Mechanical design of machine elements and machines : A failure prevention perspective

This page intentionally left blank

MECHANICAL DESIGN OF

MACHINE ELEMENTS

AND MACHINES

Second Edition

This page intentionally left blank

MECHANICAL DESIGN OF

MACHINE ELEMENTS

AND MACHINES

A Failure Prevention Perspective

Second Edition

Jack A. Collins, Henry R. Busby & George H. Staab

The Ohio State University

John Wiley & Sons

VP & EXECUTIVE PUBLISHER Don Fowley

ACQUISITIONS EDITOR Michael McDonald

PRODUCTION MANAGER Dorothy Sinclair

SENIOR PRODUCTION EDITOR Sandra Dumas

MARKETING MANAGER Christopher Ruel

SENIOR DESIGNER Kevin Murphy

PRODUCTION MANAGEMENT SERVICES Thomson Digital

EDITORIAL ASSISTANT Renata Marchione

MEDIA EDITOR Lauren Sapira

COVER PHOTO Professor Anthony Luscher

This book was set in Times Roman by Thomson Digital and printed and bound by R.R. Donnelley/Willard.

The cover was printed by Phoenix Color.

This book is printed on acid free paper. ∞

Copyright © 2010, 2003 John Wiley & Sons, Inc. All rights reserved. No part of this publication may be

reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical,

photocopying, recording, scanning or otherwise, except as permitted under Sections 107 or 108 of the 1976

United States Copyright Act, without either the prior written permission of the Publisher, or authorization

through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc. 222 Rosewood Drive,

Danvers, MA 01923, website www.copyright.com. Requests to the Publisher for permission should be

addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken,

NJ 07030-5774, (201)748-6011, fax (201)748-6008, website http://www.wiley.com/go/permissions.

Evaluation copies are provided to qualified academics and professionals for review purposes only, for use

in their courses during the next academic year. These copies are licensed and may not be sold or transferred

to a third party. Upon completion of the review period, please return the evaluation copy to Wiley. Return

instructions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel. Outside

of the United States, please contact your local representative.

ISBN-13 978-0-470-41303-6

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

Preface

This new undergraduate book, written primarily to support a Junior-Senior level sequence

of courses in Mechanical Engineering Design, takes the viewpoint that failure prevention

is the cornerstone concept underlying all mechanical design activity. The text is presented

in two parts, Part I—Engineering Principles, containing 7 chapters, and Part II—Design

Applications, containing 13 Chapters. Because of the way the book is organized it also

may be conveniently used as the basis for continuing education courses or short-courses

directed toward graduate engineers, as well as a reference book for mechanical designers

engaged in professional practice.

Organization

Part I introduces the design viewpoint and provides analytical support for the mechani￾cal engineering design task. Analysis is characterized by known material, known shape,

known dimensions and known loading. The results of analyses usually include the calcu￾lation of stresses, strains or existing safety factors. Techniques are presented for failure

mode assessment, material selection, and safety factor selection. A unique chapter on

geometry determination provides basic principles and guidelines for creating efficient

shapes and sizes. A case is made for integration of manufacturing, maintenance, and crit￾ical point inspection requirements at the design stage, before the machine is built.

Part II expands on the design viewpoint introduced in Part I. Design is a task char￾acterized by known specifications, and nothing more. The results of design usually

include picking a material, picking a design safety factor, conceiving a shape, and

determining dimensions that will safely satisfy the design specifications in the “best”

possible way.

Key Text Features

1. Comprehensive coverage of failure modes. Basic tools are introduced for recognizing

potential failure modes that may govern in any specific design scenario. At a mini￾mum, the topics of elastic deformation, yielding brittle fracture, fatigue, buckling, and

impact should be considered by the instructor.

v

1

Chapter 2 presents a condensed and simplified version of sections of Failure of Materials in Mechanical

Design: Analysis Prediction, Prevention. 2nd ed. Wiley, 1993.

