697

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.

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.

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 Divide taper per foot by 12; multiply by length of taper in inches. length of taper; and add result to small inches, and taper per diameter. foot. The taper per foot and Distance between two Subtract small diameter from large; divide two diameters in inches. given diameters in remainder by taper per foot; and multiply inches. quotient by 12. The taper per foot. Amount of taper in a cer- Divide taper per foot by 12; multiply by tain length in inches. 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



698

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. 1.5 – 1.25 1 + ( 0.75 ⁄ 24 ) 2 C = ------------------------ × ----------------------------------------- = 4.002 inches 2 0.75 ⁄ 24 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 – K2 T = 24K -------------------2 inches per foot 1 – 2K

Example:If the disk diameters are 2 and 3 inches, respectively, and the center distance is 5 inches, what is the taper per foot measured at right angles to one side? 3–2 K = ------------ = 0.1 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

1 + sin ( α ⁄ 2 ) D = d × --------------------------------- inches 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 28th Edition MEASUREMENT OVER PINS

699

1 + sin 7.5° D = 1 × --------------------------- = 1.3002 inches 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 adjacent 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: 180 – θ   sin  ----------------  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---------– d2 +d x = ----------sin θ --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


700

Machinery's Handbook 28th Edition 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, + 35°- cos 45° – 35°- + 1 X = 1.824 + ( 2 × 0.5 )  csc 45° -------------------------------------------  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 28th Edition CHECKING SHAFT CONDITIONS

Fig. 3a.

701

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)

D )2

(L – 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


702

Machinery's Handbook 28th Edition 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 28th Edition OUT OF ROUNDNESS, LOBING

703

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.


704

Machinery's Handbook 28th Edition 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 28th Edition MEASUREMENTS USING LIGHT

705

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.


706

Machinery's Handbook 28th Edition PRECISION GAGE BLOCKS Gage Block Sets

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 direct precision measurements and gaging applications, including sine-bars. 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 inch size gage block set number 1 below, 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. Gage Block Sets, Inch Sizes (Federal Specification GGG-G-15C).—Set Number 1 (81 Blocks): First Series: 0.0001 Inch Increments (9 Blocks), 0.1001 to 0.1009; Second Series: 0.001 Inch Increments (49 Blocks), 0.101 to 0.149; Third Series: 0.050 Inch Increments (19 Blocks), 0.050 to 0.950; Fourth Series: 1.000 Inch Increments (4 Blocks), 1.000 to 4.000 inch. Set Numbers 2, 3, and 4: The specification does not list a set 2 or 3. Gage block set number 4 (88 blocks), listed in the Specification, is not given here; 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. Set Number 5 (21 Blocks): First Series: 0.0001 Inch Increments (9 Blocks), 0.0101 to 0.0109; Second Series: 0.001 Inch Increments (11 Blocks), 0.010 to 0.020; One Block 0.01005 inch. Set Number 6 (28 Blocks): First Series: 0.0001 Inch Increments (9 Blocks), 0.0201 to 0.0209; Second Series: 0.001 Inch Increments (9 Blocks). 0.021 to 0.029; Third Series: 0.010 Inch Increments (9 Blocks), 0.010 to 0.090; One Block 0.02005 Inch. Long Gage Block Set Number 7 (8 Blocks): Whole Inch Series (8 Blocks), 5, 6, 7, 8, 10, 12, 16, 20 inches. Set Number 8 (36 Blocks): First Series: 0.0001 Inch Increments (9 Blocks), 0.1001 to 0.1009; Second Series: 0.001 Inch Increments (11 Blocks), 0.100 to 0.110; Third Series: 0.010 Inch Increments (8 Blocks), 0.120 to 0.190; Fourth Series: 0.100 Inch Increments (4 Blocks), 0.200 to 0.500; Whole Inch Series (3 Blocks), 1, 2, 4 Inches; One Block 0.050 inch. Set Number 9 (20 Blocks): First Series: 0.0001 Inch Increments (9 Blocks), 0.0501 to 0.0509; Second Series: 0.001 Inch Increments (10 Blocks), 0.050 to 0.059; One Block 0.05005 inch.


Machinery's Handbook 28th Edition DETERMINING HOLE COORDINATES

707

Gage Block Sets, Metric Sizes (Federal Specification GGG-G-15C).—S e t N u m b e r 1M (45 Blocks): First Series: 0.001 Millimeter Increments (9 Blocks), 1.001 to 1.009; Second Series: 0.01 Millimeter Increments (9 Blocks), 1.01 to 1.09; Third Series: 0.10 Millimeter Increments (9 Blocks), 1.10 to 1.90; Fourth Series: 1.0 Millimeter Increments (9 Blocks), 1.0 to 9.0; Fifth Series: 10 Millimeter Increments (9 Blocks), 10 to 90 mm. Set Number 2M (88 Blocks): First Series: 0.001 Millimeter Increments (9 Blocks), 1.001 to 1.009; Second Series: 0.01 Millimeter Increments (49 Blocks), 1.01 to 1.49; Third Series: 0.50 Millimeter Increments (19 Blocks), 0.5 to 9.5; Fourth Series: 10 Millimeter Increments (10 Blocks), 10 to 100; One Block 1.0005 mm. Set Number 3M: Gage block set number 3M (112 blocks) is not given here. 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 Number 4M (45 Blocks): First Series: 0.001 Millimeter Increments (9 Blocks), 2.001 to 2.009; Second Series: 0.01 Millimeter Increments (9 Blocks), 2.01 to 2.09; Third Series: 0.10 Millimeter Increments (9 Blocks), 2.1 to 2.9; Fourth Series: 1 Millimeter Increments (9 Blocks), 1.0 to 9.0; Fifth Series: 10 Millimeter Increments (9 Blocks), 10 to 90 mm. Set Numbers 5M, 6M, 7M: Set numbers 5M (88 blocks), 6M (112 blocks), and 7M (17 blocks) are not listed here. Long Gage Block Set Number 8M (8 Blocks): Whole Millimeter Series (8 Blocks), 125, 150, 175, 200, 250, 300, 400, 500 mm. Determining Hole Coordinates Table 1 on page 708 gives the lengths of chords for spacing off the circumferences of circles. The object of this table is to make possible the division of the periphery into a number of equal parts without trials with the dividers. Table 1 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 1 may be used by toolmakers when setting “buttons” in circular formation, and may be used with inch or metric dimensions. See also Determining Hole Coordinates in the ADDITIONAL material on Machinery’s Handbook 28 CD for more information on this topic. Example:Assume that it is required to divide the periphery of a circle of 20 inches diameter into thirty-two equal parts. Solution: 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. Example:Assume that it is required to divide a circle having a diameter of 61⁄2 millimeters into seven equal parts. Find the length of the chord required for spacing off the circumference. Solution: In Table 1, the length of the chord for dividing a circle of 1 millimeter diameter into 7 equal parts is 0.433884 mm. The length of chord for a circle of 61⁄2 mm diameter is 61⁄2 × 0.433884 = 2.820246 mm. Example:Assume that it is required to divide a circle having a diameter of 923⁄32 inches into 15 equal divisions. Solution: In Table 1, the length of the chord for dividing a circle of 1 inch diameter into15 equal parts is 0.207912 inch. The length of chord for a circle of 9 inches diameter is 923⁄32 × 0.207912 = 2.020645 inches.


Machinery's Handbook 28th Edition DETERMINING HOLE COORDINATES

708

Table 1. 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 × 0.382683) = 2.796098 inches.


Machinery's Handbook 28th Edition SURFACE TEXTURE

709

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.



710

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



711

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.



712

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-



713

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

o

q

r

s

t u

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.



714

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 634 and 661 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



715

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).


716


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.



717

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.



718

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.



719

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

in.

mm

in.

0.08

0.003

2.5

0.1

0.25

0.010

8.0

0.3

0.80

0.030

25.0

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 0.050a 0.075a 0.10a 0.125 0.15

1a 2a 3

0.40a 0.50 0.63

16a 20 25

4.0 5.0

160 200

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



720

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, 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.



721

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

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.


722

Machinery's Handbook 28th Edition SURFACE TEXTURE 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.


Machinery's Handbook 28th Edition ISO SURFACE FINISH STANDARDS

723

ISO Surface Finish Standards 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. ISO Surface Finish (ISO 1302).—The primary standard dealing with surface finish, ISO 1302:2002 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. Basic symbol for surface under consideration or to a specification explained elsewhere in a note. The textual indication is APA (any process allowed) Basic symbol for mate rial removal is required, for example machining. The textual indication is MRR (material removal required)

Position of complementary requirements: all values in millimeters Manufacturing method, treatment, coating or other requirement

Machining allowance (as on casting and forgings)

c

e

d b

Lay and orientation

Second texture parameter with numerical limit and band and/or sampling length. For a third or subsequent texture requirement, positions “a” and “b” are moved upward to allow room

Basic symbol where material removal is not permitted. The textual indication is NMR (no material removed) Basic symbol with all round circle added to indicate the specification applies to all surfaces in the view shown in profile (outline)

Text height

Line width for symbols d and d '

d'

c a

x'

2.5

h (ISO 3098-2)

Single texture parameter with numerical limit and band and/or sampling length

a

x

e

3.5

5

h

d b

7

10

14

20

0.25

0.35

0.5

0.7

1

1.2

2

Height for segment

x

3.5

5

7

10

14

20

28

Height for symbol segment

x'

7.5

10.5

15

21

30

42

60

Fig. 1. ISO Surface Finish Symbols.

Differences Between ISO and ANSI Surface Finish Symbology: ISO 1302, like ASME Y14.36M, 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, ISO 1302 surface finish symbols are similar to the ANSI symbols, however, with the release of the 2002 edition, the indication of some of the parameters have changed when compared to ASME Y14.36M. The proportions of the symbol in relationship to text height differs in each as


Machinery's Handbook 28th Edition ISO TEXTURAL DESCRIPTIONS

724

well. There is now less harmonization between ASME Y14.36M and ISO 1302 than has been the case previously. Table 1. Other ISO Standards Related to Surface Finish. ISO 3274:1996

“Geometrical Product Specifications (GPS) — Surface texture: Profile method — Nominal characteristics of contact (stylus) instruments.” ISO 4287:1997 “Geometrical Product Specifications (GPS) — Surface texture: Profile method — Terms, definitions and surface texture parameters.” ISO 4288:1996 “Geometrical Product Specifications (GPS) — Surface texture: Profile method — Rules and procedures for the assessment of surface texture.” ISO 8785:1998 “Geometrical Product Specifications (GPS) — Surface imperfections — Terms, definitions and parameters.” ISO 12085:1996 “Geometrical Product Specifications (GPS) — Surface texture: Profile method — Motif parameters.” ISO 13565-1:1996 “Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having stratified functional properties — Part 1: Filtering and general measurement conditions.” ISO 13565-2:1996 “Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having stratified functional properties — Part 2: Height characterization using the linear material ratio curve.” ISO 13565-3:1998 “Geometrical Product Specifications (GPS) — Surface texture: Profile method; Surfaces having stratified functional properties — Part 3: Height characterization using the material probability curve.”

Table 2. ISO Surface Parameter Symbols (ISO 4287:1997) 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

Graphic Symbology Textural Descriptions.—New to this version of ISO 1302:2002 is the ability to add textual descriptions of the graphic symbology used on drawing. This gives specifications writers a consistent means to describe surface texture specification from within a body of text without having to add illustrations. See Fig. 1 for textual application definitions, then Figs. 2- 6 for applications of this concept. turned Rz 3.1

Rz 6

Ra 1.5

3 21±0.1

0.1

0.2 A B

Fig. 2. Indication of texture requirement on a “final” workpiece, reflecting a 3 mm machining allowance.

Fig. 3. Surface Texture Indications Combined with Geometric Dimensioning and Tolerancing.


Machinery's Handbook 28th Edition ISO TEXTURAL DESCRIPTIONS

725

ISO 1302:2002 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. This edition does better illustrate how surface texture indications can be used on castings to reflect machining allowances (Fig. 2) and how symbology can be attached to geometric dimensioning and tolerancing symbology (See Fig. 3). U Rz 0.9 L Ra 0.3

MRR U Rz 0.9; L Ra 0.3

Fig. 4. Indication of Bilateral Surface Specification Shown Textually and as indicated on a Drawing. turned Rz 3.1

MRR turned Rz 3.1

Indication of a machining process and requirement for roughness shown textually and as indicated on a drawing.

Fig. 5a. Indication of Manufacturing Processes or Related Information. Fe/Ni15p Cr r Rz 0.6

NMR Fe/Ni15p Cr r; Rz 0.6

Indication of coating and roughness requirement shown textually and as indicated on a drawing.

Fig. 5b. Indication of Manufacturing Processes or Related Information. Upper (U) and lower (L) limits Filter type "X." Gaussian is the current standard (ISO 11562). Previously it was the 2RC-filter, and in the future it could change again. It is suggested that companies specify Gaussian or " 2RC" to avoid misinterpretation. Evaluation length (ln)

U "X" 0.08-0.8 / Rz8max 3.3 Transmission band as either shortwave and/or long-wave

Surface texture parameter. First letter is Profile (R, W, P). Second character is Characteristic/parameter (p, v, z, c, t, a, q, sk, ku, m,∆q , mr(c), δ c, mr). See ISO 4287

Limit value (in micrometers)

Interpretation of spec limit: 16% or max Manufacturing process

ground U "X" 0.08-0.8 / Rz8max 3.3 Surface texture lay Material removal allowed or not allowed (APA, MRR, NMR)

Fig. 6. Control Elements for Indication of Surface Texture Requirements on Drawings.


Machinery's Handbook 28th Edition ISO SURFACE FINISH RULES

726

ISO Profiles.—Profile parameters may be one of three types (ISO 4287). These include: R-profile: Defined as the evaluation length. The ISO default length ln consists of five sampling lengths lr , thus ln = 5 × lr W-profile: This parameter indicates waviness. There is no default length. P-profile: Indicates the structure parameters. The default evaluation length is defined in ISO 4288: 1996. 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. The term “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. 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. 7). 1 Upper limit of surface texture parameter

2

2

1

Fig. 7. Roughness Parameter Value Curves Showing Mean and Standard Deviation. With the "16%-rule" transmission band as default it is shown textually and in drawings as: MRR Ra 0.7; Rz1 3.3

Ra 0.7 Rz1 3.3

If the "max-rule" transmission band is applied, it is shown textually and in drawings as: MRR 0.0025-0.8 / Rz 3.0

0.0025-0.8 / Rz 3.0

Transmission band and sampling length are specified when there is no default value. The transmission band is indicated with the cut-off value of the filters in millimeters separated by a hyphen (-) with the short-wave filter first and the long-wave filter second. Again, in textual format and on drawings. MRR 0.0025-08 / Rz 3.0

0.0025-0.8 / Rz 3.0

A specification can indicate only one of the two transmission band filters. If only one is indicated, the hyphen is maintained to indicate whether the indication is the short-wave or the long-wave filter. 0.008(short-wave filter indication) -0.25

(long-wave filter indication)

Fig. 8. Indications of Transmission Band and Sampling Length in Textual Format.


Machinery's Handbook 28th Edition ISO SURFACE TEXTURE SYMBOLOGY EXAMPLES

727

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 3. 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 3, based on the use of Ra, Rz, Rz1max or RSm. Then with instrumentation, a representative sample is taken using the sampling length chosen above. The measured values are then compared to the ranges of values in Table 3 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 3, 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 3. 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 3, then both the sampling length setting and RSm values are correct and a representative measurement of the parameter can be taken.

For Rz, Rv, Rp, Rc, Rt

For R-parameters and RSm

Evaluation length, ln (mm)

For Ra, Rq, Rsk, Rku, R∆q

Curves for Periodic and Non-periodic Profiles

Sampling length, lr (mm)

Table 3. Sampling Lengths Curves for Non-periodic Profiles such as Ground Surfaces

Ra, µm

Rz, Rz1max, µm

RSm, µm

(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

Table 4. Preferred Roughness Values and Roughness Grades Roughness values, Ra µm

µin

Roughness values, Ra Previous Grade Number from ISO 1302

µm

µin

Previous Grade Number from ISO 1302 N6

50

2000

N12

0.8

32

25

1000

N11

0.4

16

N5

12.5

500

N10

0.2

8

N4 N3

6.3

250

N9

0.1

4

3.2

125

N8

0.05

2

N2

1.6

63

N7

0.025

1

N1


728

Machinery's Handbook 28th Edition ISO SURFACE TEXTURE SYMBOLOGY EXAMPLES Table 5. Examples of ISO Applications of Surface Texture Symbology Interpretation

Surface roughness is produced by milling with a bilateral tolerance between an upper limit of Ra = 55 µm and a lower limit of Ra = 6.2µm. Both apply the “16%-rule” default (ISO 4288). Both transmission bands are 0.008 - 4 mm, using default evaluation length (5 × 4 mm = 20 mm) (ISO 4288). The surface lay is circular about the center. U and L are omitted because it is obvious one is upper and one lower. Material removal is allowed. Simplified representation where surface roughness of Rz = 6.1 µm is the default for all surfaces as indicated by the Rz = 6.1 specification, plus basic symbol within parentheses. The default the “16%rule” applies to both as does the default transmission band (ISO 4288 and ISO 3274). Any deviating specification is called out with local notes such as the Ra =0.7 µm specification. The is no lay requirement and material removal is allowed. Surface roughness is produced by grinding to two upper limit specifications: Ra = 1.5 µm and limited to Rz = 6.7 µm max; The default “16%-rule,” default transmission band and default evaluation length apply to the Ra while the “max-rule”, a −2.5 mm transmission band and default evaluation length apply to the Rz. The surface lay is perpendicular relative to the plane of projection and material removal is allowed. Surface treatment is without any material removal allowed, and to a single unilateral upper limit specification of Rz = 1 µm. The default “16%-rule,” default transmission band and default evaluation length apply. The surface treatment is nickel-chrome plated to all surfaces shown in profile (outline) in the view where the symbol is applied. There is no lay requirement. Surface roughness is produced by any material removal process to one unilateral upper limit and one bilateral specification: the unilateral, Ra = 3.1 is to the default “16%-rule,” a transmission band of 0.8 mm and the default evaluation length (5 × 0.8 = 4 mm). The bilateral Rz has an upper limit of Rz = 18 µm and a lower limit of Rz = 6.5 µm. Both limits are to a transmission band of −2.5 mm with both to the default 5 × 2.5 = 12.5 mm. The symbol U and L may be indicated even if it is obvious. Surface treatment is nickel/chromium plating. There is no lay requirement.

Example

milled 0.008-4 / Ra 55 C

0.008-4 / Ra 6.2

Ra 0.7

Rz 6.1

( ) ground Ra 1.5 -2.5 / Ramax 6.7

Fe/Ni20p Cr r Rz 1

Fe/Ni10b Cr r -0.8 / Ra 3.1 U -2.5 / Rz 18 L -2.5 / Rz 6.5


Machinery's Handbook 28th Edition ISO SURFACE TEXTURE SYMBOLOGY EXAMPLES

729

Table 5. Examples of ISO Applications of Surface Texture Symbology (Continued)

2 x 45 A

Ra

A

2.5

Ra 6. Ø40

2 Ra 1.5

3x

Ø1 4

Rz

1

Surface texture symbology and dimensions may be combined on leader lines. The feature surface roughness specifications shown is obtainable by any material removal process and is single unilateral upper limit specifications respectively: Rz = 1 m, to the default “16%-rule,” default transmission band and default evaluation length (5 × λc). There is no lay requirement. Symbology can be used for dimensional information and surface treatment. This example illustrates three successive step of a manufacturing process. The first step is a single unilateral upper limit Rz = 1.7 m to the default “16%-rule,” default evaluation length (5 × λc) and default transmission band. It is obtainable by any material removal process, with no lay characteristics specified. Step two indicated with a phantom line over the whole length of the cylinder has no surface texture requirement other than chromium plating. The third step is a single unilateral upper limit of Rz = 6.5 m applied only to the first 14 mm of the cylinder surface. The default “16%-rule” applies as does default evaluation length (5 × λc) and default transmission band. Material removal is to be by grinding, with no lay characteristics specified.

Rz 50

R3

Surface texture symbology may be applied to extended extension lines or on extended projection lines. All feature surface roughness specifications shown are obtainable by any material removal process and are single unilateral upper limit specifications respectively: Ra = 1.5 m, Ra = 6.2 m and Rz = 50 m. All are to “16%-rule” default, default transmission band and default evaluation length (5 × λc). There is no lay requirement for any of the three.

Example

Ra 6.5

Interpretation Surface texture symbology may be combined with dimension leaders and witness (extension) lines. Surface roughness for the side surfaces of the keyway is produced by any material removal process to one unilateral upper limit specification, Ra = 6.5 m. It is to the default “16%-rule,” default transmission band and default evaluation length (5 × λc) (ISO 3274). There is no lay requirement. Surface roughness for the chamfer is produced by any material removal process to one unilateral upper limit specification, Ra = 2.5 m. It is to the default “16%-rule,” default transmission band and default evaluation length (5 × λc) (ISO 3274). There is no lay requirement.

Fe/Cr50 ground Rz 6.5

Rz 1.7

14


Machinery's Handbook 28th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING CUTTING TOOLS

FORMING TOOLS (Continued)

733 Terms and Definitions 733 Tool Contour 736 Relief Angles 737 Rake Angles 738 Nose Radius 739 Chipbreakers 740 Planing Tools 740 Indexable Inserts 741 Identification System 742 Indexable Insert Tool Holders 743 Standard Shank Sizes 744 Letter Symbols 745 Indexable Insert Holders 748 Sintered Carbide Tools 748 Sintered Carbide Blanks 748 Single Point Tools 748 Single-Point, Sintered-CarbideTipped Tools 750 Tool Nose Radii 751 Tool Angle Tolerances 751 Carbide Tipped Tools 751 Style A 752 Style B 753 Style C 753 Style D 754 Style E 754 Styles ER and EL 755 Style F 756 Style G 757 Indexable Insert Holders for NC 758 Insert Radius Compensation 760 Threading Tool Insert Radius

CEMENTED CARBIDES 761 Cemented Carbide 761 Carbides and Carbonitrides 762 Properties of Tungsten-CarbideBased Cutting-Tool 766 ISO Classifications of Hardmetals 766 Ceramics 769 Superhard Materials 770 Machining Data 771 Hardmetal Tooling 771 Cutting Blades

FORMING TOOLS 772 772

Dovetail Forming Tools Straight Forming Tools

775 776 777 777 777 782 783

Circular Forming Tools Circular Forming Tools Formula Top Rake Constants for Diameters Corrected Diameters Arrangement of Circular Tools Circular Cut-Off Tools

MILLING CUTTERS 784 Selection of Milling Cutters 784 Number of Teeth 785 Hand of Milling Cutters 786 Plain Milling Cutters 787 Side Milling Cutters 788 T-Slot Milling Cutters 789 Metal Slitting Saws 789 Milling Cutter Terms 791 Shell Mills 792 Multiple- and Two-Flute SingleEnd Helical End Mills 793 Regular-, Long-, and Extra LongLength, Mills 794 Two-Flute, High Helix, Regular-, Long-, Extra Long-, Mills 795 Roughing, Single-End End Mills 803 Concave, Convex, and CornerRounding Arbor-Type Cutters 805 Roller Chain Sprocket 807 Keys and Keyways 808 Woodruff Keyseat Cutters 812 Spline-Shaft Milling Cutter 812 Cutter Grinding 813 Wheel Speeds and Feeds 813 Clearance Angles 814 Rake Angles for Milling Cutters 814 Eccentric Type Radial Relief 817 Indicator Drop Method 819 Distance to Set Tooth

REAMERS 820 821 821 821 823 823 827

Hand Reamers Irregular Tooth Spacing in Reamers Threaded-end Hand Reamers Fluted & Rose Chucking Reamers Vertical Adjustment of Tooth-rest Reamer Terms and Definitions Direction of Rotation and Helix


Machinery's Handbook 28th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING REAMERS (Continued)

827 828 830 831 832 833 834 837 839 840

TWIST DRILLS AND COUNTERBORES 842 843 863 864 865 866 866 866 867 868 869 870 872 872 872 873 874 874 875 875 877 877 878 879 879

TAPS (Continued)

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

Definitions of Twist Drill Terms Types of Drills Split-Sleeve Collet Drill Drivers Three- and Four-Flute Straight Shank Core Drills Twist Drills and Centering Tools British Standard Combined Drills Drill Drivers British Std. Metric Twist Drills Gauge and Letter Sizes Morse Taper Shank Twist Drills Tolerance on Diameter Parallel Shank Jobber Twist Drills Stub Drills Steels for Twist Drills Accuracy of Drilled Holes Counterboring Interchangeable Cutters Three Piece Counterbores Sintered Carbide Boring Tools Style Designations Boring Tools Square Carbide-Tipped Square Solid Carbide Round Boring Machines, Origin

TAPS 880 Thread Form, Styles, and Types 882 Standard System of Tap Marking 882 Unified Inch Screw Taps 885 Thread Limits, Ground Thread 886 Thread Limits, Cut Thread 887 M Profile Metric Taps 887 Thread Limits, Ground Thread

888 Tap Terms 894 Tap Dimensions, Inch and Metric 897 Optional Neck and Thread Length 900 Extension Tap Dimensions 901 Fine Pitch Tap Dimensions 902 Standard Number of Flutes 903 Pulley Taps Dimensions 904 Straight and Taper Pipe Tap 904 Dimensions 905 Tolerances 905 Runout and Locational Tolerance 906 M Profile Tap D Limits (Inch) 906 M Profile Tap D Limits (mm) 907 Tap Sizes for Class 6H Threads 908 Tap Sizes, Unified 2B & 3B 909 Unified Threads Taps H Limits 914 Straight Pipe Tap Thread Limits 916 Taper Pipe Tap Thread Limits 917 Screw Thread Insert Tap Limits 920 Acme and Square-Threaded Taps 920 Acme Threads Taps 920 Adjustable Taps 920 Proportions 920 Drill Hole Sizes for Acme Threads 923 Tapping Square Threads

STANDARD TAPERS 924 Standard Tapers 924 Morse Taper 924 Brown & Sharpe Taper 925 Jarno Taper 932 British Standard Tapers 933 Morse Taper Sleeves 934 Brown & Sharpe Taper Shank 935 Jarno Taper Shanks 935 Machine Tool Spindles 936 Plug and Ring Gages 937 Jacobs Tapers and Threads 938 Spindle Noses 940 Tool Shanks 941 Draw-in Bolt Ends 942 Spindle Nose 943 V-Flange Tool Shanks 944 Retention Knobs 944 Collets 944 R8 Collet 945 Collets for Lathes, Mills, Grinders, and Fixtures 947 ER Type Collets


Machinery's Handbook 28th Edition TABLE OF CONTENTS TOOLING AND TOOLMAKING ARBORS, CHUCKS, AND SPINDLES 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 Hex Chucks for Portable Air 952 Mounted Wheels and Points 954 Shapes and Sizes

BROACHES AND BROACHING 955 The Broaching Process 955 Types of Broaches 956 Pitch of Broach Teeth 957 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

TOOL WEAR AND SHARPENING 967 968 968 968 968 969 969 970 971 971 972 972 972 972 973 973 973 974 974 974

Flank Wear Cratering Cutting Edge Chipping Deformation Surface Finish 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 Carbide Coolants for Carbide Grinding Peripheral vs. Flat Side Grinding Lapping Carbide Tools Chip Breaker Grinding Summary of Miscellaneous Points

FILES AND BURS 962 963 963 965 966 966

Definitions of File Terms File Characteristics Classes of Files Rotary Files and Burs Speeds of Rotary Files and Burs Steel Wool


Machinery's Handbook 28th Edition TOOLING AND TOOLMAKING

733

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


734

Machinery's Handbook 28th Edition 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.



735

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.


736


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



737

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.


738


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



739

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 the shoulder type. Both types have proved satisfactory when properly proportioned for a given class of work.


740


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. 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



741

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 Thickness, 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 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 * Second angle is secondary facet angle, which may vary by ± 1°.


742


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 in the primary facet length 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 top clamp or a pin lock. Screw-on type holders use a machine screw to hold the insert in the



743

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

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

Shank Dimensions for Indexable Insert Holders 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. 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 desig-



744

nated 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



745

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 beginning page 757.



746

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

•

•

P

•

•

•

N

•

•

•

P

•

•

•

N

•

•

•

N

•

•

•

N

•

•

Bore

•

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

•

•

•

•

P

•

•

N

•

•

•

•

•

P

•

•

•

•

N

•

•

•

P

•

•

•

N

•

•

N

•

•

•

•

P

•

•

•

•

T

S

B

C

C

T

•

•

•



747

Bore

Plane

•

•

•

•

•

•

P

•

•

•

•

•

•

•

N

•

•

•

•

•

P

•

•

•

•

•

N

•

•

•

P

•

•

•

N

•

•

•

P

•

•

•

N

•

•

•

N

•

•

•

P

•

•

•

N

•

•

Groove

•

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

•

N

•

•

P

•

•

N

•

•

N

•

•

N

•

•

•

P

•

•

•


Machinery's Handbook 28th Edition CARBIDE TIPS AND TOOLS

748

N

N

D

S

S

W

Plane

Bore

Chamfer

Groove

•

Trace

T

•

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

•

•

•

N

•

•

•

P

•

•

•

N

•

•

•

N

•

•

•

•

•

•

•

P

•

•

•

•

•

•

•

N

•

•

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 750. 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



749

Table 4. American National Standard Sizes and Designations for Carbide Blanks ANSI B212.1-2002 (R2007) Styleb

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

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 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

1 5⁄ 8 3⁄ 4

0000

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 4405

0405

1405

3405

1

0410

1410

3410

4410

1

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

4490

5⁄ 8 15⁄ 16 3⁄ 4

1

0490

1490

3490

1

0500

1500

3500

1

0510

1510

3510

4510

3515

4515

11⁄4 11⁄4 11⁄2

0515

1515

4500

0520

1520

3520

4520

0525

1525

3525

4525

0530

1530

3530

4530

11⁄4

0540

1540

3540

4540

3⁄ 4

0490

1490

3490

4490

11⁄2

0550

1550

3550

4550

1

Styleb T 1⁄ 16

W 1⁄ 4

L 5⁄ 16

3⁄ 32 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 3⁄ 32 1⁄ 8 5⁄ 32 5⁄ 32 3⁄ 16 1⁄ 4

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 5⁄ 16 1⁄ 4 1⁄ 2 3⁄ 8 5⁄ 8 3⁄ 4

3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 8 1⁄ 2 3⁄ 4 5⁄ 8 3⁄ 4 3⁄ 4

1

F …

5000 5030

6000 …

70000 …

1⁄ 16

…

…

7060

…

5080

6080

…

…

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

750 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 normal to the end-cutting edge. The back-rake angle is parallel to the side-cutting edge.



750

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.

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 12, 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. 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



751

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 (R2007)

Designation Style ARa

Style ALa

Shank Dimensions 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

3⁄ 4

3⁄ 4

41⁄2

2310

3⁄ 16

7⁄ 16

1

6

{

P3390, P4390

1⁄ 4

9⁄ 16

1

7⁄ 16

13⁄ 16

AR 12

AL 12

AR 16

AL 16

1

AR 20

AL 20

11⁄4

11⁄4

7

{

P3460, P4460

5⁄ 16

5⁄ 8

1

AR 24

AL 24

11⁄2

11⁄2

8

{

P3510, P4510

3⁄ 8

5⁄ 8

1

Rectangular Shank AR 44

AL 44

1⁄ 2

1

6

P2260

3⁄ 16

5⁄ 16

5⁄ 8

AR 54

AL 54

5⁄ 8

1

6

{

P3360, P4360

1⁄ 4

3⁄ 8

3⁄ 4

AR 55

AL 55

5⁄ 8

11⁄4

7

{

P3360, P4360

1⁄ 4

3⁄ 8

3⁄ 4

AR 64

AL 64

3⁄ 4

1

6

{

P3380, P4380

1⁄ 4

1⁄ 2

3⁄ 4

AR 66

AL 66

3⁄ 4

11⁄2

8

{

P3430, P4430

5⁄ 16

7⁄ 16

AR 85

AL 85

11⁄4

7

{

P3460, P4460

5⁄ 16

5⁄ 8

1

1

15⁄ 16

AR 86

AL 86

1

11⁄2

8

{

P3510, P4510

3⁄ 8

5⁄ 8

1

AR 88

AL 88

1

2

10

{

P3510, P4510

3⁄ 8

5⁄ 8

1

AR 90

AL 90

11⁄2

2

10

{

P3540, P4540

1⁄ 2

3⁄ 4

11⁄4

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.



752

Table 6. American National Standard Style B Carbide Tipped Tools with 15-degree Side-cutting-edge Angle ANSI B212.1-2002 (R2007) 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.



753

Table 7. American National Standard Style C Carbide Tipped Tools ANSI B212.1-2002 (R2007) 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

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 11⁄4

2 21⁄4 21⁄2 3 31⁄2 4 41⁄2 6 7

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⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1

1 1 11⁄4 1 11⁄2 11⁄2

6 6 7 6 8 8

Tip Designation

Thickness, T

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

1320 1400 1400 1405 1470 1475

3⁄ 16 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16

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 (R2007) 10° ± 2° Both sides 7° ± 1° Overhang

Note – Tool must pass thru slot of nominal width “A”

W 0° ± 1°

40° ± 1°

R

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⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

1

B

Shank Dimensions Height, B Length, C 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

All dimensions are in inches.



754

Table 9. American National Standard Style E, 60-degree Nose-angle, Carbide Tipped Tools ANSI B212.1-2002 (R2007)

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

31⁄2

6200

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

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 (R2007)

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 1⁄ 16 3⁄ 32 3⁄ 32 1⁄ 8 1⁄ 8 5⁄ 32

Tip Dimensions Width Length W L 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8

1⁄ 4 3⁄ 8 3⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4




755

Table 11. American National Standard Style F, Offset, End-cutting Carbide Tipped Tools ANSI B212.1-2002 (R2007)

Designation

Shank Dimensions

Tip Dimensions

Style FR

Style FL

Width A

Height B

Length C

Offset G

FR 8

FL 8 FL 10

FR 12

FL 12

1⁄ 2 5⁄ 8 3⁄ 4

31⁄2

FR 10

1⁄ 2 5⁄ 8 3⁄ 4

FR 16

FL 16

1

1

6

FR 20

FL 20

FR 24

FL 24

11⁄4 11⁄2

11⁄4 11⁄2

1⁄ 4 3⁄ 8 5⁄ 8 3⁄ 4 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

5⁄ 8 3⁄ 4 3⁄ 4 15⁄ 16

Square Shank 4 41⁄2 7 8

3⁄ 4

{

P4170, P3170

1

{

P1230, P3230

11⁄8

{

P4310, P3310

13⁄8

{

P4390, P3390

{

P4460, P3460

{

P4510, P3510

11⁄2 11⁄2

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

1

FR 86

FL 86

1

FR 90

FL 90

11⁄2

1

6

11⁄4

7

1

6

11⁄2

8

11⁄4 11⁄2

7

2

10

8

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 11⁄2 15⁄8

{

P4460, P3460

{

P4510, P3510

{

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 761 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



756

Table 12. American National Standard Style G, Offset, Side-cutting, Carbide Tipped Tools ANSI B212.1-2002 (R2007)

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.



757

Chip Breaker.—The term “chip breaker” indicates a method of forming or grinding turning tools, that will cause the chips to break up into short pieces, thus preventing the formation of long or continuous chips which would occupy considerable space and be difficult to handle. The chip-breaking form of cutting end is especially useful in turning with carbidetipped steel turning tools because the cutting speeds are high and the chip formation rapid. The chip breaker consists of a shoulder back of the cutting edge. As the chip encounters this shoulder it is bent and broken repeatedly into small pieces. Some tools have attached or “mechanical” chip breakers which serve the same purpose as the shoulder. Chipless Machining.— Chipless machining is the term applied to methods of cold forming metals to the required finished part shape (or nearly finished shape) without the production of chips (or with a minimum of subsequent machining required). Cold forming of steel has long been performed in such operations as wire-, bar-, and tube-drawing; coldheading; coining; and conventional stamping and drawing. However, newer methods of plastic deformation with greatly increased degrees of metal displacement have been developed. Among these processes are: the rolling of serrations, splines, and gears; power spinning; internal swaging; radial forging; the cold forming of multiple-diameter shafts; cold extrusion; and high-energy-rate forming, which includes explosive forming. Also, the processes of cold heading, thread rolling and rotary swaging are also considered chipless machining processes. 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 742.


758

Machinery's Handbook 28th Edition CARBIDE TIPS AND TOOLS 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



759

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


F Stylea

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

0

.0625

.0120

.0745

1⁄ 16

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



760

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 …

Z .140 .183 .239 …

All dimensions are given in inches. Courtesy of Kennametal, Inc.


Machinery's Handbook 28th Edition CEMENTED CARBIDES AND OTHER HARD MATERIALS

761

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 740 and Indexable Insert Holders for NC on page 757. The absence of brazing stresses and the “one-use” concept also means that harder, longer-lasting grades can be used.



762

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 enough, although 3 per cent is the realistic minimum) to ensure complete sintering. In gen-



763

eral, 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


764


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. 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



765

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 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


766

Machinery's Handbook 28th Edition HARDMETAL CUTTING TOOL INSERTS

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 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.


Machinery's Handbook 28th Edition Table 2. ISO Classifications of Hardmetals (Cemented Carbides and Carbonitrides) by Application Main Types of Chip Removal Symbol and Color

Designation (Grade)

Ferrous with long chips

P01

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

P30

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

767

P50

M30

K Red

Steel, steel castings

P10

P40

M Yellow

Specific Material to be Machined

CEMENTED CARBIDES AND OTHER HARD MATERI-

P Blue

Direction of Decrease in Characteristic

Groups of Applications

Broad Categories of Materials to be Machined

768

Machinery's Handbook 28th Edition CEMENTED CARBIDES AND OTHER HARD MATERIALS 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 sufficient 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,



769

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.


770


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 metal cutting 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 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.



771

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 familiar 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.


772

Machinery's Handbook 28th Edition 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 1 gives the required dimensions and angles within its range, directly without calculation.



773

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



774

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 equals 0.25. 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 ) sin Cy = R --------------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.


Machinery's Handbook 28th Edition FORMING TOOLS × 0.17365- = 0.10419 sin B = 0.375 -------------------------------------0.625

775

Angle B = 5°59′ nearly.

Angle C = 180 – ( 170° + 5°59′ ) = 4°1′ × 0.07005- = 0.25212 Dimension y = 0.625 -------------------------------------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 r =

2

2

2

( R – C – D) + C

2

(1)

If the small radius r is given and the large radius R is required, then R =

2

2

2

( r – C + 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 =

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



776

Table 2. Formulas for Circular Forming Tools a Make of Machine

Size of Machine

Brown & Sharpe

Acme

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

2 2

2

2 2 2 2 2 2 2

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

21⁄4″

1.625

0.125

r =

( 1.6202 – D ) + 0.0156

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

5⁄ ″ 8 7⁄ ″ 8

Cleveland

Radius r, Inches

11⁄4″

6″

2 2 2 2

2

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 of the expression

2

2

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



777

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 777. 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




Dia. of Tool

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

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

1⁄ Inch 2

0.8125

0.0016

…

…

0.0037

…

…

0.0069

…

…

0.0114

…

…

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

15⁄8 13⁄4


778

Table 3. Constant for Determining Diameters of Circular Forming Tools Cutting Face 1⁄8 Inch Below Center


779

Table 4a. Corrected Diameters of Circular Forming Tools Number of B. & S. Automatic Screw Machine No. 0 No. 2

Length c on Tool

No. 00

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

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

0.023 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

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. 0 No. 2

No. 00

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

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

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

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

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

1.5326 1.5306 1.5287

2.0324 2.0304 2.0284

2.7833 2.7814 2.7794

1.5267

2.0264

2.7774

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

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

0.057

1.6373

2.1372

2.8877

0.113



780

Table 4a. Corrected Diameters of Circular Forming Tools (Continued) Number of B. & S. Automatic Screw Machine No. 0 No. 2 2.0264 2.7774 2.0245 2.7755

Length c on Tool 0.113 0.114

No. 00 1.5267 1.5247

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. 0 No. 2 1.9119 2.6634 1.9103 2.6617

No. 00 1.4124 1.4107 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



781

Table 4b. Corrected Diameters of Circular Forming Tools Number of B. & S. Screw Machine

Number of B. & S. Screw Machine

No. 2

Length c on Tool

No. 0

No. 2

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

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

No. 0

0.227 0.228 0.229 0.230

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

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

… … … … … … … … … …

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

2.2932 2.2913 2.2893 2.2874 2.2854 2.2835 2.2815 2.2796 2.2776 2.2757

… … … … … … … … … …

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



782

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 rigid support is then necessary for both tools and a good supply of oil is also required. The



783

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

Form and Cut-Off

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 1102. 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

Dia. of Stock

R

Soft Brass, Copper a = 23 Deg.

Drill Rod, Tool Steel a = 12 Deg. T x 0.043 0.009

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

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.


784

Machinery's Handbook 28th Edition 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 814. 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 813. 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.



785

Example:Determine the required number of teeth in a face mill where D = 6 inches and W = 4 inches. Using Formula (1), × 6- = 10 teeth, approximately T = 6.3 --------------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), × 4 × cos 0 ° T = 12.6 --------------------------------------- = 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.



786

American National Standard Plain Milling Cutters ANSI/ASME B94.19-1997 (R2003) Nom.

Cutter Diameter Max. Min.

Range of Face Widths, Nom.a

Nom.

Hole Diameter Max. Min.

Light-duty Cuttersb 21⁄2

2.515

2.485

3⁄ , 1⁄ , 5⁄ , 3⁄ , 16 4 16 8 1⁄ , 5⁄ , 3⁄ , 1, 11⁄ , 2 8 4 2

2 and 3 3⁄ , 1⁄ , 5⁄ , 3⁄ , 16 4 16 8

1

1.00075

1.0000

1

1.00075

1.0000

3

3.015

2.985

3

3.015

2.985

5⁄ , 3⁄ , and 11⁄ 8 4 2 1⁄ , 5⁄ , 3⁄ , 2 8 4 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

3.985

3⁄ , 1⁄ , 5⁄ , 3⁄ , 8 2 8 4 1, 11⁄2 , 2, 3

11⁄4

1.2510

1.2500

1

1.00075

1.0000

1

1.0010

1.0000

4 4

4.015 4.015

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.



787

American National Standard Side Milling Cutters ANSI/ASME B94.19-1997 (R2003) 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

1

1.00075

1.0000

5

5.015

4.985

1⁄ , 5⁄ , 3⁄ , 2 8 4

11⁄4

1.2510

1.2500

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

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

1⁄ , 5⁄ , 3⁄ , 7⁄ , 1⁄ , 4 16 8 16 2 5⁄ , 3⁄ 8 4

and 7⁄8

1⁄ , 5⁄ , 3⁄ 2 8 4

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

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

4

4.015

3.985

Half Side Cuttersd 3⁄ 4

11⁄4

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 789.



788

American National Standard Staggered Teeth, T-Slot Milling Cutters with Brown & Sharpe Taper and Weldon Shanks ANSI/ASME B94.19-1997 (R2003)

Bolt Size 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4

1

Cutter Dia., D

Neck Dia., N

Face Width, W

9⁄ 16 21⁄ 32 25⁄ 32 31⁄ 32 11⁄4 15 1 ⁄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 1 1 ⁄32

With B. & S. Tapera,b Taper No.

Length, L

With Weldon Shank Dia., S

Length, L

…

…

219⁄32

…

…

211⁄16

1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 4

…

…

31⁄4

5 51⁄4

7

37⁄16

7

315⁄16

1

67⁄8 71⁄4

9

47⁄16

9

413⁄16

1 11⁄4

a For dimensions of Brown & Sharpe taper shanks, see information given on page

934. 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 (R2003)

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 21⁄2

1 11⁄8

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.



789

American National Standard Metal Slitting Saws ANSI/ASME B94.19-1997 (R2003) 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 6 8 10 12

3.015 4.015 5.015 6.015 6.015 8.015 10.015 12.015

Range of Hole Diameter Face Widths Nom. Max. Nom.a Plain Metal Slitting Sawsb 1⁄ , 3⁄ , 1⁄ , 3⁄ , 1⁄ 7⁄ 2.485 0.87575 32 64 16 32 8 8 1⁄ , 3⁄ , 1⁄ , 3⁄ , 32 64 16 32 1 1.00075 2.985 1⁄ and 5⁄ 8 32 1⁄ , 3⁄ , 1⁄ , 3⁄ , 1⁄ , 32 64 16 32 8 3.985 1 1.00075 5⁄ and 3⁄ 32 16 1⁄ , 3⁄ , 1⁄ 4.985 1 1.00075 16 32 8 1⁄ 11⁄4 1.2510 4.985 8 1⁄ , 3⁄ , 1⁄ 1 1.00075 5.985 16 32 8 1⁄ , 3⁄ 11⁄4 5.985 1.2510 8 16 1 ⁄8 7.985 1 1.00075 1⁄ 11⁄4 7.985 1.2510 8 Metal Slitting Saws with Side Teethc 1⁄ , 3⁄ , 1⁄ 7⁄ 2.485 0.87575 16 32 8 8 1⁄ , 3⁄ , 1⁄ , 5⁄ 2.985 1 1.00075 16 32 8 32 1 3 1 5 3 ⁄16 , ⁄32 , ⁄8 , ⁄32 , ⁄16 3.985 1 1.00075 1⁄ , 3⁄ , 1⁄ , 5⁄ , 3⁄ 4.985 1 1.00075 16 32 8 32 16 1⁄ 11⁄4 1.2510 4.985 8 1⁄ , 3⁄ , 1⁄ , 3⁄ 5.985 1 1.00075 16 32 8 16 1 3 1 ⁄8 , ⁄16 1 ⁄4 5.985 1.2510 1 ⁄8 7.985 1 1.00075 1⁄ , 3⁄ 11⁄4 7.985 1.2510 8 16 Metal Slitting Saws with Staggered Peripheral and Side Teethd 3 ⁄16 2.985 1 1.00075 3⁄ 3.985 1 1.00075 16 3⁄ , 1⁄ 1 1.00075 4.985 16 4 3⁄ , 1⁄ 5.985 1 1.00075 16 4 3 1 1 ⁄16 , ⁄4 1 ⁄4 1.2510 5.985 3 1 1 ⁄16 , ⁄4 1 ⁄4 7.985 1.2510 3⁄ , 1⁄ 1⁄ 1 9.985 1.2510 16 4 4 1⁄ , 5⁄ 1⁄ 1 11.985 1.5010 4 16 2 Min.

Min. 0.8750 1.0000 1.0000 1.0000 1.2500 1.0000 1.2500 1.0000 1.2500 0.8750 1.0000 1.0000 1.0000 1.2500 1.0000 1.2500 1.0000 1.2500 1.0000 1.0000 1.0000 1.0000 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



790

Milling Cutter Terms (Continued)

American National Standard Single- and Double-Angle Milling Cutters ANSI/ASME B94.19-1997 (R2003) 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.



791

American National Standard Shell Mills ANSI/ASME B94.19-1997 (R2003)

Dia., D inches

Width, W inches

11⁄4

1

11⁄2

11⁄8

13⁄4

11⁄4 13⁄8 11⁄2 15⁄8 15⁄8 13⁄4 17⁄8 21⁄4 21⁄4 21⁄4 21⁄4

2 21⁄4 21⁄2 23⁄4 3 31⁄2 4 41⁄2 5 6

Dia., H inches

Length, B inches

1⁄ 2 1⁄ 2 3⁄ 4 3⁄ 4

5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

1 1 1 11⁄4 11⁄4 11⁄2

1

11⁄2

1

11⁄2

1

2

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 1 1 ⁄4 3 1 ⁄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 3 1 ⁄16 3 1 ⁄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



792

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 (R2003)

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.



793

ANSI Regular-, Long-, and Extra Long-Length, Multiple-Flute Medium Helix Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997 (R2003)

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

W 3⁄ 8 1⁄ 2 5⁄ 8 3⁄ 4 3⁄ 4

1 1 11⁄4 13⁄8 13⁄8 15⁄8 15⁄8 15⁄8 15⁄8 15⁄8 17⁄8 17⁄8 17⁄8 17⁄8 17⁄8

Long Mills

L

Na

25⁄16

4

…

23⁄8

4

…

27⁄16

4

S

W …

L …

…

… 11⁄4

31⁄16

13⁄8 11⁄2 13⁄4

31⁄8 31⁄4 33⁄4

4

3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2

2

4

4

…

…

…

4

…

…

4

5⁄ 8

21⁄2

4

…

…

21⁄2 21⁄2 211⁄16 211⁄16 31⁄4 33⁄8 33⁄8 35⁄8 35⁄8 33⁄4 33⁄4 33⁄4

4

4

4 4

Extra Long Mills Na

S

…

…

…

…

… 3⁄ 8

…

W

L …

Na …

…

…

13⁄4

39⁄16

4

3⁄ 8 3⁄ 8

2

4

21⁄2

33⁄4 41⁄4

…

…

…

4

… 1⁄ 2

3

5

4

…

…

…

…

…

…

…

…

…

…

…

45⁄8

4

5⁄ 8

4

61⁄8

4

…

…

…

…

…

…

4 4 4 4

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 41⁄8

53⁄4 61⁄2

4

…

…

…

…

…

…

…

…

4

41⁄8

4

…

…

…

…

…

…

…

…

2

41⁄4

6

1

4

61⁄2

6

…

…

…

…

2

41⁄4

6

1

4

61⁄2

6

11⁄4

6

81⁄2

6

1 11⁄8

1

2

41⁄2

4

…

…

…

…

…

…

…

…

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

1

2

11⁄4

2

11⁄4

2

11⁄4

2

11⁄4

2

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.



794

ANSI Two-Flute, High Helix, Regular-, Long-, and Extra Long-Length, Single-End End Mills with Weldon Shanks ANSI/ASME B94.19-1997 (R2003)

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

Long Mill

Extra Long Mill

L

S

W

L

S

W

L

27⁄16

11⁄4

31⁄16

13⁄4

39⁄16

13⁄8

31⁄8

2

33⁄4

11⁄2

31⁄4

3⁄ 8 3⁄ 8 3⁄ 8

21⁄2

41⁄4

13⁄4

33⁄4

…

…

2

4

… 1⁄ 2

3

5

4

61⁄8

4

61⁄4

…

… 81⁄2

1 11⁄4

211⁄16

15⁄8

33⁄4

15⁄8

37⁄8

3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 5⁄ 8 3⁄ 4

17⁄8

41⁄8

21⁄2 21⁄2 31⁄4

21⁄2

45⁄8

3

51⁄4

…

… 4

… 61⁄2

1 11⁄4

1 11⁄4

2

41⁄2

2

41⁄2

1 11⁄4

4

11⁄2

11⁄4

2

41⁄2

11⁄4

4

2

11⁄4

2

41⁄2

11⁄4

4

61⁄2

5⁄ 8 3⁄ 4

…

61⁄2

1 11⁄4

6 6

81⁄2

61⁄2

11⁄4

8

101⁄2

…

…

…

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 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 (R2003) Right-hand Cut

Left-hand Cut

G K 1/2 K 90° H

E B

F C

45° D

A J 12°

45°

L

.015

Central With “K”

M

Dia. A

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.



795

ANSI Roughing, Single-End End Mills with Weldon Shanks, High-Speed Steel ANSI/ASME B94.19-1997 (R2003)

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 (R2003)

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 794. 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.



796

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 (R2003)

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 (R2003)

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.



797

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 (R2003)

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

…

…

…

…

…

2

3⁄ 32

2

21⁄4 21⁄4 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

Plain End

Ball End

Plain End

2

…

…

2

9⁄ 64

2

2

…

…

2

3⁄ 16 …

…

2

15⁄ 64

2

2

…

…

2

9⁄ 32

2

2

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

…

…

3⁄ 16

…

21⁄4 …

9⁄ 32 …

21⁄4 …

3⁄ 8 …

21⁄4 …

7⁄ 16

…

21⁄4 …

1⁄ 2

21⁄4

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 15⁄8

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 934.



798

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 (R2003)

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

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

Stub Length — Plain End Length of Cut. W

Shank Dia., S

1⁄ 8 3⁄ 16 1⁄ 4

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 23⁄8 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 11⁄8

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.



799

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 (R2003)

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 11⁄2 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 3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 3⁄ 8 … 1⁄ 2 … 1⁄ 2 … 5⁄ 8 … 3⁄ 4 … 1

Regular Length — Ball End W L 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.



800

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 (R2003)

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 … …

11⁄4 13⁄8 11⁄2 2 21⁄2 … 3 31⁄2 4 … 4 …

S

Extra Long Length W L

… … 33⁄16 31⁄8 31⁄4 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.



801

American National Standard Stub- and Regular-length, Four-flute, Medium Helix, Double-end End Mills with Weldon Shanks ANSI/ASME B94.19-1997 (R2003)

Dia., D

S

W

L

Dia., D

1⁄ 8

3⁄ 8

3⁄ 16

23⁄4

3⁄ 16

5⁄ 32

3⁄ 8

15⁄ 64

23⁄4

7⁄ 32

S

W

Dia., D

L

S

W

L

Stub Length 3⁄ 8

9⁄ 32

3⁄ 8

21⁄ 64

23⁄4

1⁄ 4

3⁄ 8

3⁄ 8

27⁄8

27⁄8

…

…

…

…

5⁄ 8

13⁄8

5

Regular Length 1⁄ a 8

3⁄ 8

3⁄ 8

31⁄16

11⁄ 32

3⁄ 8

3⁄ 4

31⁄2

5⁄ a 8

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 (R2003)

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.



802

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 (R2003)

Dia., C and D

Plain End L

W

2

2

2

3

53⁄4 63⁄4 73⁄4

W

Ball End L

2, 4, 6

…

…

…

2, 3

…

…

…

No. of Flutes

No. of Flutes

2

4

2, 3, 4, 6

4

2

…

…

…

5

2

6

93⁄4

2, 3, 4, 6

6

2

8

113⁄4

6

8

73⁄4 83⁄4 93⁄4 113⁄4

21⁄2

4

73⁄4

2, 3, 4, 6

…

…

…

21⁄2

…

…

…

5

83⁄4

4

21⁄2

6

93⁄4

2, 4, 6

…

…

…

21⁄2

8

113⁄4

6

…

…

…

6 2, 4 6 6

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 (R2003) Shank Dia.

Flat Length

Xa

Shank

Lengthb

1

0.925

0.515

0.330

11⁄4

29⁄32

1.156

0.515

0.400

11⁄2

211⁄16

1.406

0.515

0.455

2

31⁄4

1.900

0.700

0.455

21⁄2

31⁄2

2.400

0.700

19⁄16

0.325

0.280

1⁄ 2

125⁄32

0.440

5⁄ 8

129⁄32

3⁄ 4

21⁄32

7⁄ 8

21⁄32

0.560 0.675 0.810

Flat Xa

29⁄32

Lengthb

3⁄ 8

Dia.

Length

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.



803

Amerian National Standard Form Relieved, Concave, Convex, and Corner-Rounding Arbor-Type Cutters ANSI/ASME B94.19-1997 (R2003)

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.

Concave Cuttersc 1⁄ 8

0.1270

0.1240

21⁄4

1⁄ 4

1

1.00075

1.00000

3⁄ 16

0.1895

0.1865

21⁄4

3⁄ 8

1

1.00075

1.00000

0.2490

21⁄2

7⁄ 16

1

1.00075

1.00000

0.3115

23⁄4

9⁄ 16

1

1.00075

1.00000

5⁄ 8

1

1.00075

1.00000

1⁄ 4 5⁄ 16

0.2520 0.3145

3⁄ 8

0.3770

0.3740

23⁄4

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

7⁄ 8

0.8790

0.8730

4

13⁄8

11⁄4

1.251

1.250

1.0040

0.9980

41⁄4

19⁄16

11⁄4

1.251

1.250

1.00000

1

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

0.2480

21⁄2

1⁄ 4

1

1.00075

1.00000

5⁄ 16

1

1.00075

1.00000

1

1.00075

1.00000

1⁄ 4

0.2520

5⁄ 16

0.3145

0.3105

23⁄4

3⁄ 8

0.3770

0.3730

23⁄4

3⁄ 8

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

7⁄ 8

0.8770

0.8730

4

7⁄ 8

11⁄4

1.251

1.250

1.0020

0.9980

41⁄4

11⁄4

1.251

1.250

1

1

Corner-rounding Cuttersd 1⁄ 8

0.1260

0.1240

21⁄2

1

1.00075

1.00000

1⁄ 4

0.2520

0.2490

3

1⁄ 4 13⁄ 32

1

1.00075

1.00000

9⁄ 16

11⁄4

1.251

1.250

3⁄ 8

0.3770

0.3740

33⁄4

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.

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 807.



804

American National Standard Roughing and Finishing Gear Milling Cutters for Gears with 141⁄2 -Degree Pressure Angles ANSI/ASME B94.19-1997 (R2003)

ROUGHING Diametral Pitch

FINISHING Dia. of Cutter, D

Dia. of Hole, H

Dia. of Cutter, D

Dia. of Hole, H

5

33⁄8

6

37⁄8

1 11⁄2

6

11⁄4

8

31⁄2 31⁄8 33⁄8 27⁄8 31⁄4 27⁄8

…

…

…

Dia. of Cutter, D

Dia. of Hole, H

81⁄2

2

3

51⁄4

11⁄2

73⁄4

2 13⁄4

3

43⁄4

11⁄4

4

43⁄4 41⁄2 41⁄4 35⁄8 43⁄8 41⁄4 33⁄4

13⁄4 11⁄2 11⁄4 1 13⁄4

7

11⁄2 11⁄4

Diametral Pitch

Diametral Pitch

Roughing Gear Milling Cutters 1 11⁄4 11⁄2 13⁄4

7 61⁄2

13⁄4

4

2

61⁄2

13⁄4

4

2 21⁄2

53⁄4

11⁄2

4

61⁄8

13⁄4

5

21⁄2

53⁄4

11⁄2

5

3

55⁄8

13⁄4

5

1 11⁄4

81⁄2

2

6

37⁄8

11⁄2

14

21⁄8

73⁄4

2 13⁄4

6

31⁄2

11⁄4

16

21⁄2

6

31⁄8

21⁄8

7

35⁄8

1 11⁄2

16

13⁄4

18

23⁄8

7

33⁄8 27⁄8 31⁄2 31⁄4 27⁄8 31⁄8 23⁄4

6 7 8

1 11⁄4 1 11⁄4 1

Finishing Gear Milling Cutters

11⁄2 13⁄4 2 2 21⁄2 21⁄2 3 3 3 4 4 4 4 5 5 5 5 6

7 61⁄2 61⁄2 53⁄4 61⁄8 53⁄4 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 13⁄4 11⁄2 13⁄4 11⁄2 11⁄4 13⁄4 11⁄2 11⁄4

7 8 8 8 9 9 10 10

3 23⁄4

10

23⁄8

1 13⁄4

11

11⁄2

12

25⁄8 23⁄8 27⁄8 25⁄8 21⁄4 21⁄2

11

11⁄4

12

1 13⁄4

12 14

11⁄4

18

1 11⁄2

20

11⁄4

22

1 11⁄4

22

1 11⁄4 1 7⁄ 8

7⁄ 8

1

2 21⁄4

1

24

2 21⁄4

1

24

13⁄4

26

13⁄4

28

13⁄4 13⁄4 13⁄4 13⁄4 13⁄4 13⁄4

30 32

7⁄ 8 11⁄4

40

1

48

1

7⁄ 8

1

2 23⁄8

20

1

7⁄ 8

7⁄ 8

1

36

7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

…

…

…

…

…

…

All dimensions are in inches. All gear milling cutters are high-speed steel and are form relieved. For keyway dimensions see page 807. 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 2053. Roughing cutters are made with No. 1 cutter form only.



805

American National Standard Gear Milling Cutters for Mitre and Bevel Gears with 141⁄2 -Degree Pressure Angles ANSI/ASME B94.19-1997 (R2003) 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 807. For cutter selection see page 2092. 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 2055.

American National Standard Roller Chain Sprocket Milling Cutters

American National Standard Roller Chain Sprocket Milling Cutters ANSI/ASME B94.19-1997 (R2003) Chain Pitch 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

Dia. of Roll 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

No. of Teeth in Sprocket 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



806

American National Standard Roller Chain Sprocket Milling Cutters ANSI/ASME B94.19-1997 (R2003)(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 807. 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 2468.


Machinery's Handbook 28th Edition American National Standard Keys and Keyways for Milling Cutters and Arbors ANSI/ASME B94.19-1997 (R2003)

1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄4 11⁄2 13⁄4 2 21⁄2 3 31⁄2

Nom. Size Key (Square)

CUTTER HOLE AND KEYWAY

Arbor and Keyseat

ARBOR AND KEY

Hole and Keyway

Arbor and Key

A Max.

A Min.

B Max.

B Min.

C Max.

C Min.

Da Min.

H Nom.

Corner Radius

E Max.

E Min.

F Max.

F Min.

3⁄ 32 1⁄ 8 1⁄ 8 1⁄ 8 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

0.0947

0.0937

0.4531

0.4481

0.106

0.099

0.5578

0.020

0.0932

0.0927

0.5468

0.5408

0.1260

0.1250

0.5625

0.5575

0.137

0.130

0.6985

0.1240

0.6875

0.6815

0.1250

0.6875

0.6825

0.137

0.130

0.8225

0.1245

0.1240

0.8125

0.8065

0.1260

0.1250

0.8125

0.8075

0.137

0.130

0.9475

0.1245

0.1240

0.9375

0.9315

0.2510

0.2500

0.8438

0.8388

0.262

0.255

1.1040

0.2495

0.2490

1.0940

1.0880

0.3135

0.3125

1.0630

1.0580

0.343

0.318

1.3850

0.3120

0.3115

1.3750

1.3690

0.3760

0.3750

1.2810

1.2760

0.410

0.385

1.6660

0.3745

0.3740

1.6560

1.6500

0.4385

0.4375

1.5000

1.4950

0.473

0.448

1.9480

0.4370

0.4365

1.9380

1.9320

0.5010

0.5000

1.6870

1.6820

0.535

0.510

2.1980

0.4995

0.4990

2.1880

2.1820

0.6260

0.6250

2.0940

2.0890

0.660

0.635

2.7330

0.6245

0.6240

2.7180

2.7120

0.7510

0.7500

2.5000

2.4950

0.785

0.760

3.2650

0.7495

0.7490

3.2500

3.2440

0.8760

0.8750

3.0000

2.9950

0.910

0.885

3.8900

1⁄ 32 1⁄ 32 1⁄ 32 3⁄ 64 1⁄ 16 1⁄ 16 1⁄ 16 1⁄ 16 1⁄ 16 3⁄ 32 3⁄ 32 3⁄ 32 1⁄ 8 1⁄ 8

0.1245

0.1260

3⁄ 64 1⁄ 16 1⁄ 16 1⁄ 16 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 3⁄ 8 3⁄ 8 7⁄ 16 1⁄ 2

0.8745

0.8740

3.8750

3.8690

0.9995

0.9990

4.3750

4.3690

1.1245

1.1240

4.9380

4.9320

1.2495

1.2490

5.5000

5.4940

4

1

1.0010

1.0000

3.3750

3.3700

1.035

1.010

4.3900

41⁄2

11⁄8

1.1260

1.1250

3.8130

3.8080

1.160

1.135

4.9530

5

11⁄4

1.2510

1.2500

4.2500

4.2450

1.285

1.260

5.5150

All dimensions given in inches.


807

a D max. is 0.010 inch larger than D min.

MILLING CUTTERS

ARBOR AND KEYSEAT Nom.Arbor and Cutter Hole Dia.


808

American National Standard Woodruff Keyseat Cutters—Shank-Type StraightTeeth and Arbor-Type Staggered-Teeth ANSI/ASME B94.19-1997 (R2003)

Cutter Number 202 202 1⁄2 302 1⁄2 203 303 403 204 304 404 305 405 505 605 406

Nom. Dia.of Cutter, D 1⁄ 4 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 1⁄ 2 1⁄ 2 1⁄ 2 5⁄ 8 5⁄ 8 5⁄ 8 5⁄ 8 3⁄ 4

Width of Face, W 1⁄ 16 1⁄ 16 3⁄ 32 1⁄ 16 3⁄ 32 1⁄ 8 1⁄ 16 3⁄ 32 1⁄ 8 3⁄ 32 1⁄ 8 5⁄ 32 3⁄ 16 1⁄ 8

Length Overall, Cutter L Number 21⁄16 21⁄16 23⁄32 21⁄16 23⁄32 21⁄8 21⁄16 23⁄32 21⁄8 23⁄32 21⁄8 25⁄32 23⁄16 21⁄8

506 606 806 507 607 707 807 608 708 808 1008 1208 609 709

Shank-type Cutters Nom. Width Length Dia. of of OverCutter, Face, all, Cutter D W L Number 3⁄ 4 3⁄ 4 3⁄ 4 7⁄ 8 7⁄ 8 7⁄ 8 7⁄ 8

1 1 1 1 1 11⁄8 11⁄8

5⁄ 32 3⁄ 16 1⁄ 4 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 3⁄ 16 7⁄ 32

25⁄32 23⁄16 21⁄4 25⁄32 23⁄16 27⁄32 21⁄4 23⁄16 27⁄32 21⁄4 25⁄16 23⁄8 23⁄16 27⁄32

809 1009 610 710 810 1010 1210 811 1011 1211 812 1012 1212 …

Nom. Dia.of Cutter, D

Width of Face, W

Length Overall, L

1 1⁄8 1 1⁄8 11⁄4 11⁄4 11⁄4 11⁄4 11⁄4 13⁄8 13⁄8 13⁄8 11⁄2 11⁄2 11⁄2

1⁄ 4 5⁄ 16 3⁄ 16 7⁄ 32 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 4 5⁄ 16 3⁄ 8

2 1⁄4 2 5⁄16 23⁄16 27⁄32 21⁄4 25⁄16 23⁄8 21⁄4 25⁄16 23⁄8 21⁄4 25⁄16 23⁄8

…

…

…


Width of Face, W

Dia. of Hole, H

31⁄2 31⁄2 31⁄2 31⁄2

1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4

…

…

Arbor-type Cutters

Cutter Number


Width of Face, W

617 817 1017 1217 822

21⁄8 21⁄8 21⁄8 21⁄8 23⁄4

3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 1⁄ 4

Dia. of Hole, Cutter H Number 3⁄ 4 3⁄ 4 3⁄ 4 3⁄ 4

1

1022 1222 1422 1622 1228

Nom. Dia.of Cutter, D 23⁄4 23⁄4 23⁄4 23⁄4 31⁄2

Width of Face, W 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 3⁄ 8

Dia. of Hole, Cutter H Number 1 1 1 1 1

1628 1828 2028 2428 …

1 1 1 1 …

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 2391 through 2393. 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 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.



809

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′



810

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°

…

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

40′

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

10

77

42

70

31

62

44

53

30

40

71

40

64

41

57

8

12

78

30

72

46

66

37

59

26

49

50

72

48

67

13

61

13

54

14

45

13

14

78

56

74

9

69

2

63

6

55

19

73

26

68

46

63

46

57

59

50

38

16

79

12

75

5

70

41

65

37

59

1

73 50

69 49

65

30

60

33

54 20

18

79

22

75

45

71

53

67

27

61

43

74

5

70

33

66

46

62

26

57

20

79

30

76

16

72

44

68

52

63

47

74

16

71

6

67

44

63

52

59

3

22

79

35

76

40

73

33

69

59

65

25

74

24

71

32

68

29

65

0

60

40

24

79

39

76

59

74

9

70

54

66

44

74

30

71

53

69

6

65

56

61

59

42

20° Blank

…

48

12

34′

36

18

0

25° Blank

6

53° 57′

39° 39′

23° 18′

8

62

46

53 45

43

53

…

…

47° 0′

34° 6′

19° 33′

31° 53′

14° 31′

56

36

48

8

38

55

10

65

47

59

4

51

50

43

12

67

12

61

49

56

2

49

18

32

1

60

2

53

40

46

18

40

40

61

42

56

33

51

14

68

0

63 29

58

39

53

4

46

0

62 38

58 19

16

68

30

64

36

60

18

68

50

65

24

61

26

55

39

49

38

63

13

59

44

57

32

52

17

63

37

60

20

69

3

65 59

62

43

58

58

54 18

22

69

14

66

24

69

21

66

28

63

30

60

7

55

49

64

7

61

2

57

6

40° 54′

29° 22′

…

…

27° 47′

11° 33′

47

38

43

27

47

2

44

38

36

10

53

41

48

20

41 22

29

55

29

50

53

44

57

19

56

48

52

46

47

34

63 53

60 56

57

47

54

11

49 33

55

64

5

61

25

58

34

55

19

51

9

12

64

14

61

47

59

12

56

13

52

26

16° 32′

8

50

46

42 55

34

21°

4′

8° 41′

10

54

29

48

30

42

3

34

31

24

44

49

7

43

33

37

12

56

18

51

26

46

14

40

12

32

32

51

3

46

30

41

35

30

38

21

40

39

36

2

28

55

14

57

21

53

27

52

9

48

16

58

0

33

18

58

20

58

22 24

30° Blank

24

…

36° 34′ 17°

35° Blank …

…

24° 12′ 10°

14′

35° 32′

25° 19′

14° 3′

45

38

30

17

5

18

…

…

15

48

52

43

49

37

19

44

12

39

28

33

54 27

50

39

46

19

40 52

52 50

49 20

45

56

41

51

36 45

26

55

18

51

57

48

7

43

20

53

18

50

21

47

12

43

36

39 8

44

55

55

52

56

49

30

45

15

53

38

50

59

48

10

44

57

40

58

57

56

24

53

42

50

36

46

46

53

53

51

29

48

56

46

1

42

24

59

8

56

48

54

20

51

30

48

0

54

4

51

53

49

32

46

52

43

35

57



811

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 6

30° 48′

21° 48′

11° 58′

8

40

7

33

36

26

33

10

43

57

38

51

33

32

27

12

45

54

41

43

37

14

32

14

47

3

43

29

39

41

16

47

45

44

39

41

18

48

14

45

29

20

48

35

46

7

22

48

50

46

24

49

1

46

6

22° 45′

15° 58′

…

…

26° 34′

18° 43′

10° 11′

18° 16′

7° 23′

35

16

29

25

23

8

8°

38′

…

…

8

30

41

25 31

19

59

13° 33′

5° 20′

10

34

10

2

25

39

20

32

14

12

36

0

32 34

28

53

24

42

19 27

31 14

14

37

5

34

9

31

1

27

26

22 58

32 15

16

37

47

35

13

32

29

29

22

25

30

32

54

18

38

15

35

58

33

33

30

46

27

21

33

20

38

35

36

32

34

21

31

52

28

47

22

38

50

36

58

34

59

32

44

29

24

39

1

37

19

35

30

33

25

30

…

… 5° 58′

3

18

55

38

58

34

21

29

3

25

33

40

54

37

5

33

24

23

40

16

10

0

28

18

22

35

19

29

51

42

1

38

46

13

35

17

31

18

26

21

37

33

32

50

42

44

39

9

54

36

52

33

24

28

57

42

34

39

13

35

5

43

13

43

30

40

30

36

47

43

34

40

42

38

1

34

56

30

1

41

18

38

53

36

8

32

37

36

44

13

41

30

38

8

43

58

44

48

42

19

39

15

44

49

41

46

39

34

37

5

34

53

0

42

7

40

7

37

50

35

55

55° Blank 19° 17′

13° 30′

7°

15′

26

21

21

52

17

3

29

32

25

55

22

3

17

36

11

28 12

24

59

21

17

16 32

29 39

26

53

23

43

19 40

30

38

28

12

25

26

21

54

21

31

20

29

10

26

43

23

35

33

40

31

51

29

54

27

42

24

53

57

33

54

32

15

30

29

28

28

25

55

52

34

5

32

34

30

57

29

7

26

46

9

60° Blank 11°

12′

50°

15° 48′

50° Blank

30

60°

45° Blank

…

…

11° 30′

4° 17′ 52

65° Blank

6

16°

6′

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

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′

5

70° Blank

…

…

75° Blank

6

10° 18′

7°

9′

3°

48′

…

…

7°

38′

5°

19′

2°

50′

8

14

26

11 55

9

14

6° 9′

2° 21′

10

44

8

51

6

51

4°

…

…

10

16

25

14

21

12

8

9

37

6

30

12

14

10

40

9

1

7

8

4

49

12

17

30

15

45

13

53

11

45

9

8

13

4

11

45

10

21

8

45

6

47

14

18

9

16

38

15

1

13

11

10

55

13

34

12

26

11

13

9

50

8

7

16

18

35

17

15

15

50

14

13

12

13

13

54

12

54

11

50

10

37

9

7

18

18

53

17

42

16

26

14

59

13

13

14

8

13

14

12

17

11

12

9

51

20

19

6

18

1

16

53

15

35

13

59

14

18

13

29

12

38

11

39

10

27

22

19

15

18

16

17

15

16

3

14

35

14

25

13

41

12

53

12

0

10

54

24

19

22

18

29

17

33

16

25

15

5

14

31

13

50

13

7

12

18

11

18


Machinery's Handbook 28th Edition CUTTER GRINDING

812

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.

W sin A = ----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 removed by a hand stoning operation. Stoning also helps to reduce the roughness of grind-



813

ing 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


814


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: 45860 F C = ---------------  1.5L + -------- d ( D – d )  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



815

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

.007

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

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



816

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 Helix Angle of Cutter Flutes, H, Degrees

Radial Relief Angle, R, Degrees

12

1

0°13′

0°19′

0°22′

0°35′

2

0°26′

0°39′

0°44′

1°09′

3

0°38′

0°59′

1°06′

4

0°51′

1°18′

5

1°04′

1°38′

6

1°17′

7

18

20

30

40

45

50

52

0°50′

1°00′

1°12′

1°17′

1°41′

2°00′

2°23′

2°34′

1°44′

2°31′

3°00′

3°34′

3°50′

1°27′

2°19′

3°21′

4°00′

4°46′

5°07′

1°49′

2°53′

4°12′

5°00′

5°57′

6°23′

1°57′

2°11′

3°28′

5°02′

6°00′

7°08′

7°40′

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′

13

2°49′

4°17′

4°48′

7°36′

10°58′

13°00′

15°23′

16°28′

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′

16

3°29′

5°19′

5°57′

9°24′

13°32′

16°00′

18°52′

20°09′

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′

19

4°11′

6°23′

7°09′

11°15′

16°07′

19°00′

22°19′

23°47′

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′

22

4°55′

7°29′

8°22′

13°08′

18°44′

22°00′

25°43′

27°21′

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′

Wheel Angle, W, Degrees



817

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

.062

.00108

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

.0016

.0025

.0033

.0041

.0049

.0058

.0066

.0074

.0022

.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



818

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. Rate Angle, Deg. 1 2 3 4 5 6 7 8 9 10

Measuring Distance, inch .031

.062

.094

.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

Move cutter or indicator measuring distance. Measuring Distance, inch

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.



819

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: Diam. × Cutter Diam. × Sine of One-half the Clearance AngleOffset = Wheel --------------------------------------------------------------------------------------------------------------------------------------------------------------------Wheel Diam. + Cutter Diam. 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).


Machinery's Handbook 28th Edition REAMERS

820

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 A Reamer Blank

95

Size of Reamer

a, Inches

1⁄ 4

0.011

3⁄ 8

0.016

1

0.022

11⁄4

0.027

11⁄2

0.033

13⁄4

1⁄ 2 5⁄ 8 3⁄ 4

Size of Reamer 7⁄ 8

a, Inches

Size of Reamer

a, Inches

0.038

2

0.087

0.044

21⁄4

0.098

0.055

21⁄2

0.109

0.066

23⁄4

0.120

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.



821

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 Sizes of Reamers

Length of Threaded Part

1⁄ –5⁄ 8 16

3⁄ 8

11⁄ –1⁄ 32 2

7⁄ 16

17⁄ –3⁄ 32 4 25⁄ –1 32

No. of Threads per Inch

Dia. of Thread at Point of Reamer


Dia. of Thread at Point of Reamer

Sizes of Reamers

Length of Threaded Part

32

Full diameter −0.006

11⁄32–11⁄2

9⁄ 16

18

Full diameter −0.010

28

−0.006

117⁄32–2

9⁄ 16

18

−0.012

1⁄ 2

24

−0.008

21⁄32–21⁄2

9⁄ 16

18

−0.015

9⁄ 16

18

−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.)



822

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 23⁄4

21⁄2 21⁄2 21⁄2 21⁄2

3

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



823

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 H

E

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

No. of Teeth in Reamer

Cutter Dia. D

6

13⁄4

6

13⁄4

6 6–8

17⁄8 2

8

21⁄8

10

21⁄4

12

23⁄8

14

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

for 1⁄2-inch reamers; 5⁄16-inch 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).



824

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.



825

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.


826


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.



827

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 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

13⁄8 11⁄2

13⁄ 32 7⁄ 16 15⁄ 32 1⁄ 2 33⁄ 64 17⁄ 32 35⁄ 64 9⁄ 16

… 15⁄8

1 11⁄8

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

Large Center Dia. B 3⁄ 8

11⁄4

13⁄4 17⁄8 2 21⁄8 21⁄4 23⁄8

Drill No. C 25

Hole Depth D 7⁄ 16

1

1⁄ 2 17⁄ 32 9⁄ 16 19⁄ 32 5⁄ 8 21⁄ 32 21⁄ 32 11⁄ 16

…

Letter

…

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

20 17 12 8 5 3 2

B C E F G H

Arbor Dia. A 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

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



828

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 formation of a tapered hole. This type of bellmouthing can frequently be reduced by shortening * “Some Aspects of Reamer Design and Operation,” Metal Cuttings, April 1963.



829

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

15⁄ 16

10

25⁄8

3

8 to 10

31⁄ 32

10

25⁄8

3

8 to 10

1

101⁄2

23⁄4

3

8 to 12

6 to 8

11⁄16

101⁄2

23⁄4

3

8 to 12

1

6 to 8

11⁄8

11

27⁄8

3

8 to 12

2

6 to 8

13⁄16

11

27⁄8

3

8 to 12

6 to 8

1

1⁄ 4

3

4

8 to 12

111⁄2

3

4

8 to 12

31⁄4

4

10 to 12

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⁄ 16

7

13⁄4

1

6 to 8

1⁄ 2

8

2

1

6 to 8

17⁄ 32

8

2

1

6 to 8

9⁄ 16

8

2

1

19⁄ 32

8

2

5⁄ 8

9

21⁄4

Reamer Dia.

21⁄ 32

Length Overall A

9

21⁄4

11⁄ 16

9

21⁄4

2

6 to 8

15⁄16

23⁄ 32

9

21⁄4

2

6 to 8

13⁄8

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

…

…

…

…

…

2

11

1⁄ 2

Flute Length B

a American National Standard self-holding tapers (see Table 7a on page 931.)

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



830

Expansion Chucking Reamers—Straight and Taper Shanks ANSI B94.2-1983 (R1988) D

B A Dia of Reamer

Length, A

Flute Length,B

Shank Dia., D Max.

Min.

Dia.of Reamer

Length, A

Flute Length,B

Shank Dia.,D Max.

Min.

3⁄ 8

7

3⁄ 4

0.3105

0.3095

13⁄32

101⁄2

15⁄8

0.8745

0.8730

13⁄ 32

7

3⁄ 4

0.3105

0.3095

11⁄8

11

13⁄4

0.8745

0.8730

7⁄ 16

7

7⁄ 8

0.3730

0.3720

15⁄32

11

13⁄4

0.8745

0.8730

15⁄ 32

7

7⁄ 8

0.3730

0.3720

13⁄16

11

13⁄4

0.9995

0.9980

1⁄ 2

8

1

0.4355

0.4345

17⁄32

11

13⁄4

0.9995

0.9980

17⁄ 32

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

7⁄ 8

10

11⁄2

0.7495

0.7480

115⁄16a

14

21⁄2

1.4995

1.4980

29⁄ 32

10

11⁄2

0.7495

0.7480

2

14

21⁄2

1.4995

1.4980

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

…

…

…

…

…

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 on page 924.



831

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 1.3750 13⁄8 1.5000 11⁄2

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 2

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

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.



832

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

85⁄8 93⁄8 101⁄4 113⁄8

61⁄2 71⁄2 83⁄8 93⁄4

41⁄4 41⁄2 5 6

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.



833

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 931.)

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 1 1 ⁄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.



834

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.



835

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 1 1 ⁄8 1 1 ⁄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.


836


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 … … 11⁄16 1 … 1 ⁄8 … 13⁄16 … 11⁄4 … 15⁄16b … 13⁄8 … 17⁄16b … 11⁄2

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

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

a Reamer with straight flutes is standard only.



837

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)

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 21⁄16a 21⁄8 23⁄16a 21⁄4 23⁄8a 21⁄2a

Length Overall A 21⁄4 21⁄2 21⁄2 21⁄2 23⁄4 23⁄4 23⁄4 23⁄4 3 3 3 3 3 3 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 33⁄4 33⁄4 33⁄4 33⁄4 33⁄4 33⁄4

Flute Length B 11⁄2 13⁄4 13⁄4 13⁄4 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 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4

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.



838

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 11⁄16 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 13⁄8

a American National Standard self-holding tapers (see Table 7a on page 931.)

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)

Length Length Dia. of of OverFlute Shank all

Size of Hole

Length Length Dia. of of OverFlute Shank all

Size of Hole

D

H

Flute No.

Series No.

Diameter Range

A

B

D

H

Flute No.

00

.0600-.066

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

4

12

.3761- .407

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

0

.0661-.074

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

4

13

.4071- .439

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

1

.0741-.084

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

4

14

.4391- .470

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

2

.0841-.096

13⁄4

1⁄ 2

1⁄ 8

1⁄ 16

4

15

.4701- .505

21⁄2

11⁄4

1⁄ 2

3⁄ 16

6

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

.2821-.313

21⁄4

1

3⁄ 8

1⁄ 8

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

…

…

…

…

…

…

…

Series No.

9

Diameter Range

A

B

6

22

.8801- .942

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.



839

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 2

Straight Flutes and Squared Shank Length Flute Square Overall Length Length A B C

0.5170

33⁄4 5

21⁄4 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 0.3674 0.5170 3 65⁄16 1.4717

0.5696

1.8005

0.7444

5⁄ 16 7⁄ 16 5⁄ 8 7⁄ 8

1 11⁄8 Taper Shank No.a 0

Shank Dia. D 5⁄ 16 7⁄ 16 5⁄ 8 7⁄ 8 11⁄8 1 1 ⁄2

Square Size 0.235 0.330 0.470 0.655 0.845 1.125

Squared and Taper ShankNumber of Flutes 4 to 6 incl.

1

6 to 8 incl.

73⁄8

31⁄2

2

6 to 8 incl. 8 to 10 incl.

3

0.7748

0.9881

87⁄8

41⁄4

3

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

on page 924. 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.



840

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 1 1 ⁄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 934.

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.



841

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.


842

Machinery's Handbook 28th Edition 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



843

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.

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.



844

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

…

…

…

…

…

…

…

…

87

0.0100

0.254

5⁄ 64

2.0

3⁄ 4

19

…

…

…

…

…

…

…

…

86

0.0105

0.267

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0110

0.280

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0115

0.292

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0118

0.300

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

83

0.0120

0.305

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

82

0.0125

0.318

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0126

0.320

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

81

0.0130

0.330

3⁄ 32

2.4

3⁄ 4

19

…

…

…

…

…

…

…

…

80

0.0135

0.343

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0138

0.350

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0145

0.368

1⁄ 8

3

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0150

0.380

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0156

0.396

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0157

0.400

3⁄ 16

5

3⁄ 4

19

…

…

…

…

…

…

…

…

0.0160

0.406

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.42

0.0165

0.420

3⁄ 16

5

7⁄ 8

22

…

…

…

…

…

…

…

…

0.45

0.0177

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

…

…

…

…

…

…

…

…

91 90

0.22

0.25

85

0.28

84 0.30

0.32

0.35 79 0.38 1⁄ 64

0.40 78

77

0.55 74 0.60

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

…

…

…

…

…

…

…

…



845

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 mm

Decimal In.

mm


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

73

0.0240

0.610

5⁄ 16

8

11⁄8

29

…

…

…

…

…

…

…

…

72

0.0250

0.635

5⁄ 16

8

11⁄8

29

…

…

…

…

…

…

…

…

0.0256

0.650

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.0260

0.660

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

0.0276

0.700

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

70

0.0280

0.711

3⁄ 8

10

11⁄4

32

…

…

…

…

…

…

…

…

69

0.0292

0.742

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

0.0295

0.750

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

68

0.0310

0.787

1⁄ 2

13

13⁄8

35

…

…

…

…

…

…

…

…

1⁄ 32

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

1.200

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.250

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.300

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.321

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.350

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.397

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.400

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.450

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.500

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.511

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.550

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.588

7⁄ 8

22

17⁄8

48

13⁄4

76

5⁄ 8

16

15⁄8

41

1.600

7⁄ 8

22

17⁄8

95

11⁄ 16

17

111⁄16

43

1.613

7⁄ 8

22

17⁄8

95

11⁄ 16

17

111⁄16

43

95

11⁄ 16

17

111⁄16

43

0.65 71 0.70

0.75

0.80

0.85 65 0.90

0.95

1.00

1.05

1.20 1.25 1.30 55

0.0472 0.0492 0.0512 0.0520

1.35 54

0.0531 0.0550

1.40 1.45 1.50 53

0.0551 0.0571 0.0591 0.0595

1.55 1⁄ 16

0.0610 0.0625

1.60 52

0.0630 0.0635

1.65

0.0650

1.650

1

25

2

48 48 51

2 2 2

44 44 44 44 44 44 44 44 44 44 44

3 3 3 3 3 3 3 3 3 3 3

44

3

51

33⁄4

51

33⁄4

51

33⁄4



846


Jobbers Length

Equivalent mm

Decimal In.

mm


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

Overall L

mm

Inch

mm

0.0669

1.700

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0670

1.702

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0689

1.750

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0700

1.778

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

1.80

0.0709

1.800

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

1.85

0.0728

1.850

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0730

1.854

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0748

1.900

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0760

1.930

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

0.0768

1.950

1

25

2

51

2

51

33⁄4

95

11⁄ 16

17

111⁄16

43

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

2.527

13⁄8

35

23⁄8

60

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.578

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.600

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.642

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.700

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.705

17⁄16

37

21⁄2

64

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.779

11⁄2

38

25⁄8

67

21⁄2

64

45⁄8

117

13⁄ 16

21

113⁄16

46

2.794

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

2.800

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

2.819

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

2.870

11⁄2

38

25⁄8

67

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

2.900

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

2.946

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

3.000

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

3.048

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

1.70 51 1.75 50

49 1.90 48 1.95

44

43

2.40 41 2.46 40 2.50 39

0.0995

38

0.1015 2.60

37

0.1040 2.70

36

0.1063 0.1065

7⁄ 64

0.1094

35

0.1100 2.80

34

0.1102 0.1110

33

0.1130 2.90

32

0.1142 0.1160

3.00 31

0.1024

0.1181 0.1200



847


Jobbers Length

Equivalent mm

Decimal In.

mm


Taper Length

Flute

Overall

Flute

Overall

Flute

F

L

F

L

F

Inch

mm

Inch

mm

Inch

mm

Inch

mm

Inch

Overall L

mm

Inch

mm

0.1220

3.100

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1250

3.175

15⁄8

41

23⁄4

70

23⁄4

70

51⁄8

130

7⁄ 8

22

17⁄8

48

0.1260

3.200

15⁄8

41

23⁄4

70

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

0.1285

3.264

15⁄8

41

23⁄4

70

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

3.30

0.1299

3.300

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

3.40

0.1339

3.400

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

0.1360

3.454

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

0.1378

3.500

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

28

0.1405

3.569

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

9⁄ 64

0.1406

3.571

13⁄4

44

27⁄8

73

3

76

53⁄8

137

15⁄ 16

24

115⁄16

49

0.1417

3.600

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

0.1440

3.658

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

0.1457

3.700

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

26

0.1470

3.734

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

25

0.1495

3.797

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

0.1496

3.800

17⁄8

48

3

76

3

76

53⁄8

137

1

25

21⁄16

52

0.1520

3.861

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

0.1535

3.900

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

23

0.1540

3.912

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

5⁄ 32

0.1562

3.967

2

51

31⁄8

79

3

76

53⁄8

137

1

25

21⁄16

52

22

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

4.400

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.496

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.500

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.572

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.600

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.623

23⁄16

56

33⁄8

86

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.700

25⁄16

59

31⁄2

89

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.762

25⁄16

59

31⁄2

89

33⁄8

86

53⁄4

146

11⁄8

29

23⁄16

56

4.800

25⁄16

59

31⁄2

89

35⁄8

152

13⁄16

30

21⁄4

57

4.851

25⁄16

59

31⁄2

89

35⁄8

152

13⁄16

30

21⁄4

57

4.900

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

4.915

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

4.978

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

5.000

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

5.054

27⁄16

62

35⁄8

92

35⁄8

152

13⁄16

30

21⁄4

57

3.10 1⁄ 8

3.20 30

29 3.50

3.60 27 3.70

3.80 24 3.90

4.00

19 4.30

4.40 16

0.1770 4.50

15 14 4.70

0.1850 0.1875

4.80

11

0.1890 0.1910

4.90 10

0.1929 0.1935

9

0.1960 5.00

8

0.1811 0.1820

3⁄ 16

12

0.1772 0.1800

4.60 13

0.1732

0.1969 0.1990

92 92 92 92 92 92 92

6 6 6 6 6 6 6



848


Jobbers Length

Equivalent Decimal In.


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

0.2008

5.100

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

7

0.2010

5.105

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

13⁄ 64

0.2031

5.159

27⁄16

62

35⁄8

92

35⁄8

92

6

152

13⁄16

30

21⁄4

57

6

0.2040

5.182

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2047

5.200

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2055

5.220

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2087

5.300

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2090

5.309

21⁄2

64

33⁄4

95

35⁄8

92

6

152

11⁄4

32

23⁄8

60

0.2126

5.400

21⁄2

64

33⁄4

95

35⁄8

92

6

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

6.600

27⁄8

73

41⁄8

…

17⁄16

37

25⁄8

67

6.629

27⁄8

73

41⁄8

…

17⁄16

37

25⁄8

67

6.700

27⁄8

73

41⁄8

…

17⁄16

37

25⁄8

67

6.746

27⁄8

73

41⁄8

159

17⁄16

37

25⁄8

67

6.756

27⁄8

73

41⁄8

…

11⁄2

38

211⁄16

68

6.800

27⁄8

73

41⁄8

159

11⁄2

38

211⁄16

68

6.900

27⁄8

73

41⁄8

…

11⁄2

38

211⁄16

68

6.909

27⁄8

73

41⁄8

…

11⁄2

38

211⁄16

68

7.000

27⁄8

73

41⁄8

159

11⁄2

38

211⁄16

68

7.036

27⁄8

73

41⁄8

…

11⁄2

38

211⁄16

68

7.100

215⁄16

75

41⁄4

…

11⁄2

38

211⁄16

68

7.137

215⁄16

75

41⁄4

…

11⁄2

38

211⁄16

68

7.142

215⁄16

75

41⁄4

159

11⁄2

38

211⁄16

68

7.200

215⁄16

75

41⁄4

162

19⁄16

40

23⁄4

70

7.300

215⁄16

75

41⁄4

…

19⁄16

40

23⁄4

70

mm 5.10

5.20 5 5.30 4 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

0.2598 0.2610

6.70 17⁄ 64

0.2638 0.2656

H

0.2660 6.80 6.90

I

0.2677 0.2717 0.2720

7.00 J

0.2756 0.2770

7.10 K

0.2795 0.2810

9⁄ 32

0.2812 7.20 7.30

0.2835 0.2874

105 105

… …

105

…

105

37⁄8

105

…

105

37⁄8

105

…

105

…

105

37⁄8

105 108

… …

108

…

108

37⁄8

108 108

4 …

… …

… …

…

…

98

61⁄4

…

…

98

61⁄4

…

…

…

…

98

61⁄4

… …

… …

…

…

98

61⁄4

102

63⁄8

…

…

Inch

mm



849


Jobbers Length

Equivalent Decimal In.


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

0.2900

7.366

215⁄16

75

41⁄4

108

…

…

…

…

19⁄16

40

23⁄4

70

0.2913

7.400

31⁄16

78

43⁄8

111

…

…

…

…

19⁄16

40

23⁄4

70

0.2950

7.493

31⁄16

78

43⁄8

111

…

…

…

…

19⁄16

40

23⁄4

70

0.2953

7.500

31⁄16

78

43⁄8

111

4

102

63⁄8

162

19⁄16

40

23⁄4

70

0.2969

7.541

31⁄16

78

43⁄8

111

4

102

63⁄8

162

19⁄16

40

23⁄4

70

0.2992

7.600

31⁄16

78

43⁄8

111

…

…

…

…

15⁄8

41

213⁄16

71

0.3020

7.671

31⁄16

78

43⁄8

111

…

…

…

…

15⁄8

41

213⁄16

71

7.70

0.3031

7.700

33⁄16

81

41⁄2

114

…

…

…

…

15⁄8

41

213⁄16

71

7.80

0.3071

7.800

33⁄16

81

41⁄2

114

102

63⁄8

162

15⁄8

41

213⁄16

71

7.90

0.3110

7.900

33⁄16

81

41⁄2

114

…

…

…

15⁄8

41

213⁄16

71

0.3125

7.938

33⁄16

81

41⁄2

114

4

102

63⁄8

162

15⁄8

41

213⁄16

71

0.3150

8.000

33⁄16

81

41⁄2

114

41⁄8

105

61⁄2

165

111⁄16

43

215⁄16

75

0.3160

8.026

33⁄16

81

41⁄2

114

…

…

…

…

111⁄16

43

215⁄16

75

8.10

0.3189

8.100

35⁄16

84

45⁄8

117

…

…

…

…

111⁄16

43

215⁄16

75

8.20

0.3228

8.200

35⁄16

84

45⁄8

117

41⁄8

105

61⁄2

165

111⁄16

43

215⁄16

75

0.3230

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

0.3465

8.800

31⁄2

89

47⁄8

124

41⁄4

108

63⁄4

171

13⁄4

44

31⁄16

78

mm

L 7.40 M 7.50 19⁄ 64

7.60 N

5⁄ 16

8.00 O

P 8.30 21⁄ 64

8.40 Q

R 8.70 11⁄ 32

8.80

4 …

Inch

mm

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

9.129

31⁄2

89

47⁄8

124

41⁄4

108

63⁄4

171

13⁄4

44

31⁄16

78

9.200

35⁄8

127

41⁄4

108

63⁄4

171

113⁄16

46

31⁄8

79

9.300

35⁄8

…

113⁄16

46

31⁄8

79

9.347

35⁄8

…

113⁄16

46

31⁄8

79

9.400

35⁄8

…

113⁄16

46

31⁄8

79

9.500

35⁄8

171

113⁄16

46

31⁄8

79

9.525

35⁄8

171

113⁄16

46

31⁄8

79

9.576

35⁄8

…

17⁄8

48

31⁄4

83

9.600

33⁄4

…

17⁄8

48

31⁄4

83

9.700

33⁄4

…

17⁄8

48

31⁄4

83

9.800

33⁄4

178

17⁄8

48

31⁄4

83

9.804

33⁄4

…

17⁄8

48

31⁄4

83

9.900

33⁄4

…

17⁄8

48

31⁄4

83

9.921

33⁄4

178

17⁄8

48

31⁄4

83

10.000

33⁄4

178

115⁄16

49

35⁄16

84

S

T 9.10 23⁄ 64

0.3594 9.20 9.30

U

0.3622 0.3661 0.3680

9.40 9.50 3⁄ 8

0.3701 0.3740 0.3750

V

0.3770 9.60 9.70 9.80

W

0.3780 0.3819 0.3858 0.3860

9.90 25⁄ 64

0.3898 0.3906

10.00

0.3937

92 92 92 92 92 92

5 5 5 5 5 5

92

5

95

51⁄8

95

51⁄8

95

51⁄8

95

51⁄8

95

51⁄8

95

51⁄8

95

51⁄8

127 127

… …

127

…

127

41⁄4

127

41⁄4

127 130

… …

130

…

130

43⁄8

130

…

130

…

130

43⁄8

130

43⁄8

… …

… …

…

…

108

63⁄4

108

63⁄4

… … … 111 … … 111 111

… … … 7 … … 7 7



850


Jobbers Length

Equivalent mm

Decimal In.

mm


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

…

…

115⁄16

49

35⁄16

mm 84

178

115⁄16

49

35⁄16

84

…

115⁄16

49

35⁄16

84

178

115⁄16

49

35⁄16

84

0.3970

10.084

33⁄4

95

51⁄8

130

…

…

0.4016

10.200

37⁄8

98

51⁄4

133

43⁄8

111

Y

0.4040

10.262

37⁄8

98

51⁄4

133

…

…

13⁄ 32

0.4062

10.317

37⁄8

98

51⁄4

133

43⁄8

111

Z

0.4130

10.490

37⁄8

98

51⁄4

133

…

…

…

…

2

51

33⁄8

86

0.4134

10.500

37⁄8

98

51⁄4

133

45⁄8

117

71⁄4

184

2

51

33⁄8

86

0.4219

10.716

315⁄16

100

53⁄8

137

45⁄8

117

71⁄4

184

2

51

33⁄8

86

10.80

0.4252

10.800

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

184

21⁄16

52

37⁄16

87

11.00

0.4331

11.000

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

184

21⁄16

52

37⁄16

87

0.4375

11.112

41⁄16

103

51⁄2

140

45⁄8

117

71⁄4

184

21⁄16

52

37⁄16

87

11.20

0.4409

11.200

43⁄16

106

55⁄8

143

43⁄4

121

71⁄2

190

21⁄8

54

39⁄16

90

11.50

0.4528

11.500

43⁄16

106

55⁄8

143

43⁄4

121

71⁄2

190

21⁄8

54

39⁄16

90

0.4531

11.509

43⁄16

106

55⁄8

143

43⁄4

121

71⁄2

190

21⁄8

54

39⁄16

90

0.4646

11.800

45⁄16

110

53⁄4

146

43⁄4

121

71⁄2

190

21⁄8

54

35⁄8

92

0.4688

11.908

45⁄16

110

53⁄4

146

43⁄4

121

71⁄2

190

21⁄8

54

35⁄8

92

12.00

0.4724

12.000

43⁄8

111

57⁄8

149

43⁄4

121

73⁄4

197

23⁄16

56

311⁄16

94

12.20

0.4803

12.200

43⁄8

111

57⁄8

149

43⁄4

121

73⁄4

197

23⁄16

56

311⁄16

94

0.4844

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

X 10.20

10.50 27⁄ 64

7⁄ 16

29⁄ 64

11.80 15⁄ 32

31⁄ 64

12.50 1⁄ 2

33⁄ 64

13.20 17⁄ 32

35⁄ 64

… 7

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

14.500

413⁄16

122

65⁄8

…

25⁄8

67

41⁄8

105

0.5781

14.684

413⁄16

122

65⁄8

168

…

…

…

…

25⁄8

67

41⁄8

105

0.5807

14.750

53⁄16

132

71⁄8

181

…

…

…

…

25⁄8

67

41⁄8

105

15.000

53⁄16

132

71⁄8

…

25⁄8

67

41⁄8

105

15.083

53⁄16

132

71⁄8

…

25⁄8

67

41⁄8

105

15.250

53⁄16

132

71⁄8

…

23⁄4

70

41⁄4

108

15.479

53⁄16

132

71⁄8

…

23⁄4

70

41⁄4

108

15.500

53⁄16

132

71⁄8

…

23⁄4

70

41⁄4

108

15.750

53⁄16

132

71⁄8

…

23⁄4

70

41⁄4

108

15.875

53⁄16

132

71⁄8

…

23⁄4

70

41⁄4

108

16.000

53⁄16

132

71⁄8

…

27⁄8

73

41⁄2

114

16.250

53⁄16

132

71⁄8

…

27⁄8

73

41⁄2

114

16.271

53⁄16

132

71⁄8

…

27⁄8

73

41⁄2

144

16.500

53⁄16

132

71⁄8

…

27⁄8

73

41⁄2

114

16.669

53⁄16

132

71⁄8

…

27⁄8

73

41⁄2

114

9⁄ 16

14.50 37⁄ 64

14.75 15.00 19⁄ 32

0.5709

0.5906 0.5938

15.25 39⁄ 64

0.6004 0.6094

15.50 15.75 5⁄ 8

0.6102 0.6201 0.6250

16.00 16.25 41⁄ 64

0.6299 0.6398 0.6406

16.50 21⁄ 32

7

0.6496 0.6562

168

181 181 181 181 181 181 181 181 181 181 181 181

…

… … … … … … … … … … … …

…

… … … … … … … … … … … …

…

… … … … … … … … … … … …



851


Jobbers Length

Equivalent mm

Decimal In.

16.75

0.6594

17.00


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

43⁄ 64

17.25 11⁄ 16

17.50 45⁄ 64

18.00 23⁄ 32

18.50 47⁄ 64

19.00

mm

Inch

mm

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

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

a Fractional inch, number, letter, and metric sizes.



852

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



853

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



854

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

Thickness of Tang, J Inches

Inches 1⁄ thru 3⁄ 8 16 over 3⁄16 thru 1⁄4 1 over ⁄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

Length of Tang, K

Millimeters

Millimeters

Max.

Min.

Max.

Min.

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

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

To fit split sleeve collet type drill drivers. See page 866.



855

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

25.500

26.00 11⁄16 28.00 11⁄8

Flute Length

Overall Length

F

L

Shank Diameter A

Inch

mm

Inch

mm

Inch

mm

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

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

1.3386

34.000

41⁄2

114

71⁄8

181

1.2402

31.50

30.00

32.00 15⁄16 34.00 13⁄8

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

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

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

36.00 17⁄16 38.00

40.00 15⁄8 42.00 111⁄16 44.00 13⁄4 46.00

48.00 115⁄16 50.00 2



856

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 17⁄8 17⁄8 21⁄8 21⁄8 21⁄8 21⁄8 21⁄8 21⁄2 21⁄2 21⁄2 21⁄2 21⁄2 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 23⁄4 27⁄8 27⁄8 27⁄8 27⁄8 27⁄8 3 3 3 3 3 31⁄8 31⁄8 31⁄8 31⁄8 31⁄8 31⁄4 31⁄4 31⁄4 31⁄4 31⁄4 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 31⁄2 35⁄8 35⁄8 35⁄8

48 48 54 54 54 54 54 64 64 64 64 64 70 70 70 70 70 70 73 73 73 73 73 76 76 76 76 76 79 79 79 79 79 83 83 83 83 83 89 89 89 89 89 89 92 92 92

51⁄8 51⁄8 53⁄8 53⁄8 53⁄8 53⁄8 53⁄8 53⁄4 53⁄4 53⁄4 53⁄4 53⁄4 6 6 6 6 6 6 61⁄8 61⁄8 61⁄8 61⁄8 61⁄8 61⁄4 61⁄4 61⁄4 61⁄4 61⁄4 63⁄8 63⁄8 63⁄8 63⁄8 63⁄8 61⁄2 61⁄2 61⁄2 61⁄2 61⁄2 63⁄4 63⁄4 63⁄4 63⁄4 63⁄4 63⁄4 7 7 7

130 130 137 137 137 137 137 146 146 146 146 146 152 152 152 152 152 152 156 156 156 156 156 159 159 159 159 159 162 162 162 162 162 165 165 165 165 165 171 171 171 171 171 171 178 178 178

Morse Taper No. … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 2 … 2 …

Larger or Smaller Shanka Flute Length Overall Length F L Inch mm Inch mm … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 31⁄2 … 35⁄8 …

… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 89 … 92 …

… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 73⁄8 … 71⁄2 …

… … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 187 … 190 …



857

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 5 3 ⁄8 92 7 178 5 92 7 178 3 ⁄8 98 184 71⁄4 37⁄8 98 184 37⁄8 71⁄4 98 184 71⁄4 37⁄8 7 1 98 184 7 ⁄4 3 ⁄8 98 184 37⁄8 71⁄4 105 190 71⁄2 41⁄8 105 190 71⁄2 41⁄8 1 1 105 190 4 ⁄8 7 ⁄2 1 1 105 190 7 ⁄2 4 ⁄8 105 190 41⁄8 71⁄2 111 210 81⁄4 43⁄8 111 210 81⁄4 43⁄8 3 1 111 210 4 ⁄8 8 ⁄4 3 1 111 210 8 ⁄4 4 ⁄8 111 210 43⁄8 81⁄4 117 216 81⁄2 45⁄8 117 216 81⁄2 45⁄8 5 1 117 216 4 ⁄8 8 ⁄2 5 1 117 216 8 ⁄2 4 ⁄8 117 216 45⁄8 81⁄2 117 216 81⁄2 45⁄8 7 3 124 222 8 ⁄4 4 ⁄8 7 3 124 222 4 ⁄8 8 ⁄4 124 222 83⁄4 47⁄8 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 7 3 124 222 8 ⁄4 4 ⁄8 7 3 124 222 4 ⁄8 8 ⁄4 124 222 83⁄4 47⁄8 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 7 3 124 222 8 ⁄4 4 ⁄8 7 3 124 222 4 ⁄8 8 ⁄4 124 222 83⁄4 47⁄8 124 222 83⁄4 47⁄8 124 222 47⁄8 83⁄4 1 130 9 229 5 ⁄8 130 9 229 51⁄8 130 9 229 51⁄8 130 9 229 51⁄8 1 130 9 229 5 ⁄8 3 1 137 235 9 ⁄4 5 ⁄8 137 235 91⁄4 53⁄8 137 235 53⁄8 91⁄4 137 235 91⁄4 53⁄8 3 1 137 235 5 ⁄8 9 ⁄4 5 1 143 241 9 ⁄2 5 ⁄8 143 241 55⁄8 91⁄2 143 241 91⁄2 55⁄8 143 241 55⁄8 91⁄2 7 3 149 248 9 ⁄4 5 ⁄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 … … … … 5 1 92 190 3 ⁄8 7 ⁄2 … … … … 98 197 37⁄8 73⁄4 … … … … … … … … 98 197 37⁄8 73⁄4 … … … … … … … … 1 105 8 203 4 ⁄8 … … … … 105 8 203 41⁄8 111 197 43⁄8 73⁄4 111 197 43⁄8 73⁄4 111 197 43⁄8 73⁄4 3 3 111 197 4 ⁄8 7 ⁄4 111 197 43⁄8 73⁄4 117 8 203 45⁄8 117 8 203 45⁄8 5 117 8 203 4 ⁄8 5 117 8 203 4 ⁄8 117 8 203 45⁄8 117 8 203 45⁄8 7 1 124 210 4 ⁄8 8 ⁄4 7 1 124 210 4 ⁄8 8 ⁄4 124 210 47⁄8 81⁄4 124 210 47⁄8 81⁄4 124 210 47⁄8 81⁄4 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 130 248 51⁄8 93⁄4 … … … … 130 248 51⁄8 93⁄4 … … … … … … … … 137 10 254 53⁄8 … … … … 137 10 254 53⁄8 … … … … 143 260 55⁄8 101⁄4 … … … … 143 260 55⁄8 101⁄4 … … … … 149 267 57⁄8 101⁄2



858


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 7 3 5 ⁄8 9 ⁄4 149 248 7 3 149 248 5 ⁄8 9 ⁄4 6 152 251 97⁄8 251 6 152 97⁄8 6 152 251 97⁄8 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 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 61⁄8 103⁄4 156 273 103⁄4 61⁄8 1 3 156 273 6 ⁄8 10 ⁄4 1 3 156 273 6 ⁄8 10 ⁄4 156 273 103⁄4 61⁄8 156 273 61⁄8 103⁄4 3 162 11 279 6 ⁄8 3 162 11 279 6 ⁄8 162 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 ⁄8 165 283 111⁄8 61⁄2 165 283 61⁄2 111⁄8 165 283 111⁄8 61⁄2 1 1 165 283 6 ⁄2 11 ⁄8 5 1 168 286 11 ⁄4 6 ⁄8 168 286 65⁄8 111⁄4 168 286 65⁄8 111⁄4 168 286 111⁄4 65⁄8 7 1 175 318 6 ⁄8 12 ⁄2 175 318 121⁄2 67⁄8 175 318 67⁄8 121⁄2 181 324 123⁄4 71⁄8 1 3 181 324 7 ⁄8 12 ⁄4 1 3 181 324 12 ⁄4 7 ⁄8 181 324 71⁄8 123⁄4 184 327 71⁄4 127⁄8 184 327 127⁄8 71⁄4 1 7 184 327 7 ⁄4 12 ⁄8 3 187 13 330 7 ⁄8 187 13 330 73⁄8 187 13 330 73⁄8 187 13 330 73⁄8 1 1 190 333 13 ⁄8 7 ⁄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 … … … … 7 1 149 267 5 ⁄8 10 ⁄2 6 152 270 105⁄8 … … … … 6 152 270 105⁄8 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 61⁄8 156 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 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 3 162 12 305 6 ⁄8 … … … … … … … … … … … … 1 1 165 308 6 ⁄2 12 ⁄8 … … … … … … … … 168 311 65⁄8 121⁄4 … … … … 175 292 67⁄8 111⁄2 175 292 67⁄8 111⁄2 175 292 67⁄8 111⁄2 181 298 71⁄8 113⁄4 1 3 181 298 7 ⁄8 11 ⁄4 1 3 181 298 7 ⁄8 11 ⁄4 181 298 71⁄8 113⁄4 184 302 71⁄4 117⁄8 184 302 71⁄4 117⁄8 1 7 184 302 7 ⁄4 11 ⁄8 3 187 12 305 7 ⁄8 187 12 305 73⁄8 187 12 305 73⁄8 187 12 305 73⁄8 1 1 190 308 7 ⁄2 12 ⁄8 190 308 71⁄2 121⁄8



859

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 1 1 7 ⁄2 13 ⁄8 190 333 7 1 200 343 13 ⁄2 7 ⁄8 200 343 77⁄8 131⁄2 200 343 131⁄2 77⁄8 200 343 77⁄8 131⁄2 1 1 216 359 14 ⁄8 8 ⁄2 216 359 81⁄2 141⁄8 216 359 141⁄8 81⁄2 216 359 81⁄2 141⁄8 5 1 219 362 8 ⁄8 14 ⁄4 5 1 219 362 14 ⁄4 8 ⁄8 219 362 85⁄8 141⁄4 222 365 143⁄8 83⁄4 222 365 83⁄4 143⁄8 3 3 222 365 14 ⁄8 8 ⁄4 3 3 222 365 8 ⁄4 14 ⁄8 225 368 141⁄2 87⁄8 225 368 87⁄8 141⁄2 225 368 87⁄8 141⁄2 5 371 9 229 14 ⁄8 5 9 229 371 14 ⁄8 371 9 229 145⁄8 9 229 371 145⁄8 1 3 232 375 14 ⁄4 9 ⁄8 1 3 232 375 9 ⁄8 14 ⁄4 232 375 143⁄4 91⁄8 232 375 91⁄8 143⁄4 235 378 91⁄4 147⁄8 1 7 235 378 14 ⁄8 9 ⁄4 1 7 235 378 9 ⁄4 14 ⁄8 238 15 381 93⁄8 238 15 381 93⁄8 238 15 381 93⁄8 3 238 15 381 9 ⁄8 … … … … 238 416 93⁄8 163⁄8 244 422 165⁄8 95⁄8 … … … … 5 5 244 422 9 ⁄8 16 ⁄8 251 429 167⁄8 97⁄8 … … … … 251 429 97⁄8 167⁄8 … … … … 10 254 17 432 10 254 17 432 … … … … 257 435 171⁄8 101⁄8 1 1 257 435 10 ⁄8 17 ⁄8 … … … … 257 435 101⁄8 171⁄8 257 435 171⁄8 101⁄8 … … … … 1 1 257 435 10 ⁄8 17 ⁄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 1 1 7 ⁄2 12 ⁄8 190 308 7 1 200 318 7 ⁄8 12 ⁄2 200 318 77⁄8 121⁄2 200 318 77⁄8 121⁄2 200 318 77⁄8 121⁄2 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … 3 238 15 381 9 ⁄4 238 15 381 93⁄8 244 387 95⁄8 151⁄4 244 387 95⁄8 151⁄4 5 1 244 387 9 ⁄8 15 ⁄4 251 394 97⁄8 151⁄2 251 394 97⁄8 151⁄2 251 394 97⁄8 151⁄2 5 10 254 397 15 ⁄8 5 397 10 254 15 ⁄8 10 254 397 155⁄8 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 1 3 257 400 10 ⁄8 15 ⁄4 1 3 257 400 10 ⁄8 15 ⁄4 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 257 400 101⁄8 153⁄4 1 3 257 400 10 ⁄8 15 ⁄4 264 413 103⁄8 161⁄4



860

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 … … … … 1 1 257 435 10 ⁄8 17 ⁄8 257 435 171⁄8 101⁄8 257 435 101⁄8 171⁄8 257 435 171⁄8 101⁄8 1 1 257 435 10 ⁄8 17 ⁄8 257 435 101⁄8 171⁄8 264 441 173⁄8 103⁄8 264 441 103⁄8 173⁄8 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 3 3 264 441 17 ⁄8 10 ⁄8 264 441 173⁄8 103⁄8 264 441 103⁄8 173⁄8 260 441 173⁄8 101⁄4 1 3 260 441 10 ⁄4 17 ⁄8 1 3 260 441 17 ⁄8 10 ⁄4 260 441 101⁄4 173⁄8 260 441 101⁄4 173⁄8 1 3 260 441 17 ⁄8 10 ⁄4 1 3 260 441 10 ⁄4 17 ⁄8 260 441 173⁄8 101⁄4 260 441 101⁄4 173⁄4 257 441 173⁄8 101⁄8 1 3 257 441 10 ⁄8 17 ⁄8 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 1 3 257 441 17 ⁄8 10 ⁄8 257 441 101⁄8 173⁄8 286 476 183⁄4 111⁄4 286 476 111⁄4 183⁄4 1 3 286 476 18 ⁄4 11 ⁄4 286 476 183⁄4 111⁄4 286 476 111⁄4 183⁄4 302 495 191⁄2 117⁄8 7 1 302 495 19 ⁄2 11 ⁄8 7 1 302 495 11 ⁄8 19 ⁄2 302 495 191⁄2 117⁄8 302 495 117⁄8 191⁄2 324 518 203⁄8 123⁄4 3 3 324 518 20 ⁄8 12 ⁄4 3 3 324 518 12 ⁄4 20 ⁄8 324 518 203⁄8 123⁄4 324 518 123⁄4 203⁄8 340 537 211⁄8 133⁄8 3 1 340 537 21 ⁄8 13 ⁄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 3 1 10 ⁄8 16 ⁄4 264 413 3 1 264 413 10 ⁄4 16 ⁄4 264 413 103⁄8 161⁄4 264 413 103⁄8 161⁄4 264 413 103⁄8 161⁄4 3 1 264 413 10 ⁄8 16 ⁄4 264 413 103⁄8 161⁄4 267 419 101⁄2 161⁄2 267 419 101⁄2 161⁄2 1 1 267 419 10 ⁄2 16 ⁄2 1 1 267 419 10 ⁄2 16 ⁄2 270 422 105⁄8 165⁄8 270 422 105⁄8 165⁄8 270 422 105⁄8 165⁄8 5 5 270 422 10 ⁄8 16 ⁄8 5 5 270 422 10 ⁄8 16 ⁄8 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …



861


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 … …

537 537 537 552 552 552 552 552 622 622 622 648 …

Morse Taper No. … … … … … … … … 5 5 5 5 5

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 Inches Millimeters

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 Inches Millimeters 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

Inches 3⁄ 64 1⁄ 16 3⁄ 32 7⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4

mm

Inches

mm

Inches 3⁄ 64 1⁄ 16 3⁄ 32 7⁄ 64 5⁄ 32 3⁄ 16 7⁄ 32 1⁄ 4

1.19

0.10

2.5

1.59

0.15

3.8

2.38

0.20

5.1

2.78

0.25

6.4

3.97

0.35

8.9

4.76

0.40

10.2

5.56

0.50

12.7

6.35

0.60

15.2

Overall Length L

mm

Inches

mm

1.19

32

1.59

11⁄4 17⁄8

2.38

2

51

2.78

54

3.97

21⁄8 23⁄4

4.76

3

76

5.56

31⁄4 31⁄2

83

6.35

48

70

89



862

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

1 11⁄32 11⁄16 13⁄32 11⁄8 15⁄32 13⁄16 17⁄32 11⁄4 19⁄32

Three-Flute Drills Morse Taper No.

Four-Flute Drills

Flute Length

Overall Length

F

L

Decimal Inch

mm

A

Inch

0.2500

6.350

1

0.2812

7.142

1

27⁄8 3

0.3175

7.938

1

0.3438

8.733

0.3750

Morse Taper No.

Flute Length

Overall Length

F

L

mm

Inch

mm

A

Inch

mm

Inch

mm

73

61⁄8

156

…

…

…

…

…

76

61⁄4

159

…

…

…

…

…

31⁄8

79

63⁄8

162

…

…

…

…

…

1

31⁄4

83

61⁄2

165

…

…

…

…

…

9.525

1

31⁄2

89

171

…

…

…

…

…

0.4062

10.319

1

35⁄8

92

63⁄4 7

178

…

…

…

…

…

0.4375

11.112

1

37⁄8

98

71⁄4

184

…

…

…

…

…

0.4688

11.908

1

41⁄8

105

71⁄2

190

…

…

…

…

…

0.5000

12.700

2

43⁄8

111

81⁄4

210

2

43⁄8

111

81⁄4

210

117

216

2

222

2

222

2

124

81⁄2 83⁄4 83⁄4 83⁄4

216

2

130

9

229

2

130

9

229

137

235

2

137

2

248

2

251

2

6

152

273

3

61⁄8

156

273

3

61⁄8

156

273

3

61⁄8

156

273

3

61⁄8

156

273

3

61⁄8

156

91⁄4 91⁄2 93⁄4 97⁄8 103⁄4 103⁄4 103⁄4 103⁄4 103⁄4

235

241

45⁄8 47⁄8 47⁄8 47⁄8 51⁄8 53⁄8 55⁄8 57⁄8

117

222

124

81⁄2 83⁄4 83⁄4 83⁄4

279

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

45⁄8 47⁄8 47⁄8 47⁄8 51⁄8 53⁄8 55⁄8 57⁄8

0.7812

19.842

2

6

152

0.8125

20.638

3

61⁄8

156

0.8438

21.433

3

61⁄8

156

0.8750

22.225

3

61⁄8

156

0.9062

23.019

3

61⁄8

156

0.9375

23.812

3

61⁄8

156

91⁄4 91⁄2 93⁄4 97⁄8 103⁄4 103⁄4 103⁄4 103⁄4 103⁄4

0.9688

24.608

3

63⁄8

162

11

279

3

63⁄8

162

11

1.0000

25.400

3

63⁄8

162

11

279

3

63⁄8

162

11

279

165

283

3 3

318

4

324

4

327

4

184

111⁄8 111⁄4 121⁄2 123⁄4 127⁄8

283

286

187

13

330

4

187

13

330

190

131⁄8

333

4

190

131⁄8

333

200

131⁄2 …

343

4

200

131⁄2

343

…

4

61⁄2 65⁄8 67⁄8 71⁄8 71⁄4 73⁄8 71⁄2 77⁄8 81⁄2

165

184

111⁄8 111⁄4 121⁄2 123⁄4 127⁄8

216

141⁄8

359

1.0312

26.192

3

1.0625

26.988

3

1.0938

27.783

4

1.1250

28.575

4

1.1562

29.367

4

1.1875

30.162

4

1.2188

30.958

4

1.2500

31.750

4

61⁄2 65⁄8 67⁄8 71⁄8 71⁄4 73⁄8 71⁄2 77⁄8

1.2812

32.542

…

…

124 124

143 149

168 175 181

…

124 124

143 149

168 175 181

222 222 222

241 248 251 273 273 273 273 273

286 318 324 327



863

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

Morse Taper No.

Four-Flute Drills

Flute Length

Overall Length

F

L

Morse Taper No.

Flute Length

Overall Length

F

L

Inch 15⁄16

Decimal Inch 1.3125

mm 33.338

A …

Inch …

mm …

Inch …

mm …

A 4

Inch 85⁄8

mm 219

Inch 141⁄4

mm 362

111⁄32

1.3438

34.133

…

…

…

…

…

4

83⁄4

222

143⁄8

365

13⁄8

1.3750

34.925

…

…

…

…

…

4

87⁄8

225

141⁄2

368

113⁄32

1.4062

35.717

…

…

…

…

…

4

9

229

145⁄8

371

17⁄16

1.4375

36.512

…

…

…

…

…

4

91⁄8

232

143⁄4

375

115⁄32

1.4688

37.306

…

…

…

…

…

4

91⁄4

235

378

11⁄2

1.5000

38.100

…

…

…

…

…

4

93⁄8

238

147⁄8 15

117⁄32

1.5312

38.892

…

…

…

…

…

5

93⁄8

238

163⁄8

416

19⁄16

1.5675

39.688

…

…

…

…

…

5

95⁄8

244

165⁄8

422

119⁄32

1.5938

40.483

…

…

…

…

…

5

251

15⁄8

1.6250

41.275

…

…

…

…

…

5

97⁄8 10

254

167⁄8 17

432

121⁄32

1.6562

42.067

…

…

…

…

…

5

101⁄8

257

171⁄8

435

111⁄16

1.6875

42.862

…

…

…

…

…

5

101⁄8

257

171⁄8

435

101⁄8 101⁄8 101⁄8 101⁄8 101⁄8 103⁄8 103⁄8 103⁄8 103⁄8 103⁄8 101⁄4 101⁄8 101⁄8 111⁄4

257

171⁄8 171⁄8 171⁄8 171⁄8 171⁄8 173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 173⁄8 183⁄4

435

123⁄32 13⁄4 125⁄32 113⁄16 127⁄32 17⁄8 129⁄32 115⁄16 131⁄32

1.7188

43.658

…

…

…

…

…

5

1.7500

44.450

…

…

…

…

…

5

1.7812

45.244

…

…

…

…

…

5

1.8125

46.038

…

…

…

…

…

5

1.8438

46.833

…

…

…

…

…

5

1.8750

47.625

…

…

…

…

…

5

1.9062

48.417

…

…

…

…

…

5

1.9375

49.212

…

…

…

…

…

5

1.9688

50.008

…

…

…

…

…

5

2

2.0000

50.800

…

…

…

…

…

5

21⁄8

2.1250

53.975

…

…

…

…

…

5

21⁄4

2.2500

57.150

…

…

…

…

…

5

23⁄8

2.3750

60.325

…

…

…

…

…

5

21⁄2

2.5000

63.500

…

…

…

…

…

5

257 257 257 257 264 264 264 264 264 260 257 257 286

381

429

435 435 435 435 441 441 441 441 441 441 441 441 476

Table 8. American National Standard Drill Drivers — Split-Sleeve, Collet Type ANSI B94.35-1972 (R2005)

Taper Number

G Overall Length

H Diameter at Gage Line

J Taper per Foota

K Length to Gage Line

L Driver Projection

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

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.




864

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

Decimal Inch

Four-Flute Drills

Flute Length

Overall Length

Flute Length

F

L

F

L

mm

Inch

mm

Inch

mm

Inch

mm

Inch

mm

0.2500

6.350

95

…

…

…

…

7.142

159

…

…

…

…

0.3125

7.938

4

102

162

…

…

…

…

0.3438

8.733

105

165

…

…

…

0.3750

9.525

105

171

…

…

…

…

0.4062

10.317

111

7

178

…

…

…

…

0.4375

11.112

117

71⁄4

184

…

…

…

…

0.4688

11.908

121

71⁄2

190

…

…

…

…

0.5000

12.700

121

43⁄4

121

121

203

43⁄4

121

73⁄4 8

197

13.492

73⁄4 8

197

0.5312

203

0.5625

14.288

124

81⁄4

210

47⁄8

124

81⁄4

210

0.5938

15.083

124

83⁄4

222

47⁄8

124

83⁄4

222

0.6250

15.875

124

47⁄8

124

16.667

83⁄4 9

222

0.6562

229

51⁄8

130

83⁄4 9

229

0.6875

17.462

41⁄8 41⁄8 43⁄8 45⁄8 43⁄4 43⁄4 43⁄4 47⁄8 47⁄8 47⁄8 51⁄8 53⁄8

61⁄8 61⁄4 63⁄8 61⁄2 63⁄4

156

0.2812

33⁄4 37⁄8

0.7188

18.258

…

…

0.7500

19.050

149

0.7812

19.842

57⁄8 …

0.8125

20.638

0.8438 0.8750

98

130

…

222

91⁄4 …

235

53⁄8

137

91⁄4

235

…

55⁄8

143

91⁄2

241

248

93⁄4

248

…

57⁄8 6

149

…

93⁄4 …

152

…

…

…

…

61⁄8

156

97⁄8 10

254

21.433

…

…

…

…

61⁄8

156

10

254

22.225

…

…

…

…

61⁄8

156

10

254

0.9062

23.017

…

…

…

…

61⁄8

156

10

254

0.9375

23.812

…

…

…

…

61⁄8

156

0.9688

24.608

…

…

…

…

63⁄8

162

103⁄4 11

279

63⁄8 61⁄2 65⁄8 67⁄8 71⁄8 77⁄8

162

11

279

165

111⁄8

283

168

111⁄4 111⁄2 113⁄4 121⁄2

286

137

1

1.0000

25.400

…

…

…

…

11⁄32

1.0312

26.192

…

…

…

…

11⁄16 13⁄32 11⁄8 11⁄4

Overall Length

1.0625

26.988

…

…

…

…

1.0938

27.783

…

…

…

…

1.1250

28.575

…

…

…

…

1.2500

31.750

…

…

…

…

175 181 200

251

273

292 298 318


Machinery's Handbook 28th Edition 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


865

Decimal Equivalent



TWIST DRILLS

Size of Drill


866

Machinery's Handbook 28th Edition 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 (R2005) 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.



867

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) 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

Obsolete Drill Size 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.



868

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

101

108

114

162

168

175

182

189

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



869

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.



870

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.



871

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 56

Overall Length 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

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

All dimensions are in millimeters. Tolerances on diameters are given in Table 14.



872

3.80 4.00 4.20 4.50 4.80

16

46

18 20

49 52

22

55

24 26

58 62

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

28

66

31

70

34

74

37

79

40

84

40

84

14.00 14.50 15.00 15.50 16.00

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

Overall Length

9.50 9.80 10.00 10.20 10.50

Flute Length

62

Diameter

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

54

107

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 873 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 28th Edition COUNTERBORES

873

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


Machinery's Handbook 28th Edition COUNTERBORES

874

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

…

…

1⁄ 8

21⁄2

…

21⁄2

…

0.133

0.073

0.089

0.155

0.086

0.102

…

5⁄ 32

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 28th Edition STANDARD CARBIDE BORING TOOLS

875

Counterbore Sizes for Hex-head Bolts and Nuts.—Table 3a, page 1464, 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 (R2007) 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.



876

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 (R2007)

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

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

13⁄ 32

1⁄ 4

±.010

5⁄ 16

13⁄4

7⁄ 16

21⁄2

1⁄ 2

21⁄2

Tip Dimensions, Inches Rake Angle Deg.

Dim.Over Flat B

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 D

C

Tool Designation

D

C

SR-33

3⁄ 32

3⁄ 8

SR-55

5⁄ 32

5⁄ 8

SR-88

1⁄ 4

1

11⁄4

SR-34

3⁄ 32

1⁄ 2

SR-64

3⁄ 16

1⁄ 2

SR-810

1⁄ 4

11⁄4

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

…

…

…

A

B

C

SS-58

5⁄ 32

5⁄ 32

1

SS-610

3⁄ 16

3⁄ 16

SS-810

1⁄ 4

1⁄ 4

SS-1012

5⁄ 16

SS-1214

3⁄ 8

Tool Designation

D

C

Tool Designation

All dimensions are in inches. Tolerance on Length: Through 1 inch, + 1⁄32, − 0; over 1 inch, +1⁄16, −0.


Machinery's Handbook 28th Edition 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 (R2007)

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 (R2007) 6° ± 1° Tool Designation and Carbide Grade

G ± 1°

F Ref

W

1 D/2 ± to sharp corner 64

F ± 1°

B

T

1

6° ± 1°

C ± 16 L

H ± 0.010 6° ± 1° Along angle “G” Optional Design

SSE-58

45

SSC-610

60

SSE-610

45

SSC-810

60

SSE-810

45

SSC-1012

60 45

5⁄ 32

5⁄ 32

1

3⁄ 16

3⁄ 16

11⁄4

1⁄ 4

1⁄ 4

11⁄4

5⁄ 16

5⁄ 16

11⁄2

Side Cutting Edge Angle E,Deg.

End Cutting Edge Angle G ,Deg.

Shoulder Angle F ,Deg.

30

38

60

45

53

45

30

38

60

45

53

30

38

60

45

53

45

30

38

60

45

53

45

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

1⁄ 64

30

38

60

±.005

45

53

45

1⁄ 64

30

38

±.005

45

53

Shank Dimensions, Inches

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

R

Tip Dimensions, Inches Tip No.

T

W

L

2020

1⁄ 16

3⁄ 16

1⁄ 4

60

2040

3⁄ 32

3⁄ 16

5⁄ 16

45

2020

1⁄ 16

3⁄ 16

1⁄ 4

2060

3⁄ 32

1⁄ 4

3⁄ 8

1⁄ 4

3⁄ 8

5⁄ 16

3⁄ 8

1⁄ 32

30

38

60

±.010

45

53

45

1⁄ 32

30

38

60

2060

3⁄ 32

±.010

45

53

45

2080

3⁄ 32


877

SSE-1012

Length C

Shoulder Angle F, Deg.

60

Height B

End Cut. Edge Angle G, Deg.

SSC-58

Shank Dimensions, Inches Width A

Side Cut. Edge Angle E, Deg.

Boring Bar Angle, Deg. from Axis

Bor. Bar Angle from Axis, Deg.

Tool Designation

Tool Designation

12° ± 2° Along angle “G”

STANDARD CARBIDE BORING TOOLS

8° ± 2° 6° ± 1°

R D +0.0005 –0.0015


878

Table 6. ANSI Carbide-Tipped Square Boring Tools — ANSI B212.1-2002 (R2007) 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

E ± 1°

C ± 16

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



879

Table 7. ANSI Solid Carbide Round Boring Tools — ANSI B212.1-2002 (R2007) 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 Length Over Height C Flat B H

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

0.117

±0.005

30

38

60

45

0.149

0.117

±0.005

45

53

45

SRC-66

60

0.177

0.140

±0.005

30

38

60

SRE-66

45

5⁄ 8 5⁄ 8 3⁄ 4 3⁄ 4

0.149

SRE-55

0.177

0.140

±0.005

45

53

45

SRC-88

60

1

0.240

0.187

±0.005

30

38

60

SRE-88

45

0.187

±0.005

45

53

45

60

1 11⁄4

0.240

SRC-1010

0.300

0.235

±0.005

30

38

60

SRE-1010

45

5⁄ 32 5⁄ 32 3⁄ 16 3⁄ 16 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16

11⁄4

0.300

0.235

±0.005

45

53

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.


880

Machinery's Handbook 28th Edition TAPS

TAPS A tap is a mechanical device applied to make a standard thread on a hole. A range of tap pitch diameter (PD) limits, from which the user may select to suit local conditions, is available. Taps included in the ASME B94.9 standard are categorized according to type, style, size and chamfer, and blank design. General dimensions and tap markings are given in the standard ASME B94.9 Taps: Ground and Cut Threads (Inch and Metric Sizes) 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. The standard also gives the thread limits for taps with cut threads and ground threads. The tap thread limits and tolerances are given in Tables 2 to 4, tap dimensions for cut thread and ground thread are given in Tables 5a through 10. Pulley tap dimensions and tolerances are given in Table 12, straight and taper pipe thread tap dimensions and tolerances are given on Tables 13a and 13b, and thread limits for cut thread and ground thread taps are given in Tables 15 through 26a. Thread Form, Styles, and Types Thread Form.—The basic angle of thread between the flanks of thread measured in an axial plane is 60 degrees. The line bisecting this 60° angle is perpendicular to the axis of the screw thread. The symmetrical height of the thread form, h, is found as follows: h = 0.64951905P = 0.64951905 ---------------------------(1) n The basic pitch diameter (PD) is obtained by subtracting the symmetrical single thread height, h, from the basic major diameter as follows: Basic Pitch Diameter = D bsc – h (2) Dbsc = basic major diameter P =pitch of thread h =symmetrical height of thread n =number of threads per inch Types and Styles of Taps.—Tap type is based on general dimensions such as standard straight thread, taper and straight pipe, pulley, etc., or is based on purpose, such as thread forming and screw thread inserts (STI). Tap style is based on flute construction for cutting taps, such as straight, spiral, or spiral point, and on lobe style and construction for forming taps, such as straight or spiral. Straight Flute Taps: These taps have straight flutes of a number specified as either standard or optional, and are for general purpose applications. This standard applies to machine screw, fractional, metric, and STI sizes in high speed steel ground thread, and to machine screw and fractional sizes in high speed and carbon steel cut thread, with taper, plug, semibottom, and bottom chamfer.

BLANK Design 1

BLANK Design 3

BLANK Design 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.This standard applies to machine screw, fractional, metric, and STI sizes in high



881

speed steel ground thread, and to cut thread in machine screw and fractional sizes with plug, semibottom, and bottom chamfer.

Blank Design 1

Blank Design 2

Blank Design 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. This standard applies to machine screw and fractional sizes in high speed steel, ground thread, with plug chamfer.

Blank Design 1

Blank Design 2

Blank Design 3

Spiral Fluted Taps: These taps have right-hand helical flutes with a helix angle of 25 to 35 degrees. These features are designed to help draw chips from the hole or to bridge a keyway. This standard applies to machine screw, fractional, metric, and STI sizes in high speed steel and to ground thread with plug, semibottom, and bottom chamfer.

Blank Design 2

Blank Design 1

Blank Design 3

Fast Spiral Fluted Taps: These taps are similar to spiral fluted taps, except the helix angle is from 45 to 60 degrees.This standard applies to machine screw, fractional, metric, and STI sizes in high speed steel with plug, semibottom, and bottom chamfer.

Blank Design 1

Blank Design 2

Blank Design 3

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. This standard applies to machine screw, fractional, and metric sizes, in high speed steel, ground thread form, with plug, semibottom, and bottom entry taper.


882


Blank Design 1

Blank Design 2 Blank Design 3

Pulley Taps: These taps were originally designed for tapping line shaft pulleys by hand.Today, 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. This standard applies to fractional size and ground thread with plug and bottom chamfer.

Pipe Taps: These taps are used to produce standard straight or tapered pipe threads.This standard applies to fractional size in high speed steel, ground thread, to high speed steel and carbon steel in cut thread, and to straight pipe taps having plug chamfers and taper pipe taps.

Standard System of Tap Marking.—Ground thread taps specified in the U.S. customary system 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 specified in the U.S. customary system 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 of 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 inches, or the minimum tap pitch diameter limit is under basic pitch diameter by an even multiple of 0.0005 inches, the taps are marked “H” or “L”, respectively, followed by a limit number, determined as follows: PD – Basic PDH Limit number = Tap ---------------------------------------------0.0005 Basic PD – Tap PDL Limit number = ----------------------------------------------0.0005 The tap PD tolerances for ground threads are given in Table 2, column D; PD tolerances for cut threads are given in Table 3, column D. For standard taps, the PD limits for various H limit numbers are given in Table 20. The minimum tap PD equals the basic PD minus the



883

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 20. Tap Marking with H or L Limit Numbers Example 1: 3⁄8 -16 NC HS H1 Maximum tap PD = Basic PD + 0.0005 1 = 3--- –  0.64951904 × ------ + 0.0005 16 8  = = Minimum tap PD = = =

0.3344 + 0.0005 0.3349 Maximum tap PD – 0.0005 0.3349 – 0.0005 0.3344

Example 2: 3⁄8 -16 NC HS G L2 Minimum tap PD = Basic PD – 0.0010 1 = 3--- –  0.64951904 × ------ – 0.0010 16 8  = = Maximum tap PD = = =

0.3344 – 0.0010 0.3334 Minimum 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 from Table 2 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 the specifications in, 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. Left-Hand Taps: Taps with left-hand threads are marked “LEFT HAND” or “LH.” Example:3⁄8 -16 NC LH HS G H3.



884

Table 1. Thread Series Designations Standard Tap Marking

Product Thread Designation

Third Series

M

M

Metric Screw Threads—M Profile, with basic ISO 68 profile

M

MJ

Metric Screw Threads: MJ Profile, with rounded root of radius 0.15011P to 0.18042P (external thread only)

American National Standard References B1.13M B1.18M B1.121M

Class 5 interference-fit thread NC

NC5IF

Entire ferrous material range

B1.12

NC

NC5INF

Entire nonferrous material range

B1.12

NPS

NPSC

American Standard straight pipe threads in pipe couplings

B1.20.1

NPSF

NPSF

Dryseal American Standard fuel internal straight pipe threads

B1.20.3

NPSH

NPSH

American Standard straight hose coupling threads for joining to American Standard taper pipe threads

B1.20.7

NPSI

NPSI

Dryseal American Standard intermediate internal straight pipe threads

B1.20.3

NPSL

NPSL

American Standard straight pipe threads for loose-fitting mechanical joints with locknuts

B1.20.1

NPS

NPSM

American Standard straight pipe threads for free-fitting mechanical joints for fixtures

B1.20.1

ANPT

ANPT

Pipe threads, taper, aeronautical, national form

NPT

NPT

American Standard taper pipe threads for general use

NPTF

NPTF

Dryseal American Standard taper pipe threads

B1.20.3

NPTR

NPTR

American Standard taper pipe threads for railing joints

B1.20.1 B1.20.3

MIL-P-7105 B1.20.1

PTF

PTF

Dryseal American Standard pipe threads

PTF-SPL

PTF-SPL

Dryseal American Standard pipe threads

B1.20.3

STI

STI

Helical coil screw thread insertsfree running and screwlocking (inch series)

B18.29.1

N

UN

Constant-pitch series

B1.1

NC

UNC

Coarse pitch series

B1.1 B1.1

Unified Inch Screw Thread

NF

UNF

Fine pitch series

NEF

UNEF

Extra-fine pitch series

N

UNJ

Constant-pitch series, with rounded root of radius 0.15011P to 0.18042P (external thread only)

MIL-S-8879

NC

UNJC

Coarse pitch series, with rounded root of radius 0.15011P to 0.18042 P (external thread only)

B1.15 MIL-S-8879

NF

UNJF

Fine pitch series, with rounded root of radius 0.15011P to 0.18042P (external thread only)

B1.15 MIL-S-8879 B1.15 MIL-S-8879

B1.1

NEF

UNJEF

Extra-fine pitch series, with rounded root of radius 0.15011P to 0.18042P (external thread only)

N

UNR

Constant-pitch series, with rounded root of radius not less than 0.108P (external thread only)

B1.1

NC

UNRC

Coarse thread series, with rounded root of radius not less than 0.108P (external thread only)

B1.1

NF

UNRF

Fine pitch series, with rounded root of radius not less than 0.108P (external thread only)

B1.1

NEF

UNREF

Extra-fine pitch series, with rounded root of radius not less than 0.108P (external thread only)

B1.1

NS

UNS

Special diameter pitch, or length of engagement

B1.1



885

Table 2. Tap Thread Limits and Tolerances ASME B94.9-1999 Formulas for Unified Inch Screw Threads (Ground Thread) Max. Major Diameter = Basic Diameter + A Min. Major Diameter = Max. Maj. Dia. – B

Min. Pitch Diameter = Basic Diameter + C Max. Pitch Diameter = Min. Pitch Dia. + D

A =Constant to add = 0.130P for all pitches B =Major diameter tolerance= 0.087P for 48 to 80 tpi; 0.076P for 36 to 47 tpi; 0.065P for 4 to 35 tpi C =Amount over basic for minimum pitch diameter D =Pitch diameter tolerance C Threads per Inch

A

B

0 to 5⁄8

5⁄ to 8

80

0.0016

0.0011

0.0005

72

0.0018

0.0012

64

0.0020

0.0014

21⁄2

D Over 21⁄2

0 to 1

1 to 11⁄2

11⁄2 to 21⁄2

Over 21⁄2

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

56

0.0023

0.0016

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

48

0.0027

0.0018

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

44

0.0030

0.0017

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

40

0.0032

0.0019

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015 0.0015

36

0.0036

0.0021

0.0005

0.0010

0.0015

0.0005

0.0010

0.0010

32

0.0041

0.0020

0.0010

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015

28

0.0046

0.0023

0.0010

0.0010

0.0015

0.0005

0.0010

0.0010

0.0015 0.0015

24

0.0054

0.0027

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

20

0.0065

0.0032

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

0.0015

18

0.0072

0.0036

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

0.0015 0.0020

16

0.0081

0.0041

0.0010

0.0010

0.0015

0.0005

0.0010

0.0015

14

0.0093

0.0046

0.0010

0.0015

0.0015

0.0005

0.0010

0.0015

0.0020

13

0.0100

0.0050

0.0010

0.0015

0.0015

0.0005

0.0010

0.0015

0.0020

12

0.1080

0.0054

0.0010

0.0015

0.0015

0.0005

0.0010

0.0015

0.0020

11

0.0118

0.0059

0.0010

0.0015

0.0020

0.0005

0.0010

0.0015

0.0020

10

0.0130

0.0065

…

0.0015

0.0020

0.0005

0.0010

0.0015

0.0020

9

0.0144

0.0072

…

0.0015

0.0020

0.0005

0.0010

0.0015

0.0020

8

0.0162

0.0081

…

0.0015

0.0020

0.0005

0.0010

0.0015

0.0020

7

0.0186

0.0093

…

0.0015

0.0020

0.0010

0.0010

0.0020

0.0025

6

0.0217

0.0108

…

0.0015

0.0020

0.0010

0.0010

0.0020

0.0025

51⁄2

0.0236

0.0118

…

0.0015

0.0020

0.0010

0.0015

0.0020

0.0025

5

0.0260

0.0130

…

0.0015

0.0020

0.0010

0.0015

0.0020

0.0025

41⁄2

0.0289

0.0144

…

0.0015

0.0020

0.0010

0.0015

0.0020

0.0025

4

0.0325

0.0162

…

0.0015

0.0020

0.0010

0.0015

0.0020

0.0025

Dimensions are given in inches. The tables and formulas are used in determining the limits and tolerances for ground thread taps having a thread lead angle not in excess of 5°, unless otherwise specified. The tap major diameter must be determined from a specified tap pitch diameter, the maximum major diameter equals the minimum specified tap pitch diameter minus constant C, plus 0.64951904P plus constant A.

Maximum Major Diameter = Tap Pitch Diameter – C + 0.64951904P + A For intermediate pitches use value of next coarser pitch for C and D, use formulas for A and B. Lead Tolerance:± 0.0005 inch within any two threads not farther apart than 1 inch. Angle Tolerance: ± 20′ in half angle for 4 to 51⁄2 pitch; ± 25′ in half angle for 6 to 9 pitch, and ± 30′ in half angle for 10 to 80 pitch.



886

Table 3. Tap Thread Limits and Tolerances ASME B94.9-1999 Formulas for Unified Inch Screw Threads (Cut Thread) Min. Major Diameter = Basic Diameter + B + C Max. Major Diameter = Min. Maj. Dia. + A

Min. Pitch Diameter = Basic Diameter + B Max. Pitch Diameter = Min. Pitch Dia. + D

A =Major diameter tolerance B =Amount over basic for minimum pitch diameter C =A constant to add for major diameter: 20% of theoretical truncation for 2 to 5.5 threads per inch and 25% for 6 to 80 threads per inch D =Pitch diameter tolerance B D Diameter of Coarser than Tap (Inch) A 36 or more TPI 34 or less TPI N.F. N.F. and Finera 0 to 0.099 0.0015 0.0002 0.0005 0.0010 0.0010 0.10 to 0.249 0.0020 0.0002 0.0005 0.0015 0.0015 1⁄ to 3⁄ 0.0025 0.0005 0.0005 0.0020 0.0015 4 8 3⁄ to 5⁄ 0.0030 0.0005 0.0005 0.0025 0.0020 8 8 5⁄ to 3⁄ 0.0040 0.0005 0.0005 0.0030 0.0025 8 4 3⁄ to 1 0.0040 0.0010 0.0010 0.0030 0.0025 4 1 to 11⁄2 0.0045 0.0010 0.0010 0.0035 0.0030 11⁄2 to 2 0.0055 0.0015 0.0015 0.0040 0.0030 2 to 21⁄4 0.0060 0.0015 0.0015 0.0045 0.0035 21⁄4 to 21⁄2 0.0060 0.0020 0.0020 0.0045 0.0035 21⁄2 to 3 0.0070 0.0020 0.0020 0.0050 0.0035 over 3 0.0070 0.0025 0.0025 0.0055 0.0045 a Taps over 11⁄ inches with 10 or more threads per inch have tolerances for N.F. and finer. 2

Threads per Inch 2 21⁄2 3 31⁄2 4 41⁄2 5 51⁄2 6

C 0.0217 0.0173 0.0144 0.0124 0.0108 0.0096 0.0087 0.0079 0.0078

Threads per Inch 7 8 9 10 11 12 13 14 16

C 0.0077 0.0068 0.0060 0.0054 0.0049 0.0045 0.0042 0.0039 0.0034

Threads per Inch 18 20 22 24 26 27 28 30 32

C 0.0030 0.0027 0.0025 0.0023 0.0021 0.0020 0.0019 0.0018 0.0017

Threads per Inch 36 40 48 50 56 60 64 72 80

C 0.0015 0.0014 0.0011 0.0011 0.0010 0.0009 0.0008 0.0008 0.0007

Angle Tolerance Threads per Deviation in Deviation in Threads per Deviation in Deviation in Inch Half angle Half angle Inch Half angle Half angle 4 and coarser ± 30′ ± 45′ 10 to 28 ± 45′ ± 68′ 41⁄2 to 51⁄2 ± 35′ ± 53′ 30 and finer ± 60′ ± 90′ 6 to 9 ± 40′ ± 60′ Dimensions are given in inches. The tables and formulas are used in determining the limits and tolerances for cut thread metric taps having special diameter, special pitch, or both. For intermediate pitches use value of next coarser pitch. Lead Tolerance: ± 0.003 inch within any two threads not farther apart than 1 inch. Taps over 11⁄2 in. with 10 or more threads per inch have tolerances for N.F. and finer.



887

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 4. Tap Thread Limits and Tolerances ASME B94.9-1999 Formulas for Metric Thread (Ground Thread) Minimum major diameter = Basic diameter + W Maximum major diameter = Min. maj. dia. + X W X Y Z

= = = =

Maximum pitch diameter = Basic diameter + Y Minimum pitch diameter = Max. pitch dia. + Z

Constant to add with basic major diameter (W=0.08P) Major diameter tolerance Amount over basic for maximum pitch diameter Pitch diameter tolerance Y

P Pitch (mm) 0.30 0.35 0.40 0.45 0.50 0.60 0.70 0.75 0.80 0.90 1.00 1.25 1.50 1.75 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00

W (0.08P) 0.024 0.028 0.032 0.036 0.040 0.048 0.056 0.060 0.064 0.072 0.080 0.100 0.120 0.140 0.160 0.200 0.240 0.280 0.320 0.360 0.400 0.440 0.480

X 0.025 0.025 0.025 0.025 0.025 0.025 0.041 0.041 0.041 0.041 0.041 0.064 0.064 0.064 0.064 0.063 0.100 0.100 0.100 0.100 0.100 0.100 0.100

M1.6 to M6.3 0.039 0.039 0.039 0.039 0.039 0.052 0.052 0.052 0.052 0.052 0.065 0.065 0.065 … … … … … … … … … …

Over M6.3 to to M25 0.039 0.039 0.052 0.052 0.052 0.052 0.052 0.065 0.065 0.065 0.065 0.065 0.078 0.078 0.091 0.091 0.104 0.104 0.104 … … … …

Z Over M25 to M90 0.052 0.052 0.052 0.052 0.052 0.065 0.065 0.065 0.065 0.065 0.078 0.078 0.078 0.091 0.091 0.104 0.104 0.117 0.117 0.130 0.130 0.143 0.143

Over M90 0.052 0.052 0.052 0.052 0.065 0.065 0.065 0.078 0.078 0.078 0.091 0.091 0.091 0.104 0.104 0.117 0.130 0.130 0.143 0.143 0.156 0.156 0.156

M1.6 to M6.3 0.015 0.015 0.015 0.015 0.015 0.020 0.020 0.020 0.020 0.020 0.025 0.025 0.025 … … … … … … … … … …

Over M6.3 to to M25 0.015 0.015 0.015 0.020 0.020 0.020 0.020 0.025 0.025 0.025 0.025 0.031 0.031 0.031 0.041 0.041 0.041 0.041 0.052 0.052 … … …

Over M25 to M90 0.020 0.020 0.020 0.020 0.025 0.025 0.025 0.025 0.025 0.025 0.031 0.031 0.031 0.041 0.041 0.041 0.052 0.052 0.052 0.052 0.064 0.064 0.064

Over M90 0.020 0.020 0.025 0.025 0.025 0.025 0.025 0.031 0.031 0.031 0.031 0.041 0.041 0.041 0.041 0.052 0.052 0.052 0.064 0.064 0.064 0.064 0.064

Dimensions are given in millimeters. The tables and formulas are used in determining the limits and tolerances for ground thread metric taps having a thread lead angle not in excess of 5°, unless otherwise specified. They apply only to metric thread having a 60° form with a P/8 flat at the major diameter of the basic thread form. All calculations for metric taps are done using millimeters values as shown. When inch values are needed, they are translated from the three place millimeter tap diameters only after calculations are performed. The tap major diameter must be determined from a specified tap pitch diameter, the minimum major diameter equals the maximum specified tap pitch diameter minus constant Y, plus 0.64951905P plus constant W. Minimum major diameter = Max.tap pitch diameter – Y + 0.64951904P + W

For intermediate pitches use value of next coarser pitch. Lead Tolerance:± 0.013 mm within any two threads not farther apart than 25 mm. Angle Tolerance: ± 30′ in half angle for 0.25 to 2.5 pitch; ± 25′ in half angle for 2.5 to 4 pitch, and ± 20′ in half angle for 4 to 6 pitch.

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


888


with the letters “D” or “DU,” respectively, followed by a limit number. The limit number is determined as follows: Tap PD – Basic PD D Limit number = ----------------------------------------------0.0013 Basic PD – Tap PD DU Limit number = -----------------------------------------------0.0013 Example:M1.6 × 0.35 HS G D3 Maximum tap PD = = = = Minimum tap PD = = = M6 × 1 HS G DU4 Minimum tap PD

Basic PD + 0.0039 1.6 – ( 0.64951904 × 0.35 ) + 0.0039 1.3727 + 0.039 1.412 Maximum tap PD – 0.015 1.412 – 0.015 1.397

= = = = Maximum tap PD = = =

Basic PD – 0.052 6 – ( 0.64951904 × 1.0 ) – 0.052 5.350 – 0.052 5.298 Minimum tap PD + 0.025 5.298 + 0.025 5.323

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 1714. Actual size: The measured size of an element on an individual part. Allowance: A prescribed difference between the maximum material limits of mating parts. It is the minimum clearance or maximum interference between such parts. Basic Size: The size from which the limits are derived by application of allowance and tolerance. Bottom Top: A tap having a chamfer length of 1 to 2 pitches. 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: The gradual degrees in land height from cutting edge to heel on the chamfered portion of the land to provide radial clearance for 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. Classes 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. Concentric: Having a common center. Crest: The surface of the thread that joins the flanks of the thread and is farthest from the cylinder or cone from which the threads projects.



889

Cutter Sweep: The section removed by the milling cutter or the grinding wheel in entering or leaving a flute. Cutting Edge: The intersection of cutting edge and the major diameter in the direction of rotation for cutting which does the actual cutting. Core Diameter: The diameter of a circle that is tangent to the bottom of the flutes at a given point on the axis. Diameter, Major: It is the major cylinder on a straight thread. Diameter, Minor: It is the minor cylinder on a straight thread. Dryseal: A thread system used for both external and internal pipe threads applications designed for use where the assembled product must withstand high fluid or gas pressure without the use of sealing compound. Eccentric: Not having a common center. Eccentricity: One half of the total indicator variation (TIV) with respect to the tool axis. Entry Taper: The portion of the thread forming, where the thread forming is tapered toward the front to allow entry into the hole to be tapped. External Center: The pointed end on a tap. On bottom chamfered taps the point on the front end may be removed. Flank: The flank of a thread is the either surface connecting the crest with the root. 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 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, Spiral: A flute with uniform axial lead in a spiral path around the axis of a conical tap. Flute, Straight: A flute which forms a cutting edge lying in an axial plane. Flute, Tapered: A flute lying in a plane intersecting the tool axis at an angle. Full Indicator Movement (FIM): The total movement of an indicator where appropriately applied to a surface to measure its surface. Functional Size: The functional diameter of an external or internal thread is the PD 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. Heel: Edge of the land opposite the cutting edge. Height of Thread: The height of a thread is the distance, measured radially between the major and minor cylinders or cones, respectively. Holes, Blind: A hole that does not pass through the work piece and is not threaded to its full depth. Holes, Bottom: A blind hole that is threaded close to the bottom. 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. Internal Center: A countersink with clearance at the bottom, in one or both ends of a tool, which establishes the tool axis.



890

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. Tap Terms

Max. Tap Major Dia.

Min. Tap Major Dia.

Basic Major Dia.

Basic Height of Thread

No Relief Cutting Face

Relieved to Cutting Edge

Heel

Eccentric

Concentric

Tap Crest Basic Crest Angle of Thread Flank

Basic Pitch Dia.

Cutting Edge

Pitch

Basic Minor Dia. Base of Thread Basic Root Concentric Margin Eccentric Relief

Con-Eccentric Relief

Land

Negative Rake Angle

Zero Rake

Positive Rake Angle

Negative Rake

Radial

Positive Rake

Positive Hook

0 Deg. Hook

Negative Hook

Fig. 3. Tap Terms

Left Hand Cut: Rotation in a clockwise direction from cutting when viewed from the chamfered end of a tap. Length of Engagement: The length of engagement of two mating threads is the axial distance over which two mating threads are designed to contact. 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.



891

Tap Terms Overall Length, L Shank Length I

Thread Length I

Core Dia.

4

External Center

I

Land Width Flute

Driving Square Length

2

Truncated Center Optional Transitional Optional with Manufacturer BLANK Design 1 Overall Length, L

Thread Length I

Shank Length I4

Neck Length I1

I

External Center Neck Diameter d2

2


Truncated Neck to Shank Optional with manufacturer

BLANK Design 2 with Optional Neck Overall Length, L Shank Length I

Thread Length I

4

I

2


Truncated Center Optional

External Center

Transitional Optional with Manufacturer BLANK Design 2 (without optional neck) Overall Length Shank Thread Length Length I I4 Chamfer I5 Length

Point Dia.

Driving Square Length, I 2

Size of Square across flats

d3 Internal Center

90° Chamfer Angle

Shank Dia. d 1

Thread Lead Angle

BLANK Design 3

Fig. 1. Taps Terms

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. Neck: A section of reduced diameter between two adjacent portion of a tool. Pitch: The distance from any point on a screw thread to a corresponding point in the next thread, measured parallel to the axis and on the same side of the axis.


892


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. Point Diameter: Diameter at the cutting edge of the leading end of the chamfered section. Plug Tap: A tap having a chamfer length of 3 to 5 pitches. 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. Right Hand Cut: Rotation in clockwise direction for cutting when viewed from the chamfered end of a tap or die. Roots: The surface of the thread that joins the flanks of adjacent thread forms and is identical to cone from which the thread projects. Screw Thread: A uniform section produced by forming a groove in the form of helix on the external or the internal surface of a cylinder. Screw Thread Inserts (STI): Screw thread bushing coiled from diamond shape cross section wire. They are screwed into oversized tapped holes to size nominal size internal threads. Screw Thread Insert (STI) Taps: These taps are over the nominal size to the extent that the internal thread they produce will accommodate a helical coil screw insert, which at final assembly will accept a screw thread of the nominal size and pitch. Shank: The portion of the tool body by which it is held and driven. Shaving: The excessive removal of material from the product thread profile by the tool thread flanks caused by an axial advance per revolution less than or more than the actual lead in the tool. Size, Actual: Measured size of an element on an individual part.



893

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. Taper, Back: A gradual decrease in the diameter of the thread form on a tap from the chamfered end of the land towards the back, which creates a slight radial relief in the threads. Taper per Inch: The difference in diameter in one inch measured parallel to the axis. Taper Tap: A tap having a chamfer length of 7 to 10 pitches. Taper Thread Tap: A tap with tapered threads for producing a tapered internal thread. Thread, Angle of: The angle between the flanks of the thread measured in an axial plane. 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. Thread per Inch: The number of thread pitches in one inch of thread length. Tolerance: The total permissible variation of size or difference between limits of size. Total Indicator Variation (TIV): The difference between maximum and minimum indicator readings during a checking cycle. L

L I

I

I2

I2

d1

d1 BLANK Design 2

BLANK Design 1 L I

I2

a d1

BLANK Design 3



Over

To

Nominal Diameter, inch Machine Screw Size No. and Fractional Sizes

Decimal Equiv.

Nominal Metric Diameter

mm

inch

894

Table 5a. Standard Tap Dimensions (Ground and Cut Thread) ASME B94.9-1999 Nominal Diameter Range, inch

Tap Dimensions, inch Blank Design No.

Overall Length L

Thread Length I

Square Length I2

Shank Diameter d1

Size of Square a

0.052

0.065

0

(0.0600)

M1.6

0.0630

1

1.63

0.31

0.19

0.141

0.110

0.065

0.078

1

(0.0730)

M1.8

0.0709

1

1.69

0.38

0.19

0.141

0.110

0.078

0.091

2

(0.0860)

1

1.75

0.44

0.19

0.141

0.110 0.110

M2.0

0.0787

M2.2

0.0866 0.0984

1

1.81

0.50

0.19

0.141

…

1

1.88

0.56

0.19

0.141

0.110

0.104

3

(0.0990)

M2.5

0.104

0.117

4

(0.1120)

…

0.117

0.130

5

(0.1250)

M3.0

0.1182

1

1.94

0.63

0.19

0.141

0.110

0.130

0.145

6

(0.1380)

M3.5

0.1378

1

2.00

0.69

0.19

0.141

0.110

0.145

0.171

8

(0.1640)

M4.0

0.1575

1

2.13

0.75

0.25

0.168

0.131

0.171

0.197

10

(0.1900)

M4.5

0.1772

1

2.38

0.88

0.25

0.194

0.152

M5

0.1969

0.197

0.223

12

(0.2160)

…

…

1

2.38

0.94

0.28

0.220

0.165

0.223

0.260

1⁄ 4

(0.2500)

M6

0.2363

2

2.50

1.00

0.31

0.255

0.191

0.260

0.323

5⁄ 16

(0.3125)

M7

0.2756

2

2.72

1.13

0.38

0.318

0.238

M8

0.3150 0.3937

2

2.94

1.25

0.44

0.381

0.286

…

3

3.16

1.44

0.41

0.323

0.242

0.323

0.395

3⁄ 8

(0.3750)

M10

0.395

0.448

7⁄ 16

(0.4375)

…

0.448

0.510

1⁄ 2

(0.5000)

M12

0.4724

3

3.38

1.66

0.44

0.367

0.275

0.510

0.573

9⁄ 16

(0.5625)

M14

0.5512

3

3.59

1.66

0.50

0.429

0.322

0.573

0.635

5⁄ 8

(0.6250)

M16

0.6299

3

3.81

1.81

0.56

0.480

0.360

0.635

0.709

11⁄ 16

(0.6875)

M18

0.7087

3

4.03

1.81

0.63

0.542

0.406

0.709

0.760

3⁄ 4

(0.7500)

…

…

3

4.25

2.00

0.69

0.590

0.442

0.760

0.823

13⁄ 16

(0.8125)

M20

0.7874

3

4.47

2.00

0.69

0.652

0.489

0.823

0.885

7⁄ 8

(0.8750)

M22

0.8661

3

4.69

2.22

0.75

0.697

0.523


TAPS

0.091

Machinery's Handbook 28th Edition Table 5a. Standard Tap Dimensions (Ground and Cut Thread)(Continued) ASME B94.9-1999 Nominal Diameter Range, inch Over

To

0.885

0.948

0.948

1.010

Nominal Diameter, inch Machine Screw Size No. and Fractional Sizes 15⁄ 16


Tap Dimensions, inch

Decimal Equiv.

mm

inch

Blank Design No.

Overall Length L

Thread Length I

Square Length I2

Shank Diameter d1

Size of Square a

(0.9375)

M24

0.9449

3

4.91

2.22

0.75

0.760

0.570

1

(1.0000)

M25

0.9843

3

5.13

2.50

0.81

0.800

0.600

1.0630

3

5.13

2.50

0.88

0.896

0.672

…

3

5.44

2.56

0.88

0.896

0.672

1.1811

3

5.44

2.56

1.00

1.021

0.766

1.073

11⁄16

(1.0625)

M27

1.135

11⁄8

(1.1250)

…

1.135

1.198

13⁄16

(1.1875)

M30

1.198

1.260

11⁄4

(1.2500)

…

1.260

1.323

15⁄16

(1.3125)

M33

1.323

1.385

13⁄8

(1.3750)

…

1.358

1.448

17⁄16

(1.4375)

M36

1.448

1.510

11⁄2

(1.5000)

…

1.510

1.635

15⁄8

(1.6250)

M39

1.635

1.760

13⁄4

(1.7500)

M42

1.6535

3

1.760

1.885

17⁄8

(1.8750)

…

…

3

1.885

2.010

2

(2.0000)

M48

1.8898

3

7.63

…

3

5.75

2.56

1.00

1.021

0.766

1.2992

3

5.75

2.56

1.06

1.108

0.831

…

3

6.06

3.00

1.06

1.108

0.831

1.4173

3

6.06

3.00

1.13

1.233

0.925

…

3

6.38

3.00

1.13

1.233

0.925

1.5353

3

6.69

3.19

1.13

1.305

0.979

7.00

3.19

1.25

1.430

1.072

7.31

3.56

1.25

1.519

1.139

3.56

1.38

1.644

1.233

TAPS

1.010 1.073

Special taps greater than 1.010 inch to 1.510 inch in diameter inclusive, having 14 or more threads per inch or 1.75- mm pitch and finer, and sizes over 1.510 inch in diameter with 10 or more threads per inch or 2.5- mm pitch and finer are made to general dimensions shown in Table 10. For standard ground thread tap limits see Table 20, and Table 21 for inch and Table 16 for metric. For cut thread tap limits Table 22 and 23. Special ground thread tap limits are determined by using the formulas shown in Table 2 for unified inch screw threads and Table 4 for metric M profile screw threads. Tap sizes 0.395 inch and smaller have an external center on the thread end (may be removed on bottom taps). Sizes 0.223 inch and smaller have an external center on the shank end. Sizes 0.224 inch through 0.395 inch have truncated partial cone centers on the shank end (of diameter of shank). Sizes greater than 0.395 inch have internal centers on both the thread and shank ends. For standard thread limits and tolerances see Table 17 for unified inch screw threads and Table 19 for metric threads. For runout tolerances of tap elements see Table 14. For number of flutes see Table 11.

