The Theory of Machines

The Theory of Machines
اسم المؤلف
Thomas Beyan
التاريخ
8 يناير 2024
المشاهدات
340
التقييم
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The Theory of Machines
A Text-book for Engineering Students
By
Thomas Beyan
M.Sc. TECH. (MANCHESTER), A.M.I. MECH. E.
Senior Lecturer in Mechanical Engineering in the University and in the College of Technology, Manchester.
WITH DIAGRAMS
CONTENTS
CHAPTER
I. DEFINITIONS. SEMPLE MECHANISMS
PAGE
II. MOTION. INERTIA 14
III. VELOCITY AND ACCELERATION 68
IV. MECHANISMS WITH LOWER PAIRS . 121
V. VALVE DIAGRAMS AND VALVE GEARS 142
VI. FRICTION . 177
VII. BELT, ROPE AND CHAIN DRIVES . 223
VIII. BRAKES AND DYNAMOMETERS 248
IX. CAMS . 281
X. TOOTHED GEARING 315
XI. GEAR TRAINS 366
XII. DYNAMICS OF MACHINES. TURNING MOMENT. THE
FLYWHEEL . 412
XIII. GOVERNORS 454
XIV. BALANCING 489
XV. VIBRATIONS 532
ANSWERS TO EXAMPLES 602
BIBLIOGRAPHY . • 609
INDEX 615
INDEX
Absorption dynamometers, 265
Acceleration, 14

  • along circular path, 15
    straight line, 16
    -, angular, 16
  • centre, 90
    -, centripetal, 16
    -, Coriolis component, 102
  • diagram for link, 89
    for four-bar chain, 97
  • – for reciprocating engine, 91
  • -displacement curve, 70
    -, gyroscopic, 18
    ■- image, 89
  • of geared system, 47
  • of piston, analytical, 100
    , Fourier series for, 101
  • , Klein’s construction, 94
  • of rolling body, 45
  • -speed crave, 73
    -, tangential, 16
  • -time curve, 71
    for cam, 283
    Ackermann steering gear, 8, 134
    Addendum of tooth, 321
    , modified to avoid interference, 340
    -, standard, 328
    Adsorption, 204
    Advance, angle of, for eccentric, 144
    Amplitude of vibration, 533
    , damped vibration, 550
    -, forced vibration, 554
    at resonance, 559
    Andreau differential-stroke engine,
    86
    Angle of advance of eccentric, 144
  • of friction, limiting, 178
  • of obliquity, 321
    Angular acceleration, displacement,
    velocity, 17
  • momentum, 22
  • velocity of precession, 18
    Arc, idle, in belt drive, 230
  • of approach, 322
  • of contact, length of, 337
  • of recess, 322
    Axis, friction, 197
    Back gear, lathe, 373
    Balancing head, 524
    -, locomotive, 501, 504
  • machine, dynamic, 523
    static, 521
    Balancing of multi-cylinder in-line engine, 505, 513
  • of reciprocating masses, partial,
    499
  • of revolving masses, 489
    -, primary, 505
    -, secondary, 506
    Band and block brake, 257
  • brake, 256
    Base circle of involute wheel, 326, 330
  • pitch, 328
    Basic rack, 330
    Beam engine, 8, 122
    Bearing, ball, 216
    -, horse-shoe thrust, 192
    -, journal, 210
    -, Michell thrust, 209
    -, needle roller, 218
    -, roller, 217
    Belt creep, 230
  • drive, centrifugal stress, 226
  • -, effect of centrifugal stress on
    power transmitted, 231
    , – of gravity idler, 235
    , materials, 237
    , power transmitted, 227
    , ratio of tensions, 223
    1 tightening effect of catenary, 229
  • transmission dynamometer, 271
    Bennett’s construction for acceleration
    of piston, Q. 24, p. 118
    Bevel gearing, 315, 346
  • wheels, methods of cutting, 360
    Bevis-Gibson torsion dynamometer,
    274
    Bilgram valve diagram, 149
    Body centrode, 80
    Boswall and Brierley, experiments on
    journal bearings, 213
    Boundary friction, 204
    Brake, band, 256
    -, – and block, 257
    -, internal expanding, 255
    -, shoe, 248
    Braking of a vehicle, 260
    Brass, bedded and clearance, 213
    Broad-arrow engine, balance of, 519
    Buckingham, E., 345
    Buffer, action of, 29
    Bull engine, 10
    Cam, circular arc, 298
    -t , with oscillating roller follower, 307
    615616 INDEX
    Cam, cylindrical, 282
    -, displacement, velocity and acceleration-time curves of, 283
    -, radial, 282
    -, tangent, 302
  • with flat-faced follower, 296
    knife-edged follower, 290
    roller oscillating follower, 293
    reciprocating follower, 292
    Cams, types of, 281
    Catenary, tightening effect of, in belt
    drive, 229
    Centre, acceleration, 90
    -, instantaneous, 78, 79
  • method, instantaneous, 79
  • of percussion, 40
    Centrifugal force, 21
  • governors, 454
  • stress in belt or rope, 226
  • , effect of, on h.p.
