Tài liệu Mechanical Engineer''''s Handbook potx

Mechanical Engineer's Handbook

Academic Press Series in Engineering

Series Editor

J. David Irwin

Auburn University

This a series that will include handbooks, textbooks, and professional reference

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The series editor, J. David Irwin, is one of the best-known engineering educators in

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Published books in this series:

Control of Induction Motors

2001, A. M. Trzynadlowski

Embedded Microcontroller Interfacing for McoR Systems

2000, G. J. Lipovski

Soft Computing & Intelligent Systems

2000, N. K. Sinha, M. M. Gupta

Introduction to Microcontrollers

1999, G. J. Lipovski

Industrial Controls and Manufacturing

1999, E. Kamen

DSP Integrated Circuits

1999, L. Wanhammar

Time Domain Electromagnetics

1999, S. M. Rao

Single- and Multi-Chip Microcontroller Interfacing

1999, G. J. Lipovski

Control in Robotics and Automation

1999, B. K. Ghosh, N. Xi, and T. J. Tarn

Mechanical

Engineer's

Handbook

Edited by

Dan B. Marghitu

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

v

3.5 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 Coef®cient of Friction . . . . . . . . . . . . . . . . . . . . . . . . . . 47

5.2 Kinetic Coef®cient 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 Contents

4.7 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. De¯ection and Stiffness. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149

2.1 Springs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

2.2 Spring Rates for Tension, Compression, and Torsion . . . . . . . . 150

2.3 De¯ection Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

2.4 De¯ections 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 vii

CHAPTER 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 Contents

4. Rolling Bearings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

4.1 Generalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

4.2 Classi®cation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 ix

1.2 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 De®nitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

1.2 Systems of Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

1.3 Speci®c 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 Intensi®ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 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 Contents

2.16 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 xi

A.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

Coef®cients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 835

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 845

Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 847

xii Table of Contents

Preface

The purpose of this handbook is to present the reader with a teachable text

that includes theory and examples. Useful analytical techniques provide the

student and the practitioner with powerful tools for mechanical design. This

book may also serve as a reference for the designer and as a source book for

the researcher.

This handbook is comprehensive, convenient, detailed, and is a guide

for the mechanical engineer. It covers a broad spectrum of critical engineer￾ing topics and helps the reader understand the fundamentals.

This handbook contains the fundamental laws and theories of science

basic to mechanical engineering including controls and mathematics. It

provides readers with a basic understanding of the subject, together with

suggestions for more speci®c literature. The general approach of this book

involves the presentation of a systematic explanation of the basic concepts of

mechanical systems.

This handbook's special features include authoritative contributions,

chapters on mechanical design, useful formulas, charts, tables, and illustra￾tions. With this handbook the reader can study and compare the available

methods of analysis. The reader can also become familiar with the methods

of solution and with their implementation.

Dan B. Marghitu

xiii

Contributors

Numbers in parentheses indicate the pages on which the authors' contribu￾tions begin.

Horatiu Barbulescu, (715) Department of Mechanical Engineering,

Auburn University, Auburn, Alabama 36849

Bogdan O. Ciocirlan, (1, 51, 119, 559) Department of Mechanical Engi￾neering, Auburn University, Auburn, Alabama 36849

Nicolae Craciunoiu, (243, 559) Department of Mechanical Engineering,

Auburn University, Auburn, Alabama 36849

Cristian I. Diaconescu, (1, 51, 119, 243) Department of Mechanical

Engineering, Auburn University, Auburn, Alabama 36849

Mircea Ivanescu, (611) Department of Electrical Engineering, University

of Craiova, Craiova 1100, Romania

Dan B. Marghitu, (1, 51, 119, 189, 243, 339) Department of Mechanical

Engineering, Auburn University, Auburn, Alabama 36849

Dumitru Mazilu, (339) Department of Mechanical Engineering, Auburn

University, Auburn, Alabama 36849

Alexandru Morega, (445) Department of Electrical Engineering, ``Politeh￾nica'' University of Bucharest, Bucharest 6-77206, Romania

P. K. Raju, (339) Department of Mechanical Engineering, Auburn Univer￾sity, Auburn, Alabama 36849

xv