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Fundamentals of Machine Elements Bernard Hamrock | ||||||
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Fundamentals of Machine Elements Bernard Hamrock | ||||||
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TABLE OF CONTENTS
PART 1
FUNDAMENTALS 1
Chapter 1
INTRODUCTION 2
1.1 What Is Design? 3
1.2 Design of Mechanical Systems 4
1.3 Design as Multidisciplinary Endeavor 5
1.4 Design of Machine Elements 6
1.5 Fundamental Design Considerations 7
1.5.1 Safety in Mechanical Design 7
1.5.2 Government Codes and Industry
Standards 12
1.5.3 Manufacturing 13
1.6 Computers in Design 15
1.7 Catalogs and Vendors 17
1.8 Units 17
1.9 Unit Checks 18
1.10 Significant Figures 20
1.11 Summary 22
Chapter 2
LOAD, STRESS, AND STRAIN 27
2.1 Introduction 28
2.2 Critical Section 28
2.3 Load Classification and Sign Convention 30
2.4 Support Reactions 34
2.5 Static Equilibrium 34
2.6 Free-Body Diagram 37
2.7 Supported Beams 37
2.8 Shear and Moment Diagrams 39
2.9 Singularity Functions 41
2.10 Stress 47
2.11 Stress Element 49
2.12 Stress Tensor 50
2.13 Plane Stress 51
2.14 Mohr's Circle 55
2.15 Three-Dimensional Stresses 58
2.16 Octahedral Stresses 61
2.17 Strain 63
2.18 Strain Tensor 65
2.19 Plane Strain 66
2.20 Summary 71
Chapter 3
SOLID MATERIALS 89
3.1 Introduction 90
3.2 Ductile and Brittle Materials 91
3.2.1 Ductile Materials 91
3.2.2 Brittle Materials 92
3.3 Classification of Solid Materials 93
3.3.1 Metals 93
3.3.2 Ceramics and Glasses 94
3.3.3 Polymers and Elastomers 95
3.3.4 Composites 95
3.4 Stress-Strain Diagrams 98
3.4.1 Metals 98
3.4.2 Ceramics 101
3.4.3 Polymers 102
3.5 Properties of Solid Materials 104
3.5.1 Density 104
3.5.2 Modulus of Elasticity, Poisson's Ratio,
and Shear Modulus 106
3.5.3 Strength 111
3.5.4 Resilience and Toughness 112
3.5.5 Thermal Conductivity 114
3.5.6 Linear Thermal Expansion
Coefficient 114
3.5.7 Specific Heat Capacity 115
3.5.8 Archard Wear Constant 121
3.6 Stress-Strain Relationships 121
3.7 Two-Parameter Materials Charts 123
3.7.1 Stiffness versus Weight 123
3.7.2 Strength versus Weight 126
3.7.3 Stiffness versus Strength 128
3.7.4 Wear Rate versus Limiting Pressure 128
3.7.5 Young's Modulus versus Relative Cost 132
3.8 Summary 134
Chapter 4
NORMAL, TORSIONAL, BENDING,
AND TRANSVERSE SHEAR STRESSES AND STRAINS 139
4.1 Introduction 140
4.2 Definitions 141
4.2.1 Centroid of Area 141
4.2.2 Area Moment of Inertia 142
4.2.3 Parallel-Axis Theorem 144
4.2.4 Radius of Gyration 146
4.2.5 Section Modulus 147
4.2.6 Mass Moment of Inertia 149
4.3 Normal Stress and Strain 151
4.4 Torsion 153
4.4.1 Stress and Strain 154
4.4.2 Power Transfer 156
4.5 Bending Stress and Strain 158
4.5.1 Straight Member 158
4.5.2 Curved Member 162
4.6 Transverse Shear Stress and Strain 167
4.7 Summary 173
Chapter 5
DEFORMATION 181
5.1 Introduction 182
5.2 Moment-Curvature Relation 183
5.3 Singularity Functions 186
5.4 Method of Superposition 192
5.5 Strain Energy 195
5.5.1 Normal Stress 195
5.5.2 Shear Stress 197
5.5.3 Transverse Shear Stress 199
5.5.4 General State of Stress 200
5.6 Castigliano's Theorem 200
5.7 Summary 208
Chapter 6
FAILURE PREDICTION
FOR STATIC LOADING 219
6.1 Introduction 220
6.2 Stress Concentration 221
6.2.1 Charts 221
6.2.2 Flow Analogy 228
6.3 Fracture Mechanics 230
6.4 Modes of Crack Displacement 230