    transmitted, 231
    Centripetal acceleration, 16
  • force, 20
    Centrode, body, 80
    -, space, 80
    Chain, compound, 12
    -, double-slider crank, 11
    -, four-bar, 5, 7, 78, 97, 134, 426
    -, inverted tooth, 244
    -, kinematic, 4
    -, roller, 241
    -, slider-crank, 8
    Chain drive, 239
    , fluctuation of velocity ratio, 240
    Circle, friction, 197
    -, rolling, 323
    Circular path, motion along, 15, 20
  • pitch, 319
    Clearance in wheel teeth, 321
    Clutch, disc or plate, 193
    Co-axial gear drives, 373
    Coefficient of fluctuation of energy, 439
    of speed, 441
  • of friction, 178
    , worm gearing, 356
  • of insensitiveness, 483
  • of restitution, 27
    Collar friction, 189
    Complete constraint, 3
    Compound gear train, 367, 370
  • kinematic chain, 12
  • pendulum, 36
  • steam engine, turning moment diagram, 435
    Conical pivot, 189
    Conjugate teeth, 322
    Conservation of energy, 23
  • of momentum, 23
    Constraint, 3
    Contact, arc of, 337
    -, path of, 321, 337
    Controlling force, 476
    Coriolis component acceleration, 53,
    102
    Correction couple for inertia of connecting rod, 41
    Couple, 22, 42
    -, gyroscopic, 51
    -, representation by a vector, 495
    -, swaying, 504
    Crank and slotted lever quick-return
    motion, 10
    , acceleration of ram,
    107
    , velocity of ram, 88
    Cranks, direct and reverse, 515
    Crankshaft speed, coefficient of fluctuation of, 441
    -, fluctuation of, 437
    Creep of belt, 230
    Critical damping, 552
  • speed, 565
    Cut-off, alteration of, with Meyer
    expansion valve, 157
    -, , – simple slide valve, 156
    -, point of, 144
    Cutting wheel teeth, methods of, 356
    Cycloid, 323
    Cycloidal teeth, 323
    Cyclometer mechanism, 397
    Dalby’s method of balancing, 494
    D’Alembert’s principle, 21, 42, 419
    Damped vibration, 550
    Damping, critical, 552
    Davis steering gear, 132
    Dedendum of wheel tooth, 319
    Diametral pitch, 320
    Differential mechanism, 400
  • stroke engine, Andreau, 86
    Direct and reverse cranks, 515
    Disc clutch, 193
    Displacement, 14
    time curve, 68, 71, 73
    for cam, 283
    Dobbie Mclnnes indicator mechanism,
    130
    Double slider-crank chain, 11
    Dunkerley’s method of finding frequency of transverse vibrations,
    545
    Dynamic balancing machine, 523
  • magnifier, 556
    at resonance, 559
    Dynamical system, equivalent, 39, 418
    Dynamics, 1
    Dynamometer, absorption, 265
    -, Belt, 272
    -, Bevis-Gibson, 274
    -, Epicyclic train, 270
    -, Fottinger, 275
    -, Heenan and Froude, 267
    -, Hopkinson-Thring, 275INDEX 617
    Dynamometer, Moullin, 276
    -, Rope-brake, 266
    -, Swinging-field, 269
    -, Torsion, 273
    -, Transmission, 270
    Eccentric, equivalent or virtual, 159
    Effective force, 44, 416
  • tension, 225
    Efficiency of inclined plane, 181
  • of machine, 412
  • of screw and nut, 187
  • of spiral gearing, 349
  • of worm gearing, 356
    Effort and resistance, relation between,
    413
    -, governor, 472
    Elastic constraint, 532
  • impact, 25
  • line of shaft in torsional vibration,
    570, 576, 579, 582, 587
  • suspension, 561
    Element, 2
    Ellipse trammel, 12
    Energy, conservation of, 23
    -, kinetic, 23
  • method of finding frequency of
    transverse vibrations, 546
