Standard handbook of machine design

The purpose of the Standard Handbook of Machine Design has been, from its inception, to provide the mechanical designer, within in a single reference, the mostcomprehensive and up-to-dat

STANDARD HANDBOOK

OF MACHINE DESIGN

J o s e p h E S h i g l e y Editor mcmef

Late Professor Emeritus The University of Michigan Ann Arbor, Michigan

C h a r l e s R M i s c h k e Editor in chief

Professor Emeritus of Mechanical Engineering

Iowa State University Ames, Iowa

T h o m a s H B r o w n , Jr Editor >n chief

Faculty Associate Institute for Transportation Research and Education

North Carolina State University Raleigh, North Carolina

Third Edition

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Copyright © 2004, 1996 by The McGraw-Hill Companies, Inc All rights reserved Printed in the United States of America Except as permitted under the United States Copyright Act of 1976, no part of this publication may

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Thomas H Brown, Jr Faculty Associate, Institute for Transportation Research and

Educa-tion, North Carolina State University, Raleigh, N G (CHAR 1)

R B Bhat Associate Professor, Department of Mechanical Engineering, Concordia

Univer-sity, Montreal, Quebec, Canada (CHAP 31)

Sachindranarayan Bhaduri Associate Professor, Mechanical and Industrial Engineering

Department, The University of Texas at El Paso, El Paso, Tex (CHAP 39)

John H Bickford Retired Vice President, Manager of the Power-Dyne Division, Raymond

Engineering Inc., Middletown, Conn (CHAP 22)

Omer W Blodgett Design Consultant, The Lincoln Electric Company, Cleveland, Ohio

(CHAP 26)

Daniel M Curtis Senior Mechanical Engineer, NKF Engineering, Inc., Arlington, Va (CHAP 7) Daniel E Czernik Director of Product Engineering, Fel-Pro Inc., Skokie, 111 (CHAP 25) Joseph Datsko Professor of Mechanical Engineering Emeritus, The University of Michigan,

Ann Arbor, Mich (CHAP 32)

Raymond J Drago Senior Engineer, Advanced Power Train Technology, Boeing Vertol,

Philadelphia, Pa (CHAP 10)

K S Edwards Professor of Mechanical Engineering, The University of Texas at El Paso, Tex.

(CHAP 12)

Rudolph J Eggert Associate Professor of Mechanical Engineering, University of Idaho,

Boise, Idaho (CHAP 13)

Wolfram Funk Professor, Fachbereich Maschinenbau, Fachgebiet Maschinenelemente und

Getriebetechnik, Universitat der Bundeswehr Hamburg, Hamburg, Germany (CHAP 14)

Richard E Gustavson Technical Staff Member, The Charles Draper Laboratory, Inc.,

Cam-bridge, Mass (CHAP 3)

Harry Herman Professor of Mechanical Engineering, New Jersey Institute of Technology,

Newark, NJ (CHAP 30)

R Bruce Hopkins The Hopkins Engineering Co., Cedar Falls, Iowa (CHAP 21)

Robert J Hotchkiss Director, Gear Technology, Gleason Machine Division, Rochester, NY.

(CHAP 11)

Robert E Joerres Applications Engineering Manager, Associated Spring, Barnes Group

Inc., Bristol, Conn (CHAP 6)

Harold L Johnson Associate Professor Emeritus, School of Mechanical Engineering,

Geor-gia Institute of Technology, Atlanta, Ga (CHAP 5)

Theo J Keith, Jr Professor and Chairman of Mechanical Engineering, University of Toledo,

Toledo, Ohio (CHAP 19)

Theodore K Krenzer Director of Research and Development, Gleason Machine Division,

Rochester, NY (CHAP 11)

A R Lansdown Director, Swansea Tribology Centre, University of Swansea, United

King-dom, (CHAR 20)

Kenneth C Ludema Professor of Mechanical Engineering, Department of Mechanical

Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, Mich (CHAP 34)

Charles R Mischke Professor of Mechanical Engineering Emeritus, Iowa State University,

Ames, Iowa, (CHAPS 17,18,27,28,29,33,37)

Andrzej A Oledzki Professor Emeritus, Warsaw Technical University, Warsaw, Poland

(CHAP 4)

Richard S Sabo Manager, Educational Services, The Lincoln Electric Company, Cleveland,

Ohio (CHAR 26)

T S Sankar Professor and Chairman, Department of Mechanical Engineering, Concordia

University, Montreal, Quebec, Canada, (CHAR 31)

Howard B Schwerdlin Engineering Manager, Lovejoy, Inc., Downers Grove, 111 (CHAR 16) Joseph E Shigley Professor Emeritus, The University of Michigan, Ann Arbor, Mich.

(CHAPS 9,23,24,27,28,36,38, Appendix)

L E Torfason Professor of Mechanical Engineering, University of New Brunswick,

Freder-icton, New Brunswick, Canada (CHAR 2)

Milton G WiIIe Professor of Mechanical Engineering, Brigham Young University, Provo,

Utah, (CHAR 35)

John L Wright General Product Manager, Diamond Chain Company, Indianapolis, Ind.

(CHAR 15)

John R Zimmerman Professor of Mechanical and Aerospace Engineering, University of

Delaware, Newark, Del (CHAR 8)

Machines evolve Not biologically, of course, but they evolve nonetheless, from afragment of an idea or dream to a fully functional mechanical marvel—at least in theeyes of the designer Machine design is one of the most rewarding activities to which

a person can contribute; it is incredibly complex For some designers, their uniqueand magical designs, or machine elements, have become a legacy for future genera-tions

For most of us who are engineers, we will likely not leave a design legacy; but thejoy in using what others have devised can be intoxicating One design project leads

to another, and that project leads to yet another While this process can be hectic,sometimes at the mercy of a difficult schedule, in the end you are proud—proud ofwhat you have done in meeting the design requirements, proud to have met theschedule, and proud of how you have used the seemingly endless variety of machinedesign elements available to you

The purpose of the Standard Handbook of Machine Design has been, from its

inception, to provide the mechanical designer, within in a single reference, the mostcomprehensive and up-to-date information about what is available and how to uti-lize it effectively and efficiently The original authors, Joseph E Shigley and Charles

R Mischke, two of the most well-known and respected individuals in the cal engineering community, assembled experts in every field of machine design:mechanisms and linkages, cams, gear trains, springs, flywheels, clutches, brakes, geardesigns of every type, belts, chains, couplings, design of shafts, all manner of rollerbearings, journal bearings, lubrication selection, bolts and mechanical fasteners,welding, failure analysis, vibration, performance of engineering materials, wear, cor-rosion, and classical stress and deformation calculations This incredible wealth ofinformation, which would otherwise have to be researched in dozens of books andhundreds of scientific and professional papers, was organized by these experts intodistinct chapters, as many as 50 in the Second Edition Here in the Third Edition, the

mechani-39 chapters have been grouped into nine broad topic areas of related material Eachchapter stands on its own and, for the veteran designer, provides direct access to aspecific area of interest or need

The Standard Handbook of Machine Design is a unique reference, capturing the

breadth and depth of what we know and trust May what you discover and applyfrom these pages contribute to a successful design, one that will delight not only thedesigner but those who ultimately find value and long service in the machine thathas evolved

Thomas H Brown, Jr.