6.5 Fracture Toughness 231
6.6 Failure Prediction for Uniaxial
Stress State 234
6.7 Failure Prediction for Multiaxial
Stress State 235
6.7.1 Ductile Materials 235
6.7.2 Brittle Materials 242
6.7.3 Selecting Failure Criterion 245
6.8 Summary 250
Chapter 7
FAILURE PREDICTION FOR CYCLIC
AND IMPACT LOADING 257
7.1 Introduction 258
7.2 Fatigue 259
7.3 Cyclic Stresses 261
7.4 Strain Life Theory of Fatigue 262
7.5 Fatigue Strength 264
7.5.1 Rotating-Beam Experiments 264
7.5.2 S-N Diagrams 265
7.6 Fatigue Regimes 267
7.6.1 Low-Cycle Fatigue 268
7.6.2 High-Cycle, Finite-Life Fatigue 268
7.6.3 High-Cycle, Infinite-Life Fatigue 270
7.7 Endurance Limit Modification Factors 270
7.7.1 Stress Concentration Effects 270
7.7.2 Surface Finish Factor 273
7.7.3 Size Factor 275
7.7.4 Reliability Factor 275
7.7.5 Temperature Factor 276
7.7.6 Miscellaneous Effects 276
7.8 Cumulative Damage 279
7.9 Influence of Nonzero Mean Stress 280
7.9.1 Ductile Materials 280
7.9.2 Brittle Materials 287
7.10 Fracture Mechanics Approach
to Fatigue 288
7.11 Linear Impact Stresses and
Deformations 290
7.12 Summary 298
Chapter 8
LUBRICATION, FRICTION,
AND WEAR 307
8.1 Introduction 308
8.2 Conformal and Nonconformal Surfaces 309
8.3 Lubrication 310
8.3.1 Hydrodynamic Lubrication 310
8.3.2 Elastohydrodynamic Lubrication 311
8.3.3 Boundary Lubrication 313
8.3.4 Partial Lubrication 315
8.4 Surface Parameters 315
8.5 Film Parameter 317
8.6 Lubricant Viscosity 318
8.6.1 Absolute Viscosity 319
8.6.2 Kinematic Viscosity 321
8.6.3 Viscosity-Pressure Effects 322
8.6.4 Viscosity-Temperature Effects 326
8.7 Concentrated Loading-Deformations
and Stresses 326
8.7.1 Elliptical Contacts 327
8.7.2 Rectangular Contacts 334
8.8 Friction 336
8.8.1 Low Friction 336
8.8.2 High Friction 337
8.8.3 Laws of Dry Friction 338
8.8.4 Sliding Friction of Metals 338
8.8.5 Sliding Friction of Polymers
and Plastics 341
8.8.6 Sliding Friction of Rubber 342
8.9 Wear 342
8.9.1 Adhesive Wear 342
8.9.2 Abrasive Wear 345
8.9.3 Fatigue Wear 345
8.10 Summary 348
PART 2
MACHINE ELEMENTS 357
Chapter 9
COLUMNS 358
9.1 Introduction 359
9.2 Equilibrium Regimes 360
9.2.1 Stable Equilibrium 360
9.2.2 Neutral Equilibrium 360
9.2.3 Unstable Equilibrium 360
9.3 Concentrically Loaded Columns 362
9.3.1 Linear-Elastic Material 362
9.3.2 Inelastic Buckling 365
9.4 End Conditions 365
9.5 Euler's Buckling Criteria 367
9.6 Johnson's Buckling Criteria 368
9.7 AISC Criteria 372
9.8 Eccentrically Loaded Columns 373
9.9 Summary 379
Chapter 10
STRESSES AND DEFORMATIONS
IN CYLINDERS 385
10.1 Introduction 386
10.2 Tolerances and Fits 386
10.3 Pressurization Effects 389
10.3.1 Thin-Walled Cylinders 390
10.3.2 Thick-Walled Cylinders 393
10.4 Rotational Effects 400
10.4.1 Cylinder with Central Hole 401
10.4.2 Solid Cylinder 402
10.5 Press Fits 404
10.5.1 Hub 405
10.5.2 Shaft 406
10.5.3 Interference Fit 407
10.5.4 Force and Torque 407
10.6 Shrink Fits 409
10.7 Summary 415
Chapter 11
SHAFTING AND ASSOCIATED
PARTS 423
11.1 Introduction 424
11.2 Shaft Design Procedure 425
11.3 Static Loading 428
11.3.1 Bending Moment and Torsion 428
11.3.2 Bending Moment, Torsion, and Axial Loading 431
11.4 Cyclic Loading 432
11.4.1 Ductile Materials 432
11.4.2 Brittle Materials 437
11.5 Critical Speed of Rotating Shafts 440
11.5.1 Single-Mass System 440
11.5.2 Multiple-Mass System 442
11.6 Keys 445
11.7 Flywheels 448