2. Modern coverage of materials selection (Chapter 3). The materials selection concepts

presented introduce some new ideas and are a virtual necessity for any competent de￾sign engineer.

3. Failure theories and related topics (Chapter 5). Topics which play a significant role in

identifying failure (multiaxial states of stress and stress concentrations) are presented

as a prelude to static and fatigue failure theories as well as brittle fracture and crack

growth.

4. Guidelines for creating efficient shapes and sizes for components and machines

(Chapter 6). This important chapter, covering material rarely discussed in other

design textbooks, is a “must” for any modern course covering the design of machine

elements.

5. Concurrent engineering and “Design-for-X” ideas (Chapter 7). These are important in

modern manufacturing practice and should be introduced in a well-rounded course in

mechanical engineering design.

6. Conceptual introductions to machine elements (Chapters 8 through 19). Organized

and designed to be especially helpful to students who may have had little or no expo￾sure to machines, structures, or industrial practice, each chapter in Part II follows a

consistent introductory pattern:

• “Uses and Characteristics”—What does it look like? What does it do? What varia￾tions are available?

• “Probable failure modes”—based on practical experience.

• “Typical materials used for the application”—based on common design practice.

These introductory sections are followed in each chapter by detailed discussions about

analyzing, selecting, or designing the component under consideration.

7. Inclusion of latest available revisions of applicable codes and standards for well￾standardized elements such as gears, rolling-element bearings, V-belts, precision

roller-chain, and others. Selected up-to-date supporting data have been included for

many commercially available components, such as rolling-element bearings, V-belts,

wire rope, and flexible shafts, Many manufacturers’catalogs have been included in

the reference lists.

8. Clear sketches and detailed tables to support virtually all of the important design and

selection issues discussed.

9. Illuminating footnotes, anecdotes, experience-based observations, and contemporary￾event illustrations, to demonstrate the importance of good design decision-making.

Worked Examples and Homework Problems

Nearly 100 worked examples have been integrated with the text. Of these worked exam￾ples, about half are presented from a design viewpoint, including about 1

⁄4 of the examples

given in Part I, and about 3

⁄4 of the examples given in Part II. The remainder are presented

from the more traditional analysis viewpoint.

End-of-chapter problems have been distilled, in great measure, from real design proj￾ects encountered by the author in consulting, research, and short-course interaction with

engineers in industry, then filtered through more than three decades of student homework

assignments and design-course examinations. It is the author's hope that students (and

instructors) will find the problems interesting, realistic, instructional, challenging, and

solvable.

vi / Preface

To supplement the worked examples, a companion web site at www.wiley.com/

college/collins has been developed to provide more than 100 additional variations and

extensions of the examples worked in the text. Many of the website variations and exten￾sions require solution techniques based on standard computer codes such as MATLAB® or

Mathcad ®.

Additional instructor and student resources, such as errata listings, also are posted at

the website.

Suggestions for Course Coverage

Although it is presumed that the user has had basic courses in Physics, Materials

Engineering, Statics and Dynamics, and Strength of Materials, most concepts from these

courses that are needed for basic mechanical engineering design activity have been sum￾marized and included in Part I, primarily in Chapters 2,3, 4, and 5. Accordingly, an in￾structor has great flexibility in selecting material to be covered, depending upon the

preparation of students coming in the course. For example, if students are well prepared

in strength-of-materials concepts, only the last half of Chapter 4 needs to be covered.

Sections 4.1 through 4.5 may readily be skipped, yet the material is available for refer￾ence. Sections 4.6 through 4.10 contain important design related material not ordinarily

covered in standard strength-of-materials courses.

The three-part introduction to each “elements” chapter makes it possible to offer a

(superficial) descriptive survey course on machine elements by covering only the first few

sections of each chapter in Part II. Although such an approach would not, by itself, be

especially appropriate in educating a competent designer, it would provide the potential

for remarkable flexibility in tailoring a course sequence that could introduce the student

to all machine elements of importance (by assigning the first few sections of each chapter

of Part II), then covering in depth the chapters selected by the supervisory design-faculty￾group, or the instructor, to fit into the designated curricular time frame.

