Analysis and design of machine elements

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Analysis and Design of Machine Elements

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Analysis and Design of Machine Elements

Wei Jiang

Dalian University of Technology, China

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This edition first published 2019

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v

Contents

Preface xvii

About the Companion Website xix

Part I Fundamentals of Design and Strength Analysis 1

1 An Overview of Machine Design 3

1.1 Introduction 3

1.1.1 Machines and Machine Elements 3

1.1.2 The Scope of Machine Design 4

1.2 Machine Design 5

1.2.1 Machine Design Considerations 5

1.2.2 Machine Design Process 7

1.3 Machine Element Design 9

1.3.1 Machine Element Design Considerations 9

1.3.2 Common Failure Modes in Machine Elements 10

1.3.3 Design Criteria 11

1.3.3.1 Strength Criteria 11

1.3.3.2 Rigidity Criteria 12

1.3.3.3 Life Criteria 12

1.3.3.4 Wear Criteria 13

1.3.4 Machine Element Design Process 13

1.4 Materials and Their Properties 15

1.4.1 Types of Materials 15

1.4.1.1 Steels and Alloys 15

1.4.1.2 Cast Irons and Cast Steels 17

1.4.1.3 Nonferrous Alloys 17

1.4.1.4 Polymers 18

1.4.1.5 Composite Materials 18

1.4.2 Material Properties 18

1.4.3 Heat Treatments 19

1.4.4 Material Selection 20

1.5 Unit Systems 21

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vi Contents

1.6 Standards and Codes 22

References 23

Problems 23

2 Strength of Machine Elements 25

2.1 Fluctuating Loads and Stresses 26

2.1.1 Service Factors and Design Loads 26

2.1.2 Types of Loads 26

2.1.3 Types of Stresses 28

2.1.3.1 Static Stress 28

2.1.3.2 Completely Reversed Stress 29

2.1.3.3 Repeated Stress 29

2.1.3.4 Fluctuating Stress 29

2.2 Static Strength 29

2.2.1 Static Strength for Uniaxial Stresses 30

2.2.2 Static Strength for Combined Stresses 30

2.2.2.1 Maximum Shear Stress Theory 30

2.2.2.2 Maximum Distortion Energy Theory 31

2.3 Fatigue Strength 32

2.3.1 The Nature of Fatigue 32

2.3.2 Stress-Life Diagrams 33

2.3.3 Endurance Limit Diagrams 34

2.3.3.1 The Endurance Limit Diagram of a Material 34

2.3.3.2 The Endurance Limit Diagram of an Element 35

2.3.4 Fatigue Strength for Uniaxial Stresses with Constant Amplitude 39

2.3.5 Fatigue Strength for Uniaxial Stresses with Variable Amplitude 41

2.3.5.1 Linear Cumulative Damage Rule (Miner’s Rule) 41

2.3.5.2 Prediction of Cumulative Fatigue Damage 42

2.3.6 Fatigue Strength for Combined Stresses with Constant Amplitude 43

2.3.7 Measures to Improve Fatigue Strength 44

2.3.8 Examples of Strength Analyses 44

2.4 Contact Strength 50

2.4.1 Hertzian Contact Stresses 50

2.4.2 Surface Fatigue Failure 51

References 52

Problems 53

Part II Design Applications 57

3 Detachable Joints and Fastening Methods 59

3.1 Introduction 60

3.1.1 Applications, Characteristics and Structures 60

3.1.2 Selection of Fastening Methods 60

3.2 Screw Threads 61

3.2.1 Types of Screw Threads 61