895



896

Table 5b. Standard Tap Dimensions Tolerances (Ground and Cut Thread) ASME B94.9-1999 Nominal Diameter Range, inch Element Length overall, L

Length of thread, I

Length of thread, I2

Diameter of shank, d1

Size of square, a

Tolerance, inch

Over

To (inclusive)

Direction

Ground Thread

Cut Thread

0.5200

1.0100

±

0.0300

0.0300

1.0100

2.0000

±

0.0600

0.0600

0.0520

0.2230

±

0.0500

0.0500

0.2230

0.5100

±

0.0600

0.0600

0.5100

1.5100

±

0.0900

0.0900

1.5100

2.0000

±

0.1300

0.1300

0.0520

1.0100

±

0.0300

0.0300

1.0100

2.0000

±

0.0600

0.0600

0.0520

0.2230

−

0.0015

0.0040

0.2230

0.6350

−

0.0015

0.0050

0.6350

1.0100

−

0.0020

0.0050

1.0100

1.5100

−

0.0020

0.0070

1.5100

2.0000

−

0.0030

0.0070

0.0520

0.5100

−

0.0040

0.0040

0.5100

1.0100

−

0.0060

0.0060

1.0100

2.0000

−

0.0080

0.0080

Entry Taper Length.—Entry taper length is measured on the full diameter of the thread forming lobes and is the axial distance from the entry diameter position to the theoretical intersection of tap major diameter and entry taper angle. Beveled end threads provided on taps having internal center or incomplete threads retained when external center is removed. Whenever entry taper length is specified in terms of number of threads, this length is measured in number of pitches, P. 1 Bottom length = 1 ∼ 2 --- pitches 2 Plug length = 3 ∼ 5 pitches Entry diameter measured at the thread crest nearest the front of the tap, is an appropriate amount smaller than the diameter of the hole drilled for tapping. L I

I1

I4

L I

2

I

I2

a +0.000

d 1 -0.032 BLANK Design 2 with Optional Neck

BLANK Design 3

Optional Neck and Optional Shortened Thread Length, Ground and Cut Thread (Table 6)



Table 6. Optional Neck and Optional Shortened Thread Length (Tap Dimensions, Ground and Cut Thread) ASME B94.9-1999 Nominal Diameter, inch

Nominal Diameter, inch Machine Screw Size No. and Fractional Sizes

0.104 0.117 0.130 0.145 0.171 … 0.197 0.223

0.117 0.130 0.145 0.171 0.197 … 0.223 0.260

4 5 6 8 10 … 12 1⁄ 4

0.323 … 0.395

5⁄ 16

0.260 … 0.323 0.395

0.448

0.448

0.510

0.510

0.573

0.573

0.635

0.635

0.709

0.709

0.760

0.760

0.823

0.823

0.885

0.885 0.948

0.948 1.010

… 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1

Decimal Equiv.


Tap Dimensions, inch Square Length I2

Shank Diameter d1

Size of Square a

0.19 0.19 0.19 0.25 0.25 … 0.28 0.31

0.141 0.141 0.141 0.168 0.194 … 0.220 0.255

0.110 0.110 0.110 0.131 0.152 … 0.165 0.191

0.44 … 0.50

0.38 … 0.44

0.318 … 0.381

0.238 … 0.286 0.242

Overall Length L

Thread Length I

Neck Length I1

mm

inch

Blank Design No.

(0.2160) (0.2500)

M3.0 M3.5 M4.0 M4.5 M5.0 … M6.0

0.1181 0.1378 0.1575 0.1772 0.1969 … 0.2362

1 1 1 1 1 … 1 2

1.88 1.94 2.00 2.13 2.38 … 2.38 2.50

0.31 0.31 0.38 0.38 0.50 … 0.50 0.63

0.25 0.31 0.31 0.38 0.38 … 0.44 0.38

(0.3125) … (0.3750)

M7.0 M8.0 M10.0

0.2756 0.3150 0.3937

2 … 2

2.72 … 2.94

0.69 … 0.75

(0.1120) (0.1250) (0.1380) (0.1640) (0.1900)

(0.4375)

…

…

3

3.16

0.88

0.50

0.41

0.323

(0.5000)

M12.0

0.4724

3

3.38

0.94

…

0.44

0.367

0.275

(0.5625)

M14.0

0.5512

3

3.59

1.00

…

0.50

0.429

0.322

(0.6250)

M16.0

0.6299

3

3.81

1.09

…

0.56

0.480

0.360

(0.6875)

M18.0

0.7087

3

4.03

1.09

…

0.63

0.542

0.406

(0.7500)

…

…

3

4.25

1.22

…

0.69

0.590

0.442

(0.8125)

M20.0

0.7874

3

4.47

1.22

…

0.69

0.652

0.489

(0.8750)

M22.0

0.8661

3

4.69

1.34

…

0.75

0.697

0.523

(0.9375) (1.0000)

M24.0 M25.0

0.9449 0.9843

3 3

4.91 5.13

1.34 1.50

… …

0.75 0.75

0.760 0.800

0.570 0.600

TAPS

Over

To (inclusive)

Thread length, I, is based on a length of 12 pitches of the UNC thread series. Thread length, I, is a minimum value and has no tolerance. When thread length, I, is added to neck length, I1, the total shall be no less than the minimum thread length, I.


897

Unless otherwise specified, all tolerances are in accordance with Table 5b. For runout tolerances, see Table 14. For number of flutes seeTable 11.


898

Table 7. Machine Screw and Fractional Size Ground Thread Dimensions for Screw Thread Insert (STI) Taps ASME B94.9-1999 Tap Dimensions, inch

Threads per inch Nominal Size (STI) 1 2 3 4 5 6 8

NC

NF

Blank Design No.

64 56 48 40 40 32 … 32

… 64 56 48 … … 40 36

1 1 1 1 1 1 1 1

Overall length, L

Thread Length, I

Square Length, I2

Shank Diameter, d1

Size of Square, a

Table 5a Blank Equivalent (Reference)

1.81 1.88 1.94 2.00 2.13 2.38 2.13 2.38

0.50 0.56 0.63 0.69 0.75 0.88 0.75 0.94

0.19 0.19 0.19 0.19 0.25 0.25 0.25 0.28

0.141 0.141 0.141 0.141 0.168 0.194 0.168 0.220

0.110 0.110 0.110 0.110 0.131 0.152 0.131 0.165

No. 3 No. 4 No. 5 No. 6 No. 8 No. 10 No. 8 No. 12

10

24

32

2

2.50

1.00

0.31

0.255

0.191

1⁄ 4

12

24

…

2

2.72

1.13

0.38

0.318

0.238

5⁄ 16

1⁄ 4

20

28

2

2.72

1.13

0.38

0.318

0.238

5⁄ 16

5⁄ 16

18

24

2

2.94

1.25

0.44

0.381

0.286

3⁄ 8

3⁄ 8

16

…

3

3.38

1.66

0.44

0.367

0.275

1⁄ 2

…

24

3

3.16

1.44

0.41

0.323

0.242

7⁄ 16

14

…

3

3.59

1.66

0.50

0.429

0.322

9⁄ 16

…

20

3

3.38

1.66

0.44

0.367

0.275

1⁄ 2

13

…

3

3.81

1.81

0.56

0.480

0.360

5⁄ 8

…

20

3

3.59

1.66

0.50

0.429

0.322

9⁄ 16

12

…

3

4.03

1.81

0.63

0.542

0.406

11⁄ 16

…

18

3

3.81

1.81

0.56

0.480

0.360

5⁄ 8

11

…

3

4.25

2.00

0.69

0.590

0.442

3⁄ 4

…

18

3

4.03

1.81

0.63

0.542

0.406

11⁄ 16

10

…

3

4.69

2.22

0.75

0.697

0.523

7⁄ 8

…

16

3

4.47

2.00

0.69

0.652

0.489

9

14

3

5.13

2.50

0.81

0.800

0.600

1 11⁄4

7⁄ 16

1⁄ 2

9⁄ 16

5⁄ 8

3⁄ 4

7⁄ 8

1 11⁄8 11⁄4 13⁄8 11⁄2

13⁄ 16

8

…

3

5.75

2.56

1.00

1.021

0.766

…

12, 14 NS

3

5.44

2.56

0.88

0.896

0.672

11⁄8

7

…

3

6.06

3.00

1.06

1.108

0.831

13⁄8

…

12

3

5.75

2.56

1.00

1.021

0.766

11⁄4

7

…

3

6.38

3.00

1.13

1.233

0.925

11⁄2

…

12

3

6.06

3.00

1.06

1.108

0.831

13⁄8

6

…

3

6.69

3.19

1.13

1.305

0.979

15⁄8

…

12

3

6.38

3.00

1.13

1.233

0.925

11⁄2

6

…

3

7.00

3.19

1.25

1.430

1.072

13⁄4

…

12

3

6.69

3.19

1.13

1.305

0.979

15⁄8

These threads are larger than nominal size to the extent that the internal thread they produce will accommodate a helical coil screw inserts, which at final assembly will accept a screw thread of the nominal size and pitch. For optional necks, refer to Table 6 using dimensions for equivalent blank sizes. Ground Thread Taps: STI sizes 5⁄16 inch and smaller, have external center on thread end (may be removed on bottom taps); sizes 10 through 5⁄16 inch, will have an external partial cone center on shank end, with the length of the cone center approximately 1⁄4 of the diameter of shank; sizes larger than 5⁄16 inch may have internal centers on both the thread and shank ends. For runout tolerances of tap elements, refer to Table 14 using dimensions for equivalent blank sizes. For number of flutes, refer to Table 11 using dimensions for equivalent blank sizes. For general dimension tolerances, refer to Table 5b using Table 5a equivalent blank size.



899

Table 8. Standard Metric Size Tap Dimensions for Screw Thread Insert (STI) Taps ASME B94.9-1999 Tap Dimensions, inch Nominal Size (STI)

Thread Pitch, mm Coarse Fine

Blank Design No.

Overall length, L

Thread Length, I

Square Length, I2

Shank Diameter, d1

Size of square, a

Blank Diameter

M2.2

0.45

…

1

1.88

0.56

0.19

0.141

0.110

No.4

M2.5

0.45

…

1

1.94

0.63

0.19

0.141

0.110

No.5

M3

0.50

…

1

2.00

0.69

0.19

0.141

0.110

No.6

M3.5

0.60

…

1

2.13

0.75

0.25

0.168

0.131

No.8

M4

0.70

…

1

2.38

0.88

0.25

0.194

0.152

No.10

M5

0.80

…

2

2.50

1.00

0.31

0.255

0.191

1⁄ 4

M6

1

…

2

2.72

1.13

0.38

0.318

0.238

5⁄ 16

M7

1

…

2

2.94

1.25

0.44

0.381

0.286

3⁄ 8

M8

1.25

1

2

2.94

1.25

0.44

0.381

0.286

3⁄ 8

M10

1.5

1.25

3

3.38

1.66

0.44

0.367

0.275

1⁄ 2

…

…

3

3.16

1.44

0.41

0.323

0.242

7⁄ 16

M12

1.75

1.5

3

3.59

1.66

0.50

0.429

0.322

9⁄ 16

M14

2

…

3

4.03

1.81

0.63

0.542

0.406

11⁄ 16

…

1.5

3

3.81

1.81

0.56

0.480

0.360

5⁄ 8

2

…

3

4.25

2.00

0.69

0.590

0.442

3⁄ 4

…

1.5

3

4.03

1.81

0.63

0.542

0.406

11⁄ 16

2.5

…

3

4.69

2.22

0.75

0.697

0.523

7⁄ 8

…

2.0

3

4.47

2.00

0.69

0.652

0.489

13⁄ 16

2.5

2.0

3

4.91

2.22

0.75

0.760

0.570

15⁄ 16

3

4.69

2.22

0.75

0.697

0.523

3

5.13

2.50

0.81

0.800

0.600

M16

M18

M20

…

1.25

1.25

1.25

7⁄ 8

M22

2.5

2.0

…

1.5

3

4.91

2.22

0.75

0.760

0.570

M24

3

…

3

5.44

2.56

0.88

0.896

0.672

11⁄8

…

2

3

5.13

2.50

0.88

0.896

0.672

11⁄16

M27

3

…

3

5.75

2.56

1.00

1.021

0.766

11⁄4

…

2

3

5.44

2.56

0.88

0.896

0.672

11⁄8

3.5

…

3

6.06

3.00

1.06

1.108

0.831

13⁄8

…

2

3

5.75

2.56

1.00

1.021

0.766

11⁄4

3.5

…

3

6.38

3.00

1.13

1.233

0.925

11⁄2

…

2

3

6.06

3.00

1.06

1.108

0.831

13⁄8

M36

4

3

2

3

6.69

3.19

1.13

1.305

0.979

15⁄8

M39

4

3

2

3

7.00

3.19

1.25

1.430

1.072

13⁄4

M30

M33

1 15⁄ 16

These taps are larger than nominal size to the extent that the internal thread they produce will accommodate a helical coil screw insert, which at final assembly will accept a screw thread of the nominal size and pitch. For optional necks, use Table 6 and dimensions for equivalent blank sizes. Ground Thread Taps: STI sizes M8 and smaller, have external center on thread end (may be removed on bottom taps); STI sizes M5 through M10, will have an external partial cone center on shank end, with the length of the cone center approximately 1⁄4 of the diameter of shank; STI sizes larger than M10 inch, may have internal centers on both the thread and shank ends. For runout tolerances of tap elements, refer to Table 14 using dimensions for equivalent blank sizes. For number of flutes, refer to Table 11 using dimensions for equivalent blank sizes. For general dimension tolerances, refer to Table 5b using Table 5a equivalent blank size.



900

Table 9. Special Extension Taps ASME B94.9-1999, Appendix (Tap Dimensions, Ground and Cut Threads) L

I4

I

I2

d1+0.003 Nominal Tap Size Fractional

Machine Screw

d1 Nominal Tap Size

Shank Length I4

Pipe

Fractional

Machine Screw

Pipe

Shank Length I4

…

0-3

…

0.88

11⁄2

…

…

3.00

…

4

…

1.00

15⁄8

…

3

3.13

…

5-6

…

1.13

13⁄4

…

…

3.13

…

8

…

1.25

17⁄8

…

…

3.25

…

10-12

1⁄ to 1⁄ incl. 16 4

1.38

2

…

…

3.25

1⁄ 4

14

…

1.50

21⁄8

…

…

3.38

5⁄ 16

…

…

1.56

21⁄4

…

…

3.38

3⁄ 8

…

…

1.63

23⁄8

…

…

3.50

7⁄ 16

…

3⁄ to 1⁄ incl. 8 2

1.69

21⁄2

…

…

3.50

1⁄ 2

…

…

1.69

25⁄8

…

…

3.63

9⁄ 16

…

3⁄ 4

1.88

23⁄4

…

…

3.63

5⁄ 8

…

1

2.00

27⁄8

…

…

3.75

11⁄ 16

…

…

2.13

3

…

…

3.75

3⁄ 4

…

11⁄4

2.25

31⁄8

…

…

3.88

13⁄ 16

…

11⁄2

2.38

31⁄4

…

…

3.88

7⁄ 8

…

…

2.50

33⁄8

…

4

4.00

…

…

2.63

31⁄2

…

…

4.00

1

15⁄ 16

…

…

2.63

35⁄8

…

…

4.13

11⁄8

…

2

2.75

33⁄4

…

…

4.13

11⁄4

…

21⁄2

2.88

37⁄8

…

…

4.25

13⁄8

…

…

3.00

4

…

…

4.25

Tolerances For shank diameter, d1 for I4 length Fractional, Inch

Machine Screw

Pipe, Inch

1⁄ to 5⁄ incl. 4 8

0 to 14 incl.

1⁄ to 1⁄ incl. 16 8

−0.003

1⁄ to 4

1 incl.

−0.004

11⁄4 to 4 incl.

−0.006

11⁄ to 16

11⁄2 incl.

15⁄8 to 4 incl.

… …

Tolerances

Unless otherwise specified, special extension taps will be furnished with dimensions and tolerances as shown for machine screw and fractional taps Tables 5a, 5b, and 6, and for pipe taps in Table 13a. Exceptions are as follows: Types of centers are optional with manufacturer. Tolerances on shank diameter d1 and I4 length as shown on the above Table 9. Shank runout tolerance in applies only to the I4 length shown on the aboveTable 9.



901

Table 10. Special Fine Pitch Taps, Short Series ASME B94.9-1999, Appendix (Taps Dimensions, Ground and Cut Threads) L I4

I

I2

a

d1

Nominal Diameter Range, inch

Nominal Fractional Diameter


Taps Dimensions, inches Overall Length

Thread Length

Square Length

Shank Diameter

Size of Square

Over

To

inch

mm

L

I

I2

d1

a

1.070

1.073

11⁄16

M27

4.00

1.50

0.88

0.8960

0.672

1.073

1.135

11⁄8

…

4.00

1.50

0.88

0.8960

0.672

1.135

1.198

13⁄16

M30

4.00

1.50

1.00

1.0210

0.766

1.198

1.260

11⁄4

…

4.00

1.50

1.00

1.0210

0.766

1.260

1.323

15⁄16

M33

4.00

1.50

1.00

1.1080

0.831

1.323

1.385

13⁄8

…

4.00

1.50

1.00

1.1080

0.831

1.385

1.448

17⁄16

M36

4.00

1.50

1.00

1.2330

0.925

1.448

1.510

11⁄2

…

4.00

1.50

1.00

1.2330

0.925

1.510

1.635

15⁄8

M39

5.00

2.00

1.13

1.3050

0.979

1.635

1.760

13⁄4

M42

5.00

2.00

1.25

1.4300

1.072

1.760

1.885

17⁄8

…

5.00

2.00

1.25

1.5190

1.139

1.885

2.010

2

M48

5.00

2.00

1.38

1.6440

1.233

2.010

2.135

21⁄8

…

5.25

2.00

1.44

1.7690

1.327

2.135

2.260

21⁄4

M56

5.25

2.00

1.44

1.8940

1.420

2.260

2.385

23⁄8

…

5.25

2.00

1.50

2.0190

1.514

2.385

2.510

21⁄2

…

5.25

2.00

1.50

2.1000

1.575

2.510

2.635

25⁄8

M64

5.50

2.00

1.50

2.1000

1.575

2.635

2.760

23⁄4

…

5.50

2.00

1.50

2.1000

1.575

2.760

2.885

27⁄8

M72

5.50

2.00

1.50

2.1000

1.575 1.575

2.885

3.010

3

…

5.50

2.00

1.50

2.1000

3.010

3.135

31⁄8

…

5.75

2.00

1.50

2.1000

1.575

3.135

3.260

31⁄4

M80

5.75

2.00

1.50

2.1000

1.575

3.260

3.385

33⁄8

…

5.75

2.00

1.50

2.1000

1.575

3.385

3.510

31⁄2

…

5.75

2.00

1.50

2.1000

1.575

3.510

3.635

35⁄8

M90

6.00

2.00

1.75

2.1000

1.575

3.635

3.760

33⁄4

…

6.00

2.00

1.75

2.1000

1.575

3.760

3.885

37⁄8

…

6.00

2.00

1.75

2.1000

1.575

3.885

4.010

4

M100

6.00

2.00

1.75

2.1000

1.575

Unless otherwise specified, special taps 1.010 inches to 1.510 inches in diameter, inclusive, have 14 or more threads per inch or 1.75 mm pitch and finer. Sizes greater than 1.510 inch in diameter with 10 or more threads per inch, or 2.5 mm pitch and finer will be made to the general dimensions shown above. For tolerances see Table 5b. For runout tolerances of tap elements, see Table 14.



902

Table 11. Standard Number of Flutes (Ground and Cut Thread) ASME B94.9-1999

13⁄4 2

(1.7500) (2.0000)

Nominal Metric Dia. mm M1.6 … M2.0 M 2.5 … M3.0 M3.5 M4.0 M4.5 M5 … M6 M7 M8 M10 … M12 M14 M16 … M20 … M24 … … M30 … … … … M36 … … … …

inch 0.0630 … 0.0787 0.0984 … 0.1181 0.1378 0.1575 0.1772 0.1969 … 0.2362 0.2756 0.3150 0.3937 … 0.4724 0.5512 0.6299 … 0.7874 … 0.9449 … … 1.1811 … … … … 1.4173 … … … …

TPI/Pitch UNC NC … 64 56 48 40 40 32 32 24 … 24 20 18 18 16 14 13 12 11 10 … 9 … 8 7 … 7 … 6 … … 6 … 5 41⁄2

UNF NF 80 72 64 56 48 44 40 36 32 … 28 28 24 24 24 20 20 18 18 16 … 14 … 12 12 … … 12 … 12 … … 12 … …

Straight Flutes mm 0.35 … 0.40 0.45 0.50 0.60 0.70 0.75 0.80 … 1.00 1.00 1.25 1.50 … 1.75 2.00 2.00 … 2.5 … 3.00 … 4.00 3.50 … … … … 4.00 … … … …

Standard 2 2 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 … 4 4 6 6 6 4 4 6 6 6

Optional … … 2 2 2 2 2 2⁄ 3 2⁄ 3 2⁄ 3 2⁄ 3 2⁄ 3 2⁄ 2 2⁄ 3 3 3 3 … … … … … … … … … … … … … … … … … …

Spiral Point Standard 2 2 2 2 2 2 2 2 2 2 2 2 2 2 3 3 3 3 3 3 … … … … … … … … … … … … … … …

Optional … … … … … … … … … … … 3 3 3 … … … … … … … … … … … … … … … … … … … … …

Spiral Point Only … … … … 2 2 2 2 2 2 2 2 2 2 3 3 … … … … … … … … … … … … … … … … … … …

Reg. Spiral Flute … … … … 2 2 2 2 2 2 2 3 (optional) 3 3 3 3 … … … … … … … … … … … … … … … … … … …

Fast Spiral Flute … … … 2 2 2 2 3 3 3 3 3 3 3 3 3 3 … … … … … … … … … … … … … … … … … …

For pulley taps seeTable 12. For taper pipe see Table 13a.For straight pipe taps see Table 13a.For STI taps, use number of flutes for blank size equivalent on Table 5a.For optional flutes Table 6.


TAPS

Machine Screw Size, Nom. Fractional Dia. inch 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⁄ (0.2500) 4 … 5⁄ (0.3125) 16 3⁄ (0.3750) 8 7⁄ (0.4375) 16 1⁄ (0.5000) 2 9⁄ (0.5625) 16 5⁄ (0.6250) 8 3⁄ (0.7500) 4 … 7⁄ (0.8750) 8 … 1 (1.0000) 11⁄8 (1.1250) … 11⁄4 (1.2500) … 13⁄8 (1.3750) … … 11⁄2 (1.5000)


903

Table 12. Pulley Taps, Fractional Size (High Speed Steel, Ground Thread) ASME B94.9-1999 L

I4 I

I2

I1

a d1

+0.03

d 1 -0.03

Threads per Dia. Inch Number of NC of Tap UNC Flutes 1⁄ 20 4 4 5⁄ 18 4 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4

Length d of Shank Dia. Size b Close of Thread Neck Square of Length, Length, Length Tolerance, Shank, Square, I I I d I a 1 2 4 1 1.00 0.38 1.50 0.255 0.191 0.31

Length Overall, L 6, 8 6, 8

1.13

0.38

0.38

1.56

0.318

16

4

6, 8, 10

1.25

0.38

0.44

1.63

0.381

0.238 0.286

14

4

6, 8

1.44

0.44

0.50

1.69

0.444

0.333

13

4

6, 8, 10, 12

1.66

0.50

0.56

1.69

0.507

0.380

11

4

6, 8,10,12

1.81

0.63

0.69

2.00

0.633

0.475

10

4

10,12

2.00

0.75

0.75

2.25

0.759

0.569

Tolerances for General Dimensions Diameter Range

Tolerance

Element

Diameter Range

Tolerance

Overall length, L

1⁄ to 3⁄ 4 4

±0.06

Shank Diameter, d1a

1⁄ to 1⁄ 4 2

−0.005

Thread length, I

1⁄ to 3⁄ 4 4

±0.06

Square length, I2

1⁄ to 3⁄ 4 4

±0.03

Size of Square, ab

1⁄ to 4 5⁄ to 8

−0.004 −0.006

Neck length, I1

1⁄ to 3⁄ 4 4

c

Length of close tolerance shank, I4

1⁄ to 3⁄ 4 4

Element

1⁄ 2 3⁄ 4

d

a Shank diameter, d , is approximately the same as the maximum major diameter for that size. 1 b

Size of square, a, is equal to 0.75d1 to the nearest 0.001 in. 1 is optional with manufacturer. d Length of close tolerance shank, I , is a min. length that is held to runout tolerances per Table 14. 4 c Neck length I

These taps are standard with plug chamfer in H3 limit only. All dimensions are given in inches. These taps have an internal center in thread end. For standard thread limits see Table 20. For runout tolerances of tap elements see Table 14. L

L I

I1

I

I2

I2 d1

d1

L I

I2 d1

Straight and Taper Pipe Tap Dimensions, Ground and Cut Thread (Tables 13a and 13b)



904

Table 13a. Straight and Taper Pipe Tap Dimensions (Ground and Cut Thread) ASME B94.9-1999 Number of Flutes Nominal Size, Inch a

Threads per Inch

Regular Thread

Interrupted Thread

Length Overall, L

Thread Length, I

Square Length, I2

Shank Diameter, d1

Size of Square, a

Length Optional Neck, I1

Ground Thread NPT, NPTF, ANPT

NPSC, NPSM, NPSF

Cut Thread only

NPT

NPSC, NPSM

27

4

…

2.13

0.69

0.38

0.3125

0.234

0.375

b

…

…

…

27

4

5

2.13

0.75

0.38

0.3125

0.234

…

b, c

d, e

f, g, h

…

27

4

5

2.13

0.75

0.38

0.4375

0.328

0.375

b, c

d, e

f, g, h

a

18

4

5

2.44

1.06

0.44

0.5625

0.421

0.375

b, c

d, e

f, g, h

a

18

4

5

2.56

1.06

0.50

0.7000

0.531

0.375

b, c

d, e

f, g, h

a

14

4

5

3.13

1.38

0.63

0.6875

0.515

…

b, c

d, e

f, g, h

a

14

5

5

3.25

1.38

0.69

0.9063

0.679

…

b, c

d

f, g, h

a

1

11 1⁄2

5

5

3.75

1.75

0.81

1.1250

0.843

…

b, c

d

f, g, h

a

1 1⁄4

11 1⁄2

5

5

4.00

1.75

0.94

1.3125

0.984

…

b, c

…

f, g, h

a

1 1⁄2

11 1⁄2

7

7

4.25

1.75

1.00

1.5000

1.125

…

b, i

…

f, h

…

2

11 1⁄2

7

7

4.25

1.75

1.13

1.8750

1.406

…

b, i

…

f, h

…

2 1⁄2

8

8

…

5.50

2.56

1.25

2.2500

1.687

…

…

…

h

…

3

8

8

…

6.00

2.63

1.38

2.6250

1.968

…

…

…

h

…

a Pipe taps 1⁄ inch are furnished with large size shanks unless the small shank is specified. 8 b High-speed ground thread 1⁄ to 2 inches including noninterrupted (NPT, NPTF, and ANPT). 16 c High-speed ground thread 1⁄ to 11⁄ inches including interrupted (NPT, NPTF, and ANPT). 8 4 d High-speed ground thread 1⁄ to 1 inches including noninterrupted (NPSC, and NPSM). 8 e High-speed cut thread 1⁄ to 1inches including noninterrupted (NPSC, and NPSM). 8 f High-speed cut thread 1⁄ to 1inches including noninterrupted (NPT). 8 g High-speed cut thread 1⁄ to 11⁄ inches including interrupted (NPT). 8 4 h Carbon cut thread 1⁄ to 11⁄ inches including interrupted (NPT). 8 4 i High-speed ground thread 11⁄ to 2 inches including interrupted (NPT). 2


TAPS

1⁄ 16 1⁄ 8 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4


905

Table 13b. Straight and Taper Pipe Taps Tolerances (Ground and Cut Thread) ASME B94.9-1999 Ground Thread Nominal Diameter Range, inch To Over (inclusive)

Element Length overall, L

Length of thread, I

Length of square, I2

Diameter of shank, d1

Size of square, a

Tolerances, inch

1⁄ 16

3⁄ 4

1 1⁄ 16

2 3⁄ 4

1

11⁄4

±0.094

11⁄2

±0.125

1 1⁄ 16

2 3⁄ 4 2 1⁄ 8

1⁄ 4

1

−0.002

11⁄4

−0.002

1⁄ 16 1⁄ 4

2 1⁄ 8 3⁄ 4

1

2

−0.006 −0.008

1⁄ 16

±0.031 ±0.063 ±0.063

±0.031 ±0.063 −0.002

−0.004

Cut Thread Nominal Diameter Range, inch To Over (inclusive)

Element

Tolerances, inch

1⁄ 8

3⁄ 4

1 1⁄ 8

3 3⁄ 4

1

11⁄4

±0.094

11⁄2

±0.125

1⁄ 8 1 1⁄ 8

3 3⁄ 4 3 1⁄ 2

3⁄ 4 1⁄ 8 1⁄ 4

3

−0.009

… 3⁄ 4

−0.004

1

3

−0.008

Length overall, L

Length of thread, I

Length of square, I2 Diameter of shank, d1

Size of square, a

±0.031 ±0.063 ±0.063

±0.031 ±0.063 −0.007

−0.006

All dimensions are given in inches. The first few threads on interrupted thread pipe thread pipe taps are left full. These taps have internal centers. For runout tolerances of tap elements see Table 14. Taps marked NPS are suitable for NPSC and NPSM. These taps have 2 to 31⁄2 threads chamfer, see Table 5a. Optional neck is for manufacturing use only. For taper pipe thread limit see Table 24a. For straight pipe thread limits see Tables 23a, 23b, and 23d.

Table 14. Runout and Locational Tolerance of Tap Elements ASME B94.9-1999 a, A-B

,

, d1, A-B

A

B , c, A-B Chamfer

, d2, A-B Pitch Diameter

, da, A-B Major Diameter

Range Sizes (Inclusive) Machine Screw Shank, d1 Major diameter, da Pitch Diameter, d2

Chamfer a, c

Square, a

Metric

#0 to 5⁄16

M1.6 to M8

11⁄ to 32

4

M10 to M100

#0 to

5⁄ 16

M1.6 to M8

11⁄ to 32

4

M10 to M100

#0 to

5⁄ 16

M1.6 to M8

11⁄ to 32

4

M10 to M100

#0 to 1⁄2

M1.6 to M12

17⁄ to 32

M14 to M100

4

#0 to 1⁄2

M1.6 to M12

17⁄ to 32

M14 to M100

4

Pipe, Inch 1⁄ 16 1⁄ to 4 8 1⁄ 16 1⁄ to 4 8 1⁄ 16 1⁄ to 4 8 1⁄ to 16 1⁄ 8 1⁄ to 4 8 1⁄ to 16 1⁄ 8 1⁄ to 4 8

Total Runout FIM, Inch Ground Thread

Cut Thread

Location, Inch

0.0060

0.0010

…

0.0080

0.0016

…

0.0050

0.0010

…

0.0080

0.0016

…

0.0050

0.0010

…

0.0080

0.0016

…

0.0040

0.0020

…

0.0060

0.0030

…

…

…

0.0060

…

…

0.0080

a Chamfer should preferably be inspected by light projection to avoid errors due to indicator contact points dropping into the thread groove.



906

Table 15. Tap Thread Limits: Metric Sizes, Ground Thread (M Profile Standard Thread Limits in Inches) ASME B94.9-1999 Major Diameter (Inches)

Pitch Diameter (Inches)

Nom. Dia mm

Pitch, mm

Basic

Min.

Max.

Basic

1.6 2 2.5 3 3.5 4 4.5 5 6 7 8 10 12 14 14 16 18 20 24 30 36 42 48

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 1.25 2 1.5 2.5 3 3.5 4 4.5 5

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 0.55118 0.62992 0.70870 0.78740 0.94488 1.18110 1.41732 1.65354 1.88976

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 0.55500 0.63622 0.71350 0.79528 0.95433 1.19213 1.42992 1.66772 1.90552

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 0.55600 0.63874 0.71450 0.79780 0.95827 1.19606 1.43386 1.71102 1.98819

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 0.51920 0.57878 0.67030 0.72346 0.86815 1.09161 1.31504 1.53846 1.76189

Limit # D

3

4

5

6 7 4 7 4 7 8 9 10

D # Limit

Limit #

Min.

Max.

D

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 0.52070f 0.58075 0.67180f 0.72543 0.87063 1.0942 1.3176 1.5415 1.7649

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 0.52171f 0.58236 0.67230f 0.72705 0.8722 1.0962 1.3197 1.5436 1.7670

… … … 5 … 6 … 7 8 … 9 10 11 … … … 7 … … … … … …

D # Limit Min. … … … 0.10278a,

Max.

b

0.14185a, b

… … … 0.10787a, b

… 0.17917b, c 0.21374b, c

0.14264a, b … 0.17996b, c 0.2147b, c

0.2864b, d 0.3593b, e 0.43209e … … … 0.58075 … … … … … …

0.2875b, d 0.3605b, e 0.43331e … … … 0.58236 … … … … … …

a Minimum and maximum major diameters are 0.00102 larger than shown. b Standard D limit for thread forming taps. c Minimum and maximum major diameters are 0.00154 larger than shown. d Minimum and maximum major diameters are 0.00205 larger than shown. e Minimum and maximum major diameters are 0.00256 larger than shown. f These sizes are intended for spark plug applications; use tolerances from Table 2 column D. All dimensions are given in inches. Not all styles of taps are available with all limits listed. For calculation of limits other than those listed, see formulas in Table 4.

Table 16. Tap Thread Limits: Metric Sizes, Ground Thread (M Profile Standard Thread Limits in Millimeters) ASME B94.9-1999 Size mm

Pitch

Major Diameter Basic Min. Max.

1.6 2 2.5 3 3.5 4 4.5 5 6 7 8 10 12 14 14 16 18

0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1.00 1.00 1.25 1.50 1.75 2.00 1.25 2.00 1.50

1.60 2.00 2.50 3.00 3.50 4.00 4.50 5.00 6.00 7.00 8.00 10.0 12.0 14.0 14.0 16.0 18.0

1.628 2.032 2.536 3.040 3.548 4.056 4.560 5.064 6.121 7.121 8.10 10.12 12.14 14.01 14.16 16.16 18.12

1.653 2.057 2.561 3.065 3.573 4.097 4.601 5.105 5.351 6.351 8.164 10.184 12.204 14.164 14.224 16.224 18.184

Basic 1.373 1.740 2.208 2.675 3.110 3.545 4.013 4.480 5.391 6.391 7.188 9.026 10.863 13.188 12.701 14.701 17.026

D#

3

4

5

6 4 7 4

Pitch Diameter D # Limit Min. Max. D# 1.397 1.764 2.232 2.699 3.142 3.577 4.045 4.512 5.391 6.391 7.222 9.073 10.910 7.222f 12.751 14.751 17.063f

1.412 1.779 2.247 2.714 3.162 3.597 4.065 4.532 5.416 6.416 7.253 9.104 10.941 7.253f 12.792 14.792 17.076f

… … … 5 … 6 … 7 8 … 9 10 11 … … … …

D # Limit Min. Max. … … … 2.725a,b … 3.603a,b … 4.551b,c 5.429b,c … 7.274b,d 9.125b,d 10.975b,e … … … …

… … … 2.740a,b … 3.623a,b … 4.571b,c 5.454b,c … 7.305b,d 9.156b,d 11.006b,e … … … …



907

Table 16. (Continued) Tap Thread Limits: Metric Sizes, Ground Thread (M Profile Standard Thread Limits in Millimeters) ASME B94.9-1999 Size mm 20 24 30 36 42 48

Pitch 2.50 3.00 3.50 4.00 4.50 5.00

Major Diameter Basic Min. Max. 20.0 20.20 20.263 24.0 24.24 24.34 30.0 30.28 30.38 36.0 36.32 36.42 42.0 42.36 42.46 48.0 48.48 48.58

Basic 18.376 22.051 27.727 33.402 39.077 44.103

D# 7 8 9 10

Pitch Diameter D # Limit Min. Max. D# 18.426 18.467 … 22.114 22.155 … 27.792 27.844 … 33.467 33.519 … 39.155 39.207 … 44.182 44.246 …

D # Limit Min. Max. … … … … … … … … … … … …

a Minimum and maximum major diameters are 0.026 larger than shown. b Standard D limit for thread forming taps. c Minimum and major diameters are 0.039 larger than shown. d Minimum and major diameters are 0.052 larger than shown. e Minimum and major diameters are 0.065 larger than shown. f These sizes are intended for spark plug applications; use tolerances from Table 2 column D. Notes for Table 16: Inch translations are listed in Table 15. Limit listed in Table 16 are the most commonly used in industry. Not all styles of taps are available with all limits listed. For calculations of limits other than listed, see formulas in Table 4

Table 17. Tap Size Recommendations for Class 6H Metric Screw Threads Nominal Diameter, mm 1.6 2 2.5 3 3.5 4 4.5 5 6 7 8 10 12 14 16 20 24 30 36

Pitch, mm

Recommended Thread Limit Number

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

D3 D3 D3 D3 D4 D4 D4 D4 D5 D5 D5 D6 D6 D7 D7 D7 D8 D9 D9

Internal Threads, Pitch Diameter Min. (mm) 1.373 1.740 2.208 2.675 3.110 3.545 4.013 4.480 5.350 6.350 7.188 9.206 10.863 12.701 14.701 18.376 22.051 27.727 33.402

Max. (mm) 1.458 1.830 2.303 2.775 3.222 3.663 4.131 4.605 5.500 6.500 7.348 9.206 11.063 12.913 14.913 18.600 22.316 28.007 33.702

Min. (inch)

Max. (inch)

0.05406 0.06850 0.08693 0.10537 0.12244 0.13957 0.15789 0.17638 0.201063 0.2500 0.28299 0.35535 0.42768 0.50004 0.57878 0.72346 0.86815 1.09161 1.31504

0.05740 0.07250 0.09067 0.10925 0.12685 0.14421 0.16264 0.18130 0.21654 0.25591 0.28929 0.36244 0.43555 0.50839 0.58713 0.73228 0.87858 1.10264 1.32685

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.

Table 18. Standard Chamfers for Thread Cutting Taps ASME B94.9-1999 Chamfer length Type of tap

Straight threads taps

Bottom Semibottom Plug Taper

Min.

Max.

1P 2P 3P 7P

2P 3P 5P 10P

Chamfer length Type of tap

Taper pipe taps

Min.

Max.

2P

31⁄2 P

P = pitch. The chamfered length is measured at the cutting edge and is the axial length from the point diameter to the theoretical intersection of the major diameter and the chamfer angle. Whenever chamfer length is specified in terms of threads, this length is measured in number of pitches as shown. The point diameter is approximately equal to the basic thread minor diameter.



908

Table 19. Taps Sizes for Classes 2B and 3B Unified Screw Threads Machine Screw, Numbered, and Fractional Sizes ASME B94.9-1999 Size

Threads per Inch NC NF UNC UNF

Recommended Tap For Class of Threada Class 2Bb

Class 3Bc

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 … 14NS 7 … 7 … 6 … 6 …

… 28 … 24 … 24 … 20 … 20 … 18 … 18 … 16 … 14 … 12 14NS … 12 … 12 … 12 … 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 G H6 G H6 G H6 G H6 G H6 G H8 G H6 G H8 G H6 G H8 G H6 G H8 G H6

1 1 1 11⁄8 11⁄8 11⁄4 11⁄4 13⁄8 13⁄8 11⁄2 11⁄2

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 Recommended taps are for cutting threads only and are not for roll-form threads. b Cut thread taps in sizes #3 to 11⁄ in. NC and NF, inclusive, may be used under all normal conditions 2 and in average materials for producing Class 2B tapped holes. c Taps suited for class 3B are satisfactory for class 2B threads.

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.



Table 20. Tap Thread Limits: Machine Screw Sizes, Ground Thread ASME B94.9-1999 (Unified and American National Thread Forms, Standard Thread Limits) Pitch Diameter Threads per Inch NC NF UNF UNF

Major Diameter

H1 limit

H2 limit

H3 limit

H4 limit

H5 limit

H6 limita

H7 limitb

H8 limitc

Basic

Min.

Max.

Basic

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

56 …

… … … … … … … …

0.0600 0.0730 0.0730 0.0860 0.0860 0.0990 0.0990 0.1120

0.0605 0.0736 0.0736 0.0866 0.0866 0.0999 0.0997 0.1134

0.0616 0.0750 0.0748 0.0883 0.0880 0.1017 0.1013 0.1153

0.0519 0.0629 0.0640 0.0744 0.0759 0.0855 0.0874 0.0958

0.0519 0.0629 0.064 0.0744 … … 0.0874 0.0958

0.0524 0.0634 0.0645 0.0749 … … 0.0879 0.0963

0.0524 0.0634 0.0645 0.0749 0.0764 0.086 0.0879 0.0963

0.0529 0.0639 0.0650 0.0754 0.0769 0.0865 0.0884 0.0968

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … …

… … … … … … …

0.0978d

0.0983d

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

… … … … … … … …

…

…

36

0.1120

0.1135

0.1156

0.0940

0.094

0.0945

0.0945

0.0950

…

…

…

…

0.0960d

0.0965d

…

…

…

…

…

…

4

…

48

…

0.1120

0.1129

0.1147

0.0985

0.0985

0.0990

0.0990

0.0995

…

…

…

…

0.1005d

0.1010d

…

…

…

…

…

…

5

40

…

…

0.1250

0.1264

0.1283

0.1088

0.1088

0.1093

0.1093

0.1098

…

…

…

…

0.1108d

0.1113d

…

…

…

…

…

…

5

…

44

…

0.1250

0.1262

0.1280

0.1102

…

…

0.1107

0.1112

…

…

…

…

0.1122d

0.1127d

…

…

…

…

…

…

6

32

…

…

0.1380

0.1400

0.1421

0.1177

0.1177

0.1182

0.1182

0.1187

…

…

0.1197a

0.1202a

…

…

6

…

40

…

0.1380

0.1394

0.1413

0.1218

0.1218

0.1223

0.1223

0.1228

…

…

0.1238a

0.1243a

…

…

8

32

…

…

0.1640

0.1660

0.1681

0.1437

0.1437

0.1442

0.1442

0.1447

0.1447 0.1452

…

…

0.1457a

0.1462a

…

…

8 10 10 12 12

… 24 … 24 …

36 … 32 … 28

… … … … …

0.1640 0.1900 0.1900 0.2160 0.2160

0.1655 0.1927 0.1920 0.2187 0.2183

0.1676 0.1954 0.1941 0.2214 0.2206

0.1460 0.1629 0.1697 0.1889 0.1928

… 0.1629 0.1697 … …

… 0.1634 0.1702 … …

0.1465 0.1634 0.1702 … …

0.1470 0.1639 0.1707 … …

… 0.1639 0.1707 0.1899 0.1938

… 0.1480a 0.1649 … 0.1717 … 0.1909 … 0.1948 …

0.1485a … … … …

… 0.1654 0.1722 0.1914 0.1953

0 1 1 2 2 3 3 4

… 64 … 56 48 … 40

4

80 … 72 … 64

0.1187 0.1192 …

… … 0.1644 0.1712 0.1904 0.1943

… 0.1644 0.1712 0.1904 0.1943

0.1207 0.1212 0.1222 0.1227 …

…

…

TAPS

NS

Size

…

0.1467 0.1472 0.1482 0.1487

… … … … … 0.1659 0.1659 0.1664 … … 0.1727 0.1727 0.1732 0.1742 0.1747 0.1919 … … … … 0.1958 … … … …

a Minimum and maximum major diameters are 0.0010 larger than shown. b Minimum and maximum major diameters are 0.0020 larger than shown. c Minimum and maximum major diameters are 0.0035 larger than shown. d Minimum and maximum major diameters are 0.0015 larger than shown.


909

General notes: Limits listed in above table are the most commonly used in the industry. Not all styles of taps are available with all limits listed. For calculation of limits other than those listed, see formulas and Table 2.


910

Table 21. Tap Thread Limits: Fractional Sizes, Ground Thread ASME B94.9-1999 (Unified and American National Thread Forms, Standard Thread Limits) Major Diameter

Pitch Diameter H1 limit

Size inch

NC NF UNC UNF NS

Basic

Min.

Max.

Basic

Min.

Max.

H2 limit Min.

Max.

H3 limit Min.

Max.

H4 limit

H5 limit

H6 limita

H8 limitb

H7 limit

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

…

…

0.2195a

0.2200a

…

…

…

…

…

Max. …

…

…

…

…

…

…

…

…

0.2784a

0.2789a

…

…

0.2794c

0.2799c

…

…

…

…

…

…

0.2884c

0.2889c

…

…

0.3364a

0.3369a

…

…

0.3374c

0.3379c

…

…

…

…

…

…

0.3509c

0.3514c

…

…

…

0.3931a

0.3936a

…

…

…

…

0.3946 0.3951

1⁄ 4

20

…

…

0.2500 0.2532 0.2565 0.2175 0.2175 0.2180 0.2180 0.2185 0.2185 0.2190

1⁄ 4

…

28

…

0.2500 0.2523 0.2546 0.2268 0.2268 0.2273 0.2273 0.2278 0.2278 0.2283 0.2283 0.2288

5⁄ 16

18

…

…

0.3125 0.3161 0.3197 0.2764 0.2764 0.2769 0.2769 02774 0.2774 0.2779

5⁄ 16

…

24

…

0.3125 0.3152 0.3179 0.2854 0.2854 0.2859 0.2859 0.2864 0.2864 0.2869 0.2869 0.2874

3⁄ 8

16

…

…

0.3750 0.3790 0.3831 0.3344 0.3344 0.3349 0.3349 0.3354 0.3354 0.3359

3⁄ 8

…

24

…

0.3750 0.3777 0.3804 0.3479 0.3479 0.3484 0.3484 0.3489 0.3489 0.3494 0.3494 0.3499

7⁄ 16

14

…

…

0.4375 0.4422 0.4468 0.3911

…

…

7⁄ 16

…

20

…

0.4375 0.4407 0.4440 0.4050

…

…

0.4060 0.4065

…

…

0.4070a

0.4075a

…

…

…

…

0.4085 0.4090

1⁄ 2

13

…

…

0.5000 0.5050 0.5100 0.4500 0.4500 0.4505 0.4505 0.4510 0.4510 0.4515

…

…

0.4520a

0.4525a

…

…

…

…

0.4535 0.4540

1⁄ 2

…

20

…

0.5000 0.5032 0.5065 0.4675 0.4675 0.4680 0.4680 0.4685 0.4685 0.4690

…

…

0.4695a

0.4700a

…

…

…

…

0.4710 0.4715

9⁄ 16

12

…

…

0.5625 0.5679 0.5733 0.5084

…

…

0.5094 0.5099

…

…

0.5104a

0.5109a

…

…

0.5114c

0.5119c

…

…

9⁄ 16

…

18

…

0.5625 0.5661 0.5697 0.5264

…

…

0.5269 0.5274 0.5274 0.5279

…

…

0.5284a

0.5289a

…

…

0.5294c

0.5299c

…

…

5⁄ 8

11

…

…

0.6250 0.6309 0.6368

0.566

…

…

0.5665

0.5675

…

…

0.5680a

0.5685a

…

…

0.5690c

0.5695c

…

…

5⁄ 8

…

18

…

0.6250 0.6286 0.6322 0.5889

…

…

0.5894 0.5899 0.5899 0.5904

…

…

0.5909a

0.5914a

…

…

0.5919c

0.5924c

…

…

11⁄ 16

…

…

11

0.6875 0.6934 0.6993 0.6285

…

…

…

…

…

…

…

…

…

…

…

…

11⁄ 16

…

…

16

0.6875 0.6915 0.6956 0.6469

…

…

3⁄ 4

10

…

…

0.7500 0.7565 0.7630 0.6850

…

…

3⁄ 4

…

16

…

0.7500 0.7540 0.7581 0.7094 0.7094 0.7099 0.7099 0.7104 0.7104 0.7109

7⁄ 8

9

…

…

0.8750 0.8822 0.8894 0.8028

…

…

0.3916 0.3921 0.3921 0.3926 …

…

…

…

0.567

0.567

…

…

…

…

…

…

…

0.6295 0.6300

…

…

0.6479 0.6484

…

…

…

…

…

…

…

…

…

…

0.6855 0.6860 0.6860 0.6865

…

…

0.6870

0.6875

…

…

0.6880d

0.6885d

…

…

…

…

0.7114a

0.1119a

…

…

0.7124d

0.4129d

…

…

…

…

0.8053

0.8058

…

…

…

…

…

…

…

…

0.8043 0.8048


TAPS

Min.

Machinery's Handbook 28th Edition Table 21. (Continued) Tap Thread Limits: Fractional Sizes, Ground Thread ASME B94.9-1999 (Unified and American National Thread Forms, Standard Thread Limits) Major Diameter

Pitch Diameter H1 limit

Size inch

NC NF UNC UNF NS

Basic

Min.

Max.

Basic

Min.

Max.

H2 limit Min.

Max.

H3 limit Min.

Max.

…

…

H4 limit Min.

Max.

H5 limit

H6 limita

H8 limitb

H7 limit

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

0.8301 0.8306

…

…

…

…

…

…

…

…

7⁄ 8

…

14

…

0.8750 0.8797 0.8843 0.8286

…

…

1

8

…

…

1.0000 1.0082 1.0163 0.9188

…

…

…

…

…

…

0.9203 0.9208

…

…

0.9213

0.9218

…

…

…

…

1

…

12

…

1.0000 1.0054 1.0108 0.9459

…

…

…

…

…

…

0.9474 0.9479

…

…

…

…

…

…

…

…

1

…

…

…

1.0000 1.0047 1.0093 0.9536

…

…

…

…

…

…

0.9551 0.9556

…

…

…

…

…

…

…

…

11⁄8

7

…

1.1250 1.1343 1.1436 1.0322

…

…

…

…

…

…

1.0337 1.0342

…

…

…

…

…

…

…

…

…

1.1250 1.1304 1.1358 1.0709

…

…

…

…

…

…

1.0724 1.0729

…

…

…

…

…

…

…

…

…

1.2500 1.2593 1.2686 1.1572

…

…

…

…

…

…

1.1587 1.1592

…

…

…

…

…

…

…

…

11⁄8 11⁄4

12 7

13⁄8

12 6

13⁄8 11⁄2

12 6

…

1.2500 1.2554 1.2608 1.1959

…

…

…

…

…

…

1.1974 1.1979

…

…

…

…

…

…

…

…

…

1.3750 1.3859 1.3967 1.2667

…

…

…

…

…

…

1.2682 1.2687

…

…

…

…

…

…

…

…

…

1.3750 1.3804 1.3858 1.3209

…

…

…

…

…

…

1.3224 1.3229

…

…

…

…

…

…

…

…

…

1.5000 1.5109 1.5217 1.3917

…

…

…

…

…

…

1.3932 1.3937

…

…

…

…

…

…

…

…

11⁄2

12

…

1.5000 1.5054 1.5108 1.4459

…

…

…

…

…

…

1.4474 1.4479

…

…

…

…

…

…

…

…

13⁄4

5

…

1.7500 1.7630 1.7760 1.6201

…

…

…

…

…

…

1.6216 1.6221

…

…

…

…

…

…

…

…

2

4.5

…

2.0000 2.0145 2.0289 1.8557

…

…

…

…

…

…

1.8572 1.8577

…

…

…

…

…

…

…

…

TAPS

11⁄4

0.8291 0.8296

a Minimum and maximum major diameters are 0.0010 larger than shown. b Minimum and maximum major diameters are 0.0035 larger than shown. c Minimum and maximum major diameters are 0.0020 larger than shown.


911

d Minimum and maximum major diameters are 0.0015 larger than shown. General notes: Limits listed in Table 21 are the most commonly used in the industry. Not all styles of taps are available with all limits listed. For calculation of limits other than those listed, see formulas and Table 2.


912

Table 22. Tap Thread Limits: Machine Screw Sizes, Cut Thread ASME B94.9-1999 Unified and American National Thread Forms, Standard Thread Limits Threads per Inch

Major Diameter

Pitch Diameter

Size

NC UNC

NF UNF

NS UNS

Basic

Min.

Max.

Basic

Min.

Max.

0

…

80

…

0.0600

0.0609

0.0624

0.0519

0.0521

0.0531

1

64

…

…

0.0730

0.0739

0.0754

0.0629

0.0631

0.0641

1

…

72

…

0.0730

0.0740

0.0755

0.0640

0.0642

0.0652

2

56

…

…

0.0860

0.0872

0.0887

0.0744

0.0746

0.0756

2

…

64

…

0.0860

0.0870

0.0885

0.0759

0.0761

0.0771

3

48

…

…

0.0990

0.1003

0.1018

0.0855

0.0857

0.0867

3

…

56

…

0.0990

0.1002

0.1017

0.0874

0.0876

0.0886

4

…

…

36

0.1120

0.1137

0.1157

0.0940

0.0942

0.0957

4

40

…

…

0.1120

0.1136

0.1156

0.0958

0.0960

0.0975

4

…

48

…

0.1120

0.1133

0.1153

0.0985

0.0987

0.1002

5

40

…

…

0.1250

0.1266

0.1286

0.1088

0.1090

0.1105

6

32

…

…

0.1380

0.1402

0.1422

0.1177

0.1182

0.1197

6

…

…

36

0.1380

0.1397

0.1417

0.1200

0.1202

0.1217

6

…

40

…

0.1380

0.1396

0.1416

0.1218

0.1220

0.1235

8

32

…

…

0.1640

0.1662

0.1682

0.1437

0.1442

0.1457

8

…

36

…

0.1640

0.1657

0.1677

0.1460

0.1462

0.1477

8

…

…

40

0.1640

0.1656

0.1676

0.1478

0.1480

0.1495

10

24

…

…

0.1900

0.1928

0.1948

0.1629

0.1634

0.1649

10

…

32

…

0.1900

0.1922

0.1942

0.1697

0.1702

0.1717

12

24

…

…

0.2160

0.2188

0.2208

0.1889

0.1894

0.1909

12

…

28

…

0.2160

0.2184

0.2204

0.1928

0.1933

0.1948

14

…

…

24

0.2420

0.2448

0.2473

0.2149

0.2154

0.2174

Angle Tolerance Threads per Inch

Half Angle

20 to 28

±0°45′

Full Angle ±0°65′

30 and finer

±0°60′

±0°90′

A maximum lead error of ±0.003 inch in 1 inch of thread is permitted. All dimensions are given in inches. Thread limits are computed from Table 3.



913

Table 23. Tap Thread Limits: Fractional Sizes, Cut Thread ASME B94.9-1999 (Unified and American National Thread Forms)

Size 1⁄ 8 5⁄ 32 3⁄ 16 3⁄ 16 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 1 1 1 11⁄8 11⁄8 11⁄4 11⁄4 13⁄8 13⁄8 11⁄2 11⁄2 13⁄4 2

Threads per Inch NC NF NS UNC UNF UNS … … … … 20 … 18 … 16 … 14 … 13 … 12 … 11 … 10 … 9 … 8 … … 7 … 7 … 6 … 6 … 5 4.5

… … … … … 28 … 24 … 24 … 20 … 20 … 18 … 18 … 16 … 14 … 12 … … 12 … 12 … 12 … 12 … …

40 32 24 32 … … … … … … … … … … … … … … … … … … … … 14 … … … … … … … … … …

Major Diameter

Pitch Diameter

Basic

Min.

Max.

Basic

Min.

Max.

0.1250 0.1563 0.1875 0.1875 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 0.7500 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

0.1266 0.1585 0.1903 0.1897 0.2532 0.2524 0.3160 0.3153 0.3789 0.3778 0.4419 0.4407 0.5047 0.5032 0.5675 0.5660 0.6304 0.6285 0.7559 0.7539 0.8820 0.8799 1.0078 1.0055 1.0049 1.1337 1.1305 1.2587 1.2555 1.3850 1.3805 1.5100 1.5055 1.7602 2.0111

0.1286 0.1605 0.1923 0.1917 0.2557 0.2549 0.3185 0.3178 0.3814 0.3803 0.4449 0.4437 0.5077 0.5062 0.5705 0.5690 0.6334 0.6315 0.7599 0.7579 0.8860 0.8839 1.0118 1.0095 1.0089 1.1382 1.1350 1.2632 1.2600 1.3895 1.3850 1.5145 1.5100 1.7657 2.0166

0.1088 0.13595 0.1604 0.1672 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 1.6201 1.8557

0.1090 0.13645 0.1609 0.1677 0.2180 0.2273 0.2769 0.2859 0.3349 0.3484 0.3916 0.4055 0.4505 0.4680 0.5089 0.5269 0.5665 0.5894 0.6855 0.7099 0.8038 0.8296 0.9198 0.9469 0.9546 1.0332 1.0719 1.1582 1.1969 1.2677 1.3219 1.3927 1.4469 1.6216 1.8572

0.1105 0.1380 0.1624 0.1692 0.2200 0.2288 0.2789 0.2874 0.3369 0.3499 0.3941 0.4075 0.4530 0.4700 0.5114 0.5289 0.5690 0.5914 0.6885 0.7124 0.8068 0.8321 0.9228 0.9494 0.9571 1.0367 1.0749 1.1617 1.1999 1.2712 1.3249 1.3962 1.4499 1.6256 1.8612

Threads per Inch

Half Angle

Full Angle

41⁄2 to 51⁄2 6 to 9 10 to 28 30 to 64

±0° 35′ ±0° 40′ ±0° 45′ ±0° 60′

±0° 53′ ±0° 60′ ±0° 68′ ±0° 90′

A maximum lead error of ±0.003 inch in 1 inch of thread is permitted. All dimensions are given in inches. Thread limits are computed from Table 3.



914

Table 23a. Straight Pipe Thread Limits: NPS, Ground Thread ANSI Straight Pipe Thread Form (NPSC, NPSM) ASME B94.9-1999 Major Diameter

Threads per Inch, NPS, NPSC, NPSM

Plug at Gaging Notch

Min. G

1⁄ 8

27

0.3983

1⁄ 4

18

0.5286

3⁄ 8

18

1⁄ 2 3⁄ 4

Nominal Size, Inches

1

Pitch Diameter

Max. H

Plug at Gaging Notch E

Min. K

Max. L

0.4022

0.4032

0.3736

0.3746

0.3751

0.5347

0.5357

0.4916

0.4933

0.4938

0.6640

0.6701

0.6711

0.6270

0.6287

0.6292

14

0.8260

0.8347

0.8357

0.7784

0.7806

0.7811

14

1.0364

1.0447

1.0457

0.9889

0.9906

0.9916

111⁄2

1.2966

1.3062

1.3077

1.2386

1.2402

1.2412

Formulas for NPS Ground Thread Tapsa Minor Dia.

Threads per Inch

A

B

Max. H

Max.

27

0.0296

0.0257

Major Diameter

Nominal Size

Min. G

1⁄ 8

H − 0.0010

(K + A) − 0.0010

M−B

18

0.0444

0.0401

1⁄ to 3⁄ 4 4

H − 0.0010

(K + A) − 0.0020

M−B

14

0.0571

0.0525

1

H − 0.0015

(K + A) − 0.0021

M−B

111⁄2

0.0696

0.0647

a In the formulas, M equals the actual measured pitch diameter.

All dimensions are given in inches. Maximum pitch diameter of tap is based upon an allowance deducted from the maximum product pitch diameter of NPSC or NPSM, whichever is smaller. Minimum pitch diameter of tap is derived by subtracting the ground thread pitch diameter tolerance for actual equivalent size. Lead tolerance: A maximum lead deviation pf ± 0.0005 inch within any two threads not farther apart than one inch. Angle Tolerance: 111⁄2 to 27 threads per inch, plus or minus 30 min. in half angle. Taps made to the specifications in Table 23a are to be marked NPS and used for NPSC and NPSM.

Table 23b. Straight Pipe Thread Limits: NPSF Ground Thread ANSI Standard Straight Pipe Thread Form (NPSF) ASME B94.9-1999 Major Diameter

Pitch Diameter

Min. K 0.2772

Max. L 0.2777

Minora Dia. Flat, Max. 0.004

1⁄ 16

Threads per Inch 27

Min. G 0.3008

Max. H 0.3018

Plug at Gaging Notch E 0.2812

1⁄ 8

27

0.3932

0.3942

0.3736

0.3696

0.3701

0.004

1⁄ 4

18

0.5239

0.5249

0.4916

0.4859

0.4864

0.005

3⁄ 8

18

0.6593

0.6603

0.6270

0.6213

0.6218

0.005

1⁄ 2

14

0.8230

0.8240

0.7784

0.7712

0.7717

0.005

3⁄ 4

14

1.0335

1.0345

0.9889

0.9817

0.9822

0.005


All dimensions are given in inches. a As specified or sharper.



915

Table 23c. ASME Standard Straight Pipe Thread Limits: NPSF Ground Thread Dryseal ANSI Standard Straight Pipe Thread Form (NPSF) ASME B94.9-1999 Formulas For American Dryseal (NPSF) Ground Thread Taps Major Diameter

Pitch Diameter


Min. G

Max. H

Min. K

Max. L

Max. Minor Dia.

1⁄ 16

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

1⁄ 8

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

1⁄ 4

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

3⁄ 8

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

1⁄ 2

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

3⁄ 4

H − 0.0010

K + Q − 0.0005

L − 0.0005

E−F

M−Q

Values to Use in Formulas Threads per Inch

E

F

M

Q

0.0251 0.0035 27 Actual measured Pitch diameter of 18 0.0052 0.0395 pitch diameter plug at gaging notch 14 0.0067 0.0533 All dimensions are given in inches. Lead Tolerance: A maximum lead deviation of ±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, inclusive.

Table 23d. ANSI Standard Straight Pipe Tap Limits: (NPS)Cut Thread ANSI Straight Pipe Thread Form (NPSC) 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

Maximum pitch diameter of tap is based on an allowance deducted from the maximum product pitch diameter of NPSC. Minimum pitch diameter of tap equals maximum pitch diameter minus the tolerance. All dimensions are given in inches. Lead Tolerance: ± 0.003 inch per inch of thread. Angle Tolerance: For all pitches, tolerance will be ± 45″ for half angle and ± 68″ for full angle. Taps made to these specifications are to be marked NPS and used for NPSC thread form. Taps made to the specifications in Table 23a are to be marked NPS and used for NPSC. As the American National Standard straight pipe thread form is to be maintained, the major and minor diameters vary with the pitch diameter. Either a flat or rounded form is allowable at both the crest and the root.



916

Table 24a. Taper Pipe Thread Limits (Ground and Cut Thread: Ground Thread For NPS, NPTF, and ANPT; Cut Thread for NPT only) 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

Threads per Inch 27 27 18 18 14 11.5 11.5 11.5 11.5 8 8 20

Gage Measurement Tolerance ± Projection Cut Ground b Thread Thread Inch 0.312 0.312 0.459 0.454 0.579 0.565 0.678 0.686 0.699 0.667 0.925 0.925

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0937 0.0937 0.0937 0.0937 0.0937 0.0937

0.0625 0.0625 0.0625 0.0625 0.0625 0.0625 0.0937 0.0937 0.0937 0.0937 0.0937 0.0937

Reference Dimensions

Taper per Inch on Diametera Cut Thread Ground Thread Min.

Max.

Min.

Max.

L 1, Lengthc

Tap Drill Size NPT, ANPT, NPTF d

0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0612 0.0612

0.0703 0.0703 0.0703 0.0703 0.0677 0.0677 0.0677 0.0677 0.0677 0.0677 0.0664 0.0664

0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0599 0.0612 0.0612

0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651 0.0651

0.1600 0.1615 0.2278 0.2400 0.3200 0.3390 0.4000 0.4200 0.4200 0.4360 0.6820 0.7660

C Q 7⁄ 16 9⁄ 16 45⁄ 64 29⁄ 32 19⁄64 131⁄64 123⁄32 23⁄16 239⁄64 315⁄16

a Taper is 0.0625 inch per 1.000 inch on diameter (1:16) (3⁄ inch per 12 inches). 4 b Distance small end of tap projects through L taper ring gage. 1 c Dimension, L , thickness on thin ring gage; see ASME B1.20.1 and B1.20.5. 1 d Given sizes permit direct tapping without reaming the hole, but only give full threads for approxi-

mate L1 distance. All dimensions are given in inches. Lead Tolerance: ± 0.003 inch per inch on cut thread, and ± 0.0005 inch per inch on ground thread. Angle Tolerance: ± 40 min. in half angle and 60 min. in full angle for 8 cut threads per inch; ± 45 min. in half angle and 68 min. in full angle for 111⁄2 to 27 cut threads per inch; ±25 min. in half angle for 8 ground threads per inch; and ±30 min. in half angle for 111⁄2 to 27 ground threads per inch.

Table 24b. 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 Column I Threads per Inch 27 18 14 111⁄2 8

Tap Flat Width at Major diameter Minor diameter Major diameter Minor diameter Major diameter Minor diameter Major diameter Minor diameter Major diameter Minor diameter

Column II

NPT—Cut and Ground Thread a ANPT—Ground Thread a Min.b 0.0014 … 0.0021 … 0.0027 … 0.0033 … 0.0048 …

NPTF

Ground Thread a

Max.

Min. b

Max.

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

a 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. b Minimum minor diameter flats are not specified and may be as sharp as practicable. All dimensions are given in inches.



917

Table 25. Tap Thread Limits for Screw Thread Inserts (STI), Ground Thread, Machine Screw, and Fractional Size ASME B94.9-1999 Nominal Screw Size STI 1 2 3 4 5 6 8 10 12

Threads Per Inch

Pitch Diameter Limits

Tap Major Diameter

2B

3B

Fractional Size STI

NC

NF

Min.

Max.

H limit

Min.

Max.

H limit

Min.

Max.

… … … … … … … … … … … … … … …

64 56 … 48 … 40 … 40 32 … 32 … 24 … 24

… … 64 … 56 … 48 … … 40 … 36 … 32 …

0.0948 0.1107 0.1088 0.1289 0.1237 0.1463 0.1409 0.1593 0.1807 0.1723 0.2067 0.2022 0.2465 0.2327 0.2725

0.0958 0.1117 0.1088 0.1289 0.1247 0.1473 0.1419 0.1603 0.1817 0.1733 0.2077 0.2032 0.2475 0.2337 0.2735

H2 H2 H2 H2 H2 H2 H2 H2 H3 H2 H3 H2 H3 H3 H3

0.0837 0.0981 0.0967 0.1131 0.1111 0.1288 0.1261 0.1418 0.1593 0.1548 0.1853 0.1826 0.2180 0.2113 0.2440

0.0842 0.0986 0.0972 0.1136 0.1116 0.1293 0.1266 0.1423 0.1598 0.1553 0.1858 0.1831 0.2185 0.2118 0.2445

H1 H1 H1 H1 H1 H1 H1 H1 H2 H1 H2 H1 H2 H2 H2

0.0832 0.0976 0.0962 0.1126 0.1106 0.1283 0.1256 0.1413 0.1588 0.1543 0.1848 0.1821 0.2175 0.2108 0.2435

0.0837 0.0981 0.0967 0.1131 0.1111 0.1288 0.1261 0.1418 0.1593 0.1548 0.1853 0.1826 0.2180 0.2113 0.2440

…

1⁄ 4

20

…

0.3177

0.3187

H3

0.2835

0.2840

H2

0.2830

0.2835

…

…

…

28

0.2985

0.2995

H3

0.2742

0.2747

H2

0.2737

0.2742

…

5⁄ 16

18

…

0.3874

0.3884

H4

0.3501

0.3506

H3

0.3496

0.3501

…

…

…

24

0.3690

0.3700

H3

0.3405

0.3410

H2

0.3400

0.3405

…

3⁄ 8

16

…

0.4592

0.4602

H4

0.4171

0.4176

H3

0.4166

0.4171

…

…

…

24

0.4315

0.4325

H3

0.4030

0.4035

H2

0.4025

0.4030

…

7⁄ 16

14

…

0.5333

0.5343

H4

0.4854

0.4859

H3

0.4849

0.4854

…

…

…

20

0.5052

0.5062

H4

0.4715

0.4720

H3

0.4710

0.4715

…

1⁄ 2

13

…

0.6032

0.6042

H4

0.5514

0.5519

H3

0.5509

0.5514

…

…

…

20

0.5677

0.5687

H4

0.5340

0.5345

H3

0.5335

0.5340

…

9⁄ 16

12

…

0.6741

0.6751

H4

0.6182

0.6187

H3

0.6117

0.6182

…

…

…

18

06374

0.6384

H4

0.6001

0.6006

H3

0.5996

0.6001

…

5⁄ 8

11

…

0.7467

0.7477

H4

0.6856

0.6861

H3

0.6851

0.6856

…

…

…

18

0.6999

0.7009

H4

0.6626

0.6631

H3

0.6621

0.6626

…

3⁄ 4

10

…

0.8835

0.8850

H5

0.8169

0.8174

H3

0.8159

0.8164

…

…

…

18

0.8342

0.8352

H4

0.7921

0.7926

H3

0.7916

0.7921

…

7⁄ 8

9

…

1.0232

1.0247

H5

0.9491

0.9496

H3

0.9481

0.9486

… … … …

… 1 … …

… 8 … …

14 … 12 14 NS

0.9708 1.1666 1.1116 1.0958

0.9718 1.1681 1.1126 1.0968

H4 H6 H6 H6

0.9234 1.0832 1.0562 1.0484

0.9239 1.0842 1.0572 1.0494

H3 H4 H4 H4

0.9224 1.0822 1.0552 1.0474

0.9229 1.0832 1.0562 1.0484

…

11⁄8

7

…

…

1.3151

1.3171

H6

1.2198

1.2208

H4

1.2188

1.2198

12

1.2366

1.2376

H6

1.1812

1.1822

H4

1.1802

1.1812

…

11⁄4

7

…

1.4401

1.4421

H6

1.3448

1.3458

H4

1.3438

1.3448

…

…

…

12

1.3616

1.3626

H6

1.3062

1.3072

H4

1.3052

1.3062

…

13⁄8

6

…

1.5962

1.5982

H8

1.4862

1.4872

H6

1.4852

1.4862

…

…

…

12

1.4866

1.4876

H6

1.4312

1.4322

H4

1.4302

1.4312

…

11⁄2

6

…

1.7212

1.7232

H8

1.6112

1.6122

H6

1.6102

1.6112

…

…

…

12

1.6116

1.6126

H6

1.5562

1.5572

H4

1.5552

1.5562

These taps are over the nominal size to the extent that the internal thread they produce will accommodate a helical coil screw insert, which at final assembly will accept a screw thread of the normal size and pitch.



918

Table 26a. Tap Thread Limits ASME B94.9-1999 for Screw Thread Inserts (STI), Ground Thread, Metric Size (Inch) Metric Size STI M2.5 M3 M3.5 M4 M5 M6 M7 M8 M10

M12

M14 M16 M18

M20

M22

M24 M27 M30 M33 M36

M39

Tap Major Diameter, inch

Tap Pitch Diameter Limits, inch Tolerance Class 4H

Tolerance Class 5H and 6H

Pitch, mm

Min.

Max.

H limit

Min.

Max.

H limit

Min.

Max.

0.45 0.5 0.6 0.7 0.8 1 1 1 1.25 1 1 1.25 1.25 1.5 1.75 1.5 2 1.5 2 1.5 2 2.5 1.5 2 2.5 1.5 2 2.5 2 3 2 3 2 3.5 2 3 2 3 4 2 3 4

0.1239 0.1463 0.1714 0.1971 0.2418 0.2922 0.3316 0.3710 0.3853 0.4497 0.4641 0.4776 0.5428 0.5564 0.5700 0.6351 0.6623 0.7139 0.7410 0.7926 0.8198 0.8470 0.8713 0.8985 0.9257 0.9500 0.9773 1.0044 1.0559 1.1117 1.1741 1.2298 1.2922 1.3750 1.4103 1.4931 1.5284 1.5841 1.6384 1.6465 1.7022 1.7565

0.1229 0.1453 0.1704 0.1955 0.2403 0.2906 0.3300 0.3694 0.3828 0.4481 0.4616 0.4751 0.5403 0.5539 0.5675 0.6326 0.6598 0.7114 0.7385 0.7901 0.8173 0.8445 0.8688 0.8960 0.9232 0.9475 0.9748 1.0019 1.0534 1.1078 1.1716 1.2259 1.2897 1.3711 1.4078 1.4892 1.5259 1.5802 1.6345 1.6440 1.6983 1.7516

1 1 1 2 2 2 2 2 2 2 2 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 6 6 4 6 6

0.1105 0.1314 0.1537 0.1764 0.2184 0.2629 0.3022 0.3416 0.3480 0.4203 0.4267 0.4336 0.5059 0.5123 0.5187 0.5911 0.6039 0.6698 0.6826 0.7485 0.7613 0.7741 0.8273 0.8401 0.8529 0.9060 0.9188 0.9316 0.9981 1.0236 1.1162 1.1417 1.2343 1.2726 1.3525 1.3907 1.4706 1.4971 1.5226 1.5887 1.6152 1.6407

0.1100 0.1309 0.1532 0.1759 0.2179 0.2624 0.3017 0.3411 0.3475 0.4198 0.4262 0.4331 0.5054 0.5118 0.5182 0.5906 0.6034 0.6693 0.6821 0.7480 0.7608 0.7736 0.8268 0.8396 0.8524 0.9055 0.9183 0.9311 0.9971 1.0226 1.1152 1.1407 1.2333 1.2716 1.3515 1.3797 1.4696 1.4961 1.5216 1.5877 1.6142 1.6397

2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 6 6 6 6 6 6 6 6 6 8 8 6 8 8

0.1110 0.1319 0.1542 0.1769 0.2187 0.2634 0.3027 0.3421 0.3485 0.4208 0.4272 0.4341 0.5064 0.5128 0.5192 0.5916 0.6049 0.6703 0.6836 0.7490 0.7623 0.7751 0.8278 0.8411 0.8539 0.9065 0.9198 0.9326 0.9991 1.0246 1.1172 1.1427 1.2353 1.2736 1.3535 1.3917 1.4716 1.4981 1.5236 1.5897 1.6162 1.6417

0.1105 0.1314 0.1537 0.1764 0.2184 0.2629 0.3022 0.3416 0.3480 0.4203 0.4267 0.4336 0.5059 0.5123 0.5187 0.5911 0.6044 0.6698 0.6831 0.7485 0.7618 0.7748 0.8273 0.8406 0.8534 0.9060 0.9193 0.9321 0.9981 1.0236 1.1162 1.1417 1.2343 1.2726 1.3525 1.3907 1.4706 1.4971 1.5226 1.5887 1.6152 1.6407

These taps are over the nominal size to the extent that the internal thread they produce will accommodate a helical coil screw insert, which at final assembly will accept a screw thread of the normal size and pitch. STI basic thread dimensions are determined by adding twice the single thread height (2 × 0.64952P) to the basic dimensions of the nominal thread size. Formulas for major and pitch diameters are presented in MIL-T-21309E.



919

Table 26b. Tap Thread Limits ASME B94.9-1999 for Screw Thread Inserts (STI), Ground Thread, Metric Size (mm) Metric Size STI M2.5 M3 M3.5 M4 M5 M6 M7 M8 M10

M12

M14 M16 M18

M20

M22

M24 M27 M30 M33 M36

M39

Tap Major Diameter, mm

Tap Pitch Diameter Limits, mm Tolerance Class 4H

Tolerance Class 5H and 6H

Pitch, mm

Min.

Max.

H limit

Min.

Max.

H limit

Min.

Max.

0.45 0.5 0.6 0.7 0.8 1 1 1 1.25 1 1 1.25 1.25 1.5 1.75 1.5 2 1.5 2 1.5 2 2.5 1.5 2 2.5 1.5 2 2.5 2 3 2 3 2 3.5 2 3 2 3 4 2 3 4

3.147 3.716 4.354 5.006 6.142 7.422 8.423 9.423 9.787 11.422 11.788 12.131 13.787 14.133 14.478 16.132 16.822 18.133 18.821 20.132 20.823 21.514 22.131 22.822 23.513 24.130 24.823 25.512 26.820 28.237 29.822 31.237 32.822 34.925 35.822 37.925 38.821 40.236 41.615 41.821 43.236 44.615

3.122 3.691 4.328 4.966 6.104 7.381 8.382 9.383 9.723 11.382 11.725 12.068 13.724 14.069 14.415 16.068 16.759 18.070 18.758 20.069 20.759 21.450 22.068 22.758 23.449 24.067 24.760 25.448 26.756 28.132 29.759 31.138 32.758 34.826 35.758 37.826 38.758 40.137 41.516 41.758 43.137 44.516

1 1 1 2 2 2 2 2 2 2 2 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 6 6 4 6 6

2.807 3.338 3.904 4.481 5.547 6.678 7.676 8.677 8.839 10.676 10.838 11.013 12.850 13.012 13.175 15.014 15.339 17.013 17.338 19.012 19.337 19.662 21.013 21.339 21.664 23.012 23.338 23.663 25.352 25.999 28.351 28.999 31.351 32.324 34.354 35.324 37.353 38.026 38.674 40.353 41.026 41.674

2.794 3.325 3.891 4.468 5.535 6.665 7.663 8.664 8.827 10.663 10.825 11.001 12.837 13.000 13.162 15.001 15.326 17.000 17.325 18.999 19.324 19.649 21.001 21.326 21.651 23.000 23.325 23.650 25.352 25.974 28.326 28.974 31.326 32.299 34.324 35.298 37.328 38.001 38.649 40.328 4 1.001 41.648

2 2 2 3 3 3 3 3 3 3 3 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 5 5 6 6 6 6 6 6 6 6 6 8 8 6 8 8

2.819 3.350 3.917 4.493 5.555 6.690 7.689 8.689 8.852 10.688 10.851 11.026 12.863 13.025 13.188 15.027 15.364 17.026 17.363 19.025 19.362 19.688 21.026 21.364 21.689 23.025 23.363 23.688 25.377 26.025 28.377 29.025 31.377 32.349 34.379 35.349 37.379 38.052 38.699 40.378 41.051 41.699

2.807 3.338 3.904 4.481 5.547 6.678 7.676 8.677 8.839 10.676 10.838 11.013 12.850 13.012 13.175 15.014 15.352 17.013 17.351 19.012 19.350 19.675 21.013 21.351 21.676 23.012 23.350 23.675 25.352 25.999 28.351 28.999 31.351 32.324 34.354 35.324 37.353 38.026 37.674 40.353 41.026 41.674

These taps are over the nominal size to the extent that the internal thread they produce will accommodate a helical coil screw insert, which at final assembly will accept a screw thread of the normal size and pitch. STI basic thread dimensions are determined by adding twice the single thread height (2 × 0.64952P) to the basic dimensions of the nominal thread size. Formulas for major and pitch diameters are presented in MIL-T-21309E.


920

Machinery's Handbook 28th Edition TAPS 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, 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. 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 1826.) 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



921

Table 27. 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.

A

B

C

41⁄4

17⁄8

23⁄8

47⁄8

21⁄8

23⁄4

51⁄2 6

23⁄8

31⁄8

21⁄2

31⁄2

61⁄2

211⁄16

313⁄16

67⁄8

41⁄16

71⁄4

213⁄16 3

41⁄4

79⁄16

31⁄8

47⁄16

1

77⁄8

31⁄4

45⁄8

11⁄8

81⁄2 9

39⁄16

415⁄16

33⁄4 4

1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

11⁄4 13⁄8 11⁄2 15⁄8 13⁄4

91⁄2 10

41⁄4

D

H

I

E

F

G

H

I

17⁄8

5⁄ 8 3⁄ 4 7⁄ 8 15⁄ 16

13⁄4 2

7⁄ 8

11⁄2

1 11⁄8

13⁄4 2

0.582

21⁄4 29⁄16

11⁄4

21⁄4

0.707

51⁄4

1⁄ 2 9⁄ 16 5⁄ 8 313⁄16 11⁄ 16 3⁄ 4 3⁄ 4 13⁄ 16 13⁄ 16 7⁄ 8 15⁄ 16

51⁄2

23⁄16 21⁄2 213⁄16

K 0.520 0.645

31⁄8

1

27⁄16

0.770

11⁄16

213⁄16 3

13⁄8

35⁄16

17⁄16

2 5⁄8

0.832

31⁄2

11⁄8

31⁄8

11⁄2

23⁄4

0.895

35⁄8

13⁄16

31⁄4

19⁄16

0.957

313⁄16

11⁄4

33⁄8

15⁄8

27⁄8 3

41⁄16

15⁄16

35⁄8

13⁄4

33⁄16

1.145

45⁄16

13⁄8

37⁄8

33⁄8

1.270

1

41⁄2

17⁄16

41⁄16

17⁄8 2

31⁄2

1.395

1

11⁄2

41⁄4

21⁄8

35⁄8

1.520

1

43⁄4 5

11⁄2

41⁄2

21⁄8

1.645

1.020

101⁄2 11

41⁄2

53⁄4 6

43⁄4

61⁄4

11⁄16

53⁄16

19⁄16

411⁄16

21⁄4

37⁄8 4

113⁄8

61⁄2

11⁄16

57⁄16

19⁄16

415⁄16

21⁄4

41⁄4

1.895

1.770

17⁄8 2

113⁄4

47⁄8 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 14

51⁄2

73⁄4

13⁄4

25⁄8

51⁄8

2.520

81⁄4

11⁄4

17⁄8 2

57⁄8

53⁄4

69⁄16 7

61⁄4

51⁄2

2.770

15

61⁄4

83⁄4

11⁄4

71⁄2

2

63⁄4

23⁄4 3

53⁄4

3.020

23⁄4 3

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 pitch = 1/number of threads per inch, and: minimum diameter = basic major diameter − pitch maximum diameter = minimum minor diameter + 0.05 × pitch



922

Table 28. 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 Types of Tap

No. of Taps in Set 2

3

Acme Thread Taps

4

5

2

3

SquareThreaded Taps

4

5

Order of Tap in Set 1st

D = full diameter of tap

A R + 0.65T

B R + 0.010

2d

D

A on 1st tap − 0.005

1st

R + 0.45T

R + 0.010

2d

R + 0.80T


3d

D

A on 2d tap − 0.005

1st

R + 0.40T

R + 0.010

2d

R + 0.70T


3d

R + 0.90T

A on 2d tap − 0.005

4th

D

A on 3d tap − 0.005

1st

R + 0.37T

R + 0.010

2d

R + 0.63T


3d

R + 0.82T

A on 2d tap − 0.005

4th

R + 0.94T

A on 3d tap − 0.005

5th

D

A on 4th tap − 0.005

1st

R + 0.67T

R

2d

D


1st

R + 0.41T

R

2d

R + 0.080T


3d

D

A on 2d tap − 0.005

1st

R + 0.32T

R

2d

R + 0.62T


3d

R + 0.90T

A on 2d tap − 0.005

4th

D

A on 3d tap − 0.005

1st

R + 0.26T

R

2d

R + 0.50T


3d

R + 0.72T

A on 2d tap − 0.005

4th

R + 0.92T

A on 3d tap − 0.005

5th

D

A on 4th tap − 0.005

C 1⁄ L 8 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 5 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 5 1⁄ L 5 1⁄ L 4 1⁄ L 8 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 5 1⁄ L 4 1⁄ L 8 1⁄ L 6 1⁄ L 5 1⁄ L 5 1⁄ L 4

to 1⁄6 L to 1⁄3 L to 1⁄6 L to 1⁄4 L to 1⁄3 L

to 1⁄3 L

to 1⁄4 L to 1⁄3 L to 1⁄6 L to 1⁄3 L to 1⁄6 L to 1⁄4 L to 1⁄3 L

to 1⁄3 L

to 1⁄4 L to 1⁄3L

Example: 1⁄2 -10 Acme 2G, pitch = 1⁄10 = 0.1 minimum diameter = 0.5 − 0.1 = 0.4



923

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 pitch = 1/number of threads per inch, and: minimum diameter = basic major diameter − 0.9 × pitch maximum diameter = minimum minor diameter + 0.05 × pitch 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 dia.)] − 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 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. Collapsible Taps.—The collapsing tap shown in the accompanying illustration is one of many different designs that are manufactured. These taps are often used in turret lathe practice in place of solid taps. When using this particular style of collapsing tap, the adjustable gage A is set for the length of thread required. When the tap has been fed to this depth, the gage comes into contact with the end of the work, which causes the chasers to collapse automatically. The tool is then withdrawn, after which the chasers are again expanded and locked in position by the handle seen at the side of the holder.

Collapsing Tap

Collapsible taps do not need to be backed out of the hole at the completion of the thread, reducing the tapping time and increasing production rates.


Machinery's Handbook 28th Edition STANDARD TAPERS

924

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. 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. See more on this subject, page 935. 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. 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 corre-



925

Table 1a. Morse Stub Taper Shanks

No. of Taper

Taper per Foota

Taper per Inchb

Small End of Plug, b D

Dia. End of Socket, a A

Shank Total Length, Depth, B C

1

0.59858

0.049882

0.4314

0.475

15⁄16

2

0.59941

0.049951

0.6469

0.700

111⁄16

17⁄16

3

0.60235

0.050196

0.8753

0.938

2

13⁄4

4

0.62326

0.051938

1.1563

1.231

23⁄8

5

0.63151

0.052626 Tang

1.6526

No. of Taper 1

Radius of Mill, G 3⁄ 16

2

7⁄ 32 9⁄ 32 3⁄ 8 9⁄ 16

3 4

Diameter, H 13⁄ 32 39⁄ 64 13⁄ 16 3 1 ⁄32 19 1 ⁄32

Plug Depth, P 7⁄ 8

1.748 3 Socket Min. Depth of Tapered Hole Drilled Reamed X Y 5⁄ 29⁄ 16 32

11⁄8

21⁄16 211⁄16

Tang Thickness, E

Length, F

13⁄ 64 19⁄ 64 25⁄ 64 33⁄ 64 3⁄ 4

5⁄ 16 7⁄ 16 9⁄ 16 11⁄ 16 15⁄ 16

Tang Slot Socket End to Tang Slot, M 25⁄ 32

11⁄16

15⁄32

17⁄64

11⁄4

13⁄8

15⁄16

11⁄16

15⁄ 16

17⁄16

19⁄16

11⁄2

13⁄16

113⁄16 115⁄16 17⁄8 17⁄16 5 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.

Width, N 7⁄ 32 5⁄ 16 13⁄ 32 17⁄ 32 25⁄ 32

Length, O 23⁄ 32 15⁄ 16

11⁄8 13⁄8 13⁄4

a These are basic dimensions. b These dimensions are calculated for reference only.

sponding 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



926

Table 1b. Morse Standard Taper Shanks

No. of Taper

Taper per Foot

Taper per Inch

Small End of Plug D

Diameter End of Socket A

Shank Length B

Depth S

Depth of Hole H 21⁄32

0

0.62460

0.05205

0.252

0.3561

211⁄32

27⁄32

1

0.59858

0.04988

0.369

0.475

29⁄16

27⁄16

2

0.59941

0.04995

0.572

0.700

31⁄8

215⁄16

239⁄64

3

0.60235

0.05019

0.778

0.938

37⁄8

311⁄16

31⁄4

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

7

0.62400

3.270

115⁄8

111⁄4

105⁄64

Plug Depth P 2

Thickness t 0.1562

0.05200 2.750 Tang or Tongue Length Radius T R 1⁄ 5⁄ 4 32

21⁄8

0.2031

29⁄16

0.2500

33⁄16

0.3125

41⁄16

0.4687

53⁄16

0.6250

71⁄4

0.7500

3⁄ 8 7⁄ 16 9⁄ 16 5⁄ 8 3⁄ 4 11⁄8 13⁄8

3⁄ 16 1⁄ 4 9⁄ 32 5⁄ 16 3⁄ 8 1⁄ 2 3⁄ 4

Dia. 0.235

Keyway Width Length W L 11⁄ 9⁄ 64 16

0.343

0.218

17⁄ 32 23⁄ 32 31⁄ 32 13 1 ⁄32

0.266

2

0.781

0.328 0.484 0.656

3⁄ 4 7⁄ 8 3 1 ⁄16 1 1 ⁄4 11⁄2 13⁄4 25⁄8

25⁄32

Keyway to End K 115⁄16 21⁄16 21⁄2 31⁄16 37⁄8 415⁄16 7

25⁄8 91⁄2 1.156 10 1.1250 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.

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 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.



927

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

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

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 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

Length F 0.19 0.25 0.31 0.38 0.44 0.56 0.63 0.69 0.75 1.13

Width N 0.141 0.172 0.203 0.218 0.266 0.328 0.484 0.578 0.656 0.781

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

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.



928

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

Socket Min. Depth of Hole K

Gage Line to Tang Slot M

Thickness E

Length F

Radius of Mill G

3.69

0.312

0.56

0.28

0.78

0.08

3.31

3.25

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

5

1.748

6.13

5.88

0.625

0.75

0.38

1.41

0.13

5.31

5.25

4.94

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

Diameter H

Radius J

Keeper Slot in Shank

Drill

Ream

3.06

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

0.266

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′

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.



929

Table 4. American National Standard Nose Key Drive with Keeper Key Slot, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

Taper

A(1)

C

Q

I′

I

R

S

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

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

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

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.



930

Table 5. American National Standard Nose Key Drive with Drawbolt, Self-Holding Tapers ANSI/ASME B5.10-1994 (R2002)

Sockets Drive Key

Drive Keyway

Depth S′

Gage Line to Front of Relief T

Dia. of Relief U

Depth of Relief V

Dia. of Draw Bolt Hole d

0.50 0.50 0.50 0.50 0.50 0.75 0.75 0.75 1.00 1.00 1.00

4.75 5.50 6.25 6.94 7.69 8.38 9.13 10.56 13.50 16.31 19.00

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

Screw Holes

No. of Taper

Dia. at Gage Line Aa

Center Line to Center of Screw D

UNF 2B Hole UNF 2A Screw D′

Width R″

Width R′

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

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 … …

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

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

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

0.91 1.03 1.03 1.53

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

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

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

2–41⁄2

5.31

4.00

2.03

10.38

0.50

3.010

0.812

3.005

800

14.38

2–41⁄2

5.31

4.00

2.03

13.44

0.50

4.010

1.062

4.005

1000

17.44

2–41⁄2

5.31

4.00

2.03

16.50

0.50

4.010

1.062

5.005

20.50

2–41⁄2

5.31

4.00

2.03

19.56

0.50

4.010

1.062

6.005

1200

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.



931

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)

Origin of Series Brown & Sharpe Taper Series

Morse Taper Series

3⁄ 4

Inch per Foot Taper Series

a See illustrations above Tables 2 through 5.

All dimensions given in inches.



932

Table 7b. American National Standard Plug and Ring Gages for the Self-Holding Taper Series ANSI/ASME B5.10-1994 (R2002)

No. of Taper

Tapera per Foot

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

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

Diametera at Gage Line A

Class X Gage

Class Y Gage

Class Z Gage

Diameter at Small End A′

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.



933

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



934

Table 10. Brown & Sharpe Taper Shanks

Dia. of Plug at Small End

Plug Depth, P

Keyway from End of Spindle

Length of Keywaya

Width of Keyway

Length Diame- Thickter of ness of of Arbor Arbor Arbor Tongue Tongue Tongue

Number of Taper

Taper per Foot (inch)

1c

.50200

.20000

15⁄ 16

2c

.50200

.25000

13⁄16

…

…

111⁄64

11⁄2

1⁄ 2

.166

1⁄ 4

.220

5⁄ 32

11⁄2

…

…

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

3c

4

5

.50200

.50240

.50160

D

.31250

.35000

.45000

B & Sb Standard

Mill. Mach. Standard

Miscell.

K

S

W

T

d

t

…

…

15⁄ 16

13⁄16

3⁄ 8

.135

3⁄ 16

.170

1⁄ 8

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

8

.50100

.75000

9

.50085

.90010

10

.51612

1.04465

11

.50100

1.24995

12

.49973

1.50010

…

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

…

…

…

…

…

…

…

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.



935

Table 11. Jarno Taper Shanks

Number of Taper

Length A

Length B

Diameter C

Diameter D

Taper per foot

2

11⁄8

1

0.20

0.250

0.600

3

15⁄8

11⁄2

0.30

0.375

0.600

4

23⁄16

2

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

19

913⁄16

91⁄2

1.90

2.375

0.600

2.00

2.500

0.600

20

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, page 944, 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.



936

Table 12. American National Standard Plug and Ring Gages for Steep Machine Tapers ANSI/ASME B5.10-1994 (R2002)

Class X Gage

Class Y Gage

Class Z Gage

Diameter at Small Enda A′

Tolerances for Diameter Ab No. of Taper

Taper per Foota (Basic)

Diameter at Gage Linea A

Length Gage Line to Small End L

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.



937

Table 13. Jacobs Tapers and Threads for Drill Chucks and Spindles

Taper Series

A

B

C

Taper per Ft.

Taper Series

A

B

C

Taper per Ft.

No. 0 No. 1 No. 2 No. 2a No. 3

0.2500 0.3840 0.5590 0.5488 0.8110

0.22844 0.33341 0.48764 0.48764 0.74610

0.43750 0.65625 0.87500 0.75000 1.21875

0.59145 0.92508 0.97861 0.97861 0.63898

No. 4 No. 5 No. 6 No. 33 …

1.1240 1.4130 0.6760 0.6240 …

1.0372 1.3161 0.6241 0.5605 …

1.6563 1.8750 1.0000 1.0000 …

0.62886 0.62010 0.62292 0.76194 …

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 – 24, drill diameters 0–3⁄8 , 1⁄16 –3⁄8 , or 5⁄64 –1⁄2 inch; size 1⁄2 –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

938

Table 1. Essential Dimensions of American National Standard Spindle Noses for Milling Machines ANSI B5.18-1972 (R2004) Slot and key location X .002 total M

Usable threads

45°

45°

Z

K

X See Note 3

D min

C

.015

H

J

.015

B

A gage

H

–X–

Z

L min section Z-Z X .0004 See note 4

F

F′ F G

Keyseat Key tight fit in slot when insert key is used

G

G′ Optional Key Construction

Preferred Key Construction


STANDARD TAPERS

Max variation from gage line

Machinery's Handbook 28th Edition Table 1. (Continued) Essential Dimensions of American National Standard Spindle Noses for Milling Machines ANSI B5.18-1972 (R2004)

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

All dimensions are given in inches. Tolerances:

STANDARD TAPERS

Dia.of Spindle B

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 4: Squareness of mounting face measured near mounting bolt hole circle.


939

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.


940

Table 2. Essential Dimensions of American National Standard Tool Shanks for Milling Machines ANSI B5.18-1972 (R2004)

Tap Drill Size for Draw-in Thread O

Dia.of Neck P

1.250

0.422 0.432

0.66 0.65

1.750

0.531 0.541

0.94 0.93

45

2.250

0.656 0.666

1.19 1.18

50

2.750

0.875 0.885

1.50 1.49

60

4.250

1.109 1.119

2.28 2.27

Size. No.

Distance from Rear of Flange to End of Arbor V

30

2.75

40

3.75

0.045 0.075

45

4.38

0.105 0.135

50

5.12

0.105 0.135

8.25

0.105 0.135

Size No.

Gage Dia.of Taper N

30 40

60

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

0.625–11

0.987 0.980

1.00

1.12

2.25

0.750–10

1.268 1.260

1.00

1.50

2.75

1.000–8

1.550 1.540

1.00

1.75

3.50

1.250–7

2.360 2.350

1.75

2.25

4.25

Distance from Gage Line to Bottom of C'bore Z

Clearance of Flange from Gage Diameter W

Tool Shank Centerline to Driving Slot X

Width of Driving Slot Y

0.045 0.075

0.640 0.625

0.635 0.645

2.50

0.890 0.875

0.635 0.645

3.50

0.05 0.07

0.650 0.655

1.140 1.125

0.760 0.770

4.06

0.05 0.07

0.775 0.780

1.390 1.375

1.010 1.020

4.75

0.05 0.12

1.025 1.030

2.400 2.385

1.010 1.020

7.81

0.05 0.12

1.307 1.312

Depth of 60° Center K

Diameter of C'bore L

0.05 0.07

0.525 0.530

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)



941

Table 3. American National Standard Draw-in Bolt Ends ANSI B5.18-1972 (R2004)

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 (R2004)



942

Table 5. Essential Dimensions for American National Standard Spindle Nose with Large Flange ANSI B5.18-1972 (R2004)

Size No.

Gage Diam. of Taper A

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

50A

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

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.



943

V-Flange Tool Shanks and Retention Knobs.—Dimensions of ANSI B5.18-1972 (R2004) standard tool shanks and corresponding spindle noses are detailed on pages 938 through 941, 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

0.030 0.060 0.090 0.090 0.120 0.200

1.500

5.683

1.375

2.04

4.250

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.



944

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 Tolerances

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

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

1.25

0.25

0.125

1.50

0.31

0.125

+0.000 −0.010

±0.040

+0.010 −0.005

45

0.08

0.16

50

0.10

0.20

0.468

1.44 1.42

60

0.14

0.30

0.500

2.14 2.06

±0.010

±0.010

±0.010

Tolerances

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.

Collets R8 Collet.—The dimensions in this figure are believed reliable. However, there are variations among manufacturers of R8 collets, especially regarding the width and depth of the keyway. Some sources do not agree with all dimensions in this figure. R8 collets are not always interchangeable.


Machinery's Handbook 28th Edition COLLETS

945

5 3 Keyway − ------ Wide × ------ Deep

7 ------ – 20 UNF Thread 16

32

32

0.9375

1.2500

16° 51'

0.9495 0.9490

1.25 0.9375

3.0625 4.00

0.125

All dimensions in inches.

Bridgeport R8 Collet Dimensions

Collets Styles 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 C

A C

A C B

7

B

8

A

B

B

9

A C

A C B

B

B

11

10

12

Collet Styles

Collets for Lathes, Mills, Grinders, and Fixtures Dimensions

Max. Capacity (inches)

Collet

Style

Bearing Diam., A

Length, B

Thread, C

Round

Hex

Square

1A 1AM 1B 1C 1J 1K 2A 2AB 2AM

1 1 2 1 1 3 1 2 1

0.650 1.125 0.437 0.335 1.250 1.250 0.860 0.750 0.629

2.563 3.906 1.750 1.438 3.000 2.813 3.313 2.563 3.188

0.640 × 26 RH 1.118 × 24 RH 0.312 × 30 RH 0.322 × 40 RH 1.238 × 20 RH None 0.850 × 20 RH 0.500 × 20 RH 0.622 × 24 RH

0.500 1.000 0.313 0.250 1.063 1.000 0.688 0.625 0.500

0.438 0.875 0.219 0.219 0.875 0.875 0.594 0.484 0.438

0.344 0.719 0.188 0.172 0.750 0.719 0.469 0.391 0.344



946

Collets for Lathes, Mills, Grinders, and Fixtures (Continued) Dimensions Collet 2B 2C 2H 2J 2L 2M 2NS 2OS 2S 2VB 3AM 3AT 3B 3C 3H 3J 3NS 3OS 3PN 3PO 3S 3SC 3SS 4C 4NS 4OS 4PN 4S 5C

Style 2 1 1 1 1 4 1 1 1 2 1 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Bearing Diam., A 0.590 0.450 0.826 1.625 0.950 2 Morse 0.324 0.299 0.750 0.595 0.750 0.687 0.875 0.650 1.125 2.000 0.687 0.589 0.650 0.599 1.000 0.350 0.589 0.950 0.826 0.750 1.000 0.998 1.250

Length, B 2.031 1.812 4.250 3.250 3.000 2.875 1.562 1.250 3.234 2.438 3.188 2.313 3.438 2.688 4.438 3.750 2.875 2.094 2.063 2.063 4.594 1.578 2.125 3.000 3.500 2.781 2.906 3.250 3.281

5M 5NS 5OS 5P 5PN 5SC 5ST 5V 6H 6K 6L 6NS 6R 7B 7 B&S 7P 7R 8H 8ST 8WN 9B 10L 10P 16C

5 1 1 1 1 1 1 1 1 1 1 1 1 4 4 1 6 1 1 1 4 1 1 1

1.438 1.062 3.500 0.812 1.312 0.600 1.250 0.850 1.375 0.842 1.250 1.312 1.375 7 B&S 7 B&S 1.125 1.062 1.500 2.375 1.250 9 B&S 1.562 1.500 1.889

3.438 4.219 3.406 3.687 3.406 2.438 3.281 3.875 4.750 3.000 4.438 5.906 4.938 3.125 2.875 4.750 3.500 4.750 5.906 3.875 4.125 5.500 4.750 4.516

20W 22J 32S

1 1 1

0.787 2.562 0.703

2.719 4.000 2.563

Max. Capacity (inches) Thread, C 0.437 × 26 RH 0.442 × 30 RH 0.799 × 20 RH 1.611 × 18 RH 0.938 × 20 RH 0.375 × 16 RH 0.318 × 40 RH 0.263 × 40 RH 0.745 × 18 RH 0.437 × 26 RH 0.742 × 24 RH 0.637 × 26 RH 0.625 × 16 RH 0.640 × 26 RH 1.050 × 20 RH 1.988 × 20 RH 0.647 × 20 RH 0.518 × 26 RH 0.645 × 24 RH 0.500 × 24 RH 0.995 × 20 RH 0.293 × 36 RH 0.515 × 26 RH 0.938 × 20 RH 0.800 × 20 RH 0.660 × 20 RH 0.995 × 16 RH 0.982 × 20 RH 1.238 × 20 RHa 1.238 × 20 RH 1.050 × 20 RH 0.937 × 18 RH 0.807 × 24 RH 1.307 × 16 RH 0.500 × 26 RH 1.238 × 20 RH 0.775 × 18 RH 1.300 × 10 RH 0.762 × 26 RH 1.178 × 20 RH 1.234 × 14 RH 1.300 × 20 RH 0.375 × 16 RH 0.375 × 16 RH 1.120 × 20 RH None 1.425 × 20 RH 2.354 × 12 RH 1.245 × 16 RH 0.500 × 13 RH 1.490 × 18 RH 1.495 × 20 RH 1.875 × 1.75 mm RHb 0.775 × 6–1 cm 2.550 × 18 RH 0.690 × 24 RH

Round 0.500 0.344 0.625 1.375 0.750 0.500 0.250 0.188 0.563 0.500 0.625 0.500 0.750 0.500 0.875 1.750 0.500 0.375 0.500 0.375 0.750 0.188 0.375 0.750 0.625 0.500 0.750 0.750 1.063

Hex 0.438 0.594 0.531 1.188 0.656 0.438 0.203 0.156 0.484 0.438 0.531 0.438 0.641 0.438 0.750 1.500 0.438 0.313 0.438 0.313 0.656 0.156 0.313 0.656 0.531 0.438 0.656 0.656 0.906

Square 0.344 0.234 1.000 0.438 1.000 0.344 0.172 0.125 0.391 0.344 0.438 0.344 0.531 0.344 0.625 1.250 0.344 0.266 0.344 0.266 0.531 0.125 0.266 0.531 0.438 0.344 0.531 0.531 0.750

0.875 0.875 0.750 0.625 1.000 0.375 1.063 0.563 1.125 0.625 1.000 1.000 1.125 0.500 0.500 0.875 0.875 1.250 2.125 1.000 0.750 1.250 1.250 1.625

0.750 0.750 0.641 0.531 0.875 0.328 0.906 0.484 0.969 0.531 0.875 0.859 0.969 0.406 0.406 0.750 0.750 1.063 1.844 0.875 0.641 1.063 1.063 1.406

0.625 0.625 0.516 0.438 0.719 0.266 0.750 0.391 0.797 0.438 0.719 0.703 0.781 0.344 0.344 0.625 0.625 0.875 1.500 0.719 0.531 0.875 0.875 1.141

0.563 2.250 0.500

0.484 1.938 0.438

0.391 1.563 0.344



947

Collets for Lathes, Mills, Grinders, and Fixtures (Continued) Dimensions Collet 35J 42S 50V 52SC 115 215 315 B3 D5 GTM J&L JC LB RO RO RO RO R8

Style 1 1 8 1 1 1 1 7 7 7 9 8 10 11 12 12 11 7

Bearing Diam., A 3.875 1.250 1.250 0.800 1.344 2.030 3.687 0.650 0.780 0.625 0.999 1.360 0.687 1.250 1.250 1.250 1.250 0.950

Length, B 5.000 3.688 4.000 3.688 3.500 4.750 5.500 3.031 3.031 2.437 4.375 4.000 2.000 2.938 4.437 4.437 2.938 4.000

Max. Capacity (inches) Thread, C 3.861 × 18 RH 1.236 × 20 RH 1.125 × 24 RH 0.795 × 20 RH 1.307 × 20 LH 1.990 × 18 LH 3.622 × 16 LH 0.437 × 20 RH 0.500 × 20 RH 0.437 × 20 RH None None None 0.875 × 16 RH 0.875 × 16 RH 0.875 × 16 RH 0.875 × 16 RH 0.437 × 20 RH

Round 3.500 1.000 0.938 0.625 1.125 1.750 3.250 0.500 0.625 0.500 0.750 1.188 0.500 1.125 0.800 1.125 0.800 0.750

Hex 3.000 0.875 0.813 0.531 0.969 1.500 2.813 0.438 0.531 0.438 0.641 1.000 0.438 0.969 0.688 0.969 0.688 0.641

Square 2.438 0.719 0.656 0.438 0.797 1.219 2.250 0.344 0.438 0.344 0.516 0.813 0.344 0.781 0.563 0.781 0.563 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. Additional dimensions of the R8 collet are given on page 944.

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)

L (mm)

A (mm)

C

16 20 25 32 ERA8 ERA11 ERA16 ERA20 ERA25 ERA32

25.50 29.80 35.05 43.70 8.50 11.50 17 21 26 33 41 41 52

40 45 52 60 13.5 18 27 31 35 40 46 39 60

4.5–16 5.5–20 5.5–25 9.5–32 0.5–5 0.5–7 0.5–10 0.5–13 0.5–16 2–20 3–26 26–30 5–34

… … … … 8° 8° 8° 8° 8° 8° 8° 8° 8°

ERA40 ERA50


Machinery's Handbook 28th Edition PORTABLE GRINDING TOOLS

948

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

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

Maximum Wheel Dimensions 9500 fpm 6500 fpm Diameter Thickness Diameter Thickness D T D T 21⁄2 4

1⁄ 2 3⁄ 4

4 5

1⁄ 2 3⁄ 4

8

1

8

1

6

2

…

…

8

11⁄2

…

…

8

2

…

…

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 28th 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.



950

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

1⁄ –20 2

0.4675

0.4649

1⁄ 16

9⁄ 16

5⁄ –16 8

0.5844

0.5812

3⁄ 32

11⁄ 16

3⁄ –16 4

0.7094

0.7062

3⁄ 32

11⁄ 16

Master Plug Gage

Pitch Dia. DG

LG

Taper per Footb

No.a

DM

LM

EG

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

0.48764 0.48764 0.56051 0.62409 0.74610

0.97861 0.97861 0.76194 0.62292 0.63898

0.7500 0.87500 1.000 1.000 1.21875

a Jacobs taper number. b Calculated from E

G, DG, LG for the master plug gage. 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



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

Nominal Hexagon

Min.

Max.

B

L Max.

H

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.


952

Machinery's Handbook 28th Edition 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.

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.


Machinery's Handbook 28th Edition MOUNTED WHEELS AND POINTS

953

Fig. 1b. Standard Shapes and Sizes of Mounted Wheels and Points ANSI B74.2-1982


Machinery's Handbook 28th Edition MOUNTED WHEELS AND POINTS

954

Table 1. Shapes and Sizes of Mounted Wheels and Points ANSI B74.2-1982 Abrasive Shape Size Diameter Thickness mm mm

Abrasive Shape 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 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

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

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 Size Diameter Thickness mm mm

Abrasive Shape 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 1⁄ 16 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

W 222

25

50

1

2

W 225

30

6

11⁄4

W 226

30

10

W 228

30

20

W 230

30

30

1⁄ 4 3⁄ 8 3⁄ 4 11⁄4

W 232

30

50

W 235

40

6 13

1

W 236

40

11⁄2

W 237

40

25

2

W 238

40

40

11⁄4 11⁄4 11⁄4 11⁄4 11⁄2 11⁄2 11⁄2 11⁄2

3⁄ 4

W 242

50

25

2

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

2 1⁄ 4 1⁄ 2

1 11⁄2 1

and 1b on pages 952 and 953.


Machinery's Handbook 28th 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


956

Machinery's Handbook 28th Edition 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



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.


958


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- = 1.24 Allowable pitch = ---------------------------------------------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 1044 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.


960


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.


962

Machinery's Handbook 28th Edition 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.



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 files have 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-



964

lets of saw teeth. The blunt mill file has a uniform rectangular cross-section from tip to tang; 5) 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 diamondshaped 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



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.



966

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

1 11⁄8 11⁄4

4600 3450 2750 2300 2000 1900 1700 1600 1500 1400

Cast Iron Bronze Aluminum Speed, Revolutions per Minute 7000 15,000 20,000 5250 11,250 15,000 4200 9000 12,000 3500 7500 10,000 3100 6650 8900 2900 6200 8300 2600 5600 7500 2400 5150 6850 2300 4850 6500 2100 4500 6000

Magnesium 30,000 22,500 18,000 15,000 13,350 12,400 11,250 10,300 9750 9000

Carbide Bur Medium Fine Cut Cut Any Material 45,000 30,000 30,000 20,000 24,000 16,000 20,000 13,350 18,000 12,000 16,000 10,650 14,500 9650 13,000 8650 … … … …

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 28th 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


968

Machinery's Handbook 28th Edition TOOL SHARPENING

steel 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,



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.


970


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



971

mounted on general-purpose tool grinding machines, designed to assure the essential accuracy 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,


972


H, I, and J are used. The usual grades for roughing are I or J and for finishing H, I, and J. The 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.



973

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. 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.)


974


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 28th Edition TABLE OF CONTENTS MACHINING OPERATIONS CUTTING SPEEDS AND FEEDS 979 Introduction to Speeds and Feeds 979 Cutting Tool Materials 983 Cutting Speeds 984 Cutting Conditions 984 Selecting Cutting Conditions 984 Tool Troubleshooting 986 Cutting Speed Formulas 988 RPM for Various Cutting Speeds and Diameter

SPEED AND FEED TABLES 992 992 996 997 1001 1002 1003 1005 1007 1008 1009 1010 1013 1014 1015 1019 1020 1022 1024 1026 1027 1029 1030 1031 1036 1037 1038 1040 1041 1042 1042 1044 1045 1045 1047 1049 1050 1051

How to Use the Tables Principal Speed and Feed 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 Aluminum 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 1052 1052 1052 1052 1052 1054 1054 1055 1055 1058 1060 1060 1061 1061 1061

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 1063 Tool Wear And Tool Life Relationships 1063 Equivalent Chip Thickness (ECT) 1064 Tool-life Relationships 1068 The G- and H-curves 1069 Tool-life Envelope 1072 Forces and Tool-life 1074 Surface Finish and Tool-life 1076 Shape of Tool-life Relationships 1077 Minimum Cost 1078 Production Rate 1078 The Cost Function 1079 Global Optimum 1080 Economic Tool-life 1083 Machine Settings and Cost Calculations 1083 Nomenclature 1084 Cutting Formulas 1088 Tooling And Total Cost 1089 Optimized Data 1092 High-speed Machining Econometrics 1094 Chip Geometry in Milling 1095 Chip Thickness 1097 Forces and Tool-life 1098 High-speed Milling 1099 Econometrics Comparison


Machinery's Handbook 28th Edition TABLE OF CONTENTS MACHINING OPERATIONS SCREW MACHINE FEEDS AND SPEEDS 1101 Automatic Screw Machine Tools 1101 Knurling 1101 Revolution for Knurling 1101 Cams for Threading 1102 Cutting Speeds and Feeds 1104 Spindle Revolutions 1105 Practical Points on Cam 1106 Stock for Screw Machine Products 1108 Band Saw Blade Selection 1109 Tooth Forms 1109 Types of Blades 1110 Band Saw Speed and Feed Rate 1111 Bimetal Band Saw Speeds 1112 Band Saw Blade Break-In

CUTTING FLUIDS 1114 Types of Fluids 1114 Cutting Oils 1114 Water-Miscible Fluids 1115 Selection of Cutting Fluids 1116 Turning, Milling, Drilling and Tapping 1117 Machining 1118 Machining Magnesium 1119 Metalworking Fluids 1119 Classes of Metalworking Fluids 1119 Occupational Exposures 1120 Fluid Selection, Use, and Application 1121 Fluid Maintenance 1122 Respiratory Protection

MACHINING NONFERROUS METALS AND NON-METALLIC MATERIALS 1123 Machining Nonferrous Metals 1123 Aluminum 1124 Magnesium 1125 Zinc Alloy Die-Castings 1125 Monel and Nickel Alloys 1126 Copper Alloys 1126 Machining Non-metals 1126 Hard Rubber 1126 Formica Machining 1127 Micarta Machining 1127 Ultrasonic Machining

GRINDING FEEDS AND SPEEDS 1128 Basic Rules 1128 Wheel life T and Grinding Ratio 1129 ECT in Grinding 1130 Optimum Grinding Data 1132 Surface Finish, Ra 1133 Spark-out Time 1134 Grinding Cutting Forces 1135 Grinding Data 1136 Grindability Groups 1136 Side Feed, Roughing and Finishing 1137 Relative Grindability 1138 Grindability Overview 1138 Procedure to Determine Data 1144 Calibration of Recommendations 1146 Optimization

GRINDING AND OTHER ABRASIVE PROCESSES 1147 Grinding Wheels 1147 Abrasive Materials 1148 Bond Properties 1148 Structure 1149 ANSI Markings 1149 Sequence of Markings 1150 ANSI Shapes and Sizes 1150 Selection of Grinding Wheel 1151 Standard Shapes Ranges 1158 Grinding Wheel Faces 1159 Classification of Tool Steels 1160 Hardened Tool Steels 1164 Constructional Steels 1165 Cubic Boron Nitride 1166 Dressing and Truing 1166 Tools and Methods for Dressing and Truing 1168 Guidelines for Truing and Dressing 1169 Diamond Truing and Crossfeeds 1170 Size Selection Guide 1170 Minimum Sizes for Single-Point Truing Diamonds 1171 Diamond Wheels 1171 Shapes 1172 Core Shapes and Designations


Machinery's Handbook 28th Edition TABLE OF CONTENTS MACHINING OPERATIONS GRINDING AND OTHER ABRASIVE PROCESSES

GRINDING AND OTHER ABRASIVE PROCESSES

(Continued)

(Continued)

1172 Cross-sections and Designations 1173 Designations for Location 1174 Composition 1175 Designation Letters 1176 Selection of Diamond Wheels 1176 Abrasive Specification 1177 Handling and Operation 1177 Speeds and Feeds 1177 Grinding Wheel Safety 1177 Safety in Operating 1178 Handling, Storage and Inspection 1178 Machine Conditions 1178 Grinding Wheel Mounting 1179 Safe Operating Speeds 1180 Portable Grinders 1182 Cylindrical Grinding 1182 Plain, Universal, and LimitedPurpose Machines 1182 Traverse or Plunge Grinding 1182 Work Holding on Machines 1183 Work-Holding Methods 1183 Selection of Grinding Wheels 1184 Wheel Recommendations 1184 Operational Data 1185 Basic Process Data 1185 High-Speed 1186 Areas and Degrees of Automation 1186 Troubles and Their Correction 1190 Centerless Grinding 1191 Through-feed Method of Grinding 1191 In-feed Method 1191 End-feed Method 1191 Automatic Centerless Method 1191 Centerless Grinding 1192 Surface Grinding 1193 Principal Systems 1195 Grinding Wheel Recommendations 1196 Process Data for Surface Grinding 1196 Basic Process Data 1197 Faults and Possible Causes 1197 Vitrified Grinding Wheels 1197 Silicate Bonding Process 1197 Oilstones 1199 Offhand Grinding 1199 Floor- and Bench-Stand Grinding 1199 Portable Grinding 1199 Swing-Frame Grinding

1200 Abrasive Belt Grinding 1200 Application of Abrasive Belts 1200 Selection Contact Wheels 1200 Abrasive Cutting 1203 Cutting-Off Difficulties 1203 Honing Process 1203 Rate of Stock Removal 1204 Formula for Rotative Speeds 1204 Factors in Rotative Speed Formulas 1205 Eliminating Undesirable Honing Conditions 1205 Tolerances 1205 Laps and Lapping 1205 Material for Laps 1206 Laps for Flat Surfaces 1206 Grading Abrasives 1207 Charging Laps 1207 Rotary Diamond Lap 1207 Grading Diamond Dust 1208 Cutting Properties 1208 Cutting Qualities 1208 Wear of Laps 1208 Lapping Abrasives 1208 Effect on Lapping Lubricants 1209 Lapping Pressures 1209 Wet and Dry Lapping 1209 Lapping Tests

KNURLS AND KNURLING 1210 Knurls and Knurling 1210 ANSI Standard 1210 Preferred Sizes 1210 Specifications 1211 Cylindrical Tools 1212 Flat Tools 1212 Specifications for Flat Dies 1212 Formulas to Knurled Work 1213 Tolerances 1214 Marking on Knurls and Dies 1214 Concave Knurls

MACHINE TOOL ACCURACY 1218 1219

Degrees of Accuracy Expected with NC Machine Tool Part Tolerances


Machinery's Handbook 28th Edition TABLE OF CONTENTS MACHINING OPERATIONS CNC NUMERICAL CONTROL PROGRAMMING

CNC NUMERICAL CONTROL PROGRAMMING (Continued)

1224 1224 1225 1226 1226 1228 1229 1229 1232 1232 1232 1233 1234 1234 1234 1234 1235 1235 1235 1237 1237 1237 1238 1238 1239 1240 1245 1245

Introduction CNC Coordinate Geometry CNC Programming Process Word Address Format Program Development Control System CNC Program Data Program Structure Measurement, (G20, G21) Absolute and Incremental Programming (G90, G91) Spindle Function (S-address) Feed Rate Function (F-address) Inverse Time Feed Rate Feed Rate Override Tool Function (T-address) Tool Nose Radius Compensation Rapid Motion (G00) Linear Interpolation (G01) Circular Interpolation (G02, G03) Helical, Other Interpolation Offsets for Milling Work Offset (G54 though G59) Tool Length Offset (G43, G44) Cutter Radius Offset (G41, G42) Machining Holes Fixed Cycles Contouring Turning and Boring

1247 Thread Cutting on CNC Lathes 1247 Depth of Thread Calculations 1248 Infeed Methods 1248 Radial Infeed 1249 Compound Infeed 1249 Threading Operations 1249 Threading Cycle (G32) 1249 Threading Cycle (G76) 1250 Multi-start Threads 1250 Subprograms, Macros and Parametric Programming 1250 Subprograms 1251 Macros and Parametric Programming 1252 Basic Macro Skills 1252 Confirming Macro Capability 1252 Common Features, Functions 1253 Macro Structure 1253 Macro Definition and Call 1253 Variable Definition (G65) 1254 Types of Variables 1254 Variable Declarations and Expressions 1255 Macro Functions 1258 Branching and Looping 1258 Macro Example 1260 Axis Nomenclature 1262 Total Indicator Reading


Machinery's Handbook 28th Edition MACHINING OPERATIONS

979

CUTTING SPEEDS AND FEEDS Introduction 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.


980

Machinery's Handbook 28th Edition 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 761. 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.



981

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


982


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,



983

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


984


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 SPEEDS AND MACHINING POWER starting on page 1052. 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), 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 single-point 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 992. 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.



985

Table 1. Tool Troubleshooting Check List Problem Excessive flank wear—Tool life too short

Tool Material Carbide

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



986

Table 1. (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:

12V 12 × 252 N = ---------- = --------------------- = 120 rpm πD π×8

V 1000V N = ---------------- = 318.3 ---- rpm D πD

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. 12V 12 × 575 N = ---------- = ------------------------- = 549 rpm πD 3.1416 × 4

1000V 1000 × 175.3 N = ---------------- = ------------------------------------ = 549 rpm 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:

πDN V = ------------ fpm 12

πDN V = ------------ m/min 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. V = πDN ------------ = 12 πDN V = ------------ = 1000

π × 0.75 × 400- = 78.5 fpm ---------------------------------12 π × 19.05 × 400- = 24.9 m/min ------------------------------------1000



987

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.


Machinery's Handbook 28th Edition RPM FOR VARIOUS SPEEDS

988

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



989

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



990

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

159

191

255

318

398

477

557

637

716

16

99.5

20

79.6

95.5

127

25

63.7

76.4

102

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

109

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

45

35.4

42.4

56.6

70.7

84.9

113

141

177

212

248

283

318

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

159

90

17.7

21.2

28.3

35.4

42.4

56.6

70.7

88.4

124

141

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

130

12.2

14.7

19.6

24.5

29.4

39.2

49

61.2

73.4

85.7

106 97.9

110

119

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

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

95.5

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



991

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


992


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 and Feed 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



993

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



994

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

CELe

a

r

A'

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

Rake Angle

LA (U.S.)

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.



995

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


996


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 1006)



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

Brinell Hardness

Speed (fpm)

100–150

150

{

1132, 1137, 1139, 1140, 1144, 1146, 1151

(Leaded): 11L17, 11L18, 12L13, 12L14

{

{

Plain carbon steels: 1006, 1008, 1009, 1010, 1012, 1015, 1016, 1017, 1018, 1019, 1020, 1021, 1022, 1023, 1024, 1025, 1026, 1513, 1514

160 130

150–200

120

175–225

120

275–325

75

325–375

50

375–425

40

100–150

140

150–200

145

200–250

110

100–125

120

125–175

110

175–225

90

225–275

70


997

f s

SPEEDS AND FEEDS

1108, 1109, 1115, 1117, 1118, 1120, 1126, 1211 {

150–200 100–150

Cermet


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

998

Table 1. (Continued) Cutting Feeds and Speeds for Turning Plain Carbon and Alloy Steels

Machinery's Handbook 28th Edition 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

8 1780


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

7 1040

3 1310

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


999

325–375 375–425

f s f s f s

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

1000

Table 1. (Continued) Cutting Feeds and Speeds for Turning Plain Carbon and Alloy Steels


Table 2. Cutting Feeds and Speeds for Turning Tool Steels Uncoated HSS Material AISI Designation

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

Special purpose, low alloy: L2, L3, L6

150–200

Mold: P2, P3, P4, P5, P6, P26, P21

100–150 150–200 200–250

65

225–275

55

225–275

45

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

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

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

f s

7 385‡

3 645

10 270

5 500

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

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

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

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


1001

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



1002

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

13 815

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

Machinery's Handbook 28th Edition Table 4a. Cutting Feeds and Speeds for Turning Ferrous Cast Metals Tool Material Uncoated Carbide HSS Brinell Hardness

Material

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

120

ASTM Class 25

160–200

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

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

(Martensitic): 53004, 60003, 60004

200–255

70

(Martensitic): 70002, 70003

220–260

60

(Martensitic): 80002

240–280

50


250–320

30

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.


1003

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.


1004

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

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

{

{

175–225 225–300

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

1544 5

8 665

f s

28 115†

13 355

9070

150–200

90

200–250

80

250–300

60

175–225

80

225–250

70

250–300

55

300–350

45

350–400

30

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

Machinery's Handbook 28th Edition 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

SPEEDS AND FEEDS

Ratio of Chosen Feed to Optimum Feed

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


1005

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.


1006

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



1007

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.



1008

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

99.0 Ti

250–275

70

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

I Al-8V-5Fe

375–440

20

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



1009

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 10–20

15–20 15–30 20–25 15–25

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.


1010


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



1011

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. 12 × 85 = 108 rpm N = 12V ---------- = ------------------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.



1012

Work ar

Work Feed ar Feed

D Cutter

D Cutter

e Fig. 4.

Fig. 3.

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 Optimum feed f opt 0.008

V avg 4755 Average speed--------------------------------------- = ------------ ≈ 2.0 = ---------2320 Optimum speed V opt

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.



1013

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

CD ST and A CD ST and A

—

Alloys 360.0 and 380.0

—


—

Alloy 413 All other aluminum die-casting alloys

{

Indexable Insert Uncoated Carbide

Slit Milling



HSS

f = feed (0.001 in./tooth), s = speed (ft/min) 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

39 840 39 690

20 2390 20 2320

39 500

20 1680

39 690

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

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


Face Milling


1014

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

f s

730

f s

7 30

4 85

f s

7 25

4 70

f s

7 35

130

150–200

115

175–225

115

275–325

70

325–375

45

Slit Milling

f = feed (0.001 in./tooth), s = speed (ft/min)

Speed (fpm)

100–150

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

7

4

7

4

39

20

39

20

39

20

39

20

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

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

f s

7 30

4 85

39 185

20 350

7 465

4 735

7 800

4 39 1050 225

20 335


1015

35

90

20 830

325

140

65

39 525

4

100–150

175–225

Avg.

20 495

85

375–425

225–275

Avg. Opt.

39 265

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

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

Brinell Hardness

HSS

1016

Table 11. (Continued) Cutting Feeds and Speeds for Milling Plain Carbon and Alloy Steels

Machinery's Handbook 28th Edition 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

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

275–325

50

f s

15 5

8 20

15 45

8 170

15 80

8 240

39 190

20 305

325–375

40

375–425

25

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

20 280

175–225

75 (65)

f s

15 5

8 30

15 105

8 270

15 220

8 450

39 295

20 475

39 135

20 305

39 265

20 495

225–275

60

f s

15 5

8 25

15 50

8 175

15 85

8 255

39 200

20 320

39 70

20 210

39 115

20 290

275–325

50 (40)

f s

15 5

8 25

15 45

8 170

15 80

8 240

39 190

20 305

325–375

35 (30)

375–425

20

f s

15 5

8 20

15 40

8 155

15 75

8 225

39 175

20 280

1017

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)

Speed (fpm)

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

Brinell Hardness

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

f s

8 165

4 355

50–52 Rc

—

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

Opt.

Avg. Opt.

f s 8 15

4 45

Avg. Opt.

8 165

4 355

8 150

4 320

5 20†

3 55

8 300

Avg. Opt.

Avg. Opt.

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

1018

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 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.

Opt.

39 115

20 39 265 245

39 75

20 175

20 39 135 5†


Avg.

39 115

Avg.

20 445

20 15

20 39 265 245

20 445

1019

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

1020

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.

Machinery's Handbook 28th Edition Table 13. 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 s

7 20

Avg.

4 55

Opt.

Avg.

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.


1021

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.


1022

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

Nodular (Ductile) Iron

190–225

60

225–260

50


240–300

40

(Martensitic): 120-90-02

270–330

25

(Ferritic-Pearlitic): 80-55-06

{


SPEEDS AND FEEDS

ASTM Class 20

Machinery's Handbook 28th Edition Table 14. 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

(Medium carbon): 1030, 1040 1050

{

{

100

125–175

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, 300–350 8630, 8640, 9525, 9530, 9535

65 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

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.


1023

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

(Low-carbon alloy): 1320, 2315, 2320, 4110, 4120, 4320, 8020, 8620

100–150


1024

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 Hardness, HB

Material

1⁄ 2

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

Free malleable iron

.002

.003

.001

.002

.002

.003

.003–.008

.004

.003–.012

.002–.008

.003

.003

.001

.002

.003

.004

.003–.008

.004

.004–.012

.002–.008

.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 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

Gray cast iron

.001 .001

{ 180–220

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

Tool steel

150–200 120–180

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

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


SPEEDS AND FEEDS

AISI 1033 to 1095; 1524 to 1566

{

Machinery's Handbook 28th Edition 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 Hardness, HB

Material Pearlitic-Martensitic malleable iron

Zinc alloys (die castings) Copper alloys (brasses & bronzes)

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

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

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

135–185

.001

.002

.003

.001

.002

.003

.003

.002–.006

.004

.004–.008

.002–.007

135–185

.001

.002

.003

.001

.002

.003

.003

.003–.007

.004

.005–.008

.002–.007

Ferritic stainless steel Austenitic stainless steel

Martensitic stainless steel

.001

.002

.003

.001

.002

.002

.002

.003–.006

.003

.004–.006

.002–.007

.001

.002

.002

.001

.002

.003

.003

.003–.006

.004

.004–.010

.002–.007 .002–.007

185–225

.001

.002

.002

.001

.002

.002

.003

.003–.006

.004

.003–.008

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


1025

Monel

185–275 135–185

SPEEDS AND FEEDS

Cast steel

1⁄ 2


1026

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

0.90

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

Machinery's Handbook 28th Edition Table 15c. End, Slit, and Side Milling Speed Adjustment Factors for Radial Depth of Cut Cutting Speed, V = Vopt × Ff × Fd Vavg/Vopt

Vavg/Vopt

Maximum Feed/Tooth Factor

1.25

1.00

1.00

1.00

1.00

1.00

1.00

1.00

0.75

1.00

1.15

1.24

1.46

1.54

1.66

0.60

1.00

1.23

1.40

1.73

2.04

0.50

1.00

1.25

1.50

2.00

0.40

1.10

1.25

1.55

0.30

1.35

1.20

0.20

1.50

0.10

2.05

0.05 0.02

Maximum Feed/Tooth Factor

1.25

1.00

0.70

1.18

1.30

1.50

1.69

1.85

2.15

1.87

0.70

1.24

1.48

1.93

2.38

2.81

3.68

2.34

2.89

0.70

1.24

1.56

2.23

2.95

3.71

5.32

2.50

3.00

4.00

0.70

1.20

1.58

2.44

3.42

4.51

6.96

2.17

2.83

3.51

4.94

0.77

1.25

1.55

2.55

3.72

5.08

8.30

1.57

2.28

3.05

3.86

5.62

0.88

1.23

1.57

2.64

4.06

5.76

10.00

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

0.92

1.39

2.68

4.46

6.77

13.10

1.44

0.92

1.29

2.50

4.66

7.76

17.40

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

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

1.50

2.00

2.50

3.00

4.00

Feed Factor Ff at Maximum Feed per Tooth, Ff1

1.50

2.00

2.50

3.00

4.00

Feed Factor Ff at Minimum Feed per Tooth, Ff2

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.


1027

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

Ratio of Radial Depth of Cut to Diameter



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

1028

Table 15d. Face Milling Speed Adjustment Factors for Feed, Depth of Cut, and Lead Angle


1029

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 CB50 CC620 CC650 CC670 CC680 CC690 CT515 CT525 CD10 GC-A GC3015 GC235 GC4025 GC415 H13A S10T S1P S30T S6 SM30

Kennametal KD050 K060 K090 KYON2500 KYON2000 KYON3000 KT125 KT150 KD100 — KC910 KC9045 KC9025 KC950 K8, K4H K420, K28 K45 — K21, K25 KC710

Seco Valenite CBN20 VC721 480 — 480 Q32 — — 480 — — Q6 CM VC605 CR VC610 PAX20 VC727 — — TP100 SV310 TP300 SV235 TP200 SV325 TP100 SV315 883 VC2 CP20 VC7 CP20 VC7 CP25 VC5 CP50 VC56 CP25 VC35M

See Table 2 on page 767 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.


1030


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 17 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

1031



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

{

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

250–300

55

30

300–375 375–425

40 30

25 15

100

Threading

HSS

HSS


Brinell Hardness 125–175 175–225

150–200

Reaming

Opt.

65

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

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

{

Avg. Opt. 8 95

275–325

50

30

f 11 s 50

325–375 375–425

35 25

25 15

f s

6 85


SPEEDS AND FEEDS

Free-machining alloy steels (Resulfurized): 4140, 4150

{


HSS

1032

Table 17. Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels

Machinery's Handbook 28th Edition Table 17. Feeds and Speeds for Drilling, Reaming, and Threading Plain Carbon and Alloy Steels Drilling

Reaming

Drilling


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

20

f s

300–350

35

HSS

8 140

75 (60)

60

Threading

HSS


Speed (fpm)

175–225

200–250

Reaming

8 140

8 410

4 685

8 310

4 525


1033

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. 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

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)


HSS


1034

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 5a 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 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



1035

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 Water hardening: W1, W2, W5

150–200

HSS

Opt.

175–225

50

35

Cold work (oil hardening): O1, O2, O6, O7

175–225

45

30

30

20

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

{

(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

{

HSS

HSS

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

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

f 15 s 45

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

200–250

(Air hardening): A2, A3, A8, A9, A10

Hot work (chromium type): H10, H11, H12, H13, H14, H19

{

Threading

55

Shock resisting: S1, S2, S5, S6, S7 (High carbon, high chromium): D2, D3, D4, D5, D7

Reaming


Speed (fpm) 85


1036

Table 18. Feeds and Speeds for Drilling, Reaming, and Threading Tool Steels

Machinery's Handbook 28th Edition 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


1037

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.


1038

Table 20. 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

HSS

Uncoated

Coated


Speed (fpm)

Opt.

120–150

100

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

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

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

65 f s f s

16 80

8 90

11 85

6 180

11 235

13 50

6 50

11 70

6 150

11 195

6 405

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

Machinery's Handbook 28th Edition Table 20. 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


1039

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 All wrought aluminum alloys, 6061-T651, 5000, 6000, 7000 series All aluminum sand and permanent mold casting alloys

Reaming

Threading

HSS

HSS


HSS

1040

Table 21. Feeds and Speeds for Drilling, Reaming, and Threading Light Metals


Speed (fpm)

Opt.

CD

400

ST and A

350

350

AC

500

500

ST and A

350

Avg. Opt.

Avg. Opt.

Avg. Opt.

Avg.

400 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

Machinery's Handbook 28th Edition 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

1041


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.


1042

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 Reaming Alloy Description and UNS Alloy Material Numbers Condition

Group 1 Group 2 Group 3

A CD A CD A CD

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 threading data contained in the tables for drilling, reaming, and threading (Tables 17



1043

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 V = 35 + ------------------------------ ( 45 – 35 ) = 40 fpm 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. It will be more difficult to apply the cutting fluid at the cutting edges and to lubricate the tap


1044


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 28th Edition SPADE DRILLS

1045

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 Coolant holes

Blade retaining screw 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.


1046

Machinery's Handbook 28th Edition 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 28th Edition SPADE DRILLING

1047

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

Chisel edge angle

Web Cutting lip

Chisel edge Blade thickness

Locating slot

Rake surface

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


1048


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 1031, 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.



1049

Table 1. Feed Rates for Spade Drilling Feed—Inch 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

High-Speed

Gray Cast Iron

Ductile or Nodular Iron

Malleable Iron Ferritic Pearlitic Free Machining Stainless Steel

Stainless Steel

Aluminum Alloys Copper Alloys

…

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 0.018

(Hard)

0.010

0.012

0.014

0.016

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



1050

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 hp c = uhp  ---------- fN  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

Plain Carbon and Alloy Steel

Cast Irons Stainless Steels

Hardness 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 1031, 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 1049) 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 28th Edition TREPANNING

1051

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: πD π×2 hp c = uhp  ---------- fN = 0.94  --------------- 0.015 × 86 = 3.8  4   4  2

2

Step 3. Calculate the horsepower at the motor and provide for a 50 per cent power increase for the dull tool: hp 3.8- = 4.75 horsepower hp m = -------c- = --------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.


1052


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 Vc S 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. LT = ----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- + 0.025 1 + ---T = ----- L ×  ----V V  F c r 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 28th Edition MACHINING POWER

1053

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


1054


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 1a, and 1b can be used for all machining operations except drilling and grinding. Values given are for sharp tools. Table 1a. 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

…

{

{



1055

Table 1a. (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

Monel Metal

1.00

2.73

0.75 0.88 0.98 1.20 1.30

2.05 2.40 2.68 3.28 3.55

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 2. 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 3. 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.



1056

Table 1b. 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

All Plain Carbon Steels

80–100 100–120 120–140 140–160 160–180 180–200 200–220

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 4. Formulas for calculating the metal removal rate, Q, for different machining operations are given in Table 5. 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

(1)

P K p CQW Pm = -----c = -------------------E E

(2)

where Pc =power at the cutting tool; hp, or kW



1057

Table 2. 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 3. 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

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

Pm =power at the motor; hp, or kW Kp =power constant (see Tables 1a and 1b) Q =metal removal rate; in 3/min or cm3/s (see Table 5) C =feed factor for power constant (see Table 2) W =tool wear factor (see Table 3) E =machine tool efficiency factor (see Table 4) V =cutting speed, fpm, or m/min N =cutting speed, rpm f =feed rate for turning; in/rev or mm/rev f =feed rate for planing and shaping; in/stroke, or mm/stroke



1058

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 4. 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 5. 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 c d t 60

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 1b) C =0.94 (from Table 2) W =1.30 (from Table 3) E =0.80 (from Table 4) Q =12 Vfd = 12 × 350 × 0.016 × 0.100 (from Table 5) 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 1b) C =0.94 (from Table 2) W =1.30 (from Table 3) E =0.80 (from Table 4) V 107 3 Q = ------ fd = --------- × 0.40 × 2.54 = 1.81 cm /s (from Table 5) 60 60



1059

Pc = K p CQW = 1.69 × 0.94 × 1.81 × 1.30 = 3.74 kW P 3.74 Pm = -----c = ---------- = 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 1b) C =0.92 (From Table 2) W =1.30 (From Table 3) E =0.80 (From Table 4) Pm E 10 × 0.80 Q max = --------------- = -------------------------------------------0.85 × 0.92 × 1.30 K p CW

p CQW P = K ------------------- 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 1a) C =1.00 (From Table 2) W =1.20 (From Table 3) E =0.80 (From Table 4)



1060

Pm E 10 × 0.80 - = 12.82 in 3 /min Q max = --------------- = ------------------------------------------K p CW 0.52 × 1.00 × 1.20

p CQW P = K ------------------- m E 

Q max 12.82 = 17.1 in/min - = ---------------------f m = -----------wd 6 × 0.125

( Q = f m wd )

f max 17 - = ------------------------= 142.4 rpm N = --------0.012 × 10 ft nt

( fm = ft nt N )

πDN π × 8 × 142 V = ------------ = --------------------------- = 298.3 fpm 12 12

 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 6 through 9 are for sharp drills and the tool wear factors are given in Table 3. 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 7. 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 6. 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.



1061

Table 7. 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 6) Ff =Feed factor (See Table 8) FT =Thrust factor for drill diameter (See Table 9) FM =Torque factor for drill diameter (See Table 9) A =Chisel edge factor for torque (See Table 7) B =Chisel edge factor for thrust (See Table 7) J =Chisel edge factor for thrust (See Table 7) W =Tool wear factor (See Table 3) N =Spindle speed; rpm E =Machine tool efficiency factor (See Table 4) D =Drill diameter; in., or mm c =Chisel edge length; in., or mm (See Table 7) w =Web thickness at drill point; in., or mm (See Table 7)

(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 6) Ff =0.021 (From Table 8) FT =0.899 (From Table 9) FM =0.786 (From Table 9) A =1.085 (From Table 7) B =1.355 (From Table 7) J =0.030 (From Table 7)



1062

Table 8. Feed Factors Ff for Drilling Inch Units Feed, in./rev 0.0005 0.001 0.002 0.003 0.004 0.005 0.006 0.007 0.008 0.009 0.010

SI Metric Units

Ff

Feed, in./rev

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

Ff

Feed, mm/rev

Ff

Feed, mm/rev

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 9. Drill Diameter Factors: FT for Thrust, FM for Torque Inch Units Drill Dia., in.

FT

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

SI Metric Units

FM

Drill Dia., in.

FT

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

FM

Drill Dia., mm

FT

FM

Drill Dia., mm

FT

FM

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 3) 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 12V 12 × 101 ---------- = ----------------------- = 514 rpm πD π × 0.750 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 28th Edition MACHINING ECONOMETRICS

1063

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. 1

LIVE GRAPH

Wear, mm

Click here to view

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.


1064


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: Area ECT = ------------- (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. 1. on page 994. 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 mm, 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) equals the metal removal rate, MRR, 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: SMRR = 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: SMRR = 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 1128. 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 28th Edition MACHINING ECONOMETRICS LIVE GRAPH LIVE GRAPH

Click here to view

1065

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

200

250

300

350

400

450

500

VC (cutting speed), m/min

Fig. 2. Influence of feed per tooth on cutting time

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 (1b) lnV + n × lnT = lnC 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.


Machinery's Handbook 28th Edition MACHINING ECONOMETRICS LIVE GRAPH

1066

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..



1067

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)

x–H (4b) y = K – ------------- – z ( N 0 – L 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) 1000

LIVE GRAPH

H-CURVE

VH

G-CURVE

K = ln(VH)

Click here to view

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.



1068

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 1080. 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. 100

LIVE GRAPH

T minutes

Click here to view

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.


Machinery's Handbook 28th Edition MACHINING ECONOMETRICS LIVE GRAPH

1069

Click here to view

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. 1000

T=1 T=5 T = 15 T = 30 T = 60 T = 100 T = 300

LIVE GRAPH V, m/min

Click here to view

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-



1070

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 1092 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



1071

to calculate the tangential cutting force, torque and required machining power are found in the section ESTIMATING SPEEDS AND MACHINING POWER starting on page 1052. 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 10000

LIVE GRAPH

V = 300

Click here to view

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. 1

LIVE GRAPH

FH/FC

Click here to view

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



1072

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

1.8

Click here to view 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.



1073

For any constant speed, tool-life has a maximum at approximately the same values of ECT as has the function FH/FC. 1000

LIVE GRAPH

H-CURVE

Click here to view

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 ) 2K – y – (------------------1--- F H 4M  ln ⋅ ------- = ------------------------------------- a F C LF ------ ( 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. 1000

LIVE GRAPH

LF/L = 5

Click here to view

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:



1074

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 be taken into account, and the work material and the cutting conditions also have a significant influence. 10

LIVE GRAPH

Ra, mm

Click here to view

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 2 0.5 R a1 -------- =  ---- (6)  r 1 R a2



Click here to view

1075

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. 10

LIVE GRAPH

Ra

Click here to view

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 - – ( N 0Ra – L Ra )ln ( R a ) y = K Ra – -------------------4M Ra where KRA, HRA, MRA, NORA, and LRA are the 5 surface finish constants.



1076

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 =120

T = 45 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


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



Click here to view

1000

1077

Click here to view

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 1000

0.1

0.01

1

Fig. 17f. Tool-life for face-milling SAE 1045 steel using coated carbide 10000

LIVE GRAPH

LIVE GRAPH

Click here to view

Click here to view

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.



1078

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. CTOOL

CTOT

0.487 0.192 0.125 0.069 0.049

0.569 0.288 0.228 0.185 0.172

T 1 3 5 10 15

V 598 506 468 421 396

30

356

9.81

0.027

0.164

10.91 11.60 12.12 13.47

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 5.85 6.91 7.47 8.30 8.83

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



1079

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

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

ECT= 0.26 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



1080

1085). 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 997 and handbook Table 5b on page 1005 for turning, and Table 15e on page 1029 for milling and drilling; 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

60

TE

Click here to view

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



1081

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. 1000

LIVE GRAPH

T, minutes

Click here to view

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.



1082

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. 1000

LIVE GRAPH

Click here to view

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 T O = T V ×  ------ – 1 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.



1083

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 992 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


1084


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: rpm = 1000V ---------------- = 318V ------------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 Dist × πD t c = ----------- = ----------------- = ------------------------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: Dist × πD a t c = ------------------------- × -----------------------------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



1085

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. 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: HR T RPL $ --------C CH = ------- × T C × -----------⋅ min = $ 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 × -------------------------------60 T 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:



1086

HR TV ( C TOOL + C CH ) = ------- × T C × -----60 T HR T C TOT = ------- × T C  1 + -----V-  60 T 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: HR TV 50 9.16 ( C TOOL + C CH ) = ------- × T C × ------ = ------ × 1000 × 1.5 × ------------- = $ 417 60 T 60 27.48 Total Cost of Cutting per Batch: HR T 50 9.16- = $ 1617 C TOT = ------- × T C  1 + -----V- = ------ × 1000 × 1.5 ×  1 + -----------  60 60 T 27.48 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.



1087

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. Time for replacement of inserts TRPL, minutes

Number of inserts

Price per insert

Edges per insert

2 2

10 10

5 5

3 3

1

3

6

1

1

5

Cutter Price

Face mill 750 750 End mill 2 75 Turning 3 50

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: HR TV 50 30.466 ( C TOOL + C CH ) = ------- × T C × ------ = ------ × 1000 × 1.5 × ---------------- = $ 624 60 T 60 61 Total Cost of Cutting per Batch: HR T 50 30.466 C TOT = ------- × T C  1 + -----V- = ------ × 1000 × 1.5 ×  1 + ---------------- = $ 1874   60 60 T 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: V1 T2 200 15 n = ln ------ ÷ ln ----- = ln --------- ÷ ln ------ = 0.25 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 T E = T V ×  --- – 1 = 4 ×  ---------- – 1 = 12 minutes 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 T2 n 15 0.25 V E1 = V 2 ×  ------ = 263 ×  ------ = 278 m/min  T E  12 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


1088


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 and Feed Tables on page 992, 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 997, and for ASTM Class 20 grey cast iron using data from Table 4a on page 1003, as follows: For the 175–250 Brinell hardness range, and the hard tool grade, ln ( V 1 ⁄ V 2 ) ( 525 ⁄ 705 )- = 0.27 n = ------------------------- = ln ------------------------------C = V 1 × ( T 1 ) n = 1458 ln ( T 2 ⁄ T 1 ) ln ( 15 ⁄ 45 ) 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 )- = ln ------------------------------n = ------------------------= 0.26 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,


Machinery's Handbook 28th Edition MACHINING ECONOMETRICS ln ( V 1 ⁄ V 2 ) ( 125 ⁄ 175 )- = 0.31 n = ------------------------- = ln ------------------------------ln ( 15 ⁄ 45 ) ln ( T 2 ⁄ T 1 )

1089

C = V 1 × ( T 1 ) n = 401

For ASTM Class 20 grey cast iron, using hard ceramic, ln ( V 1 ⁄ V 2 ) ( 1490 ⁄ 2220 -) - = ln ------------------------------------= 0.36 n = ------------------------ln ( 15 ⁄ 45 ) ln ( T 2 ⁄ T 1 )

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

LIVE GRAPH

Click here to view

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 × 4 ⁄ 3 + 100 = 7.50 ---------------------------------- = $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



1090

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. 1000

LIVE GRAPH

Click here to view

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. 0.6

LIVE GRAPH

T=5 T = 22 T = 120

Click here to view0.5 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



1091

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, 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



1092

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. 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 0.00495

0.70

1.80

141

0.10802

0.05892

102

0.08665

0.01862

70

0.10393

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 1014. 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 mate-



1093

rials 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 1066). 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 1012, and Fig. 5 on page 1013. 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.



1094

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. Face Milling

End Milling

AE

hmax

ar hmax ar

hm

hm

AE fz

fz 2 ar --- cos AE = 1 – 2 × ---D

ar --- cos AE = 1 – 2 × ---D

Fig. 24.

Comparison of face milling and end milling geometryHigh-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

6.5 fz/fz0 , Face Milling

6

Click here to view 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



1095

Table 2a. Variation of Chip Thickness and fz/fz0 with ar/D Face Milling

End Milling (straight)

ecentricitye = 0 z =8 fz0 = 0.17 cosAE = 1 − 2 × (ar/D)2

z =2 fz0 = 0.17 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 1.025 0.973 0.992 0.997 0.999 1.000 1.000 1.000

0.108 0.137 0.147 0.151 0.158 0.162 0.165 0.169 0.170 0.170 0.170 0.170 0.000

5.000 3.564 2.952 2.631 1.683 1.267 1.028 0.557 0.319 0.159 0.076 0.025 0.000

1.398 1.107 1.032 1.000 0.958 0.932 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)



1096

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 correctedfor 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 correctedfor 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 =



1097

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. 1000

LIVE GRAPH

T=5 T=15 T=45 T=180

V, m/min

Click here to view

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.



1098

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

Click here to view

10000

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



1099

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

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). 100000

LIVE GRAPH

FR , mm/min.

Click here to view 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 1083). 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, $



1100

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 28th Edition SCREW MACHINE SPEEDS AND FEEDS

1101

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 1210. 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 1104 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

1102

Approximate Cutting Speeds and Feeds for Standard Automatic Screw Machine Tools—Brown and Sharpe

Machinery's Handbook 28th Edition 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.

{

Knee tools

Knurling tools {

Turret

{

Side or swing

{

Top

{

End cut

{

Pointing and facing tools Reamers and bits

Recessing tools {

1⁄ –1⁄ 16 8

Inside cut

1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 1⁄ 32 1⁄ 16 1⁄ 8 3⁄ 16

Swing tools, forming

Turning, straight and taperb Taps

…

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.


1103

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 … …


1104

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 28th Edition SCREW MACHINE CAM AND TOOL DESIGN

1105

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 1102 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.


Machinery's Handbook 28th Edition SCREW MACHINE

1106

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 28th Edition STOCK FOR SCREW MACHINES

1107

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


Machinery's Handbook 28th Edition BAND SAW BLADES

1108

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

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

11 2 13 4 1 3 2 21 4 21 2 23 4 3 3 4

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.



1109

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


1110


Cutting Rate (in.2/min)

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. 30 LIVE GRAPH Click here to view 28 26 0.75 1.5 24 22 1.5 2.5 23 20 34 18 16 46 14 12 58 10 8 8 12 6 4 2 0 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.



1111

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


1112


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). 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 table footnote on page 1112) 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 in2/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 28th Edition CUTTING FLUIDS

1113

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.

Break-In Area

% of Normal Feed

Starting Feed Rate 100 90 80 70 60 50 40 30 20 10 0 ft/min. 40 m/min. 12

in.2 100 90 80 70 60 50 40 30 20 10 0 ft/min. 40 m/min. 12

80 24

120 37

160 49

200 61

240 73

280 85

320 98

360 110

Band Speed (Machinability) Total Break-In Area Required

80 24

120 37

160 49

200 61

240 73

280 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-


1114


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



1115

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


1116


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.



1117

Cutting Fluids Recommended for Machining Operations Material to be Cut Aluminuma

Turning (or)

Mineral Oil with 10 Per cent Fat Soluble Oil

(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) Alloy

Milling

Steelsb

10 Per Cent Lard Oil with 90 Per Cent Mineral Oil

Tapping (or) (or) (or)

Soluble Oil

Brass (or)

Soluble Oil (75 to 90 Per Cent Water) 30 Per Cent Lard Oil with 70 Per Cent Mineral Oil

Tool Steels and Low-carbon Steels

Soluble Oil

Copper

Soluble Oil

Monel Metal

Soluble Oil (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.


1118


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.



1119

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.


1120


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-



1121

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-



1122

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 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 28th Edition GRINDING FEEDS AND SPEEDS

1137

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.



1138

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 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.



1139

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

100

10000

SMRR, mm3/mm/min

ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

10

LIVE GRAPH

1000

T=100 ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH

Click here to view 1 1000

T=1 min. T=10 min.


10000

V, m/min

10000

V, m/min

Fig. 1a. T–V

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

SMRR

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

10000

100

Click here to view SMRR, mm3/mm/min

T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH

ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

LIVE GRAPH

1000


1 100

1000

V, m/min

Fig. 2a. T–V

10000

100

1000

10000

V, m/min




1140

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

10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

LIVE GRAPH

T = 1 min

SMRR, mm3/mm/min

T, minutes

100

1000 T = 10 min T = 100 min ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH

Click here to view

Click here to view

1 1000

100

10000

V, m/min

Fig. 3a. T–V

1000

10000

V, m/min


Tool Life T (min)

Table 4. Group 4—Tool Steels, M1, M8, T1, H, O, L, F, 52100 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

100

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

100

10000

10

LIVE GRAPH

LIVE GRAPH


T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

T = 1 min T = 10 min 1000

T = 100 min

ECT = 17 ECT = 33 ECT = 50 ECT = 75


SMRR

1000

10000

V, m/min

Fig. 4a. T–V

100

1000

V, m/min

10000




1141

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

100

10

SMRR, mm3/mm/min

10000 ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes

SMRR

1000

LIVE GRAPH

ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH

Click here to view

Click here to view

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

SMRR

VT

SMRR

VT

SMRR

VT

SMRR

100

1600

270

1415

465

1085

540

725

540

10

2910

495

2580

850

1970

985

1315

985

1

5290

900

4690

1550

3585

1795

2395

1795

10000

100

LIVE GRAPH

10


T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

1000

ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH


1 1000

V, m/min

Fig. 6a. Group 6 Tool Steels T–V

10000

1000

10000

V, m/min




1142

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

SMRR

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

10000

T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

LIVE GRAPH

LIVE GRAPH

ETC = 17


100

ETC = 33 ETC = 50 ETC = 75

1000


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

SMRR

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

100

10000

LIVE GRAPH


T, minutes

ECT = 17 ECT = 33 ECT = 50 ECT = 75

10

LIVE GRAPH

ETC = 17 ETC = 33 ETC = 50 ETC = 75

1000


1000

V, m/min

Fig. 8a. T–V

10000

100 100

1000

10000

V, m/min




1143

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

10000

T, minutes

1000

100

LIVE GRAPH

1000

ECT = 2 ECT = 3 ECT = 5 ECT = 8

LIVE GRAPH


ECT = 2 ECT = 3 ECT = 5 ECT = 8

100


10

10000

1000

100

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

SMRR

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

10000

100

LIVE GRAPH

ECT = 2 ECT = 3 ECT = 5 ECT = 8

SMRR, mm3/mm/min

Click here to view

T, minutes

1000

100

LIVE GRAPH

ECT = 2 ECT = 3 ECT = 5 ECT = 8


10 1000

V, m/min

Fig. 10a. T–V

10000

100

1000

10000

V, m/min




1144

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 c) V10U = CU ÷ 100.26 d) 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

10000

100

LIVE GRAPH

10


ECT = 17 ECT = 33 ECT = 50 ECT = 75

T, minutes


1000

ECT = 17 ECT = 33 ECT = 50 ECT = 75

LIVE GRAPH


1 1000

V, m/min

Fig. 11a. Group 6 Tool Steels, T–V

10000

1000

10000

V, m/min




1145

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 b) V10U = CU ÷ 100.26 = 2985 ÷ 10 0.26 = 1640 m/min, and SMRR10U = 1000 × 1640 × 0.00017 = 279 mm3/mm width/min c) 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



1146 100

LIVE GRAPH

T minutes

Click here to view

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 28th Edition GRINDING WHEELS

1147

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.


1148


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 983.) 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



1149

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 B74.13“ 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 1174. 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.


1150


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.



1151

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.

CUTTING OFF (Organic bonds only) CYLINDRICAL GRINDING Between centers CYLINDRICAL GRINDING Centerless grinding wheels

1 to 48

1⁄ to 3⁄ 64 8

1⁄ to 16

6

12 to 48

1⁄ to 2

6

5 to 20

14 to 30

1 to 20

5 or 12

CYLINDRICAL GRINDING Centerless regulating wheels

8 to 14

1 to 12

INTERNAL GRINDING

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

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

2 to 3

12

SNAGGING Portable machines

3 to 8

1⁄ to 4

1

SNAGGING Portable machines (Reinforced organic bond, 17,000 sfpm)

6 or 8

3⁄ or 4

1

SNAGGING Swing frame machines

12 to 24

SURFACE GRINDING Horizontal spindle machines TOOL GRINDING Broaches, cutters, mills, reamers, taps, etc.

3⁄ to 5⁄ 8 8

1

2 to 3

31⁄2 to 12

6 to 24

1⁄ to 2

11⁄4 to 12

6 to 10

1⁄ to 1⁄ 4 2

6

5⁄ to 8

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



1152


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



1153


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



1154


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



1155


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

7⁄ 8

Throughout table large open-head arrows indicate grinding surfaces.



1156

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


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


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



1157

Table 1b. Standard Shapes and Metric Size Ranges of Grinding Wheels ANSI B74.2-1982 Size Ranges of Principal Dimensions, Millimeters Applications

D = Diam. Type 5. Wheel, recessed one

T = Thick.

H = Hole

sidea


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


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.


1158

Machinery's Handbook 28th Edition 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 hardened (Table 6) constructional steels. For the relatively rare instance where the use of a



1159

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 GROUP 1—Any area of work surface

AISI-SAE Designation of Tool Steels W1, W2, W5 S1, S2, S4, S5, S6, S7

High grindability tool and die steels

O1, O2, O6, O7

(Grindability index greater than 12)

H10, H11, H12, H13, H14 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



1160

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 2

Surfacing Straight wheels


Dry FA70-K7V 1 Over 1 to 3 Dry FA60-J8V Over 3 Dry FA46-J8V Group 2 Steels

SFA70-K7V

14 and smaller 14 and smaller Over 14 11⁄2 rim or less 3⁄ rim or less 4

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

FA60-H12VP FA54-H12VP

(for rims wider than 11⁄2 inches, go one grade softer in available specifications)



1161

Table 4. 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

First-Choice Specifications

… … … … … 8 and smaller 8 and smaller 10 and larger 14 and less 16 and larger …

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

SFA80-L6V

1⁄ to 2

1 Over 1 to 3 Over 3

Wet FA70-K5V

SFA70-K5V

Wet FA60-J8V Wet FA54-J8V

SFA60-J7V SFA54-J8V

Under 1⁄2

Dry FA80-I8V

1⁄ to 2




SFA80-K7V

Dry FA70-J8V 1 Over 1 to 3 Dry FA60-I8V Over 3 Dry FA54-I8V Group 3 Steels

SFA70-J7V

14 and smaller 14 and smaller Over 14 11⁄2 rim or less 3⁄ rim or less 4

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

FA60-G12VP FA54-G12VP

(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



1162

Table 4. 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 …

Wet FA80-L5V Wet FA60-L6V Wet FA60-L5V

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


First-Choice Specifications

1⁄ to 2


Segments Cylinders Cups

Form tool grinding

Cylindrical Internal Production grinding

Tool room grinding


Dry FA80-J8V 1 Over 1 to 3 Dry FA70-I8V Over 3 Dry FA60-I8V Group 4 Steels

SFA80-J7V

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

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

SFA70-G12VP SFA60-G12VP

(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 2

Dry FA80-J8V

C80-JV

Dry FA70-I8V Dry FA60-H8V

C70-IV C60-HV

1 Over 1 to 3 Over 3



1163

Table 4. (Continued) Grinding Wheel Recommendations for Hardened Tool Steels According to their Grindability

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 specifications)

1⁄ inches, 2

go one grade softer in available

Cutter grinding Straight wheels

…

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

…

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 Production grind- Under 1⁄2 ing 1⁄ to 1 2

Tool room grinding

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

Under 1⁄2

Dry FA100-K8V

C90-KV

…

1⁄ to 2

Dry FA90-J8V

C80-JV

…

1

Over 1 to 3

Dry FA80-I8V

C70-IV

FA80-G12VP

Over 3

Dry FA70-I8V

C60-IV

FA70-G12VP



1164

Table 5. Grinding Wheel Recommendations for Constructional Steels (Soft) Grinding Operation Surfacing Straight wheels


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

FA30-F12VP

FA24-H8V

11⁄2 rim or

Segments

less

Wet FA24-H8V

Cylinders

11⁄2 rim or

Cups

3⁄ rim 4

less

Cylindrical

Wet FA24-I8V Wet FA24-H8V

or less

Under 1⁄2 1⁄ to 2

FA24-H8V

FA30-F12VP

FA30-H8V

(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

FA30-G12VP

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

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 Cylindrical Work diameter 1 inch and smaller Over 1 inch 1 inch and smaller Over 1 inch Centerless Internal

or less

8 and smaller 8 and smaller 10 and larger

14 and smaller 14 and smaller 16 and larger 16 and larger …

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

Wet SFA54-L5V Wet SFA46-K5V Dry FA80-L6V

… … …

Under 1⁄ to 2

1⁄ 2

1

Dry FA70-K8V

…

Over 1 to 3 Over 3

Dry FA60-J8V Dry FA46-J8V

FA60-H12VP FA54-H12VP



1165

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 1171), 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. CBN 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,



1166

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 Direction of Change To increase cutting rate Coarser grain, softer bond, higher porosity To retain wheel size and/or form Finer grain, harder bond For small or narrow work surface Finer grain, harder bond For larger wheel diameter Coarser grain To improve finish on work Finer grain, harder bond, or resilient bond For increased work speed or feed rate Harder bond For increased wheel speed Generally, softer bond, except for highspeed grinding, which requires a harder bond for added wheel strength For interrupted or coarse work surface Harder bond For thin walled parts Softer bond To reduce load on the machine drive Softer bond motor 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.



1167

Table 1. 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.



1168

Table 1. 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 Dressing and Truing 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 producing fine finishes. Such variations, however, must always stay within the limits set by the


@@ @ @@ @ Machinery's Handbook 28th Edition GRINDING WHEELS

1169

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.


1170


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 28th Edition DIAMOND WHEELS

1171

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.


1172


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



1173

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. 8 — Throughout Designates wheels of solid diamond abrasive section without cores.


1174

Machinery's Handbook 28th Edition DIAMOND WHEELS Table 3. Designations for Location of Diamond Section on Diamond Wheel ANSI B74.3-1974

Designation No. and Location

Description

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.

Illustration

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.



1175

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.

Illustration

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.



1176

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

Abrasive Specification Rough: MD100-N100-B1⁄8 Finish: MD220-P75-B1⁄8 Rough: MD180-J100-B1⁄8 Finish: MD320-L75-B1⁄8

D1A1

MD150-R100-B1⁄8

D11V9

Combination: MD150-R100-B1⁄8

Multitooth Tools and Cutters (face mills, end mills, reamers, broaches, etc.) Rough: MD100-R100-B1⁄8 Sharpening and Backing off

Finish: MD220-R100-B1⁄8 D12A2

MD180-N100-B1⁄8

Saw Sharpening

D12A2

MD180-R100-B1⁄8

Surface Grinding (horizontal spindle)

D1A1

Fluting

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 28th Edition GRINDING WHEEL SAFETY

1177

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


1178


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



1179

wheels, as well as for producing accurate 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 sfpm = rpm × ------ × π 12

or

sfpm × 12 rpm = -----------------------D×π


1180


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

1151. b 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. Values in this table are for general information only.


Machinery's Handbook 28th Edition 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

1181

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

1182

Machinery's Handbook 28th Edition 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 28th Edition CYLINDRICAL GRINDING

1183

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).

A complementary work-holding device, used in conjunction with primary work holders, to provide additional support, particularly to long and/or slender parts.

Special fixtures

Single-purpose devices, designed for a particular workpiece, primarily for providing special locating elements.

Typical workpieces requiring special fixturing are, as examples, crankshafts where the holding is combined with balancing functions; or internal gears located on the pitch circle of the teeth for O.D. grinding.

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 list of grinding wheel recommendations with general validity. Instead, examples of recom-



1184

mendations 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 balance of the workpiece, as well as several grinding process conditions, such as wet or dry grinding, the manner of wheel truing, etc.



1185

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

100

0.002

0.0005 max.

1⁄ 3

1⁄ 6

150

0.002

0.0005 max.

1⁄ 3

1⁄ 6

Finishing

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 grind-


1186


ing 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 water from causing a false heavy side. Tighten wheel mounting flanges. Make sure wheel center fits spindle.



1187

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 1189. 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 1189. 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 operation and 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.


1188


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 wheel act harder. Allow work to “spark-out.” Decrease feed rate. Use proper number of



1189

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.


1190


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 28th Edition CENTERLESS GRINDING

1191

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.


1192

Machinery's Handbook 28th Edition 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.



1193

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,


1194

Machinery's Handbook 28th Edition 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



1195

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 Material Cast iron Nonferrous metal Soft steel Hardened steel, broad contact Hardened steel, narrow contact or interrupted cut General-purpose wheel Cemented carbides

Wheels less than 16 inches diameter 37C36-K8V or 23A46-I8VBE 37C36-K8V 23A46-J8VBE 32A46-H8VBE or 32A60-F12VBEP

Wheels 16 inches diameter and over 23A36-I8VBE 37C36-K8V 23A36-J8VBE 32A36-H8VBE or 32A36-F12VBEP

Horizontal-spindle, rotary-table surface grinders Wheels of any diameter 37C36-K8V or 23A46-I8VBE 37C36-K8V 23A46-J8VBE 32A46-I8VBE

32A46-I8VBE

32A36-J8VBE

32A46-J8VBE

23A46-H8VBE Diamond wheelsa

23A36-I8VBE Diamond wheelsa

23A46-I8VBE Diamond wheelsa

a General diamond wheel recommendations are listed in Table 5 on page 1176.



