E. Alfredo Campo
The Complete Part Design Handbook For Injection Molding of Thermoplastics
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E. Alfredo Campo
The Complete Part Design Handbook For Injection Molding of Thermoplastics
Hanser Publishers, Munich • Hanser Gardner Publications, Cincinnati
The Author: E. Alfredo!Campo,!1213!Cerrito!Perdido!Lane!,!El!Paso,!TX!79912,USA Distributed!in!the!USA!and!in!Canada!by Hanser!Gardner!Publications,!Inc. 6915!Valley!Avenue,!Cincinnati,!Ohio!45244-3029,!USA Fax:!(513)!527-8801 Phone:!(513)!527-8977!or!1-800-950-8977 www.hansergardner.com Distributed!in!all!other!countries!by Carl!Hanser!Verlag Postfach!86!04!20,!81631!München,!Germany Fax:!+49!(89)!98!48!09 www.hanser.de The!use!of general!descriptive!names, trademarks, etc., in!this!publication, even!if the! former! are! not! especially! identiied, is! not! to! be! taken! as! a! sign! that! such! names, as understood!by!the!Trade!Marks!and!Merchandise!Marks!Act, may!accordingly!be!used! freely!by!anyone. While!the!advice!and!information!in!this!book!are!believed!to!be!true!and!accurate!at!the date!of going!to!press, neither!the!authors!nor!the!editors!nor!the!publisher!can!accept any! legal! responsibility! for! any! errors! or! omissions! that! may! be! made. The! publisher! makes!no!warranty,!express!or!implied,!with!respect!to!the!material!contained!herein. Library!of!Congress!Cataloging-in-Publication!Data Campo,!E. Alfredo. !!The!complete!part!design!handbook!:!for!injection!molding!of!thermoplastics /!E. Alfredo!Campo. !!!!!!!p.!cm. !!Includes!index. !!ISBN-13:!978-1-56990-375-9 !!ISBN-10:!1-56990-375-1 !1.!!Injection!molding!of!plastics--Handbooks,!manuals,!etc.!2. Thermoplastics--Design--Handbooks,!manuals,!etc.!3.!!Plastics--Handbooks, manuals,!etc.!!I.!Title. !!TP1150.C36!2006 !!668.4‘23--dc22 !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!2006010219 Bibliograische!Information!Der!Deutschen!Bibliothek Die!Deutsche!Bibliothek!verzeichnet!diese!Publikation!in!der!Deutschen! Nationalbibliograie;!detaillierte!biblio-graische!Daten!sind!im!Internet!über!!abrufbar. ISBN-10:!3-446-40309-4 ISBN-13:!978-3-446-40309-3 All!rights!reserved.No!part!of this!book!may!be!reproduced!or!transmitted!in!any!form!or! by!any!means, electronic!or!mechanical, including!photocopying!or!by!any!information storage!and!retrieval!system,!without!permission!in!writing!from!the!publisher. ©!Carl!Hanser!Verlag,!Munich!2006 Production!Management:!Oswald!Immel Typeset!by!Manuela!Treindl,!Laaber,!Germany Coverconcept:!Marc!Müller-Bremer,!Rebranding,!München,!Germany Coverdesign:!MCP!•!Susanne!Kraus!GbR,!Holzkirchen,!Germany Printed!and!bound!by!Druckhaus!“Thomas!Müntzer”!GmbH,!B.!Langensalza,!Germany
V
Dedication To my wife Sandy, my son Jaime, and my daughter Michelle for the love and understanding they gave me during the six long years that it took me to produce all the original drawings, calculate examples and write this comprehensive handbook. For my uncle, Captain Jaime Merchán and my aunt Ruth Reichman for the assistance provided while attending the University of Miami. For my great grand uncle Rafael Ramirez who paid for my elementary and high school education after I lost my father at the age of five. In honor of my beloved departed brother, Leoncio, and sister in-law Becky. For my grand nephew, Alfredo Campo V. for winning the BMX world championship and the sportsman of the year in my native country Ecuador. For Richard Scott, Bob Rackley and Bill Hawkins from the Du Pont Film Department for their leadership, teaching and guidance in how to be successful in the engineering technical research and development fields. For Larry Gillespie, Director of Du Pont Engineering Polymers for providing me the opportunity to work in most of the technical positions in plastics, such as development of new compounds, economic project analysis, designs of international compounding facilities and laboratories in Japan, Mexico and Brazil. For the Du Pont Film Department, Textile Fibers Department, Engineering Polymers Department, and Du Pont do Brazil that provided me several technical assignments in Plastics during thirty years of service to the company. For all the Du Pont Plastics Customers that gave me the opportunity to improve their plastic products and optimize their injection molding manufacturing processes. E. Alfredo Campo
VII
Preface This handbook was written for the injection molding product designer who has a limited knowledge of engineering polymers. It is a guide for the designer to decide which resin and design geometries to use for the design of plastic parts. It can also offer knowledgeable advice for resin and machine selection and processing parameters. Manufacturer and end user satisfaction is the ultimate goal. This book is an indispensable, all inclusive, reference guide that can be used by any plastic product designer. There is no need to search through many books and catalogs for needed information. New illustrations, graphs and equations have been included to provide additional clarity for complex ideas. The equations have been verified to ensure correctness and not just copied from another source. Thousands of hours of research and cross referencing have gone into the completion of this work. In addition, more than 35 years of the “hands-on” experience of a plastics expert have been incorporated in this handbook. The following topics are covered: Chapter 1
Plastic Materials Selection Guide: Includes an introduction to plastic materials, the beginning of plastics, classification of polymer families. Each resin is discussed by its basic chemistry, properties, processing characteristics, advantages, disadvantages and limitations, typical applications and several product illustrations. Thermoplastic materials (35 generic families), thermoplastic elastomer materials (8 generic families), liquid injection molding of silicone, thermoset materials (16 generic families).
Chapter 2
Engineering Product Design: Starts with the introduction to structural product design principles, mechanical strength properties of thermoplastics. Centroid, section area, moment of inertia equations and tables. Beam deflection analysis methods. Structure analysis of beams, columns, flat circular plates, and torsion.
Chapter 3
Structural Design for Thermoplastics: Discusses the product wall thickness, structural rib design, sharp corners, bosses, threads, undercuts, integral life hinges, pin hinges. Encapsulation of inserts, types of metal inserts and anchorage, and electrical lead inserts.
Chapter 4
Thermoplastic Gearing Design: An introduction to and classification of gears. Standard spur, helical, bevel, and worm gears; properties required for thermoplastic molded spur gears, mounting gears on metal shafts, tolerances and mold shrinkage of gears. Plastic spur and helical gearing technology design, strength, horsepower rating, equations, tables, analysis examples and gear specification illustrations.
Chapter 5
Plastic Journal Bearing Design: An introduction to types of materials for journal bearings. Theory and design for lubrication. Design principles, performances, dimensions, clearances, molding effects, PV limits and surface finishing. Self-lubricated thermoplastic bearings. Equations, tables, and analysis examples.
VIII
Preface Chapter 6
Thermoplastic Spring Design: Introduces cantilever beam spring design, applications, and analysis examples. Locating, fixing clip, flexible hinges, and torsional spring applications. Belleville spring washers’ equations, tables, and analysis examples.
Chapter 7
Thermoplastic Pressure Vessel Design: Discusses thin- and thick-walled pressure vessels’ basic principles, equations, tables, analysis examples, design guidelines, applications, and pressure vessel regulations.
Chapter 8
Thermoplastic Assembly Methods: Joining two or more components together: assembly method is selected based on product design geometry, size, end use requirements, thermoplastic material characteristics, automatic or manual assembly operation, and manufacturing costs. Each assembly method provides a description, process sequence, advantages and limitations, typical applications, equipment, product joint design, and its variations.
Chapter 9
Thermoplastic Effects on Design: Starts discussing the polymer melt behavior, reinforcement, degradation, moisture characteristics, mold shrinkage and critical properties. The molding process effects caused by molding cycle, melt/mold temperature, injection pressure and speed, etc. on product design dimensions, surface finishing, weld line strength and impact resistance and other molding problems.
Chapter 10
Thermoplastic Injection Mold Design: Provides an introduction of injection molds, classification and effects on product design. Types of steels, chemical composition, effects of alloying, heat treatment, properties and characteristics. Types of steels used for mold bases and mold components. Cavity surfaces finish procedures and specifications. Types of injection mold designs. Cold runners (two- and three-plate molds, interchangeable mold inserts and vertical insert encapsulation mold). Hot runner molds (internally and externally heated, insulated). Mold design system and other considerations, such as number of cavities, parting line, ejection, cooling, cold runner, gating, venting, cavity inserts sidewall strength, support pillars, molded parts tolerances, mold designer check list, general specifications for mold construction are covered.
Chapter 11
Performance Testing of Thermoplastics: It introduces various tests to which thermoplastic polymers are subjected, describes their properties (statistical analysis), such as mechanical, thermal, chemical resistance, rheometer melt viscosity, soldering heat resistance, electrical, flammability, smoke generation, weathering and micro-organism resistance. Test description, procedures, apparatus, test specimen and conditioning, and their significance are discussed here.
Chapter 12
Thermoplastic Product Cost Analysis: It discusses molding process variables and capital equipment cost. Three cost analysis methods are used to estimate the molded product user’s price.
IX
Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII 1 Polymeric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Introduction to Plastic Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1 Beginning of Plastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.2 Polymer Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Thermoplastic Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 Classification of Polymers by Performance . . . . . . . . . . . . . 4 1.2.2 Molecular Structure of Plastic Materials . . . . . . . . . . . . . . . 6 1.2.3 Acrylonitrile-Butadiene-Styrene (ABS) . . . . . . . . . . . . . . . . 6 1.2.4 Acetal (POM, Polyacetal) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.5 Polymethyl Metacrylate (Acrylic, PMMA) . . . . . . . . . . . . 12 1.2.6 High Temperature Nylon (HTN) . . . . . . . . . . . . . . . . . . . . 14 1.2.7 Ionomer Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.2.8 Liquid Crystal Polymer (LCP) . . . . . . . . . . . . . . . . . . . . . . . 18 1.2.9 Polyamide (PA, Nylon) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.2.10 Polyetherimide (PEI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.2.11 Polyarylate (PAR) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 1.2.12 Polyetherether Ketone (PEEK). . . . . . . . . . . . . . . . . . . . . . . 27 1.2.13 Polycarbonate (PC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 1.2.14 Modified Polyphenylene Oxide (PPO). . . . . . . . . . . . . . . . 31 1.2.15 Polybutylene Terephthalate (PBT) . . . . . . . . . . . . . . . . . . . 33 1.2.16 Polyethylene Terephthalate (PET) . . . . . . . . . . . . . . . . . . . . 34 1.2.17 Polyethylene (PE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 1.2.18 Polytetrafluoroethylene (PTFE) . . . . . . . . . . . . . . . . . . . . . 39 1.2.19 Polyphenylene Sulfide (PPS) . . . . . . . . . . . . . . . . . . . . . . . . 44 1.2.20 Polypropylene (PP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 1.2.21 Polystyrene (PS) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 1.2.22 Polysulfone (PSU) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 1.2.23 Polyvinyl Chloride (PVC) . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 1.2.24 Styrene Acrylonitrile (SAN) . . . . . . . . . . . . . . . . . . . . . . . . . 53 1.3 Thermoplastic Elastomers (TPE) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 1.3.1 Thermoplastic Elastomer Families . . . . . . . . . . . . . . . . . . . 56 1.3.2 Thermoplastic Polyurethane Elastomer (TPU) . . . . . . . . 57 1.3.3 Styrenic Block Copolymer (SBS). . . . . . . . . . . . . . . . . . . . . 60 1.3.4 Polyolefin Thermoplastic Elastomer (TPO) . . . . . . . . . . . 62 1.3.5 Elastomeric Alloy Thermoplastic Vulcanized (TPV). . . . 65 1.3.6 Melt Processible Rubber (MPR) . . . . . . . . . . . . . . . . . . . . . 69 1.3.7 Copolyester Thermoplastic Elastomer . . . . . . . . . . . . . . . 71 1.3.8 Polyamide Thermoplastic Elastomer . . . . . . . . . . . . . . . . . 75 1.4 Liquid Injection Molding Silicone (LIM®) . . . . . . . . . . . . . . . . . . . . 77 1.4.1 LIM® Silicone Processing . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 1.5 Thermoset Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 1.5.1 Polyester Alkyd (PAK) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 1.5.2 Diallyl Phthalate/Isophthalate (DAP, DAIP) . . . . . . . . . . . 85 1.5.3 Melamine Formaldehyde (MF) . . . . . . . . . . . . . . . . . . . . . . 87 1.5.4 Cellulosic Ester . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 1.5.5 Cyanate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 1.5.6 Epoxy (EP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 1.5.7 Phenol Formaldehyde (Phenolic, PF). . . . . . . . . . . . . . . . . 94
X
Contents 1.5.8 1.5.9 1.5.10 1.5.11 1.5.12 1.5.13 1.5.14 1.5.15 1.5.16
Polybutadiene (PB) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Bismaleimide (BMI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97 Unsaturated Polyester (UP) . . . . . . . . . . . . . . . . . . . . . . . . . 98 Polyimide (PI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Polyxylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 Polyurethane (PUR). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104 Silicone (SI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 Urethane Hybrid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 Vinyl Ester (BPA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
2 Engineering Product Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 Understanding the Properties of Materials . . . . . . . . . . . . . . . . . . . 2.1.1 Plastics Selection Guidelines . . . . . . . . . . . . . . . . . . . . . . . 2.2 Structural Design of Thermoplastic Components . . . . . . . . . . . . . 2.2.1 Stress-Strain Behavior . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2.2 Tensile Testing of Viscoelastic Materials. . . . . . . . . . . . . . 2.3 Mechanical Properties of Materials . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 Tension and Compression Curves . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.5 Modulus of Elasticity (E) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.6 Stress and Strain Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7 Thermoplastics Elastic Design Method . . . . . . . . . . . . . . . . . . . . . . 2.7.1 Working Stress. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.2 Compressive Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.3 Flexural Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.4 Coefficient of Linear Thermal Expansion (α) . . . . . . . . 2.7.5 Poisson’s Ratio (υ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.6 Moisture Effects on Nylon . . . . . . . . . . . . . . . . . . . . . . . . . 2.7.7 Effects of Temperature on the Behavior of Thermoplastics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8 Stress-Strain Recovery (Hysteresis) . . . . . . . . . . . . . . . . . . . . . . . . . . 2.8.1 Creep Behavior of Thermoplastics . . . . . . . . . . . . . . . . . . 2.8.2 Creep and Rupture Under Long-Term Load . . . . . . . . . . 2.8.3 Creep and Relaxation of Thermoplastics. . . . . . . . . . . . . 2.9 Flexural Beam Stress Distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.10 Viscoelastic Modulus Design Method . . . . . . . . . . . . . . . . . . . . . . . . 2.11 Centroid, Section Area, and Moment of Inertia . . . . . . . . . . . . . . . 2.12 Radius of Gyration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13 Stress Analysis of Beams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13.1 Types of Loads. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13.2 Normal Stresses in Beams . . . . . . . . . . . . . . . . . . . . . . . . . . 2.13.3 Shearing Force . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14 Beam Deflection Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14.1 Beam Deflection by Double Integration Method . . . . . 2.14.2 Beam Deflection Moment Area Method . . . . . . . . . . . . . 2.14.3 Applications of Moment Area and Double Integration Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.14.4 Beam Deflection Superposition Method . . . . . . . . . . . . . 2.15 Column Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.15.1 Long Slender Column Critical Load (PCr) . . . . . . . . . . . . 2.15.2 Column Slenderness Ratio (L / r) . . . . . . . . . . . . . . . . . . . 2.15.3 Eccentrically Loaded Columns . . . . . . . . . . . . . . . . . . . . . 2.16 Flat Circular Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16.1 Classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16.2 Stress Analysis Methods . . . . . . . . . . . . . . . . . . . . . . . . . . .
115 115 117 120 121 122 126 129 129 130 131 132 133 134 135 136 136 137 138 138 139 139 145 147 150 158 158 158 159 164 168 169 178 179 183 188 188 188 188 194 195 195
XI
Contents 2.16.3 2.16.4 2.16.5 2.16.6
Flat Circular Plate Equations . . . . . . . . . . . . . . . . . . . . . . . Flat Circular Plate Stresses . . . . . . . . . . . . . . . . . . . . . . . . . Theory of Flexure Comparison . . . . . . . . . . . . . . . . . . . . . Circular Plates Simply Supported, Concentrated Center Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16.7 Flat Circular Plate under Concentrated Center Load . . 2.16.8 Flat Circular Plate with Fixed Edge . . . . . . . . . . . . . . . . . . 2.16.9 Flat Circular Plate Compensation Factor for Deflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.16.10 Flat Circular Plate Bending under Edge Boundaries . . . 2.17 Torsion Structural Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 Structural Designs for Thermoplastics . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Uniform and Symmetrical Wall Thickness . . . . . . . . . . . . . . . . . . . 3.1.1 Part Geometries Difficult to Mold . . . . . . . . . . . . . . . . . . 3.1.2 Wall Draft Angle per Side . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Structural Rib Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2.1 Rib Strength Analysis Method . . . . . . . . . . . . . . . . . . . . . . 3.3 Internal Sharp Corners and Notches . . . . . . . . . . . . . . . . . . . . . . . . . 3.4 Injection Molded Thermoplastic Bosses. . . . . . . . . . . . . . . . . . . . . . 3.5 Injection Molded Thermoplastic Threads . . . . . . . . . . . . . . . . . . . . 3.6 Collapsible Core for Molding Internal Threads . . . . . . . . . . . . . . . 3.7 Preferred Standard Thread Forms for Thermoplastics . . . . . . . . . 3.7.1 Thermoplastic Threads Creep Effects. . . . . . . . . . . . . . . . 3.8 Injection Molded Products with Undercuts. . . . . . . . . . . . . . . . . . . 3.9 Injection Molded Integral Life Hinges . . . . . . . . . . . . . . . . . . . . . . . 3.9.1 Injection Molded Integral Life Hinge Design . . . . . . . . . 3.9.2 Mold Design Considerations for Hinges . . . . . . . . . . . . . 3.9.3 Proper Gate Design for Life Hinges . . . . . . . . . . . . . . . . . 3.10 Conventional Types of Pin Hinges. . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11 Metal Inserts for Thermoplastic Encapsulation . . . . . . . . . . . . . . . 3.11.1 Machined Metal Threaded Insert Tolerances . . . . . . . . . 3.11.2 Thermoplastic Boss Wall Thickness for Metal Inserts. . 3.11.3 Press/Lock Slotted Metal Insert Installation After Molding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.4 Cold Forged Metal Inserts for Encapsulation . . . . . . . . . 3.11.5 Threaded Female Metal Inserts . . . . . . . . . . . . . . . . . . . . . 3.11.6 Metal Inserts Anchorage for Thermoplastic Encapsulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.11.7 Metal Insert Encapsulating Process Problems . . . . . . . . 3.11.8 Special Metal Inserts Anchorage for Encapsulation . . . 3.11.9 Electrical Lead Inserts for Encapsulation. . . . . . . . . . . . . 3.11.10 Inserts Preparation for Molding Encapsulation . . . . . . . 4 Thermoplastic Gearing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Classification of Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.1 Gears Parallel to the Shaft Axis . . . . . . . . . . . . . . . . . . . . . 4.1.2 Bevel Gears, Nonparallel and Intersecting Shafts . . . . . . 4.1.3 Hypoid Gears, Nonparallel and Nonintersecting Shafts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1.4 Gears for Straight Linear Motion . . . . . . . . . . . . . . . . . . . 4.2 Standard Injection Molded Thermoplastic Gears . . . . . . . . . . . . . 4.2.1 Selection of Thermoplastic Resins for Gears . . . . . . . . . 4.2.2 Horsepower Equations for Gears . . . . . . . . . . . . . . . . . . .
196 197 198 198 199 199 200 200 207 211 211 212 213 213 215 222 222 224 224 225 227 227 232 233 235 236 237 239 240 240 242 243 244 246 249 250 253 255 257 258 258 259 261 262 263 264 266
XII
Contents 4.2.3 Spur Gear Terminology and Definitions . . . . . . . . . . . . . Properties Required for Injection Molded Thermoplastic Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Thermoplastic Spur Gear Design Requirements . . . . . . . . . . . . . . 4.4.1 Gating Effects on Thermoplastic Gear Roundness Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.2 Multifunction Designs with Thermoplastic Gears. . . . . 4.4.3 Mounting Thermoplastic Gears on Metal Shafts . . . . . . 4.4.4 Standard Spur Gears, Equations, and Calculations . . . . 4.4.5 Spur Gear Pitch Backlash . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.6 Standard Spur Gear Tooth Size Selection . . . . . . . . . . . . 4.4.7 Standard Gear Total Composite Tolerances . . . . . . . . . . Tolerances and Mold Shrinkage of Thermoplastic Gears . . . . . . . Standard Helical Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Straight Bevel Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Standard Worm Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.8.1 Standard Worm Gear Analysis . . . . . . . . . . . . . . . . . . . . . . Plastic Gearing Technology Designs . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.1 Spur and Helical Gears PGT-1 Tooth Design . . . . . . . . . 4.10.2 Spur and Helical Gears PGT-2 Tooth Design . . . . . . . . . 4.10.3 Spur and Helical Gears PGT-3 Tooth Design . . . . . . . . . 4.10.4 Spur and Helical Gears PGT-4 Tooth Design . . . . . . . . . 4.10.5 Plastic Gearing Technology Tooth Form Design Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.6 Maximum Allowable Outside Diameter DO (Max.) . . . 4.10.7 Spur Gear Tooth Form Comparison. . . . . . . . . . . . . . . . . 4.10.8 Mating Spur Gears Tooth Form Comparison . . . . . . . . . 4.10.9 PGT Spur Mating Gears Strength Balance . . . . . . . . . . . 4.10.10 PGT Close Mesh Center Distance Between Spur Gears . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.10.11 Maximum Close Mesh Center Distance . . . . . . . . . . . . . PGT Helical Thermoplastic Gearing . . . . . . . . . . . . . . . . . . . . . . . . . 4.11.1 PGT-1 Helical Mating Gears Strength Balance . . . . . . . . 4.11.2 PGT-1 Helical Mating Gears Center Distance . . . . . . . . PGT Spur and Helical Gears Horsepower Rating . . . . . . . . . . . . . . 4.12.1 PGT Gear Horsepower Equation Basic Parameters . . . . PGT Spur and Helical Gear Specifications. . . . . . . . . . . . . . . . . . . .
308 309 314 319 322 323 324 328
5 Plastic Journal Bearing Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2 Materials Used for Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 Babbitt Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 Bronze Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 Sintered Porous Metal Journal Bearings . . . . . . . . . . . . . 5.2.4 Plugged Bronze Journal Bearings . . . . . . . . . . . . . . . . . . . 5.2.5 Carbon-Graphite Journal Bearings . . . . . . . . . . . . . . . . . . 5.2.6 Cast-iron Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7 Wooden Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.8 Rubber Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.9 Self-Lubricated Thermoplastic Journal Bearings . . . . . . 5.3 Hydrodynamics of Lubrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4 Journal Bearings Design for Lubrication . . . . . . . . . . . . . . . . . . . . . 5.5 Journal Bearing Design Principles . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 Journal Bearing Nomenclature and Equations . . . . . . . .
335 335 335 336 336 336 336 337 337 337 337 338 339 342 345 345
4.3 4.4
4.5 4.6 4.7 4.8 4.10
4.11
4.12 4.13
268 272 273 275 277 279 279 281 282 283 287 289 290 292 293 294 295 297 298 299 300 302 303 304 305
XIII
Contents
5.6 5.7 5.8 5.9 5.10 5.11 5.12
5.13
5.14 5.15
5.16
5.17
5.5.2 Thermoplastic Journal Bearing Axial Wall Thickness . . 5.5.3 Mounting Thermoplastic Journal Bearings . . . . . . . . . . Split Bushing Thermoplastic Journal Bearings . . . . . . . . . . . . . . . . Self-Centering Thermoplastic Journal Bearings . . . . . . . . . . . . . . . Journal Bearing Load Carrying Contact Surface (C) . . . . . . . . . . . Load Reaction Across the Length of Thermoplastic Bearing . . . . Injection Molded Journal Bearings Process Defects . . . . . . . . . . . . Factors Affecting Journal Bearing Performance . . . . . . . . . . . . . . . Factors Affecting Journal Bearing Dimensions . . . . . . . . . . . . . . . . 5.12.1 Length-to-Inside Diameter Ratio of Journal Bearings . 5.12.2 Types of Service and Motion of Journal Bearings . . . . . 5.12.3 Thermoplastic Journal Bearing Annealing Effects . . . . . 5.12.4 Acetal Homopolymer Moisture Absorption Effects . . . 5.12.5 TFE and Nylon 6/6 Moisture Absorption Effects . . . . . . 5.12.6 Temperature Effects on Thermoplastic Journal Bearings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12.7 Thermal Effects on Thermoplastic Journal Bearing Clearances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Journal Bearing Pressure-Velocity (PV) Limits . . . . . . . . . . . . . . . . 5.13.1 Methods to Determine the PV Limits of Plastics . . . . . . 5.13.2 Journal Bearing Coefficient of Friction . . . . . . . . . . . . . . 5.13.3 Journal Bearing Failures Due to Small Clearances. . . . . 5.13.4 Definition of Different Types of Wear . . . . . . . . . . . . . . . Mating Material Hardness and Surface Finishing. . . . . . . . . . . . . . Self-Lubricated Thermoplastic Journal Bearings . . . . . . . . . . . . . . 5.15.1 Vespel® Polyimide Bearings . . . . . . . . . . . . . . . . . . . . . . . . 5.15.2 Journal Bearing Pressure Equation . . . . . . . . . . . . . . . . . . 5.15.3 Vespel® Wear Factor Effects Caused by Temperature . . 5.15.4 Vespel® Wear Transition Temperature . . . . . . . . . . . . . . . 5.15.5 Frictional Behavior of Vespel® . . . . . . . . . . . . . . . . . . . . . . 5.15.6 Vespel® Journal Bearings Length to Inside Diameter Ratio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.15.7 Vespel® Thrust Bearing Ratio Between Diameters . . . . 5.15.8 Vespel® Journal Bearing Initial Clearance (cI) . . . . . . . . 5.15.9 Vespel® Journal Bearing Inside Diameter (dB) . . . . . . . . Teflon® (TFE) Fabric Composite Bearings . . . . . . . . . . . . . . . . . . . 5.16.1 Bearing Physical Properties . . . . . . . . . . . . . . . . . . . . . . . . 5.16.2 Bearing PV Limit Rating . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.16.3 Journal Bearing Clearances (c) . . . . . . . . . . . . . . . . . . . . . Thermoplastic Kevlar® Reinforced Bearings . . . . . . . . . . . . . . . . . .
6 Thermoplastic Molded Spring Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 Thermoplastic Molded Spring Design Considerations . . . . . . . . . 6.3 Thermoplastic Helical Compression Springs . . . . . . . . . . . . . . . . . 6.4 Thermoplastic Molded Cantilever Beam Springs . . . . . . . . . . . . . . 6.5 Cantilever Beam Spring Design Analysis . . . . . . . . . . . . . . . . . . . . . 6.5.1 Initial Modulus of Elasticity Cantilever Beam Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.2 Stress-Strain Curve Cantilever Beam Analysis Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.5.3 Empirical Data Cantilever Spring Analysis Method . . . 6.6 Thermoplastic Cantilever Spring Applications . . . . . . . . . . . . . . . . 6.7 Thermoplastic Belleville Spring Washers . . . . . . . . . . . . . . . . . . . . .
347 347 348 348 350 350 351 352 353 354 354 354 355 355 356 357 358 359 359 360 361 362 363 366 367 368 369 369 370 370 370 371 373 374 374 375 375 377 377 378 378 379 381 381 381 382 385 388
XIV
Contents 6.7.1 6.7.2 6.7.3
Acetal Homopolymer Belleville Spring Washer Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389 Belleville Spring Washer Loading Rate. . . . . . . . . . . . . . . 392 Belleville Spring Washer Long-Term Loading Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
7 Thermoplastic Pressure Vessel Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.1 Thermoplastic Thin-Walled Pressure Vessels . . . . . . . . . . . . . . . . . 7.2 Thin-Walled Cylinder Basic Principles . . . . . . . . . . . . . . . . . . . . . . . 7.3 Thick-Walled Pressure Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.1 Lame’s Equation for Thick-Walled Cylinders . . . . . . . . . 7.3.2 Maximum Stresses with Internal and External Pressures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.3.3 Maximum Stresses for Internal Pressure Only . . . . . . . . 7.4 Designing Cylinders for Cost Reduction . . . . . . . . . . . . . . . . . . . . . 7.5 Thermoplastic Pressure Vessels Design Guidelines . . . . . . . . . . . . 7.5.1 Preliminary Pressure Vessel Design. . . . . . . . . . . . . . . . . . 7.6 Testing Prototype Thermoplastic Pressure Vessels . . . . . . . . . . . . . 7.6.1 Redesign and Retesting the Pressure Vessels . . . . . . . . . . 7.7 Pressure Vessel Regulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.7.1 ASME Pressure Vessel Code . . . . . . . . . . . . . . . . . . . . . . . .
393 393 394 396 396
8 Thermoplastic Assembly Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2 Cold Heading Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.2.1 Cold Heading Procedure and Equipment . . . . . . . . . . . . 8.3 Electro Fusion Fitting System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.3.1 The SEF-System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4 Hot Plate Welding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.4.1 Hot Plate Welding Joint Design . . . . . . . . . . . . . . . . . . . . . 8.4.2 Flash or Weld Bead . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.5 Solvent and Adhesive Bonding Methods . . . . . . . . . . . . . . . . . . . . . 8.5.1 Solvents Used to Bond Thermoplastic Polymers . . . . . . 8.6 Adhesive Bonding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.1 Adhesive Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.2 Adhesive Concerns . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.6.3 Adhesives Bonding Selection . . . . . . . . . . . . . . . . . . . . . . . 8.6.4 Ultra Violet Curable Adhesives . . . . . . . . . . . . . . . . . . . . . 8.6.5 Adhesive Surface Preparation. . . . . . . . . . . . . . . . . . . . . . . 8.6.6 Adhesive Application and Curing Methods . . . . . . . . . . 8.6.7 Joint Design for Adhesive Bonding . . . . . . . . . . . . . . . . . . 8.7 Metal Fasteners Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.7.1 Thermoplastic Bosses and Self-Tapping Screws . . . . . . . 8.7.2 Thread Forming and Thread Cutting Screws . . . . . . . . . 8.8 Press Fitting Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.1 Press Fitting Interference . . . . . . . . . . . . . . . . . . . . . . . . . . 8.8.2 Circular Press Fitting Assembly Method . . . . . . . . . . . . . 8.9 Snap Fitting Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9.1 Circular Undercut Snap Fitting Joints . . . . . . . . . . . . . . . 8.9.2 Suggestions for Stripping Circular Undercut Snap Fitting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9.3 Cantilevered Latch Snap Fitting Joint. . . . . . . . . . . . . . . . 8.9.4 Cantilever Snap Fit Latch Design Guidelines . . . . . . . . . 8.9.5 Cantilever Latch Snap Fit Mathematical Model . . . . . . .
405 405 405 406 408 409 410 412 413 413 414 416 416 419 420 421 424 425 425 427 429 430 437 439 441 444 445
398 398 400 400 400 402 402 402 403
446 447 449 450
XV
Contents 8.9.6
8.10
8.11
8.12
8.13
8.14
8.15 8.16 8.17
Cantilever Snap Latch Beam Permissible Deflection (δ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.9.7 Cantilever Latch Beam Assembly Force (W) . . . . . . . . . . 8.9.8 Design and Material Considerations . . . . . . . . . . . . . . . . 8.9.9 Uniform Cross Section Cantilever Beam . . . . . . . . . . . . . 8.9.10 Tapered Cross Section Cantilever Beam . . . . . . . . . . . . . Electromagnetic Welding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.10.1 Electromagnetic Welding Process . . . . . . . . . . . . . . . . . . . 8.10.2 Electromagnetic Welding Coil Design . . . . . . . . . . . . . . . 8.10.3 Electromagnetic Welding Joint Design . . . . . . . . . . . . . . 8.10.4 Available Welding Gasket Shapes and Forms . . . . . . . . . Vibration Welding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11.1 High Frequency Vibration Welding . . . . . . . . . . . . . . . . . 8.11.2 Vibration Welding Modes . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11.3 Comparing Vibration Welding to Other Assembly Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.11.4 Vibration Welding Equipment . . . . . . . . . . . . . . . . . . . . . . 8.11.5 Vibration Welding Joint Design. . . . . . . . . . . . . . . . . . . . . 8.11.6 Vibration Welding Aligning and Fixturing . . . . . . . . . . . 8.11.7 Vibration Welding Tolerances . . . . . . . . . . . . . . . . . . . . . . 8.11.8 Vibration Welding Equipment . . . . . . . . . . . . . . . . . . . . . . Spin Welding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12.2 Basic Spin Welding Equipment . . . . . . . . . . . . . . . . . . . . . 8.12.3 Spin Welding Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.12.4 Types of Spin Welding Processes . . . . . . . . . . . . . . . . . . . . 8.12.5 Spin Welding Joint Designs . . . . . . . . . . . . . . . . . . . . . . . . 8.12.6 Spin Welding Process Suggestions. . . . . . . . . . . . . . . . . . . Ultrasonic Welding Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.13.1 Ultrasonic Welding Basic Principles . . . . . . . . . . . . . . . . . 8.13.2 Ultrasonic Welding Basic Components . . . . . . . . . . . . . . 8.13.3 Ultrasonic Welding Equipment . . . . . . . . . . . . . . . . . . . . . 8.13.4 Ultrasonic Welding Process Variables . . . . . . . . . . . . . . . . 8.13.5 Ultrasonic Welding Joint Designs . . . . . . . . . . . . . . . . . . . 8.13.6 Ultrasonic Welding Energy Director Butt Joint . . . . . . . 8.13.7 Ultrasonic Welding Method Design Limitations . . . . . . 8.13.8 Weldability of Thermoplastic Materials . . . . . . . . . . . . . . 8.13.9 Effects Caused by Thermoplastic Additives on Ultrasonic Welding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Ultrasonic Insertion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.14.1 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.14.2 Ultrasonic Insertion Configurations . . . . . . . . . . . . . . . . 8.14.3 Ultrasonic Insertion Product Design . . . . . . . . . . . . . . . . 8.14.4 Ultrasonic Insertion Equipment Requirements . . . . . . . 8.14.5 Ultrasonic Insertion Process Guidelines . . . . . . . . . . . . . Ultrasonic Stud Staking Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.15.1 Ultrasonic Stud Staking Joint Design . . . . . . . . . . . . . . . . Ultrasonic Stud Heading Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.16.1 Thermoplastic Stud Profiles for Ultrasonic Heading . . Ultrasonic Spot Welding Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . 8.17.1 Hand-Held Ultrasonic Spot Welder . . . . . . . . . . . . . . . . .
452 453 454 454 455 458 459 460 463 464 465 465 466 469 471 472 473 474 474 476 476 476 477 477 480 480 482 482 483 483 487 489 492 494 496 497 500 500 501 502 502 503 503 503 506 506 509 510
9 Thermoplastic Effects on Product Design . . . . . . . . . . . . . . . . . . . . . . . . . 511 9.1 Polymer Melt Behavior. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
XVI
Contents 9.1.1 Thermoplastics Glass Transition Temperature . . . . . . . . General Characteristics of Polymers . . . . . . . . . . . . . . . . . . . . . . . . . 9.2.1 Critical Properties of Thermoplastics. . . . . . . . . . . . . . . . Polymer Reinforcements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.1 Types of Fiber Reinforcements . . . . . . . . . . . . . . . . . . . . . 9.3.2 Isotropic Warpage of Fiber Reinforced Resins . . . . . . . . 9.3.3 Fiber Glass Reinforcement Limitations . . . . . . . . . . . . . . 9.3.4 Injection Molding Process Effects on Fiber Glass Orientation . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.5 Tensile Stress Effects Caused by Fiber Glass Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3.6 Flexural Modulus Effects Caused by Fiber Glass Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Chemical and Environmental Resistance . . . . . . . . . . . . . . . . . . . . . 9.4.1 Effects of the Environment . . . . . . . . . . . . . . . . . . . . . . . . . Types of Degradations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.1 Oxidative Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.2 Radiation Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.3 Photo Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.4 Mechanical Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5.5 Microbial Degradation . . . . . . . . . . . . . . . . . . . . . . . . . . . . Moisture Effects on Nylon Molded Parts . . . . . . . . . . . . . . . . . . . . . Aqueous Potassium Acetate for Moisture Conditioning Nylon . . Injection Molding Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Cavity Surface Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Cavity Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . . . 9.10.1 Mold and Post-Mold Shrinkage. . . . . . . . . . . . . . . . . . . . . Process Condition Effects on Mold Shrinkage . . . . . . . . . . . . . . . . Post-Mold Shrinkage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Weld Lines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
513 513 514 515 516 517 517
10 Injection Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.1 Classification of Injection Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2 Effects of Product Design on the Injection Molding Process . . . . 10.2.1 Uniform Wall Thickness . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.2 Balance Geometrical Configuration . . . . . . . . . . . . . . . . . 10.2.3 Smooth Internal Sharp Corners . . . . . . . . . . . . . . . . . . . . 10.2.4 Draft Walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.5 Feather Edges. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.6 Proportional Boss Geometries . . . . . . . . . . . . . . . . . . . . . . 10.2.7 Gate Type and Location . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.2.8 Molded Product Ejection Surface Area . . . . . . . . . . . . . . 10.2.9 Molded Product Tolerances . . . . . . . . . . . . . . . . . . . . . . . . 10.2.10 Surface Finish of Molded Product . . . . . . . . . . . . . . . . . . 10.3 Effects of Mold Design on the Injection Molding Process . . . . . . 10.3.1 Runner System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.2 Mold Cooling System. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.3 Ejector System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.4 Mold Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.3.5 Other Mold Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4 Design Considerations for Injection Molds . . . . . . . . . . . . . . . . . . . 10.4.1 Preliminary Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . 10.4.2 Detailed Mold Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.5 Types of Steels Required for Injection Molds . . . . . . . . . . . . . . . . .
545 545 546 547 547 547 547 547 548 548 548 548 549 549 549 549 550 550 550 550 551 552 553
9.2 9.3
9.4 9.5
9.6 9.7 9.8 9.9 9.10 9.11 9.12 9.13
517 518 519 520 521 522 522 522 522 522 523 523 527 528 529 530 531 533 538 541
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Contents 10.5.1 Major Steel Families . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6 Steels for Thermoplastic Injection Molds . . . . . . . . . . . . . . . . . . . . 10.6.1 General Steel Selection Procedures . . . . . . . . . . . . . . . . . . 10.6.2 Properties and Characteristics of Tool Steels . . . . . . . . . 10.6.3 Effects of Alloying Elements on Tool Steel Properties. . 10.6.4 Chemical Composition of Steels Used for Molds . . . . . 10.6.5 Effects of Alloying on Tool Steels . . . . . . . . . . . . . . . . . . . 10.6.6 Effects of Heat Treatment on Tool Steel Properties . . . . 10.6.7 Prehardened Tool Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.8 Carburizing Tool Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.9 Oil and Air Hardening Tool Steels. . . . . . . . . . . . . . . . . . . 10.6.10 Stainless Steels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.6.11 Steels Used in Thermoplastic Injection Mold Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7 Mold Cavity Surface Finishing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.7.1 Mold Surface Finishing Process Procedures . . . . . . . . . . 10.8 Thermoplastic Injection Mold Bases . . . . . . . . . . . . . . . . . . . . . . . . . 10.8.1 Standard Mold Base Components. . . . . . . . . . . . . . . . . . . 10.8.2 Functions of the Mold Base Components . . . . . . . . . . . . 10.8.3 Types of Standard Mold Bases . . . . . . . . . . . . . . . . . . . . . . 10.9 Types of Thermoplastic Injection Molds . . . . . . . . . . . . . . . . . . . . . 10.9.1 Two-Plate Molds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.9.2 Round Mate® Interchangeable Insert Molds . . . . . . . . . 10.9.3 Master Unit Die Interchangeable Insert Molds . . . . . . . 10.9.4 Three-Plate Mold Cold Runner System . . . . . . . . . . . . . . 10.9.5 Vertical Insert Mold for Thermoplastic Encapsulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.9.6 Hot Runner Molding Systems . . . . . . . . . . . . . . . . . . . . . . 10.9.7 Hot Runner Mold Temperature Control Systems . . . . . 10.9.8 Hot Runner Mold Gates (Drops) . . . . . . . . . . . . . . . . . . . 10.9.9 Types of Hot Runner Molding Systems . . . . . . . . . . . . . . 10.9.10 Thermoplastic Stack Injection Molds. . . . . . . . . . . . . . . . 10.9.11 Lost Core Thermoplastic Injection Molds. . . . . . . . . . . . 10.10 Number of Mold Cavities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.10.1 Cavity Number Limitations . . . . . . . . . . . . . . . . . . . . . . . . 10.10.2 Number of Mold Cavities Equation . . . . . . . . . . . . . . . . . 10.11 Mold Parting Line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.11.1 Flat Mold Parting Line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.11.2 Non-Flat Mold Parting Line . . . . . . . . . . . . . . . . . . . . . . . . 10.11.3 Balancing of Mold Parting Line Surfaces . . . . . . . . . . . . . 10.12 Mold Ejection Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12.1 Ejector Plate Assembly. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12.2 Ejector Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12.3 Retaining Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12.4 Ejector Sleeves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.12.5 Types of Mold Ejection Systems . . . . . . . . . . . . . . . . . . . . 10.13 Injection Mold Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.13.1 Mold Temperature Control . . . . . . . . . . . . . . . . . . . . . . . . 10.13.2 Factors Affecting Mold Cooling. . . . . . . . . . . . . . . . . . . . . 10.13.3 Effects Caused by Elevated Mold Temperature . . . . . . . 10.13.4 Effects Caused by Too Low a Mold Temperature . . . . . . 10.13.5 Mold Heat Transfer Methods . . . . . . . . . . . . . . . . . . . . . . . 10.13.6 Mold Cavity Insert Cooling . . . . . . . . . . . . . . . . . . . . . . . . 10.14 Injection Molding Machine Nozzle . . . . . . . . . . . . . . . . . . . . . . . . . .
553 557 558 559 559 559 560 562 564 566 567 568 569 571 573 578 578 579 582 583 584 585 585 586 587 588 589 590 593 601 602 606 606 606 607 607 608 610 610 611 611 611 611 612 615 616 617 617 618 618 631 639
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Contents 10.14.1 Mold Cold Runner System . . . . . . . . . . . . . . . . . . . . . . . . . 10.14.2 Determining the Injection Pressure Needed . . . . . . . . . . 10.14.3 Cold Runner Flow Tab. . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Cavity Gating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.15.1 Types of Mold Cavity Gates . . . . . . . . . . . . . . . . . . . . . . . . 10.15.2 Different Types of Hot Runner Gates . . . . . . . . . . . . . . . . Gate Molding Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Venting Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.17.1 Product Design for Venting . . . . . . . . . . . . . . . . . . . . . . . . 10.17.2 Venting Characteristics of Thermoplastic Polymers . . . 10.17.3 Mold Deposit Problems . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.17.4 How to Avoid Venting Problems . . . . . . . . . . . . . . . . . . . . 10.17.5 Planning Mold Venting . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.17.6 Mold Venting Process Problems . . . . . . . . . . . . . . . . . . . . 10.17.7 Mold Venting Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.17.8 Mold Venting Using Sintered Porous Insert Plugs . . . . . 10.17.9 Logic Seal (Negative Coolant Pressure) Mold Venting . 10.17.10 Mold Cavity Vacuum Venting System . . . . . . . . . . . . . . . Mold Cavity Insert Contact Area Strength . . . . . . . . . . . . . . . . . . . . 10.18.1 Cavity Insert Sidewall Strength . . . . . . . . . . . . . . . . . . . . . 10.18.2 Methods to Calculate the Strength of Cavity Insert Sidewall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Layout Case Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Support Pillars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Tolerances for Thermoplastic Molded Parts . . . . . . . . . . . . . . . . . . 10.21.1 Factors Affecting Dimensional Control Tolerances . . . . General Specifications for Mold Construction for Thermoplastic Injection Molding Resins . . . . . . . . . . . . . . . . . . . . . 10.22.1 Mold Design Requirements . . . . . . . . . . . . . . . . . . . . . . . . 10.22.2 Mold Drawing Standards . . . . . . . . . . . . . . . . . . . . . . . . . . 10.22.3 Required Types of Tool Steels for Mold Construction . 10.22.4 Mold Construction Requirements . . . . . . . . . . . . . . . . . . Mold Tryout – Debug – Approvals – “MQ1” Requirements. . . . . 10.23.1 Mold Tryout or Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . 10.23.2 Mold Debug Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.23.3 Approval of Molded Parts and Pre-Production Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10.23.4 Mold Cavity and Core Surface Temperatures . . . . . . . . . 10.23.5 “MQ1” Requirements . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
639 653 654 655 656 663 664 666 667 669 669 670 671 672 674 690 691 693 698 699
11 Performance Testing of Thermoplastics . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Property Data Sheet for Thermoplastics . . . . . . . . . . . . . . . . . . . . . 11.2 Tensile Testing (ASTM D-638) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.1 Tensile Testing Equipment . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.2 Tensile Test Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.3 Specimen Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.4 Tensile Strength Test Procedures . . . . . . . . . . . . . . . . . . . . 11.2.5 Tensile Modulus and Elongation . . . . . . . . . . . . . . . . . . . . 11.2.6 Molecular Orientation Effects . . . . . . . . . . . . . . . . . . . . . . 11.2.7 Crosshead Speed Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.8 Temperature Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2.9 Moisture Absorption Effects. . . . . . . . . . . . . . . . . . . . . . . . 11.2.10 Stress-Strain Effects Caused by Creep . . . . . . . . . . . . . . . 11.3 Flexural Testing (ASTM D-790) . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
723 724 725 725 726 726 726 727 728 729 729 729 730 730
10.15
10.16 10.17
10.18
10.19 10.20 10.21 10.22
10.23
700 704 705 705 707 709 709 709 711 713 720 720 720 720 720 721
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Contents
11.4
11.5
11.6
11.7
11.8
11.9
11.10 11.11 11.12
11.13
11.14
11.15 11.16 11.17 11.18
11.3.1 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.3.2 Test Procedures and Equations . . . . . . . . . . . . . . . . . . . . . 11.3.3 Modulus of Elasticity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Compressive Strength Testing (ASTM D-695) . . . . . . . . . . . . . . . . 11.4.1 Compressive Testing Apparatus . . . . . . . . . . . . . . . . . . . . . 11.4.2 Test Specimens and Conditioning. . . . . . . . . . . . . . . . . . . 11.4.3 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.4.4 Stress-Strain Tension and Compression Curves. . . . . . . Shear Strength Testing (ASTM D-732) . . . . . . . . . . . . . . . . . . . . . . . 11.5.1 Test Specimen and Apparatus . . . . . . . . . . . . . . . . . . . . . . 11.5.2 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.5.3 Significance and Limitations . . . . . . . . . . . . . . . . . . . . . . . Surface Hardness Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.6.1 Rockwell Hardness Testing (ASTM D-785-60T) . . . . . . 11.6.2 Barcol Hardness Testing (ASTM D-2583) . . . . . . . . . . . . 11.6.3 Factors Affecting the Test Results . . . . . . . . . . . . . . . . . . . Abrasion Resistance Testing (ASTM D-1044) . . . . . . . . . . . . . . . . . 11.7.1 Taber Abrasion Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.7.2 Theoretical Analysis of Wear . . . . . . . . . . . . . . . . . . . . . . . Coefficient of Friction (ASTM D-1894) . . . . . . . . . . . . . . . . . . . . . . 11.8.1 Coefficient of Friction of Thermoplastic Materials . . . . 11.8.3 Effects of Lubricants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Mold Shrinkage Test (ASTM D-955) . . . . . . . . . . . . . . . . . . . . . . . . 11.9.1 Purpose of the Mold Shrinkage Test . . . . . . . . . . . . . . . . . 11.9.2 Factors Affecting Mold Shrinkage . . . . . . . . . . . . . . . . . . . 11.9.3 Injection Molding Effects on Shrinkage. . . . . . . . . . . . . . 11.9.4 Requirements for Sampling . . . . . . . . . . . . . . . . . . . . . . . . 11.9.5 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Specific Gravity Testing (ASTM D-792) . . . . . . . . . . . . . . . . . . . . . . 11.10.1 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Density Gradient Testing (ASTM D-1505) . . . . . . . . . . . . . . . . . . . Water Absorption Testing (ASTM D-570) . . . . . . . . . . . . . . . . . . . . 11.12.1 Test Specimen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.12.2 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Impact Resistance Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.1 Pendulum Impact Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.2 Charpy Impact Testing (ASTM D-256) . . . . . . . . . . . . . . 11.13.3 Chip Impact Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.13.4 Tensile Impact Testing (ASTM D-1822) . . . . . . . . . . . . . 11.13.5 Drop Weight Impact Testing (ASTM D-3029) . . . . . . . . 11.13.6 Falling Weight Impact Testing . . . . . . . . . . . . . . . . . . . . . . 11.13.7 Instrumented Impact Testing . . . . . . . . . . . . . . . . . . . . . . . Creep, Rupture, Relaxation, and Fatigue . . . . . . . . . . . . . . . . . . . . . 11.14.1 Tensile Creep Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.14.2 Flexural Creep Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.14.3 Procedure for Applying Creep Modulus . . . . . . . . . . . . . Melting Point Test (ASTM D-795) . . . . . . . . . . . . . . . . . . . . . . . . . . Vicat Softening Point (ASTM D-1525) . . . . . . . . . . . . . . . . . . . . . . . 11.16.1 Melting Point, Glass Transition Temperature . . . . . . . . . Brittleness Temperature (ASTM D-746) . . . . . . . . . . . . . . . . . . . . . 11.17.1 Test Apparatus and Procedures . . . . . . . . . . . . . . . . . . . . . UL – Temperature Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.18.1 Relative Thermal Indices . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.18.2 Long Term Thermal Aging Index . . . . . . . . . . . . . . . . . . .
731 732 733 733 734 734 734 735 735 735 736 736 736 737 739 740 740 741 741 742 743 744 744 744 745 745 745 746 748 749 750 750 751 751 751 753 755 755 755 756 757 758 761 761 762 764 767 767 768 768 768 770 770 772
XX
Contents 11.18.3 Creep Modulus/Creep Rupture Tests . . . . . . . . . . . . . . . . 11.19 Heat Deflection Temperature (ASTM D-648). . . . . . . . . . . . . . . . . 11.19.1 Apparatus and Test Specimens . . . . . . . . . . . . . . . . . . . . . 11.19.2 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.19.3 Test Variables and Limitations . . . . . . . . . . . . . . . . . . . . . . 11.20 Soldering Heat Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.21 Coefficient of Linear Thermal Expansion Testing . . . . . . . . . . . . . 11.21.1 Test Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.22 Thermal Conductivity Testing (ASTM C-177) . . . . . . . . . . . . . . . . 11.23 Melt Flow Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.23.1 Moisture Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.24 Melt Index Testing (ASTM D-1238) . . . . . . . . . . . . . . . . . . . . . . . . . 11.24.1 Melt Flow Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.25 Capillary Rheometer Melt Viscosity Testing (ASTM D-1703) . . . 11.25.1 Melt Viscosity vs. Shear Rate Curves. . . . . . . . . . . . . . . . . 11.26 Electrical Properties Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.26.1 Underwriter’s Laboratories (UL) Yellow Cards . . . . . . . 11.26.2 How to Read and Interpret the “UL Yellow Card” . . . . . 11.26.3 “UL Insulation Systems Recognition” . . . . . . . . . . . . . . . 11.27 Electrical Insulation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.28 Electrical Resistance Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.28.1 Volume Resistivity Testing (ASTM D-257) . . . . . . . . . . . 11.28.2 Surface Resistivity Testing (ASTM D-257) . . . . . . . . . . . 11.28.3 Dielectric Strength Testing (ASTM D-149) . . . . . . . . . . . 11.28.4 Dielectric Constant Testing (ASTM D-150) . . . . . . . . . . 11.28.5 Dissipation Factor Testing (ASTM D-150) . . . . . . . . . . . 11.28.6 Arc Resistance Testing (ASTM D-495) . . . . . . . . . . . . . . . 11.28.7 High Voltage Arc Tracking Rate (UL-746 A) . . . . . . . . . . 11.28.8 Comparative Track Index Testing (ASTM D-3638/ UL 746 A) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.29 Self and Flash Ignition Temperature Testing (ASTM D-1929) . . 11.29.1 Test Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.29.2 High Current Arc Ignition Testing (UL 746A) . . . . . . . . 11.29.3 Hot Wire Coil Ignition Testing (UL 746A/ASTM D-3874) . . . . . . . . . . . . . . . . . . . . . . . . . 11.29.4 Hot Mandrel Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.29.5 Glow Wire Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.30 Flammability Characteristics of Polymers . . . . . . . . . . . . . . . . . . . . 11.30.1 Inherently Flame Retardant Polymers . . . . . . . . . . . . . . . 11.30.2 Less Flame Retardant Polymers . . . . . . . . . . . . . . . . . . . . . 11.30.3 Flammable Polymers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.31 UL 94 Flammability Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.31.1 Horizontal Burning Testing, UL 94HB. . . . . . . . . . . . . . . 11.31.2 Vertical Burning Testing, UL 94-V0, UL 94-V1, UL 94-V2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.31.3 Vertical Burning Testing, UL 94-5V, UL 94-5VA, UL 94-5VB . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.31.4 Factors Affecting UL 94 Flammability Testing . . . . . . . . 11.32 Limited Oxygen Index Testing (ASTM D-2863) . . . . . . . . . . . . . . . 11.32.1 Test Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.32.2 Factors Affecting the Test Results . . . . . . . . . . . . . . . . . . . 11.33 Smoke Generation Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.33.1 Smoke Density Testing (ASTM D-2843) . . . . . . . . . . . . . 11.34 Weathering Tests for Thermoplastic Materials . . . . . . . . . . . . . . . .
773 774 774 775 775 775 776 777 777 779 780 780 781 782 783 784 785 786 791 792 792 793 794 795 797 800 801 803 804 805 805 806 807 807 807 809 810 810 810 811 811 812 813 815 815 816 816 817 817 818
XXI
Contents 11.34.1 Weathering Creep Factors (Degradation) . . . . . . . . . . . . 11.34.2 Ultraviolet (UV) Radiation . . . . . . . . . . . . . . . . . . . . . . . . 11.34.3 Temperature. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.34.4 Moisture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.34.5 Oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.34.6 Micro-Organisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Accelerated Weathering Testing (ASTM G 23) . . . . . . . . . . . . . . . . 11.35.1 Exposure to Fluorescent UV Lamp, Condensation (ASTM G 53) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.35.2 Accelerated Weather Testing, Weather-Ometer® . . . . . . 11.35.3 Exposure to Carbon Arc Light and Water Testing (ASTM D-1499) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.35.4 Exposure to Xenon Arc Light and Water Testing (ASTM D-2565) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.35.5 Outdoor Weathering Testing of Thermoplastics (ASTM D-1435) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Fungi Resistance Testing of Thermoplastics (ASTM G 21) . . . . . Bacteria Resistance Testing of Thermoplastics (ASTM G 22) . . . Fungi and Bacteria Outdoor Exposure Resistance Limitations . .
827 828 829 829
12 Thermoplastic Product Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.1 Injection Molding Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.2 Molding Cycle Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.3 Material Handling (Regrinds) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.4 Capital Equipment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.5 Injection Molding Machine Size . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.6 Injection Molding Machine Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.7 Machine Installation and Safety Considerations . . . . . . . . . . . . . . 12.8 Auxiliary Equipment and Automation . . . . . . . . . . . . . . . . . . . . . . . 12.9 Mold Cost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.10 Molded Products Cost Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.10.1 Cost Analysis Basic Method . . . . . . . . . . . . . . . . . . . . . . . . 12.10.2 Cost Analysis Graph Method . . . . . . . . . . . . . . . . . . . . . . . 12.10.3 Advanced Cost Analysis Method . . . . . . . . . . . . . . . . . . . . 12.11 Secondary Molding Operations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12.12 Additional Manufacturing Costs . . . . . . . . . . . . . . . . . . . . . . . . . . . .
831 832 832 833 833 833 836 837 837 838 841 841 842 843 848 848
Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acronyms for Polymeric Materials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Common Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Process Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Reinforcement and Filler Acronyms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . English and Metric Units Conversion Guide. . . . . . . . . . . . . . . . . . . . . . . .
849 849 850 851 851 852 853
11.35
11.36 11.37 11.38
818 819 819 820 820 820 821 821 822 823 825
Subject Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 855 About the Author . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 869
1
1
Polymeric Materials
1.1
Introduction to Plastic Materials
Plastic materials are the ultimate tribute to man’s creativity and inventiveness. Plastics are true man-made materials. Like any other materials, they have their origin in nature. The structure of plastic materials is based on basic chemical elements such as carbon, oxygen, hydrogen, nitrogen, chlorine, and sulfur. These elements are extracted from the air, water, gas, oil, coal, and even from living plants. It was man’s inspiration to take these elements and combine them through various chemical reactions in an almost unending series of combinations to produce the rich variety of polymers known today as plastics. It is possible to create different polymers from different combinations of elements and create almost any property desired for an end product. These new polymers have similar properties to existing conventional materials but they offer greater design freedom and cost incentives for manufacturing. There are some plastics with significant property improvements over existing materials, while other polymers can only be described as unique materials with exceptional properties previously unknown to the industrial world. There are plastics that will melt at 200 °F, while other plastic materials can withstand up to 1,000 °F. The heat shields that protect astronauts travelling in space are plastic materials based on the technology known as “ablative plastics”. There are polymers used for shields that can stop a bullet. There are flexible plastic films that protect grocery products and there are rigid plastics rugged enough to serve as support beams in a building. Plastics are among the best electrical insulating materials known to mankind. However, we find another type of special plastic material capable of conducting electricity. Plastic composite materials are used for golf club shafts, while other flexible polymers are used as upholstery materials for furniture. There are impact resistant and transparent polymers used as windshields for airplanes, automobiles, and shower doors. There are also transparent packaging materials used to protect consumer items. The number of permutations possible in combining chemical elements to create plastics with different properties is almost endless. It is this diversity that has made plastics so applicable to such a broad range of end uses and products today. This polymer diversity makes it difficult to grasp the idea of a single family of materials that can provide an infinite range of properties, characteristics, and transformation processes.
1.1.1
Beginning of Plastics
Plastic materials have played an important role in the development of this modern civilization. These polymers have an extensive versatility of properties and process automation while offering several cost advantages. It is surprising to realize that a little more than a century ago there were no such plastic materials any where around the world. The plastics industry dates its beginning back to 1868, when John Wesley Hyatt mixed pyroxylin, made from cotton and nitric acid, with camphor to create an entirely different and new product called “Celluloid”. This material was the first commercial plastic material. The
7
7 7
Figure 1-1 First photographic celluloid film
2
1 Polymeric Materials development of celluloid was in response to a competition sponsored by a manufacturer of billiard balls. It came about to overcome a shortage of ivory used to produce billiard balls. With the need for a new material and a production method for this application, celluloid was developed and the plastics industry was born.
Figure 1-2 First phenolic applications
Celluloid quickly moved into other markets, including new applications such as shirt collars, cuffs and shirt fronts, dolls, combs, buttons, and window curtains used on early automobiles. However, the most important celluloid application was the first photographic film used by Eastman to produce the first motion picture film in 1882. This material is still in use by the motion picture industry today, under its chemical name of cellulose nitrate. The plastics industry took its second major step 41 years later. Dr. Leo Hendrik Baekeland introduced the first phenol formaldehyde “Phenolic” in 1909. This was the first plastic material to achieve world acceptance. What is more important, he also developed techniques for controlling and modifying the phenolformaldehyde reaction. This technology made it possible to produce useful items, such as marbleized clock bases or electric iron handles, under heat and pressure from phenolic. This process of liquefying the material to form various shapes under heat and pressure is the same process that is still in use by the industry to produce thermoset plastic materials. The third major step in plastic’s development took place in the 1920s with the introduction of cellulose acetate. This polymer was similar in structure to cellulose nitrate but safer in processing and use. Urea-formaldehyde can be processed like phenolic, but into light colored articles that were more attractive than the phenolic’s black and brown colors. Polyvinyl chloride (PVC) became the second largest selling plastic for such applications as flooring, upholstery, wire, and cable insulation, tubing, hoses, and fittings. Polyamide or nylon (Du Pont’s trade name) was first developed as a fiber material. Nylon represents one of the most important new developments in the plastic industry. The research development work of W. T. Carothers in the late 1920s made possible the introduction of the nylon technology. The tempo of plastic’s development picked up considerably in the 1930s and the 1940s. Each decade newer, more exciting, more versatile plastics came into existence. In the 1930s, the acrylic resins were introduced for signs and transparent articles. The introduction of polystyrene made this polymer the third largest selling plastic for house wares, toys, and for applications in the packaging industry. Melamine resins were also introduced for use in dishware, paints, and wet strength paper. Melamine later became a critical element (as a binder) in the development of decorative laminate kitchen counter tops, table tops, and panels. During the World War II years of the 1940s, the demand for plastics accelerated as did research into new plastics that could aid in the defense effort. Polyethylene, today the most important type of plastic, was a war time development that grew out of the need for a superior insulating material for applications such as radar cables. The thermoset polyester resins were also introduced a decade later. Radical changes in the boat building industry were also a war time development introduced for military use. Acrylonitrile-butadiene-styrene (ABS) is best known today as the plastic material used for applications such as appliance housings,
3
1.1 Introduction to Plastic Materials refrigerator liners, safety helmets, tubing, telephone handsets, and luggage. The original ABS research work was a crash program during the war for the development of synthetic rubber. By the beginning of the 1950s, plastics were on their way to being accepted by designers and engineers as basic industrial materials. This decade also saw the introduction of polypropylene following the Nobel Award winning work of Karl Ziegler in Germany and Giulio Natta in Italy for “ordering” the molecular arrangement of plastics. Also highlighting this decade was the development of acetal and polycarbonate; two plastics that, along with nylon, came to form the nucleus of a subgroup in the plastic’s family known as the “Engineering Thermoplastics”. Their outstanding impact strength, thermal and dimensional stability enabled engineering plastic resins to compete directly with metal materials. The 1960s and 1970s also had their share of new plastics’ introductions. The most important contribution was the thermoplastic polyesters used in exterior automotive parts, under the hood applications, and electrical and electronic components. Polyester bottles internally coated with high nitrile barrier resins (outstanding resistance to gas permeation) developed the new drink bottle packaging applications. During this time span, another subgroup of the plastic’s family called “High Performance Plastics” found new markets; this group includes such materials as polyimide, polyamide-imide, aromatic polyester, polyphenylene sulfide, and polyether sulfone. These materials historically met their objectives in the demanding thermal needs of aerospace and aircraft applications; reinforcing the vision of the plastic’s industry that the future is, indeed, plastics.
1.1.2
Polymer Families
Plastic materials are the result of the combination of carbon elements reacting with oxygen, hydrogen, nitrogen, and other organic and inorganic elements. These polymers have the ability to change into a liquid (melt), and are capable of being formed into shapes by the application of heat and pressure. Plastics are a family of materials, not a single kind of material. Plastics have an extensive number of polymers and compounds with each kind of material having its own unique and special type of properties. Most plastics fall into one of the following groups: thermoplastics, thermoplastic elastomers, liquid injection molding elastomers, thermosets, and thermoset rubbers. Thermoplastic resins consist of a long chain of molecules, either linear or branched, having side chains or unattached groups to other polymer molecules. Usually, the commercial shapes of the thermoplastic materials are pellets, granules or powders. These materials can be repeatedly melted by heat under pressure so they can be formed, then cooled and harden into the final desired shape. Chemical changes do not take place during the transformation process. Figure 1-3 shows a simple analogy for molding plastic resins, a wax block that can be liquified by heat, poured into a mold, then cooled to become a solid again. Thermoplastic elastomer (TPE) resins are rubbery materials with the characteristics of a thermoplastic and the performance properties of a thermoset rubber. TPEs are processed using the same thermoplastic equipment and methods, such as extrusion, injection molding, and blow molding. Liquid injection molding compounds are a family of unique products. Generally, these materials use two liquid formulations in a 1 : 1 ratio. These compounds
Figure 1-3 Thermoplastic materials analogy, wax candle
4
1 Polymeric Materials produce precision elastomeric molded parts efficiently. They use a liquid metering, mixing, and delivery system, a specially modified injection molding machine, and a high temperature precision mold. Thermoset materials have a reactive portion between the chain cross link and the long molecule’s network during polymerization. The linear polymer chains bond together to form a three-dimensional network. Therefore, once polymerized or hardened, the material cannot be softened by heating without degrading some linkages of the material. Thermoset materials in commercial form are supplied as resins, powders, and liquid monomer mixtures or as partially polymerized molding compounds. In this uncured condition, they conform to the finished shape with or without pressure and can be polymerized with chemicals or heat.
Figure 1-4 Thermoset plastics analogy, concrete
Figure 1-4 shows one of the analogies for the thermoset materials as the chemical transformation of concrete. When the cement powder blends with water and sand, the mixture becomes a thick paste compound. This mixture is then transferred to a cavity for curing and hardening to become a solid object (concrete). The chemical reaction transforms the product into concrete. The transformation processes of the concrete items are irreversible. Reprocessing concrete forms or returning to cement, sand, and water are not possible. The concrete becomes a new, different and strong material. Thermosetting materials are not reprocessable or recyclable. Thermosetting rubber materials are not covered in this book, because the technology, chemistry, part design, mold design, and processing are completely different and too intensive to review in this plastic product design handbook.
1.2
Thermoplastic Polymers
1.2.1
Classification of Polymers by Performance
Thermoplastic resin classifications divide the polymers into four family groups based on their application performance. The first is the commodity resins, which have a large consumption volume, extensive application end uses, low material cost, and limited property performances. The commodity resins include polystyrene (PS), polyethylene (PE), styrene acrylonitrile copolymer (SAN), cellulose nitrate (CN), polybutene (PB), bismaleimide (BMI), unsaturated polyester (UP), and polyvinyl chloride (PVC). The second group is classified as intermediate resins. These resins have mechanical, thermal, chemical, and electrical properties generally that are higher than the commodity resins. The basic matrix properties remain constant when modifications are made to change specific mechanical properties of the compound. This intermediate category of resins includes acrylics, thermoplastic olefin (TPO), polyphenyleneoxide (PPO), thermoplastic vulcanizate (TPV), melt procesable rubber (MPR), high impact polystyrene (HIPS), ionomers, melamine formaldehyde (MF), polyxylene, polypropylene (PP), acrylonitrilebutadiene-styrene (ABS), styrene-acrylonitrile (SAN), polyphenylene ether (PPE), polyurethane (PUR), urethane hybrid, polyester alkyd (PAK), styrenic block copolymer thermoplastic elastomers (TPR), and ultra high molecular weight polyethylene (UHMWPE). The third group is classified as engineering resins. The level of mechanical properties that qualify as engineering grade is somewhat arbitrary; a tensile
1.2 Thermoplastic Polymers strength that is not lower than 7,000 psi with a minimum modulus of elasticity of 350,000 psi are reasonable criteria. Engineering resins are fundamentally unmodified resins, whose properties are improved by compounding. A compounded resin is defined as a material containing a matrix (basic resin), additives, a reinforcing ingredient, such as fiber glass or minerals, heat and ultraviolet stabilizers, flame retardants, and other additives. Several types of compounded resins are formulated to improve specific properties required for the application. A conventional fiber glass reinforced resin contains from 10 to 55% glass fiber. The glass fibers are only 0.125 in long and a coating with a coupling agent is added to the glass fiber to obtain a bond with the matrix. The engineering resins are acetal, polyamide (nylon, PA), polycarbonate (PC), polybutylene terephthalate (PBT), polyethylene terephthalate (PET), glass fiber reinforced polypropylene, block copolyester TPE, polyamide TPE, liquid injection molding silicone, diallyl phthalate, epoxy (EP), and cyanate. The forth group is the high performance engineering resins. These resins in this category have the highest resistance retaining a high percentage of their useful mechanical properties at high temperatures, providing a longer service life of the product. They also maintain properties at higher electrical frequencies without sacrificing their chemical resistance properties when exposed to corrosive elements. These resins are also inherently flame retardant, with UL-94 flammability ratings of V0 and 5V. The high performance engineering resins include high temperature nylon (PA), liquid crystal polymers (LCP), polysulfone (PSU), fluoropolymers, polyetherimide (PEI), polyaryletherketone (PAEK), polyphenylene sulfide, silicone, and polyimide ((PMR). With few exceptions, high performance engineering resins do not have the higher Izod impact strength at room temperature that many engineering thermoplastic resins have. Competition among resin producers to capture markets has created an engineering resin supply of thousands of resin grades. The result is that there is usually more than one choice, and often several choices, available to meet the end product performance requirements. A total assessment of various grades includes product design and processing considerations. To select the best material for an application, compare the different properties and processing characteristics of several thermoplastic resins, which may meet the application requirements. However, product designers must make their resin selection based on other important characteristics of the resins, such as part design flexibility, and process performance. Generally, most resins have different performance characteristics that could create molding problems and/or part failures. Part design and process characteristics can diverge when the resin properties between grades are matched. When additives, such as flame retardants and stabilizers, are compounded into the resin, the characteristics of the matrix are modified, sometimes with a loss of some of the properties. In addition, when fiber glass or minerals are added to increase the mechanical strength properties, processibility becomes more difficult, because the rheology or viscosity of the compounded product increases, decreasing the melt flow rate (higher injection pressures and melt/mold temperature are required).
5
6
1 Polymeric Materials The economics involved in thermoplastic resin selection are complex, because the resin price is not usually the most important factor. When a thermoplastic resin is used for injection molding a close dimensional tolerance end product, the following engineering requirements are essential in reducing manufacturing costs: • Part geometry needs to be designed to produce molded components with maximum productivity. • A precision mold must be designed and constructed for fast running cycles and molding the maximum number of cavities automatically. • It is also important to select the best type, capacity, and running conditions of the injection molding machine. • Then, it is necessary to establish efficient injection molding process setup conditions for the resin being used. It is also essential that the molding and maintenance organizations are well trained, using an up-to-date technical training program provided by a qualified instructor. Material costs become increasingly significant with higher volume and less critical product requirements. Here, the resin cost represents a high percentage of the molded components finished cost. For example, common items such as business machine housings, plumbing (faucets, valves, tubing, and shower heads), kitchenware and appliance components (refrigerator liners, washing machine impellers, and vacuum cleaner housings) are price sensitive products. For these markets, the resin cost becomes a very competitive business aspect of manufacturing.
1.2.2 Amorphous molecules
Figure 1-5 Amorphous polymer molecular structure
Polymeric materials are an aggregate of long-chained molecular structures. There are two different states, one of which is comprised of high polymer compounds arranged in a crystalline structure (crystalline polymers) and the other in the form of flexible molecular chains that are entangled (amorphous polymers). However, there is no crystalline plastic material exhibiting solely a crystalline structure, but rather they have a mixed structure in which crystalline sections and amorphous sections coexist. The ratio of crystalline sections is called the material’s crystallinity. Figures 1-5 and 1-6 show the difference between these families of polymers.
1.2.3
Amorphous molecules
Molecular Structure of Plastic Materials
Acrylonitrile-Butadiene-Styrene (ABS)
Crystalline structure
The ABS resins have a well balanced set of properties for molding close dimensional control articles with an outstanding surface finishing, good impact resistance, and metal plating characteristics. ABS resins belong to a very versatile family of thermoplastic polymers. They are produced by combining three monomers: acrylonitrile, butadiene, and styrene. The chemical structure of these monomers requires each monomer to be an important component of the ABS resins. Acrylonitrile contributes heat resistance, chemical resistance, and surface hardness to the system. The butadiene contributes toughness and impact resistance, while the styrene component contributes processibility, rigidity, and strength. Figure 1-6 Semi-crystalline polymer molecular structure
ABS plastics are two-phase systems. Styrene-acrylonitrile (SAN) forms the continuous matrix phase. The second phase is composed of dispersed polybutadiene
7
1.2 Thermoplastic Polymers
General Properties of ABS Specific gravity
1.05
Tensile modulus @ 73 °F (Mpsi)
0.3
Tensile strength @ yield (Kpsi)
5.0
Notch Izod impact @ 73 °F (ft-lb/in)
2.50–12.0
Thermal limits Service temp. (°F)
167–185
Shrinkage (%)
0.4–0.7
Tg (°F)
185–240
Vicat point (°F)
237
Process temp. (°F)
410–518
Mold temp. (°F)
122–176
Drying temp. (°F)
176–185
Drying time (h)
2.0–4.0
particles, which have a layer of SAN grafted onto their surface. The binding matrix layer of SAN makes this polymer’s two phases compatible. The property balance of ABS is controlled by the ratio of the monomers and by the molecular structure of the two phases. Stabilizers, lubricants, colorants, and other additives can be added to the system, and while this makes the production of ABS very complex, it allows great flexibility in product property design. As a result of the unique morphology of ABS, hundreds of different products have been developed and are available commercially. ABS resins are grouped into two major divisions: injection molding and extrusion grades. The primary difference between these grades is their melt viscosity, which is significantly lower for injection molding resins. Within each division of ABS polymers, there are the corresponding classes of grades. Standard ABS grades are grouped by impact strength into medium, high, and very high impact grades. The standard ABS versions are available in a low surface gloss, a high surface gloss, and an ultra-high surface gloss. Specialty ABS grades include high heat, plating, clear, flame retardant, and structural foam grades. Standard grades of ABS generally meet the Underwriter’s Laboratories (UL) rating for slow burning (UL-94 HB). Flame retardant materials have UL-94 V0 at thicknesses as low as 0.062 in and UL-94 5V at thicknesses as low as 0.125 in. Clear ABS grades use methyl methacrylate providing light transmission of 72% and a haze level of 10%. Alloys of ABS-PVC are available in high and low gloss grades. Alloys of ABS-PC are available in injection molding and plating grades. ABS-SMA heat resistant alloys are available in injection molding, extrusion, and plating grade versions. Alloys of ABS-PA are also available in injection molding grades. ABS is an excellent choice for use in alloys and blends. When the plastics are combined, the positive features of each can be maintained, or even enhanced, while the negative features of each can be reduced. ABS-polycarbonate (ABSPC) and ABS-polyvinyl chloride (ABS-PVC) are well-established alloys. More recent innovations have resulted in ABS-styrene-maleic anhydride (ABS-SMA) and ABS-polyamide (ABS-PA) alloy products. ABS offers superior processibility and appearance as well as low cost, along with a good balance of engineering properties.
Figure 1-7 Portable power tool housing
8
1 Polymeric Materials Advantages • Good impact resistance (toughness) and rigidity properties • Low creep • Good dimensional stability • High strength properties • Metal coatings have excellent adherence to ABS • Transformed by conventional thermoplastic methods • A light-weight plastic material Disadvantages and Limitations Figure 1-8 Faucet chrome plated shell
• ABS is resistant to acids (except concentrated oxidizing acids), alkalis, salts, essential oils, and a wide range of food and pharmaceutical products. It is, however, attacked by many solvents, including ketone and ester. • Low dielectric strength • Only low elongation available • Low continuous service temperature • While the mechanical property of the finished part is not sensitive to moisture, its presence during processing can cause part appearance problems. Maximum suitable moisture levels of 0.2% for injection molding and 0.03% for extrusion can be reached using a dehumidifying air dryer. Typical Applications • Refrigerators: Doors and food liners for the interior surface of the refrigerator. Medium impact extrusion and molding grades, including clear ABS, are used in crisper pans, breaker strips, shelves, shelf supports, evaporator parts trays, and kick plates.
Figure 1-9 Brief case external covers
• Small Appliance Housings and Power Tool Applications: These include hair dryers, curling irons, blenders, electric can openers, coffee makers, food processors, electric fans, vacuum cleaners, electric drills, leaf blowers, and lawnmower decks. • Automotive Applications: Instrument panels, armrests, interior trim panels, seat belt retainers, glove compartment doors, and lift gates. ABS plating grades are used in wheel covers, grilles, headlight, mirror housings, and decorative trim. • Drain: Waste, vent pipes, pipe fittings, and pool filter housings. • Telecommunications: Telephone housings, mobile phones, typewriter housings, and keyboard keys. • Business and Consumer Electronics: Videocassettes, televisions, audiovisual equipment, computer housings, floppy disks, printers, and copiers. • Household Items: Countertops, sinks, and tub surrounds, roof mounted air conditioning units. – Recreational: Motorcycle fairing, sailboats, airplanes, campers, hard-sided luggage, and picnic cooler liners.
Figure 1-10 Videocassette housing
• Other Applications: Briefcases, cosmetic cases, household packaging, toys, and photographic equipment.
9
1.2 Thermoplastic Polymers
1.2.4
Acetal (POM, Polyacetal)
General Properties of Acetal Homopolymers Specific gravity
1.42
Tensile modulus @ 73 °F (Mpsi)
400.00
Tensile strength @ yield (Kpsi)
10.0
Notch Izod impact @ 73 °F (ft-lb/in)
1.30
Thermal limits service temp. (°F)
230 (short) 195 (long)
Shrinkage (%)
1.9–2.3
Tm (°F)
350
Tg (°F)
–90
Process temp. (°F)
375–450
Mold temp. (°F)
140–200
Drying temp. (°F)
N/A or not required
Drying time (h)
N/A or not required
General Properties of Acetal Copolymers Specific gravity
1.42
Tensile modulus @ 73 °F (Mpsi)
360.00
Tensile strength @ yield (Kpsi)
8.5
Notch Izod impact @ 73 °F (ft-lb/in)
1.20
Thermal limits service temp. (°F)
200 (short) 175 (long)
Shrinkage (%)
2.0–2.5
Tm (°F)
330
Tg (°F)
–90
Process temp. (°F)
340–420
Mold temp. (°F)
125–185
Drying temp. (°F)
N/A or not required
Drying time (h)
N/A or not required
Acetal resins provide a well balanced set of properties including a hard selflubricated surface, excellent chemical resistance, strength, stiffness, and toughness over a broad temperature range. The acetal homopolymer was first introduced in 1960 as a semi-crystalline form of polymerized formaldehyde forming a linear chain of molecules of oxymethylene. In the homopolymer process, the formaldehyde is separated from the water and purified to CH2O gas, which is then polymerized to the polyoxymethylene molecule. In this case, the molecule is stabilized by a reaction with acetic anhydride to give acetate end groups. The acetate capped homopolymer is less resistant to attack by base, but it has a higher melting point and mechanical advantages in strength, stiffness, toughness, hardness, creep, and fatigue than the copolymer acetal.
10
1 Polymeric Materials In the acetal copolymer process, the formaldehyde is first converted to the cyclic structure of three formaldehyde molecules, trioxane. The trioxane is separated, purified and reacted with a comonomer (ethylene oxide) to prepare polyoxymethylene that has randomly distributed –CH2–CH2 groups in the chain. This resultant raw polymer is then treated with heat and base to degrade the ends of the molecules back to a –CH2–CH2 “block” point at each end. This leaves a molecule resistant to further degradation by basic environments. The end-capping of homopolymer and copolymer chains is necessary to prevent the irreversible depolymerization of the polymer backbone during melt processing by the thermal “unzipping” of the –H–O–CH2–O–CH2– end group to a formaldehyde monomer. The homopolymer grades exhibit the highest crystallinity, with good strength, stiffness, and impact resistance. The melting point is 350 °F. The high crystallinity also provides good chemical resistance, with little or no effect seen in the material after direct exposure to common hydrocarbons, aldehydes, ketones, alcohols, and fuels. The homopolymer is also resistant to aqueous solutions with a PH range from 4–10. The homopolymer is recommended for continuous service temperature in air and water up to 220 °F. The copolymer grades have random ethyleneoxy or n-butyleneoxy units scattered throughout the polymer backbone. These comonomer units slightly disrupt the crystallinity of the polymer in the solid state, leading to slightly lowered short term strength, stiffness, impact resistance, and a melting point of 330 °F. They have good solvent resistance, because the polymer chains are not capped with an ester group and aqueous solution PH resistance is extended over a range from 4–14. The copolymer is recommended for continuous service temperatures both in air and water up to 200 °F. Acetals are strong, stiff and tough over a broad temperature range. They have good surface lubricity and a low coefficient of friction against metals, ceramics, and other plastics. They are creep and fatigue resistant because of low cold flow characteristics. The balanced properties and good solvent resistance of acetal make the ideal candidate to replace materials such as metals, thermoset polymers, wood, and ceramics. Special technology has led to impact-modified homopolymer and copolymer grades, but increased impact resistance is offset by decreased strength and stiffness. Many grades also have the approval from the Food and Drug Administration for repeated food contact, National Sanitation Foundation and Canadian Standards Association for potable water applications and Underwriter’s Laboratories UL-94 HB ratings for flammability. Special grades are also available with US Department of Agriculture approval for direct contact with meat and poultry products and Dairy and Food Industries Supply Association approval for contact with dairy products. The following grades of acetal resins are commercially available: • UV stabilized and weatherable grades,
• Low wear and low coefficient of friction grades, • Toughened and impact modified grades, • Fiber glass reinforced grades,
• Filled mineral, glass bead, milled glass filled grades, and • High melt flow grades.
11
1.2 Thermoplastic Polymers The outstanding characteristics of this polymer include stiffness, which permits the design of parts with large areas and thin cross sections; high tensile strength and creep resistance under a wide range of temperatures and humidity conditions; high fatigue resistance and resilience for applications requiring springiness and toughness. Acetal has achieved importance in applications because of a good balance of properties. Two types of acetals are available. One is a homopolymer resin with higher mechanical properties, higher end use temperatures, and higher melt flow index, and the other is a copolymer resin with better processing characteristics and impact resistance. Advantages • High mechanical properties, tensile strength, rigidity, and toughness • Glossy molded surfaces • Low static and dynamic coefficients of friction • Retains electrical and mechanical properties up to 250 °F • Low gas and vapor permeability • Approved for applications used in contact with food • Excellent chemical resistance to common hydrocarbons, aldehydes, ketones, alcohols, and fuels Disadvantages and Limitations • Poor resistance to acids and bases • High mold shrinkages • Subject to UV degradation, if special acetal grades are not used • Flammable (UL-94 HB) • Excessive process melt temperatures over 450 °F can result in significant thermal degradation of the material, with the release of formaldehyde gases • Violent thermal degradation (explosion) if acetal melt is contaminated with PVC • Difficult to bond when the acetal surface is not treated Typical Applications • Industrial: Conveyor links and slats, cams, bearings, wear stops, hose connectors, valve bodies, pumps (housings, pistons, valves and impellers) and gears. • Automotive: – Fuel handling systems: Filler caps, level sensors, floats, pumps and reservoirs – Trims: Seat belt buckle housings, window cranks, shift lever handles, knobs, buttons, mounting clips, visor mounting brackets, levers, exterior door pulls, mirror housings, brackets, bumper strip end plugs, and antenna bases – Instrument panel components: Cluster gears, bearings, housings, cable connectors, slide plates, and panel locks – Under the hood components: Fans, fan blades, dashpot housings, and tubing connectors
Figure 1-11 Automotive gasoline tank level sensor unit (Courtesy: Du Pont)
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1 Polymeric Materials • Appliances: – Refrigerators: Shelving clips, brackets, bearings, and gears – Washers and dryers: Gears, bearings, wear strips, instrument housings, and hose connectors – Dishwashers: Rack rollers, spray nozzles, soap dispensers and filter supports
Figure 1-12 Food processor conveyor belt (Courtesy: Du Pont)
Figure 1-13 Textile injection molded components (Courtesy: Du Pont)
• Home Electronics: – Keyboards: Key caps, plungers, guides, and base plates – Telephones: Push buttons, gears, bearings, and springs – Modular components: Clips, peg boards, connectors, wear strips for drawers, latch springs, and clamps – Audio and video tape players and recorders: Tape hubs, guide rollers, cams, gears, bushings, and bearings • Plumbing: – Water meters: Housings, cams, gears, dials, and pressure plates – Faucets: Underbodies, cartridges, stems, packing nuts, and waterways – Water softeners: Pump housings, pistons, impellers, and valves – Filters: Bodies, plates, and screens – Pressure regulators: Bodies, stems, knobs, and pressure plates – Potable water distributors: Fittings, drain valves, stop valves, and metal pipe adapters • Consumer: – Personnel care: Mascara, perfume, and deodorant containers, combs, aerosol valves, soap dispensers, and cosmetic applicator handles – Small appliances: Motor gears, cams, bearings, pumps, glue applicators, housings, and springs – Toys: Shells, frames, gears, bearings, cams, springs, wheels, and connectors – Sporting goods: Ski bindings, gears, bearings, guides, wear plates, clamps, pump components, valves, and buckles • Hardware: Drapery and venetian blind guides, hangers, rollers, bearings, furniture casters, slide plates and locks, tool holders, bearings, gears, and housings
Figure 1-14 Gears appliance motor (Courtesy: Du Pont)
• Irrigation: Sprinkler nozzles, arms, gears, housings, waterways, pump housings, impellers, pistons, metering valve bodies, knobs, stems, and internal components • Agriculture: Shift levers and housings, hydraulic connectors, bearings, gears, and seed application disks
1.2.5
Polymethyl Metacrylate (Acrylic, PMMA)
Polymethyl metacrylate (acrylic) polymers have outstanding optical properties, weatherability, and a full range of transparent, translucent, and opaque colors. Acrylics are comprised of polymers and copolymers in which the major monomeric belong to two families of ester-acrylates and methacrylates. Hard, clear acrylic sheets are made from methyl methacrylate, molding and extrusion resins are made in a continuous solution from methyl methacrylate copolymerized with small percentages of other acrylates or methacrylates. Methyl methacrylate is produced by a dual step process in which acetone and hydrogen cyanide react to form acetone cyanohydrin. The compound is then
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1.2 Thermoplastic Polymers
General Properties of Generic Unfilled PMMA Specific gravity
1.17
Tensile modulus @ 73 °F (Mpsi)
0.38
Tensile strength @ yield (Kpsi)
7.50
Notch Izod impact @ 73 °F (ft-lb/in)
0.30–0.50
Thermal limits service temp. (°F)
190 (short) 150 (long)
Shrinkage (%)
0.3–0.6
Tg (°F)
230
Vicat point (°F)
184
Melt flow rate (g/10 min)
0.8–2.0
Process temp. (°F)
410–575
Mold temp. (°F)
140–190
Drying temp. (°F)
165
Drying time (h)
2–4
heated with methanol in the presence of concentrated sulfuric acid to yield the monomer. Acrylic monomers polymerize by free-radical processes initiated by peroxides in the polymerization process. A monomer initiator active at elevated temperature, this reaction is vigorous and liberates tremendous heat that must be dissipated. The formulations differ in molecular weight and in their principle properties (flow rate, heat resistance, and toughness). Special formulations are available that provide matte surfaces or that absorb or transmit ultraviolet light, and a full range of transparent, translucent and opaque color resins. High impact acrylic grades for injection molding and extrusion are available. These compounds are composed of an acrylic hard phase and an acrylic modifier as the soft phase. Acrylic polymers have outstanding optical properties and weatherability. Colorless acrylic is capable of transmitting white light up to 92%, with the remaining 8% being the reflection loss, and has haze values of only 1–2%. Acrylics have outstanding resistance to the effects of sunlight and long-term exposure to the elements. The low strain optic coefficient of acrylics, coupled with their ability to be molded with very low stress, makes an ideal material for video disks. Sheet extruded from acrylic base impact modified grade has excellent thermoforming characteristics and can be stiffened by applying glass reinforced polyester to the inside surface with a spray gun to produce bathroom whirlpool tubs. High flow grade has the best transparency, because it does not contain acrylonitrile, making it suitable for medical applications in which transparency is of prime importance. Acrylic plastics can be cleaned with solutions of inorganic acids, alkalis, and aliphatic hydrocarbons. However, chlorinated and aromatic hydrocarbons, esters, and ketones will attack the acrylic plastics. Advantages • Excellent optical clarity • Excellent surface hardness
14
1 Polymeric Materials • Excellent weatherability and resistance to sunlight • Rigid with good impact strength • Excellent dimensional stability and low mold shrinkage • Thermoforming increases bi-axial toughness Disadvantages and Limitations Figure 1-15 Acrylic – medical devices
• Poor solvent resistance; attacked especially by ketones, esters, chlorocarbons, aromatic hydrocarbons, and Freon® • Combustible, continuous service temperature limited to 160 °F • Flexible grades unavailable • Moisture produces dimensional variations of the molded articles Typical Applications • Automobile: Tail lights, parking light lenses, decorative emblems, medallions, and name plates
Figure 1-16 Acrylic – typical applications
• Household: Light fixtures, picture frames, and decorative articles • Transparent Items: Available in a rainbow of sparkling colors, ideal for packaging, jewelry, and signs • Electronics: Used on print circuit board coating applications
1.2.6
High Temperature Nylon (HTN)
General Properties of HTN – 30% GR @ 50% R.H. Specific gravity
1.44
Tensile modulus @ 73 °F (Mpsi)
1,500
Tensile strength @ yield (Kpsi)
32.0
Notch Izod impact @ 73 °F (ft-lb/in)
1.80
Thermal limits service temp. (°F)
440 (short) 315 (long)
Shrinkage (%)
0.2–0.6
Tg (°F)
257
Tm (°F)
570
HDT (°F) @264 psi
510
Process temp. (°F)
580–620
Mold temp. (°F)
260–300
Drying temp. (°F)
175
Drying time (h)
2–16
There is a cost and performance gap between the engineering thermoplastic resins such as polycarbonate, nylon 6/6, acetal, and the ultrahigh performance polymers such as PEI, PEEK, LCP, and a group of relatively new resins with the convenient generic name of high temperature nylons. These HTN resins are chemically related (but not identical). The following types of HTN resins are commercially available worldwide:
1.2 Thermoplastic Polymers • Nylon (4,6) • Polyphthalamide PPA (6T/6I/66) • Nylon (6,T/D,T) • Nylon (6/6T) • Nylon (6T/6I) • Nylon (66/6T) HTN, an aliphatic aromatic polyamide line, offers many grades, variously employing glass fibers, mineral fillers, flame retardants, and impact modifiers. HTN also provides an additional 50 °F or more of high temperature service as compared to standard nylons. Although molders running nylon 6 and 6/6 will not have to change molds or machines to run HTN, they will certainly come across some processing differences. Extremely close attention must be paid to drying. Drying conventional nylons requires a moisture content of no more than 0.2%. A sealed HTN bag comes predried, but with the recommendation to predry at 175 °F for 2–16 or more hours. As with all nylons, part dimensioning must take into account both shrinkage and ambient moisture absorption by the molded parts. The mold shrinkage rates of these semi-crystalline HTN polymers are similar to the conventional nylons. Shrinkage rates range from 0.18–0.22 in/in for the unreinforced grades to 0.02–0.06 in/in for the reinforced grades. Moisture absorption will reduce shrinkage. Hot runnerless molds can be used, but individual temperature control of drops is recommended. Molds run hot, hotter than for conventional nylons, which would require electric or oil heating. The HTNs are semi-crystalline resins. By increasing the melt temperature during processing, it raises the degree of crystallinity in the polymer, consequently giving a boost to post-mold dimensional stability and an improvement of the chemical resistance of the material. There is an increase in melt viscosity with the HTN, it does not run like water, as the standard easy flow nylons do, but the advantage is less mold flashing with lower temperature molds (180 °F). One of the characteristics of the HTN resins is the fast molding cycle. These materials set up (harden) very quickly in the mold cavity before the molded parts are ejected. This family of materials may carry the name nylon, but their high performance drastically exceeds the characteristics of the traditional nylon materials. The HTN (6,T/D,T) series of polyphthalamides has a melt temperature of 570 °F and provides excellent heat resistance for heat soldering owing to its partial aromatic nature. The FR grades are flame retardant resins that have achieved UL-94 V0 rating for a 0.0031 in wall thickness. Advantages • Lower moisture absorption than nylon 6 and nylon 6/6 • Good dimensional stability • Excellent mechanical properties • Low creep characteristics • Excellent chemical resistance • High temperature performance, HTN uses part polyester and part nylon, which provides 50 °F higher melt temperature than nylon 6/6
15
16
1 Polymeric Materials • High glass transition temperature (257 °F) • Good injection molding processibility Disadvantages and Limitations • Its main weakness is low elongation. • Low crystallization (needs 300 °F mold temperature). Figure 1-17 Distribution transformer, various components (Courtesy: Du Pont)
• Problems with predrying the resin. Impact resistance and finished part appearances are adversely affected by excessive moisture during processing. Maximum suitable moisture levels of 0.2% for injection molding; needs a drying time of 2–16 h (depending on the type of compound); a dehumidifying dryer is recommended. Typical Applications • Transformer tri-clamp • Windows lift motor housing • Automotive safety: air bag sensor housings, ABS (brake sensors), speed and temperature sensors • Solenoid coil bobbins
Figure 1-18 Insulator electrical motor (Courtesy: Du Pont)
• Connector lamp sockets Automotive engine and transmission bearings, thrust washers, timing gears, valve stems and retainers, seal rings, piston skirts, and lifter wear pads
1.2.7
Ionomer Polymers
General Properties of Generic Ionomer Polymers Specific gravity
0.94
Tensile modulus @ 73 °F (Mpsi)
14–67
Tensile strength @ yield (Kpsi)
3.2–3.8
Notch Izod impact @ 73 °F (ft-lb/in)
15.0 – no break
Thermal limits service temp. (°F)
–110 +120
Melt flow rate (g/10 min)
1.1–5.0
Tm (°F)
178–205
Vicat point (°F)
135–160
HDT (°F) @ 66 psi
160–185
Process temp. (°F)
400–500
Mold temp. (°F)
40–120
Drying temp. (°F)
160–180
Drying time (h)
2–4
Ionomers are thermoplastic resins that contain metal ions along with organic chain molecules. These ions are either sodium or zinc, serve as “reversible” cross linking networks, and result in high levels of resilience and impact resistance. Ionomers are based on ethylene copolymers and contain carboxylic acid groups.
17
1.2 Thermoplastic Polymers Ionomers are supplied either as unmodified resins or as composites. The unmodified ionomers are flexible polymers that can be melt-processed at low temperatures. The ionomers can be reinforced with glass fibers to increase the strength and stiffness or filled with high loading of minerals without sacrificing useful toughness. Other additives are also used to increase the heat deflection temperature properties. The most outstanding characteristics of both the unmodified and High Performance (HP) ionomers are their impact toughness and resistance to failure at low temperatures. In the case of a HP, for instance, the notched Izod impact is approx. 8 ft-lb/in at –110 °F; there are no clean breaks in room temperature Izod impact tests. Unmodified ionomers also have demonstrated outstanding performance over many years in uses involving repeated, severe impacts, notably golf ball and bowling pin covers. The degree of cut resistance shown in golf ball applications is outstanding. The environmental resistance of ionomers is also of significance in many end uses. Ionomers are insoluble at normal end use temperatures and therefore resist etching by solvents. These unmodified ionomers are used for see-through applications because of their transparency or low haze properties. The selection of ion types is based on the specific property required. Zinc ionomers absorb less water and have better impact strength than the sodium types, but are inferior in transparency and oil resistance. The properties combine very high toughness with comparatively low modulus. The tensile strength of the polymer exhibits a well defined yield point, followed by substantial cold draw; the stress increases during the cold draw, and consequently, the energy to break is very high. The stress strain characteristic combines features of a crystalline polymer and a cured elastomeric product. The low heat deflection temperature of unmodified ionomers requires end use testing for high elevated temperature service applications. Like other flexible polymers, the ionomer polymers creep when loaded over long time periods. Mechanical properties data of a typical HP ionomer show that outstanding impact resistance is combined with moderate stiffness and yield strength. The heat deflection temperature range of 160–185 °F is adequate for many high temperature end uses, but careful testing is needed before commercial adoption. Because of their glass content, moldings of HP ionomers lack the glossy surfaces of many unreinforced plastics. The significance of this appearance factor depends entirely on the transparency of the product in use. The density of unmodified ionomers ranges from 0.94–0.96 g/cm3, while the HP ionomers have a density of approx. 1.05 g/cm3.
Figure 1-19 Golf ball (Courtesy: Du Pont)
Advantages • High impact resistance • Outstanding cut resistance • Flexible and transparent material • Excellent low temperature properties • Low melt processing temperatures • Excellent UV resistance • Excellent solvent resistance at room temperature
Figure 1-20 Bowling pin (Courtesy: Du Pont)
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1 Polymeric Materials Disadvantages and Limitations • Low heat deflection temperatures (160–185 °F) for HP ionomers • Poor surface appearance of HP ionomers • Poor creep resistance under continuous load • Limited to low temperature applications • Poor impact resistance and finished part appearances are molding problems caused by moisture absorption during processing. The resin must be predried, using a dehumidifying hopper dryer. Figure 1-21 Ski boots (Courtesy: Du Pont)
Typical Applications • Packaging: Films • Sporting Goods: Golf balls, bowling pins, ski boot’s components, sport footwear, roller skates, skis, and bowling machine components • Automotive Components: Air dams, bumper guards, metal-ionomer (foamed) laminates for decorative fascia, large tonnage brackets for engine and transmission shipment between assembly plants • Industrial: Hand tools, machine components, steps for marine ladders, and buoy applications
1.2.8
Liquid Crystal Polymer (LCP)
General Properties of Generic LCP – 30% GR Polymers Specific gravity
1.62
Tensile modulus @ 73 °F (Mpsi)
2.25
Tensile strength @ yield (Kpsi)
23.0
Notch Izod impact @ 73 °F (ft-lb/in)
1.30
Thermal limits Service temp. (°F)
400–465
Shrinkage (%)
0.2–0.5
Tm (°F)
630
Tg (°F)
250–355
HDT (°F) @ 264 psi
600
Process temp. (°F)
660–680
Mold temp. (°F)
150–230
Drying temp. (°F)
250–300
Drying time (h)
1–4.0
LCPs are a family comprised of diverse polymers, which lack chemical homogeneity found in the high temperature nylons. Most commercial LCPs are copolyesters, copolyamides, or polyester-amides, although many other linkages are possible. LCP structures range from partially aliphatic to wholly aromatic polymers. The melting point characteristics, the end use temperature properties, the chemical and solvent resistance, flammability, processibility, and cost are different for each product compound. LCPs are processed in the liquid crystalline state. All thermoplastic LCPs show one-dimensional order, which results from the semi-rigid, essentially linear
19
1.2 Thermoplastic Polymers architecture of the molecules. They are found in either the solid or nematic states. Because melt viscosity increases by a factor of two to ten when the polymer passes from the nematic to the isotropic state, processing is extremely difficult as melt temperatures approach the clearing point. One other important point is that the melt point is a very low enthalpy transition, so there is little crystallization, allowing fast cycling and low mold shrinkage. The chemical structure common to all melt processed LCPs is that of pare hydroxy benzoic acid. There are three classes of LCPs: The first is a general purpose class, which exhibits exceptional ease of processing, dimensional stability, molded part repeatability, chemical resistance, flame resistance, strength, and stiffness. The second is a more temperature resistant variant, which is not quite as easy to process, but has good dimensional stability, good chemical resistance, excellent flame resistance, and very good strength and stiffness. The third, a lower temperature performance class, is less expensive and less easily processed, but has good dimensional stability, with good strength and stiffness, less chemical resistance, and moderate flame resistance. Advantages • Cycle repeatability, tight tolerances, high melt flow for thin wall parts, warpfree parts, low mold shrinkage, and fast cycles • Molded article dimensional changes are minimal when the item is exposed to high temperatures (vapor phase or infrared soldering), without annealing • Low, controllable coefficient of thermal expansion that can be matched to glass, ceramics, and metals • LCP has inherent resistance to burn and very low smoke generation • Excellent chemical resistance to all organics, acids, and bases • Exceptional strength, stiffness, and toughness Disadvantages and Limitations
Figure 1-22 Surface mounted connector housings (Courtesy: Du Pont)
• Weld lines are very weak, because inherent stiffness of the molecules prevents their diffusion across the melt front to strengthen the weld. • Unfilled or unmodified LCP resins are so easy to orient that the surface can be abraded. The resins must be handled with extreme care. • Differences in coefficient of thermal expansion caused by different degrees and directions of molecular orientation can cause warpage. • The extremely low die swell results in a tendency to produce surface jet marks when small gates are used.
Figure 1-23 Electrical surface mounted bobbins (Courtesy: Du Pont)
• Impact resistance problems are caused by excessive amounts of moisture during processing. Maximum moisture level of 0.01% for molding is recommended, using a high temperature dehumidifying hopper dryer. Typical Applications • Dual oven handles • Electrical and electronic components • Vapor phase and infrared solderable connectors, sockets, relay and capacitor housings, active and passive molded printed wiring board components, thin walled coil forms (bobbins), brackets
Figure 1-24 Medical needle-free syringe device (Courtesy: Du Pont)
20
1 Polymeric Materials • Precise dimensions, typically required for miniaturization, where the pin spacing is very small • Semiconductor components, in which ionic contaminants are not tolerable
1.2.9 Figure 1-25 Automotive speed sensor housing (Courtesy: Du Pont)
Polyamide (PA, Nylon)
General Properties of Generic Nylon 6 – 33% GR Resins @ 50% RH Specific gravity
1.30
Tensile modulus @ 73 °F (Mpsi)
0.8
Tensile strength @ yield (Kpsi)
13.0
Notch Izod impact @ 73 °F (ft-lb/in)
3.5
Thermal limits service temp. (°F)
300 (short) 195 (long)
Shrinkage (%)
0.2–0.6
Water absorption (%) @ 24h and 73 °F
1.1
Tm (°F)
410
HDT (°F) @ 264 psi
400
Process temp. (°F)
440–550
Mold temp. (°F)
140–200
Drying temp. (°F)
175
Drying time (h)
2–20
General Properties of Generic Nylon 6/6 – 33% GR Resins @ 50% RH Specific gravity
1.38
Tensile modulus @ 73 °F (Mpsi)
0.9
Tensile strength @ yield (Kpsi)
18.0
Notch Izod impact @ 73 °F (ft-lb/in)
2.5
Thermal limits service temp. (°F)
390 (short) 265 (long)
Shrinkage (%)
0.2–0.6
Water absorption (%) @ 24h and 73 °F
0.7
Tm (°F)
491
HDT (°F) @ 66 psi @ 264 psi
500 480
Process temp. (°F)
530–580
Mold temp. (°F)
80–200
Drying temp. (°F)
175
Drying time (h)
1–16
This polymer was commercially introduced in the 1930s by Du Pont as a result of the significant research work of W. H. Carothers. Polyamides are most commonly regarded as synonymous with nylon (Du Pont’s trade name), that is, synthetic polymers that contain an amide group –CONH– as a recurring part of the chain.
21
1.2 Thermoplastic Polymers
General Properties of Generic Nylon 6/12 – 33% GR Resins @ 50% RH Specific gravity
1.32
Tensile modulus @ 73 °F (Mpsi)
0.9
Tensile strength @ yield (Kpsi)
20
Notch Izod impact @ 73 °F (ft-lb/in)
2.5
Thermal limits service temp. (°F)
305 (short) 200 (long)
Shrinkage (%)
0.2–0.6
Water absorption (%) @ 24h and 73 °F
0.16
Tm (°F)
414
HDT (°F) @ 264 psi
410
Process temp. (°F)
450–550
Mold temp. (°F)
80–200
Drying temp. (°F)
175
Drying time (h)
1–4
Nylons are made from (a) diamines and dibasic acids, (b) w-amino acids, or caprolactam. Nylon gradess are identified by a/b, which correspond to the number of C-atoms in the monomer’s diamine (a) and the number of w-amino acids (b). The most common types of resins are nylon 6, nylon 6/6, and nylon 6/12. They are made from hexamethylene diamine and the 12-carbon acid, dodecanedioic acid, or HOOC(CH2)10COOH. The molecular weights of nylons range from 11,000 to 34,000. The melting points range from 410 to 491 °F. Nylon 6/6 and nylon 6 are the most important commercial products. Other nylons are 6/9, 6/10, 6/12, 11, and 12. The more C-atoms, that is, the lower the concentration of amide groups, the lower the melting point. Nylons are modified by use of monomer mixtures leading to copolymers. These are normally less crystalline, more flexible, and more soluble than the homopolymers. Additives are used in nylons to improve thermal and photolytic stability, facilitate processing, increase flammability resistance, enhance hydrolytic resistance, and increase lubricity. Modification is an important asset. Fiber and mineral reinforcement are widely used. Blending with elastomeric modifiers has yielded nylons with improved toughness. Toughened nylon alloys or blends in the dry as-molded condition have a notched Izod impact strength of 2.5–4.5 ft-lb/in versus 1.0 ft-lb/in for unmodified nylon 6/6 or nylon 6. The supertough nylon 6/6 exhibits Izod impact values higher than 15 ft-lb/in (50% R.H.) and ductile behavior and high Izod strengths independent of test variables. Nylon is resistant to oils, greases, solvents, and bases. Nylon also has fatigue, repeated impact toughness, and abrasion resistance, plus a low coefficient of friction. Nylon also has high tensile strength properties, creep resistance, and retains most of its mechanical and electrical properties over a wide temperature range. Its limitations are high moisture pickup, with resulting changes in dimensional and mechanical properties. UL temperature’s rating for continuous service ranges from 195–265 °F.
22
1 Polymeric Materials The following types of nylon compounds are available: Lubricated, nucleated, heat stabilized, ultraviolet stabilized, hydrolytically stabilized, flame retarded, glass reinforced, Kevlar® fiber reinforced, mineral reinforced, toughened, melt flow modified, electrically conductive, and several nylon alloys. Advantages • Excellent toughness and impact resistance • Excellent abrasion resistance • Low coefficient of friction Figure 1-26 Office chair structure components (Courtesy: Du Pont)
• High tensile strength properties, creep resistance, and retention of mechanical and electrical properties over a wide temperature range. • Excellent resistance to oils, greases, solvents, and bases • Processed by all thermoplastic methods Disadvantages and Limitations • High moisture pick-up causes dimensional changes of the molded part, based on the type of polymer. • Requires UV stabilization.
Figure 1-27 Automotive engine valve cover (Courtesy: Du Pont)
• Electrical and mechanical properties are greatly influenced by polymer type, moisture content, and chemical composition. • Low impact resistance and poor finished part appearances are caused by excessive amounts of moisture during processing. Maximum suitable moisture level of 0.2% for injection molding and 0.03% for extrusion is recommended using a dehumidifying hopper dryer. Typical Applications
Figure 1-28 Automotive speed sensor (Courtesy: Du Pont)
• Transportation: This segment represents the largest single market for nylons. Applications for unreinforced materials include electrical connectors, wire jackets, emission canisters, and light duty gears for windshield wipers and speedometers. Toughened nylons are used as stone shields and trim clips. Glass reinforced nylons are used for engine fans, radiator headers, brake and power steering fluid reservoirs, valve covers, sensors, and fuel injectors. Mineral reinforced resins are used for mirror housings and tire hub covers. A combination of glass and minerals serve in exterior parts, such as fender extensions. • Electrical and Electronics: Flame retardant nylons, including those complying with Underwriter’s Laboratories UL-94 V0 requirements, play a major role in the electrical market (plugs, connectors, bobbins, wiring devices, terminal blocks, antenna mounting devices). • Appliances: Nylons are used not only for electrical components, but also for mechanical parts, housings, and other applications in power tools, washers, and various small appliances. • Telecommunication Applications: Relays, fittings, and connections.
Figure 1-29 Automotive transmission speed sensor (Courtesy: Du Pont)
• Industrial: Hammer handles, mowing machine parts, unlubricated gears, bearings, anti-friction parts, and a variety of applications requiring snap fits or spring load assembling.
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1.2 Thermoplastic Polymers • Food and Textile Processing Equipment: Pumps, valves, meters, agricultural and printing devices, business and vending machines. • Consumer Products: Toughened nylon applications such as ski boots, ice and roller skate supports, racket sports equipment, bicycle wheels, kitchen utensils, toys and photographic equipment. • Nylon Films: They are widely used for packaging meats and cheeses and for cook-in bags and pouches. Nylon films are also used as an enclosure for the thermoset fabrication of small airplane wings. • Wire and Cable Jacketing: They are used mostly as a protective layer over primary insulation. • Nylon Tubing: They are used to convey brake fluids, refrigerants, or as lining for flexible cables.
Figure 1-30 Marine radiator end caps (Courtesy: Du Pont)
• Extrusion: Sheets, rods and machining stock shapes. • Nylon 6/12 Mono-filaments: They find extensive applications in brush bristles, fishing lines, ropes, and sewing threads. They are also used for cloth stiffening, rugs, women’s nylons, and filter screens. • Nylon 11 or 12 is used to powder coat metals by means of electrostatic-spray or fluidized-bed for food handling and the pharmaceutical industries. • Encapsulated nylon for spline shafts, automotive engine timing gears.
1.2.10
Polyetherimide (PEI)
General Properties of Generic PEI – 30% GR Resins Specific gravity
1.50
Tensile modulus @ 73 °F (Mpsi)
1.30
Tensile strength @ yield (Kpsi)
24.50
Notch Izod impact @ 73 °F (ft-lb/in)
1.90
Thermal limits service temp. (°F)
392 (short) 356 (long)
Shrinkage (%)
0.2–0.7
Vicat point (°F)
426
Tg (°F)
420
HDT (°F) @ 66 psi @ 264 psi
412–415 408–420
Process temp. (°F)
640–800
Mold temp. (°F)
150–350
Drying temp. (°F)
250–300
Drying time (h)
4.0–6.0
PEIs are amorphous, high performance thermoplastic polymers that have been in use since 1982. Their chemical structure consists of repeating aromatic imide and ether units. PEIs are characterized by high strength and rigidity at room and elevated temperatures, long-term high heat resistance, highly stable dimensional and electrical properties, and broad chemical resistance. PEI resins can be meltprocessed using typical thermoplastic processing and thermoforming equipment for high volume production. Unmodified PEI is amber in color and transparent
Figure 1-31 Electrical solenoid coils encapsulated (Courtesy: Du Pont)
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1 Polymeric Materials and exhibits inherent flame resistance and low smoke generation without the use of halogenated or other types of flame retarding additives. The amorphous structure of PEIs contributes to their excellent dimensional stability, low shrinkage, and highly isotropic mechanical properties. Their high glass transition temperature (Tg) of 420 °F and high performance strength and modulus characteristics at elevated temperatures are provided by the very rigid imide groups in their chemical structure. The high Tg allows PEI to be used intermittently at 392 °F and permits short-term excursions to even higher temperatures. Higher strength and stiffness at elevated temperatures are achieved with glass or carbon fiber reinforcement. PEI unreinforced resins are rated as having 338 to 356 °F continuous end use temperatures by Underwriter’s Laboratories, Inc. and are listed as UL-94 V0, down to 0.010 in thickness. PEI resins are available either in unmodified form or reinforced with 10, 20, 30, and 40% glass fiber. Also available are grades with carbon reinforcement for high strength and static dissipation, and a series of products with internal lubricants. Other grades and blends are offered for blow molding, structural foam, and extrusion processes. PEI has been formulated to meet specific market needs, such as electromagnetic interference shielding capability and Federal Aviation Administration (FAA) heat release requirements. PEI also can be spun into fiber for use in advanced composite systems. Advantages • Excellent chemical resistance to most hydrocarbons, non-aromatic alcohols, and fully halogenated solvents • Good chemical resistance to mineral acids • Good hydrolytic stability to boiling water and steam autoclaving for sterilization (low water absorption) • Good ultraviolet radiation resistance • Good resistance to gamma radiation • Excellent electrical properties, suitable for use as a dielectric material with highly sensitive electronic components Disadvantages and Limitations • Short-term reaction when used with mild bases. Partially halogenated solvents, such as methylene chloride can be good solvents for PEIs. • The resin must be dried to less than 0.05% moisture content. • Molding process temperatures of 640–800 °F are required. • High mold temperatures are required (oil or electrical heat elements). • Price of the resin is high. Typical Applications • Automotive: Temperature and fuel sensors, air handling devices, and metallized reflectors Figure 1-32 Computer dual 50 pins connector
• Electrical and Electronics: Connectors, printed circuit boards and integrated circuit chip carriers, burn-in sockets, flexible circuitry, bobbins, and explosion proof boxes
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1.2 Thermoplastic Polymers • Packaging: Steam resistant, thermal stability, microwave resistant and compliance to Food and Drug Administration requirements • Aircraft: PEIs are used as interior materials both in sheet and molded forms. The resin is available in a variety of formulations primarily to improve chemical resistance and impact properties to meet both FAA regulations for heat release and airframe manufacturer standards for smoke and toxicity. FAA compliant blow molding grades are also available. • Industrial Applications: Corrosion resistant fluid and air handling components, mechanical couplers, and threaded fasteners. • Medical: Surgical staplers and other tool housings, handles, non-implant devices, and trays.