PREFACE TO THIRD EDITION

This Third Edition of the Standard Handbook of Machine Design has been

com-pletely reorganized as compared to its two previous editions To bring into focus theneeds of the machine design engineer, without the distractions of ancillary material,the number of chapters has been reduced from 50 in the Second Edition to 39 These

39 chapters have been carefully grouped into nine distinct sections, denoted as Parts

1 through 9 These chapter groupings were inspired primarily by a set of eight

"Machine Design Workbooks," containing much of the material in the First Edition,and published between the First and Second Editions

After a new introductory chapter, "Evolution of a Successful Design," the first ofnine sections, Part 1, "Machine Elements in Motion," presents four chapters on the

seemingly endless ways to achieve a desired motion Kinematics, or the geometry of

motion, is probably the most important step in the design process, as it sets the stagefor many of the other decisions that will be made as a successful design evolves.Whether it's a self-locking latch you are looking for, a complex cam shape, or anentire gear assembly, the information you need is here in these chapters

Part 2, "Machine Elements that Absorb and Store Energy," contains three ters presenting the classic machine elements: springs, flywheels, clutches, and brakes.Not all designs will have a need for these energy-related devices, but, when appro-priate, no other device will do the job

chap-Part 3, "Gearing," contains five chapters covering every possible gear type, frombasic spur gears to complex hypoid bevel gears sets; the intricacies of worm gearing;and the very versatile and relatively modern power screw designs

Part 4, "Power Transmission," contains four chapters directed at the requirements

of transferring motion from one rotating axis to another, whether by time-honoredbelt or chain configurations, or the wide variety of couplings used to isolate and pro-tect downstream machine elements This is also where the design of shafts, from both

a static and dynamic viewpoint, is included

Part 5, "Bearings and Lubrication," pulls together in one place the design of manytypes of roller bearings as well as the design aspects of the classic journal bearing.Bearings could not do their job without lubrication, and lubrication would be lostfrom most bearings without the proper seals Traditional and nontraditional designsare presented

Part 6, "Fastening, Joining, and Connecting," covers every conceivable type ofmechanical fastener When disassembly is not required, or when maximum strength

is needed, then the only solution is a welded connection All aspects of a welded nection are presented Many connections must prevent leakage or provide cushion-ing, so a discussion of seals and their effect on a bolted connection is provided Themating of parts without prior preassembly can be an important design requirement;therefore, this is where a detailed discussion of fits and tolerances is included.Part 7, "Load Capability Considerations," provides the designer with the rules fordetermining if a particular part will fail This determination does not have to be aprecise calculation, either under static or dynamic conditions, whether the part isacting as a beam or column, but to ignore these fundamental principles is to invite

con-disaster This section seemed like the best place to discuss vibration and, just asimportant, its control.

Part 8, "Performance of Engineering Materials," brings to bear the science ofmaterial behavior, to include the changes that take place during the manufacturingprocess Once in service, machine elements are subject to constant wear and theadverse effects of corrosion

Lastly, Part 9, "Classical Stress and Deformation Analysis," provides the designengineer with the fundamental formulas for stress, deflection, and deformation, andincludes special geometries such as curved elements and special loadings, which arefound in cylinders under internal pressure when parts are press fitted

One of the chapters included in the First and Second Editions, "Sections andShapes—Tabular Data," has been provided in this Third Edition as an appendix

It is hoped that this Third Edition provides a dependable source of relevant mation on the topics needed for the successful evolution of your design Suggestionsfor improvement are welcome and will be appreciated

infor-Thomas H Brown, Jr.

PREFACE TO FIRST EDITION

There is no lack of good textbooks dealing with the subject of machine design Thesebooks are directed primarily to the engineering student Because of this, they con-tain much theoretical material that is amenable to mathematical analysis Such top-ics are preferred by the instructor as well as the student because they appeal to thestudent's scientific, mathematical, and computer backgrounds; are well-defined top-ics with a beginning, a middle, and an end; and are easy to use in testing the student'sknowledge acquisition The limited amount of time available for academic studiesseverely limits the number of topics that can be used as well as their treatment Sincetextbooks devoted to mechanical design inevitably reflect this bias, there is greatneed for a handbook that treats the universe of machine design—not just the read-ily teachable part

The beginning designer quickly learns that there is a great deal more to ful design than is presented in textbooks or taught in technical schools or colleges.This handbook connects formal education and the practice of design engineering byincluding the general knowledge required by every machine designer

success-Much of the practicing designer's daily informational needs are satisfied by ous pamphlets or brochures, such as those published by the various standards orga-nizations Other sources include research papers, design magazines, and the variouscorporate publications concerned with specific products More often than not, how-ever, a visit to the design library or to the file cabinet will reveal that a specific pub-lication is on loan, lost, or out of date This handbook is intended to serve such needsquickly and immediately by giving the designer authoritative, up-to-date, under-standable, and informative answers to the hundreds of such questions that ariseevery day in his or her work Mathematical and statistical formulas and tabulationsare available in every design office and, for this reason, are not included in this hand-book

vari-This handbook has been written for working designers, and its place is on thedesigner's desk—not on the bookshelf It contains a great many formulas, tables,charts, and graphs, many in condensed form These are intended to give quickanswers to the many questions that seem constantly to arise

The introduction of new materials, new processes, and new analytical tools andapproaches changes the way we design machines Higher speeds, greater efficiencies,compactness, and safer, lighter-weight, and predictably reliable machines can result

if designers keep themselves up to date on technological changes This book presentsmachine design as it is practiced today; it is intended to keep the user in touch withthe latest aspects of design

Computer-aided design methods and a host of other machine-computation bilities of tremendous value to designers have multiplied in the last few years Thesehave made large and lasting changes in the way we design This book has beenplanned and written to make it easy to take advantage of machine-computationfacilities of whatever kind may be available Future developments in computer hard-ware and software will not render the content of this book obsolete

capa-This Handbook consists of the writings of 42 different contributors, all known experts in their field We have tried to assemble and to organize the 47 chap-ters so as to form a unified approach to machine design instead of a collection ofunrelated discourses This has been done by attempting to preserve the same level ofmathematical sophistication throughout and by using the same notation whereverpossible.

well-The ultimate responsibility for design decisions rests with the engineer in charge

of the design project Only he or she can judge if the conditions surrounding theapplication are congruent with the conditions which formed the bases of the pre-sentations in this Handbook, in references, or in any other literature source In view

of the large number of considerations that enter into any design, it is impossible forthe editors of this Handbook to assume any responsibility for the manner in whichthe material presented here is used in design