1196

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

Type 6 Cup Wheels

Wheel Segments

37C24-HVK

23A24-I8VBE or 23A30-G12VBEP 32A46-G8VBE or 32A36-E12VBEP

32A46-G8VBE or 32A60-E12VBEP

Hardened steel—narrow contact or interrupt cut

32A46-H8VBE

32A60-H8VBE

General-purpose use

23A30-H8VBE or 23A30-E12VBEP

37C24-HVK 23A24-I8VSM or 23A30-H12VSM 32A36-G8VBE or 32A46-E12VBEP 32A46-G8VBE or 32A60-G12VBEP 23A30-H8VSM or 23A30-G12VSM

23A24-I8VBE

…

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 Plain carbon steel

Hardness

Nitriding steels

Table Speed, fpm

Downfeed, in. per pass Finish, Rough max.

Crossfeed per pass, fraction of wheel width

Annealed, cold drawn

5500–6500 50–100

0.003

0.0005

1⁄ 4

52–65 Rc

Carburized and/or quenched and tempered

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


1⁄ 10

52 Rc max.

Alloy steels

Tool steels

Material Condition

Wheel Speed, fpm

150–275 Bhn Annealed 56–65 Rc

Quenched and tempered

200–350 Bhn Normalized, annealed 60–65 Rc

Nitrided

5500–6500 50–100

0.003

0.0005

5500–6500 50–100

0.002

0.0005

1⁄ 5

5500–6500 50–100

0.002

0.0005

1⁄ 10

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

Gray irons

52 Rc max.

As cast, annealed, and/or quenched and tempered

5000–6500 50–100

0.003

0.001

1⁄ 3

Ductile irons

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

Cast steels

Stainless steels, martensitic Aluminum alloys

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



1197

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

..

..

..

.. .. .. 䊉 .. .. .. .. .. .. .. .. ..

.. .. .. .. .. .. .. .. .. .. .. 䊉䊉

.. .. .. .. .. .. .. .. .. .. .. 䊉 ..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

..

.. .. 䊉 .. .. .. .. .. .. ..

䊉 .. .. .. .. .. .. .. .. ..

.. 䊉 .. .. .. .. .. .. .. ..

.. .. .. .. .. .. 䊉 .. .. ..

.. .. .. .. .. .. .. .. .. ..

.. .. .. 䊉䊉 .. .. .. .. ..

.. .. ..

.. .. ..

.. .. ..

..

..

..

..

..

..

䊉 .. 䊉 .. .. .. .. 䊉 .. .. .. .. ..

䊉 .. 䊉 .. .. .. .. 䊉 .. .. .. .. ..

.. .. .. .. .. .. .. .. .. .. .. .. ..

.. .. 䊉䊉䊉 .. .. .. .. .. .. .. ..

.. .. .. 䊉 .. .. .. .. 䊉䊉 .. 䊉䊉

.. 䊉 .. .. .. .. .. .. .. .. 䊉 .. ..

..

..

..

..

..

䊉

..

..

..

..

..

.. .. .. .. .. .. .. .. 䊉 ..

.. .. .. .. .. .. .. .. .. ..

.. .. .. .. .. 䊉 .. .. .. 䊉

Poor size holding

Poor finish

.. 䊉 .. 䊉 .. .. 䊉 .. 䊉 .. .. 䊉 .. ..

Scratches on surface

.. 䊉 .. 䊉 .. .. 䊉䊉 .. 䊉 .. 䊉 .. ..

Chatter marks

.. .. ..

Feed lines

.. .. 䊉

Burning or checking

.. .. ..

Burnishing of work

.. .. ..

.. .. ..

䊉䊉䊉

.. 䊉 ..

.. .. ..

Abrupt section changes

䊉

䊉

..

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

.. .. .. .. .. .. .. 䊉 .. 䊉 .. .. 䊉

.. .. .. 䊉 .. .. .. .. .. .. 䊉䊉 ..

Chuck not aligned

䊉

䊉

..

..

..

Vibrations in machine

..

..

..

..

..

Plane of movement out of parallel

䊉

䊉

..

..

..

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 .. .. ..

.. .. .. .. .. .. 䊉 .. .. ..

.. .. 䊉 .. .. .. .. .. .. ..

.. .. .. .. .. .. 䊉 .. .. ..

WORK RETAINMENT

.. .. ..

.. .. ..

Work not parallel

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

Work not flat

WORK DIMENSION

1198

Table 4. Common Faults and Possible Causes in Surface Grinding

Machinery's Handbook 28th Edition OFFHAND GRINDING

1199

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.


1200

Machinery's Handbook 28th Edition 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 and abrasive 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


Machinery's Handbook 28th Edition 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

4500–7000

Heavy or with abrasive compound

Smooth-faced rubber or cloth

20–40

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 70–90

Roughing

R/R SiC or Al2O3

24–80

5000–6500

Light


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 70–90

Roughing

R/R SiC or Al2O3

36–80

2200–4500

Light-body


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

20–30

220–320

4500–6500


Plain or finger-type cloth wheel, or free belt

Roughing

R/R Al2O3

24–60

2000–4000

None


70–90

Polishing

R/R Al2O3

80–150

4000–5500

None

Serrated rubber

30–70

R/R Al2O3

Fine Polishing Cast Iron

120–240

4000–5500

Light-body

Smooth-faced rubber

30–40

Roughing

R/R SiC or Al2O3

36–50

700–1500

Sulfur-chlorinated

Small-diameter, cog-tooth serrated rubber

70–80

Polishing

R/R SiC

60–120

1200–2000

Light-body

Standard serrated rubber

Fine Polishing

R/R SiC

120–240

1200–2000

Light-body


Fine Polishing Titanium

50 20–40

1201

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

Durometer Hardness

180–500

Fine Polishing Copper Alloys or Brass

Type

R/R Al2O3

Fine Polishing Aluminum, Cast or Fabricated

Abrasive Belta

Roughing

Fine Polishing Stainless Steel

Contact Wheel

Type of Grease Lubricant

Grit

Type of Operation

Machinery's Handbook 28th Edition ABRASIVE CUTTING

1202

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 1149). 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). 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.


Machinery's Handbook 28th Edition HONING PROCESS

1203

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 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


1204

Machinery's Handbook 28th Edition HONING PROCESS

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 × DThe 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 28th Edition LAPS AND LAPPING

1205

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


1206


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.



1207

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:


1208

Machinery's Handbook 28th Edition 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-



1209

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.


Machinery's Handbook 28th Edition KNURLS AND KNURLING

1210

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 64

Nominal Diameter, Dnt 1⁄ 2

5⁄ 8

3⁄ 4

7⁄ 8

Tracking Correction Factor Q

Straight

Diagonal

0.9864

0.0006676

0.024

0.021

Major Diameter of Knurl, Dot, +0.0000, −0.0015 0.4932

0.6165

0.7398

0.8631

Tooth Depth, h, + 0.0015, − 0.0000

1

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.



1211

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

(3)

=circular pitch on nominal diameter = π ÷ P

(4)

=circular pitch on major diameter = πDot ÷ Nt

(5)

Dot = major diameter of knurl = Dnt − (NtQ ÷ π) Q =Pnt − Pot = tracking correction factor in Formula

(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 correction 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.



1212

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 Tooth Depth, h

Diametral Pitch, P

Linear Pitch,a Pl

Straight

Diagonal

64

0.0484

0.024

96

0.0325

0.016

Tooth Depth, h

Radius at Root, R

Diametral Pitch, P

Linear Pitch,a Pl

Radius at Root, R

Straight

Diagonal

0.021

0.0070 0.0050

128

0.0244

0.012

0.010

0.0045 0.0030

0.014

0.0060 0.0040

160

0.0195

0.009

0.008

0.0040 0.0025

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.



1213

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 D w = ---------------- = ---------------------------= 0.996 inch 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


1214


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 28th Edition ACCURACY

1215

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


Next Page Machinery's Handbook 28th Edition ACCURACY

1216

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 n

1σ =

1 -----------n–1

∑ ( 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 = 1σ =

=

2 2 2 2 2 1 ------------ [ ( X 1j – X j ) + ( X 2j – X j ) + ( X 3j – X j ) + ( X 4j – X j ) + ( X 5j – X j ) ] n–1

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.


Machinery's Handbook 28th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES PUNCHES, DIES, AND PRESS WORK 1267 Sheet Metal Design 1267 Designing Sheet Metal Parts for Production 1268 Blanking and Punching 1270 Blanking and Punching Clearance 1271 Die Opening Profile 1272 Deformation Force, Deformation Work, and Force of Press 1272 Stripper Force 1273 Fine Blanking 1275 Shaving 1275 Bending 1276 Inside Bend Radius 1276 Sheet Metal 1279 Lengths of Straight Stock 1282 Drawing 1282 Mechanics of Deep Drawing 1284 Drawn Shells 1286 Drawn Cylindrical Shells 1288 Lubricants and Their Effects on Press Work 1290 Joining and Edging 1294 Steel Rule Dies 1296 Making Steel Rule Dies

ELECTRICAL DISCHARGE MACHINING 1298 EDM Terms 1300 EDM Process 1303 Electrical Control Adjustments 1304 Workpiece Materials 1304 Characteristics of Materials 1304 Electrode Materials 1305 Types of Electrodes 1306 Making Electrodes 1308 Wire EDM

IRON AND STEEL CASTINGS 1309 Material Properties 1309 Gray Cast Iron 1309 White Cast Iron 1309 Chilled Cast Iron 1309 Alloy Cast Iron 1310 Malleable-iron Castings 1310 Ductile Cast Iron 1311 Steel Castings 1311 Carbon Steel Castings

IRON AND STEEL CASTINGS (Continued)

1312 1312 1313 1313 1314 1314 1316 1317 1317 1317 1317 1318 1318 1318 1318 1319 1319 1320 1320 1320 1320 1321 1321 1321 1322 1322 1322 1322 1323 1323 1323 1324 1324 1324 1324 1325 1325 1325 1325 1325 1326 1326 1326 1328 1328 1328 1328

Mechanical Properties Alloy Steel Castings Heat-Resistant Steel Castings Corrosion-Resistant Steel Castings Casting of Metals Definitions 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


Machinery's Handbook 28th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES SOLDERING AND BRAZING

WELDING (Continued)

1329 Soldering 1329 Forms Available 1329 Fluxes for Soldering 1329 Methods of Application 1331 Ultrasonic Fluxless Soldering 1331 Brazing 1331 Filler Metals 1331 Selection of Filler Metals 1331 Fluxes for Brazing 1332 Brazing Filler Metals 1336 Steadying Work 1336 Supplying Heat 1336 Symbol Application

WELDING 1338 Welding Electrodes and Fluxes 1338 Processes 1339 Gas Metal Arc Welding (GMAW) 1339 Electrode Diameters 1340 Maximum Deposition Rates 1340 GMAW Welding of Sheet Steel 1340 Application of Shielding Gases 1342 Welding Controls 1344 GMAW Spray Transfer 1344 Deposition Rates of Electrodes 1346 Optimum Settings for GMAW 1346 Spray Transfer Voltage 1347 Flux-Cored Arc Welding 1347 Flux-Cored Welding Electrodes 1347 Gas-Shielded Electrodes 1348 Settings for FCAW Electrodes 1348 Weld Requirements 1348 Selecting an FCAW Electrode 1349 FCAW Electrodes 1350 Contact Tip Recess 1350 Porosity and Worm Tracks 1350 Welding with Various Diameter 1351 High-Deposition Electrodes 1352 Deposition Rates 1352 Vertical Up Welding 1352 Flat and Horizontal Welds 1352 Electrode Diameters and Deposition Rates 1354 Shielding Gases and FCAW Electrodes 1354 Shielded Metal Arc Welding 1354 ANSI/AWS Standard 1355 AWS E60XX Electrodes 1357 AWS E70XX Electrodes

1358 1358 1360 1361 1361 1361 1361 1361 1362 1363 1363 1363 1363 1364 1364 1364 1365 1366 1367 1367 1367 1367 1367 1368 1368 1368 1368 1368 1368 1369 1369 1369 1369 1370 1370 1370 1371 1372 1372 1373 1374 1377 1377 1378 1378 1378 1378 1379

Gas Tungsten Arc Welding GTAW Welding Current Tungsten Electrode Type Selection of GTAW Tungsten Electrode Compositions Electrode and Current Selection Current Ranges GTAW Electrodes EWP, EWZ, GTAW Electrodes Filler Metals Shielding Gases Plasma Arc Welding (PAW) Gases for Plasma Arc Welding Shielding Gases PAW Welding Equipment Applications Welding Aluminum Plasma Arc Surface Coating Plasma Arc Cutting of Metals Precision Plasma Arc Cutting Flame Cutting of Metals Arc Cutting The Cutting Torch Adjustment of Cutting Torch Metals That Can Be Cut Cutting Stainless Steel Cutting Cast Iron Mechanically Guided Torches Cutting Steel Castings Thickness of Metal Hard Facing Hard-Facing Materials High-Speed Steels Austenitic Manganese Steels Austenitic High-Chromium Irons Cobalt-Base Alloys Copper-Base Alloys Nickel-Chromium-Boron Alloys Chromium Plating Electron-Beam (EB) Welding Pipe Welding Use of Flux-cored Electrodes Complete Weld Fusion Other Methods Pipe Welding Procedure Thick-Wall, Carbon-Steel Pipes Root Welding Fill and Cover Welds


Machinery's Handbook 28th Edition TABLE OF CONTENTS MANUFACTURING PROCESSES WELDING

FINISHING OPERATIONS

(Continued)

1380

1384 1385 1390 1390

Thin-Walled Carbon Steel Pipes, Root, Fill and Cover Pass Weld and Welding Symbols ANSI Weld and Welding Symbols Basic Weld Symbols Supplementary Weld Symbols Welding Codes, Rules, Regulations, and Specifications Letter Designations for Welding ANSI Welding Symbols Nondestructive Testing Symbols

1392 1392 1392 1393 1394 1394 1395 1395 1396 1396 1397 1397 1398 1399 1400 1400 1401 1401 1401 1402 1402 1402 1402 1403 1403 1403 1403 1403 1403 1404 1404 1404

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 Heat Treatment with Lasers Materials Applicability Hardening Rates Cladding with Lasers Marking with Lasers Mask Marking Scanned-Beam Marking

1381 1381 1382 1383 1383

LASERS

1405 Power Brush Finishing 1405 Description of Brushes 1405 Use of Brushes 1405 Deburring and Producing a Radius 1406 Eliminating Undesirable Conditions 1406 Characteristics in Power Brush 1406 Polishing and Buffing 1406 Polishing Wheels 1409 Polishing Operations and Abrasives 1409 Buffing Wheels 1409 Speed of Polishing Wheels 1410 Grain Numbers of Emery 1410 Grades of Emery Cloth 1410 Etching and Etching Fluids 1410 Etching Fluids 1411 Conversion Coatings and the Coloring of Metals 1411 Passivation of Copper 1411 Coloring of Copper Alloys 1412 Coloring of Iron and Steel 1412 Anodizing Aluminum Alloys 1413 Magnesium Alloys 1413 Titanium Alloys 1413 Plating 1413 Surface Coatings 1421 Flame Spraying Process


Machinery's Handbook 28th Edition MANUFACTURING PROCESSES

1267

PUNCHES, DIES, AND PRESS WORK Designing Sheet Metal Parts for Production Sheet metal parts should be designed to satisfy the following criteria: The parts should allow high productivity rates. They should make highly efficient use of the materials involved. The production machines should be easy to service. Machines should be usable by workers with relatively basic skills. Unfortunately, very few product designers concern themselves with suitability of production, their prime concern is usually the function of the part. Design rules for parts to be produced by blanking and punching: Avoid part design with complex configurations. Use minimum dimensions of punched openings relative to material thickness given in Table 1. Use minimum distances between punched opening and rounded radius relative to material thickness given in Table 2. Design rules for parts produced by bending: Minimum bend radius should be used only if it is necessary for correct function of part. The bend radius should be larger than the thickness of the material. Use minimum distances between punched opening and bend radius given in Table 2. Flange length as shown in Table 2 needs to be h ≥ 2T. If a part has more than one bend, it is necessary to define technological data. Design rules of parts produced by drawing: Avoid very complicated parts. Make diameter of flange D less than three times the diameter of shell (D < 3d), if height h of shell is greater than twice the diameter of shell (h > 2d) as shown in Table 2. Avoid design of rectangular and square shells with bottom radii less than the corner radius in the junction area. The shortest distance between corner radii should be no less than the depth of shell. Table 1. Minimal Dimensions of Punched Openings b d b

b

b

Form of opening Material

Circle dmin =

Square bmin =

Rectangular bmin =

Oval bmin =

Stainless steel

1.50 T

1.40 T

1.20 T

1.10 T

High-carbon steel

1.20 T

1.10 T

0.90 T

0.80 T

Medium-carbon steel

1.00 T

0.90 T

0.70 T

0.60 T

Low-carbon steel

0.90 T

0.80 T

0.60 T

0.55 T

Brass and copper

0.80 T

0.70 T

0.60 T

0.55 T

Magnesium alloy at 500° F

0.25 T

0.45 T

0.35 T

0.30 T

Note: With fine punching process, minimal diameter of punched hole is (0.50 – 0.70) T.


Machinery's Handbook 28th Edition BLANKING AND PUNCHING

1268

Table 2. Minimum Distance between Punched Opening and Edges and Rounded Radius Part is

Form of opening Circle

Minimum Distance

Sketch

c≥T r ≥ 0.5T

c c

c c c

Blanked Rectangle

c ≥ 1.2T r ≥ 0.5T

c

r T

c ≥ 2T

Bent

Circle

r ≥ ( 0.5 – 1.0 )T

a

r ≥ ( 1.0 – 2.0 )T

b

r ≥ ( 2.0 – 3.0 )T

c

h

T

r

c

T

r c

c d

d ≤ ( d 1 – 2r ) D 1 ≥ ( d 1 – 2r )

Drawn

Circle

d

r1

D ≥ ( D 1 + 3T + d 2 ) c ≥ r + 0.5T

r

D

D

d2

a Al and brass b Steel c Al-alloy 6000 series

Blanking and Punching.—Blanking and punching are fabricating processes used to cut materials into forms by the use of a die. Major variables in these processes are as follows: the punch force, the speed of the punch, the surface condition and materials of the punch and die, the condition of the blade edge of the punch and die, the lubricant, and the amount of clearance.


Machinery's Handbook 28th Edition BLANKING AND PUNCHING

1269

In blanking, a workpiece is removed from the primary material strip or sheet when it is punched. The material that is removed is the new workpiece or blank. Punching is a fabricating process that removes a scrap slug from the workpiece each time a punch enters the punching die. This process leaves a hole in the workpiece (Fig. 1).

Workpiece

Blanking

Workpiece

Punching Fig. 1. Blanking and Punching

Characteristics of the blanking process include: 1) Ability to produce workpieces in both strip and sheet material during medium and mass production. 2) Removal of the workpiece from the primary material stock as a punch enters a die. 3) Control of the quality by the punch and die clearance. 4) Ability to produce holes of varying shapes quickly. Characteristics of the punching process include: 1) Ability to produce holes in both strip and sheet material during medium and mass production. 2) Ability to produce holes of varying shapes quickly. There are three phases in the process of shearing during blanking and punching as illustrated in Fig. 2. Punch

Phase I

Phase II

Work material

Phase III

Die

Fig. 2. Phases in the Process of Shearing.

In Phase I, work material is compressed across and slightly deformed between the punch and die, but the stress and deformation in the material does not exceed the plastic limit. This phase is known as the elastic phase. In Phase II, the work material is pushed farther into the die opening by the punch; at this point in the operation the material has been obviously deformed at the rim, between the cutting edges of the punch and the die. The concentration of outside forces causes plastic deformation at the rim of the material. At the end of this phase, the stress in the work material close to the cutting edges reaches a value corresponding to the material shear strength, but the material resists fracture. This phase is called the plastic phase. During Phase III, the strain in the work material reaches the fracture limit, and microcracks appear, which turn into macro-cracks, followed by separation of the parts of the workpiece. The cracks in the material start at the cutting edge of the punch on the upper side of the work material, and at the die edge on the lower side of the material; the crack propagates along the slip planes until complete separation of the part from the sheet occurs. A slight burr is generally left at the bottom of the hole and at the top of the slug. The slug is then pushed farther into the die opening. The slug burnish zone expands and is held in the die opening. The whole burnish zone contracts and clings to the punch.


Machinery's Handbook 28th Edition BLANKING AND PUNCHING CLEARANCE

1270

Blanking and Punching Clearance .—Clearance, c , is the space (per side) between the Dd – dp punch and the die opening shown in the figure, such that: c = ----------------2

dp c

Dd

Punch and Die Clearance

Ideally, proper clearance between the cutting edges enables the fractures to start at the cutting edge of the punch and the die. The fractures will proceed toward each other until they meet. The fractured portion of the sheared edge then has a clean appearance. For optimum finish of a cut edge, correct clearance is necessary. This clearance is a function of the type, thickness, and temper of the material. When clearance is not sufficient, additional layers of the material must be cut before complete separation is accomplished. With correct clearance, the angle of the fracture will permit a clean break below the burnish zone because the upper and lower fractures will extend toward one another. Excessive clearance will result in a tapered cut edge, because for any cutting operation, the opposite side of the material that the punch enters after cutting will be the same size as the die opening. Where Clearance is Applied: Whether clearance is deducted from the dimensions of the punch or added to the dimensions of the die opening depends upon the nature of the workpiece. In the blanking process (a blank of given size is required), the die opening is made to that size and the punch is made smaller. Conversely, in the punching process (when holes of a given size are required), the punch is made to the dimensions and the die opening is made larger. Therefore, for blanking, the clearance is deducted from the size of the punch, and for piercing the clearance is added to the size of the die opening. Value for Clearance: Clearance is generally expressed as a percentage of the material thickness, although an absolute value is sometimes specified. Table 3 shows the value of the shear clearance in percentages, depending on the type and thickness of the material. Table 3. Values for Clearance as a Percentage of the Thickness of the Material Material Thickness T (in.)

Material Low carbon steel Copper and soft brass Medium carbon steel 0.20% to 0.25% carbon Hard brass Hard steel, 0.40% to 0.60% carbon

< 0.040 5.0 5.0

0.040 – 0.080 6.0 6.0

0.082 – 0.118 7.0 7.0

0.122 – 0.197 8.0 8.0

0.200 – 0.275 9.0 9.0

6.0

7.0

8.0

9.0

10.0

6.0

7.0

8.0

9.0

10.0

7.0

8.0

9.0

10.0

12.0


Machinery's Handbook 28th Edition DIE PROFILE

1271

Table 4 shows absolute values for the blanking and punching clearance for high-carbon steel (0.60% to 1.0% carbon) depending on the thickness of the work material. Table 4. Absolute Values for Clearance for Blanking and Punching High-Carbon Steel Material Thickness, T (in.)

Clearance, c (in.)

Material thickness, T (in.)

Clearance, c (in.)

0.012

0.00006

0.157

0.0095

0.197

0.0009

0.177

0.0116

0.315

0.0013

0.197

0.0138

0.040

0.0016

0.236

0.0177

0.047

0.0020

0.275

0.0226

0.060

0.0026

0.315

0.0285

0.078

0.0035

0.394

0.0394

0.098

0.0047

0.472

0.0502

0.118

0.0059

0.590

0.0689

0.138

0.0077

0.748

0.0935

Effect of Clearance: Manufacturers have performed many studies on the effect of clearance on punching and blanking. Clearance affects not only the smoothness of the fracture, but also the deformation force and deformation work. A tighter blanking and punching clearance generates more heat on the cutting edge and the bulging area tightens around the punch. These effects produce a faster breakdown of the cutting edge. If the clearance increases, the bulging area disappears and the roll-over surface is stretched and will retract after the slug breaks free. Less heat is generated with increases in the blanking and punching clearance, and the edge breakdown rate is reduced. The deformation force is greatest when the punch diameter is small compared to the thickness of the work material. In one test, for example, a punching force of about 142 kN was required to punch 19 mm holes into 8 mm mild steel when the clearance was about 10 percent. With a clearance of about 4.5 per cent, the punching force increased to 147 kN and a clearance of 2.75 per cent resulted in a force of 153.5 kN. Die Opening Profile.— Die opening profiles depend on the purpose and required tolerance of the workpiece. Two opening profiles are shown in Figs. 2a and 2b. h

Fig. 2a. Opening Profile for High Quality Part

Fig. 2b. Opening for Low Accuracy Part.

The profile in Figs. 2a gives the highest quality workpiece. To allow a die block to be sharpened more times, the height h of the die block needs to be greater than the thickness of the workpiece. The value of h is given in Table 5. The die opening profile in Fig. 2b is used for making a small part with low accuracy from very soft material, such as soft thin brass. The angle of the cone α = 15′ to 45′.


Machinery's Handbook 28th Edition DEFORMATION FORCE AND WORK

1272

Table 5. Value of Dimension h Based on Material Thickness < 0.040 Height h (in.)

Work material thickness, T (in.) 0.0472 – 0.1968 0.2009 – 0.3937

0.1377

0.2559

0.4527

Angle α = 3° to 5°

Deformation Force, Deformation Work, and Force of Press .—Deformation Force: Deformation force F for punching and blanking with flat face of punch is defined by the following equation: (1) F = LTτ m = 0.8LT ( UTS ) where F = deformation force (lb) L = the total length of cutting (in) T = thickness of the material (in) τm = shear stress (lb/in2) UTS = the ultimate tensile strength of the work material lb/in2 Force of Press: Such variables as unequal thickness of the material, friction between the punch and workpiece, or dull cutting edges, can increase the necessary force by up to 30 per cent, so these variables must be considered in selecting the power requirements of the press. That is, the force requirement of the press, Fp is F p = 1.3F

(2)

The blanking and punching force can be reduced if the punch or die has bevel-cut edges. In blanking operations, bevel shear angles should be used on the die to ensure that the workpiece remains flat. In punching operations, bevel shear angles should be used on the punch. Deformation Work: Deformation work W for punching and blanking with flat face of punch is defined by the following equation: W = kFT (3) where k = a coefficient that depends on the shear strength of the material and the thickness of the material F = deformation force (lb) T = material thickness (in) Table 6. Values for Coefficient k for Some Materials Material

Shear Strength lb/in.2 35,000 – 50,000

Low carbon steel Medium carbon steel 50,000 – 70,000 0.20 to 0.25% carbon Hard steel 70,000–95,000 0.40 to 0.60% carbon Copper, annealed 21,000

< 0.040 0.70 – 0.65

Material Thickness (in) 0.040 –0.078 0.078 – 0.157 0.64 –0.60 0.58 0.50

> 0.157 0.45 – 0.35

0.60 – 0.55

0.54 – 0. 50

0.49 – 0.42

0.40 - 0.30

0.45 – 0.42

0.41 –0.38

0.36 –0.32

0.30 –0.20

0.75 – 0.69

0.70 – 0.65

0.64 –0.55

0.50 – 0.40

Stripper Force .—Elastic Stripper: When spring strippers are used, it is necessary to calculate the amount of force required to effect stripping. This force may be calculated by the following equation: 1 F s = ------------------- PT = 855PT (4) 0.00117 where Fs = stripping force (lb) P = sum of the perimeters of all the punching or blanking faces (in) T = thickness of material (in)


Machinery's Handbook 28th Edition FINE BLANKING

1273

This formula has been used for many years by a number of manufacturers and has been found to be satisfactory for most punching and blanking operations. After the total stripping force has been determined, the stripping force per spring must be found in order to establish the number and dimensions of springs required. Maximum force per spring is usually listed in the manufacturers’ catalog. The correct determined force per spring must satisfy the following relationship: Fs F max > F so > ----(5) n where Fmax = maximum force per spring (lb) FSO = stripping force per spring (lb) Fs = total stripping force (lb) n = number of springs 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 fineblanking 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 punch and die as a percentage of the thickness of material are given in Table 7. The clamping elements are sharp projections of 90-degree V-section that follow the outline of the workpiece and 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. Table 7. Values for Clearances Used in Fine-Blanking Tools as a Percentage of the Thickness of the Material. Material Thickness (in.) < 0.040 0.040 – 0.063 0.063 – 0.098 0.098 – 0.125 0.125 – 0.197 0.197 – 0.315 0.315 – 0.630

Clearance % Inside Contour 2.0 1.5 1.25 1.0 0.8 0.7 0.5

Outside Contour 1.0

0.5


1274

Machinery's Handbook 28th Edition FINE BLANKING Table 8. Dimensions for V-projections Used in Fine-Blanking Tools

V-Projections On Stripper Plate Only V-Projections On Both Stripper and Die Plate Material Thickness A h r H R V-Projections On Stripper Plate Only 0.040-0.063 0.040 0.012 0.008 … … 0.063-0.098 0.055 0.015 0.008 … … 0.098-0.125 0.083 0.024 0.012 … … 0.125-0.157 0.098 0.028 0.012 … … 0.157-0.197 0.110 0.032 0.012 … … V-Projections On Both Stripper and Die Plate 0.157–0.197 0.098 0.020 0.008 0.032 0.032 0.197–0.248 0.118 0.028 0.008 0.040 0.040 0.248–0.315 0.138 0.032 0.008 0.047 0.047 0.315–0.394 0.177 0.040 0.020 0.060 0.060 0.394–0.492 0.217 0.047 0.020 0.070 0.080 0.492–0.630 0.276 0.063 0.020 0.087 0.118 All units are in inches.

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 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 pounds (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 previously. Dimensions and positioning of the V-projection(s) are related to the material thickness,


Machinery's Handbook 28th Edition BENDING SHEET METAL

1275

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. 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. Shaving.— The edges of punched and blanked parts are generally rough and uneven. A shaving operation is used to achieve very precise clean parts. Shaving is the process of removing a thin layer of material from the inside or outside contour of a workpiece or from both sides with a sharp punch and die. Shaving a Punched Workpiece: It is necessary to provide a small amount of stock on the punched or blanked workpiece for subsequent shaving. This amount, δ, is the difference between diameters of the hole after shaving and before shaving. (6) δ = d – do where d = diameter of hole after shaving (in) d0 = diameter of hole before shaving (in) The value of δ is 0.006 to 0.0098 in. for a previously-punched hole, and 0.004 to 0.006 in. for a previously-drilled hole. The diameter of punch dp can be calculated from the formula: dp = d + ε + i

(7)

where d = diameter of hole after shaving (in.) ε =production tolerance of the hole (in.) i =amount of compensation for tightening of the hole after shaving (in.) (i = 0.0002 to 0.00067 in.) The diameter of the die Dd is D d = (1.20 to 1.30)d p

(8)

Shaving a Blanked Workpiece: Thin layers of material can be removed from a blanked surface by a process similar to punching. If the workpiece after shaving needs to have a diameter D, the punch diameter for the blanking operation is dp = D + δ (9) The die diameter for the blanking operation is d d = d p + 2c = D + δ + 2c

(10)

where D = diameter of final piece (in) c = clearance between die and punch (in) δ =amount of material for shaving (in) Bending One of the most common processes for sheet-metal forming is bending, which is used to form pieces such as L, U, or V-profiles, and also to improve the stiffness of a piece by increasing its moment of inertia. Bending metal is a uniform straining process that plastically deforms the material and changes its shape. The material is stressed above the yield strength but below the ultimate tensile strength. The surface area of the material changes only in the bending zone. "Bending" usually refers to linear deformation about one axis. Bending may be performed by air bending, bottoming bending, or coining. Air Bending: Air bending is done with the punch touching the workpiece but not bottoming it in the lower die. The profile of a die for air bending can have a right angle or an acute angle. The edges of the die with which the workpiece is in contact are rounded, and the radius of the punch will always be smaller than the bending radius.


1276


Bottoming Bending and Coining: Bottoming or coining bending is the process by which the punch and the workpiece bottom on the die. It is necessary to flatten the bottom bend area of the workpiece between the tip of the punch and bottom on the die in order to avoid springback. The tonnage required on this type of press is higher than in air bending. Inside Bend Radius .—Fig. 3 shows the terminology used in the bending process. T Bend allowance Bend angle

Inside bend radius Neutral axis

Fig. 3. Schematic illustration of terminology used in the bending process

One of the most important factors influencing the quality of bent workpieces is the inside bend radius which, must be within defined limits. Minimum Bend Radius: If the bend radius is less than Rmin given in Equation (11), particularly in harder materials, the material at the outside of the bend will tend to "orange peel." If this orange peeling, or opening of the grain, is severe enough, the metal will fracture or crack off completely in extreme cases examples. The minimum bend radius, Rmin is given by the following formula: R min = T  50 ------ – 1 r 

(11)

where T =material thickness (in.) r =percentage reduction in a tensile test for a given material (%) Maximum Bend Radius: If the bend radius is greater than Rmax given in Equation (12), the bend will be very hard to control and will spring back erratically. The amount of springback will worsen on thinner materials. When large radius bends are required an allowance should always be made for this in the tolerance of the part. To achieve permanent plastic deformation in the outer fibers of the bent workpiece the maximum bend radius must be TE R max ≤ --------------(12) 2 ( YS ) 2 where E =modulus of elasticity lb/in YS = yield strength lb/in2 T =thickness of material (in) Neutral axis: When material is formed, the deformation in the inside fibers of the material will compress during forming and the fibers of the material on the outside of the bend will expand. The material between these two regions remains neutral during forming and is referred to as the neutral axis of the material. The length of fibers along the neutral axis of the bend does not change during forming. This neutral axis is used when figuring the bend allowance for flat blank layouts. 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 10 or: L = ( 0.55 × T ) + ( 1.57 × R ) (13)



1277

For 90° bends in half-hard copper and brass, soft steel, and aluminum see Table 11 or: L = ( 0.64 × T ) + ( 1.57 × R ) (14) For 90° bends in bronze, hard copper, cold-rolled steel, and spring steel see Table 12 or: (15) L = ( 0.71 × T ) + ( 1.57 × R ) Other Bending Allowance Formulas: When bending sheet steel or brass, add from 1⁄3 to 1⁄2 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, Table 9, refers 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 hardness and other mechanical properties vary considerably. The values given in the table apply to sheet steel, aluminum, brass and bronze. Experience has demonstrated that for semi-square corners, such as those formed in a V-die, the amount to be deducted from the sum of the outside bend dimensions, shown in Fig. 8 as 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 thickness of the stock. The values of X for different gages and numbers of bends are given in the table. Application of the formula 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 that are either drawn through a block of steel made to the required shape, or are 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 example, the deduction is X = 1.33 BG. Table 9. Allowances for Bends in Sheet Metal

Formed in a Press by a V-die

Rolled or Drawn in a Draw-bench

Gage 18 16 14 13 12 11 10 18 16 14 13 12 11 10

Thickness Inches

Square Bends

Amount to be deducted from the sum of the outside bend dimensions, (in) 1 Bend

2 Bends

3 Bends

4 Bends

5 Bends

6 Bends

7 Bends

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

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

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



1278

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. 4, the angle on the drawing is 60 degrees, but the angle of bend A is 120 degrees (180 − 60 = 120); in Fig. 5, the angle of bend A is 60 degrees; in Fig. 6, angle A is 90 − 30 = 60 degrees. Formulas (13), (14), and (15) 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. 4.

Fig. 5.

Fig. 6.

Example, Showing Application of Formulas:Find the length before bending of the part illustrated by Fig. 7. Soft steel is to be used. For bend at left-hand end (180-degree bend) 180 L = [ ( 0.64 × 0.125 ) + ( 1.57 × 0.375 ) ] × --------- = 1.338 90 For bend at right-hand end (60-degree bend) 60 L = [ ( 0.64 × 0.125 ) + ( 1.57 × 0.625 ) ] × ------ = 0.707 90 Total length before bending = 3.5 + 1.338 + 0.707 = 5.545 inches

Fig. 7.

Fig. 8.

Springback: Every plastic deformation is followed by elastic recovery. As a consequence of this phenomenon, which occurs when a flat-rolled metal or alloy is cold-worked, upon release of the forming force, the material has a tendency to partially return to its original shape. This effect is called springback and is influenced not only by the tensile and yield strengths, but also by the thickness, bend radius, and bend angle. To estimate springback, an approximate formula in terms of the bend radius before springback Ri and bend radius after springback Rf is as follows R i ( YS ) 3 R i ( YS ) Ri ----- = 4  ----------------- – 3  ----------------- + 1  ET   ET  Rf

(16)

where Ri = bend radius before springback (in) Rf =bend radius after springback (in) YS = yield strength of the material lb/in2 E = modulus of elasticity of the material lb/in2 T = material thickness (in)



Table 10. 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 3⁄ 64

1⁄ 16

5⁄ 64

3⁄ 32

1⁄ 8

5⁄ 32

3⁄ 16

7⁄ 32

1⁄ 4

9⁄ 32

5⁄ 16

1⁄ 32 3⁄ 64 1⁄ 16

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

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

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 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8

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

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

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

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

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

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

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 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4

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

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

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

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

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 7⁄ 8 15⁄ 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

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

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 1 1⁄16

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⁄ 8 3⁄ 16 1⁄ 4

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

1.875

1.883

1.892

1.900

1.909

1.918

1.935

1.952

1.969

1.986

2.004

2.021

2.038

1.972

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


1279

1⁄ 32

BENDING SHEET METAL

1⁄ 64



3⁄ 64

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⁄ 8 3⁄ 16 1⁄ 4

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

1.875

1.885

1.895

1.905

1.915

1.925

1.945

1.965

1.985

1.005

2.025

2.045

2.065

1.973

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

1 1 1


BENDING SHEET METAL

1⁄ 64

1280

Table 11. 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


Table 12. Lengths of Straight Stock Required for 90-Degree Bends in Hard Copper, Bronze, Cold-Rolled Steel, and Spring Steel 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

1⁄ 32 3⁄ 64 1⁄ 16

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

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

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 7⁄ 32 1⁄ 4 9⁄ 32 5⁄ 16 11⁄ 32 3⁄ 8

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

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

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

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

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

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

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 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4

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

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

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

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

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 7⁄ 8 15⁄ 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

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

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 1 1⁄16

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⁄ 8 3⁄ 16 1⁄ 4

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

1.877

1.888

1.899

1.910

1.921

1.933

1.955

1.977

1.999

2.021

2.044

2.066

2.088

1.974

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


1281

1⁄ 32

BENDING SHEET METAL

1⁄ 64

1282

Machinery's Handbook 28th Edition DRAWING

Bending Force: The bending force is a function of the strength of the material, the length of the workpiece, and the die opening. A good approximation of the required force F is LT 2 ( UTS )F = ------------------------W where L =length of the workpiece (in) T =material thickness (in) UTS = utility tensile strength of the material lb/in2 W = die opening (in)

(17)

Drawing The drawing of metal, or deep drawing is the process by which a punch is used to force sheet metal to flow between the surfaces of a punch and a die. Many products made from sheet metals are given the required shape by using a drawing operation. A blank is first cut from flat stock, and then a shell of cylindrical, conical or special shape is produced from this flat blank by means of one or more drawing dies. Most drawn parts are of cylindrical shape, but rectangular, square, and specialized shapes are sometimes produced. With this process, it is possible to get a final part–using minimal operations and generating minimal scrap–that can be assembled without further operations. Mechanics of Deep Drawing .—As the material is drawn into the die by the punch, it flows into a three-dimensional shape. The blank is held in place with a blank holder using a fixed force. High compressive stresses act upon the metal, which without the offsetting effect of a blank holder, would result in a severely wrinkled workpiece. Wrinkling is one of the major defects in deep drawing; it can damage the dies and adversely affect part assembly and function. The prediction and prevention of wrinkling is very important. There are a number of different analytical and experimental methods that can help to predict and prevent flange wrinkling, including finite element modeling (FEM). There are many important variables in the deep drawing process but they can be classified as either: material and friction factors, or tooling and equipment factors. Important material properties such as the strain hardening coefficient (n) and normal anisotropy (R) affect deep-drawing operations. Friction and lubrication at the punch, die, and workpiece interfaces are very important in a successful deep drawing process. Unlike bending operations, in which metal is plastically deformed in a relatively small area, drawing operations impose plastic deformation over large areas and stress states are different in different regions of the part. As a starting point, consider what appear to be three zones undergoing types of deformation: 1) The flat portion of the blank that has not yet entered the die cavity (the flange) 2) The portion of the blank that is in the die cavity (the wall) 3) The zone of contact between the punch and the blank (bottom) The radial tensile stress is due to the blank being pulled into the female die, and the compressive stress, normal in the blank sheet, is due to the blank holder pressure. The punch transmits force F to the bottom of the cup, so the part of the blank that is formed into the bottom of the cup is subjected to radial and tangential tensile stress. From the bottom, the punch transmits the force through the walls of the cup to the flange. In this stressed state, the walls tend to elongate in a longitudinal direction. Elongation causes the cup wall to become thinner, which can cause the workpiece to tear. If a drawing die radius in a deep drawing operation is too small, it will cause fracture of the cup in the zone between the wall and the flange. If a punch corner radius is too small it may cause fracture in the zone between a wall and bottom of a cup. Fracture can also result from high longitudinal tensile stresses in the bottom cup, due to a high ratio between the blank diameter and the punch diameter. Parts made by deep drawing usually require sev-



1283

eral successive draws. One or more annealing operations may be required to reduce work hardening by restoring the ductile grain structure. Number of Draws: The number of successive draws n required is a function of the ratio of the part height h to the part diameter d, and is given by this formula: h n = --d

(18)

where n = number of draws h = part height, and d = part diameter The value of n for the cylindrical cup draw is given in Table 13. Table 13. Number of draws (n) for a cylindrical cup draw. h/d

< 0.6

0.6 to1.4

1.4 to 2.5

2.5 to 4.0

4.0 to 7.0

7.0 to 12.0

n

1

2

3

4

5

6

Deep Drawability : Deep drawability is the ability of a sheet metal to be formed, or drawn, into a cupped or cavity shape without cracking or otherwise failing. The depth to which metal can be drawn in one operation depends upon the quality and kind of material, its thickness, and the amount that the work material is thinned in drawing. Drawing a Cylindrical Cup Without a Flange: A general rule for determining the depth to which a cylindrical cup without a flange can be drawn in one operation is defined as the ratio of the mean diameter dm of the drawn cup to the blank diameter D. This relation is known as the drawing ratio m. The value of the drawing ratio for the first and succeeding operations is given by: dm m 1 = -------1- ; D

dm m 2 = ---------2- ; Dm 1

dm m 3 = ---------3- ;.... Dm 2

dm n m n = --------------Dm n–1

The magnitude of these ratios determines the following parameters: 1) the stresses and forces of the deep drawing processes 2) the number of successive draws 3) the blank holder force 4) the quality of the final drawn parts. Table 14 shows optimal drawing ratios for cylindrical cups of sheet steel and brass without a flange. Table 14. Optimal Ratios M for Drawing a Cylindrical Cup Without Flanges Relative Thickness of the Material 100 (%)D TTr 1.5 – 1.0 1.0 – 0.6 0.6 – 0.3 0.3 – 0.15

Drawing ratio m

2.0 - 1.5

0.15 – 0.08

m1

0.48 – 0.50

0.50 – 0.53

0.53 – 0.55

0.55 – 0.58

0.58 – 0.60

0.60 – 0.63

m2

0.73 – 0.75

0.75 – 0.76

0.76 – 0.78

0.78 – 0.79

0.79 – 0.80

0.80 – 0.82

m3

0.76 – 0.78

0.78 – 0.79

0.79 – 0.80

0.81 – 0.82

0.81 – 0.82

0.82 – 0.84

m4

0.78 – 0.80

0.80 – 0.81

0.81 – 0.82

0.82 – 0.83

0.83 – 0.85

0.85 – 0.86

m5

0.80 – 0.82

0.82 -0.84

0.84 – 0.85

0.85 – 0.86

0.86 – 0.87

0.78 – 0.90



1284

Diameters of drawing workpieces for the first and succeeding operations are given by: d 1 = m 1 D;

d 2 = m 2 d 1 ;…d i = m i d i – 1

Drawing a Cylindrical Cup With a Flange: Table 15 gives values of the drawing ratio m for the first and succeeding operations for drawing a cylindrical cup with flange. Table 15. Values of ratio m for drawing a cylindrical cup with flange

Df h Rd

Rp

d Drawing ratio m

m1

m2 m3 m4 m5

T Relative thickness of the material T r = ---- 100 (%)

Df ----d

D

2.0 - 1.5 0.51 0.49 0.47 0.45 0.42 0.37 0.32 0.73 0.75 0.78 0.80

1.1 1.3 1.5 1.8 2.0 2.5 3.0 … … … …

1.5 – 1.0 0.53 0.51 0.49 0.46 0.43 0.38 0.33 0.75 0.78 0.80 0.82

1.0 – 0.6 0.55 0.53 0.50 0.47 0.44 0.38 0.33 0.76 0.79 0.82 0.84

0.6 – 0.3 0.57 0.54 0.51 0.48 0.45 0.38 0.33 0.78 0.80 0.83 0.85

0.3 – 0.15 0.59 0.55 0.52 0.48 0.45 0.38 0.33 0.80 0.82 0.84 0.86

Diameters of drawing workpiece for the first and succeeding operations are given by d 1 = m 1 D;

…d i = m i d i – 1

d2 = m2 d1 ;

However, diameter Df needs to be accomplished in the first drawing operation if possible. Diameters of Shell Blanks: The diameters of blanks for drawing plain cylindrical shells can be obtained from Table 16 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 D =

2

d + 4dh

(19)

where D =diameter of flat blank d = diameter of finished shell h =height of finished shell. Example:If the diameter of the finished shell d, is to be 1.5 inches, and the height h, 2 inches, the trial diameter of the blank D,would be found as follows: D =

2

1.5 + 4 × 1.5 × 2 =

14.25 = 3.78 inches



1285

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

(20)

These formulas are based on the assumption that the thickness of the drawn shell is to be 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 Formulas (19) or (20) 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: ht M = ----T

(21)

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 Table 15, 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 (21): 3.75 × 0.040- = 3 inches M = ht ----- = ----------------------------T 0.050 According to Table 15, the blank diameter for a shell 2 inches in diameter and 3 inches high is 5.29 inches. Formula (21) 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 h a + ( a – b ) --t

(22)



1286

Table 16. Diameters of Blanks for Drawn Cylindrical Shells Height of Shell

Dia.. 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

3

4

4 1⁄2

5

5 1⁄2

6

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

2.70

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

2.96

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 9.41

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

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

4

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

4 1⁄2

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

11.32

4 3⁄4

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


DRAWING

2 1⁄4 2 1⁄2


1287

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 (D), can be determined by the following formula: W D = 1.1284 -----(23) 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 required 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. Forces: The punch force for drawing a cylindrical shell needs to supply the various types of work required in deep drawing, such as the work of deformation, redundant work, friction work, and the work required for ironing (if required). Force for the First Drawing Operation: The calculation of the punch force for the first drawing operation (neglecting friction) is given by the following formula: F 1 = πd m T ( UTS ) (24) 1

dm1 = mean diameter of shell after the first operation (in) T = material thickness (in) UTS = ultimate tensile strength of the material lb/in2 Force for Subsequent Drawing Operations: Subsequent drawing operations are different from the first operation: as in the deep-drawing process, the flange diameter decreases but the zone of the plastic deformation does not change. The punch force for the next drawing operation can be calculated by the approximate empirical formula as follows: D- – 0.7 F i = πd p T ( UTS ) ⋅  ---(25) d  p

where

where

dp = punch diameter (in.) D = blank diameter (in.) T = material thickness (in.) UTS = ultimate tensile strength of the material lb/in2 Shapes of Blanks for Rectangular Shells: There is no formula for determining the shape of the blank for rectangular drawing that will produce the part as drawn to print. All corner contours must be developed. However, the following conservative procedure will get the die in the final design ballpark with a minimum of trials. When laying out a blank by this method, first draw a plan view of the finished shell or lines representing the shape of the part at the bottom, the corners being given the required radius, as shown in Fig. 9. Next, insert the sides and ends, making the length L and the width W equal to the length and width of the drawn part minus twice the radius r at the corners. To provide just the right amount of material for the corners, the first step is to find what blank diameter will be required to


1288

Machinery's Handbook 28th Edition LUBRICANTS AND PRESS WORK

draw a cylindrical shell having a radius r. This diameter can be calculated by the formula for the blank diameter (D) of the cylindrical shell: D = d 2 – 4dh (26) D = blank diameter (in.) d = diameter of drawn shell (in.) h = height of shell (in.) After determining the diameter D, scribe arcs at each corner having radius R equal to onehalf of diameter D. The outline of the blank for the rectangular part is then obtained by drawing curved lines between the ends and the sides, as shown in Fig. 9. These curves should touch the arcs R. where

L h D

r

R

W

Fig. 9. Layout Design for Deep Drawn Rectangular Shell

When laying out the blank it is usually advisable to plan for a form that will produce corners a little higher than the sides. The wear of the die is at the corners, and when it occurs, the material will thicken and the drawn part will be low at the corners if no allowance for this wear has been made on the blank. Blank for Rectangular Flanged Shells: The shape of the blank for a rectangular flanged shell may be determined in practically the same way as described in the foregoing, except that the width of the flange must be considered. Referring to Fig. 9, the dimension h in the flat blank is made equal to the height of the drawn part plus the width of the flange; however, the blank diameter D for a cylindrical shell having a flange can be determined by the formula D = d 2 + 4dh (27) where D = blank diameter (in.) d = diameter of drawn shell (in.) d1 = diameter measured across the flange (in.) h = height of shell (in.) After determining diameter D and the corresponding radius R, the outline of the blank is drawn the same as for a rectangular shell without the flange. Lubricants and Their Effects on Press Work .—Most sheet-metal forming operations use lubricants to protect the die and part from excessive wear caused by scratching, scoring, welding, and galling. The physical characteristics of the lubricant and metal-forming operation involved determine the application method to be used. Methods for applying lubricant to sheet metal include dips, swabs, brushes, wipers, rollers, or recirculation. Of these, the three most common are the following: 1) Manually wiping lubricant onto a surface with a rag 2) Roll coating, during which metal blanks pass through rollers that apply the compound


Machinery's Handbook 28th Edition LUBRICANTS AND PRESS WORK

1289

3) Flooding, during which tooling and metal sheets are drenched with lubricant, and the excess liquid is recovered via a filtration and recirculation system. Lubricants for Blanking Operations: Blanking dies used for carbon and low-alloy steels are often run with only 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. 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. High-speed blanking may require heavier applications of lubrication. For sheets thicker than 1/8 in. and for stainless steel, high-pressure lubricants containing sulfurs and chlorines are often used. Lubricants for Drawing Operations: Shallow drawing and forming of steel can be done with low-viscosity oils and soap solutions, but during deep drawing, different lubrication requirements exist, from hydrodynamic lubrication in the blank holder to boundary lubrication at the drawing radius, where breakdown of the film very often occurs. Characteristic of deep drawing is the high pressure involved in the operation, on the order of 100,000 pounds per square inch (PSI) . To deal with such force, the choice of lubricant is critical to the success of the operation. Under such pressure, the drawing lubricant should cool the die and the workpiece, provide boundary lubrication between the die and the workpiece, prevent metal-to-metal adhesion or welding, and cushion the die during the drawing operation. Lubricants work by forming lubricating films between two sliding surfaces in contact with each other. When these metal surfaces are viewed under magnification, peaks and valleys become apparent, even on finely-ground surfaces. The lubricating film needs to prevent the asperities (peaks) on the two surfaces in sliding contact with each other from damaging the mating surface. Under hydrodynamic or fullfilm lubrication, two surfaces are completely separated by a fluid film, with no contact between the asperities. This condition could change as speeds vary during start-and-stop modes or if the pressure and temperature increase beyond the lubricant's film strength. Boundary lubricants work up to a certain temperature and pressure, and then the boundary additive breaks down and metal contacts metal. The working temperature varies with the type and amount of additive used and its interaction with other additives. Three types of drawing lubricants are used: 1) Drawing oils ; 2) Emulsions ; and 3) Lubricants containing both oil and solid substances. . Drawing oils become an absorbed film, and they take the form of light or soluble oils such as straight mineral oil or emulsions of soluble oil and soap, or of heavy oils, fats, and greases such as tallow or lard oil. Aqueous solutions of non-oily lubricants containing some suspended solids are called emulsions. These lubricants are not widely used in deep drawing because they contain little or no oil. Lubricants containing both oil and solid substances are used in applications involving severe drawing; these lubricants contain oily components that reduce friction and heat. The combination of the oil and the solids produces enough lubrication for severe drawing applications such as deep drawing. Deep drawing often involves ironing or thinning the wall by up to 35 per cent, and lubricant containing high proportions of chemically-active components. 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, as well as wax or soap suspensions for very large reductions. Lubricant Removal: Removing lubricant from a formed part after the deep drawing operation is important because any lubricant left behind can interfere with subsequent steps in the manufacturing of the part. Mineral oils, animal fat, and vegetable oils can be removed with an organic solvent by emulsification or saponification, or with an aqueous alkaline cleaner. Greases can also be removed from sheet metal with an organic solvent or an alka-


Machinery's Handbook 28th Edition JOINING AND EDGING

1290

line cleaner. Solids are more difficult to remove because they are not readily soluble. The presence of solids often requires that additional cleaning methods be used. Petroleum oils can raise special issues from removal through disposal. These oils require the use of alkaline cleaners for removal, which can then contaminate cleaner tanks with oil, leading to potential disposal challenges. Vegetable oils can be removed with hot water if the parts are cleaned immediately, and with a mildly to moderately alkaline cleaner if the parts are cleaned after they have been left standing for a few days. 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. Longitudinal seams also must be able to withstand 1.5 times the operating pressure without deformation. Seams must 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. Seam types must 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 it is constructed. The reinforcing members must be able resist the external deflection of the sheet, and their 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 assemblies. Sheet Metal Joints Plain Lap and Flush Lap:

Fig. 1. Plain Lap

The plain lap (Fig. 1) and flush lap (Fig. 2) 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. 2. Flush Lap

Raw and Flange Corner: The raw and flange corner (Fig. 3) is generally spot-welded, but may be riveted or soldered. For heavy gages it is tack-welded or solid-welded. Fig. 3. Raw and Flange Corner


Machinery's Handbook 28th Edition SHEET METAL JOINTS

1291

Flange and Flange Corner: The flange and flange corner (Fig. 4) 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. 4. Flange and Flange Corner

Standing Seam:

Fig. 5. Standing Seam

The standing seam (Fig. 5) 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-in. seam is normally applied for duct widths up to 42-in, and 11⁄2-in. for bigger ducts.

Groove Seam:

Fig. 6. Groove Seam

The groove seam (Fig. 6) 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. 7) has applications similar to the standing seam, and also can be used for straight-duct sections. This type of seam is mostly applied at the ends at 8″ intervals. Fig. 7. Corner Standing Seam

Double Seam:

Fig. 8. Double Corner Seam

The double corner seam (Fig. 8) at one time was the most commonly used method for duct 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. 9. Slide Corner

The slide-corner (Fig. 9) 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. 10. Button Punch Snap Lock

The button punch snap lock (Fig. 10) is a flush-type seam which may be soldered or caulked. This seam can be modified slightly for use as a “snap lock”. This type 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 material.



1292 Pittsburg:

The Pittsburg (Fig. 11) 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 the sheet. Fig. 11. Pittsburgh

Flange: The flange (Fig. 12) is an end edge stiffener. The draftsman must indicate size of 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. 12. Flange

Hem: The hem edge (Fig. 13) is a flat, finished edge. As with the flange, this hem must be designated by the draftsman. For example, drawing should show: 3⁄4″ hem out.

Fig. 13. Hem

Flat Drive Slip:

Fig. 14. Drive Slip

The drive slip 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 but should not be used for service above 2″ inches w.g.

Standing Drive Slip: H

This slip is also a slide type connection. It is made by elongating the flat drive slip and fastening standing portions 2″ from each end. The design is applicable for any length in 2″ w.g, 36″ for 3″ inch w.g., and 30″ inches at 4″ w.g. service.

Fig. 15. Standing Drive Slip

Flat Drive Slip Reinforced: This reinforcement on the flat drive slip is made by adding a transverse angle section after a fixed interval. Fig. 16. Drive Slip Reinforced

Double “S” Slip Reinforced:

Fig. 17. Double “S” Slip

The double “S” slip is used, to eliminate the problem of notching and bending, especially for large ducts. Use 24 gage sheet for 30″ width or less, and 22 gage sheet over 30″ width.

Flat “S” Slip:

Fig. 18. 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 be less than the duct gage. When it is applied on all four edges, fasten within 2″ of the corners and at 12″ maximum interval.



1293

Hemmed “S” Slip:

Fig. 19. Hemmed “S” Slip

This modified “S” slip is made 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, forming a 1 inch height slip pocket and screws at the end. Notching and bending operations on “S” slip joints can be cumbersome and costly, especially for large sizes. Tie 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. 20. Clinch-bar Slip and Flange

The clinch-bar slip and flange (Fig. 20), 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. 21. Clinch-bar Slip and Angle

The clinch bar slip and angle (Fig. 21), is similar to clinch bar slip (Fig. 20), 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. 22. 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 that may be located later. The most common matched angle connection is the angle frame, or ring (Fig. 22). The angles are fastened flush to the end of the duct.

Flanged End and Angle:

Fig. 23. Flanged Ends and Matched ∠s

The flanged end and angle (Fig. 23), 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. 24. Formed Flanges

Double flanges (Fig. 24), are similar to Fig. 12, 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 corners are used with 3⁄8″ diameter bolts.


1294

Machinery's Handbook 28th Edition STEEL RULE DIES

Double Flanges and Cleat:

Double Flanges and Cleat (Fig. 25) is identical to (Fig. 24), but has an air seal cleat. The reinforcements are attached to the duct wall on both sides of the joint. Fig. 25. Double Flanges and Cleat

Clinch-type Flanged Connections:

Fig. 26. Bead Clinch and Z Rings

Clinch-type flanged connections for round ducts, 16 ga or lighter, are shown in Fig. 26. The angles or rings can be loose, as explained in Flanged End and Angle, (Fig. 23). 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.

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. 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 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



1295

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

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


1296


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 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



1297

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 (B in Fig. 2), for the working edges of the die. Clearances for piercing punches should be similar to those used on conventional piercing dies. Pipe and Tube Bending In bending a pipe or tube, the outer part of the bend is stretched and the inner section compressed, and the pipe or tube tends to flatten or collapse. To prevent such distortion, common practice is to support the wall of the pipe or tube during the bending operation. This support may be in the form of a filling material or temporary support placed inside the pipe. Use of Filling Material.—A simple method of preventing distortion consists in using filling material inside the pipe, supporting the walls to prevent flattening at the bend. Dry sand is often used. Materials such as resin, tar, or lead are also sometimes employed. The pipe is first filled with the molten resin, lead, or low-melting-point alloy, and then after bending, the pipe is heated to melt and remove the filling material. Resin has often been used for bending small brass and copper pipes, and lead or other alloys for small iron and steel pipes. Before bending copper or brass pipe or tubing, the latter should be annealed. Alloy of Low Melting Point Used as Filler.—Filling tubes with lead may result in satisfactory bends, but the comparatively high melting point of lead often negatively effects on the physical properties of the tube. Commercial alloys such as “Cerrobend” and “Bendalloy” have melting points of about 160 degrees F. They are composed of bismuth, lead, tin, and cadmium. With these materials, tubes having a wall as thin as 0.007 inch have been bent to small radii. The metal filler conforms to the inside of the tube so closely that the tube can be bent just as though it were a solid rod. This method has been applied to the bending of copper, brass, duralumin, plain steel, and stainless steel tubes with uniform success. Tubes plated with chromium or nickel can be bent without danger of the plate flaking off. The practice usually is economical for tubes up to 2 inches in diameter. The method is considered ideal when the number of tubes of a given size or kind is more or less limited or when the bend is especially severe. When a tube-bending operation has been completed, removal of the metal filler is accomplished by heating the tube in steam, in a bath of boiling water, or in air of about the same temperature. The metal can then be drained out and used again and again. Mandrel Inside of Tube.—An internal mandrel is used for bending so that the pipe or tube is supported both externally and internally to prevent flattening. Internal mandrels are used particularly in connection with the bending of thin tubing. The mandrel may be in the form of a plain cylindrical bar that fits closely inside the tube and has a rounded end at the bending position, or it may be of special form. The ball type of mandrel has been used for many tube-bending operations. The ball is so connected to the end of its supporting arbor that it has a limited amount of movement, and partially supports the curved section of the tube. This general type of mandrel has been used both on hand-operated fixtures and on power-driven pipe- and tube-bending machines. In some cases, two or more rounded or spherical-shaped supports are used. These are linked together to provide flexibility at the bend.


1298

Machinery's Handbook 28th Edition ELECTRICAL DISCHARGE MACHINING

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



1299

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.


1300


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



1301

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


1302


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



1303

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.



1304

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

1220 1710 2696 1980

660 930 1480 1082

4442

N/A 2350 1202 2300 4748 2651 2500 2730 2750 3200 6098 790

1285 650 1260 2620 1455 1371 1500 1510 1700 3370 420

°C 2450 …

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.



1305

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 (R2001) 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 28th Edition METRIC SCREWS AND BOLTS

1500

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 13 and 15, respectively. Table 14. Basic Thread Lengths for Metric Round Head Square Neck Bolts ANSI/ASME B18.5.2.2M-1982 (R2000) 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 …

53 57 65 73 …

All dimensions are in millimeters Basic thread length B is a reference dimension intended for calculation purposes only.



1501

Table 15. Socket Head Cap Screws (Metric Series)—Length of Complete Thread ANSI/ASME B18.3.1M-1986 (R2002) Nominal Size

Length of Complete Thread, LT


Nominal Size


M1.6

15.2

M2

16.0

M6

24.0

M20

52.0

M8

28.0

M24

M2.5

60.0

17.0

M10

32.0

M30

72.0

M3

18.0

M12

36.0

M36

M4

20.0

M14

40.0

M42

96.0

M5

22.0

M16

44.0

M48

108.0

Nominal Size

84.0

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 17, for heavy hex structural bolts in Table 18, for hex lag screws in Table 16, for round head square neck bolts in Table 19, and for socket head cap screws in Table 20. 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 16. 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

䊉

…

…

…

…

…

…

…

90

䊉

䊉

䊉

䊉

䊉

10

䊉

䊉

…

…

…

…

…

…

100

䊉

䊉

䊉

䊉

䊉

12

䊉

䊉

䊉

…

…

…

…

…

110

…

䊉

䊉

䊉

䊉

14

䊉

䊉

䊉

…

…

…

…

…

120

…

䊉

䊉

䊉

䊉

16

䊉

䊉

䊉

䊉

…

…

…

…

130

…

…

䊉

䊉

䊉

20

䊉

䊉

䊉

䊉

䊉

…

…

…

140

…

…

䊉

䊉

䊉

25

䊉

䊉

䊉

䊉

䊉

䊉

…

…

150

…

…

䊉

䊉

䊉

30

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

160

…

…

䊉

䊉

䊉

35

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

180

…

…

…

䊉

䊉

40

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

200

…

…

…

䊉

䊉

45

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

220

…

…

…

…

䊉

50

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

240

…

…

…

…

䊉

60

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

260

…

…

…

…

䊉

70

…

…

䊉

䊉

䊉

䊉

䊉

䊉

280

…

…

…

…

䊉

80

…

…

䊉

䊉

䊉

䊉

䊉

䊉

300

…

…

…

…

䊉

All dimensions are in millimeters. Recommended diameter-length combinations are indicated by the symbol 䊉.



1502

Table 17. 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

䊉

…

…

…

…

…

…

…

…

…

…

10

䊉

䊉

…

…

…

…

…

…

…

…

…

12

䊉

䊉

䊉

…

…

…

…

…

…

…

…

14

䊉

䊉

䊉

䊉b

…

…

…

…

…

…

…

16

䊉

䊉

䊉

䊉

䊉b

䊉b

…

…

…

…

…

20

䊉

䊉

䊉

䊉

䊉

䊉

…

…

…

…

…

25

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

…

…

…

30

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

…

…

35

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

…

40

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

45

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

…

50

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

(55)

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉䊉

60

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

(65)

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

70

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

(75)

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

80

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

(85)

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

90

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

100

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

110

…

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

120

…

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

䊉

130

…

…

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

140

…

…

…

…

…

䊉

䊉

䊉

䊉

䊉

䊉

150

…

…

…

…

…

…

䊉

䊉

䊉

䊉

䊉

160

…

…

…

…

…

…

䊉

䊉

䊉

䊉

䊉

(170)

…

…

…

…

…

…

…

䊉

䊉

䊉

䊉

180

…

…

…

…

…

…

…

䊉

䊉

䊉

䊉

(190)

…

…

…

…

…

…

…

䊉

䊉

䊉

䊉

200

…

…

…

…

…

…

…

䊉

䊉

䊉

䊉

220

…

…

…

…

…

…

…

…

䊉

䊉

䊉

240

…

…

…

…

…

…

…

…

䊉

䊉

䊉

260

…

…

…

…

…

…

…

…

…

䊉

䊉

280

…

…

…

…

…

…

…

…

…

䊉

䊉

300

…

…

…

…

…

…

…

…

…

䊉

䊉

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 䊉. 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.



1503

Table 18. Recommended Diameter-Length Combinations for Metric Heavy Hex Structural Bolts Nominal Length, L

Nominal Diameter and Thread Pitch M16 × 2

M20 × 2.5

M22 × 2.5

M24 × 3

M27 × 3

M30 × 3.5

M36 × 4

䊉

…

䊉

䊉

… …

䊉

䊉

䊉

… … …

䊉

䊉

䊉

䊉

… … … …

䊉

䊉

䊉

䊉

䊉

… … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

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 䊉. Bolts with lengths above the heavy cross lines are threaded full length.

Table 19. 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

䊉

…

䊉

䊉

䊉

䊉

… … …

… … … … … …

䊉

䊉

䊉

… … … …

䊉

䊉

䊉

䊉

… … … … …

䊉

䊉

䊉

䊉

䊉

… … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉



1504

Table 19. (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

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … …

䊉

䊉

䊉

䊉

䊉

… … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… …

䊉䊉

a Bolts with lengths above the heavy cross lines are threaded full length. Lengths in ( ) are not recommended. All dimensions are in millimeters. Recommended diameter-length combinations are indicated by the symbol 䊉. Standard sizes for government use.

Table 20. 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

M2.5

M3

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … … … … … … … … … … … … …

䊉

䊉

䊉

M4

M5

M6

M8

M10

M12

M14

M16

M20

M24

䊉䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… … … …

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

䊉

… …

䊉

䊉

䊉

䊉

…

䊉

䊉

䊉

䊉

䊉䊉

All dimensions are in millimeters. Screws with lengths above heavy cross lines are threaded full length. Diameter-length combinations are indicated by the symbol 䊉. 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 15 footnote) are threaded full length.



1505

Table 21. American National Standard Socket Head Cap Screws Metric Series ANSI/ASME B18.3.1M-1986 (R2002)

Nom. Size and Thread Pitch 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

Body Diameter, D

Head Diameter A

Head Height H

Chamfer or Radius S

Hexagon Socket Sizea J

TransiSpline Key Socket Engage tion a Dia. ment Size M T Ba

Max

Min

Max

Min

Max

Min

Max

Nom.

Nom.

Min

Max

1.60 2.00 2.50 3.00 4.00 5.00 6.00 8.00 10.00 12.00 14.00

1.46 1.86 2.36 2.86 3.82 4.82 5.82 7.78 9.78 11.73 13.73

3.00 3.80 4.50 5.50 7.00 8.50 10.00 13.00 16.00 18.00 21.00

2.87 3.65 4.33 5.32 6.80 8.27 9.74 12.70 15.67 17.63 20.60

1.60 2.00 2.50 3.00 4.00 5.00 6.00 8.00 10.00 12.00 14.00

1.52 1.91 2.40 2.89 3.88 4.86 5.85 7.83 9.81 11.79 13.77

0.16 0.20 0.25 0.30 0.40 0.50 0.60 0.80 1.00 1.20 1.40

1.5 1.5 2.0 2.5 3.0 4.0 5.0 6.0 8.0 10.0 12.0

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

2.0 2.6 3.1 3.6 4.7 5.7 6.8 9.2 11.2 14.2 16.2

16.00 20.00 24.00 30.00 36.00 42.00 48.00

15.73 19.67 23.67 29.67 35.61 41.61 47.61

24.00 30.00 36.00 45.00 54.00 63.00 72.00

23.58 29.53 35.48 44.42 53.37 62.31 71.27

16.00 20.00 24.00 30.00 36.00 42.00 48.00

15.76 19.73 23.70 29.67 35.64 41.61 47.58

1.60 2.00 2.40 3.00 3.60 4.20 4.80

14.0 17.0 19.0 22.0 27.0 32.0 36.0

… … … … … … …

8.00 10.00 12.00 15.00 18.00 21.00 24.00

18.2 22.4 26.4 33.4 39.4 45.6 52.6

a See also Table 23.

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 15). For length of complete thread, see Table 15. For additional manufacturing and acceptance specifications, see ANSI/ASME B18.3.1M.


Machinery's Handbook 28th Edition METRIC NUTS

1506

Table 22. 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

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.

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 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.



1507

Table 23. American National Standard Hexagon and Spline Sockets for Socket Head Cap Screws—Metric Series ANSI/ASME B18.3.1M-1986 (R2002)

METRIC HEXAGON SOCKETS

METRIC SPLINE SOCKET

See Table 21 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 21 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.

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



1508

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. Table 24. American National Standard Metric Slotted Hex Nuts ANSI B18.2.4.3M-1982 (R2001)

Nominal Nut Dia. and Thread Pitch 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

Width Across Flats, S Max Min

Width Across Corners, E Max Min

Thickness, M Max Min

8.00 10.00 13.00 15.00 16.00 18.00 21.00 24.00 30.00 36.00 46.00 55.00

9.24 11.55 15.01 17.32 18.48 20.78 24.25 27.71 34.64 41.57 53.12 63.51

5.10 5.70 7.50 10.0 9.30 12.00 14.10 16.40 20.30 23.90 28.60 34.70

7.78 9.78 12.73 14.73 15.73 17.73 20.67 23.67 29.16 35.00 45.00 53.80

8.79 11.05 14.38 16.64 17.77 20.03 23.35 26.75 32.95 39.55 50.85 60.79

4.80 5.40 7.14 9.6 8.94 11.57 13.40 15.70 19.00 22.60 27.30 33.10

Bearing Face Dia., Dw Min

Unslotted Thickness, F Max Min

Width of Slot, N Max Min

Washer Face Thickness C Max Min

6.9 8.9 11.6 13.6 14.6 16.6 19.6 22.5 27.7 33.2 42.7 51.1

3.2 3.5 4.4 5.7 5.2 7.3 8.6 9.9 13.3 15.4 18.1 23.7

2.0 2.4 2.9 3.4 3.4 4.0 4.3 5.3 5.7 6.7 8.5 8.5

… … … 0.6 … … … … 0.8 0.8 0.8 0.8

2.9 3.2 4.1 5.4 4.9 6.9 8.0 9.3 12.2 14.3 16.8 22.4

1.4 1.8 2.3 2.8 2.8 3.2 3.5 4.5 4.5 5.5 7.0 7.0

… … … 0.3 … … … … 0.4 0.4 0.4 0.4

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.

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,



1509

Table 25. American National Standard Metric Hex Nuts, Styles 1 and 2 ANSI/ASME B18.2.4.1M-2002 and B18.2.4.2M-2005

Nominal Nut Dia. and Thread Pitch

Width Across Flats a, S Max Min

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 eM10 × 1.5 fM10 × 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

M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M8 × 1.25 eM10 × 1.5 fM10 × 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

Width Across Corners b, Thickness c, E M Max Min Max Min Metric Hex Nuts — Style 1 3.70 3.41 1.30 1.05 4.62 4.32 1.60 1.35 5.77 5.45 2.00 1.75 6.35 6.01 2.40 2.15 6.93 6.58 2.80 2.55 8.08 7.66 3.20 2.90 9.24 8.79 4.70 4.40 11.55 11.05 5.20 4.90 15.01 14.38 6.80 6.44 17.32 16.64 9.1 8.7 18.48 17.77 8.40 8.04 20.78 20.03 10.80 10.37 24.25 23.36 12.80 12.10 27.71 26.75 14.80 14.10 34.64 32.95 18.00 16.90 41.57 39.55 21.50 20.20 53.12 50.85 25.60 24.30 63.51 60.79 31.00 29.40 Metric Hex Nuts — Style 2 6.35 6.01 2.90 2.65 6.93 6.58 3.30 3.00 8.08 7.66 3.80 3.50 9.24 8.79 5.10 4.80 11.55 11.05 5.70 5.40 15.01 14.38 7.50 7.14 17.32 16.64 10.0 9.6 18.48 17.77 9.30 8.94 20.78 20.03 12.00 11.57 24.25 23.35 14.10 13.40 27.71 26.75 16.40 15.70 34.64 32.95 20.30 19.00 41.57 39.55 23.90 22.60 53.12 50.85 28.60 27.30 63.51 60.79 34.70 33.10

Bearing Face Dia.d, Dw Min

Washer Face Thickness d, C Max Min

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

… … … … … … … … … … … … … … 0.8 0.8 0.8 0.8

… … … … … … … … … … … … … … 0.4 0.4 0.4 0.4

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

… … … … … … … … … … … 0.8 0.8 0.8 0.8

… … … … … … … … … … … 0.4 0.4 0.4 0.4

a The width across flats shall be the distance, measured perpendicular to the axis of the nut, between two opposite wrenching flats. b A rounding or lack of fill at the junction of hex corners with the chamfer shall be permissible. c The nut thickness shall be the overall distance, measured parallel to the axis of the nut, from the top of the nut to the bearing surface, and shall include the thickness of the washer face where provided. d M16 and smaller nuts shall be double chamfered. M20 and larger nuts shall be either double chamfered or have a washer faced bearing surface and a chamfered top. e Dimensional requirements shown in bold type are in addition to or differ from ISO 4032. f When M10 hex nuts are ordered, nuts with 16 mm width across flats shall be furnished unless 15mm width across flats is specified.



1510

Table 26. American National Standard Metric Hex Flange Nuts ANSI B18.2.4.4M-1982 (R1999)

DETAIL X


Width Across Flats, S Max

Min

M5 × 0.8 8.00 7.78 M6 × 1 10.00 9.78 M8 × 1.25 13.00 12.73 M10 × 1.5 15.00 14.73 M12 × 1.75 18.00 17.73 M14 × 2 21.00 20.67 M16 × 2 24.00 23.67 M20 × 2.5 30.00 29.16 All dimensions are in millimeters.

Width Across Corners, E

Flange Dia., Dc

Bearing Circle Dia., Dw

Flange Edge Thickness, C

Thickness, M

Flange Top Fillet Radius, R

Max

Min

Max

Min

Min

Max

Min

Max

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

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 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 Combinations on page 1501 ). 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 overtapped threads in conformance with requirements specified in ASTM A563M. 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.



1511

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 27 as “all-metal” type and the third design as “top-insert” type. Table 27. American National Standard Prevailing-Torque Metric Hex Flange Nuts ANSI B18.16.3M-1998

Flange Top Fillet Radius, R

Max

Min

Max

Min

Max

Min

Max

Min

Max

Min

Min

Max

M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75 M14 × 2 M16 × 2 M20 × 2.5

10.00 13.00 15.00 18.00 21.00 24.00 30.00

9.78 12.73 14.73 17.73 20.67 23.67 29.16

11.55 15.01 17.32 20.78 24.25 27.71 34.64

11.05 14.38 16.64 20.03 23.35 26.75 32.95

7.30 9.40 11.40 13.80 15.90 18.30 22.40

5.70 7.60 9.60 11.60 13.30 15.30 18.90

8.80 10.70 13.50 16.10 18.20 20.30 24.80

8.00 9.70 12.50 15.10 17.00 19.10 23.50

14.2 17.9 21.8 26.0 29.9 34.5 42.8

12.2 15.8 19.6 23.8 27.6 31.9 39.9

1.1 1.2 1.5 1.8 2.1 2.4 3.0

0.4 0.5 0.6 0.7 0.9 1.0 1.2


Flange Dia., Dc

Nominal Dia. and Thread Pitch

Flange Edge Thickness, C

Top Insert Type

Bearing Circle Dia., Dw

All Metal Typea Width Across Flats, S

Thickness, M (All Nut Property Classes)

a Also includes metal nuts with nonmetallic inserts, plugs, or patches in their threads.

All dimensions are in millimeters.

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.



1512

Table 28. American National Standard Metric Hex Jam Nuts and Heavy Hex Nuts ANSI B18.2.4.5M-1979 (R2003) and B18.2.4.6M-1979 (R2003)

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

Bearing Face Dia., Dw

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.



Machinery's Handbook 28th Edition 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

Bearing Face Dia., Dw


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


Width Across Flats, S

a Also includes metal nuts with non-metallic inserts, plugs, or patches in their threads.



1513

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.

1514

Machinery's Handbook 28th Edition METRIC WASHERS Metric Washers

Metric Plain Washers.—American National Standard ANSI B18.22M-1981 (R2000) 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 28th Edition METRIC WASHERS

1515

Table 30. American National Standard Metric Plain Washers ANSI B18.22M-1981 (R2000) 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.


Machinery's Handbook 28th Edition CLEARANCE HOLES

1516

Clearance Holes for Bolts, Screws, and Studs The Standard ASME B18.2.8-1999, R2005 covers the recommended clearance hole sizes for #0 through 1.5 inch and M1.6 through M100 metric fasteners in three classes of clearance using a close-, normal-, and loose-fit category. The clearance hole tolerances for both inch and metric holes are based on ISO 286, ISO System of Limits and Fits, using tolerance class H12 for close-fit, H13 for normal-fit, and H14 for loose-fit clearance holes. The clearances provided by the three classes of fit are based on regularly stepped clearances as listed in Table 1a for inch and Table 2b for metric. Inch Fasteners.—The hole sizes for inch fasteners are patterned after USA common usage and the general clearances translated from the metric standard. The hole tolerances are based on the ISO System of Limits and Fits, as required by ISO 273. The tabulated drill and hole sizes, Table 1a, list the inch fastener clearance hole recommendations. The recommended drill sizes for inch fasteners are tabulated by nominal drill designation as letter, numbers, or fractional sizes. The drill sizes were selected to provide as nearly as practical a step-patterned clearance size for the minimum recommended hole (Table 1b). The maximum recommended hole size is based on standard hole tolerances. Table 1a. Clearance Holes for Inch Fasteners ASME B18.2.8-1999, R2005 Nominal Screw Size

Nominal Drill Size

Normal Hole Diameter Min. Max.

Nominal Drill Size

Close Hole Diameter Min. Max.

Nominal Drill Size

Loose Hole Diameter Min. Max.

#0 #1 #2 #3 #4 #5 #6 #8 #10 1⁄ 4

#48 #43 #38 #32 #30 5⁄ 32 #18 #9 #2 9⁄ 32

0.076 0.089 0.102 0.116 0.128 0.156 0.170 0.196 0.221 0.281

0.082 0.095 0.108 0.122 0.135 0.163 0.177 0.203 0.228 0.290

#51 #46 3⁄ 32 #36 #31 9⁄ 64 #23 #15 #5 17⁄ 64

0.067 0.081 0.094 0.106 0.120 0.141 0.154 0.180 0.206 0.266

0.071 0.085 0.098 0.110 0.124 0.146 0.159 0.185 0.211 0.272

3⁄ 32 #37 #32 #30 #27 11⁄ 64 #13 #3 B 19⁄ 64

0.094 0.104 0.116 0.128 0.144 0.172 0.185 0.213 0.238 0.297

0.104 0.114 0.126 0.140 0.156 0.184 0.197 0.225 0.250 0.311

5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

11⁄ 32 13⁄ 32 15⁄ 32 9⁄ 16 11⁄ 16 13⁄ 16 15⁄ 16 13⁄32 17⁄32 111⁄32 11⁄2 15⁄8

0.344

0.354

0.334

0.373

0.391

0.397

0.422

0.438

0.469

0.479

0.453

0.460

0.484

0.500

0.562

0.572

0.531

0.538

0.609

0.625

0.688

0.698

0.656

0.663

0.734

0.754

0.812

0.824

0.781

0.789

0.906

0.926

0.938

0.950

0.906

0.914

1.031

1.051

1.094

1.106

1.031

1.039

1.156

1.181

1.219

1.235

1.156

1.164

1.312

1.337

1.344

1.360

1.281

1.291

1.438

1.463

1.500

1.516

1.438

1.448

1.609

1.634

1.625

1.641

1.562

1.572

23⁄ 64 27⁄ 64 31⁄ 64 39⁄ 64 47⁄ 64 129⁄32 11⁄32 15⁄32 15⁄16 17⁄16 139⁄64 147⁄64

0.359

0.416

21⁄ 64 25⁄ 64 29⁄ 64 17⁄ 32 21⁄ 32 .25⁄ 32 29⁄ 32 11⁄32 15⁄32 19⁄32 17⁄16 19⁄16

0.328

0.406

1.734

1.759

1 11⁄8 11⁄4 13⁄8 11⁄2

Table 1b. Inch Clearance Hole Allowances Fit Classes

Fit Classes

Nominal Screw Size

Normal

Close

Loose

Nominal Screw Size

Normal

Close

Loose

#0 – #4

1⁄ 64

0.008

1⁄ 32

1

3⁄ 32

1⁄ 32

5⁄ 32

#5 – 7⁄16

1⁄ 32

1⁄ 64

3⁄ 64

11⁄8 , 11⁄4

3⁄ 32

1⁄ 32

3⁄ 16

1⁄ , 5⁄ 2 8

1⁄ 16

1⁄ 32

7⁄ 64

13⁄8 , 11⁄2

1⁄ 8

1⁄ 16

15⁄ 64

3⁄ , 7⁄ 4 8

1⁄ 16

1⁄ 32

5⁄ 32

…

…

…

…

Dimensions are in inches.



1517

Metric Fasteners.—The recommended drill and hole sizes for metric fasteners are tabulated in Table 2a. The minimum recommended hole is the drill size and the maximum recommended hole size is based on standard tolerances. The hole sizes for metric fasteners are in agreement with ISO 273, Fasteners-Clearance Holes for Bolts and Screws, except that ISO 273 covers fastener sizes M1 through M150. Table 2a. Clearance Holes for Metric Fasteners ASME B18.2.8-1999, R2005 Normal Nominal Screw Size M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 M14 M16 M20 M24 M30 M36 M42 M48 M56 M64 M72 M80 M90 M100

Close

Hole Diameter

Nominal Drill Size

Min.

1.8 2.4 2.9 3.4 4.5 5.5 6.6 9 11 13.5 15.5 17.5 22 26 33 39 45 52 62 70 78 86 96 107

1.8 2.4 2.9 3.4 4.5 5.5 6.6 9 11 13.5 15.5 17.5 22 26 33 39 45 52 62 70 78 86 96 107

Loose

Hole Diameter

Max.

Nominal Drill Size

Min.

1.94 2.54 3.04 3.58 4.68 5.68 6.82 9.22 11.27 13.77 15.77 17.77 22.33 26.33 33.39 39.39 45.39 52.46 62.46 70.46 78.46 86.54 96.54 107.54

1.7 2.2 2.7 3.2 4.3 5.3 6.4 8.4 10.5 13 15 17 21 25 31 37 43 50 58 66 74 82 93 104

1.7 2.2 2.7 3.2 4.3 5.3 6.4 8.4 10.5 13 15 17 21 25 31 37 43 50 58 66 74 82 93 104

Hole Diameter

Max.

Nominal Drill Size

Min.

Max.

1.8 2.3 2.8 3.32 4.42 5.42 6.55 8.55 10.68 13.18 15.18 17.18 21.21 25.21 31.25 37.25 43.25 50.25 58.3 66.3 74.3 82.35 93.35 104.35

2 2.6 3.1 3.6 4.8 5.8 7 10 12 14.5 16.5 18.5 24 28 35 42 48 56 66 74 82 91 101 112

2 2.6 3.1 3.6 4.8 5.8 7 10 12 14.5 16.5 18.5 24 28 35 42 48 56 66 74 82 91 101 112

2.25 2.85 3.4 3.9 5.1 6.1 7.36 10.36 12.43 14.93 16.93 19.02 24.52 28.52 35.62 42.62 48.62 56.74 66.74 74.74 82.87 91.87 101.87 112.87

Table 2b. Metric Clearance Hole Allowances Nominal Screw Size M1.6 M2 M2.5 M3 M4, M5 M6 M8 M10 M12-M16

Fit Classes Normal 0.2 0.4 0.4 0.4 0.5 0.6 1 1 1.5

Fit Classes

Close

Loose

Nominal Screw Size

Normal

Close

0.1 0.1 0.1 0.2 0.3 0.4 0.4 0.5 1

0.25 0.3 0.3 0.6 0.8 1 2 2 2.5

M20, M24 M30 M36, M42 M48 M56-M72 M80 M90 M100 …

2 3 3 4 6 6 6 7 …

1 1 1 2 2 2 3 4 …

Loose 4 5 6 8 10 11 11 12 …

Dimensions are in millimeters.

Recommended Substitute Drills.—If the clearance hole application is dimensioned in metric drill sizes for inch fasteners, or inch drill sizes for metric fasteners, Tables 3a and 3b list the nearest standard drill size translations for the designated drills of Tables 1a and 2a.



1518

Table 3a. Standard Metric Drills For Inch Fasteners ASME B18.2.8-1999, R2005 (Appendix 1) Nominal Screw Size, inch #0 #1 #2 #3 #4 #5 #6 #8 #10 1⁄ 4 5⁄ 16

Nominal Drill Size, mm Fit Classes Normal Close Loose 1.9 2.25 2.6 2.9 3.3 4 4.3 5 5.6 7.1 8.7

1.7 2.05 2.4 2.7 3 3.6 3.9 4.6 5.2 6.7 8.3

2.4 2.6 2.9 3.3 3.7 4.4 4.7 5.4 6 7.5 9.1

Nominal Screw Size, inch 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 1 1⁄8 1 1⁄4 1 3⁄8 1 1⁄2

Nominal Drill Size, mm Fit Classes Normal Close Loose 10.2 11.8 14.25 17.5 20.5 24 27.5 31 34 38 41

9.9 11.5 13.5 16.75 20 23 26 29.5 32.5 36.5 39.5

10.5 12.2 15.5 19 23 26 29.5 33.5 36.5 41 44

Table 3b. Standard Inch Drills For Metric Fasteners ASME B18.2.8-1999, R2005 (Appendix 1) Nominal Drill Size, inch Fit Classes Close Loose

Nominal Screw Size, mm

Normal

M1.6 M2 M2.5 M3 M4 M5 M6 M8 M10 M12 M14

#50 3⁄ 32 #33 #29 #16 7⁄ 32 G T 7⁄ 16 17⁄ 32 39⁄ 64

#51 #44 #36 1⁄ 8 #19 #4 1⁄ 4 Q Z 33⁄ 64 19⁄ 32

#47 #38 #31 9⁄ 64 #12 #1 J 25⁄ 64 31⁄ 64 37⁄ 64 21⁄ 32

Nominal Screw Size, mm M16 M20 M24 M30 M36 M42 M48 M56 M64 M72 …

Nominal Drill Size, inch Fit Classes Close Loose

Normal 11⁄ 32 55⁄ 64 1 1⁄32 1 9⁄32 1 17⁄32 1 25⁄32 2 1⁄32 2 7⁄16 2 3⁄4 3 1⁄8

43⁄ 64 53⁄ 64 63⁄ 64 1 7⁄32 1 15⁄32 1 11⁄16 1 31⁄2 2 5⁄16 2 5⁄8 2 15⁄16

47⁄ 64 15⁄ 16 1 7⁄64 1 3⁄8 1 21⁄32 1 29⁄32 2 3⁄16 2 5⁄8 2 5⁄16 3 1⁄4

…

…

…

Table 4. Recommended Clearance Holes for Metric Round Head Square Neck Bolts 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. 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. Nom. Bolt Dia., D and Thd. Pitch M5 × 0.8 M6 × 1 M8 × 1.25 M10 × 1.5 M12 × 1.75

Clearance Close

Normal

Loose

Min. Hole Diameter or Square Width, H 5.5 6.6 … … 13.0

… … 9.0 11.0 13.5

5.8 7.0 10.0 12.0 14.5

Corner Radius Rh 0.2 0.3 0.4 0.4 0.6

Nom. Bolt Dia., D and Thd. Pitch M14 × 2 M16 × 2 M20 × 2.5 M24 × 3 …

Clearance Close

Normal

Loose

Min. 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 …

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. All dimensions are in millimeters. Source: ANSI/ASME B18.5.2.2M-1982 (R2000), Appendix II


Machinery's Handbook 28th Edition HELICAL COIL SCREW THREAD INSERTS

1519

HELICAL COIL SCREW THREAD INSERTS Introduction The ASME B18.29.2M standard delineates the dimensional, mechanical, and performance data for the metric series helical coil screw thread insert and threaded hole into which it is installed. Appendices that describe insert selection, STI (screw thread insert) taps, insert installation, and removal tooling are also included. Helical coil inserts are screw thread bushings coiled from wire of diamond-shape crosssection. Inserts are screwed into STI-tapped holes to form nominal size internal threads. Inserts are installed by torquing through a diametral tang. This tang is notched for removal after installation. In the free state, they are larger in diameter than the tapped hole into which they are installed. In the assembly operation, the torque applied to the tang reduces the diameter of the leading coil and permits it to enter the tapped thread. The remaining coils are reduced in diameter as they, in turn, are screwed into the tapped hole. When the torque or rotation is stopped, the coils expand with a spring-like action anchoring the insert in place against the tapped hole. Dimensions.—Dimensions in this standard are in millimeters and apply before any coating. Symbols specifying geometric characteristics are in accordance with ASME Y14.5M. Tolerance Classes 4H5H and 5H.—Because helical coil inserts are flexible, the class of fit of the final assembly is a function of the size of the tapped hole. Helical coil STI taps are available for both tolerance class 4H5H (or class 4H6H) and class 5H tapped holes. Tolerance class 5H tapped holes provide maximum production tolerances but result in lower locking torques when screw-locking inserts are used. The higher and more consistent torques given in Table 5 are met by the screw-locking inserts when assembled and tested in tolerance class 4H5H (or class 4H6H) tapped holes. Compatibility.—Assembled helical coil inserts will mate properly with items that have M Profile external threads in accordance with ASME B1.13M. Also, due to the radius on the crest of the insert at the minor diameter, the assembled insert will mate with MJ Profile externally threaded parts with controlled radius root threads per ASME B1.21M. Types of Inserts.— Free-running inserts provides a smooth, hard, and free-running thread. Screw-locking inserts provides a resilient locking thread produced by a series of chords on one or more of the insert coils. STI-tapped Hole.—The tapped hole into which the insert is installed shall be in accordance with ASME B1.13M, except that diameters are larger to accommodate the wire cross-section of the insert (See Fig. 4.). Dimensions of the STI-tapped hole are shown in Table 1 and are calculated per General Note (c) to Table 1. Screw Thread Designation for Tapped Hole: The drawing note for the STI-threaded hole per Table 1 to accept the helical coil insert shall be in accordance with the following: Example 1: MS ×1.25-5H STI; 23.5 T per ASME B18.29.2M. Designation for a Helical Coil Insert: Helical coil inserts shall be designated by the following data, in the sequence shown: a) product name; b) designation of the standard; c) nominal diameter and thread pitch (4) nominal length; and d) insert type (free-running or screw-locking). Example 2:Helical Coil insert, ASME B18.29.2M, M8 × 1.25 × 12.0 free-running. Helical Coil insert, ASME B18.29.2M, M5 × 0.8 × 7.5 screw-locking. The recommended B18 part number (PIN) code system for helical coil inserts is included in ASME B18.24. This system may be used by user needing definitive part-numbering.


1520

Machinery's Handbook 28th Edition HELICAL COIL SCREW THREAD INSERTS PLUG STYLE TAP

BOTTOMING STYLE TAP

T

G

2 Pitch incomplete threads

4 Pitch incomplete threads

1 Pitch tap end clearance

1 Pitch tab end clearance

Fig. 4. Tapping Depth

Designation for STI-Threaded Hole Including Installed Helical Coil Insert: The drawing note for the STI-threaded hole per Table 1 having a helical coil insert installed shall be in accordance with this example. Example 3:M8 × 1.25 STI 23.5 deep; Helical Coil insert, ASME B18.29.2M, M8 × 1.25 × 12.0, free running Gages and Gaging: Acceptance of the threaded hole is determined by gaging with STI GO, NOT GO (HI), and plain cylindrical gages designed and applied in accordance with System 21 of ASME B1.3M and with ASME B1.16M. Helical Coil Insert Material.—Chemical composition of the inserts is austenitic corrosion-resistant (stainless) steel material within the limits of Table 2. Properties.—Wire, before coiling into inserts, shall have tensile strength not lower than 1035 MPa, determined in accordance with ASTM A 370. Wire shall withstand, without cracking, bending in accordance with ASTM E 290 at room temperature through an angle of 180° around a diameter equal to twice the cross-sectional dimension of the wire in the plane of the bend. The formed wire shall be of uniform quality and temper; it shall be smooth, clean, and free from kinks, waviness, splits, cracks, laps, seams, scale, segregation, and other defects that may impair the serviceability of the insert. Coatings.—At the option of the user, dry film lubricant coating can be applied to helical coil inserts.The color of dry film-lubricated inserts is dark gray to black. Lubricant shall meet requirements of Aerospace Standard SAE AS5272, type I, lubricant, solid film heat cured, and corrosion inhibiting. Coating shall be uniformly deposited on the insert with the minimum thickness being complete coverage. Maximum thickness shall be the avoidance of bridging between coils. Slight fill in between closely wound coils, which immediately separates as the coils are axially pulled apart by hand, shall not be considered bridging. Configuration and Dimensions.—Insert configurations shall be in accordance with Fig. 5, and dimensions shall be in accordance with Tables 3 and 4. Each nominal insert size is standardized in five lengths, which are multiples of the insert's nominal diameter. These are 1, 1.5, 2, 2.5, and 3 times nominal diameter. Each nominal length is the minimum through-hole length (material thickness), without countersink, into which that insert can be installed. The nominal insert length is a reference value and cannot be measured. Actual assembled length of the insert equals nominal length minus 0.5 pitch to minus 0.75 pitch, with insert installed in a basic STI threaded hole. Assembled length cannot be measured in the insert's free state.



Table 1. Screw Thread Insert Threaded Hole Data ASME B18.29.2M-2005 Countersink Diameter, M (120°±5° included angle)

Minimum Drilling Depth for Each Insert Length, G Plug Taps

Bottoming Taps

Min. Major Diam. Minor Diameter

1.5D

2D

2.5D

3D

1D

1.5D

2D

2.5D

3D

Min.

Max.

Min.

Max.

Min.

M2 × 0.4 M2.5 ×0.45 M3 × 0.5 M3.5 × 0.6 M4 × 0.7 M5 × 0.8 M6 × 1 M7 × 1 M8 × 1 M8 × 1.25 M10 × 1 M30 × 1.25 M10 × 1.5 M12 × 1.25 M12 × 1.5 M12 × 1.75 M14 × 1.5 M14 × 2 M16 × 1.5 M16 × 2 M18 × 1.5 M18 × 2 M18 × 2.5 M20 × 1.5 M20 × 2 M20 × 2.5 M22 × 1.5 M22 × 2 M22 × 2.5 M24 × 2 M24 × 3 M27 × 2

5.40 6.45 7.50 8.86 10.20 12.30 15.00 16.50 18.00 19.50 16.00 17.50 19.00 19.50 21.00 22.50 23.00 26.00 25.00 28.00 27.00 30.00 33.00 29.00 32.00 35.00 31.00 34.00 37.00 38.00 42.00 39.00

6.40 7.70 9.00 10.60 12.20 14.80 18.00 20.00 22.00 23.60 21.00 22.60 24.00 25.50 27.00 28.50 30.00 33.00 33.00 36.00 36.00 39.00 42.00 39.00 42.00 45.00 42.00 45.00 48.00 48.00 54.00 52.50

7.40 8.95 10.50 12.35 14.20 17.30 21.00 23.50 26.00 27.50 26.00 27.50 29.00 31.50 33.00 34.50 37.00 40.00 41.00 44.00 45.00 48.00 51.00 49.00 52.00 55.00 53.00 56.00 59.00 60.00 66.00 66.00

8.40 10.20 12.00 14.10 16.20 19.80 24.00 27.00 30.00 31.50 31.00 32.50 34.00 37.50 39.00 40.50 44.00 47.00 49.00 52.00 54.00 57.00 60.00 59.00 62.00 65.00 64.00 67.00 70.00 72.00 78.00 79.50

9.40 11.45 13.50 15.85 18.20 22.30 27.00 30.50 34.00 35.50 36.00 37.50 39.00 43.50 45.00 48.50 51.00 54.00 57.00 60.00 63.00 66.00 69.00 69.00 72.00 75.00 75.00 78.00 81.00 84.00 90.00 93.00

3.60 4.30 5.00 5.90 6.80 8.20 10.00 11.00 12.00 13.00 14.00 15.00 16.00 17.00 18.00 19.00 20.00 22.00 22.00 24.00 24.00 26.00 28.00 26.00 28.00 30.00 28.00 30.00 32.00 32.00 36.00 35.00

4.60 5.55 5.00 7.65 8.80 10.70 13.00 14.50 16.00 17.00 19.00 20.00 21.00 23.00 24.00 25.00 27.00 29.00 30.00 32.00 33.00 35.00 37.00 36.00 38.00 40.00 39.00 41.00 43.00 44.00 48.00 48.50

5.60 6.80 8.00 9.40 10.80 13.20 16.00 18.00 28.00 29.00 34.00 35.00 38.00 29.00 30.00 31.00 34.00 36.00 38.00 40.00 42.00 44.00 46.00 46.00 48.00 50.00 50.00 52.00 54.00 56.00 60.00 62.00

6.60 8.05 9.50 11.15 12.80 15.70 19.00 21.50 20.00 21.00 24.00 25.00 26.00 35.00 36.00 37.00 41.00 43.00 46.00 48.00 51.00 53.00 55.00 56.00 58.00 60.00 61.00 63.00 65.00 68.00 72.00 75.50

7.60 9.30 11.00 12.90 14.80 18.20 22.00 25.00 24.00 25.00 29.00 30.00 31.00 41.00 42.00 43.00 48.00 50.00 50.00 56.00 60.00 62.00 64.00 66.00 68.00 70.00 72.00 74.00 76.00 80.00 84.00 89.00

2.30 2.90 3.40 4.10 4.70 5.80 7.10 8.10 0.10 9.50 11.10 11.50 11.80 13.50 13.00 14.20 15.80 16.50 17.80 18.50 19.80 20.50 21.20 21.80 22.50 23.20 23.80 24.50 25.20 26.50 27.90 29.50

2.70 3.40 4.00 4.70 5.30 6.40 7.70 8.70 9.70 10.10 11.70 12.10 12.40 14.10 14.40 14.80 16.40 17.10 18.40 19.10 20.40 21.10 21.80 22.40 23.10 23.80 24.40 25.10 25.80 27.10 28.50 30.10

2.087 2.597 3.108 3.630 4.162 5.174 6.217 7.217 8.217 8.271 10.217 10.271 10.324 12.271 12.324 12.379 14.324 14.433 16.324 16.433 18.324 18.433 18.541 20.324 20.433 20.541 22.324 22.433 22.541 24.433 24.649 27.433

2.199 2.722 3.248 3.790 4.332 5.374 6.407 7.407 8.407 8.483 10.407 10.483 10.580 12.483 12.560 12.644 14.560 14.733 16.560 16.733 18.560 18.733 18.896 20.560 20.733 20.896 22.560 22.733 22.896 24.733 25.049 27.733

2.260 2.792 3.326 3.890 4.455 5.520 6.650 7.650 8.650 8.812 10.650 10.812 10.974 12.812 12.974 13.137 14.974 15.299 16.974 17.299 18.974 19.299 19.624 20.974 21.299 21.624 22.974 23.299 23.624 25.299 25.948 28.299

Insert Length 6H Max.

All Classes

1D

1.5D

2D

2.5D

3D

2.295 2.832 3.367 3.940 4.508 5.577 6.719 7.719 8.719 8.886 10.719 10.886 11.061 12.896 13.067 13.236 15.067 15.406 17.067 17.406 19.067 19.406 19.738 21.067 21.406 21.738 23.067 23.406 23.738 25.414 26.093 28.414

2.329 2.867 3.404 3.981 4.522 5.622 6.774 7.774 8.774 8.946 10.774 10.946 11.129 12.966 13.139 13.311 15.139 15.486 17.139 17.486 19.139 19.486 19.822 21.139 21.486 21.822 23.139 23.486 23.822 25.498 26.188 28.498

2.520 3.084 3.650 4.280 4.910 6.040 7.300 8.300 9.300 9.624 11.300 11.624 11.948 13.624 13.948 14.274 15.940 16.958 17.948 18.598 19.948 20.598 21.248 21.940 22.598 23.248 23.948 24.598 25.248 26.598 27.897 29.598

2.40 2.95 3.50 4.10 4.70 5.80 7.00 8.00 9.00 9.26 11.00 11.26 11.50 13.25 13.50 13.75 15.50 16.00 17.50 18.00 19.50 20.00 20.50 21.50 22.00 22.50 23.50 24.00 24.50 26.00 27.00 29.00

3.40 4.20 5.00 5.85 6.70 8.30 10.00 11.50 13.00 13.25 16.00 16.25 16.50 19.25 19.50 19.75 22.50 23.00 25.50 26.00 28.50 29.00 29.50 31.50 32.00 32.50 34.50 35.00 35.50 38.00 39.00 42.50

4.40 5.45 6.50 7.60 8.70 10.80 13.00 15.00 17.00 17.26 21.00 21.26 21.50 25.25 25.50 25.75 29.50 30.00 33.50 34.00 37.50 38.00 38.50 41.50 42.00 42.50 45.50 46.00 46.50 50.00 51.00 58.00

5.40 6.70 8.00 9.35 10.70 13.30 16.00 18.50 21.00 21.25 26.00 26.25 26.50 31.25 31.50 31.75 38.50 37.00 41.50 42.00 46.50 47.00 47.50 51.50 52.00 52.50 56.50 57.00 57.50 62.00 63.00 69.50

6.40 7.95 9.50 11.10 12.70 15.80 19.00 22.00 25.00 25.25 31.00 31.25 31.50 37.25 37.60 37.75 43.50 44.00 49.50 50.00 55.50 56.00 56.50 61.50 62.00 62.50 67.50 68.00 68.50 74.00 75.00 83.00

2.310 2.847 3.384 3.959 4.529 5.597 6.742 7.742 8.742 8.911 10.742 10.911 11.089 12.926 13.099 13.271 15.099 15.444 17.099 17.444 19.099 19.444 19.778 21.099 21.444 21.778 23.099 23.444 23.778 15.454 26.135 28.454


1521

1D

HELICAL COIL SCREW THREAD INSERTS

Nominal Thread Size

Minimum Tapping Depth, T

Pitch Diameter 4H 5H Max. Max.

Machinery's Handbook 28th Edition Table 1. (Continued) Screw Thread Insert Threaded Hole Data ASME B18.29.2M-2005 Countersink Diameter, M (120°±5° included angle)

Minimum Drilling Depth for Each Insert Length, G

1D 45.00 42.00 48.00 51.00 45.00 51.00 48.00 54.00 60.00 51.00 57.00

1.5D 68.50 67.00 63.00 66.00 61.60 67.60 66.00 72.00 78.00 70.50 76.50

2D 72.00 72.00 78.00 81.00 78.00 84.00 84.00 90.00 96.00 90.00 96.00

Bottoming Taps

2.5D 85.50 87.00 93.00 96.00 94.50 104.50 102.00 108.00 114.00 109.50 115.50

3D 99.00 102.00 108.00 111.00 111.00 117.00 120.00 126.00 132.00 129.00 135.00

1D 39.00 38.00 42.00 44.00 41.00 45.00 44.00 48.00 52.00 47.00 51.00

1.5D 52.50 53.00 57.00 59.00 57.50 61.50 62.00 66.00 70.00 66.50 70.50

2D 66.00 68.00 72.00 74.00 74.00 78.00 80.00 84.00 88.00 88.00 90.00

2.5D 79.50 83.00 87.00 89.00 90.50 94.50 98.00 102.00 106.00 105.50 109.50

3D 93.00 98.00 102.00 104.00 107.00 111.00 116.00 120.00 124.00 125.00 129.00

Min. Max. 30.90 31.50 32.50 33.10 33.90 34.50 34.60 35.20 35.50 36.10 36.90 37.50 38.50 39.10 39.90 40.50 41.30 41.90 41.50 42.10 42.90 43.50

Min. 27.649 30.433 30.649 30.767 33.433 33.649 36.433 36.649 36.866 39.433 39.649

Max. 28.049 30.733 31.049 31.207 33.733 34.049 36.733 37.049 37.341 39.733 40.049

Min. 28.948 31.299 31.948 32.273 34.299 34.948 37.299 37.948 28.598 40.299 40.948

Pitch Diameter 4H 5H Max. Max. 29.093 29.135 31.414 31.454 32.093 32.136 32.428 32.472 34.414 34.454 35.093 35.135 37.414 37.464 38.093 38.135 38.763 38.809 40.414 40.454 41.093 41.136

Minimum Tapping Depth, T Insert Length

6H Max. 29.188 31.489 32.188 32.628 34.498 36.188 37.498 38.188 38.873 40.498 41.188

All Classes 30.897 32.598 33.897 34.546 35.598 36.897 38.598 39.897 41.196 41.598 42.897

1D 1.5D 2D 2.5D 30.00 43.50 57.00 70.50 32.00 47.00 62.00 77.00 33.00 48.00 63.00 78.00 33.50 48.50 63.50 78.50 35.00 51.50 68.00 84.50 36.00 52.50 69.00 85.50 38.00 58.00 74.00 92.00 39.00 57.00 75.00 93.00 40.00 58.00 76.00 94.00 41.00 60.50 80.00 99.50 42.00 61.50 81.00 100.50

3D 84.00 92.00 93.00 93.50 101.00 102.00 110.00 111.00 112.00 119.00 120.00

(2) The minimum tapping depth (dimension T) is the minimum for countersink holes with insert set-down of 1.5 pitch maximum (See Fig. 4.). The dimension T = insert nominal length + 1 pitch. (3) Thread diameters are calculated as follows: Pitch diameter, min. = Pitch diameter, min. of nominal thread + 2 × H max Pitch diameter, max. = Pitch diameter, max. of nominal thread + 2 × H min Major diameter, min. = Pitch diameter min. + 0.649519 × P Minor diameter, min. = Pitch diameter min. – 0.433013 × P Minor diameter, max. = Minor diameter min. + tolerance

where Hmax and Hmin are from Table 1, and tolerance is selected from the appropriate table in ASME B1.13M with basic major diameter equal to the minimum major diameter of the STI thread.


1522

Notes: (1) The minimum drilling depths allow for a) countersinking the drilled hole to prevent a feather edge at the start of the tapped hole. b) 0.75 to 1.5 pitch of insert set-down to allow for maximum production tolerance. c) Dimensions are shown for both plug and bottoming taps. Plug taps 8 mm and smaller have a male center, and the drilled hole depth dimensions allow for this length (one-half of the diameter of the bolt). Calculation of minimum drilling depth dimension G is as follows: Plug taps 8mm and smaller, G = insert nominal length + 0.5 × nominal bolt diameter + 4 pitchs for tap chamfer + 1 pitch for tap end clearance + 1 pitch allowance for countersink and maximum insert set-down. Plug taps larger than 8 mm, G = insert nominal length + 4 pitchs for tap chamfer + 1 pitch for tap end clearance + 1 pitch allowance for countersink and maximum insert set-down. Bottoming taps, G = insert nominal length + 2 pitchs for tap chamfer + 1 pitch for tap end clearance + 1 pitch allowance for countersink and maximum insert set-down.

Minor Diameter


Nominal Thread Size M27 × 3 M30 × 2 M30 × 3 M30 × 3.5 M33 × 2 M33 × 3 M36 × 2 M36 × 3 M36 × 4 M39 × 2 M39 × 3

Plug Taps

Min. Major Diam.

Machinery's Handbook 28th Edition HELICAL COIL SCREW THREAD INSERTS Locking Feature (Note (1)] (locking inserts only)

1523

To Be Measured 30° from Tang 100° max.

J

A

P

B K

First Coil Diam. to Meet Free Diam. 210° from Tang within 20° [Note (2)] Tang

K C Number of Free Coils

Ends of Coil May Be Square or Angular

Free outer diam. 0.8

S min.

Notch to be on Top Face of First Coil Beyond Tangent Point of Tang Radius

Gage = Pitch/2 F 2

F max. 2

Min. Metal Condition Min. Metal Condition

60°

D max.

D min.

D min. H min.

+ D max. 2

D min. 2

See View L A min. flat See View L

E min.

CL of Wire Section 0.09

U V Tang Radius

H max. 2

A min. flat

D max.

D max.

R min. Tangent to Flanks

E min. 2 E max. 2

S min. Enlarged View L Typ 2 Places

E max. D G

Section K-K

Fig. 5. Insert Configuration General Notes for Fig. 5: (a) Assembled length of insert to be measured from notch. (b) Dimensions apply before supplementary coating (see Tables 3 and 4). (c) Surface texture; symbols per ASME Y14.35, requirements per ASME B46.1. (d) Dimensions and tolerancing; ASME Y14.5M. Notes: (1) Number of locking coils, spacing of locking coils, number of locking deformations, shape and orientation optional locking feature for 1, 1.5, and 2 diam. length inserts symmetrically positioned about the center of insert, and for 2.5 and 3 diam. length inserts at 1 diam. from tang end of insert. (2) Number of free coils to be counted from notch.

Inspection and Quality Assurance The inspection of inserts shall be in accordance with ASME B18.18.1M, with inspection level 3 for the 15 cycle torque test. Inspection (Nondestructive).—Inserts shall be visually examined for conformance with drawings and workmanship requirements in accordance with ASME B18.18.1M. Threads: The inserts, when assembled in STI threaded holes conforming to Table 1, shall form threads conforming to ASME B1.13M tolerance class 4H5H or 5H except for the locking feature of screw-locking inserts. The assembled insert, both types, shall accept and function with parts having external MJ threads per ASME B1.21M.



1524

Table 2. Screw Thread Insert Chemical Composition ASME B18.29.2M-2005 Check Analysis Element

Analysis,%

Under, Min.

Over, Max.

Carbon

0.15 max.

…

0.01

Manganese

2.00 max.

…

0.04

Silicon

1.00 max.

…

0.05

Phosphorous

0.045 max.

…

0.01

Sulphur

0.035 max.

…

0.005 0.20

Chromium

17.00 to 20.00

0.20

Nickel

8.00 to 10.50

0.15

0.15

Molybdenum

0.75 max.

…

0.05

Copper

0.75 max.

…

0.05

Iron

Remainder

…

…

The accuracy of the finished thread when the insert is installed depends on the accuracy of the tapped hole. If the finished tapped hole gages satisfactorily, the installed insert will be within the thread tolerance when the insert meets the requirements of the Standard. It is, therefore, not necessary to gage the installed insert. After the insert is installed, the GO thread plug gage may not enter freely because the insert may not have been fully seated in the tapped hole. However, the insert should become seated after a bolt or screw is installed and tightened. Tang Removal Notch: The tang removal notch shall be located as shown in Fig. 5 and of such depth that the part may be installed without failure of the tang and that the tang may be removed, after assembly, without affecting the function of the installed insert. Torque Test Bolts: Assembled screw-locking inserts shall be torque tested with bolts in accordance with ASME B1.13M or ASME B1.21M, cadmium plated, or having other coating with a similar coefficient of friction and hardness of 36 HRC to 44 HRC. The bolts selected for this test shall be of sufficient length so the thread runout does not enter the insert and that a minimum of one full thread extends past the end of the insert when the bolt is fully seated. Acceptability of bolt threads shall be determined based on System 22 of ASME B1.3M. Until a replacement for cadmium plating on the torque test bolts is found, and test data completed, an alternate coating/lubricant can be used to perform the torque test. Self-Locking Torque (Destructive).—The screw-locking insert, when assembled in threaded holes conforming to Table 1 and tested in accordance with the following paragraphs, shall provide a frictional lock to retain the bolt threads within the torque limits specified in Table 5. Torque Test Block and Spacer: The insert to be tested shall be installed in a tolerance class 4H5H or 4H6H threaded hole conforming to Table 1 in a test block made from 2024T4 (SAE AMS4120 or ASTM B 209M) aluminum alloy. After installation, the tang shall be removed. The surface of the test block from which the insert is assembled shall be marked “TOP” and shall be marked to indicate the radial location where the assembled insert begins. A steel spacer meeting the requirements of Fig. 6 and Table 6 shall be used for developing the bolt load. Torque Test Method: The torque test shall consist of a 15-cycle, room temperature test. A new bolt or screw and new tapped hole shall be used for each complete 15-cycle test For each of the 15 cycles, bolts shall be assembled and seated to the assembly torque specified


Machinery's Handbook 28th Edition Table 3. Screw Thread Insert Length Data ASME B18.29.2M-2005 11⁄2 × Diam.

1 × Diam. Nominal Thread Size

Assembled

Nominal

Max.

Min.

C (Ref.)

Nominal

Assembled Max.

2 1⁄2 × Diam.

2 × Diam. C

Assembled

Min.

(Ref.)

Nominal

Max.

Min.

C (Ref.)

Nominal

Assembled

3 × Diam. C

Max.

Min.

(Ref.)

Nominal

Assembled Max.

Min.

C (Ref.)

2.00

1.80

1.70

3.250

3.00

2.80

2.70

5.500

4.00

3.80

3.70

7.750

5.00

4.80

4.70

10.125

6.00

5.80

5.70

12.375

2.50

2.28

2.16

3.575

3.80

3.52

3.41

5.750

5.00

4.78

4.66

8.125

6.30

6.02

5.91

10.500

7.50

7.28

7.16

12.750

M3 × 0.5

3.00

2.75

2.62

3.750

4.50

4.25

4.12

6.375

6.00

5.75

5.62

8.875

7.50

7.25

7.12

11.375

9.00

8.75

8.62

13.875

M3.5 × 0.6

3.50

3.20

3.05

3.750

5.30

5.00

4.80

6.375

7.00

6.70

6.55

8.750

8.80

8.50

8.30

11.375

10.50

10.20

10.05

13.750

4.00

3.65

3.47

3.625

6.00

5.65

5.47

6.125

8.00

7.65

7.47

8.625

10.00

9.65

9.47

11.125

12.00

11.65

11.47

13.625

M5 × 0.8

5.00

4.60

4.40

4.125

7.50

7.10

6.90

6.875

10.00

9.60

9.40

9.625

12.50

12.10

11.90

12.375

15.00

14.60

14.40

15.125

M6 × 1

6.00

5.50

5.25

4.000

9.00

8.50

8.25

6.750

12.00

11.50

11.25

9.500

15.00

14.50

14.25

12.125

18.00

17.50

17.25

14.875

M7 × 1

7.00

6.50

6.25

4.875

10.50

10.00

9.75

8.000

14.00

13.50

13.25

11.125

17.50

17.00

16.75

14.125

21.00

20.50

20.25

17.250

M8 × 1

8.00

7.50

7.25

5.875

12.00

11.50

11.25

9.375

16.00

15.50

15.25

13.000

20.00

19.50

19.25

16.500

24.00

23.50

23.25

20.125

M8 × 1.25

8.00

7.38

7.06

4.500

12.00

11.38

11.06

7.375

16.00

15.38

15.06

10.250

20.00

19.38

19.06

13.250

24.00

23.38

23.06

16.125

M10 × 1

10.00

9.50

9.25

7.625

15.00

14.50

14.25

12.000

20.00

19.50

19.25

16.500

25.00

24.50

24.25

21.000

30.00

29.50

29.25

25.500

M10 × 1.25

10.00

9.38

9.06

5.875

15.00

14.38

14.06

9.500

20.00

19.38

19.06

13.125

25.00

24.38

24.06

16.750

30.00

29.38

29.06

20.375

M10 × 1.5

10.00

9.25

8.87

4.875

15.00

14.25

13.87

8.000

20.00

19.25

18.87

11.125

25.00

24.25

23.87

14.250

30.00

29.25

28.87

17.375

M12 × 1.25

12.00

11.38

11.06

7.250

18.00

17.38

17.06

11.625

24.00

23.38

23.06

15.875

30.00

29.38

29.06

20.250

36.00

35.38

35.06

24.500

M12 × 1.5

12.00

11.25

10.87

6.000

18.00

17.25

16.87

9.625

24.00

23.25

22.87

13.375

30.00

29.25

28.87

17.000

36.00

35.25

34.87

20.750

M12 × 1.75

12.00

11.12

10.68

5.000

18.00

17.12

16.68

8.250

24.00

23.12

22.68

11.500

30.00

29.12

28.68

14.625

36.00

35.12

34.68

17.875

M14 × 1.5

14.00

13.25

12.87

7.125

21.00

20.25

19.87

11.375

28.00

27.25

26.87

15.625

35.00

4.25

33.87

20.000

42.00

41.25

40.87

24.250

M14 × 2

14.00

13.00

12.50

5.125

21.00

20.00

19.50

8.500

28.00

27.00

26.50

11.750

35.00

34.00

33.50

15.000

42.00

41.00

40.50

18.375

M16 × 1.5

16.00

15.25

14.87

8.250

24.00

23.25

22.87

13.125

32.00

31.25

30.87

18.000

40.00

39.25

38.87

22.750

48.00

47.25

46.87

27.625

M16 × 2

16.00

15.00

14.50

6.125

24.00

23.00

22.50

9.750

32.00

31.00

30.50

13.500

40.00

39.00

38.50

17.250

48.00

47.00

46.50

21.000

M18 × 1.5

18.00

17.25

16.87

9.500

27.00

26.25

25.87

15.000

36.00

35.25

34.87

20.375

45.00

44.25

43.87

25.875

54.00

53.25

52.87

31.375

M18 × 2

18.00

17.00

16.50

7.000

27.00

26.00

25.50

11.125

36.00

35.00

34.50

15.375

45.00

44.00

43.50

19.500

54.00

53.00

52.50

23.625


1525

M4 × 0.7


M2 × 0.4 M2.5 × 0.45


Nominal Thread Size

Nominal

Assembled

11⁄2 × Diam.

Max.

Min.

C (Ref.)

Nominal

Assembled Max.

Min.

2 1⁄2 × Diam.

2 × Diam. C (Ref.)

Nominal

Assembled Max.

Min.

C (Ref.)

Nominal

Assembled

1526

Table 3. (Continued) Screw Thread Insert Length Data ASME B18.29.2M-2005 1 × Diam.

3 × Diam. C

Max.

Min.

(Ref.)

Nominal

Assembled Max.

Min.

C (Ref.)

18.00

16.75

16.12

5.375

27.00

25.75

25.12

8.875

36.00

34.75

34.12

12.250

45.00

43.75

43.12

15.625

54.00

52.75

52.12

19.000

M20 × 1.5

20.00

19.25

18.87

10.750

30.00

29.25

28.87

16.875

40.00

39.25

38.87

22.875

50.00

49.25

48.87

28.875

60.00

59.25

58.87

35.000

M20 × 2

20.00

19.00

18.50

7.875

30.00

29.00

28.50

12.500

40.00

39.00

38.50

17.250

50.00

49.00

48.50

21.875

60.00

59.00

58.50

26.500

M20 × 2.5

20.00

18.75

18.12

6.125

30.00

28.75

28.12

9.875

40.00

38.75

38.12

13.625

50.00

48.75

48.12

17.375

60.00

58.75

58.12

21.125

M22 × 1.5

22.00

21.25

20.87

11.875

33.00

32.25

31.87

18.500

44.00

43.25

42.87

25.125

55.00

54.25

53.87

31.625

66.00

65.25

64.87

38.250

M22 × 2

22.00

21.00

20.50

8.750

33.00

32.00

31.50

13.750

44.00

43.00

42.50

18.875

55.00

54.00

53.50

23.875

66.00

65.00

64.50

29.000

M22 × 2.5

22.00

20.75

20.12

6.750

33.00

31.75

31.12

10.875

44.00

42.75

42.12

14.875

55.00

53.75

53.12

19.000

66.00

64.75

64.12

23.125

M24 × 2

24.00

23.00

22.50

9.500

36.00

35.00

34.50

15.000

48.00

47.00

16.50

20.375

60.00

59.00

58.50

25.875

72.00

71.00

70.50

31.250

M24 × 3

24.00

22.50

21.75

6.125

36.00

34.50

33.75

10.000

48.00

46.50

45.75

13.750

60.00

58.50

57.75

17.500

72.00

70.50

69.75

21.375

M27 × 2

27.00

26.00

25.50

10.875

40.50

39.50

39.00

17.000

54.00

53.00

52.50

23.250

67.50

66.50

66.00

29.375

81.00

80.00

79.50

35.500

M27 × 3

27.00

25.50

24.75

7.000

40.50

39.00

38.25

11.250

54.00

52.50

51.75

15.500

67.50

66.50

65.25

19.750

81.00

79.50

78.75

24.000

M30 × 2

30.00

29.00

28.50

12.250

45.00

44.00

43.50

19.125

60.00

59.00

58.50

25.875

75.00

74.00

73.50

32.750

90.00

89.00

88.50

39.500

M30 × 3

30.00

28.50

27.75

7.875

45.00

43.50

42.75

12.500

60.00

58.50

57.75

17.125

75.00

73.50

72.75

21.875

90.00

88.50

87.75

26.500

M30 × 3.5

30.00

28.25

27.37

6.750

45.00

43.25

42.37

10.750

60.00

58.25

57.37

14.875

75.00

73.25

72.37

18.875

90.00

88.25

87.37

23.000

M33 × 2

33.00

32.00

31.50

13.625

49.50

48.50

48.00

21.125

66.00

65.00

64.50

28.625

82.50

81.50

81.00

35.000

99.00

98.00

97.50

43.500

M33 × 3

33.00

32.50

30.75

8.750

49.50

48.00

47.25

13.875

66.00

64.50

63.75

19.000

82.50

81.00

80.25

24.125

99.00

97.50

96.75

29.250

M36 × 2

36.00

35.00

34.50

15.000

54.00

53.00

52.50

23.250

72.00

71.00

70.50

31.375

90.00

89.00

88.50

39.500 108.00 107.00

106.50

47.750

M36 × 3

36.00

34.50

33.75

9.750

54.00

52.50

51.75

15.250

72.00

70.50

69.75

20.875

90.00

88.50

87.75

26.500 108.00 106.50

105.75

32.000

M36 × 4

36.00

34.00

33.00

7.125

54.00

52.00

51.00

11.375

72.00

70.00

69.00

15.625

90.00

88.00

87.00

19.875 108.00 106.00

105.00

24.250

M39 × 2

39.00

38.00

37.50

16.375

58.50

57.50

57.00

25.250

78.00

77.00

76.50

34.125

97.50

96.50

96.00

43.000 117.00 116.00

115.50

51.875

M39 × 3

39.00

37.50

36.75

10.750

58.50

57.00

56.25

15.750

78.00

76.50

75.75

22.750

97.50

96.00

95.25

28.875 117.00 115.50

114.75

34.875



M18 × 2.5

Machinery's Handbook 28th Edition Table 4. Screw Thread Insert Dimensions ASME B18.29.2M-2005 B Nominal Thread Size

D

E

H

P

U

Max.

Min.

M2 × 0.4

0.074

2.50

2.70

0.389

0.433

0.274

0.350

0.200

0.2495

0.2600

2.50

2.70

M2.5 × 0.45

0.082

3.20

3.70

0.437

0.487

0.318

0.394

0.225

0.2820

0.2920

3.05

3.65

M3 × 0.5

0.105

3.80

4.35

0.482

0.541

0.352

0.438

0.250

0.3145

0.3250

3.60

4.30

M3.5 × 0.6

1.160

4.40

4.95

0.586

0.650

0.449

0.525

0.300

0.3795

0.3900

4.25

M4 × 0.7

0.163

5.05

5.60

0.683

0.758

0.510

0.612

0.350

0.4445

0.4550

4.90

M5 × 0.8

0.209

6.25

6.80

0.775

0.866

0.598

0.700

0.400

0.5085

0.5200

6.10

6.75

3.15

4.55

0.144

0.250

2.09

1.41

0.60

M6 × 1

0.267

7.40

7.95

0.975

1.083

0.748

0.875

0.500

0.6370

0.6500

7.25

7.90

3.70

4.85

0.180

0.312

2.55

1.65

0.60 0.75

Min.

Max.

Min.

Max.

Min.

Max.

R, Min.

S, Min.

Min.

Max.

V, Max.

1.30

1.90

0.072

0.125

0.66

0.37

0.22

1.60

2.25

0.081

0.141

1.22

0.81

0.30

1.95

2.80

0.090

0.156

1.33

0'.56

0.30

4.90

2.20

3.00

0.108

0.158

1.47

0.92

0.30

5.55

2.50

3.55

0.126

0.219

1.67

1.02

0.45

Max.

Min.

M7 × 1

0.267

8.65

9.20

0.975

1.083

0.748

0.875

0.500

0.6370

0.6500

8.40

9.15

4.30

5.50

0.180

0.312

3.10

2.09

M8 × 1

0.267

9.70

10.25

0.975

1.083

0.748

0.875

0.500

0.6370

0.6500

9.20

9.65

4.75

6.50

0.180

0.312

3.58

2.27

0.75

M8 × 1.25

0.415

9.80

10.35

1.251

1.353

0.967

1.094

0.625

0.7990

0.8120

9.50

9.90

4.75

6.50

0.226

0.391

3.60

2.02

0.75

M10 × 1

0.267 11.95

12.50

0.975

1.083

0.748

0.875

0.500

0.6370

0.6500

11.10

11.55

5.50

8.00

0.180

0.312

4.90

2.95

0.75

M10 × 1.25

0.415 12.10

12.65

1.251

1.353

0.967

1.094

0.625

0.7990

0.8120

11.50

11.95

5.50

8.00

0.226

0.391

4.77

2.56

0.75

M10 × 1.5

0.511 11.95

12.50

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

11.80

12.25

5.50

8.00

0.271

0.469

4.54

2.56

0.75

M12 × 1.25

0.415 14.30

15.00

1.251

1.353

0.967

1.094

0.625

0.7990

0.8120

13.50

14.00

6.70

9.75

0.226

0.391

5.84

3.77

1.00

M12 × 1.5

0.511 14.25

14.95

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

13.80

14.30

6.70

9.75

0.271

0.469

5.58

3.50

1.20

M12 × 1.75

0.654 14.30

15.00

1.792

1.894

1.379

1.531

0.875

1.1240

1.1370

14.10

14.60

6.70

9.75

0.316

0.547

5.36

3.23

1.40 1.15

M14 × 1.5

0.511 16.55

17.25

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

15.80

16.30

7.20

11.25

0.271

0.469

6.76

4.34

M14 × 2

0.799 16.65

17.35

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

16.40

16.90

7.20

11.25

0.361

0.625

6.26

3.79

1.40

M16 × 1.5

0.511 18.90

19.60

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

17.80

18.30

8.30

12.75

0.271

0.469

7.78

5.32

1.45

0.799 18.90

19.60

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

18.40

18.90

8.30

12.75

0.361

0.625

7.30

4.76

2.70

0.511 21.05

21.75

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

19.80

20.35

9.30

14.00

0.271

0.469

8.83

6.26

1.75

M18 × 2

0.799 21.15

21.85

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

20.40

20.95

9.30

14.00

0.361

0.625

8.30

5.74

2.70


1527

M16 × 2 M18 × 1.5


Min.

Max.

Gage, F

J

A, Min.


Nominal Thread Size

A, Min.

D

E

H

J

Max.

Min.

Max.

Min.

Max.

Gage, F

Min.

Max.

Min.

M18 × 2.5

1.017 21.30

22.00

2.604

2.706

1.998

2.188

1.250

1.6110

1.6240

20.90

M20 × 1.5

0.511 23.15

24.00

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

21.80

M20 × 2

0.799 23.20

24.05

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

22.40

P

U

Min.

Max.

R, Min.

S, Min.

Min.

Max.

V, Max.

21.45

9.30

14.00

0.451

0.781

7.79

5.20

2.85

22.50

10.40

14.50

0.271

0.469

9.77

7.19

2.85

23.10

10.40

14.50

0.361

0.625

9.40

6.65

2.85

Max.

M20 × 2.5

1.017 23.55

24.40

2.604

2.706

1.998

2.188

1.250

1.6110

1.6240

22.90

23.60

10.40

14.50

0.451

0.781

8.89

6.11

2.85

M20 × 1.5

0.511 23.15

24.00

1.522

1.624

1.160

1.312

0.750

0.9615

0.9740

24.10

24.80

11.40

16.00

0.271

0.469

11.10

8.01

2.85 2.85

M22 × 2

0.799 25.60

26.50

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

24.40

25.10

11.40

16.00

0.361

0.625

10.45

7.61

M22 × 2.5

1.017 25.90

26.90

2.604

2.706

1.998

2.188

1.250

1.6110

1.6240

24.90

25.60

11.40

16.00

0.451

0.781

9.94

7.07

2.85

M24 × 2

0.799 28.10

29.10

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

26.40

27.10

12.50

16.50

0.361

0.625

11.48

8.60

2.85

M24 × 3

1.234 28.00

29.00

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

27.50

28.20

12.50

16.50

0.541

0.938

10.45

7.51

2.85

M27 × 2

0.799 31.30

32.30

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

29.40

30.10

14.00

17.50

0.361

0.625

13.14

9.93

2.85 2.85

M27 × 3

1.234 31.40

32.40

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

30.50

31.20

14.00

17.50

0.541

0.938

12.13

8.85

M30 × 2

0.799 34.50

35.70

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

32.50

33.20

15.00

19.00

0.361

0.625

14.81

11.26

2.85

M30 × 3

1.234 34.90

36.10

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

33.50

34.20

15.00

19.00

0.541

0.938

13.65

10.32

2.85

M30 × 3.5

1.451 34.90

36.10

3.687

3.789

2.833

3.062

1.750

2.2605

2.2750

34.10

34.60

15.00

19.00

0.631

1.094

13.13

9.65

2.85

M33 × 2

0.799 37.80

39.20

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

35.80

36.50

17.00

21.00

0.361

0.625

16.35

12.74

2.85

M33 × 3

1.234 38.10

39.50

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

36.50

37.20

17.00

21.00

0.541

0.938

15.19

11.78

2.85

M36 × 2

0.799 41.00

42.40

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

39.00

39.70

18.50

22.50

0.361

0.625

17.77

14.29

2.85

M36 × 3

1.234 41.30

42.70

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

39.50

40.20

18.50

22.50

0.541

0.938

16.73

13.23

2.85

M36 × 4

1.688 41.50

42.90

4.228

4.330

3.271

3.500

2.000

2.5855

2.5980

40.60

41.10

18.50

22.50

0.722

1.250

15.57

12.12

2.85

M39 × 2

0.799 44.30

45.70

2.063

2.165

1.598

1.750

1.000

1.2865

1.2990

42.30

43.00

20.00

24.00

0.361

0.625

19.28

15.77

2.85

M39 × 3

1.234 44.40

45.80

3.146

3.248

2.396

2.625

1.500

1.9360

1.9485

42.50

43.20

20.00

24.00

0.541

0.938

18.28

14.68

2.85



Min.

1528

Table 4. (Continued) Screw Thread Insert Dimensions ASME B18.29.2M-2005 B


1529

in Table 5. Bolts shall be completely disengaged from the locking coils of the insert at the end of each cycle. The test shall be run at less than 40 rpm to yield a dependable measure of torque and avoid heating of the bolt. Maximum Locking Torque: Maximum locking torque shall be the highest torque value encountered on any installation or removal cycle and shall not exceed the values specified in Table 5. Maximum locking torque readings shall be taken on the first and seventh installation cycles before the assembly torque is applied and on the 15th removal cycle. Table 5. Self Locking Torque ASME B18.29.2M-2005 Maximum Locking Torque InstalNominal Thread lation or Size Removal, N-m M2 × 0.4 0.12 M2.5 × 0.45 0.22 M3 × 0.5 0.44 M3.5 × 0.6 0.68 M4 × 0.7 0.9 M5 × 0.8 1.6 M6 × 1 3 M7 ×1 4.4 M8 × 1 6 M8 × 1.25 6 M10×1 10 M10 × 1.25 10 M10×1.5 10 M12 × 1.25 15 M12 × 1.5 15 M12 × 1.75 15 M14 × 1.5 23 M14 × 2 23 M16 × 1.5 32 M16 × 2 32 … … … … … …

Minimum Breakaway Torque, N-m 0.03 0.06 0.1 0.12 0.16 0.3 0.4 0.6 0.8 0.8 1.4 1.4 1.4 2.2 2.2 2.2 3 3 4.2 4.2 … … …

Nominal Thread Size M18 × 1.5 M18 × 2 M18×2.5 M20 × 1.5 M20 × 2 M20 × 2.5 M22 × 1.5 M22 × 2 M22 × 2.5 M24 × 2 M24 × 3 M27 × 2 M27 × 3 M30 × 2 M30 × 3 M30 × 3.5 M33 × 2 M33 × 3 M36 × 2 M36 × 3 M36 × 4 M39 × 2 M39 × 3

Maximum Locking Torque Installation or Removal, N-m 42 42 42 54 54 54 70 70 70 80 80 95 95 110 110 110 125 125 140 140 140 150 150

Minimum Breakaway Torque, N-m 5.5 5.5 5.5 7 7 7 9 9 9 11 11 12 12 14 14 14 16 16 18 18 18 20 20

Minimum Breakaway Torque: Minimum breakaway torque shall be the torque required to overcome static friction when 100% of the locking feature is engaged and the bolt or screw is not seated (no axial load). It shall be recorded at the start of the 15th removal cycle. The torque value for any cycle shall be not less than the applicable value shown in Table 5. Acceptance: The inserts shall be considered to have failed if, at the completion of any of the tests and inspection, any of the following conditions exist: a) any break or crack in the insert b) installation or removal torque exceeds the maximum locking torque value in Table 5 c) breakaway torque less than the values in Table 5 d) movement of the insert beyond 90° relative to the top surface when installing or removing the test bolt e) seizure or galling of the insert or test bolt f) tang not broken off, which interferes with the test bolt at installation g) tang breaks off during insert installation



1530

Table 6. Torque Test Spacer Dimensions ASME B18.29.2M-2005

Diameter or width

60+ 2o

Countersink Hole Diameter

diameter

Material: Steel Hardness: 45-50 HRC

Fig. 6. Torque Test Spacer

Nominal Insert Size 2 2.5 3 3.5 4 5 6 7 8 10 12 14 16 18 20 22 24 27 30 33 36 39

Minimum Diameter or Width 7.0 8.0 9.0 10.0 11.0 12.0 14.0 17.0 19.0 23.0 27.0 31.0 35.0 39.0 43.0 47.0 51.0 56.0 62.0 67.0 72.0 77.0

Hole Diameter Max. 2.3 2.8 3.5 4.0 4.5 5.5 6.5 7.6 8.6 10.7 12.7 14.8 16.8 18.8 20.8 22.8 24.8 28.3 31.3 34.3 37.3 40.3

Min. 2.1 2.6 3.3 3.8 4.3 5.3 6.3 7.3 8.3 10.4 12.4 14.4 16.4 18.4 20.4 22.4 24.4 27.9 30.9 33.9 36.9 39.9

Countersink Diameter Max. 2.7 3.3 3.8 4.3 4.9 5.9 7.0 8.4 9.5 11.5 14.5 16.5 18.5 20.7 22.7 24.7 26.7 29.8 33.8 36.8 39.8 42.8

Min. 2.5 3.1 3.6 4.1 4.7 5.7 6.8 8.2 9.2 11.2 14.2 16.2 18.2 20.4 22.4 24.4 26.4 29.4 33.4 36.4 39.4 42.4

Minimum Thickness 1.5 1.5 2.0 2.0 3.0 3.0 3.5 3.5 4.0 4.0 4.5 4.5 4.5 4.5 5.0 5.0 5.0 5.0 6.0 6.0 6.0 6.0

Insert Length Selection Engaged Length of Bolt.—Normally, the engaged length of bolt in an insert is determined by strength considerations. Material Strengths.—The standard engineering practice of balancing the tensile strength of the bolt material against the shear strength of the parent or boss material also applies to helical coil inserts. Tables 7 and 8 will aid in developing the full load value of the bolt rather than stripping the parent or tapped material.



1531

In using this table, the following factors must be considered: a) The parent material shear strengths are for room temperature. Elevated temperatures call for significant shear value reductions; compensation should be made when required. Shear values are appropriate because the parent material is subject to shearing stress at the major diameter of the tapped threads. b) When parent material shear strength falls between two tabulated values, use the lower of the two. c) Bolt thread length; overall length, insert length, and full tapped thread depth must be adequate to ensure full-thread engagement when assembled to comply with its design function. Table 7. Insert Length Selection ASME B18.29.2M-2005 Parent Material Shear Strength, MPa

Bolt Property Class 4.6

4.8

5.8

8.8

9.8

10.9

12.9 …

Insert Length in Terms of Diameters

70

3

3

3

…

…

…

100

2

2

2

3

…

…

…

150

1.5

1.5

1.5

2

2.5

2.5

3

200

1.5

1.5

1.5

2

2

2

2

250

1

1

1

1.5

1.5

1.5

1.5

300

1

1

1

1.5

1.5

1.5

1.5

350

1

1

1

1

1

1.5

1.5

Table 8. Hardness Number Conversion ASME B18.29.2M-2005 Bolt Property Max. Rockwell Class Hardness

Max. Tensile Bolt Property Max. Rockwell Strength, MPa Class Hardness

Max. Tensile Strength, MPa

4.6

95 HRB

705

9.8

36 HRC

1115

4.8

95 HRB

705

10.9

39 HRC

1215

5.8

95 HRB

705

12.9

44 HRC

1435

8.8

34 HRC

1055

Bolt strength upon which insert length recommendations are based is developed by taking the maximum hardness per ASTM F568M Carbon and Alloy Steel Externally Threaded Metric Fasteners and the equivalent tensile strength from SAE J417 Hardness Tests and Hardness Number Conversions.

Screw Thread Insert Taps.—ASME B94.9 covers design and dimensions for taps for producing Metric Series STI-threaded holes required for the installation of helical coil screw thread inserts. Threaded hole dimensions are shown in Table 1 of this standard. Helical coil screw thread insert taps are identified by the designation STI. Various types and styles of STI taps are available. General dimensions and tolerances are in accordance with ASME B94.9. Tap Thread Limits: Ground thread taps are recommended for screw thread inserts. Tap thread limits are in accordance with ASME B94.9. Basic pitch diameter used for determining values is the “Pitch Diameter, min.” from Table 1. Marking: Taps are marked in accordance with ASME B94.9. Example:M6 × 1 STI HS G H2.


1532

Machinery's Handbook 28th Edition 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 (R2005) see Tables 1 through 4 starting on page 1447, and 7 to 10 starting on page 1452. 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 1540), 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 1549 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 1535. 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, page 1723) 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 1723) 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.


Machinery's Handbook 28th Edition British Standard Whitworth (BSW) and Fine (BSF) Precision Hexagon Bolts, Screws, and Nuts A

R

F

C

B

D

G

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

Rounded End

Rolled Thread End

Alternative Hexagon Ordinary Nuts

C

E

E

0.015

A

E C

G

D

H

D

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

Alternate Hexagon Castle Nuts

A

P

N

0.015 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

0.015 G

L 30

30

Double Chamfered


30 Washer Faced

1533

30 Hexagon Slotted Nut, Full Bearing For dimensions, see Tables 1 and 2.

P C

M

120–+ 10 Enlarged View of Nut Countersink

BRITISH FASTENERS

A


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 1533. b Noted standard with BSW thread. All dimensions in inches except where otherwise noted.


BRITISH FASTENERS

Nominal Size D

Across Corners C

Diameter of Unthreaded Portion of Shank B

1534

Table 1. British Standard Whitworth (BSW) and Fine (BSF) Precision Hexagon Slotted and Castle Nuts BS 1083:1965 (obsolescent)

Machinery's Handbook 28th Edition 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

Thickness P

Castle Nuts

Lower Face to Bottom of Slot H

Total Thickness J

Lower Face to Bottom of Slot K

Slotted and Castle Nuts 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

BRITISH FASTENERS

Nominal Size D

a Not

All dimensions in inches except where otherwise noted.


1535

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 1533.

Machinery's Handbook 28th Edition BRITISH FASTENERS

1536

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


Machinery's Handbook 28th Edition 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

BRITISH FASTENERS

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.


1537

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.


BRITISH FASTENERS

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)

1538

Table 5. British Standard ISO Metric Precision Hexagon Nuts and Thin Nuts BS 3692:1967 (obsolescent)

Machinery's Handbook 28th Edition 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.

Radius (0.25 n) r

Width of Slot n

Min.

Eccentricity of the Slots

Max.

Min.

Max.

Min.

Max.

Min.

Min.

Max.

Min.

Max.

Min.

M4

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

0.27

22.00

21.67

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

25.4

30.14

24.49

25

19

24.48

18.48

21

16

20.48

15.57

15

11

14.57

10.57

4.80

3.80

4.5

3.5

1.125

0.875

0.27

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

M24

36.00

35.38

41.60

39.98

34

33.38

27

26.48

19

18.48

5.80

5.5

1.375

0.33

(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 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

(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

BRITISH FASTENERS

(M14)

a Sizes shown in parentheses are non-preferred.


1539

All dimensions are in millimeters. For illustration of hexagon slotted nuts and castle nuts see Table 3.


1540

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. All dimensions are in millimeters.

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



1541

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 (2004), “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


Machinery's Handbook 28th Edition STUDS

1542

stress at permanent set limit R 0.2 % 1 64 100 ----------------------------------------------------------------------------------- = ------ × ------ × --------10 80 1 minimum tensile strength 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 28th Edition STUDS

1543

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 1 1 ⁄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 3 1 ⁄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 5⁄ 21⁄4 25⁄8 8 5 3⁄ 3 2 ⁄8 4 7⁄ 31⁄8 35⁄8 8 1 4 31⁄2

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, 11⁄ , 8 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. Stan7 1 1 3 1 5 3 7 1 1 3 1 5 3 7 1 1 3 1 dard 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, 3 ⁄4, 3 ⁄8, 3 ⁄2 and for lengths above 31⁄2 the standard increment is 1⁄4.

All dimensions are in inches except where otherwise noted. See page 1878 for interference-fit threads.


Machinery's Handbook 28th Edition WASHERS

1544

British Standard Single Coil Rectangular Section Spring Washers Metric Series — Types B and BP BS 4464:1969 (2004)

Nom. Size &Thread Dia., d

Inside Dia.,d1 Max

Min

Width, b

Thickness, s

Outside Dia., d2 Max

Radius, r Max

k (Type BP Only)

M1.6

1.9

1.7

0.7 ± 0.1

0.4 ± 0.1

3.5

0.15

…

M2

2.3

2.1

0.9 ± 0.1

0.5 ± 0.1

4.3

0.15

…

(M2.2)

2.5

2.3

1.0 ± 0.1

0.6 ± 0.1

4.7

0.2

…

M2.5

2.8

2.6

1.0 ± 0.1

0.6 ± 0.1

5.0

0.2

…

M3

3.3

3.1

1.3 ± 0.1

0.8 ± 0.1

6.1

0.25

…

(M3.5)

3.8

3.6

1.3 ± 0.1

0.8 ± 0.1

6.6

0.25

0.15

M4

4.35

4.1

1.5 ± 0.1

0.9 ± 0.1

7.55

0.3

0.15

M5

5.35

5.1

1.8 ± 0.1

1.2 ± 0.1

9.15

0.4

0.15

M6

6.4

6.1

2.5 ± 0.15

1.6 ± 0.1

M8

8.55

8.2

3 ± 0.15

2 ± 0.1

11.7

0.5

0.2

14.85

0.65

0.3 0.3

M10

10.6

10.2

3.5 ± 0.2

2.2 ± 0.15

18.0

0.7

M12

12.6

12.2

4 ± 0.2

2.5 ± 0.15

21.0

0.8

0.4

(M14)

14.7

14.2

4.5 ± 0.2

3 ± 0.15

24.1

1.0

0.4

M16

16.9

16.3

5 ± 0.2

3.5 ± 0.2

27.3

1.15

0.4

(M18)

19.0

18.3

5 ± 0.2

3.5 ± 0.2

29.4

1.15

0.4

M20

21.1

20.3

6 ± 0.2

4 ± 0.2

33.5

1.3

0.4

(M22)

23.3

22.4

6 ± 0.2

4 ± 0.2

35.7

1.3

0.4 0.5

M24

25.3

24.4

7 ± 0.25

5 ± 0.2

39.8

1.65

(M27)

28.5

27.5

7 ± 0.25

5 ± 0.2

43.0

1.65

0.5

M30

31.5

30.5

8 ± 0.25

6 ± 0.25

48.0

2.0

0.8

(M33)

34.6

33.5

10 ± 0.25

6 ± 0.25

55.1

2.0

0.8

M36

37.6

36.5

10 ± 0.25

6 ± 0.25

58.1

2.0

0.8

(M39)

40.8

39.6

10 ± 0.25

6 ± 0.25

61.3

2.0

0.8

M42

43.8

42.6

12 ± 0.25

7 ± 0.25

68.3

2.3

0.8

(M45)

46.8

45.6

12 ± 0.25

7 ± 0.25

71.3

2.3

0.8

M48

50.0

48.8

12 ± 0.25

7 ± 0.25

74.5

2.3

0.8

(M52)

54.1

52.8

14 ± 0.25

8 ± 0.25

82.6

2.65

1.0

M56

58.1

56.8

14 ± 0.25

8 ± 0.25

86.6

2.65

1.0

(M60)

62.3

60.9

14 ± 0.25

8 ± 0.25

90.8

2.65

1.0

M64

66.3

64.9

14 ± 0.25

8 ± 0.25

93.8

2.65

1.0

(M68)

70.5

69.0

14 ± 0.25

8 ± 0.25

99.0

2.65

1.0

All dimensions are given in millimeters. Sizes shown in parentheses are non-preferred, and are not usually stock sizes.



1545

British Standard Double Coil Rectangular Section Spring Washers; Metric Series — Type D BS 4464:1969 (2004)

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)

2.4 2.6 2.9 3.6 4.1

2.1 2.3 2.6 3.3 3.8

0.9 ± 0.1 1.0 ± 0.1 1.2 ± 0.1 1.2 ± 0.1 1.6 ± 0.1

0.5 ± 0.05 0.6 ± 0.05 0.7 ± 0.1 0.8 ± 0.1 0.8 ± 0.1

4.4 4.8 5.5 6.2 7.5

0.15 0.2 0.23 0.25 0.25

M4 M5 M6 M8 M10 M12 (M14) M16 (M18) M20 (M22) M24 (M27) M30 (M33) M36 (M39) M42 M48 M56 M64

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 40.0 43.0 46.0 52.0 60.0 70.0

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 38.0 41.0 44.0 50.0 58.0 67.0

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 10 ± 0.25 10 ± 0.25 10 ± 0.25 10 ± 0.25 12 ± 0.25 12 ± 0.25

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

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

0.25 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

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.



1546

British Standard Single Coil Square Section Spring Washers; Metric Series — Type A-1 BS 4464:1969 (2004)

British Standard Single Coil Square Section Spring Washers; Metric Series — Type A-2 BS 4464:1969 (2004) 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.



1547

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

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

All dimensions are in millimeters. Nominal bolt or screw sizes shown in parentheses are nonpreferred.



1548

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.


Machinery's Handbook 28th Edition MACHINE SCREWS

1549

MACHINE SCREWS AND NUTS American National Standard Machine Screws and Machine Screw Nuts This 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 1564. 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 1719) or UNRC and UNRF Series, at option of manufacturer. Thread dimensions for sizes 0000, 000, and 00 are given in Table 7 on page 1554. 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

H

F

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.



1550

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. Cross-recessed 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.



1551

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

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

Max., Lb

SLOTTED FLAT COUNTERSUNK HEAD TYPE Head Dia., A Head Slot Height, H Width, J Min., Max., Edge Sharp Edgec 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.

Nominal Sizea or Basic Screw Dia. 4 6 8 10 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8

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.

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




1552

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

0.099 0.123 0.147

0.025 0.031 0.036

0.018 0.023 0.028

0.023 0.026 0.031

0.016 0.019 0.023

0.011 0.014 0.016

0.007 0.009 0.011

0.199 0.225 0.252

0.171 0.195 0.220

0.042 0.047 0.053

0.033 0.038 0.043

0.035 0.039 0.043

0.027 0.031 0.035

0.019 0.022 0.024

0.012 0.014 0.016

0.279 0.332 0.385

0.244 0.292 0.340

0.059 0.070 0.081

0.048 0.058 0.068

0.048 0.054 0.060

0.039 0.045 0.050

0.027 0.032 0.037

0.017 0.021 0.024

0.438 0.507 0.635

0.389 0.452 0.568

0.092 0.107 0.134

0.078 0.092 0.116

0.067 0.075 0.084

0.056 0.064 0.072

0.043 0.050 0.062

0.028 0.032 0.041

0.762 0.812 0.875

0.685 0.723 0.775

0.161 0.156 0.156

0.140 0.133 0.130

0.094 0.094 0.106

0.081 0.081 0.091

0.075 0.072 0.072

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.




1553

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

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

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 Dia., A Min.

Max.

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

Slota Depth, T

a Unless otherwise specified, hexagon head machine screws are not slotted.




1554

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.

Head Height, H 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

Slot Width, J Max. Min.


.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 Series Designat.

Class

Externalb

Nominal Sizea and Threads Per Inch 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

2

00-96 or 0.0470-96

NS

2

Internalc

Pitch Diameter

Pitch Diameter

Major Dia.

Minor Dia.

Class

Major Diameter

Min.

Max.

Tol.

Min.

.0011

.0128

2

.0169

.0181

.0012

.0210

.0340 .0325 .0286 0.272

.0014

.0232

2

.0286

.0300

.0014

.034

.0470 .0450 .0398 .0382

.0016

.0326

2

.0398

.0414

.0016

.047

.0470 .0450 .0402 .0386

.0016

.0334

2

.0402

.0418

.0016

.047

Max.

Min.

Max.

Min.

Tol.

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.



1555

Table 8. American National Standard Slotted Fillister and Slotted Drilled Fillister Head Machine Screws ANSI B18.6.3-1972 (R1991)

SLOTTED FILLISTER HEAD TYPE Nominal Size1 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

Total Head Height, O

Head Side Height, H

Head Dia., A

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.



1556

Table 9. American National Standard Slotted Oval Countersunk Head Machine Screws ANSI B18.6.3-1972 (R1991)

Nominal Sizea or Basic Screw Dia. 00 0.0470 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⁄ 0.2500 4 5⁄ 0.3125 16 3⁄ 0.3750 8 7⁄ 0.4375 16 1⁄ 0.5000 2 9⁄ 0.5625 16 5⁄ 0.6250 8 3⁄ 0.7500 4

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., Max., Edge Edge Rnded. Sharp or Flat .093 .085 .119 .099 .146 .123 .172 .147 .199 .171 .225 .195 .252 .220 .279 .244 .332 .292 .385 .340 .438 .389 .507 .452 .635 .568 .762 .685 .812 .723 .875 .775 1.000 .889 1.125 1.002 1.375 1.230

Head Side Height, H,


Ref. .028 .035 .043 .051 .059 .067 .075 .083 .100 .116 .132 .153 .191 .230 .223 .223 .260 .298 .372

Max. .042 .056 .068 .080 .092 .104 .116 .128 .152 .176 .200 .232 .290 .347 .345 .354 .410 .467 .578

Min. .034 .041 .052 .063 .073 .084 .095 .105 .126 .148 .169 .197 .249 .300 .295 .299 .350 .399 .497

Slot Depth, T

Slot Width, J Max. .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075 .084 .094 .094 .106 .118 .133 .149

Min. .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064 .072 .081 .081 .091 .102 .116 .131

Max. .023 .030 .038 .045 .052 .059 .067 .074 .088 .103 .117 .136 .171 .206 .210 .216 .250 .285 .353

Min. .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.



1557

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.

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

.009 .015 .023 .026 .035 .043 .052 .061 .069 .078 .095 .112 .130 .152 .194 .235

.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


Undercutb Dia., U Max. Min.

Undercutb Depth, X Max. Min.

.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

.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 a or Flat Ref. Max. Min. Max. Min. Sharp L 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.




1558

Table 12. Slotted Round Head Machine Screws ANSI B18.6.3-1972 (R1991) Appendix

Nominal Sizea or Basic Screw Dia.

Head Diameter, A

Head Height, H

Slot Width, J

Slot Depth, T

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

1⁄ 4

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

.041 .062 .089 .113 .138 .162 .187 .211 .236 .260 .309 .359 .408 .472

.035 .056 .080 .099 .122 .146 .169 .193 .217 .240 .287 .334 .382 .443

.022 .031 .045 .053 .061 .069 .078 .086 .095 .103 .120 .137 .153 .175

.016 .025 .036 .043 .051 .059 .067 .075 .083 .091 .107 .123 .139 .160

.008 .012 .017 .023 .026 .031 .035 .039 .043 .048 .054 .060 .067 .075

.004 .008 .010 .016 .019 .023 .027 .031 .035 .039 .045 .050 .056 .064

.017 .018 .026 .039 .044 .048 .053 .058 .063 .068 .077 .087 .096 .109

.013 .012 .018 .029 .033 .037 .040 .044 .047 .051 .058 .065 .073 .082

5⁄ 16

0.3125

.590

.557

.216

.198

.084

.072

.132

.099

3⁄ 8

0.3750

.708

.670

.256

.237

.094

.081

.155

.117

7⁄ 16

0.4375

.750

.707

.328

.307

.094

.081

.196

.148

1⁄ 2

0.5000

.813

.766

.355

.332

.106

.091

.211

.159

9⁄ 16

0.5625

.938

.887

.410

.385

.118

.102

.242

.183

5⁄ 8

0.6250

1.000

.944

.438

.411

.133

.116

.258

.195

3⁄ 4

0.7500

1.250

1.185

.547

.516

.149

.131

.320

.242

0000 000 00 0 1 2 3 4 5 6 8 10 12

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.

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. 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


Machinery's Handbook 28th Edition MINIATURE SCREWS

1559

Slotted Head Miniature Screws The ASA B18.11 standard establishes head types, their dimensions, and lengths of slotted head miniature screws, threaded in conformance with American Standard Unified Miniature Screw Threads, ASA B1.10. The standard covers threads of a nominal diameter from 0.0118 inch (0.3 mm) to 0.0551 inch (1.4 mm). Preferred diameter pitch combinations for general use are shown in bold type in the tables. Head Types.—Fillister Head: The fillister head has a flat top surface (oval crown optional) with cylindrical sides and a flat bearing surface. The head proportions are given in Table 13. Pan Head: The pan head has a flat top surface, cylindrical sides, and a flat bearing surface. The head height is less than the fillister but the head diameter is slightly larger. Head proportions are given in Table 14. Flat Head: The flat head has a flat top surface and a conical bearing surface with an included angle of approximately 100°. Head proportions are given in Table 15. Binding Head: The head height is less than the pan head but the head diameter is greater, and is intended for applications which would otherwise require washers. Head proportions are given in Table 16. Table 13. Miniature Screws – Fillister Head ASA B18.11-1961, R2005 H

L

T R

C

A

LT

J

D

UNM THREAD ASA B1.10 45Ο +- 50 OVAL CROWN OPTIONAL MIN. RADIUS 0.85 OF NOMINAL HEAD DIA.

o o

D Fillister Head Dimensions Basic H T Major A J Size Thds Head Hgt Dia. Head Dia. Slot Width Slot Depth a Desigper Max Max Min Max Min Max Min Max Min nation Inch 30 UNM 318 0.0118 0.021 0.019 0.012 0.010 0.004 0.003 0.006 0.004 35 UNM 282 0.0138 0.023 0.021 0.014 0.012 0.004 0.003 0.007 0.005 40 UNM 254 0.0157 0.025 0.023 0.016 0.013 0.005 0.003 0.008 0.006 45 UNM 254 0.0177 0.029 0.027 0.018 0.015 0.005 0.003 0.009 0.007 50 UNM 203 0.0197 0.033 0.031 0.020 0.017 0.006 0.004 0.010 0.007 55 UNM 203 0.0217 0.037 0.035 0.022 0.019 0.006 0.004 0.011 0.008 60 UNM 169 0.0236 0.041 0.039 0.025 0.021 0.008 0.005 0.012 0.009 70 UNM 145 0.0276 0.045 0.043 0.028 0.024 0.008 0.005 0.014 0.011 80 UNM 127 0.0315 0.051 0.049 0.032 0.028 0.010 0.007 0.016 0.012 90 UNM 113 0.0354 0.056 0.054 0.036 0.032 0.010 0.007 0.018 0.014 100 UNM 102 0.0394 0.062 0.058 0.040 0.035 0.012 0.008 0.020 0.016 110 UNM 102 0.0433 0.072 0.068 0.045 0.040 0.012 0.008 0.022 0.018 120 UNM 102 0.0472 0.082 0.078 0.050 0.045 0.016 0.012 0.025 0.020 140 UNM 85 0.0551 0.092 0.088 0.055 0.050 0.016 0.012 0.028 0.023 Bold face type indicates preferred sizes. See Notes for Tables 1 through 4 on page 1560. a

TO MINOR DIA MIN.

C Chamfer Max 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.008 0.008

R Radius b Min 0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006

T measured from bearing surface.

b Relative to maximum major diameter.



1560

Notes for Tables 1 through 4 Material: Corrosion resistant steels: ASTM Designation A276 CLASS 303, COND A CLASS 416, COND A, heat treat to approx 120,000-150,000 PSI (ROCKWELL C28-34) CLASS 420, COND A, heat treat to approx 220,000-240,000 PSI (ROCKWELL C50-53) Brass: Temper half hard ASTM Designation B16 Nickel Silver: Temper hard ASTM Designation B151, Alloy C Machine Finish: Machined surface roughness of heads shall be approximately 63µin. arithmetical average determined by visual comparison. Applied coatings: Corrosion resistant steel: Passivate; Brass: Bare, black oxide, or nickel flash. Nickel silver: None Notes: 1) The diameter of the unthreaded body shall not be more than the maximum major diameter nor less than the minimum pitch diameter of the thread. 2) For screw lengths four times the major diameter or less, thread length (LT) shall extend to within two threads of the head bearing surface. Screws of greater length shall have complete threads for a minimum of four major diameters. 3) Screws shall be free of all projecting burrs, observed at 3× magnification. 4) All dimensions are in inches.

Table 14. Miniature Screws – Pan Head ASA B18.11-1961, R2005 H

L

T LT

R

C

A

J

D

UNM THREAD ASA B1.10

TO MINOR o o

45Ο +- 50

DIA MIN.

o o

45Ο +- 50

Size Designation

Thds per Inch

D Basic Major Dia.,M ax

Pan Head Dimensions A Head Dia. Min

Max

Min

J Slot Width Max

Min

T Slot Depth a Max

C Chamfer

R Radius b

Min

Max

Min

30 UNM 318 0.0118 0.025 0.023 0.010 0.008 0.005 0.003 0.005 0.003 35 UNM 282 0.0138 0.029 0.027 0.011 0.009 0.005 0.003 0.006 0.004 40 UNM 254 0.0157 0.033 0.031 0.012 0.010 0.006 0.004 0.006 0.004 45 UNM 254 0.0177 0.037 0.035 0.014 0.012 0.006 0.004 0.007 0.005 50 UNM 203 0.0197 0.041 0.039 0.016 0.013 0.008 0.005 0.008 0.006 55 UNM 203 0.0217 0.045 0.043 0.018 0.015 0.008 0.005 0.009 0.007 60 UNM 169 0.0236 0.051 0.049 0.020 0.017 0.010 0.007 0.010 0.007 70 UNM 145 0.0276 0.056 0.054 0.022 0.019 0.010 0.007 0.011 0.008 80 UNM 127 0.0315 0.062 0.058 0.025 0.021 0.012 0.008 0.012 0.009 90 UNM 113 0.0354 0.072 0.068 0.028 0.024 0.012 0.008 0.014 0.011 100 UNM 102 0.0394 0.082 0.078 0.032 0.028 0.016 0.012 0.018 0.014 110 UNM 102 0.0433 0.092 0.088 0.036 0.032 0.016 0.012 0.018 0.014 120 UNM 102 0.0472 0.103 0.097 0.040 0.035 0.020 0.015 0.020 0.016 140 UNM 85 0.0551 0.113 0.107 0.045 0.040 0.020 0.015 0.022 0.018 Bold face type indicates preferred sizes. See Notes for Tables 1 through 4 on page 1560.

0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.008 0.008

0.002 0.002 0.002 0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006

a

Max

H Head Hgt





1561

Table 15. Miniature Screws – 100° Flat Head ASA B18.11-1961, R2005 H

L LT

R

T 1000 + 20

A

AV

J

D


Size Designation

Thds per Inch

D Basic Major Dia.

DIA MIN.

Head Dimensions A Head Dia. Max

Min

Av at Full Cone a at max H

H Head Hgt Max

Min

J Slot Width Max

T Slot Depth

R Radius b

Min

Max

Min

Max

30 UNM 318 0.0118 0.023 0.021 0.0285 0.007 0.005 0.004 0.003 35 UNM 282 0.0138 0.025 0.023 0.0305 0.007 0.005 0.004 0.003 40 UNM 254 0.0157 0.029 0.027 0.0348 0.008 0.006 0.005 0.003 45 UNM 254 0.0177 0.033 0.031 0.0392 0.009 0.007 0.005 0.003 50 UNM 203 0.0197 0.037 0.035 0.0459 0.011 0.008 0.006 0.004 55 UNM 203 0.0217 0.041 0.039 0.0503 0.012 0.009 0.006 0.004 60 UNM 169 0.0236 0.045 0.043 0.0546 0.013 0.010 0.008 0.005 70 UNM 145 0.0276 0.051 0.049 0.0610 0.014 0.011 0.008 0.005 80 UNM 127 0.0315 0.056 0.054 0.0696 0.016 0.012 0.010 0.007 90 UNM 113 0.0354 0.062 0.058 0.0759 0.017 0.013 0.010 0.007 100 UNM 102 0.0394 0.072 0.068 0.0847 0.019 0.015 0.012 0.008 110 UNM 102 0.0433 0.082 0.078 0.0957 0.022 0.018 0.012 0.008 120 UNM 102 0.0472 0.092 0.088 0.1068 0.025 0.020 0.016 0.012 140 UNM 85 0.0551 0.103 0.097 0.1197 0.027 0.022 0.016 0.012 Bold face type indicates preferred sizes. See Notes for Tables 1 through 4 on page 1560.

0.004 0.004 0.005 0.005 0.006 0.006 0.008 0.008 0.010 0.010 0.012 0.012 0.016 0.016

0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.008 0.008 0.010 0.010

0.005 0.005 0.006 0.006 0.008 0.008 0.010 0.010 0.012 0.012 0.016 0.016 0.020 0.020

a

Max

TO MINOR o o

45Ο +- 50

Av derived from maximum D, maximum H, and mean angle.


Specifications.—Head Height: The head heights given in the dimensional tables represent the metal measurement (after slotting). Depth of Slots: The depth of slots on fillister, pan and binding head screws is measured from the bearing surface to the intersection of the bottom of the slot with the head diameter. On heads with a conical bearing surface, the depth of slots is measured parallel to the axis of the screw from the flat top surface to the intersection of the bottom of the slot with the bearing surface. The maximum permissible concavity of the slot shall not exceed 3 per cent of the mean head diameter. Bearing Surface: The bearing surface of fillister, pan and binding head screws shall be at right angles to the axis of the body within 2°. Eccentricity: Eccentricity is defined as one half of the total indicator reading. Head Eccentricity: The heads of miniature fastening screws shall not be eccentric with the screw bodies by more than 2 per cent of the maximum head diameter or 0.001 inch, whichever is the greater. Eccentricity of Slots: Slots in miniature fastening screw heads shall not be eccentric with screw bodies by more than 5 per cent of the nominal body diameter.



