MACHINE ELEMENTS IN MECHANICAL DESIGN Fourth Etdition Robert L. Mott, RE University of Dayton ZSL.-^ 1 *^ OH THUY LQI TLTHAM KHAO PEARSON Prentice Hall Upper Saddle River, New Jersey Columbus, Ohio To my wife. Marge our children, Lyiine, Robert, Jr., and Stephen and my /Mother and Father Library of Ccmgress Cataloging in Publication Data Mott. Robert L. Machine eleinents in mechanical design / Robert L. Mott. Ith ed. p. cm. ISBN 0-13-061885-3 I. Machine design. 2. Mechanical movements. I. Title. TJ230.M68 2004 62I.8'I5—dc2I 2003042548 Editor in Chief: Stephen Helba Executive Editor: Debbie '^'arnell Editorial Assistant: Jonathan Tenthoff Production Editor: Louise N. Sette Production Supervision: Carlisle Publishers Ser\ ices Design Coordinator: Diane Ernsberger Cover Designer: Jason Moore Production Manager: Brian Fox Marketing Manager: Jimmy Stephens This book was set in Times Roman and Hehetica by Carlisle Communications. Ltd. It was printed and bound by Courier Westford. Inc. 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Pearson Education—Japan Pearson Education Malaysia Pte. Ltd. 10987654 ISBN 0-13-061885-3 Preface The objective of this book is to provide the concepts, procedures, data, and decision analy sis techniques necessary to design machine elements commonly found in mechanical de vices and systems. Students completing a course of study using this book should be able to execute original designs for machine elements and integrate the elements into a system composed of several elements. This process requires a consideration of the performance requirements of an individ ual element and ofthe interfaces between elements as they work together to form a system. For example, a gear must be designed to transmit power at a given .speed. The design must specify the number of teeth, pitch, tooth form, face width, pitch diameter, material, and method of heat treatment. But the gear design also affects, and is affected by, the mating gear, the shaft carrying the gear, and the environment in which it is to operate. Furthermore, the shaft must be supported by bearings, which must be contained in a housing. Thus, the designer should keep the complete system in mind while designing each individual ele ment. This book will help the student approach design problems in this way. This text is designed for those interested in practical mechanical design. The empha sis is on the use of readily available materials and processes and appropriate design ap proaches to achieve a safe, efficient design. It is assumed that the person using the book will be the designer, that is, the person responsible for determining the configuration of a ma chine or a part of a machine. Where practical, all design equations, data, and procedures needed to make design decisions are specified. It is expected that students using this book will have a good background in statics, strength of materials, college algebra, and trigonometry. Helpful, but not required, would be knowledge of kinematics, industrial mechanisms, dynamics, materials, and manufactur ing processes. Among the important features of this book are the following: 1. It is designed to be used at the undergraduate level in a first course in machine design. 2. The large list of topics allows the instmctor some choice in the design of the course. The format is also appropriate for a two-course sequence and as a refer ence for mechanical design project courses. 3. Students should be able to extend their efforts into topics not covered in classroom instmction because explanations of principles are straightforward and include many example problems. 4. The practical presentation of the material leads to feasible design decisions and is useful to practicing designers. 5. The text advocates and demonstrates use of computer spreadsheets in cases re quiring long, laborious solution procedures. Using spreadsheets allows the de signer to make decisions and to modify data at several points within the problem while the computer performs all computations. See Chapter 6 on columns. Chapter 9 on spur gears. Chapter 12 on shafts. Chapter 13 on shrink fits, and Chapter 19 on spring design. Other computer-aided calculation software can also be used. Ill IV Preface 6. References to other books, standards, and technical papers assist the instructor in presenting alternate approaches or extending the depth of treatment. 7. Lists of Internet sites pertinent to topics in this book are included at the end of most chapters to assist readers in accessing additional information or data about com mercial products. 