We wish to thank all contributors, domestic and foreign, for their patience andunderstanding in permitting us to fine-tune their manuscripts and for meeting andtolerating our exacting demands We are also grateful to the many manufacturerswho so generously provided us with advice, literature, and photographs Most of theartwork was competently prepared and supervised by Mr Gary Roys of Madrid,Iowa, to whom the editors are indebted

Care has been exercised to avoid error The editors will appreciate beinginformed of errors discovered, so that they may be eliminated in subsequent print-ings

Joseph E Shigley Charles R Mischke

My enduring love and appreciation goes to my wife, Miriam, who has always aged me in my many endeavors throughout our marriage Whether it is the day today support in our life together, or in my annual quest for perfection in the State Fairamateur wine competition (a Blue Ribbon in 2003), or the hope of someday having

encour-a trophy deer hencour-anging in the den, she hencour-as been steencour-adfencour-ast in her strength encour-and tion During the many months of my preoccupation with completing this project, shehas been so wonderful and understanding

devo-I am grateful for the love of my three children, Sianna, Hunter, and Elliott, whohave been so very patient through the many weekends without their Dad, and whoare a continual joy to me To my dear friend, Dr Carl Zorowski, Professor Emeritus

of Mechanical Engineering at NC State University, without whose weekly guidanceover lunch for more than a decade, my insights in mechanical engineering and themachine design process would be sorely lacking And to my new friends, and editors,Ken McCombs and Carol Levine, who have inspired me to produce the best I canproduce, and in the process given me great honor to be a part of the McGraw-Hillfamily

Thomas H Brown, Jr.

ABOUT THE EDITORS

Joseph E Shigley (deceased) was awarded the B.S.M.E and B.S.E.E degrees from

Purdue University, and an M.S from the University of Michigan He was Professor Emeritus at the University of Michigan, Fellow in the American Society of Mechan- ical Engineers, and received the Worcester Reed Warner medal in 1977 and their

Machine Design Award in 1985 He was the author of eight books, including Theory

of Machines and Mechanisms (with John J Uicker, Jr.), and Applied Mechanics of Materials Shigley began Machine Design as sole author in 1956, and it evolved into Mechanical Engineering Design He was Coeditor-in-Chief of the Standard Hand- book of Machine Design setting the model for such textbooks.

Charles R Mischke, Ph.D., is Professor Emeritus of Mechanical Engineering,

Iowa State University, Ames, Iowa He has authored many technical papers on designing to a reliability specification, computer-aided design, and design morphol-

ogy His was Coeditor-in-Chief, with XE Shigley, of the Standard Handbook of Machine Design, Second Edition, 1996.

Thomas H Brown, Jr., Ph.D., PE, is a Faculty Associate at North Carolina State

University He currently manages both the FE review program and the Civil neering PE Review Program at the University's Institute for Transportation Research and Education (ITRE) In addition to fulfilling his course development and teaching responsibilities, Dr Brown also teaches review courses for the Mechanical Engineering PE Review Program offered by the university and a private professional development firm Prior to coming to NC State, Dr Brown worked as a mechanical engineer for Scientific-Atlanta, Inc., Fluor Daniel Construction, and Burlington Industries, where he specialized in product development and machine design.

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Contents

Contributors ix

Foreword xi

Preface to Third Edition xiii

Preface to First Edition xv

Acknowledgments xvii

About the Editors xix

1 Evolution of a Successful Design 1.1 1.1 Evolution of a Design 1.1 1.2 Using the Handbook 1.2 1.3 Some Opportunities to Discover 1.3 1.4 Final Thoughts 1.8

Part I Machine Elements in Motion

2 A Thesaurus of Mechanisms 2.3

3 Linkages 3.1 3.1 Basic Linkage Concepts 3.1 3.2 Mobility Criterion 3.4 3.3 Establishing Precision Positions 3.4 3.4 Plane Four-bar Linkage 3.4

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3.5 Plane Offset Slider-crank Linkage 3.8 3.6 Kinematic Analysis of the Planar Four-bar

Linkage 3.8 3.7 Dimensional Synthesis of the Planar Four-bar

Linkage: Motion Generation 3.10 3.8 Dimensional Synthesis of the Planar Four-bar

Linkage: Crank-angle Coordination 3.18 3.9 Pole-force Method 3.20 3.10 Spatial Linkages 3.21 References 3.22

4 Cam Mechanisms 4.1 Summary 4.1 4.1 Cam Mechanism Types, Characteristics, and

Motions 4.1 4.2 Basic Cam Motions 4.6 4.3 Layout and Design; Manufacturing

Considerations 4.17 4.4 Force and Torque Analysis 4.22 4.5 Contact Stress and Wear: Programming 4.25 References 4.28

5 Gear Trains 5.1 5.1 Ordinary Gear Trains 5.1 5.2 Gear Type Selection 5.3 5.3 Planetary Gear Trains 5.5 5.4 Differential Trains 5.14 References 5.16

Part II Machine Elements That Absorb and Store

Energy

6 Springs 6.3 6.1 Introduction 6.4

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6.2 Glossary of Spring Terminology 6.4 6.3 Selection of Spring Materials 6.6 6.4 Helical Compression Springs 6.12 6.5 Helical Extension Springs 6.29 6.6 Helical Torsion Springs 6.36 6.7 Belleville Spring Washer 6.40 6.8 Special Spring Washers 6.51 6.9 Flat Springs 6.55 6.10 Constant-force Springs 6.58 6.11 Torsion Bars 6.62 6.12 Power Springs 6.63 6.13 Hot-wound Springs 6.66 References 6.69

7 Flywheels 7.1 7.1 Flywheel Usage 7.3 7.2 Sizing the Flywheel 7.3 7.3 Stress 7.13 7.4 Flywheels for Energy Storage 7.20 7.5 Strength and Safety 7.21 References 7.25

8 Clutches and Brakes 8.1 8.1 Types, Uses, Advantages, and Characteristics 8.4 8.2 Torque and Energy Considerations 8.14 8.3 Temperature Considerations 8.21 8.4 Friction Materials 8.23 8.5 Torque and Force Analysis of Rim Clutches and

Brakes 8.25 8.6 Band and Cone Brakes and Clutches 8.34 8.7 Disk Clutches and Brakes 8.40 8.8 Electromagnetic Types 8.45

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8.9 Actuation Problems 8.48 References 8.50 Suggested Reading 8.50

Part III Gearing

9 Spur Gears 9.3 9.1 Definitions 9.3 9.2 Tooth Dimensions and Standards 9.6 9.3 Force Analysis 9.7 9.4 Fundamental AGMA Rating Formulas 9.8

10 Helical Gears 10.1 10.1 Introduction 10.1 10.2 Types 10.2 10.3 Advantages 10.2 10.4 Geometry 10.5 10.5 Load Rating 10.8 References 10.57

