Machines elements : analysis and design

Machine Elements • Analysis and Design

This textbook provides undergraduate students with a basic understanding of machine element

theory, and introduces tools and techniques to facilitate design calculations for a number of

frequently encountered mechanical elements.

The material in the book is appropriate for one or two courses in Machine Elements and/or

Mechanical Engineering Design. The material is intended for students who have passed first

and second year basic courses in engineering physics, engineering mechanics and engineering

materials science.

The book is organized into 13 separate chapters, which in principle can be read independently.

The covered subjects are: Tolerances, springs, bearings, shafts, shaft-hub connections, threaded

fasteners (bolts), 2D Joint Kinematics, couplings, clutches, brakes, belt drives, gear geometry

and strength of gears.

About the authors

Peder Klit and Niels L. Pedersen are both professors in machine elements at the Department of

Mechanical Engineering, the Technical University of Denmark, DTU.

Peder Klit & Niels L. Pedersen

MACHINE ELEMENTS

ANALYSIS AND DESIGN

Machine Elements

Analysis and Design

By Peder Klit and Niels L. Pedersen

© 2014 Polyteknisk Forlag

2nd edition, 2014

ISBN 978-87-502-1068-9

Cover design by Anne Bjørlie

Printed by Livonia

Printed in Latvia 2014

All rights reserved. No part of the contents of this book may be reproduced or transmitted in

any form or by any means without the written permission of the publisher.

Polyteknisk Forlag

Anker Engelundsvej 1

DK-2800 Lyngby

Phone: +45 7742 4328

Fax: +45 7742 4354

E-mail: [email protected]

www.polyteknisk.dk

Side iii

Preface to the second edition

This book is intended to provide undergraduate students with basic understanding of machine

element theory, and to introduce tools and techniques facilitating design calculations for a

number of frequently encountered mechanical elements. The material in the book is appropriate

for a course in Machine Elements and/or Mechanical Engineering Design for students who have

passed first and second year basic courses in engineering physics, engineering mechanics and

engineering materials science.

At the end of each chapter in the book, references, which may be useful for further

studies of specific subjects or for verification, are given. Students who wish to go deeper into

the general theory of machine elements may find the following textbooks inspiring:

• Norton, R. L., "Machine Design, an integrated approach", Prentice-Hall, 2014.

• Shigley, J. E. and Mischke, C. R., "Mechanical Engineering Design", McGraw-Hill,

2004.

Students are encouraged to find supplement information from other sources such as

International and National Standards, Internet Catalogues and information provided by

companies (online or paper based). Those who are in command of the German language will

find numerous German textbooks of very high standard. Outstanding in quality is the textbooks

by Niemann and co-authors.

• Niemann, G., Winter,H., Hohn, B. "Maschinenelemente", Springer Verlag, Band I,

2005.

• Niemann, G., Winter,H., "Maschinenelemente", Springer Verlag, Band II, 2003.

• Niemann, G., Winter,H., "Maschinenelemente", Springer Verlag, Band III, 1983.

• Decker, K., "Maschinenelemente, Funktion, Gestaltung und Berechnung", Carl

Hanser Verlag, 2011

and an overall mechanical engineering reference book can be recommended as helpful during

the study, and afterwards in your professional engineering life as well:

• DUBBEL: Taschenbuch fiir den Maschinenbau, Springer Verlag, 2014.

In this second edition of the book the misprints in the first edition have been corrected

and some chapters have been extended. A new chapter on 2D joint kinematics has also been

added to the book.