11.7.1 Dynamics 448
11.7.2 Flywheel Sizing 449
11.7.3 Stresses 452
11.7.4 Materials 454
11.8 Summary 458
Chapter 12
HYDRODYNAMIC AND HYDROSTATIC BEARINGS AND SEALS 467
12.1 Introduction 469
12.2 Reynolds Equation 469
12.2.1 Derivation of Reynolds Equation 470
12.2.2 Physical Significance of Terms
in Reynolds Equation 474
12.2.3 Standard Reduced Forms 477
12.3 Thrust Slider Bearings 478
12.3.1 Mechanism of Pressure
Development 478
12.3.2 General Thrust Slider Bearing Theory 480
12.3.3 Hydrodynamic Thrust Bearings-
Neglecting Side Leakage 481
12.3.4 Operating and Performance
Parameters 489
12.3.5 Fixed-Incline Slider Bearing 492
12.3.6 Pivoted-Pad Slider Bearing 498
12.3.7 Thrust Slider Bearing Geometry 503
12.4 Journal Slider Bearings 504
12.4.1 Petrov's Equation 504
12.4.2 Journal Slider Bearing Operation 506
12.4.3 Operating and Performance
Parameters 507
12.4.4 Design Procedure 508
12.4.5 Optimization Techniques 514
12.4.6 Nonplain Configurations 514
12.5 Squeeze Film Bearings 516
12.5.1 Parallel-Surface Squeeze Film Thrust Bearing 517
12.5.2 General Comments About Squeeze Film Bearings 521
12.6 Hydrostatic Bearings 521
12.7 Gas-Lubricated Bearings 525
12.8 Summary 528
Chapter 13
ROLLING-ELEMENT BEARINGS 539
13.1 Introduction 541
13.2 Historical Overview 542
13.3 Bearing Types 543
13.3.1 Ball Bearings 543
13.3.2 Roller Bearings 546
13.4 Geometry 549
13.4.1 Ball Bearings 549
13.4.2 Roller Bearings 559
13.5 Kinematics 563
13.6 Separators 567
13.7 Static Load Distribution 568
13.7.1 Load Deflection Relationships 568
13.7.2 Radially Loaded Ball and Roller
Bearings 570
13.7.3 Thrust-Loaded Ball Bearings 573
13.7.4 Preloading 576
13.7.5 Static Load Rating 577
13.7.6 Equivalent Static Load 579
13.8 Elastohydrodynamic Lubrication 581
13.8.1 Relevant Equations 581
13.8.2 Dimensionless Grouping 582
13.8.3 Minimum-Film-Thickness Formula 584
13.9 Fatigue Life 586
13.9.1 Contact Fatigue Theory 586
13.9.2 Weibull Distribution 587
13.9.3 Dynamic Load Rating 590
13.9.4 Equivalent Dynamic Load 591
13.9.5 Life Adjustment Factors 591
13.10 Summary 603
Chapter 14
GEARS 613
14.1 Introduction 615
14.2 Types of Gear 615
14.2.1 Parallel-Axis Gears 615
14.2.2 Nonparallel, Coplanar Gears 617
14.2.3 Nonparallel, Noncoplanar Gears 617
14.3 Gear Geometry 619
14.3.1 Center Distance, Circular Pitch, and Diametral Pitch 619
14.3.2 Addendum, Dedendum,
and Clearance 623
14.3.3 Line of Action, Pressure Angle, and Gear Involute 624
14.4 Kinematics 627
14.5 Contact Ratio 628
14.6 Tooth Thickness, Backlash,
and Interference 632
14.7 Gear Trains 634
14.7.1 Single Gear Mesh 634
14.7.2 Simple Spur Gear Trains 635
14.7.3 Compound Spur Gear Trains 636
14.8 Gear Materials and Allowable Stresses 638
14.9 Loads Acting on a Gear Tooth 639
14.10 Bending Stresses in Gear Teeth 640
14.10.1 Application Factor 643
14.10.2 Size Factor 644
14.10.3 Load Distribution Factor 644
14.10.4 Dynamic Factor 644
14.11 Contact Stresses in Gears 646
14.12 Elastohydrodynamic Film Thickness 648
14.13 Helical Gears 650
14.13.1 Helical Gear Relationships 651
14.13.2 Pitches of Helical Gears 651
14.13.3 Equivalent Number of Teeth and Pressure Angle 652
14.13.4 Helical Tooth Proportions 652
14.13.5 Loads and Stresses 653
14.14 Summary 656
Chapter 15
FASTENERS AND POWER SCREWS 665
15.1 Introduction 667
15.2 Thread Terminology, Classification,
