Design of machine elements

Design of

Machine Elements

Third Edition

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About the Author

V B Bhandari retired as Professor and Head, Department of Mechanical

Engineering at Vishwakarma Institute of Technology, Pune. He holds First-Class

BE and ME degrees in Mechanical Engineering from Pune University, and his

teaching experience spans over 38 years in Government Colleges of Engineering

at Pune, Karad and Aurangabad. He was also a postgraduate teacher of Pune

University, Shivaji University and Marathwada University. Besides being a

National Scholar, he has received fi ve prizes from Pune University during his

academic career.

Professor Bhandari was a member of ‘Board of Studies in Mechanical

Engineering’ and a member of ‘Faculty of Engineering’ of Pune University.

He is a Fellow of Institution of Engineers (India), a Fellow of Institution of Mechanical Engineers

(India) and a Senior Member of Computer Society of India. He was a Fellow of Institution of Production

Engineers (India) and a Member of American Society of Mechanical Engineers (USA).

He has presented and published twenty technical papers in national and international conferences

and journals, and is also the author of Introduction to Machine Design published by Tata McGraw Hill

Education Private Limited.

Preface xvii

Visual Walkthrough xxi

1. Introduction 1

1.1 Machine Design 1

1.2 Basic Procedure of Machine Design 2

1.3 Basic Requirements of Machine Elements 3

1.4 Design of Machine Elements 4

1.5 Traditional Design Methods 8

1.6 Design Synthesis 8

1.7 Use of Standards in Design 9

1.8 Selection of Preferred Sizes 11

1.9 Aesthetic Considerations in Design 14

1.10 Ergonomic Considerations in Design 15

1.11 Concurrent Engineering 17

Short Answer Questions 19

Problems for Practice 19

2. Engineering Materials 20

2.1 Stress–Strain Diagrams 20

2.2 Mechanical Properties of Engineering Materials 23

2.3 Cast Iron 26

2.4 BIS System of Designation of Steels 29

2.5 Plain-carbon Steels 30

2.6 Free-cutting Steels 32

2.7 Alloy Steels 32

2.8 Overseas Standards 34

2.9 Heat Treatment of Steels 36

2.10 Case Hardening of Steels 37

2.11 Cast Steel 38

Contents

vi Contents

2.12 Aluminium Alloys 39

2.13 Copper Alloys 41

2.14 Die-casting Alloys 43

2.15 Ceramics 44

2.16 Plastics 45

2.17 Fibre-reinforced Plastics 48

2.18 Natural and Synthetic Rubbers 49

2.19 Creep 50

2.20 Selection of Material 51

2.21 Weighted Point Method 51

Short Answer Questions 53

3. Manufacturing Considerations in Design 55

3.1 Selection of Manufacturing Method 55

3.2 Design Considerations of Castings 57

3.3 Design Considerations of Forgings 59

3.4 Design Considerations of Machined Parts 61

3.5 Hot and Cold Working of Metals 62

3.6 Design Considerations of Welded Assemblies 62

3.7 Design for Manufacture and Assembly (DFMA) 64

3.8 Tolerances 65

3.9 Types of Fits 66

3.10 BIS System of Fits and Tolerances 67

3.11 Selection of Fits 69

3.12 Tolerances and Manufacturing Methods 69

3.13 Selective Assembly 70

3.14 Tolerances For Bolt Spacing 72

3.15 Surface Roughness 73

Short Answer Questions 73

Problems for Practice 74

4. Design Against Static Load 76

4.1 Modes of Failure 76

4.2 Factor of Safety 77

4.3 Stress–strain Relationship 79

4.4 Shear Stress and Shear Strain 80

4.5 Stresses Due To Bending Moment 81

4.6 Stresses Due To Torsional Moment 82

4.7 Eccentric Axial Loading 83

4.8 Design of Simple Machine Parts 84

4.9 Cotter Joint 85

4.10 Design Procedure for Cotter Joint 90

4.11 Knuckle Joint 94

4.12 Design Procedure for Knuckle Joint 99

4.13 Principal Stresses 104

4.14 Theories of Elastic Failure 106

Contents vii

4.15 Maximum Principal Stress Theory 107

4.16 Maximum Shear Stress Theory 108