1562

Table 16. Miniature Screws – Binding Head ASA B18.11-1961, R2005 H

L

T LT

R

C

A

J

D


TO MINOR o o

45Ο +- 50

DIA MIN.

o o

45Ο +- 50

Size Designation

Thds per Inch

40 UNM

254

D Basic Major Dia Max

Binding Head Dimensions A Head Dia. Max

Min

H Head Hgt Max

Min

J Slot Width Max

Min

0.0157 0.041 0.039 0.010 0.008 0.006

0.004

T Slot Depth a Max

R Radius

Min

Max

Max

0.005 0.003

0.002

0.004 0.002

0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006 0.008 0.008

0.004 0.004 0.004 0.006 0.006 0.008 0.008 0.010 0.010 0.012 0.012

45 UNM 254 0.0177 0.045 0.043 0.011 0.009 0.006 0.004 0.006 50 UNM 203 0.0197 0.051 0.049 0.012 0.010 0.008 0.005 0.006 55 UNM 203 0.0217 0.056 0.054 0.014 0.012 0.008 0.005 0.007 60 UNM 169 0.0236 0.062 0.058 0.016 0.013 0.010 0.007 0.008 70 UNM 145 0.0276 0.072 0.068 0.018 0.015 0.010 0.007 0.009 80 UNM 127 0.0315 0.082 0.078 0.020 0.017 0.012 0.008 0.010 90 UNM 113 0.0354 0.092 0.088 0.022 0.019 0.012 0.008 0.011 100 UNM 102 0.0394 0.103 0.097 0.025 0.021 0.016 10.012 0.012 110 UNM 102 0.0433 0.113 0.107 0.028 0.024 0.016 0.012 0.014 120 UNM 102 0.0472 0.124 0.116 0.032 0.028 0.020 0.015 0.016 140 UNM 85 0.0551 0.144 0.136 0.036 0.032 0.020 0.015 0.018 Bold face type indicates preferred sizes. See Notes for Tables 1 through 4 below. a

C Chamfer

0.004 0.004 0.005 0.006 0.007 0.007 0.008 0.009 0.011 0.012 0.014

Min

0.002 0.002 0.002 0.003 0.003 0.004 0.004 0.005 0.005 0.006 0.006


Underhead Fillets: The radius of the fillet under perpendicular bearing surface type heads shall not exceed 1⁄2 times the pitch of the thread. The radius of the fillet under conical bearing surface type heads shall not exceed 2 times the pitch of the thread. The radius of the fillet under the binding head is given in Table 16. Unthreaded Diameter: On miniature fastening screws not threaded to the head, the diameter of the unthreaded body shall not be more than the maximum major diameter of the thread nor less than the minimum pitch diameter of the thread. Length: The length of miniature screws having perpendicular bearing surface type heads shall be measured from the bearing surface to the extreme end in a line parallel to the axis of the screw. The length of screws with conical bearing surface type heads shall be measured from the top of the head to the extreme end in a line parallel to the axis of the screw. Preferred lengths are those listed in Table 17. Tolerance on Length: The length tolerance of miniature screws shall conform to the limits given in Table 17. Length of Thread: On all miniature screws having a length four times the nominal body diameter or less the threaded length shall extend to within two threads of the bearing surface of the head. Screws of greater length shall possess complete threads for a minimum of four diameters.


Machinery's Handbook 28th Edition Table 17. Miniature Screw Standard Lengths – Fillister Head, Pan Head, Binding Head, and 100° Flat Head ASA B18.11 30 UNM a

35 UNM a

Max. (0.0118)

(0.0138)

(0.0157) (0.0177 (0.0197) (0.0217) (0.0236) (0.0276) (0.0315) (0.0354) (0.0394) (0.0433) (0.0472) (0.0551)

Length (In.) Min.

40 UNM

45 UNM

50 UNM

55 UNM

60 UNM

70 UNM

80 UNM

90 UNM

100 UNM

110 UNM

120 UNM

140 UNM

0.016 0.020 30-020 b 30-025

35-025

40-025

0.021 0.025

30-025

35-025

40-025

0.027 0.032

30-032

35-032

40-032

45-032

50-032

0.035 0.040

30-040

35-040

40-040

45-040

50-040

55-040

60-040

0.044 0.050

30-050

35-050

40-050

45-050

50-050

50-050

60-050

70-050

80-050

0.054 0.060

30-060

35-060

40-060

45-060

50-060

55-060

60-060

70-060

80-060

90-060

100-060

0.072 0.080

30-080

35-080

40-080

45-080

50-080

55-080

60-080

70-080

80-080

90-080

100-080

110-080

120-080

0.092 0.100

30-100

35-100

40-100

45-100

50-100

55-100

60-100

70-100

80-100

90-100

100-100

110-100

120-100

0.110 0.120

30-120

35-120

40-120

45-120

50-120

55-120

60-120

70-120

80-120

90-120

100-120

110-120

120-120

140-120

0.150 0.160

30-160

35-160

40-160

45-160

50-160

55-160

60-160

70-160

80-160

90-160

100-160 110-160

120-160

140-160

35-200

40-200

45-200

50-200

55-200

60-200

70-200

80-200

90-200

100-200

110-200

120-200

140-200

45-250

50-250

55-250

60-250

70-250

80-250

90-250

100-250

110-250

120-250

140-250

55-320

60-320

70-320

80-320

90-320

100-320

110-320

120-320

140-320

70-400

80-400

90-400

100-400

110-400

120-400

140-400

90-500

100-500

110-500

120-500

140-500

110-600

120-600

140-600

0.188 0.200 0.238 0.250 0.304 0.320 0.384 0.400 0.480 0.500 0.580 0.600

140-100

MINIATURE SCREWS

0.020 0.025

a Sizes 30 UMN and 35 UMN are not specified for Binding Head.


1563

b Does not apply to 100° Flat Head. Bold face type indicates preferred sizes. Sizes surrounded by heavy line apply to 100° Flat Head only.

1564

Machinery's Handbook 28th Edition METRIC MACHINE SCREWS

End of Body: Miniature fastening screws shall be regularly supplied with flat ends having a chamfer of approximately 45° extending to the minor diameter of the thread as a minimum depth. Thread Series and Tolerances: The screw threads of miniature screws shall be in conformance with American Standard Unified Miniature Screw Threads, ASA B1.10-1958. Material and Finish: Miniature screws are generally supplied in ferrous and nonferrous materials, coatings and heat treatments which must be specified by the user. Coatings, when required, are limited to those of electro-plating or chemical oxidation. Designation: Screws in conformance with this standard shall be identified by the designation for thread size in conformance with American Standard ASA B1.10 followed by the nominal length in units of 1⁄1000 inch (omitting the decimal point) and the head type. Typical examples are: 60 UNM × 040 FIL HD 100 UNM × 080 PAN HD 120 UNM × 120 FLAT HD 140 UNM × 250 BIND HD Machined Finish: Roughness of the machined surfaces of heads shall not exceed 63 micro-inches arithmetical average (per ASA B46.1, Surface Texture) determined by visual comparison with roughness comparison specimens. 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 5. 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. Also see Table 6. Diameter of Body: The body diameters of metric machine screws are within the limits specified in the dimensional tables (Tables 3 through 4 and 5). 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.


Machinery's Handbook 28th Edition METRIC MACHINE SCREWS

1565

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

Nominal Screw Lengtha

Nominal Screw Length Equal to or Shorter thana

Maxd

Maxe

M2 × 0.4

6

1.0

0.4

6

M2.5 × 0.45

8

1.1

0.5

M3 × 0.5

9

1.2

0.5

M3.5 × 0.6

10

1.5

M4 × 0.7

12

M5 × 0.8

15

M6 × 1 M8 × 1.25

Nominal Screw Size and Thread Pitch

Unthreaded Lengthb

LUS

L

To and IncludOver ing

Heat-Treated Recessed Flat Countersunk Head Screws LU L

Unthreaded Lengthb

L

B

Full Form Nomi- Thread nal Lengthc Screw Length Longer Min thana

Maxd

Maxe

30

1.0

0.8

30

25.0

8

30

1.1

0.9

30

25.0

9

30

1.2

1.0

30

25.0

0.6

10

50

1.5

1.2

50

38.0

1.8

0.7

12

50

1.8

1.4

50

38.0

2.0

0.8

15

50

2.0

1.6

50

38.0

18

2.5

1.0

18

50

2.5

2.0

50

38.0

24

3.1

1.2

24

50

3.1

2.5

50

38.0

M10 × 1.5

30

3.8

1.5

30

50

3.8

3.0

50

38.0

M12 × 1.75

36

4.4

1.8

36

50

4.4

3.5

50

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.




Style B DSHa

DS

Body and Shoulder Diameter

Body 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

M3 × 0.5

3.00

2.58

3.00

2.86

2.58

0.60

0.40

6.3

5.9

5.2

M3.5 × 0.6

3.50

3.00

3.50

3.32

3.00

0.70

0.50

8.2

7.7

M4 × 0.7

4.00

3.43

4.00

3.82

3.43

0.80

0.60

9.4

8.9

M5 × 0.8

5.00

4.36

5.00

4.82

4.36

0.90

0.70

10.4

M6 × 1

6.00

5.21

6.00

5.82

5.21

1.10

0.90

12.6

R

N

Underhead Fillet Radius

T

Slot Width

Slot Depth

Max

Min

Max

Min

Max

Min

0.8

0.4

0.7

0.5

0.6

0.4

1.0

0.5

0.8

0.6

0.7

0.5

1.7

1.2

0.6

1.0

0.8

0.9

0.6

6.9

2.3

1.4

0.7

1.2

1.0

1.2

0.9

8.0

2.7

1.6

0.8

1.5

1.2

1.3

1.0

9.8

8.9

2.7

2.0

1.0

1.5

1.2

1.4

1.1

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 6.


METRIC MACHINE SCREWS

Slotted and Style A

1566

Table 2. American National Standard Slotted, Cross and Square Recessed Flat Countersunk Head Metric Machine Screws ANSI/ASME B18.6.7M-1985

Machinery's Handbook 28th Edition 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

Min

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

5.1

4.4

1.5

0.6

6.6

1.0

0.5

0.8

0.6

1.2

1.0

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

Max

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


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.


1567



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

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

a This size not specified for Type III square recessed pan heads; Type II cross recess is not specified for any size.



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


Cross and Square Recess

Slotted Nominal Screw Size and Thread Pitch

1568

Table 4. American National Standard Slotted and Cross and Square Recessed Pan Head Metric Machine Screws ANSI/ASME B18.6.7M-1985


Table 5. 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

Ea

Sa 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


DS Nominal Screw Size and Thread Pitch

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


1569

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.


Next Page

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

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 6.



Body Diameter, DS


1570

Table 5. (Continued) American National Standard Hex and Hex Flange Head Metric Machine Screws ANSI/ASME B18.6.7M-1985

Machinery's Handbook 28th Edition TABLE OF CONTENTS THREADS AND THREADING SCREW THREAD SYSTEMS 1712 Screw Thread Forms 1712 V-Thread, Sharp V-thread 1712 US Standard Screw Thread 1712 Unified Screw Thread Forms 1713 International Metric Thread 1714 ISO Metric Thread System 1714 Definitions of Screw Threads

UNIFIED SCREW THREADS 1719 American Standard for Unified Screw Threads 1719 Revised Standard 1719 Advantages of Unified Threads 1719 Thread Form 1720 Internal and External Screw Thread Design Profile 1720 Thread Series 1721 Inch Screw Thread 1722 Diameter-Pitch Combination 1723 Standard Series Combinations 1750 Coarse-Thread Series 1751 Fine-Thread Series 1751 Extra-Fine-Thread Series 1752 Constant Pitch Series 1753 4-Thread Series 1754 6-Thread Series 1755 8-Thread Series 1756 12-Thread Series 1757 16-Thread Series 1758 20-Thread Series 1759 28-Thread Series 1760 Thread Classes 1760 Coated 60-deg. Threads 1762 Screw Thread Selection 1762 Pitch Diameter Tolerance 1762 Screw Thread Designation 1763 Designating Coated Threads 1763 Designating UNS Threads 1763 Hole Sizes for Tapping 1763 Minor Diameter Tolerance 1764 Unified Miniature Screw Thread 1764 Basic Thread Form 1765 Design Thread Form 1766 Design Form Dimensions 1766 Formulas for Basic Dimensions 1767 Limits of Size and Tolerances 1768 Minimum Root Flats 1769 UNJ Profile

CALCULATING THREAD DIMENSIONS 1770 Introduction 1770 Metric Application 1770 Purpose 1771 Calculating And Rounding 1771 Rounding of Decimal Values 1771 Calculations from Formulas 1772 Examples 1772 Inch Screw Threads 1772 Metric Screw Threads 1772 Thread Form Constants

METRIC SCREW THREADS 1783 1783 1783 1783 1784 1784 1785 1785 1785 1786 1787 1791 1793 1793 1797 1797 1798 1800 1805 1805 1808 1808 1815 1815 1815 1816 1816 1817 1817 1817 1818 1818 1818

M Profile Metric Screw Threads Comparison with Inch Threads Interchangeability Definitions Basic M Profile M Crest and Root Form General Symbols M Profile Screw Thread Series Mechanical Fastener Coarse Pitch M Profile Data Limits and Fits Limits for Coated Threads Dimensional Effect of Coating Formulas for M Profile Tolerance Grade Comparisons M Profile Limiting Dimension Internal Metric Thread External Metric Thread MJ Profile Metric Screw Threads Diameter-Pitch Combinations Trapezoidal Metric Thread Comparison of ISO and DIN ISO Miniature Screw Threads British Standard Metric Threads Basic Profile Dimensions Tolerance System Fundamental Deviations Tolerance Grades Tolerance Positions Tolerance Classes Lengths of Thread Engagements Design Profiles M Designation


Machinery's Handbook 28th Edition TABLE OF CONTENTS THREADS AND THREADING METRIC SCREW THREADS

BUTTRESS THREADS

(Continued)

(Continued)

1819 Fundamental Deviation Formulas 1820 Crest Diameter Tolerance 1820 Limits and Tolerances, Table 1823 Diameter/Pitch Combinations 1823 Limits and Tolerances 1824 Diameter/Pitch Table 1825 Comparison of Thread Systems

1852 1853 1856 1856 1857 1857

ACME SCREW THREADS 1826 1826 1828 1828 1828 1828 1828 1828 1828 1828 1833 1833 1835 1835 1835 1836 1837 1837 1837 1838 1844 1844 1844 1844 1844 1844 1847 1847 1849

General Purpose Acme Threads Acme Thread Form Acme Thread Abbreviations Designation Basic Dimensions Formulas for Diameters Limiting Dimensions Single-Start Screw Thread Data Pitch Diameter Allowances Multiple Start Acme Threads Pitch Diameter Tolerances Centralizing Acme Threads Basic Dimensions Formulas for Diameters Limiting Dimensions Screw Thread Data Pitch Diameter Allowances Pitch Diameter Tolerances Tolerances and Allowances Designation Acme Centralizing Thread Stub Acme Threads Basic Dimensions Formulas for Diameters Limiting Dimensions Stub Acme Thread Designations Alternative Stub Acme Threads Former 60-Degree Stub Thread Square Thread

BUTTRESS THREADS 1850 Threads of Buttress Form 1850 British Standard Buttress Threads 1850 Lowenherz or Löwenherz Thread 1851 Buttress Inch Screw Threads 1851 Pitch Combinations 1851 Basic Dimensions 1851 Symbols and Form 1852 Buttress Thread Tolerances

Class 2 Tolerances Buttress Thread Form Allowances for Easy Assembly External Thread Allowances Buttress Thread Designations Designation Sequence

WHITWORTH THREADS 1858 British Standard Whitworth (BSW) and Fine (BSF) Threads 1858 Standard Thread Form 1858 Whitworth Standard Thread Form 1858 Tolerance Formulas 1859 Basic Dimensions

PIPE AND HOSE THREADS 1861 1861 1861 1862 1863 1863 1864 1865 1865 1865 1865 1867 1867 1867 1867 1869 1869 1870 1870 1870 1871 1871 1872 1873 1875 1875 1876 1877

American National Pipe Threads Thread Designation and Notation Taper Pipe Thread Basic Dimensions Length of Engagement Tolerances on Thread Elements Limits on Crest and Root Pipe Couplings Railing Joint Straight Pipe Threads Mechanical Joints Dryseal Pipe Thread Limits on Crest and Root Types of Dryseal Pipe Thread Limitation of Assembly Tap Drill Sizes Special Dryseal Threads Limitations for Combinations British Standard Pipe Threads Non-pressure-tight Joints Basic Sizes Pressure-tight Joints Limits of Size Hose Coupling Screw Threads Screw Thread Length Fire Hose Connection Basic Dimensions Limits of Size

OTHER THREADS 1878 Interference-Fit Threads 1879 Design and Application Data


Machinery's Handbook 28th Edition TABLE OF CONTENTS THREADS AND THREADING OTHER THREADS

MEASURING SCREW THREADS

(Continued)

(Continued)

1880 1880 1881 1882 1882 1883 1884 1884 1884 1885 1886 1886 1887 1887 1890 1891 1891 1891 1891 1892 1892 1892 1892 1892 1892 1893 1893 1893 1893 1893

1903 1904 1905

External Thread Dimension Internal Thread Dimension Engagement Lengths Allowances for Coarse Thread Tolerances for Coarse Thread Variations in Lead and Diameter Spark Plug Threads BS Spark Plugs SAE Spark Plugs Lamp Base and Socket Threads Instrument & Microscope Threads British Association Thread Instrument Makers’ Screw Thread Microscope Objective Thread Swiss Screw Thread Historical and Miscellaneous Aero-Thread Briggs Pipe Thread Casing Thread Cordeaux Thread Dardelet Thread “Drunken” Thread Echols Thread French Thread (S.F.) Harvey Grip Thread Lloyd & Lloyd Thread Lock-Nut Pipe Thread Philadelphia Carriage Bolt Thread SAE Standard Screw Thread Sellers Screw Thread

MEASURING SCREW THREADS 1894 Measuring Screw Threads 1894 Pitch and Lead of Screw Threads 1894 Thread Micrometers 1895 Ball-point Micrometers 1895 Three-wire Method 1896 Classes of Formulas 1896 Screw Thread Profiles 1896 Accuracy of Formulas 1897 Best Wire Sizes 1898 Measuring Wire Accuracy 1898 Measuring or Contact Pressure 1898 Three-Wire Formulas 1899 NIST General Formula 1900 Formulas for Pitch Diameters 1900 Effect of Small Thread Angle 1902 Dimensions Over Wires 1902 Formula Including Lead Angle

1906 1906 1907 1907 1908 1910 1911 1912 1912 1912 1915 1915 1917 1919

Measuring Whitworth Threads Buckingham Exact Formula Accuracy of Formulas Acme and Stub Acme Thread Checking Pitch Diameter Checking Thread Thickness Wire Sizes Checking Thread Angle Best Wire Diameters Taper Screw Threads Buttress Threads Thread Gages Thread Gage Classification Gages for Unified Inch Threads Thread Forms of Gages Thread Gage Tolerances Tolerances for Cylindrical Gages Formulas for Limits

TAPPING AND THREAD CUTTING 1920 Selection of Taps 1922 Tap Rake Angles 1922 Cutting Speed 1922 Tapping Specific Materials 1925 Diameter of Tap Drill 1926 Hole Size Limits 1934 Tap Drill Sizes 1935 Tap Drills and Clearance Drills 1935 Tolerances of Tapped Holes 1936 Hole Sizes before Tapping 1937 Miniature Screw Threads 1938 Tapping Drill Sizes 1938 ISO Metric Threads 1939 Clearance Holes 1940 Cold Form Tapping 1941 Core Hole Sizes 1942 Tap Drill Sizes 1942 Removing a Broken Tap 1942 Tap Drills for Pipe Taps 1942 Power for Pipe Taps 1943 High-Speed CNC Tapping 1944 Coolant for Tapping 1944 Combined Drilling and Tapping 1945 Relief Angles for Cutting Tools 1947 Lathe Change Gears 1947 Change Gears for Thread Cutting 1947 Compound Gearing


Machinery's Handbook 28th Edition TABLE OF CONTENTS THREADS AND THREADING TAPPING AND THREAD CUTTING (Continued)

1947 1948 1948 1949 1951 1951 1952

Fractional Threads Change Gears for Metric Pitches Change Gears, Fractional Ratios Quick-Change Gearbox Output Finding Accurate Gear Ratios Lathe Change-gears Relieving Helical-Fluted Hobs

THREAD ROLLING 1953 Thread-Rolling Machine 1953 Flat-Die Type 1953 Cylindrical-Die Type 1953 Rate of Production 1954 Precision Thread Rolling 1954 Steels for Thread Rolling 1954 Diameter of Blank 1954 Automatic Screw Machines 1955 Factors Governing the Diameter 1955 Diameter of Threading Roll 1955 Kind of Thread on Roll 1956 Application of Thread Roll 1956 Thread Rolling Speeds and Feeds

THREAD GRINDING 1958 Thread Grinding 1958 Wheels for Thread Grinding 1958 Single-Edge Wheel 1959 Edges for Roughing and Finishing 1959 Multi-ribbed Wheels 1960 Ribbed Wheel for Fine Pitches 1960 Solid Grinding Threads 1960 Number of Wheel Passes 1960 Wheel and Work Rotation 1961 Wheel Speeds 1961 Work Speeds 1961 Truing Grinding Wheels 1961 Wheel Hardness or Grade 1962 Grain Size 1962 Grinding by Centerless Method

THREAD MILLING 1963 Thread Milling 1963 Single-cutter Method 1963 Multiple-cutter Method 1964 Planetary Method 1964 Classes of Work 1965 Pitches of Die-cut Threads

THREAD MILLING (Continued)

1965 Changing Pitch of Screw 1965 Helical Milling 1965 Lead of a Milling Machine 1966 Change Gears for Helical Milling 1966 Short-lead Milling 1966 Helix 1967 Helix Angles 1968 Change Gears for Different Leads 1978 Lead of Helix 1981 Change Gears and Angles Determining Helix Angle 1982 For Given Lead and Diameter 1983 For Given Angle 1983 For Given Lead 1983 For Lead Given DP and Teeth 1983 Determine Lead of Tooth

SIMPLE, COMPOUND, DIFFERENTIAL, AND BLOCK INDEXING 1984 Milling Machine Indexing 1984 Hole Circles 1984 Holes in Brown & Sharpe 1984 Holes in Cincinnati 1984 Simple Indexing 1985 Compound Indexing 1986 Simple and Compound Indexing 1991 Angular Indexing 1991 Tables for Angular Indexing 1992 Angle of One Hole Moves 1993 Accurate Angular Indexing 2008 Indexing for Small Angles 2009 Differential Indexing 2009 Ratio of Gearing 2010 To Find the Indexing Movement 2010 Use of Idler Gears 2010 Compound Gearing 2011 Check Number of Divisions 2012 Simple and Different Indexing 2018 Indexing Movements of Plate 2019 Indexing High Numbers 2022 Indexing Tables 2022 Block or Multiple Indexing 2024 60-Tooth Worm Indexing 2025 Linear Indexing for Rack Cutting 2025 Linear Indexing Movements 2026 Counter Milling


1712

Machinery's Handbook 28th Edition THREADS AND THREADING

SCREW THREAD SYSTEMS Screw Thread Forms Of the various screw thread forms which have been developed, the most used are those having symmetrical sides inclined at equal angles with a vertical center line through the thread apex. Present-day examples of such threads would include the Unified, the Whitworth and the Acme forms. One of the early forms was the Sharp V which is now used only occasionally. Symmetrical threads are relatively easy to manufacture and inspect and hence are widely used on mass-produced general-purpose threaded fasteners of all types. In addition to general-purpose fastener applications, certain threads are used to repeatedly move or translate machine parts against heavy loads. For these so-called translation threads a stronger form is required. The most widely used translation thread forms are the square, the Acme, and the buttress. Of these, the square thread is the most efficient, but it is also the most difficult to cut owing to its parallel sides and it cannot be adjusted to compensate for wear. Although less efficient, the Acme form of thread has none of the disadvantages of the square form and has the advantage of being somewhat stronger. The buttress form is used for translation of loads in one direction only because of its non-symmetrical form and combines the high efficiency and strength of the square thread with the ease of cutting and adjustment of the Acme thread. V-Thread, Sharp V-thread.—The sides of the thread form an angle of 60 degrees with each other. The top and bottom or root of this thread form are theoretically sharp, but in actual practice the thread is made with a slight flat, owing to the difficulty of producing a perfectly sharp edge and because of the tendency of such an edge to wear away or become battered. This flat is usually equal to about one twenty-fifth of the pitch, although there is no generally recognized standard. Owing to the difficulties connected with the V-thread, the tap manufacturers agreed in 1909 to discontinue the making of sharp Vthread taps, except when ordered. One advantage of the V-thread is that the same cutting tool may be used for all pitches, whereas, with the American Standard form, the width of the point or the flat varies according to the pitch. The V-thread is regarded as a good form where a steam-tight joint is necessary, and many of the taps used on locomotive work have this form of thread. Some modified V-threads, for locomotive boiler taps particularly, have a depth of 0.8 × pitch. The American Standard screw thread is used largely in preference to the sharp V-thread because it has several advantages; see American Standard for Unified Screw Threads. If p = pitch of thread, and d depth of thread, then 0.866 d = p × cos 30 deg. = 0.866 × p = ------------------------------------------------------No. of threads per inch United States Standard Screw Thread.—William Sellers of Philadelphia, in a paper read before the Franklin Institute in 1864, originally proposed the screw thread system that later became known as the U. S. Standard system for screw threads. A report was made to the United States Navy in May, 1868, in which the Sellers system was recommended as a standard for the Navy Department, which accounts for the name of U. S. Standard. The American Standard Screw Thread system is a further development of the United States Standard. The thread form which is known as the American (National) form is the same as the United States Standard form. See American Standard for Unified Screw Threads. American National and Unified Screw Thread Forms.—The American National form (formerly known as the United States Standard) was used for many years for most screws, bolts, and miscellaneous threaded products produced in the United States. The American


Machinery's Handbook 28th Edition SCREW THREAD SYSTEMS

1713

National Standard for Unified Screw Threads now in use includes certain modifications of the former standard as is explained below and on page 1719. The basic profile is shown in Fig. 1 and is identical for both UN and UNR screw threads. In this figure H is the height of a sharp V-thread, P is the pitch, D and d are the basic major diameters, D2 and d2 are the basic pitch diameters, and D1 and d1 are the basic minor diameters. Capital letters are used to designate the internal thread dimensions (D, D2, D1), and lowercase letters to designate the external thread dimensions (d, d2, d1). Definitions of Basic Size and Basic Profile of Thread are given on page 1714.

Fig. 1. Basic Profile of UN and UNF Screw Threads

In the past, other symbols were used for some of the thread dimensions illustrated above. These symbols were changed to conform with current practice in nomenclature as defined in ANSI/ASME B1.7M, “Nomenclature, Definitions, and Letter Symbols for Screw Threads.” The symbols used above are also in accordance with terminology and symbols used for threads of the ISO metric thread system. International Metric Thread System.—The Système Internationale (S.I.) Thread was adopted at the International Congress for the standardization of screw threads held in Zurich in 1898. The thread form is similar to the American standard (formerly U.S. Standard), excepting the depth which is greater. There is a clearance between the root and mating crest fixed at a maximum of 1⁄16 the height of the fundamental triangle or 0.054 × pitch. A rounded root profile is recommended. The angle in the plane of the axis is 60 degrees and the crest has a flat like the American standard equal to 0.125 × pitch. This system formed the basis of the normal metric series (ISO threads) of many European countries, Japan, and many other countries, including metric thread standards of the United States. Depth d = 0.7035 P max.; 0.6855 P min. Flat f = 0.125 P Radius r = 0.0633 P max.; 0.054 P min. Tap drill dia = major dia.− pitch

P f 60° Nut

d

Screw r

International Metric Fine Thread: The International Metric Fine Thread form of thread is the same as the International system but the pitch for a given diameter is smaller. German Metric Thread Form: The German metric thread form is like the International Standard but the thread depth = 0.6945 P. The root radius is the same as the maximum for the International Standard or 0.0633 P.


Machinery's Handbook 28th Edition SCREW THREADS

1714

ISO Metric Thread System.—ISO refers to the International Organization for Standardization, a worldwide federation of national standards bodies (for example, the American National Standards Institute is the ISO national body representing the United States) that develops standards on a very wide variety of subjects. The basic profile of ISO metric threads is specified in ISO 68 and shown in Fig. 2. The basic profile of this thread is very similar to that of the Unified thread, and as previously discussed, H is the height of a sharp V-thread, P is the pitch, D and d are the basic major diameters, D2 and d2 are the basic pitch diameters, and D1 and d1 are the basic minor diameters. Here also, capital letters designate the internal thread dimensions (D, D2, D1), and lowercase letters designate the external thread dimensions (d, d2, d1). This metric thread is discussed in detail in the section METRIC SCREW THREADS starting on page 1783. Internal threads

P 8

P 2

D, d

H 8

P

60°

30°

P 2

P 4

D 2, d 2 D 1, d 1

90°

3 H 8 5 H 8 H

H 4

Axis of screw thread

External threads H=

3 × P = 0.866025404P 2

0.125H = 0.108253175P 0.250H = 0.216506351P 0.375H = 0.324759526P 0.625H = 0.541265877P

Fig. 2. ISO 68 Basic Profile

Definitions of Screw Threads The following definitions are based on American National Standard ANSI/ASME B1.7M-1984 (R2001) “Nomenclature, Definitions, and Letter Symbols for Screw Threads,” and refer to both straight and taper threads. Actual Size: An actual size is a measured size. Allowance: An allowance is the prescribed difference between the design (maximum material) size and the basic size. It is numerically equal to the absolute value of the ISO term fundamental deviation. Axis of Thread: Thread axis is coincident with the axis of its pitch cylinder or cone. Basic Profile of Thread: The basic profile of a thread is the cyclical outline, in an axial plane, of the permanently established boundary between the provinces of the external and internal threads. All deviations are with respect to this boundary. Basic Size: The basic size is that size from which the limits of size are derived by the application of allowances and tolerances. Bilateral Tolerance: This is a tolerance in which variation is permitted in both directions from the specified dimension. Black Crest Thread: This is a thread whose crest displays an unfinished cast, rolled, or forged surface. Blunt Start Thread: “Blunt start” designates the removal of the incomplete thread at the starting end of the thread. This is a feature of threaded parts that are repeatedly assembled



1715

by hand, such as hose couplings and thread plug gages, to prevent cutting of hands and crossing of threads. It was formerly known as a Higbee cut. Chamfer: This is a conical surface at the starting end of a thread. Class of Thread: The class of a thread is an alphanumerical designation to indicate the standard grade of tolerance and allowance specified for a thread. Clearance Fit: This is a fit having limits of size so prescribed that a clearance always results when mating parts are assembled at their maximum material condition. Complete Thread: The complete thread is that thread whose profile lies within the size limits. (See also Effective Thread and Length of Complete Thread.) Note: Formerly in pipe thread terminology this was referred to as “the perfect thread” but that term is no longer considered desirable. Crest: This is that surface of a thread which joins the flanks of the thread and is farthest from the cylinder or cone from which the thread projects. Crest Truncation: This is the radial distance between the sharp crest (crest apex) and the cylinder or cone that would bound the crest. Depth of Thread Engagement: The depth (or height) of thread engagement between two coaxially assembled mating threads is the radial distance by which their thread forms overlap each other. Design Size: This is the basic size with allowance applied, from which the limits of size are derived by the application of a tolerance. If there is no allowance, the design size is the same as the basic size. Deviation: Deviation is a variation from an established dimension, position, standard, or value. In ISO usage, it is the algebraic difference between a size (actual, maximum, or minimum) and the corresponding basic size. The term deviation does not necessarily indicate an error. (See also Error.) Deviation, Fundamental (ISO term): For standard threads, the fundamental deviation is the upper or lower deviation closer to the basic size. It is the upper deviation es for an external thread and the lower deviation EI for an internal thread. (See also Allowance and Tolerance Position.) Deviation, Lower (ISO term): The algebraic difference between the minimum limit of size and the basic size. It is designated EI for internal and ei for external thread diameters. Deviation, Upper (ISO term): The algebraic difference between the maximum limit of size and the basic size. It is designated ES for internal and es for external thread diameters. Dimension: A numerical value expressed in appropriate units of measure and indicated on drawings along with lines, symbols, and notes to define the geometrical characteristic of an object. Effective Size: See Pitch Diameter, Functional Diameter. Effective Thread: The effective (or useful) thread includes the complete thread, and those portions of the incomplete thread which are fully formed at the root but not at the crest (in taper pipe threads it includes the so-called black crest threads); thus excluding the vanish thread. Error: The algebraic difference between an observed or measured value beyond tolerance limits, and the specified value. External Thread: A thread on a cylindrical or conical external surface. Fit: Fit is the relationship resulting from the designed difference, before assembly, between the sizes of two mating parts which are to be assembled. Flank: The flank of a thread is either surface connecting the crest with the root. The flank surface intersection with an axial plane is theoretically a straight line. Flank Angle: The flank angles are the angles between the individual flanks 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 Diametral Displacement: In a boundary profile defined system, flank diametral displacement is twice the radial distance between the straight thread flank segments of the


1716


maximum and minimum boundary profiles. The value of flank diametral displacement is equal to pitch diameter tolerance in a pitch line reference thread system. Height of Thread: The height (or depth) of thread is the distance, measured radially, between the major and minor cylinders or cones, respectively. Helix Angle: On a straight thread, the helix angle is the angle made by the helix of the thread and its relation to the thread axis. On a taper thread, the helix angle at a given axial position is the angle made by the conical spiral of the thread with the axis of the thread. The helix angle is the complement of the lead angle. (See also page 1967 for diagram.) Higbee Cut: See Blunt Start Thread. Imperfect Thread: See Incomplete Thread. Included Angle: This is the angle between the flanks of the thread measured in an axial plane. Incomplete Thread: A threaded profile having either crests or roots or both, not fully formed, resulting from their intersection with the cylindrical or end surface of the work or the vanish cone. It may occur at either end of the thread. Interference Fit: A fit having limits of size so prescribed that an interference always results when mating parts are assembled. Internal Thread: A thread on a cylindrical or conical internal surface. Lead: Lead is the axial distance between two consecutive points of intersection of a helix by a line parallel to the axis of the cylinder on which it lies, i.e., the axial movement of a threaded part rotated one turn in its mating 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 perpendicular to the axis at the pitch line. Lead Thread: That portion of the incomplete thread that is fully formed at the root but not fully formed at the crest that occurs at the entering end of either an external or internal thread. Left-hand Thread: A thread is a left-hand thread if, when viewed axially, it winds in a counterclockwise and receding direction. Left-hand threads are designated LH. Length of Complete Thread: The axial length of a thread section having full form at both crest and root but also including a maximum of two pitches at the start of the thread which may have a chamfer or incomplete crests. Length of Thread Engagement: The length of thread engagement of two mating threads is the axial distance over which the two threads, each having full form at both crest and root, are designed to contact. (See also Length of Complete Thread.) Limits of Size: The applicable maximum and minimum sizes. Major Clearance: The radial distance between the root of the internal thread and the crest of the external thread of the coaxially assembled designed forms of mating threads. Major Cone: The imaginary cone that would bound the crests of an external taper thread or the roots of an internal taper thread. Major Cylinder: The imaginary cylinder that would bound the crests of an external straight thread or the roots of an internal straight thread. 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. (See also Major Cylinder and Major Cone.) Maximum Material Condition: (MMC): The condition where a feature of size contains the maximum amount of material within the stated limits of size. For example, minimum internal thread size or maximum external thread size. Minimum Material Condition: (Least Material Condition (LMC)): The condition where a feature of size contains the least amount of material within the stated limits of size. For example, maximum internal thread size or minimum external thread size. Minor Clearance: The radial distance between the crest of the internal thread and the root of the external thread of the coaxially assembled design forms of mating threads.



1717

Minor Cone: The imaginary cone that would bound the roots of an external taper thread or the crests of an internal taper thread. Minor Cylinder: The imaginary cylinder that would bound the roots of an external straight thread or the crests of an internal straight thread. 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. (See also Minor Cylinder and Minor Cone.) Multiple-Start Thread: A thread in which the lead is an integral multiple, other than one, of the pitch. Nominal Size: Designation used for general identification. Parallel Thread: See Screw Thread. Partial Thread: See Vanish Thread. Pitch: The pitch of a thread having uniform spacing is the distance measured parallel with its axis between corresponding points on adjacent thread forms in the same axial plane and on the same side of the axis. Pitch is equal to the lead divided by the number of thread starts. Pitch Cone: The pitch cone is an imaginary cone of such apex angle and location of its vertex and axis that its surface would pass through a taper thread in such a manner as to make the widths of the thread ridge and the thread groove equal. It is, therefore, located equidistantly between the sharp major and minor cones of a given thread form. On a theoretically perfect taper thread, these widths are equal to one-half the basic pitch. (See also Axis of Thread and Pitch Diameter.) Pitch Cylinder: The pitch cylinder is an imaginary cylinder of such diameter and location of its axis that its surface would pass through a straight thread in such a manner as to make the widths of the thread ridge and groove equal. It is, therefore, located equidistantly between the sharp major and minor cylinders of a given thread form. On a theoretically perfect thread these widths are equal to one-half the basic pitch. (See also Axis of Thread and Pitch Diameter.) Pitch Diameter: On a straight thread the pitch diameter is the diameter of the pitch cylinder. 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. Note: When the crest of a thread is truncated beyond the pitch line, the pitch diameter and pitch cylinder or pitch cone would be based on a theoretical extension of the thread flanks. Pitch Diameter, Functional Diameter: The functional diameter is the pitch diameter of an enveloping thread with perfect pitch, lead, and flank angles and having a specified length of engagement. It includes the cumulative effect of variations in lead (pitch), flank angle, taper, straightness, and roundness. Variations at the thread crest and root are excluded. Other, nonpreferred terms are virtual diameter, effective size, virtual effective diameter, and thread assembly diameter. Pitch Line: The generator of the cylinder or cone specified in Pitch Cylinder and Pitch Cone. Right-hand Thread: A thread is a fight-hand thread if, when viewed axially, it winds in a clockwise and receding direction. A thread is considered to be right-hand unless specifically indicated otherwise. Root: That surface of the thread which joins the flanks of adjacent thread forms and is immediately adjacent to the cylinder or cone from which the thread projects. Root Truncation: The radial distance between the sharp root (root apex) and the cylinder or cone that would bound the root. See also Sharp Root (Root Apex). Runout: As applied to screw threads, unless otherwise specified, runout refers to circular runout of major and minor cylinders with respect to the pitch cylinder. Circular runout, in accordance with ANSI Y14.5M, controls cumulative variations of circularity and coaxiality. Runout includes variations due to eccentricity and out-of-roundness. The amount of runout is usually expressed in terms of full indicator movement (FIM).


1718


Screw Thread: A screw thread is a continuous and projecting helical ridge usually of uniform section on a cylindrical or conical surface. Sharp Crest (Crest Apex): The apex formed by the intersection of the flanks of a thread when extended, if necessary, beyond the crest. Sharp Root (Root Apex): The apex formed by the intersection of the adjacent flanks of adjacent threads when extended, if necessary, beyond the root. Standoff: The axial distance between specified reference points on external and internal taper thread members or gages, when assembled with a specified torque or under other specified conditions. Straight Thread: A straight thread is a screw thread projecting from a cylindrical surface. Taper Thread: A taper thread is a screw thread projecting from a conical surface. Tensile Stress Area: The tensile stress area is an arbitrarily selected area for computing the tensile strength of an externally threaded fastener so that the fastener strength is consistent with the basic material strength of the fastener. It is typically defined as a function of pitch diameter and/or minor diameter to calculate a circular cross section of the fastener correcting for the notch and helix effects of the threads. Thread: A thread is a portion of a screw thread encompassed by one pitch. On a singlestart thread it is equal to one turn. (See also Threads per Inch and Turns per Inch.) Thread Angle: See Included Angle. Thread Runout: See Vanish Thread. Thread Series: Thread Series are groups of diameter/pitch combinations distinguished from each other by the number of threads per inch applied to specific diameters. Thread Shear Area: The thread shear area is the total ridge cross-sectional area intersected by a specified cylinder with diameter and length equal to the mating thread engagement. Usually the cylinder diameter for external thread shearing is the minor diameter of the internal thread and for internal thread shearing it is the major diameter of the external thread. Threads per Inch: The number of threads per inch is the reciprocal of the axial pitch in inches. Tolerance: The total amount by which a specific dimension is permitted to vary. The tolerance is the difference between the maximum and minimum limits. Tolerance Class: (metric): The tolerance class (metric) is the combination of a tolerance position with a tolerance grade. It specifies the allowance (fundamental deviation), pitch diameter tolerance (flank diametral displacement), and the crest diameter tolerance. Tolerance Grade: (metric): The tolerance grade (metric) is a numerical symbol that designates the tolerances of crest diameters and pitch diameters applied to the design profiles. Tolerance Limit: The variation, positive or negative, by which a size is permitted to depart from the design size. Tolerance Position: (metric): The tolerance position (metric) is a letter symbol that designates the position of the tolerance zone in relation to the basic size. This position provides the allowance (fundamental deviation). Total Thread: Includes the complete and all the incomplete thread, thus including the vanish thread and the lead thread. Transition Fit: A fit having limits of size so prescribed that either a clearance or an interference may result when mating parts are assembled. Turns per Inch: The number of turns per inch is the reciprocal of the lead in inches. Unilateral Tolerance: A tolerance in which variation is permitted in one direction from the specified dimension. Vanish Thread: (Partial Thread, Washout Thread, or Thread Runout): That portion of the incomplete thread which is not fully formed at the root or at crest and root. It is produced by the chamfer at the starting end of the thread forming tool. Virtual Diameter: See Pitch Diameter, Functional Diameter. Washout Thread: See Vanish Thread.


Machinery's Handbook 28th Edition UNIFIED SCREW THREADS

1719

UNIFIED SCREW THREADS American Standard for Unified Screw Threads American Standard B1.1-1949 was the first American standard to cover those Unified Thread Series agreed upon by the United Kingdom, Canada, and the United States to obtain screw thread interchangeability among these three nations. These Unified threads are now the basic American standard for fastening types of screw threads. In relation to previous American practice, Unified threads have substantially the same thread form and are mechanically interchangeable with the former American National threads of the same diameter and pitch. The principal differences between the two systems lie in: 1) application of allowances; 2) variation of tolerances with size; 3) difference in amount of pitch diameter tolerance on external and internal threads; and 4) differences in thread designation. In the Unified system an allowance is provided on both the Classes 1A and 2A external threads whereas in the American National system only the Class I external thread has an allowance. Also, in the Unified system, the pitch diameter tolerance of an internal thread is 30 per cent greater than that of the external thread, whereas they are equal in the American National system. Revised Standard.—The revised screw thread standard ANSI/ASME B1.1-1989 (R2001) is much the same as that of ANSI B1.1-1982. The latest symbols in accordance with ANSI/ASME B1.7M-1984 (R2001) Nomenclature, are used. Acceptability criteria are described in ANSI/ASME B1.3M-1992 (R2001), Screw Thread Gaging Systems for Dimensional Acceptability, Inch or Metric Screw Threads (UN, UNR, UNJ, M, and MJ). Where the letters U, A or B do not appear in the thread designations, the threads conform to the outdated American National screw threads. Advantages of Unified Threads.—The Unified standard is designed to correct certain production difficulties resulting from the former standard. Often, under the old system, the tolerances of the product were practically absorbed by the combined tool and gage tolerances, leaving little for a working tolerance in manufacture. Somewhat greater tolerances are now provided for nut threads. As contrasted with the old “classes of fit” 1, 2, and 3, for each of which the pitch diameter tolerance on the external and internal threads were equal, the Classes 1B, 2B, and 3B (internal) threads in the new standard have, respectively, a 30 per cent larger pitch diameter tolerance than the 1A, 2A, and 3A (external) threads. Relatively more tolerance is provided for fine threads than for coarse threads of the same pitch. Where previous tolerances were more liberal than required, they were reduced. Thread Form.—The Design Profiles for Unified screw threads, shown on page 1720, define the maximum material condition for external and internal threads with no allowance and are derived from the Basic Profile, shown on page 1713. UN External Screw Threads: A flat root contour is specified, but it is necessary to provide for some threading tool crest wear, hence a rounded root contour cleared beyond the 0.25P flat width of the Basic Profile is optional. UNR External Screw Threads: To reduce the rate of threading tool crest wear and to improve fatigue strength of a flat root thread, the Design Profile of the UNR thread has a smooth, continuous, non-reversing contour with a radius of curvature not less than 0.108P at any point and blends tangentially into the flanks and any straight segment. At the maximum material condition, the point of tangency is specified to be at a distance not less than 0.625H (where H is the height of a sharp V-thread) below the basic major diameter. UN and UNR External Screw Threads: The Design Profiles of both UN and UNR external screw threads have flat crests. However, in practice, product threads are produced with partially or completely rounded crests. A rounded crest tangent at 0.125P flat is shown as an option on page 1720.



1720

UN Internal Screw Thread: In practice it is necessary to provide for some threading tool crest wear, therefore the root of the Design Profile is rounded and cleared beyond the 0.125P flat width of the Basic Profile.There is no internal UNR screw thread. American National Standard Unified Internal and External Screw Thread Design Profiles (Maximum Material Condition) .— 0.125H

0.625H

0.125P

0.5P Pitch line

0.375H

H

Rounded crest optional 60 deg 30 deg

0.25P

P

0.25H

0.25H Nominal flat root design minor diameter Rounded root optional

Flanks to be straight beyond 0.25H from sharp apex of root 90 deg

Axis of external thread

0.125H 0.125P 60 deg 0.625H H

0.5P Pitch line

0.375H 0.25P

30 deg

0.6875H

0.25H

P 0.0625H 0.25H

0.1875H r = 0.108P Flanks to be straight beyond 0.25H from sharp apex of root 90 deg

Rounded crest optional

Tangency flank/root rad. UNR design minor diameter specified in dimensional tables


Min major diameter specified in dimensional tables

60° 0.25H

UN Internal 0.125P Thread (Nut) 0.125H Pitch line 0.5P

0.25P

0.125H 0.375H 0.625H 0.25H

H

0.25H

P 90 deg


(H = height of sharp V-thread = 0.86603 × pitch)

Thread Series.—Thread series are groups of diameter-pitch combinations distinguished from each other by the numbers of threads per inch applied to a specific diameter. The various diameter-pitch combinations of eleven standard series are shown in Table 2. The limits of size of threads in the eleven standard series together with certain selected combinations of diameter and pitch, as well as the symbols for designating the various threads, are given in Table 3. (Text continues on page 1750)


Machinery's Handbook 28th Edition Table 1. American Standard Unified Inch Screw Thread Form Data Depth of UNR Ext. Thd.

Truncation of Ext. Thd. Root

Truncation of UNR Ext. Thd. Rootb

Truncation of Ext. Thd. Crest

Truncation of Int. Thd. Root

Truncation of Int. Thd. Crest

n

P

0.86603P

0.54127P

0.59539P

0.21651P

0.16238P

0.10825P

0.10825P

0.2165P

80 72 64 56 48 44 40 36 32 28 27 24 20 18 16 14 13 12 111⁄2 11 10 9 8 7 6 5 41⁄2 4

0.01250 0.01389 0.01563 0.01786 0.02083 0.02273 0.02500 0.02778 0.03125 0.03571 0.03704 0.04167 0.05000 0.05556 0.06250 0.07143 0.07692 0.08333 0.08696

0.01083 0.01203 0.01353 0.01546 0.01804 0.01968 0.02165 0.02406 0.02706 0.03093 0.03208 0.03608 0.04330 0.04811 0.05413 0.06186 0.06662 0.07217 0.07531

0.00677 0.00752 0.00846 0.00967 0.01128 0.01230 0.01353 0.01504 0.01691 0.01933 0.02005 0.02255 0.02706 0.03007 0.03383 0.03866 0.04164 0.04511 0.04707

0.00744 0.00827 0.00930 0.01063 0.01240 0.01353 0.01488 0.01654 0.01861 0.02126 0.02205 0.02481 0.02977 0.03308 0.03721 0.04253 0.04580 0.04962 0.05177

0.00271 0.00301 0.00338 0.00387 0.00451 0.00492 0.00541 0.00601 0.00677 0.00773 0.00802 0.00902 0.01083 0.01203 0.01353 0.01546 0.01655 0.01804 0.01883

0.00203 0.00226 0.00254 0.00290 0.00338 0.00369 0.00406 0.00451 0.00507 0.00580 0.00601 0.00677 0.00812 0.00902 0.01015 0.01160 0.01249 0.01353 0.01412

0.00135 0.00150 0.00169 0.00193 0.00226 0.00246 0.00271 0.00301 0.00338 0.00387 0.00401 0.00451 0.00541 0.00601 0.00677 0.00773 0.00833 0.00902 0.00941

0.00135 0.00150 0.00169 0.00193 0.00226 0.00246 0.00271 0.00301 0.00338 0.00387 0.00401 0.00451 0.00541 0.00601 0.00677 0.00773 0.00833 0.00902 0.00941

0.00271 0.00301 0.00338 0.00387 0.00451 0.00492 0.00541 0.00601 0.00677 0.00773 0.00802 0.00902 0.01083 0.01203 0.01353 0.01546 0.01665 0.01804 0.01883

0.09091 0.10000 0.11111 0.12500 0.14286 0.16667 0.20000 0.22222

0.07873 0.08660 0.09623 0.10825 0.12372 0.14434 0.17321 0.19245

0.04921 0.05413 0.06014 0.06766 0.07732 0.09021 0.10825 0.12028

0.05413 0.05954 0.06615 0.07442 0.08506 0.09923 0.11908 0.13231

0.01968 0.02165 0.02406 0.02706 0.03093 0.03608 0.04330 0.04811

0.01476 0.01624 0.01804 0.02030 0.02320 0.02706 0.03248 0.03608

0.00984 0.01083 0.01203 0.01353 0.01546 0.01804 0.02165 0.02406

0.00984 0.01083 0.01203 0.01353 0.01546 0.01804 0.02165 0.02406

0.01968 0.02165 0.02406 0.02706 0.03093 0.03608 0.04330 0.04811

0.25000

0.21651

0.13532

0.14885

0.05413

0.04059

0.02706

0.02706

0.05413

Threads per Inch

Basic Flat at Int. Thd. Crestc

Maximum Ext. Thd. Root Radius

Addendum of Ext. Thd.

0.125P

0.25P

0.14434P

0.32476P

0.00156 0.00174 0.00195 0.00223 0.00260 0.00284 0.00312 0.00347 0.00391 0.00446 0.00463 0.00521 0.00625 0.00694 0.00781 0.00893 0.00962 0.01042 0.01087

0.00312 0.00347 0.00391 0.00446 0.00521 0.00568 0.00625 0.00694 0.00781 0.00893 0.00926 0.01042 0.01250 0.01389 0.01562 0.01786 0.01923 0.02083 0.02174

0.00180 0.00200 0.00226 0.00258 0.00301 0.00328 0.00361 0.00401 0.00451 0.00515 0.00535 0.00601 0.00722 0.00802 0.00902 0.01031 0.01110 0.01203 0.01255

0.00406 0.00451 0.00507 0.00580 0.00677 0.00738 0.00812 0.00902 0.01015 0.01160 0.01203 0.01353 0.01624 0.01804 0.02030 0.02320 0.02498 0.02706 0.02824

0.01136 0.01250 0.01389 0.01562 0.01786 0.02083 0.02500 0.02778

0.02273 0.02500 0.02778 0.03125 0.03571 0.04167 0.05000 0.05556

0.01312 0.01443 0.01604 0.01804 0.02062 0.02406 0.02887 0.03208

0.02952 0.03248 0.03608 0.04059 0.04639 0.05413 0.06495 0.07217

0.03125

0.06250

0.03608

0.08119

Flat at Ext. Thd. Crest and Int. Thd. Root

UNIFIED SCREW THREADS

Pitch

Depth of Sharp V-Thread

Depth of Int. Thd. and UN Ext. Thd.a

a Also depth of thread engagement. b Design profile.



1721

c Also basic flat at external UN thread root.


1722

Table 2. Diameter-Pitch Combinations for Standard Series of Threads (UN/UNR) Sizesa No. or Inches 0 (1) 2 (3) 4 5 6 8 10 (12) 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 (1 1⁄16) 1 1⁄8 (1 3⁄16) 1 1⁄4 1 5⁄16 1 3⁄8 (1 7⁄16) 1 1⁄2 (1 9⁄16) 1 5⁄8 (1 11⁄16) 1 3⁄4 (1 13⁄16) 1 7⁄8 (1 15⁄16) 2 (2 1⁄8) 2 1⁄4 (2 3⁄8) 2 1⁄2 (2 5⁄8) 2 3⁄4 (2 7⁄8) 3 (3 1⁄8) 3 1⁄4 (3 3⁄8) 3 1⁄2 (3 5⁄8) 3 3⁄4 (3 7⁄8) 4

Basic Major Dia. Inches 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 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000 1.0625 1.1250 1.1875 1.2500 1.3125 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000

Threads per Inch Series with Graded Pitches Series with Uniform (Constant) Pitches Coarse Fineb Extra finec UNC UNF UNEF 4-UN 6-UN 8-UN 12-UN 16-UN 20-UN 28-UN 32-UN … 80 Series designation shown indicates the UN thread form; however, the UNR 64 72 56 64 thread form may be specified by substituting UNR in place of UN in all 48 56 designations for external threads. 40 48 40 44 … … … … … … … … … 32 40 … … … … … … … … UNC 32 36 … … … … … … … … UNC 24 32 … … … … … … … … UNF 24 28 32 … … … … … … UNF UNEF 20 28 32 … … … … … UNC UNF UNEF 18 24 32 … … … … … 20 28 UNEF 16 24 32 … … … … UNC 20 28 UNEF 14 20 28 … … … … 16 UNF UNEF 32 13 20 28 … … … … 16 UNF UNEF 32 12 18 24 … … … UNC 16 20 28 32 11 18 24 … … … 12 16 20 28 32 … … 24 … … … 12 16 20 28 32 10 16 20 … … … 12 UNF UNEF 28 32 … … 20 … … … 12 16 UNEF 28 32 9 14 20 … … … 12 16 UNEF 28 32 … … 20 … … … 12 16 UNEF 28 32 8 12 20 … … UNC UNF 16 UNEF 28 32 … … 18 … … 8 12 16 20 28 … 7 12 18 … … 8 UNF 16 20 28 … … … 18 … … 8 12 16 20 28 … 7 12 18 … … 8 UNF 16 20 28 … … … 18 … … 8 12 16 20 28 … 6 12 18 … UNC 8 UNF 16 20 28 … … … 18 … 6 8 12 16 20 28 … 6 12 18 … UNC 8 UNF 16 20 28 … … … 18 … 6 8 12 16 20 … … … … 18 … 6 8 12 16 20 … … … … 18 … 6 8 12 16 20 … … 5 … … … 6 8 12 16 20 … … … … … … 6 8 12 16 20 … … … … … … 6 8 12 16 20 … … … … … … 6 8 12 16 20 … … 41⁄2 … … … 6 8 12 16 20 … … … … … … 6 8 12 16 20 … … 4 1⁄2 … … … 6 8 12 16 20 … … … … … … 6 8 12 16 20 … … 4 … … UNC 6 8 12 16 20 … … … … … 4 6 8 12 16 20 … … 4 … … UNC 6 8 12 16 20 … … … … … 4 6 8 12 16 20 … … 4 … … UNC 6 8 12 16 20 … … … … … 4 6 8 12 16 … … … 4 … … UNC 6 8 12 16 … … … … … … 4 6 8 12 16 … … … 4 … … UNC 6 8 12 16 … … … … … … 4 6 8 12 16 … … … 4 … … UNC 6 8 12 16 … … … … … … 4 6 8 12 16 … … … 4 … … UNC 6 8 12 16 … … …

a Sizes shown in parentheses are secondary sizes. Primary sizes of 41⁄ , 41⁄ , 43⁄ , 5, 51⁄ , 51⁄ , 53⁄ and 6 4 2 4 4 2 4 inches also are in the 4, 6, 8, 12, and 16 thread series; secondary sizes of 41⁄8, 43⁄8, 45⁄8, 47⁄8, 51⁄8, 53⁄8, 55⁄8, and 57⁄8 also are in the 4, 6, 8, 12, and 16 thread series. b For diameters over 11⁄ inches, use 12-thread series. 2 c For diameters over 111⁄ inches, use 16-thread series. 16 For UNR thread form substitute UNR for UN for external threads only.



Table 3. Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 0–80 UNF 1–64 UNC 1–72 UNF

2–64 UNF 3–48 UNC 3–56 UNF 4–40 UNC 4–48 UNF 5–40 UNC 5–44 UNF 6–32 UNC 6–40 UNF 8–32 UNC

Maxd

Min

0.0563 0.0568 0.0686 0.0692 0.0689 0.0695 0.0813 0.0819 0.0816 0.0822 0.0938 0.0945 0.0942 0.0949 0.1061 0.1069 0.1068 0.1075 0.1191 0.1199 0.1195 0.1202 0.1312 0.1320 0.1321 0.1329 0.1571 0.1580 0.1577 0.1585

— — — — — — — — — — — — — — — — — — — — — — — — — — — — — —

0.0514 0.0519 0.0623 0.0629 0.0634 0.0640 0.0738 0.0744 0.0753 0.0759 0.0848 0.0855 0.0867 0.0874 0.0950 0.0958 0.0978 0.0985 0.1080 0.1088 0.1095 0.1102 0.1169 0.1177 0.1210 0.1218 0.1428 0.1437 0.1452 0.1460

0.0496 0.0506 0.0603 0.0614 0.0615 0.0626 0.0717 0.0728 0.0733 0.0744 0.0825 0.0838 0.0845 0.0858 0.0925 0.0939 0.0954 0.0967 0.1054 0.1069 0.1070 0.1083 0.1141 0.1156 0.1184 0.1198 0.1399 0.1415 0.1424 0.1439

0.0446 0.0451 0.0538 0.0544 0.0559 0.0565 0.0642 0.0648 0.0668 0.0674 0.0734 0.0741 0.0771 0.0778 0.0814 0.0822 0.0864 0.0871 0.0944 0.0952 0.0972 0.0979 0.1000 0.1008 0.1074 0.1082 0.1259 0.1268 0.1301 0.1309

Major Diameter

Class

Allowance

Maxd

2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A 2A 3A

0.0005 0.0000 0.0006 0.0000 0.0006 0.0000 0.0006 0.0000 0.0006 0.0000 0.0007 0.0000 0.0007 0.0000 0.0008 0.0000 0.0007 0.0000 0.0008 0.0000 0.0007 0.0000 0.0008 0.0000 0.0008 0.0000 0.0009 0.0000 0.0008 0.0000

0.0595 0.0600 0.0724 0.0730 0.0724 0.0730 0.0854 0.0860 0.0854 0.0860 0.0983 0.0990 0.0983 0.0990 0.1112 0.1120 0.1113 0.1120 0.1242 0.1250 0.1243 0.1250 0.1372 0.1380 0.1372 0.1380 0.1631 0.1640 0.1632 0.1640

Pitch Diameter

Minor Diameter Class 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B 2B 3B

Min

Max

0.0465 0.0465 0.0561 0.0561 0.0580 0.0580 0.0667 0.0667 0.0691 0.0691 0.0764 0.0764 0.0797 0.0797 0.0849 0.0849 0.0894 0.0894 0.0979 0.0979 0.1004 0.1004 0.104 0.1040 0.111 0.1110 0.130 0.1300 0.134 0.1340

0.0514 0.0514 0.0623 0.0623 0.0635 0.0635 0.0737 0.0737 0.0753 0.0753 0.0845 0.0845 0.0865 0.0865 0.0939 0.0939 0.0968 0.0968 0.1062 0.1062 0.1079 0.1079 0.114 0.1140 0.119 0.1186 0.139 0.1389 0.142 0.1416


Pitch Diameter

Major Diameter

Min

Max

Min

0.0519 0.0519 0.0629 0.0629 0.0640 0.0640 0.0744 0.0744 0.0759 0.0759 0.0855 0.0855 0.0874 0.0874 0.0958 0.0958 0.0985 0.0985 0.1088 0.1088 0.1102 0.1102 0.1177 0.1177 0.1218 0.1218 0.1437 0.1437 0.1460 0.1460

0.0542 0.0536 0.0655 0.0648 0.0665 0.0659 0.0772 0.0765 0.0786 0.0779 0.0885 0.0877 0.0902 0.0895 0.0991 0.0982 0.1016 0.1008 0.1121 0.1113 0.1134 0.1126 0.1214 0.1204 0.1252 0.1243 0.1475 0.1465 0.1496 0.1487

0.0600 0.0600 0.0730 0.0730 0.0730 0.0730 0.0860 0.0860 0.0860 0.0860 0.0990 0.0990 0.0990 0.0990 0.1120 0.1120 0.1120 0.1120 0.1250 0.1250 0.1250 0.1250 0.1380 0.1380 0.1380 0.1380 0.1640 0.1640 0.1640 0.1640

1723

8–36 UNF

Min

Mine

UNR Minor Dia.,c Max (Ref.)


2–56 UNC

Internalb

Externalb


Nominal Size, Threads per Inch, and Series Designationa 10–24 UNC 10–28 UNS 10–32 UNF

12–28 UNF 12–32 UNEF 12–36 UNS 12–40 UNS 12–48 UNS 12–56 UNS 1⁄ –20 UNC 4

1⁄ –24 4 1⁄ –27 4 1⁄ –28 4

1⁄ –32 4

UNS

Min 0.1818 0.1828 0.1825 0.1831 0.1840 0.1836 0.1840 0.1847 0.1852 0.2078 0.2088 0.2085 0.2095 0.2091 0.2100 0.2096 0.2100 0.2107 0.2112 0.2367

Mine

Maxd

— — — — — — — — — — — — — — — — — — — —

0.1619 0.1629 0.1658 0.1688 0.1697 0.1711 0.1729 0.1757 0.1777 0.1879 0.1889 0.1918 0.1928 0.1948 0.1957 0.1971 0.1989 0.2017 0.2037 0.2164

Min 0.1586 0.1604 0.1625 0.1658 0.1674 0.1681 0.1700 0.1731 0.1752 0.1845 0.1863 0.1886 0.1904 0.1917 0.1933 0.1941 0.1960 0.1991 0.2012 0.2108

UNR Minor Dia.,c Max (Ref.) 0.1394 0.1404 0.1464 0.1519 0.1528 0.1560 0.1592 0.1644 0.1681 0.1654 0.1664 0.1724 0.1734 0.1779 0.1788 0.1821 0.1835 0.1904 0.1941 0.1894

0.2408 0.2419 0.2417

0.2367 — —

0.2164 0.2175 0.2218

0.2127 0.2147 0.2181

0.1894 0.1905 0.1993

Major Diameter

Class 2A 3A 2A 2A 3A 2A 2A 2A 2A 2A 3A 2A 3A 2A 3A 2A 2A 2A 2A 1A

0.1890 0.1900 0.1890 0.1891 0.1900 0.1891 0.1891 0.1892 0.1893 0.2150 0.2160 0.2150 0.2160 0.2151 0.2160 0.2151 0.2151 0.2152 0.2153 0.2489

2A 3A 2A

0.0011 0.0000 0.0011

0.2489 0.2500 0.2489

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Class 2B 3B 2B 2B 3B 2B 2B 2B 2B 2B 3B 2B 3B 2B 3B 2B 2B 2B 2B 1B

Min 0.145 0.1450 0.151 0.156 0.1560 0.160 0.163 0.167 0.171 0.171 0.1710 0.177 0.1770 0.182 0.1820 0.186 0.189 0.193 0.197 0.196

Max 0.156 0.1555 0.160 0.164 0.1641 0.166 0.169 0.172 0.175 0.181 0.1807 0.186 0.1857 0.190 0.1895 0.192 0.195 0.198 0.201 0.207

Min 0.1629 0.1629 0.1668 0.1697 0.1697 0.1720 0.1738 0.1765 0.1784 0.1889 0.1889 0.1928 0.1928 0.1957 0.1957 0.1980 0.1998 0.2025 0.2044 0.2175

Max 0.1672 0.1661 0.1711 0.1736 0.1726 0.1759 0.1775 0.1799 0.1816 0.1933 0.1922 0.1970 0.1959 0.1998 0.1988 0.2019 0.2035 0.2059 0.2076 0.2248

Min 0.1900 0.1900 0.1900 0.1900 0.1900 0.1900 0.1900 0.1900 0.1900 0.2160 0.2160 0.2160 0.2160 0.2160 0.2160 0.2160 0.2160 0.2160 0.2160 0.2500

2B 3B 2B

0.196 0.1960 0.205

0.207 0.2067 0.215

0.2175 0.2175 0.2229

0.2224 0.2211 0.2277

0.2500 0.2500 0.2500

UNS

2A

0.0010

0.2490

0.2423

—

0.2249

0.2214

0.2049

2B

0.210

0.219

0.2259

0.2304

0.2500

UNF

1A

0.0010

0.2490

0.2392

—

0.2258

0.2208

0.2064

1B

0.211

0.220

0.2268

0.2333

0.2500

UNEF

2A 3A 2A

0.0010 0.0000 0.0010

0.2490 0.2500 0.2490

0.2425 0.2435 0.2430

— — —

0.2258 0.2268 0.2287

0.2225 0.2243 0.2255

0.2064 0.2074 0.2118

2B 3B 2B

0.211 0.2110 0.216

0.220 0.2190 0.224

0.2268 0.2268 0.2297

0.2311 0.2300 0.2339

0.2500 0.2500 0.2500

3A

0.0000

0.2500

0.2440

—

0.2297

0.2273

0.2128

3B

0.2160

0.2229

0.2297

0.2328

0.2500



10–36 UNS 10–40 UNS 10–48 UNS 10–56 UNS 12–24 UNC

Internalb

Externalb Allowance 0.0010 0.0000 0.0010 0.0009 0.0000 0.0009 0.0009 0.0008 0.0007 0.0010 0.0000 0.0010 0.0000 0.0009 0.0000 0.0009 0.0009 0.0008 0.0007 0.0011

1724

Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads

Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 1⁄ –36 UNS 4

Maxd

—

0.2311

Min 0.2280

0.2491

0.2440

—

0.2329

0.2300

0.2193

0.2492

0.2447

—

0.2357

0.2330

0.2243

0.0008

0.2492

0.2451

—

0.2376

0.2350

1A

0.0012

0.3113

0.2982

—

0.2752

UN

2A 3A 2A

0.0012 0.0000 0.0012

0.3113 0.3125 0.3113

0.3026 0.3038 0.3032

0.2982 — —

UNF

3A 1A

0.0000 0.0011

0.3125 0.3114

0.3044 0.3006

2A 3A 2A

0.0011 0.0000 0.0010

0.3114 0.3125 0.3115

2A

0.0010

3A 2A

0.0000 0.0010

3A 2A

5⁄ –20 16

5⁄ –27 UNS 16 5⁄ –28 UN 16 5⁄ –32 16

UNEF

5⁄ –36 UNS 16 5⁄ –40 UNS 16 5⁄ –48 UNS 16 3⁄ –16 UNC 8

3⁄ –18 UNS 8 3⁄ –20 UN 8

Major Diameter

Class 2A

Allowance 0.0009

0.2491

2A

0.0009

2A

0.0008

2A

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Max 0.226

Min 0.2320

Max 0.2360

Min 0.2500

2B

0.223

0.229

0.2338

0.2376

0.2500

2B

0.227

0.232

0.2365

0.2401

0.2500

0.2280

2B

0.231

0.235

0.2384

0.2417

0.2500

0.2691

0.2452

1B

0.252

0.265

0.2764

0.2843

0.3125

0.2752 0.2764 0.2788

0.2712 0.2734 0.2748

0.2452 0.2464 0.2518

2B 3B 2B

0.252 0.2520 0.258

0.265 0.2630 0.270

0.2764 0.2764 0.2800

0.2817 0.2803 0.2852

0.3125 0.3125 0.3125

— —

0.2800 0.2843

0.2770 0.2788

0.2530 0.2618

3B 1B

0.2580 0.267

0.2680 0.277

0.2800 0.2854

0.2839 0.2925

0.3125 0.3125

0.3042 0.3053 0.3048

— — —

0.2843 0.2854 0.2874

0.2806 0.2827 0.2839

0.2618 0.2629 0.2674

2B 3B 2B

0.267 0.2670 0.272

0.277 0.2754 0.281

0.2854 0.2854 0.2884

0.2902 0.2890 0.2929

0.3125 0.3125 0.3125

0.3115

0.3050

—

0.2883

0.2849

0.2689

2B

0.274

0.282

0.2893

0.2937

0.3125

0.3125 0.3115

0.3060 0.3055

— —

0.2893 0.2912

0.2867 0.2880

0.2699 0.2743

3B 2B

0.2740 0.279

0.2807 0.286

0.2893 0.2922

0.2926 0.2964

0.3125 0.3125

0.0000 0.0009

0.3125 0.3116

0.3065 0.3061

— —

0.2922 0.2936

0.2898 0.2905

0.2753 0.2785

3B 2B

0.2790 0.282

0.2847 0.289

0.2922 0.2945

0.2953 0.2985

0.3125 0.3125

2A

0.0009

0.3116

0.3065

—

0.2954

0.2925

0.2818

2B

0.285

0.291

0.2963

0.3001

0.3125

2A

0.0008

0.3117

0.3072

—

0.2982

0.2955

0.2869

2B

0.290

0.295

0.2990

0.3026

0.3125

1A

0.0013

0.3737

0.3595

—

0.3331

0.3266

0.2992

1B

0.307

0.321

0.3344

0.3429

0.3750

2A 3A 2A

0.0013 0.0000 0.0013

0.3737 0.3750 0.3737

0.3643 0.3656 0.3650

0.3595 — —

0.3331 0.3344 0.3376

0.3287 0.3311 0.3333

0.2992 0.3005 0.3076

2B 3B 2B

0.307 0.3070 0.315

0.321 0.3182 0.328

0.3344 0.3344 0.3389

0.3401 0.3387 0.3445

0.3750 0.3750 0.3750

2A

0.0012

0.3738

0.3657

—

0.3413

0.3372

0.3143

2B

0.321

0.332

0.3425

0.3479

0.3750

3A

0.0000

0.3750

0.3669

—

0.3425

0.3394

0.3155

3B

0.3210

0.3297

0.3425

0.3465

0.3750


1725

Min 0.220

Class 2B


Min 0.2436

Mine

UNR Minor Dia.,c Max (Ref.) 0.2161

1⁄ –40 UNS 4 1⁄ –48 UNS 4 1⁄ –56 UNS 4 5⁄ –18 UNC 16

5⁄ –24 16

Internalb

Externalb


Nominal Size, Threads per Inch, and Series Designationa 3⁄ –24 UNF 8 3⁄ –24 UNF 8 3⁄ –27 UNS 8 3⁄ –28 UN 8

UNEF

3⁄ –36 8 3⁄ –40 8

UNS

UNS 0.390–27 UNS 7⁄ –14 UNC 16

7⁄ –16 16

Maxd

—

0.3468

Min 0.3411

0.3667 0.3678

— —

0.3468 0.3479

0.3430 0.3450

0.3243 0.3254

Major Diameter

Class 1A

0.3739

2A 3A

0.0011 0.0000

0.3739 0.3750

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Class 1B

Min 0.330

Max 0.340

Min 0.3479

Max 0.3553

Min 0.3750

2B 3B

0.330 0.3300

0.340 0.3372

0.3479 0.3479

0.3528 0.3516

0.3750 0.3750

2A

0.0011

0.3739

0.3672

—

0.3498

0.3462

0.3298

2B

0.335

0.344

0.3509

0.3556

0.3750

2A

0.0011

0.3739

0.3674

—

0.3507

0.3471

0.3313

2B

0.336

0.345

0.3518

0.3564

0.3750

3A 2A

0.0000 0.0010

0.3750 0.3740

0.3685 0.3680

— —

0.3518 0.3537

0.3491 0.3503

0.3324 0.3368

3B 2B

0.3360 0.341

0.3426 0.349

0.3518 0.3547

0.3553 0.3591

0.3750 0.3750

3A 2A

0.0000 0.0010

0.3750 0.3740

0.3690 0.3685

— —

0.3547 0.3560

0.3522 0.3528

0.3378 0.3409

3B 2B

0.3410 0.345

0.3469 0.352

0.3547 0.3570

0.3580 0.3612

0.3750 0.3750

2A

0.0009

0.3741

0.3690

—

0.3579

0.3548

0.3443

2B

0.348

0.354

0.3588

0.3628

0.3750

2A 1A

0.0011 0.0014

0.3889 0.4361

0.3822 0.4206

— —

0.3648 0.3897

0.3612 0.3826

0.3448 0.3511

2B 1B

0.350 0.360

0.359 0.376

0.3659 0.3911

0.3706 0.4003

0.3900 0.4375

2A 3A 2A

0.0014 0.0000 0.0014

0.4361 0.4375 0.4361

0.4258 0.4272 0.4267

0.4206 — —

0.3897 0.3911 0.3955

0.3850 0.3876 0.3909

0.3511 0.3525 0.3616

2B 3B 2B

0.360 0.3600 0.370

0.376 0.3717 0.384

0.3911 0.3911 0.3969

0.3972 0.3957 0.4028

0.4375 0.4375 0.4375

UNS

3A 2A

0.0000 0.0013

0.4375 0.4362

0.4281 0.4275

— —

0.3969 0.4001

0.3935 0.3958

0.3630 0.3701

3B 2B

0.3700 0.377

0.3800 0.390

0.3969 0.4014

0.4014 0.4070

0.4375 0.4375

UNF

1A

0.0013

0.4362

0.4240

—

0.4037

0.3975

0.3767

1B

0.383

0.395

0.4050

0.4131

0.4375

UNS

2A 3A 2A

0.0013 0.0000 0.0011

0.4362 0.4375 0.4364

0.4281 0.4294 0.4292

— — —

0.4037 0.4050 0.4093

0.3995 0.4019 0.4055

0.3767 0.3780 0.3868

2B 3B 2B

0.383 0.3830 0.392

0.395 0.3916 0.402

0.4050 0.4050 0.4104

0.4104 0.4091 0.4153

0.4375 0.4375 0.4375

UNS

2A

0.0011

0.4364

0.4297

—

0.4123

0.4087

0.3923

2B

0.397

0.406

0.4134

0.4181

0.4375

UNEF

2A

0.0011

0.4364

0.4299

—

0.4132

0.4096

0.3938

2B

0.399

0.407

0.4143

0.4189

0.4375

3A 2A

0.0000 0.0010

0.4375 0.4365

0.4310 0.4305

— —

0.4143 0.4162

0.4116 0.4128

0.3949 0.3993

3B 2B

0.3990 0.404

0.4051 0.411

0.4143 0.4172

0.4178 0.4216

0.4375 0.4375

3A

0.0000

0.4375

0.4315

—

0.4172

0.4147

0.4003

3B

0.4040

0.4094

0.4172

0.4205

0.4375

7⁄ –18 16 7⁄ –20 16

7⁄ –24 16 7⁄ –27 16 7⁄ –28 16

UN

Min 0.3631

Mine


7⁄ –32 16

UN



3⁄ –32 8

Internalb

Externalb Allowance 0.0011

1726


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 1⁄ –12 UNS 2

Internalb

Externalb

Major Diameter

—

0.4443

Min 0.4389

0.5000 0.4985

0.4886 0.4822

— —

0.4459 0.4485

0.4419 0.4411

0.4008 0.4069

3B 1B

0.4100 0.417

0.4223 0.434

0.4459 0.4500

0.4511 0.4597

0.5000 0.5000

0.0015 0.0000 0.0015

0.4985 0.5000 0.4985

0.4876 0.4891 0.4882

0.4822 — —

0.4485 0.4500 0.4521

0.4435 0.4463 0.4471

0.4069 0.4084 0.4135

2B 3B 2B

0.417 0.4170 0.423

0.434 0.4284 0.438

0.4500 0.4500 0.4536

0.4565 0.4548 0.4601

0.5000 0.5000 0.5000

2A

0.0014

0.4986

0.4892

—

0.4580

0.4533

0.4241

2B

0.432

0.446

0.4594

0.4655

0.5000

UNS

3A 2A

0.0000 0.0013

0.5000 0.4987

0.4906 0.4900

— —

0.4594 0.4626

0.4559 0.4582

0.4255 0.4326

3B 2B

0.4320 0.440

0.4419 0.453

0.4594 0.4639

0.4640 0.4697

0.5000 0.5000

UNF

1A

0.0013

0.4987

0.4865

—

0.4662

0.4598

0.4392

1B

0.446

0.457

0.4675

0.4759

0.5000

UNS

2A 3A 2A

0.0013 0.0000 0.0012

0.4987 0.5000 0.4988

0.4906 0.4919 0.4916

— — —

0.4662 0.4675 0.4717

0.4619 0.4643 0.4678

0.4392 0.4405 0.4492

2B 3B 2B

0.446 0.4460 0.455

0.457 0.4537 0.465

0.4675 0.4675 0.4729

0.4731 0.4717 0.4780

0.5000 0.5000 0.5000

UNS

2A

0.0011

0.4989

0.4922

—

0.4748

0.4711

0.4548

2B

0.460

0.469

0.4759

0.4807

0.5000

UNEF

2A

0.0011

0.4989

0.4924

—

0.4757

0.4720

0.4563

2B

0.461

0.470

0.4768

0.4816

0.5000

UN

3A 2A

0.0000 0.0010

0.5000 0.4990

0.4935 0.4930

— —

0.4768 0.4787

0.4740 0.4752

0.4574 0.4618

3B 2B

0.4610 0.466

0.4676 0.474

0.4768 0.4797

0.4804 0.4842

0.5000 0.5000

UNC

3A 1A

0.0000 0.0016

0.5000 0.5609

0.4940 0.5437

— —

0.4797 0.5068

0.4771 0.4990

0.4628 0.4617

3B 1B

0.4660 0.472

0.4719 0.490

0.4797 0.5084

0.4831 0.5186

0.5000 0.5625

9⁄ –14 UNS 16 9⁄ –16 UN 16

2A 3A 2A

0.0016 0.0000 0.0015

0.5609 0.5625 0.5610

0.5495 0.5511 0.5507

0.5437 — —

0.5068 0.5084 0.5146

0.5016 0.5045 0.5096

0.4617 0.4633 0.4760

2B 3B 2B

0.472 0.4720 0.485

0.490 0.4843 0.501

0.5084 0.5084 0.5161

0.5152 0.5135 0.5226

0.5625 0.5625 0.5625

2A

0.0014

0.5611

0.5517

—

0.5205

0.5158

0.4866

2B

0.495

0.509

0.5219

0.5280

0.5625

9⁄ –18 16

3A 1A

0.0000 0.0014

0.5625 0.5611

0.5531 0.5480

— —

0.5219 0.5250

0.5184 0.5182

0.4880 0.4950

3B 1B

0.4950 0.502

0.5040 0.515

0.5219 0.5264

0.5265 0.5353

0.5625 0.5625

2A 3A

0.0014 0.0000

0.5611 0.5625

0.5524 0.5538

— —

0.5250 0.5264

0.5205 0.5230

0.4950 0.4964

2B 3B

0.502 0.5020

0.515 0.5106

0.5264 0.5264

0.5323 0.5308

0.5625 0.5625

1⁄ –13 2

UNC

1⁄ –14 UNS 2 1⁄ –16 UN 2 1⁄ –18 2 1⁄ –20 2

1⁄ –24 2 1⁄ –27 2 1⁄ –28 2

1⁄ –32 2 9⁄ –12 16

UNF

Class 2A

0.4984

3A 1A

0.0000 0.0015

2A 3A 2A

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 0.410

Max 0.428

Min 0.4459

Max 0.4529

Min 0.5000


1727

Maxd

Major Diameter

Allowance 0.0016


Min 0.4870

Mine



Nominal Size, Threads per Inch, and Series Designationa 9⁄ –20 UN 16 9⁄ –24 16

UNEF

Min 0.5531

Mine

Maxd

—

0.5287

Min 0.5245


0.5544 0.5541

— —

0.5300 0.5342

0.5268 0.5303

0.5030 0.5117

Major Diameter

Class 2A

0.5612

3A 2A

0.0000 0.0012

0.5625 0.5613

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Class 2B

Min 0.508

Max 0.520

Min 0.5300

Max 0.5355

Min 0.5625

3B 2B

0.5080 0.517

0.5162 0.527

0.5300 0.5354

0.5341 0.5405

0.5625 0.5625

0.0000 0.0011

0.5625 0.5614

0.5553 0.5547

— —

0.5354 0.5373

0.5325 0.5336

0.5129 0.5173

3B 2B

0.5170 0.522

0.5244 0.531

0.5354 0.5384

0.5392 0.5432

0.5625 0.5625

0.0011

0.5614

0.5549

—

0.5382

0.5345

0.5188

2B

0.524

0.532

0.5393

0.5441

0.5625

UN

3A 2A

0.0000 0.0010

0.5625 0.5615

0.5560 0.5555

— —

0.5393 0.5412

0.5365 0.5377

0.5199 0.5243

3B 2B

0.5240 0.529

0.5301 0.536

0.5393 0.5422

0.5429 0.5467

0.5625 0.5625

UNC

3A 1A

0.0000 0.0016

0.5625 0.6234

0.5565 0.6052

— —

0.5422 0.5644

0.5396 0.5561

0.5253 0.5152

3B 1B

0.5290 0.527

0.5344 0.546

0.5422 0.5660

0.5456 0.5767

0.5625 0.6250

2A 3A 2A

0.0016 0.0000 0.0016

0.6234 0.6250 0.6234

0.6113 0.6129 0.6120

0.6052 — —

0.5644 0.5660 0.5693

0.5589 0.5619 0.5639

0.5152 0.5168 0.5242

2B 3B 2B

0.527 0.5270 0.535

0.546 0.5391 0.553

0.5660 0.5660 0.5709

0.5732 0.5714 0.5780

0.6250 0.6250 0.6250

9⁄ –32 16

5⁄ –12 8

UN

5⁄ –14 UNS 8 5⁄ –16 UN 8

3A 2A

0.0000 0.0015

0.6250 0.6235

0.6136 0.6132

— —

0.5709 0.5771

0.5668 0.5720

0.5258 0.5385

3B 2B

0.5350 0.548

0.5463 0.564

0.5709 0.5786

0.5762 0.5852

0.6250 0.6250

2A

0.0014

0.6236

0.6142

—

0.5830

0.5782

0.5491

2B

0.557

0.571

0.5844

0.5906

0.6250

5⁄ –18 8

3A 1A

0.0000 0.0014

0.6250 0.6236

0.6156 0.6105

— —

0.5844 0.5875

0.5808 0.5805

0.5505 0.5575

3B 1B

0.5570 0.565

0.5662 0.578

0.5844 0.5889

0.5890 0.5980

0.6250 0.6250

UN

2A 3A 2A

0.0014 0.0000 0.0013

0.6236 0.6250 0.6237

0.6149 0.6163 0.6156

— — —

0.5875 0.5889 0.5912

0.5828 0.5854 0.5869

0.5575 0.5589 0.5642

2B 3B 2B

0.565 0.5650 0.571

0.578 0.5730 0.582

0.5889 0.5889 0.5925

0.5949 0.5934 0.5981

0.6250 0.6250 0.6250

UNEF

3A 2A

0.0000 0.0012

0.6250 0.6238

0.6169 0.6166

— —

0.5925 0.5967

0.5893 0.5927

0.5655 0.5742

3B 2B

0.5710 0.580

0.5787 0.590

0.5925 0.5979

0.5967 0.6031

0.6250 0.6250

3A 2A

0.0000 0.0011

0.6250 0.6239

0.6178 0.6172

— —

0.5979 0.5998

0.5949 0.5960

0.5754 0.5798

3B 2B

0.5800 0.585

0.5869 0.594

0.5979 0.6009

0.6018 0.6059

0.6250 0.6250

2A

0.0011

0.6239

0.6174

—

0.6007

0.5969

0.5813

2B

0.586

0.595

0.6018

0.6067

0.6250

3A

0.0000

0.6250

0.6185

—

0.6018

0.5990

0.5824

3B

0.5860

0.5926

0.6018

0.6055

0.6250

UNF

5⁄ –20 8 5⁄ –24 8

5⁄ –27 UNS 8 5⁄ –28 UN 8



3A 2A 2A

9⁄ –27 UNS 16 9⁄ –28 UN 16

5⁄ –11 8

Internalb


1728


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 5⁄ –32 UN 8

Internalb

Externalb

Min 0.6179

Mine

Maxd

—

0.6036

Min 0.6000


Major Diameter

Class 2A

Allowance 0.0011

0.6239

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Class 2B

Min 0.591

Max 0.599

Min 0.6047

Max 0.6093

Min 0.6250

UN

3A 2A

0.0000 0.0016

0.6250 0.6859

0.6190 0.6745

— —

0.6047 0.6318

0.6020 0.6264

0.5878 0.5867

3B 2B

0.5910 0.597

0.5969 0.615

0.6047 0.6334

0.6082 0.6405

0.6250 0.6875

11⁄ –16 16

UN

3A 2A

0.0000 0.0014

0.6875 0.6861

0.6761 0.6767

— —

0.6334 0.6455

0.6293 0.6407

0.5883 0.6116

3B 2B

0.5970 0.620

0.6085 0.634

0.6334 0.6469

0.6387 0.6531

0.6875 0.6875

UN

3A 2A

0.0000 0.0013

0.6875 0.6862

0.6781 0.6781

— —

0.6469 0.6537

0.6433 0.6494

0.6130 0.6267

3B 2B

0.6200 0.633

0.6284 0.645

0.6469 0.6550

0.6515 0.6606

0.6875 0.6875

UNEF

3A 2A

0.0000 0.0012

0.6875 0.6863

0.6794 0.6791

— —

0.6550 0.6592

0.6518 0.6552

0.6280 0.6367

3B 2B

0.6330 0.642

0.6412 0.652

0.6550 0.6604

0.6592 0.6656

0.6875 0.6875

11⁄ –20 16 11⁄ –24 16

UN

3A 2A

0.0000 0.0011

0.6875 0.6864

0.6803 0.6799

— —

0.6604 0.6632

0.6574 0.6594

0.6379 0.6438

3B 2B

0.6420 0.649

0.6494 0.657

0.6604 0.6643

0.6643 0.6692

0.6875 0.6875

11⁄ –32 16

UN

3A 2A

0.0000 0.0011

0.6875 0.6864

0.6810 0.6804

— —

0.6643 0.6661

0.6615 0.6625

0.6449 0.6492

3B 2B

0.6490 0.654

0.6551 0.661

0.6643 0.6672

0.6680 0.6718

0.6875 0.6875

UNC

3A 1A

0.0000 0.0018

0.6875 0.7482

0.6815 0.7288

— —

0.6672 0.6832

0.6645 0.6744

0.6503 0.6291

3B 1B

0.6540 0.642

0.6594 0.663

0.6672 0.6850

0.6707 0.6965

0.6875 0.7500

UN

2A 3A 2A

0.0018 0.0000 0.0017

0.7482 0.7500 0.7483

0.7353 0.7371 0.7369

0.7288 — —

0.6832 0.6850 0.6942

0.6773 0.6806 0.6887

0.6291 0.6309 0.6491

2B 3B 2B

0.642 0.6420 0.660

0.663 0.6545 0.678

0.6850 0.6850 0.6959

0.6927 0.6907 0.7031

0.7500 0.7500 0.7500

UNS

3A 2A

0.0000 0.0015

0.7500 0.7485

0.7386 0.7382

— —

0.6959 0.7021

0.6918 0.6970

0.6508 0.6635

3B 2B

0.6600 0.673

0.6707 0.688

0.6959 0.7036

0.7013 0.7103

0.7500 0.7500

UNF

1A

0.0015

0.7485

0.7343

—

0.7079

0.7004

0.6740

1B

0.682

0.696

0.7094

0.7192

0.7500

UNS

2A 3A 2A

0.0015 0.0000 0.0014

0.7485 0.7500 0.7486

0.7391 0.7406 0.7399

— — —

0.7079 0.7094 0.7125

0.7029 0.7056 0.7079

0.6740 0.6755 0.6825

2B 3B 2B

0.682 0.6820 0.690

0.696 0.6908 0.703

0.7094 0.7094 0.7139

0.7159 0.7143 0.7199

0.7500 0.7500 0.7500

UNEF

2A

0.0013

0.7487

0.7406

—

0.7162

0.7118

0.6892

2B

0.696

0.707

0.7175

0.7232

0.7500

UNS

3A 2A

0.0000 0.0012

0.7500 0.7488

0.7419 0.7416

— —

0.7175 0.7217

0.7142 0.7176

0.6905 0.6992

3B 2B

0.6960 0.705

0.7037 0.715

0.7175 0.7229

0.7218 0.7282

0.7500 0.7500

UNS

2A

0.0012

0.7488

0.7421

—

0.7247

0.7208

0.7047

2B

0.710

0.719

0.7259

0.7310

0.7500

3⁄ –10 4

3⁄ –12 4 3⁄ –14 4 3⁄ –16 4

3⁄ –18 4 3⁄ –20 4

3⁄ –24 4 3⁄ –27 4


1729

11⁄ –28 16


11⁄ –12 16


Nominal Size, Threads per Inch, and Series Designationa 3⁄ –28 UN 4

0.7256

Min 0.7218

0.7500 0.7489

0.7435 0.7429

— —

0.7268 0.7286

0.7239 0.7250

0.7074 0.7117

3B 2B

0.7110 0.716

0.7176 0.724

0.7268 0.7297

0.7305 0.7344

0.7500 0.7500

0.0000 0.0017

0.7500 0.8108

0.7440 0.7994

— —

0.7297 0.7567

0.7270 0.7512

0.7128 0.7116

3B 2B

0.7160 0.722

0.7219 0.740

0.7297 0.7584

0.7333 0.7656

0.7500 0.8125

0.0000 0.0015

0.8125 0.8110

0.8011 0.8016

— —

0.7584 0.7704

0.7543 0.7655

0.7133 0.7365

3B 2B

0.7220 0.745

0.7329 0.759

0.7584 0.7719

0.7638 0.7782

0.8125 0.8125

3A 2A

0.0000 0.0013

0.8125 0.8112

0.8031 0.8031

— —

0.7719 0.7787

0.7683 0.7743

0.7380 0.7517

3B 2B

0.7450 0.758

0.7533 0.770

0.7719 0.7800

0.7766 0.7857

0.8125 0.8125

0.0000 0.0011

UN

3A 2A

UN

3A 2A

UNEF

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 0.711

Max 0.720

Min 0.7268

Max 0.7318

Min 0.7500

13⁄ –28 16

UN

3A 2A

0.0000 0.0012

0.8125 0.8113

0.8044 0.8048

— —

0.7800 0.7881

0.7767 0.7843

0.7530 0.7687

3B 2B

0.7580 0.774

0.7662 0.782

0.7800 0.7893

0.7843 0.7943

0.8125 0.8125

13⁄ –32 16

UN

3A 2A

0.0000 0.0011

0.8125 0.8114

0.8060 0.8054

— —

0.7893 0.7911

0.7864 0.7875

0.7699 0.7742

3B 2B

0.7740 0.779

0.7801 0.786

0.7893 0.7922

0.7930 0.7969

0.8125 0.8125

UNC

3A 1A

0.0000 0.0019

0.8125 0.8731

0.8065 0.8523

— —

0.7922 0.8009

0.7895 0.7914

0.7753 0.7408

3B 1B

0.7790 0.755

0.7844 0.778

0.7922 0.8028

0.7958 0.8151

0.8125 0.8750

7⁄ –10 UNS 8 7⁄ –12 UN 8

2A 3A 2A

0.0019 0.0000 0.0018

0.8731 0.8750 0.8732

0.8592 0.8611 0.8603

0.8523 — —

0.8009 0.8028 0.8082

0.7946 0.7981 0.8022

0.7408 0.7427 0.7542

2B 3B 2B

0.755 0.7550 0.767

0.778 0.7681 0.788

0.8028 0.8028 0.8100

0.8110 0.8089 0.8178

0.8750 0.8750 0.8750

2A

0.0017

0.8733

0.8619

—

0.8192

0.8137

0.7741

2B

0.785

0.803

0.8209

0.8281

0.8750

7⁄ –14 8

3A 1A

0.0000 0.0016

0.8750 0.8734

0.8636 0.8579

— —

0.8209 0.8270

0.8168 0.8189

0.7758 0.7884

3B 1B

0.7850 0.798

0.7948 0.814

0.8209 0.8286

0.8263 0.8392

0.8750 0.8750

UN

2A 3A 2A

0.0016 0.0000 0.0015

0.8734 0.8750 0.8735

0.8631 0.8647 0.8641

— — —

0.8270 0.8286 0.8329

0.8216 0.8245 0.8280

0.7884 0.7900 0.7900

2B 3B 2B

0.798 0.7980 0.807

0.814 0.8068 0.821

0.8286 0.8286 0.8344

0.8356 0.8339 0.8407

0.8750 0.8750 0.8750

UNS

3A 2A

0.0000 0.0014

0.8750 0.8736

0.8656 0.8649

— —

0.8344 0.8375

0.8308 0.8329

0.8005 0.8075

3B 2B

0.8070 0.815

0.8158 0.828

0.8344 0.8389

0.8391 0.8449

0.8750 0.8750

UNEF

2A

0.0013

0.8737

0.8656

—

0.8412

0.8368

0.8142

2B

0.821

0.832

0.8425

0.8482

0.8750

3A

0.0000

0.8750

0.8669

—

0.8425

0.8392

0.8155

3B

0.8210

0.8287

0.8425

0.8468

0.8750

7⁄ –9 8

UNF

7⁄ –16 8 7⁄ –18 8 7⁄ –20 8



—

3A 2A

13⁄ –16 16 13⁄ –20 16

Min 0.7423

Maxd

Major Diameter 0.7488

13⁄ –12 16

Major Diameter

Mine


Class 2A

UN

Internalb


3⁄ –32 4

1730


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Internalb

Externalb

Nominal Size, Threads per Inch, and Series Designationa 7⁄ –24 UNS 8

Class 2A

7⁄ –27 UNS 8 7⁄ –28 UN 8

2A

0.0012

0.8738

0.8671

—

0.8497

0.8458

0.8297

2B

0.835

0.844

0.8509

0.8560

0.8750

2A

0.0012

0.8738

0.8673

—

0.8506

0.8468

0.8312

2B

0.836

0.845

0.8518

0.8568

0.8750

3A 2A

0.0000 0.0011

0.8750 0.8739

0.8685 0.8679

— —

0.8518 0.8536

0.8489 0.8500

0.8324 0.8367

3B 2B

0.8360 0.841

0.8426 0.849

0.8518 0.8547

0.8555 0.8594

0.8750 0.8750

7⁄ –32 8

UN

Allowance 0.0012

Major Diameter Maxd 0.8738

Min 0.8666

Pitch Diameter Mine

Maxd

—

0.8467

Min 0.8426


Minor Diameter Class 2B

Min 0.830

Max 0.840

Pitch Diameter Min 0.8479

Max 0.8532

Major Diameter Min 0.8750

UN

3A 2A

0.0000 0.0017

0.8750 0.9358

0.8690 0.9244

— —

0.8547 0.8817

0.8520 0.8760

0.8378 0.8366

3B 2B

0.8410 0.847

0.8469 0.865

0.8547 0.8834

0.8583 0.8908

0.8750 0.9375

15⁄ –16 16

UN

3A 2A

0.0000 0.0015

0.9375 0.9360

0.9261 0.9266

— —

0.8834 0.8954

0.8793 0.8904

0.8383 0.8615

3B 2B

0.8470 0.870

0.8575 0.884

0.8834 0.8969

0.8889 0.9034

0.9375 0.9375

UNEF

3A 2A

0.0000 0.0014

0.9375 0.9361

0.9281 0.9280

— —

0.8969 0.9036

0.8932 0.8991

0.8630 0.8766

3B 2B

0.8700 0.883

0.8783 0.895

0.8969 0.9050

0.9018 0.9109

0.9375 0.9375

15⁄ –20 16

UN

3A 2A

0.0000 0.0012

0.9375 0.9363

0.9294 0.9298

— —

0.9050 0.9131

0.9016 0.9091

0.8780 0.8937

3B 2B

0.8830 0.899

0.8912 0.907

0.9050 0.9143

0.9094 0.9195

0.9375 0.9375

15⁄ –32 16

UN

3A 2A

0.0000 0.0011

0.9375 0.9364

0.9310 0.9304

— —

0.9143 0.9161

0.9113 0.9123

0.8949 0.8992

3B 2B

0.8990 0.904

0.9051 0.911

0.9143 0.9172

0.9182 0.9221

0.9375 0.9375

3A 1A 2A 3A 2A 1A 2A 3A 1A 2A 3A 2A 3A 2A

0.0000 0.0020 0.0020 0.0000 0.0018 0.0018 0.0018 0.0000 0.0017 0.0017 0.0000 0.0015 0.0000 0.0014

0.9375 0.9980 0.9980 1.0000 0.9982 0.9982 0.9982 1.0000 0.9983 0.9983 1.0000 0.9985 1.0000 0.9986

0.9315 0.9755 0.9830 0.9850 0.9853 0.9810 0.9868 0.9886 0.9828 0.9880 0.9897 0.9891 0.9906 0.9899

— — 0.9755 — — — — — — — — — — —

0.9172 0.9168 0.9168 0.9188 0.9332 0.9441 0.9441 0.9459 0.9519 0.9519 0.9536 0.9579 0.9594 0.9625

0.9144 0.9067 0.9100 0.9137 0.9270 0.9353 0.9382 0.9415 0.9435 0.9463 0.9494 0.9529 0.9557 0.9578

0.9003 0.8492 0.8492 0.8512 0.8792 0.8990 0.8990 0.9008 0.9132 0.9132 0.9149 0.9240 0.9255 0.9325

3B 1B 2B 3B 2B 1B 2B 3B 1B 2B 3B 2B 3B 2B

0.9040 0.865 0.865 0.8650 0.892 0.910 0.910 0.9100 0.923 0.923 0.9230 0.932 0.9320 0.940

0.9094 0.890 0.890 0.8797 0.913 0.928 0.928 0.9198 0.938 0.938 0.9315 0.946 0.9408 0.953

0.9172 0.9188 0.9188 0.9188 0.9350 0.9459 0.9459 0.9459 0.9536 0.9536 0.9536 0.9594 0.9594 0.9639

0.9209 0.9320 0.9276 0.9254 0.9430 0.9573 0.9535 0.9516 0.9645 0.9609 0.9590 0.9659 0.9643 0.9701

0.9375 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

1–8 UNC

1–10 UNS 1–12 UNF

1–14 UNSf

1–16 UN 1–18 UNS


1731

15⁄ –28 16


15⁄ –12 16


Nominal Size, Threads per Inch, and Series Designationa 1–20 UNEF

1732

Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Internalb

Externalb

Major Diameter

Maxd

— — — — — — — — —

0.9661 0.9675 0.9716 0.9747 0.9756 0.9768 0.9786 0.9797 0.9793

Min 0.9616 0.9641 0.9674 0.9707 0.9716 0.9738 0.9748 0.9769 0.9725

1.0625 1.0608

1.0475 1.0494

— —

0.9813 1.0067

0.9762 1.0010

0.9137 0.9616

3B 2B

0.9270 0.972

0.9422 0.990

0.9813 1.0084

0.9880 1.0158

1.0625 1.0625

0.0000 0.0015

1.0625 1.0610

1.0511 1.0516

— —

1.0084 1.0204

1.0042 1.0154

0.9633 0.9865

3B 2B

0.9720 0.995

0.9823 1.009

1.0084 1.0219

1.0139 1.0284

1.0625 1.0625

3A 2A

0.0000 0.0014

1.0625 1.0611

1.0531 1.0524

— —

1.0219 1.0250

1.0182 1.0203

0.9880 0.9950

3B 2B

0.9950 1.002

1.0033 1.015

1.0219 1.0264

1.0268 1.0326

1.0625 1.0625

11⁄16–20 UN

3A 2A

0.0000 0.0014

1.0625 1.0611

1.0538 1.0530

— —

1.0264 1.0286

1.0228 1.0241

0.9964 1.0016

3B 2B

1.0020 1.008

1.0105 1.020

1.0264 1.0300

1.0310 1.0359

1.0625 1.0625

11⁄16–28 UN

3A 2A

0.0000 0.0012

1.0625 1.0613

1.0544 1.0548

— —

1.0300 1.0381

1.0266 1.0341

1.0030 1.0187

3B 2B

1.0080 1.024

1.0162 1.032

1.0300 1.0393

1.0344 1.0445

1.0625 1.0625

11⁄8–7 UNC

3A 1A

0.0000 0.0022

1.0625 1.1228

1.0560 1.0982

— —

1.0393 1.0300

1.0363 1.0191

1.0199 0.9527

3B 1B

1.0240 0.970

1.0301 0.998

1.0393 1.0322

1.0432 1.0463

1.0625 1.1250

11⁄8–8 UN

2A 3A 2A

0.0022 0.0000 0.0021

1.1228 1.1250 1.1229

1.1064 1.1086 1.1079

1.0982 — 1.1004

1.0300 1.0322 1.0417

1.0228 1.0268 1.0348

0.9527 0.9549 0.9741

2B 3B 2B

0.970 0.9700 0.990

0.998 0.9875 1.015

1.0322 1.0322 1.0438

1.0416 1.0393 1.0528

1.1250 1.1250 1.1250

11⁄8–10 UNS

3A 2A

0.0000 0.0018

1.1250 1.1232

1.1100 1.1103

— —

1.0438 1.0582

1.0386 1.0520

0.9762 1.0042

3B 2B

0.9900 1.017

1.0047 1.038

1.0438 1.0600

1.0505 1.0680

1.1250 1.1250

11⁄8–12 UNF

1A

0.0018

1.1232

1.1060

—

1.0691

1.0601

1.0240

1B

1.035

1.053

1.0709

1.0826

1.1250

2A 3A

0.0018 0.0000

1.1232 1.1250

1.1118 1.1136

— —

1.0691 1.0709

1.0631 1.0664

1.0240 1.0258

2B 3B

1.035 1.0350

1.053 1.0448

1.0709 1.0709

1.0787 1.0768

1.1250 1.1250

Major Diameter

11⁄16–8 UN

Class 2A 3A 2A 2A 2A 3A 2A 3A 2A

Allowance 0.0014 0.0000 0.0013 0.0012 0.0012 0.0000 0.0011 0.0000 0.0020

0.9986 1.0000 0.9987 0.9988 0.9988 1.0000 0.9989 1.0000 1.0605

11⁄16–12 UN

3A 2A

0.0000 0.0017

11⁄16–16 UN

3A 2A

11⁄16–18 UNEF

1–24 UNS 1–27 UNS 1–28 UN 1–32 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B 3B 2B 2B 2B 3B 2B 3B 2B

Min 0.946 0.9460 0.955 0.960 0.961 0.9610 0.966 0.9660 0.927

Max 0.957 0.9537 0.965 0.969 0.970 0.9676 0.974 0.9719 0.952

Min 0.9675 0.9675 0.9729 0.9759 0.9768 0.9768 0.9797 0.9797 0.9813

Max 0.9734 0.9719 0.9784 0.9811 0.9820 0.9807 0.9846 0.9834 0.9902

Min 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0625



Min 0.9905 0.9919 0.9915 0.9921 0.9923 0.9935 0.9929 0.9940 1.0455

Mine

UNR Minor Dia.,c Max (Ref.) 0.9391 0.9405 0.9491 0.9547 0.9562 0.9574 0.9617 0.9628 0.9117

Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 11⁄8–14 UNS

Maxd

—

1.0770

Min 1.0717

1.1235

1.1141

—

1.0829

1.0779

1.0490

1.1250 1.1236

1.1156 1.1149

— —

1.0844 1.0875

1.0807 1.0828

1.0505 1.0575

0.0000 0.0014

1.1250 1.1236

1.1163 1.1155

— —

1.0889 1.0911

1.0853 1.0866

0.0000 0.0013

1.1250 1.1237

1.1169 1.1165

— —

1.0925 1.0966

1.0891 1.0924

Major Diameter

Class 2A

1.1234

UN

2A

0.0015

UNEF

3A 2A

0.0000 0.0014

11⁄8–20 UN

3A 2A

11⁄8–24 UNS

3A 2A

11⁄8–18

11⁄8–28

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Min 1.048

Max 1.064

Min 1.0786

Max 1.0855

Min 1.1250

2B

1.057

1.071

1.0844

1.0909

1.1250

3B 2B

1.0570 1.065

1.0658 1.078

1.0844 1.0889

1.0893 1.0951

1.1250 1.1250

1.0589 1.0641

3B 2B

1.0650 1.071

1.0730 1.082

1.0889 1.0925

1.0935 1.0984

1.1250 1.1250

1.0655 1.0742

3B 2B

1.0710 1.080

1.0787 1.090

1.0925 1.0979

1.0969 1.1034

1.1250 1.1250

Class 2B

2A

0.0012

1.1238

1.1173

—

1.1006

1.0966

1.0812

2B

1.086

1.095

1.1018

1.1070

1.1250

UN

3A 2A

0.0000 0.0021

1.1250 1.1854

1.1185 1.1704

— —

1.1018 1.1042

1.0988 1.0972

1.0824 1.0366

3B 2B

1.0860 1.052

1.0926 1.077

1.1018 1.1063

1.1057 1.1154

1.1250 1.1875

13⁄16–12

UN

3A 2A

0.0000 0.0017

1.1875 1.1858

1.1725 1.1744

— —

1.1063 1.1317

1.1011 1.1259

1.0387 1.0866

3B 2B

1.0520 1.097

1.0672 1.115

1.1063 1.1334

1.1131 1.1409

1.1875 1.1875

13⁄16–16 UN

3A 2A

0.0000 0.0015

1.1875 1.1860

1.1761 1.1766

— —

1.1334 1.1454

1.1291 1.1403

1.0883 1.1115

3B 2B

1.0970 1.120

1.1073 1.134

1.1334 1.1469

1.1390 1.1535

1.1875 1.1875

13⁄16–18 UNEF

3A 2A

0.0000 0.0015

1.1875 1.1860

1.1781 1.1773

— —

1.1469 1.1499

1.1431 1.1450

1.1130 1.1199

3B 2B

1.1200 1.127

1.1283 1.140

1.1469 1.1514

1.1519 1.1577

1.1875 1.1875

13⁄16–20 UN

3A 2A

0.0000 0.0014

1.1875 1.1861

1.1788 1.1780

— —

1.1514 1.1536

1.1478 1.1489

1.1214 1.1266

3B 2B

1.1270 1.133

1.1355 1.145

1.1514 1.1550

1.1561 1.1611

1.1875 1.1875

13⁄16–28 UN

3A 2A

0.0000 0.0012

1.1875 1.1863

1.1794 1.1798

— —

1.1550 1.1631

1.1515 1.1590

1.1280 1.1437

3B 2B

1.1330 1.149

1.1412 1.157

1.1550 1.1643

1.1595 1.1696

1.1875 1.1875

11⁄4–7 UNC

3A 1A

0.0000 0.0022

1.1875 1.2478

1.1810 1.2232

— —

1.1643 1.1550

1.1612 1.1439

1.1449 1.0777

3B 1B

1.1490 1.095

1.1551 1.123

1.1643 1.1572

1.1683 1.1716

1.1875 1.2500

11⁄4–8 UN

2A 3A 2A

0.0022 0.0000 0.0021

1.2478 1.2500 1.2479

1.2314 1.2336 1.2329

1.2232 — 1.2254

1.1550 1.1572 1.1667

1.1476 1.1517 1.1597

1.0777 1.0799 1.0991

2B 3B 2B

1.095 1.0950 1.115

1.123 1.1125 1.140

1.1572 1.1572 1.1688

1.1668 1.1644 1.1780

1.2500 1.2500 1.2500

11⁄4–10 UNS

3A 2A

0.0000 0.0019

1.2500 1.2481

1.2350 1.2352

— —

1.1688 1.1831

1.1635 1.1768

1.1012 1.1291

3B 2B

1.1150 1.142

1.1297 1.163

1.1688 1.1850

1.1757 1.1932

1.2500 1.2500


1733

UN

13⁄16–8


Min 1.1131

Mine


Allowance 0.0016

11⁄8–16

Internalb

Externalb


Nominal Size, Threads per Inch, and Series Designationa 11⁄4–12 UNF

1734


Externalb

Major Diameter

Maxd

—

1.1941

Min 1.1849

1.2482 1.2500 1.2484

1.2368 1.2386 1.2381

— — —

1.1941 1.1959 1.2020

1.1879 1.1913 1.1966

1.1490 1.1508 1.1634

2B 3B 2B

1.160 1.1600 1.173

1.178 1.1698 1.188

1.1959 1.1959 1.2036

1.2039 1.2019 1.2106

1.2500 1.2500 1.2500

0.0015

1.2485

1.2391

—

1.2079

1.2028

1.1740

2B

1.182

1.196

1.2094

1.2160

1.2500

0.0000 0.0015

1.2500 1.2485

1.2406 1.2398

— —

1.2094 1.2124

1.2056 1.2075

1.1755 1.1824

3B 2B

1.1820 1.190

1.1908 1.203

1.2094 1.2139

1.2144 1.2202

1.2500 1.2500

3A 2A

0.0000 0.0014

1.2500 1.2486

1.2413 1.2405

— —

1.2139 1.2161

1.2103 1.2114

1.1839 1.1891

3B 2B

1.1900 1.196

1.1980 1.207

1.2139 1.2175

1.2186 1.2236

1.2500 1.2500

11⁄4–24 UNS

3A 2A

0.0000 0.0013

1.2500 1.2487

1.2419 1.2415

— —

1.2175 1.2216

1.2140 1.2173

1.1905 1.1991

3B 2B

1.1960 1.205

1.2037 1.215

1.2175 1.2229

1.2220 1.2285

1.2500 1.2500

11⁄4–28 UN

2A

0.0012

1.2488

1.2423

—

1.2256

1.2215

1.2062

2B

1.211

1.220

1.2268

1.2321

1.2500

15⁄16–8 UN

3A 2A

0.0000 0.0021

1.2500 1.3104

1.2435 1.2954

— —

1.2268 1.2292

1.2237 1.2221

1.2074 1.1616

3B 2B

1.2110 1.177

1.2176 1.202

1.2268 1.2313

1.2308 1.2405

1.2500 1.3125

15⁄16–12 UN

3A 2A

0.0000 0.0017

1.3125 1.3108

1.2975 1.2994

— —

1.2313 1.2567

1.2260 1.2509

1.1637 1.2116

3B 2B

1.1770 1.222

1.1922 1.240

1.2313 1.2584

1.2382 1.2659

1.3125 1.3125

15⁄16–16 UN

3A 2A

0.0000 0.0015

1.3125 1.3110

1.3011 1.3016

— —

1.2584 1.2704

1.2541 1.2653

1.2133 1.2365

3B 2B

1.2220 1.245

1.2323 1.259

1.2584 1.2719

1.2640 1.2785

1.3125 1.3125

15⁄16–18 UNEF

3A 2A

0.0000 0.0015

1.3125 1.3110

1.3031 1.3023

— —

1.2719 1.2749

1.2681 1.2700

1.2380 1.2449

3B 2B

1.2450 1.252

1.2533 1.265

1.2719 1.2764

1.2769 1.2827

1.3125 1.3125

15⁄16–20 UN

3A 2A

0.0000 0.0014

1.3125 1.3111

1.3038 1.3030

— —

1.2764 1.2786

1.2728 1.2739

1.2464 1.2516

3B 2B

1.2520 1.258

1.2605 1.270

1.2764 1.2800

1.2811 1.2861

1.3125 1.3125

15⁄16–28 UN

3A 2A

0.0000 0.0012

1.3125 1.3113

1.3044 1.3048

— —

1.2800 1.2881

1.2765 1.2840

1.2530 1.2687

3B 2B

1.2580 1.274

1.2662 1.282

1.2800 1.2893

1.2845 1.2946

1.3125 1.3125

13⁄8–6 UNC

3A 1A

0.0000 0.0024

1.3125 1.3726

1.3060 1.3453

— —

1.2893 1.2643

1.2862 1.2523

1.2699 1.1742

3B 1B

1.2740 1.195

1.2801 1.225

1.2893 1.2667

1.2933 1.2822

1.3125 1.3750

2A 3A

0.0024 0.0000

1.3726 1.3750

1.3544 1.3568

1.3453 —

1.2643 1.2667

1.2563 1.2607

1.1742 1.1766

2B 3B

1.195 1.1950

1.225 1.2146

1.2667 1.2667

1.2771 1.2745

1.3750 1.3750

Major Diameter

Class 1A

Allowance 0.0018

1.2482

11⁄4–14 UNS

2A 3A 2A

0.0018 0.0000 0.0016

11⁄4–16 UN

2A

11⁄4–18 UNEF

3A 2A

11⁄4–20 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 1B

Min 1.160

Max 1.178

Min 1.1959

Max 1.2079

Min 1.2500



Min 1.2310

Mine


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 13⁄8–8 UN

Internalb

Externalb

Major Diameter

1.3503

1.2916

Min 1.2844

1.3750 1.3731

1.3600 1.3602

— —

1.2938 1.3081

1.2884 1.3018

1.2262 1.2541

3B 2B

1.2400 1.267

1.2547 1.288

1.2938 1.3100

1.3008 1.3182

1.3750 1.3750

0.0019

1.3731

1.3559

—

1.3190

1.3096

1.2739

1B

1.285

1.303

1.3209

1.3332

1.3750

0.0019 0.0000 0.0016

1.3731 1.3750 1.3734

1.3617 1.3636 1.3631

— — —

1.3190 1.3209 1.3270

1.3127 1.3162 1.3216

1.2739 1.2758 1.2884

2B 3B 2B

1.285 1.2850 1.298

1.303 1.2948 1.314

1.3209 1.3209 1.3286

1.3291 1.3270 1.3356

1.3750 1.3750 1.3750

2A

0.0015

1.3735

1.3641

—

1.3329

1.3278

1.2990

2B

1.307

1.321

1.3344

1.3410

1.3750

13⁄8–18 UNEF

3A 2A

0.0000 0.0015

1.3750 1.3735

1.3656 1.3648

— —

1.3344 1.3374

1.3306 1.3325

1.3005 1.3074

3B 2B

1.3070 1.315

1.3158 1.328

1.3344 1.3389

1.3394 1.3452

1.3750 1.3750

13⁄8–20 UN

3A 2A

0.0000 0.0014

1.3750 1.3736

1.3663 1.3655

— —

1.3389 1.3411

1.3353 1.3364

1.3089 1.3141

3B 2B

1.3150 1.321

1.3230 1.332

1.3389 1.3425

1.3436 1.3486

1.3750 1.3750

13⁄8–24 UNS

3A 2A

0.0000 0.0013

1.3750 1.3737

1.3669 1.3665

— —

1.3425 1.3466

1.3390 1.3423

1.3155 1.3241

3B 2B

1.3210 1.330

1.3287 1.340

1.3425 1.3479

1.3470 1.3535

1.3750 1.3750

13⁄8–28 UN

2A

0.0012

1.3738

1.3673

—

1.3506

1.3465

1.3312

2B

1.336

1.345

1.3518

1.3571

1.3750

17⁄16–6 UN

3A 2A

0.0000 0.0024

1.3750 1.4351

1.3685 1.4169

— —

1.3518 1.3268

1.3487 1.3188

1.3324 1.2367

3B 2B

1.3360 1.257

1.3426 1.288

1.3518 1.3292

1.3558 1.3396

1.3750 1.4375

17⁄16–8 UN

3A 2A

0.0000 0.0022

1.4375 1.4353

1.4193 1.4203

— —

1.3292 1.3541

1.3232 1.3469

1.2391 1.2865

3B 2B

1.2570 1.302

1.2771 1.327

1.3292 1.3563

1.3370 1.3657

1.4375 1.4375

17⁄16–12 UN

3A 2A

0.0000 0.0018

1.4375 1.4357

1.4225 1.4243

— —

1.3563 1.3816

1.3509 1.3757

1.2887 1.3365

3B 2B

1.3020 1.347

1.3172 1.365

1.3563 1.3834

1.3634 1.3910

1.4375 1.4375

17⁄16–16 UN

3A 2A

0.0000 0.0016

1.4375 1.4359

1.4261 1.4265

— —

1.3834 1.3953

1.3790 1.3901

1.3383 1.3614

3B 2B

1.3470 1.370

1.3573 1.384

1.3834 1.3969

1.3891 1.4037

1.4375 1.4375

17⁄16–18 UNEF

3A 2A

0.0000 0.0015

1.4375 1.4360

1.4281 1.4273

— —

1.3969 1.3999

1.3930 1.3949

1.3630 1.3699

3B 2B

1.3700 1.377

1.3783 1.390

1.3969 1.4014

1.4020 1.4079

1.4375 1.4375

17⁄16–20 UN

3A 2A

0.0000 0.0014

1.4375 1.4361

1.4288 1.4280

— —

1.4014 1.4036

1.3977 1.3988

1.3714 1.3766

3B 2B

1.3770 1.383

1.3855 1.395

1.4014 1.4050

1.4062 1.4112

1.4375 1.4375

3A

0.0000

1.4375

1.4294

—

1.4050

1.4014

1.3780

3B

1.3830

1.3912

1.4050

1.4096

1.4375

Class 2A

1.3728

13⁄8–10 UNS

3A 2A

0.0000 0.0019

13⁄8–12

UNF

1A

13⁄8–14 UNS

2A 3A 2A

13⁄8–16 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 1.240

Max 1.265

Min 1.2938

Max 1.3031

Min 1.3750


1735

Maxd

Major Diameter

Allowance 0.0022


Min 1.3578

Mine



Nominal Size, Threads per Inch, and Series Designationa 17⁄16–28 UN

1736


Externalb

Major Diameter

Maxd

—

1.4130

Min 1.4088

1.4375 1.4976

1.4310 1.4703

— —

1.4143 1.3893

1.4112 1.3772

1.3949 1.2992

3B 1B

1.3990 1.320

1.4051 1.350

1.4143 1.3917

1.4184 1.4075

1.4375 1.5000

0.0024 0.0000 0.0022

1.4976 1.5000 1.4978

1.4794 1.4818 1.4828

1.4703 — 1.4753

1.3893 1.3917 1.4166

1.3812 1.3856 1.4093

1.2992 1.3016 1.3490

2B 3B 2B

1.320 1.3200 1.365

1.350 1.3396 1.390

1.3917 1.3917 1.4188

1.4022 1.3996 1.4283

1.5000 1.5000 1.5000

3A 2A

0.0000 0.0019

1.5000 1.4981

1.4850 1.4852

— —

1.4188 1.4331

1.4133 1.4267

1.3512 1.3791

3B 2B

1.3650 1.392

1.3797 1.413

1.4188 1.4350

1.4259 1.4433

1.5000 1.5000

11⁄2–12 UNF

1A

0.0019

1.4981

1.4809

—

1.4440

1.4344

1.3989

1B

1.410

1.428

1.4459

1.4584

1.5000

11⁄2–14 UNS

2A 3A 2A

0.0019 0.0000 0.0017

1.4981 1.5000 1.4983

1.4867 1.4886 1.4880

— — —

1.4440 1.4459 1.4519

1.4376 1.4411 1.4464

1.3989 1.4008 1.4133

2B 3B 2B

1.410 1.4100 1.423

1.428 1.4198 1.438

1.4459 1.4459 1.4536

1.4542 1.4522 1.4608

1.5000 1.5000 1.5000

11⁄2–16 UN

2A

0.0016

1.4984

1.4890

—

1.4578

1.4526

1.4239

2B

1.432

1.446

1.4594

1.4662

1.5000

11⁄2–18 UNEF

3A 2A

0.0000 0.0015

1.5000 1.4985

1.4906 1.4898

— —

1.4594 1.4624

1.4555 1.4574

1.4255 1.4324

3B 2B

1.4320 1.440

1.4408 1.452

1.4594 1.4639

1.4645 1.4704

1.5000 1.5000

11⁄2–20 UN

3A 2A

0.0000 0.0014

1.5000 1.4986

1.4913 1.4905

— —

1.4639 1.4661

1.4602 1.4613

1.4339 1.4391

3B 2B

1.4400 1.446

1.4480 1.457

1.4639 1.4675

1.4687 1.4737

1.5000 1.5000

11⁄2–24 UNS

3A 2A

0.0000 0.0013

1.5000 1.4987

1.4919 1.4915

— —

1.4675 1.4716

1.4639 1.4672

1.4405 1.4491

3B 2B

1.4460 1.455

1.4537 1.465

1.4675 1.4729

1.4721 1.4787

1.5000 1.5000

11⁄2–28 UN

2A

0.0013

1.4987

1.4922

—

1.4755

1.4713

1.4561

2B

1.461

1.470

1.4768

1.4823

1.5000

19⁄16–6 UN

3A 2A

0.0000 0.0024

1.5000 1.5601

1.4935 1.5419

— —

1.4768 1.4518

1.4737 1.4436

1.4574 1.3617

3B 2B

1.4610 1.382

1.4676 1.413

1.4768 1.4542

1.4809 1.4648

1.5000 1.5625

19⁄16–8 UN

3A 2A

0.0000 0.0022

1.5625 1.5603

1.5443 1.5453

— —

1.4542 1.4791

1.4481 1.4717

1.3641 1.4115

3B 2B

1.3820 1.427

1.4021 1.452

1.4542 1.4813

1.4622 1.4909

1.5625 1.5625

19⁄16–12 UN

3A 2A

0.0000 0.0018

1.5625 1.5607

1.5475 1.5493

— —

1.4813 1.5066

1.4758 1.5007

1.4137 1.4615

3B 2B

1.4270 1.472

1.4422 1.490

1.4813 1.5084

1.4885 1.5160

1.5625 1.5625

3A

0.0000

1.5625

1.5511

—

1.5084

1.5040

1.4633

3B

1.4720

1.4823

1.5084

1.5141

1.5625

Major Diameter

Class 2A

Allowance 0.0013

1.4362

11⁄2–6 UNC

3A 1A

0.0000 0.0024

11⁄2–8 UN

2A 3A 2A

11⁄2–10 UNS

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 1.399

Max 1.407

Min 1.4143

Max 1.4198

Min 1.4375



Min 1.4297

Mine



Internalb

Externalb

Major Diameter

—

1.5203

Min 1.5151

1.5625 1.5610

1.5531 1.5523

— —

1.5219 1.5249

1.5180 1.5199

1.4880 1.4949

3B 2B

1.4950 1.502

1.5033 1.515

1.5219 1.5264

1.5270 1.5329

1.5625 1.5625

0.0000 0.0014

1.5625 1.5611

1.5538 1.5530

— —

1.5264 1.5286

1.5227 1.5238

1.4964 1.5016

3B 2B

1.5020 1.508

1.5105 1.520

1.5264 1.5300

1.5312 1.5362

1.5625 1.5625

0.0000 0.0025

1.5625 1.6225

1.5544 1.6043

— —

1.5300 1.5142

1.5264 1.5060

1.5030 1.4246

3B 2B

1.5080 1.445

1.5162 1.475

1.5300 1.5167

1.5346 1.5274

1.5625 1.6250

3A 2A

0.0000 0.0022

1.6250 1.6228

1.6068 1.6078

— 1.6003

1.5167 1.5416

1.5105 1.5342

1.4271 1.4784

3B 2B

1.4450 1.490

1.4646 1.515

1.5167 1.5438

1.5247 1.5535

1.6250 1.6250

15⁄8–10 UNS

3A 2A

0.0000 0.0019

1.6250 1.6231

1.6100 1.6102

— —

1.5438 1.5581

1.5382 1.5517

1.4806 1.5041

3B 2B

1.4900 1.517

1.5047 1.538

1.5438 1.5600

1.5510 1.5683

1.6250 1.6250

15⁄8–12 UN

2A

0.0018

1.6232

1.6118

—

1.5691

1.5632

1.5240

2B

1.535

1.553

1.5709

1.5785

1.6250

15⁄8–14 UNS

3A 2A

0.0000 0.0017

1.6250 1.6233

1.6136 1.6130

— —

1.5709 1.5769

1.5665 1.5714

1.5258 1.5383

3B 2B

1.5350 1.548

1.5448 1.564

1.5709 1.5786

1.5766 1.5858

1.6250 1.6250

15⁄8–16 UN

2A

0.0016

1.6234

1.6140

—

1.5828

1.5776

1.5489

2B

1.557

1.571

1.5844

1.5912

1.6250

15⁄8–18 UNEF

3A 2A

0.0000 0.0015

1.6250 1.6235

1.6156 1.6148

— —

1.5844 1.5874

1.5805 1.5824

1.5505 1.5574

3B 2B

1.5570 1.565

1.5658 1.578

1.5844 1.5889

1.5895 1.5954

1.6250 1.6250

15⁄8–20 UN

3A 2A

0.0000 0.0014

1.6250 1.6236

1.6163 1.6155

— —

1.5889 1.5911

1.5852 1.5863

1.5589 1.5641

3B 2B

1.5650 1.571

1.5730 1.582

1.5889 1.5925

1.5937 1.5987

1.6250 1.6250

15⁄8–24 UNS

3A 2A

0.0000 0.0013

1.6250 1.6237

1.6169 1.6165

— —

1.5925 1.5966

1.5889 1.5922

1.5655 1.5741

3B 2B

1.5710 1.580

1.5787 1.590

1.5925 1.5979

1.5971 1.6037

1.6250 1.6250

111⁄16–6 UN

2A

0.0025

1.6850

1.6668

—

1.5767

1.5684

1.4866

2B

1.507

1.538

1.5792

1.5900

1.6875

111⁄16–8 UN

3A 2A

0.0000 0.0022

1.6875 1.6853

1.6693 1.6703

— —

1.5792 1.6041

1.5730 1.5966

1.4891 1.5365

3B 2B

1.5070 1.552

1.5271 1.577

1.5792 1.6063

1.5873 1.6160

1.6875 1.6875

111⁄16–12 UN

3A 2A

0.0000 0.0018

1.6875 1.6857

1.6725 1.6743

— —

1.6063 1.6316

1.6007 1.6256

1.5387 1.5865

3B 2B

1.5520 1.597

1.5672 1.615

1.6063 1.6334

1.6136 1.6412

1.6875 1.6875

3A

0.0000

1.6875

1.6761

—

1.6334

1.6289

1.5883

3B

1.5970

1.6073

1.6334

1.6392

1.6875

Class 2A

1.5609

19⁄16–18 UNEF

3A 2A

0.0000 0.0015

19⁄16–20 UN

3A 2A

15⁄8–6 UN

3A 2A

15⁄8–8 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 1.495

Max 1.509

Min 1.5219

Max 1.5287

Min 1.5625


1737

Maxd

Major Diameter

Allowance 0.0016


Min 1.5515

Mine




1738


Externalb

Major Diameter

Maxd

—

1.6453

Min 1.6400

1.6875 1.6860

1.6781 1.6773

— —

1.6469 1.6499

1.6429 1.6448

1.6130 1.6199

3B 2B

1.6200 1.627

1.6283 1.640

1.6469 1.6514

1.6521 1.6580

1.6875 1.6875

0.0000 0.0015

1.6875 1.6860

1.6788 1.6779

— —

1.6514 1.6535

1.6476 1.6487

1.6214 1.6265

3B 2B

1.6270 1.633

1.6355 1.645

1.6514 1.6550

1.6563 1.6613

1.6875 1.6875

0.0000 0.0027

1.6875 1.7473

1.6794 1.7165

— —

1.6550 1.6174

1.6514 1.6040

1.6280 1.5092

3B 1B

1.6330 1.534

1.6412 1.568

1.6550 1.6201

1.6597 1.6375

1.6875 1.7500

13⁄4–6 UN

2A 3A 2A

0.0027 0.0000 0.0025

1.7473 1.7500 1.7475

1.7268 1.7295 1.7293

1.7165 — —

1.6174 1.6201 1.6392

1.6085 1.6134 1.6309

1.5092 1.5119 1.5491

2B 3B 2B

1.534 1.5340 1.570

1.568 1.5575 1.600

1.6201 1.6201 1.6417

1.6317 1.6288 1.6525

1.7500 1.7500 1.7500

13⁄4–8 UN

3A 2A

0.0000 0.0023

1.7500 1.7477

1.7318 1.7327

— 1.7252

1.6417 1.6665

1.6354 1.6590

1.5516 1.5989

3B 2B

1.5700 1.615

1.5896 1.640

1.6417 1.6688

1.6498 1.6786

1.7500 1.7500

13⁄4–10 UNS

3A 2A

0.0000 0.0019

1.7500 1.7481

1.7350 1.7352

— —

1.6688 1.6831

1.6632 1.6766

1.6012 1.6291

3B 2B

1.6150 1.642

1.6297 1.663

1.6688 1.6850

1.6762 1.6934

1.7500 1.7500

13⁄4–12 UN

2A

0.0018

1.7482

1.7368

—

1.6941

1.6881

1.6490

2B

1.660

1.678

1.6959

1.7037

1.7500

13⁄4–14 UNS

3A 2A

0.0000 0.0017

1.7500 1.7483

1.7386 1.7380

— —

1.6959 1.7019

1.6914 1.6963

1.6508 1.6632

3B 2B

1.6600 1.673

1.6698 1.688

1.6959 1.7036

1.7017 1.7109

1.7500 1.7500

13⁄4–16 UN

2A

0.0016

1.7484

1.7390

—

1.7078

1.7025

1.6739

2B

1.682

1.696

1.7094

1.7163

1.7500

13⁄4–18 UNS

3A 2A

0.0000 0.0015

1.7500 1.7485

1.7406 1.7398

— —

1.7094 1.7124

1.7054 1.7073

1.6755 1.6824

3B 2B

1.6820 1.690

1.6908 1.703

1.7094 1.7139

1.7146 1.7205

1.7500 1.7500

13⁄4–20 UN

2A

0.0015

1.7485

1.7404

—

1.7160

1.7112

1.6890

2B

1.696

1.707

1.7175

1.7238

1.7500

113⁄16–6 UN

3A 2A

0.0000 0.0025

1.7500 1.8100

1.7419 1.7918

— —

1.7175 1.7017

1.7139 1.6933

1.6905 1.6116

3B 2B

1.6960 1.632

1.7037 1.663

1.7175 1.7042

1.7222 1.7151

1.7500 1.8125

113⁄16–8 UN

3A 2A

0.0000 0.0023

1.8125 1.8102

1.7943 1.7952

— —

1.7042 1.7290

1.6979 1.7214

1.6141 1.6614

3B 2B

1.6320 1.677

1.6521 1.702

1.7042 1.7313

1.7124 1.7412

1.8125 1.8125

113⁄16–12 UN

3A 2A

0.0000 0.0018

1.8125 1.8107

1.7975 1.7993

— —

1.7313 1.7566

1.7256 1.7506

1.6637 1.7115

3B 2B

1.6770 1.722

1.6922 1.740

1.7313 1.7584

1.7387 1.7662

1.8125 1.8125

3A

0.0000

1.8125

1.8011

—

1.7584

1.7539

1.7133

3B

1.7220

1.7323

1.7584

1.7642

1.8125

Major Diameter

Class 2A

Allowance 0.0016

1.6859

111⁄16–18 UNEF

3A 2A

0.0000 0.0015

111⁄16–20 UN

3A 2A

13⁄4–5 UNC

3A 1A

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 1.620

Max 1.634

Min 1.6469

Max 1.6538

Min 1.6875



Min 1.6765

Mine



Internalb

Externalb

Major Diameter

—

1.7703

Min 1.7650

1.8125 1.8110

1.8031 1.8029

— —

1.7719 1.7785

1.7679 1.7737

1.7380 1.7515

3B 2B

1.7450 1.758

1.7533 1.770

1.7719 1.7800

1.7771 1.7863

1.8125 1.8125

0.0000 0.0025

1.8125 1.8725

1.8044 1.8543

— —

1.7800 1.7642

1.7764 1.7558

1.7530 1.6741

3B 2B

1.7580 1.695

1.7662 1.725

1.7800 1.7667

1.7847 1.7777

1.8125 1.8750

0.0000 0.0023

1.8750 1.8727

1.8568 1.8577

— 1.8502

1.7667 1.7915

1.7604 1.7838

1.6766 1.7239

3B 2B

1.6950 1.740

1.7146 1.765

1.7667 1.7938

1.7749 1.8038

1.8750 1.8750

3A 2A

0.0000 0.0019

1.8750 1.8731

1.8600 1.8602

— —

1.7938 1.8081

1.7881 1.8016

1.7262 1.7541

3B 2B

1.7400 1.767

1.7547 1.788

1.7938 1.8100

1.8013 1.8184

1.8750 1.8750

17⁄8–12 UN

2A

0.0018

1.8732

1.8618

—

1.8191

1.8131

1.7740

2B

1.785

1.803

1.8209

1.8287

1.8750

17⁄8–14 UNS

3A 2A

0.0000 0.0017

1.8750 1.8733

1.8636 1.8630

— —

1.8209 1.8269

1.8164 1.8213

1.7758 1.7883

3B 2B

1.7850 1.798

1.7948 1.814

1.8209 1.8286

1.8267 1.8359

1.8750 1.8750

17⁄8–16 UN

2A

0.0016

1.8734

1.8640

—

1.8328

1.8275

1.7989

2B

1.807

1.821

1.8344

1.8413

1.8750

17⁄8–18 UNS

3A 2A

0.0000 0.0015

1.8750 1.8735

1.8656 1.8648

— —

1.8344 1.8374

1.8304 1.8323

1.8005 1.8074

3B 2B

1.8070 1.815

1.8158 1.828

1.8344 1.8389

1.8396 1.8455

1.8750 1.8750

17⁄8–20

UN

2A

0.0015

1.8735

1.8654

—

1.8410

1.8362

1.8140

2B

1.821

1.832

1.8425

1.8488

1.8750

UN

3A 2A

0.0000 0.0026

1.8750 1.9349

1.8669 1.9167

— —

1.8425 1.8266

1.8389 1.8181

1.8155 1.7365

3B 2B

1.8210 1.757

1.8287 1.788

1.8425 1.8292

1.8472 1.8403

1.8750 1.9375

115⁄16–8 UN

3A 2A

0.0000 0.0023

1.9375 1.9352

1.9193 1.9202

— —

1.8292 1.8540

1.8228 1.8463

1.7391 1.7864

3B 2B

1.7570 1.802

1.7771 1.827

1.8292 1.8563

1.8375 1.8663

1.9375 1.9375

115⁄16–12 UN

3A 2A

0.0000 0.0018

1.9375 1.9357

1.9225 1.9243

— —

1.8563 1.8816

1.8505 1.8755

1.7887 1.8365

3B 2B

1.8020 1.847

1.8172 1.865

1.8563 1.8834

1.8638 1.8913

1.9375 1.9375

115⁄16–16 UN

3A 2A

0.0000 0.0016

1.9375 1.9359

1.9261 1.9265

— —

1.8834 1.8953

1.8789 1.8899

1.8383 1.8614

3B 2B

1.8470 1.870

1.8573 1.884

1.8834 1.8969

1.8893 1.9039

1.9375 1.9375

115⁄16–20 UN

3A 2A

0.0000 0.0015

1.9375 1.9360

1.9281 1.9279

— —

1.8969 1.9035

1.8929 1.8986

1.8630 1.8765

3B 2B

1.8700 1.883

1.8783 1.895

1.8969 1.9050

1.9021 1.9114

1.9375 1.9375

3A

0.0000

1.9375

1.9294

—

1.9050

1.9013

1.8780

3B

1.8830

1.8912

1.9050

1.9098

1.9375

Class 2A

1.8109

113⁄16–20 UN

3A 2A

0.0000 0.0015

17⁄8–6 UN

3A 2A

17⁄8–8 UN

3A 2A

17⁄8–10 UNS

115⁄16–6

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 1.745

Max 1.759

Min 1.7719

Max 1.7788

Min 1.8125


1739

Maxd

Major Diameter

Allowance 0.0016


Min 1.8015

Mine



Nominal Size, Threads per Inch, and Series Designationa 2–41⁄2 UNC

1740


Externalb

Major Diameter

Maxd

—

1.8528

Min 1.8385

1.9971 2.0000 1.9974 2.0000 1.9977 2.0000 1.9980 1.9982 2.0000 1.9983 1.9984 2.0000 1.9985 1.9985 2.0000 2.0609

1.9751 1.9780 1.9792 1.9818 1.9827 1.9850 1.9851 1.9868 1.9886 1.9880 1.9890 1.9906 1.9898 1.9904 1.9919 2.0515

1.9641 — — — 1.9752 — — — — — — — — — — —

1.8528 1.8557 1.8891 1.8917 1.9165 1.9188 1.9330 1.9441 1.9459 1.9519 1.9578 1.9594 1.9624 1.9660 1.9675 2.0203

1.8433 1.8486 1.8805 1.8853 1.9087 1.9130 1.9265 1.9380 1.9414 1.9462 1.9524 1.9554 1.9573 1.9611 1.9638 2.0149

1.7324 1.7353 1.7990 1.8016 1.8489 1.8512 1.8790 1.8990 1.9008 1.9133 1.9239 1.9255 1.9324 1.9390 1.9405 1.9864

2B 3B 2B 3B 2B 3B 2B 2B 3B 2B 2B 3B 2B 2B 3B 2B

1.759 1.7590 1.820 1.8200 1.865 1.8650 1.892 1.910 1.9100 1.923 1.932 1.9320 1.940 1.946 1.9460 1.995

1.795 1.7861 1.850 1.8396 1.890 1.8797 1.913 1.928 1.9198 1.938 1.946 1.9408 1.953 1.957 1.9537 2.009

1.8557 1.8557 1.8917 1.8917 1.9188 1.9188 1.9350 1.9459 1.9459 1.9536 1.9594 1.9594 1.9639 1.9675 1.9675 2.0219

1.8681 1.8650 1.9028 1.9000 1.9289 1.9264 1.9435 1.9538 1.9518 1.9610 1.9664 1.9646 1.9706 1.9739 1.9723 2.0289

2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0000 2.0625

0.0000 0.0026

2.0625 2.1224

2.0531 2.1042

— —

2.0219 2.0141

2.0179 2.0054

1.9880 1.9240

3B 2B

1.9950 1.945

2.0033 1.975

2.0219 2.0167

2.0271 2.0280

2.0625 2.1250

3A 2A

0.0000 0.0024

2.1250 2.1226

2.1068 2.1076

— 2.1001

2.0167 2.0414

2.0102 2.0335

1.9266 1.9738

3B 2B

1.9450 1.990

1.9646 2.015

2.0167 2.0438

2.0251 2.0540

2.1250 2.1250

21⁄8–12 UN

3A 2A

0.0000 0.0018

2.1250 2.1232

2.1100 2.1118

— —

2.0438 2.0691

2.0379 2.0630

1.9762 2.0240

3B 2B

1.9900 2.035

2.0047 2.053

2.0438 2.0709

2.0515 2.0788

2.1250 2.1250

21⁄8–16 UN

3A 2A

0.0000 0.0016

2.1250 2.1234

2.1136 2.1140

— —

2.0709 2.0828

2.0664 2.0774

2.0258 2.0489

3B 2B

2.0350 2.057

2.0448 2.071

2.0709 2.0844

2.0768 2.0914

2.1250 2.1250

21⁄8–20 UN

3A 2A

0.0000 0.0015

2.1250 2.1235

2.1156 2.1154

— —

2.0844 2.0910

2.0803 2.0861

2.0505 2.0640

3B 2B

2.0570 2.071

2.0658 2.082

2.0844 2.0925

2.0896 2.0989

2.1250 2.1250

3A

0.0000

2.1250

2.1169

—

2.0925

2.0888

2.0655

3B

2.0710

2.0787

2.0925

2.0973

2.1250

Major Diameter

Class 1A

Allowance 0.0029

1.9971

21⁄16–16 UNS

2A 3A 2A 3A 2A 3A 2A 2A 3A 2A 2A 3A 2A 2A 3A 2A

0.0029 0.0000 0.0026 0.0000 0.0023 0.0000 0.0020 0.0018 0.0000 0.0017 0.0016 0.0000 0.0015 0.0015 0.0000 0.0016

21⁄8–6 UN

3A 2A

21⁄8–8 UN

2–6 UN 2–8 UN 2–10 UNS 2–12 UN 2–14 UNS 2–16 UN 2–18 UNS 2–20 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 1B

Min 1.759

Max 1.795

Min 1.8557

Max 1.8743

Min 2.0000



Min 1.9641

Mine


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 3 2 ⁄16–16 UNS

Internalb

Externalb

Major Diameter

—

2.1453

Min 2.1399

2.1875 2.2471

2.1781 2.2141

— —

2.1469 2.1028

2.1428 2.0882

2.1130 1.9824

3B 1B

2.1200 2.009

2.1283 2.045

2.1469 2.1057

2.1521 2.1247

2.1875 2.2500

0.0029 0.0000 0.0026

2.2471 2.2500 2.2474

2.2251 2.2280 2.2292

2.2141 — —

2.1028 2.1057 2.1391

2.0931 2.0984 2.1303

1.9824 1.9853 2.0490

2B 3B 2B

2.009 2.0090 2.070

2.045 2.0361 2.100

2.1057 2.1057 2.1417

2.1183 2.1152 2.1531

2.2500 2.2500 2.2500

3A 2A

0.0000 0.0024

2.2500 2.2476

2.2318 2.2326

— 2.2251

2.1417 2.1664

2.1351 2.1584

2.0516 2.0988

3B 2B

2.0700 2.115

2.0896 2.140

2.1417 2.1688

2.1502 2.1792

2.2500 2.2500

21⁄4–10 UNS

3A 2A

0.0000 0.0020

2.2500 2.2480

2.2350 2.2351

— —

2.1688 2.1830

2.1628 2.1765

2.1012 2.1290

3B 2B

2.1150 2.142

2.1297 2.163

2.1688 2.1850

2.1766 2.1935

2.2500 2.2500

21⁄4–12 UN

2A

0.0018

2.2482

2.2368

—

2.1941

2.1880

2.1490

2B

2.160

2.178

2.1959

2.2038

2.2500

21⁄4–14 UNS

3A 2A

0.0000 0.0017

2.2500 2.2483

2.2386 2.2380

— —

2.1959 2.2019

2.1914 2.1962

2.1508 2.1633

3B 2B

2.1600 2.173

2.1698 2.188

2.1959 2.2036

2.2018 2.2110

2.2500 2.2500

21⁄4–16 UN

2A

0.0016

2.2484

2.2390

—

2.2078

2.2024

2.1739

2B

2.182

2.196

2.2094

2.2164

2.2500

21⁄4–18 UNS

3A 2A

0.0000 0.0015

2.2500 2.2485

2.2406 2.2398

— —

2.2094 2.2124

2.2053 2.2073

2.1755 2.1824

3B 2B

2.1820 2.190

2.1908 2.203

2.2094 2.2139

2.2146 2.2206

2.2500 2.2500

21⁄4–20 UN

2A

0.0015

2.2485

2.2404

—

2.2160

2.2111

2.1890

2B

2.196

2.207

2.2175

2.2239

2.2500

25⁄16–16 UNS

3A 2A

0.0000 0.0017

2.2500 2.3108

2.2419 2.3014

— —

2.2175 2.2702

2.2137 2.2647

2.1905 2.2363

3B 2B

2.1960 2.245

2.2037 2.259

2.2175 2.2719

2.2223 2.2791

2.2500 2.3125

23⁄8–6 UN

3A 2A

0.0000 0.0027

2.3125 2.3723

2.3031 2.3541

— —

2.2719 2.2640

2.2678 2.2551

2.2380 2.1739

3B 2B

2.2450 2.195

2.2533 2.226

2.2719 2.2667

2.2773 2.2782

2.3125 2.3750

23⁄8–8 UN

3A 2A

0.0000 0.0024

2.3750 2.3726

2.3568 2.3576

— —

2.2667 2.2914

2.2601 2.2833

2.1766 2.2238

3B 2B

2.1950 2.240

2.2146 2.265

2.2667 2.2938

2.2753 2.3043

2.3750 2.3750

23⁄8–12 UN

3A 2A

0.0000 0.0019

2.3750 2.3731

2.3600 2.3617

— —

2.2938 2.3190

2.2878 2.3128

2.2262 2.2739

3B 2B

2.2400 2.285

2.2547 2.303

2.2938 2.3209

2.3017 2.3290

2.3750 2.3750

23⁄8–16 UN

3A 2A

0.0000 0.0017

2.3750 2.3733

2.3636 2.3639

— —

2.3209 2.3327

2.3163 2.3272

2.2758 2.2988

3B 2B

2.2850 2.307

2.2948 2.321

2.3209 2.3344

2.3269 2.3416

2.3750 2.3750

3A

0.0000

2.3750

2.3656

—

2.3344

2.3303

2.3005

3B

2.3070

2.3158

2.3344

2.3398

2.3750

Class 2A

2.1859

21⁄4–41⁄2 UNC

3A 1A

0.0000 0.0029

21⁄4–6 UN

2A 3A 2A

21⁄4–8 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 2.120

Max 2.134

Min 2.1469

Max 2.1539

Min 2.1875


1741

Maxd

Major Diameter

Allowance 0.0016


Min 2.1765

Mine




1742


Externalb

Major Diameter

Maxd

—

2.3410

Min 2.3359

2.3750 2.4358

2.3669 2.4264

— —

2.3425 2.3952

2.3387 2.3897

2.3155 2.3613

3B 2B

2.3210 2.370

2.3287 2.384

2.3425 2.3969

2.3475 2.4041

2.3750 2.4375

0.0000 0.0031

2.4375 2.4969

2.4281 2.4612

— —

2.3969 2.3345

2.3928 2.3190

2.3630 2.1992

3B 1B

2.3700 2.229

2.3783 2.267

2.3969 2.3376

2.4023 2.3578

2.4375 2.5000

0.0031 0.0000 0.0027

2.4969 2.5000 2.4973

2.4731 2.4762 2.4791

2.4612 — —

2.3345 2.3376 2.3890

2.3241 2.3298 2.3800

2.1992 2.2023 2.2989

2B 3B 2B

2.229 2.2290 2.320

2.267 2.2594 2.350

2.3376 2.3376 2.3917

2.3511 2.3477 2.4033

2.5000 2.5000 2.5000

3A 2A

0.0000 0.0024

2.5000 2.4976

2.4818 2.4826

— 2.4751

2.3917 2.4164

2.3850 2.4082

2.3016 2.3488

3B 2B

2.3200 2.365

2.3396 2.390

2.3917 2.4188

2.4004 2.4294

2.5000 2.5000

21⁄2–10 UNS

3A 2A

0.0000 0.0020

2.5000 2.4980

2.4850 2.4851

— —

2.4188 2.4330

2.4127 2.4263

2.3512 2.3790

3B 2B

2.3650 2.392

2.3797 2.413

2.4188 2.4350

2.4268 2.4437

2.5000 2.5000

21⁄2–12 UN

2A

0.0019

2.4981

2.4867

—

2.4440

2.4378

2.3989

2B

2.410

2.428

2.4459

2.4540

2.5000

21⁄2–14 UNS

3A 2A

0.0000 0.0017

2.5000 2.4983

2.4886 2.4880

— —

2.4459 2.4519

2.4413 2.4461

2.4008 2.4133

3B 2B

2.4100 2.423

2.4198 2.438

2.4459 2.4536

2.4519 2.4612

2.5000 2.5000

21⁄2–16 UN

2A

0.0017

2.4983

2.4889

—

2.4577

2.4522

2.4238

2B

2.432

2.446

2.4594

2.4666

2.5000

21⁄2–18 UNS

3A 2A

0.0000 0.0016

2.5000 2.4984

2.4906 2.4897

— —

2.4594 2.4623

2.4553 2.4570

2.4255 2.4323

3B 2B

2.4320 2.440

2.4408 2.453

2.4594 2.4639

2.4648 2.4708

2.5000 2.5000

21⁄2–20 UN

2A

0.0015

2.4985

2.4904

—

2.4660

2.4609

2.4390

2B

2.446

2.457

2.4675

2.4741

2.5000

25⁄8–6 UN

3A 2A

0.0000 0.0027

2.5000 2.6223

2.4919 2.6041

— —

2.4675 2.5140

2.4637 2.5050

2.4405 2.4239

3B 2B

2.4460 2.445

2.4537 2.475

2.4675 2.5167

2.4725 2.5285

2.5000 2.6250

25⁄8–8 UN

3A 2A

0.0000 0.0025

2.6250 2.6225

2.6068 2.6075

— —

2.5167 2.5413

2.5099 2.5331

2.4266 2.4737

3B 2B

2.4450 2.490

2.4646 2.515

2.5167 2.5438

2.5255 2.5545

2.6250 2.6250

25⁄8–12 UN

3A 2A

0.0000 0.0019

2.6250 2.6231

2.6100 2.6117

— —

2.5438 2.5690

2.5376 2.5628

2.4762 2.5239

3B 2B

2.4900 2.535

2.5047 2.553

2.5438 2.5709

2.5518 2.5790

2.6250 2.6250

25⁄8–16 UN

3A 2A

0.0000 0.0017

2.6250 2.6233

2.6136 2.6139

— —

2.5709 2.5827

2.5663 2.5772

2.5258 2.5488

3B 2B

2.5350 2.557

2.5448 2.571

2.5709 2.5844

2.5769 2.5916

2.6250 2.6250

3A

0.0000

2.6250

2.6156

—

2.5844

2.5803

2.5505

3B

2.5570

2.5658

2.5844

2.5898

2.6250

Major Diameter

Class 2A

Allowance 0.0015

2.3735

27⁄16–16 UNS

3A 2A

0.0000 0.0017

21⁄2–4 UNC

3A 1A

21⁄2–6 UN

2A 3A 2A

21⁄2–8 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 2.321

Max 2.332

Min 2.3425

Max 2.3491

Min 2.3750



Min 2.3654

Mine



Internalb

Externalb

Major Diameter

—

2.5910

Min 2.5859

2.6250 2.7468

2.6169 2.7111

— —

2.5925 2.5844

2.5887 2.5686

2.5655 2.4491

3B 1B

2.5710 2.479

2.5787 2.517

2.5925 2.5876

2.5975 2.6082

2.6250 2.7500

0.0032 0.0000 0.0027

2.7468 2.7500 2.7473

2.7230 2.7262 2.7291

2.7111 — —

2.5844 2.5876 2.6390

2.5739 2.5797 2.6299

2.4491 2.4523 2.5489

2B 3B 2B

2.479 2.4790 2.570

2.517 2.5094 2.600

2.5876 2.5876 2.6417

2.6013 2.5979 2.6536

2.7500 2.7500 2.7500

3A 2A

0.0000 0.0025

2.7500 2.7475

2.7318 2.7325

— 2.7250

2.6417 2.6663

2.6349 2.6580

2.5516 2.5987

3B 2B

2.5700 2.615

2.5896 2.640

2.6417 2.6688

2.6506 2.6796

2.7500 2.7500

23⁄4–10 UNS

3A 2A

0.0000 0.0020

2.7500 2.7480

2.7350 2.7351

— —

2.6688 2.6830

2.6625 2.6763

2.6012 2.6290

3B 2B

2.6150 2.642

2.6297 2.663

2.6688 2.6850

2.6769 2.6937

2.7500 2.7500

23⁄4–12 UN

2A

0.0019

2.7481

2.7367

—

2.6940

2.6878

2.6489

2B

2.660

2.678

2.6959

2.7040

2.7500

23⁄4–14 UNS

3A 2A

0.0000 0.0017

2.7500 2.7483

2.7386 2.7380

— —

2.6959 2.7019

2.6913 2.6961

2.6508 2.6633

3B 2B

2.6600 2.673

2.6698 2.688

2.6959 2.7036

2.7019 2.7112

2.7500 2.7500

23⁄4–16 UN

2A

0.0017

2.7483

2.7389

—

2.7077

2.7022

2.6738

2B

2.682

2.696

2.7094

2.7166

2.7500

23⁄4–18 UNS

3A 2A

0.0000 0.0016

2.7500 2.7484

2.7406 2.7397

— —

2.7094 2.7123

2.7053 2.7070

2.6755 2.6823

3B 2B

2.6820 2.690

2.6908 2.703

2.7094 2.7139

2.7148 2.7208

2.7500 2.7500

23⁄4–20 UN

2A

0.0015

2.7485

2.7404

—

2.7160

2.7109

2.6890

2B

2.696

2.707

2.7175

2.7241

2.7500

27⁄8–6 UN

3A 2A

0.0000 0.0028

2.7500 2.8722

2.7419 2.8540

— —

2.7175 2.7639

2.7137 2.7547

2.6905 2.6738

3B 2B

2.6960 2.695

2.7037 2.725

2.7175 2.7667

2.7225 2.7787

2.7500 2.8750

27⁄8–8 UN

3A 2A

0.0000 0.0025

2.8750 2.8725

2.8568 2.8575

— —

2.7667 2.7913

2.7598 2.7829

2.6766 2.7237

3B 2B

2.6950 2.740

2.7146 2.765

2.7667 2.7938

2.7757 2.8048

2.8750 2.8750

27⁄8–12 UN

3A 2A

0.0000 0.0019

2.8750 2.8731

2.8600 2.8617

— —

2.7938 2.8190

2.7875 2.8127

2.7262 2.7739

3B 2B

2.7400 2.785

2.7547 2.803

2.7938 2.8209

2.8020 2.8291

2.8750 2.8750

27⁄8–16 UN

3A 2A

0.0000 0.0017

2.8750 2.8733

2.8636 2.8639

— —

2.8209 2.8327

2.8162 2.8271

2.7758 2.7988

3B 2B

2.7850 2.807

2.7948 2.821

2.8209 2.8344

2.8271 2.8417

2.8750 2.8750

27⁄8–20 UN

3A 2A

0.0000 0.0016

2.8750 2.8734

2.8656 2.8653

— —

2.8344 2.8409

2.8302 2.8357

2.8005 2.8139

3B 2B

2.8070 2.821

2.8158 2.832

2.8344 2.8425

2.8399 2.8493

2.8750 2.8750

3A

0.0000

2.8750

2.8669

—

2.8425

2.8386

2.8155

3B

2.8210

2.8287

2.8425

2.8476

2.8750

Class 2A

2.6235

23⁄4–4 UNC

3A 1A

0.0000 0.0032

23⁄4–6 UN

2A 3A 2A

23⁄4–8 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 2.571

Max 2.582

Min 2.5925

Max 2.5991

Min 2.6250


1743

Maxd

Major Diameter

Allowance 0.0015


Min 2.6154

Mine



Nominal Size, Threads per Inch, and Series Designationa 3–4 UNC

— 2.9611 — — — 2.9749 — — — — — — — — — — —

2.8344 2.8344 2.8376 2.8889 2.8917 2.9162 2.9188 2.9330 2.9440 2.9459 2.9518 2.9577 2.9594 2.9623 2.9659 2.9675 3.0139

Min 2.8183 2.8237 2.8296 2.8796 2.8847 2.9077 2.9124 2.9262 2.9377 2.9412 2.9459 2.9521 2.9552 2.9569 2.9607 2.9636 3.0045

3.1250 3.1224

3.1068 3.1074

— —

3.0167 3.0412

3.0097 3.0326

2.9266 2.9736

3B 2B

2.9450 2.990

2.9646 3.015

3.0167 3.0438

3.0259 3.0550

3.1250 3.1250

0.0000 0.0019

3.1250 3.1231

3.1100 3.1117

— —

3.0438 3.0690

3.0374 3.0627

2.9762 3.0239

3B 2B

2.9900 3.035

3.0047 3.053

3.0438 3.0709

3.0522 3.0791

3.1250 3.1250

3A 2A

0.0000 0.0017

3.1250 3.1233

3.1136 3.1139

— —

3.0709 3.0827

3.0662 3.0771

3.0258 3.0488

3B 2B

3.0350 3.057

3.0448 3.071

3.0709 3.0844

3.0771 3.0917

3.1250 3.1250

3A 1A

0.0000 0.0033

3.1250 3.2467

3.1156 3.2110

— —

3.0844 3.0843

3.0802 3.0680

3.0505 2.9490

3B 1B

3.0570 2.979

3.0658 3.017

3.0844 3.0876

3.0899 3.1088

3.1250 3.2500

2A 3A 2A

0.0033 0.0000 0.0028

3.2467 3.2500 3.2472

3.2229 3.2262 3.2290

3.2110 — —

3.0843 3.0876 3.1389

3.0734 3.0794 3.1294

2.9490 2.9523 3.0488

2B 3B 2B

2.979 2.9790 3.070

3.017 3.0094 3.100

3.0876 3.0876 3.1417

3.1017 3.0982 3.1540

3.2500 3.2500 3.2500

3A

0.0000

3.2500

3.2318

—

3.1417

3.1346

3.0516

3B

3.0700

3.0896

3.1417

3.1509

3.2500

31⁄8–6 UN 31⁄8–8 UN

3A 2A

0.0000 0.0026

31⁄8–12 UN

3A 2A

31⁄8–16 UN 31⁄4–4 UNC

3–14 UNS 3–16 UN 3–18 UNS 3–20 UN

31⁄4–6

UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 1B 2B 3B 2B 3B 2B 3B 2B 2B 3B 2B 2B 3B 2B 2B 3B 2B

Min 2.729 2.729 2.7290 2.820 2.8200 2.865 2.8650 2.892 2.910 2.9100 2.923 2.932 2.9320 2.940 2.946 2.9460 2.945

Max 2.767 2.767 2.7594 2.850 2.8396 2.890 2.8797 2.913 2.928 2.9198 2.938 2.946 2.9408 2.953 2.957 2.9537 2.975

Min 2.8376 2.8376 2.8376 2.8917 2.8917 2.9188 2.9188 2.9350 2.9459 2.9459 2.9536 2.9594 2.9594 2.9639 2.9675 2.9675 3.0167

Max 2.8585 2.8515 2.8480 2.9038 2.9008 2.9299 2.9271 2.9439 2.9541 2.9521 2.9613 2.9667 2.9649 2.9709 2.9743 2.9726 3.0289

Min 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.0000 3.1250



Min 2.9611 2.9730 2.9762 2.9790 2.9818 2.9824 2.9850 2.9851 2.9867 2.9886 2.9879 2.9889 2.9906 2.9897 2.9903 2.9919 3.1040

Maxd

Major Diameter 2.9968 2.9968 3.0000 2.9972 3.0000 2.9974 3.0000 2.9980 2.9981 3.0000 2.9982 2.9983 3.0000 2.9984 2.9984 3.0000 3.1222

3–10 UNS 3–12 UN

Major Diameter

Mine

UNR Minor Dia.,c Max (Ref.) 2.6991 2.6991 2.7023 2.7988 2.8016 2.8486 2.8512 2.8790 2.8989 2.9008 2.9132 2.9238 2.9255 2.9323 2.9389 2.9405 2.9238

Class 1A 2A 3A 2A 3A 2A 3A 2A 2A 3A 2A 2A 3A 2A 2A 3A 2A

3–8 UN

Internalb

Externalb Allowance 0.0032 0.0032 0.0000 0.0028 0.0000 0.0026 0.0000 0.0020 0.0019 0.0000 0.0018 0.0017 0.0000 0.0016 0.0016 0.0000 0.0028

3–6 UN

1744



Internalb

Externalb

Major Diameter

3.2249

3.1662

Min 3.1575

3.2500 3.2480

3.2350 3.2351

— —

3.1688 3.1830

3.1623 3.1762

3.1012 3.1290

3B 2B

3.1150 3.142

3.1297 3.163

3.1688 3.1850

3.1773 3.1939

3.2500 3.2500

0.0019

3.2481

3.2367

—

3.1940

3.1877

3.1489

2B

3.160

3.178

3.1959

3.2041

3.2500

0.0000 0.0018

3.2500 3.2482

3.2386 3.2379

— —

3.1959 3.2018

3.1912 3.1959

3.1508 3.1632

3B 2B

3.1600 3.173

3.1698 3.188

3.1959 3.2036

3.2041 3.2113

3.2500 3.2500

2A

0.0017

3.2483

3.2389

—

3.2077

3.2021

3.1738

2B

3.182

3.196

3.2094

3.2167

3.2500

UNS

3A 2A

0.0000 0.0016

3.2500 3.2484

3.2406 3.2397

— —

3.2094 3.2123

3.2052 3.2069

3.1755 3.1823

3B 2B

3.1820 3.190

3.1908 3.203

3.2094 3.2139

3.2149 3.2209

3.2500 3.2500

UN

2A

0.0029

3.3721

3.3539

—

3.2638

3.2543

3.1737

2B

3.195

3.225

3.2667

3.2791

3.3750

UN

3A 2A

0.0000 0.0026

3.3750 3.3724

3.3568 3.3574

— —

3.2667 3.2912

3.2595 3.2824

3.1766 3.2236

3B 2B

3.1950 3.240

3.2146 3.265

3.2667 3.2938

3.2760 3.3052

3.3750 3.3750

33⁄8–12 UN

3A 2A

0.0000 0.0019

3.3750 3.3731

3.3600 3.3617

— —

3.2938 3.3190

3.2872 3.3126

3.2262 3.2739

3B 2B

3.2400 3.285

3.2547 3.303

3.2938 3.3209

3.3023 3.3293

3.3750 3.3750

33⁄8–16 UN

3A 2A

0.0000 0.0017

3.3750 3.3733

3.3636 3.3639

— —

3.3209 3.3327

3.3161 3.3269

3.2758 3.2988

3B 2B

3.2850 3.307

3.2948 3.321

3.3209 3.3344

3.3272 3.3419

3.3750 3.3750

31⁄2–4 UNC

3A 1A

0.0000 0.0033

3.3750 3.4967

3.3656 3.4610

— —

3.3344 3.3343

3.3301 3.3177

3.3005 3.1990

3B 1B

3.3070 3.229

3.3158 3.267

3.3344 3.3376

3.3400 3.3591

3.3750 3.5000

31⁄2–6 UN

2A 3A 2A

0.0033 0.0000 0.0029

3.4967 3.5000 3.4971

3.4729 3.4762 3.4789

3.4610 — —

3.3343 3.3376 3.3888

3.3233 3.3293 3.3792

3.1990 3.2023 3.2987

2B 3B 2B

3.229 3.2290 3.320

3.267 3.2594 3.350

3.3376 3.3376 3.3917

3.3519 3.3484 3.4042

3.5000 3.5000 3.5000

31⁄2–8 UN

3A 2A

0.0000 0.0026

3.5000 3.4974

3.4818 3.4824

— 3.4749

3.3917 3.4162

3.3845 3.4074

3.3016 3.3486

3B 2B

3.3200 3.365

3.3396 3.390

3.3917 3.4188

3.4011 3.4303

3.5000 3.5000

31⁄2–10 UNS

3A 2A

0.0000 0.0021

3.5000 3.4979

3.4850 3.4850

— —

3.4188 3.4329

3.4122 3.4260

3.3512 3.3789

3B 2B

3.3650 3.392

3.3797 3.413

3.4188 3.4350

3.4274 3.4440

3.5000 3.5000

31⁄2–12 UN

2A

0.0019

3.4981

3.4867

—

3.4440

3.4376

3.3989

2B

3.410

3.428

3.4459

3.4543

3.5000

3A

0.0000

3.5000

3.4886

—

3.4459

3.4411

3.4008

3B

3.4100

3.4198

3.4459

3.4522

3.5000

Class 2A

3.2474

31⁄4–10 UNS

3A 2A

0.0000 0.0020

31⁄4–12

2A 3A 2A

UN

31⁄4–14 UNS 31⁄4–16 UN 31⁄4–18 33⁄8–6 33⁄8–8

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 3.115

Max 3.140

Min 3.1688

Max 3.1801

Min 3.2500


1745

Maxd

Major Diameter

Allowance 0.0026


Min 3.2324

Mine



Nominal Size, Threads per Inch, and Series Designationa 31⁄2–14 UNS

Internalb

Externalb

Maxd

—

3.4518

Min 3.4457

3.4983

3.4889

—

3.4577

3.4519

3.4238

3.5000 3.4983

3.4906 3.4896

— —

3.4594 3.4622

3.4551 3.4567

3.4255 3.4322

0.0029

3.6221

3.6039

—

3.5138

3.5041

0.0000 0.0027

3.6250 3.6223

3.6068 3.6073

— —

3.5167 3.5411

3.5094 3.5322

3A 2A

0.0000 0.0019

3.6250 3.6231

3.6100 3.6117

— —

3.5438 3.5690

35⁄8–16 UN

3A 2A

0.0000 0.0017

3.6250 3.6233

3.6136 3.6139

— —

33⁄4–4 UNC

3A 1A

0.0000 0.0034

3.6250 3.7466

3.6156 3.7109

33⁄4–6 UN

2A 3A 2A

0.0034 0.0000 0.0029

3.7466 3.7500 3.7471

33⁄4–8 UN

3A 2A

0.0000 0.0027

33⁄4–10 UNS

3A 2A

33⁄4–12 UN

Major Diameter

Class 2A

3.4982

UN

2A

0.0017

UNS

3A 2A

0.0000 0.0017

UN

2A

UN

3A 2A

35⁄8–12 UN

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Major Diameter

Min 3.423

Max 3.438

Min 3.4536

Max 3.4615

Min 3.5000

2B

3.432

3.446

3.4594

3.4669

3.5000

3B 2B

3.4320 3.440

3.4408 3.453

3.4594 3.4639

3.4650 3.4711

3.5000 3.5000

3.4237

2B

3.445

3.475

3.5167

3.5293

3.6250

3.4266 3.4735

3B 2B

3.4450 3.490

3.4646 3.515

3.5167 3.5438

3.5262 3.5554

3.6250 3.6250

3.5371 3.5626

3.4762 3.5239

3B 2B

3.4900 3.535

3.5047 3.553

3.5438 3.5709

3.5525 3.5793

3.6250 3.6250

3.5709 3.5827

3.5661 3.5769

3.5258 3.5488

3B 2B

3.5350 3.557

3.5448 3.571

3.5709 3.5844

3.5772 3.5919

3.6250 3.6250

— —

3.5844 3.5842

3.5801 3.5674

3.5505 3.4489

3B 1B

3.5570 3.479

3.5658 3.517

3.5844 3.5876

3.5900 3.6094

3.6250 3.7500

3.7228 3.7262 3.7289

3.7109 — —

3.5842 3.5876 3.6388

3.5730 3.5792 3.6290

3.4489 3.4523 3.5487

2B 3B 2B

3.479 3.4790 3.570

3.517 3.5094 3.600

3.5876 3.5876 3.6417

3.6021 3.5985 3.6544

3.7500 3.7500 3.7500

3.7500 3.7473

3.7318 3.7323

— 3.7248

3.6417 3.6661

3.6344 3.6571

3.5516 3.5985

3B 2B

3.5700 3.615

3.5896 3.640

3.6417 3.6688

3.6512 3.6805

3.7500 3.7500

0.0000 0.0021

3.7500 3.7479

3.7350 3.7350

— —

3.6688 3.6829

3.6621 3.6760

3.6012 3.6289

3B 2B

3.6150 3.642

3.6297 3.663

3.6688 3.6850

3.6776 3.6940

3.7500 3.7500

2A

0.0019

3.7481

3.7367

—

3.6940

3.6876

3.6489

2B

3.660

3.678

3.6959

3.7043

3.7500

33⁄4–14 UNS

3A 2A

0.0000 0.0018

3.7500 3.7482

3.7386 3.7379

— —

3.6959 3.7018

3.6911 3.6957

3.6508 3.6632

3B 2B

3.6600 3.673

3.6698 3.688

3.6959 3.7036

3.7022 3.7115

3.7500 3.7500

33⁄4–16 UN

2A

0.0017

3.7483

3.7389

—

3.7077

3.7019

3.6738

2B

3.682

3.696

3.7094

3.7169

3.7500

33⁄4–18 UNS

3A 2A

0.0000 0.0017

3.7500 3.7483

3.7406 3.7396

— —

3.7094 3.7122

3.7051 3.7067

3.6755 3.6822

3B 2B

3.6820 3.690

3.6908 3.703

3.7094 3.7139

3.7150 3.7211

3.7500 3.7500

31⁄2–16 31⁄2–18 35⁄8–6 35⁄8–8

Class 2B



Min 3.4879

Mine


Allowance 0.0018

1746



—

3.7637

Min 3.7538

3.8750 3.8723

3.8568 3.8573

— —

3.7667 3.7911

3.7593 3.7820

3.6766 3.7235

3B 2B

3.6950 3.740

3.7146 3.765

3.7667 3.7938

3.7763 3.8056

3.8750 3.8750

0.0000 0.0020

3.8750 3.8730

3.8600 3.8616

— —

3.7938 3.8189

3.7870 3.8124

3.7262 3.7738

3B 2B

3.7400 3.785

3.7547 3.803

3.7938 3.8209

3.8026 3.8294

3.8750 3.8750

0.0000 0.0018

3.8750 3.8732

3.8636 3.8638

— —

3.8209 3.8326

3.8160 3.8267

3.7758 3.7987

3B 2B

3.7850 3.807

3.7948 3.821

3.8209 3.8344

3.8273 3.8420

3.8750 3.8750

0.0000 0.0034 0.0034 0.0000 0.0030 0.0000 0.0027 0.0000 0.0021 0.0020 0.0000 0.0018 0.0018 0.0000 0.0021

3.8750 3.9966 3.9966 4.0000 3.9970 4.0000 3.9973 4.0000 3.9979 3.9980 4.0000 3.9982 3.9982 4.0000 4.2479

3.8656 3.9609 3.9728 3.9762 3.9788 3.9818 3.9823 3.9850 3.9850 3.9866 3.9886 3.9879 3.9888 3.9906 4.2350

— — 3.9609 — — — 3.9748 — — — — — — — —

3.8344 3.8342 3.8342 3.8376 3.8887 3.8917 3.9161 3.9188 3.9329 3.9439 3.9459 3.9518 3.9576 3.9594 4.1829

3.8300 3.8172 3.8229 3.8291 3.8788 3.8843 3.9070 3.9120 3.9259 3.9374 3.9410 3.9456 3.9517 3.9550 4.1759

3.8005 3.6989 3.6989 3.7023 3.7986 3.8016 3.8485 3.8512 3.8768 3.8988 3.9008 3.9132 3.9237 3.9255 4.1289

3B 1B 2B 3B 2B 3B 2B 3B 2B 2B 3B 2B 2B 3B 2B

3.8070 3.729 3.729 3.7290 3.820 3.8200 3.865 3.8650 3.892 3.910 3.9100 3.923 3.932 3.9320 4.142

3.8158 3.767 3.767 3.7594 3.850 3.8396 3.890 3.8797 3.913 3.928 3.9198 3.938 3.946 3.9408 4.163

3.8344 3.8376 3.8376 3.8376 3.8917 3.8917 3.9188 3.9188 3.9350 3.9459 3.9459 3.9536 3.9594 3.9594 4.1850

3.8401 3.8597 3.8523 3.8487 3.9046 3.9014 3.9307 3.9277 3.9441 3.9544 3.9523 3.9616 3.9670 3.9651 4.1941

3.8750 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.0000 4.2500

3.8720

37⁄8–8 UN

3A 2A

0.0000 0.0027

37⁄8–12 UN

3A 2A

37⁄8–16 UN

3A 2A 3A 1A 2A 3A 2A 3A 2A 3A 2A 2A 3A 2A 2A 3A 2A

4–8 UN 4–10 UNS 4–12 UN 4–14 UNS 4–16 UN 41⁄4–10 UNS

Maxd

Pitch Diameter

Minor Diameter

Pitch Diameter

Class 2B

Min 3.695

Max 3.725

Min 3.7667

Max 3.7795

Min 3.8750

2A

0.0018

4.2482

4.2379

—

4.2018

4.1956

4.1632

2B

4.173

4.188

4.2036

4.2116

4.2500

41⁄4–12 UN

0.0020 0.0000 0.0018 0.0000 0.0021

4.2480 4.2500 4.2482 4.2500 4.4979

4.2366 4.2386 4.2388 4.2406 4.4850

—

4.1874 4.1910 4.2017 4.2050 4.4259

4.1488 4.1508 4.1737 4.1755 4.3789

2B 3B 2B 3B 2B

4.178

4.1600 4.182

4.1698 4.196

— —

4.1939 4.1959 4.2076 4.2094 4.4329

4.160

41⁄2–10 UNS

2A 3A 2A 3A 2A

4.1820 4.392

4.1900 4.413

4.1959 4.1959 4.2094 4.2094 4.4350

4.2044 4.2023 4.2170 4.2151 4.4441

4.2500 4.2500 4.2500 4.2500 4.5000

41⁄2–14 UNS

2A

0.0018

4.4982

4.4879

—

4.4518

4.4456

4.4132

2B

4.423

4.438

4.4536

4.4616

4.5000

41⁄4–16 UN

— —


1747

41⁄4–14 UNS


Min 3.8538

Maxd

Major Diameter

Class 2A

4–6 UN

Major Diameter

Mine


Allowance 0.0030

4–4 UNC

Internalb

Externalb


Nominal Size, Threads per Inch, and Series Designationa 41⁄2–12 UN 41⁄2–16 UN 43⁄4–10 UNS

43⁄4–16 UN 5.00–10 UNS 5.00–14 UNS 5.00–12 UN 5.00–16 UN 51⁄4–10 UNS

Class 2A 3A 2A 3A 2A

Major Diameter Maxd 4.4980 4.5000 4.4982 4.5000 4.7478

Pitch Diameter

Min 4.4866 4.4886 4.4888 4.4906 4.7349

Mine

Maxd

—

4.4439 4.4459 4.4576 4.4594 4.6828 4.7017

4.6953

4.6939 4.6959 4.7076 4.7094 4.9328 4.9517 4.9439 4.9459 4.9576 4.9594 5.1829

4.6872 4.6909 4.7015 4.7049 4.9256 4.9453 4.9372 4.9409 4.9515 4.9549 5.1756

— — — —

2A

0.0019

4.7481

4.7378

—

2A 3A 2A 3A 2A 2A 2A 3A 2A 3A 2A

0.0020 0.0000 0.0018 0.0000 0.0022 0.0019 0.0020 0.0000 0.0018 0.0000 0.0022

4.7480 4.7500 4.7482 4.7500 4.9978 4.9981 4.9980 5.0000 4.9982 5.0000 5.2478

4.7366 4.7386 4.7388 4.7406 4.9849 4.9878 4.9866 4.9886 4.9888 4.9906 5.2349

— — — — — — — — — — —

Min 4.4374 4.4410 4.4517 4.4550 4.6756

UNR Minor Dia.,c Max (Ref.) 4.3988 4.4008 4.4237 4.4255 4.6288

Minor Diameter

Pitch Diameter Min 4.4459 4.4459 4.4594 4.4594 4.6850

Max 4.4544 4.4523 4.4670 4.4651 4.6944

Major Diameter

Class 2B 3B 2B 3B 2B

Min 4.410

Max 4.428

Min 4.5000 4.5000 4.5000 4.5000 4.7500

4.4100 4.432

4.4198 4.446

4.4320 4.642

4.4408 4.663

4.6631

2B

4.673

4.688

4.7036

4.7119

4.7500

4.6488 4.6508 4.6737 4.6755 4.8788 4.9131 4.8988 4.9008 4.9237 4.9255 5.1288

2B 3B 2B 3B 2B 2B 2B 3B 2B 3B 2B

4.660

4.678

4.6600 4.682

4.6698 4.696

4.6820 4.892 4.923 4.910 4.9100 4.932 4.9320 5.142

4.6908 4.913 4.938 4.928 4.9198 4.946 4.9408 5.163

4.6959 4.6959 4.7094 4.7094 4.9350 4.9536 4.9459 4.9459 4.9594 4.9594 5.1850

4.7046 4.7025 4.7173 4.7153 4.9444 4.9619 4.9546 4.9525 4.9673 4.9653 5.1944

4.7500 4.7500 4.7500 4.7500 5.0000 5.0000 5.0000 5.0000 5.0000 5.0000 5.2500

51⁄4–14 UNS

2A

0.0019

5.2481

5.2378

—

5.2017

5.1953

5.1631

2B

5.173

5.188

5.2036

5.2119

5.2500

51⁄4–12 UN

2A 3A 2A 3A 2A

0.0020 0.0000 0.0018 0.0000 0.0022

5.2480 5.2500 5.2482 5.2500 5.4978

5.2366 5.2386 5.2388 5.2406 5.4849

—

5.1939 5.1959 5.2076 5.2094 5.4328

5.1872 5.1909 5.2015 5.2049 5.4256

5.1488 5.1508 5.1737 5.1755 5.3788

2B 3B 2B 3B 2B

5.160

5.178

5.1600 5.182

5.1698 5.196

5.1820 5.392

5.1908 5.413

5.1959 5.1959 5.2094 5.2094 5.4350

5.2046 5.2025 5.2173 5.2153 5.4444

5.2500 5.2500 5.2500 5.2500 5.5000

51⁄4–16 UN 51⁄2–10 UNS 51⁄2–14 UNS 51⁄2–12 UN 51⁄2–16 UN

— — — —

2A

0.0019

5.4981

5.4878

—

5.4517

5.4453

5.4131

2B

5.423

5.438

5.4536

5.4619

5.5000

2A 3A 2A 3A

0.0020 0.0000 0.0018 0.0000

5.4980 5.5000 5.4982 5.5000

5.4866 5.4886 5.4888 5.4906

—

5.4439 5.4459 5.4576 5.4594

5.4372 5.4409 5.4515 5.4549

5.3988 5.4008 5.4237 5.4255

2B 3B 2B 3B

5.410

5.428

5.4100 5.432

5.4198 5.446

5.4320

5.4408

5.4459 5.4459 5.4594 5.4594

5.4546 5.4525 5.4673 5.4653

5.5000 5.5000 5.5000 5.5000

— — —



43⁄4–14 UNS 43⁄4–12 UN

Internalb

Externalb Allowance 0.0020 0.0000 0.0018 0.0000 0.0022

1748


Machinery's Handbook 28th Edition Table 3. (Continued) Standard Series and Selected Combinations — Unified Screw Threads Nominal Size, Threads per Inch, and Series Designationa 53⁄4–10 UNS 53⁄4–14 UNS 53⁄4–12 UN 53⁄4–16 UN

6–16 UN

Class 2A

Allowance 0.0022

Major Diameter Maxd 5.7478

Min 5.7349

Pitch Diameter Mine

Maxd

—

5.6828

Min 5.6754


Minor Diameter Class 2B

Min 5.642

Max 5.663

Pitch Diameter Min 5.6850

Max 5.6946

Major Diameter Min 5.7500

2A

0.0020

5.7480

5.7377

—

5.7016

5.6951

5.6630

2B

5.673

5.688

5.7036

5.7121

5.7500

2A 3A 2A 3A 2A 2A 2A 3A 2A 3A

0.0021 0.0000 0.0019 0.0000 0.0022 0.0020 0.0021 0.0000 0.0019 0.0000

5.7479 5.7500 5.7481 5.7500 5.9978 5.9980 5.9979 6.0000 5.9981 6.0000

5.7365 5.7386 5.7387 5.7406 5.9849 5.9877 5.9865 5.9886 5.9887 5.9906

—

5.6938 5.6959 5.7075 5.7094 5.9328 5.9516 5.9438 5.9459 5.9575 5.9594

5.6869 5.6907 5.7013 5.7047 5.9254 5.9451 5.9369 5.9407 5.9513 5.9547

5.6487 5.6508 5.6736 5.6755 5.8788 5.9130 5.8987 5.9008 5.9236 5.9255

2B 3B 2B 3B 2B 2B 2B 3B 2B 3B

5.660

5.678

5.6600 5.682

5.6698 5.696

5.6820 5.892 5.923 5.910 5.9100 5.932 5.9320

5.6908 5.913 5.938 5.928 5.9198 5.946 5.9408

5.6959 5.6959 5.7094 5.7094 5.9350 5.9536 5.9459 5.9459 5.9594 5.9594

5.7049 5.7026 5.7175 5.7155 5.9446 5.9621 5.9549 5.9526 5.9675 5.9655

5.7500 5.7500 5.7500 5.7500 6.0000 6.0000 6.0000 6.0000 6.0000 6.0000

— — — — — — — — —

a Use UNR designation instead of UN wherever UNR thread form is desired for external use. b Regarding combinations of thread classes, see text on page

1760.

c UN series external thread maximum minor diameter is basic for Class 3A and basic minus allowance for Classes 1A and 2A. d For Class 2A threads having an additive finish the maximum is increased, by the allowance, to the basic size, the value being the same as for Class 3A. e For unfinished hot-rolled material not including standard fasteners with rolled threads. f Formerly NF, tolerances and allowances are based on one diameter length of engagement. All dimensions in inches. Use UNS threads only if Standard Series do not meet requirements (see pages 1720, 1752, and 1763). For additional sizes above 4 inches see ASME/ANSI B1.11989 (R2001).


