ELECTROMECHANICAL DESIGN HANDBOOK

ELECTROMECHANICAL

DESIGN HANDBOOK

Ronald A. Walsh

Manager, Research and Development

Powercon Corporation

Severn, Maryland

Third Edition

McGRAW-HILL

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Library of Congress Cataloging-in-Publication Data

Walsh, Ronald A.

Electromechanical design handbook / Ronald A. Walsh. — 3rd ed.

p. cm.

ISBN 0-07-134812-3

1. Electromechanical devices—Design and construction—Handbooks,

manuals, etc. I. Title.

TJ163.W35 1999

621—dc21 99-4487

CIP

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Act of 1976, no part of this publication may be reproduced or distributed in any form or

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1234567890 DOC/DOC 90987654

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Information contained in this work has been obtained by The McGraw-

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services. If such services are required, the assistance of an appropriate

professional should be sought.

ABOUT THE AUTHOR

Ronald A. Walsh was director of research and development at the Powercon Cor-

poration in Severn, Maryland for 20 years. An industrial product designer for more

than 45 years with such companies as Bendix Radio, American Machine and

Foundry, and Martin Marietta, he holds three U.S. patents for electronic packaging

systems and mechanical devices and five copyrights. Ronald Walsh worked at Cape

Canaveral, Florida, as a liaison engineer on the Titan and Gemini aerospace vehicles

and participated in the design of the Titan, Gemini, and Apollo aerospace vehicles

and numerous manned military and commercial aircraft and military guided mis-

siles. He has worked with some of the pioneers of advanced aircraft and aerospace

vehicle design, atomic energy processing equipment, and military and commercial

electrical and electronic equipment. He is the author of the McGraw-Hill Machining

and Metalworking Handbook.

ACKNOWLEDGMENTS

In the course of compiling data and procedures for inclusion in this handbook, I selected data,

design information, and design procedures from many sources. I wish to express my gratitude

particularly to the following individuals, companies, and organizations who granted permis-

sion to use their copyrighted design data or otherwise contributed to the production of this

handbook: Ralph Siegel, president, Powercon Corporation (Severn, Maryland 21144); Alex

Feygelman, design engineer; Katrina T. Walsh; Michelle E. Walsh; Exide Corporation; THE

TIMKEN COMPANY; Boston Gear Division of IMO Industries; ALCOA (Aluminum Com-

pany of America). I am grateful also to the following societies, institutes, and specification

authorities: AISC; SMI; ANSI; ASME; AGMA; NEMA; AISI; AFBMA; IFI; ASTM; SAE;

Newark Electronics; Allied Electronics; Tandy Corporation; Bryant Electric—Division of

Westinghouse; Thermometrics, Inc.; Machine Design, a Penton publication; The Chemical

Rubber Publishing Company; Omega Engineering; T. B. Wood’s Sons, Inc.; WATLOW, Inc.;

Eastman Kodak Company; Waldes Truarc; Tinnerman Co.; Ruland Co.; PEM Inc.; Linda

Ludewig, Chief Editor, McGraw-Hill, Inc.; and Larry S. Hager, Senior Editor, McGraw-

Hill, Inc.

xxi

PREFACE

This third edition of the Electromechanical Design Handbook is again presented as a useful

working tool for product designers, design engineers, and others who are involved directly in

the product design disciplines and those in the design support groups throughout industry.

The data in this handbook cover a broad range of subjects because of the nature of elec-

tromechanical design engineering practice.

Product designers who possess general and specific practical engineering knowledge are

valuable to their particular company or organization. Those who have a broad range of prac-

tical electromechanical design knowledge not only are more secure in their jobs but can

acquire the ability to find new jobs more easily and quickly if the need arises.

I have tried to consolidate enough basic and application-specific design data and proce-

dures to allow the electromechanical designer to initiate many of the design calculations and

procedures required to begin the development of mechanical, electrical, and electronic parts,

mechanisms, assemblies, and processes. Most of the equations and techniques presented in

this handbook have been previously used and accepted as standard practice throughout

industry. At the same time, the experienced designer and student should understand that

mathematical solutions to complex industrial design engineering problems are approxima-

tions at best in many cases. The mathematical solutions to problems in some areas of design

are exact, while the solutions in others are unattainable with standard analytical procedures.

There are no problem solution substitutes more effective than the prototype and definitive

testing in proving the adequacy of a particular design or product. Some products cannot have

a prototype stage, and in these cases we rely upon accepted standards and procedures formu-

lated by the American standards organizations, and calculations and experience. The proto-

type and testing stages of product design are of prime importance to the industrial

electromechanical product designer.

The intent of this handbook is to show practical, working design data and procedures; lit-

tle emphasis is placed on theory. Successful industrial design engineers do not dwell on the-

ory; rather, they use their practical engineering training, their intelligence, and testing and

experience to solve actual industrial design problems quickly and effectively, with any means

at their disposal. This handbook does not attempt to cover all subjects relevant to design engi-

neering, only those that are used in most common and some specialized electromechanical

design applications.

This third edition contains an expanded amount of information and design data that will

prove even more useful than the first edition, which was so widely accepted in the design engi-

neering community.

For those designers who are interested in or must have information concerning the manu-

facturing practices and processes directly related to electromechanical design engineering

practices and also modern manufacturing procedures, the author recommends his McGraw-

Hill Machining and Metalworking Handbook (1999), which, together with the McGraw-Hill

Electromechanical Design Handbook, gives the product designer or design engineer an

unprecedented amount and source of practical and effective design procedures and data, as

well as manufacturing procedures and industrial processes.

American industry today, more than ever, needs people in the engineering professions

who are trained in the multiple integrated disciplines of mechanical, electrical, and electronic

xix

engineering design practices (called electromechanical design engineering, not mechatronics).