4.17 Distortion-Energy Theory 110

4.18 Selection and Use of Failure Theories 112

4.19 Levers 117

4.20 Design of Levers 118

4.21 Fracture Mechanics 128

4.22 Curved Beams 130

4.23 Thermal Stresses 135

4.24 Residual Stresses 136

Short Answer Questions 137

Problems for Practice 138

5. Design Against Fluctuating Load 141

5.1 Stress Concentration 141

5.2 Stress Concentration Factors 142

5.3 Reduction of Stress Concentration 145

5.4 Fluctuating Stresses 149

5.5 Fatigue Failure 151

5.6 Endurance Limit 152

5.7 Low-cycle and High-cycle Fatigue 153

5.8 Notch Sensitivity 154

5.9 Endurance Limit—Approximate Estimation 155

5.10 Reversed Stresses—Design for Finite and Infi nite Life 159

5.11 Cumulative Damage in Fatigue 166

5.12 Soderberg and Goodman Lines 167

5.13 Modifi ed Goodman Diagrams 168

5.14 Gerber Equation 174

5.15 Fatigue Design under Combined Stresses 177

5.16 Impact Stresses 180

Short Answer Questions 182

Problems for Practice 182

6. Power Screws 184

6.1 Power Screws 184

6.2 Forms of Threads 185

6.3 Multiple Threaded Screws 187

6.4 Terminology of Power Screw 187

6.5 Torque Requirement—Lifting Load 189

6.6 Torque Requirement—Lowering Load 189

6.7 Self-locking Screw 190

6.8 Effi ciency of Square Threaded Screw 190

6.9 Effi ciency of Self-locking Screw 192

6.10 Trapezoidal and Acme Threads 192

6.11 Collar Friction Torque 193

6.12 Overall Effi ciency 194

viii Contents

6.13 Coeffi cient of Friction 194

6.14 Design of Screw and Nut 194

6.15 Design of Screw Jack 206

6.16 Differential and Compound Screws 214

6.17 Recirculating Ball Screw 215

Short-Answer Questions 216

Problems for Practice 217

7. Threaded Joints 219

7.1 Threaded Joints 219

7.2 Basic Types of Screw Fastening 220

7.3 Cap Screws 222

7.4 Setscrews 223

7.5 Bolt of Uniform Strength 224

7.6 Locking Devices 225

7.7 Terminology of Screw Threads 227

7.8 ISO Metric Screw Threads 228

7.9 Materials and Manufacture 230

7.10 Bolted Joint—Simple Analysis 231

7.11 Eccentrically Loaded Bolted Joints in Shear 233

7.12 Eccentric Load Perpendicular to Axis of Bolt 235

7.13 Eccentric Load on Circular Base 242

7.14 Torque Requirement for Bolt Tightening 248

7.15 Dimensions of Fasteners 249

7.16 Design of Turnbuckle 251

7.17 Elastic Analysis of Bolted Joints 254

7.18 Bolted Joint under Fluctuating Load 257

Short-Answer Questions 269

Problems for Practice 269

8. Welded and Riveted Joints 272

8.1 Welded Joints 272

8.2 Welding Processes 273

8.3 Stress Relieving of Welded Joints 274

8.4 Butt Joints 274

8.5 Fillet Joints 275

8.6 Strength of Butt Welds 276

8.7 Strength of Parallel Fillet Welds 277

8.8 Strength of Transverse Fillet Welds 278

8.9 Maximum Shear Stress in Parallel Fillet Weld 281

8.10 Maximum Shear Stress in Transverse Fillet Weld 282

8.11 Axially Loaded Unsymmetrical Welded Joints 284

8.12 Eccentric Load in the Plane of Welds 285

8.13 Welded Joint Subjected to Bending Moment 290

8.14 Welded Joint Subjected to Torsional Moment 294

8.15 Strength of Welded Joints 295

Contents ix

8.16 Welded Joints Subjected to Fluctuating Forces 296

8.17 Welding Symbols 297

8.18 Weld Inspection 298

8.19 Riveted Joints 298

8.20 Types of Rivet Heads 301

8.21 Types of Riveted Joints 303

8.22 Rivet Materials 305

8.23 Types of Failure 306

8.24 Strength Equations 306

8.25 Effi ciency of Joint 307

8.26 Caulking and Fullering 307

8.27 Longitudinal Butt Joint for Boiler Shell 311

8.28 Circumferential Lap Joint for Boiler Shells 318

8.29 Eccentrically Loaded Riveted Joint 321

Short-Answer Questions 325

Problems for Practice 325

9. Shafts, Keys and Couplings 330

9.1 Transmission Shafts 330

9.2 Shaft Design on Strength Basis 331

9.3 Shaft Design on Torsional Rigidity Basis 333