6–10 UNS 6–14 UNS 6–12 UN

Internalb

Externalb

1749



1750

Coarse-Thread Series: This series, UNC/UNRC, is the one most commonly used in the bulk production of bolts, screws, nuts and other general engineering applications. It is also used for threading into lower tensile strength materials such as cast iron, mild steel and softer materials (bronze, brass, aluminum, magnesium and plastics) to obtain the optimum resistance to stripping of the internal thread. It is applicable for rapid assembly or disassembly, or if corrosion or slight damage is possible. Table 4a. Coarse-Thread Series, UNC and UNRC — Basic Dimensions

Sizes No. or Inches 1 (0.073)e 2 (0.086) 3 (0.099)e 4 (0.112) 5 (0.125) 6 (0.138) 8 (0.164) 10 (0.190) 12 (0.216)e 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 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄4 33⁄4 4

Basic Major Dia., D Inches 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 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000 1.7500 2.0000 2.2500 2.5000 2.7500 3.0000 3.2500 3.500 3.7500 4.0000

Thds. per Inch, n 64 56 48 40 40 32 32 24 24 20 18 16 14 13 12 11 10 9 8 7 7 6 6 5 41⁄2 41⁄2 4 4 4 4 4 4 4

Basic Pitch Dia.,a D2 Inches 0.0629 0.0744 0.0855 0.0958 0.1088 0.1177 0.1437 0.1629 0.1889 0.2175 0.2764 0.3344 0.3911 0.4500 0.5084 0.5660 0.6850 0.8028 0.9188 1.0322 1.1572 1.2667 1.3917 1.6201 1.8557 2.1057 2.3376 2.5876 2.8376 3.0876 3.3376 3.5876 3.8376

Minor Diameter Ext. Int. Thds.,c Thds.,d d3 (Ref.) D1 Inches 0.0544 0.0648 0.0741 0.0822 0.0952 0.1008 0.1268 0.1404 0.1664 0.1905 0.2464 0.3005 0.3525 0.4084 0.4633 0.5168 0.6309 0.7427 0.8512 0.9549 1.0799 1.1766 1.3016 1.5119 1.7353 1.9853 2.2023 2.4523 2.7023 2.9523 3.2023 3.4523 3.7023

Inches 0.0561 0.0667 0.0764 0.0849 0.0979 0.1042 0.1302 0.1449 0.1709 0.1959 0.2524 0.3073 0.3602 0.4167 0.4723 0.5266 0.6417 0.7547 0.8647 0.9704 1.0954 1.1946 1.3196 1.5335 1.7594 2.0094 2.2294 2.4794 2.7294 2.9794 3.2294 3.4794 3.7294

Lead Angle λ at Basic P.D. Deg. Min 4 31 4 22 4 26 4 45 4 11 4 50 3 58 4 39 4 1 4 11 3 40 3 24 3 20 3 7 2 59 2 56 2 40 2 31 2 29 2 31 2 15 2 24 2 11 2 15 2 11 1 55 1 57 1 46 1 36 1 29 1 22 1 16 1 11

Area of Minor Dia. at D-2hb Sq. In. 0.00218 0.00310 0.00406 0.00496 0.00672 0.00745 0.01196 0.01450 0.0206 0.0269 0.0454 0.0678 0.0933 0.1257 0.162 0.202 0.302 0.419 0.551 0.693 0.890 1.054 1.294 1.74 2.30 3.02 3.72 4.62 5.62 6.72 7.92 9.21 10.61

Tensile Stress Areab Sq. In. 0.00263 0.00370 0.00487 0.00604 0.00796 0.00909 0.0140 0.0175 0.0242 0.0318 0.0524 0.0775 0.1063 0.1419 0.182 0.226 0.334 0.462 0.606 0.763 0.969 1.155 1.405 1.90 2.50 3.25 4.00 4.93 5.97 7.10 8.33 9.66 11.08

a British: Effective Diameter. b See formula, pages 1435 and

1443.

c Design form for UNR threads. (See figure on page

1720.)

d Basic minor diameter. e Secondary sizes.

Fine-Thread Series: This series, UNF/UNRF, is suitable for the production of bolts, screws, and nuts and for other applications where the Coarse series is not applicable. External threads of this series have greater tensile stress area than comparable sizes of the Coarse series. The Fine series is suitable when the resistance to stripping of both external



1751

and mating internal threads equals or exceeds the tensile load carrying capacity of the externally threaded member (see page 1443). It is also used where the length of engagement is short, where a smaller lead angle is desired, where the wall thickness demands a fine pitch, or where finer adjustment is needed. Table 4b. Fine-Thread Series, UNF and UNRF — Basic Dimensions

Sizes No. or Inches 0 (0.060) 1 (0.073)e 2 (0.086) 3 (0.099)e 4 (0.112) 5 (0.125) 6 (0.138) 8 (0.164) 10 (0.190) 12 (0.216)e 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 3⁄ 4 7⁄ 8 1 1 1 ⁄8 11⁄4 13⁄8 11⁄2

Basic Major Dia., D Inches 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 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000

Thds. per Inch, n 80 72 64 56 48 44 40 36 32 28 28 24 24 20 20 18 18 16 14 12 12 12 12 12

Basic Pitch Dia.,a D2 Inches 0.0519 0.0640 0.0759 0.0874 0.0985 0.1102 0.1218 0.1460 0.1697 0.1928 0.2268 0.2854 0.3479 0.4050 0.4675 0.5264 0.5889 0.7094 0.8286 0.9459 1.0709 1.1959 1.3209 1.4459

Minor Diameter Ext. Int. Thds.,c Thds.,d d3 (Ref.) D1 Inches 0.0451 0.0565 0.0674 0.0778 0.0871 0.0979 0.1082 0.1309 0.1528 0.1734 0.2074 0.2629 0.3254 0.3780 0.4405 0.4964 0.5589 0.6763 0.7900 0.9001 1.0258 1.1508 1.2758 1.4008

Inches 0.0465 0.0580 0.0691 0.0797 0.0894 0.1004 0.1109 0.1339 0.1562 0.1773 0.2113 0.2674 0.3299 0.3834 0.4459 0.5024 0.5649 0.6823 0.7977 0.9098 1.0348 1.1598 1.2848 1.4098

Lead Angle λ at Basic P.D. Deg. Min 4 23 3 57 3 45 3 43 3 51 3 45 3 44 3 28 3 21 3 22 2 52 2 40 2 11 2 15 1 57 1 55 1 43 1 36 1 34 1 36 1 25 1 16 1 9 1 3

Area of Minor Dia. at D-2hb Sq. In. 0.00151 0.00237 0.00339 0.00451 0.00566 0.00716 0.00874 0.01285 0.0175 0.0226 0.0326 0.0524 0.0809 0.1090 0.1486 0.189 0.240 0.351 0.480 0.625 0.812 1.024 1.260 1.521

Tensile Stress Areab Sq. In. 0.00180 0.00278 0.00394 0.00523 0.00661 0.00830 0.01015 0.01474 0.0200 0.0258 0.0364 0.0580 0.0878 0.1187 0.1599 0.203 0.256 0.373 0.509 0.663 0.856 1.073 1.315 1.581


1443.


1720.)


Extra-Fine-Thread Series: This series, UNEF/UNREF, is applicable where even finer pitches of threads are desirable, as for short lengths of engagement and for thin-walled tubes, nuts, ferrules, or couplings. It is also generally applicable under the conditions stated above for the fine threads. See Table 4c. Fine Threads for Thin-Wall Tubing: Dimensions for a 27-thread series, ranging from 1⁄4to 1-inch nominal size, also are included in Table 3. These threads are recommended for general use on thin-wall tubing. The minimum length of complete thread is one-third of the basic major diameter plus 5 threads (+ 0.185 in.). Selected Combinations: Thread data are tabulated in Table 3 for certain additional selected special combinations of diameter and pitch, with pitch diameter tolerances based on a length of thread engagement of 9 times the pitch. The pitch diameter limits are applicable to a length of engagement of from 5 to 15 times the pitch. (This provision should not be confused with the lengths of thread on mating parts, as they may exceed the length of engagement by a considerable amount.) Thread symbols are UNS and UNRS.



1752

Table 4c. Extra-Fine-Thread Series, UNEF and UNREF — Basic Dimensions Basic Pitch Dia.,a D2

Minor Diameter Ext. Int. Thds.,c Thds.,d d3 (Ref.) D1

Basic Major Dia., D Inches 0.2160 0.2500

Thds. per Inch, n 32 32

Inches 0.1957 0.2297

Inches 0.1788 0.2128

Inches 0.1822 0.2162

5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ e 16 3⁄ 4 13⁄ e 16 7⁄ 8 15⁄ e 16

0.3125

32

0.2922

0.2753

0.2787

1

0.3750

32

0.3547

0.3378

0.3412

1

0.4375

28

0.4143

0.3949

0.3988

0.5000

28

0.4768

0.4574

0.5625

24

0.5354

0.6250

24

0.5979

0.6875

24

0.7500

Lead Angle λ at Basic P.D. Deg. Min 2 55 2 29

Area of Minor Dia. at D − 2hb Sq. In. 0.0242 0.0344

Tensile Stress Areab Sq. In. 0.0270 0.0379

57

0.0581

0.0625

36

0.0878

0.0932

1

34

0.1201

0.1274

0.4613

1

22

0.162

0.170

0.5129

0.5174

1

25

0.203

0.214

0.5754

0.5799

1

16

0.256

0.268

0.6604

0.6379

0.6424

1

9

0.315

0.329

20

0.7175

0.6905

0.6959

1

16

0.369

0.386

0.8125

20

0.7800

0.7530

0.7584

1

10

0.439

0.458

0.8750

20

0.8425

0.8155

0.8209

1

5

0.515

0.536

0.9375

20

0.9050

0.8780

0.8834

1

0

0.598

0.620

1 11⁄16e

1.0000 1.0625

20 18

0.9675 1.0264

0.9405 0.9964

0.9459 1.0024

0 0

57 59

0.687 0.770

0.711 0.799

11⁄8

1.1250

18

1.0889

1.0589

1.0649

0

56

0.871

0.901

13⁄16e

1.1875

18

1.1514

1.1214

1.1274

0

53

0.977

1.009

11⁄4

1.2500

18

1.2139

1.1839

1.1899

0

50

1.090

1.123

15⁄16e

1.3125

18

1.2764

1.2464

1.2524

0

48

1.208

1.244

13⁄8

1.3750

18

1.3389

1.3089

1.3149

0

45

1.333

1.370

17⁄16e

1.4375

18

1.4014

1.3714

1.3774

0

43

1.464

1.503

11⁄2

1.5000

18

1.4639

1.4339

1.4399

0

42

1.60

1.64

19⁄16e

1.5625

18

1.5264

1.4964

1.5024

0

40

1.74

1.79

15⁄8

1.6250

18

1.5889

1.5589

1.5649

0

38

1.89

1.94

111⁄16e

1.6875

18

1.6514

1.6214

1.6274

0

37

2.05

2.10

Sizes No. or Inches 12 (0.216)e 1⁄ 4


1443.


1720.)


Other Threads of Special Diameters, Pitches, and Lengths of Engagement: Thread data for special combinations of diameter, pitch, and length of engagement not included in selected combinations are also given in the Standard but are not given here. Also, when design considerations require non-standard pitches or extreme conditions of engagement not covered by the tables, the allowance and tolerances should be derived from the formulas in the Standard. The thread symbol for such special threads is UNS. Constant Pitch Series.—The various constant-pitch series, UN, with 4, 6, 8, 12, 16, 20, 28 and 32 threads per inch, given in Table 3, offer a comprehensive range of diameter-pitch combinations for those purposes where the threads in the Coarse, Fine, and Extra-Fine series do not meet the particular requirements of the design. When selecting threads from these constant-pitch series, preference should be given wherever possible to those tabulated in the 8-, 12-, or 16-thread series. 8-Thread Series: The 8-thread series (8-UN) is a uniform-pitch series for large diameters. Although originally intended for high-pressure-joint bolts and nuts, it is now widely used as a substitute for the Coarse-Thread Series for diameters larger than 1 inch.



1753

12-Thread Series: The 12-thread series (12-UN) is a uniform pitch series for large diameters requiring threads of medium-fine pitch. Although originally intended for boiler practice, it is now used as a continuation of the Fine-Thread Series for diameters larger than 11⁄2 inches. 16-Thread Series: The 16-thread series (16-UN) is a uniform pitch series for large diameters requiring fine-pitch threads. It is suitable for adjusting collars and retaining nuts, and also serves as a continuation of the Extra-fine Thread Series for diameters larger than 111⁄16 inches. 4-, 6-, 20-, 28-, and 32-Thread Series: These thread series have been used more or less widely in industry for various applications where the Standard Coarse, Fine or Extra-fine Series were not as applicable. They are now recognized as Standard Unified Thread Series in a specified selection of diameters for each pitch (see Table 2). Whenever a thread in a constant-pitch series also appears in the UNC, UNF, or UNEF series, the symbols and tolerances for limits of size of UNC, UNF, or UNEF series are applicable, as will be seen in Tables 2 and 3. Table 5a. 4–Thread Series, 4–UN and 4–UNR — Basic Dimensions Sizes

Primary Inches

Secondary Inches

21⁄2e 25⁄8 23⁄4e 27⁄8 3e 31⁄8 31⁄4e 33⁄8 31⁄2e 35⁄8 31⁄4e 37⁄8 4e 41⁄8 41⁄4 43⁄8 41⁄2 45⁄8 43⁄4 47⁄8 5 51⁄8 51⁄4 53⁄8 51⁄2 55⁄8 53⁄4 57⁄8 6

Basic Pitch Dia.,a D2

Minor Diameter Ext. Int. Thds.,c Thds.,d d3s (Ref.) D1

Basic Major Dia., D Inches

Inches

Inches

Inches

Lead Angle λ at Basic P.D. Deg. Min.

2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000 4.1250 4.2500 4.3750 4.5000 4.6250 4.7500 4.8750 5.0000 5.1250 5.2500 5.3750 5.5000 5.6250 5.7500 5.8750 6.0000

2.3376 2.4626 2.5876 2.7126 2.8376 2.9626 3.0876 3.2126 3.3376 3.4626 3.5876 3.7126 3.8376 3.9626 4.0876 4.2126 4.3376 4.4626 4.5876 4.7126 4.8376 4.9626 5.0876 5.2126 5.3376 5.4626 5.5876 5.7126 5.8376

2.2023 2.3273 2.4523 2.5773 2.7023 2.8273 2.9523 3.0773 3.2023 3.3273 3.4523 3.5773 3.7023 3.8273 3.9523 4.0773 4.2023 4.3273 4.4523 4.5773 4.7023 4.8273 4.9523 5.0773 5.2023 5.3273 5.4523 5.5773 5.7023

2.2294 2.3544 2.4794 2.6044 2.7294 2.8544 2.9794 3.1044 3.2294 3.3544 3.4794 3.6044 3.7294 3.8544 3.9794 4.1044 4.2294 4.3544 4.4794 4.6044 4.7294 4.8544 4.9794 5.1044 5.2294 5.3544 5.4794 5.6044 5.7294

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0

57 51 46 41 36 32 29 25 22 19 16 14 11 9 7 5 3 1 0 58 57 55 54 52 51 50 49 48 47

Area of Minor Dia. at D − 2hb Sq. In.

Tensile Stress Areab Sq. In.

3.72 4.16 4.62 5.11 5.62 6.16 6.72 7.31 7.92 8.55 9.21 9.90 10.61 11.34 12.10 12.88 13.69 14.52 15.4 16.3 17.2 18.1 19.1 20.0 21.0 22.1 23.1 24.2 25.3

4.00 4.45 4.93 5.44 5.97 6.52 7.10 7.70 8.33 9.00 9.66 10.36 11.08 11.83 12.61 13.41 14.23 15.1 15.9 16.8 17.8 18.7 19.7 20.7 21.7 22.7 23.8 24.9 26.0


1443.


1720).

d Basic minor diameter. e These are standard sizes of the UNC series.



1754

Table 5b. 6–Thread Series, 6–UN and 6–UNR—Basic Dimensions Sizes

Primary Inches

Secondary Inches

13⁄8e 17⁄16 11⁄2e 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 41⁄8 41⁄4 43⁄8 41⁄2 45⁄8 43⁄4 47⁄8 5 51⁄8 51⁄4 53⁄8 51⁄2 55⁄8 53⁄4 57⁄8 6

Basic Major Dia., D Inches 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000 4.1250 4.2500 4.3750 4.5000 4.6250 4.7500 4.8750 5.0000 5.1250 5.2500 5.3750 5.5000 5.6250 5.7500 5.8750 6.0000


Minor Diameter Int. Ext. Thds.,d Thds.,c d3 (Ref.) D1

Inches 1.2667 1.3292 1.3917 1.4542 1.5167 1.5792 1.6417 1.7042 1.7667 1.8292 1.8917 2.0167 2.1417 2.2667 2.3917 2.5167 2.6417 2.7667 2.8917 3.0167 3.1417 3.2667 3.3917 3.5167 3.6417 3.7667 3.8917 4.0167 4.1417 4.2667 4.3917 4.5167 4.6417 4.7667 4.8917 5.0167 5.1417 5.2667 5.3917 5.5167 5.6417 5.7667 5.8917

Inches 1.1766 1.2391 1.3016 1.3641 1.4271 1.4891 1.5516 1.6141 1.6766 1.7391 1.8016 1.9266 2.0516 2.1766 2.3016 2.4266 2.5516 2.6766 2.8016 2.9266 3.0516 3.1766 3.3016 3.4266 3.5516 3.6766 3.8016 3.9266 4.0516 4.1766 4.3016 4.4266 4.5516 4.6766 4.8016 4.9266 5.0516 5.1766 5.3016 5.4266 5.5516 5.6766 5.8016

Inches 1.1946 1.2571 1.3196 1.3821 1.4446 1.5071 1.5696 1.6321 1.6946 1.7571 1.8196 1.9446 2.0696 2.1946 2.3196 2.4446 2.5696 2.6946 2.8196 2.9446 3.0696 3.1946 3.3196 3.4446 3.5696 3.6946 3.8196 3.9446 4.0696 4.1946 4.3196 4.4446 4.5696 4.6946 4.8196 4.9446 5.0696 5.1946 5.3196 5.4446 5.5696 5.6946 5.8196

Lead Angle λ at Basic P.D. Deg. Min. 2 24 2 17 2 11 2 5 2 0 1 55 1 51 1 47 1 43 1 40 1 36 1 30 1 25 1 20 1 16 1 12 1 9 1 6 1 3 1 0 0 58 0 56 0 54 0 52 0 50 0 48 0 47 0 45 0 44 0 43 0 42 0 40 0 39 0 38 0 37 0 36 0 35 0 35 0 34 0 33 0 32 0 32 0 31

Area of Minor Dia. at D − 2hb Sq. In. 1.054 1.171 1.294 1.423 1.56 1.70 1.85 2.00 2.16 2.33 2.50 2.86 3.25 3.66 4.10 4.56 5.04 5.55 6.09 6.64 7.23 7.84 8.47 9.12 9.81 10.51 11.24 12.00 12.78 13.58 14.41 15.3 16.1 17.0 18.0 18.9 19.9 20.9 21.9 23.0 24.0 25.1 26.3

Tensile Stress Areab Sq. In. 1.155 1.277 1.405 1.54 1.68 1.83 1.98 2.14 2.30 2.47 2.65 3.03 3.42 3.85 4.29 4.76 5.26 5.78 6.33 6.89 7.49 8.11 8.75 9.42 10.11 10.83 11.57 12.33 13.12 13.94 14.78 15.6 16.5 17.5 18.4 19.3 20.3 21.3 22.4 23.4 24.5 25.6 26.8


1443.


1720).

d Basic minor diameter. e These are standard sizes of the UNC series.



1755

Table 5c. 8–Thread Series, 8–UN and 8–UNR—Basic Dimensions Sizes Primary Inches 1e 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8

Secondary Inches 11⁄16 13⁄16 15⁄16 17⁄16 19⁄16 111⁄16 113⁄16 115⁄16

2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4

21⁄8 23⁄8 25⁄8 27⁄8 31⁄8 33⁄8 35⁄8 37⁄8

4 41⁄4 41⁄2 43⁄4

41⁄8 43⁄8 45⁄8 47⁄8

5 51⁄4 51⁄2 53⁄4 6

51⁄8 53⁄8 55⁄8 57⁄8

Basic Major Dia.,D Inches 1.0000 1.0625 1.1250 1.1875 1.2500 1.3125 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000 4.1250 4.2500 4.3750 4.5000 4.6250 4.7500 4.8750 5.0000 5.1250 5.2500 5.3750 5.5000 5.6250 5.7500 5.8750 6.0000

Basic Pitch Dia.,a D2 Inches 0.9188 0.9813 1.0438 1.1063 1.1688 1.2313 1.2938 1.3563 1.4188 1.4813 1.5438 1.6063 1.6688 1.7313 1.7938 1.8563 1.9188 2.0438 2.1688 2.2938 2.4188 2.5438 2.6688 2.7938 2.9188 3.0438 3.1688 3.2938 3.4188 3.5438 3.6688 3.7938 3.9188 4.0438 4.1688 4.2938 4.4188 4.5438 4.6688 4.7938 4.9188 5.0438 5.1688 5.2938 5.4188 5.5438 5.6688 5.7938 5.9188

Minor Diameter Ext.Thds.,c Int.Thds.,d d3 (Ref.) D1 Inches Inches 0.8512 0.8647 0.9137 0.9272 0.9792 0.9897 1.0387 1.0522 1.1012 1.1147 1.1637 1.1772 1.2262 1.2397 1.2887 1.3022 1.3512 1.3647 1.4137 1.4272 1.4806 1.4897 1.5387 1.5522 1.6012 1.6147 1.6637 1.6772 1.7262 1.7397 1.7887 1.8022 1.8512 1.8647 1.9762 1.9897 2.1012 2.1147 2.2262 2.2397 2.3512 2.3647 2.4762 2.4897 2.6012 2.6147 2.7262 2.7397 2.8512 2.8647 2.9762 2.9897 3.1012 3.1147 3.2262 3.2397 3.3512 3.3647 3.4762 3.4897 3.6012 3.6147 3.7262 3.7397 3.8512 3.8647 3.9762 3.9897 4.1012 4.1147 4.2262 4.2397 4.3512 4.3647 4.4762 4.4897 4.6012 4.6147 4.7262 4.7397 4.8512 4.8647 4.9762 4.9897 5.1012 5.1147 5.2262 5.2397 5.3512 5.3647 5.4762 5.4897 5.6012 5.6147 5.7262 5.7397 5.8512 5.8647

Area of Lead Angle λ at Basic Minor Dia. at D − 2hb P.D. Deg. Min. Sq. In. 2 29 0.551 2 19 0.636 2 11 0.728 2 4 0.825 1 57 0.929 1 51 1.039 1 46 1.155 1 41 1.277 1 36 1.405 1 32 1.54 1 29 1.68 1 25 1.83 1 22 1.98 1 19 2.14 1 16 2.30 1 14 2.47 1 11 2.65 1 7 3.03 1 3 3.42 1 0 3.85 0 57 4.29 0 54 4.76 0 51 5.26 0 49 5.78 0 47 6.32 0 45 6.89 0 43 7.49 0 42 8.11 0 40 8.75 0 39 9.42 0 37 10.11 0 36 10.83 0 35 11.57 0 34 12.34 0 33 13.12 0 32 13.94 0 31 14.78 0 30 15.6 0 29 16.5 0 29 17.4 0 28 18.4 0 27 19.3 0 26 20.3 0 26 21.3 0 25 22.4 0 25 23.4 0 24 24.5 0 24 25.6 0 23 26.8

Tensile Stress Areab Sq. In. 0.606 0.695 0.790 0.892 1.000 1.114 1.233 1.360 1.492 1.63 1.78 1.93 2.08 2.25 2.41 2.59 2.77 3.15 3.56 3.99 4.44 4.92 5.43 5.95 6.51 7.08 7.69 8.31 8.96 9.64 10.34 11.06 11.81 12.59 13.38 14.21 15.1 15.9 16.8 17.7 18.7 19.7 20.7 21.7 22.7 23.8 24.9 26.0 27.1


1443.


1720).

d Basic minor diameter. e This is a standard size of the UNC series.



1756

Table 5d. 12-Thread series, 12-UN and 12-UNR—Basic Dimensions Sizes

Primary Inches 9⁄ e 16 5⁄ 8 3⁄ 4 7⁄ 8

1e 11⁄8e 11⁄4e 13⁄8 11⁄2e 15⁄8 13⁄4 17⁄8 2 21⁄4 21⁄2 23⁄4 3 31⁄4 31⁄2 33⁄4 4 41⁄4 41⁄2 43⁄4 5 51⁄4 51⁄2 53⁄4

Secondary Inches

11⁄ 16 13⁄ 16 15⁄ 16

11⁄16 13⁄16 15⁄16 17⁄16 19⁄16 111⁄16 113⁄16 115⁄16 21⁄8 23⁄8 25⁄8 27⁄8 31⁄8 33⁄8 35⁄8 37⁄8 41⁄8 43⁄8 45⁄8 47⁄8 51⁄8 53⁄8 55⁄8 57⁄8

6

Basic Major Dia., D Inches 0.5625 0.6250 0.6875 0.7500 0.8125 0.8750 0.9375 1.0000 1.0625 1.1250 1.1875 1.2500 1.3125 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000 4.1250 4.2500 4.3750 4.5000 4.6250 4.7500 4.8750 5.0000 5.1250 5.2500 5.3750 5.5000 5.6250 5.7500 5.8750 6.0000

Basic Pitch Dia.,a D2 Inches 0.5084 0.5709 0.6334 0.6959 0.7584 0.8209 0.8834 0.9459 1.0084 1.0709 1.1334 1.1959 1.2584 1.3209 1.3834 1.4459 1.5084 1.5709 1.6334 1.6959 1.7584 1.8209 1.8834 1.9459 2.0709 2.1959 2.3209 2.4459 2.5709 2.6959 2.8209 2.9459 3.0709 3.1959 3.3209 3.4459 3.5709 3.6959 3.8209 3.9459 4.0709 4.1959 4.3209 4.4459 4.5709 4.6959 4.8209 4.9459 5.0709 5.1959 5.3209 5.4459 5.5709 5.6959 5.8209 5.9459

Minor Diameter Ext. Int. Thds.,c Thds.,d d3 (Ref.) D1 Inches Inches 0.4633 0.4723 0.5258 0.5348 0.5883 0.5973 0.6508 0.6598 0.7133 0.7223 0.7758 0.7848 0.8383 0.8473 0.9008 0.9098 0.9633 0.9723 1.0258 1.0348 1.0883 1.0973 1.1508 1.1598 1.2133 1.2223 1.2758 1.2848 1.3383 1.3473 1.4008 1.4098 1.4633 1.4723 1.5258 1.5348 1.5883 1.5973 1.6508 1.6598 1.7133 1.7223 1.7758 1.7848 1.8383 1.8473 1.9008 1.9098 2.0258 2.0348 2.1508 2.1598 2.2758 2.2848 2.4008 2.4098 2.5258 2.5348 2.6508 2.6598 2.7758 2.7848 2.9008 2.9098 3.0258 3.0348 3.1508 3.1598 3.2758 3.2848 3.4008 3.4098 3.5258 3.5348 3.6508 3.6598 3.7758 3.7848 3.9008 3.9098 4.0258 4.0348 4.1508 4.1598 4.2758 4.2848 4.4008 4.4098 4.5258 4.5348 4.6508 4.6598 4.7758 4.7848 4.9008 4.9098 5.0258 5.0348 5.1508 5.1598 5.2758 5.2848 5.4008 5.4098 5.5258 5.5348 5.6508 5.6598 5.7758 5.7848 5.9008 5.9098

Lead Angle λ at Basic P.D. Deg. Min. 2 59 2 40 2 24 2 11 2 0 1 51 1 43 1 36 1 30 1 25 1 20 1 16 1 12 1 9 1 6 1 3 1 0 0 58 0 56 0 54 0 52 0 50 0 48 0 47 0 44 0 42 0 39 0 37 0 35 0 34 0 32 0 31 0 30 0 29 0 27 0 26 0 26 0 25 0 24 0 23 0 22 0 22 0 21 0 21 0 20 0 19 0 19 0 18 0 18 0 18 0 17 0 17 0 16 0 16 0 16 0 15

Area of Minor Dia. at D − 2hb Sq. In. 0.162 0.210 0.264 0.323 0.390 0.462 0.540 0.625 0.715 0.812 0.915 1.024 1.139 1.260 1.388 1.52 1.66 1.81 1.96 2.12 2.28 2.45 2.63 2.81 3.19 3.60 4.04 4.49 4.97 5.48 6.01 6.57 7.15 7.75 8.38 9.03 9.71 10.42 11.14 11.90 12.67 13.47 14.30 15.1 16.0 16.9 17.8 18.8 19.8 20.8 21.8 22.8 23.9 25.0 26.1 27.3

Tensile Stress Areab Sq. In. 0.182 0.232 0.289 0.351 0.420 0.495 0.576 0.663 0.756 0.856 0.961 1.073 1.191 1.315 1.445 1.58 1.72 1.87 2.03 2.19 2.35 2.53 2.71 2.89 3.28 3.69 4.13 4.60 5.08 5.59 6.13 6.69 7.28 7.89 8.52 9.18 9.86 10.57 11.30 12.06 12.84 13.65 14.48 15.3 16.2 17.1 18.0 19.0 20.0 21.0 22.0 23.1 24.1 25.2 26.4 27.5


1443.


1720.)

d Basic minor diameter. e These are standard sizes of the UNC or UNF Series.



1757

Table 5e. 16–Thread Series, 16–UN and 16–UNR—Basic Dimensions Sizes Primary Inches

Secondary Inches

3⁄ e 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ e 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 41⁄8 41⁄4 43⁄8 41⁄2 45⁄8 43⁄4 47⁄8 5 51⁄8 51⁄4 53⁄8

Minor Diameter

Basic Major Dia., D Inches

Basic Pitch Dia.,a D2 Inches

Inches

Inches

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 1.3125 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000 3.1250 3.2500 3.3750 3.5000 3.6250 3.7500 3.8750 4.0000 4.1250 4.2500 4.3750 4.5000 4.6250 4.7500 4.8750 5.0000 5.1250 5.2500 5.3750

0.3344 0.3969 0.4594 0.5219 0.5844 0.6469 0.7094 0.7719 0.8344 0.8969 0.9594 1.0219 1.0844 1.1469 1.2094 1.2719 1.3344 1.3969 1.4594 1.5219 1.5844 1.6469 1.7094 1.7719 1.8344 1.8969 1.9594 2.0844 2.2094 2.3344 2.4594 2.5844 2.7094 2.8344 2.9594 3.0844 3.2094 3.3344 3.4594 3.5844 3.7094 3.8344 3.9594 4.0844 4.2094 4.3344 4.4594 4.5844 4.7094 4.8344 4.9594 5.0844 5.2094 5.3344

0.3005 0.3630 0.4255 0.4880 0.5505 0.6130 0.6755 0.7380 0.8005 0.8630 0.9255 0.9880 1.0505 1.1130 1.1755 1.2380 1.3005 1.3630 1.4255 1.4880 1.5505 1.6130 1.6755 1.7380 1.8005 1.8630 1.9255 2.0505 2.1755 2.3005 2.4255 2.5505 2.6755 2.8005 2.9255 3.0505 3.1755 3.3005 3.4255 3.5505 3.6755 3.8005 3.9255 4.0505 4.1755 4.3005 4.4255 4.5505 4.6755 4.8005 4.9255 5.0505 5.1755 5.3005

0.3073 0.3698 0.4323 0.4948 0.5573 0.6198 0.6823 0.7448 0.8073 0.8698 0.9323 0.9948 1.0573 1.1198 1.1823 1.2448 1.3073 1.3698 1.4323 1.4948 1.5573 1.6198 1.6823 1.7448 1.8073 1.8698 1.9323 2.0573 2.1823 2.3073 2.4323 2.5573 2.6823 2.8073 2.9323 3.0573 3.1823 3.3073 3.4323 3.5573 3.6823 3.8073 3.9323 4.0573 4.1823 4.3073 4.4323 4.5573 4.6823 4.8073 4.9323 5.0573 5.1823 5.3073

Ext. Thds.,c d3 (Ref.)

Int. Thds.,d D1

Lead Angle λ at Basic P.D. Deg. Min. 3 2 2 2 1 1 1 1 1 1 1 1 1 1 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 0 0 0 0 0 0 0 0 0 0 0 0

24 52 29 11 57 46 36 29 22 16 11 7 3 0 57 54 51 49 47 45 43 42 40 39 37 36 35 33 31 29 28 26 25 24 23 22 21 21 20 19 18 18 17 17 16 16 15 15 15 14 14 13 13 13

Area of Minor Dia. at D − 2hb Sq. In.

Tensile Stress Areab Sq. In.

0.0678 0.0997 0.1378 0.182 0.232 0.289 0.351 0.420 0.495 0.576 0.663 0.756 0.856 0.961 1.073 1.191 1.315 1.445 1.58 1.72 1.87 2.03 2.19 2.35 2.53 2.71 2.89 3.28 3.69 4.13 4.60 5.08 5.59 6.13 6.69 7.28 7.89 8.52 9.18 9.86 10.57 11.30 12.06 12.84 13.65 14.48 15.34 16.2 17.1 18.0 19.0 20.0 21.0 22.0

0.0775 0.1114 0.151 0.198 0.250 0.308 0.373 0.444 0.521 0.604 0.693 0.788 0.889 0.997 1.111 1.230 1.356 1.488 1.63 1.77 1.92 2.08 2.24 2.41 2.58 2.77 2.95 3.35 3.76 4.21 4.67 5.16 5.68 6.22 6.78 7.37 7.99 8.63 9.29 9.98 10.69 11.43 12.19 12.97 13.78 14.62 15.5 16.4 17.3 18.2 19.2 20.1 21.1 22.2



1758

Table 5e. (Continued) 16–Thread Series, 16–UN and 16–UNR—Basic Dimensions Sizes Primary Inches 51⁄2

Secondary Inches 55⁄8

53⁄4 57⁄8 6

Basic Major Dia., D Inches 5.5000 5.6250 5.7500 5.8750 6.0000

Minor Diameter


Ext. Thds.,c d3 (Ref.)

Int. Thds.,d D1

Inches 5.4594 5.5844 5.7094 5.8344 5.9594

Inches 5.4255 5.5505 5.6755 5.8005 5.9255

Inches 5.4323 5.5573 5.6823 5.8073 5.9323

Lead Angle λ at Basic P.D. Deg. Min. 0 13 0 12 0 12 0 12 0 11

Area of Minor Dia. at D − 2hb Sq. In. 23.1 24.1 25.2 26.4 27.5

Tensile Stress Areab Sq. In. 23.2 24.3 25.4 26.5 27.7


1443.


1720).

d Basic minor diamter. e These are standard sizes of the UNC or UNF Series.

Table 5f. 20–Thread Series, 20–UN and 20–UNR—Basic Dimensions Sizes Primary Inches 1⁄ e 4 5⁄ 16 3⁄ 8 7⁄ e 16 1⁄ e 2 9⁄ 16 5⁄ 8 3⁄ e 4 7⁄ e 8

1e 11⁄8 11⁄14 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄4 21⁄2 23⁄4 3

Secondary Inches

11⁄ 16 13⁄ e 16 15⁄ e 16

11⁄16 13⁄16 15⁄16 17⁄16 19⁄16 111⁄16 113⁄16 115⁄16 21⁄8 23⁄8 25⁄8 27⁄8

Basic Major Dia.,D Inches 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 1.3125 1.3750 1.4375 1.5000 1.5625 1.6250 1.6875 1.7500 1.8125 1.8750 1.9375 2.0000 2.1250 2.2500 2.3750 2.5000 2.6250 2.7500 2.8750 3.0000

Basic Pitch Dia.,a D2 Inches 0.2175 0.2800 0.3425 0.4050 0.4675 0.5300 0.5925 0.6550 0.7175 0.7800 0.8425 0.9050 0.9675 1.0300 1.0925 1.1550 1.2175 1.2800 1.3425 1.4050 1.4675 1.5300 1.5925 1.6550 1.7175 1.7800 1.8425 1.9050 1.9675 2.0925 2.2175 2.3425 2.4675 2.5925 2.7175 2.8425 2.9675

Minor Diameter Int. Thds.,d Ext. Thds.,c d3 (Ref.) D1 Inches Inches 0.1905 0.1959 0.2530 0.2584 0.3155 0.3209 0.3780 0.3834 0.4405 0.4459 0.5030 0.5084 0.5655 0.5709 0.6280 0.6334 0.6905 0.6959 0.7530 0.7584 0.8155 0.8209 0.8780 0.8834 0.9405 0.9459 1.0030 1.0084 1.0655 1.0709 1.1280 1.1334 1.1905 1.1959 1.2530 1.2584 1.3155 1.3209 1.3780 1.3834 1.4405 1.4459 1.5030 1.5084 1.5655 1.5709 1.6280 1.6334 1.6905 1.6959 1.7530 1.7584 1.8155 1.8209 1.8780 1.8834 1.9405 1.9459 2.0655 2.0709 2.1905 2.1959 2.3155 2.3209 2.4405 2.4459 2.5655 2.5709 2.6905 2.6959 2.8155 2.8209 2.9405 2.9459

Lead Angle λ at Basic P.D. Deg. Min. 4 11 3 15 2 40 2 15 1 57 1 43 1 32 1 24 1 16 1 10 1 5 1 0 0 57 0 53 0 50 0 47 0 45 0 43 0 41 0 39 0 37 0 36 0 34 0 33 0 32 0 31 0 30 0 29 0 28 0 26 0 25 0 23 0 22 0 21 0 20 0 19 0 18

Area of Minor Dia. at D − 2hb Sq. In. 0.0269 0.0481 0.0755 0.1090 0.1486 0.194 0.246 0.304 0.369 0.439 0.515 0.0.598 0.687 0.782 0.882 0.990 1.103 1.222 1.348 1.479 1.62 1.76 1.91 2.07 2.23 2.40 2.57 2.75 2.94 3.33 3.75 4.19 4.66 5.15 5.66 6.20 6.77

Tensile Stress Areab Sq. In. 0.0318 0.0547 0.0836 0.1187 0.160 0.207 0.261 0.320 0.386 0.458 0.536 0.620 0.711 0.807 0.910 1.018 1.133 1.254 1.382 1.51 1.65 1.80 1.95 2.11 2.27 2.44 2.62 2.80 2.99 3.39 3.81 4.25 4.72 5.21 5.73 6.27 6.84


1443.


1720.)

d Basic minor diameter. e These are standard sizes of the UNC, UNF, or UNEF Series.



1759

Table 5g. 28–Thread Series, 28–UN and 28–UNR — Basic Dimensions Sizes

Primary Inches

Secondary Inches 12 (0.216)e

1⁄ e 4 5⁄ 16 3⁄ 8 7⁄ e 16 1⁄ e 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

Basic Major Dia., D


Inches 0.2160 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 1.3125 1.3750 1.4375 1.5000

Inches 0.1928 0.2268 0.2893 0.3518 0.4143 0.4768 0.5393 0.6018 0.6643 0.7268 0.7893 0.8518 0.9143 0.9768 1.0393 1.1018 1.1643 1.2268 1.2893 1.3518 1.4143 1.4768

Minor Diameter Ext. Int. Thds.,c Thds.,d d3 (Ref.) D1 Inches Inches 0.1734 0.1773 0.2074 0.2113 0.2699 0.2738 0.3324 0.3363 0.3949 0.3988 0.4574 0.4613 0.5199 0.5238 0.5824 0.5863 0.6449 0.6488 0.7074 0.7113 0.7699 0.7738 0.8324 0.8363 0.8949 0.8988 0.9574 0.9613 1.0199 1.0238 1.0824 1.0863 1.1449 1.1488 1.2074 1.2113 1.2699 1.2738 1.3324 1.3363 1.3949 1.3988 1.4574 1.4613

Lead Angel λ at Basic P.D. Deg. 3 2 2 1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Min. 22 52 15 51 34 22 12 5 59 54 50 46 43 40 38 35 34 32 30 29 28 26

Area of Minor Dia. at D-2hb

Tensile Stress Areab Sq. In. 0.0258 0,0364 0.0606 0.0909 0.1274 0.170 0.219 0.274 0.335 0.402 0.475 0.554 0.640 0.732 0.830 0.933 1.044 1.160 1.282 1.411 1.55 1.69

Sq. In. 0.0226 0.0326 0.0556 0.0848 0.1201 0.162 0.209 0.263 0.323 0.389 0.461 0.539 0.624 0.714 0.811 0.914 1.023 1.138 1.259 1.386 1.52 1.66


1443.


1720.)

d Basic minor diameter. e These are standard sizes of the UNF or UNEF Series.

Table 5h. 32–Thread Series, 32–UN and 32–UNR — Basic Dimensions Sizes Primary Inches

Secondary Inches

6 (0.138)e 8 (0.164)e 10 (0.190)e 12 (0.216)e 1⁄ e 4 5⁄ e 16 3⁄ e 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ 16 3⁄ 4 13⁄ 16 7⁄ 8 15⁄ 16

1

Basic Major Dia.,D Inches 0.1380 0.1640 0.1900 0.2160 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

Basic Pitch Dia.,a D2 Inches 0.1177 0.1437 0.1697 0.1957 0.2297 0.2922 0.3547 0.4172 0.4797 0.5422 0.6047 0.6672 0.7297 0.7922 0.8547 0.9172 0.9797

Minor Diameter Ext.Thds.,c Int.Thds.,d d3 (Ref.) D1 Inches Inches 0.1008 0.1042 0.1268 0.1302 0.1528 0.1562 0.1788 0.1822 0.2128 0.2162 0.2753 0.2787 0.3378 0.3412 0.4003 0.4037 0.4628 0.4662 0.5253 0.5287 0.5878 0.5912 0.6503 0.6537 0.7128 0.7162 0.7753 0.7787 0.8378 0.8412 0.9003 0.9037 0.9628 0.9662

Lead Angel λ at Basic P.D. Deg. 4 3 3 2 2 1 1 1 1 1 0 0 0 0 0 0 0

Min. 50 58 21 55 29 57 36 22 11 3 57 51 47 43 40 37 35

Area of Minor Dia. at D - 2hb Sq. In. 0.00745 0.01196 0.01750 0.0242 0.0344 0.0581 0.0878 0.1237 0.166 0.214 0.268 0.329 0.395 0.468 0.547 0.632 0.723

Tensile Stress Areab Sq. In. 0.00909 0.0140 0.0200 0.0270 0.0379 0.0625 0.0932 0.1301 0.173 0.222 0.278 0.339 0.407 0.480 0.560 0.646 0.738


1443.


1720.)

d Basic minor diameter. e These are standard sizes of the UNC, UNF, or UNEF Series.


1760


Thread Classes.—Thread classes are distinguished from each other by the amounts of tolerance and allowance. Classes identified by a numeral followed by the letters A and B are derived from certain Unified formulas (not shown here) in which the pitch diameter tolerances are based on increments of the basic major (nominal) diameter, the pitch, and the length of engagement. These formulas and the class identification or symbols apply to all of the Unified threads. Classes 1A, 2A, and 3A apply to external threads only, and Classes 1B, 2B, and 3B apply to internal threads only. The disposition of the tolerances, allowances, and crest clearances for the various classes is illustrated on page 1761. Classes 2A and 2B: Classes 2A and 2B are the most commonly used for general applications, including production of bolts, screws, nuts, and similar fasteners. The maximum diameters of Class 2A (external) uncoated threads are less than basic by the amount of the allowance. The allowance minimizes galling and seizing in high-cycle wrench assembly, or it can be used to accommodate plated finishes or other coating. However, for threads with additive finish, the maximum diameters of Class 2A may be exceeded by the amount of the allowance, for example, the 2A maximum diameters apply to an unplated part or to a part before plating whereas the basic diameters (the 2A maximum diameter plus allowance) apply to a part after plating. The minimum diameters of Class 2B (internal) threads, whether or not plated or coated, are basic, affording no allowance or clearance in assembly at maximum metal limits. Class 2AG: Certain applications require an allowance for rapid assembly to permit application of the proper lubricant or for residual growth due to high-temperature expansion. In these applications, when the thread is coated and the 2A allowance is not permitted to be consumed by such coating, the thread class symbol is qualified by G following the class symbol. Classes 3A and 3B: Classes 3A and 3B may be used if closer tolerances are desired than those provided by Classes 2A and 2B. The maximum diameters of Class 3A (external) threads and the minimum diameters of Class 3B (internal) threads, whether or not plated or coated, are basic, affording no allowance or clearance for assembly of maximum metal components. Classes 1A and 1B: Classes 1A and 1B threads replaced American National Class 1. These classes are intended for ordnance and other special uses. They are used on threaded components where quick and easy assembly is necessary and where a liberal allowance is required to permit ready assembly, even with slightly bruised or dirty threads. Maximum diameters of Class 1A (external) threads are less than basic by the amount of the same allowance as applied to Class 2A. For the intended applications in American practice the allowance is not available for plating or coating. Where the thread is plated or coated, special provisions are necessary. The minimum diameters of Class 1B (internal) threads, whether or not plated or coated, are basic, affording no allowance or clearance for assembly with maximum metal external thread components having maximum diameters which are basic. Coated 60-deg. Threads.—Although the Standard does not make recommendations for thicknesses of, or specify limits for coatings, it does outline certain principles that will aid mechanical interchangeability if followed whenever conditions permit. To keep finished threads within the limits of size established in the Standard, external threads should not exceed basic size after plating and internal threads should not be below basic size after plating. This recommendation does not apply to threads coated by certain commonly used processes such as hot-dip galvanizing where it may not be required to maintain these limits. Class 2A provides both a tolerance and an allowance. Many thread requirements call for coatings such as those deposited by electro-plating processes and, in general, the 2A allow-


1/2 PD Tolerance on Nut 1/2 Allowance (Screw only) 1/2 PD Tolerance on Screw

External Thread (Screw)

Minimum Pitch Dia. of Nut Basic Pitch Dia. of Screw ond Nut Maximum Pitch Dia. of Screw Minimum Pitch Dia. of Screw 1/2 Tolerance on Minor Dia. of Nut UNR Maximum Minor Dia of Screw Minimum Minor Dia. of Screw UNR Contour (see text) Permissible Form of UN Thread From New Tool Minimum Minor Dia. of Nut Maximum Minor Dia. of Nut UN Nominal (Max.) Minor Dia. of Screw 1/ 2 Allowance Basic Form (Screw Only)

Maximum Pitch Dia. of Nut

Minimum Major Dia. of Screw Basic Major Dia. of Screw and Nut

Maximum Major Dia. of Nut Minimum Major Dia. of Nut Maximum Major Dia. of Screw

0.25P

0.125P


1/2

PD Tolerance on Nut

1/2

PD Tolerance on Screw

Limits of Size Showing Tolerances and Crest Clearances for Unified Classes 3A and 3B and American National Classes 2 and 3

Basic Form

60°

0.250P

0.125P

1761

Copyright 2008, Industrial Press Inc., New York, NY - www.industrialpress.com Minimum Minor Dia. of Nut Maximum Minor Dia. of Nut UN Nominal (Max.) Minor Dia. of Screw

30°

UNR Maximum Minor Dia. of Screw Minimum Minor Dia. of Screw UNR Contour (see text) Permissible Form of UN Thread From New Tool

60°


Limits of Size Showing Tolerances, Allowances (Neutral Space), and Crest Clearances for Unified Classes 1A, 2A, 1B, and 2B 0.125P

1/ 2 PD Tolerance on Minor Dia. of Nut

Internal Thread (Nut)

Minimum Pitch Dia. of Nut Basic Pitch Dia. of Screw and Nut Maximum Pitch Dia. of Screw Minimum Pitch Dia. of Screw

1/ 2 Tolerance on Major Diameter of Screw

Maximum Pitch Dia. of Nut

0.125P

Minimum Major Dia. of Screw Basic Major Dia. of Screw and Nut

0.041667P

Maximum Major Dia. of Nut Minimum Major Dia. of Nut Maximum Major Dia. of Screw


0.041667P

Internal Thread (Nut) 1/2

Tolerance on Major Diameter of Screw

30°

1762


ance provides adequate undercut for such coatings. There may be variations in thickness and symmetry of coating resulting from commercial processes but after plating the threads should be accepted by a basic Class 3A size GO gage and a Class 2A gage as a NOT-GO gage. Class 1A provides an allowance which is maintained for both coated and uncoated product, i.e., it is not available for coating. Class 3A does not include an allowance so it is suggested that the limits of size before plating be reduced by the amount of the 2A allowance whenever that allowance is adequate. No provision is made for overcutting internal threads as coatings on such threads are not generally required. Further, it is very difficult to deposit a significant thickness of coating on the flanks of internal threads. Where a specific thickness of coating is required on an internal thread, it is suggested that the thread be overcut so that the thread as coated will be accepted by a GO thread plug gage of basic size. This Standard ASME/ANSI B1.1-1989 (R2001) specifies limits of size that pertain whether threads are coated or uncoated. Only in Class 2A threads is an allowance available to accommodate coatings. Thus, in all classes of internal threads and in all Class 1A, 2AG, and 3A external threads, limits of size must be adjusted to provide suitable provision for the desired coating. For further information concerning dimensional accommodation of coating or plating for 60-degree threads, see Section 7, ASME/ANSI B1.1-1989 (R2001). Screw Thread Selection — Combination of Classes.—Whenever possible, selection should be made from Table 2, Standard Series Unified Screw Threads, preference being given to the Coarse- and Fine- thread Series. If threads in the standard series do not meet the requirements of design, reference should be made to the selected combinations in Table 3. The third expedient is to compute the limits of size from the tolerance tables or tolerance increment tables given in the Standard. The fourth and last resort is calculation by the formulas given in the Standard. The requirements for screw thread fits for specific applications depend on end use and can be met by specifying the proper combinations of thread classes for the components. For example, a Class 2A external thread may be used with a Class 1B, 2B, or 3B internal thread. Pitch Diameter Tolerances, All Classes.—The pitch diameter tolerances in Table 3 for all classes of the UNC, UNF, 4-UN, 6-UN, and 8-UN series are based on a length of engagement equal to the basic major (nominal) diameter and are applicable for lengths of engagement up to 11⁄2 diameters. The pitch diameter tolerances used in Table 3 for all classes of the UNEF, 12-UN, 16UN, 20-UN, 28-UN, and 32-UN series and the UNS series, are based on a length of engagement of 9 pitches and are applicable for lengths of engagement of from 5 to 15 pitches. Screw Thread Designation.—The basic method of designating a screw thread is used where the standard tolerances or limits of size based on the standard length of engagement are applicable. The designation specifies in sequence the nominal size, number of threads per inch, thread series symbol, thread class symbol, and the gaging system number per ASME/ANSI B1.3M. The nominal size is the basic major diameter and is specified as the fractional diameter, screw number, or their decimal equivalent. Where decimal equivalents are used for size callout, they shall be interpreted as being nominal size designations only and shall have no dimensional significance beyond the fractional size or number designation. The symbol LH is placed after the thread class symbol to indicate a left-hand thread: Examples: 1⁄ –20 UNC-2A (21) or 0.250–20 UNC-2A (21) 4



1763

10–32 UNF-2A (22) or 0.190–32 UNF-2A (22) 7⁄ –20 UNRF-2A (23) or 0.4375–20 UNRF-2A (23) 16 2–12 UN-2A (21) or 2.000–12 UN-2A (21) 1⁄ –20 UNC-3A-LH (21) or 0.250–20 UNC-3A-LH (21) 4 For uncoated standard series threads these designations may optionally be supplemented by the addition of the pitch diameter limits of size. Example: 1⁄ –20 UNC-2A (21) 4 PD 0.2164–0.2127 (Optional for uncoated threads) Designating Coated Threads.—For coated (or plated) Class 2A external threads, the basic (max) major and basic (max) pitch diameters are given followed by the words AFTER COATING. The major and pitch diameter limits of size before coating are also given followed by the words BEFORE COATING. 3⁄ –10 UNC-2A (21) Example: 4 aMajor dia 0.7500 max } AFTER COATING PD 0.6850 max bMajor dia 0.7482–0.7353 } BEFORE COATING PD 0.6832–0.6773 } a Major and PD values are equal to basic and correspond to those in Table 3 for Class 3A. b Major and PD limits are those in Table 3 for Class 2A.

Certain applications require an allowance for rapid assembly, to permit application of a proper lubricant, or for residual growth due to high-temperature expansion. In such applications where the thread is to be coated and the 2A allowance is not permitted to be consumed by such coating, the thread class symbol is qualified by the addition of the letter G (symbol for allowance) following the class symbol, and the maximum major and maximum pitch diameters are reduced below basic size by the amount of the 2A allowance and followed by the words AFTER COATING. This arrangement ensures that the allowance is maintained. The major and pitch diameter limits of size before coating are also given followed by SPL and BEFORE COATING. For information concerning the designating of this and other special coating conditions reference should be made to American National Standard ASME/ANSI B1.1-1989 (R2001). Designating UNS Threads.—UNS screw threads that have special combinations of diameter and pitch with tolerance to Unified formulation have the basic form designation set out first followed always by the limits of size. Designating Multiple Start Threads.—If a screw thread is of multiple start, it is designated by specifying in sequence the nominal size, pitch (in decimals or threads per inch) and lead (in decimals or fractions). Other Special Designations.—For other special designations including threads with modified limits of size or with special lengths of engagement, reference should be made to American National Standard ASME/ANSI B1.1-1989 (R2001). Hole Sizes for Tapping.—Hole size limits for tapping Classes 1B, 2B, and 3B threads of various lengths of engagement are given in Table 2 on page 1926. Internal Thread Minor Diameter Tolerances.—Internal thread minor diameter tolerances in Table 3 are based on a length of engagement equal to the nominal diameter. For general applications these tolerances are suitable for lengths of engagement up to 11⁄2 diameters. However, some thread applications have lengths of engagement which are greater than 11⁄2 diameters or less than the nominal diameter. For such applications it may be advantageous to increase or decrease the tolerance, respectively, as explained in the Tapping Section.


1764

Machinery's Handbook 28th Edition MINIATURE SCREW THREADS American Standard for Unified Miniature Screw Threads

This American Standard (B1.10-1958, R1988) introduces a new series to be known as Unified Miniature Screw Threads and intended for general purpose fastening screws and similar uses in watches, instruments, and miniature mechanisms. Use of this series is recommended on all new products in place of the many improvised and unsystematized sizes now in existence which have never achieved broad acceptance nor recognition by standardization bodies. The series covers a diameter range from 0.30 to 1.40 millimeters (0.0118 to 0.0551 inch) and thus supplements the Unified and American thread series which begins at 0.060 inch (number 0 of the machine screw series). It comprises a total of fourteen sizes which, together with their respective pitches, are those endorsed by the American-British-Canadian Conference of April 1955 as the basis for a Unified standard among the inch-using countries, and coincide with the corresponding range of sizes in ISO (International Organization for Standardization) Recommendation No. 68. Additionally, it utilizes thread forms which are compatible in all significant respects with both the Unified and ISO basic thread profiles. Thus, threads in this series are interchangeable with the corresponding sizes in both the American-British-Canadian and ISO standardization programs. Basic Form of Thread.—The basic profile by which the design forms of the threads covered by this standard are governed is shown in Table 1. The thread angle is 60 degrees and except for basic height and depth of engagement which are 0.52p, instead of 0.54127p, the basic profile for this thread standard is identical with the Unified and American basic thread form. The selection of 0.52 as the exact value of the coefficient for the height of this basic form is based on practical manufacturing considerations and a plan evolved to simplify calculations and achieve more precise agreement between the metric and inch dimensional tables. Products made to this standard will be interchangeable with products made to other standards which allow a maximum depth of engagement (or combined addendum height) of 0.54127p. The resulting difference is negligible (only 0.00025 inch for the coarsest pitch) and is completely offset by practical considerations in tapping, since internal thread heights exceeding 0.52p are avoided in these (Unified Miniature) small thread sizes in order to reduce excessive tap breakage. Design Forms of Threads.—The design (maximum material) forms of the external and internal threads are shown in Table 2. These forms are derived from the basic profile shown in Table 1 by the application of clearances for the crests of the addenda at the roots of the mating dedendum forms. Basic and design form dimensions are given in Table 3. Nominal Sizes: The thread sizes comprising this series and their respective pitches are shown in the first two columns of Table 5. The fourteen sizes shown in Table 5 have been systematically distributed to provide a uniformly proportioned selection over the entire range. They are separated alternately into two categories: The sizes shown in bold type are selections made in the interest of simplification and are those to which it is recommended that usage be confined wherever the circumstances of design permit. Where these sizes do not meet requirements the intermediate sizes shown in light type are available. Table 1. Unified Miniature Screw Threads — Basic Thread Form Formulas for Basic Thread Form Metric units (millimeters) are used in all formulas Thread Element Symbol Formula Angle of thread Half angle of thread Pitch of thread No. of threads per inch Height of sharp V thread Addendum of basic thread Height of basic thread

2α α p n H hab hb

60° 30° 25.4/p 0.86603p 0.32476p 0.52p


Machinery's Handbook 28th Edition MINIATURE SCREW THREADS

1765

Table 2. Unified Miniature Screw Threads — Design Thread Form

Formulas for Design Thread Form (maximum material)a External Thread Internal Thread Thread Element Symbol Formula Thread Element Symbol Addendum has 0.32476p Height of engagement he Height hs 0.60p Height of thread hn Flat at crest Fcs 0.125p Flat at crest Fcn Radius at root rrs 0.158p Radius at root rrn (approx)

Formula 0.52p 0.556p 0.27456p 0.072p (approx)

a Metric units (millimeters) are used in all formulas.



1766

Table 3. Unified Miniature Screw Threads—Basic and Design Form Dimensions Basic Thread Form Threads per inch na

Pitch p

External Thread Design Form Addendum hab = has = 0.32476p

Height of Sharp V H= 0.86603p

Height hb = 0.52p

.0693 .0779 .0866 .1083 .1299 .1516 .1732 .1949 .2165 .2598

.0416 .0468 .0520 .0650 .0780 .0910 .1040 .1170 .1300 .1560

.0260 .0292 .0325 .0406 .0487 .0568 .0650 .0731 .0812 .0974

Flat at Crest Fcs = 0.125p

Height hs = 0.60p

Radius at Root rrs = 0.158p

Internal Thread Design Form Height hn = 0.556p

Flat at Crest Fcn = 0.27456p

Radius at Root rrn = 0.072p

.0126 .0142 .0158 .0198 .0237 .0277 .0316 .0356 .0395 .0474

.0445 .0500 .0556 .0695 .0834 .0973 .1112 .1251 .1390 .1668

.0220 .0247 .0275 .0343 .0412 .0480 .0549 .0618 .0686 .0824

.0058 .0065 .0072 .0090 .0108 .0126 .0144 .0162 .0180 .0216

Millimeter Dimensions … … … … … … … … … …

.080 .090 .100 .125 .150 .175 .200 .225 .250 .300

.048 .054 .060 .075 .090 .105 .120 .135 .150 .180

.0100 .0112 .0125 .0156 .0188 .0219 .0250 .0281 .0312 .0375

Inch Dimensions 3171⁄2

.003150

.00273

.00164

.00102

.00189

.00039

.00050

.00175

.00086

.00023

2822⁄9

.003543

.00307

.00184

.00115

.00213

.00044

.00056

.00197

.00097

.00026

254 2031⁄5

.003937 .004921

.00341 .00426

.00205 .00256

.00128 .00160

.00236 .00295

.00049 .00062

.00062 .00078

.00219 .00274

.00108 .00135

.00028 .00035

1691⁄3

.005906

.00511

.00307

.00192

.00354

.00074

.00093

.00328

.00162

.00043

1451⁄7

.006890

.00597

.00358

.00224

.00413

.00086

.00109

.00383

.00189

.00050

127 1128⁄9

.007874 .008858

.00682 .00767

.00409 .00461

.00256 .00288

.00472 .00531

.00098 .00111

.00124 .00140

.00438 .00493

.00216 .00243

.00057 .00064

1013⁄5

.009843

.00852

.00512

.00320

.00591

.00123

.00156

.00547

.00270

.00071

842⁄3

.011811

.01023

.00614

.00384

.00709

.00148

.00187

.00657

.00324

.00085

a In Tables 5 and 6 these values are shown rounded to the nearest whole number.

Table 4. Unified Miniature Screw Threads — Formulas for Basic and Design Dimensions and Tolerances Formulas for Basic Dimensions D = Basic Major Diameter and Nominal Size in millimeters; p = Pitch in millimeters; E = Basic Pitch Diameter in millimeters = D − 0.64952p; and K = Basic Minor Diameter in millimeters = D − 1.04p Formulas for Design Dimensions (Maximum Material) External Thread Ds = Major Diameter = D

Internal Thread Dn = Major Diameter = D + 0.072p

Es = Pitch Diameter = E

En = Pitch Diameter = E

Ks = Minor Diameter = D − 1.20p

Kn = Minor Diameter = K Formulas for Tolerances on Design Dimensionsa

External Thread (−) Major Diameter Tol., 0.12p + 0.006 Pitch Diameter Tol., 0.08p + 0.008 cMinor

Diameter Tol., 0.16p + 0.008

Internal Thread (+) bMajor

Diameter Tol., 0.168p + 0.008 Pitch Diameter Tol., 0.08p + 0.008 Minor Diameter Tol., 0.32p + 0.012

a These tolerances are based on lengths of engagement of 2⁄ D to 11⁄ D. 3 2 b This tolerance establishes the maximum limit of the major diameter of the internal thread. In prac-

tice, this limit is applied to the threading tool (tap) and not gaged on the product. Values for this tolerance are, therefore, not given in Table 5. c This tolerance establishes the minimum limit of the minor diameter of the external thread. In practice, this limit is applied to the threading tool and only gaged on the product in confirming new tools. Values for this tolerance are, therefore, not given in Table 5. Metric units (millimeters) apply in all formulas. Inch tolerances are not derived by direct conversion of the metric values. They are the differences between the rounded off limits of size in inch units.


Machinery's Handbook 28th Edition Table 5. Unified Miniature Screw Threads — Limits of Size and Tolerances Major Diam.

External Threads Pitch Diam.

Minor Diam.

Minor Diam.

Internal Threads Pitch Diam.

Pitch mm

Maxb mm

Min mm

Maxb mm

Min mm

Maxc mm

Mind mm

Minb mm

Max mm

Minb mm

Max mm

0.30 UNM 0.35 UNM 0.40 UNM 0.45 UNM 0.50 UNM 0.55 UNM 0.60 UNM 0.70 UNM 0.80 UNM 0.90 UNM 1.00 UNM 1.10 UNM 1.20 UNM 1.40 UNM

0.080 0.090 0.100 0.100 0.125 0.125 0.150 0.175 0.200 0.225 0.250 0.250 0.250 0.300 Thds. per in. 318 282 254 254 203 203 169 145 127 113 102 102 102 85

0.300 0.350 0.400 0.450 0.500 0.550 0.600 0.700 0.800 0.900 1.000 1.100 1.200 1.400 inch 0.0118 0.0138 0.0157 0.0177 0.0197 0.0217 0.0236 0.0276 0.0315 0.0354 0.0394 0.0433 0.0472 0.0551

0.284 0.333 0.382 0.432 0.479 0.529 0.576 0.673 0.770 0.867 0.964 1.064 1.164 1.358 inch 0.0112 0.0131 0.0150 0.0170 0.0189 0.0208 0.0227 0.0265 0.0303 0.0341 0.0380 0.0419 0.0458 0.0535

0.248 0.292 0.335 0.385 0.419 0.469 0.503 0.586 0.670 0.754 0.838 0.938 1.038 1.205 inch 0.0098 0.0115 0.0132 0.0152 0.0165 0.0185 0.0198 0.0231 0.0264 0.0297 0.0330 0.0369 0.0409 0.0474

0.234 0.277 0.319 0.369 0.401 0.451 0.483 0.564 0.646 0.728 0.810 0.910 1.010 1.173 inch 0.0092 0.0109 0.0126 0.0145 0.0158 0.0177 0.0190 0.0222 0.0254 0.0287 0.0319 0.0358 0.0397 0.0462

0.204 0.242 0.280 0.330 0.350 0.400 0.420 0.490 0.560 0.630 0.700 0.800 0.900 1.040 inch 0.0080 0.0095 0.0110 0.0130 0.0138 0.0157 0.0165 0.0193 0.0220 0.0248 0.0276 0.0315 0.0354 0.0409

0.183 0.220 0.256 0.306 0.322 0.372 0.388 0.454 0.520 0.586 0.652 0.752 0.852 0.984 inch 0.0072 0.0086 0.0101 0.0120 0.0127 0.0146 0.0153 0.0179 0.0205 0.0231 0.0257 0.0296 0.0335 0.0387

0.217 0.256 0.296 0.346 0.370 0.420 0.444 0.518 0.592 0.666 0.740 0.840 0.940 1.088 inch 0.0085 0.0101 0.0117 0.0136 0.0146 0.0165 0.0175 0.0204 0.0233 0.0262 0.0291 0.0331 0.0370 0.0428

0.254 0.297 0.340 0.390 0.422 0.472 0.504 0.586 0.668 0.750 0.832 0.932 1.032 1.196 inch 0.0100 0.0117 0.0134 0.0154 0.0166 0.0186 0.0198 0.0231 0.0263 0.0295 0.0327 0.0367 0.0406 0.0471

0.248 0.292 0.335 0.385 0.419 0.469 0.503 0.586 0.670 0.754 0.838 0.938 1.038 1.205 inch 0.0098 0.0115 0.0132 0.0152 0.0165 0.0185 0.0198 0.0231 0.0264 0.0297 0.0330 0.0369 0.0409 0.0474

0.262 0.307 0.351 0.401 0.437 0.487 0.523 0.608 0.694 0.780 0.866 0.966 1.066 1.237 inch 0.0104 0.0121 0.0138 0.0158 0.0172 0.0192 0.0206 0.0240 0.0273 0.0307 0.0341 0.0380 0.0420 0.0487


Maxd mm

Lead Angle at Basic Pitch Diam. deg min

0.327 0.380 0.432 0.482 0.538 0.588 0.644 0.750 0.856 0.962 1.068 1.168 1.268 1.480 inch 0.0129 0.0149 0.0170 0.0190 0.0212 0.0231 0.0254 0.0295 0.0337 0.0379 0.0420 0.0460 0.0499 0.0583

5 5 5 4 5 4 5 5 5 5 5 4 4 4 deg 5 5 5 4 5 4 5 5 5 5 5 4 4 4

Major Diam. Mine mm 0.306 0.356 0.407 0.457 0.509 0.559 0.611 0.713 0.814 0.916 1.018 1.118 1.218 1.422 inch 0.0120 0.0140 0.0160 0.0180 0.0200 0.0220 0.0240 0.0281 0.0321 0.0361 0.0401 0.0440 0.0480 0.0560

52 37 26 44 26 51 26 26 26 26 26 51 23 32 min 52 37 26 44 26 51 26 26 26 26 26 51 23 32

Sectional Area at Minor Diam. at D — 1.28p sq mm 0.0307 0.0433 0.0581 0.0814 0.0908 0.1195 0.1307 0.1780 0.232 0.294 0.363 0.478 0.608 0.811 sq in 0.0000475 0.0000671 0.0000901 0.0001262 0.0001407 0.0001852 0.000203 0.000276 0.000360 0.000456 0.000563 0.000741 0.000943 0.001257

MINIATURE SCREW THREADS

Size Designationa

a Sizes shown in bold type are preferred. b This is also the basic dimension.


1767

c This limit, in conjunction with root form shown in Table 2, is advocated for use when optical projection methods of gaging are employed. For mechanical gaging the minimum minor diameter of the internal thread is applied. d This limit is provided for reference only. In practice, the form of the threading tool is relied upon for this limit. e This limit is provided for reference only, and is not gaged. For gaging, the maximum major diameter of the external thread is applied.


1768

Table 6. Unified Miniature Screw Threads— Minimum Root Flats for External Threads

mm

No. of Threads Per Inch

0.080 0.090 0.100 0.125 0.150 0.175 0.200 0.225 0.250 0.300

318 282 254 203 169 145 127 113 102 85

Pitch

Minimum Flat at Root Frs = 0.136p

Thread Height for Min. Flat at Root 0.64p mm

Inch

mm

Inch

0.0512 0.0576 0.0640 0.0800 0.0960 0.1120 0.1280 0.1440 0.1600 0.1920

0.00202 0.00227 0.00252 0.00315 0.00378 0.00441 0.00504 0.00567 0.00630 0.00756

0.0109 0.0122 0.0136 0.0170 0.0204 0.0238 0.0272 0.0306 0.0340 0.0408

0.00043 0.00048 0.00054 0.00067 0.00080 0.00094 0.00107 0.00120 0.00134 0.00161

Internal Thread (Nut) 1/ 2 tolerance on major dia.

of external thread

1/ 2 P D tolerance on

0.52p

internal tolerance 1/ 2 P D tolerance on

0.64p 0.136p

Min minor dia. of external thread

Max minor dia. of external thread

Min minor dia. of internal thread

minor dia. tolerance on internal thread


1/2

Max major dia. of internal thread Min major dia. of internal thread Max major dia. of external thread Min major dia. of external thread Basic major dia. Max pitch diameter of internal thread Min pitch diameter of internal thread Basic pitch dia. Max pitch diameter of external thread Min pitch diameter of external thread Max pitch diameter of internal thread

external tolerance

Limits of Size Showing Tolerances and Crest Clearances for UNM Threads


Machinery's Handbook 28th Edition BRITISH UNIFIED THREADS

1769

Limits of Size: Formulas used to determine limits of size are given in Table 4; the limits of size are given in Table 5. The diagram on page 1768 illustrates the limits of size and Table 6 gives values for the minimum flat at the root of the external thread shown on the diagram. Classes of Threads: The standard establishes one class of thread with zero allowance on all diameters. When coatings of a measurable thickness are required, they should be included within the maximum material limits of the threads since these limits apply to both coated and uncoated threads. Hole Sizes for Tapping: Suggested hole sizes are given in the Tapping Section. Unified Screw Threads of UNJ Basic Profile British Standard UNJ Threads.—This British Standard BS 4084: 1978 arises from a request originating from within the British aircraft industry and is based upon specifications for Unified screw threads and American military standard MIL-S-8879. These UNJ threads, having an enlarged root radius, were introduced for applications requiring high fatigue strength where working stress levels are high, in order to minimize size and weight, as in aircraft engines, airframes, missiles, space vehicles and similar designs where size and weight are critical. To meet these requirements the root radius of external Unified threads is controlled between appreciably enlarged limits, the minor diameter of the mating internal threads being appropriately increased to insure the necessary clearance. The requirement for high strength is further met by restricting the tolerances for UNJ threads to the highest classes, Classes 3A and 3B, of Unified screw threads. The standard, not described further here, contains both a coarse and a fine pitch series of threads. BS 4084: 1978 is technically identical to ISO 3161-1977 except for Appendix A. ASME Unified Inch Screw Threads, UNJ Form.—The ASME B1.15-1995 standard is similar to Military Specification MIL-S-8879, and equivalent to ISO 3161-1977 for thread Classes 3A and 3B. The ASME B1.15-1995 standard establishes the basic profile for the UNJ thread form, specifies a system of designation, lists the standard series of diameter-pitch combinations for diameters from 0.060 to 6.00 inches, and specifies limiting dimensions and tolerances. It specifies the characteristics of the UNJ inch series of threads having 0.15011P to 0.18042P designated radius at the root of the external thread, and also having the minor diameter of the external and internal threads increased above the ASME B1.1 UN and UNR thread forms to accommodate the external thread maximum root radius. UNJ threads are similar to UN threads except for a large radius in the root, or minor diameter, of the external thread. The radius eliminates sharp corners in the minor diameter of the bolt to increase the stripping strength. The fillets or radius in sharp corners increases strength at stress points where cracking or failure may occur due to change in temperature, heavy loads, or vibration. Other dimensions are the same as the UN thread. Because the radius on the external thread increases the minor diameter of the bolt, the internal thread, or nut, is modified accordingly to permit assembly. The minor diameter of the internal thread is enlarged to clear the radius. This is the only change to the internal thread. All other dimensions are the same as standard Unified threads. Different types of tap drill sizes are required to produce UNJ thread. All tooling for external threads, thread rolls, and chasers must be made to produce a radius at the minor diameter. All runout or incomplete threads shall have a radius also. Thread conforming to the ASME B1.1 UN profile and the UNJ profile are not interchangeable because of possible interference between the UNJ external thread minor diameter and the UN internal thread minor diameter. However, the UNJ internal thread will assemble with the UN external thread.


1770

Machinery's Handbook 28th Edition CALCULATING THREAD DIMENSIONS

CALCULATING THREAD DIMENSIONS Introduction The purpose of the ASME B1.30 standard is to establish uniform and specific practices for calculating and rounding the numeric values used for inch and metric screw thread design data dimensions only. No attempt has been made to establish a policy of rounding actual thread characteristics measured by the manufacturer or user of thread gages. Covered is the Standard Rounding Policy* regarding the last figure or decimal place to be retained by a numeric value and the number of decimal places to be retained by values used in intermediate calculations of thread design data dimensions. Values calculated to this ASME B1.30 Standard for inch and metric screw thread design data dimensions may vary slightly from values shown in existing issues of ASME B1 screw thread standards and are to take precedence in all new or future revisions of ASME B1 standards as applicable except as noted in following paragraph. Metric Application.—Allowances (fundamental deviations) and tolerances for metric M and MJ screw threads are based upon formulas which appear in applicable standards. Values of allowances for standard tolerance positions and values of tolerances for standard tolerance grades are tabulated in these standards for a selection of pitches. Rounding rules specified in ASME B1.30 have not been applied to these values but have followed practices of the International Organization for Standardization (ISO). For pitches which are not included in the tables, standard formulas and the rounding rules specified herein are applicable. ISO rounding practices, for screw thread tolerances and allowances, use rounding to the nearest values in the R40 series of numbers in accordance with ISO 3 (see page 672). In some cases, the rounded values have been adjusted to produce a smooth progression. Since the ISO rounded values have been standardized internationally, for metric screw threads, it would lead to confusion if tolerances and allowances were recalculated using B1.30 rules for use in the USA. B1.30 rounding rules are, therefore, only applicable to special threads where tabulated values do not exist in ISO standards. Values calculated using the ISO R40 series values may differ from those calculated using B1.30. In such a case the special thread values generated using B1.30 take precedence. Purpose.—Thread dimensions calculated from published formulas frequently may not yield the exact values published in the standards. The difference in most cases are due to rounding policy. The ASME B1.30 standard specifies that pitch, P, values shall be rounded to eight decimal places. In Example 1 that follows on page 1772, the pitch of 28 threads per inch, 0.03571429, is correct; using 1⁄28 or 0.0357 or 0.0357142856 instead of 0.03571429 will not produce values that conform to values calculated according this standard. The rounding rules specified by the standard are not uniform, and vary by feature. Pitch is held to eight decimal places, maximum major diameter to four decimal places, and tolerances to six decimal places. In order to maintain same screw dimensions, everybody has to follow the same rounding practice. Basic profile of UN and UNF screw threads are shown on Fig. 1. Here we show two example of detail calculations of UNEF and UNS External and Internal thread, where all the ins and outs of rounding policy, formulas, and detail description is provided for better understanding, and individual to find out accurate dimensions. * It is recognized that ASME B1.30 is not in agreement with other published documents, e.g., ASME SI-

9, Guide for Metrication of Codes and Standards SI (Metric) Units, and IEEE/ASTM SI 10, Standard for Metric Practice. The rounding practices used in the forenamed documents are designed to produce even distribution of numerical values. The purpose of this document is to define the most practical and common used method of rounding numerical thread form values. Application of this method is far more practical in the rounding of thread form values.



1771

Calculating and Rounding Dimensions Rounding of Decimal Values.—The following rounding practice represents the method to be used in new or future revisions of ASME B1 thread standards. Rounding Policy: When the figure next beyond the last figure or place retained is less than 5, the figure in the last place retained is kept unchanged. Example: 1.012342

1.01234

1.012342

1.0123

1.012342

1.012

When the figure next beyond the last figure or place retained is greater than 5, the figure in the last place retained is increased by 1. Example: 1.56789

1.5679

1.56789

1.568

1.56789

1.57

When the figure next beyond the last figure or place retained is 5, and: 1) There are no figures, or only zeros, beyond the 5, the last figure should be increased by 1. Example: 1.01235

1.0124

1.0123500

1.0124

1.012345

1.01235

1.01234500

1.01235

2) If the 5 next beyond the figure in the last place to be retained is followed by any figures other than zero, the figure in the last place retained should be increased by 1. Example: 1.0123501

1.0124

1.0123599

1.0124

1.01234501

1.01235

1.01234599

1.01235

The final rounded value is obtained from the most precise value available and not from a series of successive rounding. For example, 0.5499 should be rounded to 0.550, 0.55 and 0.5 (not 0.6), since the most precise value available is less than 0.55. Similarly, 0.5501 should be rounded as 0.550, 0.55 and 0.6, since the most precise value available is more than 0.55. In the case of 0.5500 rounding should be 0.550, 0.55 and 0.6, since the most precise value available is 0.5500. Calculations from Formulas, General Rules.—1) Values for pitch and constants derived from a function of pitch are used out to eight decimal places for inch series. The eight place values are obtained by rounding their truncated ten place values. Seven decimal place values for metric series constants are derived by rounding their truncated nine place values. Values used in intermediate calculations are rounded to two places beyond the number of decimal places retained for the final value, see Tables 1 and 7. 2) Rounding to the final value is the last step in a calculation.


1772


Example 1, Rounding Inch Series: n = 28 threads per inch P = 0.0357142857 P = 0.03571429

1P = 1--- = ----n 28 ( calculated and truncated to 10 places ) ( rounded to 8 places )

Table 1. Number of Decimal Places Used in Calculations Units Inch Metric

Pitch 8 as designated

Constants 8 7

Intermediate 6 5

Final 4 3

3) For inch screw thread dimensions, four decimal places are required for the final values of pitch diameter, major diameter, and minor diameter with the exception of Class 1B and 2B internal thread minor diameters for thread sizes 0.138 and larger. The final values for the allowances and tolerances applied to thread elements are expressed to four decimal places except for external thread pitch diameter tolerance, Td2, which is expressed to six decimal places. Minor Diameter Exceptions for Internal Threads: Minimum Minor Diameter: All classes are calculated and then rounded off to the nearest 0.001 inch and expressed in three decimal places for sizes 0.138 inch and larger. For Class 3B, a zero is added to yield four decimal places. Maximum Minor Diameter: All classes are calculated before rounding, then rounded for Classes 1B and 2B to the nearest 0.001 in. for sizes 0.138 in. and larger. Class 3B values are rounded to four decimal places. 4) Metric screw threads are dimensioned in millimeters. The final values of pitch diameter, major diameter, minor diameter, allowance and thread element tolerances are expressed to three decimal places. 5) Values containing multiple trailing zeros out to the required number of decimal places can be expressed by displaying only two of them beyond the last significant digit. Example:20 threads per inch has a pitch equal to 0.05000000 and can be expressed as 0.0500. Examples Inch Screw Threads.—The formulas in the examples for inch screw threads are based on those listed in ASME B1.1, Unified Inch Screw Threads. Table 3 and Table 4 are based on a size that when converted from a fraction to a decimal will result in a number that has only four decimal places. Table 5 and Table 6 are based on a size that when converted will result in a number with infinite numbers of digits after the decimal point. Fig. 1 is provided for reference. Metric Screw Threads.—The formulas for metric screw threads are based on those listed in ASME B1.13M, Metric Screw Threads. The calculation of size limits for standard diameter/pitch combinations listed in both ISO 261 and ASME B1.13M use of the tabulated values for allowances and tolerances (in accordance with ISO 965-1). The constant values differ from those used for inch screw threads, in accordance with the policy of rounding of this standard, because metric limits of size are expressed to only three decimal places rather than four. Thread Form Constants.—For thread form data see Table 2. The number of decimal places and the manner in which they are listed should be consistent. Thread form constants printed in older thread standards are based on a function of thread height (H) or pitch (P). The equivalent of the corresponding function is also listed. There are some constants that would require these values to 8 or 7 decimal places before they would round to equivalent



1773

values. For standardization the tabulated listing of thread values based on a function of pitch has been established, with thread height used as a reference only All thread calculations are to be performed using a function of pitch (P), rounded to 8 decimal places for inch series and as designated for metric series, not a function of thread height (H). Thread height is to be used for reference only. See Table 7.

Fig. 1. Basic Profile of UN and UNF Screw Threads

Table 2. Thread Form Data Constant for Inch Series (8-place) 0.04811252P 0.05412659P 0.08660254P 0.09622504P 0.10825318P 0.12990381P 0.14433757P 0.16237976P 0.21650635P 0.28867513P 0.32475953P 0.36084392P 0.39692831P 0.43301270P 0.48713929P 0.54126588P 0.57735027P 0.59539246P 0.61343466P 0.61602540P 0.64951905P 0.72168783P 0.79385662P 0.86602540P 1.08253175P 1.19078493P 1.22686932P

Reference Values 1⁄ H 18 1⁄ H 16 1⁄ H 10 1⁄ H 9 1⁄ H 8 3⁄ H 20 1⁄ H 6 3⁄ H 16 1⁄ H 4 1⁄ H 3 3⁄ H 8 5⁄ H 12 11⁄ H 24 1⁄ H 2 9⁄ H 16 5⁄ H 8 2⁄ H 3 11⁄ H 16 17⁄ H 24

… H H H H 5⁄ H 4 11⁄ H 8 17⁄ H 12 3⁄ 4 5⁄ 6 11⁄ 12

0.0556H 0.0625H 0.1000H 0.1111H 0.1250H 0.1500H 0.1667H 0.1875H 0.2500H 0.3333H 0.3750H 0.4167H 0.4583H 0.5000H 0.5625H 0.6250H 0.6667H 0.6875H 0.7083H 0.7113H 0.7500H 0.8333H 0.9167H 1.0000H 1.2500H 1.3750H 1.4167H

Constant for Metric Series (7-place) 0.0481125P 0.0541266P 0.0866025P 0.0962250P 0.1082532P 0.1299038P 0.1443376P 0.1623798P 0.2165064P 0.2886751P 0.3247595P 0.3608439P 0.3969283P 0.4330127P 0.4871393P 0.5412659P 0.5773503P 0.5953925P 0.6134347P 0.6160254P 0.6495191P 0.7216878P 0.7938566P 0.8660254P 1.0825318P 1.1907849P 1.2268693P



1774

Table 3. External Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2A Characteristic Description

Calculation

Notes

Basic major diameter, dbsc

d bsc = --1- = 0.5 = 0.5000 2

Pitch, P

1- = 0.035714285714 = 0.03571429 P = ----28

P is rounded to eight decimal places

Maximum external major diameter (dmax) = basic major diameter (dbsc) − allowance (es)

d max = d bsc – es

es is the basic allowance

dbsc is rounded to four decimal places

d bsc = 0.5000


Allowance (es)

es = 0.300 × Td 2 for Class 2A

Td2 is the pitch diameter tolerance for Class 2A

--13

Td 2 = 0.0015D + 0.0015 LE + 0.015P

External pitch diameter tolerance Td2

--23

1 --3

= 0.0015 × 0.5 + 0.0015 9 × 0.03571429 + 0.015 ( 0.03571429 ) = 0.001191 + 0.000850 + 0.001627 = 0.003668

2 --3

LE = 9P (length of engagement) Td2 is rounded to six decimal places

Allowance (es)

es = 0.300 × 0.003668 = 0.0011004 = 0.0011

es is rounded to four decimal places

Maximum external major diameter (dmax)

d max = d base – es = 0.5000 – 0.0011 = 0.4989

dmax is rounded to four decimal places

Minimum external major diameter (dmin) = maximum external major diameter (dmax) − major diameter tolerance (Td)

d min = d max – Td

Td is the major diameter tolerance

2

Td = 0.060 3 P = 0.060 × 3 0.03571429

Major diameter tolerance (Td)

2

= 0.060 × 3 0.001276 = 0.060 × 0.108463 = 0.00650778 = 0.0065

Td is rounded to four decimal places


CALCULATING THREAD DIMENSIONS

Basic major diameter (dbsc)

Machinery's Handbook 28th Edition Table 3. (Continued) External Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2A Characteristic Description Minimum external major diameter (dmin)

= 0.492392 = 0.4924 d 2max = d max – 2 × h as h as = 0.64951905P -------------------------------2h as = 0.64951905P 2 2h as = 0.64951905 × 0.03571429 = 0.02319711

External thread addendum

Notes dmin is rounded to four decimal places

has = external thread addendum

2has is rounded to six decimal places

= 0.023197

Maximum external pitch diameter (d2max) Minimum external pitch diameter (d2min) = maximum external pitch diameter (d2max) − external pitch diameter tolerance (Td2) Minimum external pitch diameter (d2min) Maximum external UNR minor diameter (d3max) = maximum external major diameter (dmax) − double height of external UNR thread 2hs External UNR thread height (2hs)

= 0.475703 = 0.4757 d 2min = d 2max – Td 2 d 2min = d 2max – Td 2 = 0.4757 – 0.003668 = 0.472032 = 0.4720 d 3max = d max – 2 × h s 2h s = 1.19078493P = 1.19078493 × 0.03571429 = 0.042528 d 3max = d max – 2 × h s = 0.4989 – 0.042528 = 0.456372 = 0.4564

d2max is rounded to four decimal places Td2 = external pitch diameter tolerance (see previous Td2 calculation in this table) d2min is rounded to four decimal places

hs = external UNR thread height,

2hs rounded to six decimal places

d3max is rounded to four decimal places


1775

Maximum external UNR minor diameter (d3max)

d 2max = d max – 2 × h as = 0.4989 – 0.23197


Maximum external pitch diameter (d2max) = maximum external major diameter (dmax) − twice the external thread addendum (has)

Calculation d min = d max – Td = 0.4989 – 0.006508


Characteristic Description Maximum external UN minor diameter (d1max) = maximum external major diameter (dmax) − double height of external UN thread 2hs

Calculation d 1max = d max – 2 × h s

Notes

1776

Table 3. (Continued) External Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2A

For UN threads, 2hs = 2hn

2h s = 1.08253175P

Maximum external UN minor diameter (d1max)

d 1max = d max – 2 × h s = 0.4989 – 0.038662 = 0.460238 = 0.4602

2hs is rounded to six decimal places


Table 4. Internal Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2B Characteristic Description

Calculation = 1--- = 0.5 = 0.5000 2

Notes


d bsc

Pitch, P

1- = 0.035714285714 = 0.03571429 P = ----28

P is rounded to eight decimal places

Minimum internal minor diameter (D1min) = basic major diameter (Dbsc) − double height of external UN thread 2hn

D 1min = D bsc – 2h n

2hn is the double height of external UN thread

Double height of external UN thread 2hs

Minimum internal major diameter (D1min)

2h n = 1.08253175P = 1.08253175 × 0.03571429 = 0.03866185 = 0.038662 D 1min = D bsc – 2 × h n = 0.5000 – 0.038662 = 0.461338 = 0.461


2hn is rounded to six decimal places For class 2B the value is rounded to three decimal places to obtain the final values



= 1.08253175 × 0.03571429 = 0.03866185 = 0.038662

Double height of external UN thread 2hs

Machinery's Handbook 28th Edition Table 4. (Continued) Internal Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2B Characteristic Description Maximum internal minor diameter (D1max) = minimum internal minor diameter (D1min) + internal minor diameter tolerance TD1

Calculation

Minimum internal pitch diameter (D2min) = basic major diameter (Dbsc) − twice the external thread addendum (hb)

2 2

= 0.25 × 0.03571429 – 0.40 × 0.03571429 = 0.008929 – 0.000510 = 0.008419 = 0.003127 D 1max = D 1min + TD 1 = 0.461338 + 0.008419 = 0.469757 = 0.470

D 2min = D bsc – h b h b = 0.64951905P = 0.64951905 × 0.03571429

External thread addendum (hb)

= 0.02319711 = 0.023197

Minimum internal pitch diameter (D2min) Maximum internal pitch diameter (D2max) = minimum internal pitch diameter (D2min) + internal pitch diameter tolerance (TD2) External pitch diameter tolerance TD2

= 0.476803 = 0.4768 D 2max = D 2min + TD 2

TD 2 = 1.30 × ( Td 2 for Class 2A ) = 1.30 × 0.003668 = 0.0047684 = 0.0048 D 2max = D 2min + TD 2 = 0.4768 + 0.0048 = 0.4816

For the Class 2B thread D1max is rounded to three decimal places to obtain final values. Other sizes and classes are expressed in a four decimal places hb= external thread addendum

hb is rounded to six decimal places

D2min is rounded to four decimal places

TD2 = external pitch diameter tolerance Constant 1.30 is for this Class 2B example, and will be different for Classes 1B and 3B. Td2 for Class 2A (see Table 3) is rounded to six decimal places. TD2 is rounded 4 to places D2max is rounded to four decimal places


1777

Maximum internal pitch diameter (D2max)

D 2min = D bsc – h b = 0.5000 – 0.023197

TD1 is rounded to four decimal places.


Maximum internal minor diameter (D1max)

D1min is rounded to six decimal places

D 1max = D 1min + TD 1

TD 1 = 0.25P – 0.40P

Internal minor diameter tolerance TD1

Notes


Characteristic Description

Calculation

Minimum internal major diameter (Dmin) = basic major diameter (Dbsc)

Notes Dmin is rounded to four decimal places

D min = D bsc = 0.5000

Calculation

Notes

= 19 ------ = 0.296875 = 0.2969 64


d bsc

Pitch, P

1- = 0.0277777777778 = 0.02777778 P = ----36

Maximum external major diameter (dmax) = basic major diameter (dbsc) − allowance (es)

d max = d bsc – es

dbsc is rounded to four decimal places P is rounded to eight decimal places

es = 0.300 × Td 2 for Class 2A

Allowance (es) 1--3

Td 2 = 0.0015D + 0.0015 LE + 0.015P

External pitch diameter tolerance, Td2

Td2 is Pitch diameter tolerance for Class 2A

2--3

--13

= 0.0015 × 0.2969 + 0.0015 9 × 0.02777778 + 0.015 ( 0.02777778 ) = 0.001000679 + 0.00075 + 0.001375803 = 0.003126482 = 0.003127

--23

LE = 9P (length of engagement) Td2 is rounded to six decimal places

Allowance (es)

es = 0.300 × 0.003127 = 0.0009381 = 0.0009

es is rounded to four decimal places

Maximum external major diameter (dmax)

d max = d bsc – es = 0.2969 – 0.0009 = 0.2960

dmax is rounded to four decimal places



Table 5. External Inch Screw Thread Calculations for 19⁄64 -36 UNS-2A Characteristic Description

1778

Table 4. (Continued) Internal Inch Screw Thread Calculations for 1⁄2 -28 UNEF-2B

Machinery's Handbook 28th Edition Table 5. (Continued) External Inch Screw Thread Calculations for 19⁄64 -36 UNS-2A Characteristic Description Minimum external major diameter (dmin) = maximum external major diameter (dmax) − major diameter tolerance (Td)

Calculation d min = d max – Td 2

Td is the major diameter tolerance 2

= 0.060 × 0.000772 = 0.060 × 0.091736 = 0.00550416 = 0.0055 3

Td is rounded to four decimal places

Minimum external major diameter (dmin)

d min = d max – Td = 0.2960 – 0.0055 = 0.2905

dmin is rounded to four decimal places

Maximum external pitch diameter (d2max) = maximum external major diameter (dmax) − twice the external thread addendum

d 2max = d max – 2 × h as

has= external thread addendum

0.64951905Ph as = ------------------------------2h as = 0.64951905P 2 2h as = 0.64951905 × 0.02777778 = 0.0180421972


has is rounded to six decimal places

= 0.018042

Maximum external pitch diameter (d2max) Minimum external pitch diameter (d2min) = maximum external pitch diameter (d2max) − external pitch diameter tolerance (Td2) Minimum external pitch diameter (d2min)

d 2max = d max – 2h as = 0.2960 – 0.018042 = 0.277958 = 0.2780 d 2min = d 2max – Td 2 d 2min = d 2max – Td 2 = 0.2780 – 0.003127 = 0.274873 = 0.2749

d2max is rounded to four decimal places Td2 = external pitch diameter tolerance (see previous Td2 calculation in this table)


Td = 0.060 3 P = 0.060 × 3 0.02777778

Major diameter tolerance (Td)

Notes

d2min is rounded to four decimal places

1779



Characteristic Description Maximum external UNR minor diameter (d3max) = maximum external major diameter (dmax) − double height of external UNR thread 2hs

Calculation

hs= external UNR thread height,

d 3max = d max – 2h s 2h s = 1.19078493P = 1.19078493 × 0.02777778 = 0.033077362 = 0.033077

Maximum external UNR minor diameter (d3max) Maximum external UN minor diameter (d1max) = maximum external major diameter (dmax) − double height of external UN thread 2hs Double height of external UN thread 2hs

Maximum external UN minor diameter (d1max)

d 3max = d max – 2h s = 0.2960 – 0.033077 = 0.262923 = 0.2629

2hs is rounded to six decimal places


d 1max = d max – 2 × h s

For UN threads, 2hs =2hn

2h s = 1.08253175P = 1.08253175 × 0.02777778

For UN threads, 2hs = 2hn 2hs is rounded to six decimal places

= 0.030070329 = 0.030070 d 1max = d max – 2h s = 0.2960 – 0.030070 = 0.265930 = 0.2659

Maximum external UN minor diameter is rounded to four decimal places

Table 6. Internal Inch Screw Thread Calculations for 19⁄64 -28 UNS-2B Characteristic Description

Calculation

Notes

Minimum internal minor diameter (D1min) = basic major diameter (Dbsc) − double height of external UN thread 2hn

D 1min = D bsc – 2h n

2hn is the double height of external UN threads

Basic major diameter (Dbsc)

D bsc = 19 ------ = 0.296875 = 0.2969 64

This is the final value of basic major diameter (given) and rounded to four decimal places



External UNR thread height

Notes

1780

Table 5. (Continued) External Inch Screw Thread Calculations for 19⁄64 -36 UNS-2A

Machinery's Handbook 28th Edition Table 6. (Continued) Internal Inch Screw Thread Calculations for 19⁄64 -28 UNS-2B Characteristic Description Double height of external UN thread 2hs

Maximum internal minor diameter (D1max) = minimum internal minor diameter (D1min) + internal minor diameter tolerance TD1

= 0.030070329 = 0.030070

Maximum internal minor diameter (D1max) Minimum internal pitch diameter (D2min) = basic major diameter (Dbsc) − twice the external thread addendum (hb)

= 0.266830 = 0.267

D1min is rounded to six decimal places

D 1max = D 1min + TD 1 2 2

= 0.25 × 0.02777778 – 0.40 × 0.02777778 = 0.006944 – 0.000309 = 0.006635 = 0.0066 D 1max = D 1min + TD 1 = 0.266830 + 0.006635 = 0.273465 = 0.273

D 2min = D 1max – h b h b = 0.64951905P = 0.64951905 × 0.02777778


= 0.018042197 = 0.018042

Minimum internal pitch diameter (D2min)

P is rounded to eight decimal places For class 2B the value is rounded to three decimal places to obtain the final value, other sizes and classes are expressed in a four place decimal.

D 1min = D bsc – 2h n = 0.2969 – 0.030070

TD 1 = 0.25P – 0.40P

Internal minor diameter tolerance TD1

Notes

D 2min = D bsc – h b = 0.2969 – 0.018042 = 0.278858 = 0.2789

TD1 is rounded to four decimal places.

For Class 2B thread the value is rounded to three decimal places to obtain the final values. Other sizes and classes are expressed in a four decimal places hb = external thread addendum

hb is rounded to six decimal places


Minimum internal major diameter (D1min)

Calculation 2h n = 1.08253175P = 1.08253175 × 0.02777778

D2min is rounded to four decimal places

1781



Characteristic Description

Calculation

Maximum internal pitch diameter (D2max) = minimum internal pitch diameter (D2min) + internal pitch diameter tolerance (TD2)

Notes TD2 = external pitch diameter tolerance

D 2max = D 2min + TD 2

= 1.30 × 0.003127 = 0.0040651 = 0.0041

The constant 1.30 is for this Class 2B example, and will be different for Classes 1B and 3B. Td2 for Class 2A (see calculation, Table 5) is rounded to six decimal places

Maximum internal pitch diameter (D2max)

D 2max = D 2min + TD 2 = 0.2789 + 0.0041 = 0.2830

D2max is rounded to four decimal places

Minimum internal major diameter (Dmin) = basic major diameter (Dbsc)

D min = D bsc = 0.2969

Dmin is rounded to four decimal places

Table 7. Number of Decimal Places for Intermediate and Final Calculations of Thread Characteristics Symbol d D d2 D2 d1 d3 D1 D1

Dimensions Major diameter, external thread Major diameter, internal thread Pitch diameter, external thread Pitch diameter, internal thread Minor diameter, external thread Minor diameter, rounded root external thread Minor diameter, internal threads for sizes 0.138 and larger for Classes 1B and 2B only Minor diameter, internal threads for sizes smaller than 0.138 for Classes 1B and 2B, and all sizes for Class 3B

Intermediate Inch Metric … … … … … … … … … … … …

Final Inch Metric 4 3 4 3 4 3 4 3 4 3 4 3

Intermediate Inch Metric 6 N/A … … … … … … … … … …

Inch … 8 4 6 4 4

Final Metric … Note a 3 3 3 3

Symbol LE P Td Td2 TD2 TD1

Dimensions Length of thread engagement Pitch Major diameter tolerance Pitch diameter tolerance, external thread Pitch diameter tolerance, internal thread Minor diameter tolerance, internal thread Twice the external thread addendum

6

N/A

…

…

6

N/A

…

…

…

…

3

N/A

hb = 2has

…

…

4

N/A

2hs

Double height of UNR external thread

2hn

Double height of internal thread and UN external thread

6

N/A

…

…

Twice the external thread addendum

6

N/A

…

…

D1

Minor diameter, internal metric thread

…

…

es

Allowance at major pitch and minor diameters of external thread

…

…

N/A

3 3

a Metric pitches are not calculated. They are stated in the scread thread designation and are to be used out to the number of decimal places as stated.

Note: Constants based on a function of P are rounded to an 8-place decimal for inch threads and a 7-place decimal for metric threads.



TD 2 = 1.30 × ( Td 2 for Class 2A )

External pitch diameter tolerance TD2

1782

Table 6. (Continued) Internal Inch Screw Thread Calculations for 19⁄64 -28 UNS-2B

Machinery's Handbook 28th Edition METRIC SCREW THREADS M PROFILE

1783

METRIC SCREW THREADS American National Standard Metric Screw Threads M Profile American National Standard ANSI/ASME B1.13M-2005 describes a system of metric threads for general fastening purposes in mechanisms and structures. The standard is in basic agreement with ISO screw standards and resolutions, as of the date of publication, and features detailed information for diameter-pitch combinations selected as to preferred standard sizes. This Standard contains general metric standards for a 60-degree symmetrical screw thread with a basic ISO 68 designated profile. Application Comparison with Inch Threads.—The metric M profile threads of tolerance class 6H/6g (see page 1790) are intended for metric applications where the inch class 2A/2B have been used. At the minimum material limits, the 6H/6g results in a looser fit than the 2A/2B. Tabular data are also provided for a tighter tolerance fit external thread of class 4g6g which is approximately equivalent to the inch class 3A but with an allowance applied. It may be noted that a 4H5H/4h6h fit is approximately equivalent to class 3A/3B fit in the inch system. Interchangeability with Other System Threads.—Threads produced to this Standard ANSI/ASME B1.13M are fully interchangeable with threads conforming to other National Standards that are based on ISO 68 basic profile and ISO 965/1 tolerance practices. Threads produced to this Standard should be mechanically interchangeable with those produced to ANSI B1.18M-1982 (R1987) “Metric Screw Threads for Commercial Mechanical Fasteners—Boundary Profile Defined,” of the same size and tolerance class. However, there is a possibility that some parts may be accepted by conventional gages used for threads made to ANSI/ASME B1.13M and rejected by the Double-NOT-GO gages required for threads made to ANSI B1.18M. Threads produced in accordance with M profile and MJ profile ANSI/ASME B1.21M design data will assemble with each other. However, external MJ threads will encounter interference on the root radii with internal M thread crests when both threads are at maximum material condition. Definitions.—The following definitions apply to metric screw threads — M profile. Allowance: The minimum nominal clearance between a prescribed dimension and its basic dimension. Allowance is not an ISO metric screw thread term but it is numerically equal to the absolute value of the ISO term fundamental deviation. Basic Thread Profile: The cyclical outline in an axial plane of the permanently established boundary between the provinces of the external and internal threads. All deviations are with respect to this boundary. (See Figs. 1 and 5.) Bolt Thread (External Thread): The term used in ISO metric thread standards to describe all external threads. All symbols associated with external threads are designated with lower case letters. This Standard uses the term external threads in accordance with United States practice. Clearance: The difference between the size of the internal thread and the size of the external thread when the latter is smaller. Crest Diameter: The major diameter of an external thread and the minor diameter of an internal thread. Design Profiles: The maximum material profiles permitted for external and internal threads for a specified tolerance class. (See Figs. 2 and 3.) Deviation: An ISO term for the algebraic difference between a given size (actual, measured, maximum, minimum, etc.) and the corresponding basic size. The term deviation does not necessarily indicate an error.


1784


Fit: The relationship existing between two corresponding external and internal threads with respect to the amount of clearance or interference which is present when they are assembled. Fundamental Deviation: For Standard threads, the deviation (upper or lower) closer to the basic size. It is the upper deviation, es, for an external thread and the lower deviation, EI, for an internal thread. (See Fig. 5.) Limiting Profiles: The limiting M profile for internal threads is shown in Fig. 6. The limiting M profile for external threads is shown in Fig. 7. Lower Deviation: The algebraic difference between the minimum limit of size and the corresponding basic size. Nut Thread (Internal Thread): A term used in ISO metric thread standards to describe all internal threads. All symbols associated with internal threads are designated with upper case letters. This Standard uses the term internal thread in accordance with United States practice. Tolerance: The total amount of variation permitted for the size of a dimension. It is the difference between the maximum limit of size and the minimum limit of size (i.e., the algebraic difference between the upper deviation and the lower deviation). The tolerance is an absolute value without sign. Tolerance for threads is applied to the design size in the direction of the minimum material. On external threads the tolerance is applied negatively. On internal threads the tolerance is applied positively. Tolerance Class: The combination of a tolerance position with a tolerance grade. It specifies the allowance (fundamental deviation) and tolerance for the pitch and major diameters of external threads and pitch and minor diameters of internal threads. Tolerance Grade: A numerical symbol that designates the tolerances of crest diameters and pitch diameters applied to the design profiles. Tolerance Position: A letter symbol that designates the position of the tolerance zone in relation to the basic size. This position provides the allowance (fundamental deviation). Upper Deviation: The algebraic difference between the maximum limit of size and the corresponding basic size. Basic M Profile.—The basic M thread profile also known as ISO 68 basic profile for metric screw threads is shown in Fig. 1 with associated dimensions listed in Table 3. Design M Profile for Internal Thread.—The design M profile for the internal thread at maximum material condition is the basic ISO 68 profile. It is shown in Fig. 2 with associated thread data listed in Table 3. Design M Profile for External Thread.—The design M profile for the external thread at the no allowance maximum material condition is the basic ISO 68 profile except where a rounded root is required. For the standard 0.125P minimum radius, the ISO 68 profile is modified at the root with a 0.17783H truncation blending into two arcs with radii of 0.125P tangent to the thread flanks as shown in Fig. 3 with associated thread data in Table 3. M Crest and Root Form.—The form of crest at the major diameter of the external thread is flat, permitting corner rounding. The external thread is truncated 0.125H from a sharp crest. The form of the crest at the minor diameter of the internal thread is flat. It is truncated 0.25H from a sharp crest. The crest and root tolerance zones at the major and minor diameters will permit rounded crest and root forms in both external and internal threads. The root profile of the external thread must lie within the “section lined” tolerance zone shown in Fig. 4. For the rounded root thread, the root profile must lie within the “section lined” rounded root tolerance zone shown in Fig. 4. The profile must be a continuous, smoothly blended non-reversing curve, no part of which has a radius of less than 0.125P, and which is tangential to the thread flank. The profile may comprise tangent flank arcs that are joined by a tangential flat at the root.



1785

The root profile of the internal thread must not be smaller than the basic profile. The maximum major diameter must not be sharp. General Symbols.—The general symbols used to describe the metric screw thread forms are shown in Table 1. Table 1. American National Standard Symbols for Metric Threads ANSI/ASME B1.13M-2005 Symbol

Explanation

D

Major Diameter Internal Thread

D1

Minor Diameter Internal Thread

D2

Pitch Diameter Internal Thread

d

Major Diameter External Thread

d1

Minor Diameter External Thread

d2

Pitch Diameter External Thread

d3

Rounded Form Minor Diameter External Thread

P

Pitch

r

External Thread Root Radius

T

Tolerance

TD1, TD2 Td, Td2

Tolerances for D1, D2 Tolerances for d, d2

ES

Upper Deviation, Internal Thread [Equals the Allowance (Fundamental Deviation) Plus the Tolerance]. See Fig. 5.

EI

Lower Deviation, Internal Thread Allowance (Fundamental Deviation). See Fig. 5.

G, H

Letter Designations for Tolerance Positions for Lower Deviation, Internal Thread

g, h

Letter Designations for Tolerance Positions for Upper Deviation, External Thread

es

Upper Deviation, External Thread Allowance (Fundamental Deviation). See Fig. 5. In the ISO system es is always negative for an allowance fit or zero for no allowance.

ei

Lower Deviation, External Thread [Equals the Allowance (Fundamental Deviation) Plus the Tolerance]. See Fig. 5. In the ISO system ei is always negative for an allowance fit.

H

Height of Fundamental Triangle

LE

Length of Engagement

LH

Left Hand Thread

Standard M Profile Screw Thread Series.—The standard metric screw thread series for general purpose equipment's threaded components design and mechanical fasteners is a coarse thread series. Their diameter/pitch combinations are shown in Table 4. These diameter/pitch combinations are the preferred sizes and should be the first choice as applicable. Additional fine pitch diameter/pitch combinations are shown in Table 5. Table 2. American National Standard General Purpose and Mechanical Fastener Coarse Pitch Metric Thread—M Profile Series ANSI/ASME B1.13M-2005 Nom.Size 1.6 2 2.5 3 3.5 4 5

Pitch 0.35 0.4 0.45 0.5 0.6 0.7 0.8

Nom.Size 6 8 10 12 14 16 20

Pitch 1 1.25 1.5 1.75 2 2 2.5

Nom.Size

Pitch

Nom.Size

Pitch

22 24 27 30 36 42 48

2.5a 3 3a 3.5 4 4.5 5

56 64 72 80 90 100 …

5.5 6 6b 6b 6b 6b …

a For high strength structural steel fasteners only. b Designated as part of 6 mm fine pitch series in ISO 261.




Pitch P

Dedendum of Internal Thread and Addendum External Thread

Differencea

Height of InternalThread and Depth of Thread Engagement

Twice the External Thread Addendum

Differencec

H--8

H--4

--3- H 8

H--2

--5- H 8

11----H 12

0.2165064P

0.3247595P

0.4330127P

0.5412659P

Differenceb 0.711325H 0.6160254P

--3- H 4

0.1082532P

0.6495191P

0.7938566P

Height of Sharp V-Thread H 0.8660254P

0.02165 0.02706 0.03248 0.03789 0.04330 0.04871 0.05413 0.06495 0.07578 0.08119 0.08660 0.10825 0.13532 0.16238 0.18944 0.21651 0.27063 0.32476 0.37889 0.43301 0.48714 0.54127 0.59539 0.64952 0.86603

0.04330 0.05413 0.06495 0.07578 0.08660 0.09743 0.10825 0.12990 0.15155 0.16238 0.17321 0.21651 0.27063 0.32476 0.37889 0.43301 0.54127 0.64652 0.75777 0.86603 0.97428 1.08253 1.19079 1.29904 1.73205

0.06495 0.08119 0.09743 0.11367 0.12990 0.14614 0.16238 0.19486 0.22733 0.24357 0.25981 0.32476 0.40595 0.48714 0.56833 0.64952 0.81190 0.97428 1.13666 1.29904 1.46142 1.62380 1.78618 1.94856 2.59808

0.08660 0.10825 0.12990 0.15155 0.17321 0.19486 0.21651 0.25981 0.30311 0.32476 0.34641 0.43301 0.54127 0.64952 0.75777 0.86603 1.08253 1.29904 1.51554 1.73205 1.94856 2.16506 2.38157 2.59808 3.46410

0.10825 0.13532 0.16238 0.18944 0.21651 0.24357 0.27063 0.32476 0.37889 0.40595 0.43301 0.54127 0.67658 0.81190 0.94722 1.08253 1.35316 1.62380 1.89443 2.16506 2.43570 2.70633 2.97696 3.24760 4.33013

0.12321 0.15401 0.18481 0.21561 0.24541 0.27721 0.30801 0.36962 0.43122 0.46202 0.49282 0.61603 0.77003 0.92404 1.07804 1.23205 1.54006 1.84808 2.15609 2.46410 2.77211 3.08013 3.38814 3.69615 4.92820

0.12990 0.16238 0.19486 0.22733 0.25981 0.29228 0.32476 0.38971 0.45466 0.48714 0.51962 0.64952 0.81190 0.97428 1.13666 1.29904 1.62380 1.94856 2.27332 2.59808 2.92284 3.24760 3.57236 3.89711 5.19615

0.15877 0.19846 0.23816 0.27785 0.31754 0.35724 0.39693 0.47631 0.55570 0.59539 0.63509 0.79386 0.99232 1.19078 1.38925 1.58771 1.98464 2.38157 2.77850 3.17543 3.57235 3.96928 4.36621 4.76314 6.35085

0.17321 0.21651 0.25981 0.30311 0.34641 0.38971 0.43301 0.51962 0.60622 0.64952 0.69282 0.86603 1.08253 1.29904 1.51554 1.73205 2.16506 2.59808 3.03109 3.46410 3.89711 4.33013 4.76314 5.19615 6.92820

Double Height of Internal Thread

--5- H 4 1.0825318P 0.21651 0.27063 0.32476 0.37889 0.43301 0.48714 0.54127 0.64952 0.75777 0.81190 0.86603 1.08253 1.35316 1.62380 1.89443 2.16506 2.70633 3.24760 3.78886 4.33013 4.87139 5.41266 5.95392 6.49519 8.66025

a Difference between max theoretical pitch diameter and max minor diameter of external thread and between min theoretical pitch diameter and min minor diameter of internal thread. b Difference between min theoretical pitch diameter and min design minor diameter of external thread for 0.125P root radius. c Difference between max major diameter and max theoretical pitch diameter of internal thread. All dimensions are in millimeters.


METRIC SCREW THREADS M PROFILE

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8

Addendum of Internal Thread and Truncation of Internal Thread

1786

Table 3. American National Standard Metric Thread — M Profile Data ANSI/ASME B1.13M-2005 Truncation of Internal Thread Root and External Thread Crest


1787

Table 4. American National Standard Minimum Rounded Root Radius— M Profile Series ANSI/ASME B1.13M-2005 Min. Root Radius, 0.125P

Pitch P 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Min. Root Radius, 0.125P

Pitch P

0.025 0.031 0.038 0.044 0.050 0.056 0.063

0.6 0.7 0.75 0.8 1 1.25 …


Pitch P

0.075 0.088 0.094 0.100 0.125 0.156 …

1.5 1.75 2 2.5 3 3.5 …


Pitch P

0.188 0.219 0.250 0.313 0.375 0.438 …

4 4.5 5 5.5 6 8 …

0.500 0.563 0.625 0.688 0.750 1.000 …


Table 5. American National Standard Fine Pitch Metric Thread—M Profile Series ANSI/ASME B1.13M-2005 Nom. Size 8

Nom. Size

Pitch 1

Nom. Size

Pitch

Pitch

Nom. Size

Pitch 2

…

27

…

2

56

…

2

105

10

0.75

1.0

1.25

30

1.5

2

60

1.5

…

110

2

12

1

1.5

1.25

33

…

2

64

…

2

120

2 2

14

…

1.5

35

1.5

…

65

1.5

…

130

15

1

…

36

…

2

70

1.5

…

140

2

16

…

1.5

39

…

2

72

…

2

150

2

17

1

40

1.5

…

75

1.5

…

160

3

18

…

1.5

42

…

2

80

1.5

2

170

3

20

1

1.5

45

1.5

…

85

…

2

180

3

22

…

1.5

48

…

2

90

…

2

190

3

24

…

2

50

1.5

…

95

…

2

200

3

25

1.5

…

55

1.5

…

100

…

2

…


Limits and Fits for Metric Screw Threads — M Profile.—The International (ISO) metric tolerance system is based on a system of limits and fits. The limits of the tolerances on the mating parts together with their allowances (fundamental deviations) determine the fit of the assembly. For simplicity the system is described for cylindrical parts (see British Standard for Metric ISO Limits and Fits starting on page 661) but in this Standard it is applied to screw threads. Holes are equivalent to internal threads and shafts to external threads. Basic Size: This is the zero line or surface at assembly where the interface of the two mating parts have a common reference.* Upper Deviation: This is the algebraic difference between the maximum limit of size and the basic size. It is designated by the French term “écart supérieur” (ES for internal and es for external threads). Lower Deviation: This is the algebraic difference between the minimum limit of size and the basic size. It is designated by the French term “écart inférieur” (EI for internal and ei for external threads). Fundamental Deviations (Allowances): These are the deviations which are closest to the basic size. In the accompanying figure they would be EI and es. * “Basic,”

when used to identify a particular dimension in this Standard, such as basic major diameter, refers to the h/H tolerance position (zero fundamental deviation) value.



1788

Tolerance: The tolerance is defined by a series of numerical grades. Each grade provides numerical values for the various nominal sizes corresponding to the standard tolerance for that grade. In the schematic diagram the tolerance for the external thread is shown as negative. Thus the tolerance plus the fit define the lower deviation (ei). The tolerance for the mating internal thread is shown as positive. Thus the tolerance plus the fit defines the upper deviation (ES). Fits: Fits are determined by the fundamental deviations assigned to the mating parts and may be positive or negative. The selected fits can be clearance, transition, or interference. To illustrate the fits schematically, a zero line is drawn to represent the basic size as shown in Fig. 5. By convention, the external thread lies below the zero line and the internal thread lies above it (except for interference fits). This makes the fundamental deviation negative for the external thread and equal to its upper deviation (es). The fundamental deviation is positive for the internal thread and equal to its lower deviation (EI). Internal threads

P 2

D, d

H 8

P

P 8

60°

3 H 8

30° P 4

P 2

H 4

D 2, d 2

D 1, d 1

90°

5 H H 8

Axis of screw thread

External threads H=

3 ×P 2

= 0.866025P

0.125H = 0.108253P 0.250H = 0.216506P 0.375H = 0.324760P 0.625H = 0.541266P

Fig. 1. Basic M Thread Profile (ISO 68 Basic Profile)

Fig. 2. Internal Thread Design M Profile with No Allowance (Fundamental Deviation) (Maximum Material Condition). For Dimensions see Table 3



1789

Fig. 3. External Thread Design M Profile with No Allowance (Fundamental Deviation) (Flanks at Maximum Material Condition). For Dimensions see Table 3 Basic M profile Upper limiting profile for rounded root (See notes)

0.5 es

r

min = 0.125P

0.5 Td

d2 basic pitch dia.

2

P 4

Point of intersection

d3 max rounded root minor dia. Point of intersection r min = 0.125P

d1

0.5 es

Rounded root max truncation (See notes)

H 4

0.14434H min truncation d1 max flat root minor dia.

d3 min minor dia.

Fig. 4. M Profile, External Thread Root, Upper and Lower Limiting Profiles for rmin = 0.125 P and for Flat Root (Shown for Tolerance Position g) Notes: 1) “Section lined” portions identify tolerance zone and unshaded portions identify allowance (fundamental deviation). 2) The upper limiting profile for rounded root is not a design profile; rather it indicates the limiting acceptable condition for the rounded root which will pass a GO thread gage.

T d2 H 3) Max truncation = ---- – r min  1 – cos 60° – arc cos  1 – -------------  4

where





4r min 

H =Height of fundamental triangle rmin = Minimum external thread root radius Td2 = Tolerance on pitch diameter of external threasd


1790


Fig. 5. Metric Tolerance System for Screw Threads

Tolerance Grade: This is indicated by a number. The system provides for a series of tolerance grades for each of the four screw thread parameters: minor diameter, internal thread, D1; major diameter, external thread, d; pitch diameter, internal thread, D2; and pitch diameter, external thread, d2. The tolerance grades for this Standard ANSI B1.13M were selected from those given in ISO 965/1. Dimension Tolerance Grades Table D1 4, 5, 6, 7, 8 Table 8 Table 9 d 4, 6, 8 D2 4, 5, 6, 7, 8 Table 10 d2 3, 4, 5, 6, 7, 8, 9 Table 11 Note: The underlined tolerance grades are used with normal length of thread engagement.

Tolerance Position: This position is the allowance (fundamental deviation) and is indicated by a letter. A capital letter is used for internal threads and a lower case letter for external threads. The system provides a series of tolerance positions for internal and external threads. The underlined letters are used in this Standard: Internal threads External threads

G, H e, f, g, h

Table 6 Table 6

Designations of Tolerance Grade, Tolerance Position, and Tolerance Class: The tolerance grade is given first followed by the tolerance position, thus: 4g or 5H. To designate the tolerance class the grade and position of the pitch diameter is shown first followed by that for the major diameter in the case of the external thread or that for the minor diameter in the case of the internal thread, thus 4g6g for an external thread and 5H6H for an internal thread. If the two grades and positions are identical, it is not necessary to repeat the symbols, thus 4g, alone, stands for 4g4g and 5H, alone, stands for 5H5H. Lead and Flank Angle Tolerances: For acceptance of lead and flank angles of product screw threads, see Section 10 of ANSI/ASME B1.13M-2005. Short and Long Lengths of Thread Engagement when Gaged with Normal Length Contacts: For short lengths of thread engagement, LE, reduce the pitch diameter tolerance of the external thread by one tolerance grade number. For long lengths of thread engagement, LE, increase the allowance (fundamental deviation) at the pitch diameter of the external thread. Examples of tolerance classes required for normal, short, and long gage length contacts are given in the following table. For lengths of thread engagement classified as normal, short, and long, see Table 7.



1791

Table 6. American National Standard Allowance (Fundamental Deviation) for Internal and External Metric Threads ISO 965/1 ANSI/ASME B1.13M-2005 Allowance (Fundamental Deviation)a Internal Thread D 2, D 1 Pitch P 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8

External Thread d, d2

G

Hb

e

f

gc

h

EI

EI

es

es

es

es

+0.017 +0.018 +0.018 +0.019 +0.019 +0.020 +0.020 +0.021 +0.022 +0.022 +0.024 +0.026 +0.028 +0.032 +0.034 +0.038 +0.042 +0.048 +0.053 +0.060 +0.063 +0.071 +0.075 +0.080 +0.100

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

… … … … … … −0.050 −0.053 −0.056 −0.056 −0.060 −0.060 −0.063 −0.067 −0.071 −0.071 −0.080 −0.085 −0.090 −0.095 −0.100 −0.106 −0.112 −0.118 −0.140

… … … −0.034 −0.034 −0.035 −0.036 −0.036 −0.038 −0.038 −0.038 −0.040 −0.042 −0.045 −0.048 −0.052 −0.058 −0.063 −0.070 −0.075 −0.080 −0.085 −0.090 −0.095 −0.118

−0.017 −0.018 −0.018 −0.019 −0.019 −0.020 −0.020 −0.021 −0.022 −0.022 −0.024 −0.026 −0.028 −0.032 −0.034 −0.038 −0.042 −0.048 −0.053 −0.060 −0.063 −0.071 −0.075 −0.080 −0.100

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

All dimensions are in millimeters. a Allowance is the absolute value of fundamental deviation. b c

Tabulated in this standard for M internal threads. Tabulated in this standard for M external threads. Normal LE 6g 4g6g 6ha 4h6ha 6H 4H6H

Short LE 5g6g 3g6g 5h6h 3h6h 5H 3H6H

Long LE 6e6g 4e6g 6g6h 4g6h 6G 4G6G

a Applies to maximum material functional size (GO thread gage) for plated 6g and 4g6g class threads, respectively.

Material Limits for Coated Threads.—Unless otherwise specified, size limits for standard external tolerance classes 6g and 4g6g apply prior to coating. The external thread allowance may thus be used to accommodate the coating thickness on coated parts, provided that the maximum coating thickness is no more than 1⁄4 of the allowance. Thus, a 6g thread after coating is subject to acceptance using a basic size 6h GO thread gage and a 4g6g thread, a 4h6h or 6h GO thread gage. Minimum material, LO, or NOT-GO gages would be 6g and 4g6g, respectively. Where the external thread has no allowance or the allowance must be maintained after coating, and for standard internal threads, sufficient



1792

Table 7. American National Standard Length of Metric Thread Engagement ISO 965/1 and ANSI/ASME B1.13M-2005 Length of Thread Engagement Basic Major Diameter dbsc Over

Up to and incl.

1.5

2.8

2.8

5.6

5.6

11.2

11.2

22.4

22.4

45

45

90

90

180

180

355

Pitch P 0.2 0.25 0.35 0.4 0.45 0.35 0.5 0.6 0.7 0.75 0.8 0.75 1 1.25 1.5 1 1.25 1.5 1.75 2 2.5 1 1.5 2 3 3.5 4 4.5 1.5 2 3 4 5 5.5 6 2 3 4 6 8 3 4 6 8

Short LE

Normal LE

Up to and incl.

Over

0.5 0.6 0.8 1 1.3 1 1.5 1.7 2 2.2 2.5 2.4 3 4 5 3.8 4.5 5.6 6 8 10 4 6.3 8.5 12 15 18 21 7.5 9.5 15 19 24 28 32 12 18 24 36 45 20 26 40 50

0.5 0.6 0.8 1 1.3 1 1.5 1.7 2 2.2 2.5 2.4 3 4 5 3.8 4.5 5.6 6 8 10 4 6.3 8.5 12 15 18 21 7.5 9.5 15 19 24 28 32 12 18 24 36 45 20 26 40 50

Up to and incl. 1.5 1.9 2.6 3 3.8 3 4.5 5 6 6.7 7.5 7.1 9 12 15 11 13 16 18 24 30 12 19 25 36 45 53 63 22 28 45 56 71 85 95 36 53 71 106 132 60 80 118 150

Long LE Over 1.5 1.9 2.6 3 3.8 3 4.5 5 6 6.7 7.5 7.1 9 12 15 11 13 16 18 24 30 12 19 25 36 45 53 63 22 28 45 56 71 85 95 36 53 71 106 132 60 80 118 150


allowance must be provided prior to coating to ensure that finished product threads do not exceed the maximum material limits specified. For thread classes with tolerance position H or h, coating allowances in accordance with Table 6 for position G or g, respectively, should be applied wherever possible.



1793

Dimensional Effect of Coating.—On a cylindrical surface, the effect of coating is to change the diameter by twice the coating thickness. On a 60-degree thread, however, since the coating thickness is measured perpendicular to the thread surface while the pitch diameter is measured perpendicular to the thread axis, the effect of a uniformly coated flank on the pitch diameter is to change it by four times the thickness of the coating on the flank. External Thread with No Allowance for Coating: To determine gaging limits before coating for a uniformly coated thread, decrease: 1) maximum pitch diameter by four times maximum coating thickness; 2) minimum pitch diameter by four times minimum coating thickness; 3) maximum major diameter by two times maximum coating thickness; a n d 4) minimum major diameter by two times minimum coating thickness. External Thread with Only Nominal or Minimum Thickness Coating: I f n o c o a t i n g thickness tolerance is given, it is recommended that a tolerance of plus 50 per cent of the nominal or minimum thickness be assumed. Then, to determine before coating gaging limits for a uniformly coated thread, decrease: 1) maximum pitch diameter by six times coating thickness; 2) minimum pitch diameter by four times coating thickness; 3) maximum major diameter by three times coating thickness; and 4) minimum major diameter by two times coating thickness. Adjusted Size Limits: It should be noted that the before coating material limit tolerances are less than the tolerance after coating. This is because the coating tolerance consumes some of the product tolerance. In cases there may be insufficient pitch diameter tolerance available in the before coating condition so that additional adjustments and controls will be necessary. Strength: On small threads (5 mm and smaller) there is a possibility that coating thickness adjustments will cause base material minimum material conditions which may significantly affect strength of externally threaded parts. Limitations on coating thickness or part redesign may then be necessary. Internal Threads: Standard internal threads provide no allowance for coating thickness. To determine before coating, gaging limits for a uniformly coated thread, increase: 1) minimum pitch diameter by four times maximum coating thickness, if specified, or by six times minimum or nominal coating thickness when a tolerance is not specified; 2) maximum pitch diameter by four times minimum or nominal coating thickness; 3) minimum minor diameter by two times maximum coating thickness, if specified, or by three times minimum or nominal coating thickness; and 4) maximum minor diameter by two times minimum or nominal coating thickness. Other Considerations: It is essential to review all possibilities adequately and consider limitations in the threading and coating production processes before finally deciding on the coating process and the allowance required to accommodate the coating. A no-allowance thread after coating must not transgress the basic profile and is, therefore, subject to acceptance using a basic (tolerance position H/h) size GO thread gage. Formulas for M Profile Screw Thread Limiting Dimensions.—The limiting dimensions for M profile screw threads are calculated from the following formulas.



1794

Internal Threads: Min major dia. = basic major dia. + EI (Table 6) Min pitch dia. = basic major dia. − 0.6495191P (Table 3) + EI for D2 (Table 6) Max pitch dia. = min pitch dia. + TD2 (Table 10) Max major dia. = max pitch dia. + 0.7938566P (Table 3) Min minor dia. = min major dia. − 1.0825318P (Table 3) Max minor dia. = min minor dia. + TD1 (Table 8) External Threads: Max major dia. = basic major dia. − es (Table 6) (Note that es is an absolute value.) Min major dia. = max major dia. − Td (Table 9) Max pitch dia. = basic major dia. − 0.6495191P (Table 3) − es for d2 (Table 6) Min pitch dia. = max pitch dia. − Td2 (Table 11) Max flat form minor dia. = max pitch dia. − 0.433013P (Table 3) Max rounded root minor dia. = max pitch dia. − 2 × max trunc. (See Fig. 4) Min rounded root minor dia. = min pitch dia. − 0.616025P (Table 3) Min root radius = 0.125P Table 8. ANSI Standard Minor Diameter Tolerances of Internal Metric Threads TD1 ISO 965/1 ANSI/ASME B1.13M-2005 Pitch P 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8

Tolerance Grade 4

5

6a

7

8

0.038 0.045 0.053 0.063 0.071 0.080 0.090 0.100 0.112 0.118 0.125 0.150 0.170 0.190 0.212 0.236 0.280 0.315 0.355 0.375 0.425 0.450 0.475 0.500 0.630

… 0.056 0.067 0.080 0.090 0.100 0.112 0.125 0.140 0.150 0.160 0.190 0.212 0.236 0.265 0.300 0.355 0.400 0.450 0.475 0.530 0.560 0.600 0.630 0.800

… … 0.085 0.100 0.112 0.125 0.140 0.160 0.180 0.190 0.200 0.236 0.265 0.300 0.335 0.375 0.450 0.500 0.560 0.600 0.670 0.710 0.750 0.800 1.000

… … … … … … 0.180 0.200 0.224 0.236 0.250 0.300 0.335 0.375 0.425 0.475 0.560 0.630 0.710 0.750 0.850 0.900 0.950 1.000 1.250

… … … … … … … … … … 0.315 0.375 0.425 0.475 0.530 0.600 0.710 0.800 0.900 0.950 1.060 1.120 1.180 1.250 1.600

a Tabulated in this standard for M internal threads.




1795

Table 9. ANSI Standard Major Diameter Tolerances of External Metric Threads, Td ISO 965/1 ANSI/ASME B1.13M-2005 Pitch P 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1 1.25

Tolerance Grade 4

6a

8

0.036 0.042 0.048 0.053 0.060 0.063 0.067 0.080 0.090 0.090 0.095 0.112 0.132

0.056 0.067 0.075 0.085 0.095 0.100 0.106 0.125 0.140 0.140 0.150 0.180 0.212

… … … … … … … … … … 0.236 0.280 0.335

Pitch P 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8 …

Tolerance Grade 4

6a

8

0.150 0.170 0.180 0.212 0.236 0.265 0.300 0.315 0.335 0.355 0.375 0.450 …

0.236 0.265 0.280 0.335 0.375 0.425 0.475 0.500 0.530 0.560 0.600 0.710 …

0.375 0.425 0.450 0.530 0.600 0.670 0.750 0.800 0.850 0.900 0.950 1.180 …

a Tabulated in this standard for M internal threads.


Table 10. ANSI Standard Pitch-Diameter Tolerances of Internal Metric Thread, TD2 ISO 965/1 ANSI/ASME B1.13M-2005 Tolerance Grade

Basic Major Diameter, D Over

Up to and incl.

1.5

2.8

2.8

5.6

5.6

11.2

11.2

22.4

22.4

45

45

90

Pitch P 0.2 0.25 0.35 0.4 0.45 0.35 0.5 0.6 0.7 0.75 0.8 0.75 1 1.25 1.5 1 1.25 1.5 1.75 2 2.5 1 1.5 2 3 3.5 4 4.5 1.5 2 3 4 5 5.5 6

4

5

6a

7

8

0.042 0.048 0.053 0.056 0.060 0.056 0.063 0.071 0.075 0.075 0.080 0.085 0.095 0.100 0.112 0.100 0.112 0.118 0.125 0.132 0.140 0.106 0.125 0.140 0.170 0.180 0.190 0.200 0.132 0.150 0.180 0.200 0.212 0.224 0.236

… 0.060 0.067 0.071 0.075 0.071 0.080 0.090 0.095 0.095 0.100 0.106 0.118 0.125 0.140 0.125 0.140 0.150 0.160 0.170 0.180 0.132 0.160 0.180 0.212 0.224 0.236 0.250 0.170 0.190 0.224 0.250 0.265 0.280 0.300

… … 0.085 0.090 0.095 0.090 0.100 0.112 0.118 0.118 0.125 0.132 0.150 0.160 0.180 0.160 0.180 0.190 0.200 0.212 0.224 0.170 0.200 0.224 0.265 0.280 0.300 0.315 0.212 0.236 0.280 0.315 0.335 0.355 0.375

… … … … … … 0.125 0.140 0.150 0.150 0.160 0.170 0.190 0.200 0.224 0.200 0.224 0.236 0.250 0.265 0.280 0.212 0.250 0.280 0.335 0.355 0.375 0.400 0.265 0.300 0.355 0.400 0.425 0.450 0.475

… … … … … … … … … … 0.200 … 0.236 0.250 0.280 0.250 0.280 0.300 0.315 0.335 0.355 … 0.315 0.355 0.425 0.450 0.475 0.500 0.335 0.375 0.450 0.500 0.530 0.560 0.600



1796

Table 10. (Continued) ANSI Standard Pitch-Diameter Tolerances of Internal Metric Thread, TD2 ISO 965/1 ANSI/ASME B1.13M-2005 Tolerance Grade

Basic Major Diameter, D Over 90

Up to and incl. 180

180

355

Pitch P 2 3 4 6 8 3 4 6 8

4 0.160 0.190 0.212 0.250 0.280 0.212 0.236 0.265 0.300

5 0.200 0.236 0.265 0.315 0.355 0.265 0.300 0.335 0.375

6a 0.250 0.300 0.335 0.400 0.450 0.335 0.375 0.425 0.475

7 0.315 0.375 0.425 0.500 0.560 0.425 0.475 0.530 0.600

8 0.400 0.475 0.530 0.630 0.710 0.530 0.600 0.670 0.750

a Tabulated in this standard for M threads. All dimensions are in millimeters.

Table 11. ANSI Standard Pitch-Diameter Tolerances of External Metric Threads, Td2 ISO 965/1 ANSI/ASME B1.13M-2005 Basic Major Diameter, d Over

Up to and incl.

1.5

2.8

2.8

5.6

5.6

11.2

11.2

22.4

22.4

45

45

90

90

180

Pitch P 0.2 0.25 0.35 0.4 0.45 0.35 0.5 0.6 0.7 0.75 0.8 0.75 1 1.25 1.5 1 1.25 1.5 1.75 2 2.5 1 1.5 2 3 3.5 4 4.5 1.5 2 3 4 5 5.5 6 2 3 4 6 8

Tolerance Grade 3

4a

5

6a

7

8

9

0.025 0.028 0.032 0.034 0.036 0.034 0.038 0.042 0.045 0.045 0.048 0.050 0.056 0.060 0.067 0.060 0.067 0.071 0.075 0.080 0.085 0.063 0.075 0.085 0.100 0.106 0.112 0.118 0.080 0.090 0.106 0.118 0.125 0.132 0.140 0.095 0.112 0.125 0.150 0.170

0.032 0.036 0.040 0.042 0.045 0.042 0.048 0.053 0.056 0.056 0.060 0.063 0.071 0.075 0.085 0.075 0.085 0.090 0.095 0.100 0.106 0.080 0.095 0.106 0.125 0.132 0.140 0.150 0.100 0.112 0.132 0.150 0.160 0.170 0.180 0.118 0.140 0.160 0.190 0.212

0.040 0.045 0.050 0.053 0.056 0.053 0.060 0.067 0.071 0.071 0.075 0.080 0.090 0.095 0.106 0.095 0.106 0.112 0.118 0.125 0.132 0.100 0.118 0.132 0.160 0.170 0.180 0.190 0.125 0.140 0.170 0.190 0.200 0.212 0.224 0.150 0.180 0.200 0.236 0.265

0.050 0.056 0.063 0.067 0.071 0.067 0.075 0.085 0.090 0.090 0.095 0.100 0.112 0.118 0.132 0.118 0.132 0.140 0.150 0.160 0.170 0.125 0.150 0.170 0.200 0.212 0.224 0.236 0.160 0.180 0.212 0.236 0.250 0.265 0.280 0.190 0.224 0.250 0.300 0.335

… … 0.080 0.085 0.090 0.085 0.095 0.106 0.112 0.112 0.118 0.125 0.140 0.150 0.170 0.150 0.170 0.180 0.190 0.200 0.212 0.160 0.190 0.212 0.250 0.265 0.280 0.300 0.200 0.224 0.265 0.300 0.315 0.335 0.355 0.236 0.280 0.315 0.375 0.425

… … … … … … … … … … 0.150 … 0.180 0.190 0.212 0.190 0.212 0.224 0.236 0.250 0.265 0.200 0.236 0.265 0.315 0.335 0.355 0.375 0.250 0.280 0.335 0.375 0.400 0.425 0.450 0.300 0.355 0.400 0.475 0.530

… … … … … … … … … … 0.190 … 0.224 0.236 0.265 0.236 0.265 0.280 0.300 0.315 0.335 0.250 0.300 0.335 0.400 0.425 0.450 0.475 0.315 0.355 0.425 0.475 0.500 0.530 0.560 0.375 0.450 0.500 0.600 0.670



1797

Table 11. (Continued) ANSI Standard Pitch-Diameter Tolerances of External Metric Threads, Td2 ISO 965/1 ANSI/ASME B1.13M-2005 Basic Major Diameter, d Over 180

Up to and incl. 355

Pitch P 3 4 6 8

Tolerance Grade 3 0.125 0.140 0.160 0.180

4a 0.160 0.180 0.200 0.224

5 0.200 0.224 0.250 0.280

6a 0.250 0.280 0.315 0.355

7 0.315 0.355 0.400 0.450

8 0.400 0.450 0.500 0.560

9 0.500 0.560 0.630 0.710

a Tabulated in this Standard for M threads.


Tolerance Grade Comparisons.—The approximate ratios of the tolerance grades shown in Tables 8, 9, 10, and 11 in terms of Grade 6 are as follows: Minor Diameter Tolerance of Internal Thread: Grade 6 isTD1 (Table 8): Grade 4 is 0.63 TD1 (6); Grade 5 is 0.8 TD1 (6); Grade 7 is 1.25 TD1 (6); and Grade 8 is 1.6 TD1 (6). Pitch Diameter Tolerance of Internal Thread: Td2 (Table 10): Grade 4 is 0.85 Td2 (6); Grade 5 is 1.06 Td2 (6); Grade 6 is 1.32 Td2 (6); Grade 7 is 1.7 Td2 (6); and Grade 8 is 2.12 Td2 (6). It should be noted that these ratios are in terms of the Grade 6 pitch diameter tolerance for the external thread. Major Diameter Tolerance of External Thread: Td(6) (Table 9): Grade 4 is 0.63 Td (6); and Grade 8 is 1.6 Td (6). Pitch Diameter Tolerance of External Thread: Td2 (Table 11): Grade 3 is 0.5 Td2 (6); Grade 4 is 0.63 Td2 (6); Grade 5 is 0.8 Td2 (6); Grade 7 is 1.25 Td2 (6); Grade 8 is 1.6 Td2 (6); and Grade 9 is 2 Td2 (6). Standard M Profile Screw Threads, Limits of Size.—The limiting M profile for internal threads is shown in Fig. 6 with associated dimensions for standard sizes in Table 12. The limiting M profiles for external threads are shown in Fig. 7 with associated dimensions for standard sizes in Table 13. If the required values are not listed in these tables, they may be calculated using the data in Tables 3, 6, 7, 8, 9, 10, and 11 together with the preceding formulas. If the required data are not included in any of the tables listed above, reference should be made to Sections 6 and 9.3 of ANSI/ASME B1.13M, which gives design formulas.

Fig. 6. Internal Thread — Limiting M Profile. Tolerance Position H



1798

Note: “Section Lined”portions identify tolerance zone. *Dimension D in Fig. 6 is used in the design of tools, etc. For internal threads it is not normally specified. Generally, major diameter acceptance is based on maximum material condition gaging.

Fig. 7. External Thread — Limiting M Profile. Tolerance Position g Note: “Section Lined”portions identify tolerance zone and unshaded portions identify allowance (fundamental deviation.)

Table 12. Internal Metric Thread - M Profile Limiting Dimensions, ANSI/ASME B1.13M-2005 Basic Thread Designation

Toler. Class

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 M8 × 1 M10 × 0.75 M10 × 1 M10 × 1.5 M10 × 1.25 M12 × 1.75 M12 × 1.5 M12 × 1.25 M12 × 1 M14 × 2 M14 × 1.5 M15 × 1 M16 × 2 M16 × 1.5 M17 × 1 M18 × 1.5 M20 × 2.5 M20 × 1.5

6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H

Minor Diameter D1

Pitch Diameter D2

Min

Max

Min

Max

1.221 1.567 2.013 2.459 2.850 3.242 4.134 4.917 6.647 6.917 9.188 8.917 8.376 8.647 10.106 10.376 10.647 10.917 11.835 12.376 13.917 13.835 14.376 15.917 16.376 17.294 18.376

1.321 1.679 2.138 2.599 3.010 3.422 4.334 5.153 6.912 7.153 9.378 9.153 8.676 8.912 10.441 10.676 10.912 11.153 12.210 12.676 14.153 14.210 14.676 16.153 16.676 17.744 18.676

1.373 1.740 2.208 2.675 3.110 3.545 4.480 5.350 7.188 7.350 9.513 9.350 9.026 9.188 10.863 11.026 11.188 11.350 12.701 13.026 14.350 14.701 15.026 16.350 17.026 18.376 19.026

1.458 1.830 2.303 2.775 3.222 3.663 4.605 5.500 7.348 7.500 9.645 9.500 9.206 9.348 11.063 11.216 11.368 11.510 12.913 13.216 14.510 14.913 15.216 16.510 17.216 18.600 19.216

Major Diameter D Tol 0.085 0.090 0.095 0.100 0.112 0.118 0.125 0.150 0.160 0.150 0.132 0.150 0.180 0.160 0.200 0.190 0.180 0.160 0.212 0.190 0.160 0.212 0.190 0.160 0.190 0.224 0.190

Min

Maxa

1.600 2.000 2.500 3.000 3.500 4.000 5.000 6.000 8.000 8.000 10.000 10.000 10.000 10.000 12.000 12.000 12.000 12.000 14.000 14.000 15.000 16.000 16.000 17.000 18.000 20.000 20.000

1.736 2.148 2.660 3.172 3.698 4.219 5.240 6.294 8.340 8.294 10.240 10.294 10.397 10.340 12.452 12.407 12.360 12.304 14.501 14.407 15.304 16.501 16.407 17.304 18.407 20.585 20.407



1799

Table 12. (Continued) Internal Metric Thread - M Profile Limiting Dimensions, ANSI/ASME B1.13M-2005 Basic Thread Designation M20 × 1 M22 × 2.5 M22 × 1.5 M24 × 3 M24 × 2 M25 × 1.5 M27 × 3 M27 × 2 M30 × 3.5 M30 × 2 M30 × 1.5 M33 × 2 M35 × 1.5 M36 × 4 M36 × 2 M39 × 2 M40 × 1.5 M42 × 4.5 M42 × 2 M45 × 1.5 M48 × 5 M48 × 2 M50 × 1.5 M55 × 1.5 M56 × 5.5 M56 × 2 M60 × 1.5 M64 × 6 M64 × 2 M65 × 1.5 M70 × 1.5 M72 × 6 M72 × 2 M75 × 1.5 M80 × 6 M80 × 2 M80 × 1.5 M85 × 2 M90 × 6 M90 × 2 M95 × 2 M100 × 6 M100 × 2 M105 × 2 M110 × 2 M120 × 2 M130 × 2 M140 × 2 M150 × 2 M160 × 3 M170 × 3 M180 × 3 M190 × 3 M200 × 3

Toler. Class 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H 6H

Minor Diameter D1 Min 18.917 19.294 20.376 20.752 21.835 23.376 23.752 24.835 26.211 27.835 28.376 30.835 33.376 31.670 33.835 36.835 38.376 37.129 39.835 43.376 42.587 45.835 48.376 53.376 50.046 53.835 58.376 57.505 61.835 63.376 68.376 65.505 69.835 73.376 73.505 77.835 78.376 82.835 83.505 87.835 92.835 93.505 97.835 102.835 107.835 117.835 127.835 137.835 147.835 156.752 166.752 176.752 186.752 196.752

Max 19.153 19.744 20.676 21.252 22.210 23.676 24.252 25.210 26.771 28.210 28.676 31.210 33.676 32.270 34.210 37.210 38.676 37.799 40.210 43.676 43.297 46.210 48.676 53.676 50.796 54.210 58.676 58.305 62.210 63.676 68.676 66.305 70.210 73.676 74.305 78.210 78.676 83.210 84.305 88.210 93.210 94.305 98.210 103.210 108.210 118.210 128.210 138.210 148.210 157.252 167.252 177.252 187.252 197.252

Pitch Diameter D2 Min 19.350 20.376 21.026 22.051 22.701 24.026 25.051 25.701 27.727 28.701 29.026 31.701 34.026 33.402 34.701 37.701 39.026 39.077 40.701 44.026 44.752 46.701 49.026 54.026 52.428 54.701 59.026 60.103 62.701 64.026 69.026 68.103 70.701 74.026 76.103 78.701 79.026 83.701 86.103 88.701 93.701 96.103 98.701 103.701 108.701 118.701 128.701 138.701 148.701 158.051 168.051 178.051 188.051 198.051

Max 19.510 20.600 21.216 22.316 22.925 24.226 25.316 25.925 28.007 28.925 29.226 31.925 34.226 33.702 34.925 37.925 39.226 39.392 40.925 44.226 45.087 46.937 49.238 54.238 52.783 54.937 59.238 60.478 62.937 64.238 69.238 68.478 70.937 74.238 76.478 78.937 79.238 83.937 86.478 88.937 93.951 96.503 98.951 103.951 108.951 118.951 128.951 138.951 148.951 158.351 168.351 178.351 188.386 198.386

Major Diameter D Tol 0.160 0.224 0.190 0.265 0.224 0.200 0.265 0.224 0.280 0.224 0.200 0.224 0.200 0.300 0.224 0.224 0.200 0.315 0.224 0.200 0.335 0.236 0.212 0.212 0.355 0.236 0.212 0.375 0.236 0.212 0.212 0.375 0.236 0.212 0.375 0.236 0.212 0.236 0.375 0.236 0.250 0.400 0.250 0.250 0.250 0.250 0.250 0.250 0.250 0.300 0.300 0.300 0.335 0.335

Min 20.000 22.000 22.000 24.000 24.000 25.000 27.000 27.000 30.000 30.000 30.000 33.000 35.000 36.000 36.000 39.000 40.000 42.000 42.000 45.000 48.000 48.000 50.000 55.000 56.000 56.000 60.000 64.000 64.000 65.000 70.000 72.000 72.000 75.000 80.000 80.000 80.000 85.000 90.000 90.000 95.000 100.000 100.000 105.000 110.000 120.000 130.000 140.000 150.000 160.000 170.000 180.000 190.000 200.000

Maxa 20.304 22.585 22.407 24.698 24.513 25.417 27.698 27.513 30.786 30.513 30.417 33.513 35.417 36.877 36.513 39.513 40.417 42.964 42.513 45.417 49.056 48.525 50.429 55.429 57.149 56.525 60.429 65.241 64.525 65.429 70.429 73.241 72.525 75.429 81.241 80.525 80.429 85.525 91.241 90.525 95.539 101.266 100.539 105.539 110.539 120.539 130.539 140.539 150.539 160.733 170.733 180.733 190.768 200.768

a This reference dimension is used in design of tools, etc., and is not normally specified. Generally, major diameter acceptance is based upon maximum material condition gaging. All dimensions are in millimeters.



1800

Table 13. External Metric Thread—M Profile Limiting Dimensions ANSI/ASME B1.13M-2005

Tol. Class

M1.6 × 0.35 M1.6 × 0.35 M1.6 × 0.35 M2 × 0.4 M2 × 0.4 M2 × 0.4 M2.5 × 0.45 M2.5 × 0.45 M2.5 × 0.45 M3 × 0.5 M3 × 0.5 M3 × 0.5 M3.5 × 0.6 M3.5 × 0.6 M3.5 × 0.6 M4 × 0.7 M4 × 0.7 M4 × 0.7 M5 × 0.8 M5 × 0.8 M5 × 0.8 M6 × 1 M6 × 1 M6 × 1 MS × 1.25 M8 × 1.25 M8 × 1.25 M8 × 1 M8 × 1 M8 × 1 M10 × 1.5 M10 × 1.5 M10 × 1.5 M10 × 1.25 M10 × 1.25 M10 × 1.25 M10 × 1 M10 × 1 M10 × 1 M10 × 0.75 M10 × 0.75 M10 × 0.75 M12 × 1.75 M12 × 1.75 M12 × 1.75 M12 × 1.5 M12 × 1.5 M12 × 1.5 M12 × 1.25 M12 × 1.25 M12 × 1.25 M12 × 1 M12 × 1 M12 × 1 M14 × 2 M14 × 2 M14 × 2 M14 × 1.5 M14 × 1.5 M14 × 1.5 M15 × 1 M15 × 1 M15 × 1

6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g

Minor Dia.d d3

Allowancea es

Basic Thread Designation

Minor Dia.b d1

Max.

Min.

Max.

Min.

Tol.

Max.

Min.