    -, potential, 23
    -, strain, 23
    Engine, Andreau differential stroke, 86
    -, Atkinson cycle, Q. 11, p. 115
    -, beam, 8, 122
    -, broad arrow, balance of, 519
    -, opposed-piston, balance of, 508
    -, rotary, acceleration diagram, 110
    -, single-cylinder, balance of, 499, 516
    -, symmetrical, balance of, 511
    Epicyclic gear, Ford, Q. 17, p. 409
    , Humpage, 398
    trains, speed ratio of, 378, 381
    , tooth loads and torques, 387
    , Trojan, 401
    1 Wilson, 402
  • train dynamometer, 270
    Epicycloid, 323
    Equivalent dynamical system, 39
    for link, 39, 418
  • eccentric, 59, 162
  • mass for geared system, 47
    for rolling body, 45
    Exhaust lap, 142
    Expansion gear, Meyer, 157
  • plate, minimum width of, 159
    Film lubrication, 205
    of plane surfaces, 207
    of the journal bearing, 210
    Fluctuation of crankshaft speed, 437
  • of energy, 440
    Fly-press, 7
    Flywheel, size of, 442
    Followers, types of cam, 282
    Force, 18
    -, centrifugal, 21
    -, centripetal, 20
    -, closure, 4
    -, controlling, 476
    -, effective, 44, 416
    -, impulsive, 24
    -, inertia, of a link, 416
    Forced vibrations, 554
    Formed cutters for wheel teeth, 356
    Fottinger torsion dynamometer, 275
    Four-bar chain, 5, 7
  • -, acceleration diagram for, 97
    , inertia forces in, 426
    , velocity diagram for, 78
  • -speed gear box, 375
    Fourier series for velocity and acceleration of piston, 101
    Free vibrations, 532
    Frequency of vibration, longitudinal,
    533
    -, simple harmonic, 34
    , torsional 535, 570, 585
    , transverse, 534, 538, 544
    Friction, angle of, 178
  • axis, 197
    -, boundary, 204
  • circle, 197
  • of dry surfaces, 177
  • of governor, 481
  • of inclined plane, 179
  • of lubricated surfaces, 202
  • of screw-and-nut, 187
    -, rolling, 214
    Froude dynamometer, 267
    Gear box, motor car, 375
  • train, compound, 367, 370, 373
    , epicyclic, 366, 378
    , simple, 366
  • wheels, methods of manufacture,
    356
    Geared system, acceleration of, 47
    , torsional vibration of, 585
    Gearing, bevel, 315, 346, 360
    -, definitions, 319
    -, epicyclic, 378
    -, helical, 315, 345
    -, hyperboloidal, 316
    -, skew, 315
    -, spiral, 315, 347
    -, spur, 315
    -, worm, 353
    Generating pitch line, 341
  • wheel teeth, 357
    Gooch link motion, 167
    Governor, centrifugal, 454
    -, definitions, 471618 INDEX
    Governor effort, 472
  • friction, 481
    -, Hartnell, 465
    -, isochronous, 472, 480
    -, Porter, 457
  • power, 472
    -, Proell, 461
    -, spring-loaded, 464
    -, stability of, 480
    -, Watt, 456
    Grasshopper straight-line motion, 126
    Gravity idler, effect of, on belt drives,
    235
    Grooved pulley, ratio of tensions, 223
    Gyration, radius of, 21
    Gyroscope, 51
    Gyroscopic acceleration, 18
  • couple, 51
  • stabilisation, 59
    Hackworth valve gear, 170
    Hammer blow, 503
    Harmonic motion, simple, 33
    Harmonics, higher, balance of, 513
    Hart straight-line mechanism, 124
    Hartnell governor, 465
    Heenan and Froude dynamometer, 267
    Helical gearing, 315, 345
    Higher pair, 4
    Hobbing wheel teeth, 358
    Hooke’s joint, 135
    Hopkinson-Thring torsion dynamometer, 275
    Horse-power transmitted by belt or
    rope, 227, 231
    Humpage gear, 398