11 Bevel and Hypoid Gears 11.1 11.1 Introduction 11.1 11.2 Terminology 11.1 11.3 Gear Manufacturing 11.7 11.4 Gear Design Considerations 11.10 11.5 Gear-tooth Dimensions 11.19 11.6 Gear Strength 11.25 11.7 Design of Mountings 11.50

12 Worm Gearing 12.1 12.1 Introduction 12.2 12.2 Kinematics 12.3 12.3 Velocity and Friction 12.5 12.4 Force Analysis 12.5 12.5 Strength and Power Rating 12.9

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12.6 Heat Dissipation 12.12 12.7 Design Standards 12.13 12.8 Double-enveloping Gear Sets 12.18 References 12.22 Additional Reference 12.22

13 Power Screws 13.1 13.1 Introduction 13.2 13.2 Kinematics 13.3 13.3 Mechanics 13.6 13.4 Buckling and Deflection 13.8 13.5 Stresses 13.9 13.6 Ball Screws 13.10 13.7 Other Design Considerations 13.12 References 13.13

Part IV Power Transmission

14 Belt Drives 14.3 14.1 General 14.4 14.2 Flat-belt Drive 14.16 14.3 V-belt Drive 14.21 14.4 Synchronous-belt Drive 14.27 14.5 Other Belt Drives 14.37 14.6 Comparison of Belt Drives 14.39

15 Chain Drives 15.1 15.1 Types, Uses, and Characteristics 15.2 15.2 Roller Chains: Nomenclature and Dimensions 15.4 15.3 Selection of Roller-chain Drives 15.7 15.4 Lubrication and Wear 15.14 15.5 Engineering Steel Chains: Nomenclature and

Dimensions 15.18 15.6 Selection of Offset-sidebar-chain Drives 15.20

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15.7 Silent Chains: Nomenclature and Dimensions 15.25 15.8 Selection of Silent-chain Drives 15.28 References 15.32

16 Couplings 16.1 16.1 General 16.2 16.2 Rigid Couplings 16.7 16.3 Flexible Metallic Couplings 16.9 16.4 Flexible Elastomeric Couplings 16.19 16.5 Universal Joints and Rotating-link Couplings 16.25 16.6 Methods of Attachment 16.32 References 16.33 Bibliography 16.34

17 Shafts 17.1 17.1 Introduction 17.2 17.2 Distortion Due to Bending 17.3 17.3 Distortion Due to Transverse Shear 17.8 17.4 Distortion Due to Torsion 17.13 17.5 Shaft Materials 17.13 17.6 Load-induced Stresses 17.14 17.7 Strength 17.15 17.8 Critical Speeds 17.17 17.9 Hollow Shafts 17.19 References 17.21 Recommended Reading 17.21

Part V Bearings and Lubrication

18 Rolling-contact Bearings 18.3 18.1 Introduction 18.4 18.2 Load-life Relation for Constant Reliability 18.9 18.3 Survival Relation at Steady Load 18.10 18.4 Relating Load, Life, and Reliability Goal 18.11

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18.5 Combined Radial and Thrust Loadings 18.14 18.6 Application Factors 18.15 18.7 Variable Loading 18.15 18.8 Misalignment 18.18 References 18.19

19 Journal Bearings 19.1 19.1 Introduction 19.3 19.2 Bearing and Journal Configurations 19.4 19.3 Bearing Materials and Selection Criteria 19.7 19.4 Pressure Equation for a Lubricating Film 19.13 19.5 Journal Bearing Performance 19.16 19.6 Liquid-lubricated Journal Bearings 19.20 19.7 Gas-lubricated Journal Bearings 19.43 19.8 Hydrostatic Journal Bearing Design 19.52 References 19.57

20 Lubrication 20.1 20.1 Functions and Types of Lubricant 20.1 20.2 Selection of Lubricant Type 20.2 20.3 Liquid Lubricants: Principles and Requirements 20.3 20.4 Lubricant Viscosity 20.6 20.5 Boundary Lubrication 20.9 20.6 Deterioration Problems 20.12 20.7 Selecting the Oil Type 20.14 20.8 Lubricating Greases 20.17 20.9 Solid Lubricants 20.22 20.10 Gas Lubrication 20.26 20.11 Lubricant Feed Systems 20.26 20.12 Lubricant Storage 20.29 References 20.30

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21 Seals 21.1 21.1 Elastomeric Seal Rings 21.1 21.2 Seals for Rotary Motion 21.4 21.3 Seals for Reciprocating Motion 21.9 References 21.15

Part VI Fastening, Joining, and Connecting

22 Bolted and Riveted Joints 22.3 22.1 Shear Loading of Joints 22.6 22.2 Eccentric Loads on Shear Joints 22.13 22.3 Tension-loaded Joints: Preloading of Bolts 22.18 22.4 Bolt Torque Requirements 22.31 22.5 Fatigue Loading of Bolted and Riveted Joints 22.31 22.6 Programming Suggestions for Joints Loaded in

Tension 22.38 References 22.40

23 Threaded Fasteners 23.1 23.1 Screw Threads 23.1 23.2 Bolts 23.5 23.3 Screws 23.11 23.4 Nuts 23.28 23.5 Tapping Screws 23.35 Reference 23.38

24 Unthreaded Fasteners 24.1 24.1 Rivets 24.1 24.2 Pins 24.8 24.3 Eyelets and Grommets 24.10 24.4 Retaining Rings 24.16 24.5 Keys 24.24 24.6 Washers 24.26 References 24.29

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25 Gaskets 25.1 25.1 Definition 25.1 25.2 Standard Classification System for Nonmetallic

Gasket Materials 25.1 25.3 Gasket Properties, Test Methods, and Their

Significance in Gasketed Joints 25.2 25.4 Permeability Properties 25.3 25.5 Load-bearing Properties 25.7 25.6 Environmental Conditions 25.12 25.7 Gasket Design and Selection Procedure 25.13 25.8 Gasket Compression and Stress-distribution

Testing 25.22 25.9 Installation Specifications 25.23 References 25.23

26 Welded Connections 26.1 26.1 Definitions and Terminology 26.1 26.2 Basic Welding Circuit 26.2 26.3 Arc Shielding 26.2 26.4 Nature of the Arc 26.4 26.5 Overcoming Current Limitations 26.5 26.6 Commercial Arc-welding Processes 26.6 26.7 Arc-welding Consumables 26.18 26.8 Design of Welded Joints 26.23 26.9 Codes and Specifications for Welds 26.39

27 Fits and Tolerances 27.1 27.1 Introduction 27.2 27.2 Metric Standards 27.2 27.3 U.S Standard – Inch Units 27.9 27.4 Interference-fit Stresses 27.9 27.5 Absolute Tolerances 27.13 References 27.16

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Part VII Load Capability Considerations

28 Strength under Static Conditions 28.3 28.1 Permissible Stresses and Strains 28.4 28.2 Theory of Static Failure 28.5 28.3 Stress Concentration 28.9 28.4 Fracture Mechanics 28.13 28.5 Nonferrous Metals 28.19 References 28.22