See the introduction to Chap. 6 and its contents for how to effectively implement these disci-

plines. America needs more highly trained electromechanical design engineers and fewer spe-

cialists in order to more effectively compete in the national and international markets. This

has been the author’s purpose and goal in writing this volume and its companion, the

McGraw-Hill Machining and Metalworking Handbook.

Ronald A. Walsh

xx PREFACE

INTRODUCTION

If you are involved in the design of industrial, military, or consumer products and perform

mechanical, electrical, and electronic design functions, this handbook will be of value in your

work.

The handbook is not intended for specialists in the various engineering disciplines, but

rather for those designers who create the majority of general products, parts, mechanisms,

and assemblies used throughout industry.

The handbook does not attempt to show an individual how to be a designer, but does pre-

sent the basic reference data and techniques used to perform the various design functions.

The term electromechanical designer is appropriate today because many designers are

involved with components and assemblies that contain elements that are mechanical, electri-

cal, and electronic in nature, all dependently combined to form the finished product.

In many small companies, the electromechanical or product designer is responsible for

the entire product—all aspects included. It is to the designer’s advantage to be proficient in

or to have reference data pertaining to as many of the disciplines involved in product design

as possible.

Aside from containing a formidable amount of design data, the references listed in the bib-

liographies at the ends of chapters will be of assistance to many designers in carrying out their

work, as will the listings of specification and standards authorities shown in Chap. 15. As

stated in the handbook, the accumulation of accurate data is one of the basic design functions.

It was not my intent to show as many aspects of product design as possible, but to show

those methods and data that are used again and again in the course of product-design engi-

neering work. I have attempted to cover those subjects and areas which are of prime impor-

tance to the product designer, with emphasis on procuring additional information from

various expert sources, which have been listed.

The handbook also will be of value to students of engineering attending technical teaching

facilities, as it provides them with a good view of what is involved in modern product design

and how to approach many basic design problems.

Electromechanical designers today have many technological advantages over their prede-

cessors. In modern manufacturing facilities, the designer has access to accurate measuring and

testing equipment, computer-aided design stations, and high-speed and accurate manufacturing

equipment, such as computer-controlled machining centers and multistation punch presses, and

highly accurate sheet-metal cutting and bending machines. Facilities such as these allow parts to

be made consistently more accurately and at a higher rate of production than in the past.

Modern test and measuring equipment and devices, such as computers, digital oscillo-

scopes, digital multimeters and counters, pressure transducers, load cells, strain gauges, ther-

mocouples, accelerometers, and high-speed cameras, allow the modern designer to acquire

accurate answers to many design problems that would have been difficult or impossible to

solve mathematically in the past, and that are still beyond the scope of engineering design

manuals.

This equipment allows designers today to design and develop a particular product quickly,

send it onto its prototype stage, and run definitive tests to prove the adequacy and safety

of the design. Cost analyses can then be made and implemented, the prototype again tested,

and finally, the product set up for production after the engineering documentation has been

completed.

xxiii

Using this handbook will enable you to perform many preliminary design studies and cal-

culations that are necessary to define the basic requirements of the various parts, mechanisms,

and assemblies that represent or make up the designer’s concepts of the anticipated product.

On complex products, you will consult with specialists in the various engineering and sci-

entific disciplines who will assist you in your efforts. It is good design practice to also consult

the various manufacturers of purchased parts and the outside vendor producers of your

designed parts or processes, such as springs, castings, molded-plastic parts, gears, bearings,

plating, special finishes, and fabricating materials. These manufacturers are all willing and

able to assist the designer in their particular specialties.

As a conclusion to this introduction, it must be said that the majority of the credit for this

handbook is not due the author, but the thousands of individuals and companies who origi-

nated and developed the data and equations that fill the pages of this handbook. A consoli-

dation of all their efforts can only be beneficial to the practicing product designer and to

American industry.