0.019 0.000 0.019 0.019 0.000 0.019 0.020 0.000 0.020 0.020 0.000 0.020 0.021 0.000 0.021 0.022 0.000 0.022 0.024 0.000 0.024 0.026 0.000 0.026 0.028 0.000 0.028 0.026 0.000 0.026 0.032 0.000 0.032 0.028 0.000 0.028 0.026 0.000 0.026 0.022 0.000 0.022 0.034 0.000 0.034 0.032 0.000 0.032 0.028 0.000 0.028 0.026 0.000 0.026 0.038 0.000 0.038 0.032 0.000 0.032 0.026 0.000 0.026

1.581 1.600 1.581 1.981 2.000 1.981 2.480 2.500' 2.480 2.980 3.000 2.980 3.479 3.500 3.479 3.978 4.000 3.978 4.976 5.000 4.976 5.974 6.000 5.974 7.972 8.000 7.972 7.974 8.000 7.974 9.968 10.000 9.968 9.972 10.000 9.972 9.974 10.000 9.974 9.978 10.000 9.978 11.966 12.000 11.966 11.968 12.000 11.968 11.972 12.000 11.972 11.974 12.000 11.974 13.962 14.000 13.962 13.968 14.000 13.968 14.974 15.000 14.974

1.496 1.515 1.496 1.886 1.905 1.886 2.380 2.400 2.380 2.874 2.894 2.874 3.354 3.375 3.354 3.838 3.860 3.838 4.826 4.850 4.826 5.794 5.820 5.794 7.760 7.788 7.760 7.794 7.820 7.794 9.732 9.764 9.732 9.760 9.788 9.760 9.794 9.820 9.794 9.838 9.860 9.838 11.701 11.735 11.701 11.732 11.764 11.732 11.760 11.788 11.760 11.794 11.820 11.794 13.682 13.720 13.682 13.732 13.764 13.732 14.794 14.820 14.794

1.354 1.373 1.354 1.721 1.740 1.721 2.188 2.208 2.188 2.655 2.675 2.655 3.089 3.110 3.089 3.523 3.545 3.523 4.456 4.480 4.456 5.324 5.350 5.324 7.160 7.188 7.160 7.324 7.350 7.324 8.994 9.026 8.994 9.160 9.188 9.160 9.324 9.350 9.324 9.491 9.513 9.491 10.829 10.863 10.829 10.994 11.026 10.994 11.160 11.188 11.160 11.324 11.350 11.324 12.663 12.701 12.663 12.994 13.026 12.994 14.324 14.350 14.324

1.291 1.310 1.314 1.654 1.673 1.679 2.117 2.137 2.143 2.580 2.600 2.607 3.004 3.025 3.036 3.433 3.455 3.467 4.361 4.385 4.396 5.212 5.238 5.253 7.042 7.070 7.085 7.212 7.238 7.253 8.862 8.894 8.909 9.042 9.070 9.085 9.212 9.238 9.253 9.391 9.413 9.428 10.679 10.713 10.734 10.854 10.886 10.904 11.028 11.056 11.075 11.206 11.232 11.249 12.503 12.541 12.563 12.854 12.886 12.904 14.206 14.232 14.249

0.063 0.063 0.040 0.067 0.067 0.042 0.071 0.071 0.045 0.075 0.075 0.048 0.085 0.085 0.053 0.090 0.090 0.056 0.095 0.095 0.060 0.112 0.112 0.071 0.118 0.118 0.075 0.112 0.112 0.071 0.132 0.132 0.085 0.118 0.118 0.075 0.112 0.112 0.071 0.100 0.100 0.063 0.150 0.150 0.095 0.140 0.140 0.090 0.132 0.132 0.085 0.118 0.118 0.075 0.160 0.160 0.100 0.140 0.140 0.090 0.118 0.118 0.075

1.202 1.221 1.202 1.548 1.567 1.548 1.993 2.013 1.993 2.438 2.458 2.438 2.829 2.850 2.829 3.220 3.242 3.220 4.110 4.134 4.110 4.891 4.917 4.891 6.619 6.647 6.619 6.891 6.917 6.891 8.344 8.376 8.344 8.619 8.647 8.619 8.891 8.917 8.891 9.166 9.188 9.166 10.071 10.105 10.071 10.344 10.376 10.344 10.619 10.647 10.619 10.891 10.917 10.891 11.797 11.835 11.797 12.344 12.376 12.344 13.891 13.917 13.891

1.075 1.094 1.098 1.408 1.427 1.433 1.840 1.860 1.866 2.272 2.292 2.299 2.634 2.655 2.666 3.002 3.024 3.036 3.868 3.892 3.903 4.596 4.622 4.637 6.272 6.300 6.315 6.596 6.622 6.637 7.938 7.970 7.985 8.272 8.300 8.315 8.596 8.622 8.637 8.929 8.951 8.966 9.601 9.635 9.656 9.930 9.962 9.980 10.258 10.286 10.305 10.590 10.616 10.633 11.271 11.309 11.331 11.930 11.962 11.980 13.590 13.616 13.633

Pitch Diameterb c d2

Major Diameterb d



1801

Basic Thread Designation M16 × 2 M16 × 2 M16 × 2 M16 × 1.5 M16 × 1.5 M16 × 1.5 M17 × 1 M17 × 1 M17 × 1 M18 × 1.5 M18 × 1.5 M18 × 1.5 M20 × 2.5 M20 × 2.5 M20 × 2.5 M20 × 1.5 M20 × 1.5 M20 × 1.5 M20 × 1 M20 × 1 M20 × 1 M22 × 2.5 M22 × 2.5 M22 × 1.5 M22 × 1.5 M22 × 1.5 M24 × 3 M24 × 3 M24 × 3 M24 × 2 M24 × 2 M24 × 2 M25 × 1.5 M25 × 1.5 M25 × 1.5 M27 × 3 M27 × 3 M27 × 2 M27 × 2 M27 × 2 M30 × 3.5 M30 × 3.5 M30 × 3.5 M30 × 2 M30 × 2 M30 × 2 M30 × 1.5 M30 × 1.5 M30 × 1.5 M33 × 2 M33 × 2 M33 × 2 M35 × 1.5 M35 × 1.5 M36 × 4 M36 × 4 M36 × 4 M36 × 2 M36 × 2 M36 × 2 M39 × 2 M39 × 2 M39 × 2 M40 × 1.5

Tol. Class 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g

Allowancea es

Table 13. (Continued) External Metric Thread—M Profile Limiting Dimensions ANSI/ASME B1.13M-2005

0.038 0.000 0.038 0.032 0.000 0.032 0.026 0.000 0.026 0.032 0.000 0.032 0.042 0.000 0.042 0.032 0.000 0.032 0.026 0.000 0.026 0.042 0.000 0.032 0.000 0.032 0.048 0.000 0.048 0.038 0.000 0.038 0.032 0.000 0.032 0.048 0.000 0.038 0.000 0.038 0.053 0.000 0.053 0.038 0.000 0.038 0.032 0.000 0.032 0.038 0.000 0.038 0.032 0.000 0.060 0.000 0.060 0.038 0.000 0.038 0.038 0.000 0.038 0.032

Major Diameterb d Max. 15.962 16.000 15.962 15.968 16.000 15.968 16.974 17.000 16.974 17.968 18.000 17.968 19.958 20.000 19.958 19.968 20.000 19.968 19.974 20.000 19.974 21.958 22.000 21.968 22.000 21.968' 23.952 24.000 23.952 23.962 24.000 23.962 24.968 25.000 24.968 26.952 27.000 26.962 27.000 26.962 29.947 30.000 29.947 29.962 30.000 29.962 29.968 30.000 29.968 32.962 33.000 32.962 34.968 35.000 35.940 36.000 35.940 35.962 36.000 35.962 38.962 39.000 38.962 39.968

Min. 15.682 15.720 15.682 15.732 15.764 15.732 16.794 16.820 16.794 17.732 17.764 17.732 19.623 19.665 19.623 19.732 19.764 19.732 19.794 19.820 19.794 21.623 21.665 21.732 21.764 21.732 23.577 23.625 23.577 23.682 23.720 23.682 24.732 24.764 24.732 26.577 26.625 26.682 26.720 26.682 29.522 29.575 29.522 29.682 29.720 29.682 29.732 29.764 29.732 32.682 32.720 32.682 34.732 34.764 35.465 35.525 35.465 35.682 35.720 35.682 38.682 38.720 38.682 39.732

Pitch Diameterb c d2 Max. 14.663 14.701 14.663 14.994 15.026 14.994 16.324 16.350 16.324 16.994 17.026 16.994 18.334 18.376 18.334 18.994 19.026 18.994 19.324 19.350 19.324 20.334 20.376 20.994 21.026 20.994 22.003 22.051 22.003 22.663 22.701 22.663 23.994 24.026 23.994 25.003 25.051 25.663 25.701 25.663 27.674 27.727 27.674 28.663 28.701 28.663 28.994 29.026 28.994 31.663 31.701 31.663 33.994 34.026 33.342 33.402 33.342 34.663 34.701 34.663 37.663 37.701 37.663 38.994

Min. 14.503 14.541 14.563 14.854 14.886 14.904 16.206 16.232 16.249 16.854 16.886 16.904 18.164 18.206 18.228 18.854 18.886 18.904 19.206 19.232 19.249 20.164 20.206 20.854 20.886 20.904 21.803 21.851 21.878 22.493 22.531 22.557 23.844 23.876 23.899 24.803 24.851 25.493 25.531 25.557 27.462 27.515 27.542 28.493 28.531 28.557 28.844 28.876 28.899 31.493 31.531 31.557 33.844 33.876 33.118 33.178 33.202 34.493 34.531 34.557 37.493 37.531 37.557 38.844

Tol. 0.160 0.160 0.100 0.140 0.140 0.090 0.118 0.118 0.075 0.140 0.140 0.090 0.170 0.170 0.106 0.140 0.140 0.090 0.118 0.118 0.075 0.170 0.170 0.140 0.140 0.090 0.200 0.200 0.125 0.170 0.170 0.106 0.150 0.150 0.095 0.200 0.200 0.170 0.170 0.106 0.212 0.212 0.132 0.170 0.170 0.106 0.150 0.150 0.095 0.170 0.170 0.106 0.150 0.150 0.224 0.224 0.140 0.170 0.170 0.106 0.170 0.170 0.106 0.150

Minor Dia.b d1

Minor Dia.d d3

Max. 13.797 13.835 13.797 14.344 14.376 14.344 15.891 15.917 15.891 16.344 16.376 16.344 17.251 17.293 17.251 18.344 18.376 18.344 18.891 18.917 18.891 19.251 19.293 20.344 20.376 20.344 20.704 20.752 20.704 21.797 21.835 21.797 23.344 23.376 23.344 23.704 23.752 24.797 24.835 24.797 26.158 26.211 26.158 27.797 27.835 27.797 28.344 28.376 28.344 30.797 30.835 30.797 33.344 33.376 31.610 31.670 31.610 33.797 33.835 33.797 36.797 36.835 36.797 38.344

Min. 13.271 13.309 13.331 13.930 13.962 13.980 15.590 15.616 15.633 15.930 15.962 15.980 16.624 16.666 16.688 17.930 17.962 17.980 18.590 18.616 18.633 18.624 18.666 19.930 19.962 19.980 19.955 20.003 20.030 21.261 21.299 21.325 22.920 22.952 22.975 22.955 23.003 24.261 24.299 24.325 25.306 25.359 25.386 27.261 27.299 27.325 27.920 27.952 27.975 30.261 30.299 30.325 32.920 32.952 30.654 30.714 30.738 33.261 33.299 33.325 36.261 36.299 36.325 37.920



1802

Basic Thread Designation M40 × 1.5 M40 × 1.5 M42 × 4.5 M42 × 4.5 M42 × 4.5 M42 × 2 M42 × 2 M42 × 2 M45 × 1.5 M45 × 1.5 M45 × 1.5 M48 × 5 M48 × 5 M48 × 5 M48 × 2 M48 × 2 M48 × 2 M50 × 1.5 M50 × 1.5 M50 × 1.5 M55 × 1.5 M55 × 1.5 M55 × 1.5 M56 × 5.5 M56 × 5.5 M56 × 5.5 M56 × 2 M56 × 2 M56 × 2 M60 × 1.5 M60 × 1.5 M60 × 1.5 M64 × 6 M64 × 6 M64 × 6 M64 × 2 M64 × 2 M64 × 2 M65 × 1.5 M65 × 1.5 M65 × 1.5 M70 × 1.5 M70 × 1.5 M70 × 1.5 M72 × 6 M72 × 6 M72 × 6 M72 × 2 M72 × 2 M72 × 2 M75 × 1.5 M75 × 1.5 M75 × 1.5 M80 × 6 M80 × 6 M80 × 6 M80 × 2 M80 × 2 M80 × 2 M80 × 1.5 M80 × 1.5 M80 × 1.5 M85 × 2 M85 × 2

Tol. Class 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h

Allowancea es


0.000 0.032 0.063 0.000 0.063 0.038 0.000 0.038 0.032 0.000 0.032 0.071 0.000 0.071 0.038 0.000 0.038 0.032 0.000 0.032 0.032 0.000 0.032 0.075 0.000 0.075 0.038 0.000 0.038 0.032 0.000 0.032 0.080 0.000 0.080 0.038 0.000 0.038 0.032 0.000 0.032 0.032 0.000 0.032 0.080 0.000 0.080 0.038 0.000 0.038 0.032 0.000 0.032 0.080 0.000 0.080 0.038 0.000 0.038 0.032 0.000 0.032 0.038 0.000

Major Diameterb d Max. 40.000 39.968 41.937 42.000 41.937 41.962 42.000 41.962 44.968 45.000 44.968 47.929 48.000 47.929 47.962 48.000 47.962 49.968 50.000 49.968 54.968 55.000 54.968 55.925 56.000 55.925 55.962 56.000 55.962 59.968 60.000 59.968 63.920 64.000 63.920 63.962 64.000 63.962 64.968 65.000 64.968 69.968 70.000 69.968 71.920 72.000 71.920 71.962 72.000 71.962 74.968 75.000 74.968 79.920 80.000 79.920 79.962 80.000 79.962 79.968 80.000 79.968 84.962 85.000

Min. 39.764 39.732 41.437 41.500 41.437 41.682 41.720 41.682 44.732 44,764 44.732 47.399 47.470 47.399 47.682 47.720 47.682 49.732 49.764 49.732 54.732 54.764 54.732 55.365 55.440 55.365 55.682 55.720 55.682 59.732 59.764 59.732 63.320 63.400 63.320 63.682 63.720 63.682 64.732 64.764 64.732 69.732 69.764 69.732 71.320 71.400 71.320 71.682 71.720 71.682 74.732 74.764 74.732 79.320 79.400 79.320 79.682 79.720 79.682 79.732 79.764 79.732 84.682 84.720

Pitch Diameterb c d2 Max. 39.026 38.994 39.014 39.077 39.014 40.663 40.701 40.663 43.994 44.026 43.994 44.681 44.752 44.681 46.663 46.701 46.663 48.994 49.026 48.994 53.994 54.026 53.994 52.353 52.428 52.353 54.663 54.701 54.663 58.994 59.026 58.994 60.023 60.103 60.023 62.663 62.701 62.663 63.994 64.026 63.994 68.994 69.026 68.994 68.023 68.103 68.023 70.663 70.701 70.663 73.994 74.026 73.994 76.023 76.103 76.023 78.663 78.701 78.663 78.994 79.026 78.994 83.663 83.701

Min. 38.876 38.899 38.778 38.841 38.864 40.493 40.531 40.557 43.844 43.876 43.899 44.431 44.502 44.521 46.483 46.521 46.551 48.834 48.866 48.894 53.834 53.866 53.894 52.088 52.163 52.183 54.483 54.521 54.551 58.834 58.866 58.894 59.743 59.823 59.843 62.483 62.521 62.551 63.834 63.866 63.894 68.834 68.866 68.894 67.743 67.823 67.843 70.483 70.521 70.551 73.834 73.866 73.894 75.743 75.823 75.843 78.483 78.521 78.551 78.834 78.866 78.894 83.483 83.521

Tol. 0.150 0.095 0.236 0.236 0.150 0.170 0.170 0.106 0.150 0.150 0.095 0.250 0.250 0.160 0.180 0.180 0.112 0.160 0.160 0.100 0.160 0.160 0.100 0.265 0.265 0.170 0.180 0.180 0.112 0.160 0.160 0.100 0.280 0.280 0.180 0.180 0.180 0.112 0.160 0.160 0.100 0.160 0.160 0.100 0.280 0.280 0.180 0.180 0.180 0.112 0.160 0.160 0.100 0.280 0.280 0.180 0.180 0.180 0.112 0.160 0.160 0.100 0.180 0.180

Minor Dia.b d1

Minor Dia.d d3

Max. 38.376 38.344 37.065 37.128 37.065 39.797 39.835 39.797 43.344 43.376 43.344 42.516 42.587 42.516 45.797 45.835 45.797 48.344 48.376 48.344 53.344 53.376 53.344 49.971 50.046 49.971 53.797 53.835 53.797 58.344 58.376 58.344 57.425 57.505 57.425 61.797 61.835 61.797 63.344 63.376 63.344 68.344 68.376 68.344 65.425 65.505 65.425 69.797 69.835 69.797 73.344 73.376 73.344 73.425 73.505 73.425 77.797 77.835 77.797 78.344 78.376 78.344 82.797 82.835

Min. 37.952 37.975 36.006 36.069 36.092 39.261 39.299 39.325 42.920 42.952 42.975 41.351 41.422 41.441 45.251 45.289 45.319 47.910 47.942 47.970 52.910 52.942 52.970 48.700 48.775 48.795 53.251 53.289 53.319 57.910 57.942 57.970 56.047 56.127 56.147 61.251 61.289 61.319 62.910 62.942 62.970 67.910 67.942 67.970 64.047 64.127 64.147 69.251 69.289 69.319 72.910 72.942 72.970 72.047 72.127 72.147 77.251 77.289 77.319 77.910 77.942 77.970 82.251 82.289



1803

Basic Thread Designation M85 × 2 M90 × 6 M90 × 6 M90 × 6 M90 × 2 M90 × 2 M90 × 2 M95 × 2 M95 × 2 M95 × 2 M100 × 6 M100 × 6 M100 × 6 M100 × 2 M100 × 2 M100 × 2 M105 × 2 M105 × 2 M105 × 2 M110 × 2 M110 × 2 M110 × 2 M120 × 2 M120 × 2 M120 × 2 M130 × 2 M130 × 2 M130 × 2 M140 × 2 M140 × 2 M140 × 2 M150 × 2 M150 × 2 M150 × 2 M160 × 3 M160 × 3 M160 × 3 M170 × 3 M170 × 3 M170 × 3 M180 × 3 M180 × 3 M180 × 3 M190 × 3 M190 × 3 M190 × 3 M200 × 3 M200 × 3 M200 × 3 a

Tol. Class 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g 6g 6h 4g6g

Allowancea es


0.038 0.080 0.000 0.080 0.038 0.000 0.038 0.038 0.000 0.038 0.080 0.000 0.080 0.038 0.000 0.038 0.038 0.000 0.038 0.038 0.000 0.038 0.038 0.000 0.038 0.038 0.000 0.038 0.038 0.000 0.038 0.038 0.000 0.038 0.048 0.000 0.048 0.048 0.000 0.048 0.048 0.000 0.048 0.048 0.000 0.048 0.048 0.000 0.048

Major Diameterb d Max. 84.962 89.920 90.000 89.920 89.962 90.000 89.962 94.962 95.000 94.962 99.920 100.000 99.920 99.962 100.000 99.962 104.962 105.000 104.962 109.962 110.000 109.962 119.962 120.000 119.962 129.962 . 130.000 129.962 139.962 140.000 139.962 149.962 150.000 149.962 159.952 160.000 159.952 169.952 170.000 169.952 179.952 180.000 179.952 189.952 190.000 189.952 199.952 200.000 199.952

Min. 84.682 89.320 89.400 89.320 89.682 89.720 89.682 94.682 94.720 94.682 99.320 99.400 99.320 99.682 99.720 99.682 104.682 104.720 104.682 109.682 109.720 109.682 119.682 119.720 119.682 129.682 129.720 129.682 139.682 139.720 139.682 149.682 149.720 149.682 159.577 159.625 159.577 169.577 169.625 169.577 179.577 179.625 179.577 189.577 189.625 189.577 199.577 199.625 199.577

Pitch Diameterb c d2 Max. 83.663 86.023 86.103 86.023 88.663 88.701 88.663 93.663 93.701 93.663 96.023 96.103 96.023 98.663 98.701 98.663 103.663 103.701 103.663 108.663 108.701 108.663 118.663 118.701 118.663 128.663 128.701 128.663 138.663 138.701 138.663 148.663 148.701 148.663 158.003 158.051 158.003 168.003 168.051 168.003 178.003 178.051 178.003 188.003 188.051 188.003 198.003 198.051 198.003

Min. 83.551 85.743 85.823 85.843 88.483 88.521 88.551 93.473 93.511 93.545 95.723 95.803 95.833 98.473 98.511 98.545 103.473 103.511 103.545 108.473 108.511 108.545 118.473 118.511 118.545 128.473 128.511 128.545 138.473 138.511 138.545 148.473 148.511 148.545 157.779 157.827 157.863 167.779 167.827 167.863 177.779 177.827 177.863 187.753 187.801 187.843 197.753 197.801 197.843

Tol. 0.112 0.280 0.280 0.180 0.180 0.180 0.112 0.190 0.190 0.118 0.300 0.300 0.190 0.190 0.190 0.118 0.190 0.190 0.118 0.190 0.190 0.118 0.190 0.190 0.118 0.190 0.190 0.118 0.190 0.190 0.118 0.190 0.190 0.118 0.224 0.224 0.140 0.224 0.224 0.140 0.224 0.224 0.140 0.250 0.250 0.160 0.250 0.250 0.160

Minor Dia.b d1

Minor Dia.d d3

Max. 82.797 83.425 83.505 83.425 87.797 87.835 87.797 92.797 92.835 92.797 93.425 93.505 93.425 97.797 97.835 97.797 102.797 102.835 102.797 107.797 107.835 107.797 117.797 117.835 117.797 127.797 127.835 127.797 137.797 137.835 137.797 147.797 147.835 147.797 156.704 156.752 156.704 166.704 166.752 166.704 176.704 176.752 176.704 186.704 186.752 186.704 196.704 196.752 196.704

Min. 82.319 82.047 82.127 82.147 87.251 87.289 87.319 92.241 92.279 92.313 92.027 92.107 92.137 97.241 97.279 97.313 102.241 102.279 102.313 107.241 107.279 107.313 117.241 117.279 117.313 127.241 127.279 127.313 137.241 137.279 137.313 147.241 147.279 147.313 155.931 155.979 156.015 165.931 165.979 166.015 175.931 175.979 176.015 185.905 185.953 185.995 195.905 195.953 195.995

es is an absolute value.

b For coated threads with tolerance classes 6g or 4g6g, Material Limits for Coated Threads. c Functional diameter size includes the effects of all variations in pitch diameter, thread form, and profile. The variations in the individual thread characteristics such as flank angle, lead, taper, and roundness on a given thread, cause the measurements of the pitch diameter and functional diameter to vary from one another on most threads. The pitch diameter and the functional diameter on a given thread are equal to one another only when the thread form is perfect. When required to inspect either the pitch diameter, the functional diameter, or both, for thread acceptance, use the same limits of size for the appropriate thread size and class. d Dimension used in the design of tools, etc. in dimensioning external threads it is not normally specified. Generally, minor diameter acceptance is based on maximum material condition gaging. All dimensions are in millimeters.


1804


Metric Screw Thread Designations.—Metric screw threads are identified by the letter (M) for the thread form profile, followed by the nominal diameter size and the pitch expressed in millimeters, separated by the sign (×) and followed by the tolerance class separated by a dash (−) from the pitch. The simplified international practice for designating coarse pitch M profile metric screw threads is to leave off the pitch. Thus a M14 × 2 thread is designated just M14. However, to prevent misunderstanding, it is mandatory to use the value for pitch in all designations. Thread acceptability gaging system requirements of ANSI B1.3M may be added to the thread size designation as noted in the examples (numbers in parentheses) or as specified in pertinent documentation, such as the drawing or procurement document. Unless otherwise specified in the designation, the screw thread is right hand. Examples: External thread of M profile, right hand: M6 × 1 − 4g6g (22) Internal thread of M profile, right hand: M6 × 1 − 5H6H (21) Designation of Left Hand Thread: When a left hand thread is specified, the tolerance class designation is followed by a dash and LH. Example: M6 × 1 − 5H6H − LH (23) Designation for Identical Tolerance Classes: If the two tolerance class designations for a thread are identical, it is not necessary to repeat the symbols. Example: M6 × 1 − 6H (21) Designation Using All Capital Letters: When computer and teletype thread designations use all capital letters, the external or internal thread may need further identification. Thus the tolerance class is followed by the abbreviations EXT or INT in capital letters. Examples: M6 × 1 − 4G6G EXT; M6 × 1 − 6H INT Designation for Thread Fit: A fit between mating threads is indicated by the internal thread tolerance class followed by the external thread tolerance class and separated by a slash. Examples: M6 × 1 − 6H/6g; M6 × 1 − 6H/4g6g Designation for Rounded Root External Thread: The M profile with a minimum root radius of 0.125P on the external thread is desirable for all threads but is mandatory for threaded mechanical fasteners of ISO 898/I property class 8.8 (minimum tensile strength 800 MPa) and stronger. No special designation is required for these threads. Other parts requiring a 0.125P root radius must have that radius specified. When a special rounded root is required, its external thread designation is suffixed by the minimum root radius value in millimeters and the letter R. Example: M42 × 4.5 − 6g − 0.63R Designation of Threads Having Modified Crests: Where the limits of size of the major diameter of an external thread or the minor diameter of an internal thread are modified, the thread designation is suffixed by the letters MOD followed by the modified diameter limits. Examples: External thread M profile, major diameter reduced 0.075 mm. M6 × 1 − 4h6h MOD Major dia = 5.745 − 5.925 MOD

Internal thread M profile, minor diameter increased 0.075 mm. M6 × 1 − 4H5H MOD Minor dia = 5.101 − 5.291 MOD

Designation of Special Threads: Special diameter-pitch threads developed in accordance with this Standard ANSI/ASME B1.13M are identified by the letters SPL following the tolerance class. The limits of size for the major diameter, pitch diameter, and minor diameter are specified below this designation.


Machinery's Handbook 28th Edition METRIC SCREW THREADS MJ PROFILE

1805

Examples: External thread M6.5 × 1 − 4h6h − SPL (22) Major dia = 6.320 − 6.500 Pitch dia = 5.779 − 5.850 Minor dia = 5.163 − 5.386

Internal thread M6.5 × 1 − 4H5H − SPL (23) Major dia = 6.500 min Pitch dia = 5.850 − 5.945 Minor dia = 5.417 − 5.607

Designation of Multiple Start Threads: When a thread is required with a multiple start, it is designated by specifying sequentially: M for metric thread, nominal diameter size, × L for lead, lead value, dash, P for pitch, pitch value, dash, tolerance class, parenthesis, script number of starts, and the word starts, close parenthesis. Examples:

M16 × L4 − P2 − 4h6h (TWO STARTS) M14 × L6 − P2 − 6H (THREE STARTS)

Designation of Coated or Plated Threads: In designating coated or plated M threads the tolerance class should be specified as after coating or after plating. If no designation of after coating or after plating is specified, the tolerance class applies before coating or plating in accordance with ISO practice. After plating, the thread must not transgress the maximum material limits for the tolerance position H/h. M6 × 1 − 6h AFTER COATING or AFTER PLATING M6 × 1 − 6g AFTER COATING or AFTER PLATING Where the tolerance position G/g is insufficient relief for the application to hold the threads within product limits, the coating or plating allowance may be specified as the maximum and minimum limits of size for minor and pitch diameters of internal threads or major and pitch diameters for external threads before coating or plating. Examples:

Example:Allowance on external thread M profile based on 0.010 mm minimum coating thickness. M6 × 1 − 4h6h − AFTER COATING BEFORE COATING Major dia = 5.780 − 5.940 Pitch dia = 5.239 − 5.290 Metric Screw Threads—MJ Profile The MJ screw thread is intended for aerospace metric threaded parts and for other highly stressed applications requiring high temperature or high fatigue strength, or for “no allowance” applications. The MJ profile thread is a hard metric version similar to the UNJ inch standards, ANSI/ASME B1.15 and MIL-S-8879. The MJ profile thread has a 0.15011P to 0.180424P controlled root radius in the external thread and the internal thread minor diameter truncated to accommodate the external thread maximum root radius. First issued in 1978, the American National Standard ANSI/ASME B1.21M-1997 establishes the basic triangular profile for the MJ form of thread; gives a system of designations; lists the standard series of diameter-pitch combinations for diameters from 1.6 to 200 mm; and specifies limiting dimensions and tolerances. Changes included in the 1997 revision are the addition of tolerance class 4G6G and 4G5G/4g6g comparable to ANSI/ASME B1.15 (UNJ thread); the addition of tolerance class 6H/6g comparable to ANSI/ASME B1.13M; and changes in the rounding proceedure as set forth in ANSI/ASME B1.30M. Diameter-Pitch Combinations.—This Standard includes a selected series of diameterpitch combinations of threads taken from International Standard ISO 261 plus some additional sizes in the constant pitch series. These are given in Table 1. It also includes the standard series of diameter-pitch combinations for aerospace screws, bolts, nuts, and fluid system fittings as shown in Table 2.



1806

Table 1. ANSI Standard Metric Screw Threads MJ Profile Diameter-Pitch Combinations ANSI/ASME B1.21M-1997 (R2003) Nominal Diameter

Pitchs

Nominal Diameter

Choices

Pitchs

Choices

1st

2nd

Coarse

Fine

1st

2nd

Coarse

Fine

1.6 … 2.0 … 2.5 3 3.5 4 … 5 6 7 8 …

… 1.8 … 2.2 … … … … 4.5 … … … … 9

0.35 0.35 0.4 0.45 0.45 0.5 0.6 0.7 0.75 0.8 1 1 1.25 1.25

… … … … … … … … … … 0.75 0.75 1, 0.75 1, 0.75

… 55

52 … 56 58

… … 5.5 … … … 6 … … … 6 … …

3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5

…

10 …

… 11

1.5 1.5

1.25, 1, 0.75

12

…

1.75

14

…

2

…

15

…

1.25b, 1, 0.75 1.5, 1.25, 1 1.5, 1.25c, 1 1.5, 1

… 60 … … 65 … 70 … 75 … …

62 64 … 68 … 72 … 76 78

80 …

… 82

6

3a, 2, 1.5a 3, 2, 1.5

…

3a, 2, 1.5a

85

…

…

3, 2, 1.5a

90

…

6

3, 2, 1.5a

95

…

…

3, 2, 1.5a

16

…

2

1.5, 1

100

…

6

3, 2, 1.5a

…

17

…

1.5, 1

105

…

…

3, 2, 1.5a

18

…

2.5

2, 1.5, 1

110

…

…

3, 2, 1.5a

20

…

2.5

2, 1.5, 1

…

115

…

3, 2, 1.5a

22

…

2.5

2, 1.5, 1

120

…

…

3, 2, 1.5a

24

…

3

2, 1.5, 1

…

125

…

3, 2, 1.5a

…

25

…

2, 1.5, 1

130

…

…

3, 2, 1.5a

…

26

…

1.5

…

135

…

3, 2, 1.5a

27

…

3

2, 1.5, 1

140

…

…

3, 2, 1.5a

…

28

…

2, 1.5, 1

…

145

…

3, 2, 1.5a

30

…

3.5

3, 2, 1.5, 1

150

…

…

… 33 … 36 … 39 … . 45 … 50

32 … 35 … 38 … 40 42 … 48 …

… … … 4 … … … 4.5 … 5 …

2, 1.5 3, 2, 1.5 1.5 3, 2, 1.5 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5 3, 2, 1.5

… 160 … 170 … 180 … 190 … 200 …

155 … 165 … 175 … 185 … 195 … …

… … … … … … … … … … …

3, 2, 1.5a 3 3 3 3 3 3 3 3 3 3 …

a Not included in ISO 261. b Only for aircraft control cable fittings. c Only for spark plugs for engines.

All dimensions are in millimeters. Pitches in parentheses ( ) are to be avoided as far as possible.



1807

Table 2. ANSI Standard Metric Screw Threads MJ Profile, Diameter-Pitch Combinations for Aerospace ANSI/ASME B1.21M-1997 (R2003) Aerospace Screws, Bolts and Nuts Nom. Sizea 1.6 2 2.5 3 3.5 4

Pitch

Nom. Size

0.35 0.4 0.45 0.5 0.6 0.7

5 6 7 8 10 12

Pitch

Nom. Size

0.8 1 1 1 1.25 1.25

14 16 18 20 22 24

Aerospace Fluid System Fittings

Pitch

Nom. Size

1.5 1.5 1.5 1.5 1.5 2

27 30 33 36 39 …

Pitch

Nom. Size

Pitch

Nom. Size

Pitch

Nom. Size

Pitch

2 2 2 2 2 …

8 10 12 14 16 18

1 1 1.25 1.5 1.5 1.5

20 22 24 27 30 33

1.5 1.5 1.5 1.5 1.5 1.5

36 39 42 48 50 …

1.5 1.5 2 2 2 …

All dimensions are in millimeters. a For threads smaller than 1.6 mm nominal size, use miuniature screw threads (ANSI B1.10M).

Fig. 1. Internal MJ Thread Basic and Design Profiles (Top) and External MJ Thread Basic and Design Profiles (Bottom) Showing Tolerance Zones


Machinery's Handbook 28th Edition TRAPEZOIDAL METRIC THREADS

1808

Tolerances: The thread tolerance system is based on ISO 965/1, Metric Screw thread System of Tolerance Positions and Grades. Tolerances are positive for internal threads and negative for external threads, that is, in the direction of minimum material. For aerospace applications, except for fluid fittings, tolerance classes 4H5H or 4G6G and 4g6g should be used. These classes approximate classes 3B/3A in the inch system. Aerospace fluid fittings use classes 4H5H or 4H6H and 4g6g. Tolerance classes 4G5G or 4G6G and 4g6g are provided for use when thread allowances are required. These classes provide a slightly tighter fit than the inch classes 2B/2A at minimum material condition. Additional tolerance classes 6H/6g are included in this Standard to provide appropriate product selection based on general applications. These classes and the selection of standard diameter/pitch combinations are the same as those provided for the M profile metric screw threads in ANSI/ASME B1.13M. Classes 6H/6g result in a slightly looser fit than inch classes 2B/2A at minimum material condition. Symbols: Standard symbols appearing in Fig. 1 are: D =Basic major diameter of internal thread D2 =Basic pitch diameter of internal thread D1 =Basic minor diameter of internal thread d =Basic major diameter of external thread d2 =Basic pitch diameter of external thread d1 =Basic minor diameter of internal thread d3 =Diameter to bottom of external thread root radius H =Height of fundamental triangle P =Pitch Basic Designations: The aerospace metric screw thread is designated by the letters “MJ” to identify the metric J thread form, followed by the nominal size and pitch in millimeters (separated by the sign “×”) and followed by the tolerance class (separated by a dash from the pitch). Unless otherwise specified in the designation, the thread helix is right hand. Example:MJ6 × 1 − 4h6h For further details concerning limiting dimensions, allowances for coating and plating, modified and special threads, etc., reference should be made to the Standard. Trapezoidal Metric Thread Comparison of ISO and DIN Standards.—ISO metric trapezoidal screw threads standard, ISO 2904-1977, describes the system of general purpose metric threads for use in mechanisms and structures. The standard is in basic agreement with trapezoidal metric thread DIN 103. The DIN 103 standard applies a particular pitch for a particular diameter of thread, but the ISO standard applies a variety of pitchs for a particular diameter. In ISO 2904-1977, the same clearance is applied to both the major diameter and minor diameter, but in DIN 103 the clearance in the minor diameter is two or three times greater than clearance in the major diameter. A comparison of DIN 103 is given in Table 1.



P

1809

Internal Thread

30˚ ac Z

R2

R1

H4 h3

H1 R2

ac

D4

D1

d d2 d3

D2, d2

External Thread

Metric Trapezoidal Thread, ISO 2904

Terminology: The term "bolt threads" is used for external screw threads, the term "nut threads" for internal screw threads. Calculation: The value given in the International standards have been calculated by using the following formulas: H 1 = 0.5P

H 4 = H 1 + a c = 0.5P + a c

H 3 = H 1 + a c = 0.5P + a c

D 4 = d + 2a c

Z = 0.25P = H 1 ⁄ 2

D 1 = d – 2H 1 = d – p

D 3 = D – 2h 3

d 2 = D 2 = d – 2Z = d – 0.5P

R 1max. = 0.5a c

R 2max. = a c

where ac = clearance on the crest; D = major diameter for nut threads; D2 = pitch diameter for nut threads; D1 = minor diameter for nut threads; d = major diameter for bolt threads = nominal diameter; d2 = pitch diameter for bolt threads; d3 = minor diameter for bolt threads; h1 = Height of overlapping; h4 = height of nut threads; h3 = height of bolt threads; and, P = pitch. Table 1. Comparison of ISO Metric Trapezoidal Screw Thread ISO 2904-1977 and Trapezoidal Metric Screw Thread DIN 103 ISO 2904 D p ac ac h1

DIN 103 DS p b a he

Minor diameter for external thread Pitch diameter for external thread

Bolt Circle h3 = 0.50P + ac has = 0.25p D3 = d − 2h3 D2 = d − 2has

hs = 0.50P + a z = 0.25p ks = d − 2hs d2 = d − 2z

Same Same Same Same

Basic major diameter for nut thread Height of internal thread Minor diameter of internal thread

Nut Circle D4 = d + 2ac h4 = h3 D1= D − 2h1

dn = d + a + b hn = h3+ a Kn = Dn− 2hn

Not same Not same Not same

Nominal Diameter Pitch Clearances (Bolt Circle) Clearances (Nut Circle) Height of Overlapping

Comment Same Same Not same Same



1810

Table 2. ISO Metric Trapezoidal Screw Thread ISO 2904-1977 Nominal Diameter, d 8

1.5 9

10 11 12 14 16 18 20

22

24

26

28

30

32

34

36

38

40

Pitch, P

Pitch Diam. d2 = D2 7.250

Major Diam. D4 8.300

Minor Diameter d3

D1

6.200

6.500 7.500

1.5

8.250

9.300

7.200

2

8.000

9.500

6.500

7.000

1.5

9.250

10.300

8.200

8.500

2

9.000

10.500

7.500

8.000

2

10.000

11.500

8.500

9.000

3

9.500

11.500

7.500

8.000

2

11.000

12.500

9.500

10.000

3

10.500

12.500

8.500

9.000

2

13.000

14.500

11.500

12.000

3

12.500

14.500

10.500

11.000

2

15.000

16.500

13.500

14.000

3

14.500

16.500

12.500

13.000

2

17.000

18.500

15.500

16.000

4

16.000

18.500

13.500

14.000

2

19.000

20.500

17.500

18.000

4

18.000

20.500

15.500

16.000

3

20.500

22.500

18.500

19.000

5

19.500

22.500

16.500

17.000

8

18.000

23.000

13.000

14.000

3

22.500

24.500

20.500

21.000

5

21.500

24.500

18.500

19.000

8

20.000

25.000

15.000

16.000

3

24.500

26.500

22.500

23.000

5

23.500

26.500

20.500

21.000

8

22.000

27.000

17.000

18.000

3

26.500

28.500

24.500

25.000

5

25.500

28.500

22.500

23.000

8

24.000

29.000

19.000

20.000

3

28.500

30.500

26.500

27.000

6

27.000

31.000

23.000

24.000

10

25.000

31.000

19.000

20.000

3

30.500

32.500

28.500

29.000

6

29.000

33.000

25.000

26.000

10

27.000

33.000

21.000

22.000

3

32.500

34.500

30.500

31.000

6

31.000

35.000

27.000

28.000

10

29.000

35.000

23.000

24.000

3

34.500

36.500

32.500

33.000

6

33.000

37.000

29.000

30.000

10

31.000

37.000

25.000

26.000

3

36.500

38.500

34.500

35.000

7

34.500

39.000

30.000

31.000

10

33.000

39.000

27.000

28.000

3

38.500

40.500

36.500

37.000

7

36.500

41.000

32.000

33.000

10

35.000

41.000

29.000

30.000



1811

Table 2. (Continued) ISO Metric Trapezoidal Screw Thread ISO 2904-1977 Nominal Diameter, d

42

44

46

48

50

52

55

60

65

70

75

80

85

90 95 95

100

Minor Diameter

Pitch, P

Pitch Diam. d2 = D2

Major Diam. D4

d3

D1

3

40.500

42.500

38.500

39.000

7

38.500

43.000

34.000

35.000

10

37.000

43.000

31.000

32.000

3

42.500

44.500

40.500

41.000

7

40.500

45.000

36.000

37.000

12

38.000

45.000

31.000

32.000

3

44.500

46.500

42.500

43.000

8

42.000

47.000

37.000

38.000

12

40.000

47.000

33.000

34.000

3

46.500

48.500

44.500

45.000

8

44.000

49.000

39.000

40.000

12

42.000

49.000

35.000

36.000

3

48.500

50.500

46.500

47.000

8

46.000

51.000

41.000

42.000

12

44.000

51.000

37.000

38.000

3

50.500

52.500

48.500

49.000

8

48.000

53.000

43.000

44.000

12

46.000

53.000

39.000

40.000

3

53.500

55.500

51.500

52.000

9

50.500

56.000

45.000

46.000

14

48.000

57.000

39.000

41.000

3

58.500

60.500

56.500

57.000

9

55.500

61.000

50.000

51.000

14

53.000

62.000

44.000

46.000

4

63.000

65.500

60.500

61.000

10

60.000

66.000

54.000

55.000

16

57.000

67.000

47.000

49.000

4

68.000

70.500

65.500

66.000

10

65.000

71.000

59.000

60.000

16

62.000

72.000

52.000

54.000

4

73.000

75.500

70.500

71.000

10

70.000

76.000

64.000

65.000

16

67.000

77.000

57.000

59.000

4

78.000

80.500

75.500

76.000

10

75.000

81.000

69.000

70.000

16

72.000

82.000

62.000

64.000

4

83.000

85.500

80.500

81.000

12

79.000

86.000

72.000

73.000

18

76.000

87.000

65.000

67.000

4

88.000

90.500

85.500

86.000

12

84.000

91.000

77.000

78.000

18

81.000

92.000

70.000

72.000

4

93.000

95.500

90.500

91.000

12

89.000

96.000

82.000

83.000

18

86.000

97.000

75.000

77.000

4

98.000

100.500

95.500

96.000

12

94.000

101.000

87.000

88.000

20

90.000

102.000

78.000

80.000



1812


105

110

115

120

125

130

135

140

145

150

155

160

165

170

175

180

Minor Diameter

Pitch, P

Pitch Diam. d2 = D2

Major Diam. D4

d3

D1

4

103.000

105.500

100.500

101.000

12

103.000

106.000

92.000

93.000

20

95.000

107.000

83.000

85.000

4

108.000

110.500

105.500

106.000

12

104.000

111.000

97.000

98.000

20

100.000

112.000

88.000

90.000

6

112.000

116.000

108.000

109.000

14

112.000

117.000

99.000

101.000

22

104.000

117.000

91.000

93.000

6

117.000

121.000

113.000

114.000

14

113.000

122.000

104.000

106.000

22

109.000

122.000

96.000

98.000

6

122.000

126.000

118.000

119.000

14

122.000

127.000

109.000

111.000

22

114.000

127.000

101.000

103.000

6

127.000

131.000

123.000

124.000

14

123.000

132.000

114.000

116.000

22

119.000

132.000

106.000

108.000

6

132.000

136.000

128.000

129.000

14

132.000

137.000

119.000

121.000

24

123.000

137.000

109.000

111.000

6

137.000

141.000

133.000

134.000

14

133.000

142.000

124.000

126.000

24

128.000

142.000

114.000

116.000

6

142.000

146.000

138.000

139.000

14

142.000

147.000

129.000

131.000

24

133.000

147.000

119.000

121.000

6

147.000

151.000

143.000

144.000

16

142.000

152.000

132.000

134.000

24

138.000

152.000

124.000

126.000

6

152.000

156.000

148.000

149.000

16

152.000

157.000

137.000

139.000

24

143.000

157.000

129.000

131.000

6

157.000

161.000

153.000

154.000

16

152.000

162.000

142.000

144.000

28

146.000

162.000

130.000

132.000

6

162.000

166.000

158.000

159.000

16

162.000

167.000

147.000

149.000

28

151.000

167.000

135.000

137.000

6

167.000

171.000

163.000

164.000

16

162.000

172.000

152.000

154.000

28

156.000

172.000

140.000

142.000

8

171.000

176.000

166.000

167.000

16

171.000

177.000

157.000

159.000

28

161.000

177.000

145.000

147.000

8

176.000

181.000

171.000

172.000

18

171.000

182.000

160.000

162.000

28

166.000

182.000

150.000

152.000



1813


185

190

195

200

210

220

230

240

250

260

270

280

290

300

Minor Diameter

Pitch, P

Pitch Diam. d2 = D2

Major Diam. D4

d3

D1

8

181.000

186.000

176.000

177.000

18

181.000

187.000

165.000

167.000

32

169.000

187.000

151.000

153.000

8

186.000

191.000

181.000

182.000

18

181.000

192.000

170.000

172.000

32

174.000

192.000

156.000

158.000

8

191.000

196.000

186.000

187.000

18

191.000

197.000

175.000

177.000

32

179.000

197.000

161.000

163.000

8

196.000

201.000

191.000

192.000

18

191.000

202.000

180.000

182.000

32

184.000

202.000

166.000

168.000

8

206.000

211.000

201.000

202.000

20

200.000

212.000

188.000

190.000

36

192.000

212.000

172.000

174.000

8

216.000

221.000

211.000

212.000

20

210.000

222.000

198.000

200.000

36

202.000

222.000

182.000

184.000

8

226.000

231.000

221.000

222.000

20

220.000

232.000

208.000

210.000

36

212.000

232.000

192.000

194.000

8

236.000

241.000

231.000

232.000

22

229.000

242.000

216.000

218.000

36

222.000

242.000

202.000

204.000

12

244.000

251.000

237.000

238.000

22

239.000

252.000

226.000

228.000

40

230.000

252.000

208.000

210.000

12

254.000

261.000

247.000

248.000

22

249.000

262.000

236.000

238.000

40

240.000

262.000

218.000

220.000

12

264.000

271.000

257.000

258.000

24

258.000

272.000

244.000

246.000

40

250.000

272.000

228.000

230.000

12

274.000

281.000

267.000

268.000

24

268.000

282.000

254.000

256.000

40

260.000

282.000

238.000

240.000

12

284.000

291.000

277.000

278.000

24

278.000

292.000

264.000

266.000

44

268.000

292.000

244.000

246.000

12

294.000

301.000

287.000

288.000

24

288.000

302.000

274.000

276.000

44

278.000

302.000

254.000

256.000

All dimensions in millimeters


Machinery's Handbook 28th Edition TRAPEZOIDAL METRIC THREAD

1814

Trapezoidal Metric Thread — Preferred Basic Sizes DIN 103

H =1.866P hs =0.5P + a he =0.5P + a − b hn =0.5P + 2a − b has = 0.25P

Nom. & Major Diam.of Bolt, Ds 10 12 14 16 18 20 22 24 26 28 30 32 36 40 44 48 50 52 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

Pitch, P 3 3 4 4 4 4 5 5 5 5 6 6 6 7 7 8 8 8 9 9 10 10 10 10 12 12 12 12 12 14 14 14 16 16 16 18 18 18 20 20 20 22 22 22 24 24 24 26

P Nut a

has r* Ds

Pitch Diam., E 8.5 10.5 12 14 16 18 19.5 21.5 23.5 25.5 27 29 33 36.5 40.5 44 46 48 50.5 55.5 60 65 70 75 79 84 89 94 104 113 123 133 142 152 162 171 181 191 200 210 220 229 239 249 258 268 278 287

Depth of Engagement, he 1.25 1.25 1.75 1.75 1.75 1.75 2 2 2 2 2.5 2.5 2.5 3 3 3.5 3.5 3.5 4 4 4.5 4.5 4.5 4.5 5.5 5.5 5.5 5.5 5.5 6 6 6 7 7 7 8 8 8 9 9 9 10 10 10 11 11 11 12

H H/2

30˚

E

a 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.25 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5 0.5

b 0.5 0.5 0.5 0.5 0.5 0.5 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 0.75 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5 1.5

Dn Kn

b

Ks

Clearance

hn

he

hs

Bolt Bolt Depth of Minor Thread, Diam., hs Ks

Major Diam., Dn

Nut Minor Diam., Kn

6.5 8.5 9.5 11.5 13.5 15.5 16.5 18.5 20.5 22.5 23.5 25.5 29.5 32.5 36.5 39.5 41.5 43.5 45.5 50.5 54.5 59.5 64.5 69.5 72.5 77.5 82.5 87.5 97.5 105 115 125 133 143 153 161 171 181 189 199 209 217 227 237 245 255 265 273

10.5 12.5 14.5 16.5 18.5 20.5 22.5 24.5 26.5 28.5 30.5 32.5 36.5 40.5 44.5 48.5 50.5 52.5 55.5 60.5 65.5 70.5 75.5 80.5 85.5 90.5 95.5 100.5 110.5 121 131 141 151 161 171 181 191 201 211 221 231 241 251 261 271 281 291 301

7.5 9.5 10.5 12.5 14.5 16.5 18 20 22 24 25 27 31 34 38 41 43 45 47 52 56 61 66 71 74 79 84 89 99 108 118 128 136 146 156 164 174 184 192 202 212 220 230 240 248 258 268 276

1.75 1.75 2.25 2.25 2.25 2.25 2.75 2.75 2.75 2.75 3.25 3.25 3.25 3.75 3.75 4.25 4.25 4.25 4.75 4.75 5.25 5.25 5.25 5.25 6.25 6.25 6.25 6.25 6.25 7.5 7.5 7.5 8.5 8.5 8.5 9.5 9.5 9.5 10.5 10.5 10.5 11.5 11.5 11.5 12.5 12.5 12.5 13.5

Depth of Thread, hn 1.50 1.50 2.00 2.00 2.00 2.00 2.00 2.25 2.25 2.25 2.75 2.75 2.75 3.25 3.25 3.75 3.75 3.75 4.25 4.25 4.75 4.75 4.75 4.75 5.75 5.75 5.75 5.75 5.75 6.5 6.5 6.5 7.5 7.5 7.5 8.5 8.5 8.5 9.5 9.5 9.5 10.5 10.5 10.5 11.5 11.5 11.5 12.5

All dimensions are in millimeters. *Roots are rounded to a radius, r, equal to 0.25 mm for pitches of from 3 to 12 mm inclusive and 0.5 mm for pitches of from 14 to 26 mm inclusive for power transmission.


Machinery's Handbook 28th Edition ISO MINIATURE SCREW THREADS

1815

ISO Miniature Screw Threads ISO Miniature Screw Threads, Basic Form ISO/R 1501:1970 Pitch P

H = 0.866025P

0.08 0.09 0.1 0.125 0.15 0.175 0.2 0.225 0.25 0.3

0.069282 0.077942 0.086603 0.108253 0.129904 0.151554 0.173205 0.194856 0.216506 0.259808

0.554256H = 0.48P 0.038400 0.043200 0.048000 0.060000 0.072000 0.084000 0.096000 0.108000 0.120000 0.144000

0.375H = 0.324760P 0.025981 0.029228 0.032476 0.040595 0.048714 0.056833 0.064952 0.073071 0.081190 0.097428

0.320744H = 0.320744P 0.022222 0.024999 0.027777 0.034722 0.041666 0.048610 0.055554 0.062499 0.069443 0.083332

0.125H = 0.108253P 0.008660 0.009743 0.010825 0.013532 0.016238 0.018944 0.021651 0.024357 0.027063 0.032476

ISO Miniature Screw Threads, Basic Dimensions ISO/R 1501:1970 Nominal Diameter 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.70 0.80 0.90 1.00 1.10 1.20 1.40

Pitch P

Major Diameter D, d

Pitch Diameter D 2, d 2

Minor Diameter D1, d1

0.300000 0.350000 0.400000 0.450000 0.500000 0.550000 0.600000 0.700000 0.800000 0.900000 1.000000 1.100000 1.200000 1.400000

0.248039 0.291543 0.335048 0.385048 0.418810 0.468810 0.502572 0.586334 0.670096 0.753858 0.837620 0.937620 1.037620 1.205144

0.223200 0.263600 0.304000 0.354000 0.380000 0.430000 0.456000 0.532000 0.608000 0.684000 0.760000 0.860000 0.960000 1.112000

0.080 0.090 0.100 0.100 0.125 0.125 0.150 0.175 0.200 0.225 0.250 0.250 0.250 0.300

D and d dimensions refer to the nut (internal) and screw (external) threads, respectively.

British Standard ISO Metric Screw Threads BS 3643:Part 1:1981 (R2004) provides principles and basic data for ISO metric screw threads. It covers single-start, parallel screw threads of from 1 to 300 millimeters in diameter. Part 2 of the Standard gives the specifications for selected limits of size. Basic Profile.—The ISO basic profile for triangular screw threads is shown in Fig. 1. and basic dimensions of this profile are given in Table 1. Table 1. British Standard ISO Metric Screw Threads Basic Profile Dimensions BS 3643:1981 (R2004) 5⁄ H 8

=

3⁄ H 8

=

Pitch P

H= 0.086603P

0.54127P

0.32476P

H/4 = 0.21651P

H/8 = 0.10825P

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7

0.173 205 0.216 506 0.259 808 0.303 109 0.346 410 0.389 711 0.433 013 0.519 615 0.606 218

0.108 253 0.135 316 0.162 380 0.189 443 0.216 506 0.243 570 0.270 633 0.324 760 0.378 886

0.064 952 0.081 190 0.097 428 0.113 666 0.129 904 0.146 142 0.162 380 0.194 856 0.227 322

0.043 301 0.054 127 0.064 952 0.075 777 0.086 603 0.097 428 0.108 253 0.129 904 0.151 554

0.021 651 0.027 063 0.032 476 0.037 889 0.043 301 0.048 714 0.054 127 0.064 952 0.075 777


Machinery's Handbook 28th Edition BRITISH STANDARD ISO METRIC SCREW THREADS

1816

Table 1. (Continued) British Standard ISO Metric Screw Threads Basic Profile Dimensions BS 3643:1981 (R2004) 5⁄ H 8

H= 0.086603P 0.649 519 0.692 820 0.866 025 1.082 532 1.299 038 1.515 544 1.732 051 2.165 063 2.598 076 3.031 089 3.464 102 3.897 114 4.330 127 4.763 140 5.196 152 6.928 203

Pitch P 0.75 0.8 1 1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6 8a

3⁄ H 8

=

0.54127P 0.405 949 0.433 013 0.541 266 0.676 582 0.811 899 0.947 215 1.082 532 1.353 165 1.623 798 1.894 431 2.165 063 2.435 696 2.706 329 2.976 962 3.247 595 4.330 127

=

H/4 = 0.21651P 0.162 380 0.173 205 0.216 506 0.270 633 0.324 760 0.378 886 0.433 013 0.541 266 0.649 519 0.757 772 0.866 025 0.974 279 1.082 532 1.190 785 1.299 038 1.732 051

0.32476P 0.243 570 0.259 808 0.324 760 0.405 949 0.487 139 0.568 329 0.649 519 0.811 899 0.974 279 1.136 658 1.299 038 1.461 418 1.623 798 1.786 177 1.948 557 2.598 076

H/8 = 0.10825P 0.081 190 0.086 603 0.108 253 0.135 316 0.162 380 0.189 443 0.216 506 0.270 633 0.324 760 0.378 886 0.433 013 0.487 139 0.541 266 0.595 392 0.649 519 0.866 025

a This pitch is not used in any of the ISO metric standard series. All dimensions are given in millimeters.

Tolerance System.—The tolerance system defines tolerance classes in terms of a combination of a tolerance grade (figure) and a tolerance position (letter). The tolerance position is defined by the distance between the basic size and the nearest end of the tolerance zone, this distance being known as the fundamental deviation, EI, in the case of internal threads, and es in the case of external threads. These tolerance positions with respect to the basic size (zero line) are shown in Fig. 2 and fundamental deviations for nut and bolt threads are given in Table 2. Table 2. Fundamental Deviations for Nut Threads and Bolt Threads Nut Thread D2, D1

Nut Thread D2, D1

Bolt Thread d, d2 Tolerance Position

G

H

e

Bolt Thread d, d2 Tolerance Position

f

g

h

G

H

Fundamental Deviation

e

f

g

h

Fundamental Deviation

Pitch P mm

EI

EI

es

es

es

es

µm

µm

µm

µm

µm

µm

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.6 0.7 0.75 0.8 1

+17 +18 +18 +19 +19 +20 +20 +21 +22 +22 +24 +26

0 0 0 0 0 0 0 0 0 0 0 0

… … … … … … −50 −53 −56 −56 −60 −60

… … … −34 −34 −35 −36 −36 −38 −38 −38 −40

−17 −18 −18 −19 −19 −20 −20 −21 −22 −22 −24 −26

0 0 0 0 0 0 0 0 0 0 0 0

Pitch P mm

EI

EI

es

es

es

es

µm

µm

µm

µm

µm

µm

1.25 1.5 1.75 2 2.5 3 3.5 4 4.5 5 5.5 6

+28 +32 +34 +38 +42 +48 +53 +60 +63 +71 +75 +80

0 0 0 0 0 0 0 0 0 0 0 0

−63 −67 −71 −71 −80 −85 −90 −95 −100 −106 −112 −118

−42 −45 −48 −52 −58 −63 −70 −75 −80 −85 −90 −95

−28 −32 −34 −38 −42 −48 −53 −60 −63 −71 −75 −80

0 0 0 0 0 0 0 0 0 0 0 0

See Figs. 1 and 2 for meaning of symbols.



1817

Tolerance Grades.—Tolerance grades specified in the Standard for each of the four main screw thread diameters are as follows: Minor diameter of nut threads (D1): tolerance grades 4, 5, 6, 7, and 8. Major diameter of bolt threads (d): tolerance grades 4, 6, and 8. Pitch diameter of nut threads (D2): tolerance grades 4, 5, 6, 7, and 8. Pitch diameter of bolt threads (d2): tolerance grades 3, 4, 5, 6, 7, 8, and 9. Tolerance Positions.—Tolerance positions are G and H for nut threads and e, f, g, and h for bolt threads. The relationship of these tolerance position identifying letters to the amount of fundamental deviation is shown in Table 2.

D =maj. diam. of internal thread; d =maj. diam. of external th D2 =pitch diam. of internal thread; d2 =pitch diam. of internal thread; D1 =minor diam. of internal thread; d1 =minor diam. of external thread; P =Pitch; H =height of fundamental angle;

Fig. 1. Basic Profile of ISO Metric Thread

Tolerance Classes.—To reduce the number of gages and tools, the Standard specifies that the tolerance positions and classes shall be chosen from those listed in Table 3 for short, normal, and long lengths of thread engagement. The following rules apply for the choice of tolerance quality: Fine: for precision threads when little variation of fit character is needed; Medium: for general use; and Coarse: for cases where manufacturing difficulties can arise as, for example, when threading hot-rolled bars and long blind holes. If the actual length of thread engagement is unknown, as in the manufacturing of standard bolts, normal is recommended. Table 3. Tolerance Classesa,b,c for Nuts and Bolts Tolerance Classes for Nuts Tolerance Quality Fine Medium Coarse

Short …

Tolerance Position G Normal …

Long …

5Ga …

6Gc 7Gc

7Gc 8Gc

Short 4Hb 5Ha …

Tolerance Position H Normal 5Hb 6Ha,d 7Hb

Long 6Hb 7Ha 8Hb

Tolerance Classes for Bolts Tolelance Quality Fine Medium Coarse

Tolerance Position e Tolerance Position f Tolerance Position g Tolerance Position h Short Normal Long Short Normal Long Short Normal Long Short Normal Long … … … … … … … … … 3h4hc 4ha 5h4hc … … 5g6gc 6ga,d 7g6gc 5h6hc 6ea 6f a 7e6ec … 6hb 7h6hc … … … … … … … … … 9g8gc … 8gb

a First choice. b Second choice. c Third choice; these are to be avoided. d For commercial nut and bolt threads.

Note: See Table 4 for short, normal, and long categories. Any of the recommended tolerance classes for nuts can be combined with any of the recommended tolerance classes for bolts with the exception of sizes M1.4 and smaller for which the combination 5H/6h or finer shall be chosen. However, to guarantee a sufficient overlap, the finished components should preferably be made to form the fits H/g, H/h, or G/h.



1818

Table 4. Lengths of Thread Engagements for Short, Normal, and Long Categories Basic Major Diameter d

Short

Normal

Long

Basic Major Diameter d

Short

Over

Up to and Incl.

Pitch P

Up to and Incl.

Over

0.2 0.5 0.5 0.25 0.6 0.6 0.3 0.7 0.7 0.2 0.5 0.5 0.25 0.6 0.6 0.35 0.8 0.8 1.4 2.8 0.4 1 1 0.45 1.3 1.3 0.35 1 1 0.5 1.5 1.5 0.6 1.7 1.7 2.8 5.6 0.7 2 2 0.75 2.2 2.2 0.8 2.5 2.5 0.75 2.4 2.4 1 3 3 5.6 11.2 1.25 4 4 1.5 5 5 1 3.8 3.8 1.25 4.5 4.5 1.5 5.6 5.6 11.2 22.4 1.75 6 6 2 8 8 2.5 10 10 All dimensions are given in millimeters 0.99

1.4

Normal

Long

Length of Thread Engagement

Length of Thread Engagement Up to and Incl.

Over

1.4 1.7 2 1.5 1.9 2.6 3 3.8 3 4.5 5 6 6.7 7.5 7.1 9 12 15 11 13 16 18 24 30

1.4 1.7 2 1.5 1.9 2.6 3 3.8 3 4.5 5 6 6.7 7.5 7.1 9 12 15 11 13 16 18 24 30

Over

Up to and Incl.

22.4

45

45

90

90

180

180

300

Pitch P

Up to and Incl.

Over

Up to and Incl.

Over

1 1.5 2 3 3.5 4 4.5 1.5 2 3 4 5 5.5 6 2 3 4 6 3 4 6

4 6.3 8.5 12 15 18 21 7.5 9.5 15 19 24 28 32 12 18 24 36 20 26 40

4 6.3 8.5 12 15 18 21 7.5 9.5 15 19 24 28 32 12 18 24 36 20 26 40

12 19 25 36 45 53 63 22 28 45 56 71 85 95 36 53 71 106 60 80 118

12 19 25 36 45 53 63 22 28 45 56 71 85 95 36 53 71 106 60 80 118

Fig. 2. Tolerance Positions with Respect to Zero Line (Basic Size)

Design Profiles.—The design profiles for ISO metric internal and external screw threads are shown in Fig. 3. These represent the profiles of the threads at their maximum metal condition. It may be noted that the root of each thread is deepened so as to clear the basic flat crest of the other thread. The contact between the thread is thus confined to their sloping flanks. However, for nut threads as well as bolt threads, the actual root contours shall not at any point violate the basic profile. Designation.—Screw threads complying with the requirements of the Standard shall be designated by the letter M followed by values of the nominal diameter and of the pitch, expressed in millimeters, and separated by the sign ×. Example: M6 × 0.75. The absence of the indication of pitch means that a coarse pitch is specified. The complete designation of a screw thread consists of a designation for the thread system and size, and a designation for the crest diameter tolerance. Each class designation consists of: a figure indicating the tolerance grade; and a letter indicating the tolerance



1819

position, capital for nuts, lower case for bolts. If the two class designations for a thread are the same (one for the pitch diameter and one for the crest diameter), it is not necessary to repeat the symbols. As examples, a bolt thread designated M10-6g signifies a thread of 10 mm nominal diameter in the Coarse Thread Series having a tolerance class 6g for both pitch and major diameters. A designation M10 × 1-5g6g signifies a bolt thread of 10 mm nominal diameter having a pitch of 1 mm, a tolerance class 5g for pitch diameter, and a tolerance class 6g for major diameter. A designation M10-6H signifies a nut thread of 10 mm diameter in the Coarse Thread Series having a tolerance class 6H for both pitch and minor diameters. Nut (Internal Thread)

In practice the root is rounded and cleared beyond a width of P/8

H/8 30°

P/4

30° P/8

H

5/8 H

Pitch line

H/4 P/2

H/4

P

90° Axis of nut

Bolt (External Thread) H/8 P/2 5/8 H

3/8 H

P P/8

In practice the root is rounded and cleared beyond a width of P/8

30°

Pitch line

H H/4

P/8 P

90° Axis of bolt

Fig. 3. Maximum Material Profiles for Internal and External Threads

A fit between mating parts is indicated by the nut thread tolerance class followed by the bolt thread tolerance class separated by an oblique stroke. Examples: M6-6H/6g and M20 × 2-6H/5g6g. For coated threads, the tolerances apply to the parts before coating, unless otherwise specified. After coating, the actual thread profile shall not at any point exceed the maximum material limits for either tolerance position H or h. Fundamental Deviation Formulas.—The formulas used to calculate the fundamental deviations in Table 2 are: EIG = + (15 + 11P) EIH = 0 ese = −(50 + 11P) except for threads with P ≤ 0.45 mm esf = −(30 + 11P) esg = −(15 + 11P) esh = 0 In these formulas, EI and es are expressed in micrometers and P is in millimeters.



1820

Crest Diameter Tolerance Formulas.—The tolerances for the major diameter of bolt threads (Td), grade 6, in Table 5, were calculated from the formula: 3.15 T d ( 6 ) = 180 3 P 2 – ---------P In this formula, Td (6) is in micrometers and P is in millimeters. For tolerance grades 4 and 8: Td (4) = 0.63 Td (6) and Td (8) = 1.6 Td (6), respectively. The tolerances for the minor diameter of nut threads (TD1), grade 6, in Table 5, were calculated as follows: For pitches 0.2 to 0.8 mm, TD1 (6) = 433P − 190P1.22. For pitches 1 mm and coarser, TD1 (6) = 230P0.7. In these formulas, TD1 (6) is in micrometers and P is in millimeters. For tolerance grades 4, 5, 7, and 8: TD1 (4) = 0.63 TD1 (6); TD1 (5) = 0.8 TD1 (6); TD1 (7) = 1.25 TD1 (6); and TD1 (8) = 1.6 TD1 (6), respectively. Table 5. British Standard ISO Metric Screw Threads: Limits and Tolerances for Finished Uncoated Threads for Normal Lengths of Engagement BS 3643: Part 2: 1981

0.2 1 0.25 0.2 1.1 0.25 0.2 1.2 0.25 0.2 1.4 0.3 0.2 1.6 0.35 0.2 1.8 0.35 0.25 2 0.4 0.25 2.2 0.45

Minor Dia

Fund dev.

Max

Tol(−)

Max

Tol(−)

Min

4h 6g 4h 6g 4h 6g 4h 6g 4h 6g 4h 6g 4h 6g 4h 6g

0 0.017 0 0.018 0 0.017 0 0.018 0 0.017 0 0.018 0 0.017 0 0.018

1.000 0.983 1.000 0.982 1.100 1.083 1.100 1.082 1.200 1.183 1.200 1.182 1.400 1.383 1.400 1.382

0.036 0.056 0.042 0.067 0.036 0.056 0.042 0.067 0.036 0.056 0.042 0.067 0.036 0.056 0.048 0.075

0.870 0.853 0.838 0.820 0.970 0.953 0.938 0.920 1.070 1.053 1.038 1.020 1.270 1.253 1.205 1.187

0.030 0.048 0.034 0.053 0.030 0.048 0.034 0.053 0.030 0.048 0.034 0.053 0.030 0.048 0.036 0.056

0.717 0.682 0.649 0.613 0.817 0.782 0.750 0.713 0.917 0.882 0.850 0.813 1.117 1.082 0.984 0.946

4h 6g 4h 6g

0 0.017 0 0.019

1.600 1.583 1.600 1.581

0.036 0.056 0.053 0.085

1.470 1.453 1.373 1.354

0.032 0.050 0.040 0.063

1.315 1.280 1.117 1.075

4h 6g 4h 6g

0 0.017 0 0.019

1.800 1.783 1.800 1.781

0.036 0.056 0.053 0.085

1.670 1.653 1.573 1.554

0.032 0.050 0.040 0.063

1.515 1.480 1.317 1.275

4h 6g 4h 6g

0 0.018 0 0.019

2.000 1.982 2.000 1.981

0.042 0.067 0.060 0.095

1.838 1.820 1.740 1.721

0.036 0.056 0.042 0.067

1.648 1.610 1.452 1.408

4h 6g 4h 6g

0 0.018 0 0.020

2.200 2.182 2.200 2.180

0.042 0.067 0.063 0.100

2.038 2.020 1.908 1.888

0.036 0.056 0.045 0.071

1.848 1.810 1.585 1.539

Major Dia.

Pitch Dia.

Tol. Class

External Threads (Bolts) Tol. Class

Fine

Coarse

Nominal Diametera

Pitch

Internal Threads (Nuts)b Major Dia. Pitch Dia. Minor Dia Min

Max

Tol(−)

Max

Tol(−)

4H

1.000

0.910

0.040

0.821

0.038

4H 5H 4H

1.000 1.000 1.100

0.883 0.894 1.010

0.045 0.056 0.040

0.774 0.785 0.921

0.045 0.056 0.038

4H 5H 4H

1.100 1.100 1.200

0.983 0.994 1.110

0.045 0.056 0.040

0.874 0.885 1.021

0.045 0.056 0.038

4H 5H 4H

1.200 1.200 1.400

1.083 1.094 1.310

0.045 0.056 0.040

0.974 0.985 1.221

0.045 0.056 0.038

4H 5H 6H 4H

1.400 1.400 1.400 1.600

1.253 1.265 1.280 1.512

0.048 0.060 0.075 0.042

1.128 1.142 1.160 1.421

0.053 0.067 0.085 0.038

4H 5H 6H 4H

1.600 1.600 1.600 1.800

1.426 1.440 1.458 1.712

0.053 0.067 0.085 0.042

1.284 1.301 1.321 1.621

0.063 0.080 0.100 0.038

4H 5H 6H 4H 5H 4H 5H 6H 4H 5H 4H 5H 6H

1.800 1.800 1.800 2.000 2.000 2.000 2.000 2.000 2.200 2.200 2.200 2.200 2.000

1.626 1.640 1.658 1.886 1.898 1.796 1.811 1.830 2.086 2.098 1.968 1.983 2.003

0.053 0.067 0.085 0.048 0.060 0.056 0.071 0.090 0.048 0.060 0.060 0.075 0.095

1.484 1.501 1.521 1.774 1.785 1.638 1.657 1.679 1.974 1.985 1.793 1.813 1.838

0.063 0.080 0.100 0.045 0.056 0.071 0.090 0.112 0.045 0.056 0.080 0.100 0.125



1821

Table 5. (Continued) British Standard ISO Metric Screw Threads: Limits and Tolerances for Finished Uncoated Threads for Normal Lengths of Engagement BS 3643: Part 2: 1981

4h 0 6g 0.020

2.500 2.480

0.063 0.100

2.208 2.188

0.045 0.071

1.885 1.839

4h 0 0.35 6g 0.019

3.000 2.981

0.053 0.085

2.773 2.754

0.042 0.067

2.515 2.471

4h 0 6g 0.020

3.000 2.980

0.067 0.106

2.675 2.655

0.048 0.075

2.319 2.272

4h 0 0.35 6g 0.019

3.500 3.481

0.053 0.085

3.273 3.254

0.042 0.067

3.015 2.971

4h 0 6g 0.021

3.500 3.479

0.080 0.125

3.110 3.089

0.053 0.085

2.688 2.635

4h 0 6g 0.020

4.000 3.980

0.067 0.106

3.675 3.655

0.048 0.075

3.319 3.272

4h 0 6g 0.022

4.000 3.978

0.090 0.140

3.545 3.523

0.056 0.090

3.058 3.002

4h 0 6g 0.020

4.500 4.480

0.067 0.106

4.175 4.155

0.048 0.075

3.819 3.772

4h 0 6g 0.022

4.500 4.478

0.090 0.140

4.013 3.991

0.056 0.090

3.495 3.439

4h 0 6g 0.020

5.000 4.980

0.067 0.106

4.675 4.655

0.048 0.075

4.319 4.272

4h 0 6g 0.024

5.000 4.976

0.095 0.150

4.480 4.456

0.060 0.095

3.927 3.868

4h 0 6g 0.020

5.500 5.480

0.067 0.106

5.175 5.155

0.048 0.075

4.819 4.772

4h 0 0.75 6g 0.022

6.000 5.978

0.090 0.140

5.513 5.491

0.063 0.100

4.988 4.929

4h 6g 8g 4h 0.75 6g

0 0.026 0.026 0 0.022

6.000 5.974 5.974 7.000 6.978

0.112 0.180 0.280 0.090 0.140

5.350 5.324 5.324 6.513 6.491

0.071 0.112 0.180 0.063 0.100

4.663 4.597 4.528 5.988 5.929

4h 6g 8g 4h 6g 8g 4h 6g 8g

0 0.026 0.026 0 0.026 0.026 0 0.028 0.028

7.000 6.974 6.974 8.000 7.974 7.974 8.000 7.972 7.972

0.112 0.180 0.280 0.112 0.180 0.280 0.132 0.212 0.335

6.350 6.324 6.324 7.350 7.324 7.324 7.188 7.160 7.160

0.071 0.112 0.180 0.071 0.112 0.180 0.075 0.118 0.190

5.663 5.596 5.528 6.663 6.596 6.528 6.343 6.272 6.200

0.6

0.5 4 0.7

0.5 4.5 0.75

0.5 5 0.8

0.5

7 1

1

Tol. Class

Min 2.017 1.975

3.5

1.25

Tol. Class

Tol(−) 0.040 0.063

0.5

8

Minor Dia

Max 2.273 2.254

3

1

Pitch Dia.

Tol(−) 0.053 0.085

0.45

6

Major Dia. Max 2.500 2.481

2.5

5.5

External Threads (Bolts)

Fund dev. 4h 0 0.35 6g 0.019 Fine

Coarse

Nominal Diametera

Pitch

4H 5H 6H 4H 5H 6H 4H 5H 6H 5H 6H 7H 4H 5H 6H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H

Internal Threads (Nuts)b Major Dia. Pitch Dia. Minor Dia Min 2.500 2.500 2.500 2.500 2.500 2.500 3.000 3.000 3.000 3.000 3.000 3.000 3.500 3.500 3.500 3.500 3.500 3.500 4.000 4.000 4.000 4.000 4.000 4.000 4.500 4.500 4.500 4.500 4.500 4.500 5.000 5.000 5.000 5.000 5.000 5.000 5.500 5.500 5.500 6.000 6.000 6.000 6.000 6.000 6.000 7.000 7.000 7.000 7.000 7.000 7.000 8.000 8.000 8.000 8.000 8.000 8,000

Max 2.326 2.340 2.358 2.268 2.283 2.303 2.829 2.844 2.863 2.755 2.775 2.800 3.329 3.344 3.363 3.200 3.222 3.250 3.755 3.775 3.800 3.640 3.663 3.695 4.255 4.275 4.300 4.108 4.131 4.163 4.755 4.775 4.800 4.580 4.605 4.640 5.255 5.275 5.300 5.619 5.645 5.683 5.468 5.500 5.540 6.619 6.645 6.683 6.468 6.500 6.540 7.468 7.500 7.540 7.313 7.348 7.388

Tol(−) 0.053 0.067 0.085 0.060 0.075 0.095 0.056 0.071 0.090 0.080 0.100 0.125 0.056 0.071 0.090 0.090 0.112 0.140 0.080 0.100 0.125 0.095 0.118 0.150 0.080 0.100 0.125 0.095 0.118 0.150 0.080 0.100 0.125 0.100 0.125 0.160 0.080 0.100 0.125 0.106 0.132 0.170 0.118 0.150 0.190 0.106 0.132 0.170 0.118 0.150 0.190 0.118 0.150 0.190 0.125 0.160 0.200

Max 2.184 2.201 2.221 2.093 2.113 2.138 2.684 2.701 2.721 2.571 2.599 2.639 3.184 3.201 3.221 2.975 3.010 3.050 3.571 3.599 3.639 3.382 3.422 3.466 4.071 4.099 4.139 3.838 3.878 3.924 4.571 4.599 4.639 4.294 4.334 4.384 5.071 5.099 5.139 5.338 5.378 5.424 5.107 5.153 5.217 6.338 6.378 6.424 6.107 6.153 6.217 7.107 7.153 7.217 6.859 6.912 6.982

Tol(−) 0.063 0.080 0.100 0.080 0.100 0.125 0.063 0.080 0.100 0.112 0.140 0.180 0.063 0.080 0.100 0.125 0.160 0.200 0.112 0.140 0.180 0.140 0.180 0.224 0.112 0.140 0.180 0.150 0.190 0.236 0.112 0.140 0.180 0.160 0.200 0.250 0.112 0.140 0.180 0.150 0.190 0.236 0.190 0.236 0.300 0.150 0.190 0.236 0.190 0.236 0.300 0.190 0.236 0.300 0.212 0.265 0.335



1822


9

10

11

12

14

16

18

20

22

24

27

4h 1.25 6g 8g 4h 1.25 6g 8g 4h 1.5 6g 8g 4h 1.5 6g 8g 4h 1.25 6g 8g 4h 1.75 6g 8g 4h 1.5 6g 8g 4h 2 6g 8g 4h 1.5 6g 8g 4h 2 6g 8g 4h 1.5 6g 8g 4h 2.5 6g 8g 4h 1.5 6g 8g 4h 2.5 6g 8g 4h 1.5 6g 8g 4h 2.5 6g 8g 4h 2 6g 8g 4h 3 6g 8g 4h 2 6g 8g 4h 3 6g 8g

Major Dia. Fund dev. 0 0.028 0.028 0 0.028 0.028 0 0.032 0.032 0 0.032 0.032 0 0.028 0.028 0 0.034 0.034 0 0.032 0.032 0 0.038 0.038 0 0.032 0.032 0 0.038 0.038 0 0.032 0.032 0 0.042 0.042 0 0.032 0.032 0 0.042 0.042 0 0.032 0.032 0 0.042 0.042 0 0.038 0.038 0 0.048 0.048 0 0.038 0.038 0 0.048 0.048

Max 9.000 8.972 8.972 10.000 9.972 9.972 10.000 9.968 9.968 11.000 10.968 10.968 12.000 11.972 11.972 12.000 11.966 11.966 14.000 13.968 13.968 14.000 13.962 13.962 16.000 15.968 15.968 16.000 15.962 15.962 18.000 17.968 17.968 18.000 17.958 17.958 20.000 19.968 19.968 20.000 19.958 19.958 22.000 21.968 21.968 22.000 21.958 21.958 24.000 23.962 23.962 24.000 23.952 23.952 27.000 26.962 26.962 27.000 26.952 26.952

Tol(−) 0.132 0.212 0.335 0.132 0.212 0.335 0.150 0.236 0.375 0.150 0.236 0.375 0.132 0.212 0.335 0.170 0.265 0.425 0.150 0.236 0.375 0.180 0.280 0.450 0.150 0.236 0.375 0.180 0.280 0.450 0.150 0.236 0.375 0.212 0.335 0.530 0.150 0.236 0.375 0.212 0.335 0.530 0.150 0.236 0.375 0.212 0.335 0.530 0.180 0.280 0.450 0.236 0.375 0.600 0.180 0.280 0.450 0.236 0.375 0.600

Pitch Dia. Max 8.188 8.160 8.160 9.188 9.160 9.160 9.026 8.994 8.994 10.026 9.994 9.994 11.188 11.160 11.160 10.863 10.829 10.829 13.026 12.994 12.994 12.701 12.663 12.663 15.026 14.994 14.994 14.701 14.663 14.663 17.026 16.994 16.994 16.376 16.334 16.334 19.026 18.994 18.994 18.376 18.334 18.334 21.026 20.994 20.994 20.376 20.334 20.334 22.701 22.663 22.663 22.051 22.003 22.003 25.701 25.663 25.663 25.051 25.003 25.003

Tol(−) 0.075 0.008 0.190 0.075 0.118 0.190 0.085 0.132 0.212 0.085 0.132 0.212 0.085 0.132 0.212 0.095 0.150 0.236 0.090 0.140 0.224 0.100 0.160 0.250 0.090 0.140 0.224 0.100 0.160 0.250 0.090 0.140 0.224 0.106 0.170 0.265 0.090 0.140 0.224 0.106 0.170 0.265 0.090 0.140 0.224 0.106 0.170 0.265 0.106 0.170 0.265 0.125 0.200 0.315 0.106 0.170 0.265 0.125 0.200 0.315

Minor Dia Min 7.343 7.272 7.200 8.343 8.272 8.200 8.018 7.938 7.858 9.018 8.938 8.858 10.333 10.257 10.177 9.692 9.602 9.516 12.012 11.930 11.846 11.369 11.271 11.181 14.012 13.930 13.846 13.369 13.271 13.181 16.012 15.930 15.846 14.730 14.624 14.529 18.012 17.930 17.846 16.730 16.624 16.529 20.012 19.930 19.846 18.730 18.624 18.529 21.363 21.261 21.166 20.078 19.955 19.840 24.363 24.261 24.166 23.078 22.955 22.840

Tol. Class


Fine

Coarse

Nominal Diametera

Pitch

5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H

Internal Threads (Nuts)b Major Dia. Pitch Dia. Minor Dia Min 9.000 9.000 9.000 10.000 10.000 10.000 10.000 10.000 10.000 11.000 11.000 11.000 12.000 12.000 12.000 12.000 12.000 12.000 14.000 14.000 14.000 14.000 14.000 14.000 16.000 16.000 16.000 16.000 16.000 16.000 18.000 18.000 18.000 18.000 18.000 18.000 20.000 20.000 20.000 20.000 20.000 20.000 22.000 22.000 22.000 22.000 22.000 22.000 24.000 24.000 24.000 24.000 24.000 24.000 27.000 27.000 27.000 27.000 27.000 27.000

Max 8.313 8.348 8.388 9.313 9.348 9.388 9.166 9.206 9.250 10.166 10.206 10.250 11.328 11.398 11.412 11.023 11.063 11.113 13.176 13.216 13.262 12.871 12.913 12.966 15.176 15.216 15.262 14.871 14.913 14.966 17.176 17.216 17.262 16.556 16.600 16.656 19.176 0.190 19.262 18.556 18.600 18.650 21.176 21.216 21.262 20.556 20.600 20.656 22.881 22.925 22.981 22.263 22.316 22.386 25.881 25.925 25.981 25.263 25.316 25.386

Tol(−) 0.125 0.160 0.200 0.125 0.160 0.200 0.140 0.180 0.224 0.140 0.180 0.224 0.140 0.180 0.224 0.160 0.200 0.250 0.150 0.190 0.236 0.170 0.212 0.265 0.150 0.190 0.236 0.170 0.212 0.265 0.150 0.190 0.236 0.180 0.224 0.280 0.150 0.190 0.236 0.180 0.224 0.280 0.150 0.190 0.236 0.180 0.224 0.280 0.180 0.224 0.280 0.212 0.265 0.335 0.180 0.224 0.280 0.212 0.265 0.335

Max 7.859 7.912 7.982 8.859 8.912 8.982 8.612 8.676 8.751 9.612 9.676 9.751 10.859 10.912 10.985 10.371 10.441 10.531 12.612 12.676 12.751 12.135 12.210 12.310 14.612 14.676 14.751 14.135 14.210 14.310 16.612 16.676 16.751 15.649 15.774 15.854 18.612 18.676 18.751 17.649 17.744 17.854 20.612 20.676 20.751 19.649 19.744 19.854 22.135 22.210 22.310 21.152 21.252 21.382 25.135 25.210 25.310 24.152 24.252 24.382

Tol(−) 0.212 0.265 0.335 0.212 0.265 0.335 0.236 0.300 0.375 0.236 0.300 0.375 0.212 0.265 0.335 0.265 0.335 0.425 0.236 0.300 0.375 0.300 0.375 0.475 0.236 0.300 0.375 0.300 0.375 0.475 0.236 0.300 0.375 0.355 0.450 0.560 0.236 0.300 0.375 0.355 0.450 0.560 0.236 0.300 0.375 0.335 0.450 0.560 0.300 0.375 0.475 0.400 0.500 0.630 0.300 0.375 0.475 0.400 0.500 0.630



1823


2 30 3.5

2 33 3.5

36

4

39

4

Internal Threads (Nuts)b Major Dia. Pitch Dia. Minor Dia

4h 6g 8g 4h 6g 8g 4h 6g 8g 4h 6g 8g 4h 6g 8g 4h 6g 8g

Major Dia. Fund dev. 0 0.038 0.038 0 0.053 0.053 0 0.038 0.038 0 0.053 0.053 0 0.060 0.060 0 0.060 0.060

Max 30.000 29.962 29.962 30.000 29.947 29.947 33.000 32.962 32.962 33.000 32.947 32.947 36.000 35.940 35.940 39.000 38.940 38.940

Tol(−) 0.180 0.280 0.450 0.265 0.425 0.670 0.180 0.280 0.450 0.265 0.425 0.670 0.300 0.475 0.750 0.300 0.475 0.750

Pitch Dia. Max 28.701 28.663 28.663 27.727 27.674 27.674 31.701 31.663 30.663 30.727 30.674 30.674 33.402 33.342 33.342 36.402 36.342 36.342

Tol(−) 0.106 0.170 0.265 0.132 0.212 0.335 0.106 0.170 0.265 0.132 0.212 0.335 0.140 0.224 0.355 0.140 0.224 0.355

Minor Dia Min 27.363 27.261 27.166 25.439 25.305 25.183 30.363 30.261 30.166 28.438 28.305 28.182 30.798 30.654 30.523 33.798 33.654 33.523

Tol. Class


Fine

Coarse

Nominal Diametera

Pitch

5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H 5H 6H 7H

Min 30.000 30.000 30.000 30.000 30.000 30.000 33.000 33.000 33.000 33.000 33.000 33.000 36.000 36.000 36.000 39.000 39.000 39.000

Max 28.881 27.925 28.981 27.951 28.007 28.082 31.881 31.925 31.981 30.951 31.007 31.082 33.638 33.702 33.777 36.638 36.702 36.777

Tol(−) 0.180 0.224 0.280 0.224 0.280 0.355 0.180 0.224 0.280 0.224 0.280 0.355 0.236 0.300 0.375 0.236 0.300 0.375

Max 28.135 28.210 28.310 26.661 26.771 26.921 31.135 31.210 31.310 29.661 29.771 29.921 32.145 32.270 32.420 35.145 35.270 35.420

Tol(−) 0.300 0.375 0.475 0.450 0.560 0.710 0.300 0.375 0.475 0.450 0.560 0.710 0.475 0.600 0.750 0.475 0.600 0.750

a This table provides coarse- and fine-pitch series data for threads listed in Table 6 for first, second, and third choices. For constant-pitch series and for larger sizes than are shown, refer to the Standard. b The fundamental deviation for internal threads (nuts) is zero for threads in this table. All dimensions are in millimeters.

Diameter/Pitch Combinations.—Part 1 of BS 3643 provides a choice of diameter/pitch combinations shown here in Table 6. The use of first-choice items is preferred but if necessary, second, then third choice combinations may be selected. If pitches finer than those given in Table 6 are necessary, only the following pitches should be used: 3, 2, 1.5, 1, 0.75, 0.5, 0.35, 0.25, and 0.2 mm. When selecting such pitches it should be noted that there is increasing difficulty in meeting tolerance requirements as the diameter is increased for a given pitch. It is suggested that diameters greater than the following should not be used with the pitches indicated: Pitch, mm

0.5

0.75

1

1.5

2

3

Maximum Diameter, mm

22

33

80

150

200

300

In cases where it is necessary to use a thread with a pitch larger than 6 mm, in the diameter range of 150 to 300 mm, the 8 mm pitch should be used. Limits and Tolerances for Finished Uncoated Threads.—Part 2 of BS 3643 specifies the fundamental deviations, tolerances, and limits of size for the tolerance classes 4H, 5H, 6H, and 7H for internal threads (nuts) and 4h, 6g, and 8g for external threads (bolts) for coarse-pitch series within the range of 1 to 68 mm; fine-pitch series within the range of 1 to 33 mm; and constant pitch series within the range of 8 to 300 mm diameter. The data in Table 5 provide the first, second, and third choice combinations shown in Table 6 except that constant-pitch series threads are omitted. For diameters larger than shown in Table 5, and for constant-pitch series data, refer to the Standard.



1824

Table 6. British Standard ISO Metric Screw Threads — Diameter/Pitch Combinations BS 3643:Part 1:1981 (R2004) Nominal Diameter Choices

Nominal Diameter

1st

2nd

3rd

Coarse Pitch

1 … 1.2 … 1.6 … 2.0 … 2.5 3 … 4 … 5 … 6 … 8 … 10 … 12 … … 16 … … 20 … 24 … … … … 30 … … … 36 … … … 42 48 … … … 56 … … … 64 … …

… 1.1 … 1.4 … 1.8 … 2.2 … … 3.5 … 4.5 … … … 7 … … … … … 14 … … … 18 … 22 … … … 27 … … … 33 … … … 39 … 45 … … 52 … … … 60 … … … 68

… … … … … … … … … … … … … … 5.5 … … … 9 … 11 … … 15 … 17 … … … … 25 26 … 28 … 32 … 35b … 38 … 40 … … 50 … 55 … 58 … 62 … 65 …

0.25 0.25 0.25 0.3 0.35 0.35 0.4 0.45 0.45 0.5 0.6 0.7 0.75 0.8 … 1 1 1.25 1.25 1.5 1.5 1.75 2 … 2 … 2.5 2.5 2.5 3 … … 3 … 3.5 … 3.5 … 4 … 4 … 4.5 5 … 5 … 5.5 … 5.5 … 6 … 6

Choices

Fine Pitch

Constant Pitch

1st

2nd

3rd

Constant Pitch

0.2 0.2 0.2 0.2 0.2 0.2 0.25 0.25 0.35 0.35 0.35 0.5 0.5 0.5 (0.5) 0.75 0.75 1 … 1.25 … 1.25 1.5 … 1.5 … 1.5 1.5 1.5 2 … … 2 … 2 … 2 … … … … … … … … … … … … … … … … …

… … … … … … … … … … … … … … … … … 0.75 1, 0.75 1, 0.75 1, 0.75 1.5, 1 1.25 a , 1 1.5, 1 1 1.5, 1 2, 1 2, 1 2, 1 1.5, 1 2, 1.5, 1 1.5 1.5, 1 2, 1.5, 1 (3), 1.5, 1 2, 1.5 (3), 1.5 1.5 3, 2, 1.5 1.5 3, 2, 1.5 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5 4, 3, 2, 1.5

… 72 … … … 80 … … 90 … 100 … 110 … … 125 … … 140 … … … 160 … … … 180 … … … 200 … … … 220 … … … … … 250 … … … … … 280 … … … … … … …

… … … 76 … … … 85 … 95 … 105 … 115 120 … 130 … … … 150 … … … 170 … … … 190 … … … 210 … … … … … 240 … … … 260 … … … … … … … 300 … … …

70 … 75 … 78 … 82 … … … … … … … … … … 135 … 145 … 155 … 165 … 175 … 185 … 195 … 205 … 215 … 225 230 235 … 245 … 255 … 265 270 275 … 285 290 295 … … … …

6, 4, 3, 2, 1.5 6, 4, 3, 2, 1.5 4, 3, 2, 1.5 6, 4, 3, 2, 1.5 2 6, 4, 3, 2, 1.5 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3, 2 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4, 3 6, 4 6, 4 6, 4 6, 4 6, 4 6, 4 6, 4 6, 4 6, 4 6, 4 … … …

a Only for spark plugs for engines. b Only for locking nuts for bearings.

All dimensions are in millimeters. Pitches in parentheses ( ) are to be avoided as far as possible.


Machinery's Handbook 28th Edition Comparison of Metric Thread Systems Metric Series Threads — A comparison of Maximum Metal Dimensions of British ( BS 1095), French ( NF E03-104), German ( DIN 13), and Swiss ( VSM 12003) Systems Bolt

Nut

Minor Diameter

Minor Diameter

French

German

Swiss

British & German

6 7 8 9 10 11 12 14 16 18 20 22 24

1 1 1.25 1.25 1.5 1.5 1.75 2 2 2.5 2.5 2.5 3

5.350 6.350 7.188 8.188 9.026 10.026 10.863 12.701 14.701 16.376 18.376 20.376 22.051

4.863 5.863 6.579 7.579 8.295 9.295 10.011 11.727 13.727 15.158 17.158 19.158 20.590

4.59 5.59 6.24 7.24 7.89 8.89 9.54 11.19 13.19 14.48 16.48 18.48 19.78

4.700 5.700 6.376 7.376 8.052 9.052 9.726 11.402 13.402 14.752 16.752 18.752 20.102

4.60 5.60 6.25 7.25 7.90 8.90 9.55 11.20 13.20 14.50 16.50 18.50 19.80

6.000 7.000 8.000 9.000 10.000 11.000 12.000 14.000 16.000 18.000 20.000 22.000 24.000

6.108 7.108 8.135 9.135 10.162 11.162 12.189 14.216 16.216 18.270 20.270 22.270 24.324

6.100 7.100 8.124 9.124 10.150 11.150 12.174 14.200 16.200 18.250 20.250 22.250 24.300

4.700 5.700 6.376 7.376 8.052 9.052 9.726 11.402 13.402 14.752 16.752 18.752 20.102a

4.863 5.863 6.579 7.579 8.295 9.295 10.011 11.727 13.727 15.158 17.158 19.158 20.590

27

3

25.051

23.590

22.78

23.102

22.80

27.000

27.324

27.300

30 33 36 39 42 45 48 52 56 60

3.5 3.5 4 4 4.5 4.5 5 5 5.5 5.5

27.727 30.727 33.402 36.402 39.077 42.077 41.752 48.752 52.428 56.428

26.022 29.022 31.453 34.453 36.885 39.885 42.316 46.316 49.748 53.748

25.08 28.08 30.37 33.37 35.67 38.67 40.96 44.96 48.26 52.26

25.454 28.454 30.804 33.804 36.154 39.154 41.504 45.504 48.856 52.856

25.10 28.10 30.40 33.40 35.70 38.70 41.00 45.00 48.30 52.30

30.000 33.000 36.000 39.000 42.000 45.000 48.000 52.000 56.000 60.000

30.378 33.378 36.432 39.432 42.486 45.486 48.540 52.540 56.594 60.594

30.350 33.350 36.400 39.400 42.450 45.450 48.500 52.500 56.550 60.550

23.102b 25.454 28.454 30.804 33.804 36.154 39.154 41.504 45.504 48.856 52.856

26.022 29.022 31.453 34.453 36.885 39.885 42.316 46.316 49.748 53.748

Pitch

Pitch Diam.

Major Diameter

British

French

Swiss

French, German& Swiss

British

23.590

COMPARISON OF METRIC THREAD SYSTEMS

Nominal Size and Major Bolt Diam.

a The value shown is given in the German Standard; the value in the French Standard is 20.002; and in the Swiss Standard, 20.104.

All dimensions are in mm.


1825

b The value shown is given in the German Standard; the value in the French Standard is 23.002; and in the Swiss Standard, 23.104.

1826

Machinery's Handbook 28th Edition ACME SCREW THREADS

ACME SCREW THREADS American National Standard Acme Screw Threads This American National Standard ASME/ANSI B1.5-1997 is a revision of American Standard ANSI B1.5-1988 and provides for two general applications of Acme threads, namely, General Purpose and Centralizing. The limits and tolerances in this standard relate to single-start Acme threads, and may be used, if considered suitable, for multi-start Acme threads, which provide fast relative traversing motion when this is necessary. For information on additional allowances for multistart Acme threads, see later section on page 1828. General Purpose Acme Threads.—Three classes of General Purpose threads, 2G, 3G, and 4G, are provided in the standard, each having clearance on all diameters for free movement, and may be used in assemblies with the internal thread rigidly fixed and movement of the external thread in a direction perpendicular to its axis limited by its bearing or bearings. It is suggested that external and internal threads of the same class be used together for general purpose assemblies, Class 2G being the preferred choice. If less backlash or end play is desired, Classes 3G and 4G are provided. Class 5G is not recommended for new designs. Thread Form: The accompanying Fig. 1 shows the thread form of these General Purpose threads, and the formulas accompanying the figure determine their basic dimensions. Table 1 gives the basic dimensions for the most generally used pitches. Angle of Thread: The angle between the sides of the thread, measured in an axial plane, is 29 degrees. The line bisecting this 29-degree angle shall be perpendicular to the axis of the screw thread. Thread Series: A series of diameters and associated pitches is recommended in the Standard as preferred. These diameters and pitches have been chosen to meet present needs with the fewest number of items in order to reduce to a minimum the inventory of both tools and gages. This series of diameters and associated pitches is given in Table 3. Chamfers and Fillets: General Purpose external threads may have the crest corner chamfered to an angle of 45 degrees with the axis to a maximum width of P/15, where P is the pitch. This corresponds to a maximum depth of chamfer flat of 0.0945P. Basic Diameters: The max major diameter of the external thread is basic and is the nominal major diameter for all classes. The min pitch diameter of the internal thread is basic and is equal to the basic major diameter minus the basic height of the thread, h. The basic minor diameter is the min minor diameter of the internal thread. It is equal to the basic major diameter minus twice the basic thread height, 2h. Length of Engagement: The tolerances specified in this standard are applicable to lengths of engagement not exceeding twice the nominal major diameter. Major and Minor Diameter Allowances: A minimum diametral clearance is provided at the minor diameter of all external threads by establishing the maximum minor diameter 0.020 inch below the basic minor diameter of the nut for pitches of 10 threads per inch and coarser, and 0.010 inch for finer pitches. A minimum diametral clearance at the major diameter is obtained by establishing the minimum major diameter of the internal thread 0.020 inch above the basic major diameter of the screw for pitches of 10 threads per inch and coarser, and 0.010 inch for finer pitches. Major and Minor Diameter Tolerances: The tolerance on the external thread major diameter is 0.05P, where P is the pitch, with a minimum of 0.005 inch. The tolerance on the internal thread major diameter is 0.020 inch for 10 threads per inch and coarser and 0.010 for finer pitches. The tolerance on the external thread minor diameter is 1.5 × pitch diameter tolerance. The tolerance on the internal thread minor diameter is 0.05P with a minimum of 0.005 inch.



1827

ANSI General Purpose Acme Thread Form ASME/ANSI B1.5-1997 (R2004), and Stub Acme Screw Thread Form ASME/ANSI B1.8-1988 (R2006)

Fig. 1. General Purpose and Stub Acme Thread Forms

Formulas for Basic Dimensions of General Purpose and Stub Acme Screw Threads General Purpose Pitch = P = 1 ÷ No. threads per inch, n Basic thread height h = 0.5P Basic thread thickness t = 0.5P Basic flat at crest Fcn = 0.3707P (internal thread) Basic flat at crest Fcs = 0.3707P − 0.259 × (pitch dia. allowance on ext. thd.) Frn = 0.3707P − 0.259 × (major dia. allowance on internal thread) Frs = 0.3707P − 0.259 × (minor dia. allowance on ext. thread − pitch dia. allowance on ext. thread)

Stub Acme Threads Pitch = P = 1 ÷ No. threads per inch, n Basic thread height h = 0.3P Basic thread thickness t = 0.5P Basic flat at crest Fcn = 0.4224P (internal thread) Basic flat at crest Fcs = 0.4224P − 0.259 × (pitch dia. allowance on ext. thread) Frn = 0.4224P − 0.259 × (major dia. allowance on internal thread) Frs = 0.4224P − 0.259 × (minor dia. allowance on ext. thread − pitch dia. allowance on ext. thread)

Pitch Diameter Allowances and Tolerances: Allowances on the pitch diameter of General Purpose Acme threads are given in Table 4. Pitch diameter tolerances are given in Table 5. The ratios of the pitch diameter tolerances of Classes 2G, 3G, and 4G, General Purpose threads are 3.0, 1.4, and 1, respectively. An increase of 10 per cent in the allowance is recommended for each inch, or fraction thereof, that the length of engagement exceeds two diameters. Application of Tolerances: The tolerances specified are designed to ensure interchangeability and maintain a high grade of product. The tolerances on diameters of the internal thread are plus, being applied from minimum sizes to above the minimum sizes. The tolerances on diameters of the external thread are minus, being applied from the maximum sizes to below the maximum sizes. The pitch diameter (or thread thickness) tolerances for an external or internal thread of a given class are the same. The thread thickness tolerance is 0.259 times the pitch diameter tolerance.


1828


Limiting Dimensions: Limiting dimensions of General Purpose Acme screw threads in the recommended series are given in Table 2b. These limits are based on the formulas in Table 2a. For combinations of pitch and diameter other than those in the recommended series, the formulas in Table 2a and the data in Tables 4 and 5 make it possible to readily determine the limiting dimensions required. A diagram showing the disposition of allowances, tolerances, and crest clearances for General Purpose Acme threads appears on page 1827. Stress Area of General Purpose Acme Threads: For computing the tensile strength of the thread section, the minimum stress area based on the mean of the minimum pitch diameter d2 min. and the minimum minor diameter d1 max. of the external thread is used: d 2 min. + d 1 max. 2 Stress Area = 3.1416  -------------------------------------------- 4 where d2 min. and d1 max. may be computed by Formulas 4 and 6, Table 2a or taken from Table 2b. Shear Area of General Purpose Acme Threads: For computing the shear area per inch length of engagement of the external thread, the maximum minor diameter of the internal thread D1 max., and the minimum pitch diameter of the external thread D2 min., Table 2b or Formulas 12 and 4, Table 2a, are used: Shear Area = 3.1416D 1 max. [ 0.5 + n tan 14 1⁄2 ° ( D 2 min. – D 1 max. ) ] Acme Thread Abbreviations.—The following abbreviations are recommended for use on drawings and in specifications, and on tools and gages: ACME = Acme threads G =General Purpose C =Centralizing P =pitch L =lead LH = left hand Designation of General Purpose Acme Threads.—The examples listed below are given here to show how General Purpose Acme threads are designated on drawings and tools: 1.750-4 ACME-2G indicates a General Purpose Class 2G Acme thread of 1.750-inch major diameter, 4 threads per inch, single thread, right hand. The same thread, but left hand, is designated 1.750-4 ACME-2G-LH. 2.875-0.4P-0.8L-ACME-3G indicates a General Purpose Class 3G Acme thread of 2.875-inch major diameter, pitch 0.4 inch, lead 0.8 inch, double thread, right hand. Multiple Start Acme Threads.—The tabulated diameter-pitch data with allowances and tolerances relate to single-start threads. These data, as tabulated, may be and often are used for two-start Class 2G threads but this usage generally requires reduction of the full working tolerances to provide a greater allowance or clearance zone between the mating threads to assure satisfactory assembly. When the class of thread requires smaller working tolerances than the 2G class or when threads with 3, 4, or more starts are required, some additional allowances or increased tolerances or both may be needed to ensure adequate working tolerances and satisfactory assembly of mating parts. It is suggested that the allowances shown in Table 4 be used for all external threads and that allowances be applied to internal threads in the following ratios: for two-start threads, 50 per cent of the allowances shown in the Class 2G, 3G and 4G columns of Table 4; for



1829

Table 1. American National Standard General Purpose Acme Screw Thread Form — Basic Dimensions ASME/ANSI B1.5-1997 (R2004) Width of Flat

Pitch, P = 1/n

Height of Thread (Basic), h = P/2

Total Height of Thread, hs = P/2 + 1⁄2 allowancea

Thread Thickness (Basic), t = P/2

Crest of Internal Thread (Basic), Fcn = 0.3707P

Root of Internal Thread, Frn 0.3707P −0.259 × allowancea

0.06250 0.07143 0.08333 0.10000 0.12500 0.16667 0.20000 0.25000 0.33333 0.40000

0.03125 0.03571 0.04167 0.05000 0.06250 0.08333 0.10000 0.12500 0.16667 0.20000

0.0362 0.0407 0.0467 0.0600 0.0725 0.0933 0.1100 0.1350 0.1767 0.2100

0.03125 0.03571 0.04167 0.05000 0.06250 0.08333 0.10000 0.12500 0.16667 0.20000

0.0232 0.0265 0.0309 0.0371 0.0463 0.0618 0.0741 0.0927 0.1236 0.1483

0.0206 0.0239 0.0283 0.0319 0.0411 0.0566 0.0689 0.0875 0.1184 0.1431

2 11⁄2

0.50000 0.66667

0.25000 0.33333

0.2600 0.3433

0.25000 0.33333

0.1853 0.2471

0.1802 0.2419

11⁄3

0.75000

Thds. per Inch n 16 14 12 10 8 6 5 4 3 21⁄2

1 1.00000 All dimensions are in inches.

0.37500

0.3850

0.37500

0.2780

0.2728

0.50000

0.5100

0.50000

0.3707

0.3655

a Allowance is 0.020 inch for 10 threads per inch and coarser, and 0.010 inch for finer threads.

Table 2a. American National Standard General Purpose Acme Single-Start Screw Threads — Formulas for Determining Diameters ASME/ANSI B1.5-1997 (R2004) D = Basic Major Diameter and Nominal Size, in Inches. P = Pitch = 1 ÷ Number of Threads per Inch. E = Basic Pitch Diameter = D − 0.5P K = Basic Minor Diameter = D − P No. 1 2 3 4 5 6

7 8 9 10 11 12

External Threads (Screws) Major Dia., Max. = D Major Dia., Min. = D minus 0.05Pa but not less than 0.005. Pitch Dia., Max. = E minus allowance from Table 4. Pitch Dia., Min. = Pitch Dia., Max. (Formula 3) minus tolerance from Table 5. Minor Dia., Max. = K minus 0.020 for 10 threads per inch and coarser and 0.010 for finerpitches. Minor Dia., Min. = Minor Dia., Max. (Formula 5) minus 1.5 × pitch diameter tolerance from Table 5. Internal Threads (Nuts) Major Dia., Min. = D plus 0.020 for 10 threads per inch and coarser and 0.010 for finer pitches. Major Dia., Max. = Major Dia., Min. (Formula 7) plus 0.020 for 10 threads per inch and coarser and 0.010 for finer pitches. Pitch Dia., Min. = E Pitch Dia., Max. = Pitch Dia., Min. (Formula 9) plus tolerance from Table 5. Minor Dia., Min. = K Minor Dia., Max. = Minor Dia., Min. (Formula 11) plus 0.05Pa but not less than 0.005.

a If P is between two recommended pitches listed in Table 3, use the coarser of the two pitches in this

formula instead of the actual value of P.



Nominal Diameter, D

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

5⁄ 8

3⁄ 4

7⁄ 8

1

11⁄8

11⁄4

13⁄8

Threads per Incha

16

14

12

12

10

8

6

6

5

5

5

4

Limiting Diameters Classes 2G, 3G, and 4G Major Diameter

1830

Table 2b. Limiting Dimensions of ANSI General Purpose Acme Single-Start Screw Threads ASME/ANSI B1.5-1988

External Threads {

Max (D)

0.2500

0.3125

0.3750

0.4375

0.5000

0.6250

0.7500

0.8750

1.0000

1.1250

1.2500

1.3750

Min

0.2450

0.3075

0.3700

0.4325

0.4950

0.6188

0.7417

0.8667

0.9900

1.1150

1.2400

1.3625 1.1050

Classes 2G, 3G, and 4G Minor Diameter

0.1775

0.2311

0.2817

0.3442

0.3800

0.4800

0.5633

0.6883

0.7800

0.9050

1.0300

Min

0.1618

0.2140

0.2632

0.3253

0.3594

0.4570

0.5372

0.6615

0.7509

0.8753

0.9998

1.0720

Class 3G, Minor Diameter

Min

0.1702

0.2231

0.2730

0.3354

0.3704

0.4693

0.5511

0.6758

0.7664

0.8912

1.0159

1.0896 1.0940

Class 4G, Minor Diameter Class 2G, Pitch Diameter

{

Class 3G, Pitch Diameter

{


{

Min

0.1722

0.2254

0.2755

0.3379

0.3731

0.4723

0.5546

0.6794

0.7703

0.8951

1.0199

Max

0.2148

0.2728

0.3284

0.3909

0.4443

0.5562

0.6598

0.7842

0.8920

1.0165

1.1411

1.2406

Min

0.2043

0.2614

0.3161

0.3783

0.4306

0.5408

0.6424

0.7663

0.8726

0.9967

1.1210

1.2188

Max

0.2158

0.2738

0.3296

0.3921

0.4458

0.5578

0.6615

0.7861

0.8940

1.0186

1.1433

1.2430

Min

0.2109

0.2685

0.3238

0.3862

0.4394

0.5506

0.6534

0.7778

0.8849

1.0094

1.1339

1.2327

Max

0.2168

0.2748

0.3309

0.3934

0.4472

0.5593

0.6632

0.7880

0.8960

1.0208

1.1455

1.2453

Min

0.2133

0.2710

0.3268

0.3892

0.4426

0.5542

0.6574

0.7820

0.8895

1.0142

1.1388

1.2380

Min

0.2600

0.3225

0.3850

0.4475

0.5200

0.6450

0.7700

0.8950

1.0200

1.1450

1.2700

1.3950

Max

0.2700

0.3325

0.3950

0.4575

0.5400

0.6650

0.7900

0.9150

1.0400

1.1650

1.2900

1.4150

Min

0.1875

0.2411

0.2917

0.3542

0.4000

0.5000

0.5833

0.7083

0.8000

0.9250

1.0500

1.1250

Internal Threads Classes 2G, 3G, and 4G Major Diameter Classes 2G, 3G, and 4G Minor Diameter

{ {


{


{


{

Max

0.1925

0.2461

0.2967

0.3592

0.4050

0.5062

0.5916

0.7166

0.8100

0.9350

1.0600

1.1375

Min

0.2188

0.2768

0.3333

0.3958

0.4500

0.5625

0.6667

0.7917

0.9000

1.0250

1.1500

1.2500

Max

0.2293

0.2882

0.3456

0.4084

0.4637

0.5779

0.6841

0.8096

0.9194

1.0448

1.1701

1.2720

Min

0.2188

0.2768

0.3333

0.3958

0.4500

0.5625

0.6667

0.7917

0.9000

1.0250

1.1500

1.2500

Max

0.2237

0.2821

0.3391

0.4017

0.4564

0.5697

0.6748

0.8000

0.9091

1.0342

1.1594

1.2603

Min

0.2188

0.2768

0.3333

0.3958

0.4500

0.5625

0.6667

0.7917

0.9000

1.0250

1.1500

1.2500

Max

0.2223

0.2806

0.3374

0.4000

0.4546

0.5676

0.6725

0.7977

0.9065

1.0316

1.1567

1.2573


ACME SCREW THREADS

Max

Class 2G, Minor Diameter

Machinery's Handbook 28th Edition Table 2b. (Continued) Limiting Dimensions of ANSI General Purpose Acme Single-Start Screw Threads ASME/ANSI B1.5-1988 Nominal Diameter, D Threads per Incha

11⁄2

13⁄4

2

21⁄4

21⁄2

23⁄4

3

31⁄2

4

41⁄2

5

4

4

4

3

3

3

2

2

2

2

2

Limiting Diameters Classes 2G, 3G, and 4G Major Diameter

External Threads {

Max (D)

1.5000

1.7500

2.0000

2.2500

2.5000

2.7500

3.0000

3.5000

4.0000

4.5000

5.0000

Min

1.4875

1.7375

1.9875

2.2333

2.4833

2.7333

2.9750

3.4750

3.9750

4.4750

4.9750

Max

1.2300

1.4800

1.7300

1.8967

2.1467

2.3967

2.4800

2.9800

3.4800

3.9800

4.4800

Classes 2G, 3G, and 4G Minor Diameter

ACME SCREW THREADS 1831



Nominal Sizes (All Classes)

1 11⁄8 11⁄4 13⁄8 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄2 4 41⁄2 5

Basic Diameters Classes 2G, 3G, and 4G Minor Pitch Major Diameter, Diameter, Diameter, = D − h D D D 2 1 = D − 2h 0.2500 0.2188 0.1875 0.3125 0.2768 0.2411 0.3750 0.3333 0.2917 0.4375 0.3958 0.3542 0.5000 0.4500 0.4000 0.6250 0.5625 0.5000 0.7500 0.6667 0.5833 0.8750 0.7917 0.7083 1.0000 0.9000 0.8000 1.1250 1.0250 0.9250 1.2500 1.1500 1.0500 1.3750 1.2500 1.1250 1.5000 1.3750 1.2500 1.7500 1.6250 1.5000 2.0000 1.8750 1.7500 2.2500 2.0833 1.9167 2.5000 2.3333 2.1667 2.7500 2.5833 2.4167 3.0000 2.7500 2.5000 3.5000 3.2500 3.0000 4.0000 3.7500 3.5000 4.5000 4.2500 4.0000 5.0000 4.7500 4.5000

Thread Data

Pitch, P 0.06250 0.07143 0.08333 0.08333 0.10000 0.12500 0.16667 0.16667 0.20000 0.20000 0.20000 0.25000 0.25000 0.25000 0.25000 0.33333 0.33333 0.33333 0.50000 0.50000 0.50000 0.50000 0.50000

Thickness at Pitch Line, t = P/2 0.03125 0.03571 0.04167 0.04167 0.05000 0.06250 0.08333 0.08333 0.10000 0.10000 0.10000 0.12500 0.12500 0.12500 0.12500 0.16667 0.16667 0.16667 0.25000 0.25000 0.25000 0.25000 0.25000

Basic Height of Thread, h = P/2 0.03125 0.03571 0.04167 0.04167 0.05000 0.06250 0.08333 0.08333 0.10000 0.10000 0.10000 0.12500 0.12500 0.12500 0.12500 0.16667 0.16667 0.16667 0.25000 0.25000 0.25000 0.25000 0.25000

Basic Width of Flat, F = 0.3707P 0.0232 0.0265 0.0309 0.0309 0.0371 0.0463 0.0618 0.0618 0.0741 0.0741 0.0741 0.0927 0.0927 0.0927 0.0927 0.1236 0.1236 0.1236 0.1853 0.1853 0.1853 0.1853 0.1853

Lead Angle λ at Basic Pitch Diametera Classes 2G, 3G,and 4G Deg Min 5 12 4 42 4 33 3 50 4 3 4 3 4 33 3 50 4 3 3 33 3 10 3 39 3 19 2 48 2 26 2 55 2 36 2 21 3 19 2 48 2 26 2 9 1 55

Shear Areab Class 3G 0.350 0.451 0.545 0.660 0.749 0.941 1.108 1.339 1.519 1.751 1.983 2.139 2.372 2.837 3.301 3.643 4.110 4.577 4.786 5.73 6.67 7.60 8.54

Stress Areac Class 3G 0.0285 0.0474 0.0699 0.1022 0.1287 0.2043 0.2848 0.4150 0.5354 0.709 0.907 1.059 1.298 1.851 2.501 3.049 3.870 4.788 5.27 7.50 10.12 13.13 16.53

a All other dimensions are given in inches. b Per inch length of engagement of the external thread in line with the minor diameter crests of the internal thread. Figures given are the minimum shear area based on max D1 and min d2. c Figures given are the minimum stress area based on the mean of the minimum minor and pitch diameters of the external thread. See formulas for shear area and stress area on page 1828.


ACME SCREW THREADS

1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

Threads per Inch,a n 16 14 12 12 10 8 6 6 5 5 5 4 4 4 4 3 3 3 2 2 2 2 2

1832

Table 3. General Purpose Acme Single-Start Screw Thread Data ASME/ANSI B1.5-1988 Identification

Machinery's Handbook 28th Edition CENTRALIZING ACME SCREW THREADS

1833

Table 4. American National Standard General Purpose Acme Single-Start Screw Threads — Pitch Diameter Allowances ASME/ANSI B1.5-1988 Nominal Size Rangea

Allowances on External Threads b 2G c,

Class 3G,

Class 4G,

0.008 D

0.006 D

0.004 D

Class To and Above Including

Nominal Size Rangea To and Above Including

Allowances on External Threads b Class 2Gc,

Class 3G,

Class 4G,

0.008 D

0.006 D

0.004 D

0

3⁄ 16

0.0024

0.0018

0.0012

17⁄16

19⁄16

0.0098

0.0073

0.0049

3⁄ 16

5⁄ 16

0.0040

0.0030

0.0020

19⁄16

17⁄8

0.0105

0.0079

0.0052

5⁄ 16

7⁄ 16

0.0049

0.0037

0.0024

17⁄8

21⁄8

0.0113

0.0085

0.0057

7⁄ 16

9⁄ 16

0.0057

0.0042

0.0028

21⁄8

23⁄8

0.0120

0.0090

0.0060

9⁄ 16

11⁄ 16

0.0063

0.0047

0.0032

23⁄8

25⁄8

0.0126

0.0095

0.0063

11⁄ 16

13⁄ 16

0.0069

0.0052

0.0035

25⁄8

27⁄8

0.0133

0.0099

0.0066

13⁄ 16

15⁄ 16

0.0075

0.0056

0.0037

27⁄8

31⁄4

0.0140

0.0105

0.0070

15⁄ 16

11⁄16

0.0080

0.0060

0.0040

31⁄4

33⁄4

0.0150

0.0112

0.0075

11⁄16

13⁄16

0.0085

0.0064

0.0042

33⁄4

41⁄4

0.0160

0.0120

0.0080

13⁄16

15⁄16

0.0089

0.0067

0.0045

41⁄4

43⁄4

0.0170

0.0127

0.0085

15⁄16

17⁄16

0.0094

0.0070

0.0047

43⁄4

51⁄2

0.0181

0.0136

0.0091

All dimensions in inches. It is recommended that the sizes given in Table 3 be used whenever possible. a The values in columns for Classes 2G, 3G, and 4G are to be used for any size within the nominal size range shown. These values are calculated from the mean of the range. b An increase of 10 per cent in the allowance is recommended for each inch, or fraction thereof, that the length of engagement exceeds two diameters. c Allowances for the 2G Class of thread in this table also apply to American National Standard Stub Acme threads ASME/ANSI B 1.8-1988.

three-start threads, 75 per cent of these allowances; and for four-start threads, 100 per cent of these same values. These values will provide for a 0.25-16 ACME-2G thread size, 0.002, 0.003, and 0.004 inch additional clearance for 2-, 3-, and 4-start threads, respectively. For a 5-2 ACME-3G thread size the additional clearances would be 0.0091, 0.0136, and 0.0181 inch, respectively. GO thread plug gages and taps would be increased by these same values. To maintain the same working tolerances on multi-start threads, the pitch diameter of the NOT GO thread plug gage would also be increased by these same values. For multi-start threads with more than four starts, it is believed that the 100 per cent allowance provided by the above procedures would be adequate as index spacing variables would generally be no greater than on a four-start thread. In general, for multi-start threads of Classes 2G, 3G, and 4G the percentages would be applied, usually, to allowances for the same class, respectively. However, where exceptionally good control over lead, angle, and spacing variables would produce close to theoretical values in the product, it is conceivable that these percentages could be applied to Class 3G or Class 4G allowances used on Class 2G internally threaded product. Also, these percentages could be applied to Class 4G allowances used on Class 3G internally threaded product. It is not advocated that any change be made in externally threaded products. Designations for gages or tools for internal threads could cover allowance requirements as follows: GO and NOT GO thread plug gages for: 2.875-0.4P-0.8L-ACME-2G with 50 per cent of the 4G internal thread allowance. Centralizing Acme Threads.—The three classes of Centralizing Acme threads in American National Standard ASME/ANSI B1.5-1988, designated as 2C, 3C, and 4C, have limited clearance at the major diameters of internal and external threads so that a bearing at the major diameters maintains approximate alignment of the thread axis and prevents wedging on the flanks of the thread. An alternative series having centralizing control on the minor



1834

Table 5. American National Standard General Purpose Acme Single-Start Screw Threads — Pitch Diameter Tolerances ASME/ANSI B1.5-1988 Class of Thread 2Gb

3G

Class of Thread

Diameter Increment

Nom. Dia.,a D

0.006 D

0.0028 D

1⁄ 4

.00300

.00140

5⁄ 16

.00335

3⁄ 8

.00367

2Gb

4G

3G

4G

Diameter Increment

0.002 D

Nom. Dia.,a D

0.006 D

0.0028 D

0.002 D

.00100

11⁄2

.00735

.00343

.00245

.00157

.00112

13⁄4

.00794

.00370

.00265

.00171

.00122

2

.00849

.00396

.00283

7⁄ 16

.00397

.00185

.00132

21⁄4

.00900

.00420

.00300

1⁄ 2

.00424

.00198

.00141

21⁄2

.00949

.00443

.00316

5⁄ 8

.00474

.00221

.00158

23⁄4

.00995

.00464

.00332

3⁄ 4

.00520

.00242

.00173

3

.01039

.00485

.00346

7⁄ 8

.00561

.00262

.00187

31⁄2

.01122

.00524

.00374

.00600

.00280

.00200

4

.01200

.00560

.00400

.01273

.00594

.00424

.01342

.00626

.00447

…

…

1 11⁄8

.00636

.00297

.00212

41⁄2

11⁄4

.00671

.00313

.00224

5

13⁄8

.00704

.00328

.00235

…

…

Class of Thread Thds. per Inch c, n 16 14

Class of Thread

2Gb

3G Pitch Increment

4G

0.030 1 ⁄ n

0.014 1 ⁄ n

0.010 1 ⁄ n

.00750 .00802

.00350 .00374

.00250 .00267

Thds. per Inchc, n 4 3

2Gb

3G Pitch Increment

4G

0.030 1 ⁄ n

0.014 1 ⁄ n

0.010 1 ⁄ n

.01500 .01732

.00700 .00808

.00500 .00577

12

.00866

.00404

.00289

21⁄2

.01897

.00885

.00632

10

.00949

.00443

.00316

2

.02121

.00990

.00707

.02449

.01143

.00816

.02598

.01212

.00866

8

.01061

.00495

.00354

11⁄2

6

.01225

.00572

.00408

11⁄3

5 .01342 .00626 .00447 1 .03000 .01400 .01000 For any particular size of thread, the pitch diameter tolerance is obtained by adding the diameter increment from the upper half of the table to the pitch increment from the lower half of the table. Example: A 1⁄4-16 Acme-2G thread has a pitch diameter tolerance of 0.00300 + 0.00750 = 0.0105 inch. The equivalent tolerance on thread thickness is 0.259 times the pitch diameter tolerance. a For a nominal diameter between any two tabulated nominal diameters, use the diameter increment for the larger of the two tabulated nominal diameters. b Columns for the 2G Class of thread in this table also apply to American National Standard Stub Acme threads, ASME/ANSI B1.8-1988 (R2006). c All other dimensions are given in inches.

diameter is described on page 1844. For any combination of the three classes of threads covered in this standard some end play or backlash will result. Classes 5C and 6C are not recommended for new designs. Application: These three classes together with the accompanying specifications are for the purpose of ensuring the interchangeable manufacture of Centralizing Acme threaded parts. Each user is free to select the classes best adapted to his particular needs. It is suggested that external and internal threads of the same class be used together for centralizing assemblies, Class 2C providing the maximum end play or backlash. If less backlash or end play is desired, Classes 3C and 4C are provided. The requirement for a centralizing fit is that the sum of the major diameter tolerance plus the major diameter allowance on the internal thread, and the major diameter tolerance on the external thread shall equal or be less than the pitch diameter allowance on the external thread. A Class 2C external thread, which has a larger pitch diameter allowance than either a Class 3C or 4C, can be used interchangeably with a Class 2C, 3C, or 4C internal thread and fulfill this requirement. Simi-



1835

0.0945P max 45°

Basic pitch dia. h

One-half Minor dia. allowance

Min pitch dia. of screw


P 4

Max pitch dia. of screw

Max major dia. of nut Min major dia. of nut Nominal (basic) major dia. (D) Max major dia. of screw Min major dia. of screw Min depth of engagement

P 4

1/2 Pitch dia. allowance Max minor dia. of nut Min minor dia. of nut Basic minor dia. Max minor dia. of screw Min minor dia. of screw Min pitch dia. of nut Max pitch dia. of nut

One-half Minor dia. allowance

Internal Thread (Screw)

Fig. 2. Disposition of Allowances, Tolerances, and Crest Clearances for General Purpose Single-start Acme Threads (All Classes)

larly, a Class 3C external thread can be used interchangeably with a Class 3C or 4C internal thread, but only a Class 4C internal thread can be used with a Class 4C external thread. Thread Form: The thread form is the same as the General Purpose Acme Thread and is shown in Fig. 3. The formulas in Table 7 determine the basic dimensions, which are given in Table 6 for the most generally used pitches. Angle of Thread: The angle between the sides of the thread measured in an axial plane is 29 degrees. The line bisecting this 29-degree angle shall be perpendicular to the axis of the thread. Chamfers and Fillets: External threads have the crest corners chamfered at an angle of 45 degrees with the axis to a minimum depth of P/20 and a maximum depth of P/15. These modifications correspond to a minimum width of chamfer flat of 0.0707P and a maximum width of 0.0945P (see Table 6, columns 6 and 7). External threads for Classes 2C, 3C, and 4C may have a fillet at the minor diameter not greater than 0.1P Thread Series: A series of diameters and pitches is recommended in the Standard as preferred. These diameters and pitches have been chosen to meet present needs with the fewest number of items in order to reduce to a minimum the inventory of both tools and gages. This series of diameters and associated pitches is given in Table 9.



1836

Table 6. American National Standard Centralizing Acme Screw Thread Form — Basic Dimensions ASME/ANSI B1.5-1988 45-Deg Chamfer Crest of External Threads

Pitch, P

Height of Thread (Basic), h = P/2

Total Height of Thread (All External Threads) hs = h + 1⁄2 allowancea

Thread Thickness (Basic), t = P/2

0.06250 0.07143 0.08333 0.10000 0.12500 0.16667 0.20000 0.25000 0.33333 0.40000

0.03125 0.03571 0.04167 0.05000 0.06250 0.08333 0.10000 0.12500 0.16667 0.20000

0.0362 0.0407 0.0467 0.0600 0.0725 0.0933 0.1100 0.1350 0.1767 0.2100

11⁄2

0.50000 0.66667

0.25000 0.33333

11⁄3

0.75000

0.37500

1 1.00000 0.50000 All dimensions in inches. See Fig. 3.

Thds per Inch, n 16 14 12 10 8 6 5 4 3 21⁄2 2

Min Depth, 0.05P

Min Width of Chamfer Flat, 0.0707P

Max Fillet Radius, Root of Tapped Hole, 0.06P

Fillet Radius at Min or Diameter of Screws Max (All) 0.10P

0.03125 0.03571 0.04167 0.05000 0.06250 0.08333 0.10000 0.12500 0.16667 0.20000

0.0031 0.0036 0.0042 0.0050 0.0062 0.0083 0.0100 0.0125 0.0167 0.0200

0.0044 0.0050 0.0059 0.0071 0.0088 0.0119 0.0141 0.0177 0.0236 0.0283

0.0038 0.0038 0.0050 0.0060 0.0075 0.0100 0.0120 0.0150 0.0200 0.0240

0.0062 0.0071 0.0083 0.0100 0.0125 0.0167 0.0200 0.0250 0.0333 0.0400

0.2600 0.3433

0.25000 0.33333

0.0250 0.0330

0.0354 0.0471

0.0300 0.0400

0.0500 0.0667

0.3850

0.37500

0.0380

0.0530

0.0450

0.0750

0.5100

0.50000

0.0500

0.0707

0.0600

0.1000

a Allowance is 0.020 inch for 10 or less threads per inch and 0.010 inch for more than 10 threads per inch.

Fig. 3. Centralizing Acme Screw Thread Form

Basic Diameters: The maximum major diameter of the external thread is basic and is the nominal major diameter for all classes.



1837

Table 7. Formulas for Finding Basic Dimensions of Centralizing Acme Screw Threads Pitch = P = 1 ÷ No. threads per inch, n: Basic thread height h = 0.5P Basic thread thickness t = 0.5P Basic flat at crest Fcn = 0.3707P + 0.259 × (minor. diameter allowance on internal threads) (internal thread) Basic flat at crest Fcs = 0.3707P − 0.259 × (pitch diameter allowance on external thread) (external thread) Frn = 0.3707P − 0.259 × (major dia. allowance on internal thread) Frs = 0.3707P − 0.259 × (minor dia. allowance on external thread — pitch dia. allowance on external thread)


One-half minor dia. allowance (nut)

h h – 0.05P

P 4

Basic pitch dia. 1/2 pitch dia. allowance Max minor dia. of nut Min minor dia. of nut Basic minor dia. Max minor dia. of screw Min minor dia. of screw Min pitch dia. of nut Max pitch dia. of nut

Detail of fillet

P 4

0.05P

Max major dia. of nut

One-half major dia. allowance (nut)

Detail of chamfer

Symbols: P = pitch h = basic thread height

Internal Thread (Nut) rN rN = 0.06P Max

r1

Max pitch dia. of screw Min pitch dia. of screw

45°

0.067P Max 0.050P Min

Min major dia. of nut Nominal (basic) major dia. (D) Max major dia. of screw Min major dia. of screw Min depth of engagement

0.0945P Max 0.0707P Min

One half minor dia. allowance (screw) rS

rS = 0.1P max

Detail of optional fillet

Fig. 4. Disposition of Allowances, Tolerances, and Crest Clearances for Centralizing Single-Start Acme Threads—Classes 2C, 3C, and 4C

The minimum pitch diameter of the internal thread is basic for all classes and is equal to the basic major diameter D minus the basic height of thread, h. The minimum minor diameter of the internal thread for all classes is 0.1P above basic. Length of Engagement: The tolerances specified in this Standard are applicable to lengths of engagement not exceeding twice the nominal major diameter. Pitch Diameter Allowances: Allowances applied to the pitch diameter of the external thread for all classes are given in Table 10. Major and Minor Diameter Allowances: A minimum diametral clearance is provided at the minor diameter of all external threads by establishing the maximum minor diameter 0.020 inch below the basic minor diameter for 10 threads per inch and coarser, and 0.010 inch for finer pitches and by establishing the minimum minor diameter of the internal thread 0.1P greater than the basic minor diameter. A minimum diametral clearance at the major diameter is obtained by establishing the minimum major diameter of the internal thread 0.001 D above the basic major diameter. These allowances are shown in Table 12.


1838


Table 8a. American National Standard Centralizing Acme Single-Start Screw Threads — Formulas for Determining Diameters ASME/ANSI B1.5-1988 D = Nominal Size or Diameter in Inches P = Pitch = 1 ÷ Number of Threads per Inch No.

Classes 2C, 3C, and 4C External Threads (Screws)

1 2 3

Major Dia., Max = D (Basic). Major Dia., Min = D minus tolerance from Table 12, columns 7, 8, or 10. Pitch Dia., Max = Int. Pitch Dia., Min (Formula 9) minus allowance from the appropriate Class 2C, 3C, or 4C column of Table 10. Pitch Dia., Min = Ext. Pitch Dia., Max (Formula 3) minus tolerance from Table 11. Minor Dia., Max = D minus P minus allowance from Table 12, column 3. Minor Dia., Min = Ext. Minor Dia., Max (Formula 5) minus 1.5 × Pitch Dia. tolerance from Table 11. Classes 2C, 3C, and 4C Internal Threads (Nuts) Major Dia., Min = D plus allowance from Table 12, column 4. Major Dia., Max = Int. Major Dia., Min (Formula 7) plus tolerance from Table 12, columns 7, 9, or 11. Pitch Dia., Min = D minus P/2 (Basic). Pitch Dia., Max = Int. Pitch Dia., Min (Formula 9) plus tolerance from Table 11. Minor Dia., Min = D minus 0.9P. Minor Dia., Max = Int. Minor Dia., Min (Formula 11) plus tolerance from Table 12, column 6.

4 5 6

7 8 9 10 11 12

Major and Minor Diameter Tolerances: The tolerances on the major and minor diameters of the external and internal threads are listed in Table 12 and are based upon the formulas given in the column headings. An increase of 10 per cent in the allowance is recommended for each inch or fraction thereof that the length of engagement exceeds two diameters. For information on gages for Centralizing Acme threads the Standard ASME/ANSI B1.5 should be consulted. Pitch Diameter Tolerances: Pitch diameter tolerances for Classes 2C, 3C and 4C for various practicable combinations of diameter and pitch are given in Table 11. The ratios of the pitch diameter tolerances of Classes 2C, 3C, and 4C are 3.0, 1.4, and 1, respectively. Application of Tolerances: The tolerances specified are such as to insure interchangeability and maintain a high grade of product. The tolerances on the diameters of internal threads are plus, being applied from the minimum sizes to above the minimum sizes. The tolerances on the diameters of external threads are minus, being applied from the maximum sizes to below the maximum sizes. The pitch diameter tolerances for an external or internal thread of a given class are the same Limiting Dimensions: Limiting dimensions for Centralizing Acme threads in the preferred series of diameters and pitches are given in Tables 8b and 8c. These limits are based on the formulas in Table 8a. For combinations of pitch and diameter other than those in the preferred series the formulas in Tables 8b and 8c and the data in the tables referred to therein make it possible to readily determine the limiting dimension required. Designation of Centralizing Acme Threads.—The following examples are given to show how these Acme threads are designated on drawings, in specifications, and on tools and gages: Example, 1.750-6-ACME-4C:Indicates a Centralizing Class 4C Acme thread of 1.750inch major diameter, 0.1667-inch pitch, single thread, right-hand.


Machinery's Handbook 28th Edition Table 8b. Limiting Dimensions of American National Standard Centralizing Acme Single-Start Screw Threads, Classes 2C, 3C, and 4C ASME/ANSI B1.5-1988 Nominal Diameter, D

1⁄ 2

5⁄ 8

3⁄ 4

7⁄ 8

1

11⁄8

11⁄4

13⁄8

11⁄2

Threads per Incha

10

8

6

6

5

5

5

4

4

1.1250 1.1213 1.1234 1.1239 0.9050 0.8753 0.8912 0.8951 1.0165 0.9967 1.0186 1.0094 1.0208 1.0142

1.2500 1.2461 1.2483 1.2489 1.0300 0.9998 1.0159 1.0199 1.1411 1.1210 1.1433 1.1339 1.1455 1.1388

1.3750 1.3709 1.3732 1.3738 1.1050 1.0719 1.0896 1.0940 1.2406 1.2186 1.2430 1.2327 1.2453 1.2380

1.5000 1.4957 1.4982 1.4988 1.2300 1.1965 1.2144 1.2188 1.3652 1.3429 1.3677 1.3573 1.3701 1.3627

1.1261 1.1298 0.1282 0.9450 0.9550 1.0250 1.0448 1.0250 1.0342 1.0250 1.0316

1.2511 1.2550 1.2533 0.0700 1.0800 1.1500 1.1701 1.1500 1.1594 1.1500 1.1567

1.3762 1.3803 1.3785 1.1500 1.1625 1.2500 1.2720 1.2500 1.2603 1.2500 1.2573

1.5012 1.5055 1.5036 1.2750 1.2875 1.3750 1.3973 1.3750 1.3854 1.3750 1.3824

Limiting Diameters

External Threads

Class 2C, Pitch Diameter

{


{


{

0.5000 0.4975 0.4989 0.4993 0.3800 0.3594 0.3704 0.3731 0.4443 0.4306 0.4458 0.4394 0.4472 0.4426

0.6250 0.6222 0.6238 0.6242 0.4800 0.4570 0.4693 0.4723 0.5562 0.5408 0.5578 0.5506 0.5593 0.5542

0.7500 0.7470 0.7487 0.7491 0.5633 0.5371 0.5511 0.5546 0.6598 0.6424 0.6615 0.6534 0.6632 0.6574

0.8750 0.8717 0.8736 0.8741 0.6883 0.6615 0.6758 0.6794 0.7842 0.7663 0.7861 0.7778 0.7880 0.7820

Min Max Max Min Max Min Max Min Max Min Max

0.5007 0.5032 0.5021 0.4100 0.04150 0.4500 0.4637 0.4500 0.4564 0.4500 0.4546

0.6258 0.6286 0.6274 0.5125 0.5187 0.5625 0.5779 0.5625 0.5697 0.5625 0.5676

0.7509 0.7539 0.7526 0.6000 0.6083 0.6667 0.6841 0.6667 0.6748 0.6667 0.6725

0.8759 0.8792 0.8778 0.7250 0.7333 0.7917 0.8096 0.7917 0.8000 0.7917 0.7977

1.0000 0.9965 0.9985 0.9990 0.7800 0.7509 0.7664 0.7703 0.8920 0.8726 0.8940 0.8849 0.8960 0.8895 Internal Threads

Classes 2C, 3C, and 4C, Major Diameter Classes 2C and 3C, Major Diameter Class 4C, Major Diameter Classes 2C, 3C, and 4C, { Minor Diameter Class 2C, Pitch Diameter

{


{


{

1.0010 1.0045 1.0030 0.8200 0.8300 0.9000 0.9194 0.9000 0.9091 0.9000 0.9065


1839

Max Min Min Min Max Min Min Min Max Min Max Min Max Min

CENTRALIZING ACME SCREW THREADS

Classes 2C, 3C, and 4C, Major Diameter Class 2C, Major Diameter Class 3C, Major Diameter Class 4C, Major Diameter Classes 2C, 3C, and 4C, Minor Diameter Class 2C, Minor Diameter Class 3C, Minor Diameter Class 4C, Minor Diameter


Nominal Diameter, D Threads per Incha

1840

Table 8c. Limiting Dimensions of American National Standard Centralizing Acme Single-Start Screw Threads, Classes 2C, 3C, and 4C ASME/ANSI B1.5-1988 13⁄4

2

21⁄4

21⁄2

23⁄4

3

31⁄21 2

4

41⁄2

5

4

4

3

3

3

2

2

2

2

2

3.5000 3.4935 3.4972 3.4981 2.9800 2.9314 2.9574 2.9638 3.2350 3.2026 3.2388 3.2237 3.2425 3.2317

4.0000 3.9930 3.9970 3.9980 3.4800 3.4302 3.4568 3.4634 3.7340 3.7008 3.7380 3.7225 3.7420 3.7309

4.5000 4.4926 4.4968 4.4979 3.9800 3.9291 3.9563 3.9631 4.2330 4.1991 4.2373 4.2215 4.2415 4.2302

5.0000 4.9922 4.9966 4.9978 4.4800 4.4281 4.4558 4.4627 4.7319 4.6973 4.7364 4.7202 4.7409 4.7294

3.5019 3.5084 3.5056 3.0500 3.0750 3.2500 3.2824 3.2500 3.2651 3.2500 3.2608

4.0020 4.0090 4.0060 3.5500 3.5750 3.7500 3.7832 3.7500 3.7655 3.7500 3.7611

4.5021 4.5095 4.5063 4.0500 4.0750 4.2500 4.2839 4.2500 4.2658 4.2500 4.2613

5.0022 5.0100 5.0067 4.5500 4.5750 4.7500 4.7846 4.7500 4.7662 4.7500 4.7615

Limiting Diameters

External Threads


{


{


{

Max Min Min Min Max Min Min Min Max Min Max Min Max Min

1.7500 1.7454 1.7480 1.7487 1.4800 1.4456 1.4640 1.4685 1.6145 1.5916 1.6171 1.6064 1.6198 1.6122

2.0000 1.9951 1.9979 1.9986 1.7300 1.6948 1.7136 1.7183 1.8637 1.8402 1.8665 1.8555 1.8693 1.8615

2.2500 2.2448 2.2478 2.2485 1.8967 1.8572 1.8783 1.8835 2.0713 2.0450 2.0743 2.0620 2.0773 2.0685

2.5000 2.4945 2.4976 2.4984 2.1467 2.1065 2.1279 2.1333 2.3207 2.2939 2.3238 2.3113 2.3270 2.3181

2.7500 2.7442 2.7475 2.7483 2.3967 2.3558 2.3776 2.3831 2.5700 2.5427 2.5734 2.5607 2.5767 2.5676

Min Max Max Min Max Min Max Min Max Min Max

1.7513 1.7559 1.7539 1.5250 1.5375 1.6250 1.6479 1.6250 1.6357 1.6250 1.6326

2.0014 2.0063 2.0042 1.7750 1.7875 1.8750 1.8985 1.8750 1.8860 1.8750 1.8828

2.2515 2.2567 2.2545 1.9500 1.9667 2.0833 2.1096 2.0833 2.0956 2.0833 2.0921

2.5016 2.5071 2.5048 2.2000 2.2167 2.3333 2.3601 2.3333 2.3458 2.3333 2.3422

2.7517 2.7575 2.7550 2.4500 2.4667 2.5833 2.6106 2.5833 2.5960 2.5833 2.5924

3.0000 2.9939 2.9974 2.9983 2.4800 2.4326 2.4579 2.4642 2.7360 2.7044 2.7395 2.7248 2.7430 2.7325

Internal Threads Classes 2C, 3C, and 4C, Major Diameter Classes 2C and 3C, Major Diameter Class 4C, Major Diameter Classes 2C, 3C, and 4C, { Minor Diameter Class 2C, Pitch Diameter

{


{

Class 4C Pitch Diameter

{

3.0017 3.0078 3.0052 2.5500 2.5750 2.7500 2.7816 2.7500 2.7647 2.7500 2.7605

a All other dimensions are in inches. The selection of threads per inch is arbitrary and for the purpose of establishing a standard.



Classes 2C, 3C, and 4C, Major Diameter Class 2C, Major Diameter Class 3C, Major Diameter Class 4C, Major Diameter Classes 2C, 3C, and 4C, Minor Diameter Class 2C, Minor Diameter Class 3C, Minor Diameter Class 4C, Minor Diameter

Machinery's Handbook 28th Edition Table 9. American National Standard Centralizing Acme Single-Start Screw Thread Data ASME/ANSI B1.5-1988 Identification

Diameters

Thread Data

Centralizing, Classes 2C, 3C, and 4C Basic Major Diameter, D

Pitch Diameter, D2 = (D − h)

Minor Diameter, D1 = (D − 2h)

1⁄ 4

16

0.2500

0.2188

5⁄ 16

14

0.3125

3⁄ 8

12

7⁄ 16

Lead Angle λ at Basic Pitch Diametera

Pitch, P

Thickness at Pitch Line, t = P/2

Basic Height of Thread, h = P/2

Basic Width of Flat, F = 0.3707P

Deg

Min

0.1875

0.06250

0.03125

0.03125

0.0232

5

12

0.2768

0.2411

0.07143

0.03571

0.03571

0.0265

4

42

0.3750

0.3333

0.2917

0.08333

0.04167

0.04167

0.0309

4

33

12

0.4375

0.3958

0.3542

0.08333

0.04167

0.04167

0.0309

3

50

1⁄ 2

10

0.5000

0.4500

0.4000

0.10000

0.05000

0.05000

0.0371

4

3

5⁄ 8

8

0.6250

0.5625

0.5000

0.12500

0.06250

0.06250

0.0463

4

3

3⁄ 4

6

0.7500

0.6667

0.5833

0.16667

0.08333

0.08333

0.0618

4

33

7⁄ 8

6

0.8750

0.7917

0.7083

0.16667

0.08333

0.08333

0.0618

3

50

1 11⁄8

5 5

1.0000 1.1250

0.9000 1.0250

0.8000 0.9250

0.20000 0.20000

0.10000 0.10000

0.10000 0.10000

0.0741 0.0741

4 3

3 33

11⁄4

5

1.2500

1.1500

1.0500

0.20000

0.10000

0.10000

0.0741

3

10

13⁄8

4

1.3750

1.2500

1.1250

0.25000

0.12500

0.12500

0.0927

3

39

11⁄2

4

1.5000

1.3750

1.2500

0.25000

0.12500

0.12500

0.0927

3

19

13⁄4

4

1.7500

1.6250

1.5000

0.25000

0.12500

0.12500

0.0927

2

48

2 21⁄4

4 3

2.0000 2.2500

1.8750 2.0833

1.7500 1.9167

0.25000 0.33333

0.12500 0.16667

0.12500 0.16667

0.0927 0.1236

2 2

26 55

21⁄2

3

2.5000

2.3333

2.1667

0.33333

0.16667

0.16667

0.1236

2

36

23⁄4

3

2.7500

2.5833

2.4167

0.33333

0.16667

0.16667

0.1236

2

21

3 31⁄2

2 2

3.0000 3.5000

2.7500 3.2500

2.5000 3.0000

0.50000 0.50000

0.25000 0.25000

0.25000 0.25000

0.1853 0.1853

3 2

19 48

4 41⁄2

2 2

4.0000 4.5000

3.7500 4.2500

3.5000 4.0000

0.50000 0.50000

0.25000 0.25000

0.25000 0.25000

0.1853 0.1853

2 2

26 9

5

2

5.0000

4.7500

4.5000

0.50000

0.25000

0.25000

0.1853

1

55

Centralizing Classes 2C, 3C, and 4C,


1841

a All other dimensions are given in inches.


Nominal Sizes (All Classes)

Threads per Inch,a n


1842

Table 10. American National Standard Centralizing Acme Single-Start Screw Threads — Pitch Diameter Allowances ASME/ANSI B1.5-1988 Nominal Size Rangea To and Above Including 3⁄ 0 16 3⁄ 5⁄ 16 16 5⁄ 7⁄ 16 16 7⁄ 9⁄ 16 16 9⁄ 11⁄ 16 16 11⁄ 13⁄ 16 16 13⁄ 15⁄ 16 16 15⁄ 11⁄16 16 1 3 1 ⁄16 1 ⁄16 13⁄16 15⁄16 15⁄16 17⁄16

Allowances on External Threadsb Centralizing Class 2C, Class 3C, Class 4C,

0.008 D

0.006 D

0.004 D

0.0024 0.0040 0.0049 0.0057 0.0063 0.0069 0.0075 0.0080 0.0085 0.0089 0.0094

0.0018 0.0030 0.0037 0.0042 0.0047 0.0052 0.0056 0.0060 0.0064 0.0067 0.0070

0.0012 0.0020 0.0024 0.0028 0.0032 0.0035 0.0037 0.0040 0.0042 0.0045 0.0047

Nominal Size Rangea To and Above Including 17⁄16 19⁄16 17⁄8 21⁄8 23⁄8 25⁄8 27⁄8 31⁄4 33⁄4 41⁄4 43⁄4

19⁄16 17⁄8 21⁄8 23⁄8 25⁄8 27⁄8 31⁄4 33⁄4 41⁄4 43⁄4 51⁄2

Allowances on External Threadsb Centralizing Class 2C, Class 3C, Class 4C,

0.008 D

0.006 D

0.004 D

0.0098 0.0105 0.0113 0.0120 0.0126 0.0133 0.0140 0.0150 0.0160 0.0170 0.0181

0.0073 0.0079 0.0085 0.0090 0.0095 0.0099 0.0105 0.0112 0.0120 0.0127 0.0136

0.0049 0.0052 0.0057 0.0060 0.0063 0.0066 0.0070 0.0075 0.0080 0.0085 0.0091

All dimensions are given in inches. It is recommended that the sizes given in Table 9 be used whenever possible. a The values in columns for Classes 2C, 3C, and 4C are to be used for any size within the nominal size range columns. These values are calculated from the mean of the range. b An increase of 10 per cent in the allowance is recommended for each inch, or fraction thereof, that the length of engagement exceeds two diameters.

Table 11. American National Standard Centralizing Acme Single-Start Screw Threads — Pitch Diameter Tolerances ASME/ANSI B1.5-1988 Nom. Dia.,a D 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 5⁄ 8 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 13⁄8

Class of Thread and Diameter Increment 2C 3C 4C

0.006 D

0.0028 D

0.002 D

.00300 .00335 .00367 .00397 .00424 .00474 .00520 .00561 .00600 .00636 .00671 .00704

.00140 .00157 .00171 .00185 .00198 .00221 .00242 .00262 .00280 .00297 .00313 .00328

.00100 .00112 .00122 .00132 .00141 .00158 .00173 .00187 .00200 .00212 .00224 .00235

Nom. Dia.,a D 11⁄2 13⁄4 2 21⁄4 21⁄2 23⁄4 3 31⁄2 4 41⁄2 5 …

Class of Thread and Diameter Increment 2C 3C 4C

0.006 D

0.0028 D

0.002 D

.00735 .00794 .00849 .00900 .00949 .00995 .01039 .01122 .01200 .01273 .01342 …

.00343 .00370 .00396 .00420 .00443 .00464 .00485 .00524 .00560 .00594 .00626 …

.00245 .00265 .00283 .00300 .00316 .00332 .00346 .00374 .00400 .00424 .00447 …

Class of Thread and Pitch Increment Class of Thread and Pitch Increment Thds. Thds. 2C 3C 4C 2C 3C 4C per per Inch, Inch, 0.030 1 ⁄ n 0.014 1 ⁄ n 0.010 1 ⁄ n 0.030 1 ⁄ n 0.014 1 ⁄ n 0.010 1 ⁄ n n n 16 .00750 .00350 .00250 4 .01500 .00700 .00500 14 .00802 .00374 .00267 3 .01732 .00808 .00577 12 .00866 .00404 .00289 .01897 .00885 .00632 21⁄2 10 .00949 .00443 .00316 2 .02121 .00990 .00707 .02449 .01143 .00816 8 .01061 .00495 .00354 11⁄2 1 .02598 .01212 .00866 6 .01225 .00572 .00408 1 ⁄3 5 .01342 .00626 .00447 1 .03000 .01400 .01000 All dimensions are given in inches. For any particular size of thread, the pitch diameter tolerance is obtained by adding the diameter increment from the upper half of the table to the pitch increment from the lower half of the table. Example: A 0.250-16-ACME-2C thread has a pitch diameter tolerance of 0.00300 + 0.00750 = 0.0105 inch. The equivalent tolerance on thread thickness is 0.259 times the pitch diameter tolerance. a For a nominal diameter between any two tabulated nominal diameters, use the diameter increment for the larger of the two tabulated nominal diameters.


Machinery's Handbook 28th Edition Table 12. American National Standard Centralizing Acme Single-Start Screw Threads — Tolerances and Allowances for Major and Minor Diameters ASME/ANSI B1.5-1988

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 31⁄2 4 41⁄2 5

Thdsa per Inch 16 14 12 12 10 8 6 6 5 5 5 4 4 4 4 3 3 3 2 2 2 2 2

0.010 0.010 0.010 0.010 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020 0.020

0.0005 0.0006 0.0006 0.0007 0.0007 0.0008 0.0009 0.0009 0.0010 0.0011 0.0011 0.0012 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0017 0.0019 0.0020 0.0021 0.0022

0.0062 0.0071 0.0083 0.0083 0.0100 0.0125 0.0167 0.0167 0.0200 0.0200 0.0200 0.0250 0.0250 0.0250 0.0250 0.0333 0.0333 0.0333 0.0500 0.0500 0.0500 0.0500 0.0500

Tolerance on Minor Diam, b, c All Internal Threads, (Plus 0.05P) 0.0050 0.0050 0.0050 0.0050 0.0050 0.0062 0.0083 0.0083 0.0100 0.0100 0.0100 0.0125 0.0125 0.0125 0.0125 0.0167 0.0167 0.0167 0.0250 0.0250 0.0250 0.0250 0.0250

Tolerance on Major Diameter Plus on Internal, Minus on External Threads Class 2C Class 3C Class 4C External and External Internal External Internal Internal Threads, Thread, Thread, Thread, Thread,

0.0035 D

0.0015 D

0.0035 D

0.0010 D

0.0020 D

0.0017 0.0020 0.0021 0.0023 0.0025 0.0028 0.0030 0.0033 0.0035 0.0037 0.0039 0.0041 0.0043 0.0046 0.0049 0.0052 0.0055 0.0058 0.0061 0.0065 0.0070 0.0074 0.0078

0.0007 0.0008 0.0009 0.0010 0.0011 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0018 0.0018 0.0020 0.0021 0.0022 0.0024 0.0025 0.0026 0.0028 0.0030 0.0032 0.0034

0.0017 0.0020 0.0021 0.0023 0.0025 0.0028 0.0030 0.0033 0.0035 0.0037 0.0039 0.0041 0.0043 0.0046 0.0049 0.0052 0.0055 0.0058 0.0061 0.0065 0.0070 0.0074 0.0078

0.0005 0.0006 0.0006 0.0007 0.0007 0.0008 0.0009 0.0009 0.0010 0.0011 0.0011 0.0012 0.0012 0.0013 0.0014 0.0015 0.0016 0.0017 0.0017 0.0019 0.0020 0.0021 0.0022

0.0010 0.0011 0.0012 0.0013 0.0014 0.0016 0.0017 0.0019 0.0020 0.0021 0.0022 0.0023 0.0024 0.0026 0.0028 0.0030 0.0032 0.0033 0.0035 0.0037 0.0040 0.0042 0.0045


1843

a All other dimensions are given in inches. Intermediate pitches take the values of the next coarser pitch listed. Values for intermediate diameters should be calculated from the formulas in column headings, but ordinarily may be interpolated. b To avoid a complicated formula and still provide an adequate tolerance, the pitch factor is used as a basis, with the minimum tolerance set at 0.005 in. c Tolerance on minor diameter of all external threads is 1.5 × pitch diameter tolerance. d The minimum clearance at the minor diameter between the internal and external thread is the sum of the values in columns 3 and 5. e The minimum clearance at the major diameter between the internal and external thread is equal to column 4.


Size (Nom.)

Allowance From Basic Major and Minor Diameters (All Classes) Internal Thread Minor Diam, d Major Diam, e Minor All External (Plus Threads Diam, d 0.0010 D ) (Minus) (Plus 0.1P)

1844

Machinery's Handbook 28th Edition STUB ACME SCREW THREADS

Example, 1.750-6-ACME-4C-LH:Indicates the same thread left-hand. Example, 2.875-0.4P-0.8L-ACME-3C (Two Start):Indicates a Centralizing Class 3C Acme thread with 2.875-inch major diameter, 0.4-inch pitch, 0.8-inch lead, double thread, right-hand. Example, 2.500-0.3333P-0.6667L-ACME-4C (Two Start):Indicates a Centralizing Class 4C Acme thread with 2.500-inch nominal major diameter (basic major diameter 2.500 inches), 0.3333-inch pitch, 0.6667-inch lead, double thread, right-hand. The same thread left-hand would have LH at the end of the designation. Acme Centralizing Threads—Alternative Series with Minor Diameter Centralizing Control.—When Acme centralizing threads are produced in single units or in very small quantities (and principally in sizes larger than the range of commercial taps and dies) where the manufacturing process employs cutting tools (such as lathe cutting), it may be economically advantageous and therefore desirable to have the centralizing control of the mating threads located at the minor diameters. Particularly under the above-mentioned type of manufacturing, the two advantages cited for minor diameter centralizing control over centralizing control at the major diameters of the mating threads are: 1) Greater ease and faster checking of machined thread dimensions. It is much easier to measure the minor diameter (root) of the external thread and the mating minor diameter (crest or bore) of the internal thread than it is to determine the major diameter (root) of the internal thread and the major diameter (crest or turn) of the external thread; and 2) better manufacturing control of the machined size due to greater ease of checking. In the event that minor diameter centralizing is necessary, recalculate all thread dimensions, reversing major and minor diameter allowances, tolerances, radii, and chamfer. American National Standard Stub Acme Threads.—This American National Standard ASME/ANSI B1.8-1988 (R2006) provides a Stub Acme screw thread for those unusual applications where, due to mechanical or metallurgical considerations, a coarsepitch thread of shallow depth is required. The fit of Stub Acme threads corresponds to the Class 2G General Purpose Acme thread in American National Standard ANSI B1.5-1988. For a fit having less backlash, the tolerances and allowances for Classes 3G or 4G General Purpose Acme threads may be used. Thread Form: The thread form and basic formulas for Stub Acme threads are given on page 1827 and the basic dimensions in Table 13. Allowances and Tolerances: The major and minor diameter allowances for Stub Acme threads are the same as those given for General Purpose Acme threads on page 1826. Pitch diameter allowances for Stub Acme threads are the same as for Class 2G General Purpose Acme threads and are given in Table 4. Pitch diameter tolerances for Stub Acme threads are the same as for Class 2G General Purpose Acme threads given in Table 5. Limiting Dimensions: Limiting dimensions of American Standard Stub Acme threads may be determined by using the formulas given in Table 14a, or directly from Table 14b. The diagram below shows the limits of size for Stub Acme threads. Thread Series: A preferred series of diameters and pitches for General Purpose Acme threads (Table 15) is recommended for Stub Acme threads. Stub Acme Thread Designations.—The method of designation for Standard Stub Acme threads is illustrated in the following examples: 0.500-20 Stub Acme indicates a 1⁄2-inch major diameter, 20 threads per inch, right hand, single thread, Standard Stub Acme thread. The designation 0.500-20 Stub Acme-LH indicates the same thread except that it is left hand.


Machinery's Handbook 28th Edition ALTERNATIVE STUB ACME SCREW THREADS

1845

Table 13. American National Standard Stub Acme Screw Thread Form — Basic Dimensions ASME/ANSI B1.8-1988 (R2006) Width of Flat

Pitch, P = 1/n

Height of Thread (Basic), 0.3P

Total Height of Thread, 0.3P + 1⁄2 allowanceb

Thread Thickness (Basic), P/2

Crest of InternalThread (Basic), 0.4224P

Root of Internal Thread, 0.4224P −0.259 ×allowanceb

16 14 12 10 9 8 7 6 5 4 31⁄2

0.06250 0.07143 0.08333 0.10000 0.11111 0.12500 0.14286 0.16667 0.20000 0.25000 0.28571

0.01875 0.02143 0.02500 0.03000 0.03333 0.03750 0.04285 0.05000 0.06000 0.07500 0.08571

0.0238 0.0264 0.0300 0.0400 0.0433 0.0475 0.0529 0.0600 0.0700 0.0850 0.0957

0.03125 0.03571 0.04167 0.05000 0.05556 0.06250 0.07143 0.08333 0.10000 0.12500 0.14286

0.0264 0.0302 0.0352 0.0422 0.0469 0.0528 0.0603 0.0704 0.0845 0.1056 0.1207

0.0238 0.0276 0.0326 0.0370 0.0417 0.0476 0.0551 0.0652 0.0793 0.1004 0.1155

3 21⁄2

0.33333 0.40000

0.10000 0.12000

0.1100 0.1300

0.16667 0.20000

0.1408 0.1690

0.1356 0.1638

2 11⁄2

0.50000 0.66667

0.15000 0.20000

0.1600 0.2100

0.25000 0.33333

0.2112 0.2816

0.2060 0.2764

11⁄3

0.75000

0.22500

0.2350

0.37500

0.3168

0.3116

1

1.00000

0.30000

0.3100

0.50000

0.4224

0.4172

Thds. per Incha n

a All other dimensions in inches. See Fig. 1, page

1827. b Allowance is 0.020 inch for 10 or less threads per inch and 0.010 inch for more than 10 threads per inch.

Table 14a. American National Standard Stub Acme Single-Start Screw Threads — Formulas for Determining Diameters ASME/ANSI B1.8-1988 (R2006) D = Basic Major Diameter and Nominal Size in Inches D2 = Basic Pitch Diameter = D − 0.3P D1 = Basic Minor Diameter = D − 0.6P No. 1 2 3 4 5 6

7 8 9 10 11 12

External Threads (Screws) Major Dia., Max = D. Major Dia., Min. = D minus 0.05P. Pitch Dia., Max. = D2 minus allowance from the appropriate Class 2G column, Table 4. Pitch Dia., Min. = Pitch Dia., Max. (Formula 3) minus Class 2G tolerance from Table 5. Minor Dia., Max. = D1 minus 0.020 for 10 threads per inch and coarser and 0.010 for finer pitches. Minor Dia., Min. = Minor Dia., Max. (Formula 5) minus Class 2G pitch diameter tolerance from Table 5. Internal Threads (Nuts) Major Dia., Min. = D plus 0.020 for 10 threads per inch and coarser and 0.010 for finer pitches. Major Dia., Max.= Major Dia., Min. (Formula 7) plus Class 2G pitch diameter tolerance from Table 5. Pitch Dia., Min. = D2 = D − 0.3P Pitch Dia., Max. = Pitch Dia., Min. (Formula 9) plus Class 2G tolerance from Table 5. Minor Dia., Min. = D1 = D − 0.6P Minor Dia., Max = Minor Dia., Min. (Formula 11) plus 0.05P.



Nominal Diameter, D Threads per Incha

1⁄ 4

5⁄ 16

3⁄ 8

7⁄ 16

1⁄ 2

5⁄ 8

3⁄ 4

7⁄ 8

11⁄4

13⁄8

14

12

12

10

8

6

6

1 5

11⁄8

16

5

5

4

0.8750 0.8667 0.8175 0.7996 0.7550 0.7371

1.0000 0.9900 0.9320 0.9126 0.8600 0.8406

1.1250 1.1150 1.0565 1.0367 0.9850 0.9652

1.2500 1.2400 1.1811 1.1610 1.1100 1.0899

1.3750 1.3625 1.2906 1.2686 1.2050 1.1830

0.8950 0.9129 0.8250 0.8429 0.7750 0.7833

1.0200 1.0394 0.9400 0.9594 0.8800 0.8900

1.1450 1.1648 1.0650 1.0848 1.0050 1.0150

1.2700 1.2901 1.1900 1.2101 1.1300 1.1400

1.3950 1.4170 1.3000 1.3220 1.2250 1.2375

Limiting Diameters {

Pitch Dia.

{

Minor Dia.

{

Major Dia.

{

Pitch Dia.

{

Minor Dia.

External Threads

{

Max (D) Min Max Min Max Min

0.2500 0.2469 0.2272 0.2167 0.2024 0.1919

0.3125 0.3089 0.2871 0.2757 0.2597 0.2483

0.3750 0.3708 0.3451 0.3328 0.3150 0.3027

0.4375 0.4333 0.4076 0.3950 0.3775 0.3649

0.5000 0.4950 0.4643 0.4506 0.4200 0.4063

Min Max Min Max Min Max

0.2600 0.2705 0.2312 0.2417 0.2125 0.2156

0.3225 0.3339 0.2911 0.3025 0.2696 0.2732

0.3850 0.3973 0.3500 0.3623 0.3250 0.3292

0.4475 0.4601 0.4125 0.4251 0.3875 0.3917

0.5200 0.5337 0.4700 0.4837 0.4400 0.4450

11⁄2

13⁄4

2

21⁄4

21⁄2

23⁄4

3

31⁄2

4

41⁄2

5

4

4

4

3

3

3 External Threads

2

2

2

2

2

Max (D) Min Max Min Max Min

1.5000 1.4875 1.4152 1.3929 1.3300 1.3077

1.7500 1.7375 1.6645 1.6416 1.5800 1.5571

2.0000 1.9875 1.9137 1.8902 1.8300 1.8065

2.2500 2.2333 2.1380 2.1117 2.0300 2.0037

2.5000 2.4833 2.3874 2.3606 2.2800 2.2532

3.0000 2.9750 2.8360 2.8044 2.6800 2.6484

3.5000 3.4750 3.3350 3.3026 3.1800 3.1476

4.0000 3.9750 3.8340 3.8008 3.6800 3.6468

4.5000 4.4750 4.3330 4.2991 4.1800 4.1461

5.0000 4.9750 4.8319 4.7973 4.6800 4.6454

Min Max Min Max Min Max

1.5200 1.5423 1.4250 1.4473 1.3500 1.3625

1.7700 1.7929 1.6750 1.6979 1.6000 1.6125

2.0200 2.0435 1.9250 1.9485 1.8500 1.8625

2.2700 2.2963 2.1500 2.1763 2.0500 2.0667

2.5200 2.5468 2.4000 2.4268 2.3000 2.3167

2.7500 2.7333 2.6367 2.6094 2.5300 2.5027 Internal Threads 2.7700 2.7973 2.6500 2.6773 2.5500 2.5667

3.0200 3.0516 2.8500 2.8816 2.7000 2.7250

3.5200 3.5524 3.3500 3.3824 3.2000 3.2250

4.0200 4.0532 3.8500 3.8832 3.7000 3.7250

4.5200 4.5539 4.3500 4.3839 4.2000 4.2250

5.0200 5.0546 4.8500 4.8846 4.7000 4.7250

Nominal Diameter, D Threads per Incha Limiting Diameters Major Dia.

{

Pitch Dia.

{

Minor Dia.

{

Major Dia.

{

Pitch Dia.

{

Minor Dia.

