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Mechanical Engineer’s Handbook
J. David Irwin
Department of Mechanical Engineering, Auburn University, Auburn, Alabama
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Table of Contents
Preface . xiii
Contributors xv
CHAPTER 1 Statics
Dan B. Marghitu, Cristian I. Diaconescu, and Bogdan O. Ciocirlan
1. Vector Algebra 2
1.1 Terminology and Notation 2
1.2 Equality . 4
1.3 Product of a Vector and a Scalar 4
1.4 Zero Vectors 4
1.5 Unit Vectors 4
1.6 Vector Addition 5
1.7 Resolution of Vectors and Components 6
1.8 Angle between Two Vectors . 7
1.9 Scalar (Dot) Product of Vectors . 9
1.10 Vector (Cross) Product of Vectors 9
1.11 Scalar Triple Product of Three Vectors 11
1.12 Vector Triple Product of Three Vectors 11
1.13 Derivative of a Vector . 12
2. Centroids and Surface Properties 12
2.1 Position Vector 12
2.2 First Moment . 13
2.3 Centroid of a Set of Points 13
2.4 Centroid of a Curve, Surface, or Solid . 15
2.5 Mass Center of a Set of Particles 16
2.6 Mass Center of a Curve, Surface, or Solid 16
2.7 First Moment of an Area 17
2.8 Theorems of Guldinus–Pappus . 21
2.9 Second Moments and the Product of Area 24
2.10 Transfer Theorem or Parallel-Axis Theorems 25
2.11 Polar Moment of Area . 27
2.12 Principal Axes . 28
3. Moments and Couples . 30
3.1 Moment of a Bound Vector about a Point 30
3.2 Moment of a Bound Vector about a Line . 31
3.3 Moments of a System of Bound Vectors . 32
3.4 Couples . 34
v3.5 Equivalence 35
3.6 Representing Systems by Equivalent Systems 36
4. Equilibrium . 40
4.1 Equilibrium Equations 40
4.2 Supports . 42
4.3 Free-Body Diagrams . 44
5. Dry Friction . 46
5.1 Static Coefficient of Friction 47
5.2 Kinetic Coefficient of Friction . 47
5.3 Angles of Friction . 48
References . 49
CHAPTER 2 Dynamics
Dan B. Marghitu, Bogdan O. Ciocirlan, and Cristian I. Diaconescu
1. Fundamentals . 52
1.1 Space and Time 52
1.2 Numbers 52
1.3 Angular Units . 53
2. Kinematics of a Point 54
2.1 Position, Velocity, and Acceleration of a Point 54
2.2 Angular Motion of a Line 55
2.3 Rotating Unit Vector . 56
2.4 Straight Line Motion . 57
2.5 Curvilinear Motion 58
2.6 Normal and Tangential Components 59
2.7 Relative Motion 73
3. Dynamics of a Particle 74
3.1 Newton’s Second Law 74
3.2 Newtonian Gravitation . 75
3.3 Inertial Reference Frames . 75
3.4 Cartesian Coordinates 76
3.5 Normal and Tangential Components 77
3.6 Polar and Cylindrical Coordinates 78
3.7 Principle of Work and Energy 80
3.8 Work and Power . 81
3.9 Conservation of Energy . 84
3.10 Conservative Forces . 85
3.11 Principle of Impulse and Momentum 87
3.12 Conservation of Linear Momentum . 89
3.13 Impact 90
3.14 Principle of Angular Impulse and Momentum 94
4. Planar Kinematics of a Rigid Body 95
4.1 Types of Motion . 95
4.2 Rotation about a Fixed Axis 96
4.3 Relative Velocity of Two Points of the Rigid Body . 97
4.4 Angular Velocity Vector of a Rigid Body 98
4.5 Instantaneous Center . 100
4.6 Relative Acceleration of Two Points of the Rigid Body . 102
vi Table of Contents4.7 Motion of a Point That Moves Relative to a Rigid Body 103
5. Dynamics of a Rigid Body 111
5.1 Equation of Motion for the Center of Mass . 111
5.2 Angular Momentum Principle for a System of Particles . 113
5.3 Equation of Motion for General Planar Motion 115
5.4 D’Alembert’s Principle 117
References 117
CHAPTER 3 Mechanics of Materials
Dan B. Marghitu, Cristian I. Diaconescu, and Bogdan O. Ciocirlan
1. Stress . 120
1.1 Uniformly Distributed Stresses . 120
1.2 Stress Components 120
1.3 Mohr’s Circle 121
1.4 Triaxial Stress 125
1.5 Elastic Strain . 127
1.6 Equilibrium . 128
1.7 Shear and Moment 131
1.8 Singularity Functions . 132
1.9 Normal Stress in Flexure . 135
1.10 Beams with Asymmetrical Sections 139
1.11 Shear Stresses in Beams . 140
1.12 Shear Stresses in Rectangular Section Beams . 142
