اسم المؤلف
Dan B. Marghitu
التاريخ
6 سبتمبر 2018
المشاهدات
206
التقييم

Mechanical Engineer’s Handbook
Edited by
Dan B. Marghitu
Department of Mechanical Engineering, Auburn University, Auburn, Alabama
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
1.7 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
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
2.12 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
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
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
1.2 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
4.1 Generalities . 297
4.2 Classification 298
4.3 Geometry . 298
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,
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
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
6.1 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
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 847
Index
A
ABEC grade. See Annular Bearing Engineers’
Committee
Absolute temperature scales, 449
Absorption, of heat, 454, 466
Acceleration
analysis of, 211–222
angular, 55, 71
centripetal, 72
Coriolis, 72
defined, 52
normal, 78
of a point, 54–55
tangential component, 61, 78
velocity and, 211–222
Accumulators, fluid, 601–604
Action-reaction. See Newton’s laws of motion,
third law
AFBMA. See Anti-Friction Bearing Manufacturers
Association
AGMA number. See American Gear Manufacturers
Association
American Gear Manufacturers Association
(AGMA), 253
class number, 260
Analytic functions, 807–808
Angles
angular units, 53–54
degrees of, 54
of friction, 47–49
between vectors, 7
Angular acceleration, 55, 71
Angular frequency, 341
Angular impulse, 95
Angular momentum, 94
derivative of, 398
principle of, 113–115
Angular units, 53–54
Angular velocity
diagrams of, 269–270
of rigid body, 98–99
Annular Bearing Engineers’ Committee (ABEC)
Anti-Friction Bearing Manufacturers Association
(AFBMA), 304
Arc length, 68
Archimedes’ principle, 565
Area
axis of symmetry, 18
centroids, 17–20, 25
composite, 19
first moment, 17–21
parallel-axis theorem, 27
polar moment, 27–28
principal axes, 28–30
product of, 24, 27, 30
second moments, 24–25
surface properties, 17–20
Associative law, 6
Asymptotic boundary conditions, 461–462
Automotive differential, 267–268
Autonomous systems, 686
Axes
centroidal, 17–20, 25
orthogonal, 19, 76–77
principal, 28–30
of symmetry, 18–19, 24
Axial piston pump, 598
B
Backlash, 679
Ball and beam problem, 697–699
Ball-and-socket supports, 44
Bandwidth, 637–638
Barometer, 564
Base point, 36
847Beams
asymmetric sections, 139–140
bending moment, 131–132, 175
cantilevered, 134, 156, 164, 184–185, 760
channel, 177
cross-sections, 176–177
deflection of. See Deflection analysis
endurance limit, 173
fatigue analysis, 173–187
Gerber criterion, 186
Goodman lines, 178–179, 183–185
I-beams, 176
Moore tests, 173–175
rectangular, 177
shear stresses, 140–142
size factor, 176
S–N diagrams for, 173
Soderberg criterion, 183–185
strain in, 160–163
stress in, 139–143, 184
web section, 177
Bearings
ball-raceway contact, 301
characteristic number, 325
contact angle, 303
fatigue life, 310
free contact angle, 302
free endplay, 301
life requirement, 309–311
lubrication of, 318–336
misalignment angle, 302
rated capacity, 309
reliability factor, 310–311
rolling, 297–318
selection of, 317
self-aligning, 304
sliding, 297, 318–336
standard life, 310
tapered, 304
total curvature of, 302
Beat phenomenon, 355
Beat transfer, 446
Belleville springs, 296–297
Belts, 253
Bending, 175
moment, 131, 132
shear force, 131–132
singularity functions, 132
stress, 284, 295
vibration and, 393
Berkovsky-Polevikov correlation, 551
Bernoulli equation, 519–521, 572–574, 749
Bernoulli’s theorem, 573–575
Bessel equation, 798, 800, 802, 811, 813
Bessel functions, 482, 799, 813
BHN. See Brinell hardness number
Big-bang controller, 684
Bilocal problem, 801
Binomial vector, 69–70
Biot numbers, 475, 478
Blackbody, 454
Blasius number, 512
Blasius solution, 521–522
Bode diagrams, 415, 633, 648–649, 659
Body forces, 494
Boiling, 454
Bolts, 244
Boring machine, 432
systems
Boundary layer
assumptions, 503
equations for, 538
heat transfer and, 490, 502–505, 513
hydrodynamic, 490
laminar flow, 491–492
momentum equation, 504
scale analysis of, 505–508
shape factor, 506
similarity solutions for, 512–516
streamlines, 491
transition zone, 492
turbulent flow, 491–492
types of, 491
Boundary-value problem, 153, 802–807
Bound vectors, 30–36
Bourdon gage, 579
Boussinesq equation, 541
Break frequency, 635
Brinell hardness number (BHN), 279
British engineering units, 560
Brownian motion, 456
Buckingham equation, 278
Bulk modulus of elasticity, 562
Bulk temperature, 452–453
Buoyancy, 565
Buoyancy-friction balance, 540
Buoyancy-inertia balance, 541
Burnout, 518
C
Cantilevered beam, 134, 156, 164, 184–185, 760
Capacitive thermal analysis, 476–477
Capillarity, 562
Cartesian coordinates, 7, 58, 70, 76–77
848 IndexCartesian method, 202–208
Castigliano’s theorem, 163–165, 286, 390
Cauchy number, 567
Cauchy problem, 438, 717, 817
Cauchy’s function, 784–785, 788
Celsius scale, 449