29 Strength under Dynamic Conditions 29.1 29.1 Testing Methods and Presentation of Results 29.3 29.2 SN Diagram for Sinusoidal and Random

Loading 29.7 29.3 Fatigue-strength Modification Factors 29.9 29.4 Fluctuating Stress 29.18 29.5 Complicated Stress-variation Patterns 29.20 29.6 Strength at Critical Locations 29.22 29.7 Combined Loading 29.27 29.8 Surface Fatigue 29.32 References 29.35 Recommended Reading 29.36

30 Instabilities in Beams and Columns 30.1 30.1 Euler's Formula 30.2 30.2 Effective Length 30.4 30.3 Generalization of the Problem 30.6 30.4 Modified Buckling Formulas 30.7 30.5 Stress-limiting Criterion 30.8 30.6 Beam-column Analysis 30.12 30.7 Approximate Method 30.13 30.8 Instability of Beams 30.14 References 30.18

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31 Vibration and Control of Vibration 31.1 31.1 Introduction 31.1 31.2 Single-degree-of-freedom Systems 31.1 31.3 Systems with Several Degrees of Freedom 31.19 31.4 Vibration Isolation 31.28 References 31.30

Part VIII Performance of Engineering Materials

32 Solid Materials 32.3 32.1 Structure of Solids 32.3 32.2 Atomic Bonding Forces 32.4 32.3 Atomic Structures 32.6 32.4 Crystal Imperfections 32.13 32.5 Slip in Crystalline Solids 32.17 32.6 Mechanical Strength 32.19 32.7 Mechanical Properties and Tests 32.22 32.8 Hardness 32.23 32.9 The Tensile Test 32.27 32.10 Tensile Properties 32.34 32.11 Strength, Stress, and Strain Relations 32.38 32.12 Impact Strength 32.44 32.13 Creep Strength 32.45 32.14 Mechanical-property Data 32.48 32.15 Numbering Systems 32.53 References 32.57

33 Strength of Cold-worked and Heat-treated Steels 33.1 33.1 Introduction 33.2 33.2 Strength of Plastically Deformed Materials 33.3 33.3 Estimating Ultimate Strength after Plastic

Strains 33.4

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33.4 Estimating Yield Strength after Plastic Strains 33.8 33.5 Estimating Ultimate Strength of Heat-treated

Plain Carbon Steels 33.9 33.6 Estimating Ultimate Strength of Heat-treated

Low-alloy Steels 33.11 33.7 Tempering Time and Temperature Tradeoff

Relation 33.29 References 33.31 Recommended Reading 33.31

34 Wear 34.1 34.1 General Principles in Design for Wear

Resistance 34.1 34.2 Steps in Design for Wear Life Without Selecting

Materials 34.4 34.3 Wear Equations 34.6 34.4 Steps in Selecting Materials for Wear

Resistance 34.7 34.5 Material-selection Procedure 34.14 References 34.18 Bibliography 34.18

35 Corrosion 35.1 35.1 Introduction 35.1 35.2 Corrosion Rates 35.2 35.3 Metal Attack Mechanisms 35.2 35.4 Corrosion Data for Materials Selection 35.28 References 35.28

Part IX Classical Stress and Deformation Analysis

36 Stress 36.3 36.1 Definitions and Notation 36.3

Contents xvii

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36.2 Triaxial Stress 36.5 36.3 Stress-strain Relations 36.6 36.4 Flexure 36.12 36.5 Stresses Due to Temperature 36.16 36.6 Contact Stresses 36.19 References 36.24

37 Deflection 37.1 37.1 Stiffness or Spring Rate 37.2 37.2 Deflection Due to Bending 37.3 37.3 Properties of Beams 37.3 37.4 Analysis of Frames 37.3

38 Curved Beams and Rings 38.1 38.1 Bending in the Plane of Curvature 38.2 38.2 Castigliano's Theorem 38.2 38.3 Ring Segments with One Support 38.3 38.4 Rings with Simple Supports 38.10 38.5 Ring Segments with Fixed Ends 38.15 References 38.22

39 Pressure Cylinders 39.1 39.1 Introduction 39.1 39.2 Design Principles of Pressure Cylinders 39.2 39.3 Design Loads 39.3 39.4 Cylindrical Shells – Stress Analysis 39.4 39.5 Thick cylindrical shells 39.12 39.6 Thermal Stresses in Cylindrical Shells 39.14 39.7 Fabrication Methods and Materials 39.17 39.8 Design of Pressure Cylinders 39.18 References 39.21 Appendix: Sections and Shapes – Tabular Data A.1 A.1 Centroids and Center of Gravity A.1

xviii Contents

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A.2 Second Moments of Areas A.11 A.3 Structural Shapes A.14 References A.26

Index I.1

CHAPTER 1 EVOLUTION OF

A SUCCESSFUL DESIGN

Thomas H Brown, Jr., Ph.D., RE.

Faculty Associate Institute for Transportation Research and Education

North Carolina State University Raleigh, North Carolina

1.1 EVOLUTION OF A DESIGN / 1.1

1.2 USING THE HANDBOOK / 1.2

1.3 SOME OPPORTUNITIES TO DISCOVER / 1.3

1.4 FINAL THOUGHTS / 1.8

7.7 EVOLUTIONOFADESIGN

Most likely you have, right at this moment, at least one machine design project inprogress Maybe you were the originator of the design, but I suspect you inheritedthis design from others I further suspect that you have already identified elements

of the design you feel could be improved You might be under pressure from tomer service or marketing to respond to some need for change In responding suc-cessfully, either to your own observations for change or to those of others, the designwill evolve Recognizing that the evolutionary design process is decidedly complex,

cus-with a seemingly random sequence of steps, the primary purpose of Standard book of Machine Design is to make the information you need as readily accessible

Hand-and usable as possible

As an example of how a design can evolve, and to provide perspective on how theinformation in this Handbook has traditionally been used, let me review for you aproject I was given in my first job as a mechanical engineer It involved the position-ing of a microwave feed horn for a 30-ft-diameter antenna dish The original design(not mine, by the way) called for a technician to climb up onto a platform, some 20

ft off the ground, near the backside of the feed horn The technician had to loosen ahalf dozen bolts, rotate the feed horn manually, and then retighten the bolts Thisdesign worked quite well until several systems were sold to a customer providingtelecommunications along the Alaskan oil pipeline Workers were not really safegoing out in below 00F weather, with snow and ice on everything As a result of theirconcerns for safety, this customer asked that we provide remote positioning of thefeed horn from the nearby control room

The critical design requirement was that the positioning of the feed horn needed

to be relatively precise This meant that our design had to have as little backlash inthe drive mechanism as possible Being a young engineer, I was unaware of the widevariety of different drive systems, in particular their respective properties and capa-

bilities I asked one of the older engineers for some direction He suggested I use aworm drive since it cannot be back driven, and loaned me his copy of Joseph