xxiv INTRODUCTION

CONTENTS

Preface

xix

Acknowledgments xxi

Introduction xxiii

Chapter 1. Mathematics Reference and Measurement System Conversions 1.1

1.1. Plane Geometry

1.5

1.2. Transposing Equations

1.9

1.3. Algebraic Factors and Expansions

1.10

1.3.1. Imaginary Numbers / 1.12

1.3.2. Complex Numbers / 1.12

1.3.3. Trigonometric Form of a Complex Number / 1.12

1.3.4. Radicals / 1.12

1.3.5. Factorials / 1.14

1.3.6. Ratios and Proportions / 1.14

1.3.7. Summation / 1.14

1.3.8. Permutations, Combinations, and Progressions / 1.14

1.3.9. Quadratic Equations / 1.15

1.3.10. Cubic Equations / 1.15

1.3.11. General Quartic Equations / 1.16

1.4. Powers-of-Ten Notation 1.17

1.5. Logarithms 1.17

1.6. Binomial Formula 1.19

1.7. Determinants 1.19

1.7.1. Second-Order Determinants / 1.19

1.7.2. Third-Order Determinants / 1.20

1.8. Trigonometry 1.21

1.8.1. Functions of Angles in a Right Triangle / 1.21

1.8.2. Signs and Limits of Trigonometric Functions / 1.21

1.8.3. Equivalent Expressions (Identities) / 1.21

1.8.4. Solution of Triangles / 1.23

1.9. Analytic Geometry 1.27

1.9.1. Straight-Line Equations / 1.28

1.9.2. Linear Functions of Lines / 1.28

1.9.3. Equations of the Common Geometric Forms / 1.30

1.9.4. Relating Rectangular and Polar Coordinates / 1.30

1.9.5. Other Useful Curves / 1.30

1.10. Basic Calculus 1.33

1.10.1. Derivatives / 1.33

1.10.2. Differentiation Formulas for Algebraic Functions / 1.34

1.10.3. Differentiation Formulas for Transcendental Functions / 1.35

1.10.4. Applications of the Derivative / 1.35

1.10.5. Integrals and Integration / 1.38

1.10.6. Other Useful Integration Formulas / 1.39

1.10.7. Partial Derivatives / 1.40

1.10.8. Differentials / 1.42

1.10.9. Double or Iterated Integrals / 1.43

1.11. Percentages, Compound-Interest Calculations, and Engineering Economics 1.44

1.11.1. Percentages / 1.44

1.11.2. Compound Interest / 1.45

1.11.3. Engineering Economics / 1.46

1.12. The Involute Function 1.46

1.12.1. Involute Geometry / 1.47

1.12.2. Plotting the Involute Curve / 1.49

1.13. U.S. Customary and Metric (SI) Measures and Conversions

1.49

1.14. Temperature Systems 1.49

1.15. Mathematical Signs and Symbols 1.50

1.16. Factors and Prime Numbers 1.51

1.17. Newton’s Method for Solving Intractable Equations 1.51

1.18. The Greek Alphabet 1.68

1.19. Decimal Chart 1.68

1.20. Degrees and Radians Chart 1.68

Chapter 2. Practical Engineering Mechanics 2.1

2.1. Definitions and Basic Units of Mechanics 2.1

2.2. Statics 2.3

2.2.1. Resolution of Forces at 90° / 2.3

2.2.2. Resolution of Forces Not at 90° / 2.3

2.2.3. Resolution of Noncoplanar Forces / 2.4

2.2.4. Coplanar Force Systems / 2.5

2.2.5. Noncoplanar, Concurrent Force Systems / 2.6

2.2.6. Graphical Resolution of Coplanar Forces / 2.7

2.2.7. Systems in Equilibrium / 2.9

2.3. Dynamics

2.13

2.3.1. Moments of Inertia / 2.13

2.3.2. Polar Moments of Inertia of Areas / 2.13

2.3.3. Polar Moments of Inertia of Masses / 2.13

2.3.4. Moments of Complex Areas and Masses / 2.14

2.3.5. Transfer of Axes / 2.15

2.3.6. Approximate Calculations for I / 2.15

2.3.7. Moments of Plane Areas by Integration / 2.16

2.3.8. Section Modulus / 2.17

2.3.9. Radius of Gyration / 2.18

2.3.10. Center of Percussion / 2.18

2.3.11. Center of Gravity / 2.19

2.3.12. Acceleration Resulting from Unbalanced Forces / 2.19

2.3.13. Rectilinear Motion with Constant Velocity / 2.19

2.3.14. Rectilinear Motion with Constant Acceleration / 2.20

2.3.15. Rotary Motion with Constant Acceleration / 2.21

2.3.16. Torque and Angular Acceleration / 2.22

2.3.17. Kinetic Energy / 2.23

2.3.18. Potential Energy / 2.23

2.3.19. Force and Energy in a Force Field / 2.23

2.3.20. Work and Power / 2.24

2.3.21. Centrifugal Force / 2.24

2.3.22. Conversions / 2.25

2.3.23. Mechanics in Product Design / 2.25

2.3.24. Impulse and Linear Momentum / 2.30

2.3.25. Angular Impulse and Momentum / 2.30

2.3.26. Symbols Used in Mechanics / 2.30

2.3.27. Constants / 2.32

2.3.28. Newton’s Method for Solving Intractable Equations / 2.32

2.3.29. Mechanics Conversions / 2.33

vi CONTENTS

2.3.30. Reference Axes in Mechanics Problems / 2.35

2.3.31. Systematic Simplification of Complex Dynamics Problems in Industrial

Applications / 2.35

2.4. Newton’s Laws of Motion 2.39

2.5. Basic Engineering Mechanics Equations 2.39

2.5.1. Acceleration or Retarded Motion—General Equations / 2.40

2.5.2. Rotary Motion—Uniform / 2.40

2.5.3. Rotary Motion—Accelerated / 2.41

Chapter 3. Mensuration, Descriptive Geometry, and Basic Optics 3.1

3.1. Mensuration 3.1

3.1.1. Area, Volume of Irregular Plane Areas, and Solid Masses / 3.12

3.1.2. Properties of the Circle / 3.12

3.2. Basic Descriptive Geometry

3.14