Center, instantaneous, 100–101
Center of mass, 111–113
Central axis, 33
Centripetal acceleration, 72
Centroid, 12–22
area moment and, 17–20
axes and, 18, 25
cartesian coordinates of, 15
decomposition, method of, 15
first moment, 13, 17–20
Guldinus-Pappus theorems, 21–23
mass center and, 16
parallel-axis theorems, 25–26
points and, 13–15
polar moment, 27
position vector, 12
principal axes, 28–29
product of area, 24
second moments, 24
solid, 15
statics and, 12–28
surface properties, 13–15
symmetry and, 18
transfer theorems, 25–26
Chains
belts and, 253
complex, 198
kinematic, 197
simple, 198
sliding, 764
Channel section, 176
Characteristic functions, 677, 789
eigenvalues, 683–685
roots of, 351, 836–838
polynomial, 414–415
Characteristic length, 475
Chatter, 582
Chebyshev equation, 795–796, 800
Chebyshev polynomials, 796
Check valves, 592–594
Churning loss, 308
Circular angular speed, 380
Circular frequency, 341
Circular motion, 64–65
Circumferential tension, 564
Clairaut equation, 758
Closed-loop systems, 613, 649–672
Columns, 169–171
Commutative law, 6
Companion form, 692, 695
Comparison equations, 802
Complementary error function, 487
Complete integrals, 720
Complex general motion, 190
Component vectors, 7–8
Components, of machines, 243–328
Composite areas, 19
Compound relief valves, 588–590
Compression, 150–152, 165
Compression effect, 495
Concurrent forces, 37
Condensation, 454
Conduction, heat, 446, 448, 451–472
boundary conditions, 461–462
films, 452
fins and, 468–471
heat transfer, 456–458
initial conditions, 461–462
interface conditions, 461–462
semi-infinite solid bodies, 487
thermal conductivity, 452, 458–461
thermal resistance, 463
Conjugate gear, 254
Conservation effects
of energy, 84–85, 447
forces and, 85–87
of linear momentum, 89–90
of mass, 568
systems 375
Constant life fatigue diagram, 178–181
Contact ratio, gears, 258–261
Contact stresses, 147–149
Continuity equation, 493, 503, 569
Contour equation method, 269
Contour, in structure, 197
Contour mapping, 707–712
Contour method, 229–241
Control surface, 447
Control theory
bandwidth, 637–638
Bode diagrams, 648
closed-loop systems, 649–672
connection of elements, 618–619
feedback linearization, 691–694
frequency-domain performance, 631–639
frequential methods, 669–672
Index 849Control theory (continued)
Laplace transform, 707
linear feedback systems, 639–649
Lipaunov method, 688–689
logarithmic plots, 633–636
nonlinear systems, 678–695
Nyquist criterion, 641–647
P-controller performance, 651–655
polar plot, 632
pole-zero methods, 620, 649–669
robotic arm, 664–668
Routh–Hurwitz criterion, 640
signal flow diagram, 712–714
signals and, 613–615
sliding controls, 695–700
stability and, 639–649
standard controllers, 650
state variable models, 672–677
time-domain performance, 628–631
transfer functions, 616–618
Control volume, 447, 494–499
Controls, hydraulic, 580–594
Convection, heat, 446, 448, 451–454, 488–549
external forced, 488–520
external natural, 535–549
free, 535
heat transfer and, 488–555
heat transfer coefficient, 489
internal flow, 452
internal forced, 520–535
thermal boundary layer, 490
types of, 452
Cooling, Newton’s law of, 730
Cooling problem, 455
Coordinate systems, 95
cartesian, 58
cylindrical, 72–73
polar, 70
principal systems of, 459
Coriolis force, 72, 106, 109
Cosmic velocity, 725
Coulomb friction, 46–49, 346, 437
Coulombian damping, 391
Counterbalance valves, 587
Coupler, defined, 198
Couples
bound vectors and, 34
equivalent systems, 36–39
force and, 37
moments and, 30–40
simple, 34
statics and, 34–36
torque of, 34
Cracking pressure, 580
Cramer criteria, 415
Crank, defined, 146, 198
Crank slider mechanism, 227–228
Critical damping, 631
Cross product, 9–10, 223
Cryogenic systems, 446
Curl, 87, 502
Curvature, 15–17
correction factor, 286
definition of, 136
differential equation for, 720–721
envelope of, 758, 772
force and, 564
of plane curve, 152
of surface, 15–17
Curvilinear motion, 58–59
Cutting process, 440–444
Cylinders, 482, 575–577
Cylindrical bar, 481
Cylindrical coordinates, 72–73, 78–80, 87
D
D’Alembert’s principle, 364
Newton’s second law and, 226
rigid body and, 117
Damping
arbitrary, 346
coefficients of, 418, 435
complex, 391
Coulombian, 391
critical, 352, 631
damping ratio, 348
differential equations for, 705
dry, 345–347
electric motors, 418
energy dissipated, 390
external, 390–391
internal, 391
linear, 391
matrix, 403
Newton’s second law, 342
order, 629
oscillation decay, 351
overdamped system, 631
parametric, 391
transmissibility and, 371–372
underdamped system, 631
of vibrations, 343–359
viscous, 345, 347–352, 391, 398
850 IndexDams, forces on, 564
Dean–Davis scale, 322
Decay phenomena, 723, 730
Decomposition method, 15–17
Deflection analysis
beams and, 131–132, 152–153, 163, 726
Castigliano’s theorem, 163–164, 286
columns and, 165–171
compression and, 165
compression members, 171
deformation and, 3, 160–163, 389
expression for, 157
impact analysis, 157–159
maximum values, 158
springs and, 150–151
stiffness, 149–172
strain energy, 160–162
Degrees of freedom, 190
coordinates and, 193
finite, 385