3.2.2 Standards and Terminology 62

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Contents vii

3.3 Threaded Fastening Methods 64

3.3.1 Types of Threaded Fastening Methods 64

3.3.2 Threaded Fasteners 65

3.3.3 Tightening Torque and Preloading 66

3.3.4 Fastener Loosening and Locking 66

3.4 Force Analysis of Multiply Bolted Joints 67

3.4.1 Multiply Bolted Joints Subjected to Symmetric Transverse Loads 67

3.4.2 Multiply Bolted Joints Subjected to a Torque 68

3.4.3 Multiply Bolted Joints Subjected to a Symmetric Axial Load 69

3.4.4 Multiply Bolted Joints Subjected to an Overturning Moment 70

3.5 Strength Analysis 71

3.5.1 Potential Failure Modes 71

3.5.2 Strength Analysis for Shear Bolts 71

3.5.3 Strength Analysis for Tension Bolts 72

3.5.3.1 Tension Bolts Subjected to Axial Loads Only 72

3.5.3.2 Preloaded Tension Bolts Subjected to Transverse Loads 72

3.5.3.3 Preloaded Tension Bolts Subjected to Combined Preload and Static Axial

Loads 73

3.5.3.4 Preloaded Tension Bolts Subjected to Combined Preload and Variable Axial

Loads 74

3.5.4 Measures to Improve Fatigue Strength of Bolted Joints 75

3.6 Design of Bolted Joints 76

3.6.1 Introduction 76

3.6.2 Materials and Allowable Stresses 76

3.6.3 Design Criteria 78

3.6.4 Design Procedure and Guidelines 78

3.6.5 Structural Design 79

3.6.6 Design Cases 79

References 83

Problems 84

4 Detachable Fastenings for Shaft and Hub 91

4.1 Keys 91

4.1.1 Applications, Characteristics and Structure 91

4.1.2 Types of Keys 92

4.1.3 Strength Analysis 94

4.2 Splines 96

4.3 Pins 97

References 98

Problems 99

5 Permanent Connections 105

5.1 Riveting 105

5.1.1 Applications, Characteristics and Structure 105

5.1.2 Types of Rivets 105

5.1.3 Strength Analysis 106

5.1.4 Design of Riveted Joints 107

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5.2 Welding 109

5.2.1 Applications, Characteristics and Structure 109

5.2.2 Types of Welded Joints and Types of Welds 110

5.2.3 Strength Analysis 110

5.2.3.1 Butt Welds 111

5.2.3.2 Fillet Welds 111

5.2.4 Design of Welded Joints 112

5.3 Brazing, Soldering and Adhesive Bonding 113

5.3.1 Applications, Characteristics and Structure 113

5.3.2 Types of Adhesive and Their Selection 113

5.3.3 Analysis and Design of Adhesive Joints 114

References 115

Problems 115

6 Belt Drives 119

6.1 Introduction 120

6.1.1 Applications, Characteristics and Structures 120

6.1.2 Types of Belts 121

6.1.3 V-Belts 123

6.1.3.1 Terminology and Dimensions of V-Belts 123

6.1.3.2 Types of V-Belts 123

6.1.3.3 V-Belt Construction 123

6.2 Working Condition Analysis 124

6.2.1 Geometrical Relationships in Belt Drives 124

6.2.2 Force Analysis 125

6.2.2.1 Force Analysis of an Element of Belt 126

6.2.2.2 Relations Between Tight Tension F1, Slack Tension F2, Initial Tension F0 and

Effective Tension Fe 126

6.2.2.3 Critical or Maximum Effective Tension, Fec 127

6.2.2.4 Centrifugal Tension, Fc 128

6.2.3 Kinematic Analysis 128

6.2.3.1 Elastic Creep 128

6.2.3.2 Slippage of Belts 129

6.2.3.3 Speed Ratio 129