1.2.11
Figure 1-33 Spider motor armature insulator
Polyarylate (PAR)
General Properties of Generic PAR Polymers Specific gravity
1.22
Flexural modulus E (Mpsi)
0.3–0.35
σY (Kpsi)
10.0
Izod impact @ 73 °F (ft-lb/in)
4.0–4.75
Thermal limits service temp. (°F)
210
Shrinkage (%)
0.9
Vicat point (°F)
392
Tg (°F)
379
HDT (°F) @ 264 psi
300–345
Process temp. (°F)
675–735
Mold temp. (°F)
250–300
Drying temp. (°F)
250–285
Drying time (h)
3.0–8.0
Polyarylates (PAR) are a family of tough polyesters with heat, creep, and warpage resistance, ultraviolet stability, flammability resistance (without additives), and good electrical properties. PARs are aromatic polyesters derived from aromatic dicarboxylic acids and diphenols. Although both amorphous and crystalline resins have been developed, the amorphous resins have been the preferred polymer for most of the applications. The mechanical properties of amorphous PARs are similar to polycarbonates (rigid, strong, and tough). Heat deflection temperatures of 0.25 in thick amorphous PARs tested at 264 psi range from 300–345 °F. Good retention of notched Izod impact strength, after exposures of up to 300 °F for 336 hours. In addition, PARs are able to sustain loading stresses of 1,100,000 psi at 210 °F with less than 1% total strain deformation. Amorphous PARs have also shown excellent low temperature resistance and are useful as an adhesive down to –240 °F. They can withstand thermal cycling at temperatures ranging between –240 to +212 °F. Liquid crystalline PARs have a very high heat deflection temperature of 671 °F.
26
1 Polymeric Materials Amorphous PAR materials offer outstanding weatherability properties. Because excellent ultraviolet resistance is inherent in these resins, there is no need for additional ultraviolet absorbers. Under the influence of ultraviolet radiation, the polymer surface rapidly rearranges to form an o-hydroxybenzophenone structure, which provides stability against ultraviolet radiation. Mechanical as well as optical properties are retained after weathering exposure. Amorphous PARs offer good performance in all areas, including low flame spread, high oxygen index, low smoke density and relatively low amounts of toxic gases. PAR products of combustion will not contain halogen, nitrogen, sulfur, or phosphorous components commonly found in flame retardant compounds. Amorphous PARs show unusual flexural recovery or elastic rebound, the combination of this elastic recovery and thermal resistance offer opportunities for hot comb and high temperature lens applications. Unmodified, amorphous PAR materials show similar chemical resistance as other amorphous resins, such as PC. Alloying with other resins can improve the resistance to chemicals such as gasoline and ethanol. The crystalline versions of PAR show good resistance to most chemical environments. Amorphous polyarylates injection molding melt temperatures range from 675–750 °F, depending on the formulation of the alloy. The most important condition for successful PAR processing is the dryness of the resin, with no more than 0.02% moisture level being acceptable. Resins are unstable in the presence of moisture at processing temperatures. Unsatisfactory part properties result from processing wet resins. Suitable decorating procedures for PAR include screen printing, hot stamping, decal transferring, and painting. No surface pretreatment is needed. Advantages • Good heat and cold temperature resistance, impact strength, and dimensional stability • Excellent high gloss surface used for metallization applications • Excellent long-term weather resistance • Excellent gasoline and oil resistance • Excellent flammability resistance, colorability, and transparency • Excellent electrical shielding ability • Excellent gamma sterilizability Disadvantages and Limitations • The resin must be dried to moisture levels below 0.02%. • Heavy wall thickness drastically reduces the impact strength property of the molded part. • Polymer melt degradation occurs at high melt temperatures and on extended melt residence time in the processing equipment. • Slow melt flow characteristics. • Solvent resistance is only fair. Figure 1-34 Gas knob components
• Properties become unstable when submerged in hot water
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1.2 Thermoplastic Polymers Typical Applications • Automotive: Headlight housings and brake light reflectors, exterior trim parts, and alloy PAR body panels • Safety Equipment: Fire helmets, helmet face shields, mining light covers, and traffic signal lenses • Electrical and Electronic: Electrical connectors, relay housings, coil bobbins, switches, and fuse covers
Figure 1-35 Gasoline product components
• Exterior Construction and Lighting: Glazing, skylights, and transparent panels
1.2.12
Polyetherether Ketone (PEEK)
General Properties of Generic PEEK Polymers Specific gravity
1.3–1.6
Flexural modulus E (Mpsi)
0.6–3.2
σY (Kpsi)
13.0–39.0
Izod impact @ 73 °F (ft-lb/in)
1.2–1.6
Thermal limits service temp. (°F)
482
Shrinkage (%)
1.0–1.8
Tm (°F)
645
Tg (°F)
289
Thermal degradation
805
Process temp. (°F)
660–790
Mold temp. (°F)
250–430
Drying temp. (°F)
300–350
Drying time (h)
3.0
Polyetherether ketone (PEEK) is a subgroup of ketone polymer materials that is similar to polyarylether ketone (PEAK) and polyetherketone ketone (PEKK). Because of their semi-crystalline nature, PEEK resins demonstrate an excellent balance of physical properties, including strength at elevated temperature, chemical resistance, and hydrolytic and thermal stability. They offer the highest level of thermal resistance together with thermoplastic processing capability. Polyetherether ketone resins are produced as unreinforced resins, glass fiber reinforced resins, and carbon fiber reinforced resins. PEEK materials retain their mechanical properties at very high end use temperatures. The retention of flexural modulus and tensile strength properties is excellent, especially for the fiber reinforced resins. Another characteristic of PEEK-based resins is their outstanding thermal properties, the UL-94 rating for PEEK has been observed to be V0, without the addition of any flame retardant additives. PEEK resins exhibit heat deflection temperatures that make them perform well under both low and high stress conditions; the UL continuous use temperature is higher than 480 °F. The electrical property values are good for PEEK resins.
Figure 1-36 Air quick disconnect couplings
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1 Polymeric Materials Chemical resistance at elevated temperatures in various aggressive environments shows that reinforced PAEK is a chemically resistant material. The retention of tensile properties for unreinforced PAEK resins is greater than 75%. Glass reinforced PAEK resins exhibit a much higher retention rate of tensile properties but show some loss of tensile strength properties. This problem may be caused by the effects of the fiber glass coupling agent’s bonding strength with the matrix. Unreinforced PAEK resins chemically react to acids and bases. Figure 1-37 Various molded products
Reciprocating screw injection molding machines adapted to the high melt temperature and rheology of PAEK and PEEK are used to process these resins. Care must be exercised when working at these temperatures, because polymer melt degradation may occur beyond 805 °F. Its processibility is due to its semicrystalline characteristics after reaching its melting point of 645 °F. Advantages • Excellent flexural modulus and tensile strength retention • Outstanding thermal properties • Low flammability and smoke generation
Figure 1-38 Electronic wafer baskets
• UL-94 V0 rating, without flame retardant additives • UL continuous use temperature is 480 °F • Good electrical properties Disadvantages and Limitations • High resin cost • Limited type of commercial resins available • Unreinforced resins may react to acids and bases • Injection molding machines must be adapted to the high melt temperature and rheology of the polymer
Figure 1-39 Aircraft bracket support
• Polymer degradation occurs beyond the melt temperature of 805 °F Typical Applications • Aircraft and Aerospace: Engine components, cabin interior material, air ducts, and exterior parts • Electrical and Electronics: Wire and cable • Chemical Processing: Pump components and oil seals • Industrial Equipment: Journal bearing surfaces
1.2.13
Polycarbonate (PC)
Polycarbonate was introduced in 1958. PC is an amorphous engineering thermoplastic material with exceptionally high impact strength, transparency, high temperature resistance, and dimensional stability. Melt flow rate is one of the most important properties of polycarbonate. PC is produced by reacting Bisphenol A and carbonyl chloride in an interfacial process. This reaction is carried out under basic conditions in the presence of an aqueous and an organic phase. Molecular weight is controlled by a phenolic
29
1.2 Thermoplastic Polymers
General Properties of generic PC – 30% GR Polymers Specific gravity
1.40
Tensile modulus @ 73 °F (Mpsi)
1.25
Tensile strength @ yield (Kpsi)
19.00
Notch Izod impact @ 73 °F (ft-lb/in)
1.7–3.0
Thermal limits service temp. (°F)
220 265
Shrinkage (%)
0.15–0.6
Tm (°F)
267–495
Tg (°F)
293–300
Vicat point (°F)
305–310
Process temp. (°F)
430–620
Mold temp. (°F)
175–250
Drying temp. (°F)
250–260
Drying time (h)
2.0–4.0
Figure 1-40 Automotive headlamp assembly
chain stopper. Trifunctional monomers are added for increased melt strength for extrusion and blow molding applications. Polycarbonate does not have a true melting point as other crystalline polymers. It does, however, have a high glass transition temperature of 300 °F. Polycarbonate is characterized by an exceptionally high notched Izod impact strength of 12–17 ft-lb/in on a 0.125 in wall thickness. The impact strength, measured by a falling dart or a Dynatup® (dynamic impact testing equipment), is retained to temperatures as low as minus 60 °F. The heat deflection temperature of polycarbonate, at 264 psi, is 260–270 °F, this HDT can be increased to close to 320 °F when the matrix is compounded with a high heat polyphthalate carbonate. PC has low and predictable mold shrinkage characteristics. It also has good creep resistance and low moisture absorption properties. The molded surface of PC has a high gloss finishing. This material can be compounded to produce resins for sterilizability, flame retardance, and stain resistance.
Figure 1-41 PC/ABS alloy – volvo bumper
Polycarbonate has high corona resistance and insulation resistance properties, as well as a dielectric constant that is independent of temperature. Polycarbonate must be dried before processing at a drying temperature of 250–260 °F for 3–4 hours, using a dehumidifying hopper dryer. This drying is essential to reduce the moisture content to 0.02% to prevent hydrolysis during molding.
Figure 1-42 Drinking mugs and pitchers
Polycarbonate requires a high melt temperature, from 430–620 °F. The mold temperature should range between 175 and 250 °F to control surface finish. The components should be molded stress-free, using a high injection molding pressure, low injection speeds to fill the cavities, and long curing time. A great number of grades have been developed for special purposes by compounding fiber glass and mineral reinforcements with various additives. These ingredients enhance the thermal stability, ultraviolet stability, tensile strength, stiffness, and flame retardants. In addition, the color, shielding ability, Food and Drug Administration compliance, gamma sterilizability, low temperature impact, solvent resistance, wear resistance, and foameability are obtained in these resins.
Figure 1-43 Binocular housing
30
1 Polymeric Materials Polycarbonate is a versatile compounding material and is used as a basic matrix component in the production of several alloy resins. For example, polycarbonate and polyester (polyethylene terephthalate and polybutylene terephthalate), polycarbonate and ABS (acrylonitrile-butadiene-styrene), and polycarbonate and SAM (styrene-maleic anhydride) are used in alloys and blends. Advantages • High impact strength • Low flammability Figure 1-44 Air-conditioner appliance grille
• Electrical shielding ability • Gamma sterilizability • Wear resistance • High heat deflection temperatures • Good dimensional stability • Good electrical properties • Processable by all thermoplastic methods Disadvantages and Limitations • Soluble in selected chlorinated hydrocarbons • Exhibits crazing in acetone and is attacked by bases
Figure 1-45 Coil bobbins
• Its surface is relatively soft and therefore can be scratched • Ultraviolet resistance of non-ultraviolet-stabilized polycarbonate is poor. The molded part tends to yellow after long-term exposure to ultraviolet light • Heavy wall thickness drastically reduces the impact strength property of the molded part • Snap-off undercuts for assembly are not recommended • Poor stress cracking resistance • Subject to melt degradation at high processing temperatures and extended residence time, especially for the flame retardant resins • Solvent resistance is only fair Typical Applications
Figure 1-46 Motorcycle helmet shell
• Electronic and Business Equipment: Business machine housings, computer parts and peripherals, connectors, terminal blocks, and telecommunication components • Appliances: Food processors, electrical kitchen components, power tool housings, refrigerator drawers, and vacuum cleaner components • Transportation: Tail and head lights, signal light lenses and housings, runway markers, blow molded spoilers, instrument panels, and seat backs • Safety and Sports: Sports helmets, recreational vehicle hoods, windshields, head lights, boat propellers, and sun glass lenses • Food Service: Microwave cookware, serving trays, mugs, pitchers, water bottles, baby bottles, and institutional storage containers
31
1.2 Thermoplastic Polymers • Medical: Tubing connectors, dialysis components and devices, blood oxygenators, filter housings, lenses, gamma sterilization appliances, and surgical staplers • Sheet Products: Institutional and mass transit glazing signs, aircraft interior panels, and greenhouse windows • Industrial: Mailboxes, material handling containers, and highway delineations
1.2.14
Modified Polyphenylene Oxide (PPO)
General Properties of Generic PPO – 30% GR Polymers Specific gravity
1.25
Tensile modulus @ 73 °F (Mpsi)
1.10
Tensile strength @ yield (Kpsi)
14.50
Notch Izod impact @ 73 °F (ft-lb/in)
1.7–3.0
Thermal limits service temp. (°F)
200–240
Shrinkage (%)
0.20–0.60
HDT (°F) @ 66 psi @ 264 psi
280–320 275–317
Tg (°F)
302
Vicat point (°F)
230–298
Process temp. (°F)
520–600
Mold temp. (°F)
160–220
Drying temp. (°F)
200–250
Drying time (h)
2.0–4.0
Polyphenylene oxide materials are rigid, amorphous, tough, and dimensionally stable at a wide range of high temperatures. The chemical composition of the homopolymer is a poly(2,6-dimethyl-1,4-phenylene ether) or a poly[oxy-(2-6dimethyl-1,4-phenylene)]. Modified PPO resins are the result of compounding PPO with polystyrene (PS) plus various additives. Unmodified PPO resins are high temperature polymers with glass transition temperatures (Tg) of approximately 302 °F. They are very difficult to process, even at melt temperatures of 520–600 °F. The high softening point and melt viscosity of PPO are in contrast to the low softening point and melt viscosity of PS. The unique thermodynamic compatibility of PPO and PS, particularly high impact PS, or HIPS, permits these two polymers to be blended in all proportions. The blends exhibit lower viscosity and improve the processibility compared to pure PPO, as well as a single Tg (between HIPS at 212 °F and PPO at 302 °F, at all ratios). This permits tailoring of the viscosity and toughness properties of a blend to specific requirements. With the addition of rubber impact-modified HIPS provides the PPO blend with an Izod impact value higher than the blends of PPO and crystalline PS. Most blends contain 20–80% PPO, with 40–50% being the most common mixture. The HIPS impact modifier and various additives represent the compounding ingredients of the resin. To improve the chemical resistance and thermal property of the compound, PPO has been alloyed with polyamide (nylon 6/6). To increase flexural modulus and reduce mold shrinkage, glass and mineral filled modified PPO resins are available.
Figure 1-47 Laundry dryer housing
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1 Polymeric Materials The PPO modified blend formulations have the following characteristics: high tensile strength, high heat resistance, and low moisture absorption properties. Heat deflection temperatures range from 180–310 °F. Small creep rates are detected at room temperature. There is a low coefficient of thermal expansion. Notched Izod impact values range from 1.3–8 ft-lb/in. The dimensional stability of modified PPO at elevated temperatures and stress can be maintained in a number of environments, such as strong alkalies and bases, detergents, and hot water. Filled and flame retardant (FR) grades that have Underwriter’s Laboratories (UL) recognition are available. The high melt strength of modified PPO makes possible injection molding, structural foam molding, extrusion, blow molding, and thermoforming processes. Modified PPO blends make excellent insulators, because they have low loss and dissipation factors over broad temperature and frequency ranges. These materials also have inherently low dielectric constants and high dielectric strengths. High humidity conditions have little effect on these properties. Secondary operations can be performed on parts made from modified PPO resins. However, to obtain good adhesion, application of a urethane, alkyd, or acrylic base primer is recommended before painting. For electroplating, a preactivator step is necessary before catalyst deposition on the surface. Sputtering, vacuum metallizing, and hot stamping can be used for decorative purposes. Assembly techniques include the use of solvents, ultrasonic welding, vibrational welding, hot melt adhesives, thread cutting, and thread forming screws and metal inserts encapsulation. Advantages Figure 1-48 Electrical connectors
• High mechanical strength • High heat and moisture resistance • Small creep rates at room temperature • Low coefficient of thermal expansion • Good notched Izod impact • Excellent electrical properties • Good dimensional stability Disadvantages and Limitations
Figure 1-49 Office cabinet housing
• Most hydrocarbon and aromatic base substances such as esters, oils, grease, or alcohols cause stress cracks or soften PPO blends • Ultraviolet (UV) applications are not recommended • They are very difficult to process, even at high melt temperatures Typical Applications • Blow Molded Products: These resins are used for office furniture, automotive steering column covers, and appliance doors and ducts • Flame Retardant Products: They include business machine housings, decks, and enclosures
Figure 1-50 Automotive body panel
• Automotive: They include instrument panels, wheel covers, fuse blocks, trim, and windshield wiper blades
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1.2 Thermoplastic Polymers • Electrical Applications: They include fiberoptic connectors, ceiling boxes, control housings, and load centers • Industrial: Pumps, impellers, shower heads, chemical process equipment, and filter bodies • Metal Plated: Modified PPO performs well in electromagnetic interference and radio frequency interference (EMI/RFI) shielded enclosures
1.2.15
Polybutylene Terephthalate (PBT)
General Properties of Generic PBT – 30% GR Polymers Specific gravity
1.53
Tensile modulus @ 73 °F (Mpsi)
1.35
Tensile strength @ yield (Kpsi)
17.50
Notch Izod impact @ 73 °F (ft-lb/in)
0.90
Thermal limits service temp. (°F)
200–250
Shrinkage (%)
0.30–2.30
HDT (°F) @ 66 psi @ 264 psi
421–510 385–437
Tg (°F)
113–140
Tm (°F)
437
Process temp. (°F)
470–530
Mold temp. (°F)
110–200
Drying temp. (°F)
250–300
Drying time (h)
2.5–5.5
Polybutylene terephthalate is a high performance, semi-crystalline resin, one of the toughest and most versatile of all engineering thermoplastics. Strong and lightweight, this polyester is characterized by low moisture absorption, excellent electrical properties, broad chemical resistance, lubricity, durability, mechanical strength, and heat resistance. These properties are stable over a broad range of temperature and humidity conditions. The resin is commonly supplied with fiber glass and/or mineral reinforcements. Polybutylene terephthalate is produced by the transesterification of dimethyl terephthalate with butanediol. This reaction takes place by a catalyzed melt poly-condensation, resulting in a repetition of the molecular unit. PBT can be alloyed with 10–30% nylon to facilitate glass reinforcement. Moisture absorption can be reduced, processibility and mechanical properties boosted simultaneously, when PBT is alloyed with 15–25% low density polyethylene (LDPE). The addition of graft containing butadiene polymers, as well as urethanes or copolyester elastomers, reduces notch sensitivity. An enhanced gloss surface also can be achieved when PBT is blended with PET.
Figure 1-51 Automotive motor fan supports (Courtesy: Du Pont)
Advantages • Excellent resistance to water up to 122 °F temperature. It also resists most aqueous salt solutions, weak acids and bases, most organic solvents (aliphatic hydrocarbons, glycol, ethers, high molecular weight esters, and ketones), gasoline, and cleaning solutions at room temperature. This material is not attacked by most oils and greases at temperatures up to 140 °F.
Figure 1-52 Electric iron handle (Courtesy: Du Pont)
34
1 Polymeric Materials • Excellent electrical properties, including high dielectric strength and insulation resistance. It has superior arc resistance, consistent dielectric constant, and a low dissipation factor over a range of temperatures and humidity. The dielectric constant, dissipation factor is nearly independent of frequency and temperature. Underwriter’s Laboratories (UL) continuous use temperature indices for the electrical and mechanical strengths range from 248–265 °F. Disadvantages and Limitations
Figure 1-53 Motorcycle side panels (Courtesy: Du Pont)
• Sensitive to alkaline oxidizing acids, hot water, strong bases, aromatic solutions, and ketones above ambient temperatures. Solvents include trifluoroacetic acid, phenol with chlorinated aliphatic hydrocarbons, and hexafluoroisoprophenol. • Unmodified PBT is notch sensitive. High levels of glass filler make the material brittle. • Part warpage caused by different cooling rates resulting from part geometry or tool design lead to differential shrinkage. Typical Applications • Building and Construction: Housewares, lawn and garden • Automotive: Grilles, body panels, fenders, wheel covers, components for door handles, mirrors, and windows. Under the hood distributor caps, rotors, ignition components, head lamp systems, windshield wiper assemblies, water pumps, and brake systems
Figure 1-54 Automotive distributor cap (Courtesy: Du Pont)
• Electrical and Electronics: Switches, relays, motor housings, tube sockets, photoelectric cell receptacles, ballast housings, fuse cases, key caps for computer keyboards, chip carriers, and connectors • Telecommunications: Network connector devices, junction boxes, and fiberoptic buffer tubing • Material Handling: Conveyor chain links, gear wheels, bearings, monorail hangers, dunnage, collapsible part racks, foamed pallet containers, tote bins • Industrial Applications: Tubing, fittings, conduits, roof anchors, plumbing, pump impellers, sprinkler bodies and levers, pipe caps, pressure vessel housings, cable protection, and valve components • Consumer Uses: Food processor blades, vacuum cleaner parts, fans, gears, furniture, iron handles, toaster side panels, hair dryer housings, coffee makers
1.2.16
Polyethylene Terephthalate (PET)
Polyethylene terephthalate (PET) is a versatile polymer widely used in synthetic fibers, industrial and packaging films, injection molding, blow molding, and thermoforming. High strength products are possible because of the ability of the material to be oriented and crystallized.
Figure 1-55 Electric motor end frame (Courtesy: Du Pont)
Unoriented PET melt crystallizes or hardens slowly during its production. The maximum crystallization rate is obtained when the melt temperature reaches 482–490 °F. In its amorphous state, PET tends to be brittle at room temperature; then it softens above its glass transition temperature of approx. 158 °F. Molten PET is subject to hydrolytic degradation and so must be rigorously dried before melt processing. A maximum moisture content of 0.02% is recommended.
35
1.2 Thermoplastic Polymers
General Properties of Generic PET – 30% GR Polymers Specific gravity
1.67
Tensile modulus @ 73 °F (Mpsi)
1.50
Tensile strength @ yield (Kpsi)
22.00
Notch Izod impact @ 73 °F (ft-lb/in)
1.60
Thermal limits service temp. (°F)
392
Shrinkage (%)
0.20–0.90
HDT (°F) @ 66 psi @ 264 psi
392–490 435
Tg (°F)
158
Tm (°F)
482–490
Process temp. (°F)
510–565
Mold temp. (°F)
150–250
Drying temp. (°F)
250–275
Drying time (h)
2.0–4.0
Figure 1-56 Encapsulated stator motor (Courtesy: Du Pont)
PET is prepared by a reaction of either purified terephthalic acid (PTA) or dimethyl terephthalate (DMT) with ethylene glycol (EG). The high viscosity melt is converted into amorphous clear pellets by rapid quenching and cutting in water. Thermoplastic polyesters are long chain, unbranched molecules that are produced by the condensation reaction between a dibasic organic acid or ester and a glycol. PET has the stiffest polymer chain possible for a thermoplastic polyester with an outstanding combination of strength, stiffness, and melt flow properties. These special properties of PET are the basis for its broad application in areas such as electrical and electronics components, fibers, films, and drink bottles. However, the chain stiffness also retards the rate of crystallization from the melt that makes PET, by itself, unsatisfactory as a resin for injection molding. The PET injection molding grades include a proprietary crystallization system that provides the rapid crystallization needed for good moldability at normal molding temperatures.
Figure 1-57 Wheelchair structure (Courtesy: Du Pont)
Reinforced grades continue to be introduced as improvements in crystallization rates, impact, warpage and other physical properties are made. Most of the PET compounded resins are glass fiber/mineral reinforced. Glass fiber and mica are used for low warpage applications. Reinforced grade resins are available with fiber glass contents ranging from 15–55%. Several flame retardant resins meeting UL-94 V0 and V5; high impact and foamed grades are also produced. Specialty copolymers based on polyester and polycarbonate blends of PET with PBT have also been introduced. Advantages • Excellent resistance to water up to 122 °F temperature; also resists most aqueous salt solutions, weak acids and bases, gasoline, and cleaning solutions. PET is not attacked by most oils and greases • Excellent electrical properties, including high dielectric strength and insulation resistance, consistent dielectric constant, low dissipation factor. Underwriter’s Laboratories (UL) continuous use temperature index for electrical, mechanical strengths ranges from 302–392 °F
Figure 1-58 Beverage bottles (Courtesy: Du Pont)
36
1 Polymeric Materials Disadvantages and Limitations • Sensitive to alkaline oxidizing acids, hot water, strong bases above 122 °F temperature • PET requires drying of the resin from 2–4 hours at 275 °F to reach a 0.02% of moisture before processing • Part warpage caused by different cooling rates, which are a result of part geometry or tool design, leads to differential shrinkage Typical Applications Figure 1-59 Electrical coil bobbin (Courtesy: Du Pont)
• Automotive: Body panels, spoilers, door handles, distributor caps, rotors, ignition components, head lamps, and windshield wiper • Electrical and Electronic: Switches, relays, motor housings, tube sockets, ballast housings, fuse cases, chip carriers, and connectors • Consumer Uses: Vacuum cleaner parts, fans, gears, furniture, iron skirts, hair dryer housings, and coffee makers
1.2.17 Figure 1-60 Transformer spool and housing (Courtesy: Du Pont)
Polyethylene (PE)
General Properties of Generic Unfilled HDPE and LDPE Polymers
Specific gravity
HDPE
LDPE
0.94
0.91
Tensile modulus @ 73 °F (Mpsi)
0.2
0.05
Tensile strength @ yield (Kpsi)
3.75
2.25
Notch Izod impact @ 73 °F (ft-lb/in)
No break
No break
Thermal limits service temp. (°F)
158–176
140–167
Shrinkage (%)
1.1–1.4
1.1–1.4
Vicat point (°F)
255
–
Tg (°F)
–150
–150
Tm (°F)
257–275
212–230
Process temp. (°F)
400–535
360–530
Mold temp. (°F)
50–140
50–140
Drying temp. (°F)
150
150
Drying time (h)
3.0
3.0
The experimental development and testing of polyethylene polymers in the 1930s for use as a high frequency insulation for radar cables during World War II gave impetus to its commercial production. Polyethylene is available in a range of flexibilities, depending on the production process. High density polyethylene (HDPE) is the most rigid of the three basic types of PE resins (HDPE, low density polyethylene (LDPE), and linear low density polyethylene (LLDPE)). HDPE can be formed by a wide variety of thermoplastic processing methods and is particularly useful where moisture resistance and low cost are required. Polyethylene is limited by low end use temperature characteristics. There are three basic manufacturing processes for making HDPE. The slurry particle reactor process (the most widely used method), the gas phase process, and the new metallocene catalyst technology. This last process also may be used
37
1.2 Thermoplastic Polymers with standard catalysts to combine the advantages offered by both polyolefin polymerization catalysts. A new class of catalysts for polyolefins based on nickel and palladium reportedly can produce a very broad range of molecular weights and branching. Ability to incorporate a wide variety of polar and nonpolar comonomers allows the production of EVA and EMA copolymers in low pressure processes. Combinations of reactors also are used to make HDPE. The tandem reactors produce what are called bimodal molecular weight HDPE. The slurry process and gas phase process can also be used to make HDPE. Unlike LDPE, LLDPE lacks a long chain branching. Another difference is that the ethylene is copolymerized with butene, octane or hexene comonomers in the reactor. LLDPE has a narrower molecular weight distribution than LDPE. A final distinction is that LLDPE exits the reactor in a powder form and the granules are compounded with additives in an extruder and pelletized. Blow molding uses the largest amount of HDPE. About 35% is used to make blow molded products. Extruded products consume about 30%, and injection molding accounts for about 20%. High molecular weight (HMW) and HDPE resins have high strength; they are used in packaging films, sheets, pipes, and large blow and rotation molding items. Low density polyethylene (LDPE) is the second largest PE capacity in the US. Extrusion is the dominant process used with LDPE resins. Extruded products, principally films, account for 75% of LDPE sales. LDPE remains the dominant PE resin for extrusion coating and for food packaging films. LDPE is also used for injection molding, blow molding, and rotational molding. High molecular weight (HMW) LDPE film grade resins produce high gloss, high clarity film that exhibit good toughness and heat sealability. High pressure, high temperature polymerization reactors, both tubular and autoclaves, are used to make LDPE. The molecular structure of LDPE is characterized by long side branches that give the resins their combination of flexibility, clarity, and processability. 1.2.17.1
Ethylene Vinyl Acetate (EVA)
General Properties of Generic EVA Polymers Specific gravity
0.93
Flexural modulus E (Kpsi)
2.5–14.0
σY (Kpsi)
0.50–2.50
Izod impact @ 73 °F (ft-lb/in)
No break
Thermal limits service temp. (°F)
–
Shrinkage (%)
–
HDT (°F) @ 264 psi
–
Vicat point(°F)
140–200
Tm (°F)
189–223
Process temp. (°F)
285–435
Mold temp. (°F)
60–105
Drying temp. (°F)
120–14-
Drying time (h)
8.0
Figure 1-61 Tennis shoes (Courtesy: Du Pont)
Figure 1-62 Automotive carpet sound backing (Courtesy: Du Pont)
38
1 Polymeric Materials These copolymers are very flexible, tough materials with good adhesion properties. The vinyl acetate content ranges from 1–50% and the grades with more than 20% VA contents are called high EVAs. All thermoplastic end use fabrication processes can be used with EVA products. The resins also are used to make hot melt adhesives and can be compounded with other polymers. 1.2.17.2
Figure 1-63 School bus toy
Ethylene N-Butyl Acrylate (ENBA)
These copolymers are very flexible, tough, and have good tear strength, low temperature toughness, and optical properties. The butyl acrylate content of these resins ranges from 5–20%. ENBA copolymers are used in flexible packaging and extrusion coating applications. These polymers require higher heat processing temperatures, and they have low temperature properties and heat seal properties not provided by EVA copolymers. Optical properties of ENBA copolymers are comparable to those of EVA copolymers. 1.2.17.3
Ethylene Methyl Acrylate (EMA)
These copolymer resins have properties very similar to those of ENBA copolymers, but are available in FDA approved grades. As a result, the EMA copolymer resins are used in flexible food packaging where high clarity, low temperature toughness, and good tear strength are required. Figure 1-64 Blow molded crane and sandbox toy
1.2.17.4
Ethylene Ethyl Acrylate (EEA)
These copolymer resins are very tough and flexible polyolefins, which have excellent low temperature properties. The ethyl acrylate content of these resins ranges from 15–30%. The compounds with the higher percentage have properties similar to rubber materials. EEA copolymers, which are made in modified high pressure PE reactors, can be injection molded, extruded, and blow molded. The resins are used to make hot melt adhesives and are compounded with other polymers. 1.2.17.5
Figure 1-65 Resin bulk shipping container
These resins have an average molecular weight of 3–6 million. They offer excellent abrasion resistance, a low coefficient of friction, low temperature impact strength and good chemical resistance. However, these resins are difficult to process by conventional processing techniques. Compression molding generally is used to make UHMWPE parts or they are machined from rods, bars, or plates. 1.2.17.6
Figure 1-66 Kitchen ware container
Ultrahigh Molecular Weight Polyethylene (UHMWPE)
Metallocene Polyethylene (MPE)
These are made using standard catalyst technology. They claim to offer better strength, improved heat sealing characteristics, better moisture and oxygen barrier characteristics, high clarity, and greater toughness. Also, the high metallocene catalyst activity is said to virtually eliminate catalyst residues. The MPE resins are more expensive and more difficult to process than LDPE and LLDPE resins. Advantages • Low resin cost • Good impact resistance at temperatures from 104–194 °F • Good properties at low temperatures
39
1.2 Thermoplastic Polymers • Moisture and oxygen resistance • Good chemical resistance • Food grades are available • Readily processed by all thermoplastic methods Disadvantages and Limitations • High coefficient of thermal expansion
Figure 1-67 Low voltage electrical cables
• Poor UV and weathering resistance • Subject to stress cracking • Difficult to bond • Flammable Typical Applications • Packaging: Packaging films, rigid and semi-rigid packaging products • Transportation: Automotive fuel tanks • Medical: Hygiene products, medical application trays, and containers • Consumer: Toys, blow molded bottles, bottle caps, household goods, kitchen utensils • Appliances: Portable containers, outdoor furniture, and irrigation • Industrial: Pipes, connectors, buckets, containers, processing equipment, and hardware items for construction • Electrical: Wire and cable insulations
1.2.18
Polytetrafluoroethylene (PTFE)
General Properties of Generic PTFE Polymers Specific gravity
2.13–2.20
Flexural modulus E (Kpsi)
58–108
σY (Kpsi)
3.50–4.50
Coefficient of friction (73 °F)
0.02
Thermal limits service temp. (°F)
500.0
Water absorption (%)
< 0.01
Tm (°F)
648
Tg (°F)
257–266
HDT at 264 psi (°F)
132.0
Process temp. (°F)
690–710
Dielectric constant
2.10
Dielectric strength (V/mil)
500–600
Dissipation factor
< 0.0003
Figure 1-68 Car windshield fluid reservoir
40
1 Polymeric Materials Polytetrafluoroethylene (PTFE) was the first fluorocarbon resin invented by Roy J. Plunkett and introduced by E. I. Du Pont in the late 1940s. The properties of PTFE are unique and versatile. The fluorocarbon resin is created from chloroform by a series of reactions. PTFE is composed of long, straight chains of fluorinated carbons. It is the chemistry of PTFE that provides the unique characteristics of the polymer. The straight backbone of carbon atoms symmetrically surrounded by fluorine atoms provides the resin with its unique chemical, electrical, and thermal properties. Other fluoropolymer resins include fluorinated perfluoroethylene-propylene copolymer (FEP), perfluoro alkoxy alkane (PFA), ethylenetetrafluoroethylene (ETFE), polyvinylidene fluoride (PVDF), chlorotrifluoroethylene (CTFE), ethylene chlorotrifluoroethylene (ECTFE), polyvinyl fluoride (PVF), and other less important polymers. The maximum end use temperature for PTFE in continuous service is 500 °F. When exposed to flame, PTFE will burn, but it does not continue to burn when the flame is removed, because it has an exceptionally high limiting oxygen index and will not support combustion in air. Like most fluoropolymers, PTFE has outstanding electrical insulation properties. Its dielectric constant and loss factor are very low and uniform across a wide temperature and frequency range. PTFE is probably best known for its low coefficient of friction, lower than most other materials. It does not adhere to anything. PTFE is flexible, strong and tough at temperatures as low as –320 °F. It is an opaque white or bluish-white color, but it can be formed into very thin and transparent film. Its tensile strength ranges from 3,500–4,500 psi and its flexural strength is 2,000 psi. The fluorocarbon polymers are available in granular, fine powder, and water base dispersion forms (8 μ in). Granular resins are used for molding and ram extrusion. Fine powders are paste-extruded into thin sections. Dispersions are used for metal coatings and to impregnate porous structures such as fabrics. The molding techniques used for granular PTFE are similar to those for ceramics. The resin starts its transformation at ambient conditions, at pressures between 2,000 and 5,000 psi. The self supporting gel is then sintered at temperatures ranging from 690–710 °F under a controlled temperature cycle. To make tapes or sheets of PTFE (up to 0.250 in thick), a cylinder is molded and veneered. Sintering always follows compression of powder, whether the process is used to mold PTFE into sheets or billets through simple compression molding. To form multiple, simply shaped items, it is recommended to use automatic molding, or isostatic molding equipment. A flexible membrane and hydraulic pressure are used to make complicated shapes. The molecular weight of PTFE is 10 million or higher and it is about 90% crystalline before molding. It will withstand continuous exposure to a temperature near absolute zero (–525 °F) without reaction. The polymer has an initial melting point of 648 °F and although it does not char, it does begin to depolymerize at about 1,142 °F. Polytetrafluoroethylene is also highly resistant to blending with fillers and reinforcers. However, one or more fillers can be added to PTFE in some circumstances to prevent creep or cold flow from occurring when a load is applied to the soft material. Fillers are particularly desirable when PTFE is used for parts in a dynamic operation in which a high rate of wear may occur. Bonding between the PTFE and the filler particles is not possible. The filler particles
1.2 Thermoplastic Polymers are just suspended and depend on the relative movement of PTFE particles to improve the flexural modulus, creep, and wear, while decreasing the physical properties of PTFE. The fillers include fiber glass, carbon, graphite, bronze, and molybdenum disulfide. The PVDF resin can be processed in a typical thermoplastic extruder. To extrude thin wall tubing from fine powder PTFE material, the fine powder should be mixed with a volatile organic lubricant, such as naphtha or mineral spirits, to lubricate the fine powder. The lubricated fine powder is then cold-formed into a cylindrical billet, loaded into an extruder barrel, and driven by hydraulic or pneumatic ram pressure through the die. This process produces a heated continuous extrudate when a reciprocating ram slowly moves the resin through a heated die tubing. As it leaves the die, it passes through a multi-zone oven that removes the solvent and sinters the resin. Only highly corrosion resistant alloys should be used in contact with the melt during processing polytetrafluoroethylene. There are two general classes of polymers based on their process capabilities, the fluoropolymers that are able to use traditional melt processing technologies and the fluoropolymers that need special types of processing techniques. Polytetrafluoroethylene has a high melt viscosity property and the polymer never becomes fluid. At temperatures above 620 °F it becomes a self supporting gel. Because of this unusual melt characteristic, traditional thermoplastic processing equipment cannot be used. The fluoropolymer families can also be classified not only by their processing requirements, but by their chemical composition and properties. The characteristics of each fluoropolymer family are described below. 1.2.18.1
Fluorinated Perfluoroethylene Propylene (FEP)
A copolymer of hexafluoropropylene and tetrafluoroethylene is similar to PTFE in its chemical inertness, dielectric characteristics, coefficient of friction, and resistance to high heat. Its maximum temperature in continuous use is 400 °F. With a lower abrasion resistance than PTFE, it can be processed by most thermoplastic techniques and is available in pelletized grades for extrusion and molding. 1.2.18.2
Perfluoro Alkoxy Alkane (PFA)
It is produced when an alkoxy side chain is added onto a base of tetrafluoroethylene. It is similar to PTFE in thermal and chemical resistance, low coefficient of friction, and abrasion resistance. It has the same temperature range of PTFE, up to 500 °F. It can be extruded or injection molded, but to avoid stresses, PFA should be processed at high temperatures (700 °F) at slow processing rates. 1.2.18.3
Ethylenetetrafluoroethylene (ETFE)
It is a 1 : 1 alternating copolymer of ethylene and tetrafluoroethylene. It is resistant to chemicals, exhibiting only a slight swelling when exposed to some chlorinated solvents. Its service temperature ranges from –32 to 300 °F. It has excellent resistance to impact, cut through, abrasion, weather, and radiation. It also has a low dielectric constant and uniform electrical properties. The resin is processed by extrusion and injection molding, as dry nano particles, is used in fluidized bed, rotation molding, and electrostatic coating applications.
41
42
1 Polymeric Materials 1.2.18.4
Polyvinylidene Fluoride (PVDF)
This resin is one of the most rigid and abrasion resistant of the melt processible fluoropolymers. It has good chemical resistance, particularly to permeation by halogens (bromine). It can be attacked by a number of chemicals, such as hot sulfuric acid and hot amines. Some coating grades are solubilized by acetone and ethyl acetate. It has a higher dielectric constant than does PTFE, but a more limited service temperature range. Polyvinylidene fluoride resin is produced by emulsion or suspension polymerization of vinylidene fluoride. It can be extruded and injection molded on typical PVC machines. It is available as dry powder, pellets, and as a solvent base dispersion for coatings. 1.2.18.5
Chlorotrifluoroethylene (CTFE)
This resin is a melt processible fluoropolymer that substitutes every fourth fluorine atom on the PTFE chain with chlorine. This fluoropolymer can be used at cryogenic temperatures as low as –350 °F. It retains resilience after exposure to most chemicals, although it is swollen (but not attacked) by chlorinated solvents. It can be molded and extruded, but can be degraded by thermal and mechanical means. The electrical dissipation factor and dielectric constant are higher than PTFE. CTFE has excellent resistance to permeation by chemicals and can be made fully transparent, which lends to its use in packaging applications. 1.2.18.6
Ethylene Chlorotrifluoroethylene (ECTFE)
This resin is produced by copolymerizing chlorotrifluoroethylene and ethylene. Because of its 1 : 1 alternating copolymer, ECTFE has greater strength, wear and creep resistance than PTFE. It exhibits excellent chemical resistance to acids, bases, and solvents. It is attacked by hot amines and swells slightly in polar organic solvents. It matches PVDF in rigidity and abrasion resistance and surpasses it in impact strength and chemical resistance. Ethylene chlorotrifluoroethylene is the easiest to process, whether by melt extrusion, injection, or compression molding, or by dry powder coating and rotational molding. Advantages • Highly inert, no substance has been found that will dissolve PTFE • Nonflammable • Excellent resistance to nuclear radiation, ultraviolet rays, and ozone • Excellent chemical resistance, PTFE is unaffected by virtually all chemicals, acids, bases, and solvents • Low creep characteristics • Excellent electrical properties • Good mechanical strength at ambient temperature • Excellent permeability • Excellent oxidative stability • Higher temperature capability (500 °F) • Anti-stick characteristics • Low coefficient of friction Figure 1-69 High performance seals (Courtesy: Du Pont)
• Low mold shrinkage • Low water absorption
43
1.2 Thermoplastic Polymers Disadvantages and Limitations • Poor adhesive characteristics • Low mechanical strength at high temperatures • Comparatively high resin cost • Toxic by-products upon thermal decomposition • Not processable by common thermoplastic methods • Requires corrosion resistant steel for processing equipment
Figure 1-70 Submarine ball valves (Courtesy: Du Pont)
Typical Applications • Aerospace Industry: Low weight and stress crack resistance of PTFE, FEP, and ETFE are used for hose and tubing for hydraulic, fuel, oil, pneumatic, and oxygen systems. Dielectric strength, low dissipation factor, and low dielectric constant are used for printed circuit board laminates in military defence and commercial flight communications equipment. Resistance to severe chemicals, low coefficient of friction, and compressibility is used for sealing applications in turbine engines, alternators, and rotary actuators.
Figure 1-71 Automotive hoses for fuel and air conditioning (Courtesy: Du Pont)
• Automotive: Power steering and transmission seals and rings. Mechanical control cable and fuel hose linings, head gasket coatings. Shaft, compressor, and shock absorber seals. ETFE is extruded into wire harness conduit to protect wire assemblies from high engine temperatures and abrasion. It is also used in shielding applications to serve as a barrier against heat in underthe-hood applications. • Petrochemicals: Lining pipes, valves, pumps, tanks, tubing, fittings, column packing, and processing equipment.
Figure 1-72 Stadium roof covering membrane (Courtesy: Du Pont)
• Medical: Vascular grafts, cardiovascular patches, surgical membranes, soft tissue patches, sutures, ligaments, catheters, and piping systems for the laboratories. • Semiconductor Manufacturing: PFA and PVDF are used for piping, pumps, and valves in clean room fluid handling systems. Filter cartridges with PTFE or PVDF membrane elements are used for filters, which are supported by other components that are injection molded from PFA or PVDF. Wafer carriers, processing cassettes, wet bench equipment, rinse tanks, counter tops, sinks, and 55 gallon drum liners. PFA is used for packaging and shipping clean room processing chemicals, storage, and transportation of waste chemicals. • Electronic and Electrical: Code approved plenum cable, aircraft and fire alarm equipment, cables and printed circuit board substrates. • Other Applications: Nonstick cookware, coating and impregnation of valve and pump packing, coating on glass cloth provides outstanding weathering and ultraviolet radiation resistance. PTFE coated glass fabric is used as building roof covering material. Fluoropolymers are used as a breathable waterproof in protective clothing, filtration screening, and mist separators.
Figure 1-73 Internal liner valve, corrosion resistant (Courtesy: Du Pont)
44
1 Polymeric Materials
1.2.19
Polyphenylene Sulfide (PPS)
General Properties of Generic PPS – 30% GR Resins Specific gravity
1.38
Tensile modulus @ 73 °F (Mpsi)
1.70
Tensile strength @ yield (Kpsi)
22.00
Notch Izod impact @ 73 °F (ft-lb/in)
1.10
Thermal limits service temp. (°F)
450 (short) 390 (long)
Shrinkage (%)
0.6–3.5
Vicat point (°F)
530
Tm (°F)
540
HDT (°F) @ 66 psi @ 264 psi
534 507
Process temp. (°F)
600–715
Mold temp. (°F)
275–320
Drying temp. (°F)
300
Drying time (h)
3.0–6.0
Polyphenylene sulfide is an engineering thermoplastic material with an excellent combination of properties: thermal stability and unusual insolubility, chemical resistance and inherent flame resistance. It is produced commercially by the reaction of 1,4-dichlorobenzene with a suitable sulfur source, such as sodium sulfide. PPS is a semi-crystalline, aromatic polymer composed structurally of a series of alternating pare-substituted phenylene rings and divalent sulfide moieties. Polyphenylene sulfide possesses good thermal stability in which isothermal weight losses as a function of time were measured at several temperatures. These results indicate good resistance to thermal degradation up to 700 °F. Polyphenylene sulfide possesses excellent solvent resistance, being almost totally insoluble in organic solvents below 390 °F. PPS is affected only by high temperature exposure to a few organic solvents, strong mineral acids, and strong oxidizing environments. Oxidizing agents, such as peracetic acid and aqueous sodium hypochlorite, oxidize the sulfide moiety to sulfoxide and/or sulfone groups. Because of their chemical structure and ability to char when exposed to an external flame, PPS is inherently flame resistant. It possesses a high oxygen index and a low radiant flame spread index and it is classified as UL-94 V0 and UL-94 V5. The auto-ignition temperature is 1,000 °F. Glass fiber reinforcement produces injection and compression molding compounds that exhibit high tensile strength, good flexural strength, high heat deflection temperature, low elongation, and very low impact strength. A variety of pigments and mineral fillers can be added to produce several injection molding compounds, with mechanical properties ranging between the unfilled grades and the 50% glass filled compounds.
Figure 1-74 Automotive water pump impeller
Both filled and unfilled PPS grades exhibit the inherent flame resistance and excellent chemical resistance characteristics of the base resin. Results of longterm heat aging of moldings are consistent with the good thermal stability of the polymer. PPS/glass fiber and PPS/mineral fiber compounds show good retention
45
1.2 Thermoplastic Polymers of tensile properties under long-term temperature and load exposure. Because of the characteristics of PPS, aging at higher temperatures gives an even more impressive retention of properties owing to a “case hardening” surface effect caused by curing of surfaces exposed to high temperature air. Polyphenylene sulfide and its compounds possess good overall electrical (insulating) properties. The glass filled compound has a low dielectric constant and dissipation factors are retained over a broad frequency range. In addition, the dissipation factor remains low at temperatures up to 390 °F. Insulating properties are obtained by measuring the volume resistivity and the insulation resistance. These properties are also retained after exposure to high humidity environments. Arc resistance of formulations containing only glass reinforcement is not impressive but can be increased dramatically by proper choice of mineral fillers. The combination of good electrical properties and high temperature resistance has led to UL approval of PPS compounds for use at temperatures (390–450 °F) The addition of a small amount of carbon black provides an adequate ultraviolet protection to the compound.
Figure 1-75 Automotive exhaust sensor
Advantages • Capable of extended usage at 450 °F • Good radiation, solvent, and chemical resistance • Excellent dimensional stability and low water absorption • Non-burning Disadvantages and Limitations
Figure 1-76 Automotive air brake valve
• Difficult to process (high melt temperature) • Comparatively high resin cost • Fillers required to achieve good impact strength • Attacked by chlorinated hydrocarbons Typical Applications • Electrical and Electronic: Sockets, coil forms, bolt yokes, motor brush holders, connectors, integrated circuit, capacitor encapsulations, switches, electronic watch bases, and relay components • Mechanical and Chemical: Pump housings, impeller diffusers, pump veins, end plates, valve components, oil field hardware, heat shields, boiler sensors, and flow meters • Appliance: Housings, handles, internal components, microwave oven components, computer disc drives, and heat insulators • Automotive: Emission control system, censoring devices, fuel, ignition and braking systems, light sockets, cooling system, air conditioning units, and generator and alternator components
Figure 1-77 Computer pin connectors
46
1 Polymeric Materials
1.2.20
Polypropylene (PP)
General Properties of Generic Unfilled PP Homopolymer Specific gravity
0.90
Tensile modulus @ 73 °F (Mpsi)
0.17
Tensile strength @ yield (Kpsi)
4.00
Notch Izod impact @ 73 °F (ft-lb/in)
0.5–18.0
Thermal limits service temp. (°F)
212
Shrinkage (%)
0.5–2.0
Vicat point (°F)
320
Tm (°F)
329–338
HDT (°F) @ 264 psi
120–140
Process temp. (°F)
390–525
Mold temp. (°F)
85–175
Drying temp. (°F)
175
Drying time (h)
2.0–3.0
Polypropylene was introduced in the late 1950s and is the fastest growing commodity thermoplastic in the world. It is a versatile polymer used in applications from fibers, films, appliances, to automobile bumpers. PP continues to displace other materials, such as fiber glass, mineral reinforced thermoplastics and metals, in a variety of applications. Figure 1-78 Variety of injection molded products
Polypropylene is manufactured by polymerizing propylene monomer with a titanium based catalyst, a second co-catalyst (triethylaluminum) is added to initiate the polymerization reaction and hydrogen is used in the reactor to control polymer molecular weight. This reaction is produced using a slurry or gas phase type of process. There are three PP structures: isotactic, syndiotactic, and atactic. The principal structure of PP is isotactic semi-crystalline in a helical form. This structure has good mechanical properties, such as stiffness and tensile strength. These properties can be further increased with nucleating agents or with fillers, such as talc, calcium carbonate, or fiber glass.
Figure 1-79 Snap-top closure
Syndiotactic PP is produced by the monomer units inserted alternately head-totail. This structure is more flexible than the isotactic form but has better impact resistance and clarity. Atactic PP (hard wax amorphous monomer) is a by-product of the manufacturing process. This product is used in roofing tars and adhesives for the shoe industry. All forms of PP are susceptible to oxidation caused by the presence of a tertiary hydrogen. Polypropylene is stabilized against thermal degradation by the addition of primary and secondary antioxidants. Neutralizing agents are also added to stabilize the low levels of chloride ash generated during manufacturing. Other special additives are used, such as antistatic agents, slip agents, and UV stabilizers.
Figure 1-80 Compact disk jewel boxes
Polypropylene is sold commercially as homopolymers, random copolymers, or impact resistance copolymers. Physical properties range from high strength, stiffness, to a flexible polymer with lower strength but greater toughness.
47
1.2 Thermoplastic Polymers The homopolymer has the highest melting point and stiffness with a wide range of melt flow properties. The copolymers incorporate small amounts of ethylene that lower the crystallinity, producing improved impact resistance properties, more flexibility, but a lower melting point. Impact resistant copolymers are copolymerized in a reactor by adding ethylene. The copolymer acts as a plasticizer and is evenly dispersed throughout the homopolymer matrix to form a heterophasic polymer. This copolymer has very high impact resistance even at low temperatures. High impact resistance copolymers are produced by compounding the pre-blend of copolymer, additives, and ethylene-propylene or EPDM rubber. Advantages • Lighter or low density polymer (0.90 g/cm3) • High melting point (329–338 °F) • End use temperatures of 212 °F • Good chemical resistance to hydrocarbons, alcohols, and non-oxidizing reagents • Good fatigue resistance (integral life hinge closures) • Processed by all thermoplastic methods: injection molding, compression molding, blow molding, extrusion, cast films, and thermoforming
Figure 1-81 Automobile injection molded dash panel
Disadvantages and Limitations • Degraded by UV • Flammable, but flame retardant grades are available • Attacked by chlorinated solvents and aromatic solutions • Difficult to bond • Several metals accelerate oxidative degrading Typical Applications • Flexible packaging films • Biaxially oriented packaging films
Figure 1-82 Hot water dispenser bottles
• Stretched and oriented monofilament, tapes for textiles, carpeting, insulated medical fabrics and woven carpet backing • Automotive interiors, bumpers, spoilers, air vent systems, under the hood components, internal wheel guards, and bellows • Hygiene products, household goods and medical application trays, strainers, and containers • Consumer products, such as closures, over caps, trigger sprayers, rigid and semi-rigid packaging, video cassette cases, toys, and electrical hardware • Appliance housings and components, outdoor furniture, and luggage • Injection blow molded stretch bottles with excellent stiffness, impact resistance, and clarity
Figure 1-83 Electric rice cooker
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1 Polymeric Materials
1.2.21
Polystyrene (PS)
General Properties of General Purpose PS Polymers Specific gravity
Figure 1-84 Watch packaging
1.05
Tensile modulus @ 73 °F (Mpsi)
0.45
Tensile strength @ yield (Kpsi)
6.0
Notch Izod impact @ 73 °F (ft-lb/in)
0.25–0.60
Thermal limits service temp. (°F)
158 (short) 122 (long)
Shrinkage (%)
0.05–0.80
Vicat point (°F)
200–227
Tm (°F)
212
HDT (°F) @ 264 psi
190
Process temp. (°F)
390–480
Mold temp. (°F)
50–175
Drying temp. (°F)
160–200
Drying time (h)
2.0–3.0
Polystyrene (PS) has been known for well over 100 years, but its molecular nature was not clarified until about 1920, when the work of Staudinger described the material’s molecular structure. Polystyrene has been commercially produced since the late 1930s. PS is one of the most popular commodity amorphous thermoplastic resins; it has a broad range of balanced properties and an attractive price. Polystyrene is divided into semi-crystalline (general purpose) polystyrene (GPPS), rubber modified medium and high impact polystyrene (MIPS and HIPS), and expandable polystyrene (EPS). The raw materials for polystyrene are ethylene and benzene which react in a process to form ethylbenzene, which is further processed into styrene monomer; other feed stocks are acrylonitrile and butadiene rubber. A polymerization process using a thermal or catalyzed reaction of styrene monomer is used to produce an amorphous polymer. Other materials are added to the process such as rubbers, plasticizers, release agents, and stabilizers to give the polymers the desired characteristics. The formulation may also include colorants, flame retardants, UV stabilizers, or impact modifiers. GPPS is typically selected for its clarity, rigidity, and suitability for many applications. HIPS and MIPS are used where more flexibility or impact resistance is required; HIPS and MIPS contain butadiene rubber as the copolymerization agent to increase toughness, it also makes it opaque in color. Advantages
Figure 1-85 Perfume bottle
• • • • • • •
Optical clarity High gloss FDA grades are available Processable by all thermoplastic methods Low cost Good dimensional stability Good rigidity
49
1.2 Thermoplastic Polymers Disadvantages and Limitations • Flammable, but flame retarded grades are available • Poor solvent resistance, attacked by many chemicals • Homopolymers are brittle • Subject to stress and environmental cracking • Poor thermal stability Typical Applications • Single service items, such as plates, glasses, and cups • Packaging items such as cassette boxes and compact disc jewel boxes
Figure 1-86 Kitchen timer
• Consumer durables, such as housewares and cosmetic containers • Blow molded medical and pharmaceutical packaging • Extruded solid sheets, foamed or biaxially oriented sheets for thermoforming; blends with styrene butadiene rubber-block copolymer are used where clarity and toughness are desired • Shower curtain sheets, easy to color with a printable surface • Foamed food packaging articles, such as trays, takeout containers, building insulation, and construction materials • Oriented polystyrene food contact articles, such as cookie containers and chocolate trays • Molded parts and components for refrigerators and other appliances, consumer durables, such as toys, housewares, video cassettes, and micro floppy diskette housings
1.2.22
Polysulfone (PSU)
General Properties of PSU – 30% GR Polymers Specific gravity
1.46
Tensile modulus @ 73 °F (Mpsi)
1.35
Tensile strength @ yield (Kpsi)
14.50
Notch Izod impact @ 73 °F (ft-lb/in)
1.10
Thermal limits service temp. (°F)
375 (short) 350 (long)
Shrinkage (%)
0.50–0.80
Vicat point (°F)
363–387
Tg (°F)
373
HDT (°F) @ 66 psi @ 264 psi
360 350
Process temp. (°F)
600–715
Mold temp. (°F)
200–355
Drying temp. (°F)
200–320
Drying time (h)
3.0–4.0
Figure 1-87 Wine rack
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1 Polymeric Materials Polysulfone (PSU) is produced from Bisphenol A (BPA) and 4,4-dichlorodiphenylsulfone by a nucleophilic process. It is an amorphous engineering thermoplastic material with exceptionally high temperature resistance, high rigidity; it is transparent and dimensionally stable. It exhibits a significant reduction in Izod impact strength when notched; its continuous use temperature index is 350 °F. PSU has a glass transition temperature (Tg) of 373 °F. Polysulfone has been approved to be used in several medical and laboratory applications. It exhibits good chemical resistance but is sensitive to polar solvents and other solutions. Polysulfone is in compliance with the gamma sterilizability requirements. Unlike many other polymers, the melt viscosity of PSU is relatively insensitive to shear forces. The low degree of molecular orientation during injection molding slightly affects the physical properties of the molded parts, independent of flow directions of the melt flow. Polysulfone sheets or molded parts may be joined to another PSU surface or to metals by direct heat sealing, adhesive bonding, solvent fusion, hot plate welding, ultrasonic welding, or heat sealing at 700 °F. Solvent fusion is accomplished with a 5% solution of PSU in a dope of methylene chloride, followed by drying at elevated temperatures as the parts are held together. Polysulfone can be plated by an electrolysis process that imparts bond strengths. Both nickel and copper electroless processes can be employed. All molded parts must be annealed before plating. Polysulfones also can be vacuum-metallized using standard equipment and techniques. Polysulfone should be dried before processing to prevent voids, surface streaks (jetting), and splay marks caused by volatilization of absorbed water. Moisture content should be reduced to below 0.05% before processing the resin. Advantages • Heat deflection temperature of 345 °F at 264 psi • UL continuous use temperature index of 350 °F • High resistivity and dielectric strength properties • High resistance to burning without flame retardant additives • Excellent thermal stability • Excellent resistance to thermal degradation • Good chemical resistance • Highly resistant to alkalies, salt solutions, and aqueous mineral acids • Conventional thermoplastic techniques are used for transformation Figure 1-88 Artificial heart components
• Both thermosetting and thermoplastic types of polymers are available Disadvantages and Limitations • High resin cost • Poor weatherability, subject to stress cracking • Soluble in chlorinated aliphatics, such as methylene chloride, chloroform, and trichloroethylene
Figure 1-89 Syringe holder device
• It is partially dissolved in esters and ketones
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1.2 Thermoplastic Polymers • Low notched Izod impact strength • Viscosity is very temperature sensitive • Processing requires high injection molding pressures, high barrel temperatures, and high mold temperatures • It absorbs water (0.85%) Typical Applications • Construction and Building: Plated plumbing fixture and insulators
Figure 1-90 Tile flooring
• Major Appliances: Microwave oven components • Small Appliances: Plated hair dryer handles • Medical: Pans, hospital equipment, electronic parts, packaging enclosures, filters cases, and laboratory supplies that require sterilization • Housewares: Microwave oven trays, bowls, and covers
1.2.23
Polyvinyl Chloride (PVC)
Figure 1-91 Industrial boots
General Properties of Generic Rigid PVC Polymers Specific gravity
1.38
Tensile modulus @ 73 °F (Mpsi)
0.35
Tensile strength @ yield (Kpsi)
6.00
Notch Izod impact @ 73 °F (ft-lb/in)
0.40–20.0
Thermal limits service temp. (°F)
221 (short) 140 (long)
Shrinkage (%)
0.10–2.50
Vicat point (°F)
179–216
Tm (°F)
360–390
HDT (°F) @ 264 psi
140–170
Process temp. (°F)
365–400
Mold temp. (°F)
85–140
Drying temp. (°F)
160–180
Drying time (h)
2.0–3.0
Polyvinyl chloride (PVC) was introduced in the early 1930s to become a very popular material in the building and construction industry because of its properties, its competitive cost, wide processing capability, and because it can be recycled.
Figure 1-92 Structural window frames
Figure 1-93 Garage door
The two major categories of PVC resins are available: the homopolymer suspension resins and the dispersion resins. Suspension resins account for more than 90% of the total PVC market. They are produced as white powders containing coarse porous particles. When mixed with additives, the suspension resin becomes a powder blend. Suspension resins can be produced as either rigid resins for non-plasticized applications or flexible resins for plasticized applications. All PVC resins require heat stabilizers to allow processing without degrading and discoloring the polymer. Plasticizers are added to increase the flexibility
Figure 1-94 Flat wire cable
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1 Polymeric Materials of the compound. They can also improve the heat stability or improve the flame retardancy of the compound. Fillers are used to reduce the cost of the compound and improve dimensional stability (stiffness) and impact strength of the polymers. Suspension PVC resins may be blended using two types of mixers: the high intensity mixer and the ribbon blender. High intensity blenders and twin screw extruders are used for producing rigid resins. Ribbon blenders and single screw extruders are used for producing flexible resins. Figure 1-95 Electric cords
Dispersion resins account for 7% of the total PVC market. They have a very fine particle size of about 1 micron. When dispersed in plasticizers and other liquid ingredients, they form plastisols and organosols that are applied as liquid (paste) coatings and then fused with heat. Advantages • Processed by all thermoplastic methods • Wide range of flexibility, made possible by varying levels of plasticizer • Relatively low cost • Not flammable
Figure 1-96 Packaging
• Good resistance to weathering • Dimensional stability • Excellent resistance to water and aqueous solutions Disadvantages and Limitations • Attacked severely by stronger solvents, such as aromatic hydrocarbons, ketone, esters, and chlorinated solvents
Figure 1-97 Electrical plug
• Limited thermal capability • Thermal degradation of the polymer generates hydrochloric acid • Stained by sulfur compounds • Higher density than many other plastics Typical Applications • Construction: Pipe, conduit, fittings, siding windows, doors
Figure 1-98 Tubing and connections
• Residential and Commercial Building Constructions: Flexible vinyl sheet and tile flooring, wire insulation, electrical tape, rigid molded outlet boxes and covers. Wall coverings, vinyl coated fabrics and furniture upholstery sheeting, shower curtains, window shades and blinds, wall paneling, picture frames, garden hose, lawn edging, swimming pool liners, and weather stripping • Recreational and Sporting Goods: Toys and athletic footwear • Consumer Use: Appliances, luggage, handbags, baby pants, footwear, tablecloths, adhesive tape, labels, notebook covers. and credit cards • Automotive Applications: Instrument door panels, upholstery, arm rests, center consoles, vinyl tops, body moldings, floor mats, sealants, and caulks
Figure 1-99 Large pipe fitting
• Packaging and Medical Applications: Clear and opaque bottles, flexible and rigid packaging, clear food wrap film, medical gloves, blood bags, tubing, and test equipment trays
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1.2 Thermoplastic Polymers
1.2.24
Styrene Acrylonitrile (SAN)
General Properties of Generic Unreinforced SAN Polymers Specific gravity
1.06–1.08
Tensile modulus @ 73 °F (Mpsi)
0.40–0.56
Tensile strength @ yield (Kpsi)
9.0–12.0
Notch Izod impact @ 73 °F (ft-lb/in)
0.40–0.60
Thermal limits service temp. (°F)
175 (short) 190 (long)
Shrinkage (%)
0.30–0.50
Vicat point (°F)
219–235
Tg (°F)
212–250
HDT (°F) @ 66 psi @ 264 psi
165–200 170–205
Process temp. (°F)
360–550
Mold temp. (°F)
30–175
Drying temp. (°F)
160–190
Drying time (h)
2.0–4.0
Styrene acrylonitriles (SAN) are random, amorphous, linear copolymers, produced by copolymerizing styrene and acrylonitrile. The characteristics of SAN copolymers are: transparency, excellent thermal properties, good chemical resistance, hardness, dimensional stability, and load bearing capabilities. Two rubber-modified versions of SAN are olefin-modified SAN (OSA) and acrylic styrene acrylonitrile (ASA). Both polymers are softer than unmodified SAN; they are ductile and opaque materials. The two-phase terpolymers are commonly known as weatherable polymers. OSAs are produced by combining with a grafted SAN, saturated elastomeric olefin rubber backbone. ASA is a random amorphous terpolymer, produced either by a mass copolymerization process or by grafting styrene-acrylonitrile to the acrylic elastomer backbone. The resulting terpolymers (OSA and ASA) are tough and ductile. These polymers are extremely weather resistant. UV absorbers and antioxidants are used to enhance weatherability. SAN resins are normally used unmodified, although SAN can also be reinforced with glass fiber to produce materials with extremely high rigidity and enhanced thermal properties. Alloys and blends are also available. The alloy SAN/PVC improves outdoor weatherability and flame retardancy. The alloy SAN/PC enhances processibility, while retaining the physical properties of PC. The alloy SAN/butyl acrylate enhances outdoor stability. The alloy OSA/butyl acrylate offers improvements in processibility, toughness, and retention of properties with weathering. Because these polymers are hygroscopic, they absorb a small amount of moisture. Drying is recommended before processing, especially after long-term storage in a warm, humid environment. Drying for 2–4 hours at 160–190 °F with a dehumidifying hopper dryer system is suggested.
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1 Polymeric Materials Advantages • SAN is optically clear, hard, and rigid with excellent dimensional stability and good environmental stress cracking resistance. • OSA and ASA are opaque, rigid, ductile products, similar to ABS but with superior outdoor weathering characteristics and surface stability. • OSA is ideal for coextrusion as a protective cap layer over various substrates. • Improved solvent resistance over polystyrene Figure 1-100 Insulin kit case
Disadvantages and Limitations • Hygroscopic polymer requires predrying • Highly susceptible to the effects of structure orientation • Annealing heavy wall thickness parts reduces the molded-in stresses • Low thermal capability (175 °F) Typical Applications for SAN • Automotive: Instrument lenses, instrument panel supports, battery caps, probes, and cases • Construction and Building: Window panels, storm door glazing panels, plumbing fixture knobs, aerosol nozzles, and paint jars
Figure 1-101 Disposable lighter
• Appliances: Washing machine drain connectors, control panels and doors • Medical: Intravenous connectors, filter cases, and blood dialysis units • Electronics: Video cassette hubs and lenses, telephone parts, terminal boxes, and dust covers • Housewares: Glasses, bowls, mugs, cake covers, brush handles, bristles, and bathroom accessories • Packaging: Display racks, cosmetic cases, lipstick tubes and closures • Miscellaneous: Industrial battery cases, home water filters, swimming pool pump components, and disposable cigarette lighters Typical Applications for OSA and ASA
Figure 1-102 Coffee dispenser
• Automotive: Body moldings, exterior and interior trim part, bumper parts, recreational vehicle components, and pickup truck caps • Construction and Building: Home siding, trim, down-spouts, gutters, fencing, shutters and window frame components • Recreational and Leisure: Swimming pool and pump components, snowmobile housings, and outdoor furniture
1.3 Thermoplastic Elastomers (TPE)
1.3
Thermoplastic Elastomers (TPE)
A thermoplastic elastomer (TPE) is a rubbery material with the characteristics of a thermoplastic and the performance properties of a thermoset rubber. TPEs are processed by using the same thermoplastic equipment and methods,, such as extrusion, injection molding, and blow molding. The TPE resins combine the properties of rubber and thermoplastics. Charles Goodyear started the rubber industry in the 1840s, and John Wesley Hyatt, who is considered the father of the plastic industry, introduced the first plastic material in 1860. The rubber and the plastic industries have each grown and prospered in different directions, developing their materials, technology, fabrication methods, and markets. The fast development and commercialization of applications using thermoplastic elastomer resins have forced an interaction between the rubber and the plastic industries and the barriers between these two industries are shrinking continuously. The first TPE introduced to the industry was the thermoplastic polyurethane elastomer resin during the late 1950s. The styrene butadiene and styrene isoprene block copolymer resins were introduced in 1965. The introduction of the thermoplastic block copolyester elastomer resins was in the early 1970s. The block copolyester TPE was a significant technical innovation, increasing the use of these materials in new and critical applications. The next group of TPEs to be introduced was a blend of rubber and plastic (polypropylene and EPDM rubber) by the late 1970s. The elastomeric alloy thermoplastic vulcanizates (TPV) were introduced in the 1980s. The TPV vulcanization is based on oil dispersion, fillers, and an elastomeric phase (EPD) in a continuous phase of (PP) polyolefin. The elastomeric alloy melt processible rubbers (MPR) were introduced in 1985. The thermoplastic polyamide elastomers (flexible nylons) are another high performance class of TPEs, introduced in the late 1980s. Advantages Thermoplastic elastomers offer a variety of advantages over the thermoset rubbers: • Most TPEs are fully formulated, compounded, and ready for processing. Mixing, blending, or compounding is not required. • TPEs have the processing simplicity of a thermoplastic, giving more efficient processing conditions and significantly lower cost for the finished component. • TPEs offer fast molding cycles, reducing the manufacturing cost of the molded part. The TPE molding cycle is measured in seconds, compared to minutes for compression molding and vulcanization of thermoset rubbers. • Recycling of reject parts and runners (reground). The scrap material from the thermoset rubber process usually is discarded. Some thermoset manufacturing methods could generate large amounts of scrap materials equal or greater to the weight of the finished part. The reground from TPE processes can be recycled (25% maximum ratio) to give finished parts with properties as good as the virgin material.
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1 Polymeric Materials • Lower energy consumption as a result of lower injection molding cycle characteristics obtained while processing TPEs. • Better quality control and closer part dimensional tolerances obtained by injection molding parts made from TPE resins. • Lower manufacturing costs because of greater reproducibility and consistency in properties of the TPE resins. • TPEs have a lower density than most thermoset rubbers, giving additional cost savings. Both rubber and plastic are processed on a volume basis; however, both materials are bought on a weight basis. Disadvantages Thermoplastic elastomers have some disadvantages over thermoset rubbers: • New Technology: Significant thermoset rubber technology innovations have been developed for the industry (better materials, efficient equipment, automatic running molds, and faster processing cycles) to reduce manufacturing costs of the articles. • Unfamiliar Processing Equipment: The equipment required to process TPE resins is familiar to the thermoplastic processors, but this equipment is foreign to the conventional thermoset rubber fabricators. • Drying TPE resins before processing requires additional new drying equipment for the rubber processors. They also need to learn the critical operations required to process TPEs. Conventional rubber fabricators have never used any type of dryer to process thermoset rubbers. The thermoplastic fabricators are very familiar with the dryers and the manufacturing problems caused by processing a wet TPE resin. • The manufacturers offer a limited number of low hardness TPEs. The great majority of commercially available TPEs have a hardness above 60 Shore “A”. The number of available commercial TPE grades with hardness as low as 35 Shore “A” is limited. These special TPE soft grades are slowly becoming commercially available for some types of TPE alloys. • Melting the TPE resins at elevated temperatures and high injection pressures is required for the injection molding process. A thermoset rubber, on the other hand, requires low injection pressure and low temperature provided by the mold.
1.3.1
Thermoplastic Elastomer Families
The property characteristics of thermoplastic elastomers are based on the chemistry and morphology of their matrix. Thermoset rubber materials generally are reinforced with carbon black. In TPEs, the polymer matrix itself provides this reinforcement. Sometimes, it is necessary to modify the matrix structure’s molecular chain ramifications to obtain the required stiffness or hardness for the product. Chemical composition and morphology provide a rational, convenient means of categorizing the existing commercial thermoplastic elastomers. The following commercial TPE families are available: • Thermoplastic polyurethane elastomers (TPU) • Styrenic block copolymer thermoplastic elastomers (SBS)
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1.3 Thermoplastic Elastomers (TPE) • Thermoplastic elastomer alloys: – Polyolefin thermoplastic elastomeric (TPO) – Elastomeric alloy thermoplastic vulcanized (TPV) – Melt processible rubbers (MPR) • Block copolyester thermoplastic elastomers • Polyamide thermoplastic elastomers To compare the performance characteristics between the different TPE resins and the thermoset rubbers, we need to analyze the performance required for applications and the manufacturing costa. The cost and performance characteristics of the generic TPE categories are rated in the following order: starting with styrenic block copolymers, polyolefin blends, elastomeric alloys, thermoplastic polyurethanes, block copolyester elastomer, and polyamide elastomer. The thermoset rubbers also increase in both cost and performance similar to the TPE materials. When comparing thermoplastic elastomers to the corresponding thermoset rubbers, it is important to remember that the processing costs of the TPEs are significantly lower than those for thermoset rubbers, because of the efficient, fast, and automatic molding process.
1.3.2
Thermoplastic Polyurethane Elastomer (TPU)
General Properties of TPU Elastomeric Polymers Specific gravity
1.12–1.21
Tensile modulus @ 73 °F (Mpsi)
5–12 (soft) 15–145 (hard)
Tensile strength @ break (Kpsi)
1.5–7.5 (soft) 5–114 (hard)
Compression set w/o annealing (%)
60–80
Elongation break @ 73 °F (%)
450–600 (soft) 160–450 (hard)
Shore durometer hardness
70A – 98A (soft) 40D – 75D (hard)
Thermal limits service temp. (°F)
230 (short) 176 (long)
Shrinkage (%)
1.3–1.5 (soft) 0.6–0.85 (hard)
Tg (°F)
250 (soft) 320 (hard)
Process temp. (°F)
380–430 (soft) 390–450 (hard)
Mold temp. (°F)
50–150
Drying temp. (°F)
200–230
Drying time (h)
2.0–4.0
Thermoplastic polyurethane elastomers are a member of the family of polyurethanes, which were discovered by Otto Bayer in 1937. Originally, polyurethane elastomers (formed by the casting technique) were considered a material that was chemically crosslinked like the thermoset materials. Not until the late 1950s was it found that essentially linear polyurethane elastomers based on
58
1 Polymeric Materials 4,4-diphenylmethane diisocyanate could be processed like thermoplastics. The segmented structure of the polyurethane elastomer contained crystalline hard segments. This led to a completely new model for the scientific understanding of the elastomeric materials. The basic ingredients of thermoplastic polyurethanes (TPUs) are diisocyanates and long-chain and short-chain diols. The diisocyanates and short-chain diols become the basis of the hard segment structure, while the long-chain diols provide the basis of the soft segments. Because the hard and soft segments do not mix, TPU exhibits a two-phase structure. The properties of TPU can be attributed to the formation of domain micro structures. The basis of polyurethane chemistry is the reaction of isocyanates with various active hydrogen elements present in the compounds. The higher functionality of the isocyanates and the active hydrogen present in the comnpound must be used to obtain higher weight molecular polyurethane. Primarily, TPU linear polymers, consisting of a large number of urethane groups, are synthesized by the condensation of diisocyanates with short-chain diols and polyester or polyether diols. Thermoplastic polyurethanes can be categorized into polyester and polyether types. Polyester-based TPUs generally have better physical properties, such as thermo-oxidative stability and oil resistance. At a similar hardness, polyetherbased TPUs exhibit better low temperature properties, such as hydrolytic stability and resistance to microbial attack. A wide variety of TPUs, with hardness ranging from 70–90 Shore “A” and 40–75 Shore “D”, are available in either pellet or granular form. TPUs consist of an amorphous phase (soft block) and a crystalline phase (hard block), owing to the incompatibility of the adducts of short-chain versus longchain diols with diisocyanates. The hard segments are generally dispersed in the amorphous phase (continuous phase). In a typical TPU, the hard segments determine the hardness, the flexural modulus, the tear strength, and the upper use temperature, while the soft segments of the compound determine the elastic characteristics and the low use temperature properties. The load bearing properties of TPUs are a direct function of the hardness; the higher the hardness of a TPU, the better its load bearing properties. The compression set property of a polymer is its elastic recovery behavior under a specific loading or a specific deflection at various times and temperatures. Typical compression set values of annealed TPUs range from 25–50% and from 60–80% without annealing. Compression set under 25% is obtained with a deflection at 158 °F cured for 22 hours. TPUs are known to exhibit excellent resistance to abrasion. However, the abrasive wear of a TPU is considerably affected by the surface heat buildup during the test, which is believed to be related to the coefficient of friction, stress loading, and contact areas. The abrasive wear of a lubricated TPU is generally lower than that of an unlubricated one. The thermal stability of TPUs is strongly dependent on the structures of the isocyanates and chain extenders. Most TPUs are decomposed slowly at 302– 398 °F and at a measurable rate at 398–482 °F. The TPUs exhibit a loss of mechanical properties and discoloration upon exposure to sunlight. The UV stability of TPUs can be improved by the addition of UV stabilizers. Carbon black-pigmented TPUs have also been found to exhibit better UV stability.
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1.3 Thermoplastic Elastomers (TPE) Although the hydrophilic characteristics of TPU materials have prevented their use in applications where consistently high electrical insulation resistance properties are required, the use of TPUs as a protective covering for various cable applications has been increasing because of their flexibility and abrasion resistance. One advantage of TPUs is their ease of processing. They can be inexpensively processed into simple or complex semi-finished and finished goods by a variety of methods. The extrusion and injection molding techniques are two of the most important processes for the fabrication of TPUs. Other methods include calendering and solution fabrication. Thermoplastic polyurethanes absorb moisture rapidly upon exposure to atmospheric air; so they must be dried before they can be converted into acceptable finished goods. Excessive moisture content in TPUs will result in molding and extrusion difficulties. Blisters, splay marks, bubbles, foamy melt, nozzle drool, and poor physical properties are typical injection molding problems, if the TPU resins are processed wet without drying. During the extrusion process, bubbles, poor surfaces, wave forms, surging, and degradation problems are observed. Although the amount of moisture that can be tolerated in a TPU during processing may vary with the application, it is generally suggested that the moisture content be below 0.07%. Therefore, proper drying of the TPU just before processing is strongly recommended. One recommended way of drying TPUs is to use hopper dryers, which make use of hot air having a dew point below 0 °F and supply drying air at a flow rate greater than 1 lb/h The drying temperatures for TPUs normally range from 203–230 °F with residence times of 2–4 hours. Generally, the softer the TPU is, the lower the drying temperature should be. Prolonged drying should be avoided to prevent TPU discoloration. Advantages • Good physical properties
• Good thermo-oxidative stability
• Good oil, grease, and gasoline resistance • Moderate temperature resistance • Good hydrolytic stability
• Good resistance to microbial attack
Figure 1-103 Snorkels
• Excellent abrasion, wear, and tear resistance Disadvantages and Limitations • High resin cost
• Low aliphatic hydrocarbon resistance
• Low aromatic hydrocarbon resistance • High compression set properties
• Most solvents cause swelling and/or degradation • Requires UV stabilizers for outdoor applications • Poor electrical properties
• Requires drying the resin below 0.07%moisture content before the extrusion process
Figure 1-104 Swim fin
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1 Polymeric Materials Typical Applications • Automotive: Bushings and seals, steering gear parts, shock-absorber bumper, fender extension, membranes of hydro-pneumatic suspension system, grill, bumper filler, and valance panel • Hosing and tubing: Irrigation hose, garden hose, fire hose, hydraulic hose, sewer hose, fuel line hose, fuel line tubing for snowmobiles and small gas engines, pneumatic tubing, and medical tubing • Wire and cable: Air gun control cable, audio wire, camera cable, computer cable, head-set wire, interior building wire, marine cable, welder cable, military cable, communication wire, and jacketing Figure 1-105 In-Line skate wheels
• Casters: Shopping carts, food service carts, and hospital cart wheels • Film and sheet: Elastic leg and waist bands for disposable diapers, life vests, life rafts, life jackets, football liners, seals, gaskets, diaphragms, balloons, air mattresses, water beds, rainwear, surgical drapes, wheel chain pads, conveyor belts, disposable gloves, adhesive film for foam and fabrics, protective covers for industrial usage, and foam cushions • Industrial: Shoe soles and heels, belts, drive gears, wheels
Figure 1-106 Caster wheels
• General Purpose: Reinforced and unreinforced drive belts, packaging seals and gaskets, asphalt paving equipment, soft face hammer heads, wear strips, ski masks, foot holders for wind surfing boards, ski pole handles, mining screens, boots, and soles
1.3.3
Styrenic Block Copolymer (SBS)
General Properties of Generic SBS Specific gravity
0.90–1.28
Flexural modulus @ 73 °F (Mpsi)
140–1,400
Tensile strength (psi)
560–3,500
Compression set w/o annealing (%)
–
Elongation at break @ 73 °F (%)
250–820
Shore durometer hardness
36 A – 95 A 36 D – 60 D
Thermal limits service temp. (°F)
–110 to 140
Shrinkage (%)
0.3–0.6
Melt point (°F)
330
Process temp. (°F)
350–440
Mold temp. (°F)
75–90
Drying temp. (°F)
160
Drying time (h)
2.0–3.0
Styrenic thermoplastic elastomers represent a unique class of materials introduced about 1965. They have many of the physical properties of vulcanized rubbers (softness, flexibility, resilience) but are processed as thermoplastics. Styrenic thermoplastic elastomers can be processed on conventional plastic processing equipment, e.g., with injection molding, and scrap usually can be
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1.3 Thermoplastic Elastomers (TPE) recycled. The high production rate and low resin cost have given the styrenic thermoplastic elastomers a significant boost in the thermoplastic elastomers market growth. However, because the transition to the final form is reversible, some end use properties of styrenic thermoplastic elastomers (e.g., compression set, solvent resistance, and upper service temperature) are usually not as good as those of thermoset rubbers. Styrenic thermoplastic elastomers are used in areas where these end use properties are less important (e.g., footwear, wire insulation, adhesives, polymer blending, sealants, and coatings). Styrenic thermoplastic elastomers have thermoplastic properties because of their structure. They are multi-phase compositions in which the phases are chemically bonded by block copolymerization. At least one phase is a styrenic polymer that is hard at room temperature but becomes fluid when the polymer is heated, whereas another phase is a softer material that is rubber-like at room temperature. Most polymers are thermodynamically incompatible with other polymers, and such mixtures separate into two phases. This characteristic exists even when the polymeric matrix is part of the same molecule, as in the case of the poly(styrene-b-elastomer-b-styrene) block copolymers. Most of the polymer molecules have their end polystyrene segments in different domains. At room temperature, these polystyrene domains are hard and act as crosslinks, tying the elastomer chains together in a three-dimensional network. But in thermoplastic elastomers the domains lose their strength when the material is heated or dissolved in solvents, allowing the polymer to flow. When the melt is cooled or the solvent is evaporated, the domains become hard again and the network regains its original integrity. The most important property of these polymers for commercial purposes is their resemblance, at least at room temperatures, to vulcanized rubbers. Styrenic block copolymers have a tensile strength from 560–3,500 psi and elongation at break from 250–820% at room temperature. There are two reasons for these high values. The first one is that the hard polystyrene domains act as reinforcing filler, and the second takes into account the increased tensile strength, resulting from the slippage of entangled chains. The materials containing a constant polystyrene structure have demonstrated that the tensile module and tensile strengths of the styrenic block polymers are not molecular weight dependent. As long as the polystyrene molecular weight structure is high enough to cause the formation of a strong bond and a well separated structure domain. These materials must be protected against oxidative degradation and in some cases against sunlight also, depending on their end use. Combinations of hindered phenols and thiodipropionate synergists are effective antioxidants. Combinations of benzotriazoles and hindered amines are effective UV stabilizers.
Figure 1-107 Tape measurement grip
For products that do not have to be clear, titanium dioxide or carbon black pigments also provide effective UV protection. Many types of styrenic thermoplastic elastomers have been produced to meet specific end use requirements. General purpose styrenic block copolymer, soluble when compounded, improved stability. They are used for wire and cable coatings and medical applications. The hard and rigid compounds are used for injection molding and extrusion applications. Like most conventional vulcanized rubbers and unlike most thermoplastics, the styrenic thermoplastic elastomers have no commercial applications when the product is just a pure polymer. Depending on the particular requirements for each end use, they are compounded with other polymers, oils, fillers, and
Figure 1-108 Industrial boot skirt
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1 Polymeric Materials additives. In almost all cases, the products contain less than 50% of the block copolymer. Advantages • Good mechanical properties and high elongation at room temperature • Low cost resins
Figure 1-109 Diagnostic tester housing
• Thermoplastic processing equipment can be used (injection molding and extrusion) • Reground material can be recycled • Excellent impact modifier compounding ingredient Disadvantages and Limitation • Poor compression set properties • Poor solvent resistance • Poor high temperature resistance • Usage only for noncritical applications
Figure 1-110 Fish knife handle
Typical Applications • Replacements for vulcanized rubber • Injection molded articles requiring modest end use temperatures for the footwear, toys, and furniture industries • Extrusion of sheets, tubing, and wire coating • Adhesives, sealants, and coatings • Polymer blends • Impact modifier ingredient for other compounds • Viscosity index enhancer for lubricating oils • Modifiers for thermoset materials
1.3.4
Polyolefin Thermoplastic Elastomer (TPO)
TPOs resemble other TPE resins; they have properties of a thermoset rubber, but are processible in standard thermoplastic equipment. TPO products cover a range of properties, bridging the gap between rubber and plastics. The ability to use thermoplastic processing equipment allows for greater productivity and economy. The recycling of reground materials, such as runners, sprues, and rejected parts, provides a significant economic advantage. TPO materials are defined as compounds of various polyolefins, semi-crystalline plastics, and amorphous elastomers. The most common types of TPOs are composed of polypropylene (PP) and ethylene-propylene rubber (EPR). EPR may be either a copolymer of only ethylene and propylene monomers or a third monomer, the diene monomer, which provides a small amount of unsaturation in the polymer chain for sulfur crosslinking. This is called ethylene-propylenediene-monomer rubber (EPDM). Other polyolefin polymers commonly used in TPO compounds include: low density polyethylene (LDPE), high density
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1.3 Thermoplastic Elastomers (TPE)
General Properties of Generic TPO Specific gravity
0.88–0.98
Flexural modulus @ 73 °F (Kpsi)
2.7–300.0
Tensile strength @ yield (Kpsi)
0.95–4.00
Izod impact @ 73 °F (ft-lb/in)
1.00 No break
Elongation at break @ 73 °F (%)
20.0–600
Shore durometer hardness
40 D – 70 D
Thermal limits service temp. (°F)
180–212 (Stiff grade)
Shrinkage (%)
0.7–2.1
Melt point (°F)
290–330
Process temp. (°F)
360–500
Mold temp. (°F)
50–150
Drying temp. (°F)
150–225
Drying time (h)
3.0–6.0
polyethylene (HDPE), linear low density polyethylene (LLDPE), copolymers of ethylene with vinyl acetate (EVA), ethylacrylate (EEA), methyl acrylate (EMA), semi-crystalline copolymers of propylene, ethylene, and polybutene. TPO products are compounds of polyolefin polymers. Like most thermoplastic elastomers, they are composed of hard and soft domains. The exact size and shape of these domains determines the properties of the compounds. The properties of the product may be determined as much by the process of producing the compound as by the composition. An unlimited number of formulations for TPO compounds are possible because of the wide variety of polyolefin polymers used. Each of these compounds has its set of properties that may be useful in specific application. In most TPO compounds, the hard domain is isotactic propylene homopolymer or an isotactic propylene copolymer with a minor amount of ethylene as the comonomer. The ethylene monomer may be distributed either randomly in the copolymer or as blocks. Some of the segments of the polymer chain are composed of ethylene and propylene copolymers, while the other segments of the polymer chain are almost totally propylene homopolymer. The homopolymer and block copolymers have a crystalline melting point of 311–329 °F where as the random copolymers have a melting point of 293–311 °F. The relatively high melting point of the polypropylene portion of the TPO results in products that retain many of their mechanical properties at temperatures approaching the melting point of the polypropylene resin. Higher impact strength at low temperature is achieved by increasing the amount of ethylene present in the copolymer. Ethylene also reduces the rigidity of the copolymer. The crystalline melting point is depressed more sharply with increasing ethylene content in random than in block copolymers. The soft domain of the polymer chain is ethylene-propylene rubber (EPR) or ethylene-propylene-dienemonomer rubber (EPDM). Rubber materials with nearly equal amounts of ethylene and propylene are totally amorphous. The softest EPDM rubber grades are the most efficient impact modifier additives used in TPOs.
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1 Polymeric Materials Some of the other additives used in TPO compounds function by modifying the rubber phase. Hydrocarbon oil increases the softness and flexibility of a TPO compound by swelling the rubber phase. Polyethylene also increases the volume of the rubber phase, but does not have the softening effect of oils. High density polyethylene improves the impact strength at low temperatures while maintaining stiffness. In addition, a wide variety of other ingredients are used in compounding TPOs. These ingredients may include fillers, reinforcing agents, lubricants, plasticizers, heat stabilizers, antioxidants, UV stabilizers, colorants, flame retardants, foaming agents, flow modifiers, or processing aids. Figure 1-111 Roller skate wheels
Figure 1-112 Air conditioner system
Figure 1-113 Tailgate bumper
TPOs can be formulated to combine strength and toughness. TPO products are available from 40–70 Shore “D” hardness, with a flexural modulus ranging from 2,700–300,000 psi. Several factors determine the upper limit of use temperature for a TPO product. The melting point of the hard domain polymer is most important for short-term exposures. For most TPOs, the melting point of polypropylene is a limiting factor. Polypropylene homopolymers melt from 320–350 °F. Most TPO (hard/stiff) compounds will retain useful properties intermittently at temperatures up to 280 °F. For long-term exposure, the resistance of the TPO to aging effects at elevated use temperature is as important as the melting point of the hard domain polymers. The oxidative stability of TPOs is a function of the antioxidant and stabilizer additives. The most effectively stabilized TPO (hard/stiff) compounds are formulated with heat stabilizers, antioxidants, and reinforcements to withstand continuous use temperatures up to 250 °F or more. General purpose TPO (hard/stiff) compounds will retain their physical properties when used for extended periods from 180–212 °F. One of the outstanding properties of TPOs is their performance at low temperatures. TPO compounds retain their flexibility at very low temperatures. The softer TPO grades often have a low temperature brittle breaking point of less than –112 °F. Almost all TPO products retain their physical properties when exposed to sunlight and weather. TPO compounds are made without unsaturated polymers in the polymer backbone and these types of materials are not susceptible to degradation by ozone. EPDM is a weather resistant rubber. TPOs also are not particularly susceptible to fungus growth. Many grades have outstanding color retention. These specially stabilized grades, designed for unpainted automotive applications, have been exposed in Florida sun aging tests for more than two years without changing color. All TPO products are unaffected by water and exhibit fair chemical resistance to acids and bases. Hot hydrocarbon solvents tend to soften and swell TPO products. This softening and swelling is typically slight for the harder formulations but severe for the softer products. The chemically inactive surface of a TPO part makes bonding to other materials difficult. Most TPO compounds are good electrical insulating materials. They have good dielectric strength properties and they do not absorb moisture, because they are not hygroscopic. Many TPO parts that are used in automotive applications must be painted with an automotive finish to match or accent the painted finish of the other body panels. Paint systems are available that will give excellent adhesion of the paint to the TPO surface. The TPO materials do not have a molded surface that chemically reacts with the primer paint system to develop a strong and durable bond. To achieve adequate adhesion of the primer, the TPO must be modified in some way to obtain a reactive surface.
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1.3 Thermoplastic Elastomers (TPE) Advantages • Excellent electrical insulating characteristics • Can be compounded with nylon to increase end use temperatures • Excellent impact resistance • Excellent fatigue resistance • Excellent low temperature brittle point for softer grades
Figure 1-114 Bumper fascia
• Excellent moisture absorption resistance • Not susceptible to degradation by ozone • Not susceptible to fungus growth • UV resistance grades are available Disadvantages and Limitations • Fair chemical resistance to acids and bases
Figure 1-115 Instrument panel shell
• Hot hydrocarbon solvents tend to soften and swell the TPOs. This softening and swelling is slight for the harder formulations but severe for the softer products • Bonding to other materials is difficult • Reactive surface treating and a paint primer are required before painting Typical Applications • Exterior Automotive Applications: Body side trimming, body side molding, bumper covers, bumper end caps, bumper side pieces, fender liners, sight shields, stone deflectors, wheel well moldings, and valance panels • Under Hood Automotive Applications: Wiring harness protective sleeve, blow molded air duct, sound absorbing fire wall blanket, automotive high performance audio systems, such as speaker box enclosures, rocker panel covers, rub strips, and scuff plates • Wire and Cable: TPOs are used for a number of low voltage wire and cable applications. They are used for insulation and jacketing for battery booster cables, portable power supply cords, and submersible pump cable • Mechanical Goods: Seals, electrical plugs, extruded sheet, and weather strips • Impact Modifier: Polyolefin and polypropylene are used to improve the low temperature impact strength; TPO also is added to HDPE to improve stress crack resistance
1.3.5
Elastomeric Alloy Thermoplastic Vulcanized (TPV)
Vulcanized elastomeric alloys are thermoplastic elastomers composed of mixtures of two or more polymers that have received a proprietary treatment. TPV compounds tailor their characteristics during the manufacturing process. The improved TPV properties are superior to other major competitive compounds.
Figure 1-116 Bumper fascia
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1 Polymeric Materials
General Properties of Generic TPV Specific gravity
0.94–1.34
Flexural modulus @ 73 °F (Kpsi)
2.7–50.3
Tensile strength @ yield (Kpsi)
0.64–4.0
Compression set @ 22 h (%)
16–44 @ 73 °F
Elongation at break @ 73 °F (%)
330–600
Shore durometer hardness
55 A – 87 A 40 D – 50 D
Thermal limits service temp. (°F)
–75 275
Shrinkage (%)
1.5–2.5
Vicat point (°F)
206–290
Process temp. (°F)
360–410
Mold temp. (°F)
50–175
Drying temp. (°F)
150–175
Drying time (h)
2.0–4.0
EA-TPVs are a category of TPEs made of a rubber and plastic polymer mixture in which the rubber phase is highly vulcanized. The plastic phase of a TPV is a polyolefin (polypropylene) and the rubber phase is an ethylene-propylene elastomer. The first TPV (1981) was an EA-TPV, in which the plastic phase was polypropylene and the rubber phase was EPDM rubber. A subsequent TPV of polypropylene and nitrile rubber was introduced to the plastic industry. The vulcanization of the rubber phase of an EA-TPV results in numerous property improvements. Insoluble in rubber solvents, the TPV exhibits less swelling in these solvents than TPE rubber and plastic blends. This vulcanization offers several improvements in the properties of EA-TPV: • Increase in tensile strength and modulus • Decrease in compression set • Decrease in swelling caused by oils Vulcanization of the rubber phase also improves the retention of properties at elevated temperatures. The dynamic vulcanization embraces the curing of a rubber composition during its compounding and one of the ingredients of this rubber composition must be a thermoplastic resin. It is important that the mixing be continuous during the compounding step. The temperature reached during the mixing must be sufficiently high to melt the resin and effect the chemistry of the crosslinking reaction. Elastomeric alloy TPVs differ from simple elastomer blend TPEs in the degree of vulcanization of the rubber phase. The rubber TPV consists primarily of a fine dispersion of highly vulcanized EPDM rubber in a matrix of polypropylene as the continuous phase. Of equal importance for the improved properties of a TPV is the size of the particles of vulcanized EPDM. As the particle size decreases, the properties progressively improve. Typical grades range from 55–87 Shore “A” and from 40–50 Shore “D”. Service temperature ranges from a minimum of –75 °F to a maximum of 275 °F.
1.3 Thermoplastic Elastomers (TPE) The tear strength and abrasion resistance of elastomeric alloy TPVs is good but not outstanding, the tear strength increases progressively with hardness. The desirability of low or high resilience (hysteresis) will depend on the end use. Uses, where heat generation of the flexing rubber is critical, demand high resiliency; those requiring vibrational damping need low resiliency.An outstanding dynamic property of thermoplastic vulcanizates is their fatigue resistance. TPVs have a maximum use temperature in air of 275 °F for extended periods of time. This temperature is based on air aging data after 1,000 hours, 50% retention of elongation, 70% retention of tensile and hardness reduction. Accelerated outdoor aging tests on black TPVs show that they retain their performance properties for 12 months; colorable EPDM-TPVs are much less resistant to the combined effects of solar radiation, atmospheric oxygen, ozone, and other atmospheric pollutants. The resistance of EPDM-TPVs to polar fluid media is excellent. The environment ranges from a corrosive media, such as concentrated acids and alkalis, to mild media, such as aqueous salts and polar organic and inorganic fluids. As the polarity of the medium decreases, so does the resistance of the EPDM-TPVs, culminating in their poor resistance to halocarbons. Chemical resistance to hydrocarbons is fair; the resistance to saturated hydrocarbons is better; resistance to water, aqueous solutions (both acids and alkalis), and hot oils are poor. These materials cannot be recommended for service in diesel fuel above 158 °F. TPVs have fair to good resistance to industrial and automotive fluids at elevated temperatures. Thermoplastic vulcanizates have excellent electrical insulation properties, an excellent dielectric strength 400 volts/mil at a thickness of 0.080 in. The volume and surface resistivity of EPDM-TPVs are sufficiently high to justify their consideration for use as primary electrical insulators, as well as jacketing material. The dielectric constant (specific inductive capacitance) and power factors are basic limits in the selection of a primary electrical insulation material. These two parameters of flame retarded TPVs at ambient and elevated (212 °F) temperatures and the normal power transmission frequency of 60 Hz make them a good choice for electrical applications. TPVs absorb moisture, causing significant processing problems, such as internal voids, rough surface appearance, and poor dimensional control. When using a hot runnerless mold, moisture causes a dangerous buildup of high pressure steam. Therefore, moisture adsorption after exposure for 24 hours, or even less, causes significant processing problems. The recommended moisture content limit for these materials is less than 0.3% before processing. Proper drying will eliminate most of the major processing problems for these materials.
Figure 1-117 Soft-touch common handling tools
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1 Polymeric Materials It is strongly recommended that TPVs be dried again immediately before use. Desiccant drying systems are recommended for drying the resin from 2–4 hours at 150–175 °F. Hot air drying systems are not recommended, because they remove only the moisture from the surface of the resin, the interior volume of the resin does not become dried, producing uneven drying results. Advantages • Can be injection molded, extruded, compression molded, blow molded, calendered, thermoformed, and extrusion foamed Figure 1-118 Weatherstripping seal
• Good tear strength and abrasion resistance • Excellent fatigue resistance • Excellent resistance to polar fluid media • Excellent electrical insulation properties Disadvantages and Limitations • Poor UV resistance • Poor bonding, surface preparation is recommended • Chemical resistance to hydrocarbons is fair; the resistance to saturated hydrocarbons is better • Poor resistance to halocarbons
Figure 1-119 Equipment grip handle
• Poor chemical resistance to aqueous solutions (both acids and alkalis) and hot oils • TPVs cannot be recommended for service in diesel fuel above 158 °F • Fair resistance to industrial and automotive fluids at elevated temperatures Typical Applications • Automotive: Hose coverings, air inlet duct covers, gaskets, seals, convoluted boots, vibration dampeners, ignition components, window seals, cover systems connecting the distributor to the spark plugs and vibration dampeners
Figure 1-120 Automotive headlamp seal
• Architectural and Construction: Expansion joints, roofing, flooring, and weather seals around doors and windows, soft extruded TPV profile as a window glazing material, metal reinforced TPV weather stripping, and other exterior openings. • Electrical and Electronics: Insulator, jacketing material, wire and cable coverings, electrical connectors, plugs, insulators for electrical and electronic assemblies, computer hardware and software, telephones, electronic appliances, duplicating machines, and office equipment • Hose, Tubing, and Sheeting: Sheeting is used for on-site fabrication of roofing membranes, seals, and gaskets. It is also used for different types of hose and tubing, inner liners, jacketing, and hoses reinforced with a textile fiber or metal mesh
Figure 1-121 Automotive air duct
• Medical and Food Contact: Applications in direct contact with foods, beverages, pharmaceuticals, and living tissues. These applications employ special grades that comply with the regulations of the USA Food and Drug Administration. Medical devices include syringe plunger tips, drug vial
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1.3 Thermoplastic Elastomers (TPE) stoppers, aerosol valve seals, medical tubing, nursing bed sheets, and liquid dispenser pump diaphragms. All of these applications are derived from the biocompatibility and low toxicity of elastomeric alloy TPVs, both before and after sterilization • Mechanical Rubber Goods: Household appliances, industrial equipment, recreational devices, seals, gaskets, valve seats, grommets, appliance feet, bushings, toys, hand tools, ski pole grips, caster wheels used in grocery carts, toys, and small industrial equipment
1.3.6
Melt Processible Rubber (MPR)
General Properties of Generic MPR Specific gravity
1.10–1.26
Flexural modulus @ 73 °F (Kpsi)
1.10–1.40
Tensile strength @ yield (Kpsi)
1.03–1.68
Compression set @ 22 h (%)
12–18 @ 73 °F
Elongation at break @ 73 °F (%)
265–350
Shore durometer hardness
60 A – 80 A
Thermal limits service temp. (°F)
–40 to 212
Shrinkage (%)
1.5–3.0
Brittleness temp. (°F)
–132 to –105
Process temp. (°F)
300–380
Mold temp. (°F)
250–300
Drying temp. (°F)
150–200
Drying time (h)
1.0–2.0
With the introduction of the melt processible rubber (MPR) in 1985, it was possible to eliminate vulcanization, increase productivity, recycle the scrap, and minimize the dependency on the rubber compounds. MPR has the range of properties and cost savings needed to replace conventional thermoset rubber. This compound is not a thermoset material. The MPR resin produces parts that look, feel, and perform like vulcanized rubber and can be processed on equipment used for thermoplastics or thermosets. It also offers the combination of resistance to heat, oil, chemicals, and weathering. The melt processible rubber resin has been recognized as the most rubbery-like product among all the TPE families. MPRs are available in a hardness range from 60–80 Shore “A” durometers. MPR alloys are composed of proprietary ethylene interpolymers and chlorinated polyolefins, in which the ethylene interpolymer component has been partially crosslinked. Plasticizers, stabilizers, antioxidants, curing agents, and fillers can be incorporated into the resin to provide flexibility and reinforcement. The MPR polymer network is amorphous, providing a very low flexural modulus, excellent tensile strength, and linearly proportional stress-strain curve. Halogenated polyolefins are intermixed with a large number of structurally coupled ethylene interpolymers. The ethylene interpolymers are used as intermediates in MPRs. They contain functional groups that are strongly protonaccepting to promote hydrogen bonding with the alpha hydrogen atoms of the halogenated polyolefin over the entire composition range. The MPR polymer
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1 Polymeric Materials blends are single-phase systems, because they have a single glass transition temperature. As an amorphous material, the MPR exhibits no crystalline melting point. It gradually softens with increasing temperature, but does not flow at any temperature, unless also subjected to shear. By increasing the shear rate of the MPR, the melt viscosity property of the polymer increases proportionally. The polymer melt only becomes softer, but not a liquid melt. This unique polymer characteristic makes it possible for the melt to flow through small-size gates, runners, and parts with thin wall thicknesses. Increasing the temperature in the range from 300 °F–380 °F has little effect on viscosity. Little is gained in processing MPR at temperatures above 350 °F. Because of its rheology and its amorphous single-phase nature, MPR is obviously not a plastic. It has a fractional melt index, does not melt and exhibits thixotropic behavior. It has a useful plastic processing property in flowing like a thermoplastic on application of shear. Unlike plastics, it displays minimum draw-down because of elastic recovery, even at elevated temperatures. MPR provides a balance of properties, such as durability and performance sufficient to replace thermoset rubbers. MPR is unique in duplicating the feel and recovery of vulcanized rubber and in being processible on both thermoplastic and modified rubber equipment. It has outstanding oil resistance, heat aging, weatherability, and is recyclable. It has mechanical properties, tear and abrasion resistance, and a continuous temperature similar to mid-performance rubbers. MPR is used as an energy absorbing polymer, but it has limitations in applications requiring very dynamic motion and load carrying capabilities. Advantages • The most rubbery-like product of the TPEs • Blow molding, injection and compression molding, extrusion, calendering processes are possible • Excellent resistance to ultraviolet light • Low operating temperatures below –40 °F • Excellent resistance to paraffinic (ASTM oil #1) and aromatic (ASTM oil #3) oils, to gasohol (15% methanol), unleaded gasoline, diesel fuel, JP-4 jet fuel, and kerosene • Good resistance to aromatic fuel B, fuel C, and fuel A • Inert to solvents such as alcohols and ethers, and hydrocarbons, such as hexane, cyclohexane, turpentine, and fluorocarbon (Freon® 112) Figure 1-122 Wrench handle
• Excellent resistance to many lubricants, steering, and brake fluids and other hydraulic fluids Disadvantages and Limitations • Poor chemical resistance to polar fluids, including esters, aldehydes, ketones, and chlorinated solvents • Low swelling in boiling water, glycol, and water coolants, aqueous alcohols, acids, bases, and salts • Poor electrical properties
Figure 1-123 Gasoline nozzle pump
• Continuous operating end use temperature of 212 °F
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1.3 Thermoplastic Elastomers (TPE) Typical Applications • Reinforced Hoses: Low performance, high volume, such as garden hoses and automotive heater hoses • Automotive Hoses: Cover for air condition hoses and fuel lines, filler neck hoses, vent hoses, evaporative loss hoses, truck air brake hoses • Industrial Hoses: Hydraulic wire braid, hydraulic textile braid, oil suction discharge, chemical and oil transfer, agricultural spray, fire extinguisher, fuel delivery, shop vacuum hose, washing machine, and dishwasher hoses • Service Cords: Appliances, electric drills, power drills, saws, typewriters, and office machines • Control Cable: Low voltage cables for control switches and relays • Flexible Power Cable Jacket: Airport lighting, industrial plants, oil well, utility power, urban primary, and secondary network cables.
Figure 1-124 Bumper/lamp gasket
• Elastomeric Sheeting: Colorable, flexible sheeting for single ply roofing, elastomeric lining of ponds and pits for industrial waste • Molded Goods: Molded MPR articles of all shapes and forms, that require the rubbery feeling, wear, UV resistance, color and molded to metal adhesion properties • Fabric Coating: Industrial pond and pit liner, automotive fabrics, and different types of clothing • Seals, Gaskets, and Weather Stripping: Building gaskets, highway and bridge gaskets, appliance seals, automotive weather stripping, extruded profiles of varying complexity, circumferential gaskets (compression molded or die-cut from sheet stock), coextrusion composite using a MPR seal and a rigid vinyl (PVC) or other hard material as reinforcement
1.3.7
Copolyester Thermoplastic Elastomer
General Properties of Generic Block Copolyester TPE Specific gravity
1.07–1.43
Flexural modulus @ 73 °F (Kpsi)
4.7–175.0
Tensile strength @ yield (Kpsi)
1.49–7.00
Brittleness temp. (°F)
–157 to –67
Elongation at break @ 73 °F (%)
200–700
Shore durometer hardness
35 D (soft) 82 D (hard)
Thermal limits service temp. (°F)
–40 (soft) 300 (hard)
Shrinkage (%)
0.50–1.60
Tm (°F)
312–433
Process temp. (°F)
360–500
Mold temp. (°F)
90–150
Drying temp. (°F)
212
Drying time (h)
2.0–3.0
Figure 1-125 Automobile steering ring
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1 Polymeric Materials Block copolyester thermoplastic elastomers have a combination of mechanical properties, such as tensile strength, elasticity, creep resistance, and dynamic properties. These polymers are operational over a broad service temperature range without significant change in properties. They also have excellent chemical, heat, and oil resistance properties. In 1972, E. I. DuPont Company introduced a new material based on 1,4-butanediol, terephthalic acid and polytetramethylene ether glycol or polypropylene glycol. Because the building blocks behaved like high tensile strength engineering plastics and elastomers, respectively, the product combined these characteristics in proportion to the ratio of hard and soft molecular segments. The fast crystallization rate of the hard segment, combined with exceptional melt stability of the backbone, allowed these polymers to be processed like a thermoplastic material. Block copolyester elastomers stress-strain curves show why these polymers are not like thermoplastics or thermoset rubbers. They are a class of materials combining some of the strength of plastics with some of the elasticity of rubber. A distinguishing characteristic of block copolyester elastomer resins versus other flexible materials is their excellent dynamic performance, which makes these resins suitable for applications requiring long-term spring properties and flex life. Operating within their elastic limits, block copolyester elastomers are creep resistant, supporting loads for a long time without stress relaxation. They can be subjected to repeated cycles of tension and compression without significant loss of mechanical strength. Block copolyester elastomers demonstrate low hysteresis loss in dynamic applications. Product components working at low strain levels exhibit complete recovery in cyclic applications with little heat buildup. Typical melt temperatures range from 360–500 °F. As a general rule, stiffer grades have higher melting points and crystallization temperatures, yielding shorter mold cycles than those of the more flexible grades. The melting points between soft and hard grades, for example, 312 °F versus 433 °F, introduce some variations in the process conditions. The process thermal stability of copolyester elastomers permits exposure to elevated temperatures and long residence time without degrading the polymer. The different resins have a significant difference in melt rheology. Their viscosity is tailored for specific processes; the low viscosity melts are used for injection molding and extrusion, while the high viscosity melts are used for extrusion blow molding. Resistance to cut growth during flexing is outstanding, mainly because of high resilience and low heat buildup. Block copolyester elastomers rank high among thermoplastics for impact resistance; most of the compounded grades do not break by conventional notched Izod impact testing equipment. Resistance to abrasion is a complex function of tear strength, coefficient of friction, resilience, heat dissipation, and other properties. If high mechanical strength is required in an abrasive environment, copolyester elastomers will outperform any type of thermoplastic elastomer and rubber. Copolyester elastomers are used in electrical applications with less than 600 V. The following characteristics make them attractive for electrical and electronic applications: good dielectric properties, high mechanical strength, creep resist-
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1.3 Thermoplastic Elastomers (TPE) ance, spring properties, flex fatigue resistance, high impact strength, abrasion resistance, and end use service temperature range between –40 to +300 °F. Block copolyester elastomer compounds have excellent oil resistance; in several applications they have replaced materials such as polyacrylate, silicone, fluorosilicone, SBR, nitrile, and polychloroprene rubber. Block copolyester elastomer stiffer grades offer the best performance in hot hydrocarbon environments, with many resins suitable for use with hot oil, grease, fuels, and hydraulic fluids. Block copolyester elastomer resins are attacked by polar fluids at temperatures above 158 °F, even though the resins are resistant to fuels, they are not suitable for under the hood automotive applications. Hydrolytic stabilizing concentrates are available from Du Pont; this additive is blended with the virgin resin to extend service life in the presence of hot water. Many applications, such as containers, sheets, and seals, require low permeability to standard fuels. Block copolyester elastomers are rather permeable to polar molecules such as water, but are resistant to penetration by nonpolar hydrocarbons and refrigerant gases. Permeability to water vapor makes polyester elastomers useful in coating fabrics for rain resistance. The low permeability to refrigerant gases and propane is important for refrigerant hose and propane gas hose, respectively. Block copolyester elastomers are highly resistant to radiation. Block copolyester elastomer compounds do not contain plasticizer additives in their formulations. The inherent chemical purity of block copolyester elastomers makes them an excellent choice for food contact and medical applications. Block copolyester elastomers are UL-94 HB rated. Master batch additives and compounded grades are available to meet UL-94 V0 ratings. Block copolyester elastomer parts can be produced by injection molding, injection blow molding, blow molding, extrusion, and rotational molding. Film processes include casting, extrusion, and blowing. Block copolyester elastomers are subject to hydrolysis (moisture absorption) at processing temperatures. It is essential that the polymer be dried before processing. The virgin resins are supplied in moisture-proof bags with less than 0.10% moisture. The virgin material can be used directly from sealed bags. However, all reground material and resin from an open shipping bag or container exposed for more than one hour to ambient air, must be dried before processing. The material is hygroscopic and within one hour can absorb enough moisture from ambient air to cause degradation during processing. It is recommended to dry the wet resin from 2–3 h in a dehumidifying oven or hopper dryer at 212 °F.