    Hunting of governor, 472
    Hyatt roller bearing, 217
    Hyperboloidal gearing, 316
    Hypocycloid, 323
    Idle arc in belt drive, 230
    Image, acceleration, 89
    -, velocity, 77
    Impact, 24
    ■-, loss of kinetic energy during, 26
    Impulse, 24
    Impulsive force, 24
    Inclined plane, efficiency of, 181
    , friction of, 179
    with guide friction, 183
    Indicator diagram, gas or oil engine,
    433
    , steam engine, 142
  • pencil mechanisms, 128
    Inelastic impact, 25
    Inertia force of a link, 416
    — forces in the four-bar chain, 426
  • – in the reciprocating engine, 421
    -, moment of, 21
  • torque, 423, 426, 431
    Initial tension in belt drive, 227
    Inside lap, see lap, exhaust
    Instantaneous centre, 78, 79
  • – method, 79
    of acceleration, 90
    Interference in involute wheels, 329
    -, methods of eliminating, 339
    -, minimum number of teeth to avoid
    332
    Internal expanding brake, 255
    Inversion, 6
    Inversions of double-slider-crank chain,
    11
  • of slider-crank chain, 8
    Inverted tooth chain, 243
    Involute teeth, 328
    -, the, 326
    Isochronous governor, 472, 481
    Joint, Hooke’s, 135
    Joints and links, relation between
    numbers of, 5
    Journal bearing, friction of, 210
    Joy valve gear, 171
    Kinematic chain, 4
  • pair, 2
    Kinematics, 1
    Kinetic energy, 23
    , loss of, during impact, 26
    Kinetics, 1
    Kingsbury thrust bearing, 209
    Klein’s construction for acceleration of
    piston, 94
    applied to the four-bar chain, 97
    Lap, exhaust, 142
    -, steam, 142
    -, -, of expansion valve, 158
    Lathe back gear, 373
    Lead angle, 346, 349
  • of slide valve, 142
    Lenix drive, 236
    Limiting angle of friction, 178
  • ratio of the tensions, 223
    Line of contact, 4, 281, 316, 353
    Linear momentum, 18
    Link, 2
  • motion, Gooch, 167
  • -, Stephenson, 164
    Links and pairs, relation between
    numbers of, 5
    Locomotive balancing, 501
    Longitudinal vibration, 533
    Lower pair, 4
    Lubricated surfaces, friction at, 202
  • -, Tower’s experiments on, 205
    Lubrication, film, 205
  • of journal bearings, 210
  • of plane surfaces, 207INDEX 619
    Machine, 1, 6
    Magnifier, dynamic, 556
    Marshall valve gear, 171
    Mass, 18
    -, unit of, 19
    Materials, belt and rope, 237
    Mechanism, 6
    Meyer expansion gear, 157
    Michell thrust bearing, 209
    Minimum width of expansion plate, 159
    Mode of vibration, 570, 574
    Module pitch, 320
    Moment, friction, of collar or pivot, 189
    Momentum, angular, 22
    -, conservation of, 23
    -, linear, 18
    -, moment of, 22
    Morse silent chain, 243
    Motion along a circular path, 15, 20
    -, processional, 18, 52
    -, simple harmonic, 33
    -, straight line, 16,122
    Motor car gear box, 375
  • – steering gear, 8, 134
    Moullin torsion dynamometer, 276
    Needle roller bearing, 218
    Newton’s laws of motion, 18, 21, 24
    Node, 547, 569, 574
    Normal mode of vibration, 570, 574
  • pitch, 345
    Number of links in kinematic chain, 5
    Obliquity, angle of, 321
    Oiliness, 203
    Oldham shaft coupling, 11, 12
    Opposed piston engine, imbalanced
    forces in, 508
    Oscillating-cylinder engine, 8
    Outside lap, see lap, steam
    Oval valve diagram, 154
    Pair, higher, 4
    -•, kinematic, 2
    -, lower, 4
    -, screw, 3