6.2.4 Stress Analysis 130

6.2.4.1 Tensile Stress in Tight Side, ��1, and Slack Side, ��2 130

6.2.4.2 Centrifugal Stress, ��c 130

6.2.4.3 Bending Stress, ��b 130

6.2.5 Potential Failure Modes 131

6.3 Power Transmission Capacities 131

6.3.1 The Maximum Effective Tension 131

6.3.2 Power Transmission Capacity of a Single V-Belt 132

6.3.2.1 The Basic Power Rating of a Single Standard V-Belt, P0 132

6.3.2.2 The Actual Power Rating of a Single V-Belt, Pr 132

6.4 Design of Belt Drives 135

6.4.1 Introduction 135

6.4.2 Design Criteria 135

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Contents ix

6.4.3 Design Procedure and Guidelines 135

6.4.3.1 Compute Design Power, Pca 136

6.4.3.2 Specify Suitable Belt Types 136

6.4.3.3 Determine the Sheave Size 136

6.4.3.4 Confirm the Centre Distance, a and Belt Datum Length, Ld 136

6.4.3.5 Compute Contact Angle on the Small Sheave, ��1 137

6.4.3.6 Compute the Number of Belts Required to Carry the Design Power 137

6.4.3.7 Decide Initial Tension, F0 137

6.4.3.8 Compute the Force Acting on the Sheave Shaft, FQ 138

6.4.4 Design of V-Belt Sheaves 138

6.4.5 Design Cases 138

6.5 Installation and Maintenance 140

References 141

Problems 141

7 Chain Drives 147

7.1 Introduction 148

7.1.1 Applications, Characteristics and Structures 148

7.1.2 Types of Chains 148

7.2 Working Condition Analysis 151

7.2.1 Geometrical Relationships in Chain Drives 151

7.2.2 Kinematic Analysis 151

7.2.2.1 Speed Ratio 151

7.2.2.2 Angular Velocity Ratio 152

7.2.2.3 Chordal Action 153

7.2.3 Force Analysis 154

7.2.3.1 Tension in Tight Side 154

7.2.3.2 Tension in Slack Side 154

7.2.3.3 Dynamic Forces 154

7.2.4 Potential Failure Modes 155

7.3 Power Transmission Capacities 155

7.3.1 Limiting Power Curves 155

7.3.2 Actually Transmitted Power 156

7.4 Design of Chain Drives 157

7.4.1 Introduction 157

7.4.2 Materials 157

7.4.3 Design Criteria 157

7.4.4 Design Procedure and Guidelines 158

7.4.4.1 Tentatively Select the Number of Sprocket Teeth z and Speed Ratio i 158

7.4.4.2 Determine the Required Power Rating of a Single-Strand Chain, P0 159

7.4.4.3 Select Types of Chain and Pitch, p 159

7.4.4.4 Determine the Centre Distance Between the Sprocket Shafts, a and Chain

Length, Lp 160

7.4.4.5 Select an Appropriate Lubrication According to the Speed of Chain 160

7.4.4.6 Forces Acting on the Shaft 160

7.4.5 Design Cases 161

7.5 Drive Layout, Tension and Lubrication 163

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7.5.1 Drive Layout 163

7.5.2 Tensioning 163

7.5.3 Lubrication 164

References 165

Problems 165

8 Gear Drives 171

8.1 Introduction 173

8.1.1 Applications, Characteristics and Structures 173

8.1.2 Types of Gear Drives 173

8.1.3 Geometry and Terminology 175

8.2 Working Condition Analysis 178

8.2.1 Kinematic Analysis 178

8.2.1.1 Speed Ratio and Pitch Line Velocity 178

8.2.1.2 Contact Ratio 178

8.2.2 Design Loads 179

8.2.3 Potential Failure Modes 181

8.3 Strength Analysis for Spur Gears 182

8.3.1 Forces on Spur Gear Teeth 182