3.2.1. True Lengths of Lines / 3.14

3.2.2. Common Perpendicular to Two Skew Lines / 3.15

3.2.3. True Size of a Plane / 3.16

3.2.4. The Angle Between Any Two Planes / 3.16

3.2.5. Resultant of Three Concurrent, Noncoplanar Forces / 3.18

3.3. Basic Optics 3.19

3.3.1. Relative Aperture, or f Number / 3.21

3.3.2. Lensmaker’s Equation / 3.22

3.3.3. Lens Pairs / 3.23

3.3.4. Magnification with Closeup Lenses (Cameras) / 3.23

3.3.5. The Nature of Light / 3.23

3.3.6. Optical Lenses / 3.30

Chapter 4. Engineering Materials, Properties, and Uses 4.1

4.1. Irons and Steels 4.1

4.1.1. Characteristics of Plain-Carbon and Common Alloy Steels / 4.2

4.1.2. Identification of Stainless Steels / 4.4

4.2. Brinell Hardness Testing 4.4

4.3. AISI-SAE Designation System for Steels 4.4

4.4. Common Aluminum Alloys 4.5

4.5. Copper and Its Alloys 4.6

4.6. Other Common Metals and Alloys 4.7

4.7. Common Plastics 4.7

4.8. Common Plastics—Mechanical Properties 4.16

4.8.1. Petrochemical Origin of the Plastics / 4.16

4.9. Insulating Materials 4.16

4.10. Elastomers 4.16

4.11. Common Woods 4.18

4.12. Thermal Expansion of Materials 4.18

4.13. Special-Purpose Alloys 4.19

4.13.1. Material Specifications and Application Data for Important Engineering

Metals and Alloys / 4.20

4.14. Hardening Processes for Metals 4.47

4.14.1. Hardening of Steels and Beryllium Copper / 4.47

4.14.2. Testing Materials for Hardness / 4.48

4.15. Color Scale of Temperature 4.49

4.16. Standard Pipe Dimensions 4.49

4.17. Common and Formal Names of Chemicals 4.50

4.18. Conductive Properties of Various Metals and Alloys 4.50

CONTENTS vii

4.19. Electromotive Series 4.50

4.20. Chemical Symbols for Metals 4.53

4.21. The Elements 4.53

4.22. Laboratory Analysis of Materials 4.53

4.23. Obsolete SAE Steels 4.56

4.24. Identification of Plastics 4.56

4.25. Chemical Resistance of Plastics 4.56

4.26. Hardness Values of Selected Elastomers 4.56

4.26.1. Durometer Scales—Shore Hardness / 4.56

4.27. Weights and Specific Gravities of Various Solids, Liquids, and Gases

4.56

Chapter 5. Strength of Materials 5.1

5.1. Common Terms Used in Strength of Materials 5.1

5.2. Impact Stresses 5.3

5.2.1. Shock Loads and Developed Stresses / 5.3

5.3. Fatigue 5.5

5.4. Vibratory Stresses in Bars and Beams 5.5

5.5. Beams and Reactions at the Supports 5.5

5.6. Shear Diagrams 5.7

5.7. Moment Diagrams 5.8

5.8. Bending 5.9

5.9. Ultimate Strength of Beams 5.10

5.10. Torsion 5.11

5.11. Buckling and Bending Failure of Columns 5.13

5.11.1. Rankine or Gordon Equation / 5.13

5.11.2. Euler Equation / 5.13

5.12. Machine Elements Used as Columns 5.14

5.13. Moments of Inertia 5.14

5.14. Properties of Sections 5.16

5.15. Beam Equations—AISC Standard 5.28

5.16. Combined Stresses 5.46

5.17. Pressure Vessels 5.46

5.18. Eyebolt Safe Loads 5.46

5.19. Hardness Conversion Equivalents 5.47

5.20. Special Joint Applications 5.47

5.21. Converting Beam Equations for Maximum Stress at Any Point 5.55

Chapter 6. Electrical and Electronic Engineering Practices and Design Data 6.1

6.1. Terms, Conversions, Factors, Constants, and Properties 6.1

6.1.1. Common Electrical Terms / 6.1

6.1.2. Physical Constants / 6.2

6.1.3. Quantities of Electricity, Magnetism, and Light / 6.2

6.1.4. Electrical Conversion Factors / 6.3

6.1.5. Resistivity and Conductivity Conversion / 6.3

6.1.6. Prefixes for Powers of Ten / 6.6

6.1.7. Metal Weights, Melting Points, and Conductivities / 6.6

6.1.8. Dielectric Constants / 6.6

6.2. Circuit Elements 6.8

6.2.1. Basic Circuit Formulas / 6.8

6.2.2. Ohm’s Law for DC and AC Circuits / 6.17

6.3. Decibels 6.19

viii CONTENTS

6.4. Wavelength 6.19

6.5. Properties of Electrical Metals 6.20

6.6. Electrical Components 6.20

6.6.1. Resistors / 6.20

6.6.2. Capacitors / 6.21

6.6.3. Inductors / 6.26

6.6.4. Solenoids / 6.26

6.6.5. Relays / 6.34

6.6.6. Electric Motors and Codes / 6.40

6.6.7. Switches / 6.52

6.6.8. Transformers / 6.56

6.6.9. Copper Wire Current-Carrying Capacity / 6.69

6.6.10. Fusing Time Current for Copper Conductors / 6.69

6.7. Electrical Power System Components 6.72

6.7.1. Current-Carrying Capacities, Copper Conductors / 6.72

6.7.2. Heating in Electrical Conductors / 6.72

6.7.3. Short-Circuit Calculations in High-Current Busses / 6.81

6.7.4. Temperature Rise during Short Circuits / 6.83

6.7.5. Deflection and Stress Equations for Busses / 6.84

6.7.6. Insulator Systems and Materials / 6.120

6.7.7. Electrical Clearances of Conductors through Air / 6.121

6.8. Common Electronic and Electrical Terms and Definitions 6.121

6.8.1. Common Electrical and Electronic Abbreviations and Acronyms / 6.124

6.9. Electronics and Electronic Components 6.126

6.9.1. Resistors / 6.127