Shigley's book, Mechanical Engineering Design He said that Shigley's book (a

pre-cursor to this Handbook) had been his primary source of information about wormdrives, and a wealth of other machine design information As it turned out, theresulting design worked as required It not only pleased our Alaskan customer butbecame a standard on all antenna systems

I did not get a promotion as a result of the success of this new design, nor did Ireceive a raise However, I was proud, and, as you can surmise, still am I credit thissuccessful design evolution to the material on worm drives in Shigley's book Andthere is more to this story The worm drive gearbox we ultimately purchased con-tained a plastic drive element This allowed the backlash to be greater than whatcould be tolerated in positioning accuracy and did not provide the necessarystrength to break the feed horn loose from a covering of ice The original manufac-turer of the gearbox refused to change this drive element to metal for the units wewould be buying If we made the change ourselves, they said, the warranty would bevoided However, after absorbing the wealth of information on worm drives inShigley's book, I felt confident that we could make this substitution without endan-gering the reliability of the unit Also, because of Joseph Shigley's reputation in themechanical engineering community and the extensive list of references he cited, Inever felt the need to consult other sources

Another aspect of this story is also important to note In addition to the tion on worm drives, I also used Shigley's book to find comprehensive design infor-mation on the many other machine elements in the new design: gear train geometry,chain drives, couplings, roller bearings, bolted joints, welds, lubrication, corrosion,and the necessary stress and deformation calculations I needed to make All this

informa-information, and much more, was contained in the First Edition of the Standard Handbook of Machine Design, which Joseph Shigley coauthored with Charles

Mischke Now in its Third Edition, this Handbook includes the information machinedesign engineers have come to trust We hope you will find this information invalu-able as you constantly strive to improve your designs, whether by your own initia-tives, or for other reasons

7.2 USINGTHEHANDBOOK

Once the chapters for this Third Edition of the Handbook were determined, wedecided that these chapters should be organized into nine sections, denoted Parts 1through 9 Each section focuses on a distinct collection of related material Forexample, Part 3, "Gearing," contains chapters on spur gears, helical gears, bevel andhypoid gears, worm gearing, and power screws However, each chapter stands on itsown, providing direct access to a specific area of interest or need

This Handbook is a unique reference, capturing the breadth and depth of what iscurrently known about each of these design element topics The nine sections are

Part 1 Machine Elements in Motion

Part 2 Machine Elements That Absorb and Store Energy

Part 3 Gearing

Part 4 Power Transmission

Part 5 Bearings and Lubrication

Part 6 Fastening, Joining, and Connecting

Part 7 Load Capability Considerations

Part 8 Performance of Engineering Materials

Part 9 Classical Stress and Deformation Analysis

While there are many ways the nine sections could have been ordered, the orderchosen for this Third Edition provides one sequence of steps to the evolutionarydesign process For example, you might first consider the kinds of motions you needand how they might be accomplished Part 1 might help you choose a classic mecha-nism or linkage, a cam, or maybe some arrangement of gears Possibly your designneeds to absorb or store energy, so the chapters included in Part 2 would provide theinformation you need Depending on your design, Parts 3 and 4 cover virtually everytype of gear set, drive type, coupling, and the common elements related to thesedevices Part 5 covers how rotating elements might be supported, typically witheither roller- or journal-type bearings And if bearings are present, then lubricationand seals must be carefully considered

Part 6 continues the design process to the consideration of how components will

be assembled Are there structural bolts, or just mechanical fasteners, or are parts to

be welded? The coauthor of the chapter on welding is the well-known author of thepreeminent book on welding, so this Handbook should provide all the informationyou need relative to this topic The last chapter in this section presents the complexprocedure necessary to maintain proper fits and tolerances, a full-time job in itselffor some engineers Everything an engineer needs to know about this area of manu-facturing can be found in this Third Edition of the Handbook

At some point, loads will be determined, both statically and dynamically; fore, Part 7 contains the information you need to make decisions relative to the reli-ability of critical parts Information on vibration, and just as important, its control, isprovided in a chapter in this section The selection of materials is covered in Part 8and includes chapters on wear and corrosion With regard to the problems of corro-sion, one of the main components of a system I was responsible for failed due toexcessive galvanic corrosion The information contained in this Handbook helped

there-me not make that mistake again

The last section, Part 9, contains the classic information on stress and mation calculations every mechanical engineer learns in school, but finds escapesexponentially if not used regularly Here, four chapters provide every importantcalculation practicing engineers should need, and they are introduced in a mannerthat can be understood and used with confidence

defor-1.3 SOME OPPORTUNITIES TO DISCOVER

As mentioned earlier, this Third Edition of the Standard Handbook of Machine Design has been organized differently as compared to the two previous editions In

addition to grouping the chapters into nine sections, almost a dozen of the 50 ters in the Second Edition, which contained a variety of information ancillary to themachine design process, have been removed Therefore, the scope of this edition ofthe Handbook is focused on the more traditional machine design topics

chap-For those familiar with the previous editions, one chapter that was in the FirstEdition but not in the Second, "Pressure Cylinders," has been included in the Third.This additional chapter is located in Part 9, completing the information important

relative to stress and deformation analysis Also, one of the chapters in the two vious editions, "Sections and Shapes—Tabular Data," is now Appendix A.

pre-Discovering opportunities to improve or evolve your designs successfully is one

of the primary ways we expect you to use this Handbook Each chapter has erable design information and the format used is unique What follows is a discus-sion of just some of the helpful information you will find in each chapter

consid-Part 1: Machine Elements in Motion

Chapter 2 in this section is undoubtedly one of the most distinctive chapters you willfind anywhere There is page after page of diagrams of every conceivable mechanismand machine device There are snap-action mechanisms, linear actuators, fine adjust-ment devices, clamping and locating mechanisms, escapements and indexing mecha-nisms, oscillating mechanisms, ratchets and latches, reciprocating and reversingmechanisms, and couplings (see the commercial designs in Chap 16) and connectors,including slider connectors

There are devices that stop, pause, and hesitate motion, and devices that port motion between machine elements There are two pages of loading and unload-ing mechanisms, many that are commonly used for construction and earth-movingequipment, as well as bulk-handling railcars You will find path generators, functiongenerators, and even mechanical computing mechanisms, still finding a place in thiselectronic age There are speed-changing mechanisms and multidegree mechanismsthat form the basis of many robotic-type machines I hope you enjoy as much as I dojust flipping pages in this one-of-a-kind catalog of mechanical devices

trans-If a particular linkage catches your eye in Chap 2, then the information tained in Chap 3 takes you many steps further, providing all the geometry of motiondiagrams, or kinematics, you will need Details of the famous slider-crank and four-bar linkages are provided The material in this chapter might seem intimidatinggraphically, but without it, the preciseness of the motion you most likely need will bedifficult to achieve any other way

con-If your machine requires a cam to achieve its design requirements, then Chap 4contains everything about this particular device From simplified schematics to thecomplexity of cam trigonometry, everything a designer will need is here in thesepages There is even a computer program flowchart to help you develop a compre-hensive analysis of your design, whether you use a programming code like FOR-TRAN or a personal computer spreadsheet