8.3.2 Tooth Surface Fatigue Strength Analysis 184

8.3.2.1 Hertz Formula 184

8.3.2.2 Contact Stress Calculation 185

8.3.2.3 Contact Strength Analysis 186

8.3.3 Tooth Bending Strength Analysis 186

8.3.3.1 Bending Stress Calculation 187

8.3.3.2 Bending Strength Analysis 188

8.4 Strength Analysis for Helical Gears 188

8.4.1 Geometry and Terminology 189

8.4.1.1 The Geometry of a Helical Gear 189

8.4.1.2 Contact Ratio 191

8.4.1.3 Virtual Number of Teeth 192

8.4.2 Forces on Helical Gear Teeth 192

8.4.3 Tooth Surface Fatigue Strength Analysis 194

8.4.3.1 Contact Stress Calculation 194

8.4.3.2 Contact Strength Analysis 195

8.4.4 Tooth Bending Strength Analysis 195

8.4.4.1 Bending Stress Calculation 195

8.4.4.2 Bending Strength Analysis 196

8.5 Strength Analysis for Bevel Gears 196

8.5.1 Geometry and Terminology 196

8.5.2 Forces on Straight Bevel Gear Teeth 199

8.5.3 Tooth Surface Fatigue Strength Analysis 200

8.5.3.1 Contact Stress Calculation 200

8.5.3.2 Contact Strength Analysis 201

8.5.4 Tooth Bending Strength Analysis 201

8.5.4.1 Bending Stress Calculation 201

8.5.4.2 Bending Strength Analysis 202

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Contents xi

8.6 Design of Gear Drives 202

8.6.1 Introduction 202

8.6.2 Materials and Heat Treatments 202

8.6.2.1 Commonly Used Gear Materials 203

8.6.2.2 Heat Treatments 203

8.6.3 Gear Manufacturing and Quality 203

8.6.4 Allowable Stresses 204

8.6.5 Design Criteria 207

8.6.6 Design Procedure and Guidelines 207

8.6.6.1 Select Gear Type, Materials, Accuracy Grades, Heat Treatments and

Manufacturing Methods 207

8.6.6.2 Initial Selection of Design Variables 207

8.6.6.3 Design by Gear Strength 208

8.6.6.4 Geometrical Calculation 209

8.6.7 Design Cases 210

8.7 Structural Design of Gears 224

8.8 Lubrication and Efficiency 225

References 225

Problems 226

9 Wormgear Drives 233

9.1 Introduction 234

9.1.1 Applications, Characteristics and Structures 234

9.1.2 Types of Wormgear Drives 234

9.1.2.1 Cylindrical Wormgear Drives 235

9.1.2.2 Toroidal Wormgear Drives 235

9.1.2.3 Spiroid Wormgear Drives 235

9.1.3 Geometry and Terminology 235

9.1.3.1 Module m and Pressure Angle a 236

9.1.3.2 The Worm Diameter d1 and Worm Diameter Factor q 236

9.1.3.3 The Number of Threads of Worm z1 and the Number of Wormgear Teeth

z2 237

9.1.3.4 Worm Lead Angle �� and Wormgear Helix Angle �� 237

9.1.3.5 Profile Shift Coefficient x 237

9.1.3.6 Centre Distance a 237

9.2 Working Condition Analysis 239

9.2.1 Kinematic Analysis 239

9.2.1.1 Speed Ratio i and Gear Ratio u 239

9.2.1.2 Sliding Velocity Analysis 239

9.2.2 Forces on Worm and Wormgear Teeth 240

9.2.3 Potential Failure Modes 241

9.3 Load Carrying Capacities 242

9.3.1 Tooth Surface Fatigue Strength Analysis 242

9.3.2 Tooth Bending Strength Analysis 243

9.3.3 Rigidity Analysis 243

9.3.4 Efficiency and Thermal Capacity 244

9.3.4.1 Efficiency of Wormgear Drives 244

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9.3.4.2 Thermal Analysis 244