8. In addition to the emphasis on original design of machine elements, much ofthe discussion covers commercially available machine elements and devices, since many design projects require an optimum combination of new, uniquely designed parts and purchased components. 9. For some topics the focus is on aiding the designer in selecting commercially available components, such as rolling contact bearings, flexible couplings, ball screws, electric motors, belt drives, chain drives, clutches, and brakes. 10. Computations and problem solutions use both the International System of Units (SI) and the U.S. Customary System (inch-pound-second) approximately equally. The basic reference for the usage of SI units is IEEE/ASTM-SI-10 Standard for Use ofthe Intemational System of Units (SI): The Modern Metric System, which has replaced ASTM E380 and ANSI/IEEE Standard 268-1992. 11. Extensive appendices are included along with detailed tables in many chapters to help the reader to make real design decisions, using only this text. MDESIGN- The design of machine elements inherently involves extensive procedures, complex cal MECHANICAL culations, and many design decisions. Data must be found from numerous charts and ta DESIGN bles. Furthermore, design is typically iterative, requiring the designer to try several SOFTWARE options for any given element, leading to the repetition of design calculations with new INCLUDED data or new design decisions. This is especially true for complete mechanical devices IN THE BOOK containing several components as the interfaces between components are considered. Changes to one component often require changes to mating elements. Use of computer- aided mechanical design software can facilitate the design process by performing many ofthe tasks while leaving the major design decisions to the creativity and judgment ofthe designer or engineer. We emphasize that users of computer software must have a solid under standing of the principles of design and stress analysis to ensure that design deci sions are based on reliable foundations. We recommend that the software be used only after mastering a given design methodology by careful study and using man ual techniques. aiDESIGN Included in this book is the MDESIGN mechanical design software created by the TEDATA Company. Derived from the successful MDESIGN mec software produced for the European market, the U.S. version of MDESIGN employs standards and design meth ods that are typically in use in North America. Many of the textual aids and design proce dures come directly from this book. Machine Elements in Mechanical Design, Topics for which the MDESIGN software can be used as a supplement to this book include: Beam stress analysis Beam deflections Mohr's circle Columns Belt drives Chain drives Spur gears Helical gears Shafts Keys Power screws Springs Rolling contact bearings Plain surface bearings Bolted connections Fasteners Clutches Brakes Preface Special icons as shown on the preceding page are placed in the margins at places in this book where use ofthe software is pertinent. Also, the Solutions Manual, available only to instructors using this book in scheduled classes, includes guidance for use of the software. FEATURES OF The practical approach to designing machine elements in the context of complete mechan- THE FOURTH ical designs is retained and refined in this edition. An extensive amount of updating has EDITION been accomplished through the inclusion of new photographs of commercially available machine components, new design data for some elements, new or revised standards, new end-of-chapter references, listings of Internet sites, and some completely new elements. The following list summarizes the primary features and the updates. 1. The three-part structure that was introduced in the third edition has been main tained. • Part I (Chapters 1-6) focuses on reviewing and upgrading readers' understand ing of design philosophies, the principles of strength of materials, the design properties of materials, combined stresses, design for different types of load ing, and the analysis and design of columns. • Part II (Chapters 7-15) is organized around the concept ofthe design of a com plete power transmission system, covering some of the primary machine ele ments such as belt drives, chain drives, gears, shafts, keys, couplings, seals, and rolling contact bearings. These topics are tied together to emphasize