9.4 ASME Code for Shaft Design 334

9.5 Design of Hollow Shaft on Strength Basis 342

9.6 Design of Hollow Shaft on Torsional Rigidity Basis 344

9.7 Flexible Shafts 346

9.8 Keys 346

9.9 Saddle Keys 347

9.10 Sunk Keys 348

9.11 Feather Key 349

9.12 Woodruff Key 350

9.13 Design of Square and Flat Keys 350

9.14 Design of Kennedy Key 352

9.15 Splines 354

9.16 Couplings 356

9.17 Muff Coupling 357

9.18 Design Procedure for Muff Coupling 357

9.19 Clamp Coupling 359

9.20 Design Procedure for Clamp Coupling 360

9.21 Rigid Flange Couplings 362

9.22 Design Procedure for Rigid Flange Coupling 364

9.23 Bushed-pin Flexible Coupling 368

9.24 Design Procedure for Flexible Coupling 371

9.25 Design for Lateral Rigidity 376

9.26 Castigliano’s Theorem 380

x Contents

9.27 Area Moment Method 382

9.28 Graphical Integration Method 383

9.29 Critical Speed of Shafts 385

Short-Answer Questions 388

Problems for Practice 389

10. Springs 393

10.1 Springs 393

10.2 Types of Springs 393

10.3 Terminology of Helical Springs 395

10.4 Styles of End 396

10.5 Stress and Defl ection Equations 397

10.6 Series and Parallel Connections 399

10.7 Spring Materials 401

10.8 Design of Helical Springs 403

10.9 Spring Design—Trial-and-Error Method 405

10.10 Design against Fluctuating Load 405

10.11 Concentric Springs 425

10.12 Optimum Design of Helical Spring 430

10.13 Surge in Spring 432

10.14 Helical Torsion Springs 433

10.15 Spiral Springs 435

10.16 Multi-Leaf Spring 437

10.17 Nipping of Leaf Springs 439

10.18 Belleville Spring 441

10.19 Shot Peening 443

Short-Answer Questions 443

Problems for Practice 444

11. Friction Clutches 448

11.1 Clutches 448

11.2 Torque Transmitting Capacity 450

11.3 Multi-disk Clutches 456

11.4 Friction Materials 459

11.5 Cone Clutches 461

11.6 Centrifugal Clutches 465

11.7 Energy Equation 467

11.8 Thermal Considerations 469

Short-Answer Questions 470

Problems for Practice 471

12. Brakes 472

12.1 Brakes 472

12.2 Energy Equations 472

12.3 Block Brake with Short Shoe 475

12.4 Block Brake with Long Shoe 480

Contents xi

12.5 Pivoted Block Brake with Long Shoe 482

12.6 Internal Expanding Brake 485

12.7 Band Brakes 490

12.8 Disk Brakes 493

12.9 Thermal Considerations 496

Short-Answer Questions 496

Problems for Practice 497

13. Belt Drives 499

13.1 Belt Drives 499

13.2 Belt Constructions 501

13.3 Geometrical Relationships 503

13.4 Analysis of Belt Tensions 504

13.5 Condition for Maximum Power 507

13.6 Condition for Maximum Power (Alternative Approach) 507

13.7 Characteristics of Belt Drives 509

13.8 Selection of Flat-belts from Manufacturer’s Catalogue 514

13.9 Pulleys for Flat Belts 517

13.10 Arms of Cast-iron Pulley 520

13.11 V-belts 522

13.12 Selection of V-belts 534

13.13 V-grooved Pulley 535

13.14 Belt-Tensioning Methods 540

13.15 Ribbed V-belts 540

Short-Answer Questions 542

Problems for Practice 542

14. Chain Drives 544

14.1 Chain Drives 544

14.2 Roller Chains 546

14.3 Geometric Relationships 548

14.4 Polygonal Effect 549

14.5 Power Rating of Roller Chains 549

14.6 Sprocket Wheels 551

14.7 Design of Chain Drive 553

14.8 Chain Lubrication 555

14.9 Silent Chain 562

Short-Answer Questions 562

Problems for Practice 563

15. Rolling Contact Bearings 564

15.1 Bearings 564

15.2 Types of Rolling-contact Bearings 565

15.3 Principle of Self-aligning Bearing 568

15.4 Selection of Bearing-type 569

15.5 Static Load Carrying Capacity 569

xii Contents

15.6 Stribeck’s Equation 569

15.7 Dynamic Load Carrying Capacity 571

15.8 Equivalent Bearing Load 571

15.9 Load-Life Relationship 572

15.10 Selection of Bearing Life 572

15.11 Load Factor 573

15.12 Selection of Bearing from Manufacturer’s Catalogue 573

15.13 Selection of Taper Roller Bearings 580