kinematic pairs, 199
number of, 199–200
Delay term, 459
Denavit–Hartenberg algorithm, 680
Derivative vectors, 12
Determinants, 11
Diametral clearance, 300
Diametral pitch, 257
Difference, of vectors, 5
Differential, automotive, 267–268
Differential equations
constant coefficients in, 835–837
existence of solutions, 766
integrable, 726–766, 823–824
linear, 744–814, 825–837
method of elimination, 819–822
ordinary equations, 716–726
systems of, 816–837
uniqueness of solutions, 766
Differentials, gears, 267–270
Diffusion processes, 451
law of, 459
molecular, 457, 498
thermal, 457–459, 461, 488, 499
Dimensional analysis, 499, 565–567
Direct-operated relief valves, 580
Direct-way transfer function, 621
Dirichlet conditions, 358, 461–462
Discontinuity, surfaces of, 462
Dissipation, 398
Distance, of points, 13
Distortion-energy theory, 283
Distribution coefficients, 412
Distributive law, 6
Divergence, 493
Dobrovolski formula, 199
Dog trajectory, 724
Door hinges, 290
Dot product, 4, 9
Driver torque, 239
Dry damping, 345, 346–347
Dry friction, 46–49, 346, 391, 437
Duct flows, 528, 531–535
Ductile materials, 175
Duhamel integral, 368
RRR, 209, 212, 214
RRT, 205, 209
RTR, 209, 215
TRT, 216–222
Dynamics
angular impulse, 94
angular momentum prinicple, 113–114
angular motion, 55, 98–99
angular units, 53
cartesian coordinates, 76
center of mass, 111–112
conservation effects, 84–87
curvilinear motion, 58
cylindrical coordinates, 78–79
D’Alembert’s principle, 117
dynamical similitude, 567
energy and, 80
equations of motion, 115–116
impact, 90–93
impulse, 87–88
inertial reference frames, 75
instantaneous center, 100–101
kinematics of a point, 54–73
linear, 89
momentum, 87–89, 94
motion types, 95–96
Newtonian gravitation, 75
Newton’s laws. See Newton’s laws of motion
normal components, 59–72, 77
of particles, 74–94
planar kinematics, 94–110
polar coordinates, 78–79
power, 81–83
relative acceleration, 102
relative motion, 73
Index 851Dynamics (continued)
relative velocity, 97
of rigid body, 94–117
rotating unit vector, 56
straight line motion, 57
tangential components, 59–72, 77
work and, 81–83
E
Eckert solution, 519
Effective dimension, 176
Eigenvalues, 683, 685
Einstein’s theory of relativity, 75
Elasticity
constants of, 386–390, 435
Castigliano theorem, 163–165
deformation and, 3, 160–163, 389
impact and, 90–93
kinematics of, 419–429
modulus of, 128
springs and, 342
strain and, 127–128, 160–163
subsystems, 419–429
theory of, 726
Electric motors, 418, 425
Electrical oscillatory circuit, 725
Electronic gas, 460
Elimination, method of, 819
Emissivity, 454
Emulsions, 702
End conditions, 165, 168
Endurance limit, 173–177
Energy
balance, 496–499
conservation of, 84–85, 447
equation, 571
generation of, 445
kinetic, 81–84, 93, 396–397, 568
potential, 81–84, 160, 570
thermodynamics, 446–455
English units, 257–258
Enthalpy, 499, 507
Entrance region effects, 534–535
Entropy transfer, 449
Envelope, of curves, 758, 772
Epidemics, model of, 724
Equilibrium, 40–45, 128–131
body in, 40
conditions of, 40
equations of, 40–42
free-body diagrams, 44
Newton’s second law, 117
nonlinear systems, 687
static, 40–44, 129, 130
stress, 128–130
supports, 42–43
unstable, 167
Equivalence relations, 35–36
Equivalent systems, 35–40
ER fluids, 702
Escape-velocity problem, 763
Euler columns, 167–168
Euler gamma function, 812
Euler linear equations, 794
Euler number, 567
Euler’s equation, 341
Euler’s theorem, 99
Exact differential equations, 742
Existence, of solutions, 766, 770
Extended surfaces, 468–471
External convection, 535–549
External moments, 129
F
Fail-safe valves, 582
Falkner–Skan solution, 519
Family, of mechanisms, 199
Fatigue
endurance limit, 173–177
fatigue strengths, 175, 247
fluctuating stresses, 178
life fatigue diagram, 178–180
in materials, 173–187
Feedback, 613, 619, 691–694
Film coefficient, 452
Film conductance, 452
Film temperature, 539
Filters, hydraulic, 606–607
Finish, of surface, 175
Fins, 468–471
Fixed stars, 76
Fixed support, 43
Flexibility coefficient, 393
Flexible elements, 149
Flexure, 135–139
Float regulator, 613
Flotation, 565
Flow conditions, 519
Flow configurations, 549
Flow-limiting controls, 592–595
852 IndexFlow nets, 570
Fluctuating stresses, 173, 178
Fluid capacitance, 705
Fluid dynamics
absolute gage pressure, 572
Bernoulli’s theorem, 573–574
bulk modulus of elasticity, 562
buoyancy, 565
capillarity, 562
dimensional analysis, 565–567
filters, 606
flotation, 565
flow-limiting controls, 592–594
fluid characteristics, 560
fluid inertia, 705
fluid power transmitted, 604
gage pressure, 572
hydraulic cylinders, 575–577
hydraulic motors, 598–600
hydraulic similitude, 565–567
hydraulics, 572–607
hydrostatic forces, 564
piston motion, 604
pressure controls, 580–591
pumps, 595–597
representative system, 607
specific weight, 560
standard symbols, 605
statics, 563
surface tension, 562
vapor pressure, 562
viscosity, 561
Fourier law, 451, 458, 461, 469
Fourier number, 475
Fourier series, 358
Frame, 193
Free-body diagrams, 44–46, 131, 135, 156, 159,
227
Free convection, 535
Free-fixed ends, 165
Free vector, 3
Frenet formulas, 65–70