{

0.6250 0.7500 0.6188 0.7417 0.5812 0.6931 0.5658 0.6757 0.5300 0.6300 0.5146 0.6126 Internal Threads 0.6450 0.7700 0.6604 0.7874 0.5875 0.7000 0.6029 0.7174 0.5500 0.6500 0.5562 0.6583


ALTERNATIVE STUB ACME SCREW THREADS

Major Dia.

1846

Table 14b. Limiting Dimensions for American National Standard Stub Acme Single-Start Screw Threads ASME/ANSI B1.8-1988 (R2006)

Machinery's Handbook 28th Edition ALTERNATIVE CENTRALIZING ACME SCREW THREADS

1847

P′

Min minor dia. of screw Min pitch dia. of nut

Basic pitch dia.


One-half major dia. allowance

0.15P

h

Max pitch dia. of screw Min pitch dia. of screw

Max major dia. of nut Min major dia. of nut Nominal (basic) major dia. (D) Max major dia. of screw Min major dia. of screw

Min depth of engagement

One-half major dia. allowance 0.15P

1/2 Pitch dia. allowance Max minor dia. of nut Min minor dia. of nut Basic minor dia. Max minor dia. of screw Min minor dia. of screw

Basic thickness of thread, P/2


Limits of Size, Allowances, Tolerances, and Crest Clearances for American National Standard Stub Acme Threads

Alternative Stub Acme Threads.—Since one Stub Acme thread form may not meet the requirements of all applications, basic data for two of the other commonly used forms are included in the appendix of the American Standard for Stub Acme Threads. These socalled Modified Form 1 and Modified Form 2 threads utilize the same tolerances and allowances as Standard Stub Acme threads and have the same major diameter and basic thread thickness at the pitchline (0.5P). The basic height of Form 1 threads, h, is 0.375P; for Form 2 it is 0.250P. The basic width of flat at the crest of the internal thread is 0.4030P for Form 1 and 0.4353P for Form 2. The pitch diameter and minor diameter for Form 1 threads will be smaller than similar values for the Standard Stub Acme Form and for Form 2 they will be larger owing to the differences in basic thread height h. Therefore, in calculating the dimensions of Form 1 and Form 2 threads using Formulas 1 through 12 in Table 14a, it is only necessary to substitute the following values in applying the formulas: For Form 1, D2 = D − 0.375P, D1 = D − 0.75P; for Form 2, D2 = D − 0.25P, D1 = D − 0.5P. Thread Designation: These threads are designated in the same manner as Standard Stub Acme threads except for the insertion of either M1 or M2 after “Acme.” Thus, 0.500-20 Stub Acme M1 for a Form 1 thread; and 0.500-20 Stub Acme M2 for a Form 2 thread. Former 60-Degree Stub Thread.—Former American Standard B1.3-1941 included a 60-degree stub thread for use where design or operating conditions could be better satisfied by the use of this thread, or other modified threads, than by Acme threads. Data for 60Degree Stub thread form are given in the accompanying diagram.



Basic Diameters

1848

Table 15. Stub Acme Screw Thread Data ASME/ANSI B1.8-1988 (R2006) Identification

Thread Data

Major Diameter, D

Pitch Diameter, D2 = D − h

Minor Diameter, D1 = D − 2h

1⁄ 4

16

0.2500

0.2312

0.2125

5⁄ 16

14

0.3125

0.2911

3⁄ 8

12

0.3750

0.3500

7⁄ 16

12

0.4375

1⁄ 2

10

5⁄ 8

Lead Angleat Basic Pitch Diameter

Pitch, P

Thread Thickness at Pitch Line, t = P/2

Basic Thread Height, h = 0.3P

Basic Width of Flat, 0.4224P

0.06250

0.03125

0.01875

0.0264

4

54

0.2696

0.07143

0.03572

0.02143

0.0302

4

28

0.3250

0.08333

0.04167

0.02500

0.0352

4

20

0.4125

0.3875

0.08333

0.04167

0.02500

0.0352

3

41

0.5000

0.4700

0.4400

0.10000

0.05000

0.03000

0.0422

3

52

8

0.6250

0.5875

0.5500

0.12500

0.06250

0.03750

0.0528

3

52

3⁄ 4

6

0.7500

0.7000

0.6500

0.16667

0.08333

0.05000

0.0704

4

20

7⁄ 8

6

0.8750

0.8250

0.7750

0.16667

0.08333

0.05000

0.0704

3

41

11⁄8

5 5

1.0000 1.1250

0.9400 1.0650

0.8800 1.0050

0.20000 0.20000

0.10000 0.10000

0.06000 0.06000

0.0845 0.0845

3 3

52 25

11⁄4

5

1.2500

1.1900

1.1300

0.20000

0.10000

0.06000

0.0845

3

4

13⁄8

4

1.3750

1.3000

1.2250

0.25000

0.12500

0.07500

0.1056

3

30

11⁄2

4

1.5000

1.4250

1.3500

0.25000

0.12500

0.07500

0.1056

3

12

13⁄4

4

1.7500

1.6750

1.6000

0.25000

0.12500

0.07500

0.1056

2

43

2 21⁄4

4 3

2.0000 2.2500

1.9250 2.1500

1.8500 2.0500

0.25000 0.33333

0.12500 0.16667

0.07500 0.10000

0.1056 0.1408

2 2

22 50

21⁄2

3

2.5000

2.4000

2.3000

0.33333

0.16667

0.10000

0.1408

2

32

23⁄4

3

2.7500

2.6500

2.5500

0.33333

0.16667

0.10000

0.1408

2

18

3

2 2

3.0000 3.5000

2.8500 3.3500

2.7000 3.2000

0.50000 0.50000

0.25000 0.25000

0.15000 0.15000

0.2112 0.2112

3 2

12 43

41⁄2

2 2

4.0000 4.5000

3.8500 4.3500

3.7000 4.2000

0.50000 0.50000

0.25000 0.25000

0.15000 0.15000

0.2112 0.2112

2 2

22 6

5

2

5.0000

4.8500

4.7000

0.50000

0.25000

0.15000

0.2112

1

53

Nominal Sizes

1

31⁄2 4

a All other dimensions are given in inches.


Deg

Min

ALTERNATIVE CENTRALIZING ACME SCREW

Threads per Inch,a n

Machinery's Handbook 28th Edition ALTERNATIVE CENTRALIZING ACME SCREW THREADS

1849

60-Degree Stub Thread

A clearance of at least 0.02 × pitch is added to depth h to produce extra depth, thus avoiding interference with threads of mating part at minor or major diameters. Basic thread thickness at pitch line = 0.5 × pitch p; basic depth h = 0.433 × pitch; basic width of flat at crest = 0.25 × pitch; width of flat at root of screw thread = 0.227 × pitch; basic pitch diameter = basic major diameter − 0.433 × pitch; basic minor diameter = basic major diameter − 0.866 × pitch. Square Thread.—The square thread is so named because the section is square, the depth, in the case of a screw, being equal to the width or one-half the pitch. The thread groove in a square-threaded nut is made a little greater than one-half the pitch in order to provide a slight clearance for the screw; hence, the tools used for threading square-threaded taps are a little less in width at the point than one-half the pitch. The pitch of a square thread is usually twice the pitch of an American Standard thread of corresponding diameter. The square thread has been superseded quite largely by the Acme form which has several advantages. See ACME SCREW THREADS. 10-Degree Modified Square Thread: The included angle between the sides of the thread is 10 degrees (see accompanying diagram). The angle of 10 degrees results in a thread which is the practical equivalent of a “square thread,” and yet is capable of economical production. Multiple thread milling cutters and ground thread taps should not be specified for modified square threads of the larger lead angles without consulting the cutting tool manufacturer. Clearance (See Note)

Nut 0.25p

p 2

0.4563p

5˚

p 2

h 0.25p

1 Pitch 2 Diameter Allowance

G

Screw

Clearance (See Note)

In the following formulas, D = basic major diameter; E = basic pitch diameter; K = basic minor diameter; p = pitch; h = basic depth of thread on screw depth when there is no clearance between root of screw and crest of thread on nut; t = basic thickness of thread at pitch line; F = basic width of flat at crest of screw thread; G = basic width of flat at root of screw thread; C = clearance between root of screw and crest of thread on nut: E = D − 0.5p; K = D − p; h = 0.5p (see Note); t = 0.5p; F = 0.4563p; G = 0.4563p − (0.17 × C). Note: A clearance should be added to depth h to avoid interference with threads of mating parts at minor or major diameters.


Machinery's Handbook 28th Edition BUTTRESS THREADS

1850

BUTTRESS THREADS Threads of Buttress Form The buttress form of thread has certain advantages in applications involving exceptionally high stresses along the thread axis in one direction only. The contacting flank of the thread, which takes the thrust, is referred to as the pressure flank and is so nearly perpendicular to the thread axis that the radial component of the thrust is reduced to a minimum. Because of the small radial thrust, this form of thread is particularly applicable where tubular members are screwed together, as in the case of breech mechanisms of large guns and airplane propeller hubs. Fig. 1a shows a common form. The front or load-resisting face is perpendicular to the axis of the screw and the thread angle is 45 degrees. According to one rule, the pitch P = 2 × screw diameter ÷ 15. The thread depth d may equal 3⁄4 × pitch, making the flat f = 1⁄8 × pitch. Sometimes depth d is reduced to 2⁄3 × pitch, making f = 1⁄6 × pitch. f

f

P

f

P

45˚

50˚

45˚

h

3˚

5˚ 50˚

d

P

NUT d d1

d

g e

33˚

33˚

SCREW

f

f Fig. 1a.

r

Fig. 1b.

Fig. 1c.

The load-resisting side or flank may be inclined an amount (Fig. 1b) ranging usually from 1 to 5 degrees to avoid cutter interference in milling the thread. With an angle of 5 degrees and an included thread angle of 50 degrees, if the width of the flat f at both crest and root equals 1⁄8 × pitch, then the thread depth equals 0.69 × pitch or 3⁄4 d1. The saw-tooth form of thread illustrated by Fig. 1c is known in Germany as the “Sägengewinde” and in Italy as the “Fillettatura a dente di Sega.” Pitches are standardized from 2 millimeters up to 48 millimeters in the German and Italian specifications. The front face inclines 3 degrees from the perpendicular and the included angle is 33 degrees. The thread depth d for the screw = 0.86777 × pitch P. The thread depth g for the nut = 0.75 × pitch. Dimension h = 0.341 × P. The width f of flat at the crest of the thread on the screw = 0.26384 × pitch. Radius r at the root = 0.12427 × pitch. The clearance space e = 0.11777 × pitch. British Standard Buttress Threads BS 1657: 1950.—Specifications for buttress threads in this standard are similar to those in the American Standard (see page 1851) except: 1) A basic depth of thread of 0.4p is used instead of 0.6p; 2) Sizes below 1 inch are not included; 3) Tolerances on major and minor diameters are the same as the pitch diameter tolerances, whereas in the American Standard separate tolerances are provided; however, provision is made for smaller major and minor diameter tolerances when crest surfaces of screws or nuts are used as datum surfaces, or when the resulting reduction in depth of engagement must be limited; and 4) Certain combinations of large diameters with fine pitches are provided that are not encouraged in the American Standard. Lowenherz or Löwenherz Thread.—The Lowenherz thread is intended for the fine screws of instruments and is based on the metric system. The Löwenherz thread has flats at the top and bottom the same as the U.S. standard buttress form, but the angle is 53 degrees 8 minutes. The depth equals 0.75 × the pitch, and the width of the flats at the top and bottom is equal to 0.125 × the pitch. This screw thread used for measuring instruments, optical apparatus, etc., especially in Germany.


Machinery's Handbook 28th Edition ANSI BUTTRESS THREADS

1851

Löwenherz Thread Diameter Millimeters

Inches

1.0 1.2 1.4 1.7 2.0 2.3 2.6 3.0 3.5 4.0 4.5 5.0 5.5 6.0 7.0 8.0

0.0394 0.0472 0.0551 0.0669 0.0787 0.0905 0.1024 0.1181 0.1378 0.1575 0.1772 0.1968 0.2165 0.2362 0.2756 0.3150

Approximate Diameter Pitch, No. of Threads Millimeters per Inch Millimeters Inches 0.25 0.25 0.30 0.35 0.40 0.40 0.45 0.50 0.60 0.70 0.75 0.80 0.90 1.00 1.10 1.20

101.6 101.6 84.7 72.6 63.5 63.5 56.4 50.8 42.3 36.3 33.9 31.7 28.2 25.4 23.1 21.1

9.0 10.0 12.0 14.0 16.0 18.0 20.0 22.0 24.0 26.0 28.0 30.0 32.0 36.0 40.0 …

0.3543 0.3937 0.4724 0.5512 0.6299 0.7087 0.7874 0.8661 0.9450 1.0236 1.1024 1.1811 1.2599 1.4173 1.5748 …

Approximate Pitch, No. of Threads Millimeters per Inch 1.30 1.40 1.60 1.80 2.00 2.20 2.40 2.80 2.80 3.20 3.20 3.60 3.60 4.00 4.40 …

19.5 18.1 15.9 14.1 12.7 11.5 10.6 9.1 9.1 7.9 7.9 7.1 7.1 6.4 5.7 …

American National Standard Buttress Inch Screw Threads The buttress form of thread has certain advantages in applications involving exceptionally high stresses along the thread axis in one direction only. As the thrust side (load flank) of the standard buttress thread is made very nearly perpendicular to the thread axis, the radial component of the thrust is reduced to a minimum. On account of the small radial thrust, the buttress form of thread is particularly applicable when tubular members are screwed together. Examples of actual applications are the breech assemblies of large guns, airplane propeller hubs, and columns for hydraulic presses. 7°/45° Buttress Thread Form.—In selecting the form of thread recommended as standard, ANSI B1.9-1973 (R2007), manufacture by milling, grinding, rolling, or other suitable means, has been taken into consideration. All dimensions are in inches. Form of Thread: The form of the buttress thread is shown in the accompanying Figs. 2a and 2b, and has the following characteristics: a) A load flank angle, measured in an axial plane, of 7 degrees from the normal to the axis. b) A clearance flank angle, measured in an axial plane, of 45 degrees from the normal to the axis. c) Equal truncations at the crests of the external and internal threads such that the basic height of thread engagement (assuming no allowance) is equal to 0.6 of the pitch d) Equal radii, at the roots of the external and internal basic thread forms tangential to the load flank and the clearance flank. (There is, in practice, almost no chance that the thread forms will be achieved strictly as basically specified, that is, as true radii.) When specified, equal flat roots of the external and internal thread may be supplied. Table 1. American National Standard Diameter—Pitch Combinations for 7°/45° Buttress Threads ANSI B1.9-1973 (R2007) Preferred Nominal Major Diameters, Inches 0.5, 0.625, 0.75 0.875, 1.0 1.25, 1.375, 1.5 1.75, 2, 2.25, 2.5 2.75, 3, 3.5, 4

Threads per Incha (20, 16, 12) (16, 12, 10) 16, (12, 10, 8), 6 16, 12, (10, 8, 6), 5, 4 16, 12, 10, (8, 6, 5), 4

Preferred Nominal Major Diameters, Inches 4.5, 5, 5.5, 6 7, 8, 9, 10 11, 12, 14, 16 18, 20, 22, 24

Threads per Incha 12, 10, 8, (6, 5, 4), 3 10, 8, 6, (5, 4, 3), 2.5, 2 10, 8, 6, 5, (4, 3, 2.5), 2, 1.5, 1.25 8, 6, 5, 4, (3, 2.5, 2), 1.5, 1.25, 1

a Preferred threads per inch are in parentheses.



1852

Table 2. American National Standard Inch Buttress Screw Threads— Basic Dimensions ANSI B1.9-1973 (R2007)

Thds.a per Inch 20 16 12 10 8 6 5 4 3 21⁄2 2 11⁄2 11⁄4 1

Height of Crest Sharp-V Truncation, Thread,H = f= 0.89064p 0.14532p

Height of Thread, hs or hn = 0.66271p

Max. Root Truncation,b s= 0.0826p

Max. Root Radius,c r= 0.0714p

Width of Flat at Crest, F = 0.16316p

Pitch, p

Basic Height of Thread, h = 0.6p

0.0500 0.0625 0.0833 0.1000 0.1250 0.1667 0.2000 0.2500 0.3333 0.4000 0.5000 0.6667

0.0300 0.0375 0.0500 0.0600 0.0750 0.1000 0.1200 0.1500 0.2000 0.2400 0.3000 0.4000

0.0445 0.0557 0.0742 0.0891 0.1113 0.1484 0.1781 0.2227 0.2969 0.3563 0.4453 0.5938

0.0073 0.0091 0.0121 0.0145 0.0182 0.0242 0.0291 0.0363 0.0484 0.0581 0.0727 0.0969

0.0331 0.0414 0.0552 0.0663 0.0828 0.1105 0.1325 0.1657 0.2209 0.2651 0.3314 0.4418

0.0041 0.0052 0.0069 0.0083 0.0103 0.0138 0.0165 0.0207 0.0275 0.0330 0.0413 0.0551

0.0036 0.0045 0.0059 0.0071 0.0089 0.0119 0.0143 0.0179 0.0238 0.0286 0.0357 0.0476

0.0082 0.0102 0.0136 0.0163 0.0204 0.0271 0.0326 0.0408 0.0543 0.0653 0.0816 0.1088

0.8000 1.0000

0.4800 0.6000

0.7125 0.8906

0.1163 0.1453

0.5302 0.6627

0.0661 0.0826

0.0572 0.0714

0.1305 0.1632

a All other dimensions are in inches. b Minimum root truncation is one-half of maximum. c Minimum root radius is one-half of maximum.

Buttress Thread Tolerances.—Tolerances from basic size on external threads are applied in a minus direction and on internal threads in a plus direction. Pitch Diameter Tolerances: The following formula is used for determining the pitch diameter product tolerance for Class 2 (standard grade) external or internal threads: PD tolerance = 0.002

3

D + 0.00278 L e + 0.00854 p

where D =basic major diameter of external thread (assuming no allowance) Le =length of engagement p =pitch of thread When the length of engagement is taken as 10p, the formula reduces to 0.002

3

D + 0.0173 p

It is to be noted that this formula relates specifically to Class 2 (standard grade) PD tolerances. Class 3 (precision grade) PD tolerances are two-thirds of Class 2 PD tolerances. Pitch diameter tolerances based on this latter formula, for various diameter pitch combinations, are given in Table 4. Functional Size: Deviations in lead and flank angle of product threads increase the functional size of an external thread and decrease the functional size of an internal thread by the cumulative effect of the diameter equivalents of these deviations. The functional size of all buttress product threads shall not exceed the maximum-material limit. Tolerances on Major Diameter of External Thread and Minor Diameter of Internal Thread: Unless otherwise specified, these tolerances should be the same as the pitch diameter tolerance for the class used. Tolerances on Minor Diameter of External Thread and Major Diameter of Internal Thread: It will be sufficient in most instances to state only the maximum minor diameter of the external thread and the minimum major diameter of the internal thread without any tol-



1853

Form of American National Standard 7°/45° Buttress Thread with 0.6p Basic Height of Thread Engagement

Internal Thread p r s

.5G

f 90°

.5h

H

hn

.5h

he

.5G

7°

F

h .5h

45°

F

hs

0.020p radius approx. (Optional)

f s r (Basic) Pitch Dia. (E) Min Pitch Dia. of Internal Thread Max Pitch Dia. of External Thread Major Dia. of External Thread

Minor Dia. of External Thread Minor Dia. of Internal Thread (Basic) Minor Dia. (K) Nominal (Basic) Major Dia. (D)

Fig. 2a. Round Root External Thread Heavy Line Indicates Basic Form

Internal Thread p Max Corner Rounding = r

S

s

s .5 G f .5h H

hn

h

.5h

.5h

he

.5G

F

7° F

hs s

Max Corner Rounding = r (Basic) Pitch Dia. (E) Min Pitch Dia. of Internal Thread Max Pitch Dia. of External Thread Major Dia. of External Thread

45°

f

s S

0.020p Radius Approx. (Optional) (Basic) Minor Dia. (K)

Minor Dia. of External Thread Minor Dia. of Internal Thread Nominal (Basic) Major Dia. (D)

Fig. 2b. Flat Root External Thread Heavy Line Indicates Basic Form

erance. However, the root truncation from a sharp V should not be greater than 0.0826p nor less than 0.0413p. Lead and Flank Angle Deviations for Class 2: The deviations in lead and flank angles may consume the entire tolerance zone between maximum and minimum material product limits given in Table 4. Diameter Equivalents for Variations in Lead and Flank Angles for Class 3: T h e c o m bined diameter equivalents of variations in lead (including helix deviations), and flank



1854

Table 3. American National Standard Buttress Inch Screw Thread Symbols and Form Thread Element

Max. Material (Basic)

Pitch

p

Min. Material

Height of sharp-V thread

H

Basic height of thread engagement

h

= 0.89064p = 0.6p

Root radius (theoretical)(see footnote a)

r

= 0.07141p

Min. r

= 0.0357p

Root truncation

s

= 0.0826p

Min. s

= 0.5; Max. s = 0.0413p

Root truncation for flat root form

s

= 0.0826p

Min. s

= 0.5; Max. s = 0.0413p

Flat width for flat root form

S

= 0.0928p

Min. S

= 0.0464p

Allowance

G

Height of thread engagement

he

Min. he

= Max. he − [0.5 tol. on major dia. external thread + 0.5 tol. on minor dia. internal thread].

(see text) = h − 0.5G

Crest truncation

f

= 0.14532p

Crest width

F

= 0.16316p

Major diameter

D

Major diameter of internal thread

Dn

= D + 0.12542p

Max. Dn

= Max. pitch dia.of internal thread + 0.80803p

=D−G

Min. Ds

= D − G − D tol.

Major diameter of external thread

Ds

Pitch diameter

E

Pitch diameter of internal thread (see footnote b)

En

=D−h

Max. En

= D − h + PD tol.

Pitch diameter of external thread (see footnote c)

Es

=D−h−G

Min. Es

= D − h − G − PD tol.

Minor diameter

K external thread

Ks

= D − 1.32542p − G

Min. Ks

= Min. pitch dia. of external thread − 0.80803p

Minor diameter of internal thread

Kn

= D − 2h

Min. Kn

= D − 2h + K tol.

Height of thread of internal thread

hn

= 0.66271p

Height of thread ofexternal thread

hs

= 0.66271p

Pitch diameter increment for lead

∆El

Pitch diameter increment for 45° clearance flank angle

∆Eα1

Pitch diameter increment flank angle

∆Eα2

Minor diameter of

Length of engagement

for 7° load

Le

a Unless the flat root form is specified, the rounded root form of the external and internal thread shall

be a continuous, smoothly blended curve within the zone defined by 0.07141p maximum to 0.0357p minimum radius. The resulting curve shall have no reversals or sudden angular variations, and shall be tangent to the flanks of the thread. There is, in practice, almost no chance that the rounded thread form will be achieved strictly as basically specified, that is, as a true radius. b The pitch diameter X tolerances for GO and NOT GO threaded plug gages are applied to the internal product limits for En and Max. En. c The pitch diameter W tolerances for GO and NOT GO threaded setting plug gages are applied to the external product limits for Es and Min. Es.



1855

Table 4. American National Standard Buttress Inch Screw Threads Tolerances Class 2 (Standard Grade) and Class 3 (Precision Grade) ANSI B1.9-1973 (R2007) Basic Major Diameter, Inch Thds. per Inch

Pitch,a p Inch

From 0.5 thru 0.7

Over 0.7 thru 1.0

Over 1.0 thru 1.5

Over 1.5 thru 2.5

Over 2.5 thru 4

Over 4 thru 6

Over 6 thru 10

Over 10 thru 16

Over 16 thru 24

Tolerance on Major Diameter of External Thread, Pitch Diameter of External and Internal Threads, and Minor Diameter of Internal Thread, Inch

Pitchb Increment,

0.0173 p Inch

Class 2, Standard Grade 20 0.0500 16 0.0625 12 0.0833 10 0.1000 8 0.1250 6 0.1667 5 0.2000 4 0.2500 3 0.3333 2.5 0.4000 2.0 0.5000 1.5 0.6667 1.25 0.8000 1.0 1.0000 Diameter Increment,c

0.002

3

.0056 .0060 .0067 .... .... .... .... .... .... .... .... .... .... ....

.... .0062 .0069 .0074 .... .... .... .... .... .... .... .... .... ....

.... .0065 .0071 .0076 .0083 .0092 .... .... .... .... .... .... .... ....

.... .0068 .0075 .0080 .0086 .0096 .0103 .0112 .... .... .... .... .... ....

.... .0073 .0080 .0084 .0091 .0100 .0107 .0116 .... .... .... .... .... ....

.... .... .0084 .0089 .0095 .0105 .0112 .0121 .0134 .... .... .... .... ....

.... .... .... .0095 .0101 .0111 .0117 .0127 .0140 .0149 .0162 .... .... ....

.... .... .... .0102 .0108 .0118 .0124 .0134 .0147 .0156 .0169 .0188 .0202 ....

.... .... .... .... .0115 .0125 .0132 .0141 .0154 .0164 .0177 .0196 .0209 .0227

.00387 .00432 .00499 .00547 .00612 .00706 .00774 .00865 .00999 .01094 .01223 .01413 .01547 .01730

.00169 .00189 .00215 .00252 .00296 .00342 .00400 .00470 .00543

D Class 3, Precision Grade

20 16 12 10 8 6 5 4 3 2.5 2.0 1.5 1.25 1.0

0.0500 0.0625 0.0833 0.1000 0.1250 0.1667 .02000 0.2500 .03333 0.4000 0.5000 0.6667 0.8000 1.0000

.0037 .0040 .0044 .... .... .... .... .... .... .... .... .... .... ....

.... .0042 .0046 .0049 .... .... .... .... .... .... .... .... .... ....

.... .0043 .0048 .0051 .0055 .0061 .... .... .... .... .... .... .... ....

.... .0046 .0050 .0053 .0058 .0064 .0068 .0074 .... .... .... .... .... ....

.... .0049 .0053 .0056 .0061 .0067 .0071 .0077 .... .... .... .... .... ....

.... .... .0056 .0059 .0064 .0070 .0074 .0080 .0089 .... .... .... .... ....

.... .... .... .0063 .0067 .0074 .0078 .0084 .0093 .0100 .0108 .... .... ....

.... .... .... .0068 .0072 .0078 .0083 .0089 .0098 .0104 .0113 .0126 .0135 ....

.... .... .... .... .0077 .0083 .0088 .0094 .0103 .0109 .0118 .0130 .0139 .0152

a For threads with pitches not shown in this table, pitch increment to be used in tolerance formula is

to be determined by use of formula PD Tolerance = 0.002

3

D + 0.00278 L e + 0.00854 p , where:

D = basic major diameter of external thread (assuming no allowance), Le = length of engagement, and p = pitch of thread. This formula relates specifically to Class 2 (standard grade) PD tolerances. Class 3 (precision grade) PD tolerances are two-thirds of Class 2 PD tolerances. See text b When the length of engagement is taken as 10p, the formula reduces to:

0.002

3

D + 0.0173 p

c Diameter D, used in diameter increment formula, is based on the average of the range.

angle for Class 3, shall not exceed 50 percent of the Class 2 pitch diameter tolerances given in Table 4. Tolerances on Taper and Roundness: There are no requirements for taper and roundness for Class 2 buttress screw threads.



1856

The major and minor diameters of Class 3 buttress threads shall not taper nor be out of round to the extent that specified limits for major and minor diameter are exceeded. The taper and out-of-roundness of the pitch diameter for Class 3 buttress threads shall not exceed 50 per cent of the pitch-diameter tolerances. Allowances for Easy Assembly.—An allowance (clearance) should be provided on all external threads to secure easy assembly of parts. The amount of the allowance is deducted from the nominal major, pitch, and minor diameters of the external thread when the maximum material condition of the external thread is to be determined. The minimum internal thread is basic. The amount of the allowance is the same for both classes and is equal to the Class 3 pitchdiameter tolerance as calculated by the formulas previously given. The allowances for various diameter-pitch combinations are given in Table 5. Table 5. American National Standard External Thread Allowances for Classes 2 and 3 Buttress Inch Screw Threads ANSI B1.9-1973 (R2007) Basic Major Diameter, Inch Threads per Inch

Pitch, p Inch

From 0.5 thru 0.7

20 16 12 10 8 6 5 4 3 2.5 2.0 1.5 1.25 1.0

0.0500 0.0625 0.0833 0.1000 0.1250 0.1667 0.2000 0.2500 0.3333 0.4000 0.5000 0.6667 0.8000 1.0000

.0037 .0040 .0044 .... .... .... .... .... .... .... .... .... .... ....

Over 0.7 thru 1.0

Over 1.0 thru 1.5

Over 1.5 thru 2.5

Over 2.5 thru 4

Over 4 thru 6

Over 6 thru 10

Over 10 thru 16

Over 16 thru 24

Allowance on Major, Minor and Pitch Diameters of External Thread, Inch .... .0042 .0046 .0049 .... .... .... .... .... .... .... .... .... ....

.... .0043 .0048 .0051 .0055 .0061 .... .... .... .... .... .... .... ....

.... .0046 .0050 .0053 .0058 .0064 .0068 .0074 .... .... .... .... .... ....

.... .0049 .0053 .0056 .0061 .0067 .0071 .0077 .... .... .... .... .... ....

.... .... .0056 .0059 .0064 .0070 .0074 .0080 .0089 .... .... .... .... ....

.... .... .... .0063 .0067 .0074 .0078 .0084 .0093 .0100 .0108 .... .... ....

.... .... .... .0068 .0072 .0078 .0083 .0089 .0098 .0104 .0113 .0126 .0135 ....

.... .... .... .... .0077 .0083 .0088 .0094 .0103 .0109 .0118 .0130 .0139 .0152

Example Showing Dimensions for a Typical Buttress Thread.—The dimensions for a 2-inch diameter, 4 threads per inch, Class 2 buttress thread with flank angles of 7 degrees and 45 degrees are h =basic thread height = 0.1500 (Table 2) hs = hn = height of thread in external and internal threads = 0.1657 (Table 2) G =pitch-diameter allowance on external thread = 0.0074 (Table 5) Tolerance on PD of external and internal threads = 0.0112 (Table 4) Tolerance on major diameter of external thread and minor diameter of internal thread = 0.0112 (Table 4) Internal Thread: Basic Major Diameter: D = 2.0000 Min. Major Diameter: D − 2h + 2hn = 2.0314 (see Table 2) Min. Pitch Diameter: D − h = 1.8500 (see Table 2) Max. Pitch Diameter: D − h + PD Tolerance = 1.8612 (see Table 4) Min. Minor Diameter: D − 2h = 1.7000 (see Table 2) Max. Minor Diameter: D − 2h + Minor Diameter Tolerance = 1.7112 (see Table 4)



1857

External Thread: Max. Major Diameter: D − G = 1.9926 (see Table 5) Min. Major Diameter: D − G − Major Diameter Tolerance = 1.9814 (see Tables 4 and 5) Max. Pitch Diameter: D − h − G = 1.8426 (see Tables 2 and 5) Min. Pitch Diameter: D − h − G − PD Tolerance = 1.8314 (see Table 4) Max. Minor Diameter: D − G − 2hs = 1.6612 (see Tables 2 and 5) Buttress Thread Designations.—When only the designation, BUTT is used, the thread is “pull” type buttress (external thread pulls) with the clearance flank leading and the 7degree pressure flank following. When the designation, PUSH-BUTT is used, the thread is a push type buttress (external thread pushes) with the 7-degree load flank leading and the 45-degree clearance flank following. Whenever possible this description should be confirmed by a simplified view showing thread angles on the drawing of the product that has the buttress thread. Standard Buttress Threads: A buttress thread is considered to be standard when: 1) opposite flank angles are 7-degrees and 45-degrees; 2) basic thread height is 0.6p; 3) tolerances and allowances are as shown in Tables 4 and 5; and 4) length of engagement is 10p or less. Thread Designation Abbreviations: In thread designations on drawings, tools, gages, and in specifications, the following abbreviations and letters are to be used: BUTT PUSHBUTT LH P L A B Le SPL FL E TPI THD

for buttress thread, pull type for buttress thread, push type for left-hand thread (Absence of LH indicates that the thread is a right-hand thread.) for pitch for lead Note: Absence of A or B after thread class indicates for external thread that designation covers both the external and interfor internal thread nal threads. for length of thread engagement for special for flat root thread for pitch diameter for threads per inch for thread

Designation Sequence for Buttress Inch Screw Threads.—When designating singlestart standard buttress threads the nominal size is given first, the threads per inch next, then PUSH if the internal member is to push, but nothing if it is to pull, then the class of thread (2 or 3), then whether external (A) or internal (B), then LH if left-hand, but nothing if righthand, and finally FL if a flat root thread, but nothing if a radiused root thread; thus, 2.5-8 BUTT-2A indicates a 2.5 inch, 8 threads per inch buttress thread, Class 2 external, righthand, internal member to pull, with radiused root of thread. The designation 2.5-8 PUSHBUTT-2A-LH-FL signifies a 2.5 inch size, 8 threads per inch buttress thread with internal member to push, Class 2 external, left-hand, and flat root. A multiple-start standard buttress thread is similarly designated but the pitch is given instead of the threads per inch, followed by the lead and the number of starts is indicated in parentheses after the class of thread. Thus, 10-0.25P–0.5L – BUTT-3B (2 start) indicates a 10-inch thread with 4 threads per inch, 0.5 inch lead, buttress form with internal member to pull, Class 3 internal, 2 starts, with radiused root of thread.


Machinery's Handbook 28th Edition WHITWORTH THREADS

1858

WHITWORTH THREADS British Standard Whitworth (BSW) and British Standard Fine (BSF) Threads The BSW is the Coarse Thread series and the BSF is the Fine Thread series of British Standard 84:1956—Parallel Screw Threads of Whitworth Form. The dimensions given in the tables on the following pages for the major, effective, and minor diameters are, respectively, the maximum limits of these diameters for bolts and the minimum limits for nuts. Formulas for the tolerances on these diameters are given in the table below. Whitworth Standard Thread Form.—This thread form is used for the British Standard Whitworth (BSW) and British Standard Fine (BSF) screw threads. More recently, both threads have been known as parallel screw threads of Whitworth form. With standardization of the Unified thread, the Whitworth thread form is expected to be used only for replacements or spare parts. Tables of British Standard Parallel Screw Threads of Whitworth Form will be found on the following pages; tolerance formulas are given in the table below. The form of the thread is shown by the diagram. If p = pitch, d = depth of thread, r = radius at crest and root, and n = number of threads per inch, then d = 1⁄3 p × cot 27 ° 30 ′ = 0.640327p = 0.640327 ÷ n r = 0.137329p = 0.137329 ÷ n

p

It is recommended that stainless steel bolts of nominal size 3⁄4 inch and below should not be made to Close Class 55˚ limits but rather to Medium or Free Class limits. Nomir d nal sizes above 3⁄4 inch should have maximum and minir mum limits 0.001 inch smaller than the values obtained from the table. Tolerance Classes : Close Class bolts. Applies to screw threads requiring a fine snug fit, and should be used only for special work where refined accuracy of pitch and thread form are particularly required. Medium Class bolts and nuts. Applies to the better class of ordinary interchangeable screw threads. Free Class bolts. Applies to the majority of bolts of ordinary commercial quality. Normal Class nuts. Applies to ordinary commercial quality nuts; this class is intended for use with Medium or Free Class bolts. Table 1. Tolerance Formulas for BSW and BSF Threads Class or Fit Close Bolts

Medium Free

Nuts

Close Medium Normal

Major Dia. 2⁄ T 3

Tolerance in inchesa (+ for nuts, − for bolts) Effective Dia. Minor Dia.

+ 0.01 p

T + 0.01 p 3⁄ T 2

+ 0.01 p

… … …

2⁄ T 3

2⁄ T 3

T 3⁄ T 2

3⁄ T 2

2⁄ T 3

T 3⁄ T 2

+ 0.013 p

T + 0.02 p

}{

+ 0.02 p

0.2p + 0.004b 0.2p + 0.005c 0.2p + 0.007d

a The symbol T = 0.002 3 D + 0.003 L + 0.005 p , where D = major diameter of thread in inches; L = length of engagement in inches; p = pitch in inches. The symbol p signifies pitch. b For 26 threads per inch and finer. c For 24 and 22 threads per inch. d For 20 threads per inch and coarser.



1859

Table 2. Threads of Whitworth Form—Basic Dimensions

p

H6 p =1 ÷ n H =0.960491p H/6 = 0.160082p h =0.640327p e =0.0739176p r =0.137329p

r

h

e r

H

55˚

H6 Threads per Inch n 72 60 56 48 40 36 32 28 26 24 22 20 19 18 16 14 12 11 10 9 8 7 6 5 4.5 4 3.5 3.25 3 2.875 2.75 2.625 2.5

Pitch p 0.013889 0.016667 0.017857 0.020833 0.025000 0.027778 0.031250 0.035714 0.038462 0.041667 0.045455 0.050000 0.052632 0.055556 0.062500 0.071429 0.083333 0.090909 0.100000 0.111111 0.125000 0.142857 0.166667 0.20000 0.222222 0.250000 0.285714 0.307692 0.333333 0.347826 0.363636 0.380952 0.400000

Triangular Height H 0.013340 0.016009 0.017151 0.020010 0.024012 0.026680 0.030015 0.034303 0.036942 0.040020 0.043659 0.048025 0.050553 0.053361 0.060031 0.068607 0.080041 0.087317 0.096049 0.106721 0.120061 0.137213 0.160082 0.192098 0.213442 0.240123 0.274426 0.295536 0.320164 0.334084 0.349269 0.365901 0.384196

Shortening H/6 0.002223 0.002668 0.002859 0.003335 0.004002 0.004447 0.005003 0.005717 0.006157 0.006670 0.007276 0.008004 0.008425 0.008893 0.010005 0.011434 0.013340 0.014553 0.016008 0.017787 0.020010 0.022869 0.026680 0.032016 0.035574 0.040020 0.045738 0.049256 0.053361 0.055681 0.058212 0.060984 0.064033

Depth of Thread h 0.008894 0.010672 0.011434 0.013340 0.016008 0.017787 0.020010 0.022869 0.024628 0.026680 0.029106 0.032016 0.033702 0.035574 0.040020 0.045738 0.053361 0.058212 0.064033 0.071147 0.080041 0.091475 0.106721 0.128065 0.142295 0.160082 0.182951 0.197024 0.213442 0.222722 0.232846 0.243934 0.256131

Depth of Rounding e 0.001027 0.001232 0.001320 0.001540 0.0011848 0.002053 0.002310 0.002640 0.002843 0.003080 0.003366 0.003696 0.003890 0.004107 0.004620 0.005280 0.006160 0.006720 0.007392 0.008213 0.009240 0.010560 0.012320 0.014784 0.016426 0.018479 0.021119 0.022744 0.024639 0.025710 0.026879 0.028159 0.029567

Radius r 0.001907 0.002289 0.002452 0.002861 0.003433 0.003815 0.004292 0.004905 0.005282 0.005722 0.006242 0.006866 0.007228 0.007629 0.008583 0.009809 0.011444 0.012484 0.013733 0.015259 0.017166 0.019618 0.022888 0.027466 0.030518 0.034332 0.039237 0.042255 0.045776 0.047767 0.049938 0.052316 0.054932

Dimensions are in inches.

Allowances: Only Free Class and Medium Class bolts have an allowance. For nominal sizes of 3⁄4 inch down to 1⁄4 inch, the allowance is 30 per cent of the Medium Class bolt effective-diameter tolerance (0.3T); for sizes less than 1⁄4 inch, the allowance for the 1⁄4-inch size applies. Allowances are applied minus from the basic bolt dimensions; the tolerances are then applied to the reduced dimensions.



1860

Table 3. British Standard Whitworth (BSW) and British Standard Fine (BSF) Screw Thread Series—Basic Dimensions BS 84:1956 (obsolescent) Nominal Size, Inches 1⁄ a 8 3⁄ 16 1⁄ 4 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ a 16 5⁄ 8 11⁄ a 16 3⁄ 4 7⁄ 8

1 1 1⁄8 1 1⁄4 1 1⁄2 1 3⁄4 2 2 1⁄4 2 1⁄2 2 3⁄4 3 3 1⁄4 a 3 1⁄2 3 3⁄4 a 4 4 1⁄2 5 5 1⁄2 6 3⁄ a, b 16 7⁄ a 32 1⁄ 4 9⁄ a 32 5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2 9⁄ 16 5⁄ 8 11⁄ a 16 3⁄ 4 7⁄ 8

1 11⁄8 11⁄4 1 3⁄8 a 1 1⁄2 1 5⁄8 a 13⁄4 2 2 1⁄4 2 1⁄2 2 3⁄4 3 3 1⁄4 3 1⁄2 3 3⁄4 4 41⁄4

Threads per Inch

Pitch, Inches

40 24 20 18 16 14 12 12 11 11 10 9 8 7 7 6 5 4.5 4 4 3.5 3.5 3.25 3.25 3 3 2.875 2.75 2.625 2.5

0.02500 0.04167 0.05000 0.05556 0.06250 0.07143 0.08333 0.08333 0.09091 0.09091 0.10000 0.11111 0.12500 0.14286 0.14286 0.16667 0.20000 0.22222 0.25000 0.25000 0.28571 0.28571 0.30769 0.30769 0.33333 0.33333 0.34783 0.36364 0.38095 0.40000

32 28 26 26 22 20 18 16 16 14 14 12 11 10 9 9 8 8 8 7 7 6 6 6 5 5 4.5 4.5 4.5 4

0.03125 0.03571 0.03846 0.03846 0.04545 0.05000 0.05556 0.06250 0.06250 0.07143 0.07143 0.08333 0.09091 0.10000 0.11111 0.11111 0.12500 0.12500 0.12500 0.14286 0.14286 0.16667 0.16667 0.16667 0.20000 0.20000 0.22222 0.22222 0.22222 0.25000

Effective Major Depth of Diameter, Diameter, Thread, Inches Inches Inches Coarse Thread Series (BSW) 0.0160 0.1250 0.1090 0.0267 0.1875 0.1608 0.0320 0.2500 0.2180 0.0356 0.3125 0.2769 0.0400 0.3750 0.3350 0.0457 0.4375 0.3918 0.0534 0.5000 0.4466 0.0534 0.5625 0.5091 0.0582 0.6250 0.5668 0.0582 0.6875 0.6293 0.0640 0.7500 0.6860 0.0711 0.8750 0.8039 0.0800 1.0000 0.9200 0.0915 1.1250 1.0335 0.0915 1.2500 1.1585 0.1067 1.5000 1.3933 0.1281 1.7500 1.6219 0.1423 2.0000 1.8577 0.1601 2.2500 2.0899 0.1601 2.5000 2.3399 0.1830 2.7500 2.5670 0.1830 3.0000 2.8170 0.1970 3.2500 3.0530 0.1970 3.5000 3.3030 0.2134 3.7500 3.5366 0.2134 4.0000 3.7866 0.2227 4.5000 4.2773 0.2328 5.0000 4.7672 0.2439 5.5000 5.2561 0.2561 6.0000 5.7439 Fine Thread Series (BSF) 0.0200 0.0229 0.0246 0.0246 0.0291 0.0320 0.0 356 0.0400 0.0400 0.0457 0.0457 0.0534 0.0582 0.0640 0.0711 0.0711 0.0800 0.0800 0.0800 0.0915 0.0915 0.1067 0.1067 0.1067 0.1281 0.1281 0.1423 0.1423 0.1423 0.1601

0.1875 0.2188 0.2500 0.2812 0.3125 0.3750 0.4375 0.5000 0.5625 0.6250 0.6875 0.7500 0.8750 1.0000 1.1250 1.2500 1.3750 1.5000 1.6250 1.7500 2.0000 2.2500 2.5000 2.7500 3.0000 3.2500 3.5000 3.7500 4.0000 4.2500

0.1675 0.1959 0.2254 0.2566 0.2834 0.3430 0.4019 0.4600 0.5225 0.5793 0.6418 0.6966 0.8168 0.9360 1.0539 1.1789 1.2950 1.4200 1.5450 1.6585 1.9085 2.1433 2.3933 2.6433 2.8719 3.1219 3.3577 3.6077 3.8577 4.0899

Minor Diameter, Inches

Area at Bottom ofThread, Sq. in.

0.9030 0.1341 0.1860 0.2413 0.2950 0.3461 0.3932 0.4557 0.5086 0.5711 0.6220 0.7328 0.8400 0.9420 1.0670 1.2866 1.4938 1.7154 1.9298 2.1798 2.3840 2.6340 2.8560 3.1060 3.3232 3.5732 4.0546 4.5344 5.0122 5.4878

0.0068 0.0141 0.0272 0.0457 0.0683 0.0941 0.1214 0.1631 0.2032 0.2562 0.3039 0.4218 0.5542 0.6969 0.8942 1.3000 1.7530 2.3110 2.9250 3.7320 4.4640 5.4490 6.4060 7.5770 8.6740 10.0300 12.9100 16.1500 19.7300 23.6500

0.1475 0.1730 0.2008 0.2320 0.2543 0.3110 0.3363 0.4200 0.4825 0.5336 0.5961 0.6432 0.7586 0.8720 0.9828 1.1078 1.2150 1.3400 1.4650 1.5670 1.8170 2.0366 2.2866 2.5366 2.7438 2.9938 3.2154 3.4654 3.7154 3.9298

0.0171 0.0235 0.0317 0.0423 0.0508 0.0760 0.1054 0.1385 0.1828 0.2236 0.2791 0.3249 0.4520 0.5972 0.7586 0.9639 1.1590 1.4100 1.6860 1.9280 2.5930 3.2580 4.1060 5.0540 5.9130 7.0390 8.1200 9.4320 10.8400 12.1300

Tap Drill Dia. 2.55 mm 3.70 mm 5.10 mm 6.50 mm 7.90 mm 9.30 mm 10.50 mm 12.10. mm 13.50 mm 15.00 mm 16.25 mm 19.25 mm 22.00 mm 24.75 mm 28.00 mm 33.50 mm 39.00 mm 44.50 mm

Tap drill diameters shown in this column are recommended sizes listed in BS 1157:1975 and provide from 77 to 87% of full thread.

4.00 mm 4.60 mm 5.30 mm 6.10 mm 6.80 mm 8.30 mm 9.70 mm 11.10 mm 12.70 mm 14.00 mm 15.50 mm 16.75 mm 19.75 mm 22.75 mm 25.50 mm 28.50 mm 31.50 mm 34.50 mm

Tap drill sizes listed in this column are recommended sizes shown in BS 1157:1975 and provide from 78 to 88% of full thread.

a To be dispensed with wherever possible. b The use of number 2 BA threads is recommended in place of 3/16-inch BSF thread, see page

1886.


Machinery's Handbook 28th Edition AMERICAN PIPE THREADS

1861

PIPE AND HOSE THREADS The types of threads used on pipe and pipe fittings may be classed according to their intended use: 1) threads that when assembled with a sealer will produce a pressure-tight joint; 2) threads that when assembled without a sealer will produce a pressure-tight joint; 3) threads that provide free- and loose-fitting mechanical joints without pressure tightness; and 4) threads that produce rigid mechanical joints without pressure tightness. American National Standard Pipe Threads American National Standard pipe threads described in the following paragraphs provide taper and straight pipe threads for use in various combinations and with certain modifications to meet these specific needs. Thread Designation and Notation.—American National Standard Pipe Threads are designated by specifying in sequence the nominal size, number of threads per inch, and the symbols for the thread series and form, as: 3⁄8—18 NPT. The symbol designations are as follows: NPT—American National Standard Taper Pipe Thread; NPTR—American National Standard Taper Pipe Thread for Railing Joints; NPSC—American National Standard Straight Pipe Thread for Couplings; NPSM—American National Standard Straight Pipe Thread for Free-fitting Mechanical Joints; NPSL—American National Standard Straight Pipe Thread for Loose-fitting Mechanical Joints with Locknuts; and NPSH— American National Standard Straight Pipe Thread for Hose Couplings. American National Standard Taper Pipe Threads.—The basic dimensions of the ANSI Standard taper pipe thread are given in Table 1a. Form of Thread: The angle between the sides of the thread is 60 degrees when measured in an axial plane, and the line bisecting this angle is perpendicular to the axis. The depth of the truncated thread is based on factors entering into the manufacture of cutting tools and the making of tight joints and is given by the formulas in Table 1a or the data in Table 2 obtained from these formulas. Although the standard shows flat surfaces at the crest and root of the thread, some rounding may occur in commercial practice, and it is intended that the pipe threads of product shall be acceptable when crest and root of the tools or chasers lie within the limits shown in Table 2. Pitch Diameter Formulas: In the following formulas, which apply to the ANSI Standard taper pipe thread, E0 = pitch diameter at end of pipe; E1 = pitch diameter at the large end of the internal thread and at the gaging notch; D = outside diameter of pipe; L1 = length of hand-tight or normal engagement between external and internal threads; L2 = basic length of effective external taper thread; and p = pitch = 1 ÷ number of threads per inch. E 0 = D – ( 0.05D + 1.1 )p E 1 = E 0 + 0.0625L 1 Thread Length: The formula for L2 determines the length of the effective thread and includes approximately two usable threads that are slightly imperfect at the crest. The normal length of engagement, L1, between external and internal taper threads, when assembled by hand, is controlled by the use of the gages. L 2 = ( 0.80D + 6.8 )p Taper: The taper of the thread is 1 in 16, or 0.75 inch per foot, measured on the diameter and along the axis. The corresponding half-angle of taper or angle with the center line is 1 degree, 47 minutes.



1862

Table 1a. Basic Dimensions, American National Standard Taper Pipe Threads, NPT ANSI/ASME B1.20.1-1983 (R2006) L4

L5 L3

2p

Taper of Thread 1 in 16 Measured on Diameter

L1

E1 E5

E0

E3

Imperfect Threads due to Chamfer on die

V

L2

E2

D

For all dimensions, see corresponding reference letter in table. Angle between sides of thread is 60 degrees. Taper of thread, on diameter, is 3⁄4 inch per foot. Angle of taper with center line is 1°47′. The basic maximum thread height, h, of the truncated thread is 0.8 × pitch of thread. The crest and root are truncated a minimum of 0.033 × pitch for all pitches. For maximum depth of truncation, see Table 2.

Nominal Pipe Size 1⁄ 16

Outside Dia. of Pipe, D

Threads per Inch, n

Pitch of Thread, p

Pitch Diameter at Beginning of External Thread, E0

Handtight Engagement Length,a L1

Effective Thread, External

Dia.,b E1

Length,c L2

Inch

Dia., E2 Inch

0.3125

27

0.03704

0.27118

0.160

0.28118

0.2611

0.28750

1⁄ 8

0.405

27

0.03704

0.36351

0.1615

0.37360

0.2639

0.38000

1⁄ 4

0.540

18

0.05556

0.47739

0.2278

0.49163

0.4018

0.50250

3⁄ 8

0.675

18

0.05556

0.61201

0.240

0.62701

0.4078

0.63750

1⁄ 2

0.840

14

0.07143

0.75843

0.320

0.77843

0.5337

0.79179

3⁄ 4

1.050

14

0.07143

0.96768

0.339

0.98887

0.5457

1.00179

1

1.315

111⁄2

0.08696

1.21363

0.400

1.23863

0.6828

1.25630

11⁄4

1.660

111⁄2

0.08696

1.55713

0.420

1.58338

0.7068

1.60130

11⁄2

1.900

111⁄2

0.08696

1.79609

0.420

1.82234

0.7235

1.84130

2

2.375

111⁄2

0.08696

2.26902

0.436

2.29627

0.7565

2.31630

21⁄2

2.875

8

0.12500

2.71953

0.682

2.76216

1.1375

2.79062

3

3.500

8

0.12500

3.34062

0.766

3.38850

1.2000

3.41562

31⁄2

4.000

8

0.12500

3.83750

0.821

3.88881

1.2500

3.91562

4

4.500

8

0.12500

4.33438

0.844

4.38712

1.3000

4.41562

5

5.563

8

0.12500

5.39073

0.937

5.44929

1.4063

5.47862

6

6.625

8

0.12500

6.44609

0.958

6.50597

1.5125

6.54062

8

8.625

8

0.12500

8.43359

1.063

8.50003

1.7125

8.54062

10

10.750

8

0.12500

10.54531

1.210

10.62094

1.9250

10.66562

12

12.750

8

0.12500

12.53281

1.360

12.61781

2.1250

12.66562

14 OD

14.000

8

0.12500

13.77500

1.562

13.87262

2.2500

13.91562

16 OD

16.000

8

0.12500

15.76250

1.812

15.87575

2.4500

15.91562

18 OD

18.000

8

0.12500

17.75000

2.000

17.87500

2.6500

17.91562

20 OD

20.000

8

0.12500

19.73750

2.125

19.87031

2.8500

19.91562

24 OD

24.000

8

0.12500

23.71250

2.375

23.86094

3.2500

23.91562

a Also length of thin ring gage and length from gaging notch to small end of plug gage. b Also pitch diameter at gaging notch (handtight plane). c Also length of plug gage.



1863

Table 1b. Basic Dimensions, American National Standard Taper Pipe Threads, NPT ANSI/ASME B1.20.1-1983 (R2006) Nominal Pipe Size

Wrench Makeup Length for Internal Thread Length,c L3

Dia., E3

Vanish Thread, (3.47 thds.), V

Nominal Perfect External Threadsa

Overall Length External Thread, L4

Length, L5

Dia., E5

Height of Thread, h

Basic Minor Dia. at Small End of Pipe,b K0

1⁄ 16

0.1111

0.26424

0.1285

0.3896

0.1870

0.28287

0.02963

0.2416

1⁄ 8

0.1111

0.35656

0.1285

0.3924

0.1898

0.37537

0.02963

0.3339

1⁄ 4

0.1667

0.46697

0.1928

0.5946

0.2907

0.49556

0.04444

0.4329

3⁄ 8

0.1667

0.60160

0.1928

0.6006

0.2967

0.63056

0.04444

0.5676

1⁄ 2

0.2143

0.74504

0.2478

0.7815

0.3909

0.78286

0.05714

0.7013

3⁄ 4

0.2143

0.95429

0.2478

0.7935

0.4029

0.99286

0.05714

0.9105

11⁄4

0.2609 0.2609

1.19733 1.54083

0.3017 0.3017

0.9845 1.0085

0.5089 0.5329

1.24543 1.59043

0.06957 0.06957

1.1441 1.4876

11⁄2

0.2609

1.77978

0.3017

1.0252

0.5496

1.83043

0.06957

1.7265

2

0.2609

21⁄2

0.2500d

2.25272 2.70391

0.3017 0.4337

1.0582 1.5712

0.5826 0.8875

2.30543 2.77500

0.06957 0.100000

2.1995 2.6195

3

0.2500d

3.32500

0.4337

1.6337

0.9500

3.40000

0.100000

3.2406

31⁄2

0.2500

3.82188

0.4337

1.6837

1.0000

3.90000

0.100000

3.7375

4 5 6 8 10 12 14 OD 16 OD 18 OD 20 OD 24 OD

0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500

4.31875 5.37511 6.43047 8.41797 10.52969 12.51719 13.75938 15.74688 17.73438 19.72188 23.69688

0.4337 0.4337 0.4337 0.4337 0.4337 0.4337 0.4337 0.4337 0.4337 0.4337 0.4337

1.7337 1.8400 1.9462 2.1462 2.3587 2.5587 2.6837 2.8837 3.0837 3.2837 3.6837

1.0500 1.1563 1.2625 1.4625 1.6750 1.8750 2.0000 2.2000 2.4000 2.6000 3.0000

4.40000 5.46300 6.52500 8.52500 10.65000 12.65000 13.90000 15.90000 17.90000 19.90000 23.90000

0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000 0.100000

4.2344 5.2907 6.3461 8.3336 10.4453 12.4328 13.6750 15.6625 17.6500 19.6375 23.6125

1

a The length L from the end of the pipe determines the plane beyond which the thread form is imper5 fect at the crest. The next two threads are perfect at the root. At this plane the cone formed by the crests of the thread intersects the cylinder forming the external surface of the pipe. L5 = L2 − 2p. b Given as information for use in selecting tap drills. c Three threads for 2-inch size and smaller; two threads for larger sizes. d Military Specification MIL—P—7105 gives the wrench makeup as three threads for 3 in. and smaller. The E3 dimensions are then as follows: Size 21⁄2 in., 2.69609 and size 3 in., 3.31719. All dimensions given in inches. Increase in diameter per thread is equal to 0.0625/n. The basic dimensions of the ANSI Standard Taper Pipe Thread are given in inches to four or five decimal places. While this implies a greater degree of precision than is ordinarily attained, these dimensions are the basis of gage dimensions and are so expressed for the purpose of eliminating errors in computations.

Engagement Between External and Internal Taper Threads.—The normal length of engagement between external and internal taper threads when screwed together handtight is shown as L1 in Table 1a. This length is controlled by the construction and use of the pipe thread gages. It is recognized that in special applications, such as flanges for high-pressure work, longer thread engagement is used, in which case the pitch diameter E1 (Table 1a) is maintained and the pitch diameter E0 at the end of the pipe is proportionately smaller. Tolerances on Thread Elements.—The maximum allowable variation in the commercial product (manufacturing tolerance) is one turn large or small from the basic dimensions. The permissible variations in thread elements on steel products and all pipe made of steel, wrought iron, or brass, exclusive of butt-weld pipe, are given in Table 3. This table is a



1864

guide for establishing the limits of the thread elements of taps, dies, and thread chasers. These limits may be required on product threads. On pipe fittings and valves (not steel) for steam pressures 300 pounds and below, it is intended that plug and ring gage practice as set up in the Standard ANSI/ASME B1.20.1 will provide for a satisfactory check of accumulated variations of taper, lead, and angle in such product. Therefore, no tolerances on thread elements have been established for this class. For service conditions where a more exact check is required, procedures have been developed by industry to supplement the regulation plug and ring method of gaging. Table 2. Limits on Crest and Root of American National Standard External and Internal Taper Pipe Threads, NPT ANSI/ASME B1.20.1-1983 (R2006) INTERNAL THREAD Minimum Truncation

Root Minimum Truncation

H Max. h

Maximum Truncation

Minimum Truncation

Maximum Truncation

Crest Crest Maximum Truncation

Maximum Truncation

Root Minimum Truncation

EXTERNAL THREAD Threads per Inch

Height of Sharp V Thread, H

27 18 14 111⁄2 8

Height of Pipe Thread, h

Truncation, f

Width of Flat, F, Equivalent toTruncation

Max.

Min.

Min.

Max.

Min.

Max.

0.03208 0.04811 0.06186 0.07531

0.02963 0.04444 0.05714 0.06957

0.02496 0.03833 0.05071 0.06261

0.0012 0.0018 0.0024 0.0029

0.0036 0.0049 0.0056 0.0063

0.0014 0.0021 0.0027 0.0033

0.0041 0.0057 0.0064 0.0073

0.10825

0.10000

0.09275

0.0041

0.0078

0.0048

0.0090

All dimensions are in inches and are given to four or five decimal places only to avoid errors in computations, not to indicate required precision.

Table 3. Tolerances on Taper, Lead, and Angle of Pipe Threads of Steel Products and All Pipe of Steel, Wrought Iron, or Brass ANSI/ASME B1.20.1-1983 (R2006) (Exclusive of Butt-Weld Pipe) Nominal Pipe Size

1,

1⁄ , 1⁄ 16 8 1⁄ , 3⁄ 4 8 1⁄ , 3⁄ 2 4 1 1 ⁄4, 11⁄2,

2

21⁄2 and larger

Threads per Inch

Taper on Pitch Line (3⁄4 in./ft)

Lead in Length of Effective Threads

60 Degree Angle of Threads, Degrees

Max.

Min.

27

+1⁄8

−1⁄16

±0.003

18

+1⁄8

−1⁄16

±0.003

± 21⁄2 ±2

14

+1⁄8

−1⁄16

±0.003a

±2

111⁄2 8

+1⁄8

−1⁄16

±0.003a

±11⁄2

+1⁄8

−1⁄16

±0.003a

±11⁄2

a The tolerance on lead shall be ± 0.003 in. per inch on any size threaded to an effective thread length

greater than 1 in. For tolerances on height of thread, see Table 2. The limits specified in this table are intended to serve as a guide for establishing limits of the thread elements of taps, dies, and thread chasers. These limits may be required on product threads.



1865

Table 4. Internal Threads in Pipe Couplings, NPSC for Pressuretight Joints with Lubricant or Sealer ANSI/ASME B1.20.1-1983 (R2006) Nom.Pipe- Thds.per Size Inch 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

27 18 18 14 14

1

111⁄2 111⁄2

11⁄4

Minora Dia. Min. 0.340 0.442 0.577 0.715 0.925 1.161 1.506

Pitch Diameterb Min. Max. 0.3701 0.3771 0.4864 0.4968 0.6218 0.6322 0.7717 0.7851 0.9822 0.9956 1.2305 1.2468 1.5752 1.5915

Nom. Pipe

Thds. per Inch

11⁄2

111⁄2 111⁄2

2 21⁄2 3 31⁄2 4 …

8 8 8 8 …

Minora Dia. Min. 1.745 2.219 2.650 3.277 3.777 4.275 …

Pitch Diameterb Min. Max. 1.8142 1.8305 2.2881 2.3044 2.7504 2.7739 3.3768 3.4002 3.8771 3.9005 4.3754 4.3988 … …

a As the ANSI Standard Pipe Thread form is maintained, the major and minor diameters of the internal thread vary with the pitch diameter. All dimensions are given in inches. b The actual pitch diameter of the straight tapped hole will be slightly smaller than the value given when gaged with a taper plug gage as called for in ANSI/ASME B1.20.1.

Railing Joint Taper Pipe Threads, NPTR.—Railing joints require a rigid mechanical thread joint with external and internal taper threads. The external thread is basically the same as the ANSI Standard Taper Pipe Thread, except that sizes 1⁄2 through 2 inches are shortened by 3 threads and sizes 21⁄2 through 4 inches are shortened by 4 threads to permit the use of the larger end of the pipe thread. A recess in the fitting covers the last scratch or imperfect threads on the pipe. Straight Pipe Threads in Pipe Couplings, NPSC.—Threads in pipe couplings made in accordance with the ANSI/ASME B1.20.1 specifications are straight (parallel) threads of the same thread form as the ANSI Standard Taper Pipe Thread. They are used to form pressuretight joints when assembled with an ANSI Standard external taper pipe thread and made up with lubricant or sealant. These joints are recommended for comparatively low pressures only. Straight Pipe Threads for Mechanical Joints, NPSM, NPSL, and NPSH.—W h i l e external and internal taper pipe threads are recommended for pipe joints in practically every service, there are mechanical joints where straight pipe threads are used to advantage. Three types covered by ANSI/ASME B1.20.1 are: Loose-fitting Mechanical Joints With Locknuts (External and Internal), NPSL: T h i s thread is designed to produce a pipe thread having the largest diameter that it is possible to cut on standard pipe. The dimensions of these threads are given in Table 5. It will be noted that the maximum major diameter of the external thread is slightly greater than the nominal outside diameter of the pipe. The normal manufacturer's variation in pipe diameter provides for this increase. Loose-fitting Mechanical Joints for Hose Couplings (External and Internal), NPSH: Hose coupling joints are ordinarily made with straight internal and external loose-fitting threads. There are several standards of hose threads having various diameters and pitches. One of these is based on the ANSI Standard pipe thread and by the use of this thread series, it is possible to join small hose couplings in sizes 1⁄2 to 4 inches, inclusive, to ends of standard pipe having ANSI Standard External Pipe Threads, using a gasket to seal the joints. For the hose coupling thread dimensions see ANSI Standard Hose Coupling Screw Threads starting on page 1873. Free-fitting Mechanical Joints for Fixtures (External and Internal), NPSM: S t a n d a r d iron, steel, and brass pipe are often used for special applications where there are no internal pressures. Where straight thread joints are required for mechanical assemblies, straight pipe threads are often found more suitable or convenient. Dimensions of these threads are given in Table 5.



1866

Table 5. American National Standard Straight Pipe Threads for Mechanical Joints, NPSM and NPSL ANSI/ASME B1.20.1-1983 (R2006) Nominal Pipe Size 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1 11⁄4 11⁄2 2 21⁄2 3 31⁄2 4 5 6 1⁄ 8 1⁄ 4 3⁄ 8 1⁄ 2 3⁄ 4

1 11⁄4 11⁄2 2 21⁄2 3 31⁄2 4 5 6 8 10 12

Threads per Inch 27 18 18 14 14 111⁄2 111⁄2 111⁄2 111⁄2 8 8 8 8 8 8 27 18 18 14 14 111⁄2 111⁄2 111⁄2 111⁄2 8 8 8 8 8 8 8 8 8

Allowance

External Thread Major Diameter Pitch Diameter

Internal Thread Minor Diameter Pitch Diameter

Max.a Min. Max. Min. Min.a Free-fitting Mechanical Joints for Fixtures—NPSM

Max.

0.0011 0.397 0.390 0.3725 0.3689 0.358 0.364 0.0013 0.526 0.517 0.4903 0.4859 0.468 0.481 0.0014 0.662 0.653 0.6256 0.6211 0.603 0.612 0.0015 0.823 0.813 0.7769 0.7718 0.747 0.759 0.0016 1.034 1.024 0.9873 0.9820 0.958 0.970 0.0017 1.293 1.281 1.2369 1.2311 1.201 1.211 0.0018 1.638 1.626 1.5816 1.5756 1.546 1.555 0.0018 1.877 1.865 1.8205 1.8144 1.785 1.794 0.0019 2.351 2.339 2.2944 2.2882 2.259 2.268 0.0022 2.841 2.826 2.7600 2.7526 2.708 2.727 0.0023 3.467 3.452 3.3862 3.3786 3.334 3.353 0.0023 3.968 3.953 3.8865 3.8788 3.835 3.848 0.0023 4.466 4.451 4.3848 4.3771 4.333 4.346 0.0024 5.528 5.513 5.4469 5.4390 5.395 5.408 0.0024 6.585 6.570 6.5036 6.4955 6.452 6.464 Loose-fitting Mechanical Joints for Locknut Connections—NPSL … 0.409 … 0.3840 0.3805 0.362 … … 0.541 … 0.5038 0.4986 0.470 … … 0.678 … 0.6409 0.6357 0.607 … … 0.844 … 0.7963 0.7896 0.753 … … 1.054 … 1.0067 1.0000 0.964 … … 1.318 … 1.2604 1.2523 1.208 … … 1.663 … 1.6051 1.5970 1.553 … … 1.902 … 1.8441 1.8360 1.792 … … 2.376 … 2.3180 2.3099 2.265 … … 2.877 … 2.7934 2.7817 2.718 … … 3.503 … 3.4198 3.4081 3.344 … … 4.003 … 3.9201 3.9084 3.845 … … 4.502 … 4.4184 4.4067 4.343 … … 5.564 … 5.4805 5.4688 5.405 … … 6.620 … 6.5372 6.5255 6.462 … … 8.615 … 8.5313 8.5196 8.456 … … 10.735 … 10.6522 10.6405 10.577 … … 12.732 … 12.6491 12.6374 12.574 …

Min.b

Max.

0.3736 0.4916 0.6270 0.7784 0.9889 1.2386 1.5834 1.8223 2.2963 2.7622 3.3885 3.8888 4.3871 5.4493 6.5060

0.3783 0.4974 0.6329 0.7851 0.9958 1.2462 1.5912 1.8302 2.3044 2.7720 3.3984 3.8988 4.3971 5.4598 6.5165

0.3863 0.5073 0.6444 0.8008 1.0112 1.2658 1.6106 1.8495 2.3234 2.8012 3.4276 3.9279 4.4262 5.4884 6.5450 8.5391 10.6600 12.6569

0.3898 0.5125 0.6496 0.8075 1.0179 1.2739 1.6187 1.8576 2.3315 2.8129 3.4393 3.9396 4.4379 5.5001 6.5567 8.5508 10.6717 12.6686

a As the ANSI Standard Straight Pipe Thread form of thread is maintained, the major and the minor diameters of the internal thread and the minor diameter of the external thread vary with the pitch diameter. The major diameter of the external thread is usually determined by the diameter of the pipe. These theoretical diameters result from adding the depth of the truncated thread (0.666025 × p) to the maximum pitch diameters, and it should be understood that commercial pipe will not always have these maximum major diameters. b This is the same as the pitch diameter at end of internal thread, E Basic. (See Table 1a.) 1

All dimensions are given in inches. Notes for Free-fitting Fixture Threads: The minor diameters of external threads and major diameters of internal threads are those as produced by commercial straight pipe dies and commercial ground straight pipe taps. The major diameter of the external thread has been calculated on the basis of a truncation of 0.10825p, and the minor diameter of the internal thread has been calculated on the basis of a truncation of 0.21651p, to provide no interference at crest and root when product is gaged with gages made in accordance with the Standard. Notes for Loose-fitting Locknut Threads: The locknut thread is established on the basis of retaining the greatest possible amount of metal thickness between the bottom of the thread and the inside of the pipe. In order that a locknut may fit loosely on the externally threaded part, an allowance equal to the “increase in pitch diameter per turn” is provided, with a tolerance of 11⁄2 turns for both external and internal threads.


Machinery's Handbook 28th Edition DRYSEAL PIPE THREADS

1867

American National Standard Dryseal Pipe Threads for Pressure-Tight Joints.— Dryseal pipe threads are based on the USA (American) pipe thread; however, they differ in that they are designed to seal pressure-tight joints without the necessity of using sealing compounds. To accomplish this, some modification of thread form and greater accuracy in manufacture is required. The roots of both the external and internal threads are truncated slightly more than the crests, i.e., roots have wider flats than crests so that metal-to-metal contact occurs at the crests and roots coincident with, or prior to, flank contact. Thus, as the threads are assembled by wrenching, the roots of the threads crush the sharper crests of the mating threads. This sealing action at both major and minor diameters tends to prevent spiral leakage and makes the joints pressure-tight without the necessity of using sealing compounds, provided that the threads are in accordance with standard specifications and tolerances and are not damaged by galling in assembly. The control of crest and root truncation is simplified by the use of properly designed threading tools. Also, it is desirable that both external and internal threads have full thread height for the length of hand engagement. Where not functionally objectionable, the use of a compatible lubricant or sealant is permissible to minimize the possibility of galling. This is desirable in assembling Dryseal pipe threads in refrigeration and other systems to effect a pressure-tight seal. The crest and root of Dryseal pipe threads may be slightly rounded, but are acceptable if they lie within the truncation limits given in Table 6. Table 6. American National Standard Dryseal Pipe Threads—Limits on Crest and Root Truncation ANSI B1.20.3-1976 (R2003) Truncation Height of Sharp V Thread (H)

Formula

Inch

Formula

Inch

Formula

Inch

Formula

Inch

111⁄2

0.03208 0.04811 0.06180 0.07531

0.047p 0.047p 0.036p 0.040p

0.0017 0.0026 0.0026 0.0035

0.094p 0.078p 0.060p 0.060p

0.0035 0.0043 0.0043 0.0052

0.094p 0.078p 0.060p 0.060p

0.0035 0.0043 0.0043 0.0052

0.140p 0.109p 0.085p 0.090p

0.0052 0.0061 0.0061 0.0078

8

0.10825

0.042p

0.0052

0.055p

0.0069

0.055p

0.0069

0.076p

0.0095

Threads Per Inch 27 18 14

Minimum At Crest

Maximum At Root

At Crest

At Root

All dimensions are given in inches. In the formulas, p = pitch.

Types of Dryseal Pipe Thread.—American National Standard ANSI B1.20.3-1976 (R2003) covers four types of standard Dryseal pipe threads: NPTF, Dryseal USA (American) Standard Taper Pipe Thread PTF-SAE SHORT, Dryseal SAE Short Taper Pipe Thread NPSF, Dryseal USA (American) Standard Fuel Internal Straight Pipe Thread NPSI, Dryseal USA (American) Standard Intermediate Internal Straight Pipe Thread Table 7. Recommended Limitation of Assembly among the Various Types of Dryseal Threads Type

External Dryseal Thread Description

1

NPTF (tapered), ext thd

2a,e

PTF-SAE SHORT (tapered) ext thd

For Assembly with Internal Dryseal Thread Type Description 1 NPTF (tapered), int thd PTF-SAE SHORT (tapered), int thd 2a,b NPSF (straight), int thd 3a,c 4a,c,d NPSI (straight), int thd 4 NPSI (straight), int thd 1 NPTF (tapered), int thd

a Pressure-tight

joints without the use of a sealant can best be ensured where both components are threaded with NPTF (full length threads), since theoretically interference (sealing) occurs at all threads, but there are two less threads engaged than for NPTF assemblies. When straight internal threads are used, there is interference only at one thread depending on ductility of materials.


1868


b PTF-SAE SHORT internal threads are primarily intended for assembly with type 1-NPTF external threads. They are not designed for, and at extreme tolerance limits may not assemble with, type 2-PTFSAE SHORT external threads. c There is no external straight Dryseal thread. d NPSI internal threads are primarily intended for assembly with type 2-PTF-SAE SHORT external threads but will also assemble with full length type 1 NPTF external threads. e PTF-SAE SHORT external threads are primarily intended for assembly with type 4-NPSI internal threads but can also be used with type 1-NPTF internal threads. They are not designed for, and at extreme tolerance limits may not assemble with, type 2-PTF-SAE SHORT internal threads or type 3NPSF internal threads. An assembly with straight internal pipe threads and taper external pipe threads is frequently more advantageous than an all taper thread assembly, particularly in automotive and other allied industries where economy and rapid production are major considerations. Dryseal threads are not used in assemblies in which both components have straight pipe threads.

NPTF Threads: This type applies to both external and internal threads and is suitable for pipe joints in practically every type of service. Of all Dryseal pipe threads, NPTF external and internal threads mated are generally conceded to be superior for strength and seal since they have the longest length of thread and, theoretically, interference (sealing) occurs at every engaged thread root and crest. Use of tapered internal threads, such as NPTF or PTFSAE SHORT in hard or brittle materials having thin sections will minimize the possibility of fracture. There are two classes of NTPF threads. Class 1 threads are made to interfere (seal) at root and crest when mated, but inspection of crest and root truncation is not required. Consequently, Class 1 threads are intended for applications where close control of tooling is required for conformance of truncation or where sealing is accomplished by means of a sealant applied to the threads. Class 2 threads are theoretically identical to those made to Class 1, however, inspection of root and crest truncation is required. Consequently, where a sealant is not used, there is more assurance of a pressure-tight seal for Class 2 threads than for Class 1 threads. PTF-SAE SHORT Threads: External threads of this type conform in all respects with NPTF threads except that the thread length has been shortened by eliminating one thread from the small (entering) end. These threads are designed for applications where clearance is not sufficient for the full length of the NPTF threads or for economy of material where the full thread length is not necessary. Internal threads of this type conform in all respects with NPTF threads, except that the thread length has been shortened by eliminating one thread from the large (entry) end. These threads are designed for thin materials where thickness is not sufficient for the full thread length of the NPTF threads or for economy in tapping where the full thread length is not necessary. Pressure-tight joints without the use of lubricant or sealer can best be ensured where mating components are both threaded with NPTF threads. This should be considered before specifying PTF-SAE SHORT external or internal threads. NPSF Threads: Threads of this type are straight (cylindrical) instead of tapered and are internal only. They are more economical to produce than tapered internal threads, but when assembled do not offer as strong a guarantee of sealing since root and crest interference will not occur for all threads. NPSF threads are generally used with soft or ductile materials which will tend to adjust at assembly to the taper of external threads, but may be used in hard or brittle materials where the section is thick. NPSI Threads: Threads of this type are straight (cylindrical) instead of tapered, are internal only and are slightly larger in diameter than NPSF threads but have the same tolerance and thread length. They are more economical to produce than tapered threads and may be used in hard or brittle materials where the section is thick or where there is little expansion at assembly with external taper threads. As with NPSF threads, NPSI threads when assembled do not offer as strong a guarantee of sealing as do tapered internal threads.



1869

For more complete specifications for production and acceptance of Dryseal pipe threads, see ANSI B1.20.3 (Inch) and ANSI B1.20.4 (Metric Translation), and for gaging and inspection, see ANSI B1.20.5 (Inch) and ANSI B1.20.6M (Metric Translation). Designation of Dryseal Pipe Threads: The standard Dryseal pipe threads are designated by specifying in sequence nominal size, thread series symbol, and class: Examples: 1⁄8-27 NPTF-1; 1⁄8-27 PTF-SAE SHORT; and 3⁄8-18 NPTF-1 AFTER PLATING. Table 8. Suggested Tap Drill Sizes for Internal Dryseal Pipe Threads

Taper Pipe Thread Minor Diameter At Distance

Straight Pipe Thread

Drill Sizea

Minor Diameter

Size

Probable Drill Oversize Cut (Mean)

L1 From Large End

L1 + L 3 From Large End

Without Reamer

With Reamer

NPSF

NPSI

Drill Sizea

1⁄ –27 16

0.0038

0.2443

0.2374

“C” (0.242)

“A” (0.234)

0.2482

0.2505

“D” (0.246)

1⁄ –27 8

0.0044

0.3367

0.3298

“Q” (0.332)

21⁄ (0.328) 64

0.3406

0.3429

“R” (0.339)

0.4258

7⁄ (0.438) 16

27⁄ (0.422) 64

0.4422

0.4457

7⁄ (0.438) 16

9⁄ (0.563) 16

1⁄ –18 4

0.0047

0.4362

3⁄ –18 8

0.0049

0.5708

0.5604

9⁄ (0.562) 16

0.5776

0.5811

37⁄ (0.578) 64

1⁄ –14 2

0.0051

0.7034

0.6901

45⁄ (0.703) 64

11⁄ (0.688) 16

0.7133

0.7180

45⁄ (0.703) 64

0.8993

29⁄ (0.906) 32

57⁄ (0.891) 64

0.9238

0.9283

59⁄ (0.922) 64

1.1307

19⁄64 (1.141)

11⁄8 (1.125)

1.1600

1.1655

15⁄32 (1.156)

115⁄32 (1.469)

3⁄ –14 4

1–111⁄2

0.0060 0.0080

0.9127 1.1470

11⁄4–111⁄2

0.0100

1.4905

1.4742

131⁄64 (1.484)

…

…

…

11⁄2–111⁄2

0.0120

1.7295

1.7132

123⁄32 (1.719)

145⁄64 (1.703)

…

…

…

2–111⁄2

0.0160

2.2024

2.1861

23⁄16 (2.188)

211⁄64 (2.172)

…

…

…

21⁄2–8

0.0180

2.6234

2.6000

239⁄64 (2.609)

237⁄64 (2.578)

…

…

…

3–8

0.0200

3.2445

3.2211

315⁄64 (3.234)

313⁄64 (3.203)

…

…

…

a Some drill sizes listed may not be standard drills.


Special Dryseal Threads.—Where design limitations, economy of material, permanent installation, or other limiting conditions prevail, consideration may be given to using a special Dryseal thread series. Dryseal Special Short Taper Pipe Thread, PTF-SPL SHORT: Threads of this series conform in all respects to PTF-SAE SHORT threads except that the full thread length has been further shortened by eliminating one thread at the small end of internal threads or one thread at the large end of external threads.


Machinery's Handbook 28th Edition BRITISH PIPE THREADS

1870

Dryseal Special Extra Short Taper Pipe Thread, PTF-SPL EXTRA SHORT: Threads of this series conform in all respects to PTF-SAE SHORT threads except that the full thread length has been further shortened by eliminating two threads at the small end of internal threads or two threads at the large end of external threads. Limitations of Assembly: Table 9 applies where Dryseal Special Short or Extra Short Taper Pipe Threads are to be assembled as special combinations. Table 9. Assembly Limitations for Special Combinations of Dryseal Threads May Assemble witha

Thread

May Assemble withb

PTF SPL SHORT EXTERNAL PTF SPL EXTRA SHORT EXTERNAL

PTF-SAE SHORT INTERNAL NPSF INTERNAL PTF SPL SHORT INTERNAL PTF SPL EXTRA SHORT INTERNAL

NPTF or NPSI INTERNAL

PTF SPL SHORT INTERNAL PTF SPL EXTRA SHORT INTERNAL

PTF-SAE SHORT EXTERNAL

NPTF EXTERNAL

a Only when the external thread or the internal thread or both are held closer than the standard toler-

ance, the external thread toward the minimum and the internal thread toward the maximum pitch diameter to provide a minimum of one turn hand engagement. At extreme tolerance limits the shortened full-thread lengths reduce hand engagement and the threads may not start to assemble. b Only when the internal thread or the external thread or both are held closer than the standard tolerance, the internal thread toward the minimum and the external thread toward the maximum pitch diameter to provide a minimum of two turns for wrench make-up and sealing. At extreme tolerance limits the shortened full-thread lengths reduce wrench make-up and the threads may not seal.

Dryseal Fine Taper Thread Series, F-PTF: The need for finer pitches for nominal pipe sizes has brought into use applications of 27 threads per inch to 1⁄4- and 3⁄8-inch pipe sizes. There may be other needs that require finer pitches for larger pipe sizes. It is recommended that the existing threads per inch be applied to the next larger pipe size for a fine thread series, thus: 1⁄4-27, 3⁄8-27, 1⁄2-18, 3⁄4-18, 1-14, 11⁄4-14, 11⁄2-14, and 2-14. This series applies to external and internal threads of full length and is suitable for applications where threads finer than NPTF are required. Dryseal Special Diameter-Pitch Combination Series, SPL-PTF: Other applications of diameter-pitch combinations have come into use where taper pipe threads are applied to nominal size thin wall tubing. These combinations are: 1⁄2-27, 5⁄8-27, 3⁄4-27, 7⁄8-27, and 1-27. This series applies to external and internal threads of full length and is applicable to thin wall nominal diameter outside tubing. Designation of Special Dryseal Pipe Threads: The designations used for these special dryseal pipe threads are as follows: 1⁄ -27 PTF-SPL SHORT 8 1⁄ -27 PTF-SPL EXTRA SHORT 8 1⁄ -27 SPL PTF, OD 0.500 2 Note that in the last designation the OD of tubing is given. British Standard Pipe Threads British Standard Pipe Threads for Non-pressure-tight Joints.—The threads in BS 2779:1973, “Specifications for Pipe Threads where Pressure-tight Joints are not Made on the Threads”, are Whitworth form parallel fastening threads that are generally used for fastening purposes such as the mechanical assembly of component parts of fittings, cocks and valves. They are not suitable where pressure-tight joints are made on the threads. The crests of the basic Whitworth thread form may be truncated to certain limits of size given in the Standard except on internal threads, when they are likely to be assembled with external threads conforming to the requirements of BS 21 “British Standard Pipe Threads for Pressure-tight Joints” (see page 1871).



1871

For external threads two classes of tolerance are provided and for internal, one class. The two classes of tolerance for external threads are Class A and Class B. For economy of manufacture the class B fit should be chosen whenever possible. The class A is reserved for those applications where the closer tolerance is essential. Class A tolerance is an entirely negative value, equivalent to the internal thread tolerance. Class B tolerance is an entirely negative value twice that of class A tolerance. Tables showing limits and dimensions are given in the Standard. The thread series specified in this Standard shall be designated by the letter “G”. A typical reference on a drawing might be “G1⁄2”, for internal thread; “G1⁄2 A”, for external thread, class A: and “G 1⁄2 B”, for external thread, class B. Where no class reference is stated for external threads, that of class B will be assumed. The designation of truncated threads shall have the addition of the letter “T” to the designation, i.e., G 1⁄2 T and G 1⁄2 BT.

Threads per Incha

1⁄ 16

28

{

1⁄ 8

28

{

1⁄ 4

19

{

3⁄ 8

19

{

1⁄ 2

14

{

5⁄ 8

14

{

3⁄ 4

14

{

7⁄ 8

14

{

1

11

{

11⁄8

11

{

11⁄4

11

{

11

{

11⁄2

Depth of Major Thread Diameter 0.581 0.0229 0.581 0.0229 0.856 0.0337 0.856 0.0337 1.162 0.0457 1.162 0.0457 1.162 0.0457 1.162 0.0457 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582

7.723 0.3041 9.728 0.3830 13.157 0.5180 16.662 0.6560 20.955 0.8250 22.911 0.9020 26.441 1.0410 30.201 1.1890 33.249 1.3090 37.897 1.4920 41.910 1.6500 47.803 1.8820

Pitch Minor Diameter Diameter 7.142 0.2812 9.147 0.3601 12.301 0.4843 15.806 0.6223 19.793 0.7793 21.749 0.8563 25.279 0.9953 29.039 1.1433 31.770 1.2508 36.418 1.4338 40.431 1.5918 46.324 1.8238

6.561 0.2583 8.566 0.3372 11.445 0.4506 14.950 0.5886 18.631 0.7336 20.587 0.8106 24.117 0.9496 27.877 1.0976 30.291 1.1926 34.939 1.3756 38.952 1.5336 44.845 1.7656



British Standard Pipe Threads (Non-pressure-tight Joints) Metric and Inch Basic Sizes BS 2779:1973

13⁄4

Threads per Incha

11

{

2

11

{

21⁄4

11

{

21⁄2

11

{

23⁄4

11

{

3

11

{

31⁄2

11

{

4

11

{

41⁄2

11

{

5

11

{

51⁄2

11

{

6

11

{

Depth of Major Pitch Minor Thread Diameter Diameter Diameter 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582 1.479 0.0582

53.746 2.1160 59.614 2.3470 65.710 2.5870 75.184 2.9600 81.534 3.2100 87.884 3.4600 100.330 3.9500 113.030 4.4500 125.730 4.9500 138.430 5.4500 151.130 5.9500 163.830 6.4500

52.267 2.0578 58.135 2.2888 64.231 2.5288 73.705 2.9018 80.055 3.1518 86.405 3.4018 98.851 3.8918 111.551 4.3918 124.251 4.8918 136.951 5.3918 149.651 5.8918 162.351 6.3918

50.788 1.9996 56.656 2.2306 62.752 2.4706 72.226 2.8436 78.576 3.0936 84.926 3.3436 97.372 3.8336 110.072 4.3336 122.772 4.8336 135.472 5.3336 148.172 5.8336 160.872 6.3336

a The thread pitches in millimeters are as follows: 0.907 for 28 threads per inch. 1.337 for 19 threads

per inch, 1.814 for 14 threads per inch, and 2.309 for 11 threads per inch. Each basic metric dimension is given in roman figures (nominal sizes excepted) and each basic inch dimension is shown in italics directly beneath it.

British Standard Pipe Threads for Pressure-tight Joints.—T h e t h r e a d s i n B S 21:1973, “Specification for Pipe Threads where Pressure-tight Joints are Made on the Threads”, are based on the Whitworth thread form and are specified as: 1) Jointing threads: These relate to pipe threads for joints made pressure-tight by the mating of the threads; they include taper external threads for assembly with either taper or parallel internal threads (parallel external pipe threads are not suitable as jointing threads) 2) Longscrew threads: These relate to parallel external pipe threads used for longscrews (connectors) specified in BS 1387 where a pressure-tight joint is achieved by the compression of a soft material onto the surface of the external thread by tightening a back nut against a socket



1872

British Standard External and Internal Pipe Threads (Pressure-tight Joints) Metric and Inch Dimensions and Limits of Size BS 21:1973 Basic Diameters at Gage Plane

Nominal Size 1⁄ 16

No. of Threads per Incha 28

Major {

1⁄ 8

28

{

1⁄ 4

19

{

3⁄ 8

19

{

1⁄ 2

14

{

3⁄ 4

1

14

{

11

{

11⁄4

11

{

11⁄2

11

{

2

11

{

21⁄2

11

{

3

11

{

4

11

{

5

11

{

6

11

{

Gage Length

Tolerance + and − Number of Useful On Threads Gage Diameon Pipe Plane to ter of for Basic Face of TolerParallel Gage ance Int. Taper Int. (+ and −) Lengthb Thread Threads

Pitch

Minor

Basic

7.723

7.142

6.561

(43⁄8)

(1)

(71⁄8)

(11⁄4)

0.071

0.304

0.2812

0.2583

4.0

0.9

6.5

1.1

0.0028

9.728

9.147

8.566

(43⁄8)

(1)

(71⁄8)

(11⁄4)

0.071

0.383

0.3601

0.3372

4.0

0.9

6.5

1.1

0.0028

(41⁄2)

(1)

(71⁄4)

(11⁄4)

0.104

6.0

1.3

9.7

1.7

0.0041

(43⁄4)

(1)

(71⁄2)

(11⁄4)

0.104

6.4

1.3

10.1

1.7

0.0041

(41⁄2)

(1)

(71⁄4)

(11⁄4)

0.142

8.2

1.8

13.2

2.3

0.0056

(51⁄4)

(1)

(8)

(11⁄4)

0.142

9.5

1.8

14.5

2.3

0.0056

(41⁄2)

(1)

(71⁄4)

(11⁄4)

0.180

10.4

2.3

16.8

2.9

0.0071

(51⁄2)

(1)

(81⁄4)

(11⁄4)

0.180

12.7

2.3

19.1

2.9

0.0071

(51⁄2)

(1)

(81⁄4)

(11⁄4)

0.180

12.7

2.3

19.1

2.9

0.0071

(67⁄8)

(1)

(101⁄8)

(11⁄4)

0.180

15.9

2.3

23.4

2.9

0.0071

(79⁄16)

(11⁄2)

(119⁄16)

(11⁄2)

0.216

17.5

3.5

26.7

3.5

0.0085

(815⁄16)

(11⁄2)

(1215⁄16)

(11⁄2)

0.216

20.6

3.5

29.8

3.5

0.0085

(11)

(11⁄2)

(151⁄2)

(11⁄2)

0.216

25.4

3.5

35.8

3.5

0.0085

(123⁄8)

(11⁄2)

(173⁄8)

(11⁄2)

0.216

28.6

3.5

40.1

3.5

0.0085

(123⁄8)

(11⁄2)

(173⁄8)

(11⁄2)

0.216

28.6

3.5

40.1

3.5

0.0085

13.157 0.518 16.662 0.656 20.955 0.825 26.441 1.041 33.249 1.309 41.910 1.650 47.803 1.882 59.614 2.347 75.184 2.960 87.884 3.460 113.030 4.450 138.430 5.450 163.830 6.450

12.301 0.4843 15.806 0.6223 19.793 0.7793 25.279 0.9953 31.770 1.2508 40.431 1.5918 46.324 1.8238 58.135 2.2888 73.705 2.9018 86.405 3.4018 111.551 4.3918 136.951 5.3918 162.351 6.3918

11.445 0.4506 14.950 0.5886 18.631 0.7336 24.117 0.9496 30.291 1.1926 38.952 1.5336 44.845 1.7656 56.656 2.2306 72.226 2.8436 84.926 3.3436 110.072 4.3336 135.472 5.3336 160.872 6.3336

a In

the Standard BS 21:1973 the thread pitches in millimeters are as follows: 0.907 for 28 threads per inch, 1.337 for 19 threads per inch, 1.814 for 14 threads per inch, and 2.309 for 11 threads per inch. b This is the minimum number of useful threads on the pipe for the basic gage length; for the maximum and minimum gage lengths, the minimum numbers of useful threads are, respectively, greater and less by the amount of tolerance in the column to the left. The design of internally threaded parts shall make allowance for receiving pipe ends of up to the minimum number of useful threads corresponding to the maximum gage length; the minimum number of useful internal threads shall be no less than 80 per cent of the minimum number of useful external threads for the minimum gage length. Each basic metric dimension is given in roman figures (nominal sizes excepted) and each basic inch dimension is shown in italics directly beneath it. Figures in ( ) are numbers of turns of thread with metric linear equivalents given beneath. Taper of taper thread is 1 in 16 on diameter.


Machinery's Handbook 28th Edition HOSE COUPLING SCREW THREADS

1873

Hose Coupling Screw Threads ANSI Standard Hose Coupling Screw Threads.—Threads for hose couplings, valves, and all other fittings used in direct connection with hose intended for domestic, industrial, and general service in sizes 1⁄2, 5⁄8, 3⁄4, 1, 11⁄4, 11⁄2, 2, 21⁄2, 3, 31⁄2, and 4 inches are covered by American National Standard ANSI/ASME B1.20.7-1991 These threads are designated as follows: NH — Standard hose coupling threads of full form as produced by cutting or rolling. NHR — Standard hose coupling threads for garden hose applications where the design utilizes thin walled material which is formed to the desired thread. NPSH — Standard straight hose coupling thread series in sizes 1⁄2 to 4 inches for joining to American National Standard taper pipe threads using a gasket to seal the joint. Thread dimensions are given in Table 1 and thread lengths in Table 2. p p 24

INTERNAL THREAD (COUPLING SWIVEL)

h 18

h 6

f

h

MIN

BASIC MINOR DIAM.

MIN

MAX

MAX MIN

MIN

MAX

PITCH DIAM. OF EXTERNAL THREAD

p 8

MINOR DIAM. EXTERNAL THREAD

= 1 h = 0.108253p 6

MINOR DIAM. INTERNAL THREAD

p = PITCH h = BASIC THREAD HEIGHT = 0.649519p f = BASIC TRUNCATION

BASIC PITCH DIAMETER

MAX

30˚

PITCH DIAM. OF INTERNAL THREAD

EXTERNAL THREAD (NIPPLE)

h 2

60˚

MIN

MAX MAJOR DIAM. EXTERNAL THREAD

PERMISSIBLE PROFILE WITH WORN TOOL

1 2 allowance (external thread only)

BASIC MAJOR DIAM., D.

MAJOR DIAM. OF INTERNAL THREAD

MAX WITH WORN TOOL MIN

p 8

h 18

p 24 90˚

AXIS OF SCREW THREAD

Fig. 1. Thread Form for ANSI Standard Hose Coupling Threads, NPSH, NH, and NHR. Heavy Line Shows Basic Size.



Nipple (External) Thread Threads per Inch

Thread Designation

1⁄ , 5⁄ , 3⁄ 2 8 4

11.5

.75-11.5NH

1⁄ , 5⁄ , 3⁄ 2 8 4

Coupling (Internal) Thread

Pitch

Basic Height of Thread

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

Max.

Min.

.08696

.05648

1.0625

1.0455

1.0060

0.9975

0.9495

0.9595

0.9765

1.0160

1.0245

1.0725

Major Dia.

Pitch Dia.

Minor Dia.

Minor Dia.

Pitch Dia.

Major Dia.

11.5

.75-11.5NHR

.08696

.05648

1.0520

1.0350

1.0100

0.9930

0.9495

0.9720

0.9930

1.0160

1.0280

1.0680

1⁄ 2

14

.5-14NPSH

.07143

.04639

0.8248

0.8108

0.7784

0.7714

0.7320

0.7395

0.7535

0.7859

0.7929

0.8323

3⁄ 4

14

.75-14NPSH

.07143

.04639

1.0353

1.0213

0.9889

0.9819

0.9425

0.9500

0.9640

0.9964

1.0034

1.0428

1 11⁄4

11.5 11.5

1-11.5NPSH .08696 1.25-11.5NPSH .08696

.05648 .05648

1.2951 1.6399

1.2781 1.6229

1.2396 1.5834

1.2301 1.5749

1.1821 1.5269

1.1921 1.5369

1.2091 1.5539

1.2486 1.5934

1.2571 1.6019

1.3051 1.6499

11⁄2

11.5

1.5-11.5 NPSH

.08696

.05648

1.8788

1.8618

1.8223

1.8138

1.7658

1.7758

1.7928

1.8323

1.8408

1.8888

2 21⁄2

11.5 8

2-11.5NPSH 2.5-8NPSH

.08696 .12500

.05648 .08119

2.3528 2.8434

2.3358 2.8212

2.2963 2.7622

2.2878 2.7511

2.2398 2.6810

2.2498 2.6930

2.2668 2.7152

2.3063 2.7742

2.3148 2.7853

2.3628 2.8554

3 31⁄2

8 8

3-8NPSH 3.5-8NPSH

.12500 .12500

.08119 .08119

3.4697 3.9700

3.4475 3.9478

3.3885 3.8888

3.3774 3.8777

3.3073 3.8076

3.3193 3.8196

3.3415 3.8418

3.4005 3.9008

3.4116 3.9119

3.4817 3.9820

4 4

8 6

4-8NPSH 4-6NH (SPL)

.12500 .16667

.08119 .10825

4.4683 4.9082

4.4461 4.8722

4.3871 4.7999

4.3760 4.7819

4.3059 4.6916

4.3179 4.7117

4.3401 4.7477

4.3991 4.8200

4.4102 4.8380

4.4803 4.9283

All dimensions are given in inches. Dimensions given for the maximum minor diameter of the nipple are figured to the intersection of the worn tool arc with a centerline through crest and root. The minimum minor diameter of the nipple shall be that corresponding to a flat at the minor diameter of the minimum nipple equal to 1⁄24p, and may be determined by subtracting 0.7939p from the minimum pitch diameter of the nipple. (See Fig. 1) Dimensions given for the minimum major diameter of the coupling correspond to the basic flat, 1⁄8p, and the profile at the major diameter produced by a worn tool must not fall below the basic outline. The maximum major diameter of the coupling shall be that corresponding to a flat at the major diameter of the maximum coupling equal to 1⁄24p and may be determined by adding 0.7939p to the maximum pitch diameter of the coupling. (See Fig. 1) NH and NHR threads are used for garden hose applications. NPSH threads are used for steam, air and all other hose connections to be made up with standard pipe threads. NH (SPL) threads are used for marine applications.


HOSE COUPLING SCREW THREADS

Nominal Size of Hose

1874

Table 1. ANSI Standard Hose Coupling Threads for NPSH, NH, and NHR Nipples and Coupling Swivels ANSI/ASME B1.20.7-1991 (R2003)


1875

Table 2. ANSI Standard Hose Coupling Screw Thread Lengths ANSI/ASME B1.20.7-1991 (R2003)

Nominal Size of Hose

I.D. of Nipple, C

Approx. Approx. O.D. Length Length Depth Coupl. No. of of of of Thd. Thds. in Ext. Nipple, Pilot, Coupl., Length, Length Thd. L I H T T

1⁄ , 5⁄ , 3⁄ 2 8 4

Threads per Inch 11.5

25⁄ 32

11⁄16

9⁄ 16

1⁄ 8

17⁄ 32

3⁄ 8

41⁄4

1⁄ , 5⁄ , 3⁄ 2 8 4

11.5

25⁄ 32

11⁄16

9⁄ 16

1⁄ 8

17⁄ 32

3⁄ 8

41⁄4

1⁄ 2

14

17⁄ 32

13⁄ 16

1⁄ 2

1⁄ 8

15⁄ 32

5⁄ 16

41⁄4

3⁄ 4

14

25⁄ 32

11⁄32

9⁄ 16

1⁄ 8

17⁄ 32

3⁄ 8

51⁄4

1

11.5

11⁄32

19⁄32

9⁄ 16

5⁄ 32

17⁄ 32

3⁄ 8

41⁄4

11⁄4

11.5

19⁄32

15⁄8

5⁄ 8

5⁄ 32

19⁄ 32

15⁄ 32

51⁄2

11.5

117⁄32

17⁄8

5⁄ 8

5⁄ 32

19⁄ 32

15⁄ 32

51⁄2

211⁄32

3⁄ 4

3⁄ 16

23⁄ 32

19⁄ 32

63⁄4

11⁄2

11.5

21⁄32

21⁄2

8

217⁄32

227⁄32

1

1⁄ 4

15⁄ 16

11⁄ 16

51⁄2

3

8

31⁄32

315⁄32

11⁄8

1⁄ 4

11⁄16

13⁄ 16

61⁄2

31⁄2

8

317⁄32

331⁄32

11⁄8

1⁄ 4

11⁄16

13⁄ 16

61⁄2

4

8

41⁄32

415⁄32

11⁄8

1⁄ 4

11⁄16

13⁄ 16

61⁄2

4

6

4

429⁄32

11⁄8

5⁄ 16

11⁄16

3⁄ 4

41⁄2

2

All dimensions are given in inches. For thread designation see Table 1.

American National Fire Hose Connection Screw Thread.—This thread is specified in the National Fire Protection Association's Standard NFPA No. 194-1974. It covers the dimensions for screw thread connections for fire hose couplings, suction hose couplings, relay supply hose couplings, fire pump suctions, discharge valves, fire hydrants, nozzles, adaptors, reducers, caps, plugs, wyes, siamese connections, standpipe connections, and sprinkler connections. Form of Thread: The basic form of thread is as shown in Fig. 1. It has an included angle of 60 degrees and is truncated top and bottom. The flat at the root and crest of the basic thread form is equal to 1⁄8 (0.125) times the pitch in inches. The height of the thread is equal to 0.649519 times the pitch. The outer ends of both external and internal threads are terminated by the blunt start or “Higbee Cut” on full thread to avoid crossing and mutilation of thread. Thread Designation: The thread is designated by specifying in sequence the nominal size of the connection, number of threads per inch followed by the thread symbol NH.



1876

Thus, .75-8NH indicates a nominal size connection of 0.75 inch diameter with 8 threads per inch. Basic Dimensions: The basic dimensions of the thread are as given in Table 1. Table 1. Basic Dimensions of NH Threads NFPA 1963–1993 Edition Nom. Size 3⁄ 4 1 1 1 ⁄2

Threads per Inch (tpi) 8 8 9

Thread Designation 0.75-8 NH

Pitch, p 0.12500

BasicThread Height, h 0.08119

1-8 NH 1.5-9 NH

0.12500 0.11111

0.08119 0.07217

Minimum Internal Thread Dimensions Min. Minor Basic Pitch BasicMajor Dia. Dia. Dia. 1.2246 1.3058 1.3870 1.2246 1.8577

1.3058 1.9298

1.3870 2.0020

21⁄2

7.5

2.5-7.5 NH

0.13333

0.08660

2.9104

2.9970

3.0836

3 31⁄2 4 41⁄2 5 6

6 6

3-6 NH 3.5-6 NH

0.16667 0.16667

0.10825 0.10825

3.4223 4.0473

3.5306 4.1556

3.6389 4.2639

4 4

4-4 NH 4.5-4 NH

0.25000 0.25000

0.16238 0.16238

4.7111 5.4611

4.8735 5.6235

5.0359 5.7859

5-4 NH 6-4 NH

0.25000 0.25000

0.16238 0.16238

Thread Designation 0.75-8 NH

Pitch, p 0.12500

1-8 NH 1.5-9 NH

0.12500 0.11111

0.0120 0.0120

1.3750 1.9900

1.2938 1.9178

1.2126 1.8457

Nom. Size 3⁄ 4 1 11⁄2

21⁄2 3 31⁄2 4 41⁄2 5 6

4 4 Threads per Inch (tpi) 8 8 9 7.5

5.9602 6.1226 6.2850 6.7252 6.8876 7.0500 External Thread Dimensions (Nipple) Max.Major Max. Pitch Max Minor Allowance Dia. Dia. Dia. 0.0120 1.3750 1.2938 1.2126

2.5-7.5 NH

0.13333

0.0150

3.0686

2.9820

2.8954

6 6

3-6 NH 3.5-6 NH

0.16667 0.16667

0.0150 0.0200

3.6239 4.2439

3.5156 4.1356

3.4073 4.0273

4 4

4-4 NH 4.5-4 NH

0.25000 0.25000

0.0250 0.0250

5.0109 5.7609

4.8485 5.5985

4.6861 5.4361

4 4

5-4 NH 6-4 NH

0.25000 0.25000

0.0250 0.0250

6.2600 7.0250

6.0976 6.8626

5.9352 6.7002


Thread Limits of Size: Limits of size for NH external threads are given in Table 2. Limits of size for NH internal threads are given in Table 3. Tolerances: The pitch-diameter tolerances for mating external and internal threads are the same. Pitch-diameter tolerances include lead and half-angle deviations. Lead deviations consuming one-half of the pitch-diameter tolerance are 0.0032 inch for 3⁄4-, 1-, and 11⁄2-inch sizes; 0.0046 inch for 21⁄2-inch size; 0.0052 inch for 3-, and 31⁄2-inch sizes; and 0.0072 inch for 4-, 41⁄2-, 5-, and 6-inch sizes. Half-angle deviations consuming one-half of the pitch-diameter tolerance are 1 degree, 42 minutes for 3⁄4- and 1-inch sizes; 1 degree, 54 minutes for 11⁄2-inch size; 2 degrees, 17 minutes for 21⁄2-inch size; 2 degrees, 4 minutes for 3- and 31⁄2-inch size; and 1 degree, 55 minutes for 4-, 41⁄2-, 5-, and 6-inch sizes. Tolerances for the external threads are: Major diameter tolerance = 2 × pitch-diameter tolerance Minor diameter tolerance = pitch-diameter tolerance + 2h/9 The minimum minor diameter of the external thread is such as to result in a flat equal to one-third of the p/8 basic flat, or p/24, at the root when the pitch diameter of the external thread is at its minimum value. The maximum minor diameter is basic, but may be such as results from the use of a worn or rounded threading tool. The maximum minor diameter is shown in Fig. 1 and is the diameter upon which the minor diameter tolerance formula shown above is based. Tolerances for the internal threads are:



1877

Minor diameter tolerance = 2 × pitch-diameter tolerance The minimum minor diameter of the internal thread is such as to result in a basic flat, p/8, at the crest when the pitch diameter of the thread is at its minimum value. Major diameter tolerance = pitch-diameter tolerance - 2h/9 Table 2. Limits of Size and Tolerances for NH External Threads (Nipples) NFPA 1963, 1993 Edition External Thread (Nipple)

Nom. Size

Threads per Inch (tpi)

Max.

Min.

Toler.

Max.

Min.

Toler.

Minora Dia. Max.

3⁄ 4 1 1 1 ⁄2

8

1.3750

1.3528

0.0222

1.2938

1.2827

0.0111

1.2126

8 9

1.3750 1.9900

1.3528 1.9678

0.0222 0.0222

1.2938 1.9178

1.2827 1.9067

0.0111 0.0111

1.2126 1.8457

21⁄2

7.5

3.0686

3.0366

0.0320

2.9820

2.9660

0.0160

2.8954

3 31⁄2 4 41⁄2 5 6

6 6

3.6239 4.2439

3.5879 4.2079

0.0360 0.0360

3.5156 4.1356

3.4976 4.1176

0.0180 0.0180

3.4073 4.0273

4 4

5.0109 5.7609

4.9609 5.7109

0.0500 0.0500

4.8485 5.5985

4.8235 5.5735

0.0250 0.0250

4.6861 5.4361

4 4

6.2600 7.0250

6.2100 6.9750

0.0500 0.0500

6.0976 6.8626

6.0726 6.8376

0.0250 0.0250

5.9352 6.7002

Major Diameter

Pitch Diameter

a Dimensions given for the maximum minor diameter of the nipple are figured to the intersection of the worn tool arc with a center line through crest and root. The minimum minor diameter of the nipple shall be that corresponding to a flat at the minor diameter of the minimum nipple equal to p/24 and may be determined by subtracting 11h/9 (or 0.7939p) from the minimum pitch diameter of the nipple.


Table 3. Limits of Size and Tolerances for NH Internal Threads (Couplings) NFPA 1963, 1993 Edition Internal Thread (Coupling)

Nom. Size

Threads per Inch (tpi)

Min.

Max.

Toler.

Min.

Max.

Toler.

Majora Dia. Min.

3⁄ 4 1 1 1 ⁄2

8

1.2246

1.2468

0.0222

1.3058

1.3169

0.0111

1.3870

8 9

1.2246 1.8577

1.2468 1.8799

0.0222 0.0222

1.3058 1.9298

1.3169 1.9409

0.0111 0.0111

1.3870 2.0020

21⁄2 3 31⁄2 4 41⁄2 5 6

Minor Diameter

Pitch Diameter

7.5

2.9104

2.9424

0.0320

2.9970

3.0130

0.0160

3.0836

6 6

3.4223 4.0473

3.4583 4.0833

0.0360 0.0360

3.5306 4.1556

3.5486 4.1736

0.0180 0.0180

3.6389 4.2639

4 4

4.7111 5.4611

4.7611 5.5111

0.0500 0.0500

4.8735 5.6235

4.8985 5.6485

0.0250 0.0250

5.0359 5.7859

4 4

5.9602 6.7252

6.0102 6.7752

0.0500 0.0500

6.1226 6.8876

6.1476 6.9126

0.0250 0.0250

6.2850 7.0500

a Dimensions for the minimum major diameter of the coupling correspond to the basic flat (p/8), and the profile at the major diameter produced by a worn tool must not fall below the basic outline. The maximum major diameter of the coupling shall be that corresponding to a flat at the major diameter of the maximum coupling equal to p/24 and may be determined by adding 11h/9 (or 0.7939p) to the maximum pitch diameter of the coupling.


Gages and Gaging: Full information on gage dimensions and the use of gages in checking the NH thread are given in NFPA Standard No. 1963, 1993 Edition, published by the National Fire Protection Association, Batterymarch Park, Quincy, MA 02269. The information and data taken from this standard are reproduced with the permission of the NFPA.


Machinery's Handbook 28th Edition INTERFERENCE FIT THREADS

1878

OTHER THREADS Interference-Fit Threads Interference-Fit Threads.—Interference-fit threads are threads in which the externally threaded member is larger than the internally threaded member when both members are in the free state and that, when assembled, become the same size and develop a holding torque through elastic compression, plastic movement of material, or both. By custom, these threads are designated Class 5. The data in Tables 1, 2, and 3, which are based on years of research, testing and field study, represent an American standard for interference-fit threads that overcomes the difficulties experienced with previous interference-fit recommendations such as are given in Federal Screw Thread Handbook H28. These data were adopted as American Standard ASA B1.12-1963. Subsequently, the standard was revised and issued as American National Standard ANSI B1.12-1972. More recent research conducted by the Portsmouth Naval Shipyard has led to the current revision ASME/ANSI B1.12-1987 (R2003). The data in Tables 1, 2, and 3 provide dimensions for external and internal interferencefit (Class 5) threads of modified American National form in the Coarse Thread series, sizes 1⁄ inch to 11⁄ inches. It is intended that interference-fit threads conforming with this stan4 2 dard will provide adequate torque conditions which fall within the limits shown in Table 3. The minimum torques are intended to be sufficient to ensure that externally threaded members will not loosen in service; the maximum torques establish a ceiling below which seizing, galling, or torsional failure of the externally threaded components is reduced. Tables 1 and 2 give external and internal thread dimensions and are based on engagement lengths, external thread lengths, and tapping hole depths specified in Table 3 and in compliance with the design and application data given in the following paragraphs. Table 4 gives the allowances and Table 5 gives the tolerances for pitch, major, and minor diameters for the Coarse Thread Series. .125P .125H

Major Dia.

60˚

.625H H 30˚

.5P Pitch Dia.

.250H .250P

Minor Dia.

P 90˚ Axis of Screw Thread

Basic Profile of American National Standard Class 5 Interference Fit Thread


Machinery's Handbook 28th Edition INTERFERENCE FIT THREADS

1879

Internal Thread Max. Material Stud (Largest Stud)

Max. Material Tapped Hole (Smallest Tapped Hole)

External Thread

Max. Major Dia. Max. Pitch Dia. Minor Dia. (Design Form)

Min. Pitch Dia.

Max. Interference

Min. Minor Dia.

MAXIMUM INTERFERENCE

Internal Thread Min. Material Stud (Smallest Stud)

Min. Material Tapped Hole (Largest Tapped Hole)

External Thread

Major Dia. Min. Pitch Dia.

Max. Pitch Dia. Min. Interference

Max. Minor Dia. P __ 8

Min. Minor Dia.

MINIMUM INTERFERENCE Note: Plastic flow of interference metal into cavities at major and minor diameters is not illustrated.

Maximum and Minimum Material Limits for Class 5 Interference-Fit Thread

Design and Application Data for Class 5 Interference-Fit Threads.—Following are conditions of usage and inspection on which satisfactory application of products made to dimensions in Tables 1, 2, and 3 are based. Thread Designations: The following thread designations provide a means of distinguishing the American Standard Class 5 Threads from the tentative Class 5 and alternate Class 5 threads, specified in Handbook H28. They also distinguish between external and internal American Standard Class 5 Threads. Class 5 External Threads are designated as follows: NC-5 HF—For driving in hard ferrous material of hardness over 160 BHN. NC-5 CSF—For driving in copper alloy and soft ferrous material of 160 BHN or less. NC-5 ONF—For driving in other nonferrous material (nonferrous materials other than copper alloys), any hardness. Class 5 Internal Threads are designated as follows: NC-5 IF—Entire ferrous material range. NC-5 INF—Entire nonferrous material range.


Machinery's Handbook 28th Edition INTERFERENCE-FIT THREADS

1880

Table 1. External Thread Dimensions for Class 5 Interference-Fit Threads ANSI/ASME B1.12-1987 (R2003) Major Diameter, Inches

Nominal Size

NC-5 HF for driving in ferrous material with hardness greater than 160 BHN Le = 11⁄4 Diam.

NC-5 CSF for driving in brass and ferrous material with hardness equal to or less than 160 BHN Le = 11⁄4 Diam.

NC-5 ONF for driving in nonferrous except brass (any hardness) Le = 21⁄2 Diam.

Pitch Diameter, Inches

Minor Diameter, Inches

Max

Min

Max

Min

Max

Min

Max

Min

Max

0.2500–20

0.2470

0.2418

0.2470

0.2418

0.2470

0.2418

0.2230

0.2204

0.1932

0.3125–18

0.3080

0.3020

0.3090

0.3030

0.3090

0.3030

0.2829

0.2799

0.2508

0.3750–16

0.3690

0.3626

0.3710

0.3646

0.3710

0.3646

0.3414

0.3382

0.3053

0.4375–14

0.4305

0.4233

0.4330

0.4258

0.4330

0.4258

0.3991

0.3955

0.3579

0.5000–13

0.4920

0.4846

0.4950

0.4876

0.4950

0.4876

0.4584

0.4547

0.4140

0.5625–12

0.5540

0.5460

0.5575

0.5495

0.5575

0.5495

0.5176

0.5136

0.4695

0.6250–11

0.6140

0.6056

0.6195

0.6111

0.6195

0.6111

0.5758

0.5716

0.5233

0.7500–10

0.7360

0.7270

0.7440

0.7350

0.7440

0.7350

0.6955

0.6910

0.6378

0.8750– 9

0.8600

0.8502

0.8685

0.8587

0.8685

0.8587

0.8144

0.8095

0.7503

1.0000– 8

0.9835

0.9727

0.9935

0.9827

0.9935

0.9827

0.9316

0.9262

0.8594

1.1250– 7

1.1070

1.0952

1.1180

1.1062

1.1180

1.1062

1.0465

1.0406

0.9640

1.2500– 7

1.2320

1.2200

1.2430

1.2312

1.2430

1.2312

1.1715

1.1656

1.0890

1.3750– 6

1.3560

1.3410

1.3680

1.3538

1.3680

1.3538

1.2839

1.2768

1.1877

1.5000– 6

1.4810

1.4670

1.4930

1.4788

1.4930

1.4788

1.4089

1.4018

1.3127

Based on external threaded members being steel ASTM A-325 (SAE Grade 5) or better. Le = length of engagement.

Table 2. Internal Thread Dimensions for Class 5 Interference-Fit Threads ANSI/ASME B1.12-1987 (R2003) NC-5 IF Ferrous Material Minor

Nominal Size

Min

0.2500–20

0.196

0.3125–18 0.3750–16

Diam.a

NC-5 INF Nonferrous Material Minor Diam.a

Max

Tap Drill

Min

0.206

0.2031

0.196

0.252

0.263

0.2610

0.307

0.318

0.3160

0.4375–14

0.374

0.381

0.5000–13

0.431

0.5625–12 0.6250–11

Pitch Diameter

Major Diam.

Max

Tap Drill

Min

Max

Min

0.206

0.2031

0.2175

0.2201

0.2532

0.252

0.263

0.2610

0.2764

0.2794

0.3161

0.307

0.318

0.3160

0.3344

0.3376

0.3790

0.3750

0.360

0.372

0.3680

0.3911

0.3947

0.4421

0.440

0.4331

0.417

0.429

0.4219

0.4500

0.4537

0.5050

0.488

0.497

0.4921

0.472

0.485

0.4844

0.5084

0.5124

0.5679

0.544

0.554

0.5469

0.527

0.540

0.5313

0.5660

0.5702

0.6309

0.7500–10

0.667

0.678

0.6719

0.642

0.655

0.6496

0.6850

0.6895

0.7565

0.8750– 9

0.777

0.789

0.7812

0.755

0.769

0.7656

0.8028

0.8077

0.8822

1.0000– 8

0.890

0.904

0.8906

0.865

0.880

0.8750

0.9188

0.9242

1.0081

1.1250– 7

1.000

1.015

1.0000

0.970

0.986

0.9844

1.0322

1.0381

1.1343

1.2500– 7

1.125

1.140

1.1250

1.095

1.111

1.1094

1.1572

1.1631

1.2593

1.3750– 6

1.229

1.247

1.2344

1.195

1.213

1.2031

1.2667

1.2738

1.3858

1.5000– 6

1.354

1.372

1.3594

1.320

1.338

1.3281

1.3917

1.3988

1.5108

a Fourth decimal place is 0 for all sizes.

All dimensions are in inches, unless otherwise specified.

Externally Threaded Products: Points of externally threaded components should be chamfered or otherwise reduced to a diameter below the minimum minor diameter of the thread. The limits apply to bare or metallic coated parts. The threads should be free from excessive nicks, burrs, chips, grit or other extraneous material before driving.



1881

Table 3. Torques, Interferences, and Engagement Lengths for Class 5 Interference-Fit Threads ANSI/ASME B1.12-1987 (R2003) Engagement Lengths, External Thread Lengths and Tapped Hole Depthsa Interference on Pitch Diameter Nominal Size 0.2500–20

Max .0055

Min .0003

In Brass and Ferrous Le 0.312

Ts 0.375 + .125 − 0

In Nonferrous Except Brass Th min 0.375

Le 0.625

Ts 0.688 + .125 − 0

Th min 0.688

Torque at 1-1⁄4D Engagement in Ferrous Material Max, lb-ft 12

Min, lb-ft 3

0.3125–18

.0065

.0005

0.391

0.469 + .139 − 0

0.469

0.781

0.859 + .139 − 0

0.859

19

6

0.3750–16

.0070

.0006

0.469

0.562 + .156 − 0

0.562

0.938

1.031 + .156 − 0

1.031

35

10

0.4375–14

.0080

.0008

0.547

0.656 + .179 − 0

0.656

1.094

1.203 + .179 − 0

1.203

45

15

0.5000–13

.0084

.0010

0.625

0.750 + .192 − 0

0.750

1.250

1.375 + .192 − 0

1.375

75

20

0.5625–12

.0092

.0012

0.703

0.844 + .208 − 0

0.844

1.406

1.547 + .208 − 0

1.547

90

30

0.6250–11

.0098

.0014

0.781

0.938 + .227 − 0

0.938

1.562

1.719 + .227 − 0

1.719

120

37

0.7500–10

.0105

.0015

0.938

1.125 + .250 − 0

1.125

1.875

2.062 + .250 − 0

0.8750– 9

.0016

.0018

1.094

1.312 + .278 − 0

1.312

2.188

2.406 + .278 − 0

2.406

250

90

1.0000– 8

.0128

.0020

1.250

1.500 + .312 − 0

1.500

2.500

2.750 + .312 − 0

2.750

400

125

1.1250– 7

.0143

.0025

1.406

1.688 + .357 − 0

1.688

2.812

3.094 + .357 − 0

3.095

470

155

2.062

190

60

1.2500– 7

.0143

.0025

1.562

1.875 + .357 − 0

1.875

3.125

3.438 + .357 − 0

3.438

580

210

1.3750– 6

.0172

.0030

1.719

2.062 + .419 − 0

2.062

3.438

3.781 + .419 − 0

3.781

705

250

1.5000– 6

.0172

.0030

1.875

2.250 + .419 − 0

2.250

3.750

4.125 + .419 − 0

4.125

840

325

a L = Length of engagement. T = External thread length of full form thread. T = Minimum depth of e s h

full form thread in hole. All dimensions are inches.

Materials for Externally Threaded Products: The length of engagement, depth of thread engagement and pitch diameter in Tables 1, 2, and 3 are designed to produce adequate torque conditions when heat-treated medium-carbon steel products, ASTM A-325 (SAE Grade 5) or better, are used. In many applications, case-carburized and nonheat-treated medium-carbon steel products of SAE Grade 4 are satisfactory. SAE Grades 1 and 2, may be usable under certain conditions. This standard is not intended to cover the use of products made of stainless steel, silicon bronze, brass or similar materials. When such materials are used, the tabulated dimensions will probably require adjustment based on pilot experimental work with the materials involved. Lubrication: For driving in ferrous material, a good lubricant sealer should be used, particularly in the hole. A non-carbonizing type of lubricant (such as a rubber-in-water dispersion) is suggested. The lubricant must be applied to the hole and it may be applied to the male member. In applying it to the hole, care must be taken so that an excess amount of lubricant will not cause the male member to be impeded by hydraulic pressure in a blind hole. Where sealing is involved, the lubricant selected should be insoluble in the medium being sealed. For driving, in nonferrous material, lubrication may not be needed. The use of medium gear oil for driving in aluminum is recommended. American research has observed that the minor diameter of lubricated tapped holes in non-ferrous materials may tend to close in, that is, be reduced in driving; whereas with an unlubricated hole the minor diameter may tend to open up. Driving Speed: This standard makes no recommendation for driving speed. Some opinion has been advanced that careful selection and control of driving speed is desirable to obtain optimum results with various combinations of surface hardness and roughness. Experience with threads made to this standard may indicate what limitations should be placed on driving speeds.



1882

Table 4. Allowances for Coarse Thread Series ANSI/ASME B1.12-1987 (R2003)

TPI 20 18 16 14 13 12 11 10 9 8 7 6

Difference between Nom. Size and Max Major Diam of NC-5 HFa

Difference between Nom. Size and Max Major Diam. of NC-5 CSF or NC-5 ONFa

Difference between Basic Minor Diam. and Min Minor Diam. of NC-5 IFa

Difference between Basic Minor Diam. and Min Minor Diam.of NC-5 INF

Max PD Inteference or Neg Allowance, Ext Threadb

Difference between Max Minor Diam. and Basic Minor Diam., Ext Thread

0.0030 0.0045 0.0060 0.0070 0.0080 0.0085 0.0110 0.0140 0.0150 0.0165 0.0180 0.0190

0.0030 0.0035 0.0040 0.0045 0.0050 0.0050 0.0055 0.0060 0.0065 0.0065 0.0070 0.0070

0.000 0.000 0.000 0.014 0.014 0.016 0.017 0.019 0.022 0.025 0.030 0.034

0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000

0.0055 0.0065 0.0070 0.0080 0.0084 0.0092 0.0098 0.0105 0.0116 0.0128 0.0143 0.0172

0.0072 0.0080 0.0090 0.0103 0.0111 0.0120 0.0131 0.0144 0.0160 0.0180 0.0206 0.0241

a The allowances in these columns were obtained from industrial research data. b Negative allowance is the difference between the basic pitch diameter and pitch diameter value at maximum material condition.

All dimensions are in inches. The difference between basic major diameter and internal thread minimum major diameter is 0.075H and is tabulated in Table 5.

Table 5. Tolerances for Pitch Diameter, Major Diameter, and Minor Diameter for Coarse Thread Series ANSI/ASME B1.12-1987 (R2003)

TPI

PD Tolerance for Ext and Int Threadsa

Major Diam. Tolerance for Ext Threadb

Minor Diam. Tolerance for Int Thread NC-5 IF

Minor Diam. Tolerance for Int Thread NC-5 INFc

Tolerance 0.075H or 0.065P for Tap Major Diam.

20 18 16 14 13 12 11 10 9 8 7 6

0.0026 0.0030 0.0032 0.0036 0.0037 0.0040 0.0042 0.0045 0.0049 0.0054 0.0059 0.0071

0.0052 0.0060 0.0064 0.0072 0.0074 0.0080 0.0084 0.0090 0.0098 0.0108 0.0118 0.0142

0.010 0.011 0.011 0.008 0.008 0.009 0.010 0.011 0.012 0.014 0.015 0.018

0.010 0.011 0.011 0.012 0.012 0.013 0.013 0.014 0.014 0.015 0.015 0.018

0.0032 0.0036 0.0041 0.0046 0.0050 0.0054 0.0059 0.0065 0.0072 0.0093 0.0093 0.0108

a National Class 3 pitch diameter tolerance from ASA B1.1-1960. b Twice the NC-3 pitch diameter tolerance. c National Class 3 minor diameter tolerance from ASA B1.1-1960.


Relation of Driving Torque to Length of Engagement: Torques increase directly as the length of engagement and this increase is proportionately more rapid as size increases. The standard does not establish recommended breakloose torques. Surface Roughness: Surface roughnesss is not a required measurement. Roughness between 63 and 125 µin. Ra is recommended. Surface roughness greater than 125 µin. Ra may encourage galling and tearing of threads. Surfaces with roughness less than 63 µin. Ra may hold insufficient lubricant and wring or weld together.



1883

Lead and Angle Variations: The lead variation values tabulated in Table 6 are the maximum variations from specified lead between any two points not farther apart than the length of the standard GO thread gage. Flank angle variation values tabulated in Table 7 are maximum variations from the basic 30° angle between thread flanks and perpendiculars to the thread axis. The application of these data in accordance with ANSI/ASME B1.3M, the screw thread gaging system for dimensional acceptability, is given in the Standard. Lead variation does not change the volume of displaced metal, but it exerts a cumulative unilateral stress on the pressure side of the thread flank. Control of the difference between pitch diameter size and functional diameter size to within one-half the pitch diameter tolerance will hold lead and angle variables to within satisfactory limits. Both the variations may produce unacceptable torque and faulty assemblies. Table 6. Maximum Allowable Variations in Lead and Maximum Equivalent Change in Functional Diameter ANSI/ASME B1.12-1987 (R2003) External and Internal Threads Nominal Size

Allowable Variation in Axial Lead (Plus or Minus)

Max Equivalent Change in Functional Diam. (Plus for Ext, Minus for Int)

0.2500–20

0.0008

0.0013

0.3125–18

0.0009

0.0015

0.3750–16

0.0009

0.0016

0.4375–14

0.0010

0.0018

0.5000–13

0.0011

0.0018

0.5625–12

0.0012

0.0020

0.6250–11

0.0012

0.0021

0.7500–10

0.0013

0.0022

0.8750– 9

0.0014

0.0024

1.0000– 8

0.0016

0.0027

1.1250– 7

0.0017

0.0030

1.2500– 7

0.0017

0.0030

1.3750– 6

0.0020

0.0036

1.5000– 6

0.0020

0.0036

All dimensions are in inches. Note: The equivalent change in functional diameter applies to total effect of form errors. Maximum allowable variation in lead is permitted only when all other form variations are zero. For sizes not tabulated, maximum allowable variation in lead is equal to 0.57735 times one-half the pitch diameter tolerance.

Table 7. Maximum Allowable Variation in 30° Basic Half-Angle of External and Internal Screw Threads ANSI/ASME B1.12-1987 (R2003) TPI

Allowable Variation in Half-Angle of Thread (Plus or Minus)


TPI


32 28 27 24

1° 30′ 1° 20′ 1° 20′ 1° 15′

14 13 12 111⁄2

0° 55′ 0° 55′ 0° 50′ 0° 50′

8 7 6 5

0° 45′ 0° 45′ 0° 40′ 0° 40′

20 18 16

1° 10′

11

0° 50′

41⁄2

0° 40′

1° 05′ 1° 00′

10 9

0° 50′ 0° 50′

4 …

0° 40′ …

TPI


Machinery's Handbook 28th Edition SPARK PLUG THREADS

1884

Spark Plug Threads British Standard for Spark Plugs BS 45:1972 (withdrawn).—This revised British Standard refers solely to spark plugs used in automobiles and industrial spark ignition internal combustion engines. The basic thread form is that of the ISO metric (see page 1817). In assigning tolerances to the threads of the spark plug and the tapped holes, full consideration has been given to the desirability of achieving the closest possible measure of interchangeability between British spark plugs and engines, and those made to the standards of other ISO Member Bodies. Basic Thread Dimensions for Spark Plug and Tapped Hole in Cylinder Head Nom. Size

Major Dia. Pitch

Thread

Max.

Pitch Dia.

Min.

Minor Dia.

Max.

Min.

Max.

Min.

14

1.25

Plug

13.937a

13.725

13.125

12.993

12.402

12.181

14 18

1.25 1.5

Hole Plug

17.933a

14.00 17.697

13.368 16.959

13.188 16.819

12.912 16.092

12.647 15.845

18

1.5

Hole

18.00

17.216

17.026

16.676

16.376

a Not specified


The tolerance grades for finished spark plugs and corresponding tapped holes in the cylinder head are: for 14 mm size, 6e for spark plugs and 6H for tapped holes which gives a minimum clearance of 0.063 mm; and for 18 mm size, 6e for spark plugs and 6H for tapped holes which gives a minimum clearance of 0.067 mm. These minimum clearances are intended to prevent the possibility of seizure, as a result of combustion deposits on the bare threads, when removing the spark plugs and applies to both ferrous and non-ferrous materials. These clearances are also intended to enable spark plugs with threads in accordance with this standard to be fitted into existing holes. SAE Spark-Plug Screw Threads.—The SAE Standard includes the following sizes: 7⁄8inch nominal diameter with 18 threads per inch: 18-millimeter nominal diameter with a 18millimeter nominal diameter with 1.5-millimeter pitch; 14-millimeter nominal diameter with a 1.25-millimeter pitch; 10-millimeter nominal diameter with a 1.0 millimeter pitch; 3⁄ -inch nominal diameter with 24 threads per inch; and 1⁄ -inch nominal diameter with 32 8 4 threads per inch. During manufacture, in order to keep the wear on the threading tools within permissible limits, the threads in the spark plug GO (ring) gage should be truncated to the maximum minor diameter of the spark plug; and in the tapped hole GO (plug) gage to the minimum major diameter of the tapped hole. SAE Standard Threads for Spark Plugs Sizea Nom. × Pitch M18 × 1.5 M14 × 1.25 M12 × 1.25 M10 × 1.0

Major Diameter Max. 17.933 (0.07060) 13.868 (0.5460) 11.862 (0.4670) 9.974 (0.3927)

Min.

Pitch Diameter Max.

Min.

Spark Plug Threads, mm (inches) 17.803 16.959 16.853 (0.7009) (0.6677) (0.6635) 13.741 13.104 12.997 (0.5410) (0.5159) (0.5117) 11.735 11.100 10.998 (0.4620) (0.4370) (0.4330) 9.794 9.324 9.212 (0.3856) (0.3671) (0.3627)

Minor Diameter Max.

Min.

16.053 (0.6320) 12.339 (0.4858) 10.211 (0.4020) 8.747 (0.3444)

… … … … … … … …


Machinery's Handbook 28th Edition ELECTRIC SOCKET AND LAMP BASE THREAD

1885

SAE Standard Threads for Spark Plugs (Continued) Sizea Nom. × Pitch

Major Diameter Max.

M18 × 1.5

… … … … … … … …

M14 × 1.25 M12 × 1.25 M10 × 1.0

Pitch Diameter

Minor Diameter

Min. Max. Min. Tapped Hole Threads, mm (inches) 18.039 17.153 17.026 (0.7102) (0.6753) (0.6703) 14.034 13.297 13.188 (0.5525) (0.5235) (0.5192) 12.000 11.242 11.188 (0.4724) (0.4426) (0.4405) 10.000 9.500 9.350 (0.3937) (0.3740) (0.3681)

Max.

Min.

16.426 (0.6467) 12.692 (0.4997) 10.559 (0.4157) 9.153 (0,3604)

16.266 (0.6404) 12.499 (0.4921) 10.366 (0.4081) 8.917 (0.3511)

a M14 and M18 are preferred for new applications. In order to keep the wear on the threading tools within permissible limits, the threads in the spark plug GO (ring) gage shall be truncated to the maximum minor diameter of the spark plug, and in the tapped hole GO (plug) gage to the minimum major diameter of the tapped hole. The plain plug gage for checking the minor diameter of the tapped hole shall be the minimum specified. The thread form is that of the ISO metric (see page 1817). Reprinted with permission © 1990 Society of Automotive Engineers, Inc.

Lamp Base and Electrical Fixture Threads Lamp Base and Socket Shell Threads.—The “American Standard” threads for lamp base and socket shells are sponsored by the American Society of Mechanical Engineers, the National Electrical Manufacturers’ Association and by most of the large manufacturers of products requiring rolled threads on sheet metal shells or parts, such as lamp bases, fuse plugs, attachment plugs, etc. There are five sizes, designated as the “miniature size,” the “candelabra size,” the “intermediate size,” the “medium size” and the “mogul size.” Rolled Threads for Screw Shells of Electric Sockets and Lamp Bases— American Standard P R

D

R

R R

A a

b B Male or Base Screw Shells Before Assembly

Threads per Inch

Pitch P

Miniature Candelabra Intermediate Medium Mogul

14 10 9 7 4

0.07143 0.10000 0.11111 0.14286 0.25000

Miniature Candelabra Intermediate Medium Mogul

14 10 9 7 4

0.07143 0.10000 0.11111 0.14286 0.25000

Size

Depth of Radius Crest Thread D Root R 0.020 0.025 0.027 0.033 0.050

0.0210 0.0312 0.0353 0.0470 0.0906

Major Dia.

Minor Diam.

Max. A

Min. a

Max. B

Min. b

0.375 0.465 0.651 1.037 1.555

0.370 0.460 0.645 1.031 1.545

0.335 0.415 0.597 0.971 1.455

0.330 0.410 0.591 0.965 1.445

0.3775 0.470 0.657 1.045 1.565

0.3435 0.426 0.610 0.987 1.477

0.3375 0.420 0.603 0.979 1.465

Socket Screw Shells Before Assembly 0.020 0.025 0.027 0.033 0.050

0.0210 0.0312 0.0353 0.0470 0.0906

0.3835 0.476 0.664 1.053 1.577



Machinery's Handbook 28th Edition BRITISH ASSOCIATION THREADS

1886

Base Screw Shell Gage Tolerances: Threaded ring gages—“Go,” Max. thread size to minus 0.0003 inch; “Not Go,” Min. thread size to plus 0.0003 inch. Plain ring gages— “Go,” Max. thread O.D. to minus 0.0002 inch; “Not Go,” Min. thread O.D. to plus 0.0002 inch. Socket Screw Shell Gages: Threaded plug gages—“Go,” Min. thread size to plus 0.0003 inch; “Not Go,” Max. thread size to minus 0.0003 inch. Plain plug gages—“Go,” Min. minor dia. to plus 0.0002 inch; “Not Go,” Max. minor dia. to minus 0.0002 inch. Check Gages for Base Screw Shell Gages: Threaded plugs for checking threaded ring gages—“Go,” Max. thread size to minus 0.0003 inch; “Not Go,” Min. thread size to plus 0.0003 inch. Electric Fixture Thread.—The special straight electric fixture thread consists of a straight thread of the same pitches as the American standard pipe thread, and having the regular American or U. S. standard form; it is used for caps, etc. The male thread is smaller, and the female thread larger than those of the special straight-fixture pipe threads. The male thread assembles with a standard taper female thread, while the female thread assembles with a standard taper male thread. This thread is used when it is desired to have the joint “make up” on a shoulder. The gages used are straight-threaded limit gages. Instrument and Microscope Threads British Association Standard Thread (BA).—This form of thread is similar to the Whitworth thread in that the root and crest are rounded (see illustration). The angle, however, is only 47 degrees 30 minutes and the radius of the root and crest are proportionately larger. This thread is used in Great Britain and, to some extent, in other European countries for very small screws. Its use in the United States is practically confined to the manufacture of tools for export. This thread system was originated in Switzerland as a standard for watch and clock screws, and it is sometimes referred to as the “Swiss small screw thread standard.” See also Swiss Screw Thread. This screw thread system is recommended by the British Standards Institution for use in preference to the BSW and BSF systems for all screws smaller than 1⁄4 inch except that the use of the “0” BA thread be discontinued in favor of the 1⁄4-in. BSF. It is further recommended that in the selection of sizes, preference be given to even numbered BA sizes. The thread form is shown by the diagram. s 47 1 2 r H h

r

23

3

4

s

H h r s

= = = =

1.13634 × p 0.60000 × p 0.18083 × p 0.26817 × p

p British Association Thread

It is a symmetrical V-thread, of 471⁄2 degree included angle, having its crests and roots rounded with equal radii, such that the basic depth of the thread is 0.6000 of the pitch. Where p = pitch of thread, H = depth of V-thread, h = depth of BA thread, r = radius at root and crest of thread, and s = root and crest truncation.


Machinery's Handbook 28th Edition MICROSCOPE OBJECTIVE THREAD

1887

British Association (BA) Standard Thread, Basic Dimensions BS 93:1951 (obsolescent) Designation Number 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

Pitch, mm

Depth of Thread, mm

Major Diameter, mm

Bolt and Nut Effective Diameter, mm

Minor Diameter, mm

Radius, mm

1.0000 0.9000 0.8100 0.7300 0.6600 0.5900 0.5300 0.4800 0.4300 0.3900 0.3500 0.3100 0.2800 0.2500 0.2300 0.2100 0.1900

0.600 0.540 0.485 0.440 0.395 0.355 0.320 0.290 0.260 0.235 0.210 0.185 0.170 0.150 0.140 0.125 0.115

6.00 5.30 4.70 4.10 3.60 3.20 2.80 2.50 2.20 1.90 1.70 1.50 1.30 1.20 1.00 0.90 0.79

5.400 4.760 4.215 3.660 3.205 2.845 2.480 2.210 1.940 1.665 1.490 1.315 1.130 1.050 0.860 0.775 0.675

4.80 4.22 3.73 3.22 2.81 2.49 2.16 1.92 1.68 1.43 1.28 1.13 0.96 0.90 0.72 0.65 0.56

0.1808 0.1627 0.1465 0.1320 0.1193 0.1067 0.0958 0.0868 0.0778 0.0705 0.0633 0.0561 0.0506 0.0452 0.0416 0.0380 0.0344

Threads per Inch (approx.) 25.4 28.2 31.4 34.8 38.5 43.0 47.9 52.9 59.1 65.1 72.6 82.0 90.7 102 110 121 134

Tolerances and Allowances: Two classes of bolts and one for nuts are provided: Close Class bolts are intended for precision parts subject to stress, no allowance being provided between maximum bolt and minimum nut sizes. Normal Class bolts are intended for general commercial production and general engineering use; for sizes 0 to 10 BA, an allowance of 0.025 mm is provided. Tolerance Formulas for British Association (BA) Screw Threads Tolerance (+ for nuts, − for bolts) Class or Fit Bolts Nuts

Close Class 0 to 10 BA incl. Normal Class 0 to 10 BA incl. Normal Class 11 to 16 BA incl. All Classes

Major Dia.

Effective Dia.

Minor Dia.

0.15p mm 0.20p mm 0.25p mm

0.08p + 0.02 mm 0.10p + 0.025 mm 0.10p + 0.025 mm 0.12p + 0.03 mm

0.16p + 0.04 mm 0.20p + 0.05 mm 0.20p + 0.05 mm 0.375p mm

In these formulas, p = pitch in millimeters.

Instrument Makers' Screw Thread System.—The standard screw system of the Royal Microscopical Society of London, also known as the “Society Thread,” is employed for microscope objectives and the nose pieces of the microscope into which these objectives screw. The form of the thread is the standard Whitworth form. The number of threads per inch is 36. There is one size only. The maximum pitch diameter of the objective is 0.7804 inch and the minimum pitch diameter of the nose-piece is 0.7822 inch. The dimensions are as follows: outside dia. max., 0.7982 inch min., 0.7952 inch Male thread root dia. max., 0.7626 inch min., 0.7596 inch root of thread max,. 0.7674 inch min., 0.7644 inch Female thread top of thread max., 0.8030 inch min., 0.8000 inch The Royal Photographic Society Standard Screw Thread ranges from 1-inch diameter upward. For screws less than 1 inch, the Microscopical Society Standard is used. The British Association thread is another thread system employed on instruments abroad. American Microscope Objective Thread (AMO).—The standard, ANSI B1.11-1958 (R2006), describes the American microscope objective thread, AMO, the screw thread form used for mounting a microscope objective assembly to the body or lens turret of a microscope. This screw thread is also recommended for other microscope optical assem-


1888


bles as well as related applications such as photomicrographic equipment. It is based on, and intended to be interchangeable with, the screw thread produced and adopted many years ago by the Royal Microscopical Society of Great Britain, generally known as the RMS thread. While the standard is almost universally accepted as the basic standard for microscope objective mountings, formal recognition has been extremely limited. The basic thread possesses the overall British Standard Whitworth form. (See Whitworth Standard Thread Form starting on page 1858). However, the actual design thread form implementation is based on the WWII era ASA B1.6-1944 “Truncated Whitworth Form” in which the rounded crests and roots are removed. ASA B1.6-1944 was withdrawn in 1951, however, ANSI B1.11-1958 (R2006) is still active for new design. Design Requirements of Microscope Objective Threads: Due to the inherent longevity of optical equipment and the repeated use to which the objective threads are subjected, the following factors should be considered when designing microscope objective threads: Adequate clearance to afford protection against binding due to the presence of foreign particles or minor crest damage. Sufficient depth of thread engagement to assure security in the short lengths of engagement commonly encountered. Allowances for limited eccentricities so that centralization and squareness of the objective are not influenced by such errors in manufacture. Deviation from the Truncated Whitworth Thread Form: Although ANSI B1.11-1958 (R2006) is based on the withdrawn ASA B1.6-1944 truncated Whitworth standard, the previously described design requirements necessitate a deviation from the truncated Whitworth thread form. Some of the more significant modifications are: A larger allowance on the pitch diameter of the external thread. Smaller tolerances on the major diameter of the external thread and minor diameter of the internal thread. The provision of allowances on the major and minor diameters of the external thread. Thread Overview: The thread is a single start type. There is only one class of thread based on a basic major diameter of 0.800 in. and a pitch, p, of 0.027778 inch (36 threads per inch). The AMO thread shall be designated on drawings, tools and gages as “0.800–36 AMO.” Thread nomenclature, definitions and terminology are based on ANSI B1.7-1965 (R1972), “Nomenclature, Threads, and Letter Symbols for Screw Threads.” It should also be noted that ISO 8038-1:1997 “Screw threads for objectives and related nosepieces” is also based on the 0.800 inch, 36 tpi RMS thread form. Tolerances and Allowances: Tolerances are given in Table 2. A positive allowance (minimum clearance) of 0.0018 in. is provided for the pitch diamter E, major diameter D, and minor diameter, K If interchangeability with full-form Whitworth threads is not required, the allowances for the major and minor diameters are not necessary, because the forms at the root and crest are truncated. In these cases, either both limits or only the maximum limit of the major and minor diameters may be increased by the amount of the allowance, 0.0018 inch. Lengths of Engagement: The tolerances specified in Table 2 are applicable to lengths of engagement ranging from 1⁄8 in. to 3⁄8 inch, approximately 15% to 50% of the basic diameter. Microscope objective assembles generally have a length of engagement of 1⁄8 inch. Lengths exceeding these limits are seldom employed and not covered in this standard. Gage testing: Recommended ring and plug testing gage dimensions for the 0.800–36 AMO thread size can be found in ANSI B1.11–1958 (R2006), Appendix. Dimensional Terminology: Because the active standard ANSI B1.11–1958 (R2006) is based on the withdrawn ASA Truncated Whitworth standard, dimensional nomenclature is described below.


Machinery's Handbook 28th Edition MICROSCOPE OBJECTIVE THREAD pp __ __ 20

1889

The Dotted Line Indicates the Full Form British Whitworth Thread on Which the Royal Microscopical Society Thread is Based


Fc

U

1/2 Major Diameter Allowance on External Thread 1/2 Major Diameter Tolerance on External Thread

1/2 Tolerance (External Thread Only) 1/2 PD Tolerance On External Thread

Permissible Form of Thread from New Tool

Maximum Minor Diameter of Internal Thread

p __ 12

Maximum Minor Diameter of External Thread Minimum Minor Diameter of Internal Thread

Fr

Minimum Minor Diameter of External Thread

Minimum Pitch Diameter of External Thread

U

Basic Minor Diameter on British Whitworth Thread 1/2 Minor Diameter Allowance on External Thread

Basic Pitch Diameter

Maximum Pitch Diameter of External Thread

Minimum Pitch Diameter of Internal Thread

Fc Maximum Pitch Diameter of Internal Thread


1/2 Minor Diameter Tolerance on Internal Thread

External Thread

Minimum Major Diameter of

Basic Major Diameter

Maximum Major Diameter of External Thread

Maximum Major Diameter of Internal Thread

Minimum Major Diameter of Internal Thread

1/2 PD Tolerance on External Thread

55 55

Tolerances, Allowances and Crest Clearances for Microscope Objective Thread (AMO) ANSI B1.11–1958 (R2006)

Table 1. Definitions, Formulas, Basic and Design Dimensions ANSI B1.11–1958 (R2006) Symbol

Property

Formula

Dimension

Basic Thread Form α 2α n p H hb r

Half angle of thread Included angle of thread Number of threads per inch Pitch Height of fundamental triangle

… … … 1/n 0.960491p

27°30’ 55°00’ 36 0.027778 0.026680

Height of basic thread

0.640327p

0.0178

Radius at crest and root of British Standard Whitworth basic thread (not used)

0.137329p

0.0038



1890

Table 1. (Continued) Definitions, Formulas, Basic and Design Dimensions ANSI B1.11–1958 (R2006) Symbol

Property Design Thread Form

Formula

Dimension

k

Height of truncated Whitworth thread

hb – U = 0.566410p

0.0157

Fc

Width of flat at crest

0.243624p

0.0068

Fr

Width of flat at root

0.166667p

0.0046

0.073917p

0.00205

Basic truncation of crest from basic Whitworth form Basic and Design Sizes Major diameter, nominal and basic

U

D Dn

…

0.800

Major diameter of internal thread

D

0.800

Ds

Major diameter of external threada

D – 2U – G

0.7941 0.7822

E

Pitch (effective) diameter, basic

D – hb

En

Pitch (effective) diameter of internal thread

D – hb

0.7822

Es

Pitch (effective) diameter of external threadb

D – hb – G

0.7804

K

Minor diameter, basic

D – 2hb

0.7644

Kn

Minor diameter of internal thread

D – 2k

0.7685

Ks

Minor diameter of external threada

D – 2hb – G

0.7626

G

Allowance at pitch (effective) diametera, b

…

0.0018

a An allowance equal to that on the pitch diameter is also provided on the major and minor diameters

of the external thread for additional clearance and centralizing. b Allowance (minimum clearance) on pitch (effective) diameter is the same as the British RMS thread. All dimensions are in inches.

Table 2. Limits of Size and Tolerances — 0.800–36 AMO Thread ANSI B1.11–1958 (R2006) Element External thread Internal thread

Major Diameter, D

Pitch Diameter, E

Minor Diameter, K

Max.

Min.

Tol.

Max.

Min.

Tol.

Max.

Min.

Tol.

0.7941

0.7911 0.8000

0.0030 …

0.7804 0.7852

0.7774 0.7822

0.0030 0.0030

0.7626 0.7715

0.7552a 0.7865

… 0.0030

0.8092b

a Extreme minimum minor diameter produced by a new threading tool having a minimum flat of p⁄12 = 0.0023 inch. This minimum diameter is not controlled by gages but by the form of the threading tool. b Extreme maximum major diameter produced by a new threading tool having a minimum flat of p⁄20 = 0.0014 inch. This maximum diameter is not controlled by gages but by the form of the threading tool.

Tolerances on the internal thread are applied in a plus direction from the basic and design size and tolerances on the external thread are applied in a minus direction from its design (maximum material) size. All dimensions are in inches.

Swiss Screw Thread.—This is a thread system originated in Switzerland as a standard for screws used in watch and clock making. The angle between the two sides of the thread is 47 degrees 30 minutes, and the top and bottom of the thread are rounded. This system has been adopted by the British Association as a standard for small screws, and is known as the British Association thread. See British Association Standard Thread (BA) on page 1886.


Machinery's Handbook 28th Edition HISTORICAL AND MISCELANEOUS THREADS

1891

Historical and Miscellaneous Threads Aero-Thread.—The name “Aero-thread” has been applied to a patented screw thread system that is specially applicable in cases where the nut or internally threaded part is made from a soft material, such as aluminum or magnesium alloy, for the sake of obtaining lightness, as in aircraft construction, and where the screw is made from a high-strength steel to provide strength and good wearing qualities. The nut or part containing the internal thread has a 60-degree truncated form of thread. See Fig. 1. The screw, or stud, is provided with a semi-circular thread form, as shown. Between the screw and the nut there is an intermediary part known as a thread lining or insert, which is made in the form of a helical spring, so that it can be screwed into the nut. The stud, in turn, is then screwed into the thread formed by the semicircular part of the thread insert. When the screw is provided with a V-form of thread, like the American Standard, frequent loosening and tightening of the screw would cause rapid wear of the softer metal from which the nut is made; furthermore, all the threads might not have an even bearing on the mating threads. By using a thread insert which is screwed into the nut permanently, and which is made from a reasonably hard material like phosphor bronze, good wearing qualities are obtained. Also, the bearing or load is evenly distributed over all the threads of the nut since the insert, being in the form of a spring, can adjust itself to bear on all of the thread surfaces.

Fig. 1. The Basic Thread Form Used in the Aero-Thread System

Briggs Pipe Thread.—The Briggs pipe thread (now known as the American Standard) is used for threaded pipe joints and is the standard for this purpose in the United States. It derives its name from Robert Briggs. Casing Thread.—The standard casing thread of the American Petroleum Institute has an included angle of 60 degrees and a taper of 3⁄4 inch per foot. The fourteen casing sizes listed in the 1942 revision have outside diameters ranging from 41⁄2 to 20 inches. All sizes have 8 threads per inch. Rounded Thread Form: Threads for casing sizes up to 13 3⁄8 inches, inclusive, have rounded crests and roots, and the depth, measured perpendicular to the axis of the pipe, equals 0.626 × pitch − 0.007 = 0.07125 inch. Truncated Form: Threads for the 16-and 20-inch casing sizes have flat crests and roots. The depth equals 0.760 × pitch = 0.0950 inch. This truncated form is designated in the A.P.I. Standard as a “sharp thread.”


1892


Cordeaux Thread.—The Cordeaux screw thread derives its name from John Henry Cordeaux, an English telegraph inspector who obtained a patent for this thread in 1877. This thread is used for connecting porcelain insulators with their stalks by means of a screw thread on the stalk and a corresponding thread in the insulator. The thread is approximately a Whitworth thread, 6 threads per inch, the diameters most commonly used being 5⁄ or 3⁄ inch outside diameter of thread; 5⁄ inch is almost universally used for telegraph pur8 4 8 poses, while a limited number of 3⁄4-inch sizes are used for large insulators. Dardelet Thread.—The Dardelet patented self-locking thread is designed to resist vibrations and remain tight without auxiliary locking devices. The locking surfaces are the tapered root of the bolt thread and the tapered crest of the nut thread. The nut is free to turn until seated tightly against a resisting surface, thus causing it to shift from the free position (indicated by dotted lines) to the locking position. The locking is due to a wedging action between the tapered crest of the nut thread and the tapered root or binding surface of the bolt thread. This self-locking thread is also applied to set-screws and cap-screws. The holes must, of course, be threaded with Dardelet taps. The abutment sides of the Dardelet thread carry the major part of the tensile load. The nut is unlocked simply by turning it backward with a wrench. The Dardelet thread can either be cut or rolled, using standard equipment provided with tools, taps, dies, or rolls made to suit the Dardelet thread profile. The included thread angle is 29 degrees; depth E = 0.3P; maximum axial movement = 0.28 P. The major internal thread diameter (standard series) equals major external thread diameter plus 0.003 inch except for 1⁄4-inch size which is plus 0.002 inch. The width of both external and internal threads at pitch line equals 0.36 P. “Drunken” Thread.—A “drunken” thread, according to prevalent usage of this expression by machinists, etc., is a thread that does not coincide with a true helix or advance uniformly. This irregularity in a taper thread may be due to the fact that in taper turning with the tailstock set over, the work does not turn with a uniform angular velocity, while the cutting tool is advancing along the work longitudinally with a uniform linear velocity. The change in the pitch and the irregularity of the thread is so small as to be imperceptible to the eye, if the taper is slight, but as the tapers increase to, say, 3⁄4 inch per foot or more, the errors become more pronounced. To avoid this defect, a taper attachment should be used for taper thread cutting. Echols Thread.—Chip room is of great importance in machine taps and tapper taps where the cutting speed is high and always in one direction. The tap as well as the nut to be threaded is liable to be injured, if ample space for the chips to pass away from the cutting edges is not provided. A method of decreasing the number of cutting edges, as well as increasing the amount of chip room, is embodied in the “Echols thread,” where every alternate tooth is removed. If a tap has an even number of flutes, the removal of every other tooth in the lands will be equivalent to the removal of the teeth of a continuous thread. It is, therefore, necessary that taps provided with this thread be made with an odd number of lands, so that removing the tooth in alternate lands may result in removing every other tooth in each individual land. Machine taps are often provided with the Echols thread. French Thread (S.F.).—The French thread has the same form and proportions as the American Standard (formerly U. S. Standard). This French thread is being displaced gradually by the International Metric Thread System. Harvey Grip Thread.—The characteristic feature of this thread is that one side inclines 44 degrees from a line at right angles to the axis, whereas the other side has an inclination of only 1 degree. This form of thread is sometimes used when there is considerable resistance or pressure in an axial direction and when it is desirable to reduce the radial or bursting pressure on the nut as much as possible. See BUTTRESS THREADS.



1893

Lloyd & Lloyd Thread.—The Lloyd & Lloyd screw thread is the same as the regular Whitworth screw thread in which the sides of the thread form an angle of 55 degrees with one another. The top and bottom of the thread are rounded. Lock-Nut Pipe Thread.—The lock-nut pipe thread is a straight thread of the largest diameter which can be cut on a pipe. Its form is identical with that of the American or Briggs standard taper pipe thread. In general, “Go” gages only are required. These consist of a straight-threaded plug representing the minimum female lock-nut thread, and a straight-threaded ring representing the maximum male lock-nut thread. This thread is used only to hold parts together, or to retain a collar on the pipe. It is never used where a tight threaded joint is required. Philadelphia Carriage Bolt Thread.—This is a screw thread for carriage bolts which is somewhat similar to a square thread, but having rounded corners at the top and bottom. The sides of the thread are inclined to an inclusive angle of 31⁄2 degrees. The width of the thread at the top is 0.53 times the pitch. SAE Standard Screw Thread.—The screw thread standard of the Society of Automotive Engineers (SAE) is intended for use in the automotive industries of the United States. The SAE Standard includes a Coarse series, a Fine series, an 8-thread series, a 12-thread series, a 16-thread series, an Extra-fine series, and a Special-pitch series. The Coarse and Fine series, and also the 8-, 12- and 16-thread series, are exactly the same as corresponding series in the American Standard. The Extra-fine and Special-pitch series are SAE Standards only. The American Standard thread form (or the form previously known as the U. S. Standard) is applied to all SAE Standard screw threads. The Extra-fine series has a total of six pitches ranging from 32 down to 16 threads per inch. The 16 threads per inch in the Extra-fine series, applies to all diameters from 13⁄4 up to 6 inches. This Extra-fine series is intended for use on relatively light sections; on parts requiring fine adjustment; where jar and vibration are important factors; when the thickness of a threaded section is relatively small as in tubing, and where assembly is made without the use of wrenches. The SAE Special pitches include some which are finer than any in the Extra-fine series. The special pitches apply to a range of diameters extending from No. 10 (0.1900 inch) up to 6 inches. Each diameter has a range of pitches varying from five to eight. For example, a 1⁄ - inch diameter has six pitches ranging from 24 to 56 threads per inch, whereas a 6-inch 4 diameter has eight pitches ranging from 4 to 16 threads per inch. These various SAE Standard series are intended to provide adequate screw thread specifications for all uses in the automotive industries. Sellers Screw Thread.—The Sellers screw thread, later known as the ‘United States standard thread,” and now as the “American Standard,” is the most commonly used screw thread in the United States. It was originated by William Sellers, of Philadelphia, and first proposed by him in a paper read before the Franklin Institute, in April, 1864. In 1868, it was adopted by the United States Navy and has since become the generally accepted standard screw thread in the United States. Worm Threads.—The included angle of worm threads range from 29° to 60°; for singlethreaded worms 29° is common; multiple-threaded type must have larger helix and thread angles to avoid excessive under-cutting in hobbing the worm-wheel teeth. AGMA recommends 40° included thread angle for triple- and quadruple-thread worms, but many speed reducers and transmissions have 60° thread angles. The 29° angle is the same as the Acme thread, but worm thread depth is greater and widths of the flats at the top and bottom are less. If lead angle is larger than 20°, an increase in included thread angle is desirable. Worm gearing reaches maximum efficiency when lead angle is 45°, thus explaining the 60° thread angle. Thread parts of a 29° worm thread are: p = pitch; d = depth of thread = 0.6866p; t = width, top of thread = 0.335p; b = width, bottom of thread = 0.310p.


1894

Machinery's Handbook 28th Edition MEASURING SCREW THREADS

MEASURING SCREW THREADS Measuring Screw Threads Pitch and Lead of Screw Threads.—The pitch of a screw thread is the distance from the center of one thread to the center of the next thread. This applies no matter whether the screw has a single, double, triple or quadruple thread. The lead of a screw thread is the distance the nut will move forward on the screw if it is turned around one full revolution. In a single-threaded screw, the pitch and lead are equal, because the nut would move forward the distance from one thread to the next, if turned around once. In a double-threaded screw, the nut will move forward two threads, or twice the pitch, so that in this case the lead equals twice the pitch. In a triple-threaded screw, the lead equals three times the pitch, and so on. The word “pitch” is often, although improperly, used to denote the number of threads per inch. Screws are spoken of as having a 12-pitch thread, when twelve threads per inch is what is really meant. The number of threads per inch equals 1 divided by the pitch, or expressed as a formula: 1 Number of threads per inch = ----------pitch The pitch of a screw equals 1 divided by the number of threads per inch, or: 1 Pitch = --------------------------------------------------------------number of threads per inch If the number of threads per inch equals 16, the pitch = 1⁄16. If the pitch equals 0.05, the number of threads equals 1 ÷ 0.05 = 20. If the pitch is 2⁄5 inch, the number of threads per inch equals 1 ÷ 2⁄5 = 2 1⁄2. Confusion is often caused by the indefinite designation of multiple-thread screws (double, triple, quadruple, etc.). The expression, “four threads per inch, triple,” for example, is not to be recommended. It means that the screw is cut with four triple threads or with twelve threads per inch, if the threads are counted by placing a scale alongside the screw. To cut this screw, the lathe would be geared to cut four threads per inch, but they would be cut only to the depth required for twelve threads per inch. The best expression, when a multiple-thread is to be cut, is to say, in this case, “1⁄4 inch lead, 1⁄12 inch pitch, triple thread.” For single-threaded screws, only the number of threads per inch and the form of the thread are specified. The word “single” is not required. Measuring Screw Thread Pitch Diameters by Thread Micrometers.—As the pitch or angle diameter of a tap or screw is the most important dimension, it is necessary that the pitch diameter of screw threads be measured, in addition to the outside diameter.

Fig. 1.

One method of measuring in the angle of a thread is by means of a special screw thread micrometer, as shown in the accompanying engraving, Fig. 1. The fixed anvil is W-shaped to engage two thread flanks, and the movable point is cone-shaped so as to enable it to enter the space between two threads, and at the same time be at liberty to revolve. The contact



1895

points are on the sides of the thread, as they necessarily must be in order that the pitch diameter may be determined. The cone-shaped point of the measuring screw is slightly rounded so that it will not bear in the bottom of the thread. There is also sufficient clearance at the bottom of the V-shaped anvil to prevent it from bearing on the top of the thread. The movable point is adapted to measuring all pitches, but the fixed anvil is limited in its capacity. To cover the whole range of pitches, from the finest to the coarsest, a number of fixed anvils are therefore required. To find the theoretical pitch diameter, which is measured by the micrometer, subtract twice the addendum of the thread from the standard outside diameter. The addendum of the thread for the American and other standard threads is given in the section on screw thread systems. Ball-point Micrometers.—If standard plug gages are available, it is not necessary to actually measure the pitch diameter, but merely to compare it with the standard gage. In this case, a ball-point micrometer, as shown in Fig. 2, may be employed. Two types of ballpoint micrometers are ordinarily used. One is simply a regular plain micrometer with ball points made to slip over both measuring points. (See B, Fig. 2.) This makes a kind of combination plain and ball-point micrometer, the ball points being easily removed. These ball points, however, do not fit solidly on their seats, even if they are split, as shown, and are apt to cause errors in measurements. The best, and, in the long run, the cheapest, method is to use a regular micrometer arranged as shown at A. Drill and ream out both the end of the measuring screw or spindle and the anvil, and fit ball points into them as shown. Care should be taken to have the ball point in the spindle run true. The holes in the micrometer spindle and anvil and the shanks on the points are tapered to insure a good fit. The hole H in spindle G is provided so that the ball point can be easily driven out when a change for a larger or smaller size of ball point is required.

Fig. 2.

A ball-point micrometer may be used for comparing the angle of a screw thread, with that of a gage. This can be done by using different sizes of ball points, comparing the size first near the root of the thread, then (using a larger ball point) at about the point of the pitch diameter, and finally near the top of the thread (using in the latter case, of course, a much larger ball point). If the gage and thread measurements are the same at each of the three points referred to, this indicates that the thread angle is correct. Measuring Screw Threads by Three-wire Method.—The effective or pitch diameter of a screw thread may be measured very accurately by means of some form of micrometer and three wires of equal diameter. This method is extensively used in checking the accuracy of threaded plug gages and other precision screw threads. Two of the wires are placed in contact with the thread on one side and the third wire in a position diametrically opposite as illustrated by the diagram, (see table “Formulas for Checking Pitch Diameters of Screw Threads”) and the dimension over the wires is determined by means of a micrometer. An ordinary micrometer is commonly used but some form of “floating micrometer” is preferable, especially for measuring thread gages and other precision work. The floating micrometer is mounted upon a compound slide so that it can move freely in directions parallel or at right angles to the axis of the screw, which is held in a horizontal position


1896


between adjustable centers. With this arrangement the micrometer is held constantly at right angles to the axis of the screw so that only one wire on each side may be used instead of having two on one side and one on the other, as is necessary when using an ordinary micrometer. The pitch diameter may be determined accurately if the correct micrometer reading for wires of a given size is known. Classes of Formulas for Three-Wire Measurement.—Various formulas have been established for checking the pitch diameters of screw threads by measurement over wires of known size. These formulas differ with regard to their simplicity or complexity and resulting accuracy. They also differ in that some show what measurement M over the wires should be to obtain a given pitch diameter E, whereas others show the value of the pitch diameter E for a given measurement M. Formulas for Finding Measurement M: In using a formula for finding the value of measurement M, the required pitch diameter E is inserted in the formula. Then, in cutting or grinding a screw thread, the actual measurement M is made to conform to the calculated value of M. Formulas for finding measurement M may be modified so that the basic major or outside diameter is inserted in the formula instead of the pitch diameter; however, the pitch-diameter type of formula is preferable because the pitch diameter is a more important dimension than the major diameter. Formulas for Finding Pitch Diameters E: Some formulas are arranged to show the value of the pitch diameter E when measurement M is known. Thus, the value of M is first determined by measurement and then is inserted in the formula for finding the corresponding pitch diameter E. This type of formula is useful for determining the pitch diameter of an existing thread gage or other screw thread in connection with inspection work. The formula for finding measurement M is more convenient to use in the shop or tool room in cutting or grinding new threads, because the pitch diameter is specified on the drawing and the problem is to find the value of measurement M for obtaining that pitch diameter. General Classes of Screw Thread Profiles.—Thread profiles may be divided into three general classes or types as follows: Screw Helicoid: Represented by a screw thread having a straight-line profile in the axial plane. Such a screw thread may be cut in a lathe by using a straight-sided single-point tool, provided the top surface lies in the axial plane. Involute Helicoid: Represented either by a screw thread or a helical gear tooth having an involute profile in a plane perpendicular to the axis. A rolled screw thread, theoretically at least, is an exact involute helicoid. Intermediate Profiles: An intermediate profile that lies somewhere between the screw helicoid and the involute helicoid will be formed on a screw thread either by milling or grinding with a straight-sided wheel set in alignment with the thread groove. The resulting form will approach closely the involute helicoid form. In milling or grinding a thread, the included cutter or wheel angle may either equal the standard thread angle (which is always measured in the axial plane) or the cutter or wheel angle may be reduced to approximate, at least, the thread angle in the normal plane. In practice, all these variations affect the three-wire measurement. Accuracy of Formulas for Checking Pitch Diameters by Three-Wire Method.—The exact measurement M for a given pitch diameter depends upon the lead angle, the thread angle, and the profile or cross-sectional shape of the thread. As pointed out in the preceding paragraph, the profile depends upon the method of cutting or forming the thread. In a milled or ground thread, the profile is affected not only by the cutter or wheel angle, but also by the diameter of the cutter or wheel; hence, because of these variations, an absolutely exact and reasonably simple general formula for measurement M cannot be established; however, if the lead angle is low, as with a standard single-thread screw, and especially if the thread angle is high like a 60-degree thread, simple formulas that are not arranged to compensate for the lead angle are used ordinarily and meet most practical



1897

requirements, particularly in measuring 60-degree threads. If lead angles are large enough to greatly affect the result, as with most multiple threads (especially Acme or 29-degree worm threads), a formula should be used that compensates for the lead angle sufficiently to obtain the necessary accuracy. The formulas that follow include 1) a very simple type in which the effect of the lead angle on measurementM is entirely ignored. This simple formula usually is applicable to the measurement of 60-degree single-thread screws, except possibly when gage-making accuracy is required; 2) formulas that do include the effect of the lead angle but, nevertheless, are approximations and not always suitable for the higher lead angles when extreme accuracy is required; and 3) formulas for the higher lead angles and the most precise classes of work. Where approximate formulas are applied consistently in the measurement of both thread plug gages and the thread “setting plugs” for ring gages, interchangeability might be secured, assuming that such approximate formulas were universally employed. Wire Sizes for Checking Pitch Diameters of Screw Threads.—I n c h e c k i n g s c r e w threads by the 3-wire method, the general practice is to use measuring wires of the socalled “best size.” The “best-size” wire is one that contacts at the pitch line or midslope of the thread because then the measurement of the pitch diameter is least affected by an error in the thread angle. In the following formula for determining approximately the “best-size” wire or the diameter for pitch-line contact, A = one-half included angle of thread in the axial plane. × pitch = 0.5 pitch × sec A Best-size wire = 0.5 ------------------------cos A For 60-degree threads, this formula reduces to Best-size wire = 0.57735 × pitch Diameters of Wires for Measuring American Standard and British Standard Whitworth Screw Threads Wire Diameters for American Standard Threads Wire Diameters for Whitworth Standard Threads Threads per Inch

Pitch, Inch

Max.