15.14 Design for Cyclic Loads and Speeds 588

15.15 Bearing with Probability of Survival other than 90 Per Cent 592

15.16 Needle Bearings 595

15.17 Bearing Failure—Causes and Remedies 596

15.18 Lubrication of Rolling Contact Bearings 596

15.19 Mounting of Bearing 597

Short-Answer Questions 598

Problems for Practice 599

16. Sliding Contact Bearings 601

16.1 Basic Modes of Lubrication 601

16.2 Viscosity 604

16.3 Measurement of Viscosity 605

16.4 Viscosity Index 605

16.5 Petroff’s Equation 606

16.6 McKee’s Investigation 607

16.7 Viscous Flow through Rectangular Slot 608

16.8 Hydrostatic Step Bearing 609

16.9 Energy Losses in Hydrostatic Bearing 611

16.10 Reynold’s Equation 619

16.11 Raimondi and Boyd Method 622

16.12 Temperature Rise 624

16.13 Bearing Design—Selection of Parameters 625

16.14 Bearing Constructions 634

16.15 Bearing Materials 635

16.16 Sintered Metal Bearings 637

16.17 Lubricating Oils 637

16.18 Additives for Mineral Oils 639

16.19 Selection of Lubricants 640

16.20 Greases 641

16.21 Bearing Failure—Causes and Remedies 641

16.22 Comparison of Rolling and Sliding Contact Bearings 642

Short-Answer Questions 643

Problems for Practice 644

17. Spur Gears 646

17.1 Mechanical Drives 646

17.2 Gear Drives 647

xii Contents

15.6 Stribeck’s Equation 569

15.7 Dynamic Load Carrying Capacity 571

15.8 Equivalent Bearing Load 571

15.9 Load-Life Relationship 572

15.10 Selection of Bearing Life 572

15.11 Load Factor 573

15.12 Selection of Bearing from Manufacturer’s Catalogue 573

15.13 Selection of Taper Roller Bearings 580

15.14 Design for Cyclic Loads and Speeds 588

15.15 Bearing with Probability of Survival other than 90 Per Cent 592

15.16 Needle Bearings 595

15.17 Bearing Failure—Causes and Remedies 596

15.18 Lubrication of Rolling Contact Bearings 596

15.19 Mounting of Bearing 597

Short-Answer Questions 598

Problems for Practice 599

16. Sliding Contact Bearings 601

16.1 Basic Modes of Lubrication 601

16.2 Viscosity 604

16.3 Measurement of Viscosity 605

16.4 Viscosity Index 605

16.5 Petroff’s Equation 606

16.6 McKee’s Investigation 607

16.7 Viscous Flow through Rectangular Slot 608

16.8 Hydrostatic Step Bearing 609

16.9 Energy Losses in Hydrostatic Bearing 611

16.10 Reynold’s Equation 619

16.11 Raimondi and Boyd Method 622

16.12 Temperature Rise 624

16.13 Bearing Design—Selection of Parameters 625

16.14 Bearing Constructions 634

16.15 Bearing Materials 635

16.16 Sintered Metal Bearings 637

16.17 Lubricating Oils 637

16.18 Additives for Mineral Oils 639

16.19 Selection of Lubricants 640

16.20 Greases 641

16.21 Bearing Failure—Causes and Remedies 641

16.22 Comparison of Rolling and Sliding Contact Bearings 642

Short-Answer Questions 643

Problems for Practice 644

17. Spur Gears 646

17.1 Mechanical Drives 646

17.2 Gear Drives 647

Contents xiii

17.3 Classifi cation of Gears 647

17.4 Selection of Type of Gears 648

17.5 Law of Gearing 649

17.6 Terminology of Spur Gears 650

17.7 Standard Systems of Gear Tooth 653

17.8 Gear Trains 656

17.9 Interference and Undercutting 657

17.10 Backlash 658

17.11 Force Analysis 658

17.12 Gear Tooth Failures 665

17.13 Selection of Material 666

17.14 Gear Blank Design 667

17.15 Number of Teeth 670

17.16 Face Width 671

17.17 Beam Strength of Gear Tooth 672

17.18 Permissible Bending Stress 673

17.19 Effective Load on Gear Tooth 674

17.20 Estimation of Module Based on Beam Strength 677

17.21 Wear Strength of Gear Tooth 678

17.22 Estimation of Module Based on Wear Strength 680

17.23 Internal Gears 688

17.24 Gear Lubrication 690

Short-Answer Questions 690

Problems for Practice 690

18. Helical Gears 694

18.1 Helical Gears 694

18.2 Terminology of Helical Gears 694

18.3 Virtual Number of Teeth 695