Frequency, 341, 349
Frequency-domain performances, 631–639
Frequential methods, 669–672
Friction
angles of, 47–49
coefficient of, 47–48, 346, 514
Coulomb’s law of, 346
dry, 46–49, 391, 437
friction factor, 525, 527
inclined plane, 46
kinetic angle of, 49
kinetic coefficient, 47–48
rolling, 438
sliding, 438–440
static coefficent, 47
statics and, 46–47
torque, 398
vibrations and, 437–439
Froude number, 567
Fully developed flow, 523–529
Functional equation, 716
Fundamental matrix, 829–830
G
g. See Gravitational constant
Gages, 572–574, 579
Gain margin, 648
Gamma function, 812
Gases
Brownian motion, 456
equation of state, 561
ideal, 451
perfect, 499
specific weights of, 561
Gauss error function, 487
Gear pumps, 595
Gears, 253–282
AGMA Class Number, 260
belts, 253
conjugate gear-tooth action, 254
contact ratio, 258–261
defined, 253
differentials, 267–270
epicycle trains, 262–265
force analysis, 270–275
heat treated, 260
idler, 261
interference, 258–261
mating, 255
ordinary trains, 261
pitch. See Pitch, gear
planetary train, 266, 272
power transmission efficiency, 253
spurs, 253, 425
strength of teeth, 275–282
tooth geometry, 253–258, 278
General motion, 190
Generalized coordinates, 399
Generating curve, 21
Geometric similitude, 566
Gerber criteria, 183
Gerotor pumps, 595–596
Goodman diagrams, 178, 183–185
Grammian, of system, 776–777
Grashof number, 541
Index 853Gravitational constant (g), 75
Gravitational pendulum, 679
Gray surface, 454
Grease, 321
Green’s function, 804–807
Ground, defined, 193, 198
Growth phenomena, 723
Guldinus–Pappus theorems, 21–23
Gyration, 24
Gyroscopic effects, 383
H
Hagen-Poiseuille flows, 524, 526, 531, 550
Harmonic motion, 340, 345, 352, 358, 385
Heat transfer
absorption, 454, 466
Bessel functions, 482
boundary layers, 490, 502–505, 513
buoyancy-inertia balance, 541
capacitive thermal analysis, 476–477
coefficient of, 452, 489, 505
conduction, 451–454, 456–472
convection, 451–454, 488–555
cylindrical, 481–482
differential heating, 551–553
duct flows, 528, 531–535
entrance region, 534–535
equation for, 457–459
extended surfaces, 468–471
external natural, 535–549
fins, 468–471
flow conditions, 519
flow configurations, 549
flux density, 446
fully developed flow, 523–525, 528–529
heat diffusion equation, 457–458
heat function, 502
hydrodynamic entrance length, 521–523
inclined walls, 546
initial conditions, 461–462
integral method, 508–512
interface, 461–462
internal forced, 520–535
isotherms, 502, 516, 546–548
lumped capacitance method, 472–474
mechanisms of, 446
nonuniform temperature, 517
one-dimensional geometry, 481
plates, 516
pressure drop, 525–528
principles of, 445–555
rate, 455
reservoirs, 464
scale analysis, 539–541
similarity solutions, 512–516
spherical, 482
streamlines, 501–502
technical problems of, 455
thermal boundary layer, 490–491, 537–539
thermal conductivity, 459–460
thermal diffusion, 448, 461, 499
thermal resistance, 463
thermodynamics, 446–455
total, 447
turbulence, 543–544
uniform heat flux, 518
vertical wall, 542–543, 545–546
walls, 546–548
wide cavity case, 551
work rates, 447
Heisler charts, 479
Helical spring, 285
Hertzian stresses, 147
Holomorphic function, 807–808
Holzer method, 407, 409–411
Homogeneous equations, 737, 740, 774
Homogeneous plane wall, 465
Hook stresses, 284
Hooke models, 407–411, 417, 435, 441
Hooke’s law, 128, 135
Hoop tension, 564
Hurwitz criterion, 415
Hydraulics
absolute gage pressure, 572
accumulators, 601–604
actuators, 679
Bernoulli equation, 573–574
circuit symbols, 605–608
cylinders, 575–577
filters, 606
flow-limiting controls, 592–594
fluid dynamics, 572–607
gage pressure, 572
hydraulic diameter, 525–528
models, 566
motors, 598–600
piston acceleration, 604
power transmission, 604
pressure controls, 580–591
pressure gages, 579
pressure intensifiers, 578
pumps, 595–597
representative system, 607
similitude, 565–567
854 Indexstandard hydraulic symbols, 605
Hydro-cushioned valves, 583
Hydrodynamics, 437
boundary layer, 452, 489–490
entrance length, 521–523
films, 297
lubrication, 323
phenomenon, 437
problem of, 505
Hydrostatics
films, 297
forces in, 564
lubrication, 323
pressure, 495
I
I-beam section, 176
I-controller. See Integration controller
Ideal elements, 705
Ideal gas, 451
Identification method, 360
Idler, 261
Immersed bodies, 548, 549
Impact analysis, 157–160
conservation in, 90
deflection stiffness, 157–159
direct impact, 90–93
oblique impact, 93–94
perfectly plastic, 90
Impedance, 369–370
Impermeable conditions, 503
Impulse, 87–88
angular, 94
Impulse function, 614
Inclined plane, 46
Inclined walls, 546
Incompressible flow assumption, 501
Incompressible substances, 451
Inertia matrix, 403
Inertial force, 117, 224–226, 567
Inertial reference frames, 75–76, 108–111
Influence function, 786
Initial conditions, 461–462, 718
Input-output model, 675
Input-state linearization, 692
Instantaneous center, 61, 100–101
Insulation problem, 455
Integrable equations, 726–766, 823, 835
Integral method, 508–512
Integrating factors, 743
Integration constant, 153
Integration (I) controller, 651
Intensifiers, 578
Interfaces, 130, 461–462