With few exceptions, the machine element chapters (8 through 19) have been written

as stand-alone units, independent of each other, each resting upon pertinent principles dis￾cussed in Part I. This presentation philosophy affords an instructor great flexibility in for￾mulating a sequence of machine-element topics, in any order, that is compatible with his

or her priorities, philosophy, and experience.

Supplements

An instructor’s solution manual is available, providing comprehensive solutions for all

end-of-chapter problems. Please contact your local Wiley representative for details.

Acknowledgments

As time progresses, it is difficult, if not impossible, to distinguish one’s own original

thoughts from the thoughts gathered through reading and discussing the works of others.

For those who find their essence in these pages without specific reference, we wish to ex￾press our appreciation. In particular, Professor Collins expresses deep appreciation to

Professors Walter L. Starkey and the late Professor S. M. Marco, who were his professors

while he was a student. Much of their philosophy has no doubt been adopted by Professor

Collins. Professor Starkey's fertile mind created many of the innovative concepts presented

Preface / vii

in Chapters 2, 3, 6, and 7 of this text. Professor Starkey is held in the highest esteem as an

outstanding engineer, innovative designer, inspirational teacher, gentleman, and friend.

Gratitude is also expressed for colleagues at Ohio State who reviewed and contributed

to various parts of the manuscript. In particular, Professor E. O. Dobelin, Professor D. R.

Houser, Professor R. Parker, and Professor Brian D. Harper.

Reviewers always play an important role in the development of any textbook. We

would like to express our appreciation to those who reviewed the first edition of this text

and made valuable comments and suggestions for the second edition, including Richard E.

Dippery, Jr., Kettering University; Antoinette Maniatty, Rensselaer Polytechnic Institute;

Eberhard Bamberg, University of Utah; Jonathan Blotter, Brigham Young University;

Vladimir Glozman, California State Polytechnic University, Pomona; John P.H. Steele,

Colorado School of Mines; John K. Schueller, University of Florida; and Ken Youssefi,

University of California, Berkeley.

Thanks are also due to Joseph P. Hayton for seeing the benefit in pursuing a second

edition, and Michael McDonald, Editor for carrying through with the project. In addition,

we wish to thank the many other individuals in the John Wiley & Sons, Inc. organization

who have contributed their talents and energy to the production of this book.

Finally, we wish to express our thanks to our wives. In particular, Professor Collins’wife,

JoAnn, for transforming the hand-written pages into a typed manuscript for the first edition

of this text. Professor Collins wishes to dedicate his contributions in this work to his wife, Jo

Ann, his children Mike, (Julie), Jennifer, (Larry), Joan, Greg, (Heather), and his grandchil￾dren, Michael, Christen, David, Erin, Caden, and Marrec.