9.4 Design of Wormgear Drives 246

9.4.1 Introduction 246

9.4.2 Materials and Heat Treatments 246

9.4.3 Allowable Stresses 247

9.4.3.1 Allowable Contact Stresses 247

9.4.3.2 Allowable Bending Stresses 247

9.4.4 Design Criteria 249

9.4.5 Design Procedure and Guidelines 250

9.4.5.1 The Arrangement of Wormgear Drive and Selection of Accuracy Grade

Levels 250

9.4.5.2 The Selection of the Number of Worm Threads z1 and the Number of

Wormgear Teeth z2 250

9.4.5.3 Design by Wormgear Strength 250

9.4.6 Design Cases 250

9.5 Structural Design of Wormgear Drives 253

9.6 Lubrication of Wormgear Drives 253

References 254

Problems 254

10 Shafts 259

10.1 Introduction 260

10.1.1 Applications, Characteristics and Structures 260

10.1.2 Types of Shafts 260

10.2 Working Condition Analysis 262

10.2.1 Force Analysis 262

10.2.2 Stress Analysis 262

10.2.3 Deflection and Rigidity 262

10.2.4 Rotating Shaft Dynamics 264

10.2.5 Potential Failure Modes 264

10.3 Load Carrying Capacities 264

10.3.1 Strength Analysis 264

10.3.1.1 Torsional Strength Analysis 265

10.3.1.2 Combination of Torsional and Bending Strength Analysis 265

10.3.1.3 Fatigue Strength Analysis 266

10.3.1.4 Static Strength Analysis 268

10.3.2 Rigidity Analysis 268

10.3.2.1 Bending Deflections and Slopes 268

10.3.2.2 Torsional Deflections 269

10.3.3 Critical Speed Analysis 270

10.4 Design of Shafts 271

10.4.1 Introduction 271

10.4.2 Materials and Heat Treatments 271

10.4.3 Design Criteria 272

10.4.4 Design Procedure and Guidelines 272

10.4.5 Structural Design of Shafts 273

10.4.5.1 Measures to Increase Shaft Strength and Rigidity 273

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Contents xiii

10.4.5.2 Locating and Fastening Elements on a Shaft 274

10.4.5.3 Machinability and Assemblability of Shafts 275

10.4.6 Design Cases 277

References 284

Problems 284

11 Rolling Contact Bearings 291

11.1 Introduction 292

11.1.1 Applications, Characteristics and Structures 292

11.1.2 Characteristic Factors of Rolling Contact Bearings 293

11.1.2.1 Internal Clearance 293

11.1.2.2 Contact Angle �� 294

11.1.2.3 Angular Deviation �� 294

11.1.3 Types of Rolling Contact Bearings and Their Selection 295

11.1.3.1 Classification of Rolling Contact Bearings 295

11.1.3.2 Types of Rolling Contact Bearings 295

11.1.3.3 Bearing Type Selection 296

11.1.4 Designation of Rolling Contact Bearings 297

11.2 Working Condition Analysis 298

11.2.1 Kinematic Analysis 298

11.2.2 Force Analysis 299

11.2.2.1 Thrust Bearings (50000, 290000) 299

11.2.2.2 Radial Bearings (60000, 10000, 20000, N, NA) 299

11.2.2.3 Angular Contact Bearings (70000, 30000) 299

11.2.3 Stress Analysis 303

11.2.4 Potential Failure Modes 304

11.3 Life Expectancy and Load Carrying Capacities 305

11.3.1 Life Prediction under Constant Loads 305

11.3.1.1 Relations Between Bearing Load and Bearing Life 305

11.3.1.2 Modification of Life Prediction 306

11.3.1.3 Rated Life at Different Reliability 307

11.3.2 Life Prediction under Variable Loads 308

11.3.3 Static Strength Analysis 309

11.4 Design of Bearing Support Systems 310

11.4.1 Introduction 310

11.4.2 Bearing Selection 310

11.4.3 Design Procedures and Guidelines 311

11.4.4 Practical Considerations in the Application of Bearings 311

11.4.4.1 Assembly and Disassembly 311

11.4.4.2 Axial Positioning 311

11.4.4.3 Axial Retaining 313

11.4.4.4 Axial Adjustment 314

11.4.4.5 Rolling Bearing Fits 314

11.4.4.6 Preloading 314

11.4.4.7 Lubrication 314

11.4.4.8 Sealing 315

11.4.5 Design Cases 316