Figure 1-126 Headphone set spring holder
Reground ratios as high as 100% are possible, however, the reground ratio must take into account the degradation of the reground being blended with virgin material. As a general rule, the level of reground material should be less than 50% to maintain the highest polymer quality. Advantages • Hardness between 35–82 Shore “D” • Excellent dynamic performance • Excellent hysteresis flex life
Figure 1-127 Printer belt drive
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1 Polymeric Materials • Low creep recovery from deformation • Excellent flex fatigue and cut growth resistant • Excellent flexibility over broad temperature range • Good abrasion resistance • Excellent impact resistance at low temperatures Figure 1-128 Pistol holster
• High tensile strength and tear strength • Good chemical and hot oil resistance • Excellent processing characteristics • Recyclable polymer Disadvantages and Limitations • Lower compression set resistance (high deflection) than rubber
Figure 1-129 Safety air bag cover
• Lower elastic recovery at high strains compared with rubber • Poor polar fluid resistance at temperatures above 158 °F • Special compounds to optimize properties are difficult to obtain • Addition of UV stabilizers required for outdoor applications • Drying reground or wet resin is required • Different molding conditions are required for each polymer type • High resin cost
Figure 1-130 Wall anchor fastener
Typical Applications Block copolyester elastomers are well suited for applications requiring strength, flexibility, or dynamic properties. They replace rigid plastics and soft materials, such as rubber, where improved shock absorption, impact strength, flexing, sealing, spring characteristics, or silent mechanical operation are required. • Replacement of Metals: Coextruded hinges of copolyester elastomer and PVC, one piece rotomolded wheels, gear replaced cast iron in a textile braiding machine
Figure 1-131 Automotive CVJ boot
• Replacement of Cast Urethane: Automotive body parts including spoilers, air dams, CVJ boots, air bag covers, coil spring connecting brake hoses for trailer trucks, side moldings, seals, hydraulic piston actuators, and grills, railroad and large construction machinery heavy duty shock absorber stops, fluidfilled piston actuated shock absorbers for mining trucks, skiing equipment components, irrigation valve diaphragm, and coil phone cords • Replacement of Leather: Footwear, military pistol holsters, straps, soccer balls, motorcycle face masks, and sport clothing • Replacement of Rubber: Hose and tubing, compact garden hose, high pressure hydraulic hose, power drive belts for office equipment and computers • Electrical Applications: Including wire insulation, retractile wire, switches, and sealed connectors
Figure 1-132 Automotive suspension
• Specialty Products: Food contact and medical applications
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1.3 Thermoplastic Elastomers (TPE)
1.3.8
Polyamide Thermoplastic Elastomer
General Properties of Generic Polyamide TPE at 50% RH Specific gravity
0.99–1.14
Flexural modulus @ 73 °F (Kpsi)
27.0–42
Tensile strength @ yield (Kpsi)
3.00–6.90
Shrinkage (%)
0.50–2.50
Elongation at break @ 73 °F (%)
270–715
Shore durometer hardness
60 A – 90 A 25D – 63 D
Thermal limits service temp. (°F)
338–392 (hard grades)
Vicat point (°F)
140–378
Tm (°F)
300–480
Process temp. (°F)
320–537
Mold temp. (°F)
70–140
Drying temp. (°F)
160–230
Drying time (h)
4.0–10.0
The thermoplastic polyamide elastomers consist of hard and soft segments joined by amide linkages. The soft segments of the material could have polyether or polyester in the backbones of the structure. Three different chemical compounds have been developed. The creation of this new family of thermoplastic polyamide elastomers is the result of the research work of three plastics companies. The first formulation consists of an adipic acid capped hard segment block of poly (11-amino-undecanoic). The hard block is joined with a soft segment, such as polyoxyethylene glycol, polyoxypropylene glycol, or polyoxytetramethylene glycol, in a polyesterification process to form polyetheresteramide (PEEA). The second formulation is a variation, in which there are no ester linkages. The bonds between the hard and soft segments are amides. In this formulation, an amine-terminated soft segment, bis(3-aminopropyl)-polyoxytetramethylene glycol, is reacted with a dimer acid and caprolactam to form the polyetheramide (PETA). The third formulation consists of an acid terminated soft segment that is formed first by esterification of a polyoxyalkylene or other glycol. This is reacted, along with additional diacid, with a diisocyanate to form the polyesteramide (PESA), in which the hard segments are the amides formed from the additional diacid and the diisocyanate. PESA is the only formulation that incorporates substantial aromatic structures into the backbone to modify its properties. Thermoplastic polyamide elastomers exhibit properties that depend on the chemical composition of the hard (polyamide) and soft (polyether, polyester, or polyetherester) blocks as well as their segment lengths. The composition and molecular weight of the polyamide hard segment determines the polymer melting point, processing temperatures, and mechanical properties at elevated temperatures. The soft segment influences the flexibility at low temperatures and the chemical and solvent resistance. Polyether soft segments have better low temperature
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1 Polymeric Materials properties and hydrolytic stability, whereas polyester soft segments have better solvent and thermal resistance and oxidative stability. Thermoplastic polyamide elastomers hardnesses range from 60–90 Shore “A” and from 25–63 Shore “D”, at temperatures between –40 °F and 176 °F. These materials have good abrasion resistance, comparable to thermoplastic polyurethane (TPU). Thermoplastic polyamide elastomer’s tensile strength, flexural modulus, and elongation properties are higher than those of any TPE material in the same hardness range. This is a consequence of the load bearing ability of the crystalline portion of the amide hard segment domains. All of these mechanical properties show an improvement after annealing above the Tg of the amide hard segment. The thermoplastic polyesteramide elastomer is a high temperature resistant elastomer that can withstand temperatures up to 338 °F continuously and 392 °F short-term exposure, while still retaining useful mechanical properties. The PESA elastomers have good compression set properties when measured under constant low load bearing conditions. Because of their high flexural modulus and high load bearing capabilities, the high flexural modulus test conditions generate high stress levels. However, when the hard segment domain becomes reorganized, it produces higher (poor) compression set values. The PESA elastomers are very resistant to long-term dry heat aging. The tensile strength properties improved after aging for 5 days at 302 °F (annealing). Similar studies were performed for the ester-based PESA elastomers at 347 °F with only small losses in properties. With the addition of heat stabilizers, polyetheresteramides exhibit improved heat resistance characteristics. The chemical composition of the soft segment is important in determining resistance to humid aging conditions. PESA elastomers are susceptible to hydrolysis attack (reduction of properties by lowering the polymer molecular weight). Appropriate use of hydrolysis stabilizers improves the humid aging characteristics of these polymers. PESA formulations become less susceptible to hydrolysis as their hardness increases, because the ester content is reduced. PETA and PEEA polymers show excellent retention of their original tensile strength properties in humid aging tests. Aromatic polyesteramide elastomers (PESA) exhibit good resistance to UV radiation under moisture conditions. PETA and PEEA polyamide elastomers have less resistance to ultraviolet radiation. However, most of the PEEA grades are available with UV stabilization to endure at least 2,100 hours of outdoor service. The polyamide elastomers’ hard segment greatly affects the chemical and solvent resistance of a segmented block elastomer, because the hard segment domains must maintain the integrity of the polymer. The semi-crystalline amide hard segment in polyamide elastomer (PESA) has low solubility in many solvents. Polyesteramide (PESA) has good resistance to oil, fuel, grease, and phosphatebased hydraulic fluids, but it has poor resistance to chlorinated solvents. Polyamide elastomers must be dried to 0.10% (minimum) or 0.02% (optimum) moisture content (depending on the type of resin) at temperatures from 160– 230 °F with the dew point between –22 to –40 °F for 4–6 hours for virgin resin straight from the bag and for 4–10 hours if the resin is wet, using a dehumidifying hopper dryer system before processing the resin.
1.4 Liquid Injection Molding Silicone (LIM®) It is possible to recycle sprues, runners, and rejected parts of polyamide elastomer resin after regrinding and drying the material. Blending from 10–15% of reground material with virgin resin is recommended to avoid any appreciable change in the characteristics of the molded parts. However, it is not advisable to recycle any reground material in parts that have a very critical functional requirement. Advantages • Hardness range from 60 Shore “A” to 63 Shore “D” • Temperature resistance 338 °F (continuous) and 392 °F (short-term) • Good thermal aging properties • Good chemical and solvent resistance to oil, fuel, and grease • Good impact strength, flexibility at low temperatures • Good tear strength and abrasion resistance • Easy processing by injection molding • It is possible to recycle from 10–15% of reground material. Disadvantages and Limitations • Poor compression set properties • Susceptible to hydrolysis attacks and ultraviolet radiation • Poor chemical resistance to chlorinated solvents • The resin must be dried before processing Typical Applications The end use applications of this new family of thermoplastic elastomers are just beginning to emerge in the following markets: • Hoses, tubing, bellows, and boot enclosures • Wire and cable jacketing, where mechanical toughness, oil, grease, solvent, and chemical resistance are required • Low pressure seals and gaskets • Recreational ski boot components, footballs, and basketballs • Shoe sole applications
1.4
Liquid Injection Molding Silicone (LIM®)
The chemical structures of silicones are different from other polymers. Organic hydrocarbon polymers are based on a backbone of carbon-to-carbon atoms. The silicones have a backbone of silicon-to-oxygen linkages. These linkages are much stronger than those in the organic hydrocarbon polymers; they resemble the Si–O linkages found in inorganic materials, such as quartz, glass, or sand. Silicones are more resistant to attacks by high temperatures, degradation, and oxidation type processes.
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1 Polymeric Materials
General Properties of Generic LIM Silicone Rubber Specific gravity
1.12
Tensile modulus @ 73 °F (psi)
36.0–230.0
Tensile strength (Kpsi)
1.15–1.25
Tear strength (lb/in)
160–250
Elongation at break @ 73 °F (%)
400–750
Compression set 22h @ 350 °F (%)
20–40
Thermal limits service temp. (°F)
–75 to 400
Shore durometer hardness
30 A – 70 A
Dielectric strength (V/Mil)
470–530
Dielectric constant @ 1,000 Hz
3.08–3.17
Shrinkage (%)
3.00
Process temp. (°F)
302–400
Mold temp. (°F)
300–400
Silicones perform well at low temperatures and remain stable at high temperatures; they can be sticky or slippery materials; they can protect against electrical shock; or they can conduct electrical current. Liquid injection molding compounds are a family of specially formulated products used to produce precision elastomeric parts efficiently and economically, using specially modified injection molding equipment. LIM® silicones differ from conventional thermoplastic polymers in the following manner: their viscosity is low, i.e., they have high flow rate properties; the material has the tendency to generate flashing problems during the injection molding process. To avoid the flashing problems, the mold tolerances must be tighter and higher clamping forces are required for the mold. The curing chemistry characteristic makes LIM® silicone a thermoset rubber polymer. For molding, the mold must be heated between 300–400 °F. LIM® cures quickly once the temperature has been reached. Therefore, the hardness of the mold cavities must be high, the molds must operate at elevated temperatures, and the molds must be vented to ensure even filling of the cavities. LIM® silicones are elastomeric materials that do not shrink when the molded parts are still in the mold cavities. The molded parts’ shrinkage (size reduction) takes place after the parts have been ejected from the mold, when the hot parts start to cool down at room temperature. The molded parts should be ejected from the lower or moving half versus the upper or fixed half of the mold. The mold ejection techniques used for processing rigid thermoplastic materials are not recommended for ejection of LIM® silicone parts from the mold. These techniques could damage the LIM® silicone surfaces that are in contact with the mold ejection mechanism system. Most LIM® silicone rubbers show shear thinning effects. The melt viscosity properties for shear rate values are between 500 and 10,000 s–1 and are critical for maintaining production of injection molded parts. A normal injection molding machine and mold are capable of generating shear rates of this magnitude. The molding operator can adjust the process conditions to mold parts efficiently.
1.4 Liquid Injection Molding Silicone (LIM®) The melt temperature affects the viscosity and the melt flow rate. The molder has to inject LIM® (A/B mixture) quickly and completely in the heated mold cavity before the melt temperature accelerates the cure or cross linking process. Higher injection speed and shorter injection forward time will increase productivity. The injection forward time (less than 5 s) should be faster than the mold curing time. Mold temperature should be high enough to reduce the cycle time.
1.4.1
LIM® Silicone Processing
Liquid injection molding was developed from room temperature vulcanizing technology. LIM® is a family of specialty products that use two liquid formulations in a 1 : 1 ratio. These liquid injection molding components are pumped from drums into meter mixing equipment and are automatically colored, catalyzed, and then transferred to the mold without the need of post curing. These compounds are used to produce precision elastomeric parts efficiently, at a lower cost, with high volume production. However, a special modified injection molding machine, a precision high-temperature mold, and a feeding, mixing, and injection system are required. Liquid Components Feeding System • Feeder Pump: Used for feeding and metering discharge pump, the pail pump should have follower plates, driven by either hydraulic or pneumatic systems. • Metering Discharge Pump: Used for metering the constant mixing ratio of the two components by volume, this pump should be a piston or screw hydraulic type. • The pumps should be made of stainless steel, and the internal components should be protected with Teflon®; the packing materials should be made from Teflon® and Viton® (fluorocarbon rubber); the hoses should be made from Teflon®, nylon, or polyester. Other components should be made from stainless steel with a Teflon® lining. • Mixer: The mixer is used for blending the matrix with several additive materials. The mixer could be either a static type or a hydraulically driven plasticizing screw used as a mixer. • Injector: The injector supplies pressure and temperature to inject the compounded mixture in the back of the injection molding barrel. The molding machine could be either a hydraulically driven plunger type or a reciprocating plastifying screw. Injection Molding Machine Modifications • Heater bands on the injection barrel and nozzle are replaced by water cooled jackets • Use corrosion resistant steel needed for the barrel, screw, and check valve • Extension nozzles are recommended to reduce the sprue length • Mold is heated to 300–400 °F with oil or electric heaters • Injection pressures required areranging from 800–3,000 psi • High clamping pressure must be used to prevent flashing
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1 Polymeric Materials • The barrel must be modified to seal the injectors and water coolant • A valved shut-off nozzle is required to prevent drooling LIM® Mold Requirements The molds are the most important component for injection molding LIM® silicone rubber parts. Processing demands on the molds are severe because of LIM’s low viscosities or high flow rates and high cure temperatures. LIM® molds are generally operated under higher temperatures and higher injection pressures compared to compression and transfer molding processes. At 400 °F, most steels are highly susceptible to galling. It is very important that the steels for LIM® molds be corrosion resistant and hardened. Hardening the steel of the molds allows the use of thinner steel mold plates. Steel hardening is one of the techniques to maintain close tolerances at elevated temperatures and increase the useful life of the mold by reducing steel wear. LIM® Mold Design Recommendations • Chrome plated tool steel, stainless steel, and hardened aluminum • The surface treatments for the LIM® molds are: nickel-TFE coating, chrome plating, and titanium nitride coating.
Figure 1-133 Soft touch encapsulated camera (Courtesy: GE)
• The cold runner cross section should be fully round, its size between 0.062 and 0.125 in diameter. • The type of gates should be pin-point or tapered edge gates. A large full base diameter between 0.031 and 0.087 in, the gate wall surface slightly tapered towards the cavity, and the tapered gate length between 0.050 and 0.100 in. • Mold vents are needed to remove the entrapped air from the cavities and runners. The vents also remove the polymer gas produced inside the plastifying unit. The depth of the vent (cavity and runner cold slot pocket) should range from 0.001–0.002 in, the width between 0.050 and 0.200 in, the land between 0.040 and 0.062 in. The depth of the vent scape channel should range from 0.062–0.093 in until it reaches the edge of the mold. The vents should be located on the upper or moving half of the mold.
Figure 1-134 Face mask seal (Courtesy: GE)
• The temperature of the lower or fixed half of the mold should be 10 °F–30 °F lower than the temperature of the upper or moving half, making sure that the molded parts will remain on the eject side of the mold. • LIM® molds must be thoroughly cleaned and degreased before installation. Lubricants should be applied only to guide pins and bushings and not on the surfaces contacting the mold cavities. LIM® molds must be maintained and stored in a clean environment. LIM® molded parts will stick to a trace of oil or grease in the mold cavities at normal mold temperatures between 300–400 °F. Any type of dirt speck will cause galling of the mold cavity surfaces. Advantages • Excellent thermal stability • Excellent weather resistance • Good electrical properties
Figure 1-135 Various injection molded parts (Courtesy: GE)
• Excellent chemical resistance • High temperature resistance
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1.4 Liquid Injection Molding Silicone (LIM®) • Low temperature impact resistance and flexibility • Hardness range from 30–70 Shore “A” • Low coefficient of friction • Low compression set Disadvantages and Limitations • High material cost • New metering equipment is required • Modifications or dedicated injection molding machine is required
Figure 1-136 Injection mold vacuum seal (Courtesy: GE)
• Special molds and dual high temperature controller are required • Material recycling is not possible • Limited storage life (one year) for the original unopened resin at temperatures of 73 °F or below Typical Applications • Medical and Health Care: – Foley catheters: Funnel and tip – Surgical irrigation bottle: Pull tabs for surgical, irrigation bags – Respiratory apparatus: Gaskets, nose pieces, diaphragms – Skin contact devices: Ear plugs, military/industrial masks, sports goggles, diving masks, snorkels, camera eye pieces, hearing aid ear pieces, eye glass nose pads – Dental mixing cups: For mixing epoxy compounds – Baby bottle nipples: Nipples, pacifiers – Cartridge chart rollers: For scanners – Cap liners: For medical and drug laboratory containers
Figure 1-137 Extruded flexible tubing (Courtesy: GE)
• Aerospace and Military: – Electrical connectors: Connector seals – Valves: Safety relief valve for life rafts and life vests – Diaphragms: Pressure sensing device for mines • Appliances, Electrical and Industrial: – Connector seals: Connectors for refrigerators, freezer lights, air conditioners – Bellows: Sealing of outdoor electrical apparatus – Diaphragms: Pneumatic valve actuators – Switch seals: Electrical equipment used outdoors – Nozzle for welding torches: Insulation of welding nozzles – Steam irons: Tubing for water/steam – Seals for oil exploration equipment: Encapsulation down hole instrumentation – Chip carrier trays: For baking semiconductor chips – RFI-EMI shields: Binder for metallic mesh – Camera bellows: For instant cameras – Temperature probes: For toaster ovens • Automotive: – Light bulb holders: For rear lights of heavy duty trucks – Light diffusers: For illumination of dashboard instruments – Connector seals: For electronic control module
Figure 1-138 Parts molded in different processes (Courtesy: GE)
Figure 1-139 Molded roller, washers and stop bottoms (Courtesy: GE)
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1 Polymeric Materials – – – – – – – –
Figure 1-140 Electrical weather-pack seals (Courtesy: GE)
Switch seals: Power window controls Fasteners/shock absorbers: Power seal controls Light gaskets: For water-proof lights Rain gutter gaskets: For PVC gutters Nail gaskets: For automatic nail guns Mercury vapor lamp gaskets: Outdoor illumination seals Wire seals: For telephone function boxes Drip irrigation: Water flow controllers for root irrigation
• Office Equipment: – Paper moving rollers: For printers and copy machine – Keyboard pads: Nonmechanical spring action devices for computer terminals and telephones, calculators, etc.
1.5
Thermoset Polymers
Thermoset compounds are organic polymers that cure to a solid and infusible mass by forming an irreversible three-dimensional network of covalent chemical bonds. Thermoset compounds are used in many applications. Construction represents the largest single market area, consuming about half of the compounds produced. Other applications include adhesives for plywood and particle board, binders for insulation, coatings, matrix resins for laminates, and electrical molding products. Thermoset compounds are polymers with a combination of mechanical, thermal, electrical, and chemical resistance properties that allow them to compete with metals, ceramic, and thermoplastic materials. Lacking the strength and stiffness of metals, nearly all thermoset compounds contain particulates or fibrous reinforcements. Fillers, such as calcium carbonate, glass flakes, and wood flour are added to reduce cost and increase the rigidity of the cured product. Fibers, such as glass, carbon, and polyaramid increase its strength, stiffness, and cost. The amount of fillers compounded ranges between 45 and 75%. Compared to metals, thermosets possess corrosion resistance, are lighter weight, have better insulating properties, and can be processed at lower pressures and temperatures. The flow characteristics of uncured thermoset compounds can be used to form large and complex shapes in one mold, allowing part consolidation and elimination of machining costs. The advantages of metal materials are high temperature performance, thermal and electrical conductivity, isotropic properties, ductility, and dimensional control. Compared to ceramic materials, thermosets offer lighter weight, better toughness, and easier processing. Ceramic materials provide improved high temperature performance, excellent chemical resistance, and hardness. For many applications, both thermoset and engineering thermoplastic resins are viable candidates. Selection of the preferred material depends on the specific combination of required properties and processing characteristics. Thermoset compounds offer advantages in terms of reduced creep and improved solvent/ stress crack resistance. The three-dimensional polymer networks in thermosets also improve the machinability, provide low rates of gas permeability, low mold shrinkage, and high temperature performance. The low initial viscosity of thermoset compounds permits the use of large amounts of fillers or fibrous
1.5 Thermoset Polymers reinforcements, which has led to the development of many low cost compounds. Unsaturated polyester and epoxy compounds are used for large reinforced structures (tanks and boat hulls), because these products can be cured at or near room temperature at ambient pressure. Engineering thermoplastic resins have the advantage in large volume production processes, where the injection molding cycle is fast and automatic. Although cure times below one minute are possible with some thermoset compounds, injection molding cycles for engineering thermoplastics are generally faster and less affected by small changes in processing conditions. The major limitation of thermosets is their poor impact resistance. Consequently, engineering thermoplastics are increasingly being considered for structural applications that require enhanced toughness. Although many thermoset compound properties are dominated by the type and amount of reinforcement rather than the basic matrix type, interest in engineering thermoplastics is high because of the capability of recycling and cost savings in the molding process compared to thermoset compounds. Thermoset compounds have excellent heat, creep, UV, and chemical resistance; they also have excellent dimensional stability, electrical properties, surface finish and low raw material cost. The key features of the main thermoset resin families are: • Polyesters vary from extremely flexible and resilient to very hard and brittle; from water-sensitive to chemical and UV resistant; from flammable to nonburning. The polymerization depends on maleic or fumaric acid. Allylic compounds from a special class of polyesters are polymerized through the double bond of allyl phthalates. These compounds have superior heat, chemical, insulation, and abrasion resistance, good dimensional stability, and surface finish. • Phenolics in their unmodified form are extremely hard and brittle, but with alcohol modifications, they become flexible. The reinforced grades have the highest creep resistance of all plastics, while featuring low cost, excellent heat and water resistance, good chemical resistance, and electrical and mechanical properties. • Melamines exhibit excellent heat and dimensional stability, electrical insulation, and moisture resistance; they are extremely hard and scratch-resistant. Reinforced melamines are used in electrical applications; however, most applications use the unreinnforced form. • Silicones offer a unique combination of organic and inorganic properties. Their thermal stability from 500–700 °F is outstanding. They also have excellent fire, water, and chemical resistance and excellent electrical properties. Silicones require high pressure for molding and their material cost is high. • Epoxies are relatively low in molecular weight; they are outstanding for their adhesive properties, excellent electrical properties, excellent strength, thermal, and dimensional stability, and excellent chemical and wear resistance.
1.5.1
Polyester Alkyd (PAK)
Polyester alkyds are formed by the reaction of polyhydroxy compounds with unsaturated maleic acids. The resulting unsaturation in the polymer backbone
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1 Polymeric Materials
General Properties of GR PAK Specific gravity
2.40
Tensile modulus @ 73 °F (psi)
1.90–2.00
Tensile strength @ yield (Kpsi)
3.0–10.0
Elongation at break @ 73 °F (%)
2.0–6.0
HDT (°F) @ 264 psi
350–500
Thermal limits service temp. (°F)
300 (short) 250 (long)
Water absorption @ 24 h (%)
0.10–0.50
Shrinkage (%)
0.10–1.00
Notch Izod impact73 °F (ft-lb/in) @
0.20–3.20
Dielectric strength (V/Mil)
250–530
Dielectric constant @ 50 and 100 Hz
3.0–8.0
Dissipation factor @ 50 and 100 Hz
0.007–0.11
Process temp. (°F)
290–350
can be utilized to cross link the polymer and form a thermoset compound. Polyester alkyd thermoset compounds are used for injection, transfer, and compression molding. A small percentage of high viscosity monomer compounded in the resin yields a relatively high melt flow rate, suited for large and complex parts. This benefit, together with excellent electrical properties, dimensional stability, and low cost make it suitable for a variety of applications in the automotive and electrical industries. Polyester alkyd compounds can be cured without additional molding pressure and do not release water when cured. Therefore, they can be used in a variety of coating applications. Polyester alkyds are primarily electrical materials; they combine good insulating properties at temperatures up to 300 °F for intermittent and 250 °F for continuous use, low resin cost, and good insert molding characteristics for delicate and complex inserts. Polyester alkyd compounds are also reinforced with fiber glass and minerals to provide substantial improvements in physical strength, impact resistance, and during the molding process. Advantages • Lower cost resins • Excellent dimensional stability and heat aging resistance • Good electrical and mechanical properties at high temperatures • Excellent insert compression moldability and high melt flow rates • Processable by several molding methods at low pressures • Uniform mold shrinkage and fast cure cycles • Compounds are available in several grades for different processes, melt viscosities, toughness, strength, insulation resistance, and finishes.
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1.5 Thermoset Polymers Disadvantages and Limitations • Chemical resistance is marginal • Poor solvent resistance Typical Application • Small electrical components, circuit breakers, coil forms, capacitors, and resistor encapsulations
Figure 1-141 Rowing shell
• Boat hulls and other fiber reinforced items • Sheet molding laminations • Coatings and filled molding compounds • Compounds can be modified with styrene or acrylic monomers • Suitable for fiberglass composites
1.5.2
Figure 1-142 Boat hull
Diallyl Phthalate/Isophthalate (DAP, DAIP)
General Properties of DAP Specific gravity
1.94
Tensile modulus @ 73 °F (psi)
1.40
Tensile strength @ yield (Kpsi)
7.50
HDT (°F) @ 66 psi @ 264 psi
500–670 450–550
Thermal limits service temp. (°F)
430 (short) 390 (long)
Water absorption @ 24 h (%)
0.12–0.20
Shrinkage (%)
0.10–0.90
Notch Izod impact73 °F (ft-lb/in) @
1.00
Dielectric strength (V/Mil)
400–450
Dielectric constant @ 106 Hz
3.8–4.4
Volume resistivity (Ohm-cm)
1010–1016
Dissipation factor @ 106 Hz
0.011- 0.017
Process temp. (°F)
290–350
Diallyl phthalate offers a balance of electrical insulating properties, volume resistivity, dielectric strength, and arc resistance. DAP retains these properties even under long-term exposure to high heat and humidity conditions. Diallyl phthalate resins are products of the reaction of allyl alcohol and an organic acid or anhydride. The monomer diallyl phthalate can be prepared by the direct esterification of allyl alcohol and phthalic anhydride, which is then partially polymerized to a fusible resin or prepolymer by being heated with a free radical initiator. This diallyl phthalate prepolymer, combined with a free radical initiator and various fillers, constitutes a diallyl phthalate molding compound. There are two molding compound types of diallyl phthalate resins: the orthoresin diallyl phthalate (DAP) and the metaresin diallyl isophthalate (DAIP). The orthoresin is the most commonly used; it provides excellent electrical properties, while the metaresin provides superior heat resistance characteristics.
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1 Polymeric Materials The most frequently used compounds are short glass fiber reinforced, which represent approximately 70% of the market. The remaining 30% is divided fairly evenly between long glass fiber reinforced and mineral filled compounds. DAP molding compounds are available only as a filled system and are supplied complete with catalyst, pigment, and mold release. Its physical form varies with the type of reinforcement used. Mechanical properties of diallyl phthalate vary widely, depending on filler or reinforcement type and quantity. Because of its extremely stable carbon-to-carbon linkage and its tight knit three-dimensional structures, fully cured DAP is extremely resistant to creep or cold flow, moisture, strong and weak acids, alkalis, and organic solvents. Moisture has very little effect on the dielectric strength of the molded parts. Figure 1-143 Automotive distributor cap
Thermal properties may be classified into long- and short-term heat resistance. DAIP has better heat resistance than DAP, with use temperatures approximately 20 °F higher than the typical 370 °F of DAP and typically has heat deflection temperatures from 450–550 °F. DAIP has a UL temperature index of 390 °F. DAP molding compounds process extremely well, using any conventional thermoset molding equipment, such as compression, transfer, or injection molding. Diallyl phthalate molding compounds have a high degree of dimensional stability when molded. Mold temperatures may slightly affect part dimensions with differences in the coefficient of thermal expansion. The degree of cure affects several DAP properties: chemical resistance, heat deflection temperature, and most electrical properties will be reduced without proper cure.
Figure 1-144 Cook ware handle
A wide variety of molding compounds is made from these two base resins. Fillers, such as short and long glass fibers, minerals (talcs, clays, aluminum trihydrates), and synthetic fibers are compounded with the resins to obtain specific properties. Because of the catalyst systems used, DAP has a room temperature shelf life of over a year. Advantages • Excellent electrical insulating properties, volume resistivity, dielectric strength, and arc resistance Figure 1-145 Electrical bobbin
• Excellent creep or cold flow resistance under long-term exposure to high heat and humidity conditions • Good moisture resistance • Low burning and self-extinguishing grades are available • Heat deflection temperatures from 450–550 °F at 264 psi • DAIP compound has a UL temperature index of 390 °F
Figure 1-146 Computer chip housing
• Good chemical resistance to strong and weak acids, alkalis, and organic solvents. Disadvantages and Limitations • Low impact resistance • Mold temperatures and curing time are critical process parameters
Figure 1-147 Computer micro processor housings
• Expensive compound • Not recommended for use in contact with phenols and oxidizing acids
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1.5 Thermoset Polymers Typical Applications • Electrical and electronics, connectors, potting cups, switches and electrical bobbins. DAP connectors are used in aerospace or military applications (100% reliability). DAP connectors are used in communications equipment and computers, in wet or humid environments • Appliance handles • Automotive distributor caps
1.5.3
Melamine Formaldehyde (MF)
General Properties of MF Specific gravity
1.94–2.00
Tensile modulus @ 73 °F (psi)
2.40
Tensile strength @ yield (Kpsi)
5.90–7.00
HDT (°F) @ 264 psi
360–400
Thermal limits service temp. (°F)
300 (short) 170 (long)
Water absorption @ 24 h (%)
0.09–0.30
Shrinkage (%)
0.70–0.90
Notch Izod impact73 °F (ft-lb/in) @
0.25–0.35
Dielectric strength (V/Mil)
170–370
Dielectric constant @ 106 Hz
6.60–7.90
Volume resistivity (Ohm-cm)
1012
Dissipation factor @ 106 Hz
0.013–0.016
Curing temp. (°F)
310–335
Figure 1-148 Electric circuit breaker housing
Melamine formaldehyde molding compounds are produced by the reaction of the NH2 amino group with formaldehyde. Melamines are produced with α-cellulose fillers, which permit an unlimited range of colors. They exhibit excellent surface hardness and resistance to abrasion, excellent compressive strength and resistance to deformation under load. They are also good insulators and have excellent electrical and thermal resistance. Melamine formaldehyde compounds reinforced with fiber glass and/or minerals have better electrical, thermal, and impact strength properties; however, they are available in fewer colors.
Figure 1-149 Heated plate for baby food
Because melamine formaldehyde compounds filled with cellulose have been approved by the FDA for use in food contact applications, dinner ware is the single largest end use of melamine molding compounds. Melamine formaldehyde is listed in Underwriter’s Laboratories index of recognized components. The chemical resistance of melamines is poor; under elevated temperatures they are attacked by strong acids and alkalis. Urea formaldehyde is generally available only with cellulose fillers, while melamine formaldehyde molding compounds are available with cellulose, mineral, or glass fiber fillers. Melamine formaldehyde molding compounds can be compression, transfer, or injection molded. Although the materials are available in powder form, a
Figure 1-150 Office accessories
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1 Polymeric Materials granular form is preferred for most molding applications. Injection molding requires the use of equipment designed specifically for thermosets. Melamines are available in a broad range of flow rates and cure capabilities. Because water is given off during curing, the molding equipment must include a means to remove this moisture. Advantages • Melamines filled with cellulose have been approved by the Food and Drug Administration for use in food contact applications • Good insulators, both electrically and thermally Figure 1-151 Dinnerware in various colors
• Melamine fiber glass and/or mineral reinforced grades have excellent electrical properties • Excellent surface hardness, abrasion resistance, and compressive strength properties • Melamines can be processed by compression, transfer, and injection molding • Alpha cellulose filled compounds come in an unlimited range of colors and exhibit good physical and electrical properties • Melamines have excellent storage life charactersitics Disadvantages and Limitations • Melamine has poor chemical resistance to strong acids and alkalis. • Melamine filled with fiber glass or mineral are limited in color availability and their specific gravity is higher. • Moisture removal equipment is required during mold curing. Typical Applications • Electrical Industry: Circuit breaker arc chutes and a great variety of other electrical wiring devices, wall plates, switch toggles, closures, buttons, stove hardware, and small housings. • Common Applications: Dinnerware for household and institutional use, ashtrays, office accessories, clothing buttons, and jewelry
1.5.4 Figure 1-152 Extrusion profiles
Cellulosic Ester
Cellulose nitrate, more than 100 years old, is man’s first successful effort in modifying a natural polymer to improve its processibility. Celluloid and pyroxylin were two forms of this resin used in many molded components and coated articles. Also known as gun cotton, it is rarely used today in plastic applications because of its high flammability. It has been almost entirely displaced in thermoplastic applications by cellulosic thermoplastic compounds, such as cellulosic acetate (CA), cellulosic butyrate (CAB), and cellulosic proprionate (CAP). Advantages • Good electrical properties
Figure 1-153 Structure platform
• Good impact strength
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1.5 Thermoset Polymers • Good processibility • Excellent surface finish • Non-petrochemical base • Moderate resin cost Disadvantages and Limitations • Poor chemical resistance to solvents, alkaline materials, and fungus • High moisture absorption and permeability
Figure 1-154 Automotive steering wheel
• Poor long-term weatherability • Poor flammability Typical Applications • Telephone components, eyeglass frames, audio tape cases, tool handles
Eraser
• Automotive steering wheels, structure platforms • Extrusion profiles • Pens external strucrures
1.5.5
Figure 1-155 Pencil external body
Cyanate
General Properties of Cyanate Polymers Specific gravity
1.10–1.35
Tensile modulus @ 73 °F (Mpsi)
0.45–0.50
Tensile strength @ yield (Kpsi)
10.0–13.0
HDT (°F) @ 212 psi
450–500 (dry) 212–390 (wet)
Thermal limits service temp. (°F)
450 (short) 350 (long)
Water absorption long-term @ 212 °F (%)
1.30–2.40
Shrinkage (%)
0.40
Torsion toughness @ 73 °F (ft-lb/in)
0.60–1.20
Coefficient of thermal expansion (10–6 in/in/°F)
33.0–39.0
Dielectric constant @ 106 Hz
2.70–4.90
6
Dissipation factor @ 10 Hz
0.001–0.005
Flammability rating (UL-94)
V1 V0
Curing temp. (°F)
350–480
Cyanate resins, also known as cyanate esters, cyanic esters, or triazine resins, feature the polymerizable functional group –O–C≡N on an aromatic backbone. They are derived from bisphenols or polyphenols and are available as monomers, oligomers, blends, and solutions, providing an alternative to epoxy resins. Cyanate resins are chemically cures when heated. Their functionality undergoes cyclotrimerization to form symmetrically substituted triazine structures. This
Body
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1 Polymeric Materials ring-forming additional polymerization results in a thermoset network of oxygen linked triazine rings (cyanurates) and bisphenol esters/ethers. Cured cyanate resins are classified as polycyanurates, a type of polyarylate, or wholly aromatic polyester that is cross linked. The unique properties associated with cyanate resins and their ring-forming polycyanurate reaction characteristics are: • Purity. Crystalline monomers are supplied at over 99% pure. Ionic and potentially ionizable impurities are typically less than 10 ppm. • Reactivity. Cyclotrimerization rates are essentially catalyst dependent. A variety of transition metal carboxylates and chelates (latent) are available to provide a cure response ranging from one minute to shelf stable prepreg curing at 350 to 480 °F. • Compounding with Epoxy Resins. Formation of chain extending oxazoline rings and catalysis of excess epoxide permits formulation of hybrids containing up 70 to 80% epoxy resin. • Toughness and Tg. Toughness properties indicated by impact strength, fracture toughness, strain at break and adhesive peel strength are high for 480 °F Tg resins • Volume Expansion after Gelation. Increasing volume noted with conversions of over 65% eliminates stress inducing shrinkage at cure temperature. • Low Dielectric Loss. The dielectric constant (2.7–4.9) and dissipation factors (1–5 × 10–3) are unusually low for high Tg resins. • Low Moisture Absorption. Weight gain in boiling water is (1.3–2.4%). Long term stability in 212 °F water is achieved with epoxy modification. Unreinforced polymers such as cyanate homopolymers, toughened bismaleimides, epoxies of the diglycidylether and tetraglycidylamine types are cured with aromatic diamines. Polycyanurates match the toughness and adhesion of difunctional epoxies while providing elevated temperature service mid-range between the more brittle tetrafunctional epoxies and toughened bismaleimides. The epoxy-modified cyanates systems are used widely in aerospace composite applications and retain a higher percentage of original heat deflection temperature. The best performers in long term boiling water/steam environments are formulated with 1.0–1.8 epoxide equivalent. Fiber glass reinforced circuit board laminated with woven E-glass provides the following differences in performance between the unmodified cyanate resins: Dielectric loss properties are lowest for o-methylated. The flame retardant (100% epoxy) laminates, by comparison, have dielectric constant and dissipation factor values of 4.9 and 0.001, respectively. The laminates are rated self-extinguishing in the UL-94 V1 to V0 categories. The absence of halogen modification increases the onset temperature of rapid thermal degradation by approximately 212 °F. The onset temperature of the homopolymer is 765 °F, compared to 545 °F for a flame retardant blend with brominated epoxy resin. Toughness, as indicated by a 90° peel strength for one ounce copper foil cladding test, is superior for unmodified resins. Epoxy resin blends do not require curing at temperatures exceeding 350 °F and retain an excellent balance of properties at 60% modification.
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1.5 Thermoset Polymers Carbon fiber reinforced base cyanate composites have upper temperature limits of hot and wet service in the range of 265–320 °F, depending on the test temperature, conditioning, fiber form, and post cure temperature. A variety of resin physical forms, including crystalline monomers, amorphous semisolid prepolymers or oligomers, powderable hard prepolymers, solvent solutions and blends, are offered for impregnating woven and unidirectional reinforcements. Advantages • Constant mechanical properties above 85% conversion • No volatiles evolved during cure (epoxy alternative) • Short-term temperature stability to 450 °F • Long-term stability at continuous service temperatures up to 350 °F • Lower dielectric loss characteristics • Excellent adhesive strength at 480 °F • Self-extinguishing flammability rating (V1-V0) • Dicyanates provide greater toughness and increased resistance to strong solvents • Sulfur-linked structures have good solvent resistance • Low cure temperatures, increased steam resistance, and reduced cost • Prepolymers have excellent hot melt processibility characteristics • Dicyanates with Tg in the range from 465–520 °F develop higher fracture toughness and strain at break values • Dicyanates are used as an impact modifier (15–20%) for some thermoplastic polymers • Improved dimensional stability, because denser, finer circuit patterns interconnected between layers are more prone to failure from differential movement caused by dissimilar expansion coefficients and swelling in cleaning solvents, etching agents, and strippers. • Elimination of corrosion caused by resin impurities, epichlorohydrin residues, attacking conductor metals in hot and wet environments. • Lower dielectric loss characteristics reduce dielectric constant and dissipation factor in high-frequency, elevated temperature service. • Improved field reparability, needed to prevent blistering and loss of adhesion when mainframe computer boards are soldered manually. Laminate surface temperatures can reach 660 °F, resulting in rapid decomposition of brominated flame retardants. Disadvantages and Limitations • Moisture absorption • High shrinkage during curing. • Limited availability • Comparatively high cost
Figure 1-156 Electronic print circuit board
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1 Polymeric Materials Typical Applications • Adhesives and composites • Thermoplastic impact modifier (15–20%) • Printed wiring boards • Fiber glass reinforced cyanate used for large boat hulls • Composite components for aerospace applications • Replacement for epoxy resin in applications requiring high reliability
1.5.6 Figure 1-157 Boat hull
Epoxy (EP)
General Properties of Epoxy Polymers Specific gravity
1.84
Tensile modulus @ 73 °F (Mpsi)
3.00
Tensile strength @ yield (Kpsi)
18.0
HDT (°F) @ 212 psi
300–460 (dry) 212–300 (wet)
Thermal limits service temp. (°F)
450 (short) 350 (long)
Water absorption long-term @ 212 °F (%)
2.0–6.0
Shrinkage (%)
0.60
Torsion toughness @ 73 °F (ft-lb/in)
0.40–1.20
Coefficient of thermal expansion (10–6 in/in/°F)
60–70
Dielectric strength (V/Mil)
300
6
Dissipation factor @ 10 Hz
0.030
Flammability rating (UL-94)
HB V0
Curing temp. (°F)
300–430
Epoxy resins are available in a wide variety of thermosetting structures and curing agent variations. The name epoxy is for the products that have in common an epoxy ring consisting of two carbon atoms single bonded to an oxygen atom. There are two types of epoxies. Those polymers made by a reaction with epichlorohydrin are known as glycidyls, while those made by per oxidizing olefins are known as cycloaliphatics. The epoxidized phenols, or phenol glycidyl ethers, are the most commercially important resins, particularly epoxidized bisphenol A, known as the diglycidyl ether of bisphenol A (DGEBA). This resin provides an excellent balance of physical, chemical and electrical properties. Epoxidized phenol novolacs are also available in a range of viscosities. Epoxies are used in combination with a coreactant, or curing agent. Therefore, the final composite properties are influenced by the choice of coreactant. The large number of coreactants available include amines, anhydrides, acids, phenolics and amides, thereby providing a broad spectrum of performance possibilities. Figure 1-158 Bus external panels and doors
After aromatic glycidyl ethers, the epoxidized alcohols, glycols and polyols, or aliphatic glycidyl ethers, are considered most valuable. They are typically used in combination with DGEBA resin to allow better processing. These materials
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1.5 Thermoset Polymers are often very low in viscosity, which makes them highly attractive as dilutents for the more viscous phenolic base products; they can also improve flexibility and toughness properties, although this is generally at the expense of thermal and chemical resistance, particularly if the dilutent is mono functional. The most common members of this group are epoxidized butanol, known as butyl glycidyl ether and the epoxidized long chain mono alcohols. Most epoxies are thermoset materials; however, there are some situations in which high molecular weight versions of DGEBA can be used strictly as a thermoplastic, such as for coating applications to provide very flexible coatings. Most applications can be satisfied by an epoxy resin because the resin and curing agent selection is so large. For example, the cured physical properties of different epoxy systems can be modified by substituting a different curing agent (hardener) to the same epoxy. It is therefore possible to upgrade the performance of a composite structure by simply utilizing a different epoxy resin or curing agent.
Figure 1-159 Mono-train external shell structure
Physical properties can thus be varied over a wide range of rigidity and flexibility. This group of resins created the structure for the adhesive industry, as well as being used extensively in the fiber reinforced composite industries. Performance properties of the final composite depend on the resin system used. Epoxy composites have ratings from good to excellent for electrical resistance, good chemical resistance, and reasonably high glass transition temperatures. The use of fillers can often raise the Tg, reduce shrinkage, and increase the thermal conductivity and thermal resistance of the composite. The amount of filler used depends on the rheology of the system, the particle size, and the oil absorption tendency of the particular filler.
Figure 1-160 Office chair structural shell
In addition, high flexural strength may require the addition of mica or fiber glass, while silica might be best for chemical and abrasion resistance. A major weakness of epoxy resins is their poor ultraviolet resistance and weathering. Processing of high performance composites is quite complex; particularly, if a multiple-step cure schedule is required to achieve the highest possible thermal resistance in the composite structure. Epoxies used in composites are cured by an addition cross linking mechanism, which does not generate volatile byproducts. Part dimensions can be influenced by the cure, particularly if the cure temperature is too high, because a very vigorous exotherm can be generated, causing excessive shrinkage and changing the composite structure.
Figure 1-161 Electrical power line insulators
Epoxy resins are generally liquids that range from low viscosity for the epoxidized alcohols to very high viscosities for the epoxidized phenol novolac (EPN) resins. Low viscosity EPN resins have recently been developed; curing agents can be low viscosity liquids or solids, such as diaminodiphenyl sulfone. Advantages • Excellent balance of physical, thermal, chemical, and electrical properties • Convenient range of cure conditions from 73–350 °F • Thermal stability for continuous service temperatures up to 350 °F • No volatiles formed during cure • Excellent high-temperature adhesion • Suitable for all thermosetting processing methods
Figure 1-162 Bathroom solid counter top
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1 Polymeric Materials Disadvantages and Limitations • Processing high performance composites is complex • High cure temperatures cause excessive shrinkage and change the structure of the part • Poor ultraviolet resistance and weathering • Poor oxidative stability and some moisture sensitivity Figure 1-163 Epoxy coated corrosion resistant structural steel
• Specialty grades are comparatively expensive Typical Applications • High Performance Aerospace: These resins provide excellent elevated temperature resistance as well as good mechanical properties. The most commonly used epoxy resin is tetraglycidyl methylene dianiline (TGMDA). When cured with agent diaminodiphenyl sulfone, it provides excellent high performance composite structures.
Figure 1-164 Racing bicycle external shell
• General Purpose: DGEBA is the preferred material. The choice of curing agents includes aromatic and aliphatic amines or anhydrides, because they provide the best balance of cost and performance. Applications include pipes, automotive accessories, adhesives, composites, coatings, and sporting goods. • Electrical: Epoxies are used to prepare printed wiring boards and electronic encapsulations, which represent the most important applications. Because flame retardancy is a requirement in these applications, a specialty halogenated epoxy is often used. The curing agent is often an amine curing agent known as dicyandiamide, which needs a cure accelerator, such as N,N-dimethylbenzylamine.
1.5.7
Phenol Formaldehyde (Phenolic, PF)
General Properties of PF Thermosets Specific gravity
1.74–1.88
Tensile modulus @ 73 °F (Mpsi)
1.90–2.28
Tensile strength @ yield (Kpsi)
6.0–10.0
Elongation at break @ 73 °F (%)
0.20
HDT (°F) @ 264 psi
410–525
Thermal limits service temp. (°F)
450 (short) 350 (long)
Notch Izod impact @ 73 °F (ft-lb/in)
0.75–0.90
Shrinkage (%)
0.20–0.40
Dielectric constant @ 50-100 Hz
5.0–7.0
Dielectric strength (V/Mil)
300
Dissipation factor @ 106 Hz
0.030
Water absorption @ 24 h (%)
0.10–1.00
Curing temp. (°F)
330–390
1.5 Thermoset Polymers Phenolics, discovered in 1907 by Dr. Leo Baekeland, are one of the oldest types of thermosetting compounds. Phenolics are now considered the work horse of the plastics industry. Phenolic molding materials are high-performance thermoset compounds. With the heat and pressure of the molding process, PFs react to form a threedimensionally cross-linked molecular structure. This structure yields excellent dimensional and thermal stability with high load-bearing capability at elevated temperatures. Phenolics are used for close tolerance precision molded components that must function in hostile environments. Phenolic resins are products of the condensation reaction of phenol and formaldehyde. Water is the by-product of this reaction. Substituted phenols and higher aldehydes may be incorporated to achieve specific properties, such as reactivity and flexibility. A variety of phenolic resins can be produced by adjusting the formaldehyde/phenol ratio, the process temperature, and the catalyst. Two distinct types of resin are produced for use in phenolic molding materials: • Single stage (resole) resin is produced with an alkaline catalyst and a molar excess of formaldehyde. The reaction is carefully controlled to allow the production of a low-molecular weight, noncross-linked resin. Single-stage resins complete the curing reaction in a heated mold with no additional catalyst to form a three-dimensionally cross linked, insoluble, infusible polymer. • Two stage-(novolac) resin is produced by the acid catalyzed reaction of phenol and a portion of the required formaldehyde. The resulting resin product is a brittle thermoplastic at room temperature. It can be melted, but it will not cross link. Novolac can only be cured by the addition of a hardener, which is almost always formaldehyde supplied as hexamethylenetetramine (hexa). Upon heating, hexa decomposes to yield ammonia and the formaldehyde needed to complete the cross linking reaction. The unreinforced phenolic polymer is a very brittle material. However, a wide range of properties can be obtained by using a variety of fillers. These fillers and reinforcements (45–65%) of the formulations impart the mold processing properties. Lubricants, colorants, and other modifiers are also used. Wood flour or cellulosic filler yields a molding material with a balance of properties and cost effectiveness. The typical Underwriter’s Laboratories end use temperature index is 300 °F. Improved impact and toughness properties can be achieved with cellulosic fibers while maintaining a substantial creep modulus. Modification with mineral fillers up to 45% yields rigidity with improved dimensional and thermal stability. Reduced water absorption and lower coefficient of thermal expansion can also be obtained. Glass fiber reinforcement yields substantial improvement in dimensional stability, rigidity, and mechanical properties. Glass fiber reinforcement can be tailored to equal the thermal expansion of metals. The UL end use temperature index is 355 °F. Specialty grades can be formulated with graphite, Teflon®, and elastomer particles for improved toughness and/or self lubricating capabilities. Phenolic materials are available in black and brown colors. Phenolics are not stable under ultraviolet radiation. They are inert to most common solvents and weak acids and they have excellent resistance to natural oils, fats, greases, petroleum products, and automotive fluids. Resistance to strong acids and alkaline reagents is poor.
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1 Polymeric Materials Unfilled phenolic resins are available in flake, powder, or liquid form. Filled/ reinforced phenolic molding materials are available in granular, pellet, or flake form. Advantages • Moldability: Phenolics offer both processing and performance advantages; they can be molded by injection, compression, or transfer processes. • Dimensional Stability: Phenolics retain dimensional stability for an indefinite period of time under normal atmospheric conditions. • Creep Resistance: Phenolics have a high degree of resistance to deformation under load, especially at elevated temperatures. • Thermal Stability: Phenolics can withstand 300 °F continuously; certain grades are resistant to 450 °F for short periods and 350 °F for extended periods of time. • Hardness: The cross linked nature of phenolics makes them one of the hardest plastics available. • Excellent electrical insulation properties • Excellent resistance to solvents and automotive fluids • Comparatively low cost • High tensile modulus (rigid) and compressive strength • Self-extinguishing Disadvantages and Limitations • Poor chemical resistance to alkaline reagents • Requires fillers for molding compounds • Poor resistance to bases and oxidizers • Volatiles released during cure (condensation of the polymer) • Limited to dark colors because of oxidation discoloration Figure 1-165 High capacity mini compact disk (CD)
Typical Applications • Industrial: Plywood and particle board, brake and clutch linings, fiberglass, cellulose, foam insulation, grinding wheels and coated abrasives, adhesives and glues, coatings and varnishes, electrical and decorative laminates • Electrical: Wiring devices, switch gear, circuit breaker, commutators, brush holders, and connectors • Appliances: Knobs, handles, and heated components for toasters, broilers, and steam irons, motor housings, and timer cases • Automotive: Disc brake caliper pistons, power assist braking components, accessory drive pulleys, water pump housings, solenoids, ashtrays, and transmission components
Figure 1-166 Coffee maker support base
• Special Purpose: Single stage materials are also used for pump housings, vaporizers, steam irons, closures, and to hermetically seal encapsulation for electrical devices
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1.5 Thermoset Polymers
1.5.8
Polybutadiene (PB)
This thermosetting resin is cross-linked by means of its pendant vinyl group in the prepolymer stage. The hardness and cross-link density are a function of the severity of post cure time and temperature. The cross linkable polybutadiene shows surprisingly good thermal stability and electrical properties; particularly in its low dielectric constant. Some modifications have reactive terminal hydroxyl or carboxyl groups useful for other polymer hybrids, such as polyurethanes. Advantages • Good electrical properties • Low polarity Disadvantages and Limitations • High shrinkage • Thermal capability is a function of the curing conditions Typical Applications • Electrical components, particularly those that require some degree of thermal stability and low dielectric constant • High-temperature film • Tubing and hoses
1.5.9
Bismaleimide (BMI)
The bismaleimide (BMI) families of thermosetting resins are excellent materials for high-temperature aircraft and aerospace applications. The reaction of two molecules of maleic anhydride with one molecule of diamine is the processing step for manufacturing BMI polymers. The intermediate bismaleamic acid can be formed at room temperature in solvents such as methylene chloride, toluene, or dimethylformamide. The dehydration, or imidization, reaction is obtained using acetic anhydride with a catalytic of sodium acetate at 195 °F, then refluxing the intermediate acid in dimethylformamide, or heat treating the bismaleamic acid alone. The common manufacturing process for BMI is the reaction product between methylene dianiline (MDA) and maleic anhydride, which results in bis(4maleimidodiphenyl)methane (MDA BMI). To improve processibility and eliminate some of the brittleness associated with the original MDA BMI formulation, a mixture of three BMIs is used; a chain extended BMI results from the addition of the MDA BMI, MDA, and a BMI based on 2,5-diaminotoluene. Another BMI product receives a low melting point from the mixture of the BMIs; MDA, toluene diamine, and trimethyl examethylene diamine. This mixture has a low melting point range between 158 and 257 °F and is capable of impregnating reinforced cloth and fibers by using a hot air gun. This technique allows the formation of complex shapes during vacuum bagging steps. The curing, or polymerization, reaction of BMIs occurs through the maleimide double bond. This type of functionality gives rise to an addition-type curing,
Figure 1-167 Polybutadiene (PB) – applications
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1 Polymeric Materials that is, curing without the evolution of volatiles. Because BMIs are thermoset resins, final cured structures have highly cross linked networks that are infusible and insoluble. Depending on whether coreactants are absent or present, BMIs cure differently. By allowing the diallyl compound (toughening agent) to coreact with the double bond of the maleimide, better toughness is obtained. Processing BMI prepregs into parts for structural applications requires an autoclave cure and a free standing post cure. A typical cure may consist of the following steps: Autoclave cure • 1 hour at 144 °F and 100 psi. • 4 hours at 351 °F and 100 psi. • 4 hours at 399 °F and 100 psi. Post cure (free standing) • 4–24 hours at 428–500 °F with a slow cool down at 3 °F/min. Advantages • Continuous service temperature of 350 °F under moist environment conditions • Excellent high strength and corrosion resistance • Excellent high degree of hardness, lower weight, and rigidity • Excellent chemical resistance Disadvantages and Limitations • Brittleness problems • Micro cracking problems • Autoclave curing method for fabricating aerospace parts, the original BMI materials were unacceptable • Long autoclave and post cure cycles • Special manufacturing equipment and processing techniques are required Typical Applications • Aircraft and aerospace components • High temperature electronic components
1.5.10
Unsaturated Polyester (UP)
The commercial use of fiber glass reinforced thermoset unsaturated polyester resins began in 1942, when polyester resin was combined with glass fiber reinforcement to produce protective housings for radar equipment. Unsaturated polyester resins are used in a wide variety of markets, including construction, marine, and transportation, industrial, electrical, and sanitary ware. Because they are frequently used in conjunction with styrene, fabrication shops using these unsaturated polyester materials have pronounced styrene odor levels.
99
1.5 Thermoset Polymers
General Properties of UP Thermosets Specific gravity
1.75–1.90
Tensile modulus @ 73 °F (Mpsi)
1.90–2.00
Tensile strength @ yield (Kpsi)
10.0–15.0
Elongation at break @ 73 °F (%)
0.50–5.00
HDT (°F) @ 264 psi
390–400
Thermal limits service temp. (°F)
250 (short) 200 (long)
Notch Izod impact @ 73 °F (ft-lb/in)
0.70
Shrinkage (%)
0.20
Dielectric constant @ 50-100 Hz
3.8–6.0
Dielectric strength (V/Mil)
450–530
6
Dissipation factor @ 10 Hz
0.01–0.04
Water absorption @ 24 h (%)
1.00
Curing temp. (°F)
170–320
Unsaturated polyester resins are manufactured by the condensation polymerization of dibasic acids or anhydrides with dihydric alcohols with the dibasic acid or anhydride being partially or completely composed of a 1,2-ethylenically unsaturated material, such as maleic anhydride or fumaric acid. The resultant polymer can vary from a high viscosity liquid (brittle) to a low melt solid material. The polymer is then dissolved in a liquid reactive vinyl (1,2-ethylenically unsaturated) monomer such as styrene, vinyl toluene, diallyl phthalate, or methyl methacrylate to give a solution with a viscosity in the range of 2.0–20.0 Poise. Unsaturated polyester resins are used as replacements for natural materials, such as wood, concrete, marble, steel, and aluminum. Unsaturated polyester resins are commonly chosen because of their ease of fabrication, lower weight, higher strength, corrosion resistance, and lower cost. General classifications of unsaturated polyesters are based on one common building block used in the polymer chain. Descriptions for each of these five unsaturated polyester families are listed below: • Orthophthalic polyester resins are manufactured from combinations of phthalic anhydride and either maleic anhydride or fumaric acid (general purpose resins). • Isophthalic or terephthalic polyester resins are the result of a combination of isophthalic acid or terephthalic acid; they are higher quality resins with better thermal resistance, mechanical properties, chemical resistance, and higher in cost. They are easier to process and have better solubility in reactive monomers such as styrene. • Bisphenol A (BPA) fumarates are manufactured by the reaction of propoxylated or ethoxylated BPA with fumaric acid. The aromatic BPA fumarate resins have a higher degree of hardness, rigidity, good chemical resistance, and improved thermal performance. BPA fumarates are used exclusively in high performance applications.
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1 Polymeric Materials • Chlorendics use a combination of chlorendic anhydride or HET acid with maleic anhydride or fumaric acid. These polymers show some chemical resistance and flame resistance improvements because of the presence of chlorine. Figure 1-168 Racing boat hull
• Dicyclopentadiene can also be incorporated into unsaturated polyesters. The resultant alicyclic groups enhance resistance to thermal oxidative decomposition at high temperatures; these compounds are used in high temperature electrical applications. The use of a reinforcing fiber to produce an unsaturated polyester composite dramatically improves both tensile and flexural characteristics.
Figure 1-169 Surf board structure
Inorganic fillers are used in unsaturated polyester resin compounds. They improve stiffness, increase modulus, and they exhibit little effect on corrosion and are used to reduce cost. Mechanical properties at elevated temperatures show the differences in the glass transition temperature (Tg) of the various resins. The rigid and high Tg for BPA fumarate or chlorendic polyesters retain flexural strength up to 250 °F.
Figure 1-170 Automotive external panels, hoods, and doors
Figure 1-171 Racing car external shell
Polyester resins are used in elevated temperature applications, especially in electrical and corrosion resistant areas. Polyester resins have been used for many years in applications requiring resistance to chemical attack. Chlorendics are preferred for use in strong acid environments, especially at elevated temperatures, while BPA fumarate is better in strong basic solutions. However, isophthalic polyesters are the workhorse of the industry. Almost all organic polymers have good electrical properties. Thermal stability and electrical performance at elevated temperatures are directly related, by comparing the retention of dielectric strength at 390 °F with the retention of flexural strength at 390 °F. Vinyl toluene outperformed a styrene-based system in both instances. At temperatures above 390 °F, BPA fumarate outperformed isophthalic polyester when both were used with vinyl toluene. Unsaturated polyester resins are required to have some degree of resistance to burning, which can be accomplished either by simply using a filler or by incorporating halogen into the unsaturated polyester matrix. Advantages • Ease of fabrication, lower weight, higher strength, corrosion resistance, and lower cost • Isophthalic polyester resins have better thermal resistance, mechanical properties, chemical resistance (solubility in reactive monomers) • BPA fumarate resins have a higher degree of hardness, rigidity, good chemical resistance, and improved thermal performance • Chlorendic resins have excellent chemical resistance and some flame resistance • Dicyclopentadiene unsaturated polyesters are widely used in high temperature electrical applications • Tooling construction is fast, simple, and inexpensive • Non-burning halogenated grades are available
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1.5 Thermoset Polymers Disadvantages and Limitations • Orthophthalic resins have poor chemical resistance and process limitations • Orthophthalic phthalic polyester resins have very poor thermal stability performance at elevated temperatures • Isophthalic polyester resins cost more • Poor solvent resistance
Figure 1-172 Home furniture, chairs, tables, and lamps
• Pronounced styrene odor levels Typical Applications • Construction: Pipe, building panels, portable buildings, swimming pools, floor grating, and doors • Marine: Powerboats, sailboats, canoes, kayaks, gel coating, docks • Automotive: Rear lifts on vans, station wagons, sports vehicles, body panels, truck hoods, trailer panels, structural components, and seating • Industrial: Corrosion control, tanks, process vessels, pipes, fittings, valves, fans, pollution control equipment, scrubbers, hoods, blowers, ducts, stacks, ladders, linings, chutes, connections, sewer lines, and waste water treatment equipment • Electrical: Appliance covers and housings, circuit boards, insulators, and switches • Sanitary Ware: Bathtubs, shower stalls, hot tubs, spas, cultured marble, and food handling containers • Miscellaneous: Hobby castings, decorative art, buttons, bowling balls, skis, fishing rods, and nonstructural furniture parts
1.5.11
Polyimide (PI)
Polyimides are members of a class referred to as heteroaromatics; they are nylon polymers with excellent thermal capability and resistance to temperatures ranging from –270–740 °F for extended exposure times and up to 900 °F short-term for high-temperature specialty grades. PIs can resist higher temperatures better than any other unfilled polymer. Polyimides can be produced with either crosslinked molecular structures as thermosets or in linear forms as thermoplastics. Their high glass transition temperatures (Tg) require special processing methods. At the beginning, the polyimide polymers were condensation materials, but at the present time many variations have been developed and introduced to the market. Several approaches have been used to allow the thermosetting reaction to proceed by addition polymerization. Polyimides have high end use temperatures, excellent fire, chemical, and solvent resistance, low coefficient of friction, low wear, abrasion, thermal, and creep resistance, excellent electrical properties, and high mechanical strength properties. The presence of the imide ring in the structure causes some hydrolytic instability, particularly towards alkali. Polyimides are difficult to process; therefore, Du Pont manufactures the basic polyimide polymer, transforms the PI powder into a film form for the electrical industry, and laminates the film with Teflon® (the film has the trade name Kepton®). Du Pont also processes the powder into a fiber form known as Kevlar®.
Figure 1-173 Indoor spa whirlpool external shell
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1 Polymeric Materials
General Properties of PI – 40% Graphite Fiber Thermosets
Figure 1-174 Vespel® helical gear (Courtesy: Du Pont)
Figure 1-175 Vespel® ball valve seals (Courtesy: Du Pont)
Specific gravity
1.65
Flexural modulus @ 73 °F (Kpsi)
700.0
Tensile strength @ yield (Kpsi)
7.00–7.50
Notch Izod impact @ 73 °F (ft-lb/in)
0.70
HDT (°F) @ 264 psi
680
Thermal limits service temp. (°F)
900 (short) 600 (long)
Elongation at break @ 73 °F (%)
3.0
Processing temp. (°F)
690
Coeff. of thermal expansion (10–6 in/in/°F)
15.0
Coeff. of friction – metal
0.15 (stat.) 0.09 (dyn.)
Dissipation factor @ 106 Hz
0.0106 0.0034
Pressure velocity limit (psi-fpm)
300,000
Wear factor 10–10 (in3-min/ft-lb-h)
32.0
PI powder compounded with low coefficient of friction additives (Vespel®) is transformed into solid bars, plates, balls, rods, which are provided to molding manufacturers to produce custom parts. Advantages • Continuous use in air at 740 °F; intermediate exposure to temperatures as high as 900 °F for high-temperature specialty grades • Creep is almost nonexistent • Excellent electrical and temperature barriers • High stiffness and strength • Low coefficient of friction • Low wear resistance
Figure 1-176 Vespel® gear box thrust washer (Courtesy: Du Pont)
• Excellent solvent resistance • Excellent adhesion • Fire resistance • Especially suited for composite fabrication Disadvantages and Limitations • Difficult to process • Material handling difficulties • Attacked by diluted alkalis an concentrated inorganic acids • Comparatively high cost
Figure 1-177 Kepton® automotive flex print circuit (Courtesy: Du Pont)
• Brown color • Contains volatiles or solvents that must be removed during curing
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1.5 Thermoset Polymers Typical Applications • Fiber for bullet proof clothing and industrial gloves • Fiber reinforcement for automotive tires • Fiber reinforced composite laminates for speed boats, race cars, surf boards, aerospace and airplane structural components • Molding components, such as aircraft brake pads, compression seals, piston rings for transmissions, valves, thrust washers, and bearings • Refrigeration compressors, turbine engine parts, hot glas handling equipment, plasma cutting torchees, and power tools • High temperature films, flexible print circuits, capacitors, automotive electronic sensors, and high performance insulation tapes • Coatings and adhesives • High temperature wire insulation
1.5.12
Polyxylene
These polymers are unique in that they are deposited in the vapor phase by thermal decomposition of a solid dimmer into gaseous diradicals that combine on a surface to form a high molecular weight polymer film. Three variations are available: Unsubstituted, monochloro-substituted, and dichloro-substituted. Extremely thin pinhole free coatings and films may be deposited. Advantages • Ultra-thin continuous coatings • Complete coverage around and under densely spaced components • Excellent electrical properties • Dielectric strength of 5000 V/mil in thin layers • Highly resistant to organic solvents • Excellent moisture barrier for electronic assemblies Disadvantages and Limitations • Requires special vacuum deposition equipment for application • Air oxidation at temperatures above 257 °F • Difficult to remove the polymer for rework in electronic assemblies • Extra care needed in masking Typical Applications • Coatings for printed wiring assemblies • Insulation of ferrite toroids, sleeves, and bobbins • Insulation of high voltage components to prevent corona and arcing • Insulation for fine gauge magnetic wire • Protective coating for biomedical devices
Figure 1-178 Kevlar® Lotus 81 Formula One racing car (Courtesy: Du Pont)
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1 Polymeric Materials
1.5.13
Polyurethane (PUR)
General Properties of Generic PUR Thermosets Specific gravity
1.47
Tensile modulus @ 73 °F (Mpsi)
1.00
Tensile strength @ yield (Kpsi)
14.00
Notch Izod impact @ 73 °F (ft-lb/in)
2.20
Elongation at break @ 73 °F (%)
4.0
HDT (°F) @ 66 psi @264 psi
260 150
Thermal limits service temp. (°F)
120–250
Shrinkage (%)
0.30
Water absorption @ 24 h (%)
0.40
Process. Temp (°F)
450–500
Dielectric constant @ 106 Hz
3.2–4.3
Dielectric strength (V/Mil)
400–510
6
Dissipation factor @ 10 Hz
0.003 0.16
Polyurethane (PUR) was developed from polyisocyanate in Germany during Word War II. The general structure of polyurethanes is R–(NCO)n, where n typically equals 2 to 4, or even higher, and R is an aromatic or aliphatic group. The isocyanate group (R–N=C=O) reacts easily with hydroxyl groups (HO-R′). The resulting link between the two residues R and R′ are the urethane group. O N R–N = C = O + HO–R′ → R– O–C–N– R′ | H Polyurethane thermosetting resins are used in coatings, adhesives, binders, sizings, flexible foams, fibers, sealants, biomedical, and external automotive structural applications. Polyurethane is produced in the following forms: Isocyanate: The aromatic isocyanates are the most important members of this family. They are more reactive than the aliphatic types and less expensive. Toluene diisocyanate (TDI): It is the largest volume product of all isocyanates. It is a diisocyanate that is used as a mixture of 80% 2,4-isomer and 20% 2,6isomer. Diphenyl-methane-diisocyanate (MDI): It is the second largest volume aromatic diisocyanate. The commercial products contain mainly three isomers. In addition, MDI can contain components having more than two benzene rings. Polyol, Cross Linker, and Chain Extender: The counterparts for the reaction with the diisocyanates are hydroxyl or amino terminated components. Low molecular weight components are used as chain extenders or cross linkers. In combination with diisocyanate, the high temperature properties are
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1.5 Thermoset Polymers especially influenced. The flexible parts of PURs are higher molecular weight compounds. They are not only responsible for the elastic properties, but they also determine the low temperature performance of the polymer. However, they can be terminated with hydroxyl or amino groups, with a functionality of two or more. This means that chemical cross linking can also be introduced through the flexible element. The main classes of polyols are polyethers and polyesters. The polyethers are mostly derived from propylene oxide, while the polyesters are derived from adipic acid. All formulations contain additives, such as catalysts, stabilizers, blowing agents, flame retardants, mold release agents, and other nonreactive additives, such as fillers and pigments. Reaction Product PUR: The combination of the above components in different ratios, with and without water or external blowing agents, leads to a great variety of polymeric products. Because of different porosity levels, the specific gravity can range from 0.03–1.15. With different chemical compositions, the modulus of elasticity can be varied from values typical for rubber-like materials to values characteristic for engineering thermoplastics. Thermoplastic PUR: Bifunctional raw materials lead to linear PURs when secondary reactions are avoided. Certain combinations of diisocyanates and chain extenders generate PURs that are processed like thermoplastics. Flexible foam is mainly used for cushioning, mattresses, and packaging. Rigid foam is primarily used for thermal insulation; however, in a great percentage of applications, rigid foam also serves as a structural element.
Figure 1-179 Various extrusion profiles used in the home
Semirigid PUR: Semirigid PURs have a good combination of high tensile strength, high elongation, high tear resistance, and excellent flexural fatigue behavior in a broad temperature range. Low-Density Flexible RIM Systems: PURs integral skin foams with low densities are primarily used for bicycle seats and interior car parts. They are predominantly open cell foams with a tough elastic skin, which protects the foam core from mechanical damage. A void-free, smooth, soft surface is an additional advantage. Medium-Density Flexible RIM Systems: With specific gravities between 0.300– 0.700, these are typical shoe sole materials, but they have also found applications in automobile interiors. High-Density RIM Systems: Semirigid PURs, including solid RIM materials, have specific gravities from 0.70–1.15; they are mainly used for exterior automobile body parts required to withstand large elastic deformations.
Figure 1-180 Office furniture external structure
Rigid PUR: This material can be rigid block foams or rigid integral skin foams. Rigid Block Foams and Similar Systems: They have cellular structures with closed cells. Because of the cross-linked structure of the matrix material, these foams can be used at temperatures up to 250 °F, depending on the load. The most important property for rigid PUR applications is low thermal conductivity (K factor). Because the foam has a solid material content of only 3–6%, the K factor is determined by the composition of the cell gas. The normal blowing agent is CFCl3, but water is part of the formulation, leading to the production of carbon dioxide (CO2). A considerable increase in the K factor occurs if the foam is soaked with water. A water absorption of only 1% nearly doubles the thermal conductivity, and even a closed cell foam can absorb 2–5% of water.
Figure 1-181 Automotive door energy absorption
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1 Polymeric Materials Rigid Integral Skin Foams: As with semirigid integral skin foams, the density of the rigid systems can vary widely. Because they usually serve a structural purpose, their specific gravities are relatively high (0.200–0.800). Reinforced Integral Skin Foam: This polymer was introduced in the late 1970s. The main advantages of a reinforced system are higher stiffness, lower heat sag, and a smaller coefficient of thermal expansion, which allows the production of articles with tight dimensional tolerances. The fillers used are glass fibers, glass flakes, mica, and minerals. Figure 1-182 Bicycle seat
The production of filled PURs by the RIM process requires premixing the filler with the liquid components (polyol). Special tanks equipped with stirrers are used to disperse the filler. Processing filled systems requires special precautions because of their abrasiveness and high viscosities. The metering units must be equipped with mono piston pumps. Granular fillers change viscosity only slightly. Milled glass fibers are very common and can be used in concentrations up to 75% in the polyol. The effect of fillers on mechanical properties of the final foams follows the same order as observed in their influence on the viscosity of the raw materials. Granular fillers have a comparatively small effect on stiffness and the coefficient of thermal expansion.
Figure 1-183 Sandwich sailboat hull
Flake materials have a more favorable effect on these properties and improve the dimensional stability at higher temperatures. With 20% mica, for example, the Young’s modulus can be increased by a factor of 3, but tensile strength and elongation at break are reduced. An example of reinforced PUR is the product of the SRIM process (structural reaction injection molding). In fact, SRIMs are composites that contain random, unidirectional or multi-directional glass fiber mats. These mats are put into the mold, which is then closed and filled with the reactive mixture of raw materials. Because of its extremely low viscosity, the resin penetrates the reinforcing mat and solidifies the structure. This procedure allows the use of glass fiber contents of up to 70%.
Figure 1-184 Automotive fender panel
The resulting composites combine extremely high stiffness, which is typical for epoxy and polyester laminates, with the advantages of RIM (reaction injection molding) process, i.e., parts can be molded in less than one minute cycles. The manufacturer receives raw materials, such as isocyanates, polyols, blowing agents, and additives. The only exception is TPU, which is delivered as a polymer resin. The isocyanates and polyols are usually liquid. They are simultaneously metered and mixed and the reacting liquid is delivered into a mold where the reaction proceeds until the solid demolding state is reached. Additional components and additives can either be metered directly into the mixing head or prebatched into the polyol. Advantages • Integral skin foams have a porous core and a solid skin; they are produced in a wide range of stiffnesses and densities by RIM processes. • Semirigid molded foams have an open cell structure and considerable elastic hysteresis, providing good mechanical damping properties.
Figure 1-185 Acoustical foam
• Semirigid cast elastomers are solid or micro cellular, and offer high stiffness.
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1.5 Thermoset Polymers • Rigid integral skin foam has a sandwich-like structure, a porous core and a solid skin, with a transition zone between them (high stiffness and low weight). • Rigid foam has excellent thermal insulation. • The PUR family has a huge variety of properties that can be obtained by combining a relatively small number of basic components in different compositions. • PUR materials can be processed, ranging from simple hand casting to the highly sophisticated RIM processes. Both allow the production of large, complicated parts and design freedom, at relatively low costs.
Figure 1-186 Horseshoes
Disadvantages and Limitations • Diffusion barriers are required to control water absorption. Typical Applications • Integral Skin Foams: They are used in the production of interior parts that have inserts of steel or other materials, such as steering wheels, gear shift knobs, brake handles, head rests, arm rests, instrument panels, and door panels. Typical exterior body parts include spoilers and encapsulated glass, as well as body panels and fascias. • Semirigid Molded Foams: They are used in parts, such as head rests and crash pads, for which energy absorption is important. • Semirigid Cast Elastomers: Typical applications include exterior automotive body parts, elastic load transmission elements, rollers, shock absorbers, and cyclone separators.
Figure 1-187 Furniture finish panels
• Rigid Integral Skin Foams: Typical applications are skylight frames and window frame profiles, housings for personal computers, loudspeakers, televisions, radios, wind deflectors for trucks, chair shells, tables, book shelves, and furniture. • Rigid Foams: Thermal insulation for the transportation industry, such as frozen food containers for trains, trucks, aircraft, ships, warehouses, portable coolers, display cases, refrigerators, and deep freezers. The automotive industry uses rigid foam as filling to provide stiffening, sound absorption, and corrosion protection in motor and trunk hoods. Sandwich constructions are for boats, surfboards, skis, and bathroom components. Additional insulation applications for storage vessels, pipelines, doors, roofs, tanks, lightweight concrete material for wall panels, window sills, to fill the gaps between door casings and walls, and insulation for building blocks. • Others: Coatings, adhesives, binders, sizings, flexible foams, fibers, sealants, and biomedical applications.
1.5.14
Silicone (SI)
Silicones (SIs) are suitable as engineering materials for an extensive range of applications. Since their commercial introduction in the 1940s, they have become a universally useful class of materials. Their structure resembles that of silicon dioxide (SiO2) glass, which provides high temperature properties and resistance to radiation, ozone, and chemicals. The structure of SI is very different from that of organic polymers. Specifically, the polymer chain backbone consists of
Figure 1-188 Electrical insulator
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1 Polymeric Materials repeat units, whereas the polymer chain backbone of organic polymers is some configuration of repeat units. A Si–O2 bond is stronger and more flexible than a C–C or C=C bond, which makes silicone polymers chemically stronger and more flexible than organic polymers. Silicone polymers resemble the three-dimensional network structures of SiO2 (sand). Organic functionality of SI allows light cross linking between polymer chains, creating rubber elasticity.
Figure 1-189 Electrical plug weather seals
Outstanding characteristics of SI include its ability to maintain properties at both low (down to –150 °F) and high (up to 600 °F) temperatures, and its weathering and chemical resistance, physiological inertness, lubricity, excellent electrical properties, low surface tension, and compression set resistance. Silicone rubber burns to a white, non conductive ash. Burning a specimen is one method for identifying the material. Silicone Fluids The most common product is methyl silicone fluid, best known for its relatively constant viscosity over the range of its temperature resistance.
Figure 1-190 Shaft rotating seals
SIs are an important class of lubricants for industrial as well as household applications. SI greases are used in industry wherever a low temperature (–100 °F) or high temperature (445 °F) resistance is needed. At extreme temperatures, SI greases retain their characteristics. They are used in the automotive and aerospace industries in small motors, ball bearings, gear assemblies, and instrumentation. Room temperature vulcanized materials are also used in mold making because they can provide intricate part reproduction and slight undercuts. It is possible to cast polyester, polyurethane, epoxy, vinyl, and other polymers, as well as low melting metals. SI molds produce excellent prototypes and artistic castings.
Figure 1-191 Prototype mold cavity
Heat curable rubber (HCR) refers to compounded SI rubber with catalyst, color, additives mixed and milled into siloxane polymers. HCR can be extruded or molded and requires a cure time of 10 minutes at temperatures between 250 and 350 °F. For applications requiring service temperatures higher than 150 °F and dimensional stability, post curing at the service temperature or above is recommended. Before molding a catalyzed HCR compound, freshening the material through a calender mixer is recommended, depending on the storage shelf life of the compound. Advantages • Wide range of thermal capabilities • Good electrical properties • Wide variation in molecular structure for flexible or rigid systems • Transparent grades are available • Low water absorption • Inherently flame retardant • Good chemical resistance Disadvantages and Limitations • Attacked by halogenated solvents
Figure 1-192 Automotive spark plug wires
• Comparatively high cost
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1.5 Thermoset Polymers Typical Applications • Medical implants • Electronics: Room temperature vulcanized materials include potting gel, removable and permanent encapsulation, dielectric gels and/or oils, conformal coatings, calculator and computer touch pads, and insulation. Thermally and electrically conductive products are available for electromagnetic interference and radio frequency interference (EMI/RFI) shielding applications. • Molded Parts: SI is used for high temperature service or in applications that utilize their chemical and weathering resistance. It is used for seals, gaskets, and mechanical diaphragms. HCR matrices can be reinforced with fabrics or fibers for sheeting and tubes, covered roller, and conveyor belts. • Cosmetic Industry: Silicones provide the non-greasy, lubricious texture in lotions, hair preparations, antiperspirants, shaving creams, and lipstick.
Figure 1-193 Automotive engine valve cover seal
• Pharmaceutical: SI is used in ointment bases, over-the-counter medicines, and as tablet lubricants. SIs are used as reactive blocking agents for specialty syntheses of many drugs. • Industrial: Silicone fluids as anti-foaming agents include use in detergent manufacturing processes, fermentation, adhesive and sealant manufacturing, waste water treatment, boiler and cooler treatment, metal cutting fluids, agricultural chemicals, cleaning solutions, printing, paints and coatings. • Textile Industry: Yarn lubricants in high speed knitting and milling applications, ingredients in fabric finish formulations. • Paper Manufacturing Industry: Release coatings for paper to complement pressure sensitive adhesive coated paper. • Polymer Additive: Used as internal lubricants, external mold releases, and processing aids. Silicone fluids and/or silanes are ingredients in automotive polishes, furniture polishes, and masonry water repellents. • Adhesive and Sealant: SI is used for bonding metals, polymers, and ceramic substrates to one another.
1.5.15
Urethane Hybrid
Urethane acrylic polymers were developed for use in fabricating injected composites when traditional urethanes were too high in viscosity or when polyesters either required dilution with styrene or were too slow in cycle times for large volume production. These acrylamates are formed by the reaction of two liquid components, an acrylesterol and a modified diphenylmethane-4,4-diisocyanate (MDI). The first component of this polymer, the acrylesterol, is a hybrid of a urethane and an acrylic. The other component, a liquid modified MDI, contains two or more isocyanate groups that can react with the hydroxyl portion of the acrylesterol molecule. In addition, the acrylesterol reacts with itself by means of the acrylic group and other reactive groups that can be present in the acrylesterol molecule. The single hydroxyl group on the acrylesterol is very reactive with the isocyanate groups on the MDI because the activation energy necessary for this reaction is
Figure 1-194 Automotive engine gaskets
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1 Polymeric Materials relatively low. However, the urethane reaction does not form large molecular weight molecules, because the acrylesterol has only one hydroxyl that reacts. This results in a very low viscosity mixture during the initial portion of the reaction. The acrylic reaction has a higher activation energy and it requires higher temperatures to react at an appreciable rate. As the urethane is formed, the exothermic heat of reaction increases the reactant temperature until the free radical acrylic reaction is initiated. The polymer is formed rapidly through a snap cure. Appropriate catalysts are used to accelerate the urethane reaction and the free radical reaction. The resultant polymer is a highly cross linked structure. Acrylamate polymers can be tailored to provide broad processing ratios, toughness, and elongation. Combustion modified versions are also available to meet standard industry burn rate tests. Acrylamate polymers have better high temperature capabilities. They are particularly suited for mold injection into preplaced reinforcement mat. Directional reinforcement combined with continuous strand random mat provides higher strength than composites with random mat alone. The basic fabrication processes for molding acrylamate polymers include transfer molding, reaction injection molding, and use of prepregs. Reaction Injection Molding (RIM) This process consists of metering and mixing two or more liquids and injecting the mixture into a closed mold. Because the components are low in viscosity, the molding process requires low clamp pressures (less than 100 psi). SRIM Processing One difference between the SRIM and RIM processes is the method of adding a reinforcement. In SRIM, reinforcement can be provided by a random fiberglass mat or by preforms combined with bi-directional woven reinforcement placed into the mold before injecting the polymer inside the mold cavity. During injection, the chemical mixture flows through the reinforcement, wetting the fibers. As it forms, the polymer reacts with the treated surface of the reinforcing fibers. Within 1–2 minutes after injection, a finished composite can be removed from the mold. The two liquids that combine to form acrylamate acrylesterol and MDI have characteristics that are ideal for SRIM processing. The viscosity of the injected mixture of acrylesterol and MDI is only about 25.0 Poise at room temperature and even lower at mold temperature. This allows the reacting mixture to flow through the reinforcement without deforming or distorting it. Most important is that the viscosity remains low long enough for the part to be filled and the mixture to wet the reinforcing fibers. In addition, the mixture is fast reacting, for maximum productivity. Preforms have been used for many years in transfer molding. The method of making preforms uses chopped fiberglass shaped on a special screen. Air drawn through the screen holds the chopped fibers in place while a binder applied to the fibers is curing. The final preform holds the general shape of the part. Faster methods of making preforms with random continuous fibers or oriented directional fibers use the technique of thermoforming or thermoset binder molding. Thermoformable mats of continuous or directional fibers contain
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1.5 Thermoset Polymers a thermoplastic binder, which is heated to soften it. The glass mat can then be molded into shape using an inexpensive preform tool in a press. As the mat cools, the binder hardens and holds the mat in the desired shape. A heat curable binder is applied to precut fiberglass mats and the mats with binder are placed into a heated mold. The mold is closed for a short time, curing the binder. After the cure, a finished preform is removed from the mold. A prepreg is formed by reacting the two components in acetone, resulting in an acrylamate prepolymer. The cross linking reaction is avoided at this point. This solution is used to impregnate glass cloth and specialty fibers. Physical properties depend on the type and amount of reinforcement used.
Figure 1-195 Church, large upper structure
Advantages • Acrylamate resin systems produce strong and high flexural modulus fiber reinforced composites • Low density • Good performance over a wide range of temperatures • Heat deflection temperatures are in excess of 465 °F • Excellent fatigue performance Disadvantages and Limitations • Low notched Izod impact values for unreinforced resins • Reinforced resins are recommended to avoid brittle failures Typical Applications • Automotive Industry: The use of these composites for prototypes has been extended from components to whole body structures of cars and trucks. • Recreational Products: Reinforced acrylamate resins allow cost effective production of large area parts in low to medium volumes. Using resin transfer molding permits the replacement of complex, labor intensive assembly operations. • Electronics and Communication: These resins are especially advantageous in communications equipment because of the dimensional control of the molded parts and the capability of incorporating desired electronic characteristics into the composites. Electromagnetic interference/radio frequency interference (EMI/RFI) shielding can be accomplished by incorporating conductive carbon mat or metallized cloth in the composites. • Industrial Uses: These resins have been used in the aerospace industry, for agricultural equipment, and materials handling equipment.
1.5.16
Vinyl Ester (BPA)
Vinyl ester resins are unsaturated esters of epoxy compounds. The most common versions are the reaction products of methacrylic acid and Bisphenol A (BPA), an epoxy compound dissolved in styrene monomer. Corrosion resistant reinforced resins based on vinyl esters and other compounds have successfully replaced traditional materials, such as glass, carbon steel, concrete, and brick. Vinyl ester resins have many properties of epoxies combined with the processibility of a polyester. The addition of the methacrylate group allows vinyl esters to
Figure 1-196 Portable cooler insulation
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1 Polymeric Materials
General Properties of Generic BPA Thermosets Specific gravity
1.55–1.98
Tensile modulus @ 73 °F (Mpsi)
1.70
Tensile strength @ yield (Kpsi)
21.0
Notch Izod impact @ 73 °F (ft-lb/in)
6.0–20.0
Elongation at break @ 73 °F (%)
2.0
HDT (°F) @264 psi
428–550
Th ermal limits service temp. (°F)
150–210
Shrinkage (%)
8.0–9.0
Water absorption @ 24 h (%)
0.10–0.15
Process. Temp (°F)
73.0–300 6
Dielectric constant @ 10 Hz
4.58
Dielectric strength (V/Mil)
350–470
6
Dissipation factor @ 10 Hz
0.008
be cured in ways similar to the curing of unsaturated polyester compounds. The use of styrene or other reactive monomers allows low viscosities to be obtained at ambient temperature. Because of curing and material handling similarities, vinyl esters are often classified with unsaturated polyesters. The combination of excellent chemical corrosion resistance and good mechanical and material handling properties similar to those of unsaturated polyesters have made vinyl ester resins a very important product for many applications. One of the advantages of vinyl ester resins reinforced with fiber materials is that the reinforcement can be oriented in the direction requiring strength. The properties of vinyl ester resins are more important in other areas, such as fatigue resistance, retention of properties at moderate temperatures, impact resistance, and creep resistance. Chlorendic polyester retains its properties up to 210 °F. The higher residual modulus above the glass transition temperature shows that chlorendic polyester has the highest cross link density. The corrosion resistance of composites made of vinyl ester resins compares favorably with metals, thermoplastics, and unsaturated polyester compounds. Their excellent corrosion resistance is attributed to three basic factors. First, the corrosion susceptible ester linkage is shielded by a methyl group. Second, the vinyl groups are very reactive and a complete cure of the backbone is easily accomplished. Third, the epoxy backbone is very resistant to chemical attacks. The following vinyl ester products are available commercially: • BPA epoxy products are available in different molecular weights and styrene content. Cross link density decreases as molecular weight increases, because the methacrylate cross linking sectors are on the ends of the molecular chains. Vinyl ester made with a low molecular weight epoxy will have a high cross link density. When cured, this material will have a high heat deflection temperature and good solvent resistance, but lower impact resistance. Resins made with high molecular weight epoxies will have lower cross link densities, less solvent resistance, but with higher toughness.
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1.5 Thermoset Polymers • Novolac epoxy polymers have been used to improve the heat and high temperature corrosion resistance of vinyl ester resins. Novolac epoxybased vinyl esters also have improved solvent resistance. The novolac structure provides a higher aromatic content and more cross link sectors in pendant positions along the backbone of the molecule. The glass transition temperatures of these resins are 50–100 °F higher than those of conventional vinyl ester resins. Flame retardant vinyl ester resins use halogenated epoxy resins. These materials retain all the desirable properties of vinyl ester resins plus the flame retardant characteristics. • Modified vinyl ester resins are tailored to satisfy the needs of the applications. A number of vinyl ester resins, such as aliphatic polyol epoxies and epoxy esters, are available. Aliphatic polyol epoxies provide additional resiliency, impact strength, and thermal and mechanical shock resistance. Modified vinyl ester resins based on epoxy esters of dibasic acids containing carboxy terminated rubbers provide higher elongation, improved thermal and mechanical shock resistance, and improved adhesion to a variety of substrate materials. • Maleic anhydride modified vinyl esters. The additional reactive unsaturations raise the heat deflection temperature of the resin and improve the retention of properties at elevated temperatures. Processing can be based on either ambient temperature or elevated temperature cure systems. Vinyl ester resins are cured by peroxide initiated free-radical polymerization of the reactive unsaturations of styrene and the methacrylate groups. Using these ambient temperature cure systems and additives gives vinyl ester resins a wide range of gel times. Gel times from less than one minute to over three hours are possible. Some of the processes used to fabricate parts with vinyl ester resins at ambient temperature include open molding techniques, such as hands lay up and spray up, filament winding, and centrifugal casting. Vinyl ester is also used in press thermo molding. In this process, chopped glass fibers and peroxides are incorporated into the resin. Fillers and thermoplastic additives are used to control the viscosity and shrinkage characteristics during cure. When the mixture is thickened between plastic sheets, it is known as sheet molding compound (SMC). If the material is stored in sealed bags or boxes, it is referred to as bulk molding compound (BMC). The transfer molding process at high temperatures is bridging the gap between press thermo molding and open molding at room temperature. The tooling used is similar to that used in an ambient temperature cure. Because the pressure is typically less than 50 psi and is usually about 5 to 20 psi during the injection step, no pressure is used during cure, and the cure cycle can be as short as 90 seconds.
Figure 1-197 Natural gas composite tanks
Advantages of this Process • Faster cycle times than ambient temperature open molding, with a smooth finished surface on both sides of the part • Lower tooling costs than with press molding • Retention of the ability to place oriented reinforcement in the part for optimum strength • Low costs for parts of low to medium volume
Figure 1-198 Large composite tanks
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1 Polymeric Materials Polymer Advantages • Good gel flow characteristics • Toughness because of the high elongation relative to the heat deflection temperature • High cohesive strength, wet-out, and bonds well to glass fibers and many other fibrous reinforcements • Excellent processibility when using catalyst systems that have low toxicity and are easily dispersed • Excellent chemical resistance to strong acids and strong alkalis over the whole PH spectrum Figure 1-199 Water transfer composite pipes
• Vinyl ester resins are competitive in applications in which temperature and chemical corrosion resistance is required • Good mechanical strength and material handling properties • Excellent corrosion resistance Disadvantages and Limitations • High shrinkage during curing unless filled • Some systems have volatile components such as styrene Typical Applications
Figure 1-200 Army tent composite poles
• Corrosion resistant reinforced plastic parts, such as pipes, ducts, tanks, electrical equipment, linings, flooring, pumps, oil field sucker rods, process vessels, chemical waste water holding tanks, grating, plating and etching tanks, hoods, scrubbers, washer drums, exhaust stacks, and underground gasoline storage tanks • Industrial equipment for pulp and paper, chemical processing, power systems, pollution control, waste water, and mining
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2
Engineering Product Design
When designing plastic components, success will depend on one prime factor: how well we use the variety of plastic properties and the processing methods for obtaining optimum results. The designer should select the best resin, realizing that it is essential for the resin’s full potential to be exploited to ensure that the molded part will satisfy both functional and cost requirements. Plastics are governed by the same physical laws and the same rules for good design as other materials. These principles can be applied if the polymer properties are suitable for the operating environment of the product being considered. It is necessary to know and understand what the end product must do and under what circumstances it will operate, before a design analysis can be done.
2.1
Understanding the Properties of Materials
There is a big difference between the properties, processing methods, and applications of materials manufactured by various industries. There is not a single material that can be used for all applications. Each new outstanding property developed in a material opens the door for new applications, technologies, and innovations that will improve the efficiency and quality of life of the end users. Product designers should compare the properties of various groups of materials (steels, thermoplastics, aluminum alloys, rubber, etc.), because each material has different properties developed for specific applications and markets and uses different manufacturing processes. All materials have benefits and deficiencies (properties, processes, and quality), making it difficult to compare the cost of finished products made of different materials and processes. The material properties are directly related to the end use applications whether or not one material is better than another. To illustrate this point, a thermoplastic resin cannot replace a structural steel beam used in building construction; the thermoplastic resins do not have the strength, creep resistance, or melt strength to be extruded into thick walled shapes. Thermoplastic beams would also warp in all directions. However, structural beams can be made of thermoset composites, although this is expensive. In less critical applications, such as the housing industry, wood composite structural beams are replacing steel beams, because of their performance and light weight; they are easy to work with and offer a competitive price. A thermoplastic resin cannot replace the steel in automotive disc/drum brake housings, because the product requires dimensional stability, low thermal expansion, and high strength and rigidity at elevated temperatures. Thermoplastic resins do not meet the requirements. However, brake pads made of thermoset polyimide have been successfully used in airplanes. Metals cannot replace automotive rubber tires, bellows, diaphragms, or compression seals, because metals do not have the elasticity, fatigue endurance, wear resistance, and toughness of rubber. Metals are not used for light-weight and compact cellular phone housings, because metals are electrical conductors, heavy, corrosive, and expensive.
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2 Engineering Product Design
Ferrous metals Nonferrous metals Thermosets Thermoplastics 0
2
4
6
8
10
Specific gravity
Portable electrical tools and small kitchen appliance housings are no longer made of die cast steel or aluminum but have been replaced with nylon and ABS, improving toughness, electrical insulation, and styling, lowering weight and cost reduction.
Ferrous metals Nonferrous metals Thermosets Thermoplastics -460
0
500 1.000 1.500 2.000
Continuous exposure temperature (˚F.) Ferrous metals Nonferrous metals Thermosets Thermoplastics 0
50
100 150 200
Automotive engine cast iron and aluminum intake manifolds are being replaced by fiber glass reinforced nylon to improve efficiency, lower weight, creating new manufacturing processes, and cost reduction. Automotive steel bumpers, external side panels, and hoods have been replaced with TPE, thermoset composites, and PC alloys to reduce weight, improve styling, and reduce costs.
250
Tensile strength (kpsi)
Water faucet valves made of die cast steel, brass, or copper are being replaced by new designs, updated styles, and colors, using acetal, which eliminates corrosion, providing cost reduction and opening new markets. High performance, large size irrigation valves (from 1.50 to 3.0 in dia.) and small valves (0.75 and 1.00 in dia.) made of die cast steel and brass were successfully replaced with GR nylon 6/12 for the large valves and with GR nylon 6/6 or acetal for the small valves. This improved performance and reliability, eliminated corrosion, and provided cost reduction. Other low performance commercial valves made of rigid PVC (lower cost) are also produced for the irrigation market. Toilet anti-siphon (ballcock) valves made of several brass and copper components were replaced with a multi-functional design in acetal, improving performance, eliminating corrosion, and providing cost reduction. The acetal valves had excellent performance over a 30 year period.
Ferrous metals Nonferrous metals Thermosets Thermoplastics 0
5
10
15
20
25
30
Modulus of elasticity (Mpsi)
The comparison of properties is an effective tool when applied to materials in the same family. To illustrate the point that properties between different material families cannot be compared, Figure 2-1 shows several graphs using different generic property values of the different material families.
Ferrous metals Nonferrous metals Thermosets Thermoplastics 0
40
80
120 160
200
Coefficient of linear thermal expansion (in/in/˚F) x 10-6
Figure 2-1 Comparison of generic properties of materials
The ferrous metal bars include cast iron, cold rolled steels, structural steels, alloy steels, stainless steels, and tool steels. The nonferrous metal bars include magnesium, aluminum, copper, nickel and brass alloys, and titanium. The rubber bars include acrylic, butadiene, butyl, chloroprene, nitrile, silicone, urethane, EPDM, EPM, fluorocarbon, and natural rubbers. The thermoset bars include phenolics, silicones, alkyds, DAP, polyimides, aminos, unsaturated polyesters, epoxies, and urethanes. The thermoplastic bars include ABS, acrylics, acetals, nylons, LCP, PBT, PET, PS, PE, PP, PC, PPO, PEI, PEKK, PSU, PPS, PTFE, PVC, and SAN. The specific gravity graph shows the unit weight of a material compared to water and reveals that metals are two to eight times heavier than plastics. On a strength-to-weight basis, plastics have a more favorable position, as indicated by the specific gravity graph. In general, the cost of metals is much higher than plastics. The continuous exposure temperature graph shows that metals have wider temperature ranges than plastics; metals can be used at colder and at elevated temperatures. This property is used for the classification and temperature range of plastics. The tensile strength (kpsi) graph shows that metals are much stronger than plastics; metals resist higher forces when being pulled apart before breaking. The tensile strength of a plastic varies with temperature; it decreases with increasing temperature over a much smaller temperature range.
117
2.1 Understanding the Properties of Materials The modulus of elasticity (Mpsi) graph shows that metals have higher resistance to deflection for short-term, intermittent, or continuous loading than plastics. Metals have better dimensional stability at elevated temperatures than plastics. Since plastics deflect more than metals under the same loading, it is important that metal and plastic parts be loaded using different techniques. Plastics require that the load be distributed in compression mode. The coefficient of linear thermal expansion graph shows that increasing the temperature causes more dimensional changes for plastics than for metals. When plastics and metals are used together and are exposed to the same temperatures, plastic parts become larger than metals; therefore, design compensations should be provided to compensate dimensional change in plastics. The thermal conductivity graph shows that metals are good conductors of heat while plastics are excellent insulators. Despite their relatively low effective temperature range, plastics may be superior to metals as high temperature heat shields for short exposures. A plastic part exposed to a radiant heat source soon suffers surface degradation. However, this heat is not transmitted to the opposite surface as rapidly as in metals. The electrical volume resistivity graph compares only the insulation materials used in electrical applications, (metals are conductors). The dielectric strength graph shows the voltage gradient at which electrical failure or breakdown occurs as a continuous arc; the higher the value the better the material. Plastics have excellent electrical resistance properties, while metals are conductors.
2.1.1
Plastics Selection Guidelines
More than 20,000 thermoplastic grades and over 5,000 thermoset grades have been developed for the plastics industry. Because of the enormous diversity of plastic materials, the selection of the best plastic material for a given application is relatively difficult and time consuming, especially for inexperienced plastic designers. Table 2-1 provides a comparison of plastics and their properties. The table includes the most widely used unreinforced, 30% GR thermoplastic, and reinforced thermoset materials; basic mechanical, thermal and electrical properties, and process temperatures, indicating the process characteristics of the resins. Table 2-1 should be used as a preliminary plastic selection guide. The material properties listed in Table 2-1 were obtained by the resin producers by testing molded bars using ASTM procedures under laboratory conditions. Because most applications are not flat bars, but complex configurations, the actual properties will be different from the published ASTM properties. The values given are only approximate guides used to compare the values between resins for material selection and for preliminary product design calculations. To obtain precise properties for the new product design and configuration, a prototype mold is required, molding the selected materials, and testing the performance under actual service conditions. This chapter provides detailed information for all important plastics, their chemistry, characteristics, advantages, limitations, and applications. Several plastic organizations, such as ASTM, Modern Plastics, D.A.T.A., Inc., Engineering Plastics, IDES “Prospector” and all the resin suppliers provide data properties sheets.
Ferrous metals Nonferrous metals Thermosets Thermoplastics 0
0.5
1.0
1.5
2.0
2.5
Thermal conductivity (BTU/hr/ft2/˚F/in) x 103 Rubber Mica laminations Glass laminations Thermosets Thermoplastics 105 107 109 1011 1013 1015 1017 1019
Electrical volume resistivity (Ohm-cm) Rubber Mica laminations Glass laminations Thermosets Thermoplastics 0
1.0
2.0
3.0
4.0
Dielectric strength (Volt/0.001 in) x 103
Figure 2-1 (continued)
118
2 Engineering Product Design Table 2-1 Property Comparison for Selected Plastics
Tensile Modulus @ 73 °F (Mpsi)
Tensile Strength @ Yield (Kpsi)
Notch Izod Impact @ 73 °F (ft-lb/in)
Continue Expose Temperature (°F)
Processing Temperature (°F)
Dielectric Strength (Vol/Mil)
Dissipation Factor @ 1.0 × 106 Hz
ABS Unreinforced
1.05
0.30
5.00
2.50 12.00
167 185
410 518
HB
350 500
0.03 0.04
Acrylic Unreinforced
1.17
0.38
7.50
0.03 0.50
150 190
410 575
HB
450 530
0.09
Acetal Unreinforced
1.42
0.400
10.00
1.30
195 230
375 450
HB
560
0.005
HDPE Polyethylene Unreinforced
0.94
0.20
3.50
No Break
158 176
400 535
HB V2
450 500
0.0005
PP Polypropylene Homo Unfilled
0.90
0.17
4.00
0.50 20.00
212
390 525
HB V2
450 600
0.002
PS Polystyrene Unfilled
1.05
0.45
6.00
0.25 0.60
122 158
390 480
HB V2
300 600
0.004 0.0020
PVC Polyvinyl Chloride Rigid
1.38
0.35
5.90
0.40 20.00
150 185
365 400
HB V1
600 800
0.115
PC – 30% Fiber Glass
1.40
1.25
19.00
1.70 3.00
220 265
430 620
V1 V2
450
0.001
PPO – 30% Fiber Glass
1.25
1.10
14.50
1.70 2.30
200 240
520 600
HB V0
550 630
…
PBT – 30% Fiber Glass
1.53
1.35
17.50
0.90
200 250
470 530
HB V0
750
0.004
PET – 30% Fiber Glass
1.67
1.50
22.0
1.60
392
510 565
V0 5V
430
0.002
LCP – 30% Fiber Glass
1.62
2.25
23.00
1.30
430 465
660 680
V0 5V
640 1,000
0.0019
HTN – 30% Fiber Glass @ 73 °F – 50% RH
1.44
1.50
32.00
1.80
315
580 620
V2 V0
500
0.004
Nylon 6/6 – 33% GR @ 73 °F & 50% RH
1.38
0.90
18.00
2.50
265
530 580
HB V2
400
0.006
PEI – 30% Fiber Glass
1.50
1.30
24.50
1.90
356 390
640 800
V0
495 630
0.0025
PPS - 30% Fiber Glass
1.38
1.70
22.0
1.10
390 450
600 750
V0 5V
450
0.0014
PSU – 30% Fiber Glass
1.46
1.35
14.50
1.10
350 375
600 715
V0 5V
450
0.002
DAP – (TS) Fiber Glass
1.94
1.40
7.50
1.00
390 430
290 350
V1 V0
400 450
0.011 0.017
(EP) Epoxy – (TS) Fiber Glass
1.84
3.00
18.00
0.50
350 4450
300 430
HB V0
380 400
0.02 0.05
(PF) Phenolic – (TS) Fiber Glass
1.74 1.88
1.90 2.28
6.50 10.00
0.75 0.90
350 450
330 390
V1 V0
300
0.03
(UP) Polyester – (TS) Fiber Glass
1.75 1.90
1.90 2.00
10.50 15.00
0.50 18.00
200 250
170 320
V0 5V
450 530
0.01 0.04
(PI) Polyimide – (TS) Graphite Fiber
1.65
0.70
7.50
0.70
600 740
690
V0 5V
500 560
0.010 0.003
Flammability UL-94
Specific Gravity
Types of Polymers
2.1 Understanding the Properties of Materials Designer Check List
General Considerations : Performance requirements (structural, loading cycle, aesthetic, etc.) : Multifunction design : Product design for assembly : Structural load (static, dynamic, cyclic, impact, etc.) : Product tolerance specifications : Life of product : Resin selection based on performance of similar applications and end use : Product design for assembly process : Quality of product vs. process : Secondary operations : Packaging and shipping Environmental Requirements : End use temperature : Time, weather, strain, and stress cracks : Others (chemical, lubricants, water, humidity, pollution, gasoline, etc.) Design Factors : Type, frequency, direction of loads : Working stress selected (tensile, compression, flexural, combination) : Strain percentage selected : Load deformation (tensile, shear, compression, flexural, etc.) : Tensile, flexural, initial, secant, yield modulus used (temperature, creep) : Correlating the test results to end use environment conditions : Safety factor : Design product for efficient molding Economic Factors : Cost estimate of the new product : Resin cost vs. molding performance : Number of mold cavities vs. size of machine and automatic fast cycles : Eliminate secondary operations : Redesign part to simplify production
Quality Control Tests Required : Tension : Compression : Flexural : Impact (drop weight, dynatup, etc.) : Torsion, fatigue : Creep (tension, flex, temperature) : Chemical resistance : Weather (outdoors or accelerated) : UL electrical classification : UL continuous service temperature : UL temperature index : Final product UL approvals Resin Processing Characteristics : Viscosity and crystallization : Difficulties in molding the resin : Melt and mold temperature : Sensitivity to thermal degradation : Directional layout of reinforcements : Frozen stresses : Mold shrinkage control : Molding problems (flashing, voids, warpage, short shots, brittleness, tolerances, surface finishing, etc.) : Material handling : Percentage of reground (runners and rejected molded parts) allowed to mix with the virgin material : Drying the virgin resin and reground material. : Prototype molding the product (resin behavior unknown) Appearance of Product : Aesthetic product application : Dimensional control, warpage, etc. : Color matching, discoloration : Surface finishing : Weld lines, sink marks, flow lines : Parting line flash : Gate type, size, number, location : Decoration
119
120
2 Engineering Product Design If the product information and the quality of data available about a material have not been developed by the resin supplier, the designer should develop a check list by gathering all the facts related to the application. A typical designer’s check list has been included here (Table 2-2). It may be used as a guideline to develop a specific check list for any application. All aspects of the part are covered, including the product end use requirements, the structural considerations, the operating environment, the economics, and the appearance factors. This information is provided for making a quick analysis of the part requirements, such as temperature, environment, product life expectancy, and cycle and rate of loading. Designing with plastics requires maximizing the performance and efficiency of the product and the injection molding process. The following basic principles should be adopted in designing plastic products. • Design freedom is achieved using multifunctional design concepts. • When comparing materials that satisfy the requirements, remember that most metals have greater strength than plastics, and that all plastic material properties are time, temperature, and environment dependent. • Metal design principles are very different from the concepts used in plastic parts design. • Polymers are not substitutes for metals; in most designs the product geometry must be redesigned using plastic principles to be successful. We need to remember that there are no bad thermoplastic materials, only bad plastic applications.
2.2
Structural Design of Thermoplastic Components
This section will present principles for structural design of molded plastic parts. The only data provided are what is necessary to illustrate the type of information needed for analysis of plastic design structures. The mechanical properties described are the properties frequently used by designers of plastic components.
Tensile stress, σ, (psi)
E = Modulus of elasticity
P Stress limit
O
L Elastic range
Strain, ε, (%)
Figure 2-2 Stress-strain curve
Figure 2-2 shows two regions of the stress-strain curve. First, the region of low strain (O – L) will be discussed. This region is known as the elastic range; it is pertinent to applications where minimum deformation of the part under load is of prime concern. The second region of low stress (O – P) is known as the stress limit, which is important when the specimen springs back without deformation. The following discussion of creep and relaxation describes the effect of loading time on strength properties within the stress-strain curve. Specific attention is paid to creep under a constant load and relaxation from a fixed deformation. The design methods present the recommended methods for using the mechanical properties and concepts for designing with plastics. Illustrations are included to show how the equations, originally developed for metal designs, can be modified. Designing within the viscoelastic modulus utilizes modified elastic design equations. This method is normally used when deformation of the part is of prime concern. Yield design uses design principles that originate from the principles of plasticity. In this section, the yield stress is the controlling material
121
2.2 Structural Design of Thermoplastic Components variable. It is emphasized that the major difference between metal and plastic designs is the necessity of allowing for the time dependence of the mechanical properties of polymeric materials over the entire range of temperatures and environmental conditions that the part may encounter in use.
2.2.1
Stress-Strain Behavior
To understand the response of the material, design engineers have been using a set of relationships based on Hooke’s law, which states that for an elastic material, the strain (deformation) is proportional to the stress (the force intensity). Roark and Young, Timoshenko, and others have developed analyses based on elastic behavior of materials that exhibit a good approximation of simple elastic behavior over a wide range of loads and temperatures. For high stress levels and repeated loading and creep, more sophisticated analyses have been developed to deal with these types of applications. Unfortunately, Hooke’s law does not reflect accurately enough the stress-strain behavior of plastic parts and it is a poor guide to successful design, because plastics do not exhibit basic elastic behavior. Plastics require that even the simplest analysis take into account the effects of creep and nonlinear stressstrain relationships. Time is introduced as an important variable and, because polymers are strongly influenced in their physical properties by temperature, that is another important parameter to be considered.
GA1
A
Model "A"
One of the results of the viscoelastic response of polymers is to vary the relationship between the stress and strain, depending on the rate of stress application. The standard test used to determine structural properties for many materials is the analysis of the stress-strain curve. Figure 2-4 shows the slope of the curve, which is the elastic constant called Young’s modulus; the stress at which the slope of the curve deviates from the straight line is referred to as the tensile strength; and the stress at which the material fails by separation is called the ultimate tensile strength. In the case of viscoelastic behavior, the shape of the curve will depend on the rate of loading or on the rate of straining, depending on the way in which the test is performed. The modulus can vary over a range of three or four to one within the usual testing range and the material can exhibit ductile yielding at the lower straining rates. The value of the tensile strength and the ultimate strength can frequently vary by a 3 : 1 ratio.
GB1
GB2
B
B 1
2
Model "B"
Figure 2-3 Plastic resin structural models, elastic and plastic range
E = Young´s modulus or modulus of elasticity
Tensile stress, σ, (psi)
The retarded elastic response which occurs in plastic materials is best represented as a spring and dashpot acting in parallel. The creep or cold flow, which occurs in plastics, is represented by a dashpot. The combination best representing the plastic structure would be a spring and dashpot in parallel combination, in series with a dashpot. The basic elements and the combinations are shown in Figure 2-3.
2
1
In order to analyze these effects, mathematical models exhibiting the same type of response to applied forces as plastics are used. The elements that are used in such an analysis are a spring, which represents elastic response because the deflection is proportional to the applied force, and the dashpot, which is an enclosed cylinder and piston combination that allows the fluid filling the cylinder to move from in front of the piston to behind the piston through a controlled orifice.
A
GA2
Failure Ultimate tensile stress Stress limit
Elastic range
It is apparent that, when tensile tests are done on plastics, the loading rates must be specified to make sure the data have any meaning at all. It also becomes clear
Strain, ε, (%)
Figure 2-4 Young’s modulus
122
2 Engineering Product Design
Surface at specific temperature
Isochronous stress-strain curves
that such conventional data is essentially useless for the design of plastic parts, unless the end use loading rates happen to be the same as those of the test. In order to be useful, the tensile test would have to be run over a wide range of rates and the form in which the data is best presented is a three dimensional plot of stress-strain and time as illustrated in Figure 2-5.
2.2.2
Tensile Testing of Viscoelastic Materials
Creep curve
Str
ess Lo
gt
im
e
Strain
Figure 2-5 Three-dimensional graph, stress-strain-log time
In this section we will address the internal effects of forces acting on a structure. The thermoplastic components will no longer be considered to be perfectly rigid, such as in the static analysis cases. Structural design is concerned with the analysis of material strength, such as the deformations of various structures under a variety of loads. The simple tensile test is probably the most popular method for characterizing metals and so it is not surprising that it is also widely used for plastics. However, for plastics, the tensile test needs to be very carefully performed, because plastics, being viscoelastic, exhibit deformations that are very sensitive to such things as cross head speed rate in tension testing, moisture, stress level, temperature, and creep time. The stress-strain curves as shown in Figures 2-10 and 2-11 illustrate an interesting phenomenon observed in some flexible plastics, such as thermoplastic elastomers. This behavior is known as the plastic range, cold drawing, or continuous elongation of the specimen beyond the yield point without breaking. It occurs because, at low cross head speed rates, the molecular chains in the plastic have time to align themselves under the influence of the applied stress. Therefore, the plastic specimen’s molecular chains are able to align at the same rate at which the material it is being strained. The simplest case to consider is the application of a straight tensile load on a test specimen of constant cross section. The specimen is loaded at both ends with an equal force applied in opposite directions along the longitudinal axis and through the centroid cross section of the tensile test specimen. Under the action of the applied tensile forces, internal resisting forces are set up within the tensile test specimen. The tensile test assumes that the forces are applied through an imaginary plane passing along the middle of its length and oriented perpendicular to the longitudinal axis of the tensile test specimen. The magnitude of these forces must be equal and directed away from the test specimen (tension loading) to maintain an equilibrium of these forces. Typical tensile test equipment, including an extensometer, is shown in Figure 2-6. Some assumptions are made regarding the variation of these distributed internal resisting forces within the specimen. Because the applied tensile forces act through the centroid, it is assumed that they are uniform across the specimen’s cross section. The load distribution depends on the tensile test specimen geometry, dimensions, and manufacturing process. It also depends on the crystalline molecular structure of the polymer, the coupling agent used to reinforce the compound, and the flow orientation of the material reinforcement. However, to determine the mechanical properties of a polymer by performing either test in compression or tension, the cross head speed rate, at which loading is applied, has a significant influence on the physical properties obtained when running the tests at different loading rates. Ductile materials exhibit the greatest sensitivity of physical property variations at different cross head speed loading rates, whereas these effects are reduced and sometimes negligible for brittle materials.
123
2.2 Structural Design of Thermoplastic Components
Extensometer
Figure 2-6 Tensile test equipment and temperature chamber
2.2.2.1
Stress or Tensile Strength (σ)
Instead of referring to the internal force acting on some small element of the area, it is easier to use the ratio between the force acting over a unit area of the cross section. The force per unit area is termed as the stress (σ) and is expressed in units of force per unit area, e.g., lb/in2 (psi). If the forces applied to the ends of the tensile test specimen are such that the bar is in tension, then the term stress or tensile strength (σ) condition can be applied to the specimen. It is essential that the forces are applied through an imaginary plane passing through the centroid cross section area of the tensile test specimen. 2.2.2.2
Tensile Test Specimen
The tensile test specimen is held in the grips of either an electrically driven gear or hydraulic testing equipment. The electrically driven gear testing equipment is commonly used in testing laboratories for applying axial tension or compression loads. To standardize material testing procedures, the American Society for Testing Materials (ASTM) has issued standard specifications and procedures for testing various metallic, non-metallic, and thermoplastic resins in tension and compression tests. The ASTM test procedures for thermoplastic materials can be found in Chapter 11. Figure 2-7 shows a tensile test specimen specified for plastic materials. The dimensions shown are those specified by ASTM for tensile test specimens to fit the grips of the tensile test equipment. The elongations of the tensile test specimen are measured by a mechanical extensometer (see Figure 2-6), an internal gauge (micro-processor tester), or by cementing an electric resistance type strain gauge to the surface of the tensile test specimen. This resistance strain gauge consists of a number of very fine wires oriented in the axial direction of the tensile test specimen. As the test specimen elongates, the electrical resistance of the wire changes and this change of resistance is detected on a Wheatstone bridge and interpreted as elongation.