The last chapter in this section, "Gear Trains," presents all the relative speed culations for the two most common arrangements of gears: spur and planetary Also,the speed calculations for differential gear trains are presented Once these calcula-tions are made, then the detailed specifications can be made using the information

cal-in Part 3

Part 2: Machine Elements That Absorb and Store Energy

Personally, I have consulted Chap 6, "Springs," as much as any other chapter in theHandbook It contains information on every kind of spring, from the commonly usedhelical spring, with all its variations, to the unique Belleville spring washer Ellipticaland even torsion bar springs are covered In fact, basically everything I know aboutsprings is in this chapter, one of the longest in the Handbook

Flywheels are an important machine element in devices such as automobileengines and punch presses They act like an accumulator tank in an air compressorsystem, thus evening out the fluctuations in rotational motion Careful sizing is nec-essary to make sure that just the right amount of inertia is provided Too much cancause the system to be have too long a recovery period or too little inertia, causingthe system to loose too much energy between loading cycles For high-speed fly-wheels or machine elements like compressor blades, consideration of the inertialstresses developed can be important.

The late John Muir, in his book How to Keep Your Volkswagen Alive, said,

"Brakes perform a negative function, applying negative acceleration to stop the car,remaining inert when not being used." Brakes may have a negative function; how-ever, their design can be critical to a successful product Chapter 8 covers all aspects

of brakes and all aspects of what might be the opposite of brakes—clutches.Clutches are designed to transfer power evenly and gradually between two shaftsrotating at different speeds, even when one shaft is at rest There has been a greatdeal of ingenuity in the design of brakes and clutches, accounting for many patentsand commercial products Centrifugal, cone, and disk-type clutches and brakes aretwo such commercial success stories Both brakes and clutches produce significanttemperature gradients in service The design considerations associated with temper-ature variations are covered in this important chapter, including information onselecting the right clutch or brake materials for your specific application

Part 3: Gearing

One of the most fascinating sections in this Third Edition of the Handbook is Part 3,

"Gearing." Most of us as mechanical engineers will never actually be involved indesigning and manufacturing gear sets, even the simplest spur gear However, it hasalways been comforting to know that this Handbook contained everything needed if

we were ever put in the situation of having to design a set of gears Chapter 9, "SpurGears" is relatively short and straightforward, giving the impression that gears arenot that complicated Then, Chap 10, "Helical Gears," makes the point, by the extent

of the information provided, of just how complicated gear sets can be if they are to

be done correctly This is one of the longest chapters in the Handbook Anotherequally long chapter, 11, covers "Bevel and Hypoid Gears." This has always been aspecial chapter, providing insight into one of the most magical machine elements inmechanical engineering There are few vehicles on earth that do not have a differen-tial, and every differential has either a bevel or hypoid gear set All the geometry ofmotion is explained, with table after table and chart after chart of applicable formu-las and performance data for all variations and design parameters

I've already referred to the importance of the material in Chap 12, "Worm ing," in my story about the remote positioning of an antenna feed horn project As Isaid earlier, the information in this chapter was invaluable in helping me modify anexisting design to satisfy the needs of a high-profile customer

Gear-As I look back on the years I spent associated with large antenna systems, it

seems as though every aspect of these systems had me searching the Standard book of Machine Design for important information Chapter 13, "Power Screws,"

Hand-was another of those chapters I became very familiar with, since the primary tioning of the antenna dish on the satellite was accomplished by heavy duty powerscrews driven by dc motors This Handbook is where I obtained the information Ineeded

posi-Part 4: Power Transmission

This section contains four chapters directed at the requirements of transferringmotion from one rotating axis to another, whether by the time-honored belt(Chap 14) or chain (Chap 15) configurations, or by the wide variety of couplings(Chap 16) used to isolate and protect downstream machine elements This seemed

to be the best place to discuss the design of shafts (Chap 17), from both a static anddynamic viewpoint While new belt, chain, and coupling products are introducedevery year, the basic design considerations remain the same Speed ratio calcula-tions; tension adjustment schemes; and materials, many of which are composite con-structions, are universal to these machine elements Serpentine-notched belts seek

to combine the flexibility and low noise of traditional belt drives, while providing thepositional accuracy to meet strict timing requirements such as in automotive appli-cations For large horsepower transfer, metal chain and sprocket drives, usually inmultiple-strand configurations, seem the best approach—and what you need is pro-vided in this Handbook

Since lining up shafts exactly is difficult, if not impossible, the usual solution is acoupling between the shafts This is another area of intense ingenuity and cleverness,with many of the successful products highlighted in this section A complete discus-sion of universal joints and constant velocity joints is also included

Part 5: Bearings and Lubrication

One of the great inventions of the twentieth century is the roller bearing—in ular, the tapered roller bearing Roller bearings allow high speeds under relativelyheavy loads not possible before their introduction Every automobile on the roadtoday has a plethora of roller-type bearings Journal bearings, which were the pri-mary bearing type before the roller bearing, are still an important mechanical designelement The main and rod bearings in an internal combustion engine are of thejournal type Chapter 19, "Journal Bearings," is one of the longest chapters in theHandbook, punctuating the amount of design information available Its length alsoindicates the extent of the design considerations necessary for their successful use.Bearings could not do their job without lubrication, and lubrication would be lostfrom most bearings without the proper seals Traditional and nontraditional sealdesigns are presented in this section, including those operating in static conditionsand those operating between rotating parts Lubricants are another product in con-stant flux This Third Edition presents the properties and uses of the more commonand trusted oils, greases, and solid lubricants

partic-Part 6: Fastening, Joining, and Connecting

Chapter 22, "Bolted and Riveted Joints," covers the design of bolts and rivets usednot only to hold parts together in an assembly but also as structural elements Com-plex joints in tension and shear are presented, including the effect of gaskets in astructural joint Calculations for the proper preload of a structural bolt are provided.Chapters 23 and 24 cover every conceivable type of mechanical fastener Chapter

23 presents design information for threaded fasteners while Chap 24 presentsdesign information for unthreaded fasteners

If a connection must contain or keep out gases or liquids, then a gasket is usually

specified The types of gaskets typically available and their appropriate applicationcriteria are provided in Chap 25.