1.13 Torsion 143
1.14 Contact Stresses 147
2. Deflection and Stiffness 149
2.1 Springs 150
2.2 Spring Rates for Tension, Compression, and Torsion 150
2.3 Deflection Analysis 152
2.4 Deflections Analysis Using Singularity Functions . 153
2.5 Impact Analysis . 157
2.6 Strain Energy 160
2.7 Castigliano’s Theorem 163
2.8 Compression 165
2.9 Long Columns with Central Loading . 165
2.10 Intermediate-Length Columns with Central Loading . 169
2.11 Columns with Eccentric Loading . 170
2.12 Short Compression Members 171
3. Fatigue 173
3.1 Endurance Limit 173
3.2 Fluctuating Stresses 178
3.3 Constant Life Fatigue Diagram . 178
3.4 Fatigue Life for Randomly Varying Loads 181
3.5 Criteria of Failure . 183
References 187
Table of Contents viiCHAPTER 4 Theory of Mechanisms
Dan B. Marghitu
1. Fundamentals 190
1.1 Motions 190
1.2 Mobility 190
1.3 Kinematic Pairs . 191
1.4 Number of Degrees of Freedom 199
1.5 Planar Mechanisms . 200
2. Position Analysis . 202
2.1 Cartesian Method 202
2.2 Vector Loop Method 208
3. Velocity and Acceleration Analysis . 211
3.1 Driver Link 212
3.2 RRR Dyad . 212
3.3 RRT Dyad . 214
3.4 RTR Dyad . 215
3.5 TRT Dyad . 216
4. Kinetostatics . 223
4.1 Moment of a Force about a Point . 223
4.2 Inertia Force and Inertia Moment . 224
4.3 Free-Body Diagrams 227
4.4 Reaction Forces . 228
4.5 Contour Method 229
References 241
CHAPTER 5 Machine Components
Dan B. Marghitu, Cristian I. Diaconescu, and Nicolae Craciunoiu
1. Screws . 244
1.1 Screw Thread 244
1.2 Power Screws 247
2. Gears 253
2.1 Introduction . 253
2.2 Geometry and Nomenclature 253
2.3 Interference and Contact Ratio . 258
2.4 Ordinary Gear Trains . 261
2.5 Epicyclic Gear Trains . 262
2.6 Differential 267
2.7 Gear Force Analysis 270
2.8 Strength of Gear Teeth 275
3. Springs . 283
3.1 Introduction . 283
3.2 Material for Springs 283
3.3 Helical Extension Springs 284
3.4 Helical Compression Springs 284
3.5 Torsion Springs . 290
3.6 Torsion Bar Springs 292
3.7 Multileaf Springs 293
3.8 Belleville Springs 296
viii Table of Contents4. Rolling Bearings . 297
4.1 Generalities . 297
4.2 Classification 298
4.3 Geometry . 298
4.4 Static Loading 303
4.5 Standard Dimensions . 304
4.6 Bearing Selection . 308
5. Lubrication and Sliding Bearings 318
5.1 Viscosity . 318
5.2 Petroff’s Equation . 323
5.3 Hydrodynamic Lubrication Theory 326
5.4 Design Charts 328
References 336
CHAPTER 6 Theory of Vibration
Dan B. Marghitu, P. K. Raju, and Dumitru Mazilu
1. Introduction . 340
2. Linear Systems with One Degree of Freedom . 341
2.1 Equation of Motion 342
2.2 Free Undamped Vibrations . 343
2.3 Free Damped Vibrations . 345
2.4 Forced Undamped Vibrations . 352
2.5 Forced Damped Vibrations . 359
2.6 Mechanical Impedance 369
2.7 Vibration Isolation: Transmissibility 370
2.8 Energetic Aspect of Vibration with One DOF . 374
2.9 Critical Speed of Rotating Shafts 380
3. Linear Systems with Finite Numbers of Degrees of Freedom . 385
3.1 Mechanical Models 386
3.2 Mathematical Models . 392
3.3 System Model 404
3.4 Analysis of System Model 405
3.5 Approximative Methods for Natural Frequencies . 407
4. Machine-Tool Vibrations . 416
4.1 The Machine Tool as a System 416
4.2 Actuator Subsystems . 418
4.3 The Elastic Subsystem of a Machine Tool . 419
4.4 Elastic System of Machine-Tool Structure 435
4.5 Subsystem of the Friction Process . 437
4.6 Subsystem of Cutting Process . 440
References 444
CHAPTER 7 Principles of Heat Transfer
Alexandru Morega
1. Heat Transfer Thermodynamics 446
1.1 Physical Mechanisms of Heat Transfer: Conduction, Convection,
and Radiation 451
Table of Contents ix1.2 Technical Problems of Heat Transfer . 455
2. Conduction Heat Transfer 456
2.1 The Heat Diffusion Equation 457
2.2 Thermal Conductivity . 459
2.3 Initial, Boundary, and Interface Conditions . 461
2.4 Thermal Resistance 463
2.5 Steady Conduction Heat Transfer . 464