8.50 inch
0.75 inch
0.50 inch
0.125inch
Figure 2-7 Thermoplastic tensile test specimen
124
2 Engineering Product Design Stress-Strain Curves for Various Materials
Non ferrous alloys
PL
00
Med. carbon steel
Strain, ε , (%)
Figure 2-14 Stress/strain curve for reinforced resins
B Stress, σ , (psi)
Stress, σ , (psi)
0
Figure 2-11 Stress/strain curve for nonferrous alloys and cast iron materials
PL
Rubber / elastomers
Alloy steel Strain, ε , (%)
Figure 2-9 Stress/strain curve for alloy steel
0
0
Strain, ε , (%)
Figure 2-12 Stress/strain curve for rubber or elastomeric materials
Stress, σ , (psi)
PL Stress, σ , (psi)
Y
High carbon steel Strain, ε , (%)
Figure 2-10 Stress/strain curve for high carbon steel
B
PL
Unreinforced resins 0
B PL
Brittle resins
B
0
B PL
Reinforced resins
Strain, ε , (%)
ε0
Strain, ε , (%)
Figure 2-8 Stress/strain curve for medium carbon steel
0
01
Stress, σ , (psi)
0
Y Stress, σ , (psi)
Y
B
Stress, σ , (psi)
Stress, σ , (psi)
Y B
Strain, ε , (%)
Figure 2-13 Stress/strain curve for unreinforced resins
Strain, ε , (%)
Figure 2-15 Stress/strain curve for brittle resins
2.2 Structural Design of Thermoplastic Components 2.2.2.3
Strain (ε)
The elongation over the tensile test specimen gauge length is measured for any predetermined increment caused by the tensile load. From these values the elongation per unit length, called strain and denoted by ε, may be found by dividing the total elongation ∆L by the original gauge length L, i.e., ε = ∆L / L. The strain is usually expressed in units of inch per inch and consequently is dimensionless. 2.2.2.4
Stress-Strain Curve
As the tensile load is gradually increased at a cross head speed rate, the total elongation over the gauge length and the load are measured and recorded continuously at each increment of the load until fracture of the specimen takes place. Knowing the original cross sectional area of the tensile specimen, the stress (σ), may be obtained for any value of the tensile load by applying the following formula: Tensile Stress = σ = W / A where W denotes the tensile load in pounds, and A the original cross sectional area in square inches. Having obtained the numerous values of stress (σ) and strain (ε), the test results are plotted with these quantities considered as ordinate and abscissa, respectively. This is the tensile stress-strain curve or diagram of the material in tension. The stress-strain curve represents the mechanical characteristics or behavior for each type of material, therefore the stress-strain curves assume widely differing geometries for various materials. Figure 2-8 represents the stress-strain curve for a medium carbon steel, Figure 2-9 the curve for an alloy steel, Figure 2-10 the curve for a high carbon steel, Figure 2-11 the curve for nonferrous alloys and cast iron materials, and Figure 2-12 the curve for rubber or elastomeric materials. Tests conducted at room temperature using ASTM recommended proportional limits showed that polyethylene resin, PP copolymer resin, TPE resins, acetal resin, and unreinforced nylon resin (at 50% relative humidity) are materials that yield gradually until break as shown in Figure 2-13. Reinforced nylon resin (at 50% relative humidity), PC glass reinforced resin, and other compounded polymers that have limited elongation characteristics yield a curve as shown in Figure 2-14. Acrylic resin, PET glass reinforced resin, PBT glass reinforced resin, LCP, PF, PAI, PEI, PEAK, dry as molded nylon glass reinforced resins and most brittle compounded resins usually break before yielding occurs, as shown in Figure 2-15. 2.2.2.5
Hooke’s Law
For any material having a stress-strain curve of the form shown in Figure 2-16, the relation between stress and strain is linear for comparatively small values of the strain. This linear relation between elongation and tensile stress was first noticed by Sir Robert Hooke in 1678 and is called Hooke’s law. This initial linear range of action of the material is described by the following formula: Stress (σ) = Modulus of Elasticity (E) × Strain (ε) or
Strain (ε) = σ / E
where E (Modulus of Elasticity) denotes the slope or the straight line 0-PL (origin to the proportional limit) as shown in the stress-strain curve Figure 2-16.
125
126
2 Engineering Product Design E S = secant or apparent modulus 4.460 = 120.540 psi 0.037
E O = initial modulus or E = modulus of elasticity 2.875 = = 141.750 psi 0.02
σ
Y E Y = yield modulus = ε Y 5.200 = = 86.666 psi 0.06
Tensile stregth ( σ Y)
6.000 Y
Break
4.460 4.000
B
S Yield point PL Proportional limit
2.835 2.000
Elastic range
0.16
0.12
0.06
0.037
0
Strain at break ( ε B)
Yield strain ( ε Y)
1.000
0.02
Tensile stress, σ , (psi)
5.200
Plastic range Strain, ε , (%)
Figure 2-16 Stress-strain curve of a thermoplastic material
An element is subject to three mutually perpendicular stresses σx, σy, σz, which are accompanied by the strains εx, εy, εz, respectively. By superimposing the strain components arising from lateral contraction due to Poisson’s effect upon the direct strains, we obtain the general statement of Hooke’s law: εx = (1/ E )[σ x − υ (σ y + σ z )] εy = (1/ E )[σ y − υ (σ x + σ z )]
σ z = (1/ E )[σ z − υ (σ x + σ y )]
2.3
Mechanical Properties of Materials
The stress-strain curve shown in Figure 2-13 may be used to characterize several strength characteristics of thermoplastic materials. Proportional Limit (PL) The ordinate of the point PL is known as the proportional limit, i.e., the maximum stress that may be developed during a simple tension test such that the stress is a linear function of strain. For materials having stress-strain curves as shown in Figures 2-11 and 2-12, there is no defined proportional limit. Elastic Limit The ordinate of the point S (just above the proportional limit PL) is known as the elastic limit, i.e., the maximum stress that may be developed during a simple tension test such that there is no permanent or residual deformation when the load is entirely removed (see Figure 2-16). For many materials, the numerical
2.3 Mechanical Properties of Materials values of the elastic limit and the proportional limit are almost identical and the terms are sometimes used synonymously. In those cases, where the distinction between the two values is evident, the elastic limit is usually greater than the proportional limit. Elastic and Plastic Ranges The region of the stress-strain curve extending from the origin (0) to the proportional limit (PL) is called the elastic range; the region of the stress-strain curve extending from the proportional limit (PL) to the point of break (B) is called the plastic range (see Figure 2-16). Factors Affecting Elastic Properties We assumed that the elastic properties of most structural materials, when stressed below a nominal proportional limit, are constant regarding stress, unaffected by ordinary atmospheric variations of temperature, unaffected by prior applications of moderate stress, and independent of the rate of loading. When precise relations between stress and strain are important, as in product design, these assumptions cannot always be made. Thermoplastic materials exhibit a higher modulus of elasticity and a much higher proportional limit when tested rapidly (cross head speed) than when tested slowly. Absorption of moisture greatly lowers both the modulus of elasticity and the tensile strength. Rubber and thermoplastic elastomers have stress-strain curves approximately curved throughout, and neither has a definite proportional limit as shown in Figures 2-11 and 2-12. For these materials it is customary to define the modulus of elasticity (E) as the ratio of some definite stress to the corresponding strain percentage. The quantity so determined is called the secant modulus, because it represents the slope of the secant of the stress-strain diagram drawn from the origin to the point representing the stress chosen. Plasticity Plastic deformation represents an actual change in the distance between atoms in the molecular chain; plastic deformation represents a permanent change in their relative dimensions. In semi-crystalline thermoplastic materials, this permanent rearrangement consists largely of group displacements of the atoms in the crystal lattice caused by slip on planes of least resistance, thus suffering angular displacement. In amorphous thermoplastic materials, the rearrangement appears to take place through the individual shifting from positions of equilibrium of many atoms or molecules, caused by thermal agitation due to the processing energy. Yield Point (Y) The ordinate of the point Y, denoted by the yield stress σY, at which there is an increase in strain with no increase in stress, is known as the yield point of the material. After loading has progressed to the point Y, yielding is said to take place (see Figure 2-16). To define the yield point in plastics, the true stress-strain logarithmic curve must first be calculated from the conventional stress-strain curve. In the conventional stress-strain curve, strain is calculated in terms of the original length of the test specimen and stress is calculated on the basis of the original cross sectional area. As the cross sectional area of the test specimen changes during a tensile test, the true stress-strain logarithmic curve based on
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128
2 Engineering Product Design the instantaneous dimensional changes is more meaningful. The equations which convert conventional strain, ε, to logarithmic strain, ε and stress, σ, to true stress, σ are: σ = σ (1 + ε) and ε = ln (1 + ε) The following examples illustrate how these equations may be used:
True stress, (psi)
Example 2-1 12.000
Yield point Y
10.000
B
A specimen is stressed to 6,000 psi at a strain of 1.25%. What is the corresponding true stress and logarithmic strain?
B 73˚ F.
8.000
Y
6.000
True Stress = σ = 6,000 × (1 + 0.0125) = 6,075 psi
Logarithmic Strain = ε = 2.303 Log10 (1 + 0.0125) = 0.0125 or 1.25%
113˚ F.
4.000 2.000
Example 2-2 0 0
5
10
15
22
25
30
Logarithmic strain, (%)
True stress, (psi)
Figure 2-17 Unfilled nylon 6/6 tensile stress-strain curve (Courtesy: Du Pont)
12.000
True Stress = σ = 12,000 × (1 + 0.15) = 13,800 psi
Logarithmic Strain = ε = 2.303 Log10 (1 + 0.15) = 0.139 or 13.96%
Yield point Y
10.000
B 73˚ F.
8.000
By applying both equations, the true stress-logarithmic strain curves are constructed from the conventional stress-strain curve. Examples 2-1 and 2-2 show that the differences between the conventional and the true stresslogarithmic strain curves are substantial for relatively large strains and negligible for small strains within the modulus accuracy limit.
B Y
6.000
176˚ F.
4.000 2.000 0 0
2
4.5
6
8
10
12
Logarithmic strain, (%)
True stress, (psi)
Figure 2-18 Acetal homopolymer tensile stress-strain curve (Courtesy: Du Pont)
Yield point
2.000
B
Y
1.600
73˚ F.
1.200
B Y
800
176˚ F.
400 0 0
4
8
Based on the original dimensions, a specimen is stressed to 12,000 psi at a strain of 15%. What is the corresponding true stress and logarithmic strain?
12.5
16
20
24
Logarithmic strain, (%)
Figure 2-19 Polyethylene tensile stressstrain curve
In design terminology, there are many different definitions of the yield point, and therefore the danger of confusion always exists. For plastic materials that yield gradually, the yield point is determined from the true stress-logarithmic strain curve as shown in Figures 2-17, 2-18, and 2-19. The straight line between the point “Y” and point “B” is the plastic range of the tensile stress-strain curve, and the point “Y” that marks the beginning of the plastic range, is defined as the yield point. For plastic materials that yield abruptly, the yield point is defined as the maximum value (deformation or fracture) of the conventional stress-strain curve. The stress corresponding to the yield point is called the yield stress. This definition for plastic materials which yield gradually differs from the ASTM definition. Figures 2-17, 2-18 and 2-19 are the true stress-logarithmic strain curves for unfilled nylon 6/6 (50% R.H.), acetal homopolymer, and polyethylene at standard ASTM loading rates. These curves illustrate how to determine the yield point. The logarithmic yield strains are shown to be 22.00% for unfilled nylon 6/6, 4.50% for acetal homopolymer, and 12.50% for polyethylene. If a test specimen of a ductile plastic material is elongated to relatively large strains, the test specimen will neck down or elongate and the cross sectional area of the specimen becomes smaller with its structure reoriented. The stress-strain curve beyond the yield point is of little value to the designer, except that it adds confidence that the product can resist the stress loads without fracture but with deformation of the product.
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Tension and Compression Curves
In some structural calculations it is important for plastic designers to know the differences between the stress-strain curves for tension, compression, and flexure. For example, in flexural design analysis, both types of stress-strain curves are needed, because tensile and compressive stresses are present in any plastic part structure. In addition, various materials are considerably stronger in compression than in tension and flexure. The classic example of a nonmetallic material that illustrates this point is concrete. Tensile and compressive stress-strain curves are shown in Figures 2-20, 2-21, and 2-22 for dry molded and moisture conditioned (50% R.H.) unfilled nylon 6/6, acetal homopolymer, and acrylic. From these curves, obtained using the ASTM strain rates, the following conclusions can be drawn: • Tension and compression stress-strain curves at small strains are alike. • The modulus in compression is equal to the modulus in tension. • The flexural modulus is lower than the tensile modulus. • For large strains, the compressive stress is higher than the tensile stress. For example, the tensile stress at 10% strain for acetal homopolymer is 10,000 psi, while the compressive stress is 18,000 psi. Therefore, the yield stress in compression is greater than the yield stress in tension.
15.000
TENSION
10.000
Dry as molded
5.000 0.0
COMPRESSION
5.000
50% R.H. 10.000 15.000 10 8
6
4
2
0
2
4
6
8 10
Strain, (% at 73˚ F.)
Figure 2-20 Unfilled nylon 6/6 stressstrain curves, tension and compression (Courtesy: Du Pont)
Stress, (psi)
2.4
Stress, (psi)
2.5 Modulus of Elasticity (E)
10.000 5.000 0
TENSION COMPRESSION
5.000 10.000
Yield or Tensile Strength (σY ) The ordinate to the stress-strain curve such that the material has a predetermined permanent deformation or set when the load is removed is called the yield or tensile strength of the material. For the stress-strain curve shown in Figure 2-16, εY is denoted on the strain axis. The ordinate of Y represents the yield or tensile strength (σY) of the material.
15.000 18.000 10 8
6
4
2
0
2
4
6
8 10
Strain, (% at 73˚ F.)
Figure 2-21 Acetal homopolymer stressstrain curves, tension and compression (Courtesy: Du Pont)
The point B is called the breaking strength of the material (see Figure 2-16). Tangent Modulus (Et) The rate of change of stress concerning strain is known as the tangent modulus of the material. It is essentially an instantaneous modulus given by the following equation:
Stress, (psi)
Breaking Strength (B) 15.000
TENSION
10.000 5.000 0
COMPRESSION
5.000
Et = dσ / dε
10.000 15.000 5
2.5
Modulus of Elasticity (E)
The modulus of elasticity (E) is the ratio of the unit stress to the unit strain of the material in tension, or, as it is often called, Young’s modulus. Values of E for various metallic engineering materials are tabulated in machine handbooks, for engineering thermoplastic materials, the modulus of elasticity (E) is the initial modulus (Eo) shown in the stress-strain curve (Figure 2-16) and it is the highest value at room temperature and cross head loading speed rate (i.e., 0.2 in per minute), typically published and provided by the resin manufacturer’s product
4
3
2
1
0
1
2
3
4
5
Strain, (% at 73˚ F.)
Figure 2-22 Acrylic stress-strain curves, tension and compression
130
2 Engineering Product Design properties information. Because the unit strain (ε) is a pure number (percentage of a ratio of two lengths), the modulus of elasticity (E) has the same units as stress, that is lb/in2 (psi). Secant Modulus (ES) or Apparent Modulus (EA) The secant modulus (ES) is the ratio of the unit stress to the unit strain of the material. When a simple tensile force is gradually increased from the initial point “0” up to the point “S” (see Figure 2-16), this is defined as secant or apparent modulus at a predetermined working strain. The secant modulus (ES) or the tangent of the stress-strain curve from the origin “0” up to the point “S” may be calculated by dividing the secant stress (σS) by the predetermined strain (εS). The secant modulus (ES) is equivalent to 85% of the initial modulus (EO). The secant modulus (ES) is the maximum limit where the structural design principles may be applied. It is used for analyzing thermoplastic materials that have well defined elastic limits without suffering a permanent or residual deformation when the applied force returns to its original loading condition. Yield Modulus (EY ) The yield modulus (EY) is the ratio of the unit stress to the unit strain of the material. When a simple tensile force is gradually increased from the initial point “0” up to the yield point “Y” this is defined as the yield modulus. The yield modulus (EY) or the tangent of the stress-strain curve from the origin “0” up to the yield point “Y” may be calculated by dividing the yield or ultimate tensile stress (σY) by the yield strain (εY) of the curve (see Figure 2-16). It is measured in lb/in2 (psi). The yield modulus (EY) is used for determining the maximum load conditions a thermoplastic material can resist before large deformation, failure, or fracture occurs in the plastic product. Percentage Elongation at Break The increase in length (at the gauge length) after fracture divided by the initial length and multiplied by 100 is the percentage of elongation. The percentage of elongation test is performed at various temperatures and at same loading speed rates. This property is considered to be a measure of the ductility of a material.
2.6
Stress and Strain Analysis
In determining stress by mathematical analysis, it is customary to assume that the material is elastic, isotropic, homogeneous, and infinitely divisible without change in properties and that it conforms to Hooke’s law, which states that strain is proportional to stress. In fact, none of these assumptions are strictly true. A structural material is usually an aggregate of semi-crystalline or amorphous resins, fibers, minerals, and additive particles, the arrangement of which may be either random or systematic. When the arrangement is random, the material is essentially isotropic, when the arrangement is systematic, the elastic properties and strength are not equal, the properties are different in the other directions and the material is anisotropic. Finally, very careful experiments show that for all materials there is probably some set and some small deviation from Hooke’s law for any stress. These facts impose certain limitations on the conventional methods of stress analysis and must often be taken into account, but formulas for stress and strain,
2.7 Thermoplastics Elastic Design Method mathematically derived and based on the assumptions stated, give satisfactory results for nearly all problems of engineering design. If Hooke’s law holds true for the material, of which a part or structure is composed, the part or structure usually will conform proportionally to a similar law of load and deformation. The deflection of a beam or truss, the twisting of a shaft, the internal pressure in a container, etc., may in most instances be assumed proportional to the magnitude of the applied load or loads. There are two important exceptions to this rule. One is encountered when the stresses due to the loading are appreciably affected by the deformation. An example is a beam subjected to axial and transverse loads or a helical spring under severe extension. The second exception is represented by any case in which failure occurs through elastic instability, as in a slender column. Here, for loads less than the critical, elastic instability plays no part and the load deformation is linear. At the critical load the type of deformation changes, the column bending instead of merely shortening axially and the deformation becomes indeterminate. For any load beyond the critical load, failure occurs through excessive deflection.
2.7
Thermoplastics Elastic Design Method
The viscoelastic behavior of thermoplastic materials results in deformations being dependent on the time under load, the temperature, and the environmental conditions. Therefore, when structural components are to be designed using thermoplastic materials, it must be remembered that the classical equations available for the design of columns, springs, beams, plates, cylinders, etc., have been derived under the following assumptions: • The strains are small • The modulus of elasticity is constant • The strains are independent of cross head loading rate and are immediately reversible • The material is isotropic • The material behaves in the same way under tension and compression Because these assumptions are not always justified for thermoplastic materials, the equations can not be used indiscriminately. For each case, factors such as mode of deformation, service temperature, creep, injection molding conditions, environment, etc., must be considered. In particular it should be noted that the classical equations are derived using the relation: Stress (σ) = Modulus of Elasticity (E) × Strain (ε) The tensile stress-strain curves of thermoplastic materials show that the modulus of elasticity is not a constant. Several approaches have been used to allow for this and some provide very accurate results. The drawback is that the methods can be quite complex for designers. However, one method that has been widely accepted is the “Elastic Design Method”. With this method, using appropriate values of time-dependent properties, such as modulus of elasticity, stresses are selected and substituted into the classical equations. It has been found that this
131
132
2 Engineering Product Design approach gives sufficient accuracy in most cases. Provided that the values chosen for the modulus of elasticity and the stresses take into account temperature, service life of the component, and the limiting strain of the thermoplastic materials. This, of course, assumes that the limiting strain for the thermoplastic material is known. Unfortunately this is not just a value that applies for all thermoplastic materials or even for one plastic in all applications. One method is to use the tensile stress-strain curve and plot a secant modulus that is 85% of the initial tangent modulus (see Figure 2-16). However, for many thermoplastic materials this method is too restrictive and in most practical situations the limiting strain is determined in consultations between the product designer and the thermoplastic material’s manufacturer.
2.7.1
Working Stress
The above mentioned strength characteristics may be used to select the working stress. The working stress is determined merely by dividing either the stress at yield or the ultimate stress by a safety factor. Selection of the safety factor is based on the product application requirements or by the designer’s judgment and experience. Example 2-3
15.00 in. W=200 lb.
The two PET (30% glass reinforced) bars AB and CB are pinned at each end and support a load of 200 pounds as shown in Figure 2-23. The bar AB in tension should have a safety factor of 2.5, while the bar CB in compression should have a safety factor of 2.0. Determine the cross section area of these bars and also the horizontal and vertical components of displacement of point B. A free body diagram of the joint at B assumes that the unknown forces are in tension.
A
B CB =
60˚ .3 17
2i
n.
W (Load) 200.0 = = 400 lb. sin30° sin30°
AB = CB × cos30° = 400 × cos30° = 346.41 lb.
C W=200 lb.
The working stresses are 23,000 / 2.5 = 9,200 psi in tension and 23,000 / 2 = 11,500 psi in compression. The required areas are found by dividing the axial force in each bar by the allowable working stress.
B
A B 30˚
W W σ = → A= A σ
346.41 = 0.0376 in 2 9,200 400 = = 0.0347 in 2 11,500
AAB = ACB
C B Figure 2-23 Structure diagram and load components reaction, where: modulus of elasticity (E) = 1,300,000 psi, tensile strength (σ) = 23,000 psi
To analyze the displacement of point B, it is first necessary to calculate the axial deformation of each of the bars. The variation in length in tension is determined by applying the following equation:
133
2.7 Thermoplastics Elastic Design Method
∆=
W ×L A×E
346.41 × 15.00 = 0.106 in 0.0376 × 1,300,000 400.00 × 17.32 = = 0.153 in 0.0347 × 1,300,000
∆ CB
The location of the point B after deformation has occurred and the increment in bar AB or horizontal displacement is 0.106 in and also rotates as a rigid body about the pin at A. In addition, the bar CB shortens 0.153 in and also rotates about the pin at C. Figure 2-24 shows the movement of point B to its deflected location B1. The elongation of bar AB is shown by the straight line BB1. The same reasoning applies to the rotation of bar CB. From the geometry of the displacement diagram we can calculate the total vertical component straight line B1B2. ∆V =
H
∆ AB =
0.1
53
0.106 in.
in.
B1 B 30˚
V 30˚
0.106 + 0.153 × cos30° + 0.153 × sin30° = 0.489 in tan30°
∆ H = 0.106 in B2 Figure 2-24 Point “B” deflected diagram
2.7.2
Compressive Stress
Compressive properties describe the behavior of a material when it is subjected to a compressive load at a relatively low and uniform rate of loading, which tends to crush the specimen. By choosing the proper test conditions, it is possible to determine the compressive strength of the material. Compression tests for plastics are of limited design value, because plastic products (except foam) seldom deform from compressive loading alone. Compressive properties include modulus of elasticity, yield stress, deformation beyond yield point, compressive stress, and compressive strain. However, compressive stress and compressive modulus are the two properties that are used in part design, resin selection, and thermoplastic material specifications. In the case of a polymer that fails in compression by a shattering fracture, the compressive stress has a definite value. For those polymers that do not fail by a shattering fracture, the compressive stress is an arbitrary factor in determining the degree of distortion as the type of failure of the thermoplastic material. The universal testing equipment used for tensile and flexural testing can also be used for testing the compressive stress of various materials. A deflectometer or a compressometer is used to measure any change in distance between two fixed points on the test specimen at any time during the test. Figure 2-25 shows a typical specimen set up in compressive testing equipment. Compressive stress is calculated by dividing the maximum compressive load carried by the specimen during the test by the original minimum cross sectional area of the specimen. The result is expressed in psi, either at the rupture of the specimen, or at a given percentage of deformation. Modulus of elasticity or compressive modulus, like tensile and flexural modulus, is also represented by the slope of the initial straight line portion of the stress-strain curve and is calculated by dividing the change in stress by the corresponding change in strain. The method to calculate compressive modulus is the same as the tensile testing procedure.
134
2 Engineering Product Design Movable crosshead speed 0.05 inch/min.
Load direction
Specimen
Fixed head
Figure 2-25 Specimen in compressive testing equipment
It is common practice to report compressive properties with the “Compressive stress at 1% deformation”. It is believed that such values give a more accurate picture of the behavior of plastics under conditions of compression. A 1% deformation is very small and a part could recover from such a deformation and still be usable. Compressive stress at 1% deformation is calculated by dividing the force on the specimen by its original cross sectional area when it has been compressed from 1.00 in to 0.99 in (1%) in length.
2.7.3
Flexural Stress
Flexural stress is the ability of the material to withstand bending forces applied perpendicularly to its longitudinal axis. The stresses induced by the flexural load are a combination of compressive and tensile stresses. Flexural properties are reported and calculated with the maximum stress and strain that occur on the outside edge of the flexural test bar. For thermoplastic materials that break under flexural load during this test, the specimen is deflected until rupture occurs in the outer fibers. Many thermoplastic materials do not break, even after large deflection of the flexural test bar. The flexural characteristics of these resins make it hard to determine the ultimate flexural stress. In such cases, common practice is to report flexural yield stress when the maximum strain in the outer fiber of the specimen has reached 5%. Compression load Specimen Support span
6
5
4
5 3 4 1 2 0 1 3 2
Load cell
Figure 2-26 Procedure “A” specimen in the flexural testing apparatus
The flexural stress test has several advantages over the tensile stress test. If the geometry of the application is like a structural beam and the plastic component service failure occurs in the bending mode, then a flexural test is more practical for design or specification purposes than a tensile test. The tensile modulus may be different from the flexural modulus calculated from the outer fiber of the bent beam. The tensile specimen alignment is more difficult in the tensile test. Also, the tight clamping of the tensile test specimens creates stress concentration points. The small strains or deformations produced by the flexural test are sufficiently large to be measured accurately. There are two basic methods used to determine the flexural properties of thermoplastic materials. Procedure “A” is a three-point loading system utilizing center loading on a simple supported beam structure. A flexural test bar with a rectangular cross section rests on two supports 2.00 in apart and is loaded by means of a loading nose midway between the supports. The maximum axial fiber
2.7 Thermoplastics Elastic Design Method
Specimen
W 2
W 2
W 2
W 2 L 3
Load span L
L 3
Support span
Figure 2-27 Flexural stress, procedure “B”
stresses occur on a line under the loading nose. This procedure “A” is especially useful in determining flexural properties for quality control and specification purposes. A specimen in the testing apparatus is shown in Figure 2-26. Procedure “B” is a four-point loading system utilizing two load points equally spaced from their adjacent support points, with a distance between load points of one third of the support span. In this procedure “B”, the flexural test bar rests on two supports and is loaded at two points, each an equal distance from the adjacent support point. Procedure “B” is very useful in testing materials that do not fail at the point of maximum stress under a three-point loading system. The maximum axial fiber stress occurs over the area between the loading noses. This arrangement is shown in Figure 2-27. Procedure “A” is designed principally for materials that break at comparatively small deflections. Procedure “B” is designed particularly for those materials that undergo large deflections during testing. The differences between these two procedures are the strain rates (loading speed) used for these tests. The strain rate for procedure “A” is 0.01 in per minute and the strain rate for procedure “B” is 0.10 in per minute. Flexural modulus is a measure of the stiffness during the first or initial part of the bending process. The flexural modulus should be called “modulus of elasticity in bending”, but other names are also used, such as modulus of elasticity, elastic modulus, flex modulus, or simply modulus. The flexural modulus is represented by the slope of the initial straight line portion of the stress-strain curve and is calculated by dividing the change in stress by the corresponding change in strain. The procedure to calculate flexural modulus uses the three- or four-point loading deflection equations, where deflection and force are measured and recorded as with the tensile modulus calculations. When calculating the flexural modulus, several errors can be made. These are largely associated with the fact that stress-strain curves seldom have a truly straight line initial portion and considerable judgment must be used in deciding what line to draw through the stress-strain flexural curve.
2.7.4
Coefficient of Linear Thermal Expansion (α)
The coefficient of linear thermal expansion (α) is defined as the change per unit length of a straight bar subjected to a temperature change of one degree. The value of this coefficient is independent of the unit of length but does depend on the temperature scale used. Temperature changes in a structure create internal stresses just as applied loads do.
135
136
2 Engineering Product Design
2.7.5
Poisson’s Ratio (υ)
When a bar is subjected to simple tensile loading, there is an increase in the length of the bar in the direction of the load, but a decrease in the lateral dimensions perpendicular to the load. The ratio of the strain in the lateral direction to that in the axial direction is defined as Poisson’s ratio (υ). Example 2-4 A rectangular acetal bar 0.125 in thick, 1.00 in wide, and 10.00 in long is subjected to an axial tensile force of 100 lbs. Determine the decreases in the lateral cross section area of the bar due to this load. Where: Modulus of elasticity (E) = 400,000 psi Poisson’s ratio (υ) = 0.35 The loading is axial, hence the stress in the direction of the load Stress (σ ) =
W (Load) 100.00 = = 8,000 psi A (Area) 0.125 × 1.00
The simple form of Hooke’s law for axial loading states that E =
σ σ 8,000 → Axial Strain (ε) = = = 0.02 ε E 400,000
The ratio of the lateral strain to the axial strain is Poisson’s ratio υ=
Lateral Strain → Lateral Strain = υ × Axial Strain Axial Strain
Lateral strain = 0.35 × 0.02 = 0.007 Decrease in thickness = 0.125 × 0.007 = 0.000875 in Decrease in width = 1.00 ×0.007 = 0.007 in
Tensile stress, (psi)
2.7.6
Tensile testing of materials at room temperature (73 °F) has shown that most metals are characterized by a steep linear slope, a small strain, and a well defined proportional limit in the stress-strain curve. This is not the case for thermoplastic materials, they are, in general, more sensitive to moisture and temperature over long periods of time (creep), the crosshead (load) speed rate of testing, and to environmental conditions. Nylon is a good example of this behavior when it is exposed to moisture. The dry-as-molded properties of nylon should never be used to design a product. The 50% relative humidity properties of nylon are recommended for use with the product design calculations.
13.000 11.000 Dry as molded 9.000
hu mi dit y 50 % Re lat ive
7.000 5.000
e la ti ve 100% R
3.000 1.000 0
0 0.2
0.6
1.0
1.4
h u m id it
1.8
y
2.2
Moisture Effects on Nylon
2.6
3.0
Strain, (% at 73˚ F)
Figure 2-28 Unfilled nylon 6/6, stress-strain curves, moisture effects (Courtesy: Du Pont)
Figure 2-28 shows how the moisture content in the material can change the results of the stress-strain curve of unfilled nylon 6/6, thereby changing the properties such as yield stress, elongation, initial modulus, and toughness. It is very important that the designers of plastic products know under what conditions the material changes its behavior and adapt the design procedure accordingly.
137
2.7.7
Effects of Temperature on the Behavior of Thermoplastics
Thermoplastic materials are used over a wide range of temperatures and the effects of temperature on physical properties must be established before a thermoplastic material can be used for designing a particular product.
Tensile stress, (psi)
2.7 Thermoplastics Elastic Design Method
The service life of a thermoplastic molded part at a given end use temperature will be largely dependent on the requirements of the application and the material selection should be based on heat aging test data of the thermoplastic materials and on actual or simulated end use testing. The effects of temperature on the tensile properties of several thermoplastic materials are given in Figures 2-29, 2-30, 2-31, and 2-32. These stress-strain curves were established by heating the tensile test specimens in an air oven at various temperatures and using a temperature chamber mounted on the universal testing equipment (see Figure 2-3). The changes in tensile properties at various temperatures were measured, recorded, and plotted.
Tensile stress, (psi)
Nylon 6/6 toughened, 33% G. R. 35.000
. ˚F
7.000
12
2˚
6.000
15
5.000
8˚
212
F. F.
˚ F.
3.000 2.000 1.000 0 0
0.5
1.0
1.5
2.0
2.5
3.0
Tensile stress, (psi)
Strain, (%)
73˚ F.
10.000
12 2˚ F. 8.000
6.000
212˚ F . 4.000
2.000
0 0
5.0
10.0
15.0
20.0
Strain, (%)
Figure 2-29 Acetal homopolymer stressstrain curves for two strain ranges at various temperatures (Courtesy: Du Pont)
Unfilled nylon 6/6 at 50% R. H. Tensile stress, (psi)
Exposure of natural- and light-colored thermoplastic resins to elevated temperatures may result in discoloration of the molded part, depending on injection molding conditions. Thermal stabilized additives are compounded with the polymer to minimize discoloration at elevated temperatures. When the thermoplastic materials are subjected to chemicals, oils, grease, water, etc., this could also affect the tensile properties of the thermoplastic materials at elevated temperatures.
73
4.000
The nature of viscoelasticity is such that temperature is of fundamental importance. In thermoplastic materials, the primary bonds are strong covalent bonds along the molecular chains and these bonds are not affected by temperatures, unless high temperatures cause degradation. However, the secondary forces that cause the bonding chains to stay together, restricting their relative movement, may be overcome by increasing temperature. This increases the thermal motion of the molecules, changing the physical properties of the thermoplastic materials. When thermoplastic materials are subjected to elevated temperatures for prolonged periods of time in the presence of air, oxidative degradation will occur. The rate and extent of degradation depends on the type and composition of the thermoplastic material, the temperature, and the time of exposure. This effect reduces the tensile strength and toughness and can eventually lead to surface cracking and brittleness.
8.000
18.000
Yield point
16.000
- 40˚ F.
14.000 12.000 10.000
Yield point 73˚ F. dry as molded
8.000
20.000
73˚ F .
Yield point
6.000
73˚ F. 50% R.H. 200˚ F dry as molded
122˚ F.
Yield point
4.000
15.000
25 0˚ F. 2.000
10.000 0
300˚ F. dry as molded
5.000
Figure 2-31 Nylon 6/6 (toughened, 33% G.R.) stress-strain curves at various temperatures (Courtesy: Du Pont)
0 0
2.0
Strain, (%)
4.0
6.0
8.0
10.0
0
10
20
30
40
50
60
70
Strain, (%)
Figure 2-30 Unfilled nylon 6/6 (at 50% R.H.) stress-strain curves at various temperatures (Courtesy: Du Pont)
138 36.000 32.000
0 -4
28.000
Tensile stress, (psi)
Tensile stress, (psi)
2 Engineering Product Design
16.000
. ˚F
14.000
24.000
200˚ F.
12.000
. 73˚ F
20.000
10.000
16.000
8.000
12.000
6.000
8.000
4.000
4.000
2.000
30 0˚ F.
0
0 0
0.4
0.8
Strain, (%)
1.2
1.6
2.0
2.4
2.8
0
1.0
2.0
3.0
4.0
5.0
6.0
7.0
Strain, (%)
Stress, (psi)
Figure 2-32 PET 30% glass reinforced, stress-strain curves for two strain ranges at various temperatures (Courtesy: Du Pont)
8.000
2.8
Stress-Strain Recovery (Hysteresis)
7.000
Thermoplastic components are required to recover after being loaded intermittently in use. The stress-strain hysteresis curves are shown in Figure 2-33. Tensile specimens of acetal homopolymer were initially loaded using the ASTM strain rates of 0.7%, 1.5%, and 2.7%, respectively. The load was released and the strain recovery was observed. This hysteresis testing procedure was repeated five times and each tensile bar was tested to produce the same initial stress. The tensile specimen tested at 0.7% strain recovered completely. However, the other two specimens tested at higher strain rates elongated without recovering.
6.000 5.000 4.000 3.000 2.000 1.000 0 0
1
0
1
2
0
1
2
Strain, (% at 73˚ F.)
Figure 2-33 Acetal homopolymer, three stress-strain recovery tests (hysteresis) at different strain rates (Courtesy: Du Pont)
3
2.8.1
Creep Behavior of Thermoplastics
The tensile test does not provide information on the creep behavior characteristics of thermoplastic materials. Determining this property requires performing creep tests, which have been widely used to describe the deformation behavior of polymeric materials. In these tests, a constant load is applied to the material and the variation of strain with time is recorded. Normally, a logarithmic time scale is used in the secant or apparent modulus vs. time so that the time dependence after long periods can be included and used as an aid to extrapolation. This curve shows that there is typically an almost instantaneous strain followed by a gradual increase. If a material is linearly viscoelastic, then at any selected time, each line in a family of creep curves should be offset along the strain axis by the same amount. Although this type of behavior may be observed for plastics at low strains and short times, in the majority of cases, the response is nonlinear. The mechanism of creep is not completely understood, but some aspects have been interpreted based on the structures of the polymers. With thermoplastic materials, a particular atom is restricted from changing its position as a result of attractions and repulsions between atoms in the same chain or atoms in adjacent chains. It is generally considered that for an atom to change its position it must overcome an energy barrier and the probability of achieving the necessary energy is improved when a stress is applied. In a semi-crystalline material, the crystalline regions are set in an amorphous matrix. The movement of atoms can
139
2.8 Stress-Strain Recovery (Hysteresis) occur in both regions, but in the majority of cases, atom mobility is favored in the amorphous regions between the cross link chains. Thermoplastic materials have the ability to recover when the applied stress is removed and at a first approximation this can often be considered as a reversal of creep. Creep and recovery of plastics can be simulated by the use of simple structural models for materials with elasticity and plasticity. Although there are no discrete molecular structures that behave like the individual elements of the models, they help in understanding the response of these thermoplastic materials.
2.8.2
Creep and Rupture Under Long-Term Load
Most materials will creep or elongate to some extent and eventually fail under a sustained stress less than the ultimate strength (short-time). After a short time at load, the initial creep or elongation (strain) related to stress causes a redistribution in the molecular structure of the specimen; the elastic strain loses its ability to resist or recover and the viscous creep behavior takes over, resisting the load until failure. The viscous creep condition will continue until a break occurs in the specimen, unless the applied load is reduced sufficiently. Creep, caused by constant load for a long time, temperature, weather conditions, and moisture must be taken into account in product design and selecting the working stresses for the materials.
2.8.3
Creep and Relaxation of Thermoplastics
The phenomena of creep and relaxation in thermoplastic materials are of prime concern to the designers of plastic products which, in use, may be only slightly deformed yet carry a load for long periods of time. Creep will take place even at low loads and low temperature and the designer must estimate its amount. For metals, analogous behavior is usually only encountered at elevated temperatures, and therefore this situation is of less concern for metal materials. Creep and relaxation can be illustrated by loading tension on the specimen. Figure 2-34 shows a load being applied to the specimen and an initial deformation (∆LO) is observed. The permanent elongation suffered by the specimen with time under a constant load is known as the creep characteristic of the thermoplastic material. Consider a similar test bar being stressed by the same load, but in this experiment, the test bar elongation is confined to its initial deformation (∆LO) as shown in Figure 2-35. The stress level gradually decreases with time and the strain rate also decreases at a constant rate; this characteristic is known as relaxation.
L0
L0
L0
L0 +
L 0+
L 0 (t) Constant strain
L 0 (t) L0 F0
Time = 0 Figure 2-34 Creep effects
C o n st a n t fo rc e
L0
L0+
L0
Creep F0
Time = t
F0
Force decay
Time = 0
Figure 2-35 Relaxation effects
F (t)
Time = t
140
2 Engineering Product Design The creep and relaxation data are measured and presented graphically as shown in Figure 2-36. Strain
Stress
Creep
Basic creep and relaxation behaviors are measured by a simple uniaxial tension test as shown in Figure 2-37. Time-dependent creep modulus is defined: E t (Creep) =
Stress σ W /A W × L = = = Strain ε ∆/L ∆×A
E t (Relax) =
Stress σ W /A W × L = = = Strain ε ∆/L ∆×A
Relaxation Time
Figure 2-36 Constant creep and relaxation in tension
Where: W = Constant force (lb.) A = Original cross sectional area (in2) L = Original length (in) Δ = Increase in length (in)
or
∆=
W ×L A×E
W
W L
Figure 2-37
Tests have confirmed that both of the above equations are applicable when the initial strain is within the flexural modulus. This modulus is used as a checkpoint when making creep (deformation) and relaxation (force decay) calculations. It has been shown experimentally that the creep modulus and relaxation modulus are similar in magnitude and for design purposes may be assumed to be the same. That is, Et (Creep) = Et (Relax). A time-dependent modulus called the secant or apparent modulus (85% of initial modulus) is used as a safety factor. Example 2-5 Determine the apparent modulus from a creep experiment by placing a test bar in tension under a load of 150.00 pounds. The bar has an original length of 4.75 in, a width of 0.75 in, and a wall thickness of 0.10 in, or cross sectional area of 0.075 (0.75 × 0.10) in2. After one year, the increase in length is 0.031 in. Stress (σ ) =
W 150.00 = = 2,000 psi A 0.075
Strain (after 1 year) = ε(1 year) = ECreep (after 1 year) =
∆ 0.031 = = 0.0065 or 0.65% L 4.75
Stress σ 2,000 = = = 307,692 psi Strain(1 year) ε(1 year) 0.0065
The use of tensile strength, strain, and secant or apparent modulus in designing injection molded thermoplastic components is very important in the structural analysis of the product. The standard strength of material design equations are used to analyze the structure of the thermoplastic injection molded products. However, the stress, strain, and the modulus of elasticity chosen for the structure analysis of the product are selected on the basis of the service time and end use temperatures that the thermoplastic product is subjected to under load. Several types of curves have been developed by the plastic suppliers to analyze the behavior of the thermoplastic materials, when they are subjected to various temperatures under load for long periods of time (creep).
141
2.8 Stress-Strain Recovery (Hysteresis)
ABS
3.000
2.000
PP copolymer
1.000
HDPE
LDPE 0 0
1
5
4
Figure 2-38 Isochronous stress-strain curves for several resins under load after 1,000 hours at 73 °F air temperature Unfilled nylon 6/6 at 73˚ F. ur
ur
ho
ho
0
10
2.000
0h
ou
rs
5.00
1.500
s.
7
6
Strain, (%)
0.1
1 hr 10 h r s. 100 h r s. 1.00 0h r s. 10 .00 0h r s.
Tensile stress, (psi)
3
2
2.500
3.000
PP -impact copolymer
PP homopolymer
1.
Figure 2-40 shows three isochronous stress-strain curves of nylon 6/6 under load. The first set of curves shows the creep behavior of unfilled nylon 6/6 conditioned at 50% R.H. and 73 °F. The second set of curves shows the creep behavior of 33% fiber glass reinforced nylon 6/6 conditioned at 50% R.H. and 73 °F. The third set of curves shows the creep behavior of 33% fiber glass reinforced nylon 6/6 conditioned at 50% R.H. and 140 °F. These curves are used to determine the apparent modulus, tensile stress, and strain of nylon 6/6 at various periods of time. These creep properties are used for calculating the strength of the nylon 6/6 molded products at the end of the specified service time.
PVC (pipe grade)
Tensile stress, (psi)
Figure 2-39 shows four different isochronous stress-strain curves of acetal homopolymer under load in air at 73, 113, 185, and 212 °F. These curves are used to determine the apparent modulus, tensile stress, and strain of acetal homopolymer at various periods of time. These creep properties are used for calculating the stress of the acetal homopolymer molded products at the end of the service time.
4.000
Tensile stress, (psi)
Figure 2-38 shows isochronous stress-strain curves for several thermoplastic materials under load after 1,000 hours at room temperature (73 °F). These curves are only used to compare the creep behavior among these thermoplastic materials shown in the isochronous stress-strain graph.
0h
our
s
1.500
u ho
0
00 .000 urs 5 ho 00 0 . 10
0
0.5
1.0
1.5
0
3.0
3.5
ur ho
3.000
5.
0
0.1
500
2.5
Nylon 6/6, 33% G. R. at 73˚ F.
4.000
500
2.0
Strain, (%)
5.000
1.000
1.000
500
rs
1.0 10 h o u 0 0h r ho ou ur rs s
0 1.
2.000
rs
00
1.500
u ho
Tensile stress, (psi)
2.000
2.500
1 10 hour 10 hou 0 h rs ou rs
10
0.
2.500
Tensile stress, (psi)
00
0
hr
1.000
2.000
0
0.5
1.0
1.5
2.0
2.5
0
Strain, (%) at 73˚ F. air
0.5
1.0
1.5
2.0
2.5
1.000
Strain, (%) at 113˚ F. air
ou 0h 0 1.0 ours h 00 0 5. urs o h .000
ur ho 2.000
10
1.500
5
ho
ur
s
ou 0h 0 1 s our 00 h
1.000
0
0.5
1.0
1.5
Strain, (%) at 185˚ F. air
2.0
2.5
0.6
0.8
5.000 4.000 0.
3.000
1
ho
5
ur
0 .00
ur rs ho ou 0 0h . 1 10
ho
ur
s
2.000 1.000 0
0
0
0.4
Nylon 6/6, 33% G. R. at 140˚ F.
rs
s hour 1 .0 0 0 2.000 hours 3.000 hours 5.000 hours
500
500
0.2
Strain, (%)
1
Tensile stress, (psi)
ur ho
0 10
rs
0
2.500
Tensile stress, (psi)
10
s
s ur
r
1.500
1.000
ho
ou 1h
2.000
10
Tensile stress, (psi)
0 2.500
0
0.5
1.0
1.5
Strain, (%) at 212˚ F. air
Figure 2-39 Acetal homopolymer isochronous stress-strain curves, under load at four temperatures (Courtesy: Du Pont)
2.0
2.5
0
0.2
0.4
0.6
0.8
Strain, (%)
Figure 2-40 Nylon 6/6 isochronous stressstrain curves, under load, 50% R.H. at two temperatures (Courtesy: Du Pont)
4.0
142 Tensile stress, (psi)
2 Engineering Product Design 2.600 2.000 1.600
1.0
ho
ur
ur 50 ho
Figure 2-41 shows isochronous stress-strain curves of unreinforced polycarbonate under load at 203 °F. Figure 2-42 shows an isochronous strain-time creep in flexure at 4,000 psi stress curves of 30% fiber glass reinforced PET at 73, 140, and 257 °F. Both graphs are used to determine the apparent modulus and strain at various time periods.
s
our 100 h
s
1.000 600 0
0
0.5
1.0
1.5
2.0
Strain, (%)
Strain, (%)
Figure 2-41 Unfilled polycarbonate isochronous stress-strain curves, under load at 203 °F (Courtesy: General Electric Plastics)
1.8 1.6 257
1.4
Example 2-6 A container made of acetal homopolymer to store gas at 60 psi for one year or 10,000 hours. The outside diameter must not exceed 1.00 in. The maximum end use temperature is 113 °F and the maximum gas pressure is 80 psi. Determine the wall thickness and the inside diameter.
˚ F.
Solution
1.2 140˚
1.0
F.
The radial growth and mean hoop stress of a thin closed-end tube can be calculated using the following equations:
0.8
Change in radial displacement = ∆ T = (r / E T ) × (1 − υ /2) × σ h
0.6 73 ˚ F.
0.4 0.2 0 0.1
1.0
10
100
1.000
10.000
Time, (hours)
Figure 2-42 PET 30% G. R. isochronous creep flexure curves, at 4,000 psi stress at three temperatures (Courtesy: Du Pont)
Where: Mean hoop stress = σh = (P × r) / t (psi) ∆T = Total radial displacement at 10,000 hours (in) r = Tube radius (in) ET = Apparent modulus at 113 °F and 10,000 hours (psi) υ = Poisson’s Ratio (0.35) P = Maximum internal pressure (80 psi) t = Tube thickness (0.031 in) Wall thickness = 0.031 in, I. D. = 0.837 in and O. D. = 0.9 in (at 113 °F) Then: r = (0.45 + 0.418) / 2 = 0.434 in σh = (P × r) / t = (80 × 0.434) / 0.031 = 1,120 psi Apparent modulus at 10,000 hours (E10,000), 113 °F and 1,120 psi can be determined from the acetal homopolymer isochronous stress-strain curve at 113 °F, a corresponding strain value = 1.05% is found in Figure 2-39 (second set of curves). E10,000, 113 °F, 1,120 psi = σh / ε10,000 = (1,120 × 80) / 1.05 = 85,333 psi ∆10,000 = (0.434 / 85,333) × (1–0.35 / 2) × (80 × 0.434) / 0.031 = 0.0047 in or on the diameter, ∆10,000 = 2 × 0.0047 = 0.0094 in O. D.10,000 = 0.900 + 0.0094 = 0.9094 in (within tolerance).
2.8 Stress-Strain Recovery (Hysteresis)
Example 2-7 Obtain a press-fit of 0.625 in diameter steel shaft into an acetal homopolymer hub, which will require a pull-out force greater than 40 lb after 1,000 hours of exposure at 185 °F in air. A) Determine the hub dimensions. B) Determine the initial pull out force. C) Could the press-fit be accomplished at 73 °F? Solution A) Hub dimensions at 185 °F. Assume the steel shaft size variation with temperature is negligible. The apparent modulus at 1,000 hours (E1,000), 185 °F, and 1,500 psi can be determined from the acetal stress-strain creep curve long-term at 185 °F, a corresponding strain value = 1.80% is found in Figure 2-36 (third set of curves). Assume a design stress of 750 psi (safety factor of 2.0). Assume hub wall thickness is 0.125 in, hub outside diameter is 0.875 in. Hub inside diameter is calculated by finding the interference between shaft and hub which will produce a stress of 750 psi at 185 °F after 1,000 hours. Interference calculations for press-fitting plastic components used these following formulas: Interference = I = [(σd × Ds) / W] × [(W + υh) / Eh + (1 – υs) / Es] Since we assume variation of shaft size with temperature is negligible. Interference = I = [(σd × Ds) / W] × [(W + υh) / Eh] Geometry factor = W = [1 + (Ds / Dh)2] / [1 – (Ds / Dh)2] Where: I = Diameter interference (in) σd = Design stress (750 psi) Dh = Outside diameter of hub (0.875 in) Ds = Diameter of shaft (0.625 in) Eh = Tensile modulus of elasticity of hub (psi) Es = Modulus of elasticity of shaft (psi) υh = Poisson’s ratio of acetal hub (0.35) υs = Poisson’s ratio of steel shaft W = Geometry factor Then: W = [1 + (0.625 / 0.875)2] / [1 – (0.625 / 0.875)2] = 3.08 The apparent modulus at 1,000 hours (E1,000), 185 °F, and 750 psi can be determined from the acetal isochronous stress-strain at 185 °F, a corresponding strain value = 0.80% is found in Figure 2-39 (third set of curves). E500 hrs. = (750 × 100) / 0.80 = 93,750 psi
143
144
2 Engineering Product Design
Then: I = [(750 × 0.625) / 3.08] × [(3.08 + 0.35) / 93,750] = 0.00556 in Inside diameter of hub = Ds – I = 0.625–0.00556 = 0.6194 in The hub length may be calculated using the force and pressure equations to press two parts together. F = π f P Ds L, P = σd / W Where: F = Assembly force (40.0 lb) f = Coefficient of friction (0.35) P = Joint pressure (psi) Ds = Diameter of shaft (0.625 in) L = Length of press-fit surface (in) σd = Design stress (750 psi) W = Geometry factor (3.08) Combining the previous equations and solve for L: L = (F × W) / (π × f × Ds × σd) L = (40 × 3.08) / (3.14 × 0.35 × 0.625 × 750) = 0.239 in Hub dimensions are: L = 0.239 in, t = 0.125 in, I. D. = 0.6194 in. B) Pull-out load at start of 1,000 hours at 185 °F. By using the acetal stressstrain curve in Figure 2-29 at 1.0% strain, 185 °F, cross head speed 0.20 in per minute, tensile secant modulus = 250,000 psi. Now hub inside diameter will be 0.625 in at 185 °F in the press-fit condition. ε = 0.6194/0.625 = 0.991 in/in Design stress initial = σd = E185 °F × ε185 °F = 250,000 × 0.00991 = 2,477 psi Joint pressure = P = σd / W = 2,477/3.08 = 804.22 psi Force = F = π f P Ds L = 3.14 × 0.35 × 804.22 × 0.625 × 0.239 = 132.09 lbs. C) Could the press-fit be accomplished at 73 °F? I. D.185 °F = 0.6194 in before assembly? Thermal contraction from 185 to 73 °F. D73 – D185 = α × (73–185) D185 in
D73 = D185 + α × (73–185) D185 in
α = Coefficient of linear thermal expansion of acetal from 73 to 185 °F.
α = 7.2 × 10–5
D73 = 0.6194 + (7.2 × 10–5) × (–112) × 0.6194 = 0.6194–0.0049 = 0.614 in
145
2.9 Flexural Beam Stress Distribution
Calculate strain for press-fit of 0.614 in inside diameter hub of acetal homopolymer onto 0.625 in shaft of steel at 73 °F. Eh = σd / εh I = 0.625–0.614 = 0.011 in
εh = (I / Ds) × [W / (W + υh)] = (0.011 / 0.625) × [3.08 / (3.08 + 0.35)] εh = 0.0158 in/in = 1.58% From the acetal homopolymer stress-strain curve at 73 °F (see Figure 2-29, first set of curves), it is seen that this strain is well below the 4.50% yield strain and the assembly could be accomplished.
2.9
Flexural Beam Stress Distribution
The difference between metal and thermoplastic design methods lies in the selection of mechanical properties to be used in standard elastic design equations. For metal materials, these properties are relatively constant over wide ranges of temperature, time under load, and other conditions such as weather and environment. For thermoplastic materials, these properties are more sensitive to variations compared to metals under the same environmental conditions. To illustrate this behavior, consider the stress distribution of a simple three-point beam in flexure. When the beam is flexed, two symmetrical regions of stresses in opposite directions are formed at each side of the neutral plane. With one side facing the load, the fiber surface stress is in compression, while on the opposite side, facing the two supports, the surface stress is in tension. It assumes that the stress-strain curves in tension and compression are symmetrical with the same characteristics; it also assumes that the modulus of elasticity only at relatively small strains is linear in the elastic region. Therefore, the stress distribution in a beam in flexure is also symmetrical about the neutral plane; this linear stress distribution of a beam in flexure is shown in Figure 2-43 (bottom left).
Load point Compressive forces
Tensile forces
Neutral plane Support point
σcompression
σcompression
Neutral plane
σtension Equal tensile and compressive stresses
σtension Greater compressive stress than tensile stress
Figure 2-43 Flexural stress distribution of a three-point beam
146
2 Engineering Product Design When large beam deflections are caused by the load, two distinct rectangular shaped regions of stresses in opposite directions are formed at each side of the neutral plane. It assumes that the material is ductile and does not fracture until the fiber of the thermoplastic crystalline structure surface has yielded. The neutral plane is no longer in the center of the beam, because the yield stress in compression is greater than the yield stress in tension. This behavior is illustrated in Figure 2-43 top and right bottom. The standard metal beam deflection equation is modified when calculating thermoplastic beam structures. The flexural modulus of elasticity (E) is replaced with the apparent or secant modulus (ES) of the thermoplastic material. The apparent modulus (ES) is determined by using the thermoplastic isochronous stress-strain curve at the required temperature and service time of the product. Example 2-8 A bar molded of nylon 6/6, 33% fiber glass reinforced at 50% relative humidity and measuring 6.00 in length × 0.50 in width × 0.125 in thickness is to carry a center load of 5.00 lbs. The bar will rest on 2 supports on a 4.00 in span with ends free to move. Determine the maximum deflection at the center of the beam after 5,000 hours at 50% relative humidity and room temperature (73 °F). Solution 1. Calculate maximum fiber stress from stress formula. σ = (3 × W × L) / (2 × b × d2) Where: σ = Stress (psi) W = Load (5.00 lbs.) δ = Deflection (in) E = Flexural modulus or apparent modulus (psi) I = Moment of inertia (in4) b = Width of the bar (0.50 in) d = Thickness of the bar (0.125 in) L = Length of support span (4.00 in) σ = (3 × 5.00 × 4.0) / (2 × 0.50 × 0.1252) = 3,840 psi I = (b × d3) / 12 = (0.50 × 0.1253) / 12 = 8.138 × 10–5 in4 2. Calculate deflection (δ5,000 hrs.). The apparent modulus at 5,000 hours (E5,000 hrs.), 73 °F, 50% R.H., and 3,840 psi can be determined from the nylon 33% G. R. isochronous stress-strain curve (see Figure 2-37, second set of curves) as a strain of 0.68%. E5,000hrs., 3,840 psi, 73 °F = (3,840 × 100) / 0.68 = 564,705 psi. From three-point beam equation, the maximum deflection at the center is: δ = (W × L3) / (48 × E × I);
δ5,000hrs. = (5.00 × 43) / (48 × 564,705 × 8.13 × 10–5) = 0.145 in
147
2.10 Viscoelastic Modulus Design Method
2.10
Viscoelastic Modulus Design Method
0.16
Test results
0.14
The assumption made for the flexural beam deflection equations is that the deflection distribution is initially linear and remains linear with time. The validity of this assumption was checked by running a flexural beam test in the laboratory. The specimen used for the test was an acetal injection molded bar measuring 5.00 in long × 0.50 in wide × 0.125 in thick; the specimen was centrally loaded, both ends were freely supported using a 4.00 in span. The deflection caused by the load over a period of time was measured and recorded. Figure 2-44 shows that the deflection-time results are in positive agreement with the calculated and experimental values. The deflection-time curve was calculated by using the threepoint beam equation for maximum deflection; in this equation the modulus of elasticity (E) was replaced by the apparent or secant modulus (ES). Deflection = δ =
W × L3 48 × ES × I
The apparent or secant modulus value was obtained from the low strain tensile relaxation measurements. This apparent modulus was substituted in the equation and the deflection-time curve was plotted. The equations used in the calculations are applicable only if the maximum stress or corresponding initial strain is within the viscoelastic modulus boundaries. The equation for calculating the maximum stress for the beam is: Maximum stress = σ Max. =
3×W × L 2 × b × d2
The initial strain can be calculated by applying Hooke’s law, that is, by dividing the maximum stress by the initial modulus. Initial strain = εO =
σ EO
The outer fiber surface σ (stress) and the ε (strain) were calculated to be 1,500 psi and 0.41% for this experiment. Because 1,500 psi stress and 0.41% strain are less than stress and strain at the viscoelastic modulus for acetal homopolymer (stress = 5,125 psi at the start, decreasing the strength after one year and strain = 1.25%), a positive agreement between the calculated analysis and the test results were obtained. The deflection-time curves were similar in both procedures.
0.12
Deflection, (inch)
The elastic design equations that were developed for metal materials can be applied for designing injection molded thermoplastic products. The deflection equations are expressed in terms of two material variables, the modulus of elasticity (Young’s modulus) and Poisson’s ratio. The stress equations are only dependent on the load and geometry. These formulas can be converted to the appropriate time-dependent equations by replacing the modulus of elasticity with the apparent or secant time-dependent modulus and assuming that Poisson’s ratio is a constant.
0.10
Calculated values
0.08 0.06 0.04 0.02 0 0.1
1
10
100
Time, (hours at 73˚ F.)
Figure 2-44 Acetal homopolymer flex loaded beam comparison between the calculated values and test results (Courtesy: Du Pont)
1.000
148
2 Engineering Product Design
Example 2-9 Determine the deformation of an acetal homopolymer aerosol container base; the base is a circular flat plate under an internal pressure of 100.00 psi for one year at 73 °F. The slightest bulge of an initially flat bottom will cause the container to rock on its base. Hence, a skirt around the base is necessary if a flat bottom is intended for the container. The height of the skirt must be greater than the base deformation. In a round container the walls add stiffness to the base. The height for the skirt can be calculated by assuming that a simple vertical support from the walls helps the container to stand erect. Calculating the maximum deflection (δMax.) at the center of the plate requires the application of the following equation: Maximum deflection = δMax. =
3 × P × r 4 (5 − 4 υ − υ2 ) 16 × ES (1 year) × t 3
and the corresponding maximum stress (σ Max.) is: Maximum stress = σ Max. =
3 × P × r 2 (3 + υ) 8 × t2
Where: r = Radius of plate = 0.75 in t = Thickness of plate = 0.20 in Operating condition at 73 °F after one year (5,000 h) P = Internal pressure = 100.00 psi EO = Initial modulus = 410,000 psi ES (1 year) = Apparent modulus = 175,000 psi (see Example 2-10 procedure) υ = Poisson’s ratio = 0.35 δMax. =
3 × 100 × 0.754 (5 − 4 × 0.35 − 0.352 ) = 0.015 in 16 × 175,000 × 0.203
σ Max. =
3 ⋅ 100 × 0.752 (3 + 0.35) = 1,750 psi 8 × 0.202
ε=
1,750 410,000 = 0.0043 in/in = 0.43%
Because the calculated maximum initial stress and strain values are within the viscoelastic modulus of acetal homopolymer at room temperature (stress = 5,125 psi and strain = 1.25%), the calculated maximum deflection of 0.0015 in is a realistic estimated value. The height of the skirt that elevates the base should be at least 0.0015 in, so that the container will stand erect and firm.
2.10 Viscoelastic Modulus Design Method
Example 2-10 To find the radial displacement of a thermoplastic pipe under internal pressure, it is sometimes important to calculate the radial displacement of the pipe wall thickness that is under internal pressure for a specific period of time. The radial displacement (δr) and the mean hoop stress (σH) of a thin-walled closed-end pipe may be calculated by using the following equations: Radial displacement = δR = Mean hoop stress = σ H =
r ES
υ P × r 1 − 2 t
P×r t
A pipe made of unfilled nylon 6/6 operates using compressed air of 150 psi pressure; the pipe is conditioned to 50% relative humidity at 73 °F for 5,000 hours. Where: r = Mean radius of pipe = 0.50 in t = Pipe wall thickness = 0.10 in P = Internal pressure = 125 psi Environmental conditions of 50% R.H. at 73 °F after 5,000 hours EO = Initial modulus of unreinforced nylon 6/6 = 175,000 psi ES (5,000 hrs) = Apparent modulus = 76,500 psi υ = Poisson’s ratio = 0.40 To determine the apparent modulus of nylon 6/6 conditioned to 50% R.H. at 73 °F after 5,000 hours, it is necessary to obtain the isochronous curves for unfilled nylon 6/6 of 50% R.H. at 73 °F (see Figure 2-37, first set of curves). The apparent modulus after 5,000 hours is calculated by using the small original strain (strain = 0.85%) required to maintain the elongation within the elastic range limits. The stress at 0.85% strain is 650 psi after 5,000 hours. The apparent modulus is the ratio between the 650 psi stress divided by the 0.0085 strain, which equals 76,500 psi. 125 × 0.50 = 0.00326 in (1 − 0.20) × 0.10
δR =
0.50 76,500
σH =
125 × 0.50 = 625 psi 0.10
ε=
σH 625 = = 0.0037 in/in = 0.37% EO 175,000
The calculation shows that the radius of the pipe would increase by 0.00326 in after 5,000 hours. The radial displacement is realistically estimated, because the initial stress-strain did not exceed the viscoelastic modulus for nylon 6/6. The initial stress, the stress, and strain after one year are the following: σO = 1,485 psi σ(5,000 hr.) = 650 psi, ε(5,000 hr.) = 0.85%
149
150
2 Engineering Product Design
2.11
Centroid, Section Area, and Moment of Inertia
Element Moment The first moment of an element area about any axis is defined as the product of an element area and the perpendicular distance between element area and axis. Figure 2-45 shows the first moment dQx of the element da about the x-axis defined as: dQx = y da, and about the y-axis the first moment it is defined as: dQy = x da.
Y x da
Area Moment The first moment of a finite area about any axis is determined by the summation of first moments of all elements contained in the finite area about the same axis. The first moment is developed by means of an integral.
y X
O
Area moment = Qx = ∫ dQx
Figure 2-45
Area Centroid The centroid of an area is the point at which the area might be considered to be concentrated and still leave unchanged the first moment of the area about any axis. For example, a thin metal plate will balance in a horizontal plane if it is supported at a point directly under its center of gravity. The centroids of some areas are obvious. In a symmetrical figure such as a circle or square, the centroid coincides with the geometric center of the figure. Therefore x indicates the x-coordinate of the centroid. The centroid of an area is defined by the following equations, where A denotes the area. x = ∫ x da / A = Q y / A , y =
∫ y da / A = Q x / A
Example 2-11 Locate the centroid of a triangle shown in Figure 2-46. According to the coordinate system shown, the y-coordinate of the centroid is defined by the following equation
Y s
Centroid = y =
∫ y da A
dy d
Select an element such that y is constant for all points in the element. The horizontal shaded area da of the element is y s da.
y X b
Figure 2-46
Centroid = y =
∫ y s da A
151
2.11 Centroid, Section Area, and Moment of Inertia
The product y s da represents the first moment of the shaded element about the x-axis. s d−y From similar triangles it follows that = . Substituting s in above b d integral, d
Centroid = y =
d
=
0
bd 2
2 ( y d − y 2 ) dy 2 ∫ d 0
d d y3 2 y2 2 d3 d3 1 d − = − = Centroid = d 2 2 3 3 d 2 0 3 0 d 2
Y
Example 2-12
dρ
The polar coordinate system shown will be a logical choice for such a contour.
y=
Locate the centroid of a semi-circle shown in Figure 2-47. dθ r
θ
The area is approximately a rectangle and is given by: A = ρ dθ dρ
Centroid = y =
y =
∫∫ 0 0
∫∫
ρ dθ dθ
0 0
y =
Figure 2-47
∫ y da ∫ da π
( ρ dθ dρ)( ρ sin θ) π r
X
ρ
The y-coordinate of centroid is defined by the following equation:
π r
ρ sinθ
y =
b
∫ y d (d − y) dy
=
ρ3 ∫ 3 sin θ dθ 0 0
π
r
π
∫ 0
ρ2 2 dθ 0 r
=
r3 sin θ dθ 3 ∫0 π
r2 dθ 2 ∫0
2r 4r (− cos θ)0π = Centroid = = 0.424 r 3π 3π Y
Example 2-13 Locate the centroid, section area, and the moment of inertia of the shaded area remaining after the semi-circle of radius 0.375 in has been removed from the semi-circle area of radius 0.500 in, as shown in Figure 2-48.
y
The y-coordinate of the centroid of the shaded area is defined by the following equation: Centroid = y =
∫ y da A
X 0.375 r1
Figure 2-48
0.500 r2
152
2 Engineering Product Design
The numerator of this fraction may be evaluated by remembering that it represents the first moment of the entire 0.500 in semi-circular area minus the first moment of the 0.375 in semi-circular area about the x-axis. The first moment of the 0.500 in semi-circular area about the x-axis is given by the product of its area and the vertical distance from the x-axis to the centroid of this area. Similarly, for the first moment of the 0.375 in semi-cicular area, the location of the centroid, section area and the moment of inertia of each of these areas were found in the table of geometries and equations to have the following relationship: Centroid = Y =
4 (r23 − r13 ) (0.503 − 0.3753 ) = 0.424 = 0.280 in 2 2 3 π (r2 − r1 ) (0.502 − 0.3752 )
Area = A = 1.5708 (r22 + r12 ) = 1.5708 (0.502 + 0.3752 ) = 0.613 in 2 Moment of inertia = I = 0.1098 (r24 − r14 ) − (0.283 r22 × r12 )
I = 0.1098 (0.504 − 0.3754 ) − (0.283 × 0.502 × 0.3752 )
r2 − r1 r2 + r1
0.50 − 0.375 0.50 + 0.375
Moment of Inertia = I = 0.00328 in4
Composite Areas The moment of inertia of a composite area is the summation of the moments of inertia of the component areas making up the entire area. This eliminates the necessity for integration, if the area can be broken down into rectangles, triangles, circles, etc.; for each of these, the moment of inertia can be calculated. Parallel Axis Theorem Y
yG x1
xG G y1
The parallel axis theorem states that the moment of inertia of an area about any axis is equal to the moment of inertia about a parallel axis (through the centroid), plus the product of the area and the square of the perpendicular distance between the two axes. For the area shown in Figure 2-49, the axes xG and yG pass through the centroid of the plane area. The X and Y axes are parallel axes located at distances x1 and y1 from the centroidal axes. Let A denote the area of the selected cross section, I xG and I yG the moments of inertia about the axes through the centroid, and Ix and Iy the moment of inertia about the X and Y axes. The moments of inertia about both axes are represented by these equations:
O
Figure 2-49
X
Ix = I xG + A (y1)2 Iy = I yG + A (x1)2 Element Moment of Inertia The second moment, or moment of inertia of an element of area about any axis, is defined as the product of the area of the element and the square of the perpendicular distance between the element and the axis.
153
2.11 Centroid, Section Area, and Moment of Inertia The moment of inertia dIx of the element about the x-axis is: dIx = y2 da, and about the y-axis, the moment of inertia is: dIy = x2 da. Area Moment of Inertia The second moment, or moment of inertia of a finite area about any axis, is defined as the summation of moments of inertia (all elements contained in the finite area) about the same axis. The moment of inertia of the finite area about the x-axis is denoted by Ix and about the y-axis is denoted by Iy. The units of moment of inertia are the fourth power of a length (in4). Ix = ∫ d Ix =
∫ y da = ∫ x 2 da
Iy = ∫d Iy
2
Example 2-14 Determine the moment of inertia of a rectangle about an axis through the centroid and parallel to the base, as shown in Figure 2-50.
Y b
The moment of inertia I xG about the x-axis passing through the centroid is defined by the following equation: I xG =
∫y
2
da
d 2
Select an element such that y is constant for all points in the element. This side illustration shows a rectangular shaded area with the following characteristics: d /2
y3 b d3 2 = = y b y b d 3 ∫ 12 − d /2 − d /2 d /2
I xG =
dy X
G
y
d 2
Figure 2-50
Example 2-15 Determine the moment of inertia of a circle about a diameter, as shown in Figure 2-51. Y
The select shaded element of area shown in the illustration uses the polar coordinate system. The radius of the circle is r. Ix is defined as I x =
∫y
2
da . dθ
But y = ρ sin θ , and da = ρ dθ dρ . 2π r
Ix =
∫ ∫ ( ρ dθ dρ) (ρ
2
0
Ix =
r4 4
sin θ) 2
0
2π
∫ 0
sin 2 θ dθ =
dρ
r 2π
Ix =
∫ 0
π r4 4
ρ4 sin θ dθ 4 0
y
θ
X
r
ρ
2
Figure 2-51
154
2 Engineering Product Design π D4 . 64 The moment of inertia of a semicircular area about an axis coinciding with its base is half of the value of the polar moment of inertia of a solid circular area.
The diameter of the circle is D = 2 r and I x =
Ix =
1 π D4 π D4 × = = 0.0245 D 4 2 64 128
Example 2-16 Determine the moment of inertia of a circle by using the moment of inertia, area, and centroid table of equations for various cross section geometries. Table 2-2 on page 156/157 shows the following: Cross section
d
Neutral axis “y” Section area distance (in) “A” (in2) y
y=
d 2
A=
Moment of inertia “I” (in4)
π d2 π d4 = 0.7854 d 2 I = = 0.049 d 4 4 64
Example 2-17 Determine the moment of inertia of the T-section shown about a horizontal axis passing through the centroid, as shown in Figure 2-52. First, locate the centroid of the area. Then introduce the x-y coordinate system. By definition, the y-coordinate is given by the following equation: Centroid = y =
∫ y da A
The numerator of this expression represents the first moment of the entire area about the x-axis. This may be calculated by multiplying the area of each of the three component rectangles 1, 2, and 3 by the distance from the x-axis to the centroid of the particular rectangle. (0.3) (0.15) (0.075) + (0.75) (0.15) (0.375) + (0.3) (0.15) (0.075) (0.30) (0.15) + (0.75) (0.15) + (0.30) (0.15) = 0.241 in
y = 0.30
0.30 X
0.15
1
3 2 xG
0.60
Y 0.15
Figure 2-52
x1
The centroid is located 0.241 in below the x-axis. The horizontal axis passing through this point is denoted by xG in the illustration. One technique is to calculate the moment of inertia of the entire area about the x-axis, then use the parallel axis theorem to transfer this result to the xG axis. The moment of inertia about the x-axis is found as the sum of the moments of inertia about this same axis of each of the three rectangles. I x = (1/3) (0.3) (0.15)3 + (1/3) (0.15) (0.75)3 + (1/3) (0.3) (0.15)3 = 0.0217 in 4
2.11 Centroid, Section Area, and Moment of Inertia
The parallel axis theorem is used to find the moment of inertia of the entire T-section about the xG-axis. A = (0.15) (0.30) + (0.15) (0.75) + (0.15) (0.30) = 0.2025 in2 Ix = I xG + A (y1)2 0.0217 = I xG + 0.2025 (0.241)2 I xG = 0.0099 in4
Example 2-18 Determine the moment of inertia in Example 2-17, but use the table of equations for the T-section. Select the closest cross section from the table. Modify the geometry and equations to meet your requirements. The table below shows how to make these adjustments. Centroid (y) in, Section Area (A) in2, Moment of Inertia (I) in4
Cross section
y =1− n
s
m T
b
l h
+ 3 T l 2 − h (T − t ) (3 l − h)] y
a
A=
t
b T
l
1 [3 s 2 (b − T ) + 2 a m (m + 3 s) 6A
h (T + t ) + n T + a (s + n) 2
I =
1 3 [h (T + 3 t ) + 4 b n3 − 2 a m3 ] − A (l − y − n)2 12
y=
l 2 T + T 2 (b − T ) 2 (b T + h T )
T
A = bT + hT h
y
I =
y =
1 [T y 3 + b (l − y )3 − (b − T ) (l − y − T )3 ] 3
l 2 T + T 2 (b − T ) 0.752 × 0.15 + 0.152 (0.75 − 0.15) = = 0.241 in 2 (b T + h T ) 2 (0.75 × 0.15 + 0.60 × 0.15)
A = b × T + h × T = 0.75 × 0.15 + 0.60 × 0.15 = 0.2025 in2 I =
1 [T y 3 + b (l − y )3 − (b − T ) (l − y − T )3 ] 3
I =
1 [0.15 × 0.2413 + 0.735 (0.75 − 0.241)3 3 − (0.75 − 0.15) (0.75 − 0.241 − 0.15)3 ]
I = 0.0244 in4
155
156
Table 2-2 Moment of Inertia, Cross Section Area, and Neutral Axis Equations
Cross section
Centroid “y” (in)
Section area “A” (in2)
Moment of Inertia “I” (in4)
y a
y=
a 2
A = a2
I =
a4 12
y=
l 2
A = bl
I =
l b3 12
y=
l 2
A = bl
I =
l b3 12
y=
2 l 3
A=
lb 2
I =
b l3 36
y=
l (a + 2 b) 3 (a + b)
A=
l (a + b) 2
I =
l 3 (a2 + 4 a b + b2 ) 36 (a + b)
y=
l 2
A=
π l2 = 0.7854 l 2 4
I =
π l4 = 0.049 l 4 64
y=
D 2
A=
π (D 2 + l 2 ) = 0.7854 (D 2 + l 2 ) 4
I = 0.1098 (R24 − R14 ) −
0.283 R22 R12 (R2 − R1) R2 + R1
y=
4 (R23 − R13 ) (R 3 − R13 ) = 0.424 22 2 2 3 π (R2 − R1 ) (R2 − R12 )
A=
π (R22 + R12 ) = 1.5708 (R22 + R12 ) 2
I = 0.1098 (R24 − R14 ) −
0.283 R22 R12 (R2 − R1) R2 + R1
a
y d
b
y d b
y
d
b a
y
d b
y d
d
D
y y
r2
y
a
d
y=a b
A = π (a b − c l) = 3.1416 (a b − c l)
I =
π 3 (a b − c 3 l) = 0.7854 (a3 b − c 3 l) 4
I =
1 12
c
a n y
L
t
h b
s
d
l y= 2
A = l t + 2 a (s + n)
3 1 (h 4 − h 4 b l − 4 G
GFlange Slope =
h−h b−t
2 Engineering Product Design
r1
Centroid “y” (in)
Section area “A” (in2)
d
s
h
t
y
b
a
y=
I =
b 2
A = l t + 2 a (s + n)
s
a
t
I =
y h d
L
y=
n
l 2
A = l t + a (s + n)
a y
n
h b
n
L
d
s
b
h t2 G y = b − s b2 + + (b − t )2 (b + 2 t ÷ A 2 3 GFlange Slope
h−h = 2 (b − t )
I = A = l t + a (s + n)
h−h b−t
1 3 1 8 h 4 − h 4 ) b l − 12 8G h−h 2 (b − t )
1 G 2 s b3 + h t 3 + (b 4 − t 4 ) − A (b − y )2 3 2
GFlange Slope =
h−h 2 (b − t )
m
T
y = l − [3 s 2 (b − T ) + 2 a m (m + 3 s)
a
l h
G 4 3 3 4 b (l − h) + h t + 4 (b − t )
GFlange Slope =
b
s
1 12
GFlange Slope =
n
L
Moment of Inertia “I” (in4)
+ 3 T l 2 − h (T − t ) (3 l − h)] ÷ 6 A
y
A=
h (T + t ) + n T + a (s + n) 2
I =
2.11 Centroid, Section Area, and Moment of Inertia
Cross section
1 3 [h (T + 3 t ) + 4 b n3 − 2 a m3 ] − A (l − y − n)2 12
t m s
I =
y t
y=
b T n
h l
b 2
A=
h (T + t ) + n T + a (s + n) 2
a
s b3 + m T 3 + h t 3 12 a m [2 a2 (2 a + 3 T )2 ] + 36 h (T − t )[(T − t )2 + 2 (T + 2 t )2 ] + 144
t
y
a
y=a−
a
a2 + a t − t 2 2 (2 a − t )
A = t (2 a − t )
I =
1 [t y 3 + a (a − y )3 − (a − t )(a − y − t )3 ] 3
t
t d
y=
l 2
A = l t + s (b − t )
I =
t l 3 + s 3 (b − t ) 12
y=
2a − t 2
A = t [b + 2 (a − t )]
I =
b (a + c )3 − 2 l c 3 − 6 c l a2 12
s
y
b t
t
a a
c d b
y
157
158
2 Engineering Product Design
2.12
Radius of Gyration
If the moment of inertia of an area (I) about the x-axis is denoted by Ix, then the radius of gyration Rx is defined by: Rx = (Ix / A)1/2; similarly, the radius of gyration about the y-axis is given by: Ry = (Iy / A)1/2. The radius of gyration is used for comparative purposes but has no physical significance. The frequently used geometries for thermoplastic design structures have their own equations for calculating the neutral axial or centroid distance (y), the cross section area (A), and the moment of inertia (I). Table 2-2 of typical geometries and equations was developed to provide engineering assistance for structural design analysis of injection molded thermoplastic components.
2.13
Stress Analysis of Beams
The types of loads applied to beams are either forces or couples that lie in a plane, containing the longitudinal axis of the beams. The forces are understood to act perpendicular to the longitudinal axis and the plane containing the forces is assumed to be a plane of symmetry of the beam. The effects of these forces and couples acting on a beam are: • Deflections perpendicular to the longitudinal axis of the beam • Setting up both normal and shearing stresses on any cross section of the beam perpendicular to its axis.
2.13.1
Types of Loads
If couples are applied to the ends of the beam and no forces act on the beam, this is termed pure bending. For example, in Figure 2-53, a portion of the beam between the two forces is subjected to pure bending. Bending produced by forces that do not form couple is called ordinary bending. A beam subject to pure bending has only normal stresses with no shearing stresses. A beam subject to ordinary bending has both normal and shearing stresses acting within the beam. Behavior of Beams
W a
W a
Assume that a beam is composed of an infinite number of thin longitudinal fibers. Each longitudinal fiber is assumed to act independently from the other fibers, without lateral pressures or shearing stresses between the fibers. The beam shown in Figure 2-53 will deflect downward and the fibers in the lower part of the beam undergo elongation, while those in the upper part are shortened. These changes in the lengths of the fibers cause stresses in the fibers. The elongated fibers have tensile stresses acting on the fibers along the longitudinal axis of the beam, while the fibers that are shortened are subject to compressive stresses. Neutral Surface of Beams
Figure 2-53 Beam in bending by two central forces
There always exists one surface in the beam containing fibers that do not undergo any elongation or compression and is not subject to any tensile or compressive stress. This surface is called the neutral surface of the beam.
159
2.13 Stress Analysis of Beams Neutral Axis The intersection of the neutral surface with any cross section of the beam perpendicular to its longitudinal axis is called the neutral axis. All fibers on one side of the neutral axis are in a state of tension, while those on the opposite side are in compression. Bending Moment The bending moment is the sum of the moments of the external forces to one side of any cross section of the beam about an axis.
2.13.2
Normal Stresses in Beams
The normal stress of a beam is the product of a longitudinal plane of symmetrical ends subject to a bending moment (M) at a certain cross section. The normal stress acting on a longitudinal fiber at a distance y from the neutral axis of the beam is defined by the following equation: σ =
Compressive stresses
My I
where I denotes the moment of inertia of the cross sectional area about the neutral axis. Normal stresses for a beam increase from zero at the neutral axis to a maximum at the outer fibers. The stresses are tensile on one side of the neutral axis, compressive on the other. These stresses are also called bending, flexural, or fiber stresses. These stresses are shown in Figure 2-54.
Zero stress at the neutral axis Tensile stresses N. A
. y
Figure 2-54 Beam cross section, differential distribution of stresses
Example 2-19 Derive an expression for the relationship between the bending moment acting at any section in a beam and the bending stress at any point in this same section. The beam shown in Figure 2-55 is loaded by the two couples M and consequently is in static equilibrium. Since the bending moment has the same value at all points along the bar, the beam is said to be in a state of pure bending. To determine the distribution of bending stress in the beam, cut the beam by a plane passing through it in a direction perpendicular to the geometric axis of the bar. In this manner, the forces under investigation become external to the new body formed, even though they were internal effects of the original uncut body. The free body diagram of the portion of the beam to the right of this cutting plane now appears as in Figure 2-56. Evidently, a moment M must act over the cross section cut by the plane so that the left portion of the beam will be in static equilibrium. The moment M acting on the cut section represents the effect of the left portion of the beam on the right portion. Since the left portion has been removed, it must be replaced by its effect on the right portion represented by the moment M. This is the result of the moments of forces acting perpendicular to the cross section. It is now necessary to make certain assumptions to determine the nature of the variation of these forces over the cross section.
M
M
Figure 2-55
M
Figure 2-56
M
160
2 Engineering Product Design O
M
A c A
M
B d ef B
y
Figure 2-57 Beam in bending by two couples
Consider the beam to be composed of an infinite number of thin longitudinal fibers. It is assumed that every longitudinal fiber acts independently of every other fiber, that is, there are no lateral pressures or shearing stresses between adjacent fibers. Thus, each fiber is subject only to axial tension or compression. Further, it is assumed that a plane section of the beam normal to its axis before loads are applied remains plane and normal to the axis after loading. It is also assumed that the material follows Hooke’s law and that the moduli of elasticity in tension and compression are equal. Next, consider two adjacent cross sections A-A and B-B on the side of the beam, as shown in Figure 2-57. Before loading, these sections are parallel to each other. After the applied moments have acted on the beam, these sections are still planes but they have rotated about each other to the positions shown, where O represents the center of curvature of the beam. Evidently, the fibers on the upper surface of the beam are in a state of compression, while those on the lower surface have been extended slightly and are in tension. The line c-d is the trace of the surface in which the fibers do not undergo any strain during bending; this surface is called the neutral surface. Its intersection with any cross section is called the neutral axis. The elongation of the longitudinal fiber at a distance y (measured positively downward) may be found by drawing line d-e parallel to A-A. If ρ denotes the radius of curvature of the bent beam, then from the similar triangles c-O-d and e-d-f we find the strain of this fiber to be ε=
ef de y = = cd cO ρ
Therefore, the strains of the longitudinal fibers are proportional to the distance y from the neutral axis. Because Hooke’s law holds, E = σ / ε, or σ = E × ε, it immediately follows that the stresses existing in the longitudinal fibers are proportional to the distance y from the neutral axis or σ =
Ey ρ
Consider a beam of rectangular cross section, although the derivation actually holds for any cross section, that has a longitudinal plane of symmetry. In this case, these longitudinal or bending stresses are shown in Figure 2-58.
y
da
N. A
.
Figure 2-58 Beam cross section bending stresses
Let dA represent an element of area of the cross section at a distance y from the neutral axis. The stress acting on dA is given by the above expression and consequently, the force on this element is the product of the stress and the area dA. dF =
Ey dA ρ
However, the resultant longitudinal force acting over the cross section is zero (for the case of pure bending) and this condition may be expressed by the summation of all forces dF over the cross section. This is done by integration:
2.13 Stress Analysis of Beams
∫
Ey E dA = ∫ y dA = 0 ρ ρ
Evidently, ∫ y dA = 0. However, this integral represents the first moment of the area of the cross section about the neutral axis, since y is measured from that axis. But ∫ y dA = y A, where y is the distance from the neutral axis to the centroid of the cross sectional area. From this, y A = 0 and since A is not zero, then y = 0. The neutral axis always passes through the centroid of the cross section. The moment of the elemental force dF about the neutral axis is given by dM = y dF = y dA
Ey ρ
The resultant of the moments of all such elemental forces summed over the entire cross section must be equal to the bending moment M acting at that section. M = But I = M =
E y2 ∫ ρ dA
∫y
2
dA , and the bending moment is:
EI ρ
Carefully note that this moment of inertia of the cross sectional area is computed about the axis through the centroid of the cross section. Previously we had σ =
Ey ρ
Eliminating from these last two equations, we obtain: σ =
My I
This equation gives the flexural stresses in the beam. M is the bending moment at any section, I is the moment of inertia of the cross sectional area about an axis through the centroid, and y is the distance from the neutral axis to the fiber on which the stress (σ) acts. The value of y at the outer fibers of the beam is frequently denoted by c and at these fibers, the bending stresses are maximum resulting in: σ =
Mc I
161
162
2 Engineering Product Design 10.00 in
Example 2-20
75 lb
A
B
M =75 x 10 =750 in-lb
Bending moment diagram
y
1.25 in
0.187 in
Beam cross section
Figure 2-59
A 30% fiber glass reinforced PET cantilever beam, 10.00 in in length, is subjected to a concentrated load of 75.00 lbs. at the free end of the beam (A). The beam is of rectangular cross section, 0.187 in ×1.25 in. The tensile stress of this polymer is 23,000 psi. Determine the magnitude and location of the maximum tensile and compressive bending stresses. The bending moment diagram for this type of loading is found by using the following equation: It is triangular with a maximum ordinate at the supporting wall, as shown in Figure 2-59. The maximum bending moment (M) is merely the moment of the 75.00 lbs. force about an axis through point B and perpendicular to the plane of the page, multiplied by the 10.00 in in length. The bending stress (σ) at a distance y from the neutral axis, which passes through the centroid of the cross section, is σ = M y / I. In this equation, I is the moment of inertia of the cross sectional area about the neutral axis and is given by the following equation: I =
1 1 b h3 = × 0.187 × (1.25)3 = 0.03 in 4 12 12
In the supporting wall, where the bending moment reaches its maximum, the peak tensile stress which occurs at the upper fibers of the beam is: σ =
10.00 in
M y 750 × 0.625 = = 15,625 psi I 0.03
The stress required is in tension, because the beam deflects downward. At the lower fibers adjacent to the wall, the compressive stress is equal to 15,625 psi. The 23,000 psi tensile stress of the material provides an adequate design safety factor.
W = 50 lb/in
Example 2-21 A 45% glass reinforced PET cantilever beam, 10 in long, is subjected to a uniformly distributed load of 50 lb/in length. The allowable working stress in either tension or compression is 28,000 psi. If the cross section is to be rectangular, determine the dimensions if the height is to be four times greater than the width. M = 50 x 10 x 5 = 2.500 in-lb Bending moment diagram
A cantilever beam bending moment with a uniform load is parabolic, varying from zero at the free end to a maximum at the supporting wall. The loaded beam and the accompanying bending moment diagram are shown in Figure 2-60. The maximum moment at the wall is given by:
h = 4b
b Beam cross section
Figure 2-60
M(x = 10) = 50 × 10 × 5 = 2,500 lb-in The only cross section that needs to be considered for design purposes is the one where the bending moment is at maximum at the supporting wall. We wish to design a rectangular beam to a bending moment of 2,500 lb-in, with a maximum bending stress of 28,000 psi.
163
2.13 Stress Analysis of Beams
Because the cross section is to be rectangular, it will have the appearance shown in the diagram, where the width is denoted by b and the height by h = 4 b. The moment of inertia about the neutral axis, which passes through the centroid of the section, is given by the following equation: I =
1 1 b h3 = b (4 b)3 = 5.333 b 4 12 12
At the cross section of the beam adjacent to the supporting wall, the bending stress in the beam is given by σ = M y / I. The maximum bending stress in tension occurs along the upper surface of the beam, because these fibers elongate slightly and at this surface y = 2 b and σ = 28,000 psi. Then σ =
My I
or 28,000 =
2,500 × (2 b) 5,000 = 5.333 b 4 5.333 b3
from which b = 0.322 in, and h = 4 b = 1.289 in
Location of the Neutral Axis The neutral axis always passes through the centroid of the cross section. This is the same moment of inertia (I) for the normal stress equation, or the moment of inertia of the cross sectional area about an axis through the centroid of the beam. Section Modulus At the outer fibers of the beam, the value of the coordinate y is frequently denoted by the symbol c. The maximum normal stresses are defined by the following equations: σ =
Mc I
or σ =
M (I / c )
The ratio (I / c) is called the section modulus and is usually denoted by the symbol Z. The maximum normal bending stresses may then be represented by the following equation: σ =
M Z
This equation is convenient, because values of section modulus (Z) are available in handbooks for a wide range of standard structural shapes. Assumptions In the derivation of the above normal stress equations, it is assumed that a beam normal to its longitudinal axis before loading remains plane after the forces and couples have been applied. It is further assumed that the beam is initially straight and of uniform cross section. Further, that the moduli of elasticity in tension and compression are equal.
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2 Engineering Product Design
2.13.3
Shearing Force
The algebraic sum of all the vertical forces to one side of any cross section of the beam is called the shearing force at that section. Shearing Stresses in Beams When beams are subject to a shearing force (Fs) at a certain cross section, both vertical and horizontal shearing stresses (σS) are applied. The vertical shearing stresses at any cross section of a beam cause the formation of the shearing force (Fs). In the cross section of the beam shown in Figure 2-61, the vertical plane of symmetry contains the applied forces and the neutral axis passes through the centroid of the section. The coordinate y is measured from the neutral axis. The moment of inertia of the entire cross sectional area about the neutral axis is denoted by I. The shearing stress on all fibers a distance y0 from the neutral axis is defined by the following equation: σS =
Fs y da Ib ∫
Where b denotes the width of the beam at the location where the shearing stress is being calculated.
Example 2-22 In the case of a beam loaded by transverse forces acting perpendicular to the axis of the beam, not only are bending stresses parallel to the axis of the bar produced, but shearing stresses also act over cross sections of the beam perpendicular to the axis. Derive an expression for these shearing stresses with the shearing force at the section and the properties of the cross section. The theory to be developed applies only to a cross section of rectangular shape. However, the results of this analysis are used to give approximate values of the shearing stress in other cross sections having a plane of symmetry.
M + dM
M A c S
B d
B
A dx
σ =
My I
Where I is the moment of inertia of the cross section about the neutral axis.
c
yO
Let us consider an element of length dx cut from a beam as shown in Figure 2-61. We shall denote the bending moment at the left side of the element by M and that at the right side by (M + dM), as the bending moment changes slightly from one section to an adjacent section of the beam. If y is measured upward from the neutral axis, then the bending stress at the left section A-A is given by the following equation:
N. A.
b Figure 2-61 Element of length cut from the beam
This stress distribution is shown in Figure 2-61. Similarly, the bending stress at the right section B-B is: σ =
( M + dM ) y I
2.13 Stress Analysis of Beams
Let us now consider the equilibrium of the shaded element A-c-d-B-A. The force acting on an area dA of the face A-c is merely the product of the intensity of the force and the area; thus, σ da =
My dA I
The sum of all such forces over the left face A-c is found by integration. c
∫
y0
My dA I
Likewise, the sum of all normal forces over the right face d-B is given by: c
∫
y0
( M + dM ) dA I
Evidently, as these two integrals are unequal, some additional horizontal force must act on the shaded element to maintain equilibrium. Because the top face A-B is assumed to be free of any externally applied horizontal forces, the only remaining possibility is that there exists a horizontal shearing force along the lower face c-d. This represents the action of the lower portion of the beam on the shaded element. Let us denote the shearing stress along this face by σs as shown. Also, let b denote the width of the beam at the position where σs acts. Then the horizontal shearing force along the face c-d is σ S b dx . For equilibrium of the element A-c-d-B-A we have: c
∑ Fh =
∫
y0
My da − I
c
∫
y0
( M + dM ) y dA + σ S b dx = 0 I
Resulting in: σS =
1 dM − Ib dx
c
∫ y dA
y0
But, we have Fs = dM / dx, where Fs represents the shearing force (in pounds) at the section A-A (Figure 2-61). Substituting, σS =
Fs Ib
c
∫ y dA
y0
The integral in this last equation represents the first moment of the shaded cross sectional area about the neutral axis of the beam. This area is always the portion of the cross section that is above the level at which the desired shear stress acts. This first moment of area is sometimes denoted by Q in which case the above formula becomes: σS =
Fs Q Ib
165
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2 Engineering Product Design
1
m
c
dy
2
p
The shearing stress (σs) acting component is only in the horizontal direction as previously shown. However, let us consider the equilibrium of a thin element m-n-o-p of thickness t cut from any body and subject to a shearing stress σ1 on its lower face, as shown in Figure 2-62.
2
dx
n
o 1
Figure 2-62 Beam equilibrium shearing stresses
The total horizontal force on the lower face is σ1 t dx. For equilibrium of forces in the horizontal direction, an equal force, which acts in the opposite direction, must act on the upper face, hence the shear stress intensity there is also the σ1. These two forces give rise to a couple of magnitude σ1 t dx dy. The only way in which equilibrium of the element can be maintained is for another couple to act over the vertical faces. Let these faces be denoted by σ2. The total force on either vertical face moments about the center of the element we have:
∑ MC
= σ 1 t dx dy − σ 2 t dx dy = 0
or σ1 = σ 2
Thus, we have the interesting conclusion that the shearing stresses on any two perpendicular planes through a point on a body are equal. Consequently, not only are there shearing stresses (σs) acting horizontally at any point in the beam, but shearing stresses of an equal intensity also act vertically at that same point. In summary, when a beam is loaded by transverse forces, both horizontal and vertical shearing stresses arise in the beam. The vertical shearing stresses are of such magnitudes that their resultant at any cross section is exactly equal to the shearing force (Fs) at that same section. The integral c
∫ y da
y0
represents the first moment of the shaded area of the cross section about the neutral axis. The integral always represents the first moment about the neutral axis of that part of the cross sectional area of the beam between the horizontal plane, on which the shearing stress (σS) occurs and the outer face of the beam, the area between y0 and c (Figure 2-63). From the previous equation, the maximum shearing stress always occurs at the neutral axis of the beam, whereas the shearing stress at the outer fibers is always zero. This is in contrast to the distribution of normal stress over the cross section, as that varies from zero at the neutral axis to a maximum at the outer fibers. c yO
h
In a beam of rectangular cross section, the previous equation for shearing stress becomes: σS =
b
Figure 2-63 Beam cross section shearing stresses
Fs y 2 (2 I )(4 − y 02 )
Where σS denotes the shearing stress on a fiber at a distance y0 from the neutral axis and h denotes the depth of the beam. The distribution of vertical shearing stress over the rectangular cross section is parabolic, varying from zero at the outer fibers to a maximum at the neutral axis.
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2.13 Stress Analysis of Beams
Example 2-23 Using the expression for shearing stress derived in Example 2-22, determine the distribution of shearing stress in a beam of rectangular cross section. What is the maximum shearing stress in a rectangular bar? In Example 2-22, the shearing stress (σs) at a distance y0 from the neutral axis of the beam was found to be: σS =
Fs Ib
c
∫ y dA
y0
Where Fs denotes the shearing force at the cross section and b represents the width of the beam at the position where σs is acting. It is necessary to evaluate the above integral for a rectangular cross section. Let h denote the cross section height and b its width, as shown in Figure 2-64. The integral represents the first moment of the shaded area about the neutral axis. Note that this area extends from the level at which the desired shearing stress (σs) works on the outer fibers of the beam. In this manner, we find the shearing stress (σs) works on all the fibers at a distance y0 from the neutral axis. In fact, it is not necessary to integrate in such a simple case. Because the integral is known to represent the first moment of the shaded area about the neutral axis, we may calculate this first moment according to the definition. That is, the first moment of the shaded area is simply the product of the area and the perpendicular distance between the centroid of the area and the neutral axis. The area is given by: h A = b − y0 2 The distance from the centroid of the shaded region to the neutral axis is: y =
1 h + y 0 2 2
Consequently, the value of the integral representing the first moment area is: c
∫
y dA =
y0
2 1 h h 1 h b + y 0 − y 0 = − y 02 b 2 2 2 2 4
and the shearing stress (σs) at a distance y0 from the neutral axis becomes: σS =
Fs Ib
1 h2 Fs h2 2 − y 02 b − y0 = 2 I 4 2 4
From this it may be seen that the shearing stress over the cross section varies from a maximum at the neutral axis (yo = 0) to zero at the outer fibers
N.A.
yO h
b
Figure 2-64 Beam integral rectangular cross section
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2 Engineering Product Design
of the beam (yo = h / 2). This variation is shown in Figure 2-65 (bottom illustration).
N. A. h
At the neutral axis, yo = 0, the maximum shearing stress is found by substitution in the above equation to be:
b
(σ S )Max. =
Fs h2 8I
( S) Max. But, for a rectangular cross section, I = (σ S )Max. =
b h3 . Substitution results in 12
Fs h2 3F = s 3 b h 2 b h 8 12
Figure 2-65 Beam cross section variation
The maximum shearing stress in the case of a rectangular cross section is 50% greater than the average shearing stress obtained by dividing the shearing force by the cross sectional area b h.
2.14
Beam Deflection Analysis
In the previous section it was stated that lateral loads applied to a beam not only create bending and shearing stresses in the beam, but also cause the beam to deflect in a direction perpendicular to its longitudinal axis. Deformation of a beam is expressed by the deflection of the beam from its original unloaded position. The deflection is measured to the neutral surface of the deformed beam from the original neutral surface. The configuration assumed by the deformed neutral surface is known as the elastic curve of the beam. Figure 2-66 represents the beam simply supported in its original state without deformation, while Figure 2-67 represents the deformation of the beam caused by the load. The displacement δ is defined as the deflection of the beam. It is necessary to determine the deflection (δ) for every value of x along the beam, see Figure 2-67. This relation may be written as an equation that is known as the deflection curve (or elastic curve) equation of the beam.
W
Specifications for the design of beams frequently impose limitations upon the deflections as well as the stresses. Consequently, besides the calculation of stresses, it is essential that the product designer be able to calculate the beam deflection. A well designed beam must be able to carry the loads to which it will be subjected without causing undesirably large deflections and over stressing.
Figure 2-66 Beam simply supported
Y
Numerous methods are available for calculating the deflection of a beam. The most common methods are the following:
W
x
X
δ Figure 2-67 Deflected beam
• Double integration method • Moment area method • Superposition method
169
2.14 Beam Deflection Analysis
2.14.1
Beam Deflection by Double Integration Method
The following differential equation is used for calculating the bending moment of a bent beam: M =EI
dy 2 dx 2
(2-1)
Where X and Y are the coordinates of a deformed beam as shown in Figure 2-67, and where δ is the deflection of the beam (this expression is derived in Example 2-24). Here, E denotes the modulus of elasticity of the beam and I represents the moment of inertia of the beam cross section about the neutral axis, that passes through the centroid of the cross section. M represents the bending moment at the distance x from one end of the beam. This quantity is the algebraic sum of moments, caused by external forces. These moments are formed on one side of the section at a distance x from the end about an axis through this section. The moment M is a function of x and it is necessary to integrate Equation (2-1) twice to obtain an algebraic equation expressing the deflection (δ) as a function of x. Equation (2-1) is the basic differential equation that governs the deflection of all beams, irrespective of the type of applied loading. Double Integration Procedure The double integration method for calculating deflections of beams consists of integrating Equation (2-1). The first integration yields the slope dy / dx at any point in the beam and the second integration gives the deflection (δ) for any value of x. The bending moment (M) must be expressed as a function of the coordinate X before the equation can be integrated. Since the differential Equation (2-1) is of the second order, its solution must contain two constants of integration. These two constants must be evaluated from known conditions concerning the slope or deflection at certain points in the beam. For example, in the case of a cantilever beam, the constants would be determined from the conditions of zero change of slope as well as zero deflection at the wall support end of the beam. Frequently, two or more equations are necessary to describe the bending moment in the various regions along the length of a beam. For such cases, Equation (2-1) must be written for each region of the beam and integration of these equations yields two constants of integration for each region. These constants must then be determined to impose conditions of continuous deformations and slopes at the points common to adjacent regions. Sign Conventions The sign conventions for bending moment adopted previously (stresses in beam’s section) will be retained for calculating the deflection of beams. The values E and I appearing in Equation (2-1) are positive. From this equation, if M is positive for a certain value of x, then dy2 / dx2 is also positive. With the above sign convention for bending moments, it is necessary to consider the coordinate x along the length of the beam to be positive to the right and the deflection (δ) to be positive upward. This will be explained in detail in Example 2-24. With these algebraic signs, the integration of Equation (2-1) may be carried out to yield the deflection (δ) as a function of x, with the understanding that upward beam deflections are positive and downward deflections negative.
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2 Engineering Product Design Assumptions and Limitations In the derivation of Equation (2-1) it is assumed that deflections caused by shearing action are negligible compared to those caused by bending action. Also, it is assumed that the deflections are small compared to the cross sectional dimensions of the beam. Further, the beam is presumed to be straight before the application of the load (Figure 2-66). These conditions are in addition to the assumptions concerning beam theory.
Example 2-24 Obtain the differential equation of the deflection curve of a beam loaded by lateral forces. The bending moment is defined by the following equation: M =
EI ρ
(2-2)
In this equation, M denotes the bending moment acting at a particular cross section of the beam, ρ the radius of curvature to the neutral surface of the beam at this same section, E the modulus of elasticity, and I the moment of inertia of the cross sectional area about the neutral axis passing through the centroid of the cross section. We will be concerned only with those beams for which E and I are constant along the entire length of the beam, but in general, both M and ρ will be functions of x. Equation (2-1) may be written in the following form: 1 M = ρ EI
(2-3)
Where 1 / ρ in Equation (2-3) represents the curvature of the neutral surface of the beam. As M will vary along the length of the beam, the deflection curve will be of variable curvature. The heavy line shown in Figure 2-68 represents the deformed neutral surface of the bent beam. Originally, the beam coincided with the x-axis before loading and the coordinate system that is found to be most convenient is shown in Figure 2-66. The deflection δ is taken to be positive in the upward direction; hence for the particular beam shown, all deflections are negative. An expression for the curvature at any point along the deformed beam is readily available from differential calculus. The exact formula for curvature is: Y
ρ X
δ Figure 2-68 Deflected beam, simply supported
dy 2 dx 2
1 = 2 3/2 ρ dy + 1 dx
(2-4)
171
2.14 Beam Deflection Analysis
In this equation, dy / dx represents the slope of the curve at any point and for small beam deflections, this quantity, and in particular its squares, are small in comparison to unity and may reasonably be neglected. This assumption of small deflections simplifies the expression for curvature to the following form: 1 dy 2 ≈ ρ dx 2
(2-5)
For small deflections, Equation (2-3) becomes: dy 2 M = 2 E I dx
or M =EI
dy 2 dx 2
(2-6)
This is the differential equation of the deflection curve of a beam loaded by lateral forces. In solving any problem, it is necessary to integrate this equation to obtain an algebraic relationship between the deflection δ and the coordinate X along the length of the beam.
Example 2-25 Determine the deflection at every point of the cantilever beam subject to the single concentrated load W at the free end, as shown in Figure 2-69. The deformed beam is shown by the heavy line. First, it is necessary to find the reactions exerted by the supporting wall upon the beam. These are easily found from statics to be vertical load reaction W and the bending moment M = W × L. The bending moment at any cross section a distance x from the wall is given by this assumption: It is the sum of the moments of these two reactions about an axis through this section. Evidently, the upward load W produces a positive bending moment W x and the couple W L if acting alone would produce curvature of the beam. According to the sign convention, this constitutes negative bending. Hence, the bending moment M at the section x is: M = −W L + W x Y
W
The differential equation of the bent beam is: M =EI
dy 2 dx 2
L
x M=WxL
X W
Figure 2-69 Cantilever beam, free end, concentrated load
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2 Engineering Product Design
Where E denotes the modulus of elasticity of the material and I represents the moment of inertia of the cross section about the neutral axis. Substituting, EI
d2 y dx 2
= −W L + W x
(2-7)
Equation (2-7) is readily integrated once to yield the following: EI
dy W x2 = −W L + + C1 dx 2
(2-8)
Which represents the equation of the slope, where C1 denotes a constant of integration. This constant may be evaluated by use of the condition that the slope dy / dx of the beam at the wall is zero, because the beam is rigidly clamped. Therefore, (dy / dx)x = 0 = 0. Equation (2-8) is true for all values of x and y, and if the conditions at x = 0 is substituted, we obtain: 0 = 0 + 0 + C1, or C1 = 0. Next, integration of Equation (2-8) yields EIδ= −
W L x2 W x3 + + C2 2 6
(2-9)
Where C2 is a second constant of integration. Again, the condition at the supporting wall will determine this constant. There, at x = 0, the deflection (δ) is zero, because the bar is rigidly clamped. Substituting (δ) at x = 0, the condition is equal to zero, in Equation (2-9), we find that 0 = 0 + 0 + C2, or C2 = 0. Thus, Equations (2-8) and (2-9) with C1 = C2 = 0 give the slope dy / dx and deflection (δ) at any point x in the beam. The deflection is a maximum at the right end of the beam (x = L) under the load W and from Equation (2-9) is found to be: E I δ Max. = −
W L3 3
Where the negative value denotes that this point on the deflection curve lies below the X-axis. If only the magnitude of the maximum deflection at x = L is desired, it is usually denoted by deflection (δ) and we have the following equation: δMax. = −
W L3 3E I
(2-10)
173
2.14 Beam Deflection Analysis 5.00 in
Example 2-26 The cantilever beam as shown in Figure 2-69 is 5.00 in in length and with a load force W of 10.00 lb. The beam is made of acetal homopolymer with a rectangular section having 0.125 in width and 0.75 in height. The resin has a tensile strength of 10,000 psi and a modulus of elasticity of 410,000 psi at 73 °F. Determine the maximum deflection of the beam. The maximum deflection occurs at the free end of the beam under the concentrated load as shown in Figure 2-70. This deflection is downward as shown in Figure 2-70. In the derivation of this deflection equation it was assumed that the material of the beam follows Hooke’s law. In fact, from the above calculation alone there is no assurance that the material is not stressed beyond the proportional limit. If it were, then the basic beam bending equation E I (dy2 / dx2) = M would no longer be valid and the above numerical value would be meaningless. Consequently, in every problem involving beam deflections it is to be emphasized that it is necessary to determine that the maximum bending stress in the beam is below the proportional limit of the material. The moment of inertia of a rectangular cross section area is calculated by using the following equation: I =
1 1 b h3 = × 0.125 × (0.75)3 = 0.00439 in 4 12 12
Where σ denotes the bending stress, M the bending moment, y the distance from the neutral axis to the outer fibers of the beam, and I the moment of inertia of the beam cross section about the neutral axis. The maximum bending moment in this problem occurs at the supporting wall and is given by the following equation: M(Max.) = 10.00 × 5.00 = 50.00 lb-in Substituting in the deflection and bending stress equations, we have: δMax. =
10.00 × (5.00)3 W L3 = = 0.231 in 3E I 3 × 410,000 × 0.00439
σ Max. =
M y 50.00 × 0.375 = = 4,271 psi I 0.00439
Because the maximum stress is below the acetal homopolymer proportional limit (10,000 psi), the use of the beam deflection equation was justifiable.
M = 50 lb-in
Max.
10 lb
0.375 in 0.75 in
0.125 in
Figure 2-70 Cantilever beam, free end, concentrated load
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2 Engineering Product Design
Example 2-27
W = 50.00 lb/in
A cantilever beam, as shown in Figure 2-71, is made of 43% fiber glass reinforced nylon 6/6 at 73 °F with 50% relative humidity. It has a tubular cross section, 2.00 in outside diameter and 1.50 in inside diameter. The tube is 12.00 in long and carries a uniform load of 5.00 lb/in. The material has a tensile strength of 21,000 psi and a modulus of elasticity of 1,200,000 psi.
Max.
12.00 in r = 1.00 in
Calculate the maximum deflection of the beam. The maximum deflection of the cantilever beam is uniformly distributed, the load occurs at the free end and is calculated by using the following equations:
2.00 in dia
I = 0.049 (D 4 − d 4 ) = 0.049 (2.004 − 1.504 ) = 0.535 in 4
1.50 in dia
It is important to retain consistent units when substituting in such an equation. One manner of doing this is to take W in units of lb/in, L in in, E in psi, and I in in4. The maximum deflection is calculated by using the following equations:
Figure 2-71 Cantilever beam, uniformly distributed load
δMax. =
50.00 × (12.00)4 w L4 = = 0.201 in 8 E I 8 × 1,200,000 × 0.535
The maximum bending moment occurs at the supporting wall and is: M Max. = 50.00 × 12.00 × 6.00 = 3,600 lb-in. The maximum bending stress occurs at the outer fibers of the beam at this section adjacent to the wall and is given by the following equation: σ Max. =
M y 3,600 × 1.00 = = 6,728.97 psi I 0.535
As this maximum bending stress is well below the proportional limit of the material (21,000 psi), the use of the above deflection equation is valid.