both their interrelationships and their unique characteristics. Chapter 15, Completion of the Design of a Power Transmission, is a guide through detailed design deci sions such as the overall layout, detail drawings, tolerances, and fits. • Part III (Chapters 16-22) presents methods of analysis and design of several important machine elements that were not pertinent to the design of a power transmission. The.se chapters can be covered in any order or can be used as ref erence material for general design projects. Covered here are plain surface bearings, linear motion elements, fasteners, springs, machine frames, bolted connections, welded joints, electric motors, controls, clutches, and brakes. 2. The Big Picture, You Are the Designer, and Objectives features introduced in earlier editions are maintained and refined. Feedback about these features from u.sers, both students and in.structors, has been enthusiastically favorable. They help readers to draw on their own experiences and to appreciate what competencies they will acquire from the study of each chapter. Constructivist theories of learn ing espouse this approach. 3. Some ofthe new or updated topics from individual chapters are summarized here. • In Chapter 1, the discussion of the mechanical design process is refined, and several new photographs are added. Intemet sites for general mechanical de sign are included that are applicable to many later chapters. Some are for stan dards organizations, stress analysis software, and searchable databases for a wide variety of technical products and services. • Chapter 2, Materials in Mechanical Design, is refmed, notably through added material on creep, austempered ductile iron (ADI), toughness, impact energy, and the special considerations for selecting plastics. An entirely new section on materials selection has been added. The extensive list of Internet sites provides readers access to industry data for virtually all types of materials discussed in the chapter with some tied to new practice problems. vi Preface • Chapter 3, a review of Stress and Deformation Analysis, has an added review of force analysis and refinement of the concepts of stress elements, combined normal stresses, and beams with concentrated bending moments. • Chapter 5, Design for Different Types of Loading, is extensively upgraded and refined in the topics of endurance strength, design philosophy, design fac tors, predictions of failure, an overview of .statistical approaches to design, fi nite life, and damage accumulation. The recommended approach to fatigue design has been changed from the Soderberg criterion to the Goodman method. The modified Mohr method is added for members made from brittle materials. • In Chapter 7, synchronous belt drives are added and new design data for chain power ratings are included. • Chapter 9, Spur Gear Design, is refined with new photographs of gear pro duction machinery, new AGMA standards for gear quality, new discussion of functional measurement of gear quality, enhanced description of the geometry factor / for pitting resistance, more gear lubrication information, and a greatly expanded section on plastics gearing. • In Chapter 11, new information is provided for keyless hub to shaft connections ofthe Ringfeder® and polygon types, and the ComayTw universal joint. The ex tensive listing of Intemet sites provides access to data for keys, couplings, uni versal joints, and seals. • Critical speeds, other dynamic considerations, and flexible shafts are added to Chapter 12, Shaft Design. • An all-new section, Tribology: Friction, Lubrication, and Wear, is added to Chapter 16, Plain Surface Bearings. More data on pVfactors for boundary lu bricated bearings are provided. • Chapter 17 has been retitled Linear Motion Elements and includes power screws, ball screws, and linear actuators. • Refinements to Chapter 18, Fasteners, include the shear strength of threads, components of torque applied to a fastener, and methods of bolt tightening. Acknowledgments My appreciation is extended to all who provided helpful suggestions for improvements to this book. I thank the editorial staff of Prentice Hall Publishing Company, those who pro vided illustrations, and the many users of the book, both instructors and students, with whom I have had discussions. Special appreciation goes to my colleagues at the University of Dayton, Professors David Myszka, James Penrod, Joseph Untener, Philip Doepker, and Robert Wolff I also thank those who provided thoughtful