Jack A. Collins

Henry R. Busby

George H. Staab

viii / Preface

Contents

PART ONE ENGINEERING PRINCIPLES

ix

Chapter 1

Keystones of Design: Materials

Selection and Geometry Determination 1

1.1 Some Background Philosophy 1

1.2 The Product Design Team 2

1.3 Function and Form; Aesthetics and

Ergonomics 5

1.4 Concepts and Definition of Mechanical

Design 6

1.5 Design Safety Factor 7

1.6 Stages of Design 7

1.7 Steps in the Design Process 9

1.8 Fail Safe and Safe Life Design Concepts 9

1.9 The Virtues of simplicity 10

1.10 Lessons Learned Strategy 12

1.11 Machine Elements, Subassemblies, and

the Whole Machine 12

1.12 The Role of Codes and Standards in the

Design Process 13

1.13 Ethics in Engineering Design 13

1.14 Units 14

Chapter 2

The Failure Prevention Perspective 22

2.1 Role of Failure Prevention Analysis in

Mechanical Design 22

2.2 Failure Criteria 22

2.3 Modes of Mechanical Failure 23

2.4 Elastic Deformation, Yielding, and Ductile

Rupture 28

2.5 Elastic Instability and Buckling 34

Buckling of a Simple Pin-Jointed Mechanism 35

Buckling of a Pinned-End Column 36

Columns with Other End Constraints 38

Inelastic Behavior and Initially Crooked

Columns 39

Column Failure Prediction and Design

Considerations 40

Buckling of Elements Other Than Columns 43

2.6 Shock and Impact 46

Stress Wave Propagation Under Impact Loading

Conditions 46

Energy Method of Approximating Stress and

Deflection Under Impact Loading

Conditions 47

2.7 Creep and Stress Rupture 52

Predictions of Long-Term Creep Behavior 53

Creep under Uniaxial State of Stress 55

Cumulative Creep Prediction 57

2.8 Wear and Corrosion 59

Wear 59

Corrosion 64

2.9 Fretting, Fretting Fatigue, and Fretting

Wear 66

Fretting Fatigue 67

Fretting Wear 68

Minimizing or Preventing Fretting Damage 69

2.10 Failure Data and the Design Task 70

2.11 Failure Assessment and Retrospective

Design 70

2.12 The Role of Safety Factors; Reliability

Concepts 71

2.13 Selection and Use of a Design Safety

Factor 72

2.14 Determination of Existing Safety Factors

in a Completed Design: A Conceptual

Contrast 74

4.6 Stresses Caused by Curved Surfaces in

Contact 174

4.7 Load Sharing in Redundant Assemblies

and Structures 179

Machine Elements as Springs 180

4.8 Preloading Concepts 186

4.9 Residual Stresses 189

Estimating Residual Stress 190

4.10 Environmental Effects 194

Chapter 5

Failure Theories 205

5.1 Preliminary Discussions 205

5.2 Multiaxial States of Stress and Strain 205

Principal Stresses 205

Stress Cubic Equation 206

Mohr’s Circle Analogy for Stress 210

Strain Cubic Equation and Principal Strains 213

Mohr’s Circle Analogy for Strain 213

Elastic Stress-Strain Relationships

(Hooke’s Law) 214

5.3 Stress Concentration 215

Stress Concentration Effects 216

Multiple Notches 217

5.4 Combined Stress Theories of Failure 224

Maximum Normal Stress Theory

(Rankine’s Theory) 225

Maximum Shearing Stress Theory

(Tresca–Guest Theory) 226

Distortion Energy Theory

(Huber–von Mises–Hemcky Theory) 227

Failure Theory Selection 229

5.5 Brittle Fracture and Crack Propagation;

Linear Elastic Fracture Mechanics 233

5.6 Fluctuating Loads, Cumulative Damage,

and Fatigue Life 241

Fluctuating Loads and Stresses 242

Fatigue Strength and Fatigue Limit 244

Estimating S-N Curves 246

Stress-Life (S-N) Approach to Fatigue 248

Factors That May Affect S-N Curves 248

Nonzero-Mean Stress 258

Cumulative Damage Concepts and Cycle