Example 2-28 Obtain an equation for the deflection curve of the simply supported beam, subject to the concentrated load W applied at the center of the beam as shown in Figure 2-72. Y
W x X
W 2
L 2
L 2
W 2
The X-Y coordinate system is introduced. The beam deformed by the load is indicated by the heavy line. Because of symmetry, each end reaction force is W / 2. Use the equation for the bending moment at any section of a loaded beam. According to that equation, the bending moment in the left half of the beam is given by the following equation:
L Figure 2-72 Beam, simply supported, concentrated center load
M =
W L x for 0 < x < 2 2
175
2.14 Beam Deflection Analysis
The differential equation of the bent beam is M = E I EI
dy 2 . Substituting, dx 2
dy 2 W L = x for 0 < x < 2 dx 2 2
(2-11)
The first integration of Equation (2-11) yields the following: EI
dy W ( x 2 ) = + C1 dx 2 (2)
(2-12)
The slope of the beam is represented by dy / dx. Because the beam is loaded at its midpoint, the deflections are symmetric about the center of the beam (x = L / 2). This condition of symmetry tells us that the slope must be zero at x = L / 2, the tangent to the deflected beam is horizontal there. Substituting this condition: (dy /dx)x = L /2 = 0 , in Equation (2-12), we obtain: 0=
W L2 W (L2 ) + C1 or C1 = − 16 4 (4)
The slope dy / dx at any point in the beam is given by the following equation: EI
dy W (x 2 ) W L2 = − dx 4 16
(2-13)
By integrating the second time, we develop the following equation: EIδ=
W (x 3 ) W L2 − x + C2 4 (3) 16
(2-14)
The second constant of integration C2 is determined by making the value of the deflection δ at the left support of the beam to be equal to zero. Thus δx = 0 = 0. Substituting in Equation (2-14), we obtain: 0 = 0 – 0 + C2 or C2 = 0. The deflection curve of the left half of the beam is given by the following equation: EIδ=
W (x 3 ) W L2 − x 12 16
(2-15)
At this point it is to be carefully noted that it is not permissible to make use of the condition that the deflection δ is zero at the right support, δx = L = 0. This is because the bending moment equation, M = (W / 2) x, is valid only for values of x less than L / 2 (to the left of the applied load W). To the right of W, the bending moment equation contains one additional term. It would
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2 Engineering Product Design
be necessary to work with the bending moment equation in the right half of the beam if the condition δx = L = 0 were to be used. In fact, there is no need to examine deflections to the right of the load, because it is known that the deflection curve of the beam is symmetric about x = L / 2. In determining constants of integration it is permissible to use only those conditions on deflection or slope that pertain to the interval of the beam for which the bending moment equation was written. Evidently, the maximum deflection of the beam occurs at the center because of symmetry. At this center point, the maximum deflection multiplied by the modulus of elasticity and moment of inertia is defined by the following equation: E I δMax. = −
W L3 48
(2-16)
The maximum deflection at the center of the beam (without considering the algebraic sign), simply supported at each end of the beam, and subject to a centrally applied concentrated load W, the following equation is applied: δMax. = −
W L3 48 E I
(2-17)
Example 2-29 Determine the deflection equation for a simply supported beam loaded by a couple M1 at the right end of the beam as shown in Figure 2-73. First, it is necessary to determine the reactions acting on the beam. Because the applied couple M1 can be held in equilibrium only by the action of another couple, the end reactions must be forces of equal magnitude R, but opposite in direction. To find their magnitude we may write the statics equation:
∑ Mo
Y x
M1 X
= − M1 + R L = 0 or R =
The heavy line indicates the configuration of the deflected beam. The bending moment at any section a distance x from the left reaction is: M = Rx =
Y x
M1 X R
R
M1 x L
This equation is valid for all values of x. The differential equation of the deformed beam is:
L Figure 2-73 Beam, simply supported, couple loaded at one end
M1 L
EI
dy 2 M = 1 x L dx 2
(2-18)
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2.14 Beam Deflection Analysis
Integrating once, we obtain: EI
dy M (x 2 ) = 1 + C1 dx L (2)
(2-19)
There is no information available concerning the slope of the beam, making it impossible to determine C1 at this stage. It is to be noted that if there is no symmetry to the loading, then there is no reason to expect the slope to be zero at the midpoint of the beam. We integrate again and obtain: EIδ=
M1 ( x 3 ) + C1 x + C2 2 L (3)
(2-20)
At this stage, we are able to determine the constants of integration C1 and C2. It is evident that the deflection δ is zero at the left support, δx = 0 = 0. Substituting these values of x in Equation (2-20), we obtain 0 = 0 + 0 + C2 or C2 = 0. Also, the deflection δ is zero at the right support, Bdx = L = 0. Substituting these values of x and δ in Equation (2-20), we find: 0=
M1 (L3 ) + C1 L or C = − M1 L 1 6L 6
(2-21)
The deflection curve of the beam becomes the following: EIδ=
M1 ( x 3 ) M1 L − x 6L 6
(2-22)
The maximum deflection of the beam occurs at the point where the slope is zero, at that point where the tangent to the deflection curve is horizontal. The coordinate X of this point is found by setting the left side of Equation (2-19) equal to zero. Substituting the equation we obtain the following: 0=
M1 ( x 2 ) M1 L − 2L 6
or x =
L 3
(2-23)
The maximum deflection of the beam thus occurs at a distance L / 1.732 from the left reaction. The value of this deflection is found by substituting x = L / 1.732 in Equation (2-22). This substitution yields the following equations: E I δMax. =
δMax. =
M1 (L3 ) 18 L 3
−
0.0064 M1 L2 EI
M1 L2 6 3
=
M1 L2 3 27
(2-24)
(2-25)
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2 Engineering Product Design
tan
at B
B
A
tan
2.14.2
Beam Deflection Moment Area Method
The second beam deflection method, known as the moment area method, is considered an alternative procedure to the double integration method.
at A
First Moment Area Theorem dx
x
Bending moment diagram
Figure 2-74 Beam deflection and bending moment
Figure 2-74 shows that AB represents a portion of the deflection curve of a bent beam. The shaded area represents the bending moment diagram. On the deflection curve are drawn tangents at each of the points A and B as indicated. The first moment area theorem states that: The angle between the tangents at A and B is equal to the area of the bending moment diagram between these two points, divided by the product E I. If θ denotes the angle between the tangents as shown in the previous illustration, then this theorem may be stated in equation form as follows: θ=
B
M dx EI A
∫
In this equation, E represents the modulus of elasticity of the beam and I denotes the moment of inertia of the beam cross section about the neutral axis, which passes through the centroid of the cross section. M represents the bending moment at the distance x from the point B. Second Moment Area Theorem Let us consider the vertical distance between point B on the deflection curve shown above and the tangent to this curve drawn at point A. This vertical distance is denoted by δ in the illustration above. The second moment area theorem states that: The vertical distance of point B on a deflection curve from the tangent drawn to the curve at A is equal to the moment about the vertical through B (shaded area of the bending moment diagram), between A and B, divided by the product E I. This theorem is represented in an equation form as follows: δ=
B
M x dx EI A
∫
Moment Area Procedure The determination of the deflection of a specified point on a loaded beam is made according to the following procedure: • The load reactions of the beam are determined; however, for cantilever beams this step is omitted. • An approximate deflection curve is drawn. This curve must be consistent with the known conditions at the ends of the support, such as zero slope or zero deflection. • The bending moment diagram is drawn for the beam. The moment diagram is constructed by parts. The M / (E I) diagram must be used in connection
179
2.14 Beam Deflection Analysis with either of the above theorems. However, for beams of constant cross section, the M / (E I) diagram has the same shape as the ordinary bending moment diagram, except that each ordinate is divided by the product E I. For applications of beams with constant cross section, it is possible to work directly with the bending moment diagram and then divide the computed areas or moment areas by E I. Or, equivalently, the angles or deflections may be multiplied by E I when areas or moment areas of the ordinary moment diagram are used. • Convenient points A and B are selected and a tangent is drawn to the assumed deflection curve at one of these points. • The deflection of point B from the tangent at A is then calculated by the second moment area theorem. In certain simple cases, such as cantilever beams, this deflection of B from the tangent at A may actually be the desired deflection. However, in other cases, it will be necessary to apply the second moment area theorem to another point in the beam and then examine the geometric relationship between these two calculated deflections to obtain the desired deflection.
2.14.3
Applications of Moment Area and Double Integration Methods
If the deflection of only a single point of a cantilever beam is desired, the moment area method is usually more convenient than the double integration method. On the other hand, if the equation of the deflection curve of the entire beam is desired, there is no procedure superior to the double integration method. Example 2-30 The cantilever beam shown in Figure 2-75 is subject to the concentrated load W applied at the free end of the beam. Determine the deflection under the point of application of the load. In the case of a cantilever beam, the reactions at the wall need not be determined although their determination is simple. It is known that the slope and deflection at the clamped end A are each zero by definition of a cantilever beam. The heavy curved line represents a realistic deflection curve. Next, a tangent to the deflection curve is drawn at point A. In the case of a cantilever beam, this tangent coincides with the original unbent position of the bar and is represented by the straight dotted line. The deflection of point B from the tangent at A is the actual desired deflection. The deflection of the free end of the beam, B, may now be found by use of the second moment area theorem. By this theorem, the deflection of point B from the tangent drawn at A is given. The moment about the vertical line through B of the area under the bending moment diagram between A and B is divided by the product E I. In fact, because the cross section of the beam is constant along the length of the beam, it is easier to work directly with the ordinary bending moment diagram rather than with the M / (E I) diagram. Therefore, the resulting deflection must be multiplied by the product E I.
W A
tan at A
B L X
L M Max. = W x L Bending moment diagram
With the second moment area theorem, the product (E I) times the deflection of B from the tangent at A, can be calculated. By the moment of the shaded
Figure 2-75 Cantilever beam, free end, concentrated load
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2 Engineering Product Design
moment diagram about a vertical line through B, this moment (M) of area may be calculated by multiplying the area by the distance of the centroid of the area from the vertical line through B. The area of the triangular moment diagram is (L / 2) (–W L), where the negative sign is used because the bending moment is negative. The centroid of the moment diagram lies at a distance (2 L / 3) from the right end. Therefore, the moment area theorem becomes: EIδ=
W L3 1 2 (L)(−W L) L = − 3 2 3
or δ = −
W L3 3E I
Example 2-31 A cantilever beam is subject to the uniformly distributed load acting over the entire length of the beam as shown in Figure 2-76. Determine the deflection of the free end of the beam. The reactions at the end of the beam need not be determined. First, it is necessary to sketch an approximate deflection curve for the bent beam. Because the beam is clamped at the right end, evidently the slope and also the deflections at that end are each zero. The curved beam represents a deflection curve that agrees with the known conditions of zero slope and zero deflection at the right end of the beam. The maximum bending moment (M) occurs at the supporting wall and has the value (W L2) / 2, where W represents the intensity of the uniform load per unit length of the beam. In this example, the bending moment diagram is a parabola.
B
(W ) lb /u
n it le n g
th
A tan at A
L
X
L WL 2 Bending moment diagram
MMax. =
Figure 2-76 Cantilever beam, uniformly distributed load
2
Next, a tangent to the deflection curve is drawn at point A. The free end of the beam is designated as B. This tangent coincides with the original position of the beam and is represented by the straight dotted line. Therefore, the deflection of point B from the tangent drawn at A represents the desired deflection. The deflection of point B may now be found by use of the second moment area theorem. From this theorem, the deflection of point B from the tangent drawn at A is given. The moment about the vertical line through B of the area under the bending moment diagram between A and B is divided by E I. It is convenient to work with the bending moment diagram as shown in Figure 2-76 and then multiply the resulting deflection by the product E I. Therefore, by the second moment area theorem, E I times the deflection of B from the tangent at A, is given. By the moment of the shaded moment diagram about a vertical line through B, this moment of area may be calculated by multiplying the area by the distance between the centroid of the area and the vertical line through B. The area of the parabolic moment diagram is 1/3 the area of the rectangle enclosing the parabola. Therefore, the area under the moment diagram is given by the following equation: M =
1 W L2 L − 3 2
181
2.14 Beam Deflection Analysis
The centroid of the parabolic figure lies at a distance 3 L / 4 from the left end. Therefore, the second moment area theorem becomes: EIδ=
W L2 3 1 (L) − 3 2 4
W L4 L = − 8
or δ = −
W L4 8EI
The negative sign indicates that the final position of point B lies below the tangent drawn at point A.
Example 2-32 The simply supported beam has a concentrated loadapplied at its midpoint as shown in Figure 2-77. Find the maximum deflection at the center of the beam. The reaction forces at the ends of the beam are each W / 2 by symmetry. The heavy line represents the deflection curve of the beam. Because of this symmetry, the tangent drawn at the midpoint of the deflected beam will be horizontal. The midpoint of the beam is denoted as point A and the tangent drawn at A is shown by the horizontal line. The left end of the beam is designated as point B. We want to find the deflection of the beam at the midpoint, under the concentrated load W. Inspection of the bending moment diagram reveals, that this central deflection A, is identical with the deflection of point B from the tangent drawn at A. In calculating the deflection of B from the tangent at A, it is necessary to evaluate the moment. This is the area under the moment diagram between these two points about a vertical line through B; divide this quantity by the product E I. The area to be considered is the left half of the above shaded moment diagram. Look at the triangle of altitude (W L) / 4 and base L / 2. The distance from the centroid of this triangle to the vertical line through B is (2 / 3) × (L / 2), Therefore, the second moment area theorem applied between the points A and B gives the desired deflection:
L 2
W
L 2
B
EIδ=
tan at A
3
WL 1 L W L 2 L × or δ = 2 2 4 3 2 48 E I
A W 2
W 2
The deflection is positive, because point B lies above the tangent at point A. The second moment area theorem always indicates relative deflections: the deflection of one point on a beam about a tangent drawn at a second point on the beam. In this example, the displacement of B is zero. This is true, when we compare the deflection of B relative to the tangent drawn at A. Fortunately, this relative displacement is equal to the maximum displacement because of symmetry.
X L 2
L 2
MMax. =
L Bending moment diagram
Figure 2-77 Beam simply supported, concentrated load in middle
WL 4
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2 Engineering Product Design
a
b
Example 2-33
W B
D C
Wa L
Wb L
L 2 L
Figure 2-78
H
Wb 2
Wb B
D
A
Figure 2-79
By calculating the reaction of force at each end of the beam, we have the values indicated in Figure 2-75. The approximate form of the deflection curve is indicated by the heavy line. Evidently, there is no symmetry of the deflection curve about the midpoint of the beam. The right end of the beam is designated as point A, the midpoint as B, the point of application of the load (W) as C, and left end as D. It is convenient to draw the bending moment by parts. Working from right to left along the length of the beam, the moment due to the right reaction alone at any section a distance x from the right end is given by (W b x) / L. This is represented by the triangle shown in Figure 2-79. As we proceed from right to left along the beam, the effect of the downward load W on the moment diagram does not become evident until we have passed to the left of its point of application. At any section a distance x from the point A and lying to the left of load W, the bending moment due to the load W alone is given by –W b. This may be represented by the triangle shown in Figure 2-80. The bending moment diagram drawn by sections is shown in Figure 2-82.
D C
The desired deflection at the midpoint of the beam may be found by the following rather indirect use of the moment area theorem. A tangent to the deflection curve is drawn at the right end of the beam. This is designated as the tangent at point A, as shown in Figure 2-81. It is now possible to calculate the deflection of point D from the tangent at A by use of the second moment area theorem. This deflection is designated as D d in Figure 2-81. Remember that the moment area theorem provides only the relative deflections. In this example, the deflection of point D is relative to the tangent drawn at A. The absolute deflection of point D is zero, because the beam is supported at that point.
Wb
G
Figure 2-80
W D
B e tan at
A simply supported beam has a concentrated load as shown in Figure 2-78. Determine the deflection at the midpoint of the beam.
A
A
A
f
d Figure 2-81
According to the second moment area theorem, the deflection of D from the tangent drawn at A is given by the moment of the area under the moment diagram between A and D about a vertical line through D, divided by E I, where E is the modulus of elasticity and I is the moment of inertia. Therefore, taking the moment of the above triangle ADH and CDG about the vertical line through D, we obtain the following equation:
E I (D d ) = Total bending moment diagram H Wb D
C
f
Wb 2
B
A
As stated previously, B represents the midpoint of the beam. Evidently, from similar triangles, the line segment B f shown in Figure 2-81 must be exactly half the length of D d and the following equation is obtained:
Wb G
Figure 2-82
2 W b3 1 L 1 b W b L (L)(W b) + (b)(−W b) = − 3 2 3 2 6 6
E I (B f ) =
W b L2 W b3 − 12 12
183
2.14 Beam Deflection Analysis
Next, it is possible to calculate the deflection of the midpoint of the beam from the tangent drawn at A. This deflection is represented by the line segment e f in the previous figure. According to the second moment area theorem, this is given by the moment of the area under the bending moment diagram between A and B about a vertical line through B, divided by E I. This portion of the moment diagram is represented by the triangle ABF. Applying the second moment area theorem, we obtain the following equation: E I (e f ) =
1 L W b 1 L W b L2 × = 2 2 2 3 2 48
In the previous equation of the deflection curve of the beam, apparently, the midpoint deflection is represented by the line segment B e in Figure 2-81. This may be found from the following relationship: Be=Bf–ef Substituting the above values in the right side of the equation, we find the desired deflection of the midpoint.
E I (B e) =
W b L2 W b3 W b L2 − − 12 12 48
or B e =
W b L2 48 E I
4 b2 3 − 2 L
We should recognize that this is not the maximum deflection of the beam, except when a = b = L / 2. Also, it is assumed that the load W lies to the left of the midpoint of the beam. Otherwise the triangular bending moment diagram CDG in Figure 2-82 would extend to the right of the midpoint of the beam. Therefore, it would be necessary to take a portion of the deflection into account in calculating the deflection e f in Figure 2-82.
2.14.4
Beam Deflection Superposition Method
The superposition method is a process for calculating the deflections of a beam. This method calculates the deflection at any specific required location of a beam by adding together the partial effects of deflection. The specific equation required to calculate each partial deflection of the beam is based on the type of loads acting on the beam structure. The equations used in this process are the typical strength of materials design formulas. They were developed by Stephen Timoshenko, James Gere, Joseph Shigley, Fred Seely, James Smith, Raymond Roark and Warren Young, and William Nash just to name a few. These equations are found in the beam deflection equation tables in several engineering publications, such as the Machinery’s Handbook, plastic supplier’s design manuals. The basic principle of the superposition method assumes the following: If a beam is subjected to several loads, the bending moment “M” at any cross section will be equal to the sum of the bending moments M1, M2, M3, …, etc. produced by each load separately. M = M1 + M2 + M3 + …
184
2 Engineering Product Design The bending moment is defined by the following equation: M =EI
dy 2 dx 2
Therefore, the sum of the partial bending moments is obtained by the following equation: EI
dy32 dy 2 dy12 dy22 = E I + E I + E I +… dx 2 dx 2 dx 2 dx 2
After integrating the partial bending moments twice, the sum of the partial deflection is defined by the following equation: y = y1 + y 2 + y 3 + … or δ = δ1 + δ2 + δ3 + … This equation represents the total deflection at any point of the beam. The deflection can be defined as the sum of deflections caused by the separate load effects on a beam.
Example 2-34 Determine the free end deflection of a cantilever beam subjected to two types of loads using the sum of deflections superposition diagrams as shown in Figure 2-83. L
L
L W
w (lb/in)
W
w (lb/in)
4
wL 8EI
Total
Compound loads
3
=
WL 3EI
1
Equally distributed load Total
=
+ 1
2
=
2
Concentrated end load 4
Total deflection =
=
wL 8EI
3
+
WL 3EI
Figure 2-83 Beam compound loads deflection superposition diagram
The total end deflection of a cantilever beam is subjected to two types of loads. One load is a uniformly distributed load and the other a concentrated load at the end of the cantilever beam. Both of these deflection equations are found in Table 2.2
Example 2-35 Determine the deflection at point “A” of a structure with two cantilever beams having the same cross section and material but of different lengths. Both beams are connected by a free support at point “B”. The upper beam is loaded at the middle by a concentrated load. The beam structure is shown in Figure 2-84.
185
2.14 Beam Deflection Analysis
Top beam
W Bottom beam
B
A
D
L 3
L 3
L 3
L
Figure 2-84 Two cantilever beams, loaded and connected at point “B”
The beam structure must comply with the superposition process requirements. The bending moment at any cross section will be equal to the sum of the bending moments produced by the load separately on both cantilever beams. : Calculate the deflection of the top beam at pin contact point “B” by the sum of effects caused by the concentrated load “W”. L 3
W D
B L 3
L 3
W
D
L 3
3
B D
D
R
R
2
1
2L 3
Figure 2-85 Top beam superposition deflection diagrams
The top beam deflection at the pin contact point “B” is calculated by the sum of effects by the concentrated load “W”. δBTop = δ1 + δ2 + δ3 =
W (L /3)3 W (L /3)2 L R (2 L /3)3 + − 3E I 3E I 2E I 3
: The deflections of the top and bottom beams at the pin contact point “B” are the same, because the beams at this point are moving together. By balancing the deflection in both beams, the reaction force “R” is derived with the concentrated load “W” as shown in Figure 2-86. δBottom = B
δBTop = δBottom B
2L 3 D
R Bottom B
B
Figure 2-86 Top beam reaction force at pin contact point “B”
R (2 L /3)3 3E I
5W W (L /3)3 W (L /3)2 L R (2 L /3)3 R (2 L /3)3 + = →R= − 3E I 2 3 3 3 32 E I E I E I : Calculate the deflection of the bottom beam at the pin contact point “B” by the reaction load “R” caused by the top beam as shown in Figure 2-87. 3
2
5W 2 L 5W 2 L W L3 32 3 32 3 L δA = + = 3E I 2EI 3 370 E I
R =5 W 32
D 2L 3
B L
A L 3
Figure 2-87 Reaction force (B) deflects bottom beam free end
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2 Engineering Product Design Table 2-3 Beam Deflection Equations
Beam Loading
Variables
Maximum Deflection
δ=
W (2 L3 − 3 a L2 + a3 ) 6×E×I
Max. δA =
MA
W (L − a)2 = 2L
Cantilever Right End, Left End Free, Single Load a W
W × L3 , when a = 0 3×E ×I
L
A
Right End Fix, Left End Guided, Single Load a W
A
δ=
W (L − a)2 (L + 2 a) 12 × E × I
Max. δA =
L
MA
Right End Fix, Left End Support, Single Load
δ= W (L − a)2 (2 L + a) 2 L3
RA =
a W
L
RA
Cantilever Clamp Both Ends, Single Load W
RB = L B
A
a W L
RA
W × a2 (3 L − 2 a) L3
MB =
Simple Support Both Ends, Single Load
W × a (L2 − a2 )3 3 × E × I (3 L2 − a2 )2
W × L3 E×I when a = L (0.414) Max. δ = 0.0098
RA = MA
a
W (L − a)2 (L + 2 a) L3 W ×a = (L − a)2 L2
W × L3 , when a = 0 12 × E × I
δ=
2 × W (L − a)2 a3 3 × E × I (L − 2 a)2
Max. δ =
W × L3 L , when a = 192 × E × I 2
W × a2 (L − a) L2
W (L − a) L W ×a RB = L RA =
RB
δ=
L2 − a2 W ×a 3 × L × E × I 3
Max. δ =
3/2
W × L3 L , at x = a = 48 × E × I 2
Left End Guide Moment, Right End Simple Support RB = W a
A
W
M A = W (L − a)
L
MA
RA = W
RA
W
W
L
W × L3 , when a = 0 3×E ×I
RB
Simple Support both Ends with 2 Symmetrical Loads a
Max. δA =
RB = W
a RB
W × a2 (3 L − 4 a) 6×E×I W ×a Max. δ = (3 L2 − 4 a2 ) 24 × E × I Load δw =
187
2.14 Beam Deflection Analysis
Beam Loading Uniform Load, Fixed One End
Maximum Deflection
W x2 2×L W ×L Max. M = , when x = L 2
δ=
RA = W , M =
W=wxL x A
Variables
W × x2 [2 × L2 + (2 × L − x)2 ] 24 × L × E × I
Max. δA =
W × L3 , when x = L 8×E×I
L
Uniform Load, Two Simple End Supports W=wxL
L RB
Two Simple End Supports, Uniform Load, 1 Couple Guide W=wxL x MA
L RB
RA
Two Simple End Supports, Uniform Load, 2 Couple Guides W=wxL
MA
MB
x L
RA
3×W 8 5×W RB = 8 3 × x x M =W − 8 3 × L W 2 W RB = 2
RA =
Cantilever Right, Free Left End, Vertical & Transversal Loads J =
W
W 2
L x x − 6 − L
E×I L , G= P J
W (3 L × x 3 + 2 x 4 − L3 x) 48 × L × E × I
Max. δ = 0.0054
δ= 2
L 5 × W × L3 , when x = 384 × E × I 2
W × L3 , when x = 0.4215 L E×I
W × x2 (2 × L × x − L2 − x 2 ) 24 × L × E × I
Max. δ =
W × L3 L , when x = 384 × E × I 2
Max. δA =
W ( J × tan G − L), when x = L P
Max. δA =
W ×J G2 − sec G + L (tan G − G) , J 1 + 2 P
M = W × J × tan G
x
A
δ= 2
M =
W ×x (L3 + 2 × L × x 2 − x 3 ) 24 × L × E × I
Max. δ =
RA =
RB
P
δ=
W x2 M = x− 2 L
x RA
W 2 W RB = 2
RA =
L
Cantilever Right, Free Left End, Uniform & Transversal Loads J = W=wxL P A
E×I L , G= P J
M = W × J [ J (1 − sec G) + L × tan G]
x
when x = L
L
Two Simple End Supports, Uniform/2 Transversal Loads
J =
E×I L , G= P J
Max. δA =
W=wxL P
P x RA
L
RB
G M = W × J 2 sec − 1 2
when x =
W × J2 G G2 sec − 1 − , P 2 8 L 2
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2 Engineering Product Design
2.15
Column Structural Analysis
A long slender vertical bar subject to axial compression loads is known as a column. Failure of a column occurs by buckling or by lateral deflection, when the load has exceeded the maximum yield strength of the material. Buckling or failure of a column may occur even at stresses below the yield point of the material.
2.15.1 P
Long Slender Column Critical Load (PCr)
The critical load of a long slender column subjected to axial compression is the value of the axial force that is just sufficient to keep the column in a slightly deflected configuration. Figure 2-88 shows a column pinned at both ends in a buckled configuration caused by the critical load (PCr). If a long slender column of constant cross section is pinned at each end and subjected to axial compression, the critical load (PCr) that will cause buckling is given by the following equation: PCr =
P
Figure 2-88 Column, pinned ends axial loaded
π2 E I L2
Where E denotes the modulus of elasticity, I the minimum moment of inertia of the cross sectional area about an axis through the centroid, and L the length of the column. The derivation of this equation is presented in Example 2-37. This critical load (PCr) equation was first derived by a Swiss mathematician, Leonhard Euler (1707 – 1783) and the critical load (PCr) is known as Euler’s buckling load equation. This expression is not valid if the corresponding axial stress (found from the expression σCr = PCr / A, where A represents the cross sectional area of the column) exceeds the proportional limit of the material. The value of PCr represented by this equation is the failure load; consequently, a safety factor must be included to obtain a design load for the column.
2.15.2
Column Slenderness Ratio (L / r)
The slenderness ratio of a column (L / r) is determined by the length L of the column the radius r of gyration of the cross sectional area. It is recommended for use only in the range 30 < (L / r) < 120 for main members and a slenderness ratio (L / r) as high as 150 for secondary members. For the design of compression members having a high slenderness ratio, proceed according to Euler’s equation together with an appropriate safety factor. For the design of compression members having lower values of slenderness ratio, it is customary to employ any one of the many empirical formulas giving a relationship between the critical stress and the slenderness ratio of the bar. In fact, the equations usually present an expression for the working stress including a safety factor as a function of the slenderness ratio.
2.15.3
Eccentrically Loaded Columns
Although there are several methods for the rational analysis and design of an eccentrically loaded column, only one of these will be presented here. For a
189
2.15 Column Structural Analysis column subjected to a compressive force P0 acting through the centroid of the cross section together with an additional pressure P applied with an eccentricity e (measured from the centroid), the maximum stress is given by the following equation: σ =
P + Po P e c + A I
Where A represents the cross sectional area of the column and I denotes the moment of inertia of the cross sectional area about the bending axis. The distance from the neutral axis to the extreme fibers of the bar is represented by c. It is necessary to use either the A.I.S.C. specifications [σW = 17,000 – 0.485 (L / r)2] or the Chicago Building Code equation [σW = 16,000 – 70.00 (L / r)] to obtain a safe value of the allowable compressive stress for use in conjunction with this equation. Y
Example 2-36
L
Calculate the critical load for a long slender column with pinned ends loaded by an axial compressive force at each end. The line of action of the forces passes through the centroid of the cross section of the column. The critical load is defined to be the axial force that is just sufficient to hold the column in a slightly deformed configuration. Under the action of the load pressure P, the column has the deflected shape shown in Figure 2-89. It is necessary that one end of the column be able to move axially about the other end, so that lateral deflection may take place. The differential equation for the bending moment is: M =EI
dy 2 dx 2
(2-26)
The bending moment at point B having coordinates (X, Y) is the moment of the pressure P applied at the left end of the column around an axis through the point B and perpendicular to the plane of the page. This pressure produces a curvature of the column that is concave downward (negative bending), because the bending moment is defined as M = –P δ. Therefore, we have the following equation: −P δ = E I
dy 2 dx 2
(2-27)
If we define a constant in the equation: k2 =
P EI
(2-28)
we obtain: dy 2 + k 2 (δ) = 0 dx 2
(2-29)
P
P
B
X x
Figure 2-89 Column, pinned ends, axial loaded
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2 Engineering Product Design
This equation is solved by differentiating twice, multiplying by a constant, either sin k (x) or cos k (x), and setting the equation equal to zero. Using the combination of these terms, we obtain the following equation: δ = C sin k (x) + D cos k (x)
(2-30)
By the substitution of δ, as given by Equation (2-30), into Equation (2-29), it is next necessary to determine C and D. At the left end of the column, δ = 0 when x = 0. Substituting these values in Equation (2-30) we obtain the following expression: 0 = 0 + D or D = 0 At the right end of the column, δ = 0 when x = L. Substituting these values in Equation (2-30) with D = 0, we obtain: 0 = C sin k (L) Either C = 0 or (L) sin k = 0. But if C = 0, then δ is always zero and we have the configuration before the occurrence of buckling. Because we are not interested in this solution, we must take (L) sin k = 0
(2-31)
For this to be true, we must have (L) k = n radians (n = 1, 2, 3, …) Substituting k 2 =
(L)
(2-32)
P in Equation (2-32) we find: EI
2 2 P = n π or P = n π E I EI L2
(2-33)
The smallest load pressure P occurs when n = 1. The first mode of buckling where the critical pressure is (PCr), given by: PCr =
π2 E I L2
(2-34)
Example 2-37 Calculate the critical load for a column clamped at each end and axially loaded at each end and with three central support guides as shown in Figure 2-90.
Y L L 4 MO P
L 4 D
L 4
L 4 F
MO P
Figure 2-90 Column, central-supported, axial loaded, both ends fixed
X
The critical pressure load (PCr) is the axial compressive pressure (P) that is just sufficient to keep the column in a slightly deformed configuration. The moments (M0) at each end of the column cause a coupling action of the supports on the column; these moments prevent any angular rotation of the column at either end.
191
2.15 Column Structural Analysis
The deflection curve for the buckled column indicates that the central portion of the bar between points D and F correspond to the deflection of the pinnedends column discussed in Example 2-37. For the fixed end column, the length (L / 2) corresponds to the entire length (L) for the pinned-ends column. Euler’s buckling PCr for a column with pinned ends and axially loaded, Equation (2-34) in Example 2-37, is used and the length (L) is replaced by (L / 2). Assuming that the maximum stress in the column does not exceed the proportional limit of the material, PCr =
π2 E I (L /2)2
=
4 π2 E I L2
MO
Example 2-38
P
P
Calculate the critical load (PCr) for a long slender column with its base fix, free at the other end, and loaded by an axial compressive force applied at the free end, as shown in Figure 2-91. PCr is that axial compressive pressure P that is just sufficient to keep the column in a slightly deformed configuration. The moment (M0) represents the effect of the support in preventing any angular rotation of the column’s left end.
L
Figure 2-91 Column base fixed and free end axially loaded
Inspection of the deflection curve for the buckled column indicates that the entire column corresponds to one half of the deflected pinned end column, as discussed in Example 2-37 and using Equation (2-34). The critical pressure (PCr) is developed by replacing the length (L) with (2 L), we obtain the following equation: PCr =
π2 E I (2 L)2
=
π2 E I 4 L2
Example 2-39 A column made of acetal homopolymer has a cross section and dimensions as shown in Figure 2-92. The column is pinned at each end and subject to axial compression. The column is 10.00 in long. The tensile stress of acetal homopolymer is 10,000 psi and the modulus of elasticity is 410,000 psi. Determine the buckling load (PCr) using Euler’s equation.
d s y b
The minimum moment of inertia (I) of this cross section is calculated by using the following equation: I =
2 s b3 + h s 3 2 × 0.125 × 0.753 + 0.75 × 0.1253 = = 0.009 in 4 12 12
Applying the equation for buckling, the critical pressure (PCr), as given in Equation (2-34), Example 2-37, we obtain the following equation: PCr =
π2 E I 9.87 × 410,000 × 0.009 = = 360.15 lb. 100 L2
h
P Cr
s
P Cr 10.00 in
s = 0.125 in b = 0.75 in h = 0.75 in d = 1.00 in
Figure 2-92 “H” cross section, column axially loaded in pinned ends
192
2 Engineering Product Design
The area (A) of the column cross section is: A = b d − h (b − s) = 0.75 × 1.00 − 0.75 × (0.75 − 0.125) = 0.282 in 2 The critical stress (σCr) corresponding to the critical pressure (PCr) is: σ Cr =
PCr 360.15 = = 1,277.12 psi A 0.282
Therefore, the critical stress in this example is lower than the tensile stress of acetal homopolymer (10,000 psi).
Example 2-40 A long slender acetal homopolymer column with a circular cross section of 0.50 in in diameter and clamped at each end, is shown in Figure 2-90. The tensile stress of acetal homopolymer is 10,000 psi and the modulus of elasticity is 410,000 psi. Determine the minimum length for which Euler’s equation may be used to determine the buckling pressure (PCr) using a safety factor of 2.0. PCr =
4 π2 E I L2
The buckling critical pressure is: σ Cr =
PCr 4 π2 E I = A A L2
The axial stress prior to buckling is given by: σ Cr =
4 π2 E ( A r 2 ) A L2
=
4 π2 E (L / r )2
But I = A r2 where r denotes the minimum radius of gyration of the cross section. Substituting the moment of inertia values in function of the radius of gyration in the previous equation obtains: I =
π D4 3.1416 × 0.504 = = 0.003 in 4 64 64
The area is: A=
π D 2 3.1416 × 0.504 = = 0.196 in 2 4 4
The radius of gyration is: r =
I = A
0.003 = 0.124 in 0.196
193
2.15 Column Structural Analysis
Or the radius of gyration for a circular cross section is: I D 0.50 = = = 0.125 in A 4 4
r =
The minimum length for which Euler’s equation is found by setting the working stress (σW) equal to the critical stress (σCr) divided by the safety factor. σ Work =
σ Cr 10,000 4 π2 410,000 or L = 7.11 in = = Safety Factor 2.0 (L /0.125)2
The specific equations required to calculate the critical stress and critical load of the columns are based on the support and type of loads acting on the column structure. These equations are used in the strength of materials design analysis of the column. These column equations are found based on the column support fixtures, types of loading in several engineering strength of materials publications, and plastic suppliers design manuals. The Column Loading Cases and the equations in Table 2.4 were prepared using typical mounting supports, types of loading, and applications.
Table 2-4 Column Loading Cases and Equations
Column Axial Loaded at Both Pinned Ends
Column Base Fixed and Axial Loaded at Top Free End
P Cr
Column Base Fixed and Axial Loaded at Top Pinned End
P Cr
π2 × E × I L2 P = Cr A(Area)
PCr = L
σ cr
P Cr
π2 × E × I 4 × L2 P = Cr a(Area)
PCr = σ Cr
L
1.22 × π2 × E × I L2 P = Cr a(Area)
PCr = σ Cr
L
P Cr
Column base Fixed, Center Support Guides, Axial Loaded at Top Pinned End
Column Axial Loaded at Both Fixed Ends and Three Central Support Guides P Cr
P Cr
0.5 L
0.5 L
4 × π2 × E × I L2 P = Cr a(Area)
L 4 L 4 L 4 L 4
PCr = σ Cr
L
P Cr
General expressions PCr = Critical load (lb) σCr = Critical stress (psi) E = Modulus of elasticity (psi) I = Moment of inertia (in4)
A L r δ
= Cross section area (in2) = Length (in) = Radius of gyration (in) = Column deflection (in)
4 × π2 × E × I L2 P = Cr a(Area)
PCr = σ Cr
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2 Engineering Product Design
2.16
Flat Circular Plates
Flat circular plates, such as the bottom of vessels, panels, bulkheads, covers, etc., when supported around the edge and subjected to loads normal to the surface, will bend. The type of bending in plates is different from that in a beam. The plate bends in all planes normal to the plate, whereas the beam bends only in one plane. The bending of a flat circular plate in one plane is greatly influenced by the bending in all the other planes. The flat circular plate stress and deflection analysis takes into account the multiple bending; therefore, these calculations are more difficult than those for a beam structure. When the flat circular plate deflects, the middle surface (halfway between top and bottom surfaces) remains unstressed, while at other points there are biaxial stresses in the plane of the plate. Straight lines in the plate that were originally vertical remain straight but become inclined. Therefore, the intensity of either principal stress at points on any such line is proportional to the distance from the middle surface and the maximum stresses occur at the surfaces of the plate. The maximum stress analysis found by the theory of flexure of flat circular plates is usually safe. Comparing the results between a mathematical analysis and testing, we found that the flat circular plates will resist the maximum static loads in testing without being structurally damaged. These test loads were considerably higher than the analytical loads. This deviation is caused by the assumption made in the mathematical analysis that the maximum load is reached when the maximum stress at any point of the flat circular plate reaches the yield strength of the material. This fact is explained by observing how the maximum bending stresses occur only at the clamped rim during the test. The flat circular plate yields slightly before the inside surface and a redistribution of stress is produced that gives the flat circular plate an added usable strength. The equations for the flat circular plates are based on the following assumptions: • The circular plate is flat, of uniform wall thickness, and made of homogeneous isotropic material. • The wall thickness is not more than 25% of the transverse dimension and the maximum deflection is not more than 50% of the wall thickness. • All forces, loads, and reactions are normal to the plane of the flat circular plate. • The flat circular plate is not stressed beyond the elastic limit. • The plane of the flat circular plate is horizontal. There are three stages in the behavioral changes of thin and medium thickness, flat circular plates when resisting loads, particularly in the case of a plate restrained at its edges that is made of ductile material. • The stage of purely elastic strain, when the deflection of the flat circular plate is strictly proportional to the load and the deflection, because of the bending action alone. • The stage of breakdown of elastic action, when the yielding at the portions of high stress becomes sufficient to permit a large permanent elongation (cold flow deflection) of the plate. During this stage the direct tension has become an appreciable factor in the resistance of the flat circular plate.
2.16 Flat Circular Plates • The stage of direct tension, in which the tension carries the greater part of the load. During this stage the plate gradually takes a “dished” shape. If the flat circular plate is thin, the major portion of the load is carried by the direct tension even within the purely elastic stage.
2.16.1
Classification
Flat circular plates may be divided into four groups: • Thick flat circular plates, in which the shearing stresses become important, as is in the case for short and deep beam structures. • Medium thick flat circular plates, in which the bending stress is the main action, on which the useful resistance of the flat circular plate depends. • Thin flat circular plates, in which the useful strength resistance depends in part on the tension stress and the stretching action of the middle plane. • Flat circular membranes, in which the strength resistance depends exclusively on the stretching action of the middle plane. These flat circular membranes are not considered to be plates; therefore, there is no elastic bending stress resistance present in these structures. The elastic bending stress resistance of a thin flat circular plate is small. The usable strength resistance is greatly increased, because the direct stresses help to resist the load, even when “dishing” occurs. This explains why the thin flat plate structure requires properly spaced bolts around the flat circular plate edges for support and to prevent dishing.
2.16.2
Stress Analysis Methods
It is assumed that the resistance of a flat circular plate to loads is limited by the magnitude of the stresses in a flat circular plate rather than the elastic deflection. The strength of the flat circular plate rather than its stiffness is assumed to limit the maximum loads that may be applied to the plate. The main problem encountered in analyzing flat circular plates is finding a reliable relationship between the loads acting upon the flat circular plate and the significant stresses caused by the loads. Three methods have been employed in solving this problem for thin and medium thick flat circular plates: • In the first or strip method, the flat circular plate is assumed to be divided into two systems of strips at right angles to each other. Each strip acts as a beam structure. This method is useful in a qualitative analysis of the behavior in a flat circular plate, but it is less reliable for obtaining accurate quantitative results. • The second method is known as the theory of flexure of flat circular plates. This method resembles the theory of flexure for structural beams. It is assumed that the bending stress is the dominant action in the flat circular plate. It requires that the deflection of the flat circular plate be relatively small (1/2 or less than the thickness of the plate), and that the bending stresses contribute substantially to the load resistance of the flat circular plate. It is also assumed that the flat circular plate is in equilibrium and is made of an
195
196
2 Engineering Product Design ideal elastic material, and the stress and strain comply with the theory of flexure of structural beams, where the flexure stress and moment are defined by the following equations: Stress (σ) = M c / I and the differential equation is the Moment (M) = E I (dy2 / dx2) of the elastic stress-strain curve. The assumption for a flat circular plate is that every straight line drawn through the flat circular plate is normal to its middle surface before the plate is bent by the loads. Also, the flat circular plate remains straight and normal to the deflected middle surface after the plate is loaded. This method is not recommended for simple types of loading and circular shaped plates. The best method for finding the bending moment for these cases is by solving Lagrange’s equation. This method is somewhat complicated and will not be discussed in this section. When using the theory of flexure of flat circular plates, do not make allowances for the adjustments for local yielding at the clamping edges (high stress) causing a redistribution of stress. This effect increases the usable strength and added resistance to the flat circular plate, but does not take into account the design of plates, particularly flat circular plates made of ductile materials. • The third method shows the total bending moment at the dangerous section from the statics equations alone. The dangerous section is determined by observing the mode of failure from experiments. The factors by which the average stress corresponds to the total moment are multiplied to obtain the maximum stress at the dangerous section. The stress is also determined from experimental results. In this method, no attempt is made to include the effect of direct tensile stresses, which give the plate added strength as the deflection increases.
2.16.3
Flat Circular Plate Equations
Unless otherwise indicated, the equations given in Table 2.5, Parts I and II are based on very closely approximated mathematical analysis and may be accepted as sufficiently accurate so long as the assumptions stated hold true. Certain additional facts of importance in relation to these equations are as follows. Under Concentrated Load Conditions It will be noted that all the equations for the maximum stress caused by a load applied over a small area give very high values when the radius of the loaded area approaches zero. Analysis obtained by a more precise method shows that the actual maximum stress produced by a load concentrated on a very small area of radius r0 can be found by replacing r0 with its equivalent radius N (see the last case Central Circular Load, Edge Simply Supported in Table 2.5, I), which depends largely upon the wall thickness of the plate (t) and to a lesser degree on its least transverse dimension. Westergaard gives an approximate equation for this equivalent radius (N): N =
1.6 r02 + t 2 − 0.675 t
This equation, which applies to a plate of any form, may be used for all values of r0 less than fifty percent of (t), for larger values the actual r0 may be used. Use of the equivalent radius (N) can calculate the maximum stress produced by a point loading, whereas the ordinary equation would indicate that these stresses were infinite.
197
2.16 Flat Circular Plates Edge Support Conditions The equations given in Table 2.5, I and II are for various combinations of edges, simply supported and fixed. No exact edge condition is likely to be realized in ordinary construction and a condition of true edge fixity is especially difficult to obtain. Even a small horizontal force at the line of contact may appreciably reduce the stress and deflection in a simply supported plate. However, a very slight yielding at nominally fixed edges will greatly relieve the stresses there, while increasing the deflection and center stresses. Therefore, it is usually advisable to design a fixed edged plate that can carry uniform loads for somewhat higher center stresses than are indicated by theory.
2.16.4
Flat Circular Plate Stresses
Stress in flat circular plates, simply supported on a circular rim around its edge with uniformly distributed load, is defined by the following parameters: A circular flat plate of radius (a), a constant flat plate wall thickness (t), and a uniformly distributed load (w) to which the circular plate is subjected. The bending moment, about any diameter, caused by the forces that lie to one side of the vertical diametral plane, is the moment of the reaction of the supporting rim minus the moment of the downward load. The magnitude of the load on the half plate is W = (1 / 2) π a2 w and its action line passes through the centroid of the semicircular area. The centroid (y) is located at (4 a) / (3 π) from the diametral plane. The resultant force (R1) of the reaction of the supporting rim must be equal in magnitude to the load (W), but its action line passes through the centroid of the semi-circumference, therefore it acts at the distance (2 a) / π from the diametral plane as shown in Figure 2-93. The bending moment (M) about the diameter is defined by the following equations: M = R1
M =
2a 4a w π a2 2 a 4 a −W = − π 3π 2 π 3 π
w a3 3
(2-35)
(2-36)
The bending moment may be equated to the resisting moment at the diametral section. Since the resisting moment holds the bending moment in equilibrium, this expression in terms of the stress at any point in the section is unknown. If the expression for the resisting moment (M) is assumed to be the same (σ I) / c as that in a structural beam that bends in one plane only, the assumption is made that the stress at any point along a diameter is independent of the distance of the point from the center of the flat circular plate, giving us the following equations: wa σI = 3 c
W =
2a dia. 4a 3π 2a
(2-37)
π
3
a σ = w t
and c = t / 2, therefore, this equation becomes:
π a2 2
3
2at But I = 12
w
t
2
(2-38)
The value of stress (σ) in Equation (2-38) is the average bending stress of the flat circular plate surface at the diametral section.
R1 =
w
π a2 2
Figure 2-93 Flat circular plate, simply supported, and uniformly distributed load
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2 Engineering Product Design
2.16.5
Theory of Flexure Comparison
Figure 2-94, the curve C-D-E shows the stress distribution on the upper surface of a diametral section of a flat circular plate as obtained from the theory of flexure. The average stress (σ) as given by Equation (2-38) is shown by the straight line A-B. The maximum bending stress occurs at the center of the plate and can be expressed by the following equation, where υ is Poisson’s Ratio. σ Max. =
a2 3 (3 + υ) w 2 8 t
W= Approximate stress distribution
A
w π a2 2
C
σ=
3 (3 +
µ)
8
w
a2 t2 D
4 a 3π
Theoretical stress distribution
σ=
w
a2
2a
t2
π B
σ=
3 (1 4
µ)
E
w
a2 t2
R1 =
w π a2 2
Figure 2-94 Flat circular plate, flexure stress distribution under uniformly distributed load
Analyzing the average stress of a flat circular plate made of an acetal homopolymer material having a Poisson’s ratio of υ = 0.35, the maximum bending stress is greater than the average stress indicated by using Equation (2-38). However, experiments indicate that the readjustment of stress accompanying local yielding is lower than stress values given by Equation (2-38). These higher stress values become significant, particularly if the flat circular plate is made of a ductile thermoplastic material.
2.16.6
Circular Plates Simply Supported, Concentrated Center Load
Let it be assumed first that the load (W) at the center is distributed over a small concentric circular area of radius (r0), as shown in Figure 2-95. The bending moment about a diametral plane A-B (Figure 2-95) is found from the statics equations; the total rim reaction force (R1) on one half of the plate is (W / 2) and its moment arm is (2 a) / π, the total load on the semicircular area of radius (r0) is (W / 2), and its moment arm is (4 r0) / (3 π). Therefore, the bending moment at the diametral section A-B is given by the following equation:
199
2.16 Flat Circular Plates
M =
W a 2W a W a − = π π 3π
2 rO 1 − 3 a
W 2
(2-39)
The average flexural stress (σ) at the top and bottom surfaces of the flat circular plate at the diametral plane is found from the flexure equation, where (t) is the wall thickness of the plate and (a) is the radius of the plate.
2 rO
σ =
Mc = I
Wa π
2 rO t 1 − 3 a 2 2at 12
3
2
πa
4 rO 3π A
B
a
t
=
2r 3W 1− O 2 3a πt
(2-40) R1 =
W 2
Figure 2-95 Flat circular plate, simply edge supported, with concentrated center load
2.16.7
Flat Circular Plate under Concentrated Center Load
If r0 = 0 and the load is concentrated on a very small area at the center of the plate in Equation (2-40), the stress equation becomes the following: σ =
3W
π t2
(2-41)
The maximum bending stress in the flat circular plate is greater than the stress as given by Equations (2-40 and 2-41), particularly for small values of r0. However, for flat circular plates made of a ductile material and subjected to static loads, the value of stress (σ) in these equations may often be regarded as the significant stress. If the flat circular plate is made of a brittle material, or if the flat circular plate is subjected to repeated stress, the value of the significant stress is defined by the following Equation (2-42), where (K) may be assumed to be 1.50 for small values of r0 and a lesser value for larger values of r0. 3W 2r σ = K 2 1 − O 3a π t
(2-42)
The maximum theoretical values of stresses in flat circular plates as obtained by the theory of flexure of flat circular plates are shown in the equations presented in Table 2.5, Part I.
2.16.8
Flat Circular Plate with Fixed Edge
If a flat circular plate is rigidly held (fixed) so that no rotation or radial displacement occurs at the edges, the average bending moment and average bending stress at any diametral section are less than the values given by the previous equations. This is because the negative bending moment at the edge decreases the positive moment within the central portion of the flat circular plate in much the same way as in a structural beam that is fixed at its ends. The negative moment at the edge of the flat circular plate is usually greater than the moment at the center.
200
2 Engineering Product Design Under service conditions, however, the edges of flat circular plates are rarely completely “fixed”, although they usually are subjected to some restraint. A slight amount of local yielding at the fixed edge may destroy much of the effect of the restraint and thereby transfer the moment to the central part of the flat circular plate. For these reasons, the restraint at the edges of a flat circular plate is considered of less importance, particularly if the flat circular plate is made of a ductile material. A medium thickness flat circular plate with a restrained (fixed) edge will be intermediate in strength between the flat circular plate with a simply supported edge and the flat circular plate with an ideally fixed edge.
2.16.9
Flat Circular Plate Compensation Factor for Deflection
In the equations given in Table 2.5, Part I, the maximum deflection of flat circular plates made of an ideal elastic material were obtained by the use of the theory of flexure of flat circular plates. Experiments have verified these equations for uniformly distributed loads and a simply supported edge. The experiments with fixed edged under uniformly distributed loads showed that the equation for the deflection was correct for thin and medium thickness (having a thickness / radius ratio of t / a < 0.1), for deflections not larger than approx. 1/2 the flat circular plate thickness. However, for thicker flat circular plates, the measured values of deflection were much larger than those computed by the equations. Two reasons are given for this discrepancy. • First, the lack of an ideal fixed edge. • Second, the additional deflection in the thicker flat circular plates caused by the shearing stresses. Modifications are suggested for thicker flat circular plates that have a wall thickness/radius ratio of t / a > 0.1, with fixed edges subjected to uniformly distributed loads. The deflection equation marked (*) in Table 2.5, Part I should be multiplied by a compensation factor that depends on the ratio of the wall thickness (t) to the radius (a): (*) H = 1 + 5.72 (t / a)2.
2.16.10 Flat Circular Plate Bending under Edge Boundaries Table 2.5, Part II considers several applications of flat circular plates of constant wall thickness and under axisymmetric loading for several combinations of boundary conditions. Besides the equations, tabulated values of deformation and moment coefficients are given for several common loading cases, including concentrated loading and flat circular plates with circular boundaries. The cases presented in Table 2.5, Part II are expressions given for deformations and reactions at the edges of the flat circular plates, as well as general equations that allow the evaluation of deflections, slopes, moments, and shear forces at any point in the flat circular plates. Table 2.5, Part II includes several axis-symmetric loadings, such as uniformly distributed load, central circular load, load at center, and parabolically increasing normal pressure over a portion of the flat circular plates. This method of presentation permits the approximation of any reasonable axis-symmetric distributed loading by fitting an approximate second order curve to the variation in loading and solving the problem by superposition.
201
2.16 Flat Circular Plates Table 2-5 Flat Circular Plate Equations, Part I
W = Concentrated load (lb); w = Unit load (psi); M = Moment (in-lb/in); δ = Deflection (in); θ = Change in slope (radians); E = Modulus of elasticity (psi); H = Deflection factor (in.); υ = Poisson’s ratio; σ = Stress (psi); t = Wall thickness (in); a = Outer radius (in); b = Inner radius (in); d = Shaft radius; r0 = Radius of load (in); K = Plate constant Case Type
Stress and Deflection Equations (Constant Thickness)
Concentrate Center Load Edge Simply Supported
Uniform Distribute Load Edge Simply Supported
σ=
y
W 2a
edge simply supported y w
2a
3 W (1 + υ) 1 a 1 − υ r02 υ + 1 + log r − 2 υ 4 a2 2 πt 0
δMax. =
3 W a2 (1 − υ) (3 + υ) 4 π E t3
σ Max. =
3 w (3 + υ) a2 2 8 t
δMax. =
3 w a 4 (1 − υ) (5 + υ) 16 E t 3
For a > r0 y
W
Concentrated Center Load Outer Edge Fixed
2a
r02 3 W (1 + υ) a log + r0 4 a2 2 π t2
δMax. =
3 W a2 (1 − υ2 ) 4 π E t3
σ Max. =
3 w a2 4 t2
δMax. =
3 w a 4 (1 − υ2 ) 16 E t 3
y
w
Uniformly Distributed Load Outer Edge Fixed
σ Max. =
2a
δMax. = H
3 w a 4 (1 − υ2 ) 16 E t 3
For thicker flat circular plates having (t / a = 0.1), multiply the deflection equation by the constant (H), where *H = 1 + 5.72 (t / a)2. Central Couple Outer Edge Simply Supported
K =
2a
σ Max. =
2d
M
K =
2a
Central Couple Outer Edge Fixed
M
2b
2 (a − d) 1 + (υ + 1) log Ka
3M 4 π d t2
2 (0.45 a − d) 1 + (υ + 1) log 0.45 K a
σ Max.
2 1 2 a + 1 υ 3W υ a 1 log + − 1 = b μ 2 π t 2 (a2 + b2 )
δMax.
1 3 W υ2 2 − 1 (a2 υ = 4 π E t3
y
W
3M 4 π d t2
0.10 a2 (d + 0.28 a)2
σ Max. =
2d
2a
Radial Center Load Edge Simply Supported
0.49 a2 (d + 0.7 a)2
3 1 4 a 2 b 2 + 1 − b 2 ) + 1 2 υ υ a + log b 1 1 2 2 1 ( ) + − a b υ υ − 1
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2 Engineering Product Design Table 2-5 Flat Circular Plate Equations, Part II
W = Concentrated load (lb); w = Unit load (psi); M = Moment (in-lb); δ = Deflection (in); θ = Angular change (rad.); Q = shear (lb/in); E = Modulus (psi); υ = Poisson’s ratio; σ = 6M/t2 (psi); t = Wall thickness (in); a = Outer radius (in); r0 = Radius of load (in); D = E t 3 / 12 (1 – ν2); N = Equivalent radius (in); K, C, L, G = Constants (ratio-dependent) Case Type Outer and Inner Edge Simply Supported; Central Radial Load rO
W
Boundary Values δb = 0, M rb = 0, δa = 0, M ra = 0 θb =
− K θb W a
2
D Qb = K Qb W θ a = θ b C 4 + Qb
b W ro − a a δb = 0, θ b = 0, δa = 0, θa = 0
Qa = Qb
2a
Outer & Inner Edges Fixed; Change in Slope rO
O
W a2 a2 C6 − L6 D D
2a
Special Cases b/a ro / a K δMax. K θa K θb KMrb KMro
K θ D b M rb = Mrb o ; Qa = Qb a a K Qb θ o D Qb = ; δMax. = K δo θ a a2 D M ra = M rb C8 + Qb a C9 + θ o L7 a δa = 0, M ra = 0; M C = w a G17 2
Uniform Distributed Load; Edge Simply Supported g
y rO w
w (a2 − ro2 )2 8 D a (1 + υ)
2.4779
0.8114
0.70
0.70
0.10 0.50
0.3376
0.4145
0.90
0.90
0.50
0.70
K δo
–0.1071 –0.0795 –0.0586 –0.0240 –0.0290
KMrb
–2.0540
KMra
–0.6751 –1.7429 –0.8988 –5.0320 –6.3013
KQb
–0.0915 –17.0670
ro / a
0.00
1.1868 –3.5685
0.20
2.4702
0.3122
4.8176 –23.8910 –29.6041 0.40
0.60
0.80
–0.0637 –0.0576 –0.0422 –0.0230 –0.0067
K θa
0.0961
0.0886
0.0678
0.0393
0.0124
KMC
0.2062
0.1754
0.1197
0.0621
0.0177
0.40
0.60
0.80
−w 2 (3 + υ) (a − ro2 ); If ro = 0, G11 = 0.015, G14 = 0.062, G17 = 2a 16
−w a4 −w a3 − w a 4 (5 + υ) w a2 (3 + υ) w a3 G11 ; L Tθ = G14 ; δC = ; MC = ; θa = D D 64 D (1 + υ) 16 8 D (1 + υ)
Linear Increase Load; Edge Simply Supported rO
w
2a
L Tδ =
θa = Qa =
2a
L Tδ =
−W a G17 − 2 G11 2 D 1 + υ
2.9405
b/a ro / a
K δC
4
δC =
KQb
0.10 0.50 0.70 0.50 0.70 0.70 0.90 0.90 –0.0102 –0.0113 –0.0023 –0.0017 –0.0005 0.0278 0.0388 0.0120 0.0122 0.0055 –0.0444 –0.0420 –0.0165 –0.0098 –0.0048 –0.4043 –0.3819 –0.0301 –0.0178 –0.0063 0.1629 0.1689 0.1161 0.0788 0.0662
δa = 0, M ra = 0; M C = w a2 G18
ro / a K δC
4
0.00
0.20
δC =
− w a G18 − 2 G12 2 D 1 + υ
Qa =
−w (2 a2 − ro a − ro2 ) 6a
θa =
w a3 G18 (4 + υ) − 2 G15 ; If ro = 0, G12 = 0.004, G15 = 0.022, G18 = D 1 + υ 45
–0.0323 –0.0249 –0.0164 –0.0083 –0.0023
K θa
0.0512
0.0407
0.0278
0.0148
0.0043
KMC
0.0955
0.0708
0.0449
0.0222
0.0061
− w a5 − ro − w a 4 (6 + υ) w a2 (4 + υ) w a3 G12 ; δC = ; MC = ; θa = D a − ro 15 D (1 + υ) 45 15 D (1 + υ)
Central Circular Load; Edge Simply Supported 2a
For r > ro ; δ = Mr =
r
W rO
at r = a; δMax. =
Wr 1 W (3 + υ) 2 a a + ln (a − r 2 ) − 2 r 2 ln ; θ = 16 π D (1 + υ) r 4 π D (1 + υ) r
W a (a2 − r 2 ) N 2 4 (1 + υ) ln + (1 − υ) ; N = 16 π r a2 r2
or N = ro , If ro > 0.5 t ; M t =
1.6 ro2 + t 2 − 0.67 t ; If ro < 0.5 t
W a N 2 4 (1 + υ) ln + (1 − υ) 4 − 2 16 π r r
−W a2 (3 + υ) Wa W ; θ Max. = ; M Max. = 16 π D (1 + υ) 4 π D (1 + υ) 4π
a (1 + υ) ln N + 1
203
2.16 Flat Circular Plates Besides the usual loadings, Table 2.5 Part II also includes several loading cases that may be described best as externally applied conditions that force a lack of flatness into the flat circular plates. The first time we look at Table 2.5, Part II it appears to be a formidable task to calculate the strength of these structures. However, when we consider the number of cases it is possible to present in a limited space, the reason for this method of presentation becomes clear. With careful inspection, we find that the constants and functions with subscripts are the same except for the change in variables. In Table 2.5, Part II, the tabulated values in the Special Cases are listed for the preceding functions for the most frequently used denominator values of the variable ratios, such as b / a and r0 / a. Example 2-41 A flat circular plate is made of nylon 6/6 with 33% fiber glass reinforcement at 73 °F and 50% relative humidity. The radius is 3.00 in with a wall thickness of 0.25 in. The plate is simply supported around its edge and it is loaded with 500.00 lb at the center. The load is distributed through a round area of 0.125 in radius. Determine the maximum bending stress at the surface of the plate and the maximum deflection at the center of the plate. Solution
2a
This flat circular plate and loading are covered in Table 2.5, Part I, case load at center with the outer edge simply supported. The diagram and equations in Figure 2-96 were obtained from this table:
W
t = 0.250 in, w = 500 lb, a = 3.00 in, r0 = 0.125 in,
E = 900,00 psi, υ = 0.39, σ = 18,000 psi σ Max. = =
1 − υ r02 3 W (1 + υ) 1 a + − log r0 1 + υ 4 a2 2 π t2 υ + 1 3 × 500 (1 + 0.39) 1 3.00 1 − 0.39 × 0.1252 + − log 0.125 1 + 0.39 × 4 × 3.02 2 × 3.1416 × 0.252 0.39 + 1
= 10,794 psi
3 W a2 (1 − υ) (3 + υ) 3 × 500 × 3.02 (1 − 0.39) (3 + 0.39) = 4 π E t3 4 × 3.1416 × 900,00 × 0.253 = 0.158 in
δMax. =
Example 2-42 A thick flat circular plate is made of nylon 6/6 with 33% fiber glass reinforcement at 73 °F and 50% relative humidity with a radius of 4.00 in and a uniform wall thickness of 0.50 in. The plate’s outer edge is fixed and it is uniformly loaded along the round area of plate with 200.00 lb/in. Determine the maximum bending stress at the surface of the plate and the maximum deflection at the center of the plate.
Figure 2-96 Flat circular plate, concentrated center load, and simply supported edge
δ
204
2 Engineering Product Design δ
w
Solution This thick flat circular plate and type of loading is presented in Table 2.5, Part I, case Uniformly Distributed Load with the Outer Edge Fixed. The diagram and equations in Figure 2-97 were obtained from the table.
2a
Figure 2-97 Flat circular plate, uniformly distributed load, and fixed edge
Because this example case deals with a thick plate, we need to investigate if the thickness / radius ratio is greater than 0.1 to modify the maximum deflection by multiplying the value by the constant (H). t = 0.500 in, w = 200 psi, a = 4.00 in, E = 900,00 psi, υ = 0.39, σ = 18,000 psi For thicker flat circular plates with a ratio t / a > 0.1, multiply the deflection equation by the constant (H), where H = 1 + 5.72 (t / a)2. t 0.50 = = 0.125 > 0.1 a 4.00 H = 1 + 5.72 (t / a)2 = 1 + 5.72 (0.50/4.00)2 = 1.089 σ Max. = δ=
3 w a2 3 × 200 × 4.02 = = 12,223.00 psi π t2 3.1416 × 0.502
3 w a 4 (1 − υ2 ) 3 × 200 × 4.04 (1 − 0.392 ) = = 0.072 in 16 E t 3 16 × 900,00 × 0.503
δ = H x y = 1.089 × 0.072 = 0.079 in
Max.
Example 2-43 A flat circular plate, made of acetal homopolymer, has a wall thickness of 0.187 in and a 5.00 in outside diameter, and is simply supported with a uniformly distributed load of 6.0 psi. Calculate the maximum deflection in the center, the maximum stress, and the deflection equation for Figure 2-98. This flat circular plate and type of loading is presented in Table 2.5, Part II, case Uniformly Distributed Load Edge Simply Supported. First, we need to determine the maximum moment, the bending stress, the plate constant, and the deflection caused by the load. Second, we need to calculate the total deflection of the plate caused by the load, the moment, and the loading constant. Finally, we need to check the deflection at the outer edge. t = 0.187 in, w = 6.0 psi, a = 2.50 in, r0 = 0,
rO w
E = 410,000 psi, υ = 0.35, σ = 10,000 psi M Max. = M Center =
w a2 (3 + υ) 6.0 × 2.502 (3 + 0.35) = = 7.85 lb-in. 16 16
2a
Figure 2-98 Flat circular plate, uniformly distributed load with simply supported edge
σ Max. =
6 M 6 × 7.85 = = 1,339.97 psi t2 0.1872
205
2.16 Flat Circular Plates
D= δC =
E t3 410,000 × 0.1873 = = 256.66 2 12 (1 − υ ) 12 (1 − 0.352 ) −w a 4 (5 + υ) −6.0 × 2.504 (5 + 0.35) = = −0.0565 in 64 D (1 + υ) 64 × 256.66 (1 + 0.35)
The total deflection equation for the flat circular plate is: δa = δC +
MC y2 −w a4 G11 + L Ty , where for this case L Ty = D 2 D (1 + υ)
Where the constant G11 = 0.015, when r0 = 0. 7.85 × a2 6.0 × 0.015 × a 4 − 2 × 256.66 × 1.35 256.66 2 = −0.0565 + 0.01132 × a − 0.000365 × a 4
δa = −0.0565 +
Checking the deflection at the outer edge, when a = 2.50 in δa = −0.0565 + 0.01132 ⋅ 2.502 − 0.000365 ⋅ 2.504 = −0.0565 + 0.07075 − 0.01425 = 0.0
Example 2-44 A flat circular plate is made of acetal homopolymer with a wall thickness of 0.125 in and 4.00 in outside diameter. It is mounted in a fixture to produce a sudden change in slope in the radial direction of 0.05 radiant at a radius of 0.75 in. It is then clamped between two flat fixtures as shown in Figure 2-99. Calculate the maximum bending stress. This is an example of forcing a known change in slope into a flat circular plate, clamped (fixed) at both inner and outer edges. This flat circular plate and type of loading is presented in Table 2.5, Part II, case Outer and Inner Edge Fixed and Change in Slope, where: θ0 = 0.05, b / a = 0.10, r0 / a = 0.50 and Poisson’s ratio of υ = 0.35. t = 0.125 in, a = 1.50 in, b = 0.15 in, r0 = 0.75 in,
θ0 = 0.05 rad., θb = 0.0 rad., δb = 0.0 in, E = 410,000 psi,
υ = 0.35, σ = 10,000 psi D=
Qb =
3
Et 410,000 × 0.125 = = 76.04 12 (1 − υ2 ) 12 (1 − 0.352 )
K Mrb × θ × D −2.054 × 0.05 × 76.04 = = −5.20 lb-in. 1.50 a
K Qb × θ × D a2
θO 2a 4.00 dia.
3
M rb =
rO
=
−0.0915 × 0.05 × 76.04 = −0.154 lb/in. 1.502
0.125
0.15 r.
0.05 rad.
1.50 r.
0.75 r.
Figure 2-99 Flat circular plate having a change in slope with both outer and inner edges fixed
206
2 Engineering Product Design
M ra = M rb C8 + Qb a C9 + θ0
D L7 a
= −5.20 × C8 + (−0.154) × a × C9 + σ Max. =
0.05 × 76.04 L7 a
6 × M rb 6 × 5.20 = = 1,996.80 psi 2 t 0.1252
δMax. = K y0 θ r0 = −0.1071 × 0.05 × 1.50 = 0.008 in
Example 2-45 A flat circular plate, made of acetal homopolymer, has a wall thickness of 0.250 in and 5.00 in outside diameter, it is simply supported at the outer edge and subjected to two types of loads. One center load provides a uniform pressure over a diameter of 0.0625 in. The other is axis-symmetrically loaded with a distributed load that increases linearly from the center to the outside radius rO = 1.00 in;, this load has a value of 10.00 psi at the outer edge. Calculate the maximum bending stress. This example requires analyzing two different cases and to superposition the results. The first case is the linear increase of the distributed load with simply outer edge supported (Figure 2-100), the second case is the central circular uniform load with simply supported outer edge (Figure 2-101). Both cases are presented in Table 2.5, Part II. t = 0.250 in, a = 2.50 in, r01 = 1.00 in, r02 = 0.031 in, E = 410,000 psi, υ = 0.35, σ = 10,000 psi
From the special case data, the following variable ratios are obtained: rO1 w
r01 / a = 1 / 2.5 = 0.40, K yC = –0.0164, K θa = 0.0278, KMC = 0.0449 D=
2a
Figure 2-100 First case: Linear decreasing distributed load and edge simply supported
E t3 410,000 × 0.2503 = = 608.38 12 (1 − υ2 ) 12 (1 − 0.352 )
δ = K yC
w a4 −0.0164 × 10 × 2.54 = = 0.0105 in D 608.38
M = K MC w a2 = 0.0449 × 10 × 2.52 = 2.80 lb-in. 2a r P
δMax. =
− P a2 (3 + υ) − P × 2.502 (3 + 0.35) = = 0.0105 in 16 π D (1 + υ) 16 × π × 608.38 (1 + 0.35)
P = −20.76 lb. rO2
Figure 2-101 Second case: Center uniformly circular load and edge simply supported
The second moment component is calculated by using the equations provided in Table 2.5, Part II, case Central Circular Loading and Simply Outer Edge Supported.
207
2.17 Torsion Structural Analysis
N =
2 1.6 r02 + t 2 − 0.675 t =
1.6 × 0.032 + 0.252 − 0.675 × 0.25
= 0.085 in P a −20.76 (1 + υ) ln + 1 = 4π N 4π = −9.19 lb-in.
M Max. =
σ Max. =
2.17
2.50 (1 + 0.35) ln 0.085 + 1
6 M 6 (−9.19 + 2.80) = = −613.44 psi t2 0.2502
Torsion Structural Analysis
A bar is rigidly clamped at one end and twisted at the other end by a torque T = F × d, applied in a plane perpendicular to the axis. Plane sections remain plane and radii remain straight. There is at any point a shear stress (τ) on the plane of the section; the magnitude of this stress is proportional to the distance from the center of the section and its direction is perpendicular to the radius drawn through the point. The deformation and stresses are shown in Figure 2-102. In addition to these deformations and shear stresses, there are the longitudinal strain and stress. The longitudinal strain is reduced while the stress is in tension on the outside and a balancing compression stress is exerted on the inside. Assumptions The torsion equations are based on the following assumptions: • The bar is straight, of uniform circular cross section (solid or tubing), and of homogeneous isotropic material. • The bar is loaded only by equal and opposite twisting couples, which are applied at its ends in a normal direction to its axis. • The bar is not stressed beyond the elastic limit of the material. Angle of Twist (θ) If a shaft of length (L) is subjected to a constant twisting moment (T) along its length, then θ is the angle through which only one end of the bar will be twisted. Twisting Moment (T) The twisting moment T for any section along the bar is defined to be the algebraic sum of the moments of the applied couples that lie to one side of the section in question. Shearing Strain If a bar is marked on the surface (unloaded), then after the twisting moment (T) has been applied, this line moves as shown in Figure 2-102. The angle (θ) is
d T=Fxd
F
L
Figure 2-102 Deformation and stress under torque
208
2 Engineering Product Design measured in radians; the final and original position of the generator is defined as the shearing strain at the surface of the bar. Shearing Stress (τ) For a solid circular cross section bar, let T = Twisting moment; L = Length of the bar; r0 = Radius; J = Polar moment of inertia; τ = Shear stress; θ = Angle of twist (radians); G = Modulus of rigidity. Then: θ = (T L)/(G J ) ; τ Max. = (T r0 )/ J By substituting for J = (π r04 )/2 in the equation above for a solid circular cross section with radius r0, the following equations are obtained: θ = (2 T L)/(π r04 G) ; τ Max. = (2 T )/(π r03 ) For a circular tube cross section with outer radius r0 and inner radius ri: θ = (2 T L)/ π (r04 − ri4 ) G] ; τ Max. = (2 T r0 )/[π (r04 − ri4 )] The torsional stiffness of the bar can be expressed by the general equation: θ = (T L) / (G K), where K is a factor dependent on the bar cross section. For cross section bars, the factor K is equivalent to the polar moment of inertia J. In Table 2-6, the equations for the factor K and for the maximum shear stress (τMax.) for a variety of cross section bars are given. Example 2-46 Compare the strength and stiffness of a circular injection molded tube made of a plastic material, 1.00 in outside diameter and 0.187 in wall thickness, versus an extruded solid circular bar of the same material with the same diameter. The strengths of both cross sections will be compared by using the twisting moments (T) required to produce the same shear stress. The stiffness will be compared by using the values of factor (K) for both cross sections. For the circular tube bar: K = π (r04 − ri4 )/2 = 3.1416 (0.504 − 0.3134 )/2 = 0.083 in 4 T = τ π (r04 − ri4 )/(2 r0 ) = τ × 3.1416 (0.504 − 0.3134 )/(2 × 0.50) = τ × 0.166 lb-in.
For the solid circular bar: K = π r 4 /2 = 3.1416 × 0.504 /2 = 0.098 in 4 T = (τ π r 3 )/2 = τ × 3.1416 × 0.503 /2 = τ × 0.196 lb-in. The solid circular cross section bar is therefore 1.182 times as stiff as the circular tube cross section bar and 1.18 times as strong.
209
2.17 Torsion Structural Analysis Table 2-6 Torsion Equations
Constant K in θ =
Cross section
TL KG
Shear stress max.
Solid circle 2rO
K =
π rO4 2
τ Max. =
K =
π (rO4 − ri4 ) 2
τ Max. =
2T π rO3
Circular tube
ri
rO
2 T rO
π (rO4 − ri4 )
Solid ellipse 2rS
K =
π rL3 rS3 rL2 + rS2
τ Max. =
2T π rL rS2
τ Max. =
T 0.208 a3
2rL
Solid square a
K = 0.1406 a 4 a
Solid rectangle a
K =
b a3 a 5.33 − 3.36 16 b
T (3 b + 1.8 a) a4 τ Max. = − 1 4 b2 a2 12 b
b
θ = Angle of twist (radians); T = Twisting moment (lb-in); τ = Shear stress (psi); G = Modulus of rigidity (psi); J = Polar moment of inertia (in4); K = Constant equivalent to J (in4); ro = Outer radius (in); ri = Inner radius (in); rS = Elliptical short radius (in); rL = Elliptical large radius (in); a = Height (in); b = Width (in).
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211
3
Structural Designs for Thermoplastics
3.1
Uniform and Symmetrical Wall Thickness
Poor design
The ultimate design rule for injection molding thermoplastic products is to ensure that the wall thickness is uniform and symmetrical.
Molding problems
Non-uniform and/or heavy wall thicknesses can cause serious warpage and dimensional control problems in the injection molded products. Heavy wall sections cause not only internal shrinkage, voids, and surface sink marks, but also nonuniform shrinkage resulting in poor dimensional control and warpage problems. Figure 3-1 shows a poor cross section design of perpendicular corner walls that causes molding problems, such as differential shrinkage, warpage (concave) of both walls, and internal voids in the corner of the thicker wall. The last two designs are recommended to avoid these molding problems.
Sharp corner
Warpage
Voids
Good design
Good design
Figure 3-2 shows a heavy wall cross section design that could cause molding problems and the recommended design using a thin wall and proportional ribs.
r.
r.
Figure 3-3 shows a nonuniform wall section that should be replaced with a thin uniform wall having the same strength of the original heavy wall section. Figure 3-4 shows another poor and the recommended uniform wall design. Figures 3-5 and 3-6 show cross sections of two nonuniform wall designs and the recommended designs with a uniform wall thickness to avoid warpage, internal voids, long molding cycles, and surface sink marks.
Poor design
Seat
R.
Figure 3-1 Perpendicular walls, end corner designs
Good design
Figure 3-2 Heavy wall vs. thin uniform ribbed wall designs
Poor design
Good design
Figure 3-5 Nonuniform wall vs. thin uniform wall designs
Poor design
Good design
Figure 3-3 Nonuniform wall vs. thin uniform wall designs
Poor design
Good design
Figure 3-4 Nonuniform wall vs. thin uniform wall designs
Poor design
Good design
Figure 3-6 Nonuniform wall vs. thin uniform wall designs
212
3 Structural Designs for Thermoplastics Poor design
3.1.1
Part Geometries Difficult to Mold
The most serious defects caused by part geometry during the injection molding process are warpage, internal voids, surface finishing, dimensional control, and sink marks. Molding problems
Good design
These problematic part geometries are illustrated in Figure 3-7, which shows a poor design of a uniform wall thickness rectangular tray. The tray top surface corners are warped upward, while the vertical side walls are warped inward. The recommended design calls for a small crown on the top surface and the side walls to compensate for the warpage, with radii in all corners and a uniformly tapered wall starting from the center (thicker wall for gating) until the side wall ends. Figure 3-8 shows a poor design of a square box. The vertical side walls of the molded box are warped inwards. The recommended design calls for a small crown on the side walls to compensate for the warpage and radii in all corners. Figures 3-9, 3-10 and 3-11 show poor designs. The molded vertical walls are warped. The proper designs have tapered walls and radii in all corners.
Figure 3-7 Problematic rectangular tray design
Poor design
Molding problems
Poor design
Good design
Figure 3-9 Problematic electrical bobbin (spool) design
Poor design
Molding problems
Good design
Molding problems
Figure 3-10 Problematic “U” beam design
Good design Poor design
Good design
Figure 3-8 Problematic square box design
Figure 3-11 Problematic structural beam design
Molding problems
Good design
213
3.2 Structural Rib Design
3.1.2
Wall Draft Angle per Side
Draft angles for internal and external walls are essential to the ejection of the molded parts from the mold. External walls require smaller draft angles than the internal walls. Thermoplastic material expands in volume inside the plastifying unit and the solid material is transformed into a flowing melt. Then, the hot melt is injected inside the mold. The cold temperature inside the cavities initiates cooling-off and shrinking the hot melt. The amount of shrinkage of a molded part is a product of the mold shrinkage characteristics of the polymer, the part wall thickness, injection/packing time, mold temperature, and cooling time. During the shrinkage process, the molded part’s external walls shrink away from the cavity’s external walls, while the internal walls shrink in around the core surface or walls. Semi-crystalline thermoplastic materials have higher mold shrinkage characteristics than amorphous materials. Parts made of semi-crystalline materials require higher draft angles for their internal walls, while amorphous materials that have lower mold shrinkage characteristics, require higher draft angles for their external walls, lower mold temperatures, and longer cooling times. When a molded part requires an internal wall with a minimum draft angle, it is recommended to have an efficient mold temperature control, with mold cavities and cores made of hardening tool steel, well polished in the direction of ejection and low coefficient of friction surface coating on the cores. For external walls without texture made of either unreinforced or reinforced resins, a minimum draft angle of 0° 15′ to 0° 30′ is recommended. For internal walls, a minimum draft angle per wall of 0° 30′ to 1.0° is recommended. For parts made of mineral/fiber glass reinforced resins having internal walls without texture less than 1.00 in deep, a minimum draft angle per wall of 1.0° to 1.0° 30′ is recommended. For internal walls without texture deeper than 1.00 in, a minimum draft angle per wall of 1.0° 30′ to 3.0° is recommended. Figure 3-12 shows the equation to calculate the mold cavity external wall draft dimension per side, based on the draft angle and the cavity depth.
3.2
Structural Rib Design
When designing injection molding products with thermoplastic materials, it is critical to maintain uniform thin and symmetrical wall thicknesses. Nonuniform wall thickness can cause serious warpage, sink marks, and dimensional control problems. If greater strength or stiffness is required for a product design, it is more economical to use proportional ribs and thin base walls rather than thickwalled sections. For products requiring good surface appearance, the proper selection of thermoplastic materials is very important. For many resins, the use of ribs should be avoided, because they produce sink marks on the external surface and this defect becomes very noticeable on the molded product. If ribbing is necessary in a surface appearance application, the base wall thickness of the rib should be 40 to 50% of the base wall thickness, with a draft angle per wall of 0° 45′. There are several resins on the market that have good surface appearance behind the rib area, for example, PVC, ABS, PC, LCP, PBT, PET, among others. The sink mark problem could be improved by hiding the sink marks behind an external texture, letter, or surface undulation. For applications requiring uniform base
Draft angle ( ˚) Draft = L x tan ( ˚)
L
Figure 3-12 Mold cavity wall draft angle per side
214
3 Structural Designs for Thermoplastics Base wall thickness
R.
Sink mark
Differential thermal warpage
Heavy cross section area
Voids
Molding problems
Rib thickness
Poor design
Rib wall thinner than the base wall Two thinner ribs better than one
Good design
Good design
Neck down at rib intersection
Base wall Rib
Base wall Rib
Neck down at rib intersection
Good design
Base wall
Partially connected rib
Base wall Rib
Rib bridge connector Rib bridge connector
Good design
The upper sides of base wall and the rib are not connected, just a small lower area of the base wall and the rib are attached with a reduce neck down wall section
Figure 3-13 Poor rib design, molding problems, and recommendations
215
3.2 Structural Rib Design walls and ribs, the use of heavy wall sections must be avoided, which can not only cause sink marks, but also internal voids, molded-in stresses, and nonuniform mold shrinkage. Figure 3-13 shows some typical injection molding problems caused by a poor rib design.When the thermoplastic material and the product application allow design changes, the design recommendations will help to overcome this problem. The upper sides of base wall and the rib are not connected, just a small lower area of the base wall and the rib are attached with a reduced neck down wall section. The ribs should be 40% of the base structure wall and a draft angle per wall of 0° 45′ should be used, if a good surface appearance is required for the application. When using reinforced thermoplastic materials and the application does not require a good finish, the ribs should be between 60 to 100% of the base wall and a draft angle per wall of 1° should be used. For structural foam applications where good surface finishing is not required,a rib wall equal to the base wall thickness and a draft angle of 1.0°per wall should be, used.
3.2.1
Rib Strength Analysis Method
0˚ 45' T= 0.4 W
Ribs are reinforcements used to improve the strength and rigidity of injection molded thermoplastic products. Ribs have been the key to the successful replacement of metals by engineering thermoplastics. Properly designed and located ribs not only increase the load-carrying ability of thermoplastic structural sections, but also lower manufacturing costs, increase cycle times, eliminate the use of heavy wall thickness that cause sink marks, reduce heat spots in the mold, lower warpage, and improve the dimensional control of the molded products. Rib design can be troublesome, especially when the product designer has to rely on guess work to determine the strength, geometry, size, and spacing of the ribs. Three basic rib designs have been developed for the plastics industry based on the type of thermoplastic resins and product application requirements. The first rib design provides a good surface appearance, the second rib design is for structural applications that do not require good finish and are made of reinforced resins, the third rib design is for structural applications with poor surface finishing and are made of reinforced or foam resins. Figure 3-14 shows these rib designs. The rib strength analysis method requires the aid of computerized graphs to calculate the stress and the deflection of complex structures and predict the behavior of a ribbed thermoplastic structure. Four full size computerized graphs for calculating stress and deflection of a symmetrical tapered (1°) rib, where the rib wall thickness is either 60 or 100% of the base structure uniform wall, can be found in Figures 3-15, 3-16, 3-17, and 3-18.
W
Surface appearance rib design 1˚ T= 0.6 W
H
0.03 R.
W
Structural reinforced resins rib design 1˚
Each graph is a composite of several curves and is expressed as a dimensionless ratio to permit calculations in either the Standard International or English units. The graph curves are comparisons between the cross section moment of inertia of a hypothetical flat rectangular plate and the ribbed wall structure.
T= W
0.03 R.
The wall thickness of a rectangular plate would be based on the calculations an engineer might make in substituting thermoplastic for other materials in a structure that must withstand a specified load. When the width of a rectangular cross section wall is analyzed, it is divided into smaller equal sections and the moment of inertia for a single section is calculated and compared with that of its ribbed equivalent structure. The sum of the small section moments of inertia is equal to that of the original rectangular cross section.
H
0.03 R.
H
W
Structural reinforced or foam resins rib design Figure 3-14 Three rib design geometries
216
3 Structural Designs for Thermoplastics R.
1˚ H
W
WS 0.6W B
B
10
9 0.62 8
1.87 5 2.5 4
5.0 6.25 7.5 10 12.5 15 20 25 37.5 50 75 150
3
2
Computer programmed curves for calculating stress of an injection molded plastic ribbed structure, with a tapered rib, lower wall thickness equal to 60% of the base structure wall thickness
1
BEQ
3.75
W
Wall thickness for stress
1.25
6
W
WS
Base equivalent width
1.0
7
0 0
1
2
3
4
5
6
7
8
9
10
H Height of rib W
Figure 3-15 Rib (60%) stress analysis graph
R.
1˚ H
W
WD 0.6W B
B
10
0.62 9
1.0 1.25
8
5
4
Computer programmed curves for calculating deflection of an injection molded plastic ribbed structure, with a tapered rib, lower wall thickness equal to 60% of the base structure wall thickness Figure 3-16 Rib (60%) deflection analysis graph
W
WD
3
150
2
1
0 0
1
2
3
4
5
6
H Height of rib W
7
8
9
10
Base equivalent width
3.75 5.0 6.25 7.5 10 12.5 15 20 25 37.5 50 75
6
W
2.5
BEQ
Wall thickness for deflection
1.87 7
217
3.2 Structural Rib Design R.
1˚ H
W
WS W B
B
10 1.0
9
2.5
5
3.75 5.0 6.25 7.5 10 12.5 15 20 25 37.5 50 75
3
2
1
W
6
BEQ
1.87
4
W
WS
Wall thickness for stress
7
Base equivalent width
1.25
8
Computer programmed curves for calculating stress of an injection molded plastic ribbed structure, with a tapered rib, lower wall thickness equal to 100% of the base structure wall thickness
150 0 0
1
2
3
4
5
6
7
8
9
10
Figure 3-17 Rib (100%) stress analysis graph
H Height of rib W R.
1˚ H
W
WD W
B
B
10 1.25 9 1.87 2.5
8
10 12.5 15
5
20 25
4
37.5 50 75
W
WD
3
Base equivalent width
6
W
5.0 6.25 7.5
BEQ
Wall thickness for deflection
3.75 7
150 2
1
0 0
1
2
3
4
5
6
H Height of rib W
7
8
9
10
Computer programmed curves for calculating deflection of an injection molded plastic ribbed structure, with a tapered rib, lower wall thickness equal to 100% of the base structure wall thickness Figure 3-18 Rib (100%) deflection analysis graph
218
3 Structural Designs for Thermoplastics The equations for the ribbed structure and the rectangular cross sections are developed to compare the equivalent terms used in the equations. t = T − 2 H × tan(θ°)
Draft angle ( ˚) t
A (Area) = B × W + H
R.
T
H (T + t ) 2
W
3 B W 2 + 3 H t (H + 2 W ) + H (T − t )(H + 3 W ) y (Centroid) = H + W − 6A
B
I (Moment of Inertia) =
1 [4 B W 3 + H 3 (3 t + T )] − A (H − y )2 12
WD = Wall thickness for deflection, WS = Wall thickness for stress W D or W S
I (Moment of Inertia) =
B
Z (Section Modulus) =
B WD3 (or B WS3 ) 12
B WD2 (or B WS2 ) 6
To define one of the smaller sections of the whole structure, the term Base Equivalent Width (BEQ) is used and is equivalent to the base width divided by the number of ribs. BEQ =
Total Base Width B = Number of Ribs N
Using these equations, the thickness ratios for the types of ribbed structures used in designs of thermoplastic products are determined. These equations are programmed to develop the family of curves shown in Figures 3-15 to 3-18. The results were plotted for a symmetrical tapered (1°) rib thickness equal to either 60 or 100% of the structure base wall thickness. The curves in the computerized graphs are given in terms of wall thickness for deflection (WD / W) or wall thickness for stress (WS / W). The abscissa is expressed in terms of the rib height (H / W). It is important to use the height of the rib rather than the total height of the structure [(H + W) / W]. Examples 3-1, 3-2, and 3-3 illustrate step by step how to use the computerized graphs to simplify the ribbed structure calculations for deflection and stress. Example 3-1 An injection molded nylon 6/6 part with 33% fiber glass reinforcement is being considered as a replacement for an aluminum plate. The replacement must have a stiffness at least equivalent to the 0.156 in thick aluminum plate. One side can be ribbed, but in order to fit the existing housing, the overall thickness must not exceed 1.00 in. Aluminum has a modulus of elasticity of EA = 10,300,000 psi, while the modulus of elasticity for 33%
219
3.2 Structural Rib Design
fiber glass reinforced nylon 6/6 (50% relative humidity at 73 °F) has a value of EN = 900,000 psi. We selected a typical base wall thickness for nylon 6/6; W = 0.10 in. To achieve equal or greater stiffness, the deflection under a given load for the reinforced nylon 6/6 part must not exceed the deflection of the aluminum part under the same loading conditions. The deflection formula is proportional to 1 / (E · I), where E is the modulus of elasticity of the material and I is the cross section moment of inertia. I is proportional to the third power of the rib wall thickness (WD3). The equivalent wall thickness for deflection of a plain, flat reinforced nylon 6/6 part can be determined by the following calculation: 1 1 = 3 E A × WA E N × WN3 1/ 3
E × WA3 WN = A EN
1/ 3
10,300,000 × 0.1563 = 900,000
= 0.351 in
The reinforced nylon 6/6 part equivalent wall thickness for deflection is WD = 0.351 in, but because this heavy wall thickness is not economical or practical for injection molding, we select a structural base wall thickness of W = 0.10 in with a base ribbed wall thickness of T = 0.06 in (60% W). Because the maximum structure height allowable is 1.00 in, the maximum rib height is H = 1.00 – 0.10 = 0.90 in. In order to use the rib (60% W) deflection analysis graph correctly, the height (H), the equivalent base width (BEQ), and the wall thickness for deflection (WD) values must be divided by the ribbed base structure wall thickness (W). 8.40 Alumin um pla
WD 0.351 = = 3.51 W 0.100
te
14.00
H 0.90 = = 9.0 W 0.10 Then, from Figure 3-16 we obtain:
0.156
1.00
BEQ / W = 28 or BEQ = 28 · 0.10 = 2.8 8.40
The number of ribs required for the 8.40 in height is 8.40 / 2.8 = 3 ribs. For the 14 in width it is 14 / 2.8 = 5 ribs. Figure 3-19 shows the original aluminum plate and the replacement ribbed structure made of reinforced nylon 6/6. Because the ribs intersect, the reinforced nylon 6/6 structure will be more rigid than the aluminum plate, thus providing an additional design safety factor.
Nylon 6
/6, 33%
reinforc ed
14.00
0.10
Figure 3-19 Aluminum plate and the equivalent nylon 6/6 design
220
3 Structural Designs for Thermoplastics
P (load) = 70.00 psi
0.15 inch 10.0 inches
4.0 inches
Example 3-2 A copper cantilever beam plate, fixed at one end and subjected to a uniformly distributed load of 70 psi, is shown in Figure 3-20. Calculate the equivalent ribbed cross section in acetal homopolymer, its deflection, and stress. The modulus of elasticity for copper is: EC = 15,600,000 psi
Figure 3-20 Cantilever copper beam
The modulus of elasticity for acetal homopolymer is: EA = 410,000 psi Designing for the equivalent deflection, the equation is reduced to: 1 1 = 3 EC × WC E A × WA3 1/ 3
E × WC3 WA = C EA
or
1/ 3
15,600,000 × 0.153 = 410,000
= 0.50 in
A wall thickness of 0.50 in is not practical for thermoplastic structures, because of processing difficulties; therefore, an acetal homopolymer ribbed section is recommended. Modifying the known data in terms applicable for the computerized graphs and assuming a typical base structural wall thickness for injection molding of W = 0.12 in, calculate for a cantilever beam with nine equally spaced ribs. WA 0.50 = = 4.16 W 0.12 BEQ =
4.00 BEQ 0.44 B = = 3.70 = = 0.44 or W 0.12 N 9.00
From Figure 3-16, we obtain: H / W = 5.50, or H = 5.50 · 0.12 = 0.66 in. Applying the H / W = 5.50 and the BEQ / W = 3.70 to Figure 3-15, we obtain: WS / W = 2.75, or WS = 2.75 · 0.12 = 0.33 in. Calculate the moment of inertia and section modulus for the ribbed structure. I =
B × WA3 4.00 × 0.503 = = 0.041 in 4 12 12
Z =
B × WS2 4.00 × 0.332 = = 0.0726 in 3 6 6
221
3.2 Structural Rib Design
Maximum deflection of the cantilever beam at the free end: δMax. =
P × L3 70 × 10.03 = = 0.52 in 8 × E × I 8 × 410,000 × 0.041
Maximum stress of the cantilever beam at the fixed end: σ Max. =
P×L 70 × 10 = = 4820.93 psi 2 × Z 2 × 0.0726
Because the acetal homopolymer has a tensile strength value of 10,000 psi, a design safety factor of 2.0 is obtained for this example.
Example 3-3 Calculate the deflection and stress for the structure shown in Figure 3-21. The ends are simply supported, with a uniformly distributed load and it is made of 30% fiber glass reinforced polyester (PET). Substitute the known data: BEQ =
B 2.50 = = 0.625 N 4.00
H = 0.75 − 0.12 = 0.63
BEQ 0.625 = = 5.20 W 0.12 H 0.63 = = 5.25 W 0.12
From Figures 3-17 and 3-18, the following results are found: WD /W = 4.30 or WD = 4.30 · 0.12 = 0.516 in WS / W = 2.70 or WS = 2.70 · 0.12 = 0.324 in
P (load) = 150.0 psi
Determine the moment of inertia and section modulus: I =
B × WD3 2.50 × 0.5163 = = 0.0286 in 4 12 12
Z =
B × WS2 2.50 × 0.3242 = = 0.0437 in 3 6 6
20.00 inch
2.50
Maximum deflection in the middle of the beam: δMax. =
0.12
5 × P × L3 5 × 150 × 20.03 = = 0.42 in 384 × E × I 384 × 1,300,000 × 0.0286
Because 30% fiber glass reinforced polyester (PET) has an approximate tensile strength value of 17,000 psi, a design safety factor of 2.0 is obtained in this example.
0.12 0.75
1˚
Figure 3-21 Beam, uniformly distributed load, ends simply supported
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3 Structural Designs for Thermoplastics
3.3 Internal sharp corner
Poor design Pullout force Pullout force
Failure
Operational problem
r.
R.
Internal Sharp Corners and Notches
Internal sharp corners and notches are the leading cause of failure in injection molded thermoplastic parts. They are caused by the abrupt rise in stress concentrations in the internal sharp corners and are a function of the product design geometry, mold design, and the construction quality used in the mold. Figure 3-22 illustrates the failure problems caused by internal sharp corners and provides design recommendations to eliminate the internal sharp corner problems. All materials are notch-sensitive when subjected to high stresses at the notch and internal sharp corners result in crack failure. To avoid this problem, it is necessary to calculate the stress concentration factors for all internal corners and to check that all internal sharp corners are within safe stress limits. Figure 3-23 shows how to calculate the stress concentration factor of a cantilever beam and the ratio between the internal radius and the part wall thickness. With this graph, the internal radius dimension can be determined and should be approx. 50% of the part wall thickness. The internal radius should have a good surface finish, providing a streamlined path for the melt flow, improving the impact strength, and resulting in easier ejection of the parts. The radii also give added life to the mold by reducing cavitation in the cavity’s metal surface. The minimum recommended internal radius is 0.031 in.
Good design Stress concentration factor
3.0
Figure 3-22 Internal sharp corner
Cantilever beam internal radius stress concentration factor graph
2.5
2.0
Cantilever beam P = Applied load R = Internal radius T = Wall thickness
P
Recommended
R. 1.5
0.2
0.5
0.6
0
0.4
1.0
Figure 3-23 Stress concentration factor vs. radius/wall thickness (Courtesy: Du Pont)
0.8
1.0
1.2
1.4
R.
T
Internal radius/part wall thickness (R/T)
3.4
Injection Molded Thermoplastic Bosses
Bosses are thermoplastic cylinders attached to a side wall or end corners. Special self-tapping screws are used to mount other components. The boss’s outside and hole’s inside diameters are based on size, depth and type of screws, pullout torque requirements, resin modulus of elasticity, creep, and boss weld line strength. Figure 3-24 shows operational problems when the wall of the boss is either too thick or too thin. The recommended design takes into account the melt flow path around the correct boss wall and compensates for the low weld line strength with a rib. The use of large and long screws is not recommended; it is best to split the load using two or more smaller bosses to eliminate the heavy wall problems. Figure 3-25 shows the difficulties caused by large screws and provides design recommendations. When the boss is attached directly to a back wall or end corner molding, dimensional and breakage problems occur. Figures 3-26 and 3-27 show these operational problems, the recommended designs also shown eliminate these difficulties.
223
3.4 Injection Molded Thermoplastic Bosses
Boss wall too heavy Boss wall too thick
Poor design Poor design
Voids Hole size smaller
Warpage
Sink mark
Operational problems
Voids
Sink marks
Operational problems
Boss wall too thin
Poor design Good design split the load
Weld line failure
Figure 3-25 Thick boss walls cause problems that can be solved by using two smaller screws
Operational problems Correct boss wall thickness Rib Heavy cross sectional area Melt flow entrance
Voids
Rib
Sink marks
Neck down
Weld line
Poor design
Good design Figure 3-24 Boss wall thickness problems and recommended design
Good design
Operational problems
Figure 3-26 Molded bosses connected to a back wall
Heavy cross section area
Rib
Rib
Voids
Sink marks
Poor design
Molding problems
Figure 3-27 Molded bosses connected to an end corner
Good design
Good design
224
3 Structural Designs for Thermoplastics
3.5 Angled pins
Injection Molded Thermoplastic Threads
Internal and external threads can be manually or automatically molded into thermoplastic products; the speed cycle depends on the complexity of the mold. External threads are automatically molded by using the parting line of a two-plate mold or the parting line formed by angled pin slides as shown in Figure 3-28. Internal threads are molded by an automatic thread unscrewing device; the core moves forward for injection and retracts unscrewing the core from the molded product for ejection. Figure 3-29 illustrates the functional steps of this device.
Slides
Figure 3-30 illustrates a manual method used for threaded core inserts to encapsulate the threads where both items are ejected from the mold. Inserts are manually unscrewed for further use in the molding process.
Figure 3-28 External thread slides
3.6
Figure 3-29 Unscrew system
Manual core set-up
Gate
Collapsible Core for Molding Internal Threads
The collapsible core is a major breakthrough for injection molding thermoplastic products requiring internal threads, undercuts, and protrusions. This device incorporates only three moving parts, utilizing conventional mold movements. The collapsible core makes it possible to mold products that were previously considered impossible to mold. Products with internal protrusions, interrupted threads, and undercuts can be injection molded for high or low volume production applications. For conventional internal threaded products, the automatic operation of the collapsible core could reduce the injection molding cycle up to 30%. Root diameter of threads
Mold closed Core & part ejected Ejector pins
Cavity insert
Cavity
Molded cap Shut-off
Core insert
Stripper insert Collapsible core
Mold open
Collapsing segments
Figure 3-30 Manual process for molding internal threads
Positive collapse sleeve
Cooling hole
Ejector plate assembly
Figure 3-31 Collapsible core process for molding internal threads (Courtesy: DME)
Collapsible core open mold closed
Collapsible core closed mold open
225
3.7 Preferred Standard Thread Forms for Thermoplastics Figure 3-31 illustrates the collapsible core’s major advantages for injection molding thermoplastic quality end caps requiring internal threads without difficulty. The collapsible core makes it possible to design a simple mold that is easier to run in problematic product applications.
3.7
Preferred Standard Thread Forms for Thermoplastics
Several types of standard thread forms have been developed for common metal screw applications. The preferred types of thread forms for thermoplastic applications are those that have the largest internal radius with the load bearing face nearly perpendicular and with the highest depth thread. In the following, the standard thread forms are presented starting from the best to the worst for thermoplastic applications. The thread form selection will make a large difference in the performance of the thermoplastic part. The use of internal tapered (pipe) threads for any type of thermoplastic applications should be avoided. Buttress Threads The buttress threads are unique types of threads that are not symmetrical around a cross section center line; they are the preferred type of threads for thermoplastic applications. Buttress threads have advantages in load bearing applications where the load is in one direction only. Because the load bearing face is nearly perpendicular to the axis of the screw, the loads are transferred almost entirely along the axis rather than in the radial direction. The buttress threads have a standard root radius ranging from 0.035 to 0.070 × pitch. The largest possible root radius is suggested for thermoplastic products. Figure 3-32 shows the buttress thread details and applications. P (Pitch = 2 x screw dia./15) f (Flat = 0.125 x P) d (Depth = 0.75 x P)
45˚
r (Root radius from 0.035 to 0.070 x P)
Thread start (0.03 inch)
Thread end (0.03 inch)
Thread start (0.03 inch)
Figure 3-32 Buttress thread details and applications
226
3 Structural Designs for Thermoplastics (Depth of V-thread = 1.136 x P) s (Root & crest truncation = 0.26 x P) 47.5˚
r
d
s
H
British Association Standard Thread This thread form is recommended by the British Standards Institute for all screws smaller than ¼ in in diameter. This thread form, details are shown in Figure 3-33, is well suited for thermoplastic applications because of its thread face angle of 47.5° and its large root radius of 0.180 × pitch.
P r (Radius = 0.180 x P) (Depth of thread = 0.60 x P)
Figure 3-33 British Association standard thread details
(Depth = 0.640 x P)
The Whitworth thread form is an excellent thread design for thermoplastic applications, although this thread is being phased out in the industry. This type of thread, shown in Figure 3-34, has a generous radius of 0.137 × pitch at the root of each thread, which reduces the stress concentration effect.
American National or Unified Threads P
The unified thread shown in Figure 3-35 is the most common thread form used in designs. For a thermoplastic to metal thread joint, only coarse threads should be used to prevent cross threading and damage to the thermoplastic thread.
d 55˚
r (Radius = 0.137 x P)
Figure 3-34 Whitworth thread details
(Flat = 0.125 x P) P
f
Whitworth Threads
ACME Threads The ACME thread is used for power transmitting applications. This thread form, as shown in Figure 3-36, causes high stress concentration factors in the flat root sharp corners, the hoop stress developed will concentrate at the weakest point and cause failure either immediately or over a period of time. This type of thread is not recommended for use for any type of thermoplastic applications.
d 60˚
Square Threads (Depth = 0.613 x P)
Figure 3-35 Unified thread details
(Depth = 0.5 x P) P
29˚ d
V-Threads The V-thread, as shown in Figure 3-38, is the worst screw thread form for thermoplastic applications. The sharp notch at the root of the thread causes extreme stress concentration factors (3.0 to 5.0), producing catastrophic product failure.
t (Width of thread = 0.5 x P)
Figure 3-36 ACME thread details
P
0.5 P
Square threads, as shown in Figure 3-37, are used for power transmission applications, such as jack power screws, because of their efficiency in transmitting power. They are not recommended for thermoplastic applications due to the stress concentrations induced into the base threads, causing the threads to shear off.
0.5 P
Figure 3-37 Square thread details
227
3.8 Injection Molded Products with Undercuts
3.7.1
Thermoplastic Threads Creep Effects
When threading assemblies between metal to thermoplastic, it is preferable to have the metal part external to the thermoplastic part. The male thread should be on the thermoplastic part. Careful considerations should be made in a metal/plastic assembly, because of the large difference in the coefficients of linear thermal expansions of these materials. Thermal stresses created by this difference will result in creep of the thermoplastic part over a long time, if the assembly is subject to temperature fluctuations or if the end use temperature is elevated. If the plastic part must be external to the metal, a metal backup sleeve may be needed.
3.8
Injection Molded Products with Undercuts
Injection molded thermoplastic products may have undercuts for functional reasons or for decorative effects. Undercuts in an injection molded product application will increase tooling costs and lead to longer injection molding cycles. When undercuts in a chamfered molded product are less than 5% of the diameter, it may be possible to strip or eject the product out of the mold cavity. However, if this solution is contemplated, the mold must be designed to operate so that ejection takes place only when the thin walled molded product is free to expand or compress. In such cases, it may be necessary to provide the mold with an ejection ring or plate, rather than ejector pins. The only suitable geometry for internal undercuts is circular. Other shapes, such as rectangular, can not be stripped because of the high stress concentrations. Several other mold undercut release techniques are available for thermoplastic products with undercuts greater than 5% of the diameter to avoid injection molding problems. Following are design suggestions for stripping undercuts: • The undercut thermoplastic product must be free to stretch or compress. • The undercut should be rounded and chamfered to permit easy slippage of the thermoplastic product over the core of the mold and to minimize stress concentration during the ejection stripping action. • Adequate mold ejection contact area should be provided to prevent penetrating or collapsing of thin walled thermoplastic product during the stripping action. • Some permanent deformation may occur when the undercut is stripped. The deformation depends on the thermoplastic product, mold design, and injection molding process variables. • Acetal Homopolymer Resins. It is possible to strip the thermoplastic products from the cavities, see Figures 3-39 and 3-40, if the undercuts are less than 5% of the diameter and are chamfered. Only circular geometries are suitable for undercuts. Other shapes, such as rectangles, have high stress concentrations in the corners which prevent successful stripping. Other methods should be used to obtain a satisfactory thermoplastic product for undercuts greater than 5%.
P
d 60˚
(Depth = 0.866 x P)
Figure 3-38 V-thread details
228
3 Structural Designs for Thermoplastics
Allowable internal undercuts (A - B) x 100 B
B
= % u ndercut
B A
A
Figure 3-39 Internal undercuts for injection molded products (Courtesy: Du Pont)
Allowable external undercuts
C B
(A - B) x 100
= % undercut
C
A Mold closed
C B A
Figure 3-40 External undercuts for injection molded products (Courtesy: Du Pont)
Core pin closed
Undercut Mold open Plastic part
Core pins mating face
Core pin open
Figure 3-41 Core pins internal undercuts
Core
Cavity insert
Plastic part
Ejector wedge
Ejected molded part
Figure 3-42 Ejector wedge internal undercut
• Unreinforced Nylon 6/6 Resins. Injection molded nylon 6/6 products having an undercut between 6 and 10% usually can be stripped from the mold. To calculate the allowable undercut see Figures 3-39 and 3-40. The allowable undercut will vary with thickness and diameter. The undercut should be chamfered to ease the removal from the mold and to prevent over-stressing of the molded nylon 6/6 product. • Reinforced Nylon 6/6 Resins. For glass reinforced nylon 6/6 resins, a collapsible core or split cavity undercut is recommended to minimize high stress conditions during the stripping action, see Figures 3-39 and 3-40. The undercut should be rounded and limited to 1%, if stripping from a 100 °F mold, or 2% from a 200 °F mold temperature. Internal Undercuts Using Core Pins and Ejector Wedge Internal undercuts can be injection molded by using two separate core pins or an ejector wedge that srips the thermoplastic product from the mold, as shown in Figures 3-41 and 3-42. The mold must be designed to permit the necessary deflection of the part as it is stripped from the undercut. This is a very practical method, but flash must be controlled where the two core pins or the ejector wedge meet.
229
3.8 Injection Molded Products with Undercuts Internal Undercuts Using an Offset Ejector Pin
Mold closed Cavity insert
Figure 3-43 shows another method for molding internal undercuts using an offset ejector pin side movement, produced by the ejector plate assembly and the adjoining wall of the cavity. Offset ejector pins are used for internal side wall undercuts, but have limitations on the depth and size of the internal undercuts. UniLifter® Undercut Ejection System
Mold lower half cavity insert
This undercut releasing system uses standard components for simplified mold design and construction. Designs using angles from 5° to 10° will typically yield the best results. Angles up to 15° are permissible by using lifter guides in the bottom of the support plate, or whenever less than half of the core blades are bearing in the core insert. It is recommended that guided ejection be used in all designs.
Offset ejector pin Ejector plate assembly
Figure 3-44 illustrates the mold design and operation of the undercut releasing system.
Mold closed
Molded part
Offset ejector pin side movement
Ejection
Figure 3-43 Internal undercut, offset ejector pin side movement
Mold open
Figure 3-44 UniLifter ejector bar undercut (Courtesy: DME)
230
3 Structural Designs for Thermoplastics
Angled pin Heel block
Slide
Stop block Wear plate Slide retainer
Figure 3-45 External side undercuts using an angled pin slide
External Side Undercuts Using an Angled Pin Slide In this mold design, as shown in Figure 3-45, the side cavity block is attached to a carriage mounted in guides on the moving half of the mold. A suitable extension is machined in the fixed mold half, adjacent to the cavity, to accommodate the side cavity assembly when the mold is closed. This mold design offers a positive lock applied by the locking heel to the side cavity assembly when the mold is closed. External Side Undercuts with Slides Actuated Hydraulically Figure 3-46 shows that both slides are actuated hydraulically and this system is not dependent on the opening movement of the mold. The slides in this mold design can be operated automatically by the operating control panel of the machine. This mold design does not rely on the hydraulic locking force alone to keep the slides closed during the melt injection in the mold cavities. It is better to use a locking plate assembly for large side projected area slides to avoid the use of heavy duty larger diameter hydraulic cylinders. However, if the total projected area of the undercut is relatively small, this system should be a good design option, the mold design and construction is considerably simplified.
Locking plate
Mounting plate Slides
Wear plate Hydraulic actuator
Slides
Core
Ram
Figure 3-46 External side undercuts, hydraulic actuation of slides
231
3.8 Injection Molded Products with Undercuts External Radial Undercuts with Angled Pin Slides In this system, two hardened steel angle pins mounted in the fixed mold plate, control the slide cams. The slides are on the moving mold plate. Figure 3-47 shows a typical mold used to produce bobbins (spools); the top illustration shows the slides in the closed position. As the mold opens, the angled pins force the external cavity slide cams to move outwards, sliding on the mold plate as shown in the middle illustration. Once the angled pins move further out from the slide cams (mold fully open), the slide cam’s movement ceases immediately. The moving half of the mold causes the ejector sleeve system to operate and the molded bobbin is ejected from the mold automatically.
Mold closed, locking plate on both slides
Intermediate position of slides
Mold open, sleeve ejects the bobbin
Figure 3-47 External undercut with angled pin slides actuation
232
3 Structural Designs for Thermoplastics
3.9
Injection Molded Integral Life Hinges
The injection molding of integral hinge offers a unique concept that has been successfully applied for the production of a variety of containers, cases, and similar products. Figure 3-48 illustrates the concept of producing complete integral hinge enclosures in one single operation, capitalizing on the functional advantage and an economical incentive in the manufacturing of the products.
180 ˚ Integral hinge, open position
Multi-part design is the main reason for implementing this technique in articles containing one or more integral hinges. However, this concept is considered difficult because of the complex interaction of the many factors influencing the functional properties, and in particular the appearance, of the integral hinge enclosure. This section attempts to give an insight into the possibilities for, and the limitations of using injection molded thermoplastic integral hinge products. Considering the numerous possibilities in the product design and types of applications, it is obvious that the overall design aspects can only be discussed in general terms. The integral hinge is sometimes recognized as a separate device.
180 ˚ Integral hinge, closed position
90˚ Integral hinges, open positions
Figure 3-48 Injection molded integral life hinge applications
One aspect that should be considered is that the hinge acts as a second gate for the part of the box behind the hinge. The thin section formed by the hinge web (thickness between 0.001 and 0.015 in) causes a considerable pressure loss during the injection filling process of the hinge and lid. Rectangular or square boxes provided with straight sidewalls are prone to distortions with inward bending of the sidewalls of both box and lid. Consequently, the lid of the box, which is almost always the part behind the hinge, is very sensitive to the occurrence of mold shrinkage defects. It is therefore advisable to select a wall thickness for the lid that is smaller than for the box. The extent of the reduction in wall thickness in the hinge limits the possibility of filling the lid cavity. For the same reason, incorporation of ribs, bosses, etc. in the lid should be avoided. Even with correct gating, sink marks occur on the lid’s surface opposite the ribs and bosses. It is difficult and sometimes impossible to prevent these sink marks. The best remedy is to hide this defect is to use a surface texture. The following factors affect the quality of molded integral life hinges: • Geometry and size of the injection molded life hinge • Product wall thickness and melt flow distribution • Presence of melt flow dividers and/or ribs • Locking mechanism used in the product • Surface finish required for the product • Life hinge design, quantity, location, and length of the hinge • Life hinge mold design, number of cavities, size and location of the gates, and mold cooling system • Processing conditions, type, conditions, and size of the injection molding machine used • Type of thermoplastic resin used
233
3.9 Injection Molded Integral Life Hinges
3.9.1
Injection Molded Integral Life Hinge Design
For injection molded integral life hinge applications requiring a long flex life, it is essential that in designing the hinge section, optimum orientation of the polymer melt is achieved. The melt viscosity of the polymer used and the processing conditions are important parameters that influence the overall design of the life hinge and mold. Consequently, these factors set corresponding limits to the web thickness and land length of the hinge. As thickness does not influence the flex life of a correctly designed hinge, this dimension is mainly chosen to suit the required stiffness and the angle through which the life hinge enclosure must operate. The hinge should be thin enough to allow easy bending through the angle of normal use, but thick enough to retain a sufficiently stiff connection between the box and the lid enclosure. For containers and cases that normally operate at zero load, the hinge web thickness should range from 0.010 to 0.015 in. For light duty applications, a hinge web thickness of 0.015 to 0.020 in can be used. For long hinges, the thickness should be kept within narrow tolerances in order to prevent adverse effects of nonuniform melt flow through the hinge section. In general, it can be said that for 0.010 to 0.015 in thick hinges, the tolerances should be kept at ±0.0008 in. With a continuous hinge, the memory effect often results in a generally unwanted self-opening tendency of the enclosure. This tendency increases with thicker hinges and greater length. For some applications, this self-opening tendency can be an advantage, provided that it does not interfere with the container’s closing. An example where this characteristic is an advantage is the lid springs that open by a gentle pressure on the front of the enclosure. The land length should be properly dimensioned. Too short a land length may lead to insufficient back pressure generated during the injection mold filling. This in turn may result in nonuniform flow of the melt through the hinge. Weld lines may occur in the hinge section that will lead to premature failure of the hinge. On the other hand, too long a land length will cause a high pressure drop with the risk of shrinkage defects in the lid or even short shots. The land length of the hinge should be at least three times its thickness. If the ratio is less than 3 : 1, weld lines are likely to occur in the hinge, flexing will create considerable stress, and the flex life of the hinge will be reduced considerably. As a general guide, a land length of 0.030 to 0.060 in should be provided; however, this can be increased if greater angular movement is needed. Preferably, the inner shoulders of the hinge should be slightly recessed in order to ensure optimum fit of the box and lid at the closing line. Because of necking-in of the polymer, hinge thickness and land length are slightly changed when the hinge is flexed for the first time. Stress concentration initiated by internal sharp corners or notches near the hinge area should be avoided. Therefore, all corners of the hinge area should be well rounded, with the hinge surfaces polished and smooth. This aspect should be carefully considered when, for instance, the hinge surfaces are provided with a leather grain or other types of surface textures. A minimum shoulder radius in the hinge of 0.015 in is recommended. Figure 3-49 shows a faulty hinge design often encountered in practice. In addition to the presence of sharp corners, this design shows the disadvantage that the hinge will most probably not bend along the desired line and/or bending will occur
0.01 to 0.015 inch
Box
Lid
Figure 3-49 Incorrect life hinge design
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3 Structural Designs for Thermoplastics Lid
Only suitable for non critical applications 0.01 to 0.015 inch
0.01 to 0.015 Box
Lid
Figure 3-50 Incorrect life hinge design
0.03 R.
0.010 to 0.015 R. 0.03 to 0.06 Box
0.010 0.015 0.010
0.015 R.
Figure 3-52 Good angled polypropylene life hinge R. 0.03 R. Box
Recess for closing 0.010 0.015
0.02
0.01 0.063
0.03 R.
Box
Lid
1˚ Draft angle per wall (Typ.)
Figure 3-51 Good standard polypropylene life hinge
Lid 0.04
0.04
along different lines. This will result in a twisted hinge, poor closing of the box, and premature failure of the hinge. The design in Figure 3-50 is better, but is not recommended for long hinges and enclosures requiring relatively wide hinges. This type of hinge is only suitable for short hinges in noncritical applications.