Copenhagen, June 2014

Peder Klit and Niels L. Pedersen

Side iv

Side v

Contents

Preface to the second edition iii

Contents v

1 Limits, fits and surface properties 1

1.1 Introduction 1

1.2 Geometrical tolerances 1

1.2.1 Specifying geometrical tolerances 2

1.2.2 Toleranced features 3

1.3 Surface texture 4

1.3.1 Surface Texture Parameters 5

1.3.2 Surface Texture Parameters 5

1.4 Tolerances on lengths, diameters, angles 9

1.4.1 Dimensions and tolerances 10

1.4.2 Fits 11

1.4.3 The quality function deployment 12

1.4.4 Functional dimensioning 12

1.4.5 Dimension chains 15

1.5 The ISO-tolerance system 17

1.5.1 Introduction 17

1.5.2 Field of application 17

1.5.3 Terms and definitions 17

1.5.4 Tolerances and deviations 19

1.5.5 Preferred numbers 20

1.5.6 Standard tolerance grades IT1 to IT16 21

1.5.7 Formula for standard tolerances in grades IT5 to IT16 22

1.6 Nomenclature 23

1.7 References 24

2 Springs 25

2.1 Introduction 25

2.2 The design situation 25

2.3 Helical springs 26

2.3.1 Formulas for helical springs 27

2.3.2 Stress curvature correction factor 29

2.3.3 Material properties 30

2.3.4 Relaxation 30

2.3.5 Types of load 30

2.3.6 Dynamic loading 31

2.3.7 Optimization 32

Side vi

2.3.8 Compression springs 34

2.3.9 Growing mean diameter of helix 34

2.3.10 Natural frequency 34

2.3.11 Buckling of spring 34

2.3.12 Statically loaded cold-formed compression spring 36

2.3.13 Statically loaded hot-formed compression spring 36

2.3.14 Dynamically loaded cold-formed compression spring 37

2.3.15 Dynamically loaded hot-formed compression spring 37

2.3.16 Extension springs 37

2.3.17 Initial tension 38

2.3.18 Statically loaded cold-formed extension springs 38

2.3.19 Statically loaded hot-formed extension springs 38

2.3.20 Dynamically loaded cold-formed extension springs 38

2.3.21 Dynamically loaded hot-formed extension springs 39

2.3.22 Ends of extension springs 39

2.4 Belleville springs or coned-disk springs 40

2.4.1 Formulas for Belleville springs 40

2.5 Helical torsion springs 42

2.5.1 Methods of loading 42

2.5.2 Binding effects 43

2.5.3 Formulas for helical torsion springs 44

2.6 Spiral springs 45

2.6.1 Clamped outer end 45

2.6.2 Simply supported outer end 47

2.7 Supplementary literature 49

2.8 Nomenclature 49

2.9 References 51

3 Rolling element bearings 53

3.1 Introduction 53

3.2 Bearing types 53

3.2.1 Available space 53

3.2.2 Loads 54

3.2.3 Combined load 55

3.2.4 Misalignment 58

3.2.5 Speed 58

3.2.6 Stiffness 58

3.2.7 Axial displacement 58

3.3 Load carrying capacity and life 59

3.3.1 Basic load ratings 59

3.3.2 Life 60

3.3.3 Basic rating life equation 60

3.3.4 Requisite basic rating life 61

3.3.5 Adjusted rating life equation 61

3.3.6 Combination of life adjustment factors <22 and <23 64

3.3.7 SKF Life Theory 64

3.4 Calculation example 67

3.5 Calculation of dynamic bearing loads 69

3.5.1 Gear trains 69

3.5.2 Belt drives 69

Side vii

3.5.3 Equivalent dynamic bearing load 69

3.5.4 Constant bearing load 69

3.5.5 Fluctuating bearing load 70

3.5.6 Requisite minimum load 71

3.6 Selecting static loaded bearing 71

3.6.1 Stationary bearing 72

3.6.2 Static load rating 72

3.6.3 Requisite basic static load rating 73

3.7 Radial location of bearings - Selection of fit 73

3.8 Bearing lubrication 76

3.9 Nomenclature 78

3.10 References 79

4 Shafts 81

4.1 Introduction 81

4.1.1 Terminology 81

4.2 Types of load 82

4.3 Shaft design considerations 83

4.3.1 Possible modes of failure 83