Interference gears, 258–261
Intermediate-length columns, 169–170
Internal damping, 391
Internal forced convection, 520–535
Internal forces, 129
Internal gears, 260
Internal heat term, 459
Internal moments, 129
International (SI) system, 53, 74, 257, 560
International Standard Organization (ISO), 245
Invariants, 797
Involute, of circle, 254
Irrotational flow, 568
ISO. See International Standard Organization
Isoclines, 720
Isoflux wall transfer, 546
Isogonal trajectories, 721
Isothermal transfer, 516, 532–534, 546, 548
J
Jacks, screw-type, 248
Jacobian matrix, 682
Johnson formula, 169
Joints, 192
Joule heating, 458, 466
K
Kelvin scale, 449
Kinematic chains, 223
class, 192
closed, 197–198, 230
decoupling of, 229
degrees of freedom, 199
elastic subsystem, 419–429
equilibrium conditions, 231
force closed, 197
full, 193
higher, 196
lower, 196
mixed, 198
moment equation, 239
monocontour, 230
open, 198
order of, 197
pairs, 191–198, 228–237
pin, 234, 236, 237
ramification point, 232, 236
reaction forces, 235–236
rotation, 233
slider, 234, 235
translational, 233, 235
Index 855Kinematics
chains. See Kinematic chains
diagrams of, 192
planar. See Planar kinematics
of points, 54–73
of rigid body, 94–110
similitude, 566
viscosity, 503, 562
Kinetic energy, 81, 396–397
change in, 81, 84
material points, 397
perfectly elastic impact, 93
principle of, 568
Kinetostatics, 223–229
contour method, 229
free-body diagrams, 227
inertia moment, 224–226
moments of force, 223
reaction forces, 227
L
Lagrange equations, 402, 757
Lagrange method, 396–398, 435, 783, 829–835
Lagrange model, 399
Laminar flow, 491
Laplace transforms, 615, 707–713
Lathes, 432
Lattice vibrations, 457, 460
Leakage equation, 732
Legendre equation, 800, 810
Leonhard criteria, 415
Lewis equation, 276
L’Hospital rule, 352
Liapunov methods, 689–691
Light, velocity of, 75
Limit cycles, 685
Line, motion of, 55
Line of action, 2
Linear damage rule, 181
Linear damping, 391
Linear equations
constant coefficients, 790–796, 835–845
differential equations, 744–814, 825–837
homogeneous, 789–792
integrable combinations, 835
nonhomogeneous, 782–789, 792–794
second-order, 796–816
systems of, 825
zeros of solutions, 801
Linear hydraulic motor, 419
Linear impulse, 87
Linear momentum, 74, 87, 89–90
Linear operator, 777, 826
Linear springs, 83, 150
Linear systems, 342
degrees of freedom, 341, 385–416
feedback in, 639–649
torques in, 342
Liouville formula, 777, 796, 798, 830
Lipschitz condition, 817
area and, 20
central, 169–170
centroid and, 20
diagram, 156
eccentric, 170–171
intensity, 132
randomly varying, 181–183
Logarithmic plots, 633–636
Long columns, 165–168
Loop structures, 197
Lorentz constant, 460
Lubrication
films, 297, 437
hydrodynamic, 323, 326–328
hydrostatic, 323
nonpetroleum-base, 322
sliding bearings, 318–328
Lumped capacitance models, 472–475
Lumped masses model, 393–394, 417, 430, 432
M
Mach number, 567
Machines
components of, 243–328
gears, 253–275
mounting of, 435–436
Reuleaux definition, 198
rolling bearings, 297–308
screws, 244–247
sliding bearings, 318–328
springs, 283–296
as a system, 416–417
vibrations of, 416–444
Macroscopic motion, 488
Magnification factor, 363–365
Manometers, 564
Mass, 74
Mass center, 16–17
Mass conservation principle, 493, 523, 537
Mass-damper-spring system, 679
Mass geometry, 392
856 IndexMaterial points, 392–397
Materials
beams. See Beams
Castigliano theorem, 163–164
compression, 165
constant life fatigue diagram, 178–180
contact, 147–148
deflection analysis, 149–171
elastic strain, 127
endurance limit, 173–177
equilibrium, 128–130
fatigue, 173–187
flexure, 135–138
fluctuating stresses, 178
impact analysis, 157–159
mechanics of, 119–187
Mohr’s circle, 121–124
shear moment, 131
shear stresses, 140–142
short compression members, 171
singularity functions, 132, 153
spring rates, 150–151
strain energy, 160–162
stress, 120–147
torsion, 143–146
Maximum principle, 801
Mayer’s law, 451
Mechanical impedance, 369–370
Mechanisms
Cartesian method, 202–207
contour method, 229
defined, 198
degrees of freedom, 199
differential equations for, 703–707
free-body diagrams, 227
inertia moment, 224–226
kinematic pairs, 191–198
kinetostatics, 223–229
materials and, 119–197
mechanical models, 386–392
mobility, 190–191, 199
moments of a force, 223
oscillators, 725
planar, 200
position analysis, 200–208
reaction forces, 227
theory of, 189–240
vector loop method, 208–210
velocity acceleration analysis, 211–216
Melting, 518
Milling machine, 432
Minimum moment, 34
Modifying factors, 173
Module, defined, 257
Mohr-Maxwell method, 389
Mohr’s circle, 121–125
Molecular diffusivity, 457, 498
Moments, 131–132, 223
bending, 132
of bound systems, 30–33
couples and, 30–40
defined, 223
external, 129
first, 13, 17–21
internal, 129
kinematic pairs, 239
minimum, 34
statics and, 30–32
sum of, 115, 226
of systems, 30–33
Momentum, 87–88
angular, 94
balance, 493–496
boundary layer, 504
equation for, 537
flux, 495
impulse and, 87–88
linear, 74
principle of, 568
streamwise, 503
Monatomic gases, 460
Moore test, 173–177
Motion. See Newton’s laws of motion
Motor oils, 321