Counting 266

Multiaxial Cyclic Stress 272

Fracture Mechanics (F-M) Approach to Fatigue 273

Crack Initiation Phase 273

Crack Propagation and Final Fracture Phases 276

x / Contents

2.15 Reliability: Concepts, Definitions, and

Data 76

System Reliability, Reliability Goals, and

Reliability Allocation 80

Reliability Data 83

2.16 The Dilemma of Reliability Specification

versus Design Safety Factor 84

Chapter 3

Materials Selection 93

3.1 Steps in Materials Selection 93

3.2 Analyzing Requirements of the

Application 93

3.3 Assembling Lists of Responsive

Materials 94

3.4 Matching Responsive Materials to

Application Requirements; Rank Ordered

Data Table Method 105

3.5 Matching Responsive Materials to

Application Requirements; Ashby chart

Method 114

Chapter 4

Response of Machine Elements to Loads

and Environments; Stress, Strain, and

Energy Parameters 123

4.1 Loads and Geometry 123

4.2 Equilibrium Concepts and Free-Body

Diagrams 123

4.3 Force Analysis 124

4.4 Stress Analysis; Common Stress Patterns

for Common Types of Loading 126

Direct Axial Stress 128

Bending; Load, Shear, and Moment

Diagrams 128

Bending; Straight Beam with Pure Moment 133

Bending; Initially Curved Beams 137

Bending; Straight Beam with Transverse

Forces 142

Direct Shear Stress and Transverse Shear

Stress 142

Torsional Shear; Circular Cross Section 150

Torsional Shear; Noncircular Cross Section 152

Torsional Shear; Shear Center in Bending 157

Surface Contact Stress 160

4.5 Deflection Analysis Common Types of

Loading 161

Stored Strain Energy 162

Castigliano’s Theorem 164

Design Issues in Fatigue Life Prediction 280

Fatigue Stress Concentration Factors and

Notch Sensitivity Index 280

5.7 Multiaxial States of Cyclic Stress and

Multiaxial Fatigue Failure Theories 283

Chapter 6

Geometry Determination 305

6.1 The Contrast in Objectives Between

Analysis and Design 305

6.2 Basic Principles and Guidelines for

Creating Shape and Size 306

Direct Load Path Guideline 306

Tailored-Shape Guideline 307

Triangle-Tetrahedron Guideline 308

Buckling Avoidance Guideline 309

Hollow Cylinder and I-Beam Guideline 310

Conforming Surface Guideline 310

Lazy-Material Removal Guideline 311

Merging Shape Guideline 313

Strain Matching Guideline 313

Load Spreading Guideline 314

Contents / xi

6.3 Critical Sections and Critical Points 315

6.4 Transforming Combined Stress Failure

Theories into Combined Stress Design

Equations 317

6.5 Simplifying Assumptions: The Need and

the Risk 318

6.6 Iteration Revisited 319

6.7 Fits, Tolerances, and Finishes 323

Chapter 7

Design-Stage Integration of Manufacturing

and Maintenance Requirements 333

7.1 Concurrent Engineering 333

7.2 Design for Function, Performance, and

Reliability 334

7.3 Selection of the Manufacturing Process 334

7.4 Design for Manufacturing (DFM) 337

7.5 Design for Assembly (DFA) 337

7.6 Design for Critical Point Accessibility,

Inspectability, Disassembly, Maintenance,

and Recycling 339

Chapter 8

Power Transmission Shafting; Couplings,

Keys, and Splines 341

8.1 Uses and Characteristics of shafting 341

8.2 Potential Failure Modes 343

8.3 Shaft Materials 344

8.4 Design Equations–Strength Based 345

8.5 Design Equations–Deflection Based 353

8.6 Shaft Vibration and Critical Speed 358

8.7 Summary of Suggested Shaft Design

Procedure; General Guidelines for Shaft

Design 360

8.8 Couplings, Keys, and Splines 361

Rigid Couplings 361