0.08
Figure 3-53 Medical tablet dispenser life hinge design
Figures 3-51 and 3-52 are typical illustrations of polypropylene life hinge designs recommended for boxes and cases. Closing direction
H
0.010 0.015 0.020 to 0.040
L > 2H Lid Box
Figure 3-54 Video cassette case life hinge design
Box
Instead of using one long hinge it is sometimes better to use an interrupted hinge, reducing the self-opening tendency. It should be kept in mind, however, that a noncontinuous hinge gives rise to the occurrence of weld lines in the lid. Where extra resistance to torque or tearing is required, the thickness of the hinge web may be increased to 0.020 in. All transitions in the hinge web thickness should be adequately radiused (minimum 0.015 in). Figure 3-54 shows in principle the hinge design that is being successfully used for storage cases of video cassettes. The advantage of this design is that the gap between box and lid is masked by the hinge itself.
Closing direction 0.03 R. 0.06
A characteristic inherent in the use of polypropylene integral hinges is an imperfect fit of the box rear wall and lid. It is difficult to achieve an exact fit, therefore the rear wall of the closed box shows a slight gap between the box and lid beside the hinge. This defect can be minimized and often eliminated by providing a slight recess (approximate 0.010 in) in the rear wall of the box part where the hinge section is located as shown in Figure 3-53.
0.047 0.010 Lid 0.015 Total flex angle 180˚
Figure 3-55 Medicine box life hinge design
The life hinge construction illustrated in Figure 3-55 is a small box for medicine tablets. All sidewalls, including the rear wall of the box, are convex to prevent distortions. Because the hinge should be straight, the convexity of the rear wall affects the overall hinge design. The hinge will extend outside the rear wall of the box to a greater extent than with a straight rear wall.
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3.9 Injection Molded Integral Life Hinges
3.9.2
Mold Design Considerations for Hinges
Lid
The most important factor in mold design is the gating system. The selection of the number, size, and location of the gates is governed by technical, aesthetic, and economic considerations. However, the following conditions should be fulfilled: • The gate or gates should be located on the largest section of the enclosure, i.e., on the normally the box. • The major cavity should be completely filled before the melt flow reaches the restricted hinge area.
Box Figure 3-56 Film gate in box front wall
• Polymer flow in the hinge section should be perpendicular to the hinge line and should be as even as possible. This also applies when a multiple gate system is used. • With multiple gate systems, gates should not be located on either side close to the hinge, in order to prevent the formation of weld lines in the hinge. The ideal method of gating for shallow boxes is to use either a film gate or two individual edge gates located in the front wall of the box as shown in Figures 3-56 and 3-57. Especially with the film gate, mold filling is very uniform, resulting in optimum flow of the melt through the hinge. In practice, however, neither of the systems is favored, because their location in the front wall will obstruct the construction of the locking mechanism of the box. In addition, with single cavity molds, both systems require the use of a hot runner or insulated runner mold, resulting in a relatively costly mold. The simplest and most suitable gating system applicable to both shallow and deep boxes is to locate the gate(s) at the bottom of the box. Figure 3-58 shows the gate close to the hinge area causing difficulty in filling the part; this gate location is not recommended. The disadvantage of this gate location is that the melt reaches the hinge section before the first cavity is filled, restricting uniform melt flow distribution and melt flow orientation through the hinge. Because of the resultant higher pressure loss, a greater amount of shrinkage defects in the lid of the box can be expected. The choice between a single or a multi-gate system is mainly a matter of experience. In order to ensure that the first cavity is completely filled first, the gate for shallow boxes should be located as shown in Figure 3-59. With increasing box height, the gate can be moved toward the long axis of symmetry, which coincides with this line for deep boxes as shown in Figure 3-60. Figure 3-61 shows the correct location of the gates for a relatively shallow box. It can be seen that for this gating system the same principles apply as for the single gate system. When using multi-gate systems, attention should be given to balancing the melt flow to minimize the formation of weld lines. Sometimes incorporation of thicker sections in the lid (e.g., ribs or bosses) is unavoidable. Especially with relatively large and high boxes, undesirable shrinkage defects in the appearance surface are likely to occur. As shown in Figure 3-62, it is possible in these cases to gate the article on both sides of the hinge. Attention must be given to the weld line formation and that filling of the first part of the lid takes place from the cavity forming the box in order to ensure the quality of the hinge. This can be achieved by means of a multiple gate system in the box and a single gate in the lid.
Lid Weld Line
Box Figure 3-57 Two edge gates in box front wall
Box, integral hinge and lid Lid
Gate
Box
Gate Figure 3-58 Hinge, poor gate location
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3 Structural Designs for Thermoplastics Gate locations for weld line strength
Deep box
Box Gate (A) 1 2
Gate
Shallow box
Lid
Gate Gate (A)
Lid
Lid
1 4 1 3
2 3
Figure 3-61 Hinge, good multi-gate system on box
2/3
1/3
Box Gate locations for weld line strength Box Lid
Gate Figure 3-59 Hinge, good gate location
Box ½
½ Gate
Figure 3-60 Hinge, good gate location
Gate (A) 1 2
Gate (A)
Gate (B)
1 4 1 2
2 3
Figure 3-62 Integral hinge good multi-gate system on box and lid
Short hinge (1)
Box Gate Weld line
Lid
Gate
Short hinge (2)
Figure 3-63 Two gates on box with two short life hinges
Gate
Gate
In those cases where it is desirable to reduce the self-opening of the lid arising from the memory effect of a continuous hinge section, interrupted small hinges can be used as shown in Figure 3-63. With respect to the location of the gates, the same rules are applicable here as discussed for continuous hinges. Because noncontinuous hinges give rise to the formation of one or more weld lines in the second cavity, special attention should be given to the correct balancing of the individual sections of the hinge and venting of the mold. Occasionally, opening and closing of the box is accomplished by means of a two-hinge construction as shown in Figure 3-64. In this case, the gate(s) should be located in the central section forming the rear wall of the box. Wall thickness of this section should be approximately 25% greater than the wall thickness for the box and lid.
3.9.3
Proper Gate Design for Life Hinges
In this section, some other aspects regarding the design of the mold, as well as the effect of processing conditions and polymer choice in the performance of hinged boxes are discussed.
Long hinge (1)
Box
The size of the box gates (A) should be equal and considerably greater than that used for partial filling of the lid (B). Moreover, the lid gate should be located at the maximum possible distance from the hinge. The mutual sizes of the gates should be established by trial and error and can be checked from the location of the resultant weld line in the lid and by producing short shots.
Small shallow boxes used for the packaging of medicine tablets, cosmetics, etc. are most economically produced in multi-cavity molds. In these cases, proper gate design is very important. Lid
Long hinge (2)
Figure 3-64 Two gates on base with two long life hinges
In practice, it can be seen that when using a two or four cavity mold layout, the gate (usually an edge gate) is located in the sidewall close to the hinge section as shown in Figure 3-65. This system is only suitable for boxes of optimum design and should be avoided for critical designs, i.e., boxes with thin straight side walls requiring a relatively long flex life of the hinge. With this gate location, the resistance to filling the first cavity may become greater than the resistance to
237
3.10 Conventional Types of Pin Hinges flow through the hinge part located near the gate. This will obviously result in uneven flow of the melt over the whole length of the hinge and create the risk of producing warped boxes, showing a very limited flex life of the hinge due to occurrence of weld lines.
Weld line fail
Box
Lid
The best gating system with multi-cavity molds should be considered for each individual case. Sometimes it is possible to locate the gates in the center of the front wall of the boxes, but generally a system (as shown in Figure 3-66) gives the best compromise between all conflicting requirements. Edge gate
Because of their well known advantages, edge gates are preferred to other types of gates for multi-cavity mold layouts. Moreover, by using an edge gate, any shrinkage defects occurring in the lid or the box can be minimized. This type of gate enables a more flexible control of the injection filling rate. The correct size of the edge gate should be dimensioned by having a gate land of 0.040 in and a gate depth of 50% of the box wall thickness; the gate width is established by trial and error, depending on the polymer melt viscosity. A good procedure is to start with a small gate; the size can then be enlarged as necessary.
Lid
Box
Lid
Runner
Edge gate
Lid
3.10
Box
Box
Sprue
A sprue gate is used in exceptional cases, e.g., for high and relatively narrow boxes where fast filling is required in order to minimize the pressure loss in the gated cavity (long melt flow path) so that adequate pressure will be available to fill the lid cavity.
Figure 3-65 Hinge enclosure incorrect edge gate location
Box
Conventional Types of Pin Hinges
Injection molded thermoplastic hinges can be inexpensive and practical. The main idea behind their design is to make the products as simple as possible and to avoid using metal hardware. There is a trade-off between the intricacy of a mold and the cost of assembly and finishing. For production volumes of more than 100,000 parts per year, it is definitely worthwhile to build an intricate mold that eliminates all the finishing processes. For small volume productions, trial runs and prototypes, the mold should be simple. The molded products can be drilled, heat staked, and hand fitted together. Since there is sliding between mating parts, the hinge acts as a bearing. If the hinge is to be truly durable, at least one side of it should be made of nylon 6/6 or acetal homopolymer materials. The following methods of hinge formation do not require metal hardware in the hinge and are suitable for mass productions. Insert Molded Post Hinges A post made of nylon 6/6 can be insert-molded into a different material to form a strong and precise hinge. The nylon 6/6 post must be perfectly round and very smooth. The hinge will have enough friction to stay in any open position. With the proper selection of material, a hinge with an insert-molded post can last practically forever. Side Core Insert Mold Hinge Design If a small box has only two posts and socket hinges, the box can be molded with the posts interlocked in the sockets by using side cores in the mold as shown in Figure 3-67. Lid and box are molded in an interlock position. The thin steel sleeve from core separates the shaft on the lid from the bearing on the box.
Figure 3-66 Runner and mold layout, four hinge enclosures
Lid
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3 Structural Designs for Thermoplastics
Lid Snap-in pins into side holes
Lid
Core
Core Core Box
Figure 3-68 typical snap-in pin hinge used in audio cassettes
Box
Lid and box are molded in an interlock position.The thin steel sleeve from core separates the shaft on the lid from the bearing on the box. Figure 3-67 Small box with two posts and lid with socket hinges
Snap-In Pin Hinge Design In many injection molded and blow molded cases, snap-in hinges work quite well. Figure 3-68 is a typical snap-in pin hinge used in audio cassette and compact disk cases made from polystyrene. These types of hinges can be molded so that they snap together during assembly. Sometimes, they consist of a pin that is supported at both ends molded into one part, and a “C”-shaped receptacle or semicircular opposing flanges with interference so that the sides are deflected by the pin as it is inserted as shown in Figure 3-69.
Snap-in pins into holders
Standard Lug and Pin Hinge Design Figure 3-69 Enclosure case with rear snapin hinges
Top
Bottom
There are a variety of pin and hinge designs that can be injection molded into thermoplastic parts. Alternating flanges with semicircular section geometries can be used in place of a tube so that slides and cams in the tool will not be needed. Pins are often molded with flat sections, which are beyond the normal range of rotation so that the pin can be inserted from the side. It is also possible to mold alternating semicircular flanges into both parts and then insert a separate metal or thermoplastic pin through the center. Pin and hinges can be designed so that the tube slides down over the pin and is locked in place when the hinge is closed but can be lifted off when the hinge is all the way open. This is often desired when cover removal is necessary for service of the internal components as shown in Figure 3-70. Co-extruded Thermoplastic Hinge Design
Pin
Engineering thermoplastic elastomers are process compatible with a number of other thermoplastic materials and adhere well to materials such as polyvinyl chloride. This fact suggests the possibility of using co-processing to arrive at designs that incorporate the properties of more than one thermoplastic. Coextrusion and insert molding are two obvious possibilities.
Figure 3-70 Standard lug and pin hinge
In some situations, the use of a small amount of engineering thermoplastic elastomer may provide the most cost effective solution to a design problem. An examples is the co-extruded hinge shown in Figure 3-71, which incorporates a flexible film as a hinge of copolyester thermoplastic elastomer with two rigid support sections of PVC.
Lugs and pin hinge cross section Top
Bottom
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3.11 Metal Inserts for Thermoplastic Encapsulation
Copolyester hinge
Blind hole
Open hole
Blind hole counterbored
Blind hole protruding
PVC
Figure 3-71 Thermoplastic co-extruded hinge designs (Courtesy: Du Pont)
The high tear resistance, outstanding flex life, and excellent low temperature properties of copolyester thermoplastic elastomers performing as thermoplastic hinges creates opportunities that were previously beyond the capability of thermoplastics. Also, this efficient hinge design combines the different properties of each material, enabling different kinds of functions to be included in a hinge made in a single operation.
3.11
Metal Inserts for Thermoplastic Encapsulation
Protruding shaft
Protruding screw
Figure 3-72 Metal threaded and shaft inserts for plastic encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
The use of inserts in the injection molding process of thermoplastics presents some difficulties. Where inserts are required to add strength to the hold down screws, adding life to the screw thread, or when covers must be frequently removed for electrical conduction or other reasons, it must be realized that the encapsulation of inserts will slow down the molding cycle. It also requires a special type of injection molding machine, different mold and processing conditions, all adding to the manufacturing cost of the product. However, good design practices demonstrate that some types of inserts may be installed after molding. These metal inserts may be added by automatic means at a rate faster than is possible by incorporating such parts in the molding operation. For example, a tapped hole in the thermoplastic with a machine screw can be replaced with a self-tapping screw, with resultant savings in the cost of the injection molded products.
Drawn-pin
Drawn-shell
Several kinds of inserts are used in the injection molding process, including, metal inserts made by machining, by metal cold forging, by sheet metal stamping, and by sheet metal drawn processes. Several types of metal insert designs are shown in Figures 3-72 and 3-73. Maintaining a uniform accuracy in various dimensions of metal inserts has always been a problem for the plastics injection molding industry and for the metal insert manufacturers, mainly because of the lack of design information and standardization of metal insert dimensions.
Drawn-eyelet Figure 3-73 Metal drawn inserts for thermoplastic encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
240
3 Structural Designs for Thermoplastics Table 3-1 Machined Metal Screw Insert Tolerances
K E
45˚ B1
F C
H
B
A
G
D J
K E 45˚
Screw type
Description
Tolerance
A A1 A2
Tap size “American National” – “Class 2” Major diameter Minor diameter “regular” tolerance Minor diameter “precision” tolerance
(±) 0.002 in (±) 0.0005 in
B B1
Minor depth and major length diameter Number unusable threads top and bottom
C C1
Length “regular” tolerance Length “precision” tolerance Length of body male insert
(±) 0.010 in (±) 0.001 in (±) 0.010 in
D
Thread chamfer
45° · 0.003 in
E
Body chamfer
45° · 0.06 in
F
Coarse diamond knurl
G
Length of sealing diameter minimum
0.03 in
H H1
Length of usable thread 1.5 × diameter Length of usable thread
(H1 + B1 = B)
J
Sealing diameter tolerance
(±) 0.002 inch
K
Minimum bar stock diameter
F G
C1
B
H1
B2
D
A2 A1 J
Figure 3-74 Machined metal threaded insert tolerances (Courtesy: The Society of the Plastics Industry, Inc.)
3.11.1
Machined Metal Threaded Insert Tolerances
Dimensions and tolerances for typical metal female and male inserts are shown in Figure 3-74 and in Table 3-1. This data base used for machining as a single operation on an automatic metal screw inserts machine was compiled by the National Screw Machine Products Association. For dimensions A-2 (minor diameter) and C (overall length) the maximum “standard” tolerance should be specified whenever possible. However, for closer tolerances,“precision dimensions” can be specified when necessary. To maintain the “precision” tolerance, reaming and other additional operations will be necessary, at additional metal insert cost. If steel inserts are required and the recommended tolerances cannot be used in design without several modifications, the cost of this special steel insert will be higher than the common inserts made of brass, copper or aluminum. The minimum wall thickness of metal inserts depends on the accuracy of the insert mold shut-off dimensions. The stress produced by the thermoplastic mold shrinkage, combined with the injection molding pressure, may collapse the thin wall of the metal insert so that the mold shut-off diameter will be out of specified tolerances.
3.11.2
Thermoplastic Boss Wall Thickness for Metal Inserts
The thermoplastic boss wall thickness required around inserts depends on: • The proper metal insert design for thermoplastic encapsulation • Type of resin (thermoplastic or thermosetting)
241
3.11 Metal Inserts for Thermoplastic Encapsulation • The type of resin within each group • The mold shrinkage rate of the resin • The modulus of elasticity (rigidity) of the resin • The coefficient of linear thermal expansion of the resin • The coefficient of linear thermal expansion of the metal insert • End use temperature under which the product will have to function • Product dimensional changes caused by the post mold shrinkage and the moisture absorption characteristics of the resin • The resin creep characteristics (loss of properties) caused by aging of the product under load Very often, the thermoplastic injection molded product is designed first and the important metal inserts then fitted into the remaining space. If metal inserts are required for the application, they should be designed first, and then the thermoplastic encapsulated product should be designed around the metal inserts. The shape, geometry, and requirements for the metal insert control the thermoplastic wall thickness to a high degree, especially when the metal inserts are of irregular shape (rectangular, square, hexagonal, star, or of any other shape having sharp corners). The most important properties of the resin are: the modulus of elasticity, the viscosity characteristics for filling and packing the mold cavity with an optimum injection pressure, a longer melt crystallization rate, good melt adhesion characteristics, high elongation rate, and low polymer melt/ mold processing temperatures. All these resin characteristics are very important for encapsulating metal inserts without cracking or moving the insert. No one property of the resin will solve the encapsulation molding problems. For instance, if using a resin having a low mold shrinkage rate of 0.002 in/in but with a low elongation rate and a high modulus of elasticity (rigid), the encapsulated molded product will crack. Resins with a higher mold shrinkage rate of 0.010 in/in but with a good elongation rate are capable of being stretched around the metal insert and will not crack despite a thin boss wall thickness. It is difficult to set up thermoplastic boss standards (wall thickness around the insert and for the wall located underneath the insert) in relationship to the outside diameter of the metal inserts. Every encapsulated product presents different problems and must be engineered according to the design of the metal insert and the thermoplastic resin used. Figures 3-75, 3-76, and 3-77 show the metal insert orientation, the minimum clearance, and the problems caused by improper base wall thickness underneath the metal inserts. Parting line
Parting line
0.12 inch min.
Minimum distance between the inserts to avoid mold heat spots Figure 3-76 Inserts minimum clearance
Thin base wall
Blisters, poor surface finish
Thick base wall
Parting line
Voids
Good design (perpendicular)
Poor design (oblique)
Fair design (parallel)
Figure 3-75 Mold parting line orientation for metal inserts
Sink mark
Figure 3-77 Insert base wall thickness problems
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3 Structural Designs for Thermoplastics Table 3-2 Plastic Boss Dimensions for Metal Insert Encapsulation B D
T
Metal insert Outside diameter “D” (in)
Unreinforced thermoplastic
Reinforced thermoplastic
Boss dia. “B” (in)
Thickness “T” (in)
Boss dia. “B” (in)
Thickness “T” (in)
0.156 0.187 0.218 0.250 0.281 0.343
0.312 0.344 0.406 0.453 0.484 0.578
0.062 0.062 0.078 0.078 0.093 0.093
0.312 0.360 0.422 0.500 0.531 0.609
0.062 0.062 0.078 0.078 0.093 0.109
Table 3-2 shows recommendations for round metal inserts (common insert sizes), the boss diameters, and the wall thickness for the section underneath the insert, required for the thermoplastic resins.
3.11.3
Press/Lock Slotted Metal Insert Installation After Molding
It is often more economical to assemble metal inserts into the product after its removal from the mold than encapsulating the metal inserts during the molding operation. Press/lock slotted metal inserts should be installed promptly after the molded product is removed from the mold (within 3 minutes, preferably immediately), in order to take advantage of the subsequent mold shrinkage of the thermoplastic, which will promote insert anchorage. Usually, the inserts are placed and pressed in with the aid of a suitably designed fixture mounted in a small arbor press or punch press; allowing more than one insert to be be pressed in simultaneously. When an insert is to be pressed in after molding, the mold must be designed to provide a hole to receive it; the size of this hole must be designed on the basis of the size of the insert, the normal mold shrinkage of the thermoplastic, and any further allowance necessary to ensure anchorage. For small metal inserts, the diameter of the hole should be designed to be 0.001 in to 0.002 in smaller than the diameter of the insert, after completing the total shrinkage or when the product is at room temperature. For large metal inserts, and particularly when there is only a thin wall of thermoplastic surrounding the insert, an extra allowance for anchorage is not needed; on the contrary, the diameter of the hole may have to be designed on the basis of as little as 50% of the normal mold shrinkage factor in order to prevent cracking of the thermoplastic around the insert.
243
3.11 Metal Inserts for Thermoplastic Encapsulation Inserts with either coarse diamond or straight knurls can be pressed in satisfactorily. For some special applications, a coating of adhesive/sealer may be applied to the metal insert to promote anchorage and to ensure an airtight joint. For leakproof joint applications, the use of an “O” ring around the insert is recommended. A new type of insert (illustrated in Figure 3-78) has extended the practice of pressing in inserts. It can be pressed in with a single punch at the press, without the use of special fixtures. It reduces rejection rate and increases the rate of production. This press/lock slotted metal insert consists of an internal threaded brass circular shield ring insert with four slots/knurled ears and a spreader screw. This brass insert can be fed by hand or by machine into the thermoplastic molded hole. The spreader screw is then threaded downwards, putting the screw pressure on the four slots/knurled ears’ surfaces. The slots expand the shield against the wall of the hole, without harming the internal threads. When the spreader screw has reached the end of its travel, the brass insert is locked into position by a shoulder on the inside of the insert shield.
Spreader screw
Slot ear insert Molded hole
The diameter of the hole to receive the press/lock insert should be 0.002 in greater than shield size. The bottom of the hole, upon which the insert rests, must be flat. As with all inserts, maximum torque strength is achieved when the screw is long enough to utilize all of the threads of the insert and at the same time short enough so that the underside of its head comes down tight on the surface.
3.11.4
Cold Forged Metal Inserts for Encapsulation
Large volumes of cold forging inserts are needed to compete economically with other processes. Secondary operations are required for this process, such as turning, drilling, tapping, and others.
Plastic part
Pressed-in slot ear insert
Shield
The tolerances of cold forging inserts are the same as those for screw machined inserts, when machining, drilling, reaming, or tapping is involved. There are no specific formulas to control the diameters and widths of the collar’s dimensions with respect to the shank, or controlling the external geometry, such as ribs, shut-off shoulder, etc., which may be combined with other symmetrical or asymmetrical shapes in one piece. The solution for each problem should be reached through cooperation between the product designer, tool engineer, process engineer, manufacturing, resin supplier, and the insert manufacturer. Types of Materials Used for Cold Forged Inserts
Slot ears closed Spreader screw expands slot ears
Almost any metal can be cold forged, but the following materials are preferred in the order they are listed: • Aluminum and aluminum alloys • Brass • Copper and copper alloys • Carbon steels • Alloy steels • Stainless steel
Slot ears locked
Figure 3-78 Press/lock slot ears insert post molding installation
244
3 Structural Designs for Thermoplastics Tolerances without Finishing Operations Tolerances for any dimension such as length or diameter vary with the material and with the sizes and proportions of the insert, as they in turn determine the equipment or method of heading to be used. In general, the following tolerances can be considered for commercial inserts without needing finishing operations, although in some cases, special care must be exercised to meet the required specifications: Length shoulder Radii (R.) Sealing diameter Sealing diameter draft
(±) 0.010 in 0.03 in (±) 0.020 in (±) 1°
(maximum) (minimum) (minimum) (maximum)
Tolerances with Finishing Operations Figure 3-79 Commercial threaded female metal inserts for plastics
Whatever tolerance is needed can be met by adding finishing operations. For example, aircraft studs, bolts, and special components are commonly made in production today to tolerances as close as (±) 0.0005 in.
Sharp corners
3.11.5 Shrink stress
Poor design
Sharp corners
Shrink stress
Threaded Female Metal Inserts
Designing injection molded thermoplastic products requiring threaded female metal inserts for encapsulation requires a lot of planning and preliminary engineering work. The product design engineer, tool engineer, process engineer, manufacturing, resin supplier, and the insert manufacturer must cooperate to obtain simplicity of design, which will result in the production of satisfactory products and will promote economical production. Figure 3-79 shows four typical commercial threaded female metal inserts used with thermoplastic products. Typical applications for these inserts are electrical bobbins, purge solenoid magnetic spools, and ABS sensors; leads and insert connections are encapsulated inside of the plastic. Figure 3-80 shows three designs that could affect the performance of the thermoplastic product encapsulating one of these metal insert designs. Differential Shrinkage Effects on Encapsulation
Fair design
Figure 3-81 shows the after-molding effects on encapsulation caused by the high mold shrinkage of the thermoplastic resins and the small dimensional changes of the metal insert.
Metal insert
R.
R.
Plastic part
Differential shrinkage
Good design Figure 3-80 Threaded female metal insert design variations
Figure 3-81 Encapsulation effects caused by differential shrinkage
245
3.11 Metal Inserts for Thermoplastic Encapsulation Coefficient of Thermal Expansion Effects on Material Selection The correct selection of metals for inserts is essential, because of the differences in the coefficient of linear thermal expansion between the various metals and thermoplastics. The values for the coefficient of linear thermal expansion for fiber glass reinforced thermoplastic resins are controlled by the following parameters: • Fiber glass orientation during the injection molding process • Base polymer thermal properties • Additives compounded with the polymer • Process/equipment required to compound the polymer The coefficient of linear thermal expansion for a polymer oriented parallel to the melt flow direction (also known as MD) is generally the smaller value reported by the plastics suppliers. The fiber glass becomes chemically coupled and anchored with the polymer and provides reinforcement to the polymer, thus restricting changes of dimensions of the molded part. However, these benefits are only applicable to sections of the molded part that have been aligned towards the MD direction. The coefficient of linear thermal expansion increases with the fiber glass orientation angle changing from parallel or 0° (MD minimum) to perpendicular or 90° (TD maximum).
Table 3-3 Coefficient of Linear Thermal Expansion (0 °C to 200 °C) – (cm x cm/°C)
Materials
Coefficient · 10–6
Engineering Thermoplastic Nylon 6/6, unreinforced Nylon 6/6, FR. unreinforced Nylon 6/6, reinforced Nylon 6/6, FR. reinforced Nylon 4/6, FR. reinforced HTN Nylon, reinforced Nylon 6/12, reinforced PBT, reinforced PET, reinforced PPS, reinforced LCP, reinforced
70 MD – NA TD 60–70 MD – NA TD 20 MD – 55 TD 20 MD – 55 TD 25 MD – 60 TD 15 MD – 45 TD 23 MD – 50 TD 25 MD – 60 TD 25 MD – 60 TD 22 MD – 55 TD 14 MD – 40 TD
Metals Aluminum 2S (99.2% Al) Brass (67% Cu, 33% Zn) Bronze (90% Cu, 10% Zn) Phosphor bronze Phosphor bronze 30 (95.5% Cu, 4% Sn, 1% Zn) Copper (99.9+%) Steel (99% Fe, 1% C) Cold roll steel Stainless steel (90.2% Fe, 8% Cr, .4% Mn, .12% C) Monel (60% Ni, 12% Fe, 11% Cr, 2% Mn) Nickel Silver (92.5% Ag, 7.5% Cu) Solder, half and half Zinc (95% Zn, 5% Al)
23.94 18.5 18.8 16.8 18.90 17.71 12 14 11 14 12.9 18 24 28
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3 Structural Designs for Thermoplastics The coefficient of linear thermal expansion for the transverse direction of melt flow (perpendicular to the orientation of the fiber glass, also known as TD), has a much higher value than the coefficient for the MD direction. It is very close to the coefficient of linear thermal expansion value reported for the unreinforced polymers. The fiber glass oriented in the direction perpendicular to the melt flow provides very little reinforcement for the polymer (a slight improvement provided by the fiber glass TD cross section areas). Plastics suppliers do not publish the coefficient of linear thermal expansion for the transverse direction. These properties are available from the suppliers’ technical service departments. The coefficient of linear thermal expansion for common thermoplastic resins and metals are shown in Table 3-3.
3.11.6
Metal Inserts Anchorage for Thermoplastic Encapsulation
Firm and permanent anchorage of metal screw inserts is essential and because there is no chemical or natural adherence between thermoplastics and metal inserts, anchorage must be obtained by mechanical means. The slight anchorage that is obtained by the mold shrinkage of thermoplastic around the metal screw insert is never sufficient. Metal inserts must be anchored sufficiently to prevent turning when torque is applied and to prevent pulling out of the thermoplastic when subjected to tension. Internal stresses in the encapsulated thermoplastic must be kept to a minimum.
Flashing fill threads
Poor torque resistance
Poor design
Insert shoulder seals-off flashing
Coarse knurl anchorage
Good design Figure 3-82 Metal screw inserts anchorage for encapsulation
In the early days of plastics, it was customary to use hexagon metal stock for inserts. Other than in some special applications, this is mechanically incorrect. Hexagonal stock provides torsional anchorage only. Grooves must be machined to obtain sufficient anchorage in tension. Combinations of sharp corners and grooves on hexagonal stock set up certain internal stresses in the thermoplastic, which often result in cracking. In almost all applications, round metal stock is recommended, so that a coarse diamond knurling can be obtained. Coarse diamond knurling provides the most satisfactory anchorage from the standpoint of torque and tension and minimizes possible cracking around the insert. Knurling of metal inserts is best accomplished in screw machines with end knurling tools. Grooves can be used in conjunction with a coarse diamond knurl. Sharp corners must be avoided when machining the grooves. When using grooves, one wide groove in the center of the insert is preferred over two grooves. The center groove allows the thermoplastic material to shrink or creep toward the center and minimizes the formation of strain in the encapsulated molded product. Figures 3-82, 3-83, 3-84, 3-85, 3-86, 3-87, and 3-88 show poor and good anchorage designs, selection of metal insert designs required for the thermoplastic encapsulation and types of anchorage for round bars and flat sheet metal inserts.
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3.11 Metal Inserts for Thermoplastic Encapsulation Horizontal seal only No seal or shoulder
Poor design
0.125 min.
Improved design
Limited vertical & horizontal seals 0.062 min.
Horizontal & vertical seals
Protruding metal screw inserts should have a shoulder to seal out any thermoplastic flashing around the insert threads during molding.
Good design
Best design
Figure 3-83 Selection of metal screw inserts for encapsulation
Dual protruding screw inserts should have a shoulder extend above the top and below the bottom of the molded part to prevent flashing on the threads. Mold misalignment may cause damage to the mold when closing. Figure 3-84 Dual protruding metal screw insert for encapsulation
Metal insert in bosses should extend to within one material thickness of the opposite wall. Ribs can be added for additional strength to the boss weld line. Poor desig n
Good design
Figure 3-85 Threaded metal insert boss design for encapsulation
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3 Structural Designs for Thermoplastics No seal or shoulder
Horizontal seal only
Poor design
Improved design
Limited vertical & horizontal seals
Horizontal & vertical seals
Good design
Best design
Threaded metal inserts should have a shoulder to seal out any thermoplastic flashing that might be forced inside the insert threads during molding encapsulation. Figure 3-86 Selection of threaded metal inserts for encapsulation
Typical anchoring designs used to encapsulate the sheet metal stamping inserts with thermoplastic. Figure 3-87 Types of sheet metal stamping inserts for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
Typical anchoring designs used to encapsulate the round cold metal forged insert bars with thermoplastic. Figure 3-88 Types of cold metal forged inserts for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
3.11 Metal Inserts for Thermoplastic Encapsulation
3.11.7
Metal Insert Encapsulating Process Problems
3.11.7.1
Metal Insert Floating (Movement)
The floating of metal inserts can be controlled or prevented by applying the following procedures: • The retaining pins that hold the insert in position may be tapered slightly, starting the taper at the fillet and carrying it up to 1/3 of the length of the pin. If too much taper is allowed, making the insert too tight on the retaining pin, the insert may pull out of the encapsulated thermoplastic material. • The surface holding the retaining pin should be machined using a coarse straight knurl to improve the holding strength between the retaining pin and the insert holding area. • Split retaining pins are practical for holding blind hole inserts. • An extended circular shoulder should be provided on the insert to obtain a good sealed-off area; this shoulder bore in the fixed half of the mold allows the proper positioning of the insert. This technique is ideal for preventing the insert from floating, although it is not permissible when inserts must be flush with the mold parting line surface of the thermoplastic material. • For male screw metal inserts, a tapered hole can be provided for a drive fit, if close accuracy of the inserts is maintained. In this case, 0.0005 to 0.001 in for the depth of the hole is sufficient. • When precise location of the metal insert is essential, removable threaded pins are provided in the mold. Inserts are screwed into these pins. Subsequent removal of the flash from the thread is in most cases avoided. However, this procedure increases the cost of the mold, causing a longer molding cycle and higher production costs. 3.11.7.2
Thermoplastic Melt Flashing Inside the Insert Blind Hole
Thermoplastic melt flashing inside the insert blind hole is not as frequent as with the open hole type of inserts. Flashing is caused by loose retaining pins which allow the insert to move with the melt flow, poor mold insert surface, or knurling on the entire outside diameter of the insert, leaving extended burrs on the face, which do not permit the insert to rest flat on the surface of the mold or the surface of the retaining pin. It is good practice to provide a slight recess in the mold, accommodating the outside diameter of the insert. When the shoulder diameter of the retaining pin is the same as that of the insert and sharp corners can be retained in the hole, an 0.003/0.005 in increase in depth is sufficient to prevent flashing. It is desirable for the insert to protrude above the thermoplastic product surface, especially when electrical contacts are made. 3.11.7.3
Protruding Metal Insert Encapsulation Process
Protruding threaded metal inserts are frequently required and are encapsulated in thermoplastics for specific purposes. In most cases, the protruding section is used for assembly or for bearing points where a mechanical action is required. In special cases, especially with large metal inserts where the product encapsulated in thermoplastic is subjected to considerable torque in order to obtain a tight connection, the protruding section is necessary.
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3 Structural Designs for Thermoplastics Hex metal insert
Smooth hex metal insert
Round metal insert
Radius all hex corners
Sharp corners
Circular shoulder Cracks
Bead Holes
Shrinkage stresses cause molding problems
Coating
Poor design
Holes
Good design
Figure 3-89 Protruding metal inserts encapsulation process
Figure 3-89 shows the process of encapsulating a protruding circular shoulderthreaded metal insert in thermoplastic part. Using a hexagonal metal insert can cause high stress concentration factors and product failure or cracks in the thermoplastic around the hex insert’s sharp corners.
Bead
Coating
Fair design
Coating
Figure 3-90 Thin tubular metal insert anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
3.11.8
Special Metal Inserts Anchorage for Encapsulation
For thermoplastic encapsulation applications where the product wall thickness is limited, the metal insert anchorage design is provided by a coarsely diamond knurled circular metal insert with a protruded shoulder without any sharp corners. A groove can be added to increase anchorage for tension. However, sharp corners must be avoided. When encapsulating a hexagonal metal insert with a protruded circular shoulder, all sharp corners must be eliminated and a circular groove be provided at the center of the external surface of the insert for tension anchorage. Thin Tubular Metal Insert Anchorage for Encapsulation
Countersunk holes
These inserts are extremely difficult to anchor properly. When the tubular insert is located away from the molded part, it is possible to provide round holes or invert a bead from the tubular insert which will act as a satisfactory anchorage. The bead can be used outside or inside of the inserts as shown in Figure 3-90. When encapsulating the inside or outside of a tubular metal insert and a good joint is required, it is necessary to apply a thin coating to the metal insert surface (secondary operation) using an elastomeric polymer (liquid injection molding silicone, neoprene, vinyl, or a coupling agent) to improve the bonding strength between the thermoplastic and the thin tubular metal insert surface.
Angled lugs anchorage
Flat Plate Metal Insert Anchorage for Encapsulation
Figure 3-91 Flat plate metal insert anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
Flat plate metal inserts can be anchored by means of countersunk holes wherever it is permissible, or the section can be partially cut out and bent over to provide anchorage. All edges of the insert should be bevelled, except when certain sections of the insert are not required for the functioning of the product, as shown on Figure 3-91. When the flat plate metal inserts must be thick, angled
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3.11 Metal Inserts for Thermoplastic Encapsulation end lugs can be extruded and slightly flared to provide satisfactory anchorage. Anchorage may also be obtained by spot welding lugs to the underside of the flat plate metal insert. Drawn Shell Metal Insert Anchorage for Encapsulation When using a drawn shell metal insert slotted in the middle in a thermoplastic product with minimum wall thickness, extreme caution must be exercised to provide proper anchorage for encapsulation. Figure 3-92, top illustration, shows a poor anchorage design, because it allows insufficient thermoplastic product wall thickness to avoid cracking. The middle illustration shows a fair anchorage design, because the encapsulated thermoplastic product has a chance to slide (flashing) over the insert without providing good anchorage. The bottom illustration provides the best possible anchorage, the drawn shell metal insert slotted in the middle has an 80° shutoff parting line and the insert has been flared slightly, providing good anchorage. With this design, the encapsulated thermoplastic product actually has a chance to anchor the insert and to creep while shrinking. Drawn Pin Metal Insert Anchorage for Encapsulation Figure 3-93, left illustration, shows a poor anchorage design; the drawn pin open end metal insert is encapsulated with thermoplastic during the molding operation and then the insert is countersunk after molding. A slight bead has been provided as an undercut for anchorage of the insert. This type of anchorage is basically useless for holding the insert properly.
Poor design
Fair design ˚
80
Good design Figure 3-92 Drawn shell metal insert anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
The middle illustration shows a good anchorage design for this type of insert; piercing pins should be provided in the mold, so that the insert can be pierced during the molding operation. The insert is flared out to provide proper anchorage and the necessary thermoplastic countersink molded hole is formed. The right illustration shows the best anchorage design; the drawn pin open end metal insert is encapsulated with thermoplastic. Partial anchorage is obtained
Anchorage folding lugs
Poor design
Good design
Best design
Figure 3-93 Drawn pin metal insert anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
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3 Structural Designs for Thermoplastics
Anchorage lugs
by shearing and folding two lug segments of the insert during the molding operation. To minimize thermoplastic melt flashing into the insert, the floating pressure type of piercing pins are recommended as part of the mold. Large Drawn Shell Metal Insert Anchorage for Encapsulation
Tap threads after molding
Figure 3-94 shows a large drawn shell metal insert encapsulated with thermoplastic. In this application, the thread length or the insert space is limited. Because the drawn shell metal insert is thin, approx. 50% of the thread depth is used. The four flared lugs of the insert provide satisfactory anchorage for encapsulation. However, it is impossible to provide sealing surfaces if a threaded insert is used, because the hot thermoplastic melt flashes into the internal threads of the insert. Therefore, tapping threads inside the encapsulated insert after molding is recommended for satisfactory results. Large Surface Metal Insert Anchorage for Encapsulation
Anchorage lugs
Figure 3-94 Drawn shell metal insert anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
To encapsulate one or more large surface metal inserts on one side of a circular thermoplastic product, as shown in Figure 3-95, the circular inserts should have at least two grooves for anchorage. To retain the inserts in the mold, locating cavity grooves in one half of the mold are used; to avoid movement of the inserts during melt injection, fixed retainer pins in the other half of the mold are used, which cause holes in the surface “B”. Special action retainer pins are used to plug the holes, the pins are moved forward to retain the inserts at mold closing, then the melt is injected in the cavity; just before the packing time starts, the retainer pins are retracted, allowing the melt to fill the holes before mold ejection.
Metal inserts
Delay ejection retainer pins
Surface "A"
Surface "B"
Figure 3-95 Large surface metal inserts anchorage for encapsulation (Courtesy: The Society of the Plastics Industry, Inc.)
These inserts cause nonuniform mold shrinkage and warpage of the product. Surface “A” becomes convex while surface “B” becomes concave after the part is allowed to cool and age. If a flat surface is required, the encapsulated product should be annealed after molding and, as the last step, the surface should be machined. Poor design
Delay ejection retainer pins
Good design Figure 3-96 Irregular shaped metal inserts anchorage to encapsulate
Irregular Shape Metal Insert Anchorage for Encapsulation These irregularly shaped metal inserts cause great difficulties in encapsulation. Figure 3-96, top, is a poor design, where a long “U” shaped insert is partially encapsulated, causing the one-piece insert to float, molded-in stresses (differential shrinkage/thermal expansion), and cracking of the thermoplastic. The bottom illustration is a good design, where two separated inserts are supported by either fixed or delayed ejection retainer pins. This design has several advantages, among them better encapsulated product dimensional control, product free of moldedin stresses, improved quality control, reduction of product defects, and better process efficiency in long molding production runs.
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3.11 Metal Inserts for Thermoplastic Encapsulation
3.11.9
Electrical Lead Inserts for Encapsulation
If electrical contacts are required for the application, the insert can be made solid, flat, thin, and narrow. The electrical lead insert should be curved (serpentine like, winding curves) to compensate (a slight give in the curved insert) for the thermoplastic melt shrinkage around the insert, as shown in Figure 3-97. Straight inserts do not provide a firm and permanent anchorage required for a good joint between the electrical lead and the encapsulated thermoplastic product.
Electrical leads with 90° directional bends reduce the encapsulation problems caused by the different coefficient of linear thermal expansions of metal and thermoplastic. Top view A
When a long electrical lead type insert is used, it is advisable to provide an anchorage in the middle of the insert by means of retainer pins with a coarse diamond knurl on the clamping surface. The center anchorage will allow the thermoplastic melt to creep along the surface of the insert while it is shrinking toward the center. Where dimensional accuracy is required, full allowance for the differential shrinkage of the materials should be made. Leakproof Encapsulation of Various Inserts Because of the difference in the behavior between thermoplastics and metals (e.g., difference in the coefficient of linear thermal expansion) and the problems of providing proper insert anchorage, it is impossible for the insert to remain airtight within the thermoplastic, even under low injection pressures. When several inserts are used to encapsulate a leakproof product, special processing techniques are used to withstand high internal injection pressures, while retaining a leakproof joint. A leakproof encapsulated joint between two materials can be obtained by controlling the insert and the encapsulated product expansion and contraction. It is necessary that the inserts (before encapsulation) be precoated with a thin elastomeric adhesive and the walls around the insert be thin and uniform to compensate for the difference in the coefficient of linear thermal expansions.
Electrical leads A Cross section view "A - A" Lead insertion mold guides
Electrical leads Scale = 2:1
Figure 3-97 Electrical leads multidirectional bends encapsulation (Courtesy: Delphi Automotive Systems)
A few successful techniques for leakproof joints of inserts encapsulated with thermoplastics are reviewed. The external surface of the insert should be modified for anchorage with two or more grooves, about 0.03 in wide and 0.02 in deep. The front or anchorage of the insert should be dipped in neoprene, polyvinyl chloride acetate, or other rubbery material, and then cured before using. This will supply sufficient coating on the insert to give it the necessary cushioning action. It is also possible, especially on round inserts, to provide a large enough groove in the anchorage head of the insert so that a high temperature “O”-ring can be used. Under normal encapsulated molding conditions, the “O”-ring will produce satisfactory leakproof results. For some applications, such as the bobbin shown in Figure 3-98, a retaining groove for the “O”-ring is molded on the thermoplastic bobbin insert, sealing the metal can insert and providing a leakproof joint to stop the thermoplastic melt flow inside the bobbin wound wires during the encapsulation. Encapsulation of Reinforced Metal Inserts It is necessary to encapsulate the metal inserts with thermoplastics to reinforce the product, providing greater strength, rigidity, safety and accuracy. Rather than molding a thermoplastic product with a thick wall, which can cause severe operational problems, using correctly designed inserts will not only produce greater rigidity with a minimum product wall thickness, but it will also assist in maintaining better dimensional accuracy.
"O" ring viton Thermoplastic encapsulation
Thermoplastic insert electrical bobbin Metal can Electrical insert lead
Figure 3-98 Leakproof thermoplastic bobbin insert encapsulation (Courtesy: Delphi Automotive Systems)
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3 Structural Designs for Thermoplastics Figures 3-99 and 3-100 show encapsulated thermoplastic gears on hexagonal and square metal inserts. Figure 3-101 shows encapsulated thermoplastic pulley, using a ball bearing as an insert. These illustrations show typical poor product and insert designs, operational problems caused by insert sharp corners and thermoplastic mold shrinkage, and design recommendations to overcome the cracking problems. Hex metal insert
High stress concentration
Circular metal insert
Functional problems
Good design
Cracks
Poor design
Figure 3-99 Encapsulated thermoplastic gear on metal insert hub (Courtesy: Du Pont)
Square metal insert
High stress concentration
Reduced stress level
Cracks
Poor design
Functional problems
Good design
Figure 3-100 Encapsulated plastic gear on metal insert square hub (Courtesy: Du Pont)
Post molding shrinkage Double edge seal
Single edge seal
Cracks Encapsulated thermoplastic
Ball bearing
Open end for plastic expansion
Poor design
Functional problems
Figure 3-101 Encapsulated thermoplastic pulley on ball bearing (Courtesy: Du Pont)
Good design
3.11 Metal Inserts for Thermoplastic Encapsulation Nonmetallic Inserts for Encapsulation Inserts made of various materials are used successfully in encapsulation applications with thermoplastic polymers. Wooden or preformed inserts, for example, in bowling pins or golf balls use a core that is encapsulated with Surlyn resin to improve the surface finishing, hardness, scratch resistance, color, and toughness of the product, as shown in Ionomer Surlyn Applications, Chapter 1, page 17. The use of wooden inserts in applications, such as doorknobs or automobile gear shift knobs, saves considerable material and shortens the encapsulation molding cycle.
3.11.10 Inserts Preparation for Molding Encapsulation Cleaning the Inserts Proper cleaning or washing of inserts prior to molding encapsulation is essential, particularly when using metal screw machine inserts. If inserts are improperly washed, even though they appear clean, there may be loose metal chips hanging on to the threads or fine metal dust in the knurls. The latter is often rolled onto the surface by the process of knurling and it is not easily washed off, but it will be loosened by the melt flow of the thermoplastic. These metal chips may flow up to the surface and impair the appearance of the molded product. The most serious difficulty, however, is in electrical applications, where a small particle or a slight amount of metal dust may cause a total electrical breakdown. Grease and oil also are detrimental to the appearance of molded products and should be thoroughly washed off. Cleaning processes are divided into three types: • Mechanical, including hand polishing, tumbling, sandblasting, or washing with solvent or alkali • Chemical, removal of iron rust and silver tarnish by an acid bath • Use of electrolytic cleaners
Oil and machining chips can best be removed by a well-stirred alkali bath followed by a rinse with hot water, except where the nature of the metal, such as aluminum, rules out the alkali in favor of degreasing with a solvent. In many cases, a reasonable amount of tarnish can do no harm, but where the function or the appearance of the piece demands chemically clean inserts, an acid dip is necessary. For brass and bronze, a mixture of nitric and sulfuric acids or nitric alone is commonly used. Silver tarnish can be removed with nitric acid or a diluted solution of one of the cyanides. Trisodium phosphate can efficiently remove iron rust. Preheating the Metal Inserts Large inserts should be preheated (above the mold cavity temperature if possible) prior to molding encapsulation. This will allow the maximum expansion and improve the melt flow and delay the crystallization rate of the thermoplastic. With thermoplastic materials, preheating of inserts will reduce the possibility of weak weld lines, which often result in cracking of the thermoplastic after molding. Cleaning Flash from Metal Inserts Most of the difficulty with flash can be avoided in the design of the thermoplastic product and the insert by providing good sealing areas so that the melt flow of
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3 Structural Designs for Thermoplastics thermoplastic is shut off. However, even with the best design there will be some material on the inserts, especially when the mold wears or close tolerance on inserts is not maintained. Several methods are recommended to minimize this flashing problem, e.g., lubricating the insert prior to molding encapsulation with wax, soap, grease, or oil. Plating or hardening the inserts minimizes the tendency to produce flash. To remove the flash, cut the flashing area, using special deflashing tools close to the molded product and peel it off. Burn the flashing area using a small flame from a low temperature portable torch, designed for trouble shooting the nozzle/melt freeze-off in an injection molding machine. For some polymers, a mild solution of caustic soda will loosen the flashing area so that it can be easily removed. This method, however, requires extreme caution because extended contact or too strong a solution will harm the surface of the molded product and loosen the insert anchorage. Relieving Molded-In Stresses Considerable stresses are created in thermoplastic molded encapsulated products of irregular design, such as those having both thin and thick sections and especially those with metal inserts. The best method to relieve stresses is to allow the molded encapsulated product to cool slowly. The ideal situation would be to carry the molded encapsulated product on a conveyor through an oven that has various stages of temperatures, starting at 122 °F below the melting point of the polymer, then gradually decreasing until the molded encapsulated product is cooled to room temperature. The next best method requires two ovens, one at approximately 225 °F and the second at 150 °F. The molded encapsulated product remains in each oven successively until its temperature is reduced to oven temperature. The final step is cooling to room temperature. In the case of thermoplastic materials, molding stresses are relieved by using an air oven, or submerging in a liquid solution at suitable recommended temperatures and procedures. Following are guidelines for the design of inserts for molding encapsulation: • Design the product without inserts if at all possible. • Do not encapsulate an insert unless the mold was designed for it. • Do not use an open hole or internal threaded insert if it can be avoided. • Do not leave sharp corners on inserts. Chamfer wherever possible. • Do not encapsulate inserts without proper anchorage. • Do not flatten inserts if the insert is loose on the retaining pin. • Do not inject thermoplastic melt or flashing into the insert to hold it on the retaining pin, this will damage the mold, necessitating repairs. • Do not encapsulate inserts unless they are clean. • Do not use the metal drawn type eyelet inserts unless necessary. • Do not design the product with a very thin wall for the base of the insert. This wall will corrugate and appear like a blister caused by a high heat spot. • Do not design the product with a very thick wall for the base of the insert; this can produce sink marks and internal voids. • Do not allow a very thin wall around the insert, the boss will crack.
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4
Thermoplastic Gearing Design
Gears are used to transmit power and/or angular motion from one shaft to another. Examples of power gearing are the transmission and differential gears in automobiles and the gears in electric kitchen appliances and hand drills. Some gears, such as the gears between the hour and minute hands of a clock and the gears in some cameras used to focus the lenses from the range finder, are used primarily to transmit angular motion. Most gears used to transmit angular motion also transmit some power, such as in telescopes and radar drives. In this chapter, we will review the gear technology that is of importance when considering methods of gear manufacture. Gear manufacturing processes can be grouped into the following categories. • Molding Injection molding thermoplastic or powdered metal molding and casting: the completely formed gear is made in a mold having the shape of the final gear, where the material is forced into the mold cavity in a melt or liquid form. • Metal Removal Such as milling, hobbing, and shaping, which cut the tooth spaces into prepared gear blanks leaving the desired teeth. • Finishing Processes Such as shaving, grinding, and lapping, which improve the accuracy and surface finish of previously prepared gear teeth. • Chipless Methods Cold rolling, used for small worms, some gears, and splines; hot rolling used for larger gears and other proprietary processes in which gears are formed by squeezing and/or rolling with forming gears; impact forging in which metal is forced into a gear shaped die by extreme impact. The selection of a specific manufacturing process to produce gears is influenced by the type of gear to be made. Because of the complex nature of gears, considering their accuracy requirements and the exacting demands in the shape of their teeth, the manufacturing processes are highly specialized. This limits the kinds and sizes of gears that can be produced on any one machine or with a single process. When evaluating processes that may be used to manufacture gears, it is desirable to understand the geometry of the gears to be made. Without exception, every manufacturing process imposes compromises on the production of perfect gears. The determination of the degree to which a gear can be compromised requires an understanding of its geometry so that the exact effects of the compromise can be evaluated. Many product designers and manufacturers feel that gears designed to very strict standards can be manufactured only with special gear molds. In fact, the involute gear tooth form is one of the most versatile geometries known to thermoplastic gearing engineering design. With a reasonable knowledge of involute geometry, the product designer can apply standard gear mold designs to an extremely wide variety of tooth forms, solving many special problems, none of which appear to be standard by ordinary engineering techniques.
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4 Thermoplastic Gearing Design In this chapter, we will review the classification and application of gears, the standard spur and helical gear technology developed for metal applications, the new gear tooth forms “Plastic Gear Technology” (PGT) developed for injection molded thermoplastic gears, molding and operational problems caused by gear design/gating, engineering analysis methods to demonstrate how to calculate these special tooth forms by working several examples to calculate the strength, size, and tolerances of gears and finally, several illustrations of gear design documentation required to design/construct the mold and for molding production quality control standards of the gear.
4.1
Classification of Gears
To understand gearing, it is desirable to classify the more important characteristics of the gear application, such as the relationship of the shaft axes on which the gears are mounted. Shafts may be parallel or nonparallel to the shaft axis. If non-parallel, they may be intersecting or nonintersecting.
4.1.1
Gears Parallel to the Shaft Axis
Spur Gears Injection molded thermoplastic spur gears are the most common type of gears; they have a cylindrical form and the involuted teeth are parallel to the axis.
Figure 4-1 Spur gears
The American National Standard (ANSI B6.1-1968) provides two involute spur gear tooth forms. These two forms are identical, except than one has a 20° and the other has a 25° pressure angle while both tooth forms have a minimum allowable tooth number of 18. A gear tooth standard is established by specifying the tooth proportions of the basic rack. In recent years, the established standard of 20° pressure angle has become the universal standard spur gear tooth form. Figure 4-1 shows a typical spur gear set. Helical Gears
Figure 4-2 Helical gears
Helical gears have a cylindrical shape with an envoluted tooth form. The gear teeth may lie in one or two rows around the structure. The helical gear tooth orientation in the pinion and gear must be of opposite hand. The tooth elements are helixes about the axis of the gear. Figure 4-2 shows a large helical gear set. The American National Standard (ANSI B6.7-1967) provides a 20° tooth form for helical gears of 20 diametrical pitch and finer. The tooth proportions of fine pitch helical gear teeth are based on the normal diametral pitch and are the same as for fine pitch spur gears. Single Helical Gears
Figure 4-3 Single helical gears
If the teeth lie in a single row, the gear is called single helical. Injection molded thermoplastic single helical gear systems are used for low speed/torque applications, especially with the pinions encapsulated around metal shafts. Figure 4-3 shows a typical large single helical gear set. In recent years, this application has increased with the introduction of new thermoplastic materials developed for the gear market.
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4.1 Classification of Gears Double Helical Gears If the teeth lie in two rows, separated by a narrow toothless zone, the gears are called double helical gears. The helixes are of opposite hands. Because of the limited strength of the plastic materials, they are not recommended for these types of gears, because the double helical gears are used in large and high torque transmission applications as shown in Figure 4-4. Herringbone Gears Herringbone gears are cylinders with two rows of helical teeth that join in the middle, the gears have a herringbone appearance, thus their name.
Figure 4-4 Double helical gears
Because of the limited strength of the plastic materials, they are not recommended for these types of gears; most herringbone gears are used in large and high torque transmission applications. Herringbone gears are used when a smooth, continuous action is essential, as in high speed drives. These high speeds are encountered in marine transmission gears, particularly in connection with steam turbine and electric motor drives. Figure 4-5 shows a typical herringbone gear set. Internal Gears Internal gears have a cylindrical shape with envoluted teeth and have either spur or helical teeth. By definition, a left handed internal helical gear is one that meshes with a left hand mating pinion. An internal gear is like a standard spur gear turned “outside in”, as shown in Figure 4-6. To avoid interference in the tooth form, the gear’s internal diameter is increased and the mating pinion outside diameter is also made larger. Injection molded thermoplastic internal gears are commonly used in many applications, such as in the planetary gear system drives and others.
4.1.2
Figure 4-5 Herringbone gears
Bevel Gears, Nonparallel and Intersecting Shafts
Bevel Gears Conical in form, the profiles of the teeth are of specially generated forms, depending on the application, economics, and other factors. There is a variety of special tooth profile forms identified as follows:
Figure 4-6 Internal gears
Straight Bevel Gears Straight bevel gears have straight tooth elements that, if extended, would pass through the point of intersection of their axes. Injection molded thermoplastic straight bevel pinion gears are commonly used in many low speed/torque transmission applications. These straight bevel teeth forms, as shown in Figure 4-7, are the most commonly used in gear reduction applications, but their tooth sides are tapered so that they would intersect the axis at a common point called the pitch cone apex if the bevel pinion is extended inward.
Figure 4-7 Straight bevel gears
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4 Thermoplastic Gearing Design Spiral Bevel Gears Spiral bevel gears have curved oblique teeth on which contact begins gradually and continues smoothly from end to end. They mesh with a rolling contact similar to straight bevel gears. Spiral bevel gears run smoothly, quieter, and with reduced vibrations at high speeds. Injection molded thermoplastic spiral bevel pinion gears have limited use in low speed/torque transmission applications, because of the mold complexity. Figure 4-8 shows these types of gears. Figure 4-8 Spiral bevel gears
Zerol Bevel Gears The teeth of Zerol bevel gears are curved but lie in the same general direction as the teeth of straight bevel gears. The face cone elements of the Zerol bevel gears do not pass through the pitch cone apex but are approximately parallel to the root cone element of the mating gear to provide uniform tooth clearance. Injection molded thermoplastic Zerol bevel gears have a limited number of applications, because they are not commonly used. Figure 4-9 shows a typical Zerol bevel gear set. Crown Gears
Figure 4-9 Zerol bevel gears
Crown gears have teeth forms either straight or curved that lie in a plane pitch surface. Plastic materials are not used for this gear system. Skew Bevel Gears Skew bevel gears are similar to the crown gears, except that the tooth forms are straight and oblique, as shown in Figure 4-10. Thermoplastic materials are not used for this gear system. Miter Gears Miter gears are similar to bevel gears, having an equal number of teeth with axes at right angles. The specialized miter gear tooth forms are:
Figure 4-10 Skew bevel gears
• Coniflex, which has straight, crowned teeth. • Formate, in which the gear member of the pair has nongenerated teeth, usually with straight profiles and the pinion has generated teeth that are conjugate to the gear. • Revacycle, which has straight teeth generated by a special process with a special tooth form. Face Gears Face gears consist of a spur or helical pinion in combination with a conjugate gear of disk form; the axes are at right angles, either intersecting or nonintersecting. Injection molded thermoplastic face pinion gears have limited use in low speed/ torque transmission applications. Figure 4-11 shows a typical face gear set.
Figure 4-11 Face gears
261
4.1 Classification of Gears
4.1.3
Hypoid Gears, Nonparallel and Nonintersecting Shafts
Hypoid Gears Hypoid gears are similar to bevel gears, but operate on nonintersecting axes. They have tooth forms that are curved and oblique. The tooth surfaces of both gear and pinion are cut or generated by the same or similar tools. Hypoid gears resemble spiral bevel gears, except that the axis of the pinion is offset relative to the gear axis. If there is sufficient offset, the shafts may pass one another, permitting the use of a compact straddle mounting on the gear and pinion. The advantage of this design is that the pinion diameter is increased which makes it stronger than a spiral bevel pinion. Because of the limited strength of the plastic materials and complexity of the mold, they are not recommended for these types of gears. Hypoid gears, as shown in Figure 4-12, are used in high gear reduction and high torque transmission applications.
Figure 4-12 Hypoid gears
Worm Gears The worm gear system consists of a worm pinion and a worm gear with their axes at right angles to each other. Cylindrical Worm Gears
Figure 4-13 Cylindrical worm gear
A cylindrical worm gear has a tooth form like the threads of a screw. The tooth form commonly used is an involute helicoid. The cylindrical worm gears have one or more involuted helicoid threads like the screw threads on a cylinder, as shown in Figure 4-13. Hour Glass Worm Gears The hour glass worm gears, as shown in Figure 4-14, have one or more threads with their diameters increasing from the middle section towards both ends of the threads, conforming to the curvature of the mating worm pinion gear. The hour glass worm gears are also termed enveloping worm gears.
Figure 4-14 Hour glass worm gear
Single Enveloping Worm Gears A single enveloping worm gear is a mate to a worm. A worm gear that is completely conjugate to its worm has a single involuted helicoid contact surface; this type of gear interaction is termed as single enveloping. These types of worm gears are injection molded from thermoplastic polymers for many automotive and electrical gear reducer applications. The single enveloping worm gear reduction ratio between the speed of the worm gear and the speed of the worm wheel may range from 1.5 to 100. Worm gears having high ratios are not very efficient as transmitters of power because of the effect of the low lead angle. The single enveloping worm gears are not used when the primary purpose is to transmit power efficiently. Figure 4-15 shows a typical single enveloping worm gear set. Double Enveloping Worm Gears A double enveloping worm gear system consists of an hour glass worm mated with a fully conjugated throated worm gear. The contact between the worm and the worm wheel is theoretically a line contact; however, due to the tooth
Figure 4-15 Single enveloping worm gears
262
4 Thermoplastic Gearing Design deflection under load, the contact line is increased to a narrow contact zone. The larger tooth bearing area and multiple tooth contact increases the load carrying capacity, using smaller sizes of worm gears. Because of the limited strength of the plastic materials and the complexity of the mold, they are not recommended for these types of gears. Double enveloping worm gears are used in high gear reduction ratios and high torque transmission applications. Figure 4-16 shows a typical double enveloping worm gear. Figure 4-16 Double enveloping worm gear
Crossed Axial Helical Gears The crossed axial helical gears operate on crossed axes and may have the teeth oriented in the same or opposite direction. Figure 4-17 shows a crossed axial helical gear set. Injection molded thermoplastic crossed axial helical gears have limited used in low speed/torque transmission applications only. Spiroid Gears Spiroid gears, as shown in Figure 4-18, have their axes at right angles to each other. The pinion member is conical in shape and the mating member is a facetype gear. They have tooth forms that are curved and oblique. Figure 4-17 Crossed axial helical gears
The Spiroid gears resemble the spiral bevel gears, except that the axis of the pinion is offset relative to the face-type of gear axis. The advantages of the Spiroid gears are the high gear reduction ratios, fast operating speeds, and high torque transmission performance. Because of the limited strength of plastics and the complexity of the mold, they are not recommended for use in Spiroid gear applications. Helicon and Planoid Gears These types of gears are members of the Spiroid family, a Helicon pinion gear is a Spiroid pinion gear without a taper tooth form.
Figure 4-18 Spiroid gears
4.1.4
Gears for Straight Linear Motion
Spur Rack Gear A spur rack gear is a straight bar having a rectangular cross section area with a spur tooth form, spaced along a straight line and perpendicular to the top surface of the bar. Spur Pinion Gear
Figure 4-19 Spur rack and pinion gears
The spur pinion gear has a cylindrical form with involuted straight teeth at right angles to the direction of motion. These types of gears, as shown in Figure 4-19, have a metal insert centrally located for mounting a shaft. The insert has been encapsulated with a thermoplastic material using an injection molding process. Helical Rack Gear A helical rack gear is a straight bar having a rectangular cross section area with a helical tooth form that is oblique to the direction of motion, spaced along a straight line, and perpendicular to the top surface of the bar.
4.2 Standard Injection Molded Thermoplastic Gears
4.2
Standard Injection Molded Thermoplastic Gears
Thermoplastics are very good materials for low speed, light load gears for reasons of economy, performance, production efficiency, and lower weight. Engineering thermoplastic polymers are well suited for gears because of their combination of thermal, mechanical, electrical, environmental resistance, and flame retardant properties. Gear loads are transmitted during the gear motion by mating teeth which mesh with each other. This action tends to bend the teeth and subject them to a certain sliding motion. The wear characteristics and lubricity of the gear material are very important. All gear types (spur, worm, bevel, helical, annular internal, and external) experience some combination of these rolling and sliding forces. In general, wear resistance is critical for the tooth form and the dimensional stability is critical for overall gear performance. The limits of performance for the injection molded thermoplastic gears are determined by the following parameters: • Environmental temperature generated on the teeth by friction • Bending stresses on the tooth root • Fatigue or impact resistance • Wear resistance and coefficient of friction • Chemical resistance It is only a question of operating conditions, whether an engineering thermoplastic material can be considered a good candidate for a gear. If it appears that an engineering thermoplastic material will meet the specified requirements, a product designer must realize that the use of an engineering thermoplastic material also provides a number of advantages and design flexibilities that cannot be achieved when using metal materials, such as: • Post machining operations or removing of burrs are not required • Possible combination of gears with other elements, such as springs, bearings, ratchets, cams, and other gears • Corrosion resistance • Electrical insulation • Better dry running behavior than metal materials • Lower noise levels Thermoplastic gears can be molded by using special thermoplastic compounds developed for gear applications. In spite of the introduction of many new materials, the majority of applications still require gears made from acetal homopolymer and nylon 6/6. With the recent introduction of these new materials, such as Kevlar® fiber reinforced acetal homopolymer, nylon 6/6, PET and co-polyester elastomers, high performance gears are produced with these resins. In special circumstances, polycarbonate, polysulfone, polyurethane, and thermoplastic elastomer resins have been used for injection molded gears. Compounded thermoplastic materials have been modified to improve their mechanical properties. The reinforcements used in thermoplastic materials
263
264
4 Thermoplastic Gearing Design for gears are fiber glass and Kevlar® fibers. The additives compounded with the plastic matrix to reduce the coefficient of friction and to improve the wear resistance properties are zinc or aluminum stearate, polytetrafluoroethylene (TFE) Teflon® powders and fibers, silicones, graphite, and molybdenum disulfide. Fiber reinforcements increase the tensile strength, the modulus of elasticity; they also improve the dimensional stability of the gears and the end use temperature of the molded gears. Powders do not improve the mechanical strength properties; they reduce the mold shrinkage properties improving the dimensional control of the molded gears. Fiber glass and Kevlar® reinforcement with coupling agents increases the level of mechanical properties, reduces the moisture absorption characteristics, and also reduces the coefficient of linear thermal expansion to one third of the original matrix polymer value. Engineering thermoplastics containing both fiber reinforcement and internal low coefficient of friction additives are very important for gear applications. The following specialty compounded resins were developed for gear applications: High viscosity acetal homopolymer, Kevlar® reinforced acetal, chemically lubricated acetal, acetal with TFE Teflon® fibers, unfilled nylon 6/6 internally lubricated, unreinforced nylon 6/6 with a molybdenum disulfide, Kevlar® reinforced nylon 6/6, Kevlar® reinforced PET, unreinforced copolyester elastomer, Kevlar® reinforced copolyester elastomer, unreinforced lubricated polycarbonate, glass reinforced polycarbonate, lubricated polysulfone and polyurethane.
4.2.1
Selection of Thermoplastic Resins for Gears
As with any other material, the selection of injection molding thermoplastic resins is governed by the size and nature of the load to be transmitted, the speed, the life required, the environment in which the gear will operate, the type of lubrication, and the degree of precision necessary. The horsepower Eq. 4-1, 4-2 and 4-3 used for gear analysis in conjunction with Tables 4-1 to 4-3 will help to determine, which of the thermoplastic resins are good gear materials in terms of the mechanical strength required. These equations do not consider the end use temperature, the impact strength, coefficient of friction to reduce heat dissipation, the coefficient of linear thermal expansion, wear resistance, dimensional stability, or injection molding conditions. The equations are simple variations of the Lewis equations and assume the use of standard tooth forms used in metal gears. The results are conservative, but are of sufficient accuracy to help in making a decision of whether a further in-depth study is warranted. The design analysis will require machining prototype gears, testing the gears using the same specifications and requirements (load, velocity, endurance, temperature, environmental conditions) of the gears designed for the specific application under review. The safety stress is calculated by dividing the tensile stress (Table 4-2) by a safety factor (e.g., 1.50), assuming initial lubrication. The values given for tensile strength of fiber glass reinforced plastics should be used with discretion. The values for fiber glass reinforced materials are superior to those for unreinforced thermoplastics, which are excellent for certain gear applications. For other applications, requiring greater strength, the fiber glass decreases the wear resistance, dimensional control (differential mold shrinkage); the teeth are rigid, they do not flex the way we expect from a thermoplastic gear.
265
4.2 Standard Injection Molded Thermoplastic Gears Table 4-1 Gear Service Factors (SF)
Type of load
Occasional 1/2 hour/day
Intermittent 3 hours/day
8 to 10 hours/day
24 hours/day
Heavy shock Medium shock Light shock Steady
1.25 1.00 0.80 0.50
1.50 1.25 1.00 0.080
1.75 1.50 1.25 1.00
2.00 1.75 1.50 1.25
Table 4-2 Physical Properties of Thermoplastics
UL max. temperature °F
Coef. of linear thermal expansion, 10–5 in./lin. °F
2.3
200
6.8
M94 0.20 R120
–
Kevlar® reinforced acetal
14.3
6.5
5.0
200
6.8
M94 0.62 R120
3.9
Chem. lubricated acetal
9.5
4.1
1.4
200
6.8
M94 0.10 R120
–
Acetal with TFE fiber
6.9
4.2
0.7
200
6.8
M94 0.08 R120
–
Nylon 6/6 lubricated
10.2
1.8
1.2
250
5.0
M59 0.44 R108
22.9
Nylon 6/6 with MOS2
10.5
4.08
0.9
250
5.0
M57 0.18 R108
–
Kevlar® reinforced nylon
17.3
8.02
1.2
–
–
–
0.39
6.00
Glass reinforced nylon 6/6
18
9.0
2.5
310
1.3
M101
–
–
Kevlar® reinforced PET
14.8
8.33
1.6
356
–
–
0.26
0.50
Copolyester elastomer
4.7
0.01
–
275
–
–
0.77
420
Kevlar® copolyester TPE
4.7
0.05
–
275
–
–
0.68
1.1
Polycarbonate lubricated
8.7
3.15
15.0
250
3.7
M74 R120
–
–
Glass reinforced PC
19.0
11.0
2.0
–
1.2
M92 R120
–
–
Polysulfone
10.2
3.9
1.3
298
3.0
M69 R120
–
–
Polyurethane
3.9
0.01
–
240
–
–
1.05
380
Wear rate, 10–5 in./hr.
Notched Izod impact (ft-lb/in)
3.8
Static coef. of friction
Flexural modulus (105 psi)
10
High viscosity acetal
Rockwell hardness
Tensile strength (103 psi)
Thermoplastic resins
266
4 Thermoplastic Gearing Design Table 4-3 Lewis Tooth Form Factor (Y)
Number of teeth
14.5° involute or cycloidal
20° full depth involute
20° stub tooth involute
20° internal full depth Pinion
Gear
12 13 14 15 16 17 18 19 20 21 22 24 26 28 30 34 38 43 50 60 75 100 150 300 Rack
0.210 0.220 0.226 0.236 0.242 0.251 0.261 0.273 0.283 0.289 0.292 0.298 0.307 0.314 0.320 0.327 0.336 0.346 0.352 0.358 0.364 0.371 0.377 0.383 0.390
0.245 0.261 0.276 0.289 0.295 0.302 0.308 0.314 0.320 0.327 0.330 0.336 0.346 0.352 0.358 0.371 0.383 0.396 0.408 0.421 0.434 0.446 0.459 0.471 0.484
0.311 0.324 0.339 0.348 0.361 0.367 0.377 0.386 0.393 0.399 0.405 0.415 0.424 0.430 0.437 0.446 0.456 0.462 0.474 0.484 0.496 0.506 0.518 0.534 0.550
0.327 0.327 0.330 0.330 0.333 0.342 0.349 0.358 0.364 0.371 0.374 0.383 0.393 0.399 0.405 0.415 0.424 0.430 0.437 0.446 0.452 0.462 0.468 0.478 –
– – – – – – – – – – – – – 0.691 0.679 0.660 0.644 0.628 0.613 0.597 0.581 0.565 0.550 0.534 –
4.2.2
Horsepower Equations for Gears
Spur gear HP (external and internal) HP =
σS × F × Y × V 55 (600 + V ) P × SF
(4-1)
Helical gear HP (external and internal) HP =
σS × F × Y × V 423 (78 + V 0.5 ) PN × SF
(4-2)
Straight bevel gear HP HP =
(σ S × F × Y × V ) (C − F ) 55 (600 + V ) P × C × SF
Where: σS = Gear safety stress. σS = σ / Safety factor (psi) σ = Material tensile stress (psi) F = Tooth face width (in) Y = Lewis tooth form factor (Table 4-3) V = Velocity at pitch circle diameter (fpm) P = Diametral pitch PN = Normal diametral pitch SF = Service factor C = Close mesh center distance between gears (in)
(4-3)
4.2 Standard Injection Molded Thermoplastic Gears
Example 4-1 Determine the thermoplastic material for a spur gear that transmits 0.125 horse power (HP) at 320 revolutions per minute (RPM). The gear will run under a steady load for eight hours per day. Basic information for a standard spur gear: Number of teeth (N) Diametral pitch (P) Pressure angle (φ) Pitch diameter (DP) Face width of teeth (F) Transmission load (HP) Gear rotation (RPM) Tooth velocity (V) Service factor (SF) Lewis tooth form factor (Y) Tensile stress (σ) Safety working stress (σS)
70 32 20° 2.1875 0.375 in 0.125 HP 320 RPM fpm 1.0 (Table 4-1) 0.430 (Table 4-3) psi psi
Solution Calculate the spur gear tooth velocity (V): V =
(RPM) × π × DP 320 × 3.1416 × 2.1875 = = 183.26 fpm 12 12
Spur gear horsepower (Equation 4-1): HP =
σ × F ×Y ×V 55 (600 + V ) P × SF
Spur gear tooth tensile stress: 55 (600 + V ) P × SF × (HP) 55 (600 + 183.26) 32 × 1.0 × 0.125 = F ×Y ×V 0.375 × 0.430 × 183.26 = 5,831.37 psi
σ =
The safety working stress: σ S = 5,831.37 × 2 = 11,662.75 psi There are several fiber reinforced thermoplastic materials that could be used for molding the gear based only on Table 4-2. However, other physical and chemical properties of these thermoplastics must be studied depending to the environment in which the spur gear is to operate: e.g., whether these thermoplastic materials need to resist lubricants (oil, grease, etc.), UV and pollution exposure from the weather, they need to be dimensionally stable at high velocities, have excellently wear resistance characteristics and a low coefficient of friction in relation to the material of construction used for the mating gear.
267
268
4 Thermoplastic Gearing Design
4.2.3
Spur Gear Terminology and Definitions Outside dia. (DO)
Pitch dia. (Dp)
Working depth (hK)
Base dia. (Db)
Clearance (c)
Driv
e r ge ar
Pitch point
Pressure angle ( )
Line of action
p To
lan
d
e Fa c nk Fl a
Addendum (a) Dedendum (b)
h idt ew Fa c (F)
Whole depth (ht) Circular pitch (p)
Ro
Circular tooth thickness (t)
ot dia . (D
Fillet radius (rf)
)
R
Dri
ve n gear
Figure 4-20 Standard spur gear terminology
Addendum (a): The height of a gear tooth outside the pitch circle; the radial distance from the pitch circle to the outside diameter of the addendum circle, numerically equal to the reciprocal of the diametral pitch. Addendum circle: The circle at the top of the gear tooth. AGMA number: A number indicating the relative quality of a gear as specified by the American Gear Manufacturers Association, a higher number indicating higher quality. Angle of action: The angle through which one tooth travels from the time it first reaches its mating tooth on the line of action until contact ceases. This is divided into the angle of approach and the angle of recess. Backlash: The amount by which a tooth space exceeds the thickness of the meshing tooth, provided to compensate for thermal expansion; the difference between tooth thickness and tooth space as measured on the pitch circle. Base circle diameter (Db): The diameter of the base circle. Base pitch: The normal pitch of an involute gear; the distance between two successive parallel involutes which form the profiles of two adjacent teeth, equal to the circumference of the base circle divided by the number of teeth on the gear. Center distance (C): The distance between the centers of the mating gears. Circular pitch (p): The length of an arc of the pitch circle that corresponds to one tooth interval, equal to the circumference of the pitch circle divided by the number of teeth on the gear. Circular tooth thickness (t): The thickness of a single tooth measured along the pitch circle; for an unmodified tooth, equal to one-half the circular pitch.
269
4.2 Standard Injection Molded Thermoplastic Gears Clearance (c): A small space provided so that the top of a meshing tooth will not touch the bottom land of the other gear as it passes the line of centers. Dedendum (b): The depth of a tooth space below the pitch circle; the radial distance from the pitch circle to the root circle, equal to the addendum plus the tooth clearance. Diametral pitch (P): The ratio of the number of teeth to the pitch diameter of a gear, representative of the number of teeth per inch of pitch diameter (DP). P=
NG + NP π×C
(4-4)
Face width (F): The surface of a gear tooth lying between the pitch circle and the addendum circle. Fillet radius (rf ): The radius of curvature of the corner where a tooth joins the root circle. This corner is radiused with extra material to reduce the build-up of stress concentrations. Flank: The surface of a gear tooth between the root diameter (DR) and the pitch diameter (DP). Gear ratio: The ratio of the number of teeth in the gear to the number of teeth in the pinion. Interference: A term relating to conditions that permit contact between mating teeth away from the line of action to interfere with the transmission of uniform motion. Involute: A system of gearing; the principal profile of a gear tooth; a curve generated on a circle, the normal of which are all tangent to that circle. Line of action: The line along which correct contact between mating teeth is made, resulting in transmission of uniform motion from one gear to another. Number of teeth in gear (NG): The total number of teeth of the gear. Number of teeth in pinion (NP): The total number of teeth of the pinion. Outside diameter (DO): The external diameter of the gear. Pitch circle: A circle that represents a smooth disc that would transmit the desired relative motion by friction. Pitch diameter (DP): The diameter of the pitch circles of mating gears. Pressure angle (φ): The angle between the line of action and a line perpendicular to the common center line of two mating gears or the angle cutting the tooth face at the pitch point and the tooth face itself. The most common pressure angles are 14.5°, 20°, and 25°, of which 20° is the most commonly used. Root circle: The circle at the bottom of the tooth spaces in a gear. Root diameter (DR): The diameter of the root circle. Whole depth of tooth (ht): The total depth of the tooth space in a gear measured radially between the addendum circle and the root circle. Working depth of tooth (hK): The depth that the teeth of one gear extend into the spaces of its mating gear, equal to the sum of the addenda of mating gears; also equal to the whole depth minus the clearance.
270
4 Thermoplastic Gearing Design Spur Gear Tooth Stress For standard injection molded thermoplastic spur gear designs, as with any other material, it is advisable to calculate the increase in gear size at the highest end use temperature and provide sufficient backlash to prevent binding. Since the mechanical properties of the engineering thermoplastic resins are temperaturedependent, the load-bearing capacity of the injection molded thermoplastic spur gear decreases with increasing temperature, depending on the thermal characteristics of the material selected. Spur gears are also very susceptible to stress build-ups at the roots of the teeth caused by shock loading. Careful consideration has to be given to the notch impact sensitivity of the engineering thermoplastic material selected for the application. It is best to extend a full radius at the tooth root of the gear. Backlash can effectively allow for dimensional changes in the gears. Radii at the tooth root can improve the shock load compatibility. One of the advantages with the teeth of an injection molded thermoplastics spur gear is that the teeth bend without causing flexural stress or fracture; the endurance limit of the material should be used when designing to allow for cyclic reduction of mechanical stress. The spur gear tooth form, however, does not conform to the idealized configuration of the three point bending tests used to determine the flexural strength by ASTM D790. Therefore, it is often preferable to use the tensile strength of the thermoplastic material and to provide a greater margin of safety. Gear Safety Stress (σ S ) =
Maximum Tensile Strength of the Plastic Safety Factor
Spur Gear Tooth Tangential Force The spur gear tooth load limits or the design requirements can be calculated using the Lewis equation: W =
W
σS × F × t 2 6 × ht
σS =
6 × W × ht F × t2
where W is the tangential force at the end of tooth, F is the uniform face width of tooth, ht is the whole depth of the tooth decreasing towards the loaded end. The outline of the tooth form is equivalent to a parabola with vertex at the loaded end.
F
Spur Gear Tooth Transferred Torque Torque is transferred by a gear through the tangential forces acting on the gear teeth. If only one tooth of each gear in contact at or near the pitch point is carrying the entire load, a simple method of calculating the tangential force on a gear tooth is given by:
t
W =
σS × F × Y P
(4-5)
W =
2×T DP
(4-6)
ht
Figure 4-21 Tooth tangential force
271
4.2 Standard Injection Molded Thermoplastic Gears Rearranging: T =
σ S × DP × F × Y 2×P
(4-7)
Where: T σS t ht F W Dp F Y P
= Torque of gears (in-lb) = Safety working stress (psi) = Circular tooth thickness = Tooth whole depth = Tooth face width = Tangential force on tooth (lb) = Pitch diameter (in) = Face width of tooth (in) = Lewis tooth form factor = Diametral pitch
Many gears are subjected to a “stall torque” that is significantly higher than the actual operating torque. It is advisable to use the yield stress of the material at the operating temperature, calculating the bending stress of a cantilever tooth. Factors Affecting Spur Gear Tooth Loading To calculate the gear tooth load accurately, several factors must be known: • The spur gear reduction ratio • The center distance limits • The spur gear or pinion operating speed • The spur gear or pinion horsepower or torque • The type and duration (time) of loading • The Maximum Operating Temperature • The type of operating service requirement • Type of lubrication The spur gear reduction ratio is determined by the desired rate of motion between the driving (or input) spur gear and the driven (or output) spur gear. The center distance is set by the space allocated between the spur gear and the pinion. The speed of either the driving spur gear or the driven spur gear must be known, as well as either the horsepower or the torque to be transmitted. The expected spur gear service life should be stated along with the operating conditions (type of loading, duration, temperature, environment, and lubrication). In addition, the spur gear pressure angle and the diametral pitch are critical factors, because they determine the size and form of the spur gear teeth and, consequently, the load sharing ability and the strength of the teeth. The most common spur gear pressure angles are 14.5°, 20°, and 25°, with the 20° pressure angle being used most often. The 20° pressure angle has a higher load bearing ability than the 14.5° angle and it allows fewer pinion teeth to be used, avoiding the undercutting of the gear teeth before it becomes a manufacturing concern.
272
4 Thermoplastic Gearing Design
4.3
Properties Required for Injection Molded Thermoplastic Gears
Injection molded thermoplastic spur gears depend on similar properties as those used in the principles of design established for standard metal gears. However, the mechanical, thermal, and creep characteristics of the thermoplastic polymers make it essential to adhere to these properties more rigidly than would necessarily be the case in designing metal spur gears that will be machined. The coefficients of linear thermal expansion of reinforced thermoplastics are approximated in 1/3 of those of unreinforced resins. The expansion of metal gears with an increase in temperature is not a significant design concern to take into consideration. However, for injection molded thermoplastic spur gears, it is necessary to calculate the amount by which thermoplastic gears will expand at the highest temperature to which they will be subjected and to provide sufficient backlash between the teeth to prevent binding. For some hygroscopic thermoplastic polymers, such as nylons, the size of the gear increases slightly when absorbing moisture. This dimensional change in nylon gears is rarely a problem, but additional backlash should be allowed between the teeth if the gear mechanism may be unused for long periods in damp ambient operating conditions. The teeth of heavily loaded metal spur gears in critical drives are given a degree of tip relief and have full fillet root radii to reduce fatigue stresses. These modifications should also be specified for the teeth of all thermoplastic spur gears. In designing a pair of metal spur gears, variations in both gear teeth addendum lengths are frequently used. If the pinion has a small number of teeth, these teeth may be undercut. Undercutting weakens the strength of the gear teeth, causes wear, and reduces the life expectancy of the gear. The undercutting process can be eliminated by increasing the addendum of the pinion teeth and decreasing addendum of the gear teeth. The elimination of undercutting is beneficial and it is recommended in the design of injection molded thermoplastic spur gears, because it provides better tooth strength and gear design flexibility. Injection molded thermoplastic spur gears offer several benefits. The designer is freed from many of the limitations imposed by using machine tools to make the blanks, standard lobs and cutters, in shapers to form the teeth of metal gears. The expensive machining and assembly operations are eliminated by designing the gear as an integral part of the mechanism, allowing desirable modifications to the standard tooth to be specified without increasing the price of the gear with little or no additional cost for the molding tool. Today, there are instrument mechanism gears of such complexity being molded that their fabrication in metal would not be economically feasible. Consulting with the tool, process, and manufacturing engineers, the resin supplier’s technical assistants, and the mold maker before the final gear designs are approved may well result in considerable cost savings in the overall project by combining several features in a single multifunction injection molded gear design.
273
4.4 Thermoplastic Spur Gear Design Requirements
4.4
Thermoplastic Spur Gear Design Requirements
Single cavity mold Web = H x 1.1
When designing thermoplastic gears, it must be remembered that the gears are not only supposed to fulfil the expected mechanical function, but that they should also be dimensioned in a way to facilitate correct and efficient injection molding operations. The simpler the geometric shape, the easier it will be to fill the cavity properly and, if required, to achieve tight tolerances.
Whole depth (H)
Hub = H x 1.2
Two ideal spur gears and gate designs are shown in Figures 4-22 and 4-23. To provide mechanical strength, the rim wall section supporting the spur gear teeth should be at least the same tooth whole depth dimension (H). The vertical cross sections below the rim and hub wall thickness depend on the functional requirements of the gear, the type of gate, and the location of the gate. Figure 4-22 shows a diaphragm gate, centrally located at the spur gear hub; a wall thickness 20% larger than the rim and 10% larger for the vertical web section is preferred. Figure 4-23 shows a three or four pin point gate (requires a threeplate mold) located in the spur gear web; the web wall thickness should be 20% larger than the rim and the hub wall thickness should be 10% larger than the rim. Proportionally distributed wall thicknesses of the gear and the correct type of gate are recommended to obtain excellent dimensional control, including close TIR tolerances, without warpage.
Sprue Sprue puller
Rim (H)
Figure 4-22 Spur gear with sprue diaphragm gate
Multi-cavities, 3 plate mold Web = H x 1.2
Thermoplastic Spur Gear Classic Designs Whole depth (H)
Figures 4-24, 4–25, and 4–26 show three spur gear case designs illustrating a poor spur gear design, molding problems caused by an inadequate gear design, and design recommendations to overcome these types of molding problems.
Hub = H x 1.1
Spur Gear Case Design “A” Figure 4-24, left illustration, shows a spur gear with a thin wall thickness web that does not allow the rim to pack. The middle illustration shows internal voids around the rim, caused when the thin web froze-off and the rim could not be filled with more thermoplastic melt. The internal voids cause higher shrinkage than in the rest of the gear, producing poor dimensional control (roundness) and the middle of the tooth face width becomes concave. The right illustration shows proportional wall thickness as recommended for the gate type in Figures 4-22 and 4-23.
Thin web
Sucker pin
Pin point gate Rim (H)
Figure 4-23 Spur gear with 3 or 4 pin point gates
Sink teeth (concaved)
Gate
Voids
Poor design
Operational problems
Figure 4-24 Spur gear case design “A”
Recommended design
274
4 Thermoplastic Gearing Design
Web warpage
Web offset Voids Hub, heavy wall section Hub sink surface
Poor design
Operational problems
Recommended design
Figure 4-25 Spur gear case design “B”
Spur Gear Case Design “B” Figure 4-25, left illustration, shows a gear with a heavy hub wall thickness, with the web located at the rim’s edge. The middle illustration shows operational problems, with internal voids around the hub, because the heavy hub wall cannot be packed. The voids high shrinkage causes the hub’s inside diameters to sink. The offset web causes warping of the gear (uneven mold heat distribution), poor dimensional control (roundness), and bending of the tooth’s face width. The right illustration shows the recommended gear design, a uniform and balanced wall thickness, a distributed web that controls both mold halves’ cooling temperature in the cavities, keeping mold shrinkage well under control. Spur Gear Case Design “C” Figure 4-26 left illustration, shows a heavy web wall with some material removed by the four holes. The middle illustration shows operational problems, voids inside the web, because the heavy wall of the web cannot be packed. The web and hub voids cause high mold shrinkage, warping both sides of the teeth, poor dimensional control (roundness), sink marks on the hub’s outside and inside diameter. The right illustration shows the recommended design, with the web wall and cross sections uniformly/equally spaced, so that they function like four proportional webs/ribs to support the rim and the spur gear teeth.
Voids
Voids
Hub sink Web sink Teeth sink
Poor design Figure 4-26 Spur gear case design “C”
Operational problems
Recommended design
275
4.4 Thermoplastic Spur Gear Design Requirements
4.4.1
Gating Effects on Thermoplastic Gear Roundness Dimensions
High shear rates produce two effects that significantly affect the spur gear performance. The plastic molecules become aligned as a result of the high shear rates so that the melt in the walls is highly oriented in the melt flow direction. This effect is undesirable, because the strength in the direction perpendicular to the flow direction is reduced and the gear has a tendency to crack along the weld line. The other effect is the dimensional change caused by the orientation of the melt flow. Figure 4-27 shows the gear elongation and compression problems caused by an edge gate located on the spur gear tooth. When the melt flow is split by the core of the gear hub, both melt fronts, which are the coldest part of the melt, are reunited at the back side of the core causing a weld line area that is the weakest section of the gear. The flow direction of the melt has the higher injection pressure, causing less mold shrinkage (larger dimensions). The pressure perpendicular to the flow direction is lower, causing higher mold shrinkage (smaller dimensions). The mold shrinkage becomes more pronounced with fiber reinforced thermoplastics; the fiber oriented in the flow direction does not compress and has lower shrinkage, while the flow in the perpendicular direction has higher mold shrinkage. Figure 4-28 shows a single pin point gate located in the web wall of the spur gear. This type of gate requires a three-plate mold to break the gate and to mold automatically. A hot drop gate from hot runnerless molds can also be used for molding gears. This type of gating causes the same molding problems as the edge gate, but provides better results, because the gate is more centrally located. The weld line is improved and the differential mold shrinkage is reduced. The molded gears have better TIR (roundness) than the edge gate shown in Figure 4-27.
Weld line Transverse flow compression
Melt flow behavior
Edge gate
Flow direction elongation
Figure 4-27 Single edge gate on the spur gear tooth width
Weld line Web Reduced compression
Gate
Melt flow behavior
Figure 4-28 Single pin point gate on the spur gear web wall
Reduce elongation
276
4 Thermoplastic Gearing Design Hub
Gate
Weld line
Figure 4-29 shows a pin point gate located in the hub wall of the spur gear. This type of gate requires a three-plate mold to break the gate and to mold automatically. Some hot drop gates from hot runnerless mold systems can also be used for molding gears. This type of gating causes the same molding problems as the single pin point gate in the web, but provides better results, because the gate is more centrally located. It has a stronger weld line, better warpage control, and reduces differential shrinkages caused by the melt flow or fiber orientation. Molded gears have better TIR (roundness) than the two previous cases (Figures 4-27 and 4-28). Figure 4-30 shows a spur gear with three pin point gates equally spaced around a circle in the web wall of the gear. To avoid molded-in stresses and premature freeze-off of the gates, a diffuser (circular indentation) is provided behind each gate on the web’s back side. This gating requires a three-plate mold to run a multi-cavity tool automatically. Hot drop gates from some hot runnerless molds are also used for injection molded thermoplastic spur gears. This type of gating is very common in molding close precision tolerances for high velocity gear applications. This system provides strong weld lines, better warpage control, and minimum differential shrinkages caused by the melt flow or fiber orientation.
Melt flow behavior
Less compression
Figure 4-31 shows a sprue diaphragm gate being used for molding a single cavity spur gear on a two-plate mold. It may also be used for molding multi-cavity gears using some hot runnerless molds. This type of gate allows uniform melt filling, equal pressure, shrinkage, and melt flow distribution inside the cavity. The sprue diaphragm gate allows the best precision dimensional control (roundness) without weld lines. The diaphragm gate disk connected to the sprue requires a post molding operation to remove the diaphragm gate disk and sprue from the inside diameter of the hub. For the multi-cavity hot runnerless molds, it requires a post molding operation to remove only the diaphragm gate disk.
Less elongation
Pin point gate
Figure 4-29 Single pin point gate on the spur gear hub wall
Weld line (strong)
Diffuser
Sucker pin Web wall
Melt flow behavior
Figure 4-30 Three pin point or runnerless gates on gear web wall
Diaphragm gate disk Sprue puller Sprue or hot mold runnerless drop Melt flow behavior
Figure 4-31 Sprue diaphragm gate in the middle of spur gear hub
Hub
277
4.4 Thermoplastic Spur Gear Design Requirements
4.4.2
Multifunction Designs with Thermoplastic Gears
The most important advantage of injection molded thermoplastic gears is the possibility of multifunctional designs, reducing the number of components for a given device. Figures 4-32, 4-33, 4-34, and 4-35 show multifunctional design applications. • Figure 4-32 shows a multifunctional gear system; a spur gear made of acetal homopolymer is provided with two molded-in springs, acting on a ratchet wheel that is combined with the second spur gear made of unreinforced nylon 6/6. These types of ratchets function without any problems, as long as the springs in the ratchets are intermittently working and releasing the load in a free stage position, avoiding creep problems of the spring arms. • Figure 4-33 shows a multifunctional gear design made of acetal homopolymer; the gear teeth are protected against impact loads, by connecting the hub and the rim by properly dimensioned flexible elements. This principle is used on printing wheels to obtain consistent printing results in spite of injection molding dimensional discrepancies.
Nylon 6/6 spur gear
Spring arm
Ratchet
Ratchet
Acetal spur gear & spring arm
Figure 4-32 Two spur gears combined with two spring ratchets
Flexible elements
Figure 4-33 Self-centring and flexible spur gear, printing wheel
278
4 Thermoplastic Gearing Design • Figure 4-34 shows a gear design system for a backlash-free motion transmission between two gears. The main gear is equipped with four molded-in springs fitting into corresponding slot pockets on the second gear. When assembled with the pinion, the two tooth crowns are slightly offset, causing the springs to be loaded and thus suppress any backlash. The stress relaxation caused by the creep effects on the spring arms decreases the spring arms’ resistant stresses. This backlash-free gear principle is adequate for only small torques, such as in instrument dials or clock adjusting mechanisms. • Torque limiting devices are often very useful for thermoplastic gear applications to prevent tooth damage when overloading occurs (for instance on high torque transmissions, such as meat grinders, can openers, and hand tool drills). Figure 4-35 shows one solution of many other possible designs. In this torque limiting device, it is essential that the pivoting springs do not remain accidentally in the loaded position. In this design, the torque limiting is achieved by three pivoting springs and radial guiding pockets.
Pinion gear Slot pocket Main gear
Spring arm Second gear
Figure 4-34 Backlash-free thermoplastic gear system (Courtesy: Du Pont)
Pivoting spring
Pocket
Figure 4-35 Torque limiting thermoplastic gear system (Courtesy: Du Pont)
279
4.4 Thermoplastic Spur Gear Design Requirements A product designer must be aware that it is difficult to combine both design conditions (precision and multifunction) in a thermoplastic gear. Either the application requires an accurate gear, using the simple symmetrical shape or it combines as many functions as possible in one part, resulting in a more complicated shape with less accuracy.
4.4.3
Mounting Thermoplastic Gears on Metal Shafts
There are several methods for mounting thermoplastic gears on metal shafts. Some of these methods work well for metal gears, but cause severe problems with thermoplastic gears. Figure 4-36 shows the hubs of a plastic gear drilled and tapped for a metal set screw; the plastic threads can be stripped by the pull out force of the set screw, when the set screw is torqued against the metal shaft. Figure 4-37 shows a metal-threaded insert ultrasonically welded in the gear hub for a metal set screw; the metal insert is stripped from the plastic hub by the pullout force of the set screw when the set screw is torqued against the metal shaft. Recommended methods for mounting plastic gears on metal shafts include coarse knurling the metal shaft and encapsulating the plastic gear around the shaft as shown in Figure 4-38. Figure 4-39 shows a method of drilling a hole through the plastic hub and metal shaft, and then a dowel pin is inserted through the assembly. Figure 4-40 shows a method of drilling and pressing a dowel pin on the shaft, then the two snap locks molded in the plastic gear hub are snapped and locked together for mounting the plastic gear to the dowel pin and metal shaft.
Plastic gear
Set screw
Metal shaft
Hub
Figure 4-36 Set screw threaded on gear hub
Metal threaded insert ultrasonic welded
Hub
Set screw Plastic gear
Metal shaft
Figure 4-37 Ultrasonic welded metal insert and set screw on the gear hub
Plastic gear
4.4.4
Standard Spur Gears, Equations, and Calculations
Knurled shaft
Example 4-2 A pair of gears having a ratio of 3 is to be used at a center distance (C) of 8.48 in. If one gear (NG) has 60 teeth and the other (NP) has 20 teeth, determine the diametral pitch (P).
Metal shaft
Solution Figure 4-38 Encapsulated knurled metal shaft with plastic gear
To calculate the diametral pitch, select Equation 4-7. Diametral pitch (P) = t =
π 2P
Dowel pin Hub
Plastic gear
Dowel pin
Metal shaft
Plastic gear
Snap lock
Metal shaft
Figure 4-40 Dowel pin pressed metal shaft and snap lock hu
Hub
Figure 4-39 Dowel pin drilled through plastic hub and shaft
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4 Thermoplastic Gearing Design Table 4-4 Standard Spur Gear Equations Knowing the Diametral Pitch (P)
Coarse – Pitch lower than 20
Fine – Pitch higher than 20
Addendum
a=
1.000 P
a=
1.000 P
Dedendum
b=
2.000 P
b=
1.20 + 0.002 P
Working depth
hK =
2.000 P
hK =
2.000 P
Whole depth
ht =
2.250 P
ht =
2.20 + 0.002 P
Circular tooth thickness
t =
π 2P
t =
π 2P
Clearance
c=
0.250 P
c=
0.200 + 0.002 P
Pitch diameter
DP =
N P
DP =
N P
Outside diameter
DO =
N +2 P
DO =
N +2 P
Root diameter
DR =
N − 2.5 P
DR =
N − 2.2 + 0.004 P
Fillet radius
rf =
0.30 P
rf =
0.30 P
Example 4-3 Find the circular tooth thickness on the pitch circle of a 20°, full depth involute tooth having a diametral pitch (P) of 12. The circular tooth thickness is given by the equation in Table 4-4: t =
π 3.1416 = = 0.1309 in 2×P 2 × 12
Example 4-4 Find the outside diameter (DO) on the tooth circle of a 20°, full depth involute tooth having a diametral pitch (P) of 12 and number of teeth (N) of 40. The outside diameter is given by the equation in Table 4-4: (DO ) =
N + 2 40 + 2 = = 3.50 in P 12
281
4.4 Thermoplastic Spur Gear Design Requirements
4.4.5
Spur Gear Pitch Backlash
Figure 4-41 shows a pitch backlash or the tangential clearance between two meshing teeth flanks. The backlash is known as “circumferential play” or “tangential clearance”; backlash is generally defined as the distance by which tooth space exceeds tooth thickness, as measured on the pitch circle. The purpose of backlash is to prevent gears from binding or seizing-up by making simultaneous contact on both sides of meshing teeth. The pitch backlash prevents the mating teeth from binding and it is influenced by the following factors:
Pitch circles Pitch backlash or tangential clearance
Figure 4-41 Pitch backlash between mating spur gears
• Operating temperatures • Coefficient of linear thermal expansion • Mounting tolerances • Type of gear loading • Center distance tolerances • Tooth shape, size, complexity and accuracy (roundness) • Post molding dimensional changes • Type of lubrication • Run-out tolerances of shaft bearings • Speed and running conditions Gears operating under moderate loads and at moderate speeds at room temperature will be less affected by small variations in backlash. At high load, high speed or high temperatures, gears should have both greater tooth accuracy and additional backlash to compensate for the coefficient of linear thermal expansion. For thermoplastic gears at room temperature, the following backlash values are suggested: This is only a starting point, since the operating temperature is dependent on other factors, such as gear load, running speed, and tooth size. Gears operating at room temperature at high permissible loads and speeds can experience a rise in tooth temperature of 100 °F. Any heat management method at the tooth surfaces will decrease binding caused by insufficient backlash. One method is through continual lubrication. Another is a thermoplastic gear with a metal mate having a higher heat dissipation factor. Backlash may be increased by extending the center distance of mating gears. This provides an advantage of more clearance between the outside diameter of one gear and the base diameter of the other, allowing for expansion at high temperatures without radial interference. However, increasing center distance causes the teeth to mesh outside the pitch circle, which can result in greater wear. Insufficient pitch backlash may go as far as to cause seizing and rapid spur gear failure during operation. In addition, the specified center distance can be affected by other factors. If, for example, other components of the gear assembly are injection molded of thermoplastics, their dimensions may change over time due to the coefficient of linear thermal expansion or post mold shrinkage from
Table 4-5 Backlash Values for Thermoplastic Gears
Diametral pitch (P)
Pitch backlash (in)
16 20 32
0.004–0.006 0.003–0.005 0.002–0.004
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4 Thermoplastic Gearing Design high temperatures. The type of gears can also influence the center distance, as with bearing run-out caused by the axial thrust of helical gears. Therefore, providing pitch backlash by means of increased center distance is a method that should be approached with the utmost caution. 3P
4P
5P
The pitch backlash and center distance measurements and adjustments should be made under actual operating conditions over time, using injection molded prototypes to accurately predict the performance of the thermoplastic gears. It is essential to measure and adjust the correct pitch backlash at operating temperature and under real working conditions. Many gears, even though correctly designed and molded, fail as a result of incorrect backlash at operating conditions. When the gear housing is also injection molded of thermoplastics, the same considerations apply to this product. The values can be different, because the gear and housing have different geometries and the housing may be molded in another resin. Consequently, the center distances may also vary and influence the pitch backlash. It is often easier to determine the center distance after having produced and measured the gears. It is important to note that this procedure may produce more wear as the gears will no longer mesh exactly on the theoretical pitch circle.
6P
Measuring, testing, and adjusting the pitch backlash using the same end use conditions is essential for a successful thermoplastic gear application.
4.4.6
7P
Standard Spur Gear Tooth Size Selection
The standard spur gear tooth size or the diametral pitch (P) is determined as a function of allowable bending stress and general operating conditions. 8P
From a strictly functional and technical point of view, there is no reason to choose a bigger spur gear tooth size than required. However, the selection of thermoplastic gears is more conservative than for metal gears.
9P
For a given pitch diameter, a smaller spur gear tooth size is often chosen for the following reasons: • Additional load distribution safety
10 P
• Less critical injection molding tolerances • Less sensitivity to thermal variations, post mold shrinkage, and dimensional stability
12 P
Figure 4-42 shows the standard spur or helical gear tooth sizes of the most common diametral pitches (P). These spur or helical gear teeth are drawn using a full size scale; they can be used to quickly scale the overall size and tooth form details of standard spur or helical gears.
14 P
16 P
It can safely be said that the smallest standard spur gear tooth profile that fulfils the strength requirements is usually the best solution.
18 P
20 P
Figure 4-42 Standard spur gear tooth size per diametral pitch (P) (full size)
When standard spur gear testing is used for the tooth size selection, accelerated tests at speeds higher than required of a given application are of no value. Increased temperature may cause rapid failure, while under normal working conditions the part may perform well.
4.4 Thermoplastic Spur Gear Design Requirements Test conditions should always be chosen to simulate the real running conditions. The following examples further explain the need for meaningful end use testing. • Appliance thermoplastic gears under a high load that operate only intermittently: the gears should not be tested continuously; use cycles that allow the whole gear assembly device to cool down to room temperature between each test cycle. • Window blinds thermoplastic gears operate infrequently at reduced speeds: these gears can be tested at the same speed continuously; when increasing the tooth surface temperature, the test results are of no value. • Automotive windshield wiper thermoplastic gears reach their maximum working temperature quickly, at which they operate most of their service life. These thermoplastic gears should be tested continuously. Injection molded thermoplastic gears operate very closely to the endurance limit of the resin and the breaking torque test should not be considered as valid in all cases. If the breaking torque proves to be 8 to 10 times the operating load, it can usually be taken as an indication that it will provide a long service life in use. If two mating spur gears have standard circular tooth thicknesses and are brought into close mesh, the distance between their centers will be half the sum of their standard circular pitch. However, two spur gears having standard circular tooth thicknesses can operate at the standard center distance only if both spur gears were perfect. Any errors in the spur gears would cause the tooth face surface to bind at some point in their rotation. The pitch backlash must be checked before all tests. Once a thermoplastic gear has failed during the test, it is almost impossible to determine whether an incorrect pitch backlash was partially or entirely responsible for the failure. The successful development of an injection molded thermoplastic gear requires sound experience, careful product design, detailed study in selecting the best injection molding thermoplastic resin, gear tooth form selection, gear assembly analysis (tolerances), proper gear data (documentation), excellent mold design and construction, correct injection molding process, and meaningful tests.
4.4.7
Standard Gear Total Composite Tolerances
The total composite tolerances of a gear are the summation of the following dimensional variables: • Pitch tolerance • Profile tolerance • Run-out tolerance (roundness) • Lateral run-out tolerance (wobble) The sum of the pitch tolerance and the profile tolerance of a gear is known as the tooth-to-tooth composite tolerance. When the run-out tolerance is added to the tooth-to-tooth composite tolerance, this value is called the total composite tolerance of a gear. When an injection molded thermoplastic gear is loaded in the center, the center distance measuring instrument must be in close mesh with the master spur gear.
283
284
4 Thermoplastic Gearing Design
Tooth to tooth composite Total composite tolerance tolerance
Run-out tolerance
One revolution of test gear
Figure 4-43 Gear total composite tolerance graph test results
By rotating the test gear in close mesh with a master gear of known accuracy in a variable center distance fixture, the run-out tolerance, the tooth-to-tooth composite tolerance, and the total composite tolerance can be determined by measuring and plotting the radial displacements as shown in the general test graph results in Figure 4-43. There are various types of center distance measuring instruments available. The simpler models are equipped with a dial indicator and require the operator to measure and plot the radial displacements as the gear is rotated manually through 360° in close mesh with the master gear. Figure 4-44 shows a manual center distance measuring instrument. The more sophisticated models trace the radial displacements through an electronic device on a moving chart. The American Gear Manufacturers Association has developed a system to classify the dimensional accuracy of standard gear tooth forms by a number in accordance with their maximum tooth-to-tooth and the total composite tolerances allowed for the standard gears. This number is known as the AGMA Quality Number specified for the standard gear. The AGMA Quality Numbers, the tooth-to-tooth composite tolerances, the run-out tolerances, and the total composite tolerances, corresponding to the diametral pitch, the number of teeth, and the pitch diameter of a standard gear are listed in the American Gear Manufacturers Association Handbook, the Machinery’s Handbook, and other reference manuals. If a standard spur gear is assigned an AGMA Quality Number of Q7, with a diametrical pitch of 20, number of teeth 18, and a pitch diameter is 0.90, to meet these requirements, the standard spur gear maximum run-out tolerance should be 0.0008 in, the maximum tooth-to-tooth composite tolerance 0.0019 in, and the maximum total composite tolerance 0.0027 in. Figure 4-45 shows the measuring instrument test results of an injection molded thermoplastic standard spur gear in close mesh with the master spur gear. The errors in the test gear are at the maximums allowed by these tolerances. Testing gear
Master gear
0.0019 inch
Cent Dista er nce
Figure 4-44 Gear center distance manual measuring instrument
0.0027 inch
Figure 4-45 Measuring instrument spur gear tolerances test results
0.0008 inch
285
4.4 Thermoplastic Spur Gear Design Requirements To allow for the tolerances in two mating gears, either the operating center distance must be made greater than the calculated close mesh center distance by an amount equal to the sum of half the total composite tolerances, or the circular tooth thicknesses must be thinned by an equivalent amount. AGMA Quality Numbers must be chosen for a pair of mating gears at an early stage in the design procedure and the finished gears must be inspected by being run in close mesh with a master gear, to ensure that the maximum tolerances allowed are not exceeded. Together with the gear drawing, gear data documentation should be a part of the design, where the “gear testing radius” is specified. The center distance between the gears and the test radius is calculated in Example 4-5. This gear testing radius has maximum and minimum values corresponding to the maximum and minimum values of the calculated circular tooth thickness and the maximum total composite tolerance. Example 4-5 A standard spur gear has 72 teeth, a diametral pitch of 32, and a pressure angle of 20°. The gear is required to have an accuracy corresponding to AGMA Quality Number Q7. The standard pitch diameter is 2.250 in. Calculate the testing radius. Assume that the gear will be inspected by being run in close mesh with a master gear having 64 teeth, a pitch diameter of 2.00 in, and a circular tooth thickness of (1.5708 / 32) = 0.0491 in. From the AGMA it is found that the tooth-to-tooth composite tolerance is 0.0014 in and the total composite tolerance is 0.0032 in. The standard spur gear has a circular tooth thickness of (1.5708 / 32 – 0.0032) = 0.0459 in maximum and (0.0459 – 0.0014) = 0.0445 in minimum. First we need to calculate the center distance between the gears, when the standard spur gear circular tooth thickness is at 0.0459 in and 0.0445 in. C=
(N G + N M ) cos φ 2 × P × cos φ1
(4-8)
Where: C = Close mesh center distance (in) NG = Number of teeth in gear NM = Number of teeth in master gear P = Diametral pitch φ = Pressure angle (degrees) P (t G + t M ) − π φ1 = Angle whose involute is = + inv φ NG + NM tG = Circular tooth thickness of gear (in) tM = Circular tooth thickness of master gear (in) NG = 72, NM = 64, φ = 20°, P = 32, tG = 0.0459 / 0.0445, tM = 0.0491 inv φ1 =
32 (0.0459 + 0.0491) − 3.1416 + 0.014904 = 0.0141564 72 + 64
φ1 = 19.66° , cos φ1 = 0.9417 , C = inv φ1 =
(72 + 64) × 0.939692 = 2.1204 2 × 32 × 0.9417
32 (0.0445 + 0.0491) − 3.1416 + 0.014904 = 0.013827 72 + 64
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4 Thermoplastic Gearing Design
φ1 = 19.51 , cos φ1 = 0.94258 , C = Close mesh center distance (C) =
(72 + 64) × 0.939692 = 2.1184 2 × 32 × 0.94258
2.1204 in 2.1184
To complete the calculation, half the total composite tolerance is added to the maximum close mesh center distance, half is subtracted from the minimum, and from both results, half the pitch diameter of the master gear is subtracted. 2.1204 + (0.0032/2) − (2.0000/2) = 1.122 2.1184 − (0.0032/2) − (2.0000/2) = 1.116 Testing Radius =
1.122 in 1.116
Figure 4-46 shows the circular tooth thickness and testing radius tolerances between the gears, the measurement results were superimposed for comparison. Figure 4-46 shows the test radius tolerance as the difference between the maximum test radius of a standard spur gear and the minimum test radius of the master gear. The circular tooth thickness of a standard spur gear differs from the master gear by an amount equivalent to the radial tolerance displacement caused by the tooth thickness difference found in both gears. If the total composite tolerance in each gear is less than what is allowed by the tolerance, then the radial tolerance displacement could be greater than the difference between the maximum and minimum calculated circular tooth thicknesses as specified on the drawing. Therefore, the standard spur gear would be acceptable if the testing radius checked within the maximum and minimum specified values. This is the reason why the circular tooth thickness of a gear appears on the drawing as a “basic specification” rather than being included in the “manufacturing and inspection” data and why it is referred to as the “calculated” circular tooth thickness. It is also the reason why the measurement over pins has a proviso to the effect that this measurement is to be used “for set-ups only”. After choosing the number of teeth for a standard spur gear, the tooth form, the helix angle, and the AGMA Quality Number and after having determined the tooth thickness, the remaining gear data is obtained by a mathematical computation of the gear assembly system, including the various tolerances required for the design.
Maximum testing radius Maximum center distance Radial tolerance caused by tooth thickness difference Minimum center distance Minimum testing radius
Figure 4-46 Measuring test tolerances comparison between gears
Testing radius tolerance
4.5 Tolerances and Mold Shrinkage of Thermoplastic Gears Specifying the circular tooth thickness and accuracy of a thermoplastic gear with a testing radius precludes any possibility of misinterpretations and makes inspection a simple and quick operation. If the gear checks within the maximum and minimum values specified for the testing radius and if it satisfies the total composite and tooth-to-tooth maximum tolerances, the gear design is correct. Because bevel gears and worm gears are commonly manufactured as mating pairs, designing and specifying injection molded thermoplastic gears present problems not encountered with spur and helical gears. The gear project requires close working communication between the gear mold maker and the manufacturer of the metal pinion or worm before completing the design.
4.5
Tolerances and Mold Shrinkage of Thermoplastic Gears
Molded thermoplastic gears are as accurate as metal machined gears. Whether a molded thermoplastic gear or metal machined gear is characterized by AGMA Quality Number Q8, both gears meet the same tolerances. However, thermoplastic gears have not yet been molded to the highest precision obtainable by machining; gears requiring such precision represent a very small percentage of the gear markets. Fine-pitch instrument gears are molded to tolerances that would have been considered impossible to achieve in the past. For example, a four-cavity mold for a fine-pitch spur gear made of acetal homopolymer produced gears that were within the tolerances of AGMA Quality Number Q12. The tooth-to-tooth composite tolerance was 0.0003 in, with a total composite tolerance of 0.0005 in or less. All materials shrink when they are transformed from a solid cold state to a hot transitional liquid melt and back again to a solid state, as the material cools off to room temperature. As a consequence, all mold cavities must be made larger than the molded gears to compensate for the mold shrinkage effects caused by the thermoplastic polymers. For example, if a molded gear is to have an outside diameter of 1.500 in and the thermoplastic resin has a mold shrinkage of 0.020 in/in, the outside diameter of the cavity must be 1.530 in. In the design and fabrication of an injection mold for thermoplastic resins, the gear cavity for the mold should be constructed using different fabricating procedures than those used to cut the teeth in the gear if it were to be machined. It is necessary to cut an oversized mold gear cavity that, in turn, would be used to transform the melt into the correct size gear. If the gear cavity is not oversized, it will result in a smaller gear with serious dimensional problems. Figure 4-47, left illustration, shows an enlargement of a standard spur gear tooth form (dotted line) having a diametral pitch of 32, a pressure angle of 20°, and the profile of a standard oversize spur gear tooth form. The right illustration shows the profile of an injection molded thermoplastic spur gear tooth form obtained from an oversize gear cavity and a standard spur gear tooth form (dotted line). The injection molded thermoplastic spur gear tooth form is considerably different from the standard spur gears. It is thicker at the root and thinner at the tip; it has a larger pressure angle of 25°, as shown in Figure 4-47, right illustration.