6.9.2. Capacitors / 6.128

6.9.3. Inductors / 6.128

6.9.4. Transistors / 6.129

6.9.5. Diodes / 6.132

6.9.6. Varistors / 6.140

6.9.7. Thermistors / 6.141

6.9.8. Varactors / 6.144

6.9.9. Integrated Circuits / 6.144

6.9.10. Solid-State Semiconductor and IC Package Identification / 6.172

6.9.11. Electronic Component Data and IC Circuit Manuals / 6.172

6.10. Printed-Circuit Boards

6.172

6.10.1. Materials / 6.172

6.10.2. Determining Track Width on Copper PCs / 6.172

6.10.3. Prototype Fabrication of PC Boards / 6.174

6.11. Electrochemical Battery Systems 6.183

6.11.1. Battery Design Applications / 6.183

6.11.2. Characteristics of Battery Systems / 6.186

6.11.3. Battery Cross-Referencing / 6.187

6.11.4. Typical Curves and Procedures for Standby Battery Systems / 6.187

6.11.5. Battery Charger Systems / 6.190

6.11.6. Battery Systems for Automotive Power / 6.190

6.12. Electrical Measuring Instruments 6.206

6.12.1. Thermocouples and Their Characteristics / 6.206

6.12.2. Thermocouple Principles / 6.206

6.12.3. Strain Gauges / 6.207

6.12.4. Load Cells / 6.210

6.13. Electrical and Electronic Test Instruments 6.210

6.13.1. The Versatile Oscilloscope / 6.212

6.13.2. Voltage and Frequency Measurements Using the Oscilloscope / 6.213

6.13.3. The Oscilloscope as a Bridge Null Indicator / 6.214

6.14. Electronic Packaging Techniques 6.215

6.15. Basic Electric Circuit Analysis and Procedures—DC and AC 6.221

6.15.1. Basic RCL Characteristics / 6.224

6.15.2. Circuit Analysis Laws, Theorems, and Methods / 6.224

CONTENTS ix

6.15.3. Basic Three-Phase AC Electrical Power Circuits / 6.245

6.15.4. The Fundamental Vector Analysis Relationships and Coordinate

Transformations / 6.248

6.15.5. Complex Quantities / 6.249

6.15.6. Basic Vector Algebra / 6.249

6.16. Bridge Circuits for Electrical Element Measurements: R, C, and L 6.249

6.17. Electrical and Electronic Symbols 6.254

6.18. International Electrical and Electronic Component Trademarks 6.254

6.19. Fusing Wire Sizes and Materials 6.261

6.20. Short Circuits in Electric Power Distribution Equipment (Switchgear) 6.261

6.20.1. Short-Circuit Calculations for Electric Power Distribution Systems / 6.262

6.21. Electrical and Electronic Reference Data 6.269

6.22. Vector Algebra for AC Electric Circuits 6.280

Chapter 7. Comprehensive Spring Design 7.1

7.1. Introduction to Spring Design 7.1

7.1.1. Spring Design Procedures / 7.4

7.2. Compression and Extension Springs 7.4

7.2.1. Solid Height of Compression Springs / 7.5

7.2.2. Initial Tension in Close-Wound Extension Springs / 7.6

7.2.3. Active Coils (Compression Springs) / 7.7

7.2.4. Conical Compression Springs / 7.7

7.2.5. Spring Energy Content / 7.8

7.2.6. Expansion of Compression Springs When Deflected / 7.11

7.2.7. Compression Spring Features / 7.11

7.3. Torsion Springs 7.11

7.3.1. Symbols for Torsion Springs / 7.13

7.3.2. Torsion Spring Reduction of Diameter / 7.13

7.4. Spiral Torsion Springs 7.13

7.4.1. Spring Energy (Torsion and Coil Springs) / 7.14

7.4.2. Symbols for Spiral Torsion Springs / 7.15

7.5. Flat Springs 7.15

7.6. Spring Washers 7.16

7.7. Belleville Washers (Disk Springs) 7.18

7.7.1. Simple Belleville Applications / 7.19

7.8. Hair Springs 7.20

7.9. Torsion Bars 7.21

7.10. Allowable Working Stresses in Springs 7.23

7.11. Spring End Types 7.23

7.11.1. Preferred Ends / 7.23

7.11.2. Special Ends / 7.24

7.12. Spring Materials Data 7.24

7.12.1. Materials and Properties / 7.24

7.12.2. Minimum Yield Strength of Spring Wire / 7.24

7.12.3. Poisson’s Ratios for Spring Materials / 7.24

7.13. Spring Calculations and Sample Designs 7.28

7.13.1. Calculation Examples / 7.28

7.13.2. Spring Design by Programmable Calculator / 7.30

7.14. Spring Rate Curves 7.31

7.15. Spring Drawings or Forms 7.31

7.15.1. Simplified Spring Drawings / 7.31

7.15.2. Spring Tolerances / 7.35

7.15.3. Spring Material Analysis / 7.35

7.16. Heat Treatment and Postbaking of Electroplated Springs 7.36

x CONTENTS

7.16.1. Heat Treatment of Springs / 7.36

7.16.2. Electroplating Springs / 7.38

7.16.3. Postbaking Electroplated Springs / 7.38

7.17. Dynamics of Helical Compression and Extension Springs 7.38

7.18. Spring Rates for Spring Combinations 7.40

7.19. Final Notes on Spring Design 7.41

7.20. Spring Terminology for Design and Manufacturing 7.43

7.21. Elastomer Springs 7.46

Chapter 8. Machine Element Design and Mechanisms 8.1

8.1. Power Transmission Components and Design Procedures 8.1

8.1.1. Belts and Sheaves / 8.2

8.1.2. Standard V-Belts / 8.2

8.1.3. V-Belt Drive Calculations / 8.3

8.1.4. Belt Drive Design Procedures / 8.5

8.1.5. Timing Belts / 8.7

8.2. Chains and Sprockets

8.9

8.2.1. Horsepower Capacity of Chain Drives / 8.11