Flexible Coupling 362

Keys, Splines, and Tapered Fits 365

Chapter 9

Pressurized Cylinders; Interference Fits 382

9.1 Uses and Characteristics of Pressurized

Cylinders 382

9.2 Interference Fit Applications 382

9.3 Potential Failure Modes 383

9.4 Materials for Pressure Vessels 383

9.5 Principles from Elasticity Theory 384

9.6 Thin-Walled Cylinders 385

9.7 Thick-Walled Cylinders 386

9.8 Interference Fits: Pressure and Stress 392

9.9 Design for Proper Interference 396

Chapter 10

Plain Bearings and Lubrication 403

10.1 Types of Bearings 403

10.2 Uses and Characteristics of Plain

Bearings 403

10.3 Potential Failure Modes 404

10.4 Plain Bearing Materials 405

10.5 Lubrication Concepts 405

10.6 Boundary-Lubricated Bearing Design 406

10.7 Hydrodynamic Bearing Design 409

Lubricant Properties 410

PART TWO DESIGN APPLICATIONS

Tightening Torque; Fastener Loosening 507

Multiply Bolted Joints; Symmetric and

Eccentric Loading 509

13.5 Rivets 517

Rivet Materials 517

Critical Points and Stress Analysis 518

13.6 Welds 522

Base Metals, Filler Materials, and Weldability 526

Butt Welds 528

Fillet Welds 529

13.7 Adhesive Bonding 538

Joint Design 538

Structural Adhesive Materials 540

Chapter 14

Springs 546

14.1 Uses and Characteristics of Springs 546

14.2 Types of Springs 546

14.3 Potential Failure Modes 548

14.4 Spring Materials 549

14.5 Axially Loaded Helical-Coil Springs;

Stress, Deflection, and Spring Rate 552

Deflection and Spring Rate 557

Buckling and Surging 559

14.6 Summary of Suggested Helical-Coil

Spring Design Procedure, and General

Guidelines for Spring Design 562

14.7 Beam Springs (Leaf Springs) 568

14.8 Summary of Suggested Leaf Spring

Design Procedure 574

14.9 Torsion Bars and Other Torsion Springs 578

14.10 Belleville (Coned-Disk) Springs 581

14.11 Energy Storage in Springs 582

Chapter 15

Gears and Systems of Gears 594

15.1 Uses and Characteristics of Gears 594

15.2 Types of Gears; Factors in Selection 595

15.3 Gear Trains; Reduction Ratios 600

15.4 Potential failure Modes 605

15.5 Gear Materials 607

15.6 Spur Gears; Tooth Profile and Mesh

Geometry 608

Involute Profiles and Conjugate Action 609

Gearing Nomenclature; Tooth Shape and

Size 610

Gear-Tooth Systems 612

Mesh Interactions 614

xii / Contents

Loading, Friction, and Lubricant Flow

Relationships 410

Thermal Equilibrium and Oil Film Temperature

Rise 416

Design Criteria and Assumptions 419

Suggested Design Procedure 420

10.8 Hydrostatic Bearing Design 425

Chapter 11

Rolling Element Bearings 429

11.1 Uses and Characteristics of Rolling

Element Bearings 429

11.2 Types of Rolling Element Bearings 430

11.3 Potential Failure Modes 433

11.4 Bearing Materials 433

11.5 Bearing Selection 434

Basic Load Ratings 435

Reliability Specifications 435

Suggested Selection Procedure for Steady

Loads 436

Suggested Selection Procedure for Spectrum

Loading 448

Lubrication 451

11.6 Preloading and Bearing Stiffness 453

11.7 Bearing Mounting and Enclosure 457

Chapter 12

Power Screw Assemblies 462

12.1 Uses and Characteristics of Power

Screws 462

12.2 Potential Failure Modes 466

12.3 Materials 466

12.4 Power Screw Torque and Efficiency 467

12.5 Suggested Power Screw Design Procedure 473

12.6 Critical Points and Thread Stresses 474

Chapter 13

Machine Joints and Fastening Methods 485

13.1 Uses and Characteristics of Joints in

Machine Assemblies 485