reviews of the prior edition: Marian Barasch, Hudson Valley Community College; Ismail Fidan, Tennessee Tech Univer sity; Paul Unangst, Milwaukee School of Engineering; Richard Alexander, Texas A&M University; and Gary Qi, The University of Memphis. I especially thank my students—past and present—for their encouragement and their positive feedback about this book. Robert L Mott Contents PART I Principles of Design and Stress 2-9 Tool Steels 54 Analysis 1 2-10 Cast Iron 54 2-11 Powdered Metals 56 1 The Nature of Mechanical Design 2 2-12 Aluminum 57 2-13 Zinc Alloys 59 The Big Picture 3 2-14 Titanium 60 You Are the Designer 9 2-15 Copper, Brass, and Bronze 60 1-1 Objectives of This Chapter 9 2-16 Nickel-Based Alloys 61 1-2 The Mechanical Design Process 9 2-17 Plastics 61 1-3 Skills Needed in Mechanical Design 11 2-18 Composite Materials 65 1-4 Functions, Design Requirements, and Evaluation Criteria 11 2-19 Materials Selection 77 1-5 Example of the Integration of Machine References 78 Elements into a Mechanical Design 14 Internet Sites 79 1-6 Computational Aids in This Book 17 Problems 80 1-7 Design Calculations 17 1-8 Preferred Basic Sizes, Screw Threads, and 3 Stress and Deformation Analysis 83 Standard Shapes 18 The Big Picture 84 1-9 Unit Systems 24 You Are the Designer 85 1-10 Distinction among Weight, Force, and Mass 26 3-1 Objectives of This Chapter 89 References 27 3-2 Philosophy of a Safe Design 89 Internet Sites 27 3-3 Representing Stresses on a Stress Element 89 Problems 28 3-4 Direct Stresses: Tension and Compression 90 3-5 Deformation under Direct Axial Loading 92 2 Materials in Mechanical Design 29 3-6 Direct Shear Stress 92 3-7 Relationship among Torque, Power, and The Big Picture 30 Rotational Speed 94 You Are the Designer 31 3-8 Torsional Shear Stress 95 2-1 Objectives of This Chapter 32 3-9 Torsional Deformation 97 2-2 Properties of Materials 32 3-10 Torsion in Members Having Noncircular Cross 2-3 Classification of Metals and Alloys 44 Sections 98 2-4 Variability of Material Properties Data 45 3-11 Torsion in Closed, Thin-Walled Tubes 100 2-5 Carbon and Alloy Steel 46 3-12 Open Tubes and a Comparison with Clo.sed 2-6 Conditions for Steels and Heat Treatment 49 Tubes 100 2-7 Stainless Steels 53 3-13 Vertical Shearing Stress 102 2-8 Structural Steel 54 3-14 Special Shearing Stress Formulas 104 VII Contents Vlll 3-15 Stress Due to Bending 105 5-6 Design Philosophy 182 3-16 Flexural Center for Beams 107 5-7 Design Factors 185 3-17 Beam Deflections 108 5-8 Predictions of Failure 186 3-18 Equations for Deflected Beam Shape 110 5-9 Design Analysis Methods 193 3-19 Beams with Concentrated Bending 5-10 General Design Procedure 197 Moments 1 12 5-11 Design Examples 200 3-20 Combined Normal Stresses: Superposition 5-12 Statistical Approaches to Design 213 Principle 1 17 5-13 Finite Life and Damage Accumulafion 3-21 Stress Concentrations 119 Method 214 3-22 Notch Sensitivity and Strength Reduction References 218 Factor 122 Problems 219 References 123 Internet Sites 123 6 Columns 229 Problems 123 The Big Picture 230 4 Combined Stresses and You Are the Designer 231 Mohr's Circle 135 6-1 Objectives of This Chapter 231 The Big Picture 136 6-2 Properties of the Cross Section of a Column 232 You Are the Designer 136 6-3 End Fixity and Effective Length 232 4-1 Objectives of This Chapter 138 6-4 Slenderness Ratio 234 4-2 General Case of Combined Stress 138 6-5 Transition Slenderness Ratio 234 4-3 Mohr's Circle 145 6-6 Long Column Analysis: The Euler Formula 235 4-4 Mohr's Circle Practice Problems 151 6-7 Short Column Analysis: The J. B. Johnson 4-5 Case When Both Principal Stresses Have the Formula 239 Same Sign 155 6-8 Column Analysis Spreadsheet 241 4-6 Mohr's Circle for Special Stress Conditions 158 6-9 Efficient Shapes for Column Cross Sections 244 4-7 Analysis of Complex Loading Conditions 161 6-10 The Design of Columns 245 6-11 Crooked Columns 250 References 162 Internet Site 162 6-12 Eccentrically Loaded Columns 251 Problems 162 References 257 Problems 257 5 Design for Different Types of Loading 163 The Big Picture 164 PART II Design of a Mechanical Drive 261 You Are the Designer 166 5-1 Objectives of This Chapter 166 7 Belt Drives and Chain Drives 264 5-2 Types of Loading and Stress Ratio 166 The Big Picture 265 5-3 Endurance Strength 172 You Are the Designer 267 5-4 Estimated Actual Endurance Strength, .v,' 173 7-1 Objecfives of This Chapter 267 5-5 Example Problems for Estimating Actual Endurance Strength 181 7-2 Types of Belt Drives 268