Motors, 598–601
Multileaf springs, 292–296
N
Natural frequency, 345
Navier-Stokes equation, 493–496
Net momentum fluxes, 495
Neumann condition, 461–462
Neutral axis, 135
Newtonian equation, 567
Newtonian fluids, 495, 561
Newtonian gravitation, 75
Newtonian reference frame, 74–76, 108–111
Newton’s, law of cooling, 730
Newton’s, law of viscous flow, 318–323
Index 857Newton’s laws of motion
second law, 74–77, 80, 87, 108–112, 117,
224–226
cartesian coordinates, 76–77
D’Alembert’s principle, 226
damping and, 342
equilibrium equation, 117
reference frames, 74–76, 108–111
relative motion, 111
third law, 89, 112, 130
Newton’s method, 392–396
No-slip conditions, 503, 524
Nonautonomous system, 686
Nondimensional temperature, 478
Nonhomogeneous linear equations, 784
Nonlinear controllers, 691–695
Nonlinear equations of motion, 346
Nonlinear springs, 150
Nonlinear systems, 678–691
Normal component, of force, 59–73, 77–78
Normal stress, 120, 135–139, 494, 495, 726
Normal vector, 68
Null entropy interaction, 449
Numerical methods, 171
Nusselt number, 507, 515, 540
Nuts, 244
Nyquist criterion, 415, 641–647, 711
O
Oberbeck–Boussinesq approximation, 539
Octahedral shear stress, 127
Oils, 297, 322
Oldham coupling, 599
Open-loop control system, 620–621
Operator notation, 106
Operatorial equation, 716
Orientation, 4, 12, 70
Orthogonal vectors, 7, 19
Oscillations. See Vibrations
Osculating plane, 66–67
Overdamped system, 631
Overheating, 518
Overshoot, 628, 654
P
P-controller. See Proportional controllers
P-discriminant curve (PDC), 772
Pappus theorems, 22–23
Parabolic formula, 169
Parabolic mirror, 738
Parachutes, motion of, 748
Parallel-axis theorem, 25–27
Parallel forces, 38
Parametric damping, 391
Partial differential equation, 716
PD controller. See Proportional-derivative
controller
PDC. See P-discriminant curve
Peltier effects, 466
Perfect gas, 499
Perfectly elastic impact, 93
Perfectly plastic impact, 90
Periodic stress, 173
Petroff equation, 323
Phase margin, 648
Phase plane method, 681–682
Phase space, 817
Piezometers, 564
Pin support, 42
Pinion gear, 255
Piston-type accumulator, 602–604
Pitch, gear
diameter, 255, 257, 271, 298
English units, 257
line velocity, 271
pitch point, 270
pitch circles, 255–256
screws, 244
Planar kinematics, of a rigid body
angular momentum and, 113–114
angular velocity vector, 98–99
D’Alembert’s principle, 117
equations of motion, 115–116
instantaneous center, 100–101
motion types, 95–96
point relative to body, 103–110
relative acceleration and, 102
relative velocity and, 97
Planar mechanisms, 200–202
Planar motion, 59–64, 115–117, 397
Planar supports, 42–43
Plane of symmetry, 15
Plane wall, 465, 467
Plastic impact, 90
Plastic springs, 283
Pohlhausen method, 516, 519
Pohlhausen-von Karman method, 508
Point, kinematics of, 54–73, 103–110
Points, centroid of, 13–15
Poisson equation, 527
Poisson problem, 524–525
Poisson ratio, 128, 297
Poisson relations, 104
Polar coordinates, 78–80
binomial vectors, 70
858 Indexcoordinate systems, 70–71
orientation and, 70
potential energy, 85
velocity in, 70
Polar diagram, of vibration, 416
Polar moment, of area, 27–28
Polar plot representation, 632–633
Pole-zero methods, 620, 649–669
Poles, of system, 621
Polytropic gas equation, 603
Position analysis, 200–208
Position, of a point, 54–55
Position vector, 12–13
Potential energy, 84, 570
polar coordinates, 85
of spring, 85–86
strain energy and, 160
of weight, 86–87
Power, 572
defined, 82
generation of, 445
transmission of, 253, 598–600, 604
work and, 81–83
Power screws, 247–253
Prandtl number, 491, 507, 511, 516, 540
Prandtl–Pohlhausen analysis, 520
Presses, 248
Pressure
angle, 256
controls, 580–591
defined, 563
gages, 579
hydraulic diameter, 525–528
intensifiers, 578
pressure drop, 525–528
valves, 591
Principal axes, 28–30
Principal directions, 122
Product of area, 24
parallel-axis theorem, 27
principal axes, 30
second moments and, 24
Product, vector, 4–6
Projectile problem, 77
Proportional (P) controllers, 650–655
Propulsion, 445
Pumps, 595–598
Pure shear, 120
Pure substance, 450
Q
Quasicircular frequency, 349
R
Raimondi–Boyd charts, 328, 334
Ramification point, 236
Random vibrations, 456
Rayleigh function, 398
Rayleigh group, 540
Rayleigh method, 379, 411–414
Reaction forces, 227–229, 235
Reactions, in supports, 42
Reciprocating machines, 352
Rectangular section beams, 142–143
Rectangular vectors, 7
Recurrence relations, 409
Redundancy, degree of, 45
Reference frames
cartesian coordinates, 7, 58
fixed stars, 76
inertial, 75–76, 108–111
moving, 107
Newton’s second law and, 76
relativity and, 73–75
rigid body motion, 95
secondary, 111
types of, 95
Regularity, 461–462
Relative acceleration, 102
Relative motion, 73
Relative velocity, 97
Relativity, theory of, 73–75
Relaxation phenomenon, 728
Relief valves, 580, 582, 588–590
Repeated stress, 173
Representative system, 598–600
Resistivity, of metal, 460
Resolution, of vectors, 6
Resonance, 405
curve of, 355
frequency of, 637
harmonics and, 358
Rest point, of system, 819
Restitution, coefficient of, 92
Resultants, vector, 5, 19
Reverse free flow, 585–587