Min.

Pitch-Line Contact

Max.

Min.

Pitch-Line Contact

4 41⁄2

0.2500 0.2222

0.2250 0.2000

0.1400 0.1244

0.1443 0.1283

0.1900 0.1689

0.1350 0.1200

0.1409 0.1253

5 51⁄2

0.2000 0.1818

0.1800 0.1636

0.1120 0.1018

0.1155 0.1050

0.1520 0.1382

0.1080 0.0982

0.1127 0.1025

6 7 8 9 10 11 12 13 14 16 18 20 22 24 28 32 36 40

0.1667 0.1428 0.1250 0.1111 0.1000 0.0909 0.0833 0.0769 0.0714 0.0625 0.0555 0.0500 0.0454 0.0417 0.0357 0.0312 0.0278 0.0250

0.1500 0.1283 0.1125 0.1000 0.0900 0.0818 0.0750 0.0692 0.0643 0.0562 0.0500 0.0450 0.0409 0.0375 0.0321 0.0281 0.0250 0.0225

0.0933 0.0800 0.0700 0.0622 0.0560 0.0509 0.0467 0.0431 0.0400 0.0350 0.0311 0.0280 0.0254 0.0233 0.0200 0.0175 0.0156 0.0140

0.0962 0.0825 0.0722 0.0641 0.0577 0.0525 0.0481 0.0444 0.0412 0.0361 0.0321 0.0289 0.0262 0.0240 0.0206 0.0180 0.0160 0.0144

0.1267 0.1086 0.0950 0.0844 0.0760 0.0691 0.0633 0.0585 0.0543 0.0475 0.0422 0.0380 0.0345 0.0317 0.0271 0.0237 0.0211 0.0190

0.0900 0.0771 0.0675 0.0600 0.0540 0.0491 0.0450 0.0415 0.0386 0.0337 0.0300 0.0270 0.0245 0.0225 0.0193 0.0169 0.0150 0.0135

0.0939 0.0805 0.0705 0.0626 0.0564 0.0512 0.0470 0.0434 0.0403 0.0352 0.0313 0.0282 0.0256 0.0235 0.0201 0.0176 0.0156 0.0141


1898

Machinery's Handbook 28th Edition MEASURING SCREW THREAD

These formulas are based upon a thread groove of zero lead angle because ordinary variations in the lead angle have little effect on the wire diameter and it is desirable to use one wire size for a given pitch regardless of the lead angle. A theoretically correct solution for finding the exact size for pitch-line contact involves the use of cumbersome indeterminate equations with solution by successive trials. The accompanying table gives the wire sizes for both American Standard (formerly, U.S. Standard) and the Whitworth Standard Threads. The following formulas for determining wire diameters do not give the extreme theoretical limits, but the smallest and largest practicable sizes. The diameters in the table are based upon these approximate formulas. Smallest wire diameter = 0.56 × pitch American Standard

Largest wire diameter = 0.90 × pitch Diameter for pitch-line contact = 0.57735 × pitch Smallest wire diameter = 0.54 × pitch

Whitworth

Largest wire diameter = 0.76 × pitch Diameter for pitch-line contact = 0.56369 × pitch

Measuring Wire Accuracy.—A set of three measuring wires should have the same diameter within 0.0002 inch. To measure the pitch diameter of a screw-thread gage to an accuracy of 0.0001 inch by means of wires, it is necessary to know the wire diameters to 0.00002 inch. If the diameters of the wires are known only to an accuracy of 0.0001 inch, an accuracy better than 0.0003 inch in the measurement of pitch diameter cannot be expected. The wires should be accurately finished hardened steel cylinders of the maximum possible hardness without being brittle. The hardness should not be less than that corresponding to a Knoop indentation number of 630. A wire of this hardness can be cut with a file only with difficulty. The surface should not be rougher than the equivalent of a deviation of 3 microinches from a true cylindrical surface. Measuring or Contact Pressure.—In measuring screw threads or screw-thread gages by the 3-wire method, variations in contact pressure will result in different readings. The effect of a variation in contact pressure in measuring threads of fine pitches is indicated by the difference in readings obtained with pressures of 2 and 5 pounds in checking a thread plug gage having 24 threads per inch. The reading over the wires with 5 pounds pressure was 0.00013 inch less than with 2 pounds pressure. For pitches finer than 20 threads per inch, a pressure of 16 ounces is recommended by the National Bureau of Standards, now National Institute of Standards and Technology (NIST). For pitches of 20 threads per inch and coarser, a pressure of 2 1⁄2 pounds is recommended. For Acme threads, the wire presses against the sides of the thread with a pressure of approximately twice that of the measuring instrument. To limit the tendency of the wires to wedge in between the sides of an Acme thread, it is recommended that pitch-diameter measurements be made at 1 pound on 8 threads per inch and finer, and at 2 1⁄2 pounds for pitches coarser than 8 threads per inch. Approximate Three-Wire Formulas That Do Not Compensate for Lead Angle.—A general formula in which the effect of lead angle is ignored is as follows (see accompanying notation used in formulas): M = E – T cot A + W ( 1 + csc A )

(1)

This formula can be simplified for any given thread angle and pitch. To illustrate, because T = 0.5P, M = E − 0.5P cot 30° + W(1 + 2), for a 60-degree thread, such as the American Standard, M = E – 0.866025P + 3W



1899

The accompanying table contains these simplified formulas for different standard threads. Two formulas are given for each. The upper one is used when the measurement over wires, M, is known and the corresponding pitch diameter, E, is required; the lower formula gives the measurement M for a specified value of pitch diameter. These formulas are sufficiently accurate for checking practically all standard 60-degree single-thread screws because of the low lead angles, which vary from 1° 11′ to 4° 31′ in the American Standard Coarse-Thread Series. Bureau of Standards (now NIST) General Formula.—Formula (2), which follows, compensates quite largely for the effect of the lead angle. It is from the National Bureau of Standards Handbook H 28 (1944), now FED-STD-H28. The formula, however, as here given has been arranged for finding the value of M (instead of E). 2

M = E – T cot A + W ( 1 + csc A + 0.5 tan B cos A cot A )

(2)

This expression is also found in ANSI/ASME B1.2-1983 (R2007). The Bureau of Standards uses Formula (2) in preference to Formula (1) when the value of 0.5W tan2 B cos A cot A exceeds 0.00015, with the larger lead angles. If this test is applied to American Standard 60-degree threads, it will show that Formula (1) is generally applicable; but for 29degree Acme or worm threads, Formula (2) (or some other that includes the effect of lead angle) should be employed. Notation Used in Formulas for Checking Pitch Diameters by Three-Wire Method A =one-half included thread angle in the axial plane An =one-half included thread angle in the normal plane or in plane perpendicular to sides of thread = one-half included angle of cutter when thread is milled (tan An = tan A × cos B). (Note: Included angle of milling cutter or grinding wheel may equal the nominal included angle of thread, or may be reduced to whatever normal angle is required to make the thread angle standard in the axial plane. In either case, An = one-half cutter angle.) B =lead angle at pitch diameter = helix angle of thread as measured from a plane perpendicular to the axis, tan B = L ÷ 3.1416E D =basic major or outside diameter E =pitch diameter (basic, maximum, or minimum) for which M is required, or pitch diameter corresponding to measurement M F =angle required in Formulas (4b), (4d), and (4e) G =angle required in Formula (4) H =helix angle at pitch diameter and measured from axis = 90° − B or tan H = cot B Hb =helix angle at Rb measured from axis L =lead of thread = pitch P × number of threads S M =dimension over wires P =pitch = 1 ÷ number of threads per inch Rb =radius required in Formulas (4) and (4e) S =number of “starts” or threads on a multiple-threaded worm or screw T =0.5 P = width of thread in axial plane at diameter E Ta =arc thickness on pitch cylinder in plane perpendicular to axis W =wire or pin diameter



1900

Formulas for Checking Pitch Diameters of Screw Threads The formulas below do not compensate for the effect of the lead angle upon measurement M, but they are sufficiently accurate for checking standard single-thread screws unless exceptional accuracy is required. See accompanying information on effect of lead angle; also matter relating to measuring wire sizes, accuracy required for such wires, and contact or measuring pressure. The approximate best wire size for pitch-line contact may be obtained by the formula

W = 0.5 × pitch × sec 1⁄2 included thread angle For 60-degree threads, W = 0.57735 × pitch. Form of Thread

Formulas for determining measurement M corresponding to correct pitch diameter and the pitch diameter E corresponding to a given measurement over wires.a

American National Standard Unified

When measurement M is known, E = M + 0.86603P – 3W

British Standard Whitworth

When measurement M is known, E = M + 0.9605P – 3.1657W

British Association Standard Lowenherz Thread Sharp V-Thread International Standard

When pitch diameter E is used in formula, M = E – 0.86603P + 3W The American Standard formerly was known as U.S. Standard.

When pitch diameter E is used in formula, M = E – 0.9605P + 3.1657W When measurement M is known, E = M + 1.1363P – 3.4829W When pitch diameter E is used in formula, M = E – 1.1363P + 3.4829W When measurement M is known, E = M + P – 3.2359W When pitch diameter E is used in formula, M = E – P + 3.2359W When measurement M is known, E = M + 0.86603P – 3W When pitch diameter E is used in formula, M = E – 0.86603P + 3W Use the formula above for the American National Standard Unified Thread.

Pipe Thread

See accompanying paragraph on Buckingham Exact Involute Helicoid Formula Applied to Screw Threads.

Acme and Worm Threads

See Buckingham Formulas page 1904; also Three-wire Measurement of Acme and Stub Acme Thread Pitch Diameter.

Buttress Form of Thread

Different forms of buttress threads are used. See paragraph on Three-Wire Method Applied to Buttress Threads.

a The wires must be lapped to a uniform diameter and it is very important to insert in the rule or formula the wire diameter as determined by precise means of measurement. Any error will be multiplied. See paragraph on Wire Sizes for Checking Pitch Diameters of Screw Threads on page 1897.

Why Small Thread Angle Affects Accuracy of Three-Wire Measurement.—In measuring or checking Acme threads, or any others having a comparatively small thread angle A, it is particularly important to use a formula that compensates largely, if not entirely, for the effect of the lead angle, especially in all gage and precision work. The effect of the lead angle on the position of the wires and upon the resulting measurement M is much greater in a 29-degree thread than in a higher thread angle such, for example, as a 60-degree thread. This effect results from an increase in the cotangent of the thread angle as this angle becomes smaller. The reduction in the width of the thread groove in the normal plane due



1901

to the lead angle causes a wire of given size to rest higher in the groove of a thread having a small thread angle A (like a 29-degree thread) than in the groove of a thread with a larger angle (like a 60-degree American Standard). Acme Threads: Three-wire measurements of high accuracy require the use of Formula (4). For most measurements, however, Formula (2) or (3) gives satisfactory results. The table on page 1907 lists suitable wire sizes for use in Formulas (2) and (4). Values of Constants Used in Formulas for Measuring Pitch Diameters of Screws by the Three-wire System No. of Threads per Inch 21⁄4 23⁄8 21⁄2 25⁄8 23⁄4 27⁄8 3 31⁄4 31⁄2 4 41⁄2 5 51⁄2 6 7 8 9 10 11 12 13 14 15 16

American Standard Unified and Sharp V-Thread 0.866025P 0.38490 0.36464 0.34641 0.32992 0.31492 0.30123 0.28868 0.26647 0.24744 0.21651 0.19245 0.17321 0.15746 0.14434 0.12372 0.10825 0.09623 0.08660 0.07873 0.07217 0.06662 0.06186 0.05774 0.05413

Whitworth Thread 0.9605P 0.42689 0.40442 0.38420 0.36590 0.34927 0.33409 0.32017 0.29554 0.27443 0.24013 0.21344 0.19210 0.17464 0.16008 0.13721 0.12006 0.10672 0.09605 0.08732 0.08004 0.07388 0.06861 0.06403 0.06003

No. of Threads per Inch 18 20 22 24 26 28 30 32 34 36 38 40 42 44 46 48 50 52 56 60 64 68 72 80

American Standard Unified and Sharp V-Thread 0.866025P 0.04811 0.04330 0.03936 0.03608 0.03331 0.03093 0.02887 0.02706 0.02547 0.02406 0.02279 0.02165 0.02062 0.01968 0.01883 0.01804 0.01732 0.01665 0.01546 0.01443 0.01353 0.01274 0.01203 0.01083

Whitworth Thread 0.9605P 0.05336 0.04803 0.04366 0.04002 0.03694 0.03430 0.03202 0.03002 0.02825 0.02668 0.02528 0.02401 0.02287 0.02183 0.02088 0.02001 0.01921 0.01847 0.01715 0.01601 0.01501 0.01412 0.01334 0.01201

Constants Used for Measuring Pitch Diameters of Metric Screws by the Three-wire System Pitch in mm

0.866025P in Inches

W in Inches

Pitch in mm

0.866025P in Inches

W in Inches

Pitch in mm

0.866025P in Inches

W in Inches

0.2

0.00682

0.00455

0.75

0.02557

0.01705

3.5

0.11933

0.07956

0.25

0.00852

0.00568

0.8

0.02728

0.01818

4

0.13638

0.09092

0.3

0.01023

0.00682

1

0.03410

0.02273

4.5

0.15343

0.10229

0.35

0.01193

0.00796

1.25

0.04262

0.02841

5

0.17048

0.11365

0.4

0.01364

0.00909

1.5

0.05114

0.03410

5.5

0.18753

0.12502

0.45

0.01534

0.01023

1.75

0.05967

0.03978

6

0.20457

0.13638

0.5

0.01705

0.01137

2

0.06819

0.04546

8

0.30686

0.18184

0.6

0.02046

0.01364

2.5

0.08524

0.05683

…

…

…

0.7

0.02387

0.01591

3

0.10229

0.06819

…

…

…

This table may be used for American National Standard Metric Threads. The formulas for American Standard Unified Threads on page 1900 are used. In the table above, the values of 0.866025P and W are in inches so that the values for E and M calculated from the formulas on page 1900 are also in inches.



1902

Dimensions Over Wires of Given Diameter for Checking Screw Threads of American National Form (U.S. Standard) and the V-Form Dia. of Thread 1⁄ 4 1⁄ 4 1⁄ 4 1⁄ 4 5⁄ 16 5⁄ 16 5⁄ 16 5⁄ 16 3⁄ 8 3⁄ 8 3⁄ 8 7⁄ 16 7⁄ 16 1⁄ 2 1⁄ 2 1⁄ 2 9⁄ 16 9⁄ 16 5⁄ 8 5⁄ 8 5⁄ 8 11⁄ 16 11⁄ 16 3⁄ 4 3⁄ 4 3⁄ 4 13⁄ 16 13⁄ 16

No. of Threads per Inch 18 20 22 24 18 20 22 24 16 18 20 14 16 12 13 14 12 14 10 11 12 10 11 10 11 12 9 10

Wire Dia. Used 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.035 0.040 0.040 0.040 0.050 0.050 0.050 0.050 0.050 0.050 0.050 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070 0.070

Dimension over Wires VU.S. Thread Thread 0.2588 0.2708 0.2684 0.2792 0.2763 0.2861 0.2828 0.2919 0.3213 0.3333 0.3309 0.3417 0.3388 0.3486 0.3453 0.3544 0.3867 0.4003 0.3988 0.4108 0.4084 0.4192 0.4638 0.4793 0.4792 0.4928 0.5057 0.5237 0.5168 0.5334 0.5263 0.5418 0.5682 0.5862 0.5888 0.6043 0.6618 0.6835 0.6775 0.6972 0.6907 0.7087 0.7243 0.7460 0.7400 0.7597 0.7868 0.8085 0.8025 0.8222 0.8157 0.8337 0.8300 0.8541 0.8493 0.8710

Dia. of Thread 7⁄ 8 7⁄ 8 7⁄ 8 15⁄ 16 15⁄ 16

1 1 11⁄8 11⁄4 13⁄8 11⁄2 15⁄8 13⁄4 17⁄8 2 21⁄4 21⁄2 23⁄4 3

No. of Threads per Inch 8 9 10 8 9 8 9 7 7 6 6 51⁄2 5 5 41⁄2 41⁄2 4 4

31⁄4 31⁄2 33⁄4 4

31⁄2 31⁄2 31⁄4 3 3

41⁄4 41⁄2 43⁄4 5 …

27⁄8 23⁄4 25⁄8 21⁄2 …

Wire Dia. Used 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.090 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.150 0.200 0.200 0.250 0.250 0.250 0.250 0.250 0.250 0.250 …

Dimension over Wires VU.S. Thread Thread 0.9285 0.9556 0.9525 0.9766 0.9718 0.9935 0.9910 1.0181 1.0150 1.0391 1.0535 1.0806 1.0775 1.1016 1.1476 1.1785 1.2726 1.3035 1.5363 1.5724 1.6613 1.6974 1.7601 1.7995 1.8536 1.8969 1.9786 2.0219 2.0651 2.1132 2.3151 2.3632 2.5170 2.5711 2.7670 2.28211 3.1051 3.1670 3.3551 3.4170 3.7171 3.7837 3.9226 3.9948 4.1726 4.2448 4.3975 4.4729 4.6202 4.6989 4.8402 4.9227 5.0572 5.1438 … …

Buckingham Simplified Formula which Includes Effect of Lead Angle.—T h e F o r mula (3) which follows gives very accurate results for the lower lead angles in determining measurement M. However, if extreme accuracy is essential, it may be advisable to use the involute helicoid formulas as explained later. M = E + W ( 1 + sin A n )

(3)

where

T × cos B W = ---------------------cos A n

(3a)

Theoretically correct equations for determining measurement M are complex and cumbersome to apply. Formula (3) combines simplicity with a degree of accuracy which meets all but the most exacting requirements, particularly for lead angles below 8 or 10 degrees and the higher thread angles. However, the wire diameter used in Formula (3) must conform to that obtained by Formula (3a) to permit a direct solution or one not involving indeterminate equations and successive trials. Application of Buckingham Formula: In the application of Formula (3) to screw or worm threads, two general cases are to be considered. Case 1: The screw thread or worm is to be milled with a cutter having an included angle equal to the nominal or standard thread angle that is assumed to be the angle in the axial plane. For example, a 60-degree cutter is to be used for milling a thread. In this case, the



1903

Table for Measuring Whitworth Standard Threads by the Three-wire Method Dia. of Thread


Dia. of Wire Used

Dia. Measured over Wires

Dia. of Thread


Dia. of Wire Used

Dia. Measured over Wires

1⁄ 8

40

0.018

0.1420

21⁄4

4

0.150

2.3247

3⁄ 16

24

0.030

0.2158

23⁄8

4

0.150

2.4497

1⁄ 4

20

0.035

0.2808

21⁄2

4

0.150

2.5747

5⁄ 16

18

0.040

0.3502

25⁄8

4

0.150

2.6997

3⁄ 8

16

0.040

0.4015

23⁄4

31⁄2

0.200

2.9257

7⁄ 16

14

0.050

0.4815

27⁄8

31⁄2

0.200

3.0507

1⁄ 2

12

0.050

0.5249

3

31⁄2

0.200

3.1757

9⁄ 16

12

0.050

0.5874

31⁄8

31⁄2

0.200

3.3007

5⁄ 8

11

0.070

0.7011

31⁄4

31⁄4

0.200

3.3905

11⁄ 16

11

0.070

0.7636

33⁄8

31⁄4

0.200

3.5155

3⁄ 4

10

0.070

0.8115

31⁄2

31⁄4

0.200

3.6405

13⁄ 16

10

0.070

0.8740

35⁄8

31⁄4

0.200

3.7655

9

0.070

0.9187

33⁄4

3

0.200

3.8495

7⁄ 8 15⁄ 16

9

0.070

0.9812

37⁄8

3

0.200

3.9745

1 11⁄16

8 8

0.090 0.090

1.0848 1.1473

4 41⁄8

3 3

0.200 0.200

4.0995 4.2245

11⁄8

7

0.090

1.1812

41⁄4

27⁄8

0.250

4.4846

13⁄16

7

0.090

1.2437

43⁄8

27⁄8

0.250

4.6096

11⁄4

7

0.090

1.3062

41⁄2

27⁄8

0.250

4.7346

15⁄16

7

0.090

1.3687

45⁄8

27⁄8

0.250

4.8596

13⁄8

6

0.120

1.4881

43⁄4

23⁄4

0.250

4.9593

17⁄16

6

0.120

1.5506

47⁄8

23⁄4

0.250

5.0843

11⁄2

6

0.120

1.6131

5

23⁄4

0.250

5.2093

19⁄16

6

0.120

1.6756

51⁄8

23⁄4

0.250

5.3343

15⁄8

5

0.120

1.6847

51⁄4

25⁄8

0.250

5.4316

111⁄16

5

0.120

1.7472

53⁄8

25⁄8

0.250

5.5566

13⁄4

5

0.120

1.8097

51⁄2

25⁄8

0.250

5.6816

113⁄16

5

0.120

1.8722

55⁄8

25⁄8

0.250

5.8066

17⁄8

41⁄2

0.150

1.9942

53⁄4

21⁄2

0.250

5.9011

115⁄16

41⁄2

0.150

2.0567

57⁄8

21⁄2

0.250

6.0261

2

41⁄2

0.150

2.1192

6

21⁄2

0.250

6.1511

21⁄8

41⁄2

0.150

2.2442

…

…

…

…


thread angle in the plane of the axis will exceed 60 degrees by an amount increasing with the lead angle. This variation from the standard angle may be of little or no practical importance if the lead angle is small or if the mating nut (or teeth in worm gearing) is formed to suit the thread as milled. Case 2: The screw thread or worm is to be milled with a cutter reduced to whatever normal angle is equivalent to the standard thread angle in the axial plane. For example, a 29degree Acme thread is to be milled with a cutter having some angle smaller than 29 degrees (the reduction increasing with the lead angle) to make the thread angle standard in the plane of the axis. Theoretically, the milling cutter angle should always be corrected to suit the normal angle; but if the lead angle is small, such correction may be unnecessary. If the thread is cut in a lathe to the standard angle as measured in the axial plane, Case 2 applies in determining the pin size W and the overall measurement M.


1904


In solving all problems under Case 1, angle An used in Formulas (3) and (3a) equals onehalf the included angle of the milling cutter. When Case 2 applies, angle An for milled threads also equals one-half the included angle of the cutter, but the cutter angle is reduced and is determined as follows: tan A n = tan A × cos B The included angle of the cutter or the normal included angle of the thread groove = 2An. Examples 1 and 2, which follow, illustrate Cases 1 and 2. Example 1 (Case 1):Take, for example, an Acme screw thread that is milled with a cutter having an included angle of 29 degrees; consequently, the angle of the thread exceeds 29 degrees in the axial section. The outside or major diameter is 3 inches; the pitch, 1⁄2 inch; the lead, 1 inch; the number of threads or “starts,” 2. Find pin size W and measurement M. Pitch diameter E = 2.75; T = 0.25; L = 1.0; An = 14.50° tan An = 0.258618; sin An = 0.25038; and cos An = 0.968148. 1.0 tan B = -------------------------------- = 0.115749 B = 6.6025° 3.1416 × 2.75 × 0.993368- = 0.25651 inch W = 0.25 -------------------------------------0.968148 M = 2.75 + 0.25651 × ( 1 + 0.25038 ) = 3.0707 inches Note: This value of M is only 0.0001 inch larger than that obtained by using the very accurate involute helicoid Formula (4) discussed on the following page. Example 2 (Case 2):A triple-threaded worm has a pitch diameter of 2.481 inches, pitch of 1.5 inches, lead of 4.5 inches, lead angle of 30 degrees, and nominal thread angle of 60 degrees in the axial plane. Milling cutter angle is to be reduced. T = 0.75 inch; cos B = 0.866025; and tan A = 0.57735. Again use Formula (3) to see if it is applicable. tan An = tan A × cos B = 0.57735 × 0.866025 = 0.5000; hence An = 26.565°, making the included cutter angle 53.13°, thus cos An = 0.89443 and sin An = 0.44721. 0.75 × 0.866025- = 0.72618 inch W = -------------------------------------0.89443 M = 2.481 + 0.72618 × ( 1 + 0.44721 ) = 3.532 inches Note: If the value of measurement M is determined by using the following Formula (4) it will be found that M = 3.515 + inches; hence the error equals 3.532 − 3.515 = 0.017 inch approximately, which indicates that Formula (3) is not accurate enough here. The application of this simpler Formula (3) will depend upon the lead angle and thread angle (as previously explained) and upon the class of work. Buckingham Exact Involute Helicoid Formula Applied to Screw Threads.—W h e n extreme accuracy is required in finding measurement M for obtaining a given pitch diameter, the equations that follow, although somewhat cumbersome to apply, have the merit of providing a direct and very accurate solution; consequently, they are preferable to the indeterminate equations and successive trial solutions heretofore employed when extreme precision is required. These equations are exact for involute helical gears and, consequently, give theoretically correct results when applied to a screw thread of the involute helicoidal form; they also give very close approximations for threads having intermediate profiles. Helical Gear Equation Applied to Screw Thread Measurement: In applying the helical gear equations to a screw thread, use either the axial or normal thread angle and the lead angle of the helix. To keep the solution on a practical basis, either thread angle A or An, as the case may be, is assumed to equal the cutter angle of a milled thread. Actually, the pro-



1905

file of a milled thread will have some curvature in both axial and normal sections; hence angles A and An represent the angular approximations of these slightly curved profiles. The equations that follow give the values needed to solve the screw thread problem as a helical gear problem. 2R b -+W M = -----------cos G tan A n tan A- = ------------tan F = ----------(4a) tan B sin B TT a = ----------tan B

(4c)

(4)

E R b = --- cos F 2

tan H b = cos F × tan H

T W π inv G = -----a + inv F + -------------------------- – --E 2R b cos H b S

(4b)

(4d) (4e)

The tables of involute functions starting on page 110 provide values for angles from 14 to 51 degrees, used for gear calculations. The formula for involute functions on page 109 may be used to extend this table as required. Example 3:To illustrate the application of Formula (4) and the supplementary formulas, assume that the number of starts S = 6; pitch diameter E = 0.6250; normal thread angle An = 20°; lead of thread L = 0.864 inch; T = 0.072; W = 0.07013 inch. L 0.864 tan B = ------- = ---------------- = 0.44003 B = 23.751° πE 1.9635 Helix angle H = 90° – 23.751° = 66.249° tan A tan F = -------------n- = 0.36397 ------------------- = 0.90369 F = 42.104° sin B 0.40276 E 0.6250 R b = --- cos F = ---------------- × 0.74193 = 0.23185 2 2 T 0.072 - = 0.16362 T a = ------------ = -----------------tan B 0.44003 tan H b = cos F tan H = 0.74193 × 2.27257 = 1.68609 H b = 59.328° The involute function of G is found next by Formula (4e). 0.16362 0.07013 3.1416 inv G = ------------------- + 0.16884 + ------------------------------------------------------ – ---------------- = 0.20351 0.625 2 × 0.23185 × 0.51012 6 Since 0.20351 is outside the values for involute functions given in the tables on pages 110 through 113 use the formula for involute functions on page 109 to extend these tables as required. It will be found that 44 deg. 21 min. or 44.350 degrees is the angular equivalent of 0.20351; hence, G = 44.350 degrees. 2R b × 0.23185 + 0.07013 = 0.71859 inch M = ------------ + W = 2---------------------------cos G 0.71508 Accuracy of Formulas (3) and (4) Compared.—With the involute helicoid Formula (4) any wire size that makes contact with the flanks of the thread may be used; however, in the preceding example, the wire diameter W was obtained by Formula (3a) in order to compare Formula (4) with (3) . If Example (3) is solved by Formula (3) , M = 0.71912; hence the difference between the values of M obtained with Formulas (3) and (4) equals 0.71912 - 0.71859 = 0.00053 inch. The included thread angle in this case is 40 degrees. If Formulas


1906


(3) and (4) are applied to a 29-degree thread, the difference in measurements M or the error resulting from the use of Formulas (3) will be larger. For example, with an Acme thread having a lead angle of about 34 degrees, the difference in values of M obtained by the two formulas equals 0.0008 inch. Three-wire Measurement of Acme and Stub Acme Thread Pitch Diameter.—F o r single- and multiple-start Acme and Stub Acme threads having lead angles of less than 5 degrees, the approximate three-wire formula given on page 1898 and the best wire size taken from the table on page 1907 may be used. Multiple-start Acme and Stub Acme threads commonly have a lead angle of greater than 5 degrees. For these, a direct determination of the actual pitch diameter is obtained by using the formula: E = M − (C + c) in conjunction with the table on page 1908. To enter the table, the lead angle B of the thread to be measured must be known. It is found by the formula: tan B = L ÷ 3.1416E1 where L is the lead of the thread and E1 is the nominal pitch diameter. The best wire size is now found by taking the value of w1 as given in the table for lead angle B, with interpolation, and dividing it by the number of threads per inch. The value of (C + c)1 given in the table for lead angle B is also divided by the number of threads per inch to get (C + c). Using the best size wires, the actual measurement over wires M is made and the actual pitch diameter E found by using the formula: E = M − (C + c). Example:For a 5 tpi, 4-start Acme thread with a 13.952° lead angle, using three 0.10024inch wires, M = 1.1498 inches, hence E = 1.1498 − 0.1248 = 1.0250 inches. Under certain conditions, a wire may contact one thread flank at two points, and it is then advisable to substitute balls of the same diameter as the wires. Checking Thickness of Acme Screw Threads.—In some instances it may be preferable to check the thread thickness instead of the pitch diameter, especially if there is a thread thickness tolerance. A direct method, applicable to the larger pitches, is to use a vernier gear-tooth caliper for measuring the thickness in the normal plane of the thread. This measurement, for an American Standard General Purpose Acme thread, should be made at a distance below the basic outside diameter equal to p/4. The thickness at this basic pitch-line depth and in the axial plane should be p/2 − 0.259 × the pitch diameter allowance from the table on page 1828 with a tolerance of minus 0.259 × the pitch diameter tolerance from the table on page 1833. The thickness in the normal plane or plane of measurement is equal to the thickness in the axial plane multiplied by the cosine of the helix angle. The helix angle may be determined from the formula: tangent of helix angle = lead of thread ÷ (3.1416 × pitch diameter) Three-Wire Method for Checking Thickness of Acme Threads.—The application of the 3-wire method of checking the thickness of an Acme screw thread is included in the Report of the National Screw Thread Commission. In applying the 3-wire method for checking thread thickness, the procedure is the same as in checking pitch diameter (see Three-wire Measurement of Acme and Stub Acme Thread Pitch Diameter), although a different formula is required. Assume that D = basic major diameter of screw; M = measurement over wires; W = diameter of wires; S = tangent of helix angle at pitch line; P = pitch; T = thread thickness at depth equal to 0.25P. T = 1.12931 × P + 0.25862 × ( M – D ) – W × ( 1.29152 + 0.48407S 2 ) This formula transposed to show the correct measurement M equivalent to a given required thread thickness is as follows: W × ( 1.29152 + 0.48407S ) + T – 1.12931 × P M = D + ---------------------------------------------------------------------------------------------------------------0.25862 2



1907

Wire Sizes for Three-Wire Measurement of Acme Threads with Lead Angles of Less than 5 Degrees Threads per Inch 1 11⁄3 11⁄2 2 21⁄2 3 4

Best Size 0.51645 0.38734

Max. 0.65001 0.48751

Min. 0.48726 0.36545

Threads per Inch 5 6

Best Size 0.10329 0.08608

Max. 0.13000 0.10834

Min. 0.09745 0.08121

0.34430

0.43334

0.32484

8

0.06456

0.08125

0.06091

0.25822 0.20658

0.32501 0.26001

0.24363 0.19491

10 12

0.05164 0.04304

0.06500 0.05417

0.04873 0.04061

0.17215 0.12911

0.21667 0.16250

0.16242 0.12182

14 16

0.03689 0.03228

0.04643 0.04063

0.03480 0.03045

Wire sizes are based upon zero helix angle. Best size = 0.51645 × pitch; maximum size = 0.650013 × pitch; minimum size = 0.487263 × pitch.

Example:An Acme General Purpose thread, Class 2G, has a 5-inch basic major diameter, 0.5-inch pitch, and 1-inch lead (double thread). Assume the wire size is 0.258 inch. Determine measurement M for a thread thickness T at the basic pitch line of 0.2454 inch. (T is the maximum thickness at the basic pitch line and equals 0.5P, the basic thickness, −0.259 × allowance from Table 4, page 1833.) 0.258 × [ 1.29152 + 0.48407 × ( 0.06701 ) 2 ] + 0.2454 – 1.12931 × 0.5 M = 5 + --------------------------------------------------------------------------------------------------------------------------------------------------------------------0.25862 = 5.056 inches Testing Angle of Thread by Three-Wire Method.—The error in the angle of a thread may be determined by using sets of wires of two diameters, the measurement over the two sets of wires being followed by calculations to determine the amount of error, assuming that the angle cannot be tested by comparison with a standard plug gage, known to be correct. The diameter of the small wires for the American Standard thread is usually about 0.6 times the pitch and the diameter of the large wires, about 0.9 times the pitch. The total difference between the measurements over the large and small sets of wires is first determined. If the thread is an American Standard or any other form having an included angle of 60 degrees, the difference between the two measurements should equal three times the difference between the diameters of the wires used. Thus, if the wires are 0.116 and 0.076 inch in diameter, respectively, the difference equals 0.116 − 0.076 = 0.040 inch. Therefore, the difference between the micrometer readings for a standard angle of 60 degrees equals 3 × 0.040 = 0.120 inch for this example. If the angle is incorrect, the amount of error may be determined by the following formula, which applies to any thread regardless of angle: A sin a = -----------B–A where A =difference in diameters of the large and small wires used B =total difference between the measurements over the large and small wires a =one-half the included thread angle Example:The diameter of the large wires used for testing the angle of a thread is 0.116 inch and of the small wires 0.076 inch. The measurement over the two sets of wires shows a total difference of 0.122 inch instead of the correct difference, 0.120 inch, for a standard angle of 60 degrees when using the sizes of wires mentioned. The amount of error is determined as follows: 0.040 - = 0.040 sin a = -------------------------------------------- = 0.4878 0.122 – 0.040 0.082 A table of sines shows that this value (0.4878) is the sine of 29 degrees 12 minutes, approximately. Therefore, the angle of the thread is 58 degrees 24 minutes or 1 degree 36 minutes less than the standard angle.



1908

Best Wire Diameters and Constants for Three-wire Measurement of Acme and Stub Acme Threads with Large Lead Angles, 1–inch Axial Pitch 1-start threads

2-start threads

2-start threads

3-start threads

Lead angle, B, deg.

w1

(C + c)1

w1

(C + c)1

Lead angle, B, deg.

w1

(C + c)1

w1

(C + c)1

5.0 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 6.0 6.1 6.2 6.3 6.4 6.5 6.6 6.7 6.8 6.9 7.0 7.1 7.2 7.3 7.4 7.5 7.6 7.7 7.8 7.9 8.0 8.1 8.2 8.3 8.4 8.5 8.6 8.7 8.8 8.9 9.0 9.1 9.2 9.3 9.4 9.5 9.6 9.7 9.8 9.9 10.0

0.51450 0.51442 0.51435 0.51427 0.51419 0.51411 0.51403 0.51395 0.51386 0.51377 0.51368 0.51359 0.51350 0.51340 0.51330 0.51320 0.51310 0.51300 0.51290 0.51280 0.51270 0.51259 0.51249 0.51238 0.51227 0.51217 0.51206 0.51196 0.51186 0.51175 0.51164 0.51153 0.51142 0.51130 0.51118 0.51105 0.51093 0.51081 0.51069 0.51057 0.51044 0.51032 0.51019 0.51006 0.50993 0.50981 0.50968 0.50955 0.50941 0.50927 0.50913

0.64311 0.64301 0.64291 0.64282 0.64272 0.64261 0.64251 0.64240 0.64229 0.64218 0.64207 0.64195 0.64184 0.64172 0.64160 0.64147 0.64134 0.64122 0.64110 0.64097 0.64085 0.64072 0.64060 0.64047 0.64034 0.64021 0.64008 0.63996 0.63983 0.63970 0.63957 0.63944 0.63930 0.63916 0.63902 0.63887 0.63873 0.63859 0.63845 0.63831 0.63817 0.63802 0.63788 0.63774 0.63759 0.63744 0.63730 0.63715 0.63700 0.63685 0.63670

0.51443 0.51435 0.51427 0.51418 0.51410 0.51401 0.51393 0.51384 0.51375 0.51366 0.51356 0.51346 0.51336 0.41327 0.51317 0.51306 0.51296 0.51285 0.51275 0.51264 0.51254 0.51243 0.51232 0.51221 0.51209 0.51198 0.51186 0.51174 0.51162 0.51150 0.51138 0.51125 0.51113 0.51101 0.51088 0.51075 0.51062 0.51049 0.51035 0.51022 0.51008 0.50993 0.50979 0.50965 0.50951 0.50937 0.50922 0.50908 0.50893 0.50879 0.50864

0.64290 0.64279 0.64268 0.64256 0.64245 0.64233 0.64221 0.64209 0.64196 0.64184 0.64171 0.64157 0.64144 0.64131 0.64117 0.64103 0.64089 0.64075 0.64061 0.64046 0.64032 0.64017 0.64002 0.63987 0.63972 0.63957 0.63941 0.63925 0.63909 0.63892 0.63876 0.63859 0.63843 0.63827 0.63810 0.63793 0.63775 0.63758 0.63740 0.63722 0.63704 0.63685 0.63667 0.63649 0.63630 0.63612 0.63593 0.63574 0.63555 0.63537 0.63518

10.0 10.1 10.2 10.3 10.4 10.5 10.6 10.7 10.8 10.9 11.0 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 12.0 12.1 12.2 12.3 12.4 12.5 12.6 12.7 12.8 12.9 13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15.0

0.50864 0.50849 0.50834 0.50818 0.50802 0.40786 0.50771 0.50755 0.50739 0.50723 0.50707 0.50691 0.50674 0.50658 0.50641 0.50623 0.50606 0.50589 0.50571 0.50553 0.50535 0.50517 0.50500 0.50482 0.50464 0.50445 0.50427 0.50408 0.50389 0.50371 0.50352 0.50333 0.50313 0.50293 0.50274 0.50254 0.50234 0.50215 0.50195 0.50175 0.50155 0.50135 0.50115 0.50094 0.50073 0.50051 0.50030 0.50009 0.49988 0.49966 0.49945

0.63518 0.63498 0.63478 0.63457 0.63436 0.63416 0.63395 0.63375 0.53354 0.63333 0.63313 0.63292 0.63271 0.63250 0.63228 0.63206 0.63184 0.63162 0.63140 0.63117 0.63095 0.63072 0.63050 0.63027 0.63004 0.62981 0.62958 0.62934 0.62911 0.62888 0.62865 0.62841 0.62817 0.62792 0.62778 0.62743 0.62718 0.62694 0.62670 0.62645 0.62621 0.62596 0.62571 0.62546 0.62520 0.62494 0.62468 0.62442 0.62417 0.62391 0.62365

0.50847 0.50381 0.50815 0.50800 0.50784 0.50768 0.50751 0.50735 0.50718 0.50701 0.50684 0.50667 0.50649 0.50632 0.50615 0.50597 0.50579 0.50561 0.50544 0.50526 0.50507 0.50488 0.50470 0.50451 0.50432 0.50413 0.50394 0.50375 0.50356 0.50336

0.63463 0.63442 0.63420 0.63399 0.63378 0.63356 0.63333 0.63311 0.63288 0.63265 0.63242 0.63219 0.63195 0.63172 0.63149 0.63126 0.63102 0.63078 0.63055 0.63031 0.63006 0.62981 0.62956 0.62931 0.62906 0.62881 0.62856 0.62830 0.62805 0.62779

For these 3-start thread values see table on following page.

All dimensions are in inches. Values given for w1 and (C + c)1 in table are for 1-inch pitch axial threads. For other pitches, divide table values by number of threads per inch. Courtesy of Van Keuren Co.



1909

Best Wire Diameters and Constants for Three-wire Measurement of Acme and Stub Acme Threads with Large Lead Angles—1-inch Axial Pitch Lead angle, B, deg.

3-start threads

4-start threads

4-start threads

(C + c)1

w1

(C + c)1

Lead angle, B, deg.

3-start threads

w1

w1

(C + c)1

w1

(C + c)1

13.0 13.1 13.2 13.3 13.4 13.5 13.6 13.7 13.8 13.9 14.0 14.1 14.2 14.3 14.4 14.5 14.6 14.7 14.8 14.9 15.0 15.1 15.2 15.3 15.4 15.5 15.6 15.7 15.8 15.9 16.0 16.1 16.2 16.3 16.4 16.5 16.6 16.7 16.8 16.9 17.0 17.1 17.2 17.3 17.4 17.5 17.6 17.7 17.8 17.9 …

0.50316 0.50295 0.50275 0.50255 0.50235 0.50214 0.50194 0.50173 0.50152 0.50131 0.50110 0.50089 0.50068 0.50046 0.50024 0.50003 0.49981 0.49959 0.49936 0.49914 0.49891 0.49869 0.49846 0.49824 0.42801 0.49778 0.49754 0.49731 0.49707 0.49683 0.49659 0.49635 0.49611 0.49586 0.49562 0.49537 0.49512 0.49488 0.40463 0.49438 0.49414 0.49389 0.49363 0.49337 0.49311 0.49285 0.49259 0.49233 0.49206 0.49180 …

0.62752 0.62725 0.62699 0.62672 0.62646 0.62619 0.62592 0.62564 0.62537 0.62509 0.62481 0.62453 0.62425 0.62397 0.62368 0.62340 0.62312 0.62883 0.62253 0.62224 0.62195 0.62166 0.62137 0.62108 0.62078 0.62048 0.62017 0.61987 0.61956 0.61926 0.61895 0.61864 0.61833 0.61801 0.61770 0.61738 0.61706 0.61675 0.61643 0.61611 0.61580 0.61548 0.61515 0.61482 0.61449 0.61416 0.61383 0.61350 0.61316 0.61283 …

0.50297 0.50277 0.50256 0.50235 0.50215 0.50194 0.50173 0.50152 0.50131 0.50109 0.50087 0.50065 0.50043 0.50021 0.49999 0.49977 0.49955 0.49932 0.49910 0.49887 0.49864 0.49842 0.49819 0.49795 0.49771 0.49747 0.49723 0.49699 0.49675 0.49651 0.49627 0.49602 0.49577 0.49552 0.49527 0.49502 0.49476 0.49451 0.49425 0.49400 0.49375 0.49349 0.49322 0.49296 0.49269 0.49243 0.49217 0.49191 0.49164 0.49137 …

0.62694 0.62667 0.62639 0.62611 0.62583 0.62555 0.62526 0.62498 0.62469 0.62440 0.62411 0.62381 0.62351 0.62321 0.62291 0.62262 0.62232 0.62202 0.62172 0.62141 0.62110 0.62080 0.62049 0.62017 0.61985 0.61953 0.61921 0.61889 0.61857 0.61825 0.61793 0.61760 0.61727 0.61694 0.61661 0.61628 0.61594 0.61560 0.61526 0.61492 0.61458 0.61424 0.61389 0.61354 0.61319 0.61284 0.61250 0.61215 0.61180 0.61144 …

18.0 18.1 18.2 18.3 18.4 18.5 18.6 18.7 18.8 18.9 19.0 19.1 19.2 19.3 19.4 19.5 19.6 19.7 19.8 19.9 20.0 20.1 20.2 20.3 20.4 20.5 20.6 20.7 20.8 20.9 21.0 21.1 21.2 21.3 21.4 21.5 21.6 21.7 21.8 21.9 22.0 22.1 22.2 22.3 22.4 22.5 22.6 22.7 22.8 22.9 23.0

0.49154 0.49127 0.49101 0.49074 0.49047 0.49020 0.48992 0.48965 0.48938 0.48910 0.48882 0.48854 0.48825 0.48797 0.48769 0.48741 0.48712 0.48638 0.48655 0.48626 0.48597 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

0.61250 0.61216 0.61182 0.61148 0.61114 0.61080 0.61045 0.61011 0.60976 0.60941 0.60906 0.60871 0.60835 0.60799 0.60764 0.60729 0.60693 0.60657 0.60621 0.60585 0.60549 … … … … … … … … … … … … … … … … … … … … … … … … … … … … … …

0.49109 0.49082 0.49054 0.49027 0.48999 0.48971 0.48943 0.48915 0.48887 0.48859 0.48830 0.48800 0.48771 0.48742 0.48713 0.48684 0.48655 0.48625 0.48596 0.48566 0.48536 0.48506 0.48476 0.48445 0.48415 0.48384 0.48354 0.48323 0.48292 0.48261 0.48230 0.48198 0.481166 0.48134 0.48103 0.48701 0.48040 0.48008 0.47975 0.47943 0.47910 0.47878 0.47845 0.47812 0.47778 0.47745 0.47711 0.47677 0.47643 0.47610 0.47577

0.61109 0.61073 0.61037 0.61001 0.60964 0.69928 0.60981 0.60854 0.60817 0.60780 0.60742 0.60704 0.60666 0.60628 0.60590 0.60552 0.60514 0.60475 0.60437 0.60398 0.60359 0.60320 0.60281 0.60241 0.60202 0.60162 0.60123 0.60083 0.60042 0.60002 0.59961 0.49920 0.59879 0.59838 0.59797 0.59756 0.59715 0.59674 0.59632 0.59590 0.59548 0.59507 0.59465 0.59422 0.59379 0.59336 0.52993 0.59250 0.59207 0.59164 0.59121

All dimensions are in inches. Values given for w1 and (C + c)1 in table are for 1-inch pitch axial threads. For other pitches divide table values by number of threads per inch. Courtesy of Van Keuren Co.


1910


Measuring Taper Screw Threads by Three-Wire Method.—When the 3-wire method is used in measuring a taper screw thread, the measurement is along a line that is not perpendicular to the axis of the screw thread, the inclination from the perpendicular equaling one-half the included angle of the taper. The formula that follows compensates for this inclination resulting from contact of the measuring instrument surfaces, with two wires on one side and one on the other. The taper thread is measured over the wires in the usual manner except that the single wire must be located in the thread at a point where the effective diameter is to be checked (as described more fully later). The formula shows the dimension equivalent to the correct pitch diameter at this given point. The general formula for taper screw threads follows: E – ( cot a ) ⁄ 2N + W ( 1 + csc a ) M = --------------------------------------------------------------------------sec b where M =measurement over the 3 wires E =pitch diameter a =one-half the angle of the thread N =number of threads per inch W =diameter of wires; and b =one-half the angle of taper. This formula is not theoretically correct but it is accurate for screw threads having tapers of 3⁄4 inch per foot or less. This general formula can be simplified for a given thread angle and taper. The simplified formula following (in which P = pitch) is for an American National Standard pipe thread: – ( 0.866025 × P ) + 3 × WM = E -----------------------------------------------------------------1.00049 Standard pitch diameters for pipe threads will be found in the section “American Pipe Threads,” which also shows the location, or distance, of this pitch diameter from the end of the pipe. In using the formula for finding dimension M over the wires,the single wire is placed in whatever part of the thread groove locates it at the point where the pitch diameter is to be checked. The wire must be accurately located at this point. The other wires are then placed on each side of the thread that is diametrically opposite the single wire. If the pipe thread is straight or without taper, M = E – ( 0.866025 × P ) + 3 × W Application of Formula to Taper Pipe Threads: To illustrate the use of the formula for taper threads, assume that dimension M is required for an American Standard 3-inch pipe thread gage. Table 1a starting on page 1862 shows that the 3-inch size has 8 threads per inch, or a pitch of 0.125 inch, and a pitch diameter at the gaging notch of 3.3885 inches. Assume that the wire diameter is 0.07217 inch: Then when the pitch diameter is correct 3.3885 – ( 0.866025 × 0.125 ) + 3 × 0.07217 M = -------------------------------------------------------------------------------------------------------- = 3.495 inches 1.00049 Pitch Diameter Equivalent to a Given Measurement Over the Wires: The formula following may be used to check the pitch diameter at any point along a tapering thread when measurement M over wires of a given diameter is known. In this formula, E = the effective or pitch diameter at the position occupied by the single wire. The formula is not theoretically correct but gives very accurate results when applied to tapers of 3⁄4 inch per foot or less. E = 1.00049 × M + ( 0.866025 × P ) – 3 × W Example:Measurement M = 3.495 inches at the gaging notch of a 3-inch pipe thread and the wire diameter = 0.07217 inch. Then



1911

E = 1.00049 × 3.495 + ( 0.866025 × 0.125 ) – 3 × 0.07217 = 3.3885 inches Pitch Diameter at Any Point Along Taper Screw Thread: When the pitch diameter in any position along a tapering thread is known, the pitch diameter at any other position may be determined as follows: Multiply the distance (measured along the axis) between the location of the known pitch diameter and the location of the required pitch diameter, by the taper per inch or by 0.0625 for American National Standard pipe threads. Add this product to the known diameter, if the required diameter is at a large part of the taper, or subtract if the required diameter is smaller. Example:The pitch diameter of a 3-inch American National Standard pipe thread is 3.3885 at the gaging notch. Determine the pitch diameter at the small end. The table starting on page 1862 shows that the distance between the gaging notch and the small end of a 3-inch pipe is 0.77 inch. Hence the pitch diameter at the small end = 3.3885 − (0.77 × 0.0625) = 3.3404 inches. Three-Wire Method Applied to Buttress Threads The angles of buttress threads vary somewhat, especially on the front or load-resisting side. Formula (1), which follows, may be applied to any angles required. In this formula, M = measurement over wires when pitch diameter E is correct; A = included angle of thread and thread groove; a = angle of front face or load-resisting side, measured from a line perpendicular to screw thread axis; P = pitch of thread; and W = wire diameter. P A- – a × csc -AM = E – ------------------------------------------- + W 1 + cos  -2  tan a + tan ( A – a ) 2

(1)

For given angles A and a, this general formula may be simplified as shown by Formulas (3) and (4). These simplified formulas contain constants with values depending upon angles A and a. Wire Diameter: The wire diameter for obtaining pitch-line contact at the back of a buttress thread may be determined by the following general Formula (2): cos a W = P  ----------------------  1 + cos A

(2)

45-Degree Buttress Thread: The buttress thread shown by the diagram at the left, has a front or load-resisting side that is perpendicular to the axis of the screw. Measurement M equivalent to a correct pitch diameter E may be determined by Formula (3): M = E – P + ( W × 3.4142 )

(3)

Wire diameter W for pitch-line contact at back of thread = 0.586 × pitch.


1912

Machinery's Handbook 28th Edition THREAD GAGES

50-Degree Buttress Thread with Front-face Inclination of 5 Degrees: T h i s b u t t r e s s thread form is illustrated by the diagram at the right. Measurement M equivalent to the correct pitch diameter E may be determined by Formula (4): M = E – ( P × 0.91955 ) + ( W × 3.2235 ) (4) Wire diameter W for pitch-line contact at back of thread = 0.606 × pitch. If the width of flat at crest and root = 1⁄8 × pitch, depth = 0.69 × pitch. American National Standard Buttress Threads ANSI B1.9-1973: This buttress screw thread has an included thread angle of 52 degrees and a front face inclination of 7 degrees. Measurements M equivalent to a pitch diameter E may be determined by Formula (5): M = E – 0.89064P + 3.15689W + c (5) The wire angle correction factor c is less than 0.0004 inch for recommended combinations of thread diameters and pitches and may be neglected. Use of wire diameter W = 0.54147P is recommended. Measurement of Pitch Diameter of Thread Ring Gages.—The application of direct methods of measurement to determine the pitch diameter of thread ring gages presents serious difficulties, particularly in securing proper contact pressure when a high degree of precision is required. The usual practice is to fit the ring gage to a master setting plug. When the thread ring gage is of correct lead, angle, and thread form, within close limits, this method is quite satisfactory and represents standard American practice. It is the only method available for small sizes of threads. For the larger sizes, various more or less satisfactory methods have been devised, but none of these have found wide application. Screw Thread Gage Classification.—Screw thread gages are classified by their degree of accuracy, that is, by the amount of tolerance afforded the gage manufacturer and the wear allowance, if any. There are also three classifications according to use: 1) Working gages for controlling production; 2) inspection gages for rejection or acceptance of the finished product; a n d 3) reference gages for determining the accuracy of the working and inspection gages. American National Standard for Gages and Gaging for Unified Inch Screw Threads ANSI/ASME B1.2-1983 (R2007).—This standard covers gaging methods for conformance of Unified Screw threads and provides the essential specifications for applicable gages required for unified inch screw threads. The standard includes the following gages for Product Internal Thread: GO Working Thread Plug Gage for inspecting the maximum-material GO functional limit. NOT GO (HI) Thread Plug Gage for inspecting the NOT GO (HI) functional diameter limit. Thread Snap Gage—GO Segments or Rolls for inspecting the maximum-material GO functional limit. Thread Snap Gage—NOT GO (HI) Segments or Rolls for inspecting the NOT GO (HI) functional diameter limit. Thread Snap Gages—Minimum Material: Pitch Diameter Cone Type and Vee and Thread Groove Diameter Type for inspecting the minimum-material limit pitch diameter. Thread-Setting Solid Ring Gage for setting internal thread indicating and snap gages. Plain Plug, Snap, and Indicating Gages for checking the minor diameter of internal threads. Snap and Indicating Gages for checking the major diameter of internal threads. Functional Indicating Thread Gage for inspecting the maximum-material GO functional limit and size and the NOT GO (HI) functional diameter limit and size.



1913

Minimum-Material Indicating Thread Gage for inspecting the minimum-material limit and size. Indicating Runout Thread Gage for inspecting runout of the minor diameter to pitch diameter. In addition to these gages for product internal threads, the Standard also covers differential gaging and such instruments as pitch micrometers, thread-measuring balls, optical comparator and toolmaker's microscope, profile tracing instrument, surface roughness measuring instrument, and roundness measuring equipment. The Standard includes the following gages for Product External Thread: GO Working Thread Ring Gage for inspecting the maximum-material GO functional limit. NOT GO (LO) Thread Ring Gage for inspecting the NOT GO (LO) functional diameter limit. Thread Snap Gage—GO Segments or Rolls for inspecting the maximum-material GO functional limit. Thread Snap Gage—NOT GO (LO) Segments or Rolls for inspecting the NOT GO (LO) functional diameter limit. Thread Snap Gages—Cone and Vee Type and Minimum Material Thread Groove Diameter Type for inspecting the minimum-material pitch diameter limit. Plain Ring and Snap Gages for checking the major diameter. Snap Gage for checking the minor diameter. Functional Indicating Thread Gage for inspecting the maximum-material GO functional limit and size and the NOT GO (LO) functional diameter limit and size. Minimum-Material Indicating Thread Gage for inspecting the minimum-material limit and size. Indicating Runout Gage for inspecting the runout of the major diameter to the pitch diameter. W Tolerance Thread-Setting Plug Gage for setting adjustable thread ring gages, checking solid thread ring gages, setting thread snap limit gages, and setting indicating thread gages. Plain Check Plug Gage for Thread Ring Gage for verifying the minor diameter limits of thread ring gages after the thread rings have been properly set with the applicable threadsetting plug gages. Indicating Plain Diameter Gage for checking the major diameter. Indicating Gage for checking the minor diameter. In addition to these gages for product external threads, the Standard also covers differential gaging and such instruments as thread micrometers, thread-measuring wires, optical comparator and toolmaker's microscope, profile tracing instrument, electromechanical lead tester, helical path attachment used with GO type thread indicating gage, helical path analyzer, surface roughness measuring equipment, and roundness measuring equipment. The standard lists the following for use of Threaded and Plain Gages for verification of product internal threads: Tolerance: Unless otherwise specified all thread gages which directly check the product thread shall be X tolerance for all classes. GO Thread Plug Gages: GO thread plug gages must enter and pass through the full threaded length of the product freely. The GO thread plug gage is a cumulative check of all thread elements except the minor diameter.


1914


NOT GO (HI) Thread Plug Gages: NOT GO (HI) thread plug gages when applied to the product internal thread may engage only the end threads (which may not be representative of the complete thread). Entering threads on product are incomplete and permit gage to start. Starting threads on NOT GO (HI) plugs are subject to greater wear than the remaining threads. Such wear in combination with the incomplete product threads permits further entry of the gage. NOT GO (HI) functional diameter is acceptable when the NOT GO (HI) thread plug gage applied to the product internal thread does not enter more than three complete turns. The gage should not be forced. Special requirements such as exceptionally thin or ductile material, small number of threads, etc., may necessitate modification of this practice. GO and NOT GO Plain Plug Gages for Minor Diameter of Product Internal Thread: (Recommended in Class Z tolerance.) GO plain plug gages must completely enter and pass through the length of the product without force. NOT GO cylindrical plug gage must not enter. The standard lists the following for use of Thread Gages for verification of product external threads: GO Thread Ring Gages: Adjustable GO thread ring gages must be set to the applicable W tolerance setting plugs to assure they are within specified limits. The product thread must freely enter the GO thread ring gage for the entire length of the threaded portion. The GO thread ring gage is a cumulative check of all thread elements except the major diameter. NOT GO (LO) Thread Ring Gages: NOT GO (LO) thread ring gages must be set to the applicable W tolerance setting plugs to assure that they are within specified limits. NOT GO (LO) thread ring gages when applied to the product external thread may engage only the end threads (which may not be representative of the complete product thread) Starting threads on NOT GO (LO) rings are subject to greater wear than the remaining threads. Such wear in combination with the incomplete threads at the end of the product thread permit further entry in the gage. NOT GO (LO) functional diameter is acceptable when the NOT GO (LO) thread ring gage applied to the product external thread does not pass over the thread more than three complete turns. The gage should not be forced. Special requirements such as exceptionally thin or ductile material, small number of threads, etc., may necessitate modification of this practice. GO and NOT GO Plain Ring and Snap Gages for Checking Major Diameter of Product External Thread: The GO gage must completely receive or pass over the major diameter of the product external thread to ensure that the major diameter does not exceed the maximum-material-limit. The NOT GO gage must not pass over the major diameter of the product external thread to ensure that the major diameter is not less than the minimum-materiallimit. Limitations concerning the use of gages are given in the standard as follows: Product threads accepted by a gage of one type may be verified by other types. It is possible, however, that parts which are near either rejection limit may be accepted by one type and rejected by another. Also, it is possible for two individual limit gages of the same type to be at the opposite extremes of the gage tolerances permitted, and borderline product threads accepted by one gage could be rejected by another. For these reasons, a product screw thread is considered acceptable when it passes a test by any of the permissible gages in ANSI B1.3 for the gaging system that are within the tolerances. Gaging large product external and internal threads equal to above 6.25-inch nominal size with plain and threaded plug and ring gages presents problems for technical and economic reasons. In these instances, verification may be based on use of modified snap or indicating gages or measurement of thread elements. Various types of gages or measuring



1915

devices in addition to those defined in the Standard are available and acceptable when properly correlated to this Standard. Producer and user should agree on the method and equipment used. Thread Forms of Gages.—Thread forms of gages for product internal and external threads are given in Table 1. The Standard ANSI/ASME B1.2-1983 (R2007) also gives illustrations of the thread forms of truncated thread setting plug gages, the thread forms of full-form thread setting plug gages, the thread forms of solid thread setting ring gages, and an illustration that shows the chip groove and removal of partial thread. Building Up Worn Plug Gages.—Plug gages which have been worn under size can be built up by chromium plating and then lapped to size. Any amount of metal up to 0.004 or 0.005 inch can be added to a worn gage. Chromium oxide is used in lapping chromium plated gages, or other parts, to size and for polishing. When the chromium plating of a plug gage has worn under size, it may be removed by subjecting it to the action of muriatic acid. The gage is then built up again by chromium plating and lapped to size. When removing the worn plating the gage should be watched carefully and the action of the acid stopped as soon as the plating has been removed in order to avoid the roughening effect of the acid on the steel. Thread Gage Tolerances.—Gage tolerances of thread plug and ring gages, thread setting plugs, and setting rings for Unified screw threads, designated as W and X tolerances, are given in Table 4. W tolerances represent the highest commercial grade of accuracy and workmanship, and are specified for thread setting gages; X tolerances are larger than W tolerances and are used for product inspection gages. Tolerances for plain gages are given in Table 2. Determining Size of Gages: The three-wire method of determining pitch diameter size of plug gages is recommended for gages covered by American National Standard B1.2, described in Appendix B of the 1983 issue of that Standard. Size limit adjustments of thread ring and external thread snap gages are determined by their fit on their respective calibrated setting plugs. Indicating gages and thread gages for product external threads are controlled by reference to appropriate calibrated setting plugs. Size limit adjustments of internal thread snap gages are determined by their fit on their respective calibrated setting rings. Indicating gages and other adjustable thread gages for product internal threads are controlled by reference to appropriate calibrated setting rings or by direct measuring methods. Interpretation of Tolerances: Tolerances on lead, half-angle, and pitch diameter are variations which may be taken independently for each of these elements and may be taken to the extent allowed by respective tabulated dimensional limits. The tabulated tolerance on any one element must not be exceeded, even though variations in the other two elements are smaller than the respective tabulated tolerances. Direction of Tolerance on Gages: At the maximum-material limit (GO), the dimensions of all gages used for final conformance gaging are to be within limits of size of the product thread. At the functional diameter limit, using NOT GO (HI and LO) thread gages, the standard practice is to have the gage tolerance within the limits of size of the product thread. Formulas for Limits of Gages: Formulas for limits of American National Standard Gages for Unified screw threads are given in Table 5. Some constants which are required to determine gage dimensions are tabulated in Table 3.



1916

Table 1. Thread Forms of Gages for Product Internal and External Threads

THREAD GAGES



1917

Table 2. American National Standard Tolerances for Plain Cylindrical Gages ANSI/ASME B1.2-1983 (R2007) Tolerance Classa

Size Range XX

Above

To and Including

0.020 0.825 1.510 2.510 4.510 6.510 9.010

0.825 1.510 2.510 4.510 6.510 9.010 12.010

.00002 .00003 .00004 .00005 .000065 .00008 .00010

X

Y

Z

ZZ

.00010 .00012 .00016 .00020 .00025 .00032 .00040

.00020 .00024 .00032 .00040 .00050 .00064 .00080

Tolerance .00004 .00006 .00008 .00010 .00013 .00016 .00020

.00007 .00009 .00012 .00015 .00019 .00024 .00030

a Tolerances apply to actual diameter of plug or ring. Apply tolerances as specified in the Standard. Symbols XX, X, Y, Z, and ZZ are standard gage tolerance classes.


Table 3. Constants for Computing Thread Gage Dimensions ANSI/ASME B1.2-1983 (R2007) Threads per Inch

Pitch, p

0.060 3 p 2 + 0.017p

.05p

.087p

Height of Sharp VThread, H = .866025p

H/2 = .43301p

H/4 = .216506p

80

.012500

.0034

.00063

.00109

.010825

.00541

.00271

72

.013889

.0037

.00069

.00122

.012028

.00601

.00301

64

.015625

.0040

.00078

.00136

.013532

.00677

.00338

56

.017857

.0044

.00089

.00155

.015465

.00773

.00387

48

.020833

.0049

.00104

.00181

.018042

.00902

.00451

44

.022727

.0052

.00114

.00198

.019682

.00984

.00492

40

.025000

.0056

.00125

.00218

.021651

.01083

.00541

36

.027778

.0060

.00139

.00242

.024056

.01203

.00601

32

.031250

.0065

.00156

.00272

.027063

.01353

.00677

28

.035714

.0071

.00179

.00311

.030929

.01546

.00773

27

.037037

.0073

.00185

.00322

.032075

.01604

.00802

24

.041667

.0079

.00208

.00361

.036084

.01804

.00902

20

.050000

.0090

.00250

.00435

.043301

.02165

.01083

18

.055556

.0097

.00278

.00483

.048113

.02406

.01203

16

.062500

.0105

.00313

.00544

0.54127

.02706

.01353

14

.071429

.0115

.00357

.00621

.061859

.03093

.01546

13

.076923

.0122

.00385

.00669

.066617

.03331

.01665

12

.083333

.0129

.00417

.00725

.072169

.03608

.01804

111⁄2

.086957

.0133

.00435

.00757

.075307

.03765

.01883

11

.090909

.0137

.00451

.00791

.078730

.03936

.01968

10

.100000

.0146

.00500

.00870

.086603

.04330

.02165

9

.111111

.0158

.00556

.00967

.096225

.04811

.02406

8

.125000

.0171

.00625

.01088

.108253

.05413

.02706

7

.142857

.0188

.00714

.01243

.123718

.06186

.03093

6

.166667

.0210

.00833

.01450

.144338

.07217

.03608

5

.200000

.0239

.01000

.01740

.173205

.08660

.04330

41⁄2

.222222

.0258

.01111

.01933

.192450

.09623

.04811

4

.250000

.0281

.01250

.02175

.216506

.10825

.05413

All dimensions are given in inches unless otherwise specified.



1918

Table 4. American National Standard Tolerance for GO, HI, and LO Thread Gages for Unified Inch Screw Thread Tolerance on Leada Thds. per Inch

To & incl. 1⁄ in. 2 Dia.

Above 1⁄ in. 2 Dia.

80, 72 64 56 48 44, 40 36 32 28, 27 24, 20 18 16 14, 13 12 111⁄2 11 10 9 8 7 6 5 41⁄2 4

.0001 .0001 .0001 .0001 .0001 .0001 .0001 .00015 .00015 .00015 .00015 .0002 .0002 .0002 .0002 … … … … … … … …

.00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .0002 .0002 .0002 .0002 .00025 .00025 .00025 .0003 .0003 .0003 .0003 .0003

80, 72 64 56, 48 44, 40 36 32, 28 27, 24 20 18 16, 14 13, 12 111⁄2 11, 10 9 8, 7 6 5, 41⁄2 4

.0002 .0002 .0002 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0004 .0004 .0004 .0004

.0002 .0002 .0002 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0004 .0004 .0004 .0004

Tol. on Thread Halfangle (±), minutes

Tol. on Major and Minor Diams.b

Tolerance on Pitch Diameterb Above Above Above 1⁄ to 2 11⁄2 to 4 to 11⁄2 in. 8 in. 4 in. Dia. Dia. Dia.

Above 8 to 12 in.c Dia.

.0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .0001 .00015 .00015 .00015 .00015 … … … … … … … …

.00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .00015 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 … … …

… … .0002 .0002 .0002 .0002 .0002 .0002 .0002 .0002 .00025 .00025 .00025 .00025 .00025 .0025 .00025 .00025 .00025 .00025 .00025 .00025 .00025

… … … … … … .00025 .00025 .00025 .00025 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003

… … … … … … .0003 .0003 .0003 .0003 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004

.0002 .0002 .0002 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0004 .0004 … …

.0002 .0002 .0002 .0002 .0002 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0003 .0004 .0004 … …

… … .0003 .0003 .0003 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0004 .0005 .0005 .0005 .0005

… … … … … .0005 .0005 .0005 .0005 .0006 .0006 .0006 .0006 .0006 .0006 .0006 .0006 .0006

… … … … … .0006 .0006 .0006 .0006 .0008 .0008 .0008 .0008 .0008 .0008 .0008 .0008 .0008


Above 1⁄ to Above 2 4 in. 4 in. Dia. Dia. W GAGES


20 20 20 18 15 12 12 8 8 8 8 6 6 6 6 6 6 5 5 5 4 4 4

.0003 .0003 .0003 .0003 .0003 .0003 .0003 .0005 .0005 .0005 .0006 .0006 .0006 .0006 .0006 … … … … … … … …

30 30 30 20 20 15 15 15 10 10 10 10 10 10 5 5 5 5

.0003 .0004 .0004 .0004 .0004 .0005 .0005 .0005 .0005 .0006 .0006 .0006 .0006 .0007 .0007 .0008 .0008 .0009

.0003 … .0004 … .0004 … .0004 … .0004 … .0004 … .0005 .0007 .0005 .0007 .0005 .0007 .0005 .0007 .0006 .0009 .0006 .0009 .0006 .0009 .0006 .0009 .0006 .0009 .0006 .0009 .0007 .0011 .0007 .0011 .0007 .0011 .0008 .0013 .0008 .0013 .0008 .0013 .0009 .0015 X GAGES .0003 … .0004 … .0004 … .0004 … .0004 … .0005 .0007 .0005 .0007 .0005 .0007 .0005 .0007 .0006 .0009 .0006 .0009 .0006 .0009 .0006 .0009 .0007 .0011 .0007 .0011 .0008 .0013 .0008 .0013 .0009 .0015

a Allowable variation in lead between any two threads not farther apart than the length of the standard gage as shown in ANSI B47.1. The tolerance on lead establishes the width of a zone, measured parallel to the axis of the thread, within which the actual helical path must lie for the specified length of the thread. Measurements are taken from a fixed reference point, located at the start of the first full thread, to a sufficient number of positions along the entire helix to detect all types of lead variations. The amounts that these positions vary from their basic (theoretical) positions are recorded with due respect to sign. The greatest variation in each direction (±) is selected, and the sum of their values, disregarding sign, must not exceed the tolerance limits specified for W gages. b Tolerances apply to designated size of thread. The application of the tolerances is specified in the Standard. c Above 12 in. the tolerance is directly proportional to the tolerance given in this column below, in the ratio of the diameter to 12 in.

All dimensions are given in inches unless otherwise specified.



1919

Table 5. Formulas for Limits of American National Standard Gages for Unified Inch Screw Threads ANSI/ASME B1.2-1983 (R2007) No. 1

Thread Gages for External Threads GO Pitch Diameter = Maximum pitch diameter of external thread. Gage tolerance is minus.

2

GO Minor Diameter = Maximum pitch diameter of external thread minus H/2. Gage tolerance is minus.

3

NOT GO (LO) Pitch Diameter (for plus tolerance gage) = Minimum pitch diameter of external thread. Gage tolerance is plus.

4

NOT GO (LO) Minor Diameter = Minimum pitch diameter of external thread minus H/4. Gage tolerance is plus.

5

GO = Maximum major diameter of external thread. Gage tolerance is minus.

6

NOT GO = Minimum major diameter of external thread. Gage tolerance is plus.

7

GO Major Diameter = Minimum major diameter of internal thread. Gage tolerance is plus.

Plain Gages for Major Diameter of External Threads

Thread Gages for Internal Threads

8

GO Pitch Diameter = Minimum pitch diameter of internal thread. Gage tolerance is plus.

9

NOT GO (HI) Major Diameter = Maximum pitch diameter of internal thread plus H/2. Gage tolerance is minus.

10

NOT GO (HI) Pitch Diameter = Maximum pitch diameter of internal thread. Gage tolerance is minus.

11

GO = Minimum minor diameter of internal thread. Gage tolerance is plus.

12

NOT GO = Maximum minor diameter of internal thread. Gage tolerance is minus.

13

GO Major Diameter (Truncated Portion) = Maximum major diameter of external thread (= minimum major

Plain Gages for Minor Diameter of Internal Threads

Full Form nd Truncated Setting Plugs

diameter of full portion of GO setting plug) minus minus.

( 0.060 3 p 2 + 0.017p )

. Gage tolerance is

14

GO Major Diameter (Full Portion) = Maximum major diameter of external thread. Gage tolerance is plus.

15

GO Pitch Diameter = Maximum pitch diameter of external thread. Gage tolerance is minus.

16

aNOT GO (LO) Major Diameter (Truncated Portion) = Minimum pitch diameter of external thread plus H/2. Gage tolerance is minus.

17

NOT GO (LO) Major Diameter (Full Portion) = Maximum major diameter of external thread provided major diameter crest width shall not be less than 0.001 in. (0.0009 in. truncation). Apply W tolerance plus for maximum size except that for 0.001 in. crest width apply tolerance minus. For the 0.001 in. crest width, major diameter is equal to maximum major diameter of external thread plus 0.216506p minus the sum of external thread pitch diameter tolerance and 0.0017 in.

18

NOT GO (LO) Pitch Diameter = Minimum pitch diameter of external thread. Gage tolerance is plus.

19

bGO

Solid Thread-setting Rings for Snap and Indicating Gages Pitch Diameter = Minimum pitch diameter of internal thread. W gage tolerance is plus.

20

GO Minor Diameter = Minimum minor diameter of internal thread. W gage tolerance is minus.

21

bNOT

22

NOT GO (HI) Minor Diameter = Maximum minor diameter of internal thread. W gage tolerance is minus.

GO (HI) Pitch Diameter = Maximum pitch diameter of internal thread. W gage tolerance is minus.

a Truncated portion is required when optional sharp root profile is used. b Tolerances greater than W tolerance for pitch diameter are acceptable when internal indicating or snap gage can accommodate a greater tolerance and when agreed upon by supplier and user.

See data in Screw Thread Systems section for symbols and dimensions of Unified Screw Threads.


1920

Machinery's Handbook 28th Edition TAPPING

TAPPING AND THREAD CUTTING Selection of Taps.—For most applications, a standard tap supplied by the manufacturer can be used, but some jobs may require special taps. A variety of standard taps can be obtained. In addition to specifying the size of the tap it is necessary to be able to select the one most suitable for the application at hand. The elements of standard taps that are varied are: the number of flutes; the type of flute, whether straight, spiral pointed, or spiral fluted; the chamfer length; the relief of the land, if any; the tool steel used to make the tap; and the surface treatment of the tap. Details regarding the nomenclature of tap elements are given in the section TAPS starting on page 880, along with a listing of the standard sizes available. Factors to consider in selecting a tap include: the method of tapping, by hand or by machine; the material to be tapped and its heat treatment; the length of thread, or depth of the tapped hole; the required tolerance or class of fit; and the production requirement and the type of machine to be used. The diameter of the hole must also be considered, although this action is usually only a matter of design and the specification of the tap drill size. Method of Tapping: The term hand tap is used for both hand and machine taps, and almost all taps can be applied by the hand or machine method. While any tap can be used for hand tapping, those having a concentric land without the relief are preferable. In hand tapping the tool is reversed periodically to break the chip, and the heel of the land of a tap with a concentric land (without relief) will cut the chip off cleanly or any portion of it that is attached to the work, whereas a tap with an eccentric or con-eccentric relief may leave a small burr that becomes wedged between the relieved portion of the land and the work. This wedging creates a pressure towards the cutting face of the tap that may cause it to chip; it tends to roughen the threads in the hole, and it increases the overall torque required to turn the tool. When tapping by machine, however, the tap is usually turned only in one direction until the operation is complete, and an eccentric or con-eccentric relief is often an advantage. Chamfer Length: Three types of hand taps, used both for hand and machine tapping, are available, and they are distinguished from each other by the length of chamfer. Taper taps have a chamfer angle that reduces the height about 8–10 teeth; plug taps have a chamfer angle with 3–5 threads reduced in height; and bottoming taps have a chamfer angle with 11⁄2 threads reduced in height. Since the teeth that are reduced in height do practically all the cutting, the chip load or chip thickness per tooth will be least for a taper tap, greater for a plug tap, and greatest for a bottoming tap. For most through hole tapping applications it is necessary to use only a plug type tap, which is also most suitable for blind holes where the tap drill hole is deeper than the required thread. If the tap must bottom in a blind hole, the hole is usually threaded first with a plug tap and then finished with a bottoming tap to catch the last threads in the bottom of the hole. Taper taps are used on materials where the chip load per tooth must be kept to a minimum. However, taper taps should not be used on materials that have a strong tendency to work harden, such as the austenitic stainless steels. Spiral Point Taps: Spiral point taps offer a special advantage when machine tapping through holes in ductile materials because they are designed to handle the long continuous chips that form and would otherwise cause a disposal problem. An angular gash is ground at the point or end of the tap along the face of the chamfered threads or lead teeth of the tap. This gash forms a left-hand helix in the flutes adjacent to the lead teeth which causes the chips to flow ahead of the tap and through the hole. The gash is usually formed to produce a rake angle on the cutting face that increases progressively toward the end of the tool. Since the flutes are used primarily to provide a passage for the cutting fluid, they are usually made narrower and shallower thereby strengthening the tool. For tapping thin work-



1921

pieces short fluted spiral point taps are recommended. They have a spiral point gash along the cutting teeth; the remainder of the threaded portion of the tap has no flute. Most spiral pointed taps are of plug type; however, spiral point bottoming taps are also made. Spiral Fluted Taps: Spiral fluted taps have a helical flute; the helix angle of the flute may be between 15 and 52 degrees and the hand of the helix is the same as that of the threads on the tap. The spiral flute and the rake that it forms on the cutting face of the tap combine to induce the chips to flow backward along the helix and out of the hole. Thus, they are ideally suited for tapping blind holes and they are available as plug and bottoming types. A higher spiral angle should be specified for tapping very ductile materials; when tapping harder materials, chipping at the cutting edge may result and the spiral angle must be reduced. Holes having a pronounced interruption such as a groove or a keyway can be tapped with spiral fluted taps. The land bridges the interruption and allows the tap to cut relatively smoothly. Serial Taps and Close Tolerance Threads: For tapping holes to close tolerances a set of serial taps is used. They are usually available in sets of three: the No. 1 tap is undersize and is the first rougher; the No. 2 tap is of intermediate size and is the second rougher; and the No. 3 tap is used for finishing. The different taps are identified by one, two, and three annular grooves in the shank adjacent to the square. For some applications involving finer pitches only two serial taps are required. Sets are also used to tap hard or tough materials having a high tensile strength, deep blind holes in normal materials, and large coarse threads. A set of more than three taps is sometimes required to produce threads of coarse pitch. Threads to some commercial tolerances, such as American Standard Unified 2B, or ISO Metric 6H, can be produced in one cut using a ground tap; sometimes even closer tolerances can be produced with a single tap. Ground taps are recommended for all close tolerance tapping operations. For much ordinary work, cut taps are satisfactory and more economical than ground taps. Tap Steels: Most taps are made from high speed steel. The type of tool steel used is determined by the tap manufacturer and is usually satisfactory when correctly applied except in a few exceptional cases. Typical grades of high speed steel used to make taps are M-1, M2, M-3, M-42, etc. Carbon tool steel taps are satisfactory where the operating temperature of the tap is low and where a high resistance to abrasion is not required as in some types of hand tapping. Surface Treatment: The life of high speed steel taps can sometimes be increased significantly by treating the surface of the tap. A very common treatment is oxide coating, which forms a thin metallic oxide coating on the tap that has lubricity and is somewhat porous to absorb and retain oil. This coating reduces the friction between the tap and the work and it makes the surface virtually impervious to rust. It does not increase the hardness of the surface but it significantly reduces or prevents entirely galling, or the tendency of the work material to weld or stick to the cutting edge and to other areas on the tap with which it is in contact. For this reason oxide coated taps are recommended for metals that tend to gall and stick such as non-free cutting low carbon steels and soft copper. It is also useful for tapping other steels having higher strength properties. Nitriding provides a very hard and wear resistant case on high speed steel. Nitrided taps are especially recommended for tapping plastics; they have also been used successfully on a variety of other materials including high strength high alloy steels. However, some caution must be used in specifying nitrided taps because the nitride case is very brittle and may have a tendency to chip. Chrome plating has been used to increase the wear resistance of taps but its application has been limited because of the high cost and the danger of hydrogen embrittlement which can cause cracks to form in the tool. A flash plate of about .0001 in. or less in thickness is applied to the tap. Chrome-plated taps have been used successfully to tap a variety of fer-



1922

rous and nonferrous materials including plastics, hard rubber, mild steel, and tool steel. Other surface treatments that have been used successfully to a limited extent are vapor blasting and liquid honing. Rake Angle: For the majority of applications in both ferrous and nonferrous materials the rake angle machined on the tap by the manufacturer is satisfactory. This angle is approximately 5 to 7 degrees. In some instances it may be desirable to alter the rake angle of the tap to obtain beneficial results and Table 1 provides a guide that can be used. In selecting a rake angle from this table, consideration must be given to the size of the tap and the strength of the land. Most standard taps are made with a curved face with the rake angle measured as a chord between the crest and root of the thread. The resulting shape is called a hook angle. Table 1. Tap Rake Angles for Tapping Different Materials Material

Rake Angle, Degrees

Material

Rake Angle, Degrees

Cast Iron

0–3

Aluminum

Malleable Iron

5–8

Brass

2–7

Naval Brass

5–8 5–12

Steel

8–20

AISI 1100 Series

5–12

Phosphor Bronze

Low Carbon (up

5–12

Tobin Bronze

5–8

Manganese Bronze

5–12

to .25 per cent) Medium Carbon, Annealed

5–10

(.30 to .60 per cent) Heat Treated, 225–283

0–8

Brinell. (.30 to .60 per cent) High Carbon and

0–5

High Speed Stainless Titanium

8–15 5–10

Magnesium

10–20

Monel

9–12

Copper

10–18

Zinc Die Castings

10–15

Plastic Thermoplastic

5–8

Thermosetting

0–3

Hard Rubber

0–3

Cutting Speed.—The cutting speed for machine tapping is treated in detail on page 1042. It suffices to say here that many variables must be considered in selecting this cutting speed and any tabulation may have to be modified greatly. Where cutting speeds are mentioned in the following section, they are intended only to provide a guideline to show the possible range of speeds that could be used. Tapping Specific Materials.—The work material has a great influence on the ease with which a hole can be tapped. For production work, in many instances, modified taps are recommended; however, for toolroom or short batch work, standard hand taps can be used on most jobs, providing reasonable care is taken when tapping. The following concerns the tapping of metallic materials; information on the tapping of plastics is given on page 600. Low Carbon Steel (Less than 0.15% C): These steels are very soft and ductile resulting in a tendency for the work material to tear and to weld to the tap. They produce a continuous chip that is difficult to break and spiral pointed taps are recommended for tapping through holes; for blind holes a spiral fluted tap is recommended. To prevent galling and welding, a liberal application of a sulfur base or other suitable cutting fluid is essential and the selection of an oxide coated tap is very helpful. Low Carbon Steels (0.15 to 0.30% C): The additional carbon in these steels is beneficial as it reduces the tendency to tear and to weld; their machinability is further improved by cold drawing. These steels present no serious problems in tapping provided a suitable cutting fluid is used. An oxide coated tap is recommended, particularly in the lower carbon range.



1923

Medium Carbon Steels (0.30 to 0.60% C): These steels can be tapped without too much difficulty, although a lower cutting speed must be used in machine tapping. The cutting speed is dependent on the carbon content and the heat treatment. Steels that have a higher carbon content must be tapped more slowly, especially if the heat treatment has produced a pearlitic microstructure. The cutting speed and ease of tapping is significantly improved by heat treating to produce a spheroidized microstructure. A suitable cutting fluid must be used. High Carbon Steels (More than 0.6% C): Usually these materials are tapped in the annealed or normalized condition although sometimes tapping is done after hardening and tempering to a hardness below 55 Rc. Recommendations for tapping after hardening and tempering are given under High Tensile Strength Steels. In the annealed and normalized condition these steels have a higher strength and are more abrasive than steels with a lower carbon content; thus, they are more difficult to tap. The microstructure resulting from the heat treatment has a significant effect on the ease of tapping and the tap life, a spheroidite structure being better in this respect than a pearlitic structure. The rake angle of the tap should not exceed 5 degrees and for the harder materials a concentric tap is recommended. The cutting speed is considerably lower for these steels and an activated sulfur-chlorinated cutting fluid is recommended. Alloy Steels: This classification includes a wide variety of steels, each of which may be heat treated to have a wide range of properties. When annealed and normalized they are similar to medium to high carbon steels and usually can be tapped without difficulty, although for some alloy steels a lower tapping speed may be required. Standard taps can be used and for machine tapping a con-eccentric relief may be helpful. A suitable cutting fluid must be used. High-Tensile Strength Steels: Any steel that must be tapped after being heat treated to a hardness range of 40–55 Rc is included in this classification. Low tap life and excessive tap breakage are characteristics of tapping these materials; those that have a high chromium content are particularly troublesome. Best results are obtained with taps that have concentric lands, a rake angle that is at or near zero degrees, and 6 to 8 chamfered threads on the end to reduce the chip load per tooth. The chamfer relief should be kept to a minimum. The load on the tap should be kept to a minimum by every possible means, including using the largest possible tap drill size; keeping the hole depth to a minimum; avoidance of bottoming holes; and, in the larger sizes, using fine instead of coarse pitches. Oxide coated taps are recommended although a nitrided tap can sometimes be used to reduce tap wear. An active sulfur-chlorinated oil is recommended as a cutting fluid and the tapping speed should not exceed about 10 feet per minute. Stainless Steels: Ferritic and martensitic type stainless steels are somewhat like alloy steels that have a high chromium content, and they can be tapped in a similar manner, although a slightly slower cutting speed may have to be used. Standard rake angle oxide coated taps are recommended and a cutting fluid containing molybdenum disulphide is helpful to reduce the friction in tapping. Austenitic stainless steels are very difficult to tap because of their high resistance to cutting and their great tendency to work harden. A workhardened layer is formed by a cutting edge of the tap and the depth of this layer depends on the severity of the cut and the sharpness of the tool. The next cutting edge must penetrate below the work-hardened layer, if it is to be able to cut. Therefore, the tap must be kept sharp and each succeeding cutting edge on the tool must penetrate below the work-hardened layer formed by the preceding cutting edge. For this reason, a taper tap should not be used, but rather a plug tap having 3–5 chamfered threads. To reduce the rubbing of the lands, an eccentric or con-eccentric relieved land should be used and a 10–15 degree rake angle is recommended. A tough continuous chip is formed that is difficult to break. To control this chip, spiral pointed taps are recommended for through holes and low-helix angle spiral fluted taps for blind holes. An oxide coating on the tap is very helpful and a sulfur-


1924


chlorinated mineral lard oil is recommended, although heavy duty soluble oils have also been used successfully. Free Cutting Steels: There are large numbers of free cutting steels, including free cutting stainless steels, which are also called free machining steels. Sulfur, lead, or phosphorus are added to these steels to improve their machinability. Free machining steels are always easier to tap than their counterparts that do not have the free machining additives. Tool life is usually increased and a somewhat higher cutting speed can be used. The type of tap recommended depends on the particular type of free machining steel and the nature of the tapping operation; usually a standard tap can be used. High Temperature Alloys: These are cobalt or nickel base nonferrous alloys that cut like austenitic stainless steel, but are often even more difficult to machine. The recommendations given for austenitic stainless steel also apply to tapping these alloys but the rake angle should be 0 to 10 degrees to strengthen the cutting edge. For most applications a nitrided tap or one made from M41, M42, M43, or M44 steel is recommended. The tapping speed is usually in the range of 5 to 10 feet per minute. Titanium and Titanium Alloys: Titanium and its alloys have a low specific heat and a pronounced tendency to weld on to the tool material; therefore, oxide coated taps are recommended to minimize galling and welding. The rake angle of the tap should be from 6 to 10 degrees. To minimize the contact between the work and the tap an eccentric or con-eccentric relief land should be used. Taps having interrupted threads are sometimes helpful. Pure titanium is comparatively easy to tap but the alloys are very difficult. The cutting speed depends on the composition of the alloy and may vary from 40 to 10 feet per minute. Special cutting oils are recommended for tapping titanium. Gray Cast Iron: The microstructure of gray cast iron can vary, even within a single casting, and compositions are used that vary in tensile strength from about 20,000 to 60,000 psi (160 to 250 Bhn). Thus, cast iron is not a single material, although in general it is not difficult to tap. The cutting speed may vary from 90 feet per minute for the softer grades to 30 feet per minute for the harder grades. The chip is discontinuous and straight fluted taps should be used for all applications. Oxide coated taps are helpful and gray cast iron can usually be tapped dry, although water soluble oils and chemical emulsions are sometimes used. Malleable Cast Iron: Commercial malleable cast irons are also available having a rather wide range of properties, although within a single casting they tend to be quite uniform. They are relatively easy to tap and standard taps can be used. The cutting speed for ferritic cast irons is 60–90 feet per minute, for pearlitic malleable irons 40–50 feet per minute, and for martensitic malleable irons 30–35 feet per minute. A soluble oil cutting fluid is recommended except for martensitic malleable iron where a sulfur base oil may work better. Ductile or Nodular Cast Iron: Several classes of nodular iron are used having a tensile strength varying from 60,000 to 120,000 psi. Moreover, the microstructure in a single casting and in castings produced at different times vary rather widely. The chips are easily controlled but have some tendency to weld to the faces and flanks of cutting tools. For this reason oxide coated taps are recommended. The cutting speed may vary from 15 fpm for the harder martensitic ductile irons to 60 fpm for the softer ferritic grades. A suitable cutting fluid should be used. Aluminum: Aluminum and aluminum alloys are relatively soft materials that have little resistance to cutting. The danger in tapping these alloys is that the tap will ream the hole instead of cutting threads, or that it will cut a thread eccentric to the hole. For these reasons, extra care must be taken when aligning the tap and starting the thread. For production tapping a spiral pointed tap is recommended for through holes and a spiral fluted tap for blind holes; preferably these taps should have a 10 to 15 degree rake angle. A lead screw tapping machine is helpful in cutting accurate threads. A heavy duty soluble oil or a light base mineral oil should be used as a cutting fluid.



1925

Copper Alloys: Most copper alloys are not difficult to tap, except beryllium copper and a few other hard alloys. Pure copper is difficult because of its ductility and the ductile continuous chip formed, which can be hard to control. However, with reasonable care and the use of medium heavy duty mineral lard oil it can be tapped successfully. Red brass, yellow brass, and similar alloys containing not more than 35 per cent zinc produce a continuous chip. While straight fluted taps can be used for hand tapping these alloys, machine tapping should be done with spiral pointed or spiral fluted taps for through and blind holes respectively. Naval brass, leaded brass, and cast brasses produce a discontinuous chip and a straight fluted tap can be used for machine tapping. These alloys exhibit a tendency to close in on the tap and sometimes an interrupted thread tap is used to reduce the resulting jamming effect. Beryllium copper and the silicon bronzes are the strongest of the copper alloys. Their strength combined with their ability to work harden can cause difficulties in tapping. For these alloys plug type taps should be used and the taps should be kept as sharp as possible. A medium or heavy duty water soluble oil is recommended as a cutting fluid. Other Tapping Lubricants.—The power required in tapping varies considerably with different lubricants. The following lubricants reduce the resistance to the cut when threading forged nuts and hexagon drawn material: stearine oil, lard oil, sperm oil, rape oil, and 10 per cent graphite with 90 per cent tallow. A mixture of cutting emulsion (soluble oil) with water reduces resistance to threading action well. A few emulsions are almost as good as animal and vegetable oils, but the emulsion used plays an important part; the majority of emulsions do not give good results. A large volume of lubricant gives somewhat better results than a small quantity, especially in the case of the thinner oils. Kerosene, turpentine, and graphite proved unsuitable for tapping steel. Mineral oils not mixed with animal and vegetable oils, and ordinary lubricating and machine oils, are wholly unsuitable. For aluminum, kerosene is recommended. For tapping cast iron use a strong solution of emulsion; oil has a tendency to make cast-iron chips clog in the flutes, preventing the lubricant from reaching the tap cutting teeth. For tapping copper, milk is a good lubricant. Diameter of Tap Drill.—Tapping troubles are sometimes caused by tap drills that are too small in diameter. The tap drill should not be smaller than is necessary to give the required strength to the thread as even a very small decrease in the diameter of the drill will increase the torque required and the possibility of broken taps. Tests have shown that any increase in the percentage of full thread over 60 per cent does not significantly increase the strength of the thread. Often, a 55 to 60 per cent thread is satisfactory, although 75 per cent threads are commonly used to provide an extra measure of safety. The present thread specifications do not always allow the use of the smaller thread depths. However, the specification given on a part drawing must be adhered to and may require smaller minor diameters than might otherwise be recommended. The depth of the thread in the tapped hole is dependent on the length of thread engagement and on the material. In general, when the engagement length is more than one and one-half times the nominal diameter a 50 or 55 per cent thread is satisfactory. Soft ductile materials permit a slightly larger tapping hole than brittle materials such as gray cast iron. It must be remembered that a twist drill is a roughing tool that may be expected to drill slightly oversize and that some variations in the size of the tapping holes are almost inevitable. When a closer control of the hole size is required it must be reamed. Reaming is recommended for the larger thread diameters and for some fine pitch threads. For threads of Unified form (see American National and Unified Screw Thread Forms on page 1712) the selection of tap drills is covered in the section Factors Influencing Minor Diameter Tolerances of Tapped Holes on page 1935, and the hole size limits are given in Table 2. Tables 3 and 4 give tap drill sizes for American National Form threads based on 75 per cent of full thread depth. For smaller-size threads the use of slightly larger drills, if permissible, will reduce tap breakage. The selection of tap drills for these threads also may be based on the hole size limits given in Table 2 for Unified threads that take lengths of engagement into account.



1926

Table 2. Recommended Hole Size Limits Before Tapping Unified Threads Classes 1B and 2B

Class 3B Length of Engagement (D = Nominal Size of Thread)

Thread Size

To and Including 1⁄ D 3

Above 1⁄3D to 2⁄3D


11⁄2D

To and Including Above 1⁄ D to 3D 3 Recommended Hole Size Limits



Above 11⁄2D to 3D

Max

Min

Max

Min

Maxb

Min

Max

Mina

Max

Min

Max

Min

Maxb

Min

Max

0.0465 0.0561 0.0580 0.0667 0.0691 0.0764 0.0797 0.0849 0.0894 0.0979 0.1004 0.104 0.111 0.130 0.134 0.145 0.156 0.171 0.177 0.182 0.196

0.0500 0.0599 0.0613 0.0705 0.0724 0.0804 0.0831 0.0894 0.0931 0.1020 0.1042 0.109 0.115 0.134 0.138 0.150 0.160 0.176 0.182 0.186 0.202

0.0479 0.0585 0.0596 0.0686 0.0707 0.0785 0.0814 0.0871 0.0912 0.1000 0.1023 0.106 0.113 0.132 0.136 0.148 0.158 0.174 0.179 0.184 0.199

0.0514 0.0623 0.0629 0.0724 0.0740 0.0825 0.0848 0.0916 0.0949 0.1041 0.1060 0.112 0.117 0.137 0.140 0.154 0.162 0.179 0.184 0.188 0.204

0.0479 0.0585 0.0602 0.0699 0.0720 0.0805 0.0831 0.0894 0.0931 0.1021 0.1042 0.109 0.115 0.134 0.138 0.150 0.160 0.176 0.182 0.186 0.202

0.0514 0.0623 0.0635 0.0737 0.0753 0.0845 0.0865 0.0939 0.0968 0.1062 0.1079 0.114 0.119 0.139 0.142 0.156 0.164 0.181 0.186 0.190 0.207

0.0479 0.0585 0.0602 0.0699 0.0720 0.0806 0.0833 0.0902 0.0939 0.1036 0.1060 0.112 0.117 0.137 0.140 0.152 0.162 0.178 0.184 0.188 0.204

0.0514 0.0623 0.0635 0.0737 0.0753 0.0846 0.0867 0.0947 0.0976 0.1077 0.1097 0.117 0.121 0.141 0.144 0.159 0.166 0.184 0.188 0.192 0.210

0.0465 0.0561 0.0580 0.0667 0.0691 0.0764 0.0797 0.0849 0.0894 0.0979 0.1004 0.1040 0.1110 0.1300 0.1340 0.1450 0.1560 0.1710 0.1770 0.1820 0.1960

0.0500 0.0599 0.0613 0.0705 0.0724 0.0804 0.0831 0.0894 0.0931 0.1020 0.1042 0.1091 0.1148 0.1345 0.1377 0.1502 0.1601 0.1758 0.1815 0.1858 0.2013

0.0479 0.0585 0.0596 0.0686 0.0707 0.0785 0.0814 0.0871 0.0912 0.1000 0.1023 0.1066 0.1128 0.1324 0.1359 0.1475 0.1581 0.1733 0.1794 0.1837 0.1986

0.0514 0.0623 0.0629 0.0724 0.0740 0.0825 0.0848 0.0916 0.0949 0.1041 0.1060 0.1115 0.1167 0.1367 0.1397 0.1528 0.1621 0.1782 0.1836 0.1877 0.2040

0.0479 0.0585 0.0602 0.0699 0.0720 0.0805 0.0831 0.0894 0.0931 0.1021 0.1042 0.1091 0.1147 0.1346 0.1378 0.1502 0.1601 0.1758 0.1815 0.1855 0.2013

0.0514 0.0623 0.0635 0.0737 0.0753 0.0845 0.0865 0.0939 0.0968 0.1062 0.1079 0.1140 0.1186 0.1389 0.1416 0.1555 0.1641 0.1807 0.1857 0.1895 0.2067

0.0479 0.0585 0.0602 0.0699 0.0720 0.0806 0.0833 0.0902 0.0939 0.1036 0.1060 0.1115 0.1166 0.1367 0.1397 0.1528 0.1621 0.1782 0.1836 0.1873 0.2040

0.0514 0.0623 0.0635 0.0737 0.0753 0.0846 0.0867 0.0947 0.0976 0.1077 0.1097 0.1164 0.1205 0.1410 0.1435 0.1581 0.1661 0.1831 0.1878 0.1913 0.2094

1⁄ –28 4 1⁄ –32 4 1⁄ –36 4 5⁄ –18 16 5⁄ –24 16 5⁄ –32 16 5⁄ –36 16 3⁄ –16 8

0.211

0.216

0.213

0.218

0.216

0.220

0.218

0.222

0.2110

0.2152

0.2131

0.2171

0.2150

0.2190

0.2169

0.2209

0.216

0.220

0.218

0.222

0.220

0.224

0.222

0.226

0.2160

0.2196

0.2172

0.2212

0.2189

0.2229

0.2206

0.2246

0.220

0.224

0.221

0.225

0.224

0.226

0.225

0.228

0.2200

0.2243

0.2199

0.2243

0.2214

0.2258

0.2229

0.2273

0.252

0.259

0.255

0.262

0.259

0.265

0.262

0.268

0.2520

0.2577

0.2551

0.2604

0.2577

0.2630

0.2604

0.2657

0.267

0.272

0.270

0.275

0.272

0.277

0.275

0.280

0.2670

0.2714

0.2694

0.2734

0.2714

0.2754

0.2734

0.2774

0.279

0.283

0.281

0.285

0.283

0.286

0.285

0.289

0.2790

0.2817

0.2792

0.2832

0.2807

0.2847

0.2822

0.2862

0.282

0.286

0.284

0.288

0.285

0.289

0.287

0.291

0.2820

0.2863

0.2824

0.2863

0.2837

0.2877

0.2850

0.2890

0.307

0.314

0.311

0.318

0.314

0.321

0.318

0.325

0.3070

0.3127

0.3101

0.3155

0.3128

0.3182

0.3155

0.3209


TAPPING

Mina 0–80 1–64 1–72 2–56 2–64 3–48 3–56 4–40 4–48 5–40 5–44 6–32 6–40 8–32 8–36 10–24 10–32 12–24 12–28 12–32 1⁄ –20 4

Machinery's Handbook 28th Edition Table 2. (Continued) Recommended Hole Size Limits Before Tapping Unified Threads Classes 1B and 2B


Thread Size


11⁄2D




Above 11⁄2D to 3D

Max 0.335

Min 0.333

Max 0.338

Min 0.335

Maxb 0.340

Min 0.338

Max 0.343

Mina 0.3300

Max 0.3336

Min 0.3314

Max 0.3354

Min 0.3332

Maxb 0.3372

Min 0.3351

Max 0.3391

0.341

0.345

0.343

0.347

0.345

0.349

0.347

0.351

0.3410

0.3441

0.3415

0.3455

0.3429

0.3469

0.3444

0.3484

0.345

0.349

0.346

0.350

0.347

0.352

0.349

0.353

0.3450

0.3488

0.3449

0.3488

0.3461

0.3501

0.3474

0.3514

0.360

0.368

0.364

0.372

0.368

0.376

0.372

0.380

0.3600

0.3660

0.3630

0.3688

0.3659

0.3717

0.3688

0.3746

0.383

0.389

0.386

0.391

0.389

0.395

0.391

0.397

0.3830

0.3875

0.3855

0.3896

0.3875

0.3916

0.3896

0.3937

0.399

0.403

0.401

0.406

0.403

0.407

0.406

0.410

0.3990

0.4020

0.3995

0.4035

0.4011

0.4051

0.4017

0.4067

0.417

0.426

0.421

0.430

0.426

0.434

0.430

0.438

0.4170

0.4225

0.4196

0.4254

0.4226

0.4284

0.4255

0.4313

0.410

0.414

0.414

0.424

0.414

0.428

0.424

0.433

0.4100

0.4161

0.4129

0.4192

0.4160

0.4223

0.4192

0.4255

0.446

0.452

0.449

0.454

0.452

0.457

0.454

0.460

0.4460

0.4498

0.4477

0.4517

0.4497

0.4537

0.4516

0.4556

0.461

0.467

0.463

0.468

0.466

0.470

0.468

0.472

0.4610

0.4645

0.4620

0.4660

0.4636

0.4676

0.4652

0.4692

0.472

0.476

0.476

0.486

0.476

0.490

0.486

0.495

0.4720

0.4783

0.4753

0.4813

0.4783

0.4843

0.4813

0.4873

0.502

0.509

0.505

0.512

0.509

0.515

0.512

0.518

0.5020

0.5065

0.5045

0.5086

0.5065

0.5106

0.5086

0.5127

0.517

0.522

0.520

0.525

0.522

0.527

0.525

0.530

0.5170

0.5209

0.5186

0.5226

0.5204

0.5244

0.5221

0.5261

0.524

0.528

0.526

0.531

0.528

0.532

0.531

0.535

0.5240

0.5270

0.5245

0.5285

0.5261

0.5301

0.5277

0.5317

0.527

0.536

0.532

0.541

0.536

0.546

0.541

0.551

0.5270

0.5328

0.5298

0.5360

0.5329

0.5391

0.5360

0.5422

0.535

0.544

0.540

0.549

0.544

0.553

0.549

0.558

0.5350

0.5406

0.5377

0.5435

0.5405

0.5463

0.5434

0.5492

0.565

0.572

0.568

0.575

0.572

0.578

0.575

0.581

0.5650

0.5690

0.5670

0.5711

0.5690

0.5730

0.5711

0.5752

0.580

0.585

0.583

0.588

0.585

0.590

0.588

0.593

0.5800

0.5834

0.5811

0.5851

0.5829

0.5869

0.5846

0.5886

0.586

0.591

0.588

0.593

0.591

0.595

0.593

0.597

0.5860

0.5895

0.5870

0.5910

0.5886

0.5926

0.5902

0.5942

0.597

0.606

0.602

0.611

0.606

0.615

0.611

0.620

0.5970

0.6029

0.6001

0.6057

0.6029

0.6085

0.6057

0.6113

0.642

0.647

0.645

0.650

0.647

0.652

0.650

0.655

0.6420

0.6459

0.6436

0.6476

0.6454

0.6494

0.6471

0.6511

0.642

0.653

0.647

0.658

0.653

0.663

0.658

0.668

0.6420

0.6481

0.6449

0.6513

0.6481

0.6545

0.6513

0.6577

0.660

0.669

0.665

0.674

0.669

0.678

0.674

0.683

0.6600

0.6652

0.6626

0.6680

0.6653

0.6707

0.6680

0.6734

0.682

0.689

0.686

0.693

0.689

0.696

0.693

0.700

0.6820

0.6866

0.6844

0.6887

0.6865

0.6908

0.6886

0.6929

0.696

0.702

0.699

0.704

0.702

0.707

0.704

0.710

0.6960

0.6998

0.6977

0.7017

0.6997

0.7037

0.7016

0.7056

0.711

0.716

0.713

0.718

0.716

0.720

0.718

0.722

0.7110

0.7145

0.7120

0.7160

0.7136

0.7176

0.7152

0.7192

0.722

0.731

0.727

0.736

0.731

0.740

0.736

0.745

0.7220

0.7276

0.7250

0.7303

0.7276

0.7329

0.7303

0.7356


1927

Mina 0.330

TAPPING

3⁄ –24 8 3⁄ –32 8 3⁄ –36 8 7⁄ –14 16 7⁄ –20 16 7⁄ –28 16 1⁄ –13 2 1⁄ –12 2 1⁄ –20 2 1⁄ –28 2 9⁄ –12 16 9⁄ –18 16 9⁄ –24 16 9⁄ –28 16 5⁄ –11 8 5⁄ –12 8 5⁄ –18 8 5⁄ –24 8 5⁄ –28 8 11⁄ –12 16 11⁄ –24 16 3⁄ –10 4 3⁄ –12 4 3⁄ –16 4 3⁄ –20 4 3⁄ –28 4 13⁄ –12 16




Classes 1B and 2B

1928

Table 2. (Continued) Recommended Hole Size Limits Before Tapping Unified Threads Class 3B Length of Engagement (D = Nominal Size of Thread) Thread Size




11⁄2D




Above 11⁄2D to 3D

Max 0.752

Min 0.749

Max 0.756

Min 0.752

Maxb 0.759

Min 0.756

Max 0.763

Mina 0.7450

Max 0.7491

Min 0.7469

Max 0.7512

Min 0.7490

Maxb 0.7533

Min 0.7511

Max 0.7554

0.758

0.764

0.761

0.766

0.764

0.770

0.766

0.772

0.7580

0.7623

0.7602

0.7642

0.7622

0.7662

0.7641

0.7681

0.755

0.767

0.761

0.773

0.767

0.778

0.773

0.785

0.7550

0.7614

0.7580

0.7647

0.7614

0.7681

0.7647

0.7714

0.785

0.794

0.790

0.799

0.794

0.803

0.799

0.808

0.7850

0.7900

0.7874

0.7926

0.7900

0.7952

0.7926

0.7978

0.798

0.806

0.802

0.810

0.806

0.814

0.810

0.818

0.7980

0.8022

0.8000

0.8045

0.8023

0.8068

0.8045

0.8090

0.807

0.814

0.811

0.818

0.814

0.821

0.818

0.825

0.8070

0.8116

0.8094

0.8137

0.8115

0.8158

0.8136

0.8179

0.821

0.827

0.824

0.829

0.827

0.832

0.829

0.835

0.8210

0.8248

0.8227

0.8267

0.8247

0.8287

0.8266

0.8306

0.836

0.840

0.838

0.843

0.840

0.845

0.843

0.847

0.8360

0.8395

0.8370

0.8410

0.8386

0.8426

0.8402

0.8442

0.847

0.856

0.852

0.861

0.856

0.865

0.861

0.870

0.8470

0.8524

0.8499

0.8550

0.8524

0.8575

0.8550

0.8601

0.870

0.877

0.874

0.881

0.877

0.884

0.881

0.888

0.8700

0.8741

0.8719

0.8762

0.8740

0.8783

0.8761

0.8804

0.883

0.889

0.886

0.891

0.889

0.895

0.891

0.897

0.8830

0.8873

0.8852

0.8892

0.8872

0.8912

0.8891

0.8931

1–8 1–12 1–14 1–16 1–20 1–28 1 1 ⁄16–12

0.865 0.910 0.923 0.932 0.946 0.961 0.972

0.878 0.919 0.931 0.939 0.952 0.966 0.981

0.871 0.915 0.927 0.936 0.949 0.963 0.977

0.884 0.924 0.934 0.943 0.954 0.968 0.986

0.878 0.919 0.931 0.939 0.952 0.966 0.981

0.890 0.928 0.938 0.946 0.957 0.970 0.990

0.884 0.924 0.934 0.943 0.954 0.968 0.986

0.896 0.933 0.942 0.950 0.960 0.972 0.995

0.8650 0.9100 0.9230 0.9320 0.9460 0.9610 0.9720

0.8722 0.9148 0.9271 0.9366 0.9498 0.9645 0.9773

0.8684 0.9123 0.9249 0.9344 0.9477 0.9620 0.9748

0.8759 0.9173 0.9293 0.9387 0.9517 0.9660 0.9798

0.8722 0.9148 0.9271 0.9365 0.9497 0.9636 0.9773

0.8797 0.9198 0.9315 0.9408 0.9537 0.9676 0.9823

0.8760 0.9173 0.9293 0.9386 0.9516 0.9652 0.9798

0.8835 0.9223 0.9337 0.9429 0.9556 0.9692 0.9848

11⁄16–16

0.995

1.002

0.999

1.055

1.002

1.009

1.055

1.013

0.9950

0.9991

0.9969

1.0012

0.9990

1.0033

1.0011

1.0054

11⁄16–18

1.002

1.009

1.005

1.012

1.009

1.015

1.012

1.018

1.0020

1.0065

1.0044

1.0085

1.0064

1.0105

1.0085

1.0126

11⁄8–7

0.970

0.984

0.977

0.991

0.984

0.998

0.991

1.005

0.9700

0.9790

0.9747

0.9833

0.9789

0.9875

0.9832

0.9918

11⁄8–8

0.990

1.003

0.996

1.009

1.003

1.015

1.009

1.021

0.9900

0.9972

0.9934

1.0009

0.9972

1.0047

1.0010

1.0085

11⁄8–12

1.035

1.044

1.040

1.049

1.044

1.053

1.049

1.058

1.0350

1.0398

1.0373

1.0423

1.0398

1.0448

1.0423

1.0473

11⁄8–16

1.057

1.064

1.061

1.068

1.064

1.071

1.068

1.075

1.0570

1.0616

1.0594

1.0637

1.0615

1.0658

1.0636

1.0679

11⁄8–18

1.065

1.072

1.068

1.075

1.072

1.078

1.075

1.081

1.0650

1.0690

1.0669

1.0710

1.0689

1.0730

1.0710

1.0751

11⁄8–20 11⁄8–28 13⁄16–12

1.071

1.077

1.074

1.079

1.077

1.082

1.079

1.085

1.0710

1.0748

1.0727

1.0767

1.0747

1.0787

1.0766

1.0806

1.086

1.091

1.088

1.093

1.091

1.095

1.093

1.097

1.0860

1.0895

1.0870

1.0910

1.0886

1.0926

1.0902

1.0942

1.097

1.106

1.102

1.111

1.106

1.115

1.111

1.120

1.0970

1.1023

1.0998

1.1048

1.1023

1.1073

1.1048

1.1098


TAPPING

Mina 0.745

13⁄ –16 16 13⁄ –20 16 7⁄ –9 8 7⁄ –12 8 7⁄ –14 8 7⁄ –16 8 7⁄ –20 8 7⁄ –28 8 15⁄ –12 16 15⁄ –16 16 15⁄ –20 16



Thread Size

13⁄16–16


11⁄2D




Above 11⁄2D to 3D

Max 1.127

Min 1.124

Max 1.131

Min 1.127

Maxb 1.134

Min 1.131

Max 1.138

Mina 1.1200

Max 1.1241

Min 1.1219

Max 1.1262

Min 1.1240

Maxb 1.1283

Min 1.1261

Max 1.1304

1.127

1.134

1.130

1.137

1.134

1.140

1.137

1.143

1.1270

1.1315

1.1294

1.1335

1.1314

1.1355

1.1335

1.1376

1.095

1.109

1.102

1.116

1.109

1.123

1.116

1.130

1.0950

1.1040

1.0997

1.1083

1.1039

1.1125

1.1082

1.1168

1.115

1.128

1.121

1.134

1.128

1.140

1.134

1.146

1.1150

1.1222

1.1184

1.1259

1.1222

1.1297

1.1260

1.1335

1.160

1.169

1.165

1.174

1.169

1.178

1.174

1.183

1.1600

1.1648

1.1623

1.1673

1.1648

1.1698

1.1673

1.1723

1.182

1.189

1.186

1.193

1.189

1.196

1.193

1.200

1.1820

1.1866

1.1844

1.1887

1.1865

1.1908

1.1886

1.1929

1.190

1.197

1.193

1.200

1.197

1.203

1.200

1.206

1.1900

1.1940

1.1919

1.1960

1.1939

1.1980

1.1960

1.2001

1.196

1.202

1.199

1.204

1.202

1.207

1.204

1.210

1.1960

1.1998

1.1977

1.2017

1.1997

1.2037

1.2016

1.2056

1.222

1.231

1.227

1.236

1.231

1.240

1.236

1.245

1.2220

1.2273

1.2248

1.2298

1.2273

1.2323

1.2298

1.2348

1.245

1.252

1.249

1.256

1.252

1.259

1.256

1.263

1.2450

1.2491

1.2469

1.2512

1.2490

1.2533

1.2511

1.2554

1.252

1.259

1.256

1.262

1.259

1.265

1.262

1.268

1.2520

1.2565

1.2544

1.2585

1.2564

1.2605

1.2585

1.2626

1.195

1.210

1.203

1.221

1.210

1.225

1.221

1.239

1.1950

1.2046

1.1996

1.2096

1.2046

1.2146

1.2096

1.2196

1.240

1.253

1.246

1.259

1.253

1.265

1.259

1.271

1.2400

1.2472

1.2434

1.2509

1.2472

1.2547

1.2510

1.2585

1.285

1.294

1.290

1.299

1.294

1.303

1.299

1.308

1.2850

1.2898

1.2873

1.2923

1.2898

1.2948

1.2923

1.2973

1.307

1.314

1.311

1.318

1.314

1.321

1.318

1.325

1.3070

1.3116

1.3094

1.3137

1.3115

1.3158

1.3136

1.3179

1.315

1.322

1.318

1.325

1.322

1.328

1.325

1.331

1.3150

1.3190

1.3169

1.3210

1.3189

1.3230

1.3210

1.3251

1.347

1.354

1.350

1.361

1.354

1.365

1.361

1.370

1.3470

1.3523

1.3498

1.3548

1.3523

1.3573

1.3548

1.3598

1.370

1.377

1.374

1.381

1.377

1.384

1.381

1.388

1.3700

1.3741

1.3719

1.3762

1.3740

1.3783

1.3761

1.3804

1.377

1.384

1.380

1.387

1.384

1.390

1.387

1.393

1.3770

1.3815

1.3794

1.3835

1.3814

1.3855

1.3835

1.3876

1.320

1.335

1.328

1.346

1.335

1.350

1.346

1.364

1.3200

1.3296

1.3246

1.3346

1.3296

1.3396

1.3346

1.3446

1.365

1.378

1.371

1.384

1.378

1.390

1.384

1.396

1.3650

1.3722

1.3684

1.3759

1.3722

1.3797

1.3760

1.3835

1.410

1.419

1.4155

1.424

1.419

1.428

1.424

1.433

1.4100

1.4148

1.4123

1.4173

1.4148

1.4198

1.4173

1.4223

1.432

1.439

1.436

1.443

1.439

1.446

1.443

1.450

1.4320

1.4366

1.4344

1.4387

1.4365

1.4408

1.4386

1.4429

1.440

1.446

1.443

1.450

1.446

1.452

1.450

1.456

1.4400

1.4440

1.4419

1.4460

1.4439

1.4480

1.4460

1.4501

1.446

1.452

1.449

1.454

1.452

1.457

1.454

1.460

1.4460

1.4498

1.4477

1.4517

1.4497

1.4537

1.4516

1.4556

1.495

1.502

1.499

1.506

1.502

1.509

1.506

1.513

1.4950

1.4991

1.4969

1.5012

1.4990

1.5033

1.5011

1.5054

1.502

1.509

1.505

1.512

1.509

1.515

1.512

1.518

1.5020

1.5065

1.5044

1.5085

1.5064

1.5105

1.5085

1.5126


1929

Mina 1.120

TAPPING

13⁄16–18 11⁄4–7 11⁄4–8 11⁄4–12 11⁄4–16 11⁄4–18 11⁄4–20 15⁄16–12 15⁄16–16 15⁄16–18 13⁄8–6 13⁄8–8 13⁄8–12 13⁄8–16 13⁄8–18 17⁄16–12 17⁄16–16 17⁄16–18 11⁄2–6 11⁄2–8 11⁄2–12 11⁄2–16 11⁄2–18 11⁄2–20 19⁄16–16 19⁄16–18




Classes 1B and 2B

1930





11⁄2D




Above 11⁄2D to 3D

Max 1.498

Min 1.494

Max 1.509

Min 1.498

Maxb 1.515

Min 1.509

Max 1.521

Mina 1.4900

Max 1.4972

Min 1.4934

Max 1.5009

Min 1.4972

Maxb 1.5047

Min 1.5010

Max 1.5085

1.535

1.544

1.540

1.549

1.544

1.553

1.549

1.558

1.5350

1.5398

1.5373

1.5423

1.5398

1.5448

1.5423

1.5473

1.557

1.564

1.561

1.568

1.564

1.571

1.568

1.575

1.5570

1.5616

1.5594

1.5637

1.5615

1.5658

1.5636

1.5679

1.565

1.572

1.568

1.575

1.572

1.578

1.575

1.581

1.5650

1.5690

1.5669

1.5710

1.5689

1.5730

1.5710

1.5751

1.620

1.627

1.624

1.631

1.627

1.634

1.631

1.638

1.6200

1.6241

1.6219

1.6262

1.6240

1.6283

1.6261

1.6304

1.627

1.634

1.630

1.637

1.634

1.640

1.637

1.643

1.6270

1.6315

1.6294

1.6335

1.6314

1.6355

1.6335

1.6376

1.534

1.551

1.543

1.560

1.551

1.568

1.560

1.577

1.5340

1.5455

1.5395

1.5515

1.5455

1.5575

1.5515

1.5635

1.615

1.628

1.621

1.634

1.628

1.640

1.634

1.646

1.6150

1.6222

1.6184

1.6259

1.6222

1.6297

1.6260

1.6335

1.660

1.669

1.665

1.674

1.669

1.678

1.674

1.683

1.6600

1.6648

1.6623

1.6673

1.6648

1.6698

1.6673

1.6723

1.682

1.689

1.686

1.693

1.689

1.696

1.693

1.700

1.6820

1.6866

1.6844

1.6887

1.6865

1.6908

1.6886

1.6929

1.696

1.702

1.699

1.704

1.702

1.707

1.704

1.710

1.6960

1.6998

1.6977

1.7017

1.6997

1.7037

1.7016

1.7056

1.745

1.752

1.749

1.756

1.752

1.759

1.756

1.763

1.7450

1.7491

1.7469

1.7512

1.7490

1.7533

1.7511

1.7554

1.740

1.752

1.746

1.759

1.752

1.765

1.759

1.771

1.7400

1.7472

1.7434

1.7509

1.7472

1.7547

1.7510

1.7585

1.785

1.794

1.790

1.799

1.794

1.803

1.799

1.808

1.7850

1.7898

1.7873

1.7923

1.7898

1.7948

1.7923

1.7973

1.807

1.814

1.810

1.818

1.814

1.821

1.818

1.825

1.8070

1.8116

1.8094

1.8137

1.8115

1.8158

1.8136

1.1879

1.870

1.877

1.874

1.881

1.877

1.884

1.881

1.888

1.8700

1.8741

1.8719

1.8762

1.8740

1.8783

1.8761

1.8804

1.759

1.777

1.768

1.786

1.777

1.795

1.786

1.804

1.7590

1.7727

1.7661

1.7794

1.7728

1.7861

1.7794

1.7927

2–8 2–12 2–16 2–20 21⁄16–16

1.865 1.910 1.932 1.946 1.995

1.878 1.919 1.939 1.952 2.002

1.871 1.915 1.936 1.949 2.000

1.884 1.924 1.943 1.954 2.006

1.878 1.919 1.939 1.952 2.002

1.890 1.928 1.946 1.957 2.009

1.884 1.924 1.943 1.954 2.006

1.896 1.933 1.950 1.960 2.012

1.8650 1.9100 1.9320 1.9460 1.9950

1.8722 1.9148 1.9366 1.9498 1.9991

1.8684 1.9123 1.9344 1.9477 1.9969

1.8759 1.9173 1.9387 1.9517 2.0012

1.8722 1.9148 1.9365 1.9497 1.9990

1.8797 1.9198 1.9408 1.9537 2.0033

1.8760 1.9173 1.9386 1.9516 2.0011

1.8835 1.9223 1.9429 1.9556 2.0054

21⁄8–8

1.990

2.003

1.996

2.009

2.003

2.015

2.009

2.021

1.9900

1.9972

1.9934

2.0009

1.9972

2.0047

2.0010

2.0085

21⁄8–12

2.035

2.044

2.040

2.049

2.044

2.053

2.049

2.058

2.0350

2.0398

2.0373

2.0423

2.0398

2.0448

2.0423

2.0473

21⁄8–16 23⁄16–16 21⁄4–41⁄2

2.057

2.064

2.061

2.068

2.064

2.071

2.068

2.075

2.0570

2.0616

2.0594

2.0637

2.0615

2.0658

2.0636

2.0679

2.120

2.127

2.124

2.131

2.127

2.134

2.131

2.138

2.1200

2.1241

2.1219

2.1262

2.1240

2.1283

2.1261

2.1304

2.009

2.027

2.018

2.036

2.027

2.045

2.036

2.054

2.0090

2.0227

2.0161

2.0294

2.0228

2.0361

2.0294

2.0427


TAPPING

Mina 1.490

15⁄8–12 15⁄8–16 15⁄8–18 111⁄16–16 111⁄16–18 13⁄4–5 13⁄4–8 13⁄4–12 13⁄4–16 13⁄4–20 113⁄16–16 17⁄8–8 17⁄8–12 17⁄8–16 115⁄16–16 2–41⁄2

15⁄8–8



Thread Size




11⁄2D




Above 11⁄2D to 3D

Min 2.121

Max 2.134

Min 2.128

Maxb 2.140

Min 2.134

Max 2.146

Mina 2.1150

Max 2.1222

Min 2.1184

Max 2.1259

Min 2.1222

Maxb 2.1297

Min 2.1260

Max 2.1335

2.160

2.169

2.165

2.174

2.169

2.178

2.174

2.182

2.1600

2.1648

2.1623

2.1673

2.1648

2.1698

2.1673

2.1723

2.182

2.189

2.186

2.193

2.189

2.196

2.193

2.200

2.1820

2.1866

2.1844

2.1887

2.1865

2.1908

2.1886

2.1929

2.196

2.202

2.199

2.204

2.202

2.207

2.204

2.210

2.1960

2.1998

2.1977

2.2017

2.1997

2.2037

2.2016

2.2056

2.245

2.252

2.249

2.256

2.252

2.259

2.256

2.263

2.2450

2.2491

2.2469

2.2512

2.2490

2.2533

2.2511

2.2554

2.285

2.294

2.290

2.299

2.294

2.303

2.299

2.308

2.2850

2.2898

2.2873

2.2923

2.2898

2.2948

2.2923

2.2973

2.307

2.314

2.311

2.318

2.314

2.321

2.318

2.325

2.3070

2.3116

2.3094

2.3137

2.3115

2.3158

2.3136

2.3179

2.370

2.377

2.374

2.381

2.377

2.384

2.381

2.388

2.3700

2.3741

2.3719

2.3762

2.3740

2.3783

2.3761

2.3804

2.229

2.248

2.238

2.258

2.248

2.267

2.258

2.277

2.2290

2.2444

2.2369

2.2519

2.2444

2.2594

2.2519

2.2669

2.365

2.378

2.371

2.384

2.378

2.390

2.384

2.396

2.3650

2.3722

2.3684

2.3759

2.3722

2.3797

2.3760

2.3835

2.410

2.419

2.415

2.424

2.419

2.428

2.424

2.433

2.4100

2.4148

2.4123

2.4173

2.4148

2.4198

2.4173

2.4223

2.432

2.439

2.436

2.443

2.439

2.446

2.443

2.450

2.4320

2.4366

2.4344

2.4387

2.4365

2.4408

2.4386

2.4429

2.446

2.452

2.449

2.454

2.452

2.457

2.454

2.460

2.4460

2.4498

2.4478

2.4517

2.4497

2.4537

2.4516

2.4556

2.535

2.544

2.540

2.549

2.544

2.553

2.549

2.558

2.5350

2.5398

2.5373

2.5423

2.5398

2.5448

2.5423

2.5473

2.557

2.564

2.561

2.568

2.564

2.571

2.568

2.575

2.5570

2.5616

2.5594

2.5637

2.5615

2.5658

2.5636

2.5679

2.479

2.498

2.489

2.508

2.498

2.517

2.508

2.527

2.4790

2.4944

2.4869

2.5019

2.4944

2.5094

2.5019

2.5169

2.615

2.628

2.621

2.634

2.628

2.640

2.634

2.644

2.6150

2.6222

2.6184

2.6259

2.6222

2.6297

2.6260

2.6335

2.660

2.669

2.665

2.674

2.669

2.678

2.674

2.683

2.6600

2.6648

2.6623

2.6673

2.6648

2.6698

2.6673

2.6723

2.682

2.689

2.686

2.693

2.689

2.696

2.693

2.700

2.6820

2.6866

2.6844

2.6887

2.6865

2.6908

2.6886

2.6929

2.785

2.794

2.790

2.809

2.794

2.803

2.809

2.808

2.7850

2.7898

2.7873

2.7923

2.7898

2.7948

2.7923

2.7973

2.807

2.814

2.811

2.818

2.814

2.821

2.818

2.825

2.8070

2.8116

2.8094

2.8137

2.8115

2.8158

2.8136

2.8179

3–4 3–8 3–12 3–16 31⁄8–12

2.729 2.865 2.910 2.932 3.035

2.748 2.878 2.919 2.939 3.044

2.739 2.871 2.915 2.936 3.040

2.758 2.884 2.924 2.943 3.049

2.748 2.878 2.919 2.939 3.044

2.767 2.890 2.928 2.946 3.053

2.758 2.884 2.924 2.943 3.049

2.777 2.896 2.933 2.950 3.058

2.7290 2.8650 2.9100 2.9320 3.0350

2.7444 2.8722 2.9148 2.9366 3.0398

2.7369 2.8684 2.9123 2.9344 3.0373

2.7519 2.8759 2.9173 2.9387 3.0423

2.7444 2.8722 2.9148 2.9365 3.0398

2.7594 2.8797 2.9198 2.9408 3.0448

2.7519 2.8760 2.9173 2.9386 3.0423

2.7669 2.8835 2.9223 2.9429 3.0473

31⁄8–16

3.057

3.064

3.061

3.068

3.064

3.071

3.068

3.075

3.0570

3.0616

3.0594

3.0637

3.0615

3.0658

3.0636

3.0679


1931

Max 2.128

TAPPING

Mina 2.115

21⁄4–12 21⁄4–16 21⁄4–20 25⁄16–16 23⁄8–12 23⁄8–16 27⁄16–16 21⁄2–4 21⁄2–8 21⁄2–12 21⁄2–16 21⁄2–20 25⁄8–12 25⁄8–16 23⁄4–4 23⁄4–8 23⁄4–12 23⁄4–16 27⁄8–12 27⁄8–16

21⁄4–8


Classes 1B and 2B

1932





11⁄2D




Above 11⁄2D to 3D

Max 2.998

Min 2.989

Max 3.008

Min 2.998

Maxb 3.017

Min 3.008

Max 3.027

Mina 2.9790

Max 2.9944

Min 2.9869

Max 3.0019

Min 2.9944

Maxb 3.0094

Min 3.0019

Max 3.0169

3.115

3.128

3.121

3.134

3.128

3.140

3.134

3.146

3.1150

3.1222

3.1184

3.1259

3.1222

3.1297

3.1260

3.1335

3.160

3.169

3.165

3.174

3.169

3.178

3.174

3.183

3.1600

3.1648

3.1623

3.1673

3.1648

3.1698

3.1673

3.1723

3.182

3.189

3.186

3.193

3.189

3.196

3.193

3.200

3.1820

3.1866

3.1844

3.1887

3.1865

3.1908

3.1886

3.1929

3.285

3.294

3.290

3.299

3.294

3.303

3.299

3.299

3.2850

3.2898

3.2873

3.2923

3.2898

3.2948

3.2923

3.2973

3.307

3.314

3.311

3.318

3.314

3.321

3.317

3.325

3.3070

3.3116

3.3094

3.3137

3.3115

3.3158

3.3136

3.3179

3.229

3.248

3.239

3.258

3.248

3.267

3.258

3.277

3.2290

3.2444

3.2369

3.2519

3.2444

3.2594

3.2519

3.2669

3.365

3.378

3.371

2.384

3.378

3.390

3.384

3.396

3.3650

3.3722

3.3684

3.3759

3.3722

3.3797

3.3760

3.3835

3.410

3.419

3.415

3.424

3.419

3.428

3.424

3.433

3.4100

3.4148

3.4123

3.4173

3.4148

3.4198

3.4173

3.4223

3.432

3.439

3.436

3.443

3.439

3.446

3.443

3.450

3.4320

3.4366

3.4344

3.4387

3.4365

3.4408

3.4386

3.4429

3.535

3.544

3.544

3.549

3.544

3.553

3.549

3.553

3.5350

3.5398

3.5373

3.5423

3.5398

3.5448

3.5423

3.5473

3.557

3.564

3.561

3.568

3.567

3.571

3.568

3.575

3.5570

3.5616

3.5594

3.5637

3.5615

3.5658

3.5636

3.5679

3.479

3.498

3.489

3.508

3.498

3.517

3.508

3.527

3.4790

3.4944

3.4869

3.5019

3.4944

3.5094

3.5019

3.5169

3.615

3.628

3.615

3.634

3.628

3.640

3.634

3.646

3.6150

3.6222

3.6184

3.6259

3.6222

3.6297

3.6260

3.6335

3.660

3.669

3.665

3.674

3.669

3.678

3.674

3.683

3.6600

3.6648

3.6623

3.6673

3.6648

3.6698

3.6673

3.6723

3.682

3.689

3.686

3.693

3.689

3.696

3.693

3.700

3.6820

3.6866

3.6844

3.6887

3.6865

3.6908

3.6886

3.6929

3.785

3.794

3.790

3.799

3.794

3.803

3.799

3.808

3.7850

3.7898

3.7873

3.7923

3.7898

3.7948

3.7923

3.7973

3.807

3.814

3.811

3.818

3.814

3.821

3.818

3.825

3.8070

3.8116

3.8094

3.8137

3.8115

3.8158

3.8136

3.8179

4–4 4–8 4–12 4–16 41⁄4–4

3.729 3.865 3.910 3.932 3.979

3.748 3.878 3.919 3.939 3.998

3.739 3.871 3.915 3.936 3.989

3.758 3.884 3.924 3.943 4.008

3.748 3.878 3.919 3.939 3.998

3.767 3.890 3.928 3.946 4.017

3.758 3.884 3.924 3.943 4.008

3.777 3.896 3.933 3.950 4.027

3.7290 3.8650 3.9100 3.9320 3.9790

3.7444 3.8722 3.9148 3.9366 3.9944

3.7369 3.8684 3.9123 3.9344 3.9869

3.7519 3.8759 3.9173 3.9387 4.0019

3.7444 3.8722 3.9148 3.9365 3.9944

3.7594 3.8797 3.9198 3.9408 4.0094

3.7519 3.8760 3.9173 3.9386 4.0019

3.7669 3.8835 3.9223 3.9429 4.0169

41⁄4–8

4.115

4.128

4.121

4.134

4.128

4.140

4.134

4.146

4.1150

4.1222

4.1184

4.1259

4.1222

4.1297

4.1260

4.1335

41⁄4–12

4.160

4.169

4.165

4.174

4.169

4.178

4.174

4.183

4.1600

4.1648

4.1623

4.1673

4.1648

4.1698

4.1673

4.1723

41⁄4–16

4.182

4.189

4.186

4.193

4.189

4.196

4.193

4.200

4.1820

4.1866

4.1844

4.1887

4.1865

4.1908

4.1886

4.1929

41⁄2–4

4.229

4.248

4.239

4.258

4.248

4.267

4.258

4.277

4.2290

4.2444

4.2369

4.2519

4.2444

4.2594

4.2519

4.2669


TAPPING

Mina 2.979

31⁄4–8 31⁄4–12 31⁄4–16 33⁄8–12 33⁄8–16 31⁄2–4 31⁄2–8 31⁄2–12 31⁄2–16 35⁄8–12 35⁄8–16 33⁄4–4 33⁄4–8 33⁄4–12 3⁄ –16 4 37⁄8–12 37⁄8–16

31⁄4–4



Thread Size




11⁄2D




Above 11⁄2D to 3D

Max 4.378

Min 4.371

Max 4.384

Min 4.378

Maxb 4.390

Min 4.384

Max 4.396

Mina 4.3650

Max 4.3722

Min 4.3684

Max 4.3759

Min 4.3722

Maxb 4.3797

Min 4.3760

Max 4.3835

4.410

4.419

4.419

4.424

4.419

4.428

4.424

4.433

4.4100

4.4148

4.4123

4.4173

4.4148

4.4198

4.4173

4.4223

4.432

4.439

4.437

4.444

4.439

4.446

4.444

4.455

4.4320

4.4366

4.4344

4.4387

4.4365

4.4408

4.4386

4.4429

4.615

4.628

4.621

4.646

4.628

4.640

4.646

4.646

4.6150

4.6222

4.6184

4.6259

4.6222

4.6297

4.6260

4.6335

4.660

4.669

4.665

4.674

4.669

4.678

4.674

4.683

4.6600

4.6648

4.6623

4.6673

4.6648

4.6698

4.6673

4.6723

4.682

4.689

4.686

4.693

4.689

4.696

4.693

4.700

4.6820

4.6866

4.6844

4.6887

4.6865

4.6908

4.6886

4.6929

5–8 5–12 5–16 51⁄4–8

4.865 4.910 4.932 5.115

4.878 4.919 4.939 5.128

4.871 4.915 4.936 5.121

4.884 4.924 4.943 5.134

4.878 4.919 4.939 5.128

4.890 4.928 4.946 5.140

4.884 4.924 4.943 5.134

4.896 4.933 4.950 5.146

4.8650 4.9100 4.9320 5.1150

4.8722 4.9148 4.9366 5.1222

4.8684 4.9123 4.9344 5.1184

4.8759 4.9173 4.9387 5.1259

4.8722 4.9148 4.9365 5.1222

4.8797 4.9198 4.9408 5.1297

4.8760 4.9173 4.9386 5.1260

4.8835 4.9223 4.9429 5.1335

51⁄4–12

5.160

5.169

5.165

5.174

5.169

5.178

5.174

5.183

5.1600

5.1648

5.1623

5.1673

5.1648

5.1698

5.1673

5.1723

51⁄4–16

5.182

5.189

5.186

5.193

5.189

5.196

5.193

5.200

5.1820

5.1866

5.1844

5.1887

5.1865

5.1908

5.1886

5.1929

51⁄2–8

5.365

5.378

5.371

5.384

5.378

5.390

5.384

5.396

5.3650

5.3722

5.3684

5.3759

5.3722

5.3797

5.3760

5.3835

51⁄2–12 51⁄2–16 53⁄4–8 53⁄4–12 53⁄4–16

5.410

5.419

5.415

5.424

5.419

5.428

5.424

5.433

5.4100

5.4148

5.4123

5.4173

5.4148

5.4198

5.4173

5.4223

5.432

5.439

5.436

5.442

5.439

5.446

5.442

5.450

5.4320

5.4366

5.4344

5.4387

5.4365

5.4408

5.4386

5.4429

5.615

5.628

5.621

5.634

5.628

5.640

5.634

5.646

5.6150

5.6222

5.6184

5.6259

5.6222

5.6297

5.6260

5.6335

5.660

5.669

5.665

5.674

5.669

5.678

5.674

5.683

5.6600

5.6648

5.6623

5.6673

5.6648

5.6698

5.6673

5.6723

5.682

5.689

5.686

5.693

5.689

5.696

5.693

5.700

5.6820

5.6866

5.6844

5.6887

5.6865

5.6908

5.6886

5.6929

6–8 6–12 6–16

5.865 5.910 5.932

5.878 5.919 5.939

5.871 5.915 5.935

5.896 5.924 5.943

5.878 5.919 5.939

5.890 5.928 5.946

5.896 5.924 5.943

5.896 5.933 5.950

5.8650 5.9100 5.9320

5.8722 5.9148 5.9366

5.8684 5.9123 5.9344

5.8759 5.9173 5.9387

5.8722 5.9148 5.9365

5.8797 5.9198 5.9408

5.8760 5.9173 5.9386

5.8835 5.9223 5.9429

a This is the minimum minor diameter specified in the thread tables, page b This is the maximum minor diameter specified in the thread tables, page

TAPPING

Mina 4.365

41⁄2–12 41⁄2–16 43⁄4–8 43⁄4–12 43⁄4–16

41⁄2–8

1723. 1723.

All dimensions are in inches. For basis of recommended hole size limits see accompanying text. As an aid in selecting suitable drills, see the listing of American Standard drill sizes in the twist drill section. For amount of expected drill oversize, see page 873.

1933



1934

Table 3. Tap Drill Sizes for Threads of American National Form Screw Thread

Commercial Tap Drillsa

Screw Thread

Commercial Tap Drillsa

Root Diam.

Size or Number

Decimal Equiv.

27

0.4519

15⁄ 32

0.4687

9⁄ –12 16

0.4542

31⁄ 64

0.4844

18

0.4903

33⁄ 64

0.5156

0.0635

27

0.5144

17⁄ 32

0.5312

49

0.0730

5⁄ –11 8

0.5069

17⁄ 32

0.5312

0.0678

49

0.0730

12

0.5168

35⁄ 64

0.5469

7⁄ –48 64

0.0823

43

0.0890

18

0.5528

37⁄ 64

0.5781

1⁄ –32 8

0.0844

3⁄ 32

0.0937

27

0.5769

19⁄ 32

0.5937

40

0.0925

38

0.1015

11⁄ –11 16

0.5694

19⁄ 32

0.5937

9⁄ –40 64

0.1081

32

0.1160

16

0.6063

5⁄ 8

0.6250

5⁄ –32 32

0.1157

1⁄ 8

0.1250

3⁄ –10 4

0.6201

21⁄ 32

0.6562

36

0.1202

30

0.1285

12

0.6418

43⁄ 64

0.6719

11⁄ –32 64

0.1313

9⁄ 64

0.1406

16

0.6688

11⁄ 16

0.6875

3⁄ –24 16

0.1334

26

0.1470

27

0.7019

23⁄ 32

0.7187

32

0.1469

22

0.1570

13⁄ –10 16

0.6826

23⁄ 32

0.7187

13⁄ –24 64

0.1490

20

0.1610

7⁄ –9 8

0.7307

49⁄ 64

0.7656

7⁄ –24 32

0.1646

16

0.1770

12

0.7668

51⁄ 64

0.7969

32

0.1782

12

0.1890

14

0.7822

13⁄ 16

0.8125

15⁄ –24 64

0.1806

10

0.1935

18

0.8028

53⁄ 64

0.8281

1⁄ –20 4

0.1850

7

0.2010

27

0.8269

27⁄ 32

0.8437

24

0.1959

4

0.2090

9

0.7932

53⁄ 64

0.8281

27

0.2019

3

0.2130

1–8

0.8376

7⁄ 8

0.8750

28

0.2036

3

0.2130

12

0.8918

59⁄ 64

0.9219

32

0.2094

7⁄ 32

0.2187

14

0.9072

15⁄ 16

0.9375

5⁄ –18 16

0.2403

F

0.2570

27

0.9519

31⁄ 32

0.9687

20

0.2476

17⁄ 64

0.2656

11⁄8– 7

0.9394

63⁄ 64

0.9844

24

0.2584

I

0.2720

12

1.0168

13⁄64

1.0469

27

0.2644

J

0.2770

11⁄4– 7

1.0644

17⁄64

1.1094

32

0.2719

9⁄ 32

0.2812

12

1.1418

111⁄64

1.1719

3⁄ –16 8

0.2938

5⁄ 16

0.3125

13⁄8– 6

1.1585

17⁄32

1.2187

20

0.3100

21⁄ 64

0.3281

12

1.2668

119⁄64

1.2969

24

0.3209

Q

0.3320

11⁄2– 6

1.2835

111⁄32

1.3437

27

0.3269

R

0.3390

12

1.3918

127⁄64

1.4219

7⁄ –14 16

0.3447

U

0.3680

15⁄8– 51⁄2

1.3888

129⁄64

1.4531

20

0.3726

25⁄ 64

0.3906

13⁄4– 5

1.4902

19⁄16

1.5625

24

0.3834

X

0.3970

17⁄8– 5

1.6152

111⁄16

1.6875

27

0.3894

Y

0.4040

2 – 41⁄2

1.7113

125⁄32

1.7812

1⁄ –12 2

0.3918

27⁄ 64

0.4219

21⁄8– 41⁄2

1.8363

129⁄32

1.9062

13

0.4001

27⁄ 64

0.4219

21⁄4– 41⁄2

1.9613

21⁄32

2.0312

20

0.4351

29⁄ 64

0.4531

23⁄8– 4

2.0502

21⁄8

2.1250

24

0.4459

29⁄ 64

0.4531

21⁄2– 4

2.1752

21⁄4

2.2500

Outside Diam. Pitch

Root Diam.

Size or Number

Decimal Equiv.

1⁄ –64 16

0.0422

3⁄ 64

0.0469

72

0.0445

3⁄ 64

0.0469

5⁄ –60 64

0.0563

1⁄ 16

0.0625

72

0.0601

52

3⁄ –48 32

0.0667

50

Outside Diam. Pitch

15⁄ – 16

a These tap drill diameters allow approximately 75 per cent of a full thread to be produced. For small

thread sizes in the first column, the use of drills to produce the larger hole sizes shown in Table 2 will reduce defects caused by tap problems and breakage.



1935

Table 4. Tap Drills and Clearance Drills for Machine Screws with American National Thread Form Size of Screw No. or Diam.

Decimal Equiv.

0

.060

1

.073

2

.086

3

.099

4

.112

5

.125

6

.138

8

.164

10

.190

12

.216

14

.242

1⁄ 4

.250

5⁄ 16 3⁄ 8 7⁄ 16 1⁄ 2

No. of Threads per Inch 80 64 72 56 64 48 56 36a 40 48 40 44 32 40 32 36 24 32 24 28 20a 24a 20 28 18 24 16 24

Tap Drills Drill Size

Decimal Equiv.

3⁄ 64

.0469 .0595 .0595 .0700 .0700 .0785 .0820 .0860 .0890 .0935 .1015 1040 .1065 .1130 .1360 .1360 .1495 1590 .1770 .1820 .1935 .2010 .2010 .2130 .2570 .2720 .3125 .3320

.4375

14 20

53 53 50 50 47 45 44 43 42 38 37 36 33 29 29 25 21 16 14 10 7 7 3 F I 5⁄ 16 Q U 25⁄ 64

.500

13 20

27⁄ 64 29⁄ 64

.3125 .375

Clearance Hole Drills Close Fit

Free Fit

Drill Size

Decimal Equiv.

Drill Size

52

.0635

50

Decimal Equiv. .0700

48

.0760

46

.0810

43

.0890

41

.0960

37

.1040

35

.1100

32

.1160

30

.1285

30

.1285

29

.1360

27

.1440

25

.1495

18

.1695

16

.1770

9

.1960

7

.2010

2

.2210

1

.2280

D

.2460

F

.2570

F

.2570

H

.2660

P

.3230

Q

.3320

W

.3860

X

.3970

.3680 .3906

29⁄ 64

.4531

15⁄ 32

.4687

.4219 .4531

33⁄ 64

.5156

17⁄ 32

.5312

a These screws are not in the American Standard but are from the former A.S.M.E. Standard.

The size of the tap drill hole for any desired percentage of full thread depth can be calculated by the formulas below. In these formulas the Per Cent Full Thread is expressed as a decimal; e.g., 75 per cent is expressed as .75. The tap drill size is the size nearest to the calculated hole size. For American Unified Thread form: 1.08253 × Per Cent Full Thread Hole Size = Basic Major Diameter – ---------------------------------------------------------------------------Number of Threads per Inch For ISO Metric threads (all dimensions in millimeters): Hole Size = Basic Major Diameter – ( 1.08253 × Pitch × Per Cent Full Thread ) The constant 1.08253 in the above equation represents 5H/8 where H is the height of a sharp V-thread (see page 1712). (The pitch is taken to be 1.) Factors Influencing Minor Diameter Tolerances of Tapped Holes.—As stated in the Unified screw thread standard, the principle practical factors that govern minor diameter tolerances of internal threads are tapping difficulties, particularly tap breakage in the small sizes, availability of standard drill sizes in the medium and large sizes, and depth (radial) of engagement. Depth of engagement is related to the stripping strength of the thread assembly, and thus also, to the length of engagement. It also has an influence on the tendency toward disengagement of the threads on one side when assembly is eccentric. The amount of possible eccentricity is one-half of the sum of the pitch diameter allowance and toler-


1936


ances on both mating threads. For a given pitch, or height of thread, this sum increases with the diameter, and accordingly this factor would require a decrease in minor diameter tolerance with increase in diameter. However, such decrease in tolerance would often require the use of special drill sizes; therefore, to facilitate the use of standard drill sizes, for any given pitch the minor diameter tolerance for Unified thread classes 1B and 2B threads of 1⁄4 inch diameter and larger is constant, in accordance with a formula given in the American Standard for Unified Screw Threads. Effect of Length of Engagement of Minor Diameter Tolerances: There may be applications where the lengths of engagement of mating threads is relatively short or the combination of materials used for mating threads is such that the maximum minor diameter tolerance given in the Standard (based on a length of engagement equal to the nominal diameter) may not provide the desired strength of the fastening. Experience has shown that for lengths of engagement less than 2⁄3D (the minimum thickness of standard nuts) the minor diameter tolerance may be reduced without causing tapping difficulties. In other applications the length of engagement of mating threads may be long because of design considerations or the combination of materials used for mating threads. As the threads engaged increase in number, a shallower depth of engagement may be permitted and still develop stripping strength greater than the external thread breaking strength. Under these conditions the maximum tolerance given in the Standard should be increased to reduce the possibility of tapping difficulties. The following paragraphs indicate how the aforementioned considerations were taken into account in determining the minor diameter limits for various lengths of engagement given in Table 2. Recommended Hole Sizes before Tapping.—Recommended hole size limits before threading to provide for optimum strength of fastenings and tapping conditions are shown in Table 2 for classes 1B, 2B, and 3B. The hole size limit before threading, and the tolerances between them, are derived from the minimum and maximum minor diameters of the internal thread given in the dimensional tables for Unified threads in the screw thread section using the following rules: 1) For lengths of engagement in the range to and including 1⁄3D, where D equals nominal diameter, the minimum hole size will be equal to the minimum minor diameter of the internal thread and the maximum hole size will be larger by one-half the minor diameter tolerance. 2) For the range from 1⁄3D to 2⁄3D, the minimum and maximum hole sizes will each be one quarter of the minor diameter tolerance larger than the corresponding limits for the length of engagement to and including 1⁄3D. 3) For the range from 2⁄3D to 11⁄2D the minimum hole size will be larger than the minimum minor diameter of the internal thread by one-half the minor diameter tolerance and the maximum hole size will be equal to the maximum minor diameter. 4) For the range from 11⁄2D to 3D the minimum and maximum hole sizes will each be onequarter of the minor diameter tolerance of the internal thread larger than the corresponding limits for the 2⁄3D to 11⁄2D length of engagement. From the foregoing it will be seen that the difference between limits in each range is the same and equal to one-half of the minor diameter tolerance given in the Unified screw thread dimensional tables. This is a general rule, except that the minimum differences for sizes below 1⁄4 inch are equal to the minor diameter tolerances calculated on the basis of lengths of engagement to and including 1⁄3D. Also, for lengths of engagement greater than 1⁄ D and for sizes 1⁄ inch and larger the values are adjusted so that the difference between 3 4 limits is never less than 0.004 inch. For diameter-pitch combinations other than those given in Table 2, the foregoing rules should be applied to the tolerances given in the dimensional tables in the screw thread sec-



1937

tion or the tolerances derived from the formulas given in the Standard to determine the hole size limits. Selection of Tap Drills: In selecting standard drills to produce holes within the limits given in Table 2 it should be recognized that drills have a tendency to cut oversize. The material on page 873 may be used as a guide to the expected amount of oversize. Table 5. Unified Miniature Screw Threads—Recommended Hole Size Limits Before Tapping Thread Size

Internal Threads Minor Diameter Limits

Lengths of Engagement To and including 2⁄3D


Above 11⁄2D to 3D

Recommended Hole Size Limits Pitch

Min

Max

Min

Max

Min

Max

Min

Designation

mm

mm

mm

mm

mm

mm

mm

mm

mm


0.080 0.090 0.100 0.100 0.125 0.125 0.150 0.175 0.200 0.225 0.250 0.250 0.250 0.300 Thds. per in. 318 282 254 254 203 203 169 145 127 113 102 102 102 85

0.217 0.256 0.296 0.346 0.370 0.420 0.444 0.518 0.592 0.666 0.740 0.840 0.940 1.088

0.254 0.297 0.340 0.390 0.422 0.472 0.504 0.586 0.668 0.750 0.832 0.932 1.032 1.196

0.226 0.267 0.307 0.357 0.383 0.433 0.459 0.535 0.611 0.687 0.763 0.863 0.963 1.115

0.240 0.282 0.324 0.374 0.402 0.452 0.482 0.560 0.640 0.718 0.798 0.898 0.998 1.156

0.236 0.277 0.318 0.368 0.396 0.446 0.474 0.552 0.630 0.708 0.786 0.886 0.986 1.142

0.254 0.297 0.340 0.390 0.422 0.472 0.504 0.586 0.668 0.750 0.832 0.932 1.032 1.196

0.245 0.287 0.329 0.379 0.409 0.459 0.489 0.569 0.649 0.729 0.809 0.909 1.009 1.169

0.264 0.307 0.351 0.401 0.435 0.485 0.519 0.603 0.687 0.771 0.855 0.955 1.055 1.223

inch 0.0085 0.0101 0.0117 0.0136 0.0146 0.0165 0.0175 0.0204 0.0233 0.0262 0.0291 0.0331 0.0370 0.0428

inch 0.0100 0.0117 0.0134 0.0154 0.0166 0.0186 0.0198 0.0231 0.0263 0.0295 0.0327 0.0367 0.0406 0.0471

inch 0.0089 0.0105 0.0121 0.0141 0.0150 0.0170 0.0181 0.0211 0.0241 0.0270 0.0300 0.0340 0.0379 0.0439

inch 0.0095 0.0111 0.0127 0.0147 0.0158 0.0178 0.0190 0.0221 0.0252 0.0283 0.0314 0.0354 0.0393 0.0455

inch 0.0093 0.0109 0.0125 0.0145 0.0156 0.0176 0.0187 0.0217 0.0248 0.0279 0.0309 0.0349 0.0388 0.0450

inch 0.0100 0.0117 0.0134 0.0154 0.0166 0.0186 0.0198 0.0231 0.0263 0.0295 0.0327 0.0367 0.0406 0.0471

inch 0.0096 0.0113 0.0130 0.0149 0.0161 0.0181 0.0193 0.0224 0.0256 0.0287 0.0319 0.0358 0.0397 0.0460

inch 0.0104 0.0121 0.0138 0.0158 0.0171 0.0191 0.0204 0.0237 0.0270 0.0304 0.0337 0.0376 0.0415 0.0481

Designation 0.30 UNM 0.35 UNM 0.40 UNM 0.45 UNM 0.50 UNM 0.55 UNM 0.60 UNM 0.70 UNM 0.80 UNM 0.90 UNM 1.00 UNM 1.10 UNM 1.20 UNM 1.40 UNM

Max

As an aid in selecting suitable drills, see the listing of American Standard drill sizes in the twist drill section. Thread sizes in heavy type are preferred sizes.

Hole Sizes for Tapping Unified Miniature Screw Threads.—Table 5 indicates the hole size limits recommended for tapping. These limits are derived from the internal thread minor diameter limits given in the American Standard for Unified Miniature Screw Threads ASA B1.10-1958 and are disposed so as to provide the optimum conditions for tapping. The maximum limits are based on providing a functionally adequate fastening for the most common applications, where the material of the externally threaded member is of a strength essentially equal to or greater than that of its mating part. In applications where, because of considerations other than the fastening, the screw is made of an appreciably



1938

weaker material, the use of smaller hole sizes is usually necessary to extend thread engagement to a greater depth on the external thread. Recommended minimum hole sizes are greater than the minimum limits of the minor diameters to allow for the spin-up developed in tapping. In selecting drills to produce holes within the limits given in Table 5 it should be recognized that drills have a tendency to cut oversize. The material on page 873 may be used as a guide to the expected amount of oversize. British Standard Tapping Drill Sizes for Screw and Pipe Threads.—British Standard BS 1157:1975 (2004) provides recommendations for tapping drill sizes for use with fluted taps for various ISO metric, Unified, British Standard fine, British Association, and British Standard Whitworth screw threads as well as British Standard parallel and taper pipe threads. Table 6. British Standard Tapping Drill Sizes for ISO Metric Coarse Pitch Series Threads BS 1157:1975 (2004) Standard Drill Sizesa

Standard Drill Sizesa Recommended Nom. Size and Thread Diam. M1 M 1.1 M 1.2 M 1.4 M 1.6 M 1.8 M2 M 2.2 M 2.5 M3 M 3.5 M4 M 4.5 M5 M6 M7 M8 M9 M 10 M 11

Size

Theoretical Radial Engagement with Ext. Thread (Per Cent)

0.75 0.85 0.95 1.10 1.25 1.45 1.60 1.75 2.05 2.50 2.90 3.30 3.70 4.20 5.00 6.00 6.80 7.80 8.50 9.50

81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 86.8 81.5 81.5 81.5 78.5 78.5 81.5 81.5

Alternative

Recommended

Size


Nom. Size and Thread Diam.

0.78 0.88 0.98 1.15 1.30 1.50 1.65 1.80 2.10 2.55 2.95 3.40 3.80 4.30 5.10 6.10 6.90 7.90 8.60 9.60

71.7 71.7 71.7 67.9 69.9 69.9 71.3 72.5 72.5 73.4 74.7 69.9b 76.1 71.3b 73.4 73.4 71.7b 71.7b 76.1 76.1

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

Alternative

Size


Size


10.20 12.00 14.00 15.50 17.50 19.50 21.00 24.00 26.50 29.50 32.00 35.00 37.50 40.50 43.00 47.00 50.50 54.50 58.00 62.00

83.7 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5 81.5

10.40 12.20 14.25 15.75 17.75 19.75 21.25 24.25 26.75 29.75 … … … … … … … … … …

74.5b 73.4b 71.3c 73.4c 73.4c 73.4c 74.7b 74.7b 75.7b 75.7b … … … … … … … … … …

a These tapping drill sizes are for fluted taps only. b For tolerance class 6H and 7H threads only. c For tolerance class 7H threads only.

Drill sizes are given in millimeters.

In the accompanying Table 6, recommended and alternative drill sizes are given for producing holes for ISO metric coarse pitch series threads. These coarse pitch threads are suitable for the large majority of general-purpose applications, and the limits and tolerances for internal coarse threads are given in the table starting on page 1824. It should be noted that Table 6 is for fluted taps only since a fluteless tap will require for the same screw thread a different size of twist drill than will a fluted tap. When tapped, holes produced with drills of the recommended sizes provide for a theoretical radial engagement with the external thread of about 81 per cent in most cases. Holes produced with drills of the alternative sizes provide for a theoretical radial engagement with the external thread of about 70 to 75



1939

per cent. In some cases, as indicated in Table 6, the alternative drill sizes are suitable only for medium (6H) or for free (7H) thread tolerance classes. When relatively soft material is being tapped, there is a tendency for the metal to be squeezed down towards the root of the tap thread, and in such instances, the minor diameter of the tapped hole may become smaller than the diameter of the drill employed. Users may wish to choose different tapping drill sizes to overcome this problem or for special purposes, and reference can be made to the pages mentioned above to obtain the minor diameter limits for internal pitch series threads. Reference should be made to this standard BS 1157:1975 (2004) for recommended tapping hole sizes for other types of British Standard screw threads and pipe threads. Table 7. British Standard Metric Bolt and Screw Clearance Holes BS 4186: 1967 Nominal Thread Diameter 1.6 2.0 2.5 3.0 4.0 5.0 6.0 7.0 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

Clearance Hole Sizes Close Medium Free Fit Fit Fit Series Series Series 1.7 1.8 2.0 2.2 2.4 2.6 2.7 2.9 3.1 3.2 3.4 3.6 4.3 4.5 4.8 5.3 5.5 5.8 6.4 6.6 7.0 7.4 7.6 8.0 8.4 9.0 10.0 10.5 11.0 12.0 13.0 14.0 15.0 15.0 16.0 17.0 17.0 18.0 19.0 19.0 20.0 21.0 21.0 22.0 24.0 23.0 24.0 26.0 25.0 26.0 28.0 28.0 30.0 32.0 31.0 33.0 35.0 34.0 36.0 38.0 37.0 39.0 42.0 40.0 42.0 45.0 43.0 45.0 48.0 46.0 48.0 52.0 50.0 52.0 56.0

Nominal Thread Diameter 52.0 56.0 60.0 64.0 68.0 72.0 76.0 80.0 85.0 90.0 95.0 100.0 105.0 110.0 115.0 120.0 125.0 130.0 140.0 150.0 … … … … …

Clearance Hole Sizes Close Medium Free Fit Fit Fit Series Series Series 54.0 56.0 62.0 58.0 62.0 66.0 62.0 66.0 70.0 66.0 70.0 74.0 70.0 74.0 78.0 74.0 78.0 82.0 78.0 82.0 86.0 82.0 86.0 91.0 87.0 91.0 96.0 93.0 96.0 101.0 98.0 101.0 107.0 104.0 107.0 112.0 109.0 112.0 117.0 114.0 117.0 122.0 119.0 122.0 127.0 124.0 127.0 132.0 129.0 132.0 137.0 134.0 137.0 144.0 144.0 147.0 155.0 155.0 158.0 165.0 … … … … … … … … … … … … … … …


British Standard Clearance Holes for Metric Bolts and Screws.—The dimensions of the clearance holes specified in this British Standard BS 4186:1967 have been chosen in such a way as to require the use of the minimum number of drills. The recommendations cover three series of clearance holes, namely close fit (H 12), medium fit (H 13), and free fit (H 14) and are suitable for use with bolts and screws specified in the following metric British Standards: BS 3692, ISO metric precision hexagon bolts, screws, and nuts; BS 4168, Hexagon socket screws and wrench keys; BS 4183, Machine screws and machine screw nuts; and BS 4190, ISO metric black hexagon bolts, screws, and nuts. The sizes are in accordance with those given in ISO Recommendation R273, and the range has been extended up to 150 millimeters diameter in accordance with an addendum to that recommendation. The selection of clearance holes sizes to suit particular design requirements


1940


can of course be dependent upon many variable factors. It is however felt that the medium fit series should suit the majority of general purpose applications. In the Standard, limiting dimensions are given in a table which is included for reference purposes only, for use in instances where it may be desirable to specify tolerances. To avoid any risk of interference with the radius under the head of bolts and screws, it is necessary to countersink slightly all recommended clearance holes in the close and medium fit series. Dimensional details for the radius under the head of fasteners made according to BS 3692 are given on page 1537; those for fasteners to BS 4168 are given on page 1601; those to BS 4183 are given on pages 1575 through 1579. Cold Form Tapping.—Cold form taps do not have cutting edges or conventional flutes; the threads on the tap form the threads in the hole by displacing the metal in an extrusion or swaging process. The threads thus produced are stronger than conventionally cut threads because the grains in the metal are unbroken and the displaced metal is work hardened. The surface of the thread is burnished and has an excellent finish. Although chip problems are eliminated, cold form tapping does displace the metal surrounding the hole and countersinking or chamfering before tapping is recommended. Cold form tapping is not recommended if the wall thickness of the hole is less than two-thirds of the nominal diameter of the thread. If possible, blind holes should be drilled deep enough to permit a cold form tap having a four thread lead to be used as this will require less torque, produce less burr surrounding the hole, and give a greater tool life. The operation requires 0 to 50 per cent more torque than conventional tapping, and the cold form tap will pick

Machinery's Handbook

Handbook

Materials Handbook (Handbook)

ASM Handbook: Volume 8: Mechanical Testing and Evaluation (Asm Handbook) (Asm Handbook) (Asm Handbook) (Asm Handbook)

WiMAX Handbook

ModSecurity Handbook

Radio Handbook

Piping Handbook

Antenna handbook

Karate Handbook

Biosimilars Handbook

Radar Handbook

Salesforce Handbook

Homelessness Handbook

Textile Handbook

Chitin handbook

Aerogels Handbook

Hydrothermal Handbook

ASM Handbook: Volume 7: Powder Metal Technologies and Applications (Asm Handbook) (Asm Handbook) (Asm Handbook)

Oxford American Handbook of Urology (Oxford Handbook)

Visualization Handbook

Electromagnetics Handbook

EFL Handbook

TOAD Handbook

Communications Handbook

Tannin Handbook

Compressor handbook

Insulation Handbook

Satellite Handbook

Machinery's Handbook

Handbook

Materials Handbook (Handbook)

ASM Handbook: Volume 8: Mechanical Testing and Evaluation (Asm Handbook) (Asm Handbook) (Asm Handbook) (Asm Handbook)

WiMAX Handbook

ModSecurity Handbook

Radio Handbook

Piping Handbook

Antenna handbook

Karate Handbook

Biosimilars Handbook

Radar Handbook

Salesforce Handbook

Homelessness Handbook

Textile Handbook

Chitin handbook

Aerogels Handbook

Hydrothermal Handbook

ASM Handbook: Volume 7: Powder Metal Technologies and Applications (Asm Handbook) (Asm Handbook) (Asm Handbook)

Oxford American Handbook of Urology (Oxford Handbook)

Visualization Handbook

Electromagnetics Handbook

EFL Handbook

TOAD Handbook

Communications Handbook

Tannin Handbook

Compressor handbook

Insulation Handbook

Satellite Handbook

Recommend Documents