2.6 Heat Transfer from Extended Surfaces (Fins) . 468
2.7 Unsteady Conduction Heat Transfer . 472
3. Convection Heat Transfer . 488
3.1 External Forced Convection . 488
3.2 Internal Forced Convection . 520
3.3 External Natural Convection . 535
3.4 Internal Natural Convection . 549
References 555
CHAPTER 8 Fluid Dynamics
Nicolae Craciunoiu and Bogdan O. Ciocirlan
1. Fluids Fundamentals 560
1.1 Definitions 560
1.2 Systems of Units 560
1.3 Specific Weight . 560
1.4 Viscosity 561
1.5 Vapor Pressure . 562
1.6 Surface Tension . 562
1.7 Capillarity . 562
1.8 Bulk Modulus of Elasticity 562
1.9 Statics . 563
1.10 Hydrostatic Forces on Surfaces . 564
1.11 Buoyancy and Flotation . 565
1.12 Dimensional Analysis and Hydraulic Similitude 565
1.13 Fundamentals of Fluid Flow . 568
2. Hydraulics . 572
2.1 Absolute and Gage Pressure 572
2.2 Bernoulli’s Theorem 573
2.3 Hydraulic Cylinders 575
2.4 Pressure Intensifiers 578
2.5 Pressure Gages . 579
2.6 Pressure Controls 580
2.7 Flow-Limiting Controls 592
2.8 Hydraulic Pumps 595
2.9 Hydraulic Motors 598
2.10 Accumulators 601
2.11 Accumulator Sizing . 603
2.12 Fluid Power Transmitted . 604
2.13 Piston Acceleration and Deceleration . 604
2.14 Standard Hydraulic Symbols 605
2.15 Filters 606
x Table of Contents2.16 Representative Hydraulic System . 607
References 610
CHAPTER 9 Control
Mircea Ivanescu
1. Introduction . 612
1.1 A Classic Example . 613
2. Signals . 614
3. Transfer Functions . 616
3.1 Transfer Functions for Standard Elements . 616
3.2 Transfer Functions for Classic Systems . 617
4. Connection of Elements . 618
5. Poles and Zeros . 620
6. Steady-State Error . 623
6.1 Input Variation Steady-State Error . 623
6.2 Disturbance Signal Steady-State Error 624
7. Time-Domain Performance . 628
8. Frequency-Domain Performances . 631
8.1 The Polar Plot Representation . 632
8.2 The Logarithmic Plot Representation . 633
8.3 Bandwidth 637
9. Stability of Linear Feedback Systems . 639
9.1 The Routh–Hurwitz Criterion 640
9.2 The Nyquist Criterion . 641
9.3 Stability by Bode Diagrams . 648
10. Design of Closed-Loop Control Systems by Pole-Zero Methods . 649
10.1 Standard Controllers 650
10.2 P-Controller Performance 651
10.3 Effects of the Supplementary Zero 656
10.4 Effects of the Supplementary Pole 660
10.5 Effects of Supplementary Poles and Zeros . 661
10.6 Design Example: Closed-Loop Control of a Robotic Arm . 664
11. Design of Closed-Loop Control Systems by Frequential Methods 669
12. State Variable Models . 672
13. Nonlinear Systems . 678
13.1 Nonlinear Models: Examples 678
13.2 Phase Plane Analysis . 681
13.3 Stability of Nonlinear Systems . 685
13.4 Liapunov’s First Method . 688
13.5 Liapunov’s Second Method . 689
14. Nonlinear Controllers by Feedback Linearization . 691
15. Sliding Control . 695
15.1 Fundamentals of Sliding Control . 695
15.2 Variable Structure Systems . 700
A. Appendix . 703
A.1 Differential Equations of Mechanical Systems . 703
Table of Contents xiA.2 The Laplace Transform 707
A.3 Mapping Contours in the s-Plane . 707
A.4 The Signal Flow Diagram 712
References 714
APPENDIX Differential Equations and Systems of Differential
Equations
Horatiu Barbulescu
1. Differential Equations . 716
1.1 Ordinary Differential Equations: Introduction . 716
1.2 Integrable Types of Equations . 726
1.3 On the Existence, Uniqueness, Continuous Dependence on a
Parameter, and Differentiability of Solutions of Differential
Equations . 766
1.4 Linear Differential Equations 774
2. Systems of Differential Equations 816
2.1 Fundamentals 816
2.2 Integrating a System of Differential Equations by the
Method of Elimination 819
2.3 Finding Integrable Combinations . 823
2.4 Systems of Linear Differential Equations . 825
2.5 Systems of Linear Differential Equations with Constant
Coefficients 835
References 845
Index

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