When disassembly is not required or when maximum strength is needed, then ally the only solution to connecting separate parts is a weld All aspects of a weldedconnection are presented in Chap 26 This chapter begins with the basic principles ofthe arc welding process, followed by the various commercial processes, includingexhaustive information on the materials used in welding This chapter also includesthe information needed to design a welded joint to be as strong, or stronger, than thematerials being welded together Since failure of welded joints has had such a highimpact on the safety of the public, many national codes and industry specificationshave been established and must be met These are covered in detail in Chap 26

usu-As mentioned earlier, the ongoing effort in manufacturing to hold to a high dard of quality requires a thorough understanding of the factors in fits and toler-ances Chapter 27 presents the standards of fit universally accepted and thecomplications associated with a buildup of tolerances in an assembly

stan-Part 7: Load Capability Considerations

Chapter 28 covers static theories of failure, from the theories for ductile materials tobrittle materials Charts for determining stress concentration factors for variousdesign geometries are provided In contrast, Chap 29 covers dynamic theories offailure, including the determination of endurance limits For various design factors,such as surface roughness, size, loading, temperature, and a host of miscellaneousfactors, the Marin equation is used to modify the endurance limit determined fromexperiment Alternating and fluctuating loading are considered, including combinedloading considerations

Machine elements in compression must be analyzed to protect against buckling

or sudden collapse Chapter 30 covers all aspects of compression loading of beamsand columns, from Euler's formulas to complex beam-column analysis

Chapter 31 covers mechanical vibration, from the forced vibration of dampedsingle-degree-of-freedom systems to multi-degree-of-freedom systems Torsionalvibration and vibration isolation are presented

Part 8: Performance of Engineering Materials

This section contains four chapters focused on the decisions associated with theselection of materials for the critical parts in a design Chapter 32 is a summary ofthe science of material behavior, including the procedures used to determine variousmaterial properties It is one of the longer chapters in the Handbook Chapter 33focuses on the properties and engineering considerations of the most common mate-rial in machines—steel Whatever manufacturing is process used, everything needed

in designing with steel is provided

Once in service, machine elements are subject to constant wear and the adverseeffects of corrosion Chapters 34 and 35, respectively, cover the important aspects ofwear and corrosion It would seem a shame to spend so much time on the otheraspects of design only to be blindsided by these two factors Corrosion, especiallygalvanic, is insidious and only careful selection of mating materials will avoid disas-

ter Chapter 35 contains a listing from "A" for acetone to "W" for water relative to

their adverse reaction to other chemicals

Part 9: Classical Stress and Deformation Analysis

This last section in the Third Edition provides the mechanical design engineer withthe fundamental formulas for stress (Chap 36) and deflection of beams (Chap 37).This section also includes the stress and deformation of special geometries, such ascurved beams and rings (Chap 38), and the stress and deformation of pressurizedcylinders (Chap 39), which are developed as a result of internal pressure or from theeffects of a press or shrink fit

Appendix

As indicated earlier, one of the chapters included in the First and Second Editions,

"Sections and Shapes—Tabular Data," has been provided in this Third Edition as anAppendix Here are found the properties of common cross-sectional areas used invarious mechanical elements, particularly beams, and the properties of standardstructural shapes, such as rectangular tubing, channels, angles, and variations on theI-beam

1.4 FINALTHOUGHTS _ _ _ _ _ _ _ _ _

The process of creating or improving a mechanical system is an adventure Like alladventures, machine design has its complications and logistics When we are suc-cessful meeting these difficult challenges, the pride and feeling of accomplishmentare so exhilarating they might be compared to how Sir Edmund Hillary must havefelt after his successful assault on Everest Or how Sir Henry Royce, of the famousmotorcar company Rolls-Royce, felt when he was knighted While knighthoodmight not be one of our rewards for success, the recognition we receive is no less sig-nificant in our careers as design engineers—bringing admiration and respect fromour peers and considerable personal satisfaction and enjoyment

Adventures also have their heroes In the field of machine design, no two viduals stand out more than Joseph Shigley and Charles Mischke Their professionalpartnership has been synonymous with machine design for 20 years, and JosephShigley has been a household word in mechanical engineering for over 40 years We

indi-hope the wealth of information contained in this Third Edition of the Standard Handbook of Machine Design, and the way in which it is presented, will provide the

necessary resources for your design projects

P • A • R • T • 1 MACHINE ELEMENTS

IN MOTION

GLOSSARY OF SYMBOLS

R Re volute pair or pin joint

P Prismatic pair or sliding joint

C Cylinder pair for joints that allow rotation and sliding along the cylinderaxis

G Spheric pair (globe) for ball joints

SL Screw pair with lead L

F Planar pair (flat) for a joint that maintains two planes in contact

SUMMARr

This chapter is intended to be used as an idea generator Following the adage that apicture is worth 1000 words, this chapter was assembled with millions of "words" infigures and virtually none using the alphabet I have taken the liberty of varyingdimensions to better show the principle of operation You should not scale the fig-ures, but follow the regular synthesis procedure to determine the proper dimensionsfor the application in mind

In this chapter a new notation is used for the kinematic representation of joints

or pairs in a linkage

* Readers will note a difference in the style and character of the figures in this chapter When this manuscript was received, the illustrations, all conceived and executed by Professor Torfason, were seen to be original and unique We asked for and received from the publishers special permission to reproduce them exactly as they were drawn—EDS.

COLLATERAL READING

L J Kamm, Designing Cost-Efficient Mechanisms, McGraw-Hill, New York, 1990.

FIGURE 2.1 Snap-action mechanisms These mechanisms are bistable elements in machines.

They are used in switches to quickly make and break electric circuits and for fastening items.

(a) Snap-action toggle switch; (b) to (h) seven variations of snap-action switches; (i) circuit breaker;

(;') to (o), spring clips.

FIGURE 2.2 Linear actuators These are devices that cause a straight-line displacement

between two machine elements, (a) Lead screw; (b) worm gear with stationary nut; (c) worm gear with stationary screw; (d) single-acting hydraulic cylinder; (e) double-acting hydraulic cylinder; (/) telescoping hydraulic cylinder; (g) hydraulic cylinder with positional feedback; (h) hydraulic cylinder with floating link feedback.

FIGURE 2.3 Fine adjustments I Fine adjustments for stationary mechanisms are mechanisms

that make a small change in the position of a mechanical member, (a), (b) Screw adjustments; (c), (d) differential screws; (e) Chinese windlass; (/) differential hoist; (g) worm gear and screw; (h) worm gears in series; (i) lever; (/) levers in series; (Jc) toggle mechanism; (/) screws to adjust angular position; (m), (n) eccentric cranks; (o) wedges; (p) harmonic drive.

FIGURE 2.4 Fine adjustments II Fine adjustments for moving

mecha-nisms are adjusting devices which control the motion of linkages such as

stroke, etc., while the mechanism is in motion, (a), (b) Differential gear adjustment; (c) adjustable-stroke engine; (d) adjustable stroke of shaper mechanism; (e) ball and disk speed changer; (J) adjusting fixed center of

linkage for changing motion properties.

FIGURE 2.5 Clamping mechanisms These devices are used to hold items for machining

operations or to exert great forces for embossing or printing, (a) C clamp; (b) screw clamp; (c) cam clamp; (d) double cam clamp; (e) vise; (/) cam-operated clamp; (g) double cam- actuated clamp; (h) double wedge; (i) to (/) toggle press; (m) vise grips; (n) toggle clamp; (o) collet; (p) rock crusher.