8.2.2. Conveyor Applications for Roller Chains / 8.12

8.3 Shafts and Shafting Materials

8.14

8.3.1. Torsion in Shafts / 8.14

8.3.2. Bending in Shafts (Linear Deflection) / 8.15

8.3.3. Bending Stresses in Shafts / 8.16

8.3.4. Torsional Stresses in Shafts / 8.17

8.3.5. Critical Speeds of Shafts / 8.18

8.3.6. Shaft Polar Moment and Polar Section Modulus / 8.22

8.3.7. Standard Keyways and Setscrews for Shafts / 8.22

8.3.8. Shaft Overhung Loads / 8.22

8.3.9. Shafting Applications, Materials, and Heat Treatment / 8.25

8.3.10. Hardness Ranges—Shafting / 8.25

8.4. Couplings 8.26

8.4.1. Hooke’s Coupling (Cardan Universal Joint) / 8.26

8.4.2. Sleeve Couplings / 8.28

8.4.3. Flanged and Flexible Couplings / 8.28

8.5. Clutches 8.28

8.5.1. Power Transmitted by Disk Clutches / 8.28

8.5.2. Cone Clutches / 8.35

8.5.3. Electromagnetic Clutches / 8.35

8.5.4. Shock Absorbers—Calculations and Selection / 8.41

8.6. Power Screws 8.42

8.6.1. Power Screw Loads and Efficiencies for Square, V, and Acme Threads / 8.44

8.6.2. Load Capabilities of Power Screws / 8.44

8.6.3. Lead Screws and Design Calculations / 8.46

8.7. Ratchets and Ratchet Gearing 8.47

8.7.1. Ratchet Gear Design / 8.48

8.7.2. Methods for Layout of Ratchet Gear Systems / 8.49

8.7.3. Calculating the Pitch and Face Width of Ratchet-Wheel Teeth / 8.51

8.8. Gearing and Design Procedures 8.51

8.8.1. Gears in Common Use and Manufacturing Methods / 8.53

8.8.2. Gear Action and Definitions / 8.55

8.8.3. Pressure Angles and the Diametral Pitch System / 8.56

8.8.4. Module Gear System (Metric Standard) / 8.57

8.8.5. Gear Types, Geometries, Measurements, and Calculations / 8.58

8.8.6. Spur Gears / 8.59

8.8.7. Stem Pinions / 8.67

8.8.8. Internal Gears / 8.67

CONTENTS xi

8.8.9. Helical Gears / 8.69

8.8.10. Straight Miter and Bevel Gears / 8.72

8.8.11. Spiral Miter and Bevel Gears / 8.77

8.8.12. Worm Gears / 8.78

8.8.13. Other Gear Systems / 8.84

8.8.14. Zerol Bevel Gears / 8.85

8.8.15. Hypoid Gears / 8.85

8.8.16. Face Gears / 8.85

8.8.17. Crossed-Helical Gears / 8.85

8.8.18. Double-Enveloping Worm Gears / 8.86

8.8.19. Spiroid Gears / 8.86

8.8.20. Gear Tooth Gauges / 8.87

8.9. Gear Materials and Hardness Ranges 8.88

8.9.1. Plastic Gears and Materials / 8.88

8.9.2. Ferrous and Nonferrous Gear Materials

and Their Characteristics and Processes / 8.90

8.9.3. Gear Quality Numbers (AGMA) / 8.90

8.9.4. AGMA Gear Specification Sample Sheet / 8.91

8.10. Forces and Wear Loads in Gearing Systems 8.91

8.10.1. Forces in Gear Systems (Bearing Loads) / 8.92

8.10.2. Nomenclature (Bearing Forces) / 8.108

8.10.3. Vertical, Horizontal, Radial Reactions (Shaft on Two Supports) / 8.109

8.11. Gear Loads and Design Procedures 8.110

8.11.1. Spur Gear Loads and Design Procedures / 8.110

8.11.2. Helical Gear Loads and Design Procedures / 8.115

8.11.3. Bevel Gear Loads and Design Procedures / 8.117

8.11.4. Worm Gear Loads and Design Procedures / 8.119

8.12. Epicyclic Gearing

8.122

8.12.1. Speed-Ratio Definition and Number of Teeth in Epicyclic Systems / 8.124

8.12.2. Epicyclic Drive Train Calculations for Simple Planetary Systems / 8.125

8.13. Gear-Train Calculations

8.135

8.13.1. Gear-Train Design Procedures / 8.136

8.13.2. Force Ratios for Gear Trains / 8.138

8.14. Differential Gearing

8.138

8.15. Sprockets: Geometry and Dimensioning

8.139

8.16. Ratchets

8.142

8.17. Gear Design Programs for PCs and CAD Stations

8.142

8.18. Keyways and Setscrews for Gear Shafts

8.142

8.19. Calculations for Power, Torque, Force, Velocity, and RPM 8.142

8.20. Additional Gear Data and References 8.142

8.21. Gear Wear and Failure 8.143

8.22. Gear Manufacturing Processes 8.145

8.23. Gear Lubrication 8.146

8.24. Gear Summary Sheets 8.146

8.25. Cams: Development, Layout, and Design 8.146

8.25.1. Cam Motions / 8.146

8.25.2. Uniform-Motion Cam Layout / 8.148

8.25.3. Accelerated-Motion Cam Layout / 8.149

8.25.4. Cylindrical Cam Layout / 8.149

8.25.5. Eccentric Cams / 8.150

8.25.6. The Cam Follower / 8.151

8.25.7. Pressure Angle of the Cam Follower / 8.152

8.25.8. Contact Stresses between Follower and Cam / 8.156

8.25.9. Cam Torque / 8.158

8.25.10. Cam Manufacture / 8.158

8.25.11. Dynamic Analysis of Cams during Operation / 8.159

8.25.12. Various Cam Types or Designs / 8.159

xii CONTENTS

8.26. Antifriction Bearings 8.161

8.26.1. Plain Bearings: Sleeve and Flanged (Journal) / 8.162

8.26.2. Selection of Plain Bearings by PV Calculations / 8.165

8.26.3. Plain Bearing Wear Life Calculations / 8.166

8.26.4. Heat Dissipation in Plain Bearings / 8.167

8.26.5. Standard Specifications for Babbitt Metal Bearings / 8.167

8.27. Rolling-Element Antifriction Bearings 8.168