18.4 Tooth Proportions 696

18.5 Force Analysis 697

18.6 Beam Strength of Helical Gears 702

18.7 Effective Load on Gear Tooth 702

18.8 Wear Strength of Helical Gears 703

18.9 Herringbone Gears 706

18.10 Crossed Helical Gears 708

Short-Answer Questions 709

Problems for Practice 710

19. Bevel Gears 711

19.1 Bevel Gears 711

19.2 Terminology of Bevel Gears 713

19.3 Force Analysis 715

19.4 Beam Strength of Bevel Gears 720

19.5 Wear Strength of Bevel Gears 722

19.6 Effective Load on Gear Tooth 722

xiv Contents

19.7 Spiral Bevel Gears 727

Short-Answer Questions 728

Problems for Practice 728

20. Worm Gears 730

20.1 Worm Gears 730

20.2 Terminology of Worm Gears 731

20.3 Proportions of Worm Gears 733

20.4 Force Analysis 735

20.5 Friction in Worm Gears 737

20.6 Selection of Materials 741

20.7 Strength Rating of Worm Gears 742

20.8 Wear Rating of Worm Gears 744

20.9 Thermal Considerations 745

Short-Answer Questions 747

Problems for Practice 747

21. Flywheel 749

21.1 Flywheel 749

21.2 Flywheel and Governor 750

21.3 Flywheel Materials 750

21.4 Torque Analysis 751

21.5 Coeffi cient of Fluctuation of Energy 752

21.6 Solid Disk Flywheel 753

21.7 Rimmed Flywheel 755

21.8 Stresses in Rimmed Flywheel 756

Short-Answer Questions 767

Problems for Practice 767

22. Cylinders and Pressure Vessels 768

22.1 Thin Cylinders 768

22.2 Thin Spherical Vessels 769

22.3 Thick Cylinders—Principal Stresses 770

22.4 Lame’s Equation 771

22.5 Clavarino’s and Birnie’s Equations 772

22.6 Cylinders with External Pressure 774

22.7 Autofrettage 775

22.8 Compound Cylinder 775

22.9 Gaskets 779

22.10 Gasketed Joint 780

22.11 Unfi red Pressure Vessels 783

22.12 Thickness of Cylindrical and Spherical Shells 785

22.13 End Closures 785

22.14 Openings in Pressure Vessel 791

Short-Answer Questions 794

Problems for Practice 794

Contents xv

23. Miscellaneous Machine Elements 796

23.1 Oil Seals 796

23.2 Wire Ropes 797

23.3 Stresses in Wire Ropes 800

23.4 Rope Sheaves and Drums 804

23.5 Buckling of Columns 806

Short-Answer Questions 812

Problems for Practice 812

24. Statistical Considerations in Design 814

24.1 Frequency Distribution 814

24.2 Characteristics of Frequency Curves 816

24.3 Measures of Central Tendency and Dispersion 817

24.4 Probability 819

24.5 Probability Distribution 819

24.6 Normal Curve 821

24.7 Population Combinations 823

24.8 Design and Natural Tolerances 825

24.9 Reliability 829

24.10 Probabilistic Approach to Design 830

Short-Answer Questions 840

Problems for Practice 841

25. Design of IC Engine Components 843

25.1 Internal Combustion Engine 843

25.2 Cylinder and Cylinder Liner 844

25.3 Bore and Length of Cylinder 845

25.4 Thickness of Cylinder Wall 845

25.5 Stresses in Cylinder Wall 846

25.6 Cylinder Head 847

25.7 Design of Studs for Cylinder Head 847

25.8 Piston 853

25.9 Piston Materials 854

25.10 Thickness of Piston Head 854

25.11 Piston Ribs and Cup 855

25.12 Piston Rings 856

25.13 Piston Barrel 857

25.14 Piston Skirt 858

25.15 Piston Pin 858

25.16 Connecting Rod 867

25.17 Buckling of Connecting Rod 868

25.18 Cross-section for Connecting Rod 869

25.19 Big and Small End Bearings 871

xvi Contents

25.20 Big End Cap and Bolts 873

25.21 Whipping Stress 875

25.22 Crankshaft 880

25.23 Design of Centre Crankshaft 881

25.24 Centre Crankshaft at Top-Dead Centre Position 881

25.25 Centre Crankshaft at Angle of Maximum Torque 883

25.26 Side Crankshaft at Top-Dead Centre Position 892

25.27 Side Crankshaft at Angle of Maximum Torque 895

25.28 Valve-Gear Mechanism 903

25.29 Design of Valves 904

25.30 Design of Rocker Arm 906

25.31 Design of Valve Spring 910

25.32 Design of Push Rod 911

Short-Answer Questions 922

Problems for Practice 923

References 927

Index 930