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عدد المساهمات : 2041 التقييم : 3379 تاريخ التسجيل : 21/01/2012 العمر : 47 الدولة : مصر العمل : مدير الصيانة بشركة تصنيع ورق الجامعة : حلوان
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أخوانى فى الله أحضرت لكم كتاب 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 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 847 xii Table of Contents Preface 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 See also Newton’s laws of motion Accumulators, fluid, 601–604 Acme threads, 247, 251 Action-reaction. See Newton’s laws of motion, third law Addendum circle, 256–257 Adiabatic processes, 603 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 RRR dyad and, 3 Annular Bearing Engineers’ Committee (ABEC) grades, 304 Anti-Friction Bearing Manufacturers Association (AFBMA), 304 ABEC grades, 304 Arc length, 68 Archimedes’ principle, 565 Area axis of symmetry, 18 centroids, 17–20, 25 composite, 19 first moment, 17–21 loading curve, 20 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 rotation about, 21, 23, 96 of symmetry, 18–19, 24 See also Cartesian coordinates Axial loading, 175 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 loading analysis, 165–171, 177 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 ABEC grades, 304–305 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 Bladder accumulators, 603 Blasius number, 512 Blasius solution, 521–522 Bode diagrams, 415, 633, 648–649, 659 Body forces, 494 Boiling, 454 Bolts, 244 Boring machine, 432 Boundary conditions, 461–462. See also specific 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 Cascade connection, 618 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 Central loading, 165–170 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 loading curve, 20 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 steady, 464–467 thermal conductivity, 452, 458–461 thermal resistance, 463 unsteady, 472–488 See also Heat transfer 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 steady-state error, 623–624 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 See also Heat transfer; specific parameters 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 Critical load, 165, 167 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 instantaneous radius of, 61 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 dead zone, 347 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 Dead zone, 347 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 central loading, 165–169 columns and, 165–171 compression and, 165 compression members, 171 deformation and, 3, 160–163, 389 eccentric loading, 170 expression for, 157 impact analysis, 157–159 maximum values, 158 springs and, 150–151 stiffness, 149–172 strain energy, 160–162 See also Beams 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 See also specific concepts, methods, types 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 link, 200, 203, 212 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 Dyad structures, 201 links, 202 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 rotation about axis, 96 straight line motion, 57 tangential components, 59–72, 77 work and, 81–83 See also specific concepts, models E Eccentric loading, 170–171 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 See also specific parameters, models Electric motors, 418, 425 Electrical oscillatory circuit, 725 Electromagnetic radiation, 454 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 See also specific systems, parameters 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 See also specific systems 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 randomly varying loads, 181–182 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 Gradient, defined, 87 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 Hadamard problem, 461 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 radiation, 451–454 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 unsteady, 472–488 vertical wall, 542–543, 545–546 walls, 546–548 wide cavity case, 551 work rates, 447 See also specific effects, parameters 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 See also specific parameters, systems Hydrostatics films, 297 forces in, 564 lubrication, 323 pressure, 495 See also specific parameters, systems I I-beam section, 176 I-controller. See Integration controller Ideal elements, 705 Ideal gas, 451 Ideal radiator, 454 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 See also specific parameters 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 Lead, 245 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 Loading area and, 20 central, 169–170 centroid and, 20 diagram, 156 eccentric, 170–171 intensity, 132 load factor, 19–20 loading curve, 19–20 randomly varying, 181–183 See also Stresses 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 See also specific types, concepts 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 central loading, 165–169 compression, 165 constant life fatigue diagram, 178–180 contact, 147–148 deflection analysis, 149–171 eccentric loading, 170 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 randomly varying loads, 181–182 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 See also specific concepts, methods 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 See also specific topics, types Melting, 518 Metric threads, 245 Milling machine, 432 Minimum moment, 34 Mobility, 190–191. See also Degrees of freedom Modifying factors, 173 Module, defined, 257 Mohr-Maxwell method, 389 Mohr’s circle, 121–125 Molecular diffusivity, 457, 498 Moments, 131–132, 223 about a line, 31–32 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 Multiple-threaded screw, 245 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 See also Dynamics; specific systems 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 See also Gears 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 rotation about axis, 96 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 Quadratures, 726 Quasicircular frequency, 349 R Radian unit, 53–54, 341 Radiation, 446, 448, 451–454 Radiator, 468 Radioactivity, 729 Radius of curvature, 61 Raimondi–Boyd charts, 328, 334 Ramification point, 236 Random vibrations, 456 Randomly varying loads, 181–183 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 See also Coordinate systems 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 rotation about axis, 96 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 about axis, 96 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 RRR dyad, 209, 212–214 RRT dyad, 205 RTR dyad, 209, 215 Runge–Kutta scheme, 513 S S–N diagram, 173 S-plane contours, 702–712 Saddle points, 684 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 Acme threads, 251 diameter, 244 efficiency, 250 jacks, 248 multiple-threaded, 245 pitch, 244 power, 247–253 self-locking, 250 square threads, 251 unified system, 246 See also specific types, threads Secant column formula, 171 Second moments area, 24–25, 29 maximized, 29 parallel-axis theorem, 26 transfer theorem, 26–27 Section modulus, 137 Self-adjoint equation, 797–798, 800 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 loading, 162 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 contact radius, 147 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 Square threads, 247–248, 251 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 loading, 303–304 moments, 30–32 surface properties, 12–28 vector algebra for, 1–12 See also specific concepts, methods Steady-state error, 623–628 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 Temperature, 446, 456, 478. See also Heat transfer Tensile testing machines, 248 Tension, spring rates, 150–152 Tension load, 120 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 See also Heat transfer Thermometer, 449 Thomson effects, 466 Threads, 247 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 See also Moments 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 TRT dyad, 216–222 Turbulence, 491–492, 543–544 Twist, angle of, 143 U Undamped circular frequency, 345 Underdamped system, 631 Unified threads, 245–247 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 load, critical, 167 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 Unsteady conduction, 472–488 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 addition, 4 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 Velocity head, 572 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 Wear load, 279 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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