8.27.1. Load Ratings and Fatigue Life for Ball and Roller Bearings / 8.171

8.27.2. Allowances for Fits (Applicable to Antifriction Bearings, etc.) / 8.172

8.28. Selection of Bearings: Sources and Procedures 8.173

8.28.1. Bearing Sources / 8.173

8.28.2. Bearing Loads in Mechanical Systems / 8.176

8.29. Mechanisms and Linkages: Design, Operating Principles, and Analysis 8.176

8.29.1. Basic and Compound Mechanisms / 8.177

8.29.2. Space Mechanisms / 8.183

8.29.3. Linkages / 8.213

8.29.4. Linkage Analysis / 8.213

8.30. Mechanism and Linkage Applications 8.222

8.31. Columns Used as Machine Elements 8.226

8.32. Stresses Due to Interference or Force Fits in Mechanisms 8.227

8.32.1. Forces and Torques for Force Fits / 8.230

8.32.2. Shrink-Fit Assemblies / 8.230

8.32.3. Interference-Fit Pressures and Stresses / 8.231

8.32.4. Forces and Vector Forces on Taper Keys or Wedges / 8.232

8.33. Limits and Fits: U.S. Customary and SI (Metric) Standards

8.233

Chapter 9. Pneumatics, Hydraulics, Air Handling, and Heat

9.1

9.1. Pneumatics

9.1

9.1.1. Pressure, Volume, and Temperature of Air / 9.1

9.1.2. Adiabatic and Isothermal Compression or Expansion of Air / 9.2

9.1.3. Work or Energy Requirements for Air Compression / 9.2

9.1.4. Horsepower Requirements for Air Compression / 9.3

9.1.5. Airflow in Pipes / 9.3

9.1.6. Compressed Airflow in Pipes / 9.4

9.1.7. Stresses in Pressurized Cylinders / 9.4

9.1.8. Gas Constants / 9.5

9.2 Basic Hydraulics 9.5

9.2.1. Fluid Flow, Pressure, and Volume Equivalents / 9.5

9.2.2. Basic Fluid Power Equations / 9.6

9.2.3. Hydraulic Application Equations (Fluid Flow in Channels and Pipes) / 9.8

9.2.4. Hydraulic- and Air-Line Sizes and Thread Connections / 9.10

9.3. Air-Handling Data 9.10

9.3.1. Basic Laws for Air-Moving Equipment / 9.10

9.3.2. Air-Moving Equations / 9.12

9.4. Transmission of Heat 9.13

9.4.1. Ventilation and Air Quality / 9.14

9.5 Specific Heat (Thermal Capacity) 9.14

9.5.1. Properties of Liquids / 9.14

9.6. Temperatures of Mixtures and Heat Requirements 9.15

9.6.1. Heat Required to Raise Temperature of Materials / 9.16

9.6.2. Heat Equivalents / 9.16

9.7. Heat Losses 9.17

9.7.1. Fan Requirements for Enclosed Equipment / 9.18

9.7.2. Sizing Heat Exchangers and Air Conditioners / 9.19

9.7.3. Enclosure Cooling with Fans, Fins, and Radiation / 9.21

CONTENTS xiii

9.8. Viscosity Equivalents: Universal Viscosity Measuring Systems 9.22

9.9. Hydraulic and Pneumatic Component Systems 9.24

Chapter 10. Fastening and Joining Techniques and Design Data 10.1

10.1. Threaded Fasteners: Bolts, Screws, and Nuts

10.1

10.1.1. Dimensions of Bolts, Screws, Nuts, and Washers / 10.2

10.1.2. Grade Classification and Strength of Standard Bolts, Screws, and Nuts / 10.8

10.1.3. Tightening Torques and Clamp Loads of the Different Grades and Sizes of

Machine Bolts / 10.8

10.1.4. Setscrews, Self-Tapping, Thread-Forming, and Wood Screws / 10.14

10.1.5. Wrench Clearances for Design Applications / 10.16

10.2. Thread Systems: American Standard and Metric (60° V) 10.17

10.2.1. Unified and Metric Thread Data / 10.29

10.3. Rivets

10.49

10.3.1. Basic Stresses in Riveted Joints / 10.50

10.3.2. General Sizing of Rivets / 10.53

10.4. Pins

10.53

10.4.1. Clevis Pins / 10.53

10.4.2. Cotter Pins / 10.53

10.4.3. Spring Pins (Roll Pins) / 10.54

10.4.4. Spiral Spring Pins (Coiled Spring Pins) / 10.54

10.4.5. Taper Pins / 10.55

10.4.6. Dowel Pins (Hardened and Ground Machine Type) / 10.55

10.4.7. Grooved Pins / 10.55

10.4.8. Quick-Release Pins / 10.56

10.5. Retaining Rings

10.57

10.5.1. X Washers (Split Washers) / 10.59

10.6. Set, Clamp, and Split Collars 10.60

10.7. Machinery Bushings, Shims, and Arbor Spacers 10.65

10.8. Specialty Fasteners 10.66

10.9. Welding, Brazing, and Soldering 10.73

10.9.1. Welding / 10.73

10.9.2. Brazing / 10.90

10.9.3. Soldering / 10.91

10.10. Adhesive Bonding 10.93

Chapter 11. Sheet-Metal Design, Layout, and Fabrication Practices 11.1

11.1. Carbon and Low-Alloy Steel Sheets 11.1

11.2. Nonferrous Sheet Metal 11.3

11.3. Machinery for Sheet-Metal Fabrication 11.4

11.3.1. Modern Sheet-Metal Manufacturing Machinery / 11.4

11.4. Gauging Systems 11.7

11.4.1. Aluminum Sheet-Metal Standard Thicknesses / 11.7

11.5. Sheet-Metal Fabrication Methods 11.8

11.5.1. Sheet-Metal Cutting Methods / 11.9

11.5.2. Sheet-Metal Punching Methods / 11.10

11.5.3. Sheet-Metal Forming Methods / 11.10

11.6. Sheet-Metal Flat Patterns 11.12

11.6.1. Setback or J Chart for Determining Bend Deductions / 11.16

11.6.2. Bend Radii for Aluminum Alloy and Steel Sheet (Average) / 11.18

11.7. Sheet-Metal Developments and Transitions 11.19

11.7.1. Skin Development / 11.19

11.7.2. Canted-Station Skin Development (Bulkheads at an Angle to Axis) / 11.20