Revolution, 21, 23
Reynolds equation, 328
Reynolds number, 505, 524, 567
Riccati equation, 751, 798
Index 859Rigid bodies
acceleration of, 102–103
angular momentum, 113–114
angular velocity, 98–100
D’Alembert’s principle, 117
definition of, 95
dynamics of, 111–117
equations of motion, 115–116
instantaneous center of, 100–101
motion types, 95–96
planar kinematics of, 94–110
point relative to, 103–110
reference frame, 95
relative velocity of, 97–98
Rigid element, 149
Rigidity, modulus of, 128
Robin condition, 461–462
Robotics, 664–669, 680, 694
Rocker, defined, 198
Roller supports, 42
Rolling bearings, 297–318
Rolling friction, 438
Rolling slider, 437–438
Root-finding techniques, 171
Rotation, 190, 352, 397, 418
angular speed, 380
critical speed, 380–384
instantaneous axis of, 99
kinematic pairs, 233
shafts, 145, 380–384, 725, 726
torque, 145
unbalance and, 356
unit vector, 56–57
Rotational damper system, 702
Rotational spring, 705
Rotors, 409–411
Rounded-fixed ends, 165
Rounded-rounded ends, 165
Routh–Hurwitz criterion, 640
Routh stability criteria, 415
Runge–Kutta scheme, 513
S
S–N diagram, 173
S-plane contours, 702–712
SAE. See Society of Automotive Engineers
Saybolt seconds, 319
Saybolt viscosity, 319
Scalar product, 9, 11
Scalars, 4, 6–7
Scale analysis, 499–501, 505–508, 539–541
Scaling, 499
Schlichting method, 522
Screws
diameter, 244
efficiency, 250
jacks, 248
pitch, 244
power, 247–253
self-locking, 250
unified system, 246
Secant column formula, 171
Second moments
area, 24–25, 29
maximized, 29
parallel-axis theorem, 26
transfer theorem, 26–27
Section modulus, 137
Self-alignment, 381
Self-centering, 381
Self-locking screws, 250
Self-similar profiles, 512
Semi-infinite solid bodies, 487
Sense, of vectors, 4, 12
Separable equations, 735
Separable variables, 726
Sequence valves, 585, 590–591
Settling time, 655
Shape factor, 506
Shaper mechanism, 210
Shaping machine, 399
Shear, 131–132
beams and, 140–142
bending moment, 132
direct shear effects, 286
helical spring, 285
moment, 131
multiplication factor, 286
octahedral, 127
pure, 120
shear layer, 541
singularity functions, 132
strain energy, 162
stress, 120, 140–142, 285, 490, 494
viscous flow and, 319
Shock absorbers, 347
860 IndexShort compression members, 171–172
SI units, 53, 74, 257, 560
Signal flow diagram, 712–714
Signals, control theory and, 613–615
Significant digits, 52
Silicone oils, 322
Similarity analysis, 512–519
Similarity variable, 542
Simple couple, 34
Singular integral curve, 772
Singular point, in phase plane, 682–683
Singular solutions, 772–774
Singularities, of system, 621
Singularity functions, 132–135, 153–157
Sinusoidal input, 615
Sinusoidal stress, 179
Size factor, 176
Skeleton diagram, 192
Slenderness ratio, 167, 169, 172
Slider joints, 436–437
Sliding bearings, 297
Sliding controls, 695–703
Sliding friction, 438–440
Sliding pairs, 234–235
Society of Automotive Engineers (SAE), 320
Soderberg criterion, 183
Solar energy, 445
Sommerfield number, 325
Space, defined, 52
Sparrow analysis, 522
Spatial motion formulas, 65–70
Specific energy, 498
Specific enthalpy, 499
Specific heat, 450, 459
Specific internal energy, 450
Specific weight, 560
Spheres, heat transfer, 482
Spool-type controls, 582–584
Springs, 150, 283–296
Belleville springs, 296–297
compression of, 150–152
distortion-energy theory, 283
elastic constant for, 388
elastic force of, 374–375
ends, 288
extension, 284
helical, 284–290
linear, 83, 150
linear characteristic, 374–375
mass-damper system, 617–618
materials for, 283
mechanical work and, 374–375
multileaf, 292–296
nonlinear, 150
potential energy, 85–86, 374–375
rates, 150–151, 287–288
spring constant, 150, 287, 388
spring index, 286
stiffness, 150, 342, 386
tension, 150–152
torsion, 150–152, 290–293
Spur gears, 253, 425
Stability
analysis of, 414–415
criteria for, 415
of linear feedback systems, 639–649
of nonlinear systems, 685–688
vibration and, 414–415
Standard controllers, 650
Standard hydraulic symbols, 605
State variable models, 669–672
Static coefficient of friction, 47
Statics
centroids, 12–28
couples, 34–36
equilibrium in, 40–44, 129, 130
fluid dynamics, 563
friction and, 46–47
moments, 30–32
surface properties, 12–28
vector algebra for, 1–12
Steam turbine, 333
Stefan-Boltzmann law, 454
Step input, 615
Stick-slip phenomenon, 438–439
Stiffness, deflection and, 149–172
Stiffness matrix, 393, 403
Straight line motion, 57–58, 77
Strain energy, 127–128, 160–162
Strains, principal, 128
Streamfunction, 501
Streamlines, 491, 501–502, 569
Streamwise momentum equation, 503
Strengths, of points, 13
Stress, 120
alternating, 173, 178
beams and, 139–143
components of, 120–121
contact, 147–149
elastic strain, 127
equilibrium and, 128–130
flexure and, 135–138
fluctuating, 178
Index 861Stress (continued)
materials and, 120–147
Mohr circle, 121–124
normal, 120, 726
periodic, 173
principal, 122
randomly varying, 181
shear, 120, 131, 140–142
singularity functions, 132, 153
sinusoidal, 179
three-dimensional, 120
torsion, 143–146
triaxial, 125–127
uniformly distributed, 120
Stretching effect, 495
Sturm comparison theorem, 801