    •-, sliding, 3
    -, turning, 3
    Pairs, links and, relation between
    numbers of, 5
    Pantograph, 121, 129
    Parallel motion, 126
    Partial balance of reciprocating masses,
    499
    Peaucellier straight-line mechanism,
    123
    Pencil mechanisms, indicator, 128
    Pendulum, compound, 36
  • pump, 10
    Pendulum, simple, 35
    -, torsion, 37
    Percussion, centre of, 40
    Periodic time, 551
    Phase lag, 556, 558
    Piston valve, 143
    Pitch, base, 328
  • circle, 319
    -•, circular, 319
  • cone, 316, 346, 360
    -, diametral, 320
  • line, 319
  • module, 320
    -, normal, 345
  • point, 319
  • surface, 316, 319
    Pivot friction, 189
    Plane surfaces, lubrication of, 207
    Plate clutch, 193
    Poise, 203
    Porter governor, 457
    Potential energy, 23
    Pound weight, 19
    Poundal, 19
    Power, 22
  • of governor, 472
  • transmitted by belt or rope, 227
    Precession, velocity of, 18
    Pressure angle, 321
    Proell Governor, 461
    Profile of wheel teeth, 319
    Prony brake, 265
    Pump, pendulum, 10
    Quick-return motion, crank and slotted
    lever, 10
    , -, acceleration diagram, 107
    , – – -, instantaneous centres, 88
    , Whitworth, 9
    Rack, basic, 330
    -, involute, 329
    Radial cam, 282
  • valve gears, 168. See reversing
    gears, link motions
    Radius of gyration, 21
    Rayleigh, Lord, 539
    Recess, arc of, 322
    Reciprocating engine mechanism, 1, 81,
    85, 91
  • -, single-cylinder, imbalanced
    forces, 499
  • mass, inertia of, 497, 516
    , partial balance of, 499
    Rectangular valve diagram, 153
    Relative velocity, 75
    method, 75
    Resistance, effort and, 413620 INDEX
    Resistant body, 2
    Resonance, 522, 558
    -, amplitude at, 559
    Restitution, coefficient of, 27
    Reuleaux valve diagram, 147
    Reversing gear, Gooch, 167
    , Hackworth, 170
  • -, Joy, 172
    , Marshall, 171
    , Stephenson, 164
  • -, Walschaert, 169
    Revolving mass, balance of, 489
    Ritterhaus’s construction for acceleration of piston, Q. 24, p. 118
    Robert’s straight-line motion, 128
    Roller bearing, 217
  • chain, 241
    Rolling body, acceleration of, 45
  • circle, 323
  • friction, 214
    Rope brake dynamometer, 266
  • drive, see belt drives
    Ropes, cotton, 238
    -, wire, 239
    Rotary engine, 11
  • -, acceleration diagram, 110
    Scotch yoke, 12
    Scott-Russell straight-line motion, 125
    Screw and nut, friction of, 187
  • cutting, change wheels for, 369
  • pair, 3
    Sensitiveness of governor, 471
    Shaft angle of spiral gears, 347
    -, torsional stiffness of, 534
    -, torsionally equivalent, 569
    -. uniform, transverse vibration of,
    538
    -•, whirling of, 567
  • with several loads, vibration of, 544
  • with single load, whirling of, 565
    Shaping of wheel teeth, 356
    Shoe brake, 248
    Silent chain, 243
    Simple harmonic motion, 33
    vibration, 532
  • pendulum, 35
    Skew gear, 315
    Slide valve, 143
    Slider-crank chain, 8
    Sliding pair, 3
  • velocity of wheel teeth, 319
    of worm gear, 355
    Slip of belt or rope, 230
    Slug, unit of mass, 20
    Space centrode, 80
    Speed, 15
    -, coefficient of fluctuation of, 441
  • -displacement curve, 70
  • -time curve, 68, 71, 73
    Spiral angle, 349
    Spiral bevel gear, 361
  • gearing, 317, 347
    , design of, 350
    , efficiency of, 349