11.8. Developing Flat Patterns 11.21

xiv CONTENTS

CONTENTS xv

11.9. Stiffening Sheet-Metal Parts 11.21

11.10. Sheet-Metal Faying Surfaces 11.22

11.11. Design Points for Sheet-Metal Parts 11.23

11.12. Typical Transitions and Developments 11.25

11.12.1. Developing a Truncated Right Pyramid / 11.25

11.12.2. Developing an Oblique Pyramid / 11.26

11.12.3. Developing a Truncated Right Cylinder / 11.26

11.12.4. Developing a Truncated Right Circular Cone / 11.27

11.12.5. Developing an Oblique Cone / 11.28

11.12.6. Conical Connection between Two Cylindrical Pipes / 11.29

11.12.7. Developing Transition Pieces / 11.30

11.12.8. Triangulation of Warped Surfaces / 11.30

11.13. Sheet-Metal Fabrication Practices 11.32

11.14. Light-Gauge Sheet-Metal Structural Forms: Dimensions and Strengths 11.36

11.15. The Effects of Cold Working Steel 11.37

11.16. Advanced Sheet-Metal Cutting Methods and Special Die Forming 11.57

11.17. Sheet-Metal Angled Corner-Flange Notching: Flat-Pattern Development 11.62

11.17.1. Calculating Angular Bent-Flange Corner Notching / 11.64

Chapter 12. Castings, Moldings, Extrusions, and Powder-Metal Technology 12.1

12.1. Castings 12.1

12.1.1. Sand Casting / 12.2

12.1.2. Shell Casting / 12.4

12.1.3. Carbon Dioxide Casting / 12.5

12.1.4. Plaster Mold Casting / 12.6

12.1.5. Composite Mold Casting / 12.6

12.1.6. Investment Casting / 12.6

12.1.7. Ceramic Mold Casting / 12.6

12.1.8. Permanent Mold Casting / 12.7

12.1.9. Die Casting / 12.8

12.1.10. Evaporative Pattern Casting (EPC) / 12.8

12.1.11. Slush Casting / 12.9

12.2. Ferrous Metal Alloys Used in Casting

12.9

12.2.1. Gray Iron Castings / 12.9

12.2.2. Ductile Iron Castings / 12.9

12.2.3. Malleable Iron Castings / 12.9

12.2.4. Steel and Alloy Steel Castings / 12.10

12.3. Representative Casting Metals and Alloys 12.10

12.4. ASTM-Listed Cast Irons and Steels 12.10

12.4.1 ASTM—Cast Irons and Cast Steels / 12.11

12.5 Plastic Moldings 12.12

12.5.1. Prototypes of the Plastics / 12.16

12.5.2. Properties and Characteristics of Modern Plastics / 12.17

12.5.3. Design of Molded Plastic Parts / 12.17

12.5.4. Plastics Molding Machinery and Molds / 12.17

12.6. Extrusions 12.19

12.7. Powder-Metal Technology 12.23

12.7.1. Design of Powder-Metal Parts / 12.24

12.8. Table for Squares, Hexagons, and Octagons 12.25

12.9. Design Guides for Cast and Molded Metal Plastics and Parts 12.25

Chapter 13. Engineering Finishes, Plating Practices, and Specifications 13.1

13.1. Finishes 13.1

13.2. Corrosion of Metals: Principles 13.3

13.3. Electroplating Data and Specifications 13.5

13.3.1. Electroplating and Oxide Layer Thickness Ranges / 13.5

13.3.2. Anodic Coating Thickness (Anodized Parts) / 13.7

13.3.3. Electroplating Thicknesses and Specifications / 13.7

13.3.4. Plating Metals: Characteristics and Properties / 13.9

13.3.5. Summary of Plating and Finishing / 13.10

13.4. Coloring Processes for Metals and Alloys 13.12

13.5. Coloring Metals (Ferrous and Nonferrous) 13.12

13.6. Etching Metals 13.14

13.7. Anodizing 13.15

13.8. Paint Finishing 13.18

13.8.1. Estimating Paint Film Thickness and Coverage / 13.19

Chapter 14. Manufacturing Machinery and Dimension and Tolerancing

Practices 14.1

14.1. Manufacturing Machinery and Machine Tools 14.1

14.1.1. Typical Manufacturing Machinery, Equipment, and Tools / 14.2

14.2. Basic Dimensioning and Tolerancing Procedures 14.14

14.2.1. General Dimensioning and Tolerancing Practices / 14.14

14.2.2. Tolerance Accumulation / 14.15

14.2.3. Dimensioning per ANSI Y14.5M-1982 / 14.16

14.2.4. ANSI Y14.5M-1982 Tolerancing Practices / 14.21

14.2.5. Direct Tolerancing Methods / 14.24

14.2.6. Positional Tolerancing / 14.24

14.2.7. Examples of ANSI Y14.5M-1982 Dimensioning and Tolerancing Practices / 14.24

14.2.8. Design Notes on Dimensioning and Tolerancing / 14.24

14.2.9. Symbols Used in ANSI Y14.5M-1982 and ISO Dimensioning and

Tolerancing / 14.26

14.2.10. Typical Industrial Design Engineering Drawings / 14.27

Chapter 15. Subjects of Importance to the Design Engineer 15.1

15.1. Societies, Associations, Institutes, and Specification Authorities 15.1

15.2. ANSI Standards Applicable to Product Design Engineering and Manufacturing

Processes and Inspection 15.3

15.3. Approval Associations and Their Trademarks 15.10

15.4. Frequently Used Mechanical, Electrical, and Electronic Standards 15.10

15.5. United States Patents 5.13

15.6. Product Liability 15.16

15.7. Prototypes of Products 15.20

15.8. Computers in Design 15.21

15.9. Electromechanical System Design 15.22

15.10. Quality-Control Systems 15.29

15.11. Test Laboratories 15.30

15.12. Engineering Drawing Sizes and Formats 15.34

Index I.1

xvi CONTENTS