13.2 Selection of Joint Type and Fastening

Method 485

13.3 Potential Failure Modes 487

13.4 Threaded Fasteners 488

Screw Thread Standards and Terminology 489

Threaded Fastener Materials 492

Critical Points and Thread Stresses 494

Preloading Effects; Joint Stiffness and Gasketed

Joints 497

15.7 Gear Manufacturing; Methods, Quality,

and Cost 618

Gear Cutting 618

Gear Finishing 620

Cutter Path Simulation, Mesh Deflection,

and Profile Modification 621

Accuracy Requirements, Measurement Factors,

and Manufacturing Cost Trends 622

15.8 Spur Gears; Force Analysis 624

15.9 Spur Gears; Stress Analysis and Design 626

Tooth Bending: Simplified Approach 626

Tooth Bending: Synopsis of AGMA Refined

Approach 631

Surface Durability: Hertz Contact Stresses and

Surface Fatigue Wear 639

Surface Durability: Synopsis of AGMA Refined

Approach 641

15.10 Lubrication and Heat Dissipation 645

15.11 Spur Gears; Summary of Suggested

Design Procedure 647

15.12 Helical Gears; Nomenclature, Tooth

Geometry, and Mesh Interaction 648

15.13 Helical Gears; Force Analysis 653

15.14 Helical Gears; Stress Analysis and

Design 654

15.15 Helical Gears; Summary of Suggested

Design Procedure 656

15.16 Bevel Gears; Nomenclature, Tooth

Geometry, and Mesh Interaction 662

15.17 Bevel Gears; Force Analysis 665

15.18 Bevel Gears; Stress Analysis and Design 666

15.19 Bevel Gears; Summary of Suggested

Design Procedure 668

15 20 Worm Gears and Worms; Nomenclature,

Tooth Geometry, and Mesh Interaction 675

15.21 Worm Gears and Worms; Force Analysis

and Efficiency 679

15.22 Worm Gears and Worms; Stress Analysis

and Design 682

15.23 Worm Gears and Worms; Suggested

Design Procedure 684

Chapter 16

Brakes and Clutches 701

16.1 Uses and Characteristics of Brakes

and Clutches 701

16.2 Types of Brakes and Clutches 702

16.3 Potential Failure Modes 704

16.4 Brake and Clutch Materials 704

Contents / xiii

16.5 Basic Concepts for Design of Brakes

and Clutches 705

16.6 Rim (Drum) Brakes with Short Shoes 708

16.7 Rim (Drum) Brakes with Long Shoes 719

16.8 Band Brakes 727

16.9 Disk Brakes and Clutches 732

Uniform Wear Assumption 733

Uniform Pressure Assumption 735

16.10 Cone Clutches and Brakes 738

Chapter 17

Belts, Chains, Wire Rope, and Flexible

Shafts 746

17.1 Uses and Characteristics of Flexible

Power Transmission Elements 746

17.2 Belt Drives; Potential Failure Modes 750

17.3 Belts; Materials 752

17.4 Belt Drives; Flat Belts 752

17.5 Belt Drives; V-Belts 757

17.6 Belt Drives; Synchronous Belts 769

17.7 Chain Drives; Potential Failure Modes 769

17.8 Chain Drives; Materials 770

17.9 Chain Drives; Precision Roller Chain 771

17.10 Roller Chain Drives; Suggested Selection

Procedure 774

17.11 Chain Drives; Inverted-Tooth Chain 779

17.12 Wire Rope; Potential Failure Modes 779

17.13 Wire Rope; Materials 782

17.14 Wire Rope; Stresses and Strains 782

17.15 Wire Rope; Suggested Selection

Procedure 786

17.16 Flexible Shafts 791

Chapter 18

Flywheels and High-Speed Rotors 798

18.l Uses and Characteristics of Flywheels 798

18.2 Fluctuating Duty Cycles, Energy

Management, and Flywheel inertia 799

18.3 Types of Flywheels 804

18.4 Potential Failure Modes 805

18.5 Flywheel Materials 805

18.6 Spoke-and-Rim Flywheels 806

Stresses in a Rotating Free Ring 807

Bending Stresses in Flywheel Rim 808

Spoke-Axial Tensile Stresses 809

18.7 Disk Flywheels of Constant Thickness 809

18.8 Disk Flywheels of Uniform Strength 815