and Designation 667
15.3 Power Screws 670
15.3.1 Forces and Torque 672
15.3.2 Power and Efficiency 675
15.3.3 Self-Locking Screws 677
15.4 Threaded Fasteners 679
15.4.1 Types of Threaded Fastener 679
15.4.2 Load Analysis of Bolts and Nuts 680
15.4.3 Stiffness Parameters 681
15.4.4 Strength 686
15.4.5 Bolt Preload-Static Loading 688
15.4.6 Bolt Preload-Dynamic Loading 691
15.4.7 Gasketed Joints 693
15.5 Riveted Fasteners 694
15.6 Welded Joints 701
15.6.1 Parallel and Transverse Loading 702
15.6.2 Torsional Loading 702
15.6.3 Bending 704
15.6.4 Weld Strength 705
15.6.5 Fatigue Strength of Welds 708
15.7 Adhesive Bonding 709
15.8 Integrated Snap Fasteners 713
15.9 Summary 719
Chapter 16
SPRINGS 735
16.1 Introduction 736
16.2 Spring Materials 737
16.3 Helical Compression Springs 741
16.3.1 Torsional Shear Stress 742
16.3.2 Transverse Shear Stress 742
16.3.3 Combined Torsional and Transverse Shear Stresses 742
16.3.4 Deflection 744
16.3.5 End Conditions and Spring Length 745
16.3.6 Buckling and Surge 748
16.3.7 Cyclic Loading 751
16.4 Helical Extension Springs 755
16.5 Helical Torsion Springs 760
16.6 Leaf Springs 765
16.7 Belleville Springs 768
16.8 Summary 772
Chapter 17
BRAKES AND CLUTCHES 781
17.1 Introduction 782
17.2 Thrust Disk Clutches 784
17.2.1 Uniform Pressure Model 784
17.2.2 Uniform Wear Model 785
17.3 Cone Clutches 788
17.3.1 Uniform Pressure Model 789
17.3.2 Uniform Wear Model 790
17.4 Block, or Short-Shoe, Brakes 791
17.5 Long-Shoe, Internal, Expanding
Rim Brakes 794
17.5.1 Self-Energizing Shoe 796
17.5.2 Deenergizing Shoe 797
17.6 Long-Shoe, External, Contracting
Rim Brakes 801
17.7 Symmetrically Loaded Pivot-Shoe
Brakes 803
17.8 Band Brakes 807
17.9 Slip Clutches 810
17.10 Temperature Considerations 810
17.11 Summary 814
Chapter 18
FLEXIBLE MACHINE ELEMENTS 826
18.1 Introduction 827
18.2 Flat Belts 827
18.2.1 Belt Length 828
18.2.2 Belt Forces 829
18.2.3 Slip 832
18.3 Synchronous Belts 832
18.4 V-Belts 833
18.4.1 Input Normal Power Rating 835
18.4.2 Drive Size 836
18.4.3 Arc Correction Factor 836
18.4.4 Design Power Rating and Center
Distance 837
18.5 Wire Ropes 841
18.5.1 Tensile Stress 842
18.5.2 Bending Stress 844
18.5.3 Bearing Pressure 845
18.5.4 Fatigue 846
18.6 Rolling Chains 849
18.6.1 Operation of Rolling Chains 849
18.6.2 Kinematics 850
18.6.3 Chordal Rise 851
18.6.4 Chain Length 851
18.6.5 Power Rating 852
18.6.6 Selection of Sprocket Size and Center
Distance 854
18.7 Summary 858
Chapter 19
DESIGN PROJECTS 867
19.1 Introduction 869
19.2 Design of Vertical Mixer 869
19.2.1 Kinematics of Agitator Gears 871
19.2.2 Power Transmission System 873
19.2.3 Further Notes 874
19.3 Roller Coaster Braking System 874
19.3.1 Brake Pad-Fin Interaction 875
19.3.2 Brake Actuation System 877
19.3.3 Cylinder Mounting Bolts 880
19.4 Car Brake Dimensioning 881
19.4.1 Deceleration and Braking Force 882
19.4.2 Brake Dimensions 885
19.4.3 Self-Locking 888
19.5 Summary 888
Appendix A
MATERIAL PROPERTIES 899
Appendix B
STRESS-STRAIN RELATIONSHIPS 904
B.1 Laws of Stress Transformation 904
B.2 Laws of Strain Transformation 906
B.3 Hooke's Law Generalized 906
B.4 Physical Significance of Elastic Material
Constants 915
B.5 Stress-Strain Equations in Terms of Modulus
of Elasticity and Poisson's Ratio 918
B.6 Summary 921
Index 923
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