287
288
4 Thermoplastic Gearing Design Standard spur gear tooth form
Standard oversize spur gear tooth form Oversize mold cavity thermoplastic gear
Figure 4-47 Different spur gear tooth forms comparison
It is obvious that the mold shrinkage of the teeth in the tool cavity must be carefully compensated for so that, when the molded thermoplastic gear solidifies and becomes stable, the gear will have the correct tooth form. The mold design of a helical gear is more complicated; the axial (cross flow direction) mold shrinkage is quite different from the radial (melt flow direction) mold shrinkage. Compensating correctly for the mold shrinkage in a gear requires the mold designer to thoroughly understand gear geometry, gating, mold venting, cooling, processing, and to have considerable experience with the mold shrinkage behavior of thermoplastics. The importance of correctly compensating for the mold shrinkage of the thermoplastic resins cannot be over-emphasized. For example, the gear center distance measuring instrument tolerance test results shown in Figure 4-45 show that this gear can have a total composite tolerance of 0.0027 in and a tooth to tooth composite tolerance of 0.0019 in. If the tooth-to-tooth composite tolerance is at the maximum, the run-out tolerance must be held to 0.0008 in. But if the tooth-to-tooth composite tolerance is reduced to 0.0005 in, an amount easily achieved if the mold gear cavity is correctly designed and accurately constructed, the run-out tolerance can go as high as 0.0022 in. Because it is more difficult to control run-out tolerance than tooth-to-tooth composite tolerance, it is important that the thermoplastic molded gear tooth form be as accurate as possible (several degrees more accurate than a comparable machined metal gear). Mold shrinkage does not need to affect accuracy other than for the very minor variations in mold shrinkage that occur during the production molding run. It is not an uncommon practice for product designers to specify close tolerances for the outside diameters of thermoplastic gears and leave everything else wide open. This is probably done in the mistaken belief that the outside diameter of a molded gear is a measure of overall accuracy and therefore this is the easiest dimension to measure. In fact, this close outside diameter tolerance ensures that all the tolerances present in a lot of molded gears will have the same tolerance magnitude from one gear to the next gear. Except in rare cases, the outside diameter of a gear is, within limits, a matter of no consequence. If it is specified that the circular tooth thickness of a molded gear is to be held to +0.000/–0.001 in, then the outside diameter must be allowed to vary within a tolerance band of at least 0.0027 inch in the case of 20° pressure angle gears for AGMA Quality Numbers Q7. To specify close tolerances for the outside diameter of a molded gear, except where the outside diameter is functional as in pump gears, these close tolerances can make for unnecessarily high tooling costs and increase the molding cost of the gear, without obtaining the performance required for the gears. It cannot be emphasized strongly enough that the accuracy of thermoplastic gears should be specified for AGMA Quality Numbers and should be inspected by the center distance measuring method.
289
4.6 Standard Helical Gears
4.6
Standard Helical Gears
A helical gear is essentially a spur gear with teeth slanting across its face in a cylindrical spiral, or helix, to the axis. Helical gears are preferred over spur gears in many applications because of their smoother, quieter operation with fewer tendencies to squeak. However, they require not only perfect tooth profiles but also exactly matching helix angles. These requirements can be difficult to fulfil, particularly when mating gears are made of dissimilar materials. Helical gears generate axial thrust that may create problems. It is advisable to use helix angles not greater than 15°. Compared to a spur gear having the same tooth size, a helical gear provides slightly improved tooth strength. As small helix angles are most commonly used, this fact can be neglected when determining the diametral pitch and it should only be considered as an additional safety factor. Helical gears have teeth that are formed on a spiral that winds around the axis of the shaft running through the gear (as opposed to spur gear teeth that are formed parallel to this axis). They are high efficiency gears (98–99%) and are typically used when high speeds and high horsepower are involved. The gear helix may be either left or right handed and can have various helix angles. These angles cause the pair of gears to exert end thrust on the bearings that carry the shafts on which the gears are mounted. Provisions should be made to compensate for thrust in the bearings. The design equations for helical gears are similar to those for spur gears, with a modification to account for the helix angle. This overlap is what gives helical gears their excellent smooth and quiet operation. The involute tooth profile is normally used for helical gears as small variances in center distance will not affect tooth action. Helical gears require perfect tooth profiles and exactly equal helix angles for proper performance. Table 4-6 Basic Helical Gear Equations for Known Diametral Pitch (P)
Find
Rules
Equations
Addendum
Divide 1 by the pitch diameter
a=
Lead to tooth helix
Multiply the pitch diameter by 3.1416 by cot of tooth helix angle
L = π × DP × cot ψ
Center distance
Add the pitch diameters of both gears and divide by 2
C=
DP1 + DP2 2
Whole depth of tooth
Divide 2.157 by the diametral pitch
ht =
2.157 P
Tooth thickness at pitch line
Divide 1.571 by the diametral pitch
t =
Pitch diameter
Divide the number of teeth by pitch dia. × cos of tooth helix angle
DP =
Outside diameter
Add twice the addendum to the pitch diameter
DO = DP + 2 × a
1.000 P
1.571 P N P × cos ψ
290
4 Thermoplastic Gearing Design
4.7
Standard Straight Bevel Gears
Standard straight bevel gears are widely used in applications involving power transmission, for right angle drives, and for providing high efficiency in operation. They may also be used to transmit power between shafts at any angle. Bevel gears can be made with either straight or spiral teeth, which taper in both thickness and height to almost zero at the axis of the gear. Figure 4-48 shows a standard straight bevel gear; the teeth are formed with all elements on planes that intersect at the axis of the gear. Bevel gear teeth are tapered in both thickness and height, with the outer portion (the heel) longer than the inner part (or toe). Table 4-7 is used for calculating the common variables required for the pinion and gear. Bevel gears exert both axial thrust and radial loads on the shaft-support bearings. If bevel gears have too few teeth, undercutting can be a problem. Bevel gear geometry can lead to molding and/or functional problems. On heavily loaded large bevel gears, thrust load on the tooth crown may become considerably stressed and the use of ribs is not recommended.
Pitch apex to back Pitch apex to crown
Crown to back
Crown Dedendum angle Pitch apex
ce
tan
is ed
Face angle
Shaft angle
n Co
PINION
Roo ang t le Pitch angle
Face width
GEAR Uniform clearance
Pitch diameter
Back cone
Ba ck co ne dis tan ce
Outside diameter
Figure 4-48 Standard system straight bevel gear nomenclature
291
4.7 Standard Straight Bevel Gears Table 4-7 20° Straight Bevel Gear for 90° Shaft Angle Equations
Item
Pinion
Gear
Working depth
hK =
2.000 P
hK =
2.000 P
Whole depth
ht =
2.188 + 0.002 P
ht =
2.188 + 0.002 P
Pitch diameter
DP =
Pitch angle
β = tan −1
Cone distance
CD =
Circular pitch
p=
Addendum
aP = hK − aG
Dedendum
bP =
Clearance
c = ht − hK
Dedendum angle
δP = tan −1
Face angle
γ F = γ + δG
ϕF = ϕ − δP
Root angle
γ R = γ − δP
ϕR = ϕ − δG
Outside diameter
DOP = DP + 2 aP cos γ
DOP = DG + 2 aP cos γ
Pitch apex to crown
XP =
Circular thickness
tP = p − tG
Chordal addendum
aCP = aP +
Tooth angle
3438 t P + bP tan φ CD 2
3438 t P + bP tan φ CD 2
Limit piont width
CD − F (t G − 2 bP tan φ) CD
CD − F (t G − 2 bP tan φ) CD
NP P
NG P
DG = NP NG
DP 2 sin ϕ
π P
ϕ = 90° − β
CD =
p=
2.188 − aP P
DP 2 sin ϕ
π P
bG =
2.188 − aG P
c = ht − hK
bP CD
DG − aP sin γ 2
δG = tan −1
XG =
tG = t P2 cos γ 4 DP
bG CD
DP − aG sin γ 2 p − (aP − aG ) tan φ 2
aCG = aG +
t G2 cos ϕ 4 DG
292
4 Thermoplastic Gearing Design
4.8
Unreinforced nylon 6/6 worm pinion
Standard Worm Gears
Most machined worm gears are made with a throated shape that provides a contact line of a certain length on the worm. Because this system cannot easily be applied on injection molded thermoplastic gears, a simple helical gear is normally used. Consequently, the load is transmitted on very small contact points that could lead to excessive pressure, surface temperature, and wear. Therefore, a helical gear meshing with a worm has limited possibilities and should be investigated carefully. Various attempts have been made, aimed at improving wear and increasing power transmission by changing the contact points to contact lines. Figure 4-49 shows a practical application demonstrating the use of an unreinforced nylon 6/6 for the worm pinion and acetal homopolymer for the worm gear.
Acetal homopolymer one piece worm gear
Figure 4-49 One-piece thermoplastic worm gearing system
Nine radial slide cores
Figure 4-49 shows a one-piece injection molded worm gear made of high viscosity acetal homopolymer, meshing with a worm pinion made of unreinforced nylon 6/6 for a hand operated device. The undercut resulting from the throated shape amounts to about 4% and can therefore be ejected from the mold without problems. It is noteworthy that this particular worm with seven leads cannot be molded in a two plate mold with the parting line in the center. Because the lead angle of 31° being greater than the typical pressure angle of 20°, this results in an undercut along the parting line. Therefore, the worm must be unscrewed from the mold. This principle of injection molding and ejecting a one-piece worm gear from the mold is used in several applications, even though it requires good processing experience and skill to design and to construct the proper tool. Figure 4-50 shows an automotive windshield wiper gear made of high viscosity acetal homopolymer, injection molded in a different way. Because of the undercut of about 7% and the rigid structure, ejecting the worm gear from the mold becomes impossible. To compensate for this deficiency, the mold is made with nine radial slide cores, each of which covers six teeth. This injection molding procedure produces an excellent worm gear, but the worm gear mold only has a single cavity, causing rather high tooling and manufacturing costs. Figure 4-51 shows another automotive windshield wiper with a half throated worm gear that is based on an intermediate solution. It is composed of a half throated and a helical gear portion. The tooth contact takes place on the curved section, while the helical part merely improves the tooth strength and the stall torque. Though not ideal, this solution nevertheless offers a significant advantage over a simple standard helical gear.
Figure 4-50 Worm gear mold with nine radial slide cores
Figure 4-52 shows a split snap-fitted worm gear made of acetal homopolymer. The two worm gear halves are designed in such a way that each component is injection molded using the same mold cavity. The two worm gear halves are post-mold assembled by rotating 180° until facing each other and pressing both components until they are snap-fitted together. The snap fit mechanism provides the centering action with the teeth perfectly aligned by means of lugs fitting into corresponding holes. A single cavity provides a complete gear assembly that is held together by means of snap fits, ultrasonic welding, or rivets. The worm gears can be made as wide as necessary, limited only by proper meshing. Split snapfitted worm gears are especially recommended for larger worm gear diameters that require high performance in the end use application.
Figure 4-51 Half throated worm gear
The following limitations should be kept in mind when designing split snapfitted worm gears compared to standard helical gears:
293
4.8 Standard Worm Gears • Higher tooling cost • Requirement of perfect centering of the worm pinion and the gear. Even small displacements cause the load to be carried by only a portion of the tooth width, resulting in increased wear or rapid failure. • The worm gear drive is more sensitive to discrepancies of the lead angles, which must match perfectly. • The worm pinion and the gear must be assembled in a certain way. If, for instance, the worm pinion is mounted first into the housing, the split snapfitted worm gear or the half throated worm gear can only be added in a radial direction, while a standard helical gear can be mounted from the side.
4.8.1
Radial snap hole Radial snap arm
Standard Worm Gear Analysis
Except for very slow running and hand operated worm gear drives, the power transmission is essentially limited by the heat build-up on the tooth surfaces. Temperature rise is not only a result of speed and load, but is also influenced by other factors, such as overall design, heat dissipation through the housing, additional cooling by external fan blowers, or heat being carried into the gear from the electric motor. Another important factor is the efficiency of the initial lubrication, which very often determines the total service life. For the type of worm gears commonly used with thermoplastic materials (a single threaded worm and a helical worm gear), point contact occurs between the meshing teeth and limits the ability of these gear systems to carry high loads. This point contact can be increased by the various worm gear designs discussed previously. Since the teeth on the helical worm gear are weaker than the threads of the worm gears, the maximum output torque of the worm will be limited by the torque capacity of the helical worm gear. The same common equations presented for helical gears can be applied for worm gears. A liberal safety factor (2–3) should be applied to take into account the stress concentration caused by theoretical point contact. An additional problem in worm gearing is the high sliding velocity that increases tooth temperatures and results in a lower yield strength and higher tooth wear rate. Therefore, it is suggested that the use of acetal homopolymer in the worm pinions or worm gears be restricted to low loading and reduced rubbing velocities of less than 250 feet per minute for these applications. For moderate operating conditions, a worm gear made of acetal homopolymer may be used successfully with a metal worm pinion. As a guide, it is suggested that the maximum rubbing velocity of the worm gear be limited to 250 feet per minute for continuous operation and initial lubrication. The equation used to determine the rubbing velocity is: VR =
Left half worm gear
DP × n 12 × cos α
Where: VR = Rubbing velocity (fpm) DP = Worm pitch diameter (in) n = Worm speed (rpm) α = Lead angle (degrees)
(4-9)
Figure 4-52 Split snap-fitted acetal homopolymer worm gear
Right half worm gear
294
4 Thermoplastic Gearing Design A rubbing velocity of about 500 feet per minute may be used for worm gears made of acetal homopolymer, when continuously lubricated worm gears or intermittent operations have been provided for the gearing application.
4.10
Plastic Gearing Technology Designs
Designing injection molded thermoplastic gears and establishing the manufacturing and quality control requirements for the production gears involves spending an extensive amount of engineering time working on complex gearing calculations. The designer will need several gear handbooks and standards, thermoplastic material specifications and molding characteristics, a set of mathematical tables, a computer or a calculator, and countless hours to spend trying to arrive at a satisfactory gear design. The design of injection molded thermoplastic gears requires consideration of the following important factors: • The power to be transmitted • The gear ratio required • The selection of the type of gear and the tooth design geometry • The type of thermoplastic resin for injection molding • The tolerances required for the gear • The center distance dimension tolerances and alignment for the housing to be manufactured, the bearing run-out tolerances • The end use temperature and the type of lubrication The ABA Tool & Die Company, Inc. and its affiliate Plastic Gearing Technology, Inc. from Manchester, Connecticut have developed four tooth form design systems known as PGT-1, PGT-2, PGT-3, and PGT-4 in addition to the standard gear tooth forms for thermoplastic gears. Plastic Gearing Technology Inc. has also developed a Plastics Gearing Design Manual and a PGT Computer Program. The company also offers thermoplastic gear and mold design services, precision mold making, and custom molding services. The PGT gear tooth form design systems are used only for spur and helical gears. The required equations, several gear design example calculations, and the gear design drawing specifications are presented for the PGT systems. The injection molding process provides gear design freedom. The product designers are free to introduce any gear tooth design geometries and choose the correct diametral pitch for the application. These departures from the standard gear design do not increase the manufacturing costs of the injection molded gears. When a gear tooth deflects under load, the trailing tooth is out of position for truly smooth engagement with the oncoming tooth of the mating gear. All thermoplastic gear tooth designs should be given a degree of tip relief. The teeth are gradually thinned from halfway up the addendum to the tip, providing a relieved effect. The gear teeth are also given a full fillet radius between two teeth at the root. This full fillet root radius can increase the fatigue strength and service performance of the thermoplastic gear using the PGT systems.
4.10 Plastic Gearing Technology Designs
4.10.1
Spur and Helical Gears PGT-1 Tooth Design
The standard fine-pitch metal gears provide a relatively greater amount of clearance between the tooth tips and the roots of mating standard metal gears, than the standard coarse pitch gears. Greater clearance is required for the standard fine pitch gears to improve the gear wear resistance of the tips after prolonged use. PGT-1 tooth design for spur and helical thermoplastic gears functions perfectly with a standard mating gear tooth form having either a fine pitch or a coarse pitch. The fine pitch gears include all gears of 20 diametral pitch (P) and higher, the coarse pitch gears include all gears with diametral pitches (P) of less than 20. Figure 4-53 shows the spur and helical PGT-1 tooth form design for 20° pressure angle, together with the PGT-1 tooth form equations that were developed by Plastic Gearing Technology Inc. for calculating the various gear dimensions. PGT-1 tooth form fine-pitch gears used for instrument gear applications should have teeth that are longer than the standard gear tooth form. The relatively large coefficients of linear thermal expansion of injection molded thermoplastic gears make the use of longer PGT-1 tooth forms mandatory for most thermoplastic gears employed in instrument movements. A pair of PGT-1 tooth form finepitch mating gears must be designed so they will not bind at the highest end use temperatures. Injection molded thermoplastic PGT-1 tooth form fine-pitch gears are used in electric clocks, control mechanisms, meters, cameras, and similar applications. Tables 4-8, 4-9, 4-10, and 4-11 show the precalculated values for the minimum circular tooth thickness (t), outside diameter (DO), and root diameters (DR) per the most common number of teeth (N) that were developed using a 1.0 diametral pitch (P). For other gears of different diametral pitches, divide the selected value by the diametral pitch specified.
295
296
4 Thermoplastic Gearing Design 1
DP
a=
= 20°
2P
90°
1 P
1.0469 h= P
ht =
2.33 P
R= 4 p rf=
0.43 P
b=
1.33 P
p=2xt 2.3329 - (0.0426 x N) P 1 DO = [(N - 2.3158) + 2.7475 x t x P], D P = D O - 2 a, P 1 DR = [(N - 6.9758) + 2.7475 x t x P] P (Up to 18 teeth) t =
P = Diametral pitch, p = Circular pitch, 20° = Pressure angle (φ), a = Addendum, b = Dedendum, ht = Whole depth, rf = Fillet radius, h = Depth straight tangent with fillet radius, t = Circular tooth thickness, N = Teeth number, DR = Root diameter, DO = Outside diameter, DP = Pitch diameter, R = Tangent relief tooth tip radius. Figure 4-53 Thermoplastic gear PGT-1 tooth design (Courtesy: Plastic Gearing Technology Inc.)
Table 4-8 PGT-1 Thermoplastic Gear Tooth Design Data (Courtesy: Plastic Gearing Technology Inc.)
Number of teeth (N)
Min. circular tooth thickness (t × P) in
Outside diameter (DO × P) in
Root diameter (DR × P) in
6 7 8 9 10 11 12 13 14 15 16 17 18
2.0773 2.0347 1.9921 1.9495 1.9069 1.8643 1.8217 1.7791 1.7365 1.6939 1.6513 1.6087 1.5708
8.9254 9.9477 10.9578 11.9577 12.9234 13.8064 14.6893 15.5723 16.4553 17.3382 18.2212 19.1041 20.0000
4.7316 5.6145 6.4975 7.3805 8.2634 9.1464 10.0293 11.9123 11.7952 12.6782 13.5611 14.4441 15.3400
297
4.10 Plastic Gearing Technology Designs
4.10.2
Spur and Helical Gears PGT-2 Tooth Design
1
a=
= 20°
2P
DP
90° h=
1.15 P
1.248 P
ht =
2.63 P
R= 4 p rf=
0.352 P
b=
1.48 P
p=2xt t=
2.4793 - (0.0426 x N) (Up to 22 teeth) P
DO =
1 [(N - 2.0158) + 2.7475 x t x P], P
DR =
1 [(N - 7.2758) + 2.7475 x t x P] P
D P = D O - 2 a,
P = Diametral pitch, p = Circular pitch, 20° = Pressure angle (φ), a = Addendum, b = Dedendum, ht = Whole depth, rf = Fillet radius, h = Depth straight tangent with fillet radius, t = Circular tooth thickness, N = Teeth number, DR = Root diameter, DO = Outside diameter, DP = Pitch diameter, R = Tangent relief tooth tip radius Figure 4-54 Thermoplastic gear PGT-2 tooth design (Courtesy: Plastic Gearing Technology Inc.)
Table 4-9 Thermoplastic Gear PGT-2 Tooth Design (Courtesy: Plastic Gearing Technology Inc.)
Number of teeth (N)
Min. circular tooth thickness (t × P) in
Outside diameter (DO × P) in
Root diameter (DR × P) in
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22
2.2237 2.1811 2.1385 2.0959 2.0533 2.0107 1.9681 1.9255 1.8829 1.8403 1.7977 1.7551 1.7125 1.6699 1.6273 1.5847 1.5708
9.0970 10.1247 11.1398 12.1446 13.1405 14.1287 15.3915 16.0852 17.0549 18.0196 18.9234 19.8064 20.6893 21.5723 22.4552 23.3382 24.3000
4.8338 5.7168 6.5997 7.4827 8.3656 9.2486 10.1316 11.0145 11.8975 12.7804 13.6634 14.5463 15.4293 16.3123 17.1952 18.0782 19.0400
298
4 Thermoplastic Gearing Design
4.10.3
Spur and Helical Gears PGT-3 Tooth Design
1 2P
DP
= 20°
a=
90°
R=
4
1.25 P
1.380 h= P
ht =
2.83 P
p rf=
.30 P
b=
1.58 P
p=2xt t=
DO =
2.5768 - (0.0426 x N) (Up to 24 teeth) P
1 [(N - 1.8158) + 2.7475 x t x P], P
D P = D O - 2 a,
1 [(N - 7.4758) + 2.7475 x t x P] P P = Diametral pitch, p = Circular pitch, 20° = Pressure angle (φ), a = Addendum, b = Dedendum, ht = Whole depth, rf = Fillet radius, h = Depth straight tangent with fillet radius, t = Circular tooth thickness, N = Teeth number, DR = Root diameter, DO = Outside diameter, DP = Pitch diameter, R = Tangent relief tooth tip radius DR =
Figure 4-55 Thermoplastic gear PGT-3 tooth design (Courtesy: Plastic Gearing Technology Inc.)
Table 4-10 Thermoplastic Gear PGT-3 Tooth Design (Courtesy: Plastic Gearing Technology Inc.)
Number of teeth (N)
Min. circular tooth thickness (t × P) in
Outside diameter (DO × P) in
Root diameter (DR × P) in
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24
2.3212 2.2786 2.2360 2.1934 2.1508 2.1082 2.0656 2.0230 1.9804 1.9378 1.8952 1.8526 1.8100 1.7674 1.7248 1.6822 1.6396 1.5970 1.5708
9.3103 10.2413 11.2597 12.2677 13.2666 14.2577 15.2419 16.2200 17.1924 18.1598 19.1226 20.0810 21.0355 21.9863 22.9231 23.8061 24.6890 25.5720 26.5000
4.9017 6.1447 6.6676 7.5466 8.4335 9.3165 10.1994 11.0824 11.9653 12.8483 13.7313 14.6142 15.4792 16.3801 17.2631 18.1460 19.0290 19.9120 20.8400
299
4.10 Plastic Gearing Technology Designs
4.10.4
Spur and Helical Gears PGT-4 Tooth Design
1 2P
= 20°
DP
a=
1.35 P
90°
R= 4 p
rf=
0.248 P
h=
1.520 P
b=
ht =
3.03 P
1.68 P
p=2xt t= DO =
2.6751 - (0.0426 x N) (Up to 26 teeth) P
1 [(N - 1.6158) + 2.7475 x t x P], P
D P = D O - 2 a,
1 [(N - 7.6758) + 2.7475 x t x P] P P = Diametral pitch, p = Circular pitch, 20° = Pressure angle (φ), a = Addendum, b = Dedendum, ht = Whole depth, rf = Fillet radius, h = Depth straight tangent with fillet radius, t = Circular tooth thickness, N = Teeth number, DR = Root diameter, DO = Outside diameter, DP = Pitch diameter, R = Tangent relief tooth tip radius DR =
Figure 4-56 Thermoplastic gear PGT-4 tooth design (Courtesy: Plastic Gearing Technology Inc.) Table 4-11 Thermoplastic Gear PGT-4 Tooth Design (Courtesy: Plastic Gearing Technology Inc.)
Number of teeth (N)
Min. circular tooth thickness (t × P) in
Outside diameter (DO × P) in
Root diameter (DR × P) in
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26
2.4195 2.3769 2.3343 2.2917 2.2491 2.2065 2.1639 2.1213 2.0787 2.0361 1.9935 1.9509 1.9083 1.8657 1.8231 1.7805 1.7379 1.6953 1.6527 1.6101 1.5708
9.3236 10.3580 11.3795 12.3907 13.3926 14.3867 15.3737 16.3545 17.3296 18.2996 19.2650 20.2260 21.1830 22.1363 23.0861 24.0326 24.9760 25.9164 26.8541 27.7891 28.7000
4.9718 5.8547 6.6377 7.5936 8.5036 9.3826 10.2695 11.1525 12.0354 12.9184 13.8013 14.6843 15.5673 16.4502 17.3332 18.2161 19.0991 19.9820 20.8650 21.7479 22.6400
300
4 Thermoplastic Gearing Design PGT-4
PGT-3
PGT-2 PGT-1 DO STANDARD
DP t
rf DR (Scale = 25.00
1.00)
Gear of 20 (P) diametral pitch, 13 (N) teeth and 20° ( ) pressure angle
Figure 4-57 Standard vs. PGT system spur gear tooth comparison
Table 4-12 Standard and PGT Gear Tooth Form Comparison (Scale = 25.00 : 1.00) Gear of 20 (P) diametral pitch, 13 (N) teeth, and 20° (φ) pressure angle
Tooth form
Outside Circular tooth dia. (DO) thickness (t)
Pitch dia. (DP)
Root dia. (DR)
Fillet radius (rf )
Standard
0.07854
0.7500
0.6500
0.5250
0.0150
PGT-1 PGT-2 PGT-3 PGT-4
0.08890 0.09630 0.10115 0.10606
0.7786 0.8042 0.8110 0.8177
0.6786 0.6892 0.6860 0.6827
0.5456 0.5507 0.5541 0.5576
0.0215 0.0176 0.0150 0.0124
4.10.5
Plastic Gearing Technology Tooth Form Design Variables
Circular Tooth Thickness (t) The tooth thickness of a standard spur gear is always specified as being the circular tooth thickness on the standard pitch circle. But, for the PGT tooth form system, the circular tooth thickness will depend on the number of teeth times a constant divided by the diametral pitch. The PGT tooth form systems increase in thickness based on the incremental increase of the constant; therefore, the circular tooth thickness for PGT-4 is wider than PGT-3, PGT-2, or PGT-1, as shown in Figure 4-57. The addendum of each PGT tooth form is lengthened by a constant divided by the diametral pitch. The PGT-4 has a longer addendum, while PGT-1 has a shorter addendum; however, longer than the standard gear. In other words, the longer the addendum, the thicker the circular tooth thickness.
4.10 Plastic Gearing Technology Designs There is a direct relationship between the circular tooth thickness specified for a spur gear and the outside and root diameters. This relationship can best be explained by working through a calculation example.
Example 4-6 A spur gear has 16 teeth, a diametral pitch of 24 and the PGT-1 tooth design. The PGT-1 circular tooth thickness is 1.6513 ÷ 24 = 0.0688 in (using Table 4-8). Calculate the outside and root diameters. 1) Determine the standard pitch circle diameter (see Table 4-4). N = 16, P = 24, Standard pitch circle diameter (DP) = N/P = 16 / 24 = 0.6666 2) Determine the standard addendum (see Table 4-4). Standard addendum (a) = 1/P = 1 / 24 = 0.04166 in 3) Determine the standard circular tooth thickness (see Table 4-4). Standard circular tooth thickness (t) = π / (2 × P) t = 3.1415926 / (2 × 24) = 0.06545 in 4) The PGT-1 circular tooth thickness specified is 0.0688 in. The increase over the standard is 0.0688–0.06545 = 0.00335 in. To achieve this increase, the line of action is held back by 0.00335 ÷ 2 tan φ, where φ is the pressure angle. The pressure angle of the PGT-1 tooth design is 20°, therefore the line of action is held back by the following amount: 0.00335 / (2 × 0.36397023) = 0.0046 in 5) The standard addendum is 0.04166 in. The addendum corresponding to the specified PGT-1 circular tooth thickness of 0.0688 in is the standard addendum plus the amount of the line of action that has been held back. Addendum (a) = 0.04166 + 0.0046 = 0.04626 in 6) Determine the outside diameter (DO). The outside diameter of a gear is the standard pitch diameter (DP) plus two addendums (a). Outside diameter (DO) = 0.666 + (2 × 0.04626) = 0.7585 in 7) Determine the root diameter (DR). The root diameter (DR) is the outside diameter (DO) minus two whole depths (ht). Find the PGT-1 whole depth (ht) by using the equation in Figure 4-53 Whole depth (ht) = 2.33 / P = 2.33 / 24 = 0.09708 in Root diameter (DR) = 0.7585 – (2 × 0.09708) = 0.5643 in Generating the teeth by a line of action is only one of a number of methods employed to form involute teeth, but the relationship between the circular tooth thickness, the outside and root diameters applies no matter how the teeth are formed.
301
302
4 Thermoplastic Gearing Design Given the circular tooth thickness of a gear having one of the four PGT tooth form designs, the outside and root diameters are readily obtained by using the appropriate equations given in Figures 4-53, 4-54, 4-55, and 4-56). Example 4-7 Determine the outside and root diameters of the gear in the previous Example 4-6 by using PGT-1 equations. This gear has (N) 16 teeth, a diametral pitch (P) of 24, and a circular tooth thickness (t) of 0.0688 in. P = 24, N = 16, t = 0.0688 in Outside diameter (Figure 4-53) DO = (1/P) × [(N – 2.3158) + 2.7475 × t × P] DO = (1/24) × [(16–2.3158) + 2.7475 × 0.0688 × 24] = 0.7592 in Root diameter (Figure 4-53) DR = (1/P) × [(N – 6.9758) + 2.7475 × t × P] DR = (1/24) × [(16–6.9758) + 2.7475 × 0.0688 × 24] = 0.565 in
4.10.6
Maximum Allowable Outside Diameter DO (Max.)
If the two involute curves forming the profile of a tooth are continued out, they will eventually cross and the tooth will be pointed. If a gear has a small number of teeth and an enlarged tooth thickness, the teeth may become pointed at a diameter less than the outside diameter given by the DO equation. To avoid specifying an outside diameter impossible to attain, Equation 4-10 is used as a check. The smaller value obtained by calculating DO and DO (Max.) is the outside diameter specified. Equation 4-10 provides the maximum outside diameter that will still provide the teeth with an adequate top land for all four PGT tooth form designs. DO (Max.) =
N × 0.93969262 P × 1.017 × cos φ1
(4-10)
Where: DO (Max.) = Maximum allowable outside diameter (in) N = Number of teeth P = Diametral pitch t = Circular tooth thickness (in) (t × P) φ1 = Angle whose involute is = N + 0.01490438 Example 4-8 A spur gear has 10 teeth (N), a diametral pitch of 44 (P), PGT-1 tooth design, and a circular tooth thickness (t) of 0.0433. Find the outside and the root diameter. Outside diameter (Figure 4-53) DO = (1/P) × [(N – 2.3158) + 2.7475 × t × P] DO = (1/44) × [(10–2.3158) + 2.7475 × 0.0433 × 44] = 0.2936 in
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4.10 Plastic Gearing Technology Designs
Maximum outside diameter DO (Max.) =
N × 0.93969262 P × 1.017 × cos φ1
Inv φ1 = (t × P) / (N + 0.01490438) = (0.0433 × 44) / (10 + 0.01490438) = 0.1902364 φ1 = 43°32′, cos φ1 = 0.72497 DO (Max.) =
10 × 0.93969262 = 0.2896 in 44 × 1.017 × 0.72497
The outside diameter to be specified should be the smaller calculated dimension obtained by these two equations (0.2896 in). DR = (1/P) × [(N – 6.9758) + 2.7475 × t × P] (Figure 4-53) DR = (1/44) × [(10–6.9758) + 2.7475 × 0.0433 × 44] = 0.1878 in
4.10.7
Spur Gear Tooth Form Comparison
If a standard gear has a small number of teeth, the base circle will be greater than the root diameter. Because no tooth action can take place below the base circle, that section of the tooth inside the base circle is nonfunctional. To accommodate the tip of the mating tooth, the nonfunctional lower portion is undercut. Undercutting the teeth is not recommended, it weakens the teeth and causes premature wear of the gear. Figures 4-58 and 4-59 show two separate spur gear tooth forms. Both gears have the same number of teeth and the same diametral pitch. The gear tooth in Figure 4-58 has the standard circular tooth thickness (t = π / 2 P). For the gear tooth in Figure 4-59 (PGT-1), the circular tooth thickness has been increased above the standard. The PGT-1 tooth is a better design; it has a more functional profile and the undercut is reduced significantly. The equations to determine the minimum circular tooth thickness, shown in Figure 4-53, were developed to ensure adequate involute profiles and to avoid the objectionable undercutting of the teeth in the gears.
t Standard
Figure 4-58 Standard gear circular tooth thickness
Example 4-9 A spur gear has 12 teeth (N), a diametral pitch (P) of 32, and PGT-2 tooth design. Find the minimum circular tooth thickness (t), outside diameter (DO), and the root diameter (DR). 1) Minimum circular tooth thickness (t), see Figure 4-54 t =
2.4793 − (0.0426 × N ) 2.4793 − (0.0426 × 12) = = 0.0615 in P 32
2) Outside diameter (DO), see Figure 4-54 DO = (1/P) × [(N – 2.0158) + 2.7475 × t × P] DO = (1/32) × [(12–2.0158) + 2.7475 × 0.0615 × 32] = 0.4809 in Check for the maximum possible outside diameter DO (Max.), Equation 4-10
t Increased
Figure 4-59 PGT-1 design, circular tooth thickness increased
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4 Thermoplastic Gearing Design
DO (Max.) = Inv φ1 =
N × 0.93969262 P × 1.017 × cos φ1
t×P 0.0615 × 32 = = 0.16379 N + 0.0149 12 + 0.0149
φ1 = 41°44′, cos φ1 = 0.74625 DO (Max.) =
12 × 0.93969262 = 0.4643 in 32 × 1.017 × 0.74625
The smaller outside diameter obtained by using both calculations should be the one specified for the gear, DO = 0.4643 in. 3) Root Diameter (DR), see Figure 4-54 DR = (1/P) × [(N – 7.2758) + 2.7475 × t × P] DR = (1/32) × [(12–7.2758) + 2.7475 × 0.0615 × 32] = 0.3166 in
4.10.8
Mating Spur Gears Tooth Form Comparison
To obtain the best performance of a low tensile strength thermoplastic gear, it is essential that the gears used in power drives be designed so that the teeth are as strong as possible. This can be done by modifying the geometry or the tooth form. A gear tooth is a cantilevered beam. The two mating spur gears should have equal circular tooth thicknesses and strength at their roots, where the root fillet radius is as large as possible and tangent to the flanks of the teeth.
Example 4-10 Two mating spur gears made of the same material, see Figure 4-60, have a diametrical pitch (P) of 32, the pinion has 13 teeth (NP), and the gear has 60 teeth (NG). Determine both circular tooth thicknesses of the gears for equal strength. The standard circular tooth thickness of both gears is 0.0491 in. The pinion teeth are weaker than the gear and are capable of transmitting only 60% of the load. To design equal strength for both gears it is important to arrive at the right circular tooth thickness. Figure 4-61 shows two modified tooth profiles of a 13-tooth pinion and a 60-tooth gear; both mating gears have a diametral pitch of 32. Because the pinion has less than 26 teeth, the PGT-4 tooth design can be used for the pinion. For the 60-tooth gear, the standard circular tooth thickness should be used. tP =
2.6751 − (0.0426 × N ) 2.6751 − (0.0426 ×13) = = 0.066 or 0.064 in P 32
tG =
t P × htG 0.064 × 0.07075 = = 0.048 in 0.09468 htP
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4.10 Plastic Gearing Technology Designs Standard pinion 13 teeth
Standard gear 60 teeth 0.064 inch (tP)
htP= 3.03/P = 3.03/32 = 0.09468
Standard circular tooth thickness 3.1416 t= π = = 0.0491 inch 2 x 32 2P
0.0491 (tP)
0.0491 (tG)
PGT-4 pinion 13 teeth
Figure 4-60 Standard mating spur pinion and gear
The teeth used on both gears are designed to have balanced strength. By applying the equation found in Figure 4-56, the pinion minimum circular tooth thickness is calculated to be 0.066 in. To achieve equal strength, the pinion circular tooth thickness was increased from the standard of 0.0491 in to 0.064 in for the PGT-4 tooth form and the gear circular tooth thickness was reduced from the standard of 0.0491 in to 0.048 in, by multiplying the pinion circular tooth thickness with the whole depth gear/pinion ratio.
4.10.9
PGT Spur Mating Gears Strength Balance
The following Equations 4-11, 4-12, 4-13, 4-14, 4-15, and 4-16 are used to calculate the circular tooth thickness of a pair of mating spur gears to achieve balanced tooth strength. These equations are valid only for spur gears of PGT-1 tooth form design. The longer whole depth teeth (ht) of the PGT-2, PGT-3, and PGT-4 tooth form designs do not require the coarser pitch gears used in power drives. These equations provide answers for any ratio and all combinations of number of teeth, but for a power drive it is advisable for the pinions to have at least 12 teeth. Pinions with less than 12 teeth will have reduced outside diameters. Equations 4-11 and 4-12 give specific values for the circular tooth thickness required of both spur pinion and gear. Equations 4-15 and 4-16 are needed to calculate the circular tooth thickness of the gear at the very beginning of the design. These equations then give the circular tooth thickness of the pinion. Spur Pinions and Gears with Less than 35 Teeth, Circular Tooth Thickness tP =
2.3329 − 0.0219 × N P P
(4-11)
tG =
2.3329 − 0.0219 × N G P
(4-12)
Spur Pinion with Less than 35 Teeth, Gear with 35 Teeth or More, Circular Tooth Thicknesses tP =
2.3329 − 0.0219 × N P P
(4-13)
tG =
N G 2.1922 − 0.0066 × N P + Inv φ2 − 0.01490438 P N G − 2.0938
(4-14)
htG= 2.20/P + 0.002 = 2.20/32 + 0.002 = 0.07075
0.048 inch (hG)
Standard gear 60 teeth
Figure 4-61 PGT-4 pinion and standard gear for equal strength
306
4 Thermoplastic Gearing Design Spur Pinion and Gear Both with 35 Teeth or More, Circular Tooth Thickness N × (N G − 2.0938) t G 0.0149 − Inv φG + tP = P N P − 2.0938 P NG 0.0149 − Inv φP − NP P
tG =
π 2P
(4-15)
(4-16)
Where: tP = Pinion circular tooth thickness (in) tG = Gear circular tooth thickness (in) NP = Pinion number of teeth NG = Gear number of teeth P = Diametral pitch 0.9396 × N P φP = cos −1 N P − 2.0938 0.9396 × N G φG = cos −1 N G − 2.0938
Example 4-11 A pinion with 14 teeth (NP) drives a gear of 28 teeth (NG) made of the same material. The diametral pitch (P) is 20 and the PGT-1 tooth form is required. Determine the circular tooth thickness of both the pinion and gear for balanced tooth strength. Because both gears have less than 35 teeth, Equations 4-11 and 4-12 are used. tP =
2.3329 − 0.0219 × N P 2.3329 − 0.0219 × 14 = = 0.1013 in P 20
tG =
2.3329 − 0.0219 × N G 2.3329 − 0.0219 × 28 = = 0.086 in P 20
Circular tooth thickness of pinion (tP) = 0.1013 in Circular tooth thickness of gear (tG) = 0.086 in
Example 4-12 A pinion having 10 teeth (NP) drives a gear of 44 teeth (NG), both gears are made of the same material. The diametral pitch (P) is 18 and the PGT-1 tooth design is required. Determine the circular tooth thickness of both the pinion and gear for balanced tooth strength. Because the pinion has less than 35 teeth and the gear more than 35 teeth, Equations 4-13 and 4-14 are used.
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4.10 Plastic Gearing Technology Designs
tP =
2.3329 − 0.0219 × N P 2.3329 − 0.0219 × 10 = = 0.1174 in P 18
tG =
N G 2.1922 − 0.0066 × N P + Inv φ2 − 0.01490438 P N G − 2.0938
0.9396 × N G φG = cos −1 = cos −1 N G − 2.0938
0.9396 × 44 = 9.40° 44 − 2.0938
Inv φG = 0.00194 tG =
44 2.1922 − 0.0066 × 10 + 0.00194 − 0.0149 = 0.0923 in 18 44 − 2.0938
Circular tooth thickness of pinion (tP) = 0.1174 in Circular tooth thickness of gear (tG) = 0.0923 in
Example 4-13 A pinion having 36 teeth (NP) drives a gear of 72 teeth (NG). The diametral pitch (P) is 24 and the PGT-1 tooth design is required. Determine the circular tooth thickness of both the pinion and gear for balanced tooth strength. Since both gears have more than 35 teeth, Equations 4-15 and 4-16 are used. N × (N G − 2.0938) t G 0.0149 − Inv φG tP = P N + − 2.0938 N P G P 0.0149 − Inv φP − NP P 0.9396 × N G φP = cos −1 = cos −1 N P − 2.0938
0.9396 × 36 = 4.60° 36 − 2.0938
Inv φP = 0.0021182 0.9396 × N G 0.9396 × 72 φG = cos −1 = cos −1 = 14.60° 72 − 2.0938 N G − 2.0938
Inv φG = 0.005642 Standard circular tooth thickness (tG) =
π 3.1416 = = 0.06545 in 2 P 2 × 24
36 (72 − 2.0938) 0.065 0.015 − 0.0056 0.015 − 0.00212 tP = − 36 72 + − 36 2.0938 24 24 = 0.076 in
Circular tooth thickness of pinion (tP) = 0.076 in Circular tooth thickness of gear (tG) = 0.06545 in
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4 Thermoplastic Gearing Design
4.10.10 PGT Close Mesh Center Distance Between Spur Gears When two standard spur gears are brought into close mesh, the distance between their centers is half the sum of their standard pitch diameters and is referred to as the standard center distance. But it is rare for a pair of standard gears to be the best combination for a given drive. A pair of involute gears will function at widely varying center distances. The center distance at which a pair of mating spur gears operates should be regarded as a variable that can be manipulated to achieve the best possible drive. The center distance at which a pair of PGT tooth form design gears are in close mesh is determined by using Equation 4-17. C=
(N1 + N 2 ) × 0.46984631 P × cos φ1
(4-17)
Where: C = Close mesh center distance (in) N1 = Number of teeth in the first gear N2 = Number of teeth in the second gear P = Diametral pitch t1 = Circular tooth thickness of the first gear (in) t2 = Circular tooth thickness of the second gear (in) P (t1 + t 2 ) − π φ1 = Angle whose involute is + 0.01490438 N1 + N 2 Example 4-14 Two mating gears have the basic specifications given by the table below. Determine the center distance at which they will be in close mesh. Gear parameters
First gear
Second gear
Number of teeth (N) Diametral pitch (P) Tooth form design Standard pitch diameter (DP) Standard circular tooth Thickness (t)
10 32 PGT-1 0.3125 0.0595
40 32 PGT-1 1.250 0.01965
N1 = 10, N2 = 40, P = 32, t1 = 0.0595, t2 = 0.01965.
P (t1 + t 2 ) π + 0.01490438 N1 + N 2 32 (0.0595 + 0.0196) − 3.1416 = + 0.01490438 = 0.00273 10 + 40
Inv φ1 =
φ1 = 5.25°
cos φ1 = 0.995805 (N1 + N 2 ) × 0.46984631 P × cos φ1 (10 + 40) × 0.46984631 = = 0.73722 in 32 × 0.995805
Close Mesh Center Distance C =
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4.10 Plastic Gearing Technology Designs
4.10.11 Maximum Close Mesh Center Distance The close mesh center distance computed in Example 4-14 using Equation 417 assumes perfection in the gears and any type of bearings employed. It also assumes the gears and the housing in which they are mounted are made of stable materials. The gears’ and bearings’ run-out affects the tolerances of the assembly; in addition the gears and the housing will also change because of the environment, causing the close mesh center distance to vary from high to low tolerances. The minimum operating center distance specified for the housing must be equal to, or greater than, the maximum close mesh center distance, otherwise the gears may bind. The designer needs to know the tolerances specified for the gears, bearings and housing, the dimensional changes caused by the materials used for the fabrication of the gears and housing, and the nature of the environment. All these changes of dimensions must be taken into account during the gear design calculations to determine the maximum and minimum operating close mesh center distance. The sum of the tolerances in the teeth is called the tooth-to-tooth composite tolerance. The composite tolerance plus the run-out in the gear is called the total composite tolerance. This tolerance system was developed by the American Gear Manufacturers Association classifying a gear by AGMA Quality Number in accordance with the accuracy required. The system is presented, in detail, in the “Gear Handbook”, American Gear Manufacturers Association Publication 390.03. If specifications require that the gears in the previous Example 4-14 are to be to the accuracy of AGMA Quality Number Q7, from the “Gear Manual” it can be found that the first gear has a maximum total composite tolerance of 0.0027 in and the second gear has a maximum total composite tolerance of 0.0031 in. The close mesh center distance is calculated to be 0.73722 in. If the tolerances in the gears are at the maximum allowed by the tolerances, these tolerances would cause the close mesh center distance to go from a high of 0.74012 in to a low of 0.73432 in. To allow for these maximum permissible tolerances, the operating close mesh center distance must not be less than 0.74012 in. To allow for the tolerances in each of two mating gears, the minimum operating center distance must exceed the calculated close mesh center distance by half the sum of the total composite tolerances of the gears. Because the coefficients of linear thermal expansion of the thermoplastic materials are relatively high and some thermoplastics expand as they pick up moisture, these factors must also be taken into consideration in arriving at the minimum operating center distance. Finally, if the gears are mounted on shafts running in bearings, the maximum allowable run out of the bearings must be taken into account. Assuming that the gears are inspected in a relative humid environment and at a room temperature of 73 °F, the minimum operating center distance (c) must exceed the calculated close mesh center distance and the required increase in center distance (∆c) is expressed by the following Equation 4-18: ∆c =
α × N1 Tol1 + Tol 2 α × N2 + C (T − 70) 1 + 2 − αH 2 N1 + N 2 N1 + N 2 ∆ DW1 × N1 ∆ DW2 × N 2 + + + TIR N1 + N 2 N1 + N 2
(4-18)
310
4 Thermoplastic Gearing Design Where: ∆c = Required increase in center distance (in) Tol1 = First gear total composite tolerance (in) Tol2 = Second gear total composite tolerance (in) C = Close mesh center distance (in) T = Maximum application end use temperature (°F) α1 = Coefficient of linear thermal expansion of first gear (in/in/°F) α2 = Coefficient of linear thermal expansion of second gear (in/in/°F) αH = Coefficient of linear thermal expansion of housing (in/in/°F) N1 = Number of teeth in first gear N2 = Number of teeth in second gear ∆DW1 = Dimensional change due to moisture absorption first gear (in/in) ∆DW2 = Dimensional change due to moisture absorption second gear (in/in) TIR = Maximum allowable run-out of bearings (in) The coefficients of linear thermal expansion and the dimensional change caused by the moisture absorption of the thermoplastic polymers are found in the technical manuals issued by the plastic resins suppliers. Unfortunately, information about expansion caused by moisture absorption is not so readily available. In the case of applications where the gears will not be exposed immediately to conditions of high humidity, the expansion of most thermoplastic materials is small and gradual. This expansion can be discounted, being offset by the equally small and gradual mold shrinkage that occurs as molding stresses are relieved. If the gears are to be molded of one of the more hygroscopic thermoplastic resins and if conditions are such that there could be a high percentage of moisture absorption for a long period of time and high temperatures, it is advisable to consult with the plastic supplier’s technical department to determine what allowance, in terms of in/in, should be made for the melt flow and perpendicular to the flow directions.
Example 4-15 The first gear in Example 4-14 has 10 teeth and the second gear has 40 teeth. The gears need to have the accuracy required by AGMA Quality Number Q7. The maximum total composite tolerances are 0.0027 in and 0.0031 in, respectively. The first gear is to be molded of an unreinforced nylon 6/6 having a coefficient of linear thermal expansion of 5.0 × 10–5 in/in/°F. The second gear is molded of a high viscosity acetal homopolymer having a coefficient of linear thermal expansion of 6.8 × 10–5 in/in/°F. Considering the environment, in which the gears will operate, it has been determined that expansion of the unreinforced nylon 6/6 due to water absorption could be 0.003 in/in and that of the acetal homopolymer 0.0005 in/in. The housing is made of glass reinforced nylon 6/6 having a coefficient of linear thermal expansion of 1.3 × 10–5 in/in/°F. The gear shafts run in bearings concentric (TIR) to 0.0005 in. The maximum temperature to which the gears will be subjected is 150 °F. Determine the minimum operating center distance to be specified for the housing design. It has already been determined in Example 4-14, that the gears will be in close mesh at a center distance of 0.73722 in. The calculation employed to arrive at this center distance allowed for no tolerances in the gears, assuming they were conditioned at 50% relative humidity and at a temperature of 73 °F.
311
4.10 Plastic Gearing Technology Designs Increase in center distance ∆c: ∆c =
α × N1 α × N2 Tol1 + Tol 2 + C (T − 70) 1 + 2 − αH + + 2 N N N N 1 2 1 2 ∆ DW1 × N1 ∆ DW2 × N 2 + + + TIR N1 + N 2 N1 + N 2
Tol1 = 0.0027 in Tol2 = 0.0031 in C = 0.73722 in T = 150 °F α1 = 5.0 · 10–5 = 0.00005 (in/in/°F) α2 = 6.8 · 10–5 = 0.000045 (in/in/°F) α H = 1.3 · 10–5 = 0.00001 (in/in/°F) N1 = 15 N2 = 60 ∆DW1 = 0.003 in/in ∆DW2 = 0.0005 in/in TIR = 0.0005 in ∆c =
0.0027 + 0.0031 2 0.00005 × 10 0.000068 × 40 + 0.737 (150 − 73) + − 0.00001 + + 40 10 10 40 0.003 × 10 0.0005 × 40 + + + 0.0005 40 + 10 10 + 40
= 0.0029 + 0.00325 + 0.0005 = 0.00665 in Minimum center distance (C) = 0.73722 + 0.00665 = 0.74387 in The specified circular tooth thickness of the mating gears in Example 4-14 determined the close mesh center distance. When the minimum operating center distance is fixed by requirements of the gear’s mechanism, it becomes necessary to establish the circular tooth thicknesses such that the close mesh center distance is less than the minimum operating decrease in the center distance by c. ∆c is again calculated using Equation 4-18, but the value given for C is now the minimum operating center distance. This will introduce a tolerance, because C should have the value of the unknown close mesh center distance, but the tolerance is so small it can be considered negligible. ∆c is then subtracted from the minimum operating center distance. The answer is the close mesh center distance used in Equation 4-18 to get the sum of the circular tooth thicknesses for a given close mesh center distance. t1 + t 2 =
(N1 + N 2 )(inv φ1 − 0.0149043) + π P
Where: t1 = Circular tooth thickness of first gear (in) t2 = Circular tooth thickness of second gear (in) N1 = Number of teeth in first gear
(4-19)
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4 Thermoplastic Gearing Design
N2 = Number of teeth in second gear P = Diametral pitch C = Close mesh center distance (in) (N + N 2 ) × 0.46984631 φ1 = cos −1 1 P×C Example 4-16 The gears in Examples 4-14 and 4-15 are required to operate at a fixed minimum operating center distance of 0.7315 in. Determine the sum of the circular tooth thicknesses of each gear. Substituting 0.7315 in for 0.73722 in as the value for close mesh center distance (C), ∆c =
0.0027 + 0.0031 2 0.00005 × 10 0.000068 × 40 + 0.7315 (150 − 73) + − 0.00001 40 + 10 10 + 40 0.003 × 10 0.0005 × 40 + + + 0.0005 40 + 10 10 + 40
= 0.0029 + 0.003231 + 0.00005 = 0.00295 in Close mesh center distance (C) = 0.7315–0.00295 = 0.73445 in The circular tooth thicknesses must be such that, if the gears and bearings were perfect and the gears and housing made of stable materials, the gears would be in close mesh at 0.73445 in. The sum of circular tooth thicknesses for close mesh center distance is calculated by employing Equation 4-19. N1 = 10, N2 = 40, P = 32, C = 0.73445 (N + N 2 ) × 0.46984631 φ1 = cos −1 1 P×C (10 + 40) × 0.46984631 = cos −1 = cos −1 (0.99957) = 1.65° × 32 0.73445 Inv φ1 = 0.00051 (N1 + N 2 ) (inv φ1 − 0.0149043) + π P (10 + 40) (0.00051 − 0.0149043) + 3.1416 = = 0.0756 in 32
t1 + t 2 =
From Table 4-8, a gear having 10 teeth, a diametral pitch of 32, and the PGT-1 tooth form design is required to have a minimum circular tooth thickness of 1.9069 / 32 = 0.0595 in. Allowing for a discrepancy of +0.0010 / –0.0000 inches, the maximum becomes 0.0605 in, the maximum tooth thickness of the second gear is 0.0756–0.0605 = 0.0151 in. The standard circular tooth thickness of a gear having a diametral pitch of 32 is 0.0491 in. The reduction to 0.0151 in, although large, is acceptable, as the teeth will have no undercut.
4.10 Plastic Gearing Technology Designs
Example 4-17 The first gear has 15 teeth (N1), the second gear has 18 teeth (N2), a diametral pitch (P) of 32, and the minimum operating center distance is fixed at 0.5156 in. Determine the sum of circular tooth thicknesses of each gear. The total composite tolerance of the second gear is now 0.0027 in ∆c =
0.0027 + 0.0027 2 0.00005 × 15 0.000068 × 18 + 0.5156 (150 − 73) + − 0.000013 + + 18 15 15 18 0.003 × 15 0.0005 × 18 + + + 0.0005 18 + 15 15 + 18
= 0.0027 + 0.00269 + 0.0005 = 0.00589 in Close mesh center distance (C) = 0.5156–0.00589 = 0.5097 in t1 + t 2 =
(15 + 18)(inv φ1 − 0.0149043) + 3.1416 32
(15 + 18) × 0.46984631 −1 φ1 = cos −1 = cos (0.9508026) = 18.047° 32 × 0.5097 Inv φ1 = 0.01084731 t1 + t 2 =
(15 + 18) (0.01084731 − 0.0149043) + 3.1416 = 0.0940 in 32
According to Table 4-8, the circular tooth thickness of the first gear with 15 teeth is 1.6939 / 32 = 0.0529 in. The circular tooth thickness of the second gear is 0.0940–0.0529 = 0.0410 in. But, from the same Table 4-8, a gear having 18 teeth must have a circular tooth thickness of no less than 1.5708 / 32 = 0.04908 in to avoid an undesirable amount of undercut. The circular tooth thickness of the first gear could be reduced to (π / 2 P) or 3.1416 / (2 × 32) = 0.049 in and the second gear to 0.0940–0.049 = 0.0450 in. The gears would function, but their performance would not be satisfactory. A better design solution should be implemented, such as the use of a finer diametral pitch for the mating gears as illustrated in Example 4-18.
Example 4-18 Let the diametral pitch (P) of the gears in Example 4-17 be changed from 32 to 32.8. Determine the sum of circular tooth thicknesses. Both gears now have a total composite tolerance of 0.0028 in. ∆c = 0.0028 + 0.00269 + 0.0005 = 0.00599 in
313
314
4 Thermoplastic Gearing Design
Close mesh center distance (C) = 0.5156–0.00599 = 0.5096 in
t1 + t 2 =
(15 + 18)(inv φ1 − 0.0149043) + 3.1416 32.8
(15 + 18) × 0.46984631 −1 φ1 = cos −1 = cos (0.92743031) = 21.962° 32.8 × 0.5096 Inv φ1 = 0.01994651 t1 + t 2 =
(15 + 18) (0.01994651 − 0.0149043) + 3.1416 = 0.1009 in 32.8
From Table 4-8, the minimum circular tooth thickness of the first gear, which has 15 teeth and a diametral pitch of 32.8 is 1.5708 / 32.8 = 0.0478 in, say, 0.0488 in maximum and 0.0468 in minimum. The sum of the circular tooth thicknesses is 0.1009 in; therefore, the circular tooth thickness of the second gear is 0.1009–0.0488 = 0.0521 in. From Table 4-8, the minimum circular tooth thicknesses of a 18-toothed gear and a diametral pitch of 32.8 is 1.5708 / 32.8 = 0.0478 in. The diametral pitch of 32.8 was arrived at by trial and error, using Equation 4-19. This example demonstrates the freedom in designing special PGT gear tooth form designs and manufacturing thermoplastic gears by injection molding. A diametral pitch of 32.8 is required, instead of 32 initially specified.
There is nothing to be gained economically by specifying a diametral pitch of 32 and much to be lost. Rigid adherence to what is considered the “standard” diametral pitch could cause performance problems of the mating gears. Investigate the best diametral pitch as illustrated to improve the operating performance of the gear system.
4.11
PGT Helical Thermoplastic Gearing
A helical gear differs from a spur gear in that the teeth, instead of being parallel to the axis of the shaft on which the gear is mounted, are formed on a spiral that winds around the axis. Included in the data of a helical gear are three additional requirements that are not specifications of a spur gear. These are the helix angle, the direction of the helix, either right hand or left hand, and the lead. Mating helical gears on parallel shafts have the same helix angle but opposite hands of the helix. The lead of a helical gear is the distance between a point on the tooth flank and the 360° spiral path that ends in the axis plane. Figure 4-62 shows that the lead (L) is equal to the circumference of a circle containing the point multiplied by the cotangent of the helix angle (ψ).
315
4.11 PGT Helical Thermoplastic Gearing
ψ No rm al
Lead (L) =
pl
π x DP x cot ψ
an e
ψ Axial plane DP
πx
DP
Figure 4-62 Helical gear enveloped view
The helix angle of a helical gear is always specified as the helix angle at the standard pitch circle. The lead (L) is calculated by using Equation 4-20. L = π × DP × cot ψ
(4-20)
Where: L = Lead π = 3.1416 DP = Standard pitch diameter ψ = Helix angle (degrees) The basic principle of load transfer in a rotating helical gear is that it is done through the gear tooth. Because helical gears have their teeth lined-up in the direction of a helix angle, the load moves through the angled tooth face width. Therefore, the helical gears transfer the load by using two basic directional planes, one in the normal plane and the other in the axial plane. Figure 4-63 shows the helical gear top view, the two cross section planes, and their relationship to one another, together with their ruling equations and commonly used terminology. P = Pn × cos ψ DP =
N Ν = P Pn × cos ψ
Where: ψ = Helix angle P = Diametral pitch Pn = Normal diametral pitch DP = Standard pitch diameter N = Number of teeth pn p = Circular pitch = cos ψ pn = Normal circular pitch tan φn φ = tan −1 = Pressure angle cos ψ φn = Normal pressure angle
Helical gear top view
(4-21) (4-22)
ψ
φn pn
ane l pl a rm no ion t c e ss s Cro
p
φ
Cross section axial plane
Figure 4-63 Helical gear plane views and equations
316
4 Thermoplastic Gearing Design The tooth form of a helical gear is specified as the tooth form conforming to the basic rack in the normal plane. For all helical gears having helix angles of not more than 23° and operating on parallel shafts, the tooth form specified is the same as that for spur gears. This is not a requirement, but it permits the use of spur gear lines of actions to generate the teeth in helical gears. While the injection molded thermoplastic gears do not require machined hobs that are a necessity for the metal gears, there was no good reason to depart from what has become an accepted practice in the world of gear engineering. As with spur gears, a pair of mating helical gears must have an adequate contact area ratio. Helical gears have a helical overlap that serves as an additional contact area to transfer higher loads and smooth performance. Helical gear axial pitch (px) is the lead (L) divided by number of teeth (N). px = L / N px =
π Pn × sin ψ
(4-23) (4-24)
Where: px = Axial pitch L = Lead N = Number of teeth Pn = Normal diametral pitch ψ = Helix angle (degrees) A helical gear having a face width equal to its axial pitch has a helical overlap of 1.0. To obtain the benefits from the use of helical gears, the helical overlap should be approximately 2.0. In other words, the helical gear face width should be twice the axial pitch, or as close to that dimension as other design considerations permit. It is this helical overlap, or face width contact area ratio, that makes the helical gears superior to spur gears for drives requiring the maximum torque to be transferred, smooth performance, and a quiet operation. Unlike spur gears, the helical gears cause thrust forces on the bearings carrying the shafts on which the gears are mounted. The amount of thrust force increases with the helix angle and high helix angles require special helical gear tooth forms. The injection molded thermoplastic helical gears of a helix angle should be kept between 13 and 23°. Given a choice, it is recommended that a helix angle of 18° be specified for the helical gears. No specific explanation can be offered for this recommendation, but from experience it seems that helical gears having a helix angle of 18° have demonstrated excellent performance in critical applications. Everything discussed previously about spur gears holds true for helical gears. The PGT-1 tooth form design is usually specified for helical gears, although there may be occasions when the longer tooth of PGT-2 tooth form design can be advantageous. The spur gear equations are modified to account for the helix angle. They could be used to design spur gears by giving the helix angle a value of zero. Given the normal circular tooth thickness of a helical gear, the outside, root diameters and minimum normal circular tooth thickness are obtained by using the following PGT helical gear equations in the tables below (Courtesy: ABA/PGT).
317
4.11 PGT Helical Thermoplastic Gearing Table 4-13 PGT-1 Tooth Helical Gear Design Equations
Outside diameter
DO =
1 N − 2.3158 + (2.7475 × t n ) Pn cos ψ
Root diameter
DR =
1 N − 6.9758 + (2.7475 × t n ) Pn cos ψ
Minimum normal Circular tooth Thickness
tn =
1 Pn
N × (1 − cos2 φ 2.3329 − 2.7475 × cos ψ
Table 4-14 PGT-2 Tooth Helical Gear Design Equations
Outside diameter
DO =
1 N − 2.0158 + (2.7475 × t n ) Pn cos ψ
Root diameter
DR =
1 N − 7.2758 + (2.7475 × t n ) Pn cos ψ
Minimum normal Circular tooth Thickness
tn =
1 Pn
N × (1 − cos2 φ 2.4793 − 2.7475 × cos ψ
Where: DO = Outside diameter (in) DR = Root diameter (in) Pn = Normal diametral pitch N = Number of teeth tn = Minimum normal circular tooth thickness (in) ψ = Helix angle (degrees) 0.36397023 φ = tan −1 cos ψ Example 4-19 A helical gear has 38 teeth (N), a normal diametral pitch (Pn) of 32, a helix angle (ψ) of 18°, the PGT-1 tooth form design, and a normal circular tooth thickness (tn) of 0.0475 in. Determine the outside and root diameters. Pn = 32, N = 38, tn = 0.0475, ψ = 18° DO = =
DR = =
1 N − 2.3158 + (2.7475 × t n ) Pn cos ψ 1 38 − 2.3158 + (2.7475 × 0.0475) = 1.3067 in 32 0.95105652 1 N − 6.9758 + (2.7475 × t n ) Pn cos ψ 1 32
38 − 6.9758 + (2.7475 × 0.0475) = 1.1611 in 0.95105652
318
4 Thermoplastic Gearing Design
Given the normal circular tooth thickness of a helical pinion having a small number of teeth, the maximum outside diameters that will provide an adequate top land is obtained by using the following equation. DO (Max.) =
N × cos φ Pn × cos ψ × 1.017 × cos φ1
Where: DO (Max.) = Maximum outside diameter (in) tn = Normal circular tooth thickness (in) ψ = Helix angle (degrees) 0.36397023 φ = tan −1 cos ψ t × Pn + Inv φ Inv φ1 = n N
Example 4-20 A helical pinion has 10 teeth (N), a normal diametral pitch (Pn) of 32, a helix angle (ψ) of 18°, and a normal circular tooth thickness (tn) of 0.0666 in. Determine the maximum outside diameter. N = 10, Pn = 32, ψ = 18°, cos ψ = 0.95105652 0.36397023 = tan −1 φ = tan −1 cos ψ
0.36397023 = 20.9419° 0.95105652
cos φ = 0.93394337 Inv φ = 0.01719592 Inv φ1 =
t n × Pn 0.0666 × 32 + Inv φ = + 0.01719592 = 0.23031 N 10
φ1 = 45.8404° cos φ1 = 0.697165 N × cos φ Pn × cos ψ × 1.017 × cos φ1 10 × 0.93394337 = = 0.4328 in 32 × 0.951056 × 1.017 × 0.662745
DO (Max.) =
Find the outside diameter using the other equation: DO = =
1 N − 2.3158 + (2.7475 × t n ) Pn cos ψ 1 10 − 2.3158 + (2.7475 × 0.0666) = 0.4391 in 32 0.95105652
The outside diameter of 0.4328 in should be specified for the helical gear, because it is the smaller outside diameter value obtained by the two equations.
319
4.11 PGT Helical Thermoplastic Gearing
Example 4-21 A helical gear has 16 teeth (N), a normal diametral pitch (Pn) of 24, a helix angle (ψ) of 18°, and the PGT-1 tooth form design. Determine the minimum normal circular tooth thickness required to avoid undercutting of the teeth. Pn = 24, N = 16, ψ = 18°, cos ψ = 0.95105652 0.36397023 = tan −1 φ = tan −1 cos ψ
0.36397023 = 20.9419° 0.95105652
cos φ = 0.93394337 cos2φ = 0.87225022 Normal circular tooth thickness: tn = =
4.11.1
N × (1 − cos2 φ 2.3329 − 2.7475 × cos ψ
1 Pn
1 16 × (1 − 0.87225) 2.3329 − = 0.0646 in 24 2.7475 × 0.951056
PGT-1 Helical Mating Gears Strength Balance
The number of teeth, the normal diametral pitch, the pressure angle, and the helix angle of a pair of mating PGT-1 helical gears are used to calculate the normal circular tooth thicknesses. The gear material bending stress multiplied by the ratio between the tooth whole depth divided by the normal circular tooth thicknesses should be equal to the balanced strength of both helical gears. The following group of equations should be used, based on the number of teeth obtained by Equation 4-25. Number of teeth (N) =
2.0938 × cos ψ 1 − cos φ
(4-25)
Helical pinion and gear less than 30 teeth, normal circular tooth thickness t nP =
1 Pn
0.36397023 × N P × (1 − cos φ) 2.3329 − cos ψ
(4-26)
t nG =
1 Pn
0.36397023 × N G × (1 − cos φ) 2.3329 − cos ψ
(4-27)
Helical pinion has less than 30 teeth and gear has 30 teeth or more, to calculate the normal circular tooth thicknesses 0.36397023 × N P × (1 − cos φ) 2.3329 − cos ψ
t nP =
1 Pn
t nG =
NG Pn
Pn × B × cos ψ N − (2.0938 × cos ψ) + Inv φG − Inv φ G
(4-26)
(4-28)
320
4 Thermoplastic Gearing Design Helical pinion and gear have 30 teeth or more, to calculate the normal circular tooth thicknesses N × N G − (2.0938 × cos ψ) t nG Inv φ − Inv φP t nP = P + Pn N P − (2.0938 × cos ψ) N G
(4-29)
Inv φ − Inv φP − NP Pn
t nG =
B=
NG Pn × B × cos ψ + Inv φG − Inv φ Pn N G − (2.0938 × cos ψ)
N P × cos φ Pn × t nP + Inv φ Pn × cos ψ N P
N P × cos φ φP = cos −1 N P − (2.0938 × cos ψ) N G × cos φ φG = cos −1 N G − (2.0938 × cos ψ)
Where: Pn = Normal diametral pitch B = Helical tooth thickness constant N = Number of teeth (determining which equation to use) ψ = Helix angle (degrees) NP = Number of teeth in pinion NG = Number of teeth in gear tnP = Normal circular tooth thickness of pinion (in) tnG = Normal circular tooth thickness of gear (in) 0.36397023 φ = Pressure angle = tan −1 cos ψ Example 4-22 A helical pinion having 10 teeth (NP) drives the gear having 24 teeth (NG). The normal diametral pitch (Pn) is 24, and the helix angle (ψ) is 18°. The PGT-1 tooth form design is required. Determine the normal circular tooth thicknesses for a balanced tooth’s strength. Pn = 24, NP = 10, NG = 24, ψ = 18°, cos ψ = 0.95105652 0.36397023 0.36397023 φ = tan −1 = tan −1 = 20.9419° 0.951056532 cos ψ cos φ = 0.93394337 N =
2.0938 × cos ψ 2.0938 × 0.95105652 = = 30.146 or 30 teeth 1 − cos φ 1 − 0.93394337
4.11 PGT Helical Thermoplastic Gearing
Because both helical pinion and gear have less than 30 teeth, Equations 4-26 and 4-27 are selected to calculate the normal circular tooth thicknesses of the pinion and the gear to obtain a balanced strength for both teeth. 0.36397023 × N P × (1 − cos φ) 2.3329 − cos ψ 1 0.36397023 × 10 × (1 − 0.93394337) = 2.3329 − = 0.0866 in 24 0.95105652
t nP =
1 Pn
0.36397023 × N G × (1 − cos φ) 2.3329 − cos ψ 1 0.36397023 × 24 × (1 − 0.93394337) = 2.3329 − = 0.0719 in 24 0.95105652
t nG =
1 Pn
Normal circular tooth thickness of pinion = 0.0866 in Normal circular tooth thickness of gear = 0.0719 in
Example 4-23 A helical pinion having 16 teeth (NP) drives a gear having 36 teeth (NG). The normal diametral pitch (Pn) is 24, and the helix angle (ψ) is 18°. The PGT-1 tooth form design is required. Determine the normal circular tooth thicknesses for a balanced tooth’s strength. Because the pinion has less than 30 teeth and the gear has more than 30 teeth, select Equations 4-26 and 4-28. Pn = 24, NP = 16, NG = 36, cos φ = 0.93394, cos ψ = 0.951056, φ = 20.9419°, inv φ = 0.01719592 0.36397023 × N P × (1 − cos φ) 2.3329 − cos ψ 1 0.36397023 × 16 × (1 − 0.93394337) = 2.3329 − = 0.0847 in 24 0.95105652
t nP =
1 Pn
N G × cos φ φG = cos −1 N G − (2.0938 × cos ψ) 36 × 0.93394337 −1 = cos −1 = cos (0.988628) = 8.75° − × 36 (2.0938 0.95105652) Inv φG = 0.000099842 B= =
N P × cos φ Pn × t nP + Inv φ Pn × cos ψ N P 16 × 0.93394337 24 × 0.0847 + 0.01719592 = 0.0901137 24 × 0.95105652 16
321
322
4 Thermoplastic Gearing Design
Pn × B × cos ψ + inv φG − inv φ − × N ψ (2.0938 cos ) G 36 24 × 0.0901137 × 0.95105652 = + 0.00009984 − 0.01719592 24 36 − (2.0938 × 0.95105652) = 0.0694 in
t nG =
NG Pn
Normal circular tooth thickness of pinion = 0.0847 in Normal circular tooth thickness of gear = 0.0694 in
4.11.2
PGT-1 Helical Mating Gears Center Distance
Given the number of teeth for the mating helical pinion and gear, the diametral pitch, the helix angle, and the PGT-1 tooth form design, the center distance at which the gears are in close mesh is determined by Equation 4-30. Center distance = C =
(N P + N G ) × cos φ 2 × Pn × cos ψ × cos φP
(4-30)
Where: N = Number of teeth, determined by Equation 4-25 ψ = Helix angle (degrees) NP = Number of teeth in pinion NG = Number of teeth in gear tnP = Normal circular tooth thickness of pinion (in) tnG = Normal circular tooth thickness of gear (in) 0.36397023 φ = Pressure angle = tan −1 cos ψ P (t + t nG ) − π φP = Angle whose involute is n nP + Inv φ NP + NG Example 4-24 Two mating PGT-1 helical gears have the basic specifications given below. Find the center distance at which they will be in close mesh. Specifications
Pinion
Gear
Number of teeth (N)
14
38
Normal diametral pitch (Pn)
32
32
Helix angle (ψ)
18°
18°
Tooth form design
PGT-1
PGT-1
Normal circular tooth thickness on standard pitch circle (tn)
0.0618
0.0372
NP = 14, NG = 36, Pn = 32, tnP = 0.0618, tnG = 0.0372, ψ = 18°, cos = 0.95105652
0.36397023 = tan −1 φ = tan −1 cos ψ
0.36397023 = 20.9419° 0.95105652
323
4.12 PGT Spur and Helical Gears Horsepower Rating cos φ = 0.93394337 Inv φ = 0.01719592 Inv φP = =
Pn (t nP + t nG ) − π + Inv φ NP + NG 32 (0.0618 + 0.0372) − 3.1416 + 0.01719592 = 0.0177 14 + 38
φP = 21.166 cos φP = 0.932538 (N P + N G ) cos φ (14 + 38) × 0.93394337 = 2 × Pn × cos ψ × cos φP 2 × 32 × 0.95105652 × 0.932538 = 0.8556 in
C=
Close mesh center distance = 0.8556 in
4.12
PGT Spur and Helical Gears Horsepower Rating
In this section, a more sophisticated equation will be formulated specifically for use in estimating the load carrying capacity of injection molded thermoplastic spur and helical gears, designed conforming to the Plastic Gearing Technology Tooth System. Because of the number of various thermoplastic materials developed for gear applications, it is suggested that the technical representative of the plastic supplier under consideration be consulted. It is desirable to obtain the most recent information on their materials’ load bearing strength capacity, coefficient of friction, wear, mold shrinkage, and the injection molding characteristics of the thermoplastics. The fundamental horsepower Equation 4-31 is valid for spur and helical injection molded thermoplastic gears. HP =
DP × F × n × J × σ × K T × K L 126,000 × P × SF × K S
Where: HP = Horsepower DP = Operating pitch diameter of gear dP = Operating pitch diameter of pinion NG = Number of teeth of gear NP = Number of teeth of pinion F = Effective face width (in) n = Speed (rpm) J = PGT gear system geometry factor (Table 4-15) σ = Tensile stress of the thermoplastic material (psi) KT = Temperature factor T = Maximum application temperature of the gears (°F) KL = Life factor P = Diametral pitch SF = Service factor (Table 4-16)
(4-31)
324
4 Thermoplastic Gearing Design KS = Safety factor Number of Teeth of Gear (N G ) R = Ratio = Number of Teeth of Pinion (N P ) dP =
2×C R +1
(4-32)
DP =
2×C ×R R +1
(4-33)
4.12.1
PGT Gear Horsepower Equation Basic Parameters
Operating Pitch Diameter (DP , dP) The operating pitch diameter of a pinion and gear cannot be determined until it is meshing with its mate at a definite operating center distance. Knowing the operating center distance and the numbers of teeth in two mating gears, the operating pitch diameters are obtained by using Equations 4-32 and 4-33. The gear having the lesser number of teeth is referred to as the pinion and its mate as the gear. Effective face width (F) F = Effective face width that is in contact with the mating gear. Speed (n) n = Number of revolutions turned in one minute. Table 4-15 PGT Gear System Geometry Factor (J) (Courtesy: ABA/PGT)
Tooth design
PGT-1
PGT-2
Geometry factor (J)
0.75
0.65
PGT gear system geometry factor (J) The geometry factors (J) for PGT-1 and PGT-2 tooth form designs are given in Table 4-15. Tensile stress of the thermoplastic (σ) The tensile stress of the injection molding thermoplastic resin may be obtained from the resin supplier’s published properties information, either directly from the technical representative, or from the marketing technical organization of the specific injection molding thermoplastic chosen for the gear application. Temperature factor (KT ) The temperature factor allows for the decrease in the tensile stress of a thermoplastic material with an increase in temperature. KT = 1.0 – [(T – 73) × 0.003] Life factor (KL) The life factor adjusts the horsepower rating for the number of cycles required of the gear before it fails. KL = 1.0 – (log M / 5) Where: M = HP rating failure requirements =
n × Hours to Failure × 60 1,000,000
325
4.12 PGT Spur and Helical Gears Horsepower Rating Normal diametral pitch (P) P = Diametral pitch of a spur or helical gears. PGT gear system service factor (SF) The service factor takes into account the nature of the load on the mechanism driven by the gears. The service factor value is obtained from the table below. Table 4-16 PGT Gear System Service Factor (SF) (Courtesy: ABA/PGT)
Type of load
Occasional 1/2 hour/day
Intermittent 3 hours/day
8–10 hours/day
24 hours/ day
Steady Light shock Medium shock Heavy Shock
0.50 0.80 1.00 1.25
0.80 1.00 1.25 1.50
1.00 1.25 1.50 1.75
1.25 1.50 1.75 2.00
Safety factor (KS) The value given to the safety factor ranges from 1.0 to 3.0, sometimes even higher than that. As long as the gears have an adequate contact ratio and a high percentage of recess action, they are designed as specified for a power drive and have teeth of balanced strength, they have some degree of lubrication and the designer has complete confidence in the data relating to the properties of the injection molding thermoplastic materials to be used for the gears, then there is no reason why the safety factor should be greater than 1.0. If a high degree of reliability is desired, the safety factor could be increased to 1.25 or, possibly, 1.50. On the other hand, if the designer has found it necessary to make compromises because of circumstances beyond his or her control, then the extent to which the gears have been weakened must be assessed and the safety factor increased accordingly. Prototype gears for testing can be produced from a single cavity MUD universal frame tool at a reasonable price. No amount of theorizing can substitute for testing prototype gears in the mechanism they will be required to drive and under the conditions to which they will be subjected in the field. Example 4-25 A pair of helical gears is designed for a speed-reducing drive in a domestic appliance. The pinion and gear have 14 and 38 teeth, respectively and a normal diametral pitch of 32. The PGT-1 tooth design is specified and the teeth are designed to have balanced strength. The operating center distance is 0.8556 in, with a pinion and gear face width of 0.800 inches. The pinion rotates at a speed of 1,800 rpm. The drive operates intermittently for one or two hours per day and is subject to light shock loading. A life of 3,000 hours is required. The helical gears are grease-lubricated. The pinion is injection molded of a thermoplastic material having a tensile stress of 9,500 psi and the gear is made of a thermoplastic material having a tensile stress of 8,000 psi. Determine the horsepower rating for the helical pinion: HP =
DP × F × n × J × σ × K T × K L 126,000 × P × SF × K S
326
4 Thermoplastic Gearing Design
1) Operating pitch diameter (dP) C = 0.8556 , R = dP =
NG 38 = = 2.714 NP 14
2 × C 2 × 0.8556 = = 0.46 R +1 2.714 + 1
2) Effective face width (F) F = 0.800 in 3) Speed (n) n = 1,500 rpm 4) PGT gear system geometry factor (J) J = 0.75 (from Table 4-15) 5) Tensile stress of the thermoplastic (σ) σ = 9,500 psi 6) Temperature factor (KT) T = 175 °F K T = 1.0 − [(T − 73) × 0.003] = 1.0 − [(175 − 73) × 0.003] = 0.694 7) Life factor (KL) K L = 1.0 − (log M /5) M =
n × Hours to Failure × 60 1,000,000
n = 1,800 rpm Hours to failure = 3,000 M =
1,800 × 3,000 × 60 = 324 1,000,000
K L = 1.0 − log (324 /5) = 0.484 8) Normal diametral pitch (P) P = 32 9) PGT gear system service factor (SF) SF = 1.0 (from Table 4-16)
4.12 PGT Spur and Helical Gears Horsepower Rating
10) The factor of safety (KS) The pinion and gear are designed for a power drive and have balanced tooth strength. The contact ratio is 2.714 and there is 75% recess action. A degree of lubrication is provided. A safety factor of 1.2 would be adequate for good reliability. KS = 1.2 HP (Gear) = =
DP × F × n × J × σ × K T × K L 126,000 ⋅ P ⋅ SF ⋅ K S 0.46 × 0.80 × 1,800 × 0.75 × 9,500 × 0.694 × 0.484 = 0.327 126,000 × 32 × 1.0 × 1.2
Example 4-26 Determine the horsepower rating for the gear in Example 4-25. HP (Gear) =
DP × F × n × J × σ × K T × K L 126,000 × P × SF × K S
1) Operating pitch diameter (DP) DP =
2 × C × R 2 × 0.8556 × 2.714 = = 1.120 R +1 2.714 + 1
2) Effective face width (F) F = 0.800 in 3) Speed (n) n = 1,800/2.714 = 663.22 rpm 4) PGT gear system geometry factor (J) J = 0.75 (from Table 4-15) 5) Tensile stress of the thermoplastic (σ) σ = 8,000 psi 6) Temperature factor (KT) T = 175 °F K T = 1.0 − [(T − 73) × 0.003] = 1.0 − [(175 − 73) × 0.003] = 0.694 7) Life factor (KL) K L = 1.0 − (log M /5)
327
328
4 Thermoplastic Gearing Design
M =
n × Hours to Failure × 60 1,000,000
n = 663.22 rpm Hours to failure = 3,000 M =
663.22 × 3,000 × 60 = 119.38 1,000,000
K L = 1.0 − log (119.38/5) = 0.545 8) Normal diametral pitch (P) P = 32 9) PGT gear system service factor (SF) SF = 1.0 (from Table 4-16) 10) Safety Factor (KS) KS = 1.2 HP (Gear) =
DP × F × n × J × σ × K T × K L 126,000 × P × SF × K S
1.120 × 0.80 × 663.22 × 0.75 × 8,000 × 0.694 × 0.545 126,000 × 32 × 1.0 × 12 = 0.278
=
The horsepower rating for the helical pinion is 0.327, and it is higher than the rating for the helical gear (0.278). To establish the horsepower rating for the drive, select the lower calculated value of the helical pinion and gear. The calculated horsepower rating of the drive is 0.278.
4.13
PGT Spur and Helical Gear Specifications
The final step in designing a gear is the preparation of a drawing which lists the gear documentation. The data must be specified in a way that there is no possibility of misinterpretation. This might appear to be self-evident, but all too often, ambiguity in writing gear specifications has resulted in costly and timeconsuming changes to be performed to the expensive gear mold. There are three types of data specifications on the gear documentation: • The first group consists of data basic to the design of the gear; • The second group consists of data used in the injection molding and inspection • The third group consists of engineering reference data. Table 4-17 is based on the American Gear Manufacturers Association, Standards Department; this table may be used as a gear designer’s checklist for the various documentation that accompanies a gear drawing.
329
4.13 PGT Spur and Helical Gear Specifications
X
X
Diametral pitch
X
Normal diametral pitch
X
X
Basic specifications
4 5
X
Transverse pressure angle
6 X
7
Helix angle
X
8
Hand of helix
X
9
Standard pitch diameter
X
X
10
Tooth form
X
X
11
Addendum
X
12
Whole depth
X
13
Max. calculation of circular thickness on standard pitch circle
X
Max. calculation of normal circular thickness on standard pitch circle
Manufacturing and inspection
3 X
Normal pressure angle
Engineering reference
1 2
Transverse diametral pitch Pressure angle
Item number
Number of teeth
Optional
Gear design documentation
Helical gear
Type of data
Spur gear
Table 4-17 Spur and Helical Gears Designer Check List (Courtesy: American Gear Manufactures Association)
14 X
15
Gear testing radius
X
X
16
A.G.M.A. quality class
X
X
17
Maximum total composite error
X
X
18
Maximum tooth-to-tooth composite error
X
X
19
Testing pressure (oz) Master gear specifications
X X
X
Measure over two 0.xxx diameter pins (for setup only) Outside diameter (preferably shown on drawing of gear)
21 X
X
20
X
22 23
Maximum root diameter
X
24
Active profile diameter
X
25
Surface roughness of active profile
X
26
Mating gear part number
X
27
Number of teeth in mating gear
X
28
Minimum operating center distance
X
29
330
4 Thermoplastic Gearing Design Tables 4-18 and 4-19 are illustration tables for the data that should appear on the drawing of a PGT-1 tooth design pinion and spur gear. The last two specification tables (Tables 4-20 and 4-21) are illustration tables for the data that should appear on the drawing of a PGT-1 tooth design helical pinion and gear. The gear documentation is presented in a format recommended by the American Gear Manufacturers Association. Some of the information is redundant; however, it is provided for the convenience of the personnel in manufacturing and inspection departments. The PGT tooth form design is best specified by including it on the dimensioned drawing of the basic gear. The basic gear documentation for the PGT system tooth form design is based on 1.0 diametral pitch (Tables 4-8, 4-9, 4-10, and 4-11), for other diametral pitch sizes, the given values should be divided by the required diametral pitch to obtain the circular tooth thickness, the outside diameter, and the root diameter. During the gear inspection, performance requires that the injection molded thermoplastic gear be brought into close mesh with a master gear of known accuracy in a center distance measuring instrument. The testing radius of the gear is the center distance, as measured, less half the pitch circle diameter of the master gear. As the gear is rotated with the master through 360°, the center distance and, as a consequence, the testing radius will vary from a high to a low value (see Figure 4-45). For the gear to be acceptable, the high and low values must be within the maximum and minimum tolerance limits specified. The specifications of the master gear are supplied by the gear mold maker; consequently, the master gear should not be purchased at the time the gear drawing is being prepared. In that event, the testing radius specified can be the value that would apply if the master were a theoretically perfect gear of a known pitch circle diameter, or if the gears were to be rotated in close mesh with a standard gear. Once the master gear is available, it is preferable to change the testing radius to conform to the specifications supplied and to specify the master gear to be used by a tool number. To determine the testing radius to be specified in the documentation, the close mesh center distance is calculated by employing the center distance (C) equation. Two calculations are made: one for the maximum and the other for the minimum calculated circular tooth thickness of the gear. To the maximum center distance is added half the total composite tolerance and from the minimum is subtracted half the total composite tolerance. These are the maximum and minimum values of the close mesh center distance that are obtained as the gear is rotated with the master gear using a center distance measuring instrument. To obtain the maximum and minimum values of the testing radius half the pitch circle diameter of the master is subtracted from the maximum and minimum values of the close mesh center distance. If the prototype plastic machined gears prove to be unsatisfactory in testing, gear changes are made by a few adjustments to the settings of the machine used to cut the teeth. But, for injection molding the first samples of thermoplastic gear changes are considered only after the prototype or the production mold has been built. If the injection molded thermoplastic gear requires design modifications on the mold, these unexpected changes are both time-consuming and costly. It is essential, therefore, that the final design of an injection molded thermoplastic gear be the result of close study and that the data appearing on the drawing be exact and specified, so that there is no possibility of data misinterpretation.
331
4.13 PGT Spur and Helical Gear Specifications Table 4-18 PGT Spur Pinion Specifications Example (Courtesy: Plastics Gearing Technology, Inc.)
Engineering references
Manufacturing and inspection
Basic specifications
Spur pinion documentation
Values
Number of teeth
15
Diametral pitch
76
Pressure angle
20°
Standard pitch diameter
0.1974
Tooth form
PGT-4
Addendum
0.0178
Whole depth
0.0399
Calculated normal circular tooth Thickness on standard pitch circle
0.0278 Max. 0.0268 Min.
Gear testing radius
0.1093 Max. 0.1059 Min.
AGMA quality number
Q7
Maximum total composite tolerance
0.0021
Max. tooth-to-tooth composite tolerance
0.0015
Master gear specifications
152 T, 0.0207 CTT
Testing pressure (oz)
5
Diameter of measuring pin
0.025
Measurement over two pins (setup only)
0.2475 Max. 0.2458 Min.
Outside diameter
0.2440 Max. 0.2410 Min.
Maximum root diameter
0.1728
Mating Gear Part Number
Gear
Number of teeth in mating gear
120
Operating center distance
0.8780 Max. 0.8750 Min.
332
4 Thermoplastic Gearing Design Table 4-19 PGT Spur Gear Specifications Example (Courtesy: Plastics Gearing Technology, Inc.)
Engineering references
Manufacturing and inspection
Basic Specifications
Spur gear documentation
Values
Number of teeth
120
Diametral pitch
76
Pressure angle
20°
Standard pitch diameter
1.5789
Tooth form
PGT-4
Addendum
0.0178
Whole depth
0.0399
Calculated normal circular tooth Thickness on standard pitch circle
0.0017 Max. 0.0007 Min.
Gear testing radius
0.7630 Max. 0.7590 Min.
AGMA quality number
Q7
Maximum total composite tolerance
0.0025
Max. tooth-to-tooth composite tolerance
0.0012
Master gear specifications
152 T, 0.0207 CTT
Testing pressure (oz)
5
Diameter of measuring pin
0.028
Measurement over two pins (setup only)
1.5777 Max. 1.5744 Min.
Outside diameter
1.5630 Max. 1.5580 Min.
Maximum root diameter
1.4826
Mating gear part number
Pinion
Number of teeth in mating gear
15
Operating center distance
0.8780 Max. 0.8750 Min.
333
4.13 PGT Spur and Helical Gear Specifications Table 4-20 PGT Helical Pinion Specifications Example (Courtesy: Plastics Gearing Technology, Inc.)
Engineering references
Manufacturing and inspection
Basic specifications
Helical pinion documentation
Values
Number of teeth
15
Normal diametral pitch
16
Normal pressure angle
20°
Helix angle
18°
Hand of helix angle
R.H.
Standard pitch diameter
0.9857
Tooth form
PGT-1
Addendum
0.0625
Whole depth
0.1456
Calculated normal circular tooth Thickness on standard pitch circle
0.1221 Max. 0.1201 Min.
Gear testing radius
0.5259 Max. 0.5191 Min.
AGMA quality number
Q7
Maximum total composite tolerance
0.0043
Max. tooth-to-tooth composite tolerance
0.0021
Master gear specifications
N = 30, tn = 0.0982
Testing pressure (oz)
15
Diameter of measuring pin
0.110
Measurement over two pins (setup only)
1.1835 Max. 1.1798 Min.
Lead
9.5310
Outside diameter
1.1770 Max. 1.1710 Min.
Maximum root diameter
0.8853
Mating gear part number
Gear
Number of teeth in mating gear
45
Operating center distance
2.0160 Max. 2.0110 Min.
334
4 Thermoplastic Gearing Design Table 4-21 PGT Helical Gear Specifications Example (Courtesy: Plastics Gearing Technology, Inc.)
Engineering references
Manufacturing and inspection
Basic specifications
Helical gear documentation
Values
Number of teeth
45
Normal diametral pitch
16
Normal pressure angle
20°
Helix angle
18°
Hand of helix angle
L.H.
Standard pitch diameter
2.9572
Tooth form
PGT-1
Addendum
0.0625
Whole depth
0.1456
Calculated normal circular tooth Thickness on standard pitch circle
0.0961 Max. 0.0941 Min.
Gear testing radius
1.4781 Max. 1.4707 Min.
AGMA quality number
Q7
Maximum total composite tolerance
0.0047
Max. tooth-to-tooth composite tolerance
0.0017
Master gear specifications
N = 30, tn = 0.0982
Testing pressure (oz)
15
Diameter of measuring pin
0.110
Measurement over two pins (setup only)
3.1095 Max. 3.1044 Min.
Lead
28.5930
Outside diameter
3.0770 Max. 3.0710 Min.
Maximum root diameter
2.7853
Mating gear part number
Pinion
Number of teeth in mating gear
15
Operating center distance
2.0160 Max. 2.0110 Min.
335
5
Plastic Journal Bearing Design
5.1
Introduction
A journal bearing is a simple device for providing support and radial positioning while permitting rotation of a shaft. It is the oldest bearing device known to man, yet it is as modern as the latest materials and technologies available today. A great variety of plastic materials can be used for journal bearings. These materials include a number of composites, such as acetal homopolymer, acetal with Teflon® powder, chopped fiber and fabric, unreinforced and internally lubricated or with molydisulfide nylon 6/6, nylon 66 with Teflon® powder, chapped fiber, fabric, polysulfone with glass fiber and Teflon®, polycarbonate with glass fiber and Teflon®, PTFE, sintered metals, wood, rubber, bronze, among others. Bearing types range from simple thermoplastic sleeve bearings to some exceedingly complex gas-lubricated high-speed rotor bearings. The journal bearing is inherently quiet in operation, because it has no moving parts. With proper selection, installation and lubrication, it does not fail suddenly. Wear, if any, is gradual and replacement of worn bearings can be scheduled when equipment is normally idle. These bearings are uniquely suited to conditions involving oscillating or longitudinal movement. Journal bearings are subject to their environments and must be properly selected and used with proper control of shaft tolerances, housings, mounting or installation procedures, lubrication, and so forth. Plastic journal bearings can be divided into two general groups, based on the technical requirements, which can be entirely different: • Injection molded, compression molded, and machined sleeve bearings that are pressed or mounted into metal or thermoplastic housings. The main requirements in these cases are, first of all, excellent bearings and wear properties. Impact resistance and tensile strength as well as dimensional stability are considerations of lesser importance. • Composite journal bearings are exposed to wear, as a part of a larger unit, e.g., a gear box, spherical joint bearings, and others. In these applications, all mechanical and physical properties of the composite journal bearings are extremely important.
5.2
Materials Used for Journal Bearings
Numerous materials are employed to meet the needs of special applications. Although babbitt and bronze are the materials used in many applications, the technology is rapidly changing, particularly with the advent of new thermoplastics, sintered metals, and plastic composites. The selection of the most desirable material for a particular application can become a complex decision; however, there are certain applications in which a particular type of material excels.
336
5 Plastic Journal Bearing Design
5.2.1
Babbitt Journal Bearings
Babbitt journal metal bearings are universally accepted as providing reasonable capacity and dependable service, often under adverse conditions. Babbit is a relatively soft bearing material, therefore it minimizes the danger of scoring or damage of large expensive shafts or rotors. Babbitt can often be repaired quickly on the spot by rescraping, pouring of new metal, and so forth. The actual bearing operating temperature must not exceed 200 °F. Babbitt journal metal bearings are used for applications involving light to moderate loadings; bronze is required for heavier loadings or higher temperatures.
5.2.2
Bronze Journal Bearings
Bronze journal bearings are suitable for heavier loads with capacities ranging from 75 to 200% higher than Babbitt, depending on the specific ranges of loads and speeds. Bronze bearings withstand higher shock loads than Babbitt bearings, permit slightly higher speed of operation, and are used at operating temperatures up to 300 °F. Bronze is a harder material than babbitt and therefore has a greater tendency to score or damage journals if there are malfunctions. Field repair of a bronze bearing generally requires replacement of the bronze bearing bushing.
5.2.3
Sintered Porous Metal Journal Bearings
An increasingly popular bearing material is sintered porous metal, which is usually a bronze alloy, iron alloy, and stainless steel. Sintered porous metals provide an excellent design for boundary lubrication conditions. In the fabrication of this type of bearing, the powdered metal alloy is first pressed in dies to a controlled density and then sintered at high temperature in a reducing atmosphere. Any subsequent machining of the part must be controlled with proper tooling and machining techniques so that the open pore structure is maintained. The sintered porous metal journal bearing material functions somewhat like a sponge, wherein the lubricant is retained in the voids. These voids normally make up about 20% of the volume of the sintered porous metal journal bearing. Oils used for impregnation should be non-gumming types, resistant to oxidation. In operation, the development of heat or pressure between the shaft and the plain bearing initiates a capillary action, bringing a measured quantity of oil to the surface for lubrication. This type of bearing will function until the supply of lubricant contained within the sintered porous metal journal bearing is exhausted. An additional supply of lubricant is provided in a wicking type material surrounding the sintered porous metal journal bearing, with provision for additional replenishment through the oil supply reservoir.
5.2.4
Plugged Bronze Journal Bearings
The plugged bronze journal bearing is a hybrid combining the characteristics of cast bronze and carbon-graphite. The basic bronze bearing is provided with a series of holes or grooves that are filled with plugs of a solid lubricant compound of carbon-graphite, metallic oxides, waxes, or organic salts. These individual solid lubricant reservoirs are uniformly spaced around the plugged bronze journal bearing to provide a continuous distribution of a uniform film of low friction solid lubricant over the entire contact surface. This self lubricating plugged
5.2 Materials Used for Journal Bearings bronze journal bearing is generally suitable for temperatures up to 500 °F and is less susceptible to shock than the pure carbon-graphite bearing.
5.2.5
Carbon-Graphite Journal Bearings
Carbon-graphite is utilized for journal bearing applications, in particular at temperatures up to 700 °F or even higher, when the use of conventional bearings and lubricants is next to impossible. This journal bearing utilizes a carbongraphite bushing (liner). The carbon-graphite bearing is entirely self-lubricating; in essence, the bearing itself is the lubricant. In service, this solid lubricant is gradually consumed with shaft and bearing clearance gradually increasing as the solid lubricant is used. These types of carbon-graphite journal bearings have been applied in ovens, dryers, furnaces, and so forth, where loads are light and speeds low. They are often used in environmental applications because of the basic inertness of the carbon-graphite material. As an extreme example, the carbon-graphite journal bearings have been used successfully in pumps transporting molten salt at 1200 °F.
5.2.6
Cast-iron Journal Bearings
Cast-iron journal bearings are low in cost and very suitable for many moving shafts and oscillating or reciprocating arms supporting light loads. The lubricating characteristics of cast iron are attributed to the free graphite flakes present in the alloy. With the use of cast-iron journal bearings, higher shaft clearance is usually provided. Any large wear particles or extraneous debris will not jam the clearance space and seize the bearing. These bearings have been applied in temperatures as high as 1000 °F under light loads and at slow speed intermittent operation.
5.2.7
Wooden Journal Bearings
Wooden journal bearings are still used in a remarkably large number of applications. Light duty machinery frequently employs small oil impregnated hard maple bearings. For heavy duty operations in water or other liquids, lignum vitae wooden bearings are employed. Native only to the Caribbean, lignum vitae is the hardest of all woods. Its specific gravity of 1.25 and closely interwoven grain structures give the wood a high resistance to wear, compression, and splitting. This material has a resin content of 30% by volume, providing a remarkable self lubricating quality. It is unaffected by salt water, mild acids, alkalis, oils, bleaching compounds, and liquid phosphorous and is often used in chemical processing and food processing industries. The operating temperatures for wooden journal bearing should not exceed 150 °F.
5.2.8
Rubber Journal Bearings
Rubber has been a surprisingly effective journal bearing material when immersed in water and other liquids. It is especially useful for light loads accompanied by abrasive conditions, such as sand and grit. For example, water lubricated rubber journal bearings for propeller shafts of ships operating in shallow sandy water have demonstrated better results concerning wear than bronze or wooden bearings. The rubber must never run dry, even when starting and the shaft must be particularly smooth. The inner surface of the rubber journal bearing is fluted to provide passage for the coolant lubricant and to improve distribution.
337
338
5 Plastic Journal Bearing Design
5.2.9
Self-Lubricated Thermoplastic Journal Bearings
Self-lubricated thermoplastic bearings offer a growing class of designs, having a low coefficient of friction, reduced wear rates, resistance to impact and vibration, elimination of lubrication, and cleanliness. The different plastic bearing families are: The Teflon® fabric composite bearings with metal support backing, Vespel® bearings, and the thermoplastic bearings reinforced with Kevlar® chopped fibers. The compounded thermoplastic resins commonly used for journal bearing applications are fluorocarbons, nylon 6/6, acetal homopolymer, high density polyethylene, polypropylene, polysulfone, reinforced polycarbonate, and phenolic. These thermoplastic composites are engineered for self lubricated bearings and have different properties such as friction, strength, heat resistance, chemical resistance, wear, cost, and so forth. These materials are commonly used in journal bearing applications involving corrosives, abrasives, and lubrication problems. Requirements of reliability, serviceability, and cost in electro-mechanical data processing machines make optimum material selection, design, and fabrication a necessity. Because of these requirements, the use of self lubricating materials has become increasingly important. For several years, certain types of thermoplastic materials such as nylon 6/6 and acetal homopolymer have been used in self lubricating journal bearing applications because of the following desirable properties: • Low coefficient of friction against steel • Good wear resistance • Quiet operation • Operable without lubrication • Easily fabricated at low cost • Low density • Extended design freedom Most thermoplastic journal bearings are self lubricated, or they are only initially lubricated. Occasionally, thermoplastic journal bearings are used with complete hydrodynamic lubrication. The procedure for designing a fully lubricated thermoplastic journal bearing is more dependent on the properties of the lubricant than upon the properties of the bearing material. This is particularly true for hydrodynamically lubricated metal bearings. The design information presented here is for self lubricated thermoplastic journal bearings. Although the data applies specifically to journal bearings, it appears that it can also be used conservatively for plane surface or thrust bearings. In recent years, new polymers and a vast variety of composite materials have been introduced, many supposedly with excellent bearing properties. Because their wear surface has such excellent lubricity, Teflon® fabric bearings never need lubrication. The lubrication is inherent in the bearing surface so there is no danger of these bearings drying out and thus causing shaft seizure and costly repairs. Various additive compounds such as graphite, molybdenum disulfide, aluminum, calcium and other stearates, Teflon®, TFE fluorocarbon powder/fibers, and
5.3 Hydrodynamics of Lubrication petroleum hydrocarbons have been used singly and in combination as low coefficient of friction additives for thermoplastics to reduce friction and improve their bearing characteristics.
5.3
Hydrodynamics of Lubrication
The classic hydrodynamic lubrication is the most desired mode of operation for a journal bearing. The principle of the load-carrying lubricant film is straight forward, although the mathematical equations become complex. As the shaft revolves within the bearing, the motion of the shaft forces the lubricant to flow in the direction of rotation. In the area of highest loads, the shaft is displaced from the geometric center of the bearing by the applied loads. As the distance between shaft and bearing decreases at the load zone, a wedge-shaped clearance is created, ranging from the high clearance space opposite the load zone to the minimum clearance space at the load zone. The lubricant entrained by the shaft and carried into the diminishing clearance wedge is squeezed severely. The lubricant used with the journal bearing is essentially incompressible; a pressure is developed within the oil film that is sufficient to support the applied load. So long as the fluid film wedge is of sufficient thickness to prevent metal to plastic contact between shaft and sleeve, the bearing is operating with perfect fluid film lubrication. The load carrying ability of the full film lubricant wedge is largely dependent on lubricant viscosity and the relative velocity between shaft and bearing. With insufficient velocity and/or viscosity, the lubricant wedge will not develop. Direct contact will occur between the shaft and journal bearing’s surface, with the separating film of lubricant being wholly or partially excluded. Where operating speeds are insufficient to produce hydrodynamic lubrication, the hydrostatic principle of lubrication is often employed. With hydrostatic lubrication the necessary pressure to support the applied load is provided from an external source. With the hydrostatic principle, a separating oil film can be maintained even with a stationary bearing. Boundary lubrication, thin film lubrication, or partial film lubrication are synonymous terms applied to a prevalent condition of lubrication. These terms are descriptive of a lubrication regime in which the separating film of lubricant exists over only part of the load bearing surface and part of the load is carried by direct contact of the shaft and bearing material. The characteristics of the lubricant and the sliding surfaces become the factors in determining overall friction of the bearing. With such lubrication, different journal bearing materials have different coefficient of friction characteristics under the same operating conditions. Proper selection of shaft and journal bearing materials and lubricant combinations is necessary for successful operation in the boundary lubrication regime. The correct combination results in an absorbed layer of lubricant on the surfaces of both the shaft and the bearing. This layer of lubricant may be of the chemically active type or the molecular attraction polar type film. These absorbed layers are extremely thin, often mono-molecular in nature. With overloading, improper material selection, or improper lubricant selection, the absorbed layers will be disrupted, resulting in extreme boundary lubrication. An extreme boundary lubrication condition, if permitted to continue, marks the beginning of the breakdown of the shaft or the bearing surface or both. The three basic conditions of a journal bearing/shaft interface as shown in Figure 5-1 include, fluid film, boundary, and extreme boundary lubrication.
339
340
5 Plastic Journal Bearing Design Journal bearings designed for full film lubrication often pass through an extreme boundary lubrication phase during periods of starting and stopping. In some cases, such bearings are hydrostatically lubricated during starting and stopping periods.
FLUID FILM Velocity
Fluid film
Adsorbed boundary layer Mating surface completely separated by a fluid film of lubricant. BOUNDARY Velocity
Absorbed boundary layer Mating surface separated by two absorbed boundary
Journal bearings are generally designed for a specific type of lubricant, i.e., grease, oil, or solid lubricant. For journal bearings designed for oil lubrication, the viscosity of the oil is the most important factor for satisfactory lubrication. The oil viscosity governs the operating temperature of the bearing, the rate of flow of lubricant through the bearing, and the fluid film thickness or load carrying capacity of the bearing. The optimum oil viscosity for a given bearing application can be a very difficult value to establish. The optimum depends on journal bearing loading conditions, bearing design, bearing clearances, operating temperature, oil supply methods, and so forth. If oil viscosity is too low, full film lubrication will not be attained and a boundary or extreme boundary lubrication regime will prevail. With an oil viscosity that is too high, the bearing will be unable to pump the oil or develop the oil wedge and the result again will be boundary or extreme boundary lubrication. Fortunately, in most applications, the range between these two viscosity levels is broad and the oil viscosity selection is not critical. For most applications of ring oiling bearings at normal ambient temperatures and operation within normal load and speed limits, the oil viscosity should range between 100 and 200 SUS at the estimated operating temperature. When operating conditions are severe and involve variable and somewhat unpredictable loading conditions, EP additive oils are beneficial. These oil types will provide a thin molecular film to prevent or minimize metal to plastic contact in boundary lubrication conditions.
layers of lubricant. EXTREME BOUNDARY Velocity
Metal to plastic contact Mating surface in direct metal to plastic contact at various high points.
Figure 5-1 Boundary conditions for lubrication
Many rigid journal bearings are designed for grease lubrication. Because of its apparent high viscosity, grease is retained in the journal bearing longer than oil, primarily because of a reduced side leakage effect. Grease, in many cases, will provide true hydrodynamic full film lubrication and because of its high apparent viscosity and its consistency it will function more effectively in the boundary lubrication regime. This protects the journal bearings in start up and shut down operations or in a slow speed operation, where velocities are not sufficient for developing a hydrodynamic film. In many instances, grease fortified with solid lubricant additives has been proven beneficial in extreme boundary lubrication conditions. Solid lubricants can be beneficial as additives to oils or grease and they are also coming into increasing use as pure solid lubricants. Probably the best known types are graphite and molydisulfide. With the use of solid lubricants, the ruling principles are entirely different from those of the fluid or grease lubricants. There is no lubricant wedge and the action is primarily a friction phenomenon, with the solid lubricant on the bearing surfaces providing a low coefficient of friction characteristic. Solid lubricants are sometimes used in loose powder form and in this state they must have the ability to form a film on the surface to be lubricated. This characteristic is exhibited by MOS2, graphite in moist air, zinc stearate, and other compounds. In the bonded film or solid form, dry lubricants have been found effective when properly applied. The performance of the solid lubricant is limited by the wear life of the film, which must be replenished as it wears away or erodes to extend life of the system. In the case of the solid graphite bushing, the bearing itself is the lubricant and is gradually consumed during the gradual shear and wear of the structure. The most promising area of application for increased development of solid lubricants is in the field of high temperature lubrication and lubrication in vacuum.
5.3 Hydrodynamics of Lubrication Lubricant determinations are usually governed by the type of journal bearing selected, as most journal bearings are designed for a specific type of lubricant. The method of applying lubricants may vary from simple oil cups, grease cups, or fittings to completely automatic systems. The preferred method relates to the nature of the application and the economics of providing the lubricants to journal bearings at the required rate. When determining whether the journal bearings need to be lubricated, the following points should be considered: • A one-time lubrication, consisting of an initial greasing or use of dry lubricant, generally reduces break in wear and improves overall wear resistance. • Lubrication of the journal bearings can increase the PV limit by reducing the coefficient of friction and helping to remove wear debris. Circulation of the lubricant can further increase the PV limit by cooling the journal bearing. • Lubrication with a chemically compatible fluid to wet the journal bearing surfaces will reduce both friction and wear rates. The amount of reduction increases with increasing fluid film thickness, which in turn increases with fluid viscosity and surface velocity and decreases with increasing bearing pressure. Application geometry will also affect the reduction of friction. Even thin film lubricants can reduce dry wear rates by a factor of 10 or more. Thick films, which cause complete separation of the solid mating surfaces, can theoretically reduce wear to negligible proportions. • The frictional behavior of a journal bearing system using thin film lubrication is determined by the properties of the bearing material as well as by the properties of the lubricant. Frictional behavior is determined exclusively by the lubricant properties with thick film lubrication. • Unlubricated journal bearings should have surface grooves to carry wear debris out of the interface. In lubricated systems the grooves can help increase the supply of lubricant. The effect of grooving on the journal bearing pressure should be considered. • Because some types of resins do not wet, water is not an effective thin film or boundary lubricant for these types of journal bearing materials. In fact, water can adversely affect the wear rate for these journal bearing materials. However, periodic contamination by casual water should not cause any problems. • Purging an unlubricated Vespel® journal bearing with nitrogen gas can reduce wear rates to less than 20% of the corresponding rate in air. In addition, operation in nitrogen can increase the wear transition temperature by at least 100 °F above the value in air. • For applications in dirty environments, sealing or purging should be considered to prevent journal bearing surface contamination. The lubrication makes a big difference in the friction between the two rubbing surfaces and the clearance of the journal bearing. While an acetal homopolymer bearing can be run without any lubrication, this should be done only when absolutely necessary. Even varying degrees of lubrication affect performance and clearances. Continuous lubrication will allow tighter tolerance limits and provide optimum performance. Occasional lubrication will give higher performance than unlubricated surfaces, but clearances must be the same as for no lubrication at all.
341
342
5 Plastic Journal Bearing Design Lubrication, even if applied only at installation, will give improvements over completely unlubricated performance limits. Increasing lubrication decreases the need for larger clearances and raises performance limits.
5.4
Journal Bearings Design for Lubrication
Experience has shown that the service life of a properly dimensioned and designed journal bearing can be increased to several times the normal span, if correct lubrication is provided to the journal bearing. In many cases, it is possible to prevent entry of dirt without excessive cost, thus ensuring effective and longlasting lubrication at the same time. Journal Bearing Lubricated Felt Ring Design Figure 5-2 shows two illustrations of integrally injection molded annular grooves into which felt rings soaked in oil can be placed. The axial annular grooves or pockets are either molded at the edge of the journal bearing housing wall or they could be subsequently machined after molding if needed. Journal Bearing Felt Snapped-On Ring Design Figure 5-3 shows a felt ring which is fitted into an annular recess and secured by a snapped-on ring. The annular recess does not have to be machined after molding the snap ring and the journal bearing. Lubricated Axial Oil Wick with Debris Pocket Figure 5-4 shows how an axial groove for an oil wick on the journal bearing can provide very good results. The second axial groove is a pocket for accumulating the abraded particles once the effect of lubrication has disappeared and the bearing runs dry. This type of journal bearing design can solve many operation problems and it is used in many applications.
Lubricated annular felt ring
The journal bearing should be dimensioned for dry running and in addition should be provided with an initial lubrication. This does not allow a higher load (initial lubrication is only effective over a limited time period), but it does considerably prolong the effective service life. In case higher bearing temperatures are expected, selection of the lubricant must be carried out very carefully in order to avoid any chemical reaction. Lubricated Axial Groove Oil Wick with Seal Lubricated annular felt ring
Figure 5-5 shows the heavy journal bearing of an agricultural machine and the oil chamber with spin-welded end cup and labyrinth seals. The snap-fitted oil plug can be removed to add oil and snap back on the oil chamber. Lubricated Oil Wick Connected to Rod Bearing Figure 5-6 shows a heavy-duty integral connecting rod bearing that was injection molded with an oil chamber and spring-welded end cap. The lubricated wick element provides lubrication to the journal bearing continuously.