    , graphical solution of, 352
    Spring-controlled governors, 464
    Spur gearing, 315
    definitions, 319
    , methods of manufacture, 356
    — -, standard proportions for, 328
    Stabilisation, gyroscopic, 59
    Stability of governor, 472, 480
    Static balancing machine, 521
  • friction, 178
    Statics, 1
    Steam lap, 142
    Steering, condition for correct, 132
  • gear, Ackermann, 8, 134
    , Davis, 132
    Stephenson link motion, 164
    Stiffness, torsional, 534
    Stodola’s method, transverse vibration,
    546
    Stone-crusher mechanism, 79
    Straight-line motions, approximate,
    125
    , exact, 122
    Strain energy, 23
    Successful constraint, 3
    Surface contact, 4
    Swaying couple, 504
    Swift, H. W., 230
    Swinging-field dynamometer, 269
    Tangent cam, 302
    Tangential acceleration, 16
  • velocity, 15
    Taper roller bearing, 217
    Tchebicheff straight-line motion, 127
    Teeth, conjugate, 322
    –, cycloidal, 323
    -, interference between, 329
    -, involute, 328
  • of chain wheels, 242, 245
    Tension, centrifugal, 226
    -, initial, 277
    -, total, 232
    Tensions, limiting ratio of, 225
    Thompson indicator mechanism, 130
    Three centres in line theorem, 84
    , applications of, 85
    Thrust bearing, ball, 217
    , horse-shoe, 192
  • -, Kingsbury, 209
    , Michell, 209
    Torque, gas, 434
    -, inertia, 431
    -, -, of connecting rod, 423
    -, -, four-bar chain, 426
    -, -, reciprocating engine, 421, 431
    -, steam, 430INDEX 621
    Torsion dynamometers, 273
    Torsional stiffness of shaft, 534
  • vibration, 534, 568
    , damped, 553
    of geared system, 585
    multi-rotor system, 574
    -. – -, graphical method of
    solving, 582
    Tower, Beauchamp, 205
    Tractive effort, variation of, in locomotives, 504
    Trammel, ellipse, 12
    Transmissibility, 562
    Transmission dynamometers, 270
    Transverse vibration, 533
    , several loads on shaft, 544
    , uniformly-loaded shaft, 538
    Tredgold’s approximation, 347
    Trojan epicyclic gear box, 401
    Turning moment diagram, compound
    steam engine, 435
    , multi-cylinder gas engine,
    436
    , single-cylinder gas engine,
    433
    -, – steam engine, 431
  • pair, 3
    Universal joint, 135
    Valve, piston, 143
  • diagram, Bilgram, 149
    , oval, 154
    , rectangular, 153
  • -, Reuleaux, 147
    -, slide, 143
    Variation of tractive effort in locomotive, 504
    Vector representation of a couple, 51,
    495
  • solution, epicyclic gear trains, 385
    , vibration problems, 556
    Vee-belt, materials, 238
    , ratio of tensions, 223
    Vee-thread, friction of, 187
    Vehicle, braking of, 260
    Velocity, 14
    -, angular, 16
  • image, 77
  • of piston, Fourier series for, 101
  • of sliding, wheel teeth, 319
  • ratio in chain drive, 240
    -, relative, 75
    time curve for cam, 283
    Vibration, amplitude of forced, 554
    -, damped, 550
    -, forced, 554
    -, free, 532
    -, frequency of, longitudinal, 533
    -, – of, torsional, 534, 568
    -, – of, transverse, 533, 538, 544
    Virtual eccentric, link motion, 162,
    165
    , Meyer expansion gear, 159
  • -, offset line of stroke, 162
    , radial valve gear, 168
    Viscosity, 203
    Von-Hefner Alteneck transmission
    dynamometer, 272
    Waimann, K., Graphical solution of
    torsional vibration