4.4 Static loading 83

4.5 Design for fatigue (cyclic load/dynamic load) 87

4.5.1 Stress concentration 87

4.5.2 S-N curve or Wohler curve 89

4.5.3 Estimation of endurance level 90

4.5.4 Fluctuating load 91

4.6 Design for shaft deflections 94

4.7 Design for critical shaft speeds 95

4.8 Suggested design procedure, based on shaft yielding 97

4.9 Nomenclature 97

4.10 References 98

5 Shaft-hub Connections 99

5.1 Introduction 99

5.2 Positive connections 99

5.2.1 Pinned and taper-pinned joints 99

5.2.2 Parallel keys and Woodruff Keys 100

5.2.3 Splined joints 100

5.2.4 Prestressed shaft-hub connections 100

5.2.5 Failure of positive connections 101

5.3 Connection with force (Transmission by friction) 102

5.3.1 Cone interference fit 102

5.3.2 Interference fit with spacers 103

5.3.3 Interference fit (press and shrink fits) 104

5.4 Design modification/optimization 110

5.4.1 Spline design 113

5.5 Nomenclature 116

5.6 References 117

Side viii

6 Threaded Fasteners 119

6.1 Introduction 119

6.2 Characteristics of screw motion 119

6.3 Types of thread 120

6.4 Types of bolts and nuts 124

6.5 Material specification for bolts and nuts 125

6.6 Force and torque to preload a bolt 126

6.7 Deflection in joints due to preload 130

6.8 Superposition of preload and working loads 138

6.9 Failure of bolted connections 141

6.10 Design modification/optimization 143

6.11 Nomenclature 144

6.12 References 146

7 Couplings and universal joints 147

7.1 Introduction to couplings 147

7.2 Functional characteristics 147

7.2.1 Shaft elongation or shaft division 148

7.2.2 Misaligned shafts or angular deviation 148

7.2.3 Man-operated engagement or disengagement 149

7.2.4 Torque-sensitive clutches 149

7.2.5 Speed-sensitive clutches 149

7.2.6 Directional (one-way) clutches, overrun clutches 151

7.3 Permanent torsionally stiff couplings 152

7.3.1 Rigid couplings 152

7.3.2 Universal joints and other special joints 155

7.4 Permanent elastic couplings 162

7.4.1 General purpose 162

7.4.2 Selection procedures 163

7.4.3 Damping 166

7.4.4 Max coupling torque for squirrel-cage motor 167

7.5 Overload couplings and safety couplings 168

7.6 Nomenclature 168

7.7 References 169

8 Clutches 171

8.1 Friction clutches 171

8.1.1 Torque transmission (static) 172

8.1.2 Transient slip in friction clutches during engagement 174

8.1.3 Dissipated energy in the clutch 179

8.1.4 Layout design of friction clutches 181

8.2 Automatic clutches 181

8.2.1 Speed-sensitive clutches (centrifugal clutches) 181

8.2.2 Directional (one-way) clutches, overrun clutches 183

8.3 Nomenclature 185

8.4 References 186

Side ix

9 Brakes 187

9.1 Drum brakes 188

9.1.1 Self-energizing 188

9.1.2 Braking torque and friction radius 189

9.1.3 Wear and normal pressure for parallel guided shoe 190

9.1.4 Wear and normal pressure for non-pivoted long shoe 192

9.1.5 Wear and normal pressure for pivoted long shoe 193

9.2 Disc brakes 194

9.3 Cone brakes 195

9.3.1 Uniform pressure model 196

9.3.2 Uniform wear model 196

9.4 Band brakes 197

9.5 Nomenclature 198

10 Belt Drives 201

10.1 Introduction 201

10.1.1 Reasons for choosing belt drives 202

10.2 The belts 202

10.3 Belt drive geometry (kinematics) 203

10.4 Belt forces 205

10.4.1 Flat belt 205

10.4.2 V-belt 207

10.4.3 Including inertia 208

10.5 Belt stress (flat belt) 211

10.6 Optimization of belt-drives 213

10.7 Plot of the belt forces 214

10.8 Nomenclature 216

10.9 References 217

11 The geometry of involute gears 219