Figure 5-2 Journal bearing lubricated felt ring design (Courtesy: Du Pont)
343
5.4 Journal Bearings Design for Lubrication
Snap fitted ring
Lubricated felt ring
Figure 5-3 Journal bearing lubricated felt snapped-on ring design (Courtesy: Du Pont)
Lubrication axial oil wick on groove
Debris pocket
Metal shaft
Journal plastic bearing
Figure 5-4 Lubricated axial oil wick with debris collection pocket (Courtesy: Du Pont)
Journal plastic bearing Oil wick Labyrinth seal Oil plug
Metal shaft
Lubrication groove
Spin weld end cup Oil chamber
Housing
Figure 5-5 Lubricated oil wick on axial groove with labyrinth seal
344
5 Plastic Journal Bearing Design Oil plug
Oil chamber
Spin welded end cap
Oil wick
Rod bearing housing Debris trap grooves
Figure 5-6 Oil wick lubricated integral connecting rod bearing
Journal plastic bearing Lubrication axial and thrust grooves
Metal shaft
Axial/thrust debris trap grooves
Figure 5-7 Axial and thrust grooves for journal bearing lubrication (Courtesy: Du Pont)
Axial and Thrust Grooves for Journal Bearing Lubrication Perpendicular round holes for lubrication/debris trap
Wear problems can influence journal bearing design decisions. One such influencing factor is provision of axial and thrust grooves as shown in Figure 5-7. Although this solution does not decrease the rate of wear, it increases considerably the service life of the journal bearing by eliminating the abrasive influence of the abraded particles from the shaft, journal bearing, and of dust. Journal Bearing with Round Holes for Lubrication/Debris Trap
Figure 5-8 Round holes for journal bearing lubrication/debris trap (Courtesy: Du Pont)
When the journal bearing has a very thin wall thickness, the use of axial grooves is not always possible. A minimum of six perpendicular round holes made as deep as technically feasible through the journal bearing wall thickness is recommended. The holes’ diameter should be approx. 10% of the journal bearing diameter. The perpendicular holes provide the same lubrication and debris trap effects as the grooves (see Figure 5-8). Naturally, the grooves or holes will be molded integrally, even if the bore is subsequently machined.
345
5.5 Journal Bearing Design Principles
5.5
Journal Bearing Design Principles
There are many methods for designing journal bearings. Bearing design may be as simple as merely finding a standard size, low cost journal bearing to fit both the shaft and the housing without making an analysis. The designer then writes an instruction sheet, in which the user is told to squirt oil into the journal bearing occasionally. If the journal bearing fails, the user did not take care proper of it. On the other hand, the design of an aircraft engine journal bearing might require a very careful design study. Details concerning the material, construction, assembly, and lubrication will be studied very closely. A whole series of relations between the variables might be obtained to plot curves showing the effect of changing each variable. To obtain the maximum reliability, the load life curve would be studied closely and recommendations made for replacing after a specified number of engine hours.
5.5.1
Journal Bearing Nomenclature and Equations
Figure 5-9 shows a journal bearing assembly, basic equations, and variables required to calculate the journal bearing geometry depending on the end use conditions. The following information will assist in making design decisions:
L
• Journal bearing resins (properties, bearing technical information)
N V
• The number of units to be injection molded • Type of load and its characteristics, whether steady or alternating, predictable or unpredictable • Rotating speed and speed mode characteristics • Journal bearing, shaft and housing design drawings to be available, together with the information concerning making changes • The method of lubrication using force, splash, ring, or wick feed • Type of lubricant used and its operating temperature limits After reviewing the preceding information, the following tentative decisions must be made to complete the journal bearing design: • Journal bearing resin price and manufacturing molding cost • The method of analysis; whether to use the hydrodynamic theory, experimental methods, or some other method • Required assumptions to be used in the analysis, e.g., to avoid side oil leakage or operating maximum temperature • The desired journal bearing life expectancy • If the load is variable or unpredictable, analysis may be necessary in order to obtain a realistic load value on which to base the design • The shaft and journal bearing dimensions, DB, dB, DS, c, t, L • Tolerances used in the journal bearing design analysis.
W
DS dB
c
DB t
Figure 5-9 Journal bearing design assembly and equations
346
5 Plastic Journal Bearing Design V = π × dB × N
(5-1)
W dB × L
(5-2)
P=
PV = Pressure velocity limits (psi-ft/min) DB = Bearing outside diameter (in) dB = Bearing inside diameter (in) DS = Shaft outside diameter (in) c = Clearance bearing/shaft (in) L = Length of bearing (in) t = Bearing wall thickness (in) N = Rotating speed (rpm) V = Surface velocity (ft/min) W = Static load (lb) P = Pressure bearing (psi) The coefficients of friction, power loss, minimum lubricant film thickness, oil flow, and temperature rises can be calculated, using any of the procedures illustrated in this chapter or any other procedure selected by the designer as appropriate to the particular problem. When the analysis is completed, the tentative decisions are adjusted according to the results; then the analysis is repeated again, until the independent variables have values that are satisfactory to the designer. For a simple injection molded thermoplastic journal bearing design, a single set of calculations may be sufficient. The designer uses the results of the analysis to alter his preliminary decisions and fixes the design at that point. This design procedure is satisfactory when the designer has experience on which to base these alterations. However, in important applications, the experienced designer will usually carry the design study to much greater detail. Nothing is quite so basic to the design of a thermoplastic journal bearing as the proper running clearance between the shaft outside diameter and the journal bearing inside diameter. These clearances are much larger for thermoplastic journal bearings than for metal bearings. However, such clearances are necessary and beneficial in many ways. Resilience and vibration absorption of the thermoplastic journal bearing aid in overcoming possible disadvantages of large clearances. For thermoplastic journal bearings, generous clearances contribute to improved service life, particularly in the case of unlubricated bearings. Clearances of as much as 0.015 in/in of shaft outside diameter are recommended for thermoplastic journal bearing designs. Basic clearance for a completely unlubricated thermoplastic journal bearing should not be less than 0.005 in/in of shaft outside diameter. The basic clearance for a continuously lubricated thermoplastic journal bearing can be as little as 0.004–0.007 in/in of shaft outside diameter. For thermoplastic journal bearing diameters up to 3.00 in, the clearance can range from 0.008– 0.015 in/in of shaft outside diameter. Several design and service factors influence the clearance requirements. The applicability of each factor should be considered before the final design.
347
5.5 Journal Bearing Design Principles
5.5.2
Thermoplastic Journal Bearing Axial Wall Thickness
Sheet metal housing
D
The thermoplastic journal bearing’s wall thickness should be as thin as possible, offering the following advantages: • Improving the dissipation of frictional heat • Reducing the journal bearing running clearance variations resulting from thermal and moisture related dimensional changes
Plastic bearing
D + 3%
3 lobes bearing
• Reducing the journal bearing distortion under high loading Thermoplastic journal bearing wall thicknesses range from 0.040–0.125 in for most typical applications.
Plastic bearing
5.5.3
Figure 5-10 Journal bearing, three-lobes assembly
Mounting Thermoplastic Journal Bearings
The following illustrations show a few possible solutions for securing thermoplastic journal bearings in sheet metal housings. In the case of low loads and speeds, the thermoplastic journal bearing can simply be snapped into a hole in the metal sheet and retained by an undercut as shown in Figure 5-10. However, the edges of the hole must not be sharp, because this would damage or shear off the undercut. Also, stamping burrs could make a proper snap-in impossible. The thermoplastic journal bearing can have an annotated groove around its periphery. From the point of view of molding technology, the solution shown in Figure 5-10 is preferred. Here the thermoplastic journal bearing is molded with three lobes equally spaced, where the shoulder is interrupted. In this way, simple axial ejection from the mold without undercuts is possible. Figure 5-11 shows a better solution, in which the stamped aperture is at the same time provided with a deep drawn collar providing better guidance of the thermoplastic journal bearing, especially if it is longer. This mounting design requires three or four snap fittings with a slit in the middle; the undercut can be increased to 5%. Figure 5-12 shows that riveted-on bearings can become necessary, especially in case of wide operating temperature ranges, when loosening of the part is not acceptable. Metal rivets can be formed by ultrasonic riveting. Figure 5-13 shows a direct encapsulation of a journal bearing on a sheet metal housing. It is only economical if a number of other components are needed for assembly and can be molded-on at the same time. Using a vertical molding machine and a three-plate mold with three or four pin-point gates to control run-out dimensions, it is possible to encapsulate close tolerance sheet metal inserts. Thermoplastic journal bearings can be installed either by press-fitting or with commercial adhesives. To press-fit a thermoplastic journal bearing into a metal housing, the suggested practice is to use a low interference fit. After it is pressed into place, the bore of the bearing will be reduced by 90% of the calculated diametral interference, which will result in a small compressive load in the journal bearing wall. A typical interference fit is 0.5%; however, press fit interference should be adjusted to the needs of the application.
D
Plastic bearing Sheet metal Stamped housing Snap fitting
D + 5%
Figure 5-11 Snap-fitted journal bearing assembly
Sheet metal housing
Plastic bearing
Ultrasonic riveting
Figure 5-12 Riveted plastic bearing assembly
Sheet metal housing
Encapsulated plastic bearing
Figure 5-13 Encapsulated plastic bearing
348
5 Plastic Journal Bearing Design Waved split journal bearing
5.6
Split Bushing Thermoplastic Journal Bearings
Split bushing thermoplastic journal bearings, as shown in Figure 5-14, are mostly used for reduced loads, low speeds, and for an oscillating movement.
Spiral split journal bearing
Split bushing thermoplastic journal bearings are less susceptible to thermal and humidity conditions, because their clearances are only influenced by changes in wall thickness. In addition, assembly is simpler because no press-fit is used. Split bushing thermoplastic journal bearings must be secured against rotation in the housing. Their use generally means a simplification and is especially recommended for all manually operated and intermittently used shafts, such as rotating roller cranks, window actuators, hinges, locks, wheel suspensions, and similar applications.
5.7
Self-Centering Thermoplastic Journal Bearings
Self-centering thermoplastic journal bearings are easy to integrate, with their end caps having a snap-fit joint or several other functions without higher costs. The designer has a wide variety of new design possibilities, which allow ingenious and simple solutions. Figure 5-15 shows a mounting flange of a small motor with a flexible suspension (self-centering) of the bearing to a limited extent. Slot split journal bearing
Figure 5-16 shows a small elastically suspended (self-centering) journal bearing, encapsulated into a sheet metal housing for the rotation of a metal shaft. Figure 5-17 shows a Thomson Spacer Nyliner® bearing, designed to permit the utilization of the advantages of unreinforced and internal lubricated nylon 6/6. The unique cone self-centering design eliminates the need for wide clearances to prevent seizures caused by thermal expansion. Figure 5-18 shows a connecting rod ball joint bearing housing with a snap-fit securing ring, made of unreinforced nylon 6/6. The ball joint bearing is made of acetal homopolymer, ensuring low wear and friction even without lubrication. Figure 5-19 is similar in design to Figure 5-18, but with a spin welded securing ring for high axial loads.
Straight split journal bearing
Core Self-centering suspension Metal shaft
Snap-fit Mounting end flange
Figure 5-14 Split bushing thermoplastic journal bearings
Figure 5-15 Flexible suspension thermoplastic end flange bearing
349
5.7 Self-Centering Thermoplastic Journal Bearings
Encapsulated sheet metal housing
Metal shaft Self-centering suspension
Figure 5-16 Elastic suspended thermoplastic end journal bearing
"C" lock ring Snap-fit ring, nylon 6/6
Metal shaft Ball joint bearing housing, nylon 6/6 Acetal, ball joint bearing
Figure 5-18 Snap-Fit connecting rod end ball joint bearing
"C" lock ring
Spin welded ring, nylon 6/6 Sphere retainer, nylon 6/6
Acetal, ball joint bearing
Ball joint bearing housing, nylon 6/6 Metal shaft
Figure 5-19 Spin welded connecting rod end ball joint bearing
Figure 5-17 Thomson spacer Nyliner® bearing (Courtesy: Thomson)
350
5 Plastic Journal Bearing Design Equal load distribution by shaft
Clearance Load W
Load W
Rotating Stationary journal bearing
shaft Rotating metal shaft
Rotating shaft
C Integrally cantilever thermoplastic bearing & housing
C
Figure 5-20 Stationary bearing load carrying contact surface
Uneven load reaction of bearing
Clearance
Bearing deflection
Fixed
Rotating journal bearing
shaft
Fixed shaft
Reaction R R
R Reaction Reaction
C
C
Figure 5-21 Rotating bearing load carrying contact surface Figure 5-22 Uneven load reaction across the length of a bearing
5.8
Journal Bearing Load Carrying Contact Surface (C)
Rib W
W
T Rotating shaft
Integrally ribbed cantilever thermoplastic bearing & housing
In the case of a stationary journal bearing and a rotating shaft, the load carrying contact surface will increase with increasing wear. Should the clearance between the shaft outside diameter and inside diameter of the bearing be too high initially, the specific surface pressure can be several times that of the calculated theoretical value. Wear in such a case will be rapid, as shown in Figures 5-20. In the case of a stationary shaft and a rotating journal bearing (for example a roller), the load carrying contact surface will decrease with increasing wear and running conditions will deteriorate, as shown in Figures 5-21. It can be seen that good distribution of the load requires as low an initial clearance as possible.
Rib (60% T)
5.9
Figure 5-23 Equal spaced reinforced ribs around bearing
Load Reaction Across the Length of Thermoplastic Bearing
Figure 5-22 shows a uniform shaft load transferred to a cantilever flexible injection molded thermoplastic journal bearing, causing an uneven load reaction along the length of the integral journal bearing. Unequal distribution of the reaction load can cause high specific spots (edge loads), leading to the destruction of the journal bearing in a short time. As the safety factor is generally small for the thermoplastic journal bearings, this point should be given special attention.
351
5.10 Injection Molded Journal Bearings Process Defects Irregularly molded skin, warpage, inexact geometries of the bore as well as faulty assembly are the main reasons for an uneven distribution of the load. Because thermoplastics are elastic materials, the specific reaction loads can vary considerably in integrally injection molded thermoplastic journal bearings. Figure 5-23 shows an integral cantilever thermoplastic journal bearing supported by ribs and Figure 5-24 shows a thermoplastic journal bearing that is externally rib-supported. The thin ribs around the bearing distribute the load uniformly to the housing. This technique controls warpage and alignment, but a post molding machining operation is the best solution for critical run-out dimensional control. Figure 5-24 Thermoplastic housing with external ribbed bearing
5.10
Injection Molded Journal Bearings Process Defects
An incorrectly designed bearing will be impossible to mold correctly, even by the best molding processors. It is therefore the task of the designer to design all parts with the behavior of thermoplastics during injection molding in mind, in order to avoid warpage and to stay within the required tolerances. A single edge-gated journal bearing having a thick and broad shoulder will always show distortion and warpage, as shown in Figure 5-25. When the journal bearing is single edge-gated at the flange (Figure 5-25), a more or less pronounced ovality is to be expected, especially if the first stage injection speed and pressure are too high, or if the molding material has excessive mold shrinkage characteristics. If no subsequent machining of the bore has been provided for, the load at the bearing edge will always be higher than expected. Some thick walled or thick shoulder journal bearings, as shown in Figures 5-26 and 5-27, are the results of molding process problems. These molded bearings have shrinkage, warpage, and sink mark defects in the thicker cross sections, causing dimensional control problems; therefore these design techniques should be avoided.
Thick wall
A correct journal bearing design geometry with the appropriate type, size, and location of the gate, as shown in Figure 5-28, meets the following conditions:
Molding process dimensional defect problems
Molding problems
Single edge gate
Smaller diameter
Oval elongated circle
Shrinkage, warpage
Figure 5-25 Gate process effects on molded journal bearing
Sink marks
Figure 5-26 Molded effects on thick-walled journal bearing
352
5 Plastic Journal Bearing Design • The wall thickness is about 10% of the shaft diameter. Under no circumstances should it be more than 0.250 in.
Thick shoulder
• Using a sprue diaphragm or spider gate, three-plate molds with three or more individual pin point gates or a hot runnerless mold with several gate drops is recommended. Should the bearing bore be subsequently machined, the gates should be placed on the inside of the bore so that they can be removed in the same operation. • A continuous and uniform bearing flange (shoulder) should be replaced by individual small lugs that will not cause deformation of the bore. Molding problems
The remarks concerning incorrect molding are of course just as valid for journal bearings that are integrally molded with metal plate inserts or housings. Journal bearings and other components integrally molded of self-lubricating resins should also be molded at process conditions correctly selected for these thermoplastic resins, otherwise serious molding defects may appear on the molded journal bearing:
Smaller diameter
• Orange peel defects on the bearing surface (internal and external)
Shrinkage, warpage
• Conical, oval, or sunken journal bearing inside diameter • An excessive amount of post-mold shrinkage; the journal bearing inside diameter may become smaller even if subsequently bored by machining
Figure 5-27 Molded effects on thick shoulder journal bearing
• Tolerances may be too wide.
T = 0.040 - 0.125 inch Sprue
As the geometrical accuracy is decisive for the behavior of a journal bearing, its bore should always be machined as long as the economics of the part allows it. With this measure, the above sources of failure introduced by faulty bearing, gate, mold designs, and processing conditions can be corrected to produce high quality control journal bearings. The post-mold shrinkage can also be controlled by annealing the journal bearings in an oil bath at a temperature just below the melting point of the resin.
Sprue puller
Gate depth = (40 - 60%) T Gate length = 0.040 inch Spider gate (3 eq. spaces)
5.11
Factors Affecting Journal Bearing Performance
Throughout this chapter, references are made to various conditions of lubrication. The descriptions of these terms are reviewed in the following, because they may be different for thermoplastic and metal journal bearings: • No Lubrication or completely unlubricated refers to a condition in which both the journal bearing and the shaft are wiped dry with a solvent. After solvent cleaning, the shaft and bearing are handled with gloves to avoid contamination with skin oils. No lubricant is added after installation or during the entire running operation.
Gate width = 75% T
Figure 5-28 Segmented flanges bearing with sprue spider gate
• Initial Lubrication or lubricated at installation refers to the small amount of oil added when the journal bearing is assembled, but none thereafter. For example, three to five drops of oil for 1.00 in outside diameter shafts are a typical amount added.
5.12 Factors Affecting Journal Bearing Dimensions • Repeated Lubrication refers to a condition that goes beyond initial lubrication in that a few drops of oil are added infrequently during operation. This can be compared to a condition of occasional maintenance. • Continuous Lubrication refers to a constant supply of lubricant. Under this condition the coefficient of friction and the wear rate are the lowest. This condition can approach boundary, hydrodynamic, or even force lubrication. Under continuous lubrication, the PV values are the highest. When testing a journal bearing, the use of duplicate bearings for each run is recommended rather than using a single bearing for all test conditions. The test can then best simulate field conditions. This practice will eliminate unavoidable wear problems that might not be possible to determine in the field. Because gradual increases of load and speed will raise the allowable PV value limit, failure in the field may occur, if such a gradual initial wear-in period is not considered. In a journal bearing application, many factors are interrelated so that it is difficult to separate them and distinguish between individual causes and results. The frictional properties of the self-lubricated thermoplastic journal bearings are influenced by load, speed, and lubrication. The frictional properties influence the wear rate, ambient running temperature, and performance such as drag and power loss. The effect of reduced clearance or increased angular contact is most evident in journal bearings, where the ends have bowed in slightly to produce a “barrel” effect. This effect can also be caused by stress relief of the molded thermoplastic bearing. If localized wear or if seizing occurs after the bearing has run successfully, these previous conditions may be the cause. The test samples should be inspected for roundness, and preferably be annealed and wiped clean. In most cases, correctly injection molded journal bearings will not exhibit these deficiencies.
5.12
Factors Affecting Journal Bearing Dimensions
Post-mold shrinkage, temperature, moisture, and load over time (creep) are frequently overlooked in journal bearing product design. The causes of dimensional changes are common to all materials, even if the values are small. The basic engineering principles are the same for self-lubricated resins as with any other material. Knowing the design properties of these materials enables the product designer to predict the effects caused by environment and load over time. The operating limits of a thermoplastic journal bearing are more sensitive to velocity than to bearing pressure. However, there are compressive stress limits that should be considered in a well designed bearing. The proportional stress limit (elastic range) at a tested strain and temperature is used for design analysis. These proportional stress limits are only a small percentage of the compressive strengths of the materials and are purposely limited to low values to prevent excessive deformation at high temperatures. For cool or light duty journal bearings, deformation is negligible. However, for journal bearings designed to operate near the limiting PV conditions, the proportional stress limits should be increased only after cautious experimentation.
353
354
5 Plastic Journal Bearing Design The physical property reductions under load and time (creep) are characteristics of thermoplastic materials. Their behavior is similar to that experienced with metals at high temperatures. For practical design purposes, the deformation at less than 1% strain after a one year period reaches a magnitude approximately equal to that of the initial strain. To estimate total deformation, the isochronous stress-strain curves at various temperatures are used for this analysis (see Chapter 2).
5.12.1
Length-to-Inside Diameter Ratio of Journal Bearings
A length-to-inside diameter ratio of 1 : 1 is recommended for journal bearing designs. For applications where the length exceeds the inside diameter, the journal bearing suffers localized spot wear and the spot melting of the bearing increases, probably caused by localized dimensional inaccuracies. In cases where the inside diameter exceeds the length, heat transfer usually becomes less effective (as if the wall thickness was too thick), causing higher wear of the journal bearing.
5.12.2
Types of Service and Motion of Journal Bearings
The clearance between the inside diameter of the journal bearing and the outside diameter of the shaft allow it to perform under the following conditions: • In intermittent operation • In frequent start-stop motion • In reciprocal motion • In linear or helical sliding motion • In occasional peak loading conditions • In air, water, or oil cooled operation Thermoplastic journal bearings submitted to these types of services or motion usually perform above the minimum PV value limit for unlubricated journal bearings, depending on the product design, the dimensional tolerances, the type of thermoplastic material used, and the manufacturing process.
5.12.3
Thermoplastic Journal Bearing Annealing Effects
Because thermoplastic molded journal bearings have been transformed from the stage of a polymer melt to a solid form by cooling, some residual stresses may be frozen-in. Over time, these stresses may relieve themselves. In a journal bearing, this is usually evidenced by reduction in clearance and subsequent seizing up of the journal bearing. The frozen-in stresses in the molded journal bearing can be relieved by applying heat. This process is referred to as annealing; a hot air oven or a hot oil bath are used (preferred). Annealing in oil also provides lubrication to the journal bearings. The annealing temperature should be higher than the expected service or ambient running temperature. The recommended annealing temperatures should be 50 °F (±3 °F) lower than the melting point of the resins. Care should be taken that the oil temperature does not exceed the recommended
355
5.12 Factors Affecting Journal Bearing Dimensions
Annealing of the self-lubricated journal bearings should be carried out without air, preferably by immersion in a suitable annealing oil. The oil should be stable at the annealing temperature; it should not attack chemically, nor give off noxious vapors. Refined mineral oils (“Primol D”, “Uniflo”, or “Nujol”) have been found to be satisfactory for this process. Annealed journal bearings should be removed from the oil bath and cooled in air to room temperature, preferably in a draft free container. Accelerated cooling should be avoided, as it might introduce new thermal stress into the skin of the hot thermoplastic journal bearings. Post-molding annealing operations control the journal bearing’s dimensional variations and lubrication, assuming the correct processing conditions and design have been performed. However, post-molding annealing is an additional operation and should be avoided whenever feasible.
30 25
Annealing time, (minutes)
temperatures for longer than 1 minute for each 0.020 in of wall thickness, as it may cause deterioration of the physical properties of the journal bearing or cause warpage.
20 15 10 5 0 0
0.20
0.40
0.60
0.80
1.00
1.20
Part wall thickness, (inch)
Figure 5-29 Acetal homopolymer annealing time vs. wall thickness (Courtesy: Du Pont)
Figure 5-29 shows the annealing characteristics of acetal homopolymer resin.
Acetal Homopolymer Moisture Absorption Effects
The strain recovery and creep resistance of self-lubricated thermoplastic materials are excellent, particularly under high temperature and humidity conditions. The loads allowable for operation should be below the stress level causing deformation over time (creep). Therefore, self-lubricated thermoplastic resins seldom need design allowances to compensate for the creep variations.
Moisture content, (%)
1.6 1.2
se er
d
in
wa
te
r 1.3 1 .2
Figure 5-31 shows the time it takes for a part made from acetal homopolymer to change its dimensions based on the percent of moisture absorption at various temperatures. It can be seen that only prolonged service time while immersed in hot water (moisture and temperature) or similar conditions will cause dimensional changes.
2.0
1.10 th 1. 9 ng Le 0. 0.8 7 ase 0. cre In % 0.5 0.6 0.4 3 0. 0.2 1 0. 0 0.
Self-lubricated thermoplastic materials are affected by moisture from the environment. Although acetal homopolymer shows excellent stability over a wide range of humidity conditions, the dimensional changes of parts made from acetal homopolymer caused by service moisture content should be included in the journal bearing designs. Figure 5-30 shows a graph used to calculate approximate dimensional changes caused by temperature and moisture absorption of the acetal homopolymer resin.
Im
0.8 0.4
m
100% R.H.
50% R.H.
0 0
40
80
120
160
200
Temperature, (˚F.)
Figure 5-30 Acetal increase in length due to moisture vs. temperature (Courtesy: Du Pont)
2.0 Immersion in water (212˚ F.)
Moisture absorbed, (%)
5.12.4
1.6
5.12.5
TFE and Nylon 6/6 Moisture Absorption Effects
Unreinforced Teflon® TFE resin does not absorb moisture, therefore, it does not change dimensions with moisture variations. However, TFE reinforced composites may be subject to dimensional changes, depending on the type and percentage of reinforcement compounded with the basic resins. Unreinforced nylon 6/6 resins absorb moisture from the atmosphere and working environment. When the journal bearing clearance is 0.015 in/in, the moisture variations that cause dimensional changes in an air environment are not a problem. However, when the clearances are below 0.012 in/in, or the bearings are immersed in water, environmental effects should be considered in the design.
Immersion in water (140˚ F.)
1.2 Immersion in water (73˚ F.)
0.8 83% R.H. (73˚ F.)
0.4 50% R.H. (73˚ F.) 12% R.H. (73˚ F.) 0 0
10
20
30
40
50
60
Time, (days)
Figure 5-31 Acetal homopolymer moisture absorption vs. time at various temperatures and relative humidities (Courtesy: Du Pont)
356
5 Plastic Journal Bearing Design Nylon 6/6 journal bearings dry as molded normally contain less than 0.27% moisture by weight. Exposed to air at 73 °F and 50% relative humidity, the molded bearings will reach an equilibrium moisture content of 2.50%. The rate of moisture absorption and the resulting rate of dimensional change are relatively low. Preconditioning the journal bearings in boiling water or heating them in a salt solution of potassium acetate in water minimizes dimensional changes of nylon 6/6 in service. This procedure brings nylon 6/6 to an equilibrium moisture content at a faster rate and adjusts the journal bearings to the equilibrium dimensions of the anticipated service conditions.
5.12.6
Temperature Effects on Thermoplastic Journal Bearings
Temperature enters into the design of clearances for two reasons: all plastics have a coefficient of linear thermal expansion roughly ten fold that of metals and plastics dissipate heat very slowly compared with metals. One of the first steps in the product design should be to determine the temperature range over which the journal bearing must operate, using the upper and lower expected environmental temperatures at maximum velocity. Without the use of thermocouples, it is difficult to measure actual equilibrium running temperature of the journal bearings. However, if the journal bearing is at all within the suggested pressure-velocity (PV) value limit, the equilibrium running temperature should not be critical. Thermal expansion must be considered for both lubricated and unlubricated journal bearings. Some designs may offer a partial solution but, basically, thermal expansion must be included until tests show that more latitude in clearances can be employed because of cooling or good heat dissipation through the shaft and housing. The coefficient of linear thermal expansion of acetal homopolymer is 4.5 × 10–5 per °F. The greater the temperature range over which a journal bearing of acetal homopolymer must work, the greater the expansion involved. The journal bearings should have a minimum clearance of 0.005 in/in at the lowest service temperature at which operation is expected. Thermal expansion will work two ways: over the inside diameter and over the length of the journal bearing. The length should be free, unrestricted at one end to allow for thermal expansions. If the journal bearing is restricted at both ends and localized wear or spot melting occurs during testing, this is caused by an end compressive effect. Either longitudinal or diametral clearance should be enlarged. The low heat conductivity of self-lubricated journal bearings is the reason for quick heat build-up and possible spot melting or overall melting under excessive loads or small clearances. Therefore, the wall thickness of a journal bearing should be as thin as the design allows. The thinner the journal bearing wall, the better the heat transfer through the housing and the metal shaft.
357
5.12 Factors Affecting Journal Bearing Dimensions
5.12.7
Thermal Effects on Thermoplastic Journal Bearing Clearances
Thermal changes can cause a self-lubricated thermoplastic journal bearing to seize and consequently lead to its immediate destruction. If considerable changes of temperature are expected, it will be necessary to check their influence on the clearance of the journal bearing and to carry out suitable design modifications as necessary. For a journal bearing made of self-lubricated thermoplastic incoporated in a larger structure, as shown in Figure 5-32, the test data were developed using an acetal homopolymer journal bearing to determine the increased clearance with increasing temperature. The clearance should be specified and tested in relation to the lowest ambient temperature expected for the application. For example, the acetal homopolymer journal bearing inside diameter of 1.200 in will increase by 0.0024 in given an increase in temperature of 76 °F. Figure 5-33 shows a journal bearing made of self-lubricated acetal homopolymer pressed into a metal housing. The journal bearing clearance will decrease with increasing temperature as the wall expands toward the interior or inside diameter of the journal bearing. These dimensional changes can be neglected when using normal wall thicknesses. For example, given a wall thickness of 0.120 in and an increase in temperature of 105 °F, the clearance will decrease by only 0.00075 in. Should frequent temperature changes over a wide temperature range be expected, a journal bearing made of acetal homopolymer should not be secured by a press fit alone, as over time all of the retaining force will disappear. The temperature rise produced by friction in an acetal homopolymer journal bearing will depend on the coefficient of friction and the pressure-velocity (PV) value limit, therefore the heat conduction cannot be predicted with certainty. Therefore, it will be advantageous to determine the temperature of the journal bearing experimentally, for high loads and insufficient cooling applications.
176
0.024
"d" dia.
Inside diameter increase, (inch)
140 0.016
105 86 76 68
0.008
60 0.004
50 0.0024 0.0016
0.0008
Integrally journal bearing and housing 0.0003
0.40
0.80
1.20
1.60
2.40
Inside diameter, "d" (inch)
Figure 5-32 Inside diameter increase vs. size and temperature changes (Courtesy: Du Pont)
3.15
4.00
Temperature increase, (°F.)
0.04
358
5 Plastic Journal Bearing Design
"d" dia.
Clearance "d" dia. Decrease, (inch)
T
Metal housing
140
0.0016 105 90
0.0008
70 60
0.0004 50
0.00024
Temperature increase, (°F.)
176
0.0024
Bearing pressed in metal housing
0.00016
0.00008
0.00004
Acetal bearing
0.02
0.04
0.06
0.08
0.12
0.20
Wall thickness, "T" (inch)
Figure 5-33 Clearance decrease vs. thickness and temperature changes (Courtesy: Du Pont)
For acetal homopolymer journal bearings, the maximum operating surface temperature caused by friction and external environmental conditions should not exceed 158–176 °F. For journal bearings made of unreinforced and internally lubricated nylon 6/6 resins, the journal bearing maximum operating surface temperature should not exceed 176–212 °F. If a good journal bearing performance and long service life are required for acetal homopolymer and unreinforced/internally lubricated nylon 6/6 resins, the maximum recommended end use temperatures for both types of compounded polymers should be included in the journal bearing designs.
5.13
The two most important criteria in the design of thermoplastic journal bearings are PV limits and wear. The PV limit of a thermoplastic in a given environment tells the designer if the material will work in the application. To be successful, the designer must have a basis for the prediction of the wear rate; otherwise, a prototype test for each new thermoplastic journal bearing is required.
500 Acetal homopolymer Mating material 1040 steel Finishing 16 RMS Hardness 22 R C Temperature (73˚ F.) No lubrication
Pressure, (psi)
400
300
The PV limit is the product of pressure (psi) and velocity (fpm). Figure 5-34 shows the PV limits curve for acetal homopolymer resin. The connecting points of limiting pressure and limiting velocity on pressure versus velocity coordinates describe the PV limits curve. This graph is developed for a specific type of resin and is useful to figure out the limits of the material when either the pressure or velocity is known.
200
Working area
100
Journal Bearing Pressure-Velocity (PV) Limits
PV limit 0 0
100
200
300
400
500
Velocity,(fpm)
Figure 5-34 Acetal homopolymer “PV” limit curve (Courtesy: Du Pont)
Any compounded plastic bearing resin sliding against another material surface without the assistance of a lubricant (oil, grease, etc.) at a given ambient temperature has a PV limit. The PV limit is caused by the plastic’s surface frictional temperature reaching or exceeding a critical PV value.
359
5.13 Journal-Bearing Pressure Velocity (PV) Limits Because the frictional heating caused by the sliding motion depends on the pressure, velocity, and coefficient of friction, the surface temperature will depend on the same variables if heat loss parameters are unchanged. Measurement of surface temperature at various combinations of pressure and velocity would appear to be an excellent basis for determining the PV limit of a plastic. However, temperature affects compressive strain and compressive set under loads, so the maximum surface temperature at which a plastic will operate satisfactorily at high pressure and low velocity is not necessarily the same for low pressure and high velocity. The relation between a polymer’s surface temperature and its PV limit is an important notion, because it points out several factors in sliding element design. A plastic’s PV limit is decreased by increased ambient temperature and increased by decreased ambient temperature. This means that the PV limit of a plastic must approach zero as the ambient temperature approaches the critical temperature. Conversely, a plastic’s PV limit can be increased tremendously through cooling. Consideration should be given to providing an adequate heat transfer in all plastic journal bearing applications by using a thin wall thickness or by using a plastic compounded resin with conductive additives or reinforcements to improve the poor heat transfer properties of polymers. The plastic’s surface temperature is obviously important. However, a detailed study is not considered practical, because the journal bearing surface temperatures are difficult to measure accurately and the use of this approach requires the designer to predict the surface temperature of each application.
50
Acetal homopolymer
5.13.1
Methods to Determine the PV Limits of Plastics
• Pressure Stepping Test With this method, a series of tests is conducted at several constant velocities. In each test, the contact pressure is increased in small increments, measuring the sample’s temperature and coefficient of friction, until a pressure is reached at which temperature and coefficient of friction equilibrium cannot be obtained or there are other signs of failure. Through proper selection of initial pressure and pressure increments, the duration of each test is reduced so that the effect of wear will be reduced. The highest pressure at which satisfactory operation is obtained multiplied by the test velocity gives the PV limit for the particular plastic at ambient temperature. • Wear Test Series The second method is to conduct wear tests at a series of pressures at several velocities. The results of each series are plotted as wear rate (or wear factor) versus pressure. The pressure at which this curve changes slope radically is the limiting pressure for the test velocity and ambient temperature. Examples of the wear test series curves for acetal homopolymer and TFE are shown in Figure 5-35.
5.13.2
Journal Bearing Coefficient of Friction
The coefficient of friction is of prime concern to the bearing product designer. Yet, predicting accurately a specific coefficient of friction for a plastic journal bearing is impossible. However, enough data have been developed to show the approximate levels of coefficient of friction under most bearing conditions.
Wear factor, "K" (x 10-10)
40
Carbon filled TFE
30
20
10
0 0
40
80
120
160
Pressure, (psi) Mating material 1040 steel Finishing 16 RMS Hardness 22 RC Rubbing velocity 100 fpm Temperature 73˚ F. No lubrication
Figure 5-35 Acetal and TFE “PV” limits, wear test series curves (Courtesy: Du Pont)
360
5 Plastic Journal Bearing Design Teflon® has an exceptionally low coefficient of friction at speeds lower than 20 fpm and at loads higher than 25 lbs. Under such conditions, a coefficient of friction as low as 0.15 can be attained with thermoplastic compounds modified with a low percentage of coefficient of friction additives. Unreinforced Teflon® TFE polymers running against steel have the lowest coefficients of friction of all materials – as low as 0.04. The static coefficient of friction is less than the dynamic coefficient of friction. There are no slip-sticks, only smooth operation and easy breakaway. Unreinforced and internally lubricated nylon 6/6 has a coefficient of friction of 0.20–0.40. Acetal homopolymer has a lower coefficient of friction, between 0.15 and 0.35. The static and dynamic coefficients of friction of acetal homopolymer are equal. Therefore, these journal bearings have low starting friction. Journal bearing tests have shown that there is no linear relationship between the wear factor and the coefficient of friction. The smaller the clearance and the higher the coefficient of friction, the higher the wear rate. A high coefficient of friction causes frictional heat build-up fast enough to cause partial or complete melting of the inside surface of the journal bearing. However, a small clearance may increase the angular contact of the journal bearing with the shaft, in which case the coefficients of friction will be higher.
5.13.3
Journal Bearing Failures Due to Small Clearances
A thermoplastic journal bearing subjected to excessive loads and speeds or small clearances with the shaft, fails because of a rapid heat build-up beyond the melting point. Figure 5-36 shows a small-clearance acetal homopolymer journal bearing. The internal surface temperature exceeded the melting point of the resin, causing surface imperfections due to the frictional heat build up during the test.
Figure 5-36 Overheated acetal bearing surface caused by small clearance (Courtesy: Du Pont)
Most thermoplastic journal bearing failures show that excessive loads and high speeds cause the wear rate to increase in a linear proportion to the increase in loads and speeds. If wear occurs under allowable loads and speeds, this is caused by a small clearance between the bearing inside diameter and the shaft. The excessive pressure-velocity or small clearance is the primary cause for frictional heat build-up. This condition is far above the maximum limit for the material, causing rapid wear and failure of the thermoplastic journal bearing. Nevertheless, even under normal pressure-velocity conditions, well within allowable PV limits, unsatisfactory wear rates can occur due to a small bearing clearance, the lack of lubrication, or the presence of metal debris, dust, rust, sand, and so forth. The cause of higher than expected journal bearing wear can also be the improper metal shaft mating surface (hardness and finishing). The following examples describe some combinations used for journal bearing resins and shaft materials without using a lubricant: • Acetal Homopolymer Bearing to Steel Shaft Acetal homopolymer bearings on steel shafts provide good performance, the lowest coefficients of friction, and the lowest wear rates.
5.13 Journal-Bearing Pressure Velocity (PV) Limits • Acetal Homopolymer Bearing to Aluminum Shaft The coefficient of friction is higher than steel. Aluminum shaft corrosion occurs in salt water and severely increases the wear of the acetal homopolymer. Aluminum has the tendency to flake off, introducing minute particles in the bearing interface area, rapidly increasing wear. • Acetal Homopolymer Bearing to Acetal Homopolymer Shaft This combination is not the most desirable. When two equally low heat conducting materials are mated, the heat build-up is more severe. Under very light load and reduced speed conditions, this combination does well, but it produces squeaks, because high loads in an unlubricated operation produce tiny loose wear particles. • Acetal Homopolymer Bearing to Nylon 6/6 Shaft This combination offers good performance, because the frictional similarity and chemical dissimilarity of these two materials offer ideal design characteristics when a bearing of acetal homopolymer runs against a high strength nylon 6/6 shaft.
5.13.4
Definition of Different Types of Wear
The theory of solid friction and wear has been developed in great detail by Tabor, Bowden, Rabinowicz. Most theoretical studies on friction and wear have been conducted for combinations of metals and plastic materials. Adhesive Wear Whenever two materials are brought into contact, attractive forces tend to hold them together. When the surfaces are separated, the break does not occur at the original interface; rather, a cohesive failure may occur in one material. This transferred material may later transfer back to its original surface, forming loose wear particles. Adhesive wear generally produces finely divided wear particles and may transfer loose wear material to the mating surface. The resulting surface is quite smooth. Adhesive wear usually has a low wear rate; however, rapid wear and transfer from a polymer surface to a metal shaft have been observed for severe operating conditions. Abrasive Wear Abrasive wear occurs when a rough hard surface, or a soft surface containing hard particles, slides on a softer surface. These conditions generally produce a series of grooves in the softer surface and the displaced material usually forms loose wear particles. The same type of wear occurs when two smooth surfaces slide against each other in the presence of abrasive particles. Abrasive wear normally produces larger wear particles than adhesive wear, occurs at a faster rate, and produces a relatively rough wear surface. This type of wear is typical when a bearing surface becomes contaminated with abrasive particles, either from the environment or from an accumulation of wear particles. Corrosive Wear Corrosive wear results when sliding occurs in a corrosive atmosphere. Many materials form a surface film that slows or stops corrosion. However, if this film is continuously removed due to wear, corrosion of the base material will continue. Since many polymers are resistant to common corrosive chemicals, plastic bearings are often specified for corrosive environments.
361
362
5 Plastic Journal Bearing Design Thermoplastic journal bearings should be broken in for best wear performance. Fifteen minutes at one half the service conditions are usually more than satisfactory for nylon 6/6 or acetal homopolymer journal bearings. With journal bearings made of Teflon® TFE fluorocarbon, break-in time is even less. If a fifteen minute break-in period is impractical for the assembly process, reduce the design PV limit to a lower level of significance in the break-in period. The break-in period can be eliminated either by applying a few drops of oil (initial lubrication) between the mating surface of the journal bearing inside diameter and the shaft outside diameter, or by annealing the journal bearings in oil at temperatures and time recommended by the resin supplier, without removing the oil from the inside surface of the journal bearing.
5.14
Mating Material Hardness and Surface Finishing
The wear performance of thermoplastic journal bearings can be substantially affected by the hardness of the mating material and its surface finish. The wear rate can be reduced by increasing the hardness and decreasing the mating surface finish. A fine polish finishing operation of the steel shaft should be in the same direction as the journal bearing motion on the mating surface. Thrust bearing tester data without lubrication
Wear factor, (K)
1.2
1.0
0.8
0.6 20
30
40
50
60
Hardness, RC
0
10
20
30
Finishing, micro-inch (RMS)
Figure 5-37 Metal shaft hardness and finishing vs. plastic wear factor
40
Because lubricants are not needed in plastic bearing applications, metal shaft corrosion can be a problem. Stainless steel or other noncorrosive materials with proper hardness and finishing are recommended. If common steel alloys are used, it is recommended that they be chrome-plated. Where design limits permit, hard anodized or aluminum with a TFE hard surface spray coating of the shaft may be used. Aluminum and zinc are not good mating surfaces for plastic bearings because the softness of these materials can lead to rapid wear. Die cast aluminum with high silica content is very abrasive to plastics and the porosity of chrome plating may cause greater wear than a fine polished steel surface. The metal surface of the shaft should be as hard and smooth as is practical. The shaft surface finishing for plastic bearings is not as critical as the one required for some metal bearings. During the Teflon® TFE fabric bearing break-in, it is believed that the shaft becomes coated with a thin film of Teflon®. Sliding occurs primarily between the Teflon® coated shaft and the Teflon® TFE fabric. However, to prevent excessive wear, the surface finishing on the shaft should be better than 32 micro inches (RMS), a finish of 16 micro inches (RMS) being preferred. Plastic shafts are not a good mating material for plastic bearings; if used, the application should be limited to low PV limits. The softness of a plastic bearing mating surface can lead to high wear. Because plastics are relatively poor thermal conductors, the plastic-to-plastic bearing interfaces will run hotter than plastic-to-metal interfaces. The metal-to-plastic bearing interfaces have a higher PV limit than the plastic-to-plastic bearing interfaces. Plastic materials are poor heat conductors and it is necessary to provide means to carry away the frictional heat generated at the bearing/shaft interface. Figure 5-37 shows the effects of steel shaft hardness and finishing vs. wear factor for an unlubricated thrust plastic bearing.
5.15 Self-Lubricated Thermoplastic Journal Bearings
5.15
Self-Lubricated Thermoplastic Journal Bearings
One of the characteristics of self-lubricated thermoplastic materials is the low heat conductivity. Most thermoplastic materials have approximately the same thermal conductivity, although low friction additives and reinforcements are compounded to change this property of thermoplastic materials. Typical reinforcing materials are fiber glass and aramid fibers. The loading levels vary from 10–40% by volume. Low coefficient of friction additives are compounded with the matrix resins. Some of these additives are graphite, molybdenum disulfide, aluminum and calcium stearate, Teflon® TFE fluorocarbon powder or fiber, silicone, carbon and aramid fibers. Designing plastic journal bearings is similar to the procedures used for the metal bearings. The same basic engineering theories and equations are applicable. The functional properties of these thermoplastic self-lubricated bearing materials include the following: • When completely lubricated, the thermoplastic self-lubricated bearings perform similarly or better than metal bearings • They can be used with little or no lubrication at all • They have very low coefficients of friction (0.30 for unlubricated and 0.04 for the thermoplastics self-lubricated) • The self-lubricated thermoplastics show no slip-stick behavior because there is no noticeable difference between the static and dynamic coefficients of friction against steel surfaces Self-lubricated thermoplastic materials have other desirable engineering characteristics. They exhibit low creep and low deformation under loads even at high humidity and temperatures. With their high strength, they have enough resilience for press-fitting, snap-fitting, good impact strength, and a tendency to dampen vibrations produced by the journal bearing assembly. Self-lubricated thermoplastic journal bearings should not run hotter than the melting point. For example, acetal homopolymer journal bearings should not be used continuously above 176 °F and intermittently up to 200 °F. There is no accurate way of calculating the performance of a bearing, even if all the design parameters are known; the mating surface operating temperature of the bearing and shaft is difficult to measure. However, an approximation can be reached which shows if a bearing will do well in an application. The PV limit is the product of the pressure load (psi) on the projected bearing area (in2) and the running velocity (fpm). Since the velocity, the total pressure load, and the shaft diameter are known, the PV limit value can be calculated. From this value, the design physical dimensions and tolerances for the journal bearing and shaft needed for a specific application can be determined. Most journal bearing applications are subjected occasionally to unexpected loads and vibration. It is considered good practice to limit the PV value to only 75% of the rated limit. For example, designing an acetal homopolymer bearing to operate at a velocity between 100 and 200 fpm, it is recommended to select a PV limit of 3,000 (Table 5-1) multiplied by 0.75 = 2,250 psi-fpm.
363
364
5 Plastic Journal Bearing Design The pressure versus velocity graphs of unreinforced nylon 6/6 and acetal homopolymer resins as determined by the limiting PV equations are shown in Figure 5-38.
70
Acetal @ 0.005 in./in. clearance PV1.20 = 7.600 psi-fpm
Bearing pressure, (psi)
60 50
Nylon 6/6 @ 0.015 in/in. clearance PV1.47 = 40,000 psi-fpm
40
Self-lubricated bar stock plastic materials can be machined to make prototype journal bearings that can be used for testing under the required end use conditions. The calculations should only be used to decide the design feasibility and to confirm the results found in the plastic bearing prototype tests.
30 20 10 0 0
100
200
300
400
500
600
700
Velocity, (fpm)
Figure 5-38 Pressure-velocity graph per limiting PV equations (Courtesy: Du Pont)
800
Self-lubricated plastic materials for bearing applications include: phenolic, acetal homopolymer, nylon 6/6, fluorocarbon, polycarbonate, polysulfone, polypropylene, and ultrahigh molecular weight polyethylene. These materials are used with heat treated (20–45 RC) and polished (16–32 RMS) steel shafts. For some specific applications, plastics such as phenolic, polycarbonate, polysulfone, acetal homopolymer, and nylon 6/6 are compounded with low coefficient of friction additives used to decrease friction, such as fluorocarbon (10–25% by weight), silicone lubricant (2% by weight), graphite, molybdenum disulfide, and stearates. Aramid fibers and minerals are also used to increase strength, dimensional stability, and to decrease shrinkage. The design objectives for bearings are usually a long life, high efficiency, or both. Wear and friction are the major concerns in the design of bearings. The factors that control the performance of a bearing are pressure, velocity, lubrication, temperature, surface hardness, and finishing of the shaft. Nylon 6/6 and Teflon® TFE fluorocarbon bearings have a tendency to cold-flow under moderate pressure loads. The product of pressure and velocity (PV) is the power rating of the bearing per unit area. The product of PV and the coefficient of friction is the energy dissipation (or the rate of heat generation). The wear rate is the product of the wear factor and PV. Increasing the bearing material hardness with reinforcements or metal support backing (composite bearings) can reduce the coefficient of friction and the wear factor of a journal bearing. Self-lubricated thermoplastics are sensitive to heat. When the temperature rises above the melting point, the wear rate increases considerably. The best method of heat removal is by using oil or water through the metal shaft. The wear factor means the volume rate of material loss in a time period (in3/h). The bearing pressure is the load divided by the projected area of the bearing (psi). Table 5-1 shows the maximum operational conditions of several bearing materials.
Table 5-1 Plastic Bearing Materials Operating Limits
Bearing Material
Maximum pressure (psi)
Maximum temp. (°F)
Maximum velocity (fpm)
Maximum PV limit (psi-fpm)
Phenolic
6,000
200
2,500
15,000
Unreinforced nylon 6/6
1,000
200
1,000
3,000
500 2,500 60,000
500 500 350
50 1,000 150
1,000 10,000 25,000
Polycarbonate
1,000
220
1,000
3,000
Acetal homopolymer
1,000
180
1,000
3,000
Fluorocarbon Fluorocarbon (reinforced) Fluorocarbon (fabric)
365
5.15 Self-Lubricated Thermoplastic Journal Bearings Table 5-2 Coefficient of Friction and Wear Factor
Bearing material
Shaft
Wear factor (K 10–10)
Coefficient of friction Static
Dynamic
10,200 65 45
0.50 0.30 0.25
0.45 0.25 0.20
1,150 800
0.60 0.35
0.46 0.30
Acetal homopolymer Acetal homopolymer Acetal homopolymer (20% TFE)
Acetal Steel Steel
Unreinforced nylon 6/6 Unreinforced nylon 6/6
Nylon 6/6 Steel
Nylon 6/6 (20% TFE) Nylon 6/6 (30% glass, 15% TFE)
Steel Steel
30 45
0.25 0.35
0.18 0.26
Polysulfone (30% glass, 15% TFE)
Steel
65
0.40
0.28
Polycarbonate Polycarbonate (30% glass, 15% TFE)
Steel Steel
2,500 70
0.60 –
0.45 –
Table 5-2 shows the wear factor and coefficient of friction (static and dynamic) of several thermoplastic materials. The wear factor and coefficient of friction properties are not directly related. For example, some brake packing materials produce very high friction but have low wear, while a low coefficient of friction material may wear rapidly. Wear factors of 200 or less are considered very good for most design applications. For bearings operating at a very low speed, or intermittent durations, wear is not a problem. Examples of thermoplastic bearings in such applications are: nylon 6/6 sliding pads and rollers used for furniture drawers, acetal homopolymer bearings used in door hinges, electrical appliances, and light duty wheels, fluorocarbon sliding pads used between overhead highways and their supporting pillars to allow for thermal expansion, fluorocarbon bearings used in automobile steering linkages and food processing equipment. Fluorocarbon fabric composite bearings have the highest load, temperature, and PV limit ratings, while phenolic bearings have the highest speed ratings. Phenolic bearings are used in marine propeller shafts and hydroelectric turbine shafts. Thermoplastic Journal Bearing Clearances Clearances for thermoplastic journal bearings are greater than those for metals to compensate for dimensional changes. More than half of all bearing problems are the results of insufficient clearances. Increasing the clearances achieved the required performance in many applications. Their resilience and vibration absorption help these materials in overcoming the disadvantages caused by larger clearances. The recommended clearances for best performance of thermoplastic journal bearings operating in air at room temperature should be 0.005 in/in minimum, preferring a larger clearance up to 0.015 in/in. In very few cases, it is advisable to specify a diametral clearance of less than 0.004 in/in, even for small outside diameter shafts and plastic bearing applications.
366
5 Plastic Journal Bearing Design
5.15.1
Vespel® Polyimide Bearings
Vespel® bearings made of polyimide polymers do well with or without lubrication under operating conditions that destroy most other types of journal bearings and cause severe wear problems for metal journal bearings. Vespel® bearings reduce abrasion, corrosion, adhesion, fatigue, and wear problems that are typical for the conventional metal bearings, especially when they are operating without lubricants. The performances of some journal bearings in a given application depend on the following conditions: • The operating environment • Load or pressure on the bearing surface • Sliding velocity of the mating surface compared with the bearing • Hardness and finish of the mating surface • Frictional behaviour of the bearing material • Bearing thickness and the material’s ability to dissipate frictional heat • Coefficient of linear thermal expansion of the bearing material Vespel® journal bearings have a higher pressure-velocity (PV) limit than most high performance engineering thermoplastic materials. Vespel® bearings are operated over a wide range of temperatures. They have excellent stress properties, outstanding creep resistance, abrasion resistance, and low coefficients of friction. They exhibit excellent chemical resistance and have performed successfully in the following adverse environments: • Air and inert gasses at 700 °F • Gamma and electron beam radiation • High vacuum (10–10 torr) W
dS
• Liquid hydrogen and refrigerant (R-12, 134A)
Rotating shaft
N
• Hydraulic fluids and jet fuels
When a bearing is subjected to increasing PV, it will eventually fail (PV limits). The failure point is usually manifested by an abrupt increase in the wear rate of the bearing material.
Journal bearing
As long as the mechanical strength of the journal bearing material is not exceeded, the temperature of the journal bearing surface is generally the most important factor in determining the PV limit. The parameters affecting a journal bearing operating surface temperature are: the coefficient of friction and thermal conductivity of the journal bearing material, lubrication, ambient temperature, running clearance, hardness, and surface finish of the mating steel shaft.
DB Projected area (dB x L)
L dB
Figure 5-39 Journal bearing configuration model (Courtesy: Du Pont)
Analysis of the plastic material requires calculating whether the PV in the application, derived from the journal bearing configuration model as shown in Figure 5-39, is below 75% (safety factor) of the PV limit of the plastic journal bearing material. It is usually prudent to allow a generous safety margin in determining PV limits, because the real operating conditions for journal bearings are often more rigorous than the calculated or experimental conditions.
367
5.15 Self-Lubricated Thermoplastic Journal Bearings
5.15.2
Journal Bearing Pressure Equation
The journal bearing pressure P is determined by dividing the static load W per the projected surface area A that the journal bearing must withstand in operation.
P=
Static Load W = Projected Area dB × L
(5-3)
Where: P = Pressure bearing (psi) W = Static load (lb) DB = Journal bearing outside diameter (in) dB = Journal bearing inside diameter (in) DS = Shaft outside diameter (in) L = Journal bearing length (in) A = Journal bearing projected area = dB × L (in2) N = Shaft rotation speed (rpm) Thrust Bearing Pressure Equation The thrust bearing pressure P is determined by dividing the static load W per the projected surface area A that the thrust bearing must withstand in operation.
P=
Static Load 4×W = Projected Area π (D 2 − d 2 )
(5-4)
Where: P = Thrust pressure (psi) W = Static load (lb) d = Thrust bearing inside diameter (in) DM = Thrust bearing average diameter (in) D = Thrust bearing outside diameter (in) A = Thrust bearing surface area (in2) N = Rotating thrust plate speed (rpm)
Rotating thrust plate
Thrust bearing N
W
For either Vespel® bearing configuration, the pressure (P) should not exceed the allowable values at room temperature, as shown in Table 5-3: D
Table 5-3 Vespel® Allowable Static Bearing Pressure (Courtesy: Du Pont)
Material
Vespel® SP-1
Vespel® SP-21
Vespel® SP-22
Vespel® SP-211
Fabrication
Mach
Direct
Mach
Direct
Mach
Direct
Mach
Direct
Pressure, psi
7,400
4,800
6,600
4,900
6,000
3,700
5,400
4,000
DM d
Table 5-4 Bearing Velocity (V) Equations
Type of service
Journal bearing
Thrust bearing
Continuous rotation
V = π (DS × N )
V = π (DM × N )
Oscillatory motion
V = π (DS × N ) (θ° /180)
V = π (DM × N ) (θ° /180)
Thrust bearing surface area
π A=
4
( D 2 - d 2)
Figure 5-40 Thrust bearing configuration model (Courtesy: Du Pont)
368
5 Plastic Journal Bearing Design Where: V = Bearing surface velocity (in/min) N = Bearing speed of rotation (rpm) DM = Thrust bearing average diameter = (D + d) / 2 (in) D = Thrust bearing outside diameter (in) d = Thrust bearing inside diameter (in) DS = Journal bearing shaft outside diameter (in) θ° = Bearing angle of oscillation (degrees) Table 5-5 Plastic Materials PV Limit and Temperature (Courtesy: Du Pont)
Material
Reinforcements
PV Limit (psi-fpm)
Max. Temp. (°F)
Vespel® SP-21
15% Graphite
300,000
740
Vespel® SP-22
40% Graphite
300,000
740
Vespel® SP-211
15% Graphite + 10% TFE
100,000
500
PTFE PTFE PTFE PTFE
Unreinforced 15–25% Glass fiber 25% Carbon fiber 60% Bronze
1,800 12,500 20,000 18,500
500 500 500 500
Nylon 6/6
Unreinforced
3,000
215
Acetal homo. Acetal homo.
Unreinforced 20% TFE fiber
3,000 7,000
176 176
Pressure-Velocity (PV) Equation PV (psi-fpm) = P (psi) × V (in/min) / 12
5.15.3
(5-5)
Vespel® Wear Factor Effects Caused by Temperature
The PV limit is a very useful parameter in determining the suitability of a material for a bearing application. However, the contact pressure and the sliding velocity alone do not adequately describe the characteristics of the bearing materials. The operating temperature, bearing geometry, and mating material surface also play a significant role in the wear behavior of the bearings. The temperature is generally the most important parameter, because it not only affects the coefficient of friction but also determines the usable combinations of pressure and sliding velocity, or the PV limit. The wear factors of Vespel® bearings can be moderate even at high PV values, if sufficient cooling is provided to the bearing. Wear can be severe at any PV value if the operating temperature is too high. The wear factor of a Vespel® bearing operating at temperatures below its limit can be predicted analytically or experimentally. The wear factor is derived from an equation relating the volume of material removed by wear in a given service time per unit of load and surface velocity. Wear volume (in3) = ν = K × W × V × ST Where: K = Wear factor (in3-min./ft-lb-h) W = Static load (lb)
(5-6)
369
5.15 Self-Lubricated Thermoplastic Journal Bearings ST = Service time (h) V = Bearing surface velocity (in/min) For flat surfaces, Equation 5-6 is modified: Wear depth (in) = χ = K × P × V × ST
(5-7)
Where: P = Contact pressure (psi) K = Wear factor (in3-min./ft-lb-h) ST = Service time (h) V = Bearing surface velocity (in/min)
Vespel® Wear Transition Temperature
Figure 5-41 shows the Vespel® SP-21 bearing wear factor versus surface temperature in air. The wear factor is essentially constant over a wide range of operating conditions, because the bearing surface temperature does not exceed the wear transition temperature.
5.15.5
Frictional Behavior of Vespel®
Temperature, pressure, and velocity all affect the dynamic coefficient of friction of plastic materials. Typical coefficients of friction at various PV conditions for several self-lubricated Vespel® polyimide compounds are shown in Table 5-6 (Courtesy: Du Pont). The coefficients of friction for Vespel® SP-21 and Vespel® SP-211 undergo a transition at a temperature of 300 °F, similar to that of unreinforced nylon 6/6, as shown in Figure 5-42. Below this temperature the frictional forces drop sharply in the range between 380 and 700 °F. The coefficients of friction of both Vespel® materials are independent of temperature. The friction transition is not associated with wear transition.
Table 5-6 Vespel® Coefficient of Friction (Courtesy: Du Pont)
PV conditions Static P = 50 psi, V = 500 fpm P = 100 psi, V = 100 fpm P = 100 psi, V = 300 fpm P = 100 psi, V = 1,000 fpm P = 1,000 psi, V = 315 fpm
SP-21
SP-22
SP-211
0.12
0.15
0.30
0.11 0.10 0.09 0.07 0.04
0.12 – 0.10 0.09 –
0.12 0.11 – 0.08 –
Steel thrust bearing tester in air PV values between 1.000 and 500.000 (psi-fpm) Wear factor, "K" x 10-10 (in3 -min/ft-lb-hr)
The wear rate of a plastic material operating in air is proportional to the product of pressure and velocity (PV), if the surface temperature does not exceed a critical value called “Wear Transition Temperature”. Above the wear transition temperature, wear increases dramatically. For Vespel® SP-21 material, the wear transition temperature ranges between 900 and 1,000 °F in a vacuum or gasses, and in air it ranges between 700 and 750 °F.
250.0
Vespel SP-21 unlubricated
200.0
150.0
100.0
50.0
0 32
212
390
570
750
930
Surface temperature, (˚F.)
Figure 5-41 Vespel® SP-21 wear factor vs. surface temperature (Courtesy: Du Pont)
Coefficient of friction, (ƒ)
5.15.4
Against an unlubricated carbon steel 0.40
Vespel SP-211
0.30 0.20
Vespel SP-21
0.10 0 32
212
390
570
750
930
Surface temperature, (˚F.)
Figure 5-42 Vespel coefficient of friction vs. surface temperature (Courtesy: Du Pont)
370
5 Plastic Journal Bearing Design
Wear factor, "K" x 10-10 (in3 -min/ft-lb-hr)
100.0 90.0 80.0
The product designer must compensate for the higher frictional forces, caused during the start up and each restart of the bearing. First, the Vespel® polyimide bearing transfers a polymer layer to the mating surface only at start up. Second, the transition temperature must be compensated for the different types of Vespel® compounds, as shown in Figure 5-43. During the restart, breaking-in a new layer is not necessary under service conditions, but the transition temperature is reversible and will continue to operate at each restart.
Vespel SP-21
Vespel SP-211
70.0 60.0 50.0 40.0 30.0 20.0 10.0 0 32
212
390
570
750
930
Surface temperature, (˚F.)
Figure 5-43 Vespel wear factor vs. surface temperature against an unlubricated carbon steel (Courtesy: Du Pont)
DB
5.15.6
Vespel® Journal Bearings Length to Inside Diameter Ratio
For optimum performance of Vespel® journal bearings (using Figure 5-44 as a geometric model), the length per inside diameter (L / dB) ratio should be between 0.75 and 1.25. If a long journal bearing is required in an application, we recommend substituting the long bearing with two shorter journal bearings separated by an air gap in the middle. Small L / dB ratios offer the following advantages: • More efficient debris removal (air gaps in the middle) • Less sensitivity to shaft deflection and misalignment • Better frictional heat dissipation
dB
• Cost advantages due to lower fabrication costs of short bearings
L
Figure 5-44 Journal bearing length to inside diameter ratio
d
5.15.7
D
For optimum performance of Vespel® thrust bearings (using Figure 5-45 as a geometric model), it is recommended that the thrust bearing outside diameter per inside diameter ratio (D / d) does not exceed a value of 2. Ratios greater than 2 can cause overheating at the outside edge; problems may arise from lack of flatness and trapping wear debris within the thrust bearing mating surfaces.
5.15.8 Figure 5-45 Vespel thrust bearing ratio between diameters
Vespel® Thrust Bearing Ratio Between Diameters
Vespel® Journal Bearing Initial Clearance (cI)
Vespel® polyimide compounds have much lower coefficients of linear thermal expansion than some alloy steels and most other thermoplastic materials. For optimum performance, the typical clearance between the Vespel® journal bearing inside diameter and the shaft outside diameter should be between 0.3 and 0.5% of the shaft diameter. Usually, heavier loads require larger clearances. Diametral clearances for Vespel® journal bearings do not have to be adjusted for moisture, because Vespel® polyimide absorbs very little moisture. The initial journal bearing clearances should be calculated by allowing for the circumferential thermal expansion of journal bearing, shaft, and housing. cI = DS × (α S × ∆TS + c) + 2 t × α B × ∆TB
(5-8)
371
5.15 Self-Lubricated Thermoplastic Journal Bearings
5.15.9
Vespel® Journal Bearing Inside Diameter (dB)
Vespel® journal bearing inside diameters dB can be calculated by using the following equation: dB = DS (1 + αS × ∆TS) + c + 2 t × αB × ∆TB – DH × αH × ∆TH
(5-9)
Where: DS = Shaft outside diameter (in) DH = Housing inside diameter (in) cI = Journal bearing initial clearance (in) c = Journal bearing typical clearance (in) αS = Shaft material coefficient of thermal expansion (in/in/°F) αB = Bearing material coefficient of thermal expansion (in/in/°F) αH = Housing material coefficient of thermal expansion (in/in/°F) t = Journal bearing wall thickness (in) ∆TS = Shaft temperature variations (°F) ∆TB = Journal bearing temperature variations (°F) ∆TH = Housing temperature variations (°F) Table 5-7 Vespel® Coefficient of Linear Thermal Expansion (Courtesy: Du Pont)
Material
Vespel® SP-1
Vespel® SP-21
Vespel® SP-22 Vespel® SP-211
Fabrication
Mach
Direct
Mach
Direct
Mach
Direct
Mach
Direct
30
28
27
23
21
15
30
23
α, 10 in/in/°F –6
Example 5-1: Vespel® Journal Bearing Design An automotive gear box device needs a Vespel® journal bearing design analysis to meet the following requirements: : Two journal bearings operating on a 1.50 in diameter shaft must support a total load of 4,000 lbs and operate at temperatures ranging between 73 and 525 °F. : The maximum journal bearing length is 1.50 in and the maximum allowable clearance between the bearing inside diameter and the shaft outside diameter is 0.017 in, in hot or cold conditions. : To prevent the contamination of sensitive surroundings, the bearings cannot be lubricated and they must operate without service 40 hours per week for three years. : The gear box shaft rotates at 20 rpm, the operating sequence is intermittent, 5% running and 95% in stop mode. Determine if Vespel® SP-21 journal bearings will meet these requirements. Solution 1) Determine the maximum journal bearing temperature Refer to Table 5-5: the maximum surface temperature of Vespel® SP-21 in air is 740 °F. The differential surface temperature between 740 °F and 525 °F should be 215 °F.
372
5 Plastic Journal Bearing Design
2) Calculate the PV limit 2.1) Calculate the bearing pressure: P=
2,000 (lb./bearing) W = = 889 psi L × DS 1.50 in × 1.50 in
2.2) Calculate the surface shaft velocity: V =
π × DS × N π × 1.50 × 20 = = 7.85 fpm 12 12
PV = 889 psi · 7.85 fpm = 6,978 psi-fpm At this low PV (6,978 psi-fpm), Vespel® SP-21 (300,000 psi-fpm), the PV value will not be critical, especially considering the intermittent operation. 3) Calculate the wear depth (χ) 3.1) Calculate the running time (ST): ST = 0.05 · 40 h/week × 52 week/yr × 3 yr = 312 h Wear depth (χ) = K × PV × ST Wear factor K (33 × 10–10 in-min/ft-lb-h) according to Figure 5-43 Wear depth (χ) = 33 × 10–10 × 6,978 × 312 = 0.0071 in This wear depth is less than the maximum allowable clearance of 0.017 in. The clearance and the wear depth difference are enough to adapt the thermal expansion, therefore, Vespel® SP-21 journal bearings meet the requirements for this application. 4) Calculate the journal bearing clearance Practical experience and good judgment lead to the assumption that the shaft diameter, journal bearing surface inside diameter, bearing outside diameter, and the housing will all reach different operating temperatures. The following assumptions are made: : The journal bearing contact surface reaches 100 °F higher than the gear box temperature (525 °F + 100 °F = 625 °F) : The journal bearing body average temperature is only 50 °F higher than the gear box (525 °F + 50 °F = 575 °F) : The housing remains at ambient temperature and restrains the journal bearing securely : The journal bearing surface inside diameter will expand inward when the temperature rises : The shaft surface outside diameter will expand outward With these assumptions, the initial room temperature clearance (cI) can be calculated by using Equation 5-8: cI = DS (αS × ∆TS + c) + 2 t × αB × ∆TB
5.16 Teflon® (TFE) Fabric Composite Bearings
Where: cI = Journal bearing initial clearance (in) DS = Shaft outside diameter (1.50 in) c = Journal bearing typical clearance (0.002 in) t = Journal bearing wall thickness (0.0625 in) αS = Shaft coefficient of thermal expansion (6 × 10–6 in/in/°F) αB = Bearing coefficient of thermal expansion (23 × 10–6 in/in/°F) ∆TS = Shaft temperature variation (625–73 = 552 °F) ∆TB = Journal bearing temperature variation (575–73 = 502 °F) We select the Vespel® journal bearing wall thickness (t) to be 0.0625 in. CI = 1.5 [(6 × 10−6 ) (552) + 0.002] + (2 × 0.0625 × 23 × 10−6 ) (502) = 1.5 (0.0053) + 0.0014 = 0.00796 + 0.0014 = 0.0093 in 5) Calculate the maximum journal bearing clearance The maximum journal bearing clearance is equal to the initial clearance (cI) plus the wear depth after three years. Maximum clearance = Initial clearance (cI) + Wear depth (χ) = 0.0093 + 0.0071 = 0.0164 in Therefore, the Vespel® journal bearings satisfy the maximum clearance specifications of 0.017 in to operate without lubrication at the given elevated temperature (525 °F) for the automotive gear box requirements.
5.16
Teflon® (TFE) Fabric Composite Bearings
Teflon® TFE woven fabrics have been made into a variety of bearing types, including spherical, ball joint, thrust, and journal bearings. In addition, nonwoven and knitted fabrics also have been used for special applications. There are two basic requirements for the successful use of the Teflon® TFE fabric as a bearing surface: • An adequate bond of the Teflon® TFE fabric to the substrate • Adequate support of the individual fibers or fiber bundles in the fabric Teflon® TFE woven fabrics can be bonded very satisfactorily with conventional adhesives or bonding techniques by use of a double fabric in which one face is composed of cotton, an easily bondable fiber, and the other face composed in part or totally of Teflon® TFE fabric. Another method is to modify the surface tension of the face of a twill fabric of Teflon® TFE fiber. The raised fibers in the fabric are trapped in a suitable adhesive, forming a mechanical bond. Many fabric structures have been used adequately to support the Teflon® TFE fiber in the bearing. The type of bonding agent used is one that has good load bearing properties and is applied so that good penetration of the voids of the fabric is obtained. Phenolformaldehyde resins are effective, because of their load carrying ability.
373
374
5 Plastic Journal Bearing Design
Figure 5-46 Teflon® filament weaving for composite bearing (Courtesy: Du Pont)
Metal backing
Teflon® filament weaving creates structures of exceptional strength to support the bearing surface. These are, by their nature, truly concentric and have no seam or overlap. They can handle high radial and longitudinal stresses while supporting bearing pressure loads of 60,000 psi. They are also resistant to shock loading and abrasion. Their high strength makes possible the use of thin walled (0.062–0.125 in) composite bearings with a coefficient of linear thermal expansion similar to steel that also allows the dissipation of heat through the metal shafts. Low coefficient of friction and high load carrying capacity come naturally with the Teflon® fabrics used for composite bearing surfaces. With tensile strengths 20 times greater than straight PTFE resins, they have excellent cold flow resistance and have shown some remarkable wear characteristics. Figures 5-46 and 5-47 show Teflon® composite bearing structures.
5.16.1
Fabric Adhensive
Figure 5-47 Teflon® fabric composite bearing (Courtesy: Du Pont)
Bearing Physical Properties
Teflon® fabric bearings are made by the most advanced fabrication processes under strict quality control. This ensures uniformly high strength in the supporting structures and a strong bond to the Teflon® filament bearing surface. These structures will support a bearing load pressure of up to 60,000 psi, and the bearings meet operating requirements of high load pressures or high speeds in rotational and stroking movements and in oscillation applications. Teflon® fabric bearings have exceptional dimensional stability. A boiling water test produced no swelling or shrinkage. The linear thermal expansion is similar to steel and in fact less than some steels. The thin wall of the bearings helps the heat transfer away from the bearing, through the metal shaft surfaces. The bearings may be used in applications requiring operating temperatures from –300 °F to +350 °F. The specific gravity is lower than for bronze or carbon steel and is lower than other plastics.
5.16.2
Bearing PV Limit Rating
For many years, the plastics industry has used the pressure-velocity (PV) limit for evaluating performance of Teflon® fabric composite journal bearings. Knowing the PV limit of a bearing, a designer can determine the loads and surface running speeds under which a bearing can safely operate. However, there is another factor to consider. Heat generated by friction is a major cause of polymeric degradation. The rise in temperature is dependent on the running speed and is not a linear function of the PV limit. To evaluate the operating conditions of a composite journal bearing, a designer needs to know the approximate temperature generated at the wear surface. For Teflon® fabric bearings this temperature can be as high as 350 °F. As a guideline, a Teflon® fabric bearing has a maximum 25,000 PV limit. However, test results run at 15,000 PV gave only 0.002 in total wear after 10,000,000 cycles, with a 25° oscillation motion at 600 cycles per minute and a radial load of 343 pounds.
5.17 Thermoplastic Kevlar® Reinforced Bearings
5.16.3
Journal Bearing Clearances (c)
The effect of clearances on wear may not be as critical for Teflon® fabric composite journal bearings as for self-lubricated plastic or metal bearings. However, an important design consideration is allowance for linear thermal expansion of the Teflon® fabric composite journal bearing backing support, subjected to a wide range of service temperatures or continuous operation at surface speeds above 150 feet per minute. Table 5-8 provides clearance guidelines for sleeve bearings of Teflon® fabric composite journal bearings in plastic housings. Table 5-8 Journal Bearing Clearances (c) (Courtesy: Du Pont)
Shaft diameter (in)
Clearance (in)
0.50
0.001–0.003
1.00
0.002–0.005
2.00
0.004–0.007
Smaller clearances may be used when working with metal-backed bearing supports, as the coefficient of linear thermal expansion of the thin layer of Teflon® can usually be ignored. Heavy Equipment Applications On crawler type tractors, heavy earth moving equipment, and farm machinery, Teflon® fabric composite journal bearings with their freedom from oil and grease are right at home in the dusty and sandy conditions in which this equipment operates. These bearings have no problems with rust, corrosion, and they do not need oil or grease seals that require more space and add cost.
5.17
Thermoplastic Kevlar® Reinforced Bearings
Thermoplastic resins that are reinforced with Kevlar® aramid chopped fibers are injection moldable composites. Kevlar® possesses a combination of physical properties that cannot be found in any other commercially available fiber. Using Kevlar® composites, design engineers have a new family of superior wear and abrasion resistant thermoplastic materials from which to choose. The advantages offered by Kevlar® aramid chopped fibers include: • Superior wear resistance • Non-abrasive bearing inside surface • Significantly improved mechanical properties • Higher PV limit • Higher operational temperatures • Lighter bearing weight • Excellent process characteristics without wear on equipment and molds • Greatly improved machinability
375
376
5 Plastic Journal Bearing Design Several thermoplastic resins reinforced with Kevlar® aramid fibers are commercially produced for the plastic industry, among them acetal homopolymer with 15% Kevlar®, nylon 6/6 with 17.5% Kevlar®, PET with 17.5% Kevlar®, polyphenylene sulfide (modified) with 25% Kevlar®, polypropylene with 17.5% Kevlar®, copolyester elastomer with 10% Kevlar®, and TPE polyurethane with 10% Kevlar®. All these composites are produced as injection moldable pellets ranging in size from 0.25 to 0.375 in. The addition of Kevlar® fortifies the positive characteristics of the matrix resins, while reducing the abrasion wear problems. For superior wear resistance, Kevlar® aramid fiber composites are the nonabrasive answer. Many thermoplastic composites can achieve low wear rates by using a reinforcement that adds to their strength and/or stiffness. Most, however, also show a correspondingly high abrasiveness to the bearing surface. Kevlar® aramid fiber thermoplastic composites are the exception. The tough, strong reinforcing material makes the product extremely wear resistant without excessive galling to the mating wear surfaces. In addition, it improves mechanical properties and increases the operational temperature capabilities. In tests conducted using unreinforced nylon 6/6, erosion of the steel washer was more than 40 times greater than for nylon 6/6 reinforced with Kevlar® aramid fibers. Nylon 6/6 parts wore 70% faster than nylon 6/6 parts reinforced with Kevlar®. Wear tests using unreinforced nylon 6/6 molded parts and nylon 6/6 molded parts reinforced with Kevlar® resulted in equally dramatic performance differences. Both parts were tested for 240 hours at a pressure of 250 psi and a velocity of 10 ft/min. The final wear factor for unreinforced nylon 6/6 was 917. For nylon 6/6 parts reinforced with Kevlar®, the wear factor was 239, resulting in unreinforced nylon 6/6 wearing four times faster than nylon 6/6 reinforced with Kevlar® aramid fibers. Figure 5-48 Components made from thermoplastic materials reinforced with kevlar aramid fibers (Courtesy: Du Pont)
Figure 5-48 shows several applications made of thermoplastic materials reinforced with Kevlar® aramid fibers.
377
6
Thermoplastic Molded Spring Design
6.1
Introduction
Thermoplastic resins, such as acetal homopolymer, nylon 6/6, polyethylene, polypropylene, TPE, and other materials have excellent flexibility, hysteresis, and mechanical properties for injection molding flexible products that function as springs. With these materials, thermoplastic springs can be incorporated into multifunctional product components, reducing the number of parts required for the application, lowering manufacturing, assembly, and inventory costs. Thermoplastic molded spring applications include cameras, water pressure systems, irrigation, printing mechanisms, door closures, electrical lock connectors, pen caps, tubing flow metering, transportation equipment, a wide range of general industrial devices, and consumer products. The most critical material requirements for injection molded thermoplastic springs include rigidity, good fatigue resistance, high load carrying capacity, minimum creep, self-lubricity, and ease to process into thin, complex multifunctional components. Depending on the specific end use application, thermoplastic molded springs may be required to perform under a wide range of temperatures, in a corrosive atmosphere, or under other hostile environmental conditions. One of the most frequently selected thermoplastic resins for spring applications is acetal homopolymer. This polymer provides the best balance set of mechanical properties and molding process conditions. Other low creep resistance and high strength thermoplastic resins, such as polyethylene, polypropylene, TPE, polycarbonate, unreinforced, and glass fiber reinforced nylon 6/6 are also used for springs. To ensure a thermoplastic molded spring’s effective performance over the life of the product, they should be designed to operate at zero strain in the normal relaxed position. Springs should not be designed to flex, storing mechanical energy on a continuous basis, because, even under low stress levels, the continuous load will cause a reduction in its spring characteristics over a long period. Thermoplastic molded springs should be designed to work for intermittent loading and without strain the rest of the time. Several types of thermoplastic molded springs have been used in many critical applications. Case histories of commercial applications and some general observations on these spring families are presented in this chapter. These spring families include helical compression and extension, cantilever, leaf, helical torsion, spiral torsion, belleville, lock, and wave washers.
378
6 Thermoplastic Molded Spring Design
6.2
Thermoplastic Molded Spring Design Considerations
Injection molded thermoplastic spring characteristics should meet the following considerations: • Compensate for temperature and chemical environment effects on the mechanical properties of the thermoplastic springs • Design thermoplastic springs for intermittent loads without exceeding the proportional stress limit and fatigue resistance under the end use operating conditions for the service life of the product • Sharp corners should be avoided, use generous fillet radiuses Helical compression
Helical extension
Single leaf spring
• Spring designs based on constant strength cantilever beam equations operate at lower levels of stress than other spring families Not many injection molding thermoplastic materials satisfy all these spring requirements. For instance, reinforced materials that have appreciable ultimate yield strength and a high modulus of elasticity, also have some reduced elastic recoveries under significant strains; therefore, these materials are not recommended for spring applications. The selection of the most suitable injection molding thermoplastic resin for spring applications requires a very careful examination of the properties, the ambient operating conditions (temperature, chemical resistance, etc.), types of loading, and additional requirements of the spring application, such as creep, wear resistance, dimensional tolerances, spring design complexity, molding process, and so forth.
Belleville washer
Wave washer
Acetal homopolymer, polycarbonate, and unreinforced nylon 6/6 resins possess a combination of properties that make them particularly suitable for the production of flexible and elastic components with the spring characteristics.
6.3
Lock washer
Thermoplastic Helical Compression Springs
Free Load ed
Fixed
Free
Loaded
Helical torsion
Spiral torsion
Figure 6-1 Common types of metal spring designs
The use of injection molding thermoplastic materials for helical compression springs is restricted to very special applications. The most elementary and least demanding application is the polyethylene spring on the stopper for pharmaceutical containers. Polyethylene is not used in precision spring applications, because the force provided by a polyethylene spring is very low and requires a considerable deflection. Helical springs are ideal for the metal wire winding process; however, these geometries are very difficult for injection molding. Figure 6-1 shows common types of metal springs available on the market. Figure 6-2 shows a molded helical compression spring for a pen actuator (difficult), a reticulated notion, where the curved beams are converted into a bending spring (small strain) with higher spring constant, and a system using Belleville spring washers that provide the operating characteristics of a helical compression spring. Thermoplastic springs have a very low spring constant compared with metal helical springs of the same dimensions. It is very important that spring constant value four the round cross section of metal helical springs is used for metal springs
379
6.4 Thermoplastic Molded Cantilever Beam Springs only and not for compression springs made of thermoplastic material. This is because of the considerable value difference of G (material torsional modulus of elasticity) between the metallic and thermoplastic materials. Pen actuator spring
For example, the ratio between the torsional modulus of elasticity (G) of steel and acetal homopolymer is:
W
G (Steel) 8,500 = = 63 G (Acetal Homopolymer) 135 Calculating a thermoplastic helical spring’s compression is possible by using the engineering equations for metal springs. However, the design and construction of the mold are difficult, complex, and expensive. Running and maintaining the mold in production creates too many manufacturing problems. Reticulated spring
6.4
Thermoplastic Molded Cantilever Beam Springs
Injection molded thermoplastic cantilever springs are the most common type of springs made and used in many applications. There are considerable advantages compared with the use of metals, even more so when the fundamental rules of multifunction designs are adopted. Figure 6-3 shows four types of cantilever spring designs and a stress versus weight comparison graph using the classical cantilever beam equations. The graph is a comparison between the different cantilever spring geometries that produce an equivalent spring rate. The cantilever spring (A) has a constant rectangular cross section and an initial spring rate calculated from the deflection equation for a cantilever beam (W / δ = E I / L3) where W is the load and δ is the deflection at the free end of the beam. The other cantilever springs were designed to provide an identical spring rate, using the equations for constant strength beams. This results in lower stress levels and, sometimes, in a reduction in spring weight. For example, in the cantilever spring (B) the stress is 75% of that developed in cantilever spring (A) and the weight is reduced by 25%. This weight reduction can be very important as a cost savings factor when a large injection molding production run is contemplated.
Stack of belleville springs
Figure 6-2 Thermoplastic molded compression spring illustrations
b W g "A"
h
Spring "B
Tensile stress, (x 103 psi)
Sprin
W
" h
L
L
b b
b
2
A
B C D
1
W
W Sprin
3
Sprin
g "C"
g "D
"
2.25 h L
h L
4.50
Spring weight, (grams)
Figure 6-3 Cantilever springs, tensile stress vs. weight comparison
6.75
380
6 Thermoplastic Molded Spring Design If sheet metal stamping or forming operations are considered for fabrication, the sheet metal manufacturing cost is more expensive than for the thermoplastic injection molding process. ε=
σ E
(6-1)
σ =
WL Z
(6-2)
I=
b h3 12
(6-3)
Z =
b h2 6
(6-4)
W =
Z×E×ε L
(6-5)
Where: δ = Deflection (in) σ = Stress (psi) Z = Section modulus (in3) ε = Strain of beam at root (in/in) E = Modulus of elasticity (psi) W = Force of deflection (lb) L = Length of beam (in) b = Width of beam (in) h = Beam thickness at root (in) I = Moment of inertia (in4) Figure 6-4 shows four cantilever beam spring geometries with their deflection equations used in the analysis of thermoplastic and metal materials. More detailed information about cantilever latch beams and the strain limits for common types of resins can be found in Chapter 8.
W h
b
W
h
b
L δ = 0.67 x
ε x L2 h
b 4
L 4 x W x L3 b x h3 x E
δ =
ε x L2 δ = 0.86 x h
δ =
W
W
b
5.15 x W x L3 b x h3 x E
h b h
h 2
L δ = 1.09 x
ε x L2 h
δ =
6.50 x W x L3 b x h3 x E
L δ = 1.33 x
ε x L2 h
Figure 6-4 Cantilever spring geometries and deflection equations
δ =
8.00 x W x L3 b x h3 x E
6.5 Cantilever Beam Spring Design Analysis
6.5
Cantilever Beam Spring Design Analysis
Several methods are used to analyze cantilever beam springs. Computer analysis, which requires the use of one of several available programs, is the latest method. One type of software program uses the classic cantilever beams equations. Another type employs graphical models of cantilever beams. A more sophisticated type of software uses a drawing program to create a scale model of the completed product, then a second stress analysis software program calculates the stress and deflection of the computer model using the product required end use service conditions. In addition, this software program also analyzes the dynamic characteristics of the thermoplastic material, such as the stress-strain curves at different temperatures, moisture absorption, and creep. The computer analysis methods are not discussed in this design handbook. Here, three spring analysis methods will be examined. Reference will be made to flexible springs, in view of their practical importance for thermoplastic materials. Only springs loaded instantaneously and in normal environmental conditions will be considered.
6.5.1
Initial Modulus of Elasticity Cantilever Beam Analysis Method
This method is an approximation only for small strains, since it ignores certain properties of injection molding thermoplastic resins. The same equations as for metals are employed for calculating the initial modulus of elasticity. Because of the viscoelastic behavior of thermoplastic materials, the modulus of elasticity decreases with increased strain, an error in calculation is made which becomes greater as the strain increases. This method takes into account this error by fixing a maximum limit (safety factor) or the “strain limit,” that has been established experimentally at 25%. For example, for acetal homopolymer cantilever springs the strain limit is 1.25% and the stress at 73 °F is 6,750 psi. The “strain limit” has a typical value for each material and is independent of the temperature. It has been proven experimentally that, within its “strain limit,” every thermoplastic material has practically complete elastic recovery. To calculate the deflection of a cantilever spring made of a thermoplastic material using this method of calculation, • Determine the deflection according to the elasticity equations applicable to metals, using the initial elastic modulus • Calculate the corresponding strain percentage. If the result is lower than the strain limit of the thermoplastic material in question, the calculation is within the permissible 25% error. Otherwise, a more accurate method of calculation must be used.
6.5.2
Stress-Strain Curve Cantilever Beam Analysis Method
This method of calculation also uses the classical equations developed for metals, but takes into consideration the secant modulus rather than the initial modulus. In this way, the typical shape of the stress-strain curve is taken into account, which was the main cause of the unreliability in this calculation, particularly for relatively high stresses.
381
382
6 Thermoplastic Molded Spring Design
6.5.3
Empirical Data Cantilever Spring Analysis Method
This method is based on experimental test data, obtained by stressing small samples injection molded of acetal homopolymer resins and measuring the actual deflection at the free end of the cantilever beam using various loads. With this method of calculation, the uncertainties caused by the stress distribution in the cross section areas are eliminated, which is very important in high stress conditions. Acetal Homopolymer Cantilever Spring Empirical Data The experimental test spring rates for acetal homopolymer cantilever springs are plotted in Figure 6-5. Deflection (δ) Length (L) at 73˚ F. and intermittent loading 2.000 Maximum stress 1.000 600
8 .0 0 0
4.0 00
800
L /h = 4 10 .00
9.0
2.000
0
400
00
200
6 .0 0 0
L /h = 6
100 80
L /h = 8
Spring rate, WM/δ, (psi)
60
8.88
L
40 L /h = 10 L /h = 12 20 L /h = 14 10
L /h = 16
8
L /h = 18
6
L /h = 20 L /h = 22
4
L /h = 24
W
b
L /h = 26 L /h = 28
2
δ h
Figure 6-5 Empirical data of acetal homopolymer cantilever spring (Courtesy: Du Pont)
1 0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
383
6.5 Cantilever Beam Spring Design Analysis
Example 6-1: Initial Modulus of Elasticity Analysis Method An acetal homopolymer cantilever spring is required to support a 2.0 lb load when deflected 0.600 in. The length of the cantilever spring is 1.50 in, the width is 0.375 in, and wall thickness is 0.0714 in. This example is used to illustrate the differences in the calculations among the three analysis methods for acetal homopolymer spring calculations. The initia modulus of elasticity for acetal homopolymer is: E = 410,000 psi : Calculate the moment of inertia (I): I = (b h3) / 12 = (0.375 × 0.07143) / 12 = 0.0000113 in4 : Calculate the spring load (W): W = (3 × δ × E × I) / L3 W = (3 × 0.60 × 410,000 × 0.0000113) / 1.503 = 2.487 lb : Calculate the section modulus (Z): Z = (b h2) / 6 = (0.375 × 0.07142) / 6 = 0.000318 in3 : Calculate the maximum stress (σ): σ = (W × L) / Z = (2.487 × 1.50) / 0.000318 = 11,731 psi : Calculate the spring strain (ε): ε = σ / E = 11,731 / 410,000 = 0.0286 = 2.86% The 2.86% value considerably exceeds the strain limit of 1.25% allowable for acetal homopolymer resins. Consequently, a more accurate calculation is necessary: 9 8
Calculate the load of the cantilever beam spring using the stress-strain curve analysis method and data from Example 6-1. From the stress-strain curve for acetal homopolymer shown in Figure 6-6 we see that with a strain of 1.25% the unit average tensile stress is 6,750 psi, which is a value below the yield point of the material (10,000 psi). Applying the cantilever beam Equation 6-2, the stress from Figure 6-6, L and Z from Example 6-1: W = (σ × Z) / L W = (6,750 × 0.000318) / 1.50 = 1.431 lb The force exerted by the spring is 1.431 lb rather than 2.487 lb.
122˚ F.
6.75
Tensile stress, (1.000 psi)
Example 6-2: Stress-Strain Curve Analysis Method
6
158˚ F.
5 212˚ F.
4 3 2 1 0 0
1.25
2
3
Strain, (%)
Figure 6-6 Stress-strain curve for acetal homopolymer (Courtesy: Du Pont)
Service temperature, (˚ F.)
73˚ F.
384
6 Thermoplastic Molded Spring Design
Example 6-3: Empirical Data Analysis Method An acetal homopolymer cantilever spring is required to support a 2.0 lb load when deflected 0.600 in. The length of the cantilever spring is 1.50 in and the width is 0.375 in. Calculate the cantilever spring wall thickness using the empirical data analysis method. L = 1.50 in W = 2.0 lb b = 0.375 in δ = 0.600 in : Calculate the modifier load (WM): WM = W / b = 2.0 / 0.375 = 5.33 (lb/in)
: Calculate the spring rate (WM / δ): WM / δ = 5.33 / 0.600 = 8.88 (psi)
: Calculate the deflection/length ratio (δ / L): δ / L = 0.600 / 1.50 = 0.40
Find the intersection of the values for WM / δ = 8.88 (psi) and δ / L = 0.40 from the spring rate graph (Figure 6-5); these data provide the value for L / h. L / h = 20 : Calculate the cantilever spring wall thickness (h): h = L / 20 = 1.50 / 20 = 0.075 in Read off the maximum stress value from the empirical data graph from δ / L = 0.40 and the L / h = 20 (Figure 6-5): σMax = 7,250 psi A comparison of the three analysis methods used in Examples 6-1 through 6-3 shows that the initial modulus of elasticity analysis method contains an error about 62% too high in comparison with the empirical data analysis method in the estimating of the load exerted by the spring. The stress-strain curve analysis method error was 7% too low in comparison with the empirical data analysis method. The initial modulus of elasticity analysis method is more accurate, although not exact, largely because the data for the secant modulus was obtained from a tensile stress-strain curve, whereas the behavior of acetal homopolymer under bending stress is better. Note that within certain values of deflection the three methods give varying results, because of possible differences in the rate of application of the load and of crystallinity in the resin. It should also be noted that, within the normal design limits, calculation errors may even be lower than deviations of behavior due to injection molding factors (crystallinity) and the loading speed factor. Suitable testing is crucial, especially when carried out on a prototype injection molded spring under the same production conditions and tested under the actual conditions of use.
385
6.6 Thermoplastic Cantilever Spring Applications Deciding the actual load exerted by the cantilever spring is very important, in addition to the need to conduct tests to evaluate the useful life of the spring under actual working conditions (always being aware of strains lower than the limits for acetal homopolymer (1.25%) and for unreinforced nylon 6/6 at 50% RH (0.8%))
6.6
Thermoplastic Cantilever Spring Applications
With the introduction of engineering thermoplastic materials, many cantilever spring applications have been commercialized. Thermoplastic materials are different from metals; consequently, the cantilever spring designs for injection molding thermoplastic materials take advantage of the characteristics of these polymers, such as the flexibility of the components that function as a spring and the multi-functional design capabilities of a complex component (gears, cams, etc.). This allows cost savings in the number of parts, fewer assembly operations, and less inventory. In addition, certain properties can be used to the advantage of thermoplastic materials, such as resistance to corrosion, chemicals and wear, low coefficient of friction, low specific gravity, low noise, self-lubrication, electrical insulation, multi-functional design, lower manufacturing costs, etc.
Spring tongue Cam
Thermoplastic Spring Ratchet Applications The following illustrations show different injection molded thermoplastic spring ratchet and flexing applications. Figure 6-7 shows a component from the mechanism of a cash register. The outer disc carries three flexible tongues that act as springs allowing the central cam to rotate clockwise, but not in the counterclockwise direction. Figure 6-8 shows a garden spray; in the trigger a thermoplastic spring is arranged to set the rotation of an integral ratchet wheel with a cam. The trigger moves a lever that drives the upper piston that regulates how much water is discharged by the spray. Figure 6-9 shows a gear wheel with flexible spring spokes molded in a single component. Figure 6-10 shows three spring ratchets and gear wheels with pointers for an instrument mechanism.
Wheel
Figure 6-7 Three spring ratchets for a cash register machine
Lever
Trigger
Spring
Figure 6-8 Garden sprayer with spring ratchet water regulator
Figure 6-9 Gear wheel with flexible spring spokes
Figure 6-10 Three spring ratchets on gear wheel pointer
386
6 Thermoplastic Molded Spring Design Internal gear Spring
Rotor
Ratchet
Figure 6-11 Two spring ratchet gear systems
Figure 6-11 shows an electric meter assembly mechanism with an acetal homopolymer internal gear; two small ratchets made of metal are actuated by two springs made of acetal homopolymer. The springs are injection molded integrally with the central rotor. The springs are only 0.020 in thick for a working length of about 0.625 in. Figure 6-12 shows a portable tape labeling device. A spring ratchet mechanism is used for feeding the strip tape; the spring operating the ratchet was injection molded as an integral part of the trigger. Figure 6-13 shows an adding machine locating spring print gear. Figure 6-14 shows a gear and a spring ratchet with a tailpiece that exerts a counter force to eliminate backlash of the gear. The spring ratchet is preloaded on top of the gear teeth. The small and repeated deflections of the spring ratchet during the gear rotation cause negligible creep effects on material strength. Thermoplastic Locating Spring, Shock-Absorbing Applications
Gear Spring ratchet
Trigger
Figure 6-12 Labeling device spring ratchet tape feeder
Figure 6-15 shows a thermoplastic printing ring integrally injection molded with a locating spring. The rotating printing ring stops at the point mark position when the locating spring tongue enters or the spring backs inside a blank-marked slot of the printing ring. Figure 6-16 shows the mechanism for a locking cap of an automotive gasoline tank filling tube. When the cap is in the locked position the cap rotates idly, as the locating springs and the override cams avoid overtensioning the cap. Figure 6-17 shows a film projector door handle locating spring that controls the rotation of the handle. Figure 6-18 shows a lock mechanism with shock absorbing spring, which functions in both horizontal directions. Locating spring tongue Locating spring
Locating spring
Central cam
Figure 6-13 Adding machine locating spring print-out gear
Figure 6-15 Printing ring locating spring
Figure 6-16 Locating springs, automobile gasoline tank cap
Figure 6-17 Film projector door handle locating springs
Figure 6-18 Lock mechanism with shock-absorbing spring
Spring ratchet Back lash spring
Ratchet gear
Figure 6-14 Gear backlash spring ratchet mechanism
Internal teeth
387
6.6 Thermoplastic Cantilever Spring Applications Figure 6-19 shows a cable stretcher system with a spring mechanism. Figure 6-20 shows a hose clamp adjustment mechanism for mounting various sizes of hoses. This type of hose clamp makes the installation and clamping of the hose simple, secure, fast, and safe. Figure 6-21 shows the body of an electrical switch, in which the pivoted on-off button is positioned by a locating spring. When the button is pushed down to either side, a direct indentation on the status of the switch is provided. Figure 6-22 shows an automotive roof light with snap springs to assemble the lens. Figure 6-23 shows an electrical slider switch with a leaf spring mechanism.
Figure 6-19 Cable stretcher system with spring mechanism
Thermoplastic Fixing Clip Spring Applications The following illustrations show injection molded thermoplastic fixing clip spring applications. These fixing clip spring applications are subjected to a permanent type of loading. They are designed for minimal stress loading of the fixing clip springs, taking into account the eventual strength reduction over a long time (creep) and operating temperature conditions.
Locking spring Spring
Figure 6-24 shows a simple fixing clip spring for a pen cap. Figure 6-25 shows a spring clip holder, where the fixing clip spring is in the closed position. Figure 6-26 shows a film projector locating compression spring, used to detect if the film projector is loaded. Figure 6-27 shows a medical tubing flow regulator for controlling the medication flow rate.
Hose
Figure 6-20 Hose clamp system with ratchet locking springs
On-off bottom
Fixing clip spring Pivot
Figure 6-24 Common pen cap with retainer fixing clip spring
Figure 6-25 Spring clip holder
Figure 6-21 Electrical switch locating position control spring
Clip spring flow position adjustment
Figure 6-22 Automotive roof light with snap springs
Slider switch
Leaf spring
Figure 6-26 Film projector locating compression spring
Figure 6-27 Medical tubing flow regulator
Figure 6-23 Electrical slider switch with spring mechanism
388
6 Thermoplastic Molded Spring Design Flexible hinge
Pivot snap
Figure 6-28 Pivoted flexible spring hinge clothespin
Flexible spring hinge
Thermoplastic Flexible Hinge Applications Combining the elasticity of some injection molding thermoplastics with their high resistance to repeated flexing, it is possible to manufacture ingenious devices, as shown in the following illustrations. The function of a flexible hinge is to remain open and strain-free when it is not in service; but when in operation, the flexible hinge provides a differential spring force for clamping or returning to its original position. Figure 6-28 shows an integrally molded thermoplastic flexible hinge clothespin. Figure 6-29 shows an encapsulated thermoplastic flexible hinge staple remover. Figure 6-30 shows a thermoplastic flexible hinge tap tool for recharging air conditioner refrigerant of cars. Figure 6-31 shows a flexible hinge door catch device used to keep the door closed. Thermoplastic Torsional Springs
Metal teeth
Figure 6-29 Flexible spring hinge staple remover
Flexible hinge can refrigerant holder
Outlet
Locking guides
Figure 6-30 Flexible hinge tool for charging refrigerant of cars
Injection molded thermoplastic torsional springs are not commonly used in commercial applications. Thermoplastic torsional springs could provide new design opportunities in applications requiring intermittent load-bearing conditions. By the simple process of fixing a thermoplastic flat bar (Figure 6-32) at one end and applying torque at the other end, a spring action is produced by the torsional effect and the flat bar’s tendency to return to its original free loading position. A thermoplastic torsional spring is subjected to the action of a bending moment, producing a normal stress and responds correctly to varying load conditions. The thickness of the flat bar, its design, and the choice of a thermoplastic material with the ideal mechanical properties is critical. The properties required for some torsional spring applications are good fatigue resistance, spring like (hysteresis) characteristics, high rigidity, and good creep resistance. Figure 6-33 shows a heavy-duty torsional spring transmission shaft for an industrial grass mower tractor.
6.7
Thermoplastic Belleville Spring Washers
The Belleville spring washer takes its name from Julien Belleville, a French engineer who secured an English patent in the spring of 1866. His development was used largely in recoil mechanisms for artillery and buffer components used for railway applications.
Door catch
Flexible hinge door handle
Belleville spring washers, as shown in Figure 6-34, are convex round discs with a hole in the center having a saucer shape. Under load, they flatten, resuming their original shape when the pressure is released. Mounted in series, back to back or nested on a rod, they provide a simple substitute for other types of springs.
Figure 6-31 Flexible hinge used to keep doors closed Free end torque
Fixed end
Figure 6-32 Flat bar torsional spring design
Figure 6-33 Grass mower tractor torsional spring transmission shaft (Courtesy: Du Pont)
Figure 6-34 Thermoplastic molded belleville spring washers
389
6.7 Thermoplastic Belleville Spring Washers Copolyester thermoplastic elastomers, acetal homopolymer, and nylon 6/6 are some materials employed in the fabrication of Belleville spring washers, used for applications requiring high spring loads and small deflections. Belleville spring washers injection molded from acetal homopolymer are especially desirable in demanding applications, requiring nonmagnetic and electrical insulation properties. Some potential end use applications are as a replacement for helical springs in switches and relays or return springs for push buttons on computer and control panels where nonmagnetic materials are essential. They also provide a toggle action for electrical and mechanical control levers. Belleville spring washers can be deflected from their original, convex shape to a concave shape, snapping inside out. They snap back to their original shape only when pressure is exerted in the opposite direction.
6.7.1
Acetal Homopolymer Belleville Spring Washer Analysis
Belleville spring washers injection molded from acetal homopolymer are used for testing the performance and comparing the experimental data to those obtained by using standard engineering equations developed for Belleville spring washers. Belleville spring washers of different sizes using the geometric model shown in Figure 6-35 were injection molded from acetal homopolymer. Each size of Belleville spring washer was tested using an Instron testing machine at a loading speed rate of 0.05 in per minute to develop the load and deflection empirical data. Standard equations were used to calculate loads and deflections for each spring size. Subsequently, the results were compared for both types of analysis methods. Belleville spring washer equation W =
E×δ δ (H − δ) H − t + t 3 3 2 D (1 − υ2 ) 4 d ×
(6-6)
Where: W E δ υ t H D d
= Compression load (lb) = Material modulus of elasticity (psi) = Belleville spring washer deflection (in) = Material Poisson’s ratio = Belleville spring washer wall thickness (in) = Belleville spring washer height (in) = Belleville spring washer outside diameter (in) = Belleville spring washer inside diameter (in)
Figures 6-36 through 6-44 are the plotted results for the compression load “W” (lb) vs. the deflection “δ” (in) obtained in both analysis methods. The solid lines in the spring graphs are the empirical data test results and the dashed lines are the calculated results generated by a computer analysis program.
W t H d D
Figure 6-35 Belleville spring washer geometric model
390
6 Thermoplastic Molded Spring Design
90
100
2.00 Dia. 1.25 Dia.
0.10
90
80 t = 0.10
Compression load "W," (lb.)
60 50 40 t = 0.07
30 20 10
80
80
70
70
60
t = 0.10
50 40 30 t = 0.07 20
0 0.05
0.10
0
0.05
50 40 30
Compression load "W," (lb.)
Compression load "W," (lb.)
60
0.20
180
80
t = 0.10
20
t = 0.03
Figure 6-39
0.10
2.00 Dia. 180
140
140
120
t = 0.10
100 80 t = 0.07
60 40
t = 0.03
0.20 0.5 Dia.
120
t = 0.10
100 80
t = 0.07
60 40 20
0
t = 0.03
0 0
0.05 0.10 0.15 0.20 0.25 0.30 Deflection "δ," (inch)
0.05 Deflection "δ," (inch)
200
2.00 Dia. 0.85 Dia.
160
20
10
0
0
0.10
160
t = 0.07
0
t = 0.07 20
Figure 6-38
200 2.00 Dia. 1.25 Dia.
70
30
Deflection "δ," (inch)
100 0.20
40
t = 0.03
Figure 6-37
90
t = 0.10
50
0
Deflection "δ," (inch)
Figure 6-36
0.5 Dia.
60
t = 0.03
0 0
0.10
10
10
t = 0.03
2.00 Dia.
90
Compression load "W," (lb.)
Compression load "W," (lb.)
70
100
2.00 Dia. 0.85 Dia.
0.10
Compression load "W," (lb.)
100
0.05 0.10 0.15 0.20 0.25 0.30
0
0.05 0.10 0.15 0.20 0.25 0.30
Deflection "δ," (inch)
Figure 6-40
Deflection "δ," (inch)
Figure 6-41 2.00 Dia.
2.00 Dia. 1.25 Dia.
360
280
240 200 t = 0.07
160 120
t = 0.03 80
Compression load "W," (lb.)
t = 0.10
0.30 320
0.30
320
280 Compression load "W," (lb.)
2.00 Dia. 0.85 Dia.
360
0.30
320
0.50 Dia.
400
280
t = 0.10
240
240 200 t = 0.07 160 120 t = 0.03
80
Compression load "W," (lb.)
400
200
t = 0.07 120 80
40
40
40
0
0
0
0
0.05 0.10 0.15 0.20 0.25 0.30 Deflection "δ," (inch)
Figure 6-42
0
0.05 0.10 0.15 0.20 0.25 0.30 Deflection "δ," (inch)
Figure 6-43
t = 0.09
160
t = 0.05 0
0.05 0.10 0.15 0.20 0.25 0.30 Deflection "δ," (inch)
Figure 6-44
391
6.7 Thermoplastic Belleville Spring Washers Reviewing the results found in Figures 6-36 to 6-44, using the empirical data and standard equation, it can be seen that the standard equation analysis method causes some type of error, especially for thick Belleville spring washers requiring large deflections. For example, for a 0.030 in wall thickness and a deflection of 0.100 in, the error is approx. 12%. For a 0.100 in wall thickness and a deflection of 0.100 in, the error is approx. 20%. Since the primary goal for using acetal homopolymer Belleville spring washers is to achieve high levels of spring rates and to be able to predict these values accurately, the standard equation, even when calculated by a computer program, does not produce accurate enough results. However, using the empirical data method and the graphs (Figures 6-36 to 6-44) will produce results that are accurate within a range of ±5%.
Example 6-4 W
Calculate the compression load (W) at a deflection (δ) of 0.060 in when the Belleville spring washer has the dimensions shown in Figure 6-45. To calculate the compression load (W), the Belleville spring washer requires a deflection of 0.060 in. Using the empirical data method, we select the spring graph in Figure 6-39 that has the same dimension. The compression load (W) value of 24.00 lb is found for a deflection (δ) of 0.060 in and the wall thickness curve (t) of 0.03 in.
0.030 inches 0.20 inches 1.25 inches 2.00 inches
Figure 6-45 Belleville spring washer
Example 6-5 Calculate the Belleville spring washer height (H) that will produce a compression load (W) of 26.00 lb at a deflection (δ) of 0.050 in, when the Belleville spring washer has an increasing spring force with deflection and the dimensions show in Figure 6-46. Figures 6-36 to 6-44 were developed using 0.10, 0.20, and 0.30 in heights; however, we need to calculate a new height different from those used in the graphs. Reviewing the Belleville spring graphs, Figures 6-37 and 6-43 can be used to calculate the height: Spring graph Figure 6-37 D d t H δ W
= 2.00 in outside diameter = 0.85 in inside diameter = 0.03 in wall thickness = 0.10 in spring height = 0.05 in deflection = 5.00 lb load
Spring graph Figure 6-43 D d t H δ W
= 2.00 in outside diameter = 0.85 in inside Diameter = 0.03 in wall thickness = 0.30 in spring height = 0.05 in deflection = 57.00 lb load
From Figure 6-37, we obtain a load of W = 5.00 lb and the height of H = 0.10 in and from Figure 6-43 we obtain a load of W = 57.00 lb and the height of H = 0.30 in. Interpolating both loads, we obtain the desired compression load (W) = (5.00 + 57.00) / 2 = 31.00 lb By interpolating both spring heights, we obtain the desired spring height (H) = (0.10 + 0.30) / 2 = 0.20 in.
W 0.030 inches H
0.85 inches 2.00 inches
Figure 6-46 Belleville spring washer
392
6 Thermoplastic Molded Spring Design
Load Ratio, WA/WC
1.20
1.10
1.00 0.05
0.50 5.00 Axial loading rate, (inch per minute)
50.00
Figure 6-47 Load ratio WA / WC vs. axial loading rate
6.7.2
Belleville Spring Washer Loading Rate
A characteristic of most thermoplastic materials is their sensitivity to the loading rates; this effect should be considered in any Belleville spring washer calculations. Figure 6-47 is a graph of the axial loading rate versus the ratio of the true load (WA) to the calculated load (WC). An axial loading rate of 0.05 in/min was used to develop the values for load and deflection shown in the graph. The appropriate load ratios can be found for speed rates between 0.005 to 50 in/min for converting the load to a realistic value. For example, if the axial loading rate is 5.0 in/min, the ratio WA / WC is 1.13, showing a realistic load 13% higher than the calculated load value (WC).
6.7.3
Belleville Spring Washer Long-Term Loading Characteristics
Acetal homopolymer and copolyester thermoplastic elastomer Belleville spring washers have an excellent recovery rate (hysteresis) from the applied compression loads. However, if a thermoplastic Belleville spring washer is constantly loaded or stressed for a long period at higher temperatures, the thermoplastic materials will be subjected to the effects of creep or loss of mechanical properties. Therefore, the load versus deflection characteristics of thermoplastic Belleville spring washers will be reduced, causing inferior performances of the product with lower than expected values. Acetal homopolymer and copolyester thermoplastic elastomer Belleville spring washers are not recommended for any application that requires the energy to be stored or continuous loading expecting a constant spring reaction force, and these materials will not perform under these requirements. The use of thermoplastic Belleville spring washers should be limited only to intermittent loads or deflection applications.
393
7
Thermoplastic Pressure Vessel Design
7.1
Thermoplastic Thin-Walled Pressure Vessels
The term thin-walled or thin-shelled pressure vessel describes a hollow cylinder in which the circumferential stress (frequently called hoop stress) in the wall is assumed to be constant throughout the thickness of the wall when the cylinder is subjected to an internal or external fluid pressure. Thermoplastic materials have been used for the fabrication of many pressure vessel devices, such as toilet flush valves, spray paint containers, butane lighters, irrigation sprayers and valves, brake master cylinders, radiator end cores, garden hoses, tubing, end connections, pumps, and so forth. Figures 7-1 and 7-2 illustrate some of these pressure vessel applications.
Water spray gun
Figure 7-1 Thermoplastics pressure vessel applications (Courtesy: Du Pont)
Figure 7-2 Thermoplastic pressure vessel applications
394
7 Thermoplastic Pressure Vessel Design
7.2
The circumferential stress (a) in a thin-walled cylinder subjected to an internal pressure (P) per unit area is found by applying an equation of equilibrium to the forces acting on the half cylinder shown in Figure 7-3. The length is uniform, wall thickness is (t), and inside radius is (r).
t 2r x P r P
da
Thin-Walled Cylinder Basic Principles
da
P × 2 r = 2 ∫ σ da
Figure 7-3 Thin-walled cylinder mathematical model
(7-1)
But under the assumed conditions, ∫ σ da = a σ = t σ . Therefore, Barlow’s Equation is:
t
σ =
P×r t
(7-2)
r
Spherical Closed End Thin-Walled Pressure Vessels P
r
To calculate the stress of a cylindrical pressure vessel with a spherical base, under uniform internal pressure, using Figure 7-4 as a model, the maximum stress equation should be applied:
Figure 7-4 Spherical closed end thin-walled pressure vessel
σ Max. =
P×r 2×t
(7-3)
Flat Closed End Thin-Walled Pressure Vessel
r
To find the maximum stress of a cylindrical pressure vessel with a circular flat bottom base, under uniform internal pressure and using Figure 7-5 as a model, the following equations should be applied:
t P
Center deflection:
3 × P × r4 2 δ= (1 − υ ) 16 × E × t 3
Maximum moment:
M Max. =
Maximum stress:
σ Max. =
P
Figure 7-5 Flat closed end thin-walled pressure vessel
P × r2 8
(7-4)
(7-5)
6 × M 0.75 × P × r 2 = t2 t2
(7-6)
Example 7-1 The shank/riser toilet flush valve shown in Figure 7-6 needs to withstand a 2,000 psi burst pressure and 120 psi continuous internal pressure for 10 years. The burst pressure would be the controlling factor for the design, rather than the continuous pressure. The material selected for this application is acetal homopolymer with a tensile strength of 10,000 psi. Calculate the wall thickness of the shank/riser by using Barlow’s equation (Equation 7-2). Barlow’s Equation σ =
P×r t
or t =
P × r 2,000 × r = = 0.20 r σ 10,000
The stress for the shank/riser wall thickness at 120 psi pressure over ten years is calculated by using the isochronous creep stress/time long-term pipe test
7.2 Thin- Walled Cylinder Basic Principles
data shown in Figure 7-7. For 10 ycars the tensile stress is 1,750 psi. The wall thickness can be calculated as t, = (120 x r) 1 1,750 = 0.068 r. The burst pressure wall thickness t , = 0.20 r is the control bctor for dimensioning, because the wall: thickness for burst pressure requires 0.20 10.068 = 2.94 times the wall thickness calculated to retain the 110 psi internal pressure
over 10 ycars.
The shanklriser outside diameter at the base (left is theside) root diameter of the threads, and its wall thickness is t = 0.20 x 0.453 = 0.0906 in. Because its t = 0.20 the toy (right side) outside diameter is smaller, wall thickness x 0.375 = 0.075 in, without considering the reinforcement by the caused perpendicular wall of the toilet valve housing. twoThese shanklriser inside diameters form a tapered wall, which not only provides the efficientmost design, but aIso helps during the part ejection from the long core of the mold. To improve the molding process efficiency,the long core requires the surface to be hardened to 60 R,, the surface to be coated with a low coefficient of friction mold release and polished in the longitudinal direction (a RMS). The core requires alsoan independent water cooling system. The shanklriser is to he gated at the flange (thicker width wall sectinn equal 0.156 to i n ) using an insulated runnerless mold with three cavities.
Figure?-6 Acetal homopolymer shank/riser toilet flush valve
Internal pressure at 73" f.
10.000
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