Superposition, 358, 368, 385, 487, 782, 828
Supports, 42–46
Surface factor, 175
Surface of revolution, 21
Surface properties, 12–28
Surface tension, 562–564
Swimmer problem, 738
Switching surface, 696
Symbols, standard, 605
Symmetry, axis of, 24
System group, 200
Systems, of equations, 816–837
T
Tangent vector, 68
Tangential component of force, 59–78
Taylor approximation, 401, 458, 469, 493
Tensile testing machines, 248
Tension, spring rates, 150–152
Tension moment, 409
Thermal boundary layer, 489–491, 537–539
Thermal time constant, 473
Thermodynamics, 446–455
equilibrium in, 448
first principle of, 447
heat transfer, 446
second principle of, 449
Thermometer, 449
Thomson effects, 466
Acme, 247
fasteners, 244
fatigue strengths, 247
ISO and, 245
metric, 245
right hand assumption, 245
screws, 244
unified series, 245, 246
Three-dimensional supports, 44
Time, defined, 52
Time derivative, 12
Time-domain performance, 628–631
Torque, 67–68, 143–147
couple and, 34
damping, 342
defined, 223
differentials, 268
elastic strain, 342
formula, 69
friction, 398
rotating shaft, 145
spring rates, 150–152
stress and, 143–146
technological, 272
torsion springs, 290
vector, 143
wrench, 36
Total differential equations, 742
Transfer functions, 613–618, 707
Transfer theorems, 25–27
Transitivity, 36
Translation, 190
Translational pair, 233, 235
Transmissibility coefficient, 373
Transmission systems, 679
Transport mechanisms, 452
Transport theorem, 106
Trigonometric identities, 28
Triple product, vector, 11
Turbulence, 491–492, 543–544
Twist, angle of, 143
U
Undamped circular frequency, 345
Underdamped system, 631
Uniform body, 17
Uniform flow, 503, 569
Uniform heat flux, 518
Uniformly distributed stresses, 120
Uniqueness of solutions, 766, 770
Uniqueness theorem, 501
Unit conversions, 53
Unit vectors, 4
angular motion of, 56
binomial vectors, 70
862 Indexcartesian, 62
determinant form, 11
normal, 60
orthogonality of, 67
rotating, 56–57
tangent direction, 60
time derivative of, 56
Units, systems of, 74, 560
Universal constant, of ideal gas, 451
Universal function, 478
Universal gravitational constant, 75
V
Vacuum, defined, 563
Valves
check, 592–594
compound, 588–590
counterbalance, 587
hydraulics, 580–592
hydro-cushioned, 583
pressure-reducing, 591
relief, 580, 582, 588–590
sequence, 585
spool-type, 584
venting, 590
Vane pumps, 597
Vapor pressure, 562
Variable separation method, 478
Variable structure systems, 700–703
Variation of parameters, 783, 829–835
Vectors
angle between, 7–8
angular velocity, 98–99
associativity and, 6
bound, 3
characteristics of, 2
commutativity and, 6
cross product, 9–10
derivative of, 12, 106
direction of, 2
distributivity and, 6
equality of, 4
fields, 501
free, 3
functions, 12
line of action, 2
magnitude of, 2
orientation of, 2
point of application of, 3
position, 12–13
position analysis, 208–210
representations of, 2
resolution of, 6
scalar product, 9
scalars and, 4
sense of, 2
statics, 1–12
transmissible, 3
triple product, 11
unit, 4, 11, 56–60, 62, 67
zero vectors, 4
Velocity, 218, 269
acceleration analysis, 211–222
defined, 52
of a point, 54–55
polar coordinates, 70
Venting valve, 590
Veresceaghin method, 390
Versor. See Unit vectors
Vibrations
actuator subsystems, 418
arbitrary exciting force, 358–359
bending and, 393
centrifugal exciting force, 356–357, 364
conservative systems, 375
cutting process, 440–443
damping and, 340–369, 375–379
elastic subsystem, 419–437
energetic aspect, 374–379
equation of, 725, 791
equation of motion and, 342
finite degrees of freedom and, 385–407
free, 340, 342–352
free undamped, 343–345
friction process, 437–439
harmonic motion, 340
Holzer method, 409
isolation mountings, 283
isolation of, 370–374
linear shafts, 429
machine tool, 416–444
magnification factor, 365
mechanical impedance, 369
mechanical models, 386–391
natural frequencies, 407–415
nonharmonic exciting force, 358
with one degree of freedom, 374–379
phase angle, 364
polar diagram, 416
rotating shafts and, 374–379
self-excited, 441
simple harmonic, 359–364, 375
stability, 414–415
steps for solving problems, 385
superposition of, 385
Index 863Vibrations (continued)
system model, 404–405
theory of, 339–444
transmissibility of, 370–374
undamped, 352–359, 377
Viscometer, 319
Viscosity, 318–323
absolute, 319
boundary conditions, 503
coefficient of, 342
damping, 342, 345, 347–352, 391, 398
dissipation, 498
dynamic, 319
fluid dynamics, 561
kinematic, 319, 503
of liquids, 562
resistance force, 342
shear stress, 495
temperature and, 562
unit of, 319
viscous flow, 318–323
Volumetric expansion, 539
W
Wall
friction coefficienct, 490, 506, 517
heat flux, 518
no-slip conditions, 524
nonuniform temperature, 517
shear stress, 490, 505
temperature conditions, 503
unheated starting section, 516
Weber number, 568
Weibull equation, 311
Weight, 83–87
Wide cavity case, 551
Wide channel limit, 549
Wiedemann–Franz law, 460
Work, 80–84, 450
Wrench, 36, 38–40
Wronskian determinant, 776–779, 796, 829–831
Y
Yielding line, 185
Young modulus, 419
Z
Zeebeck effects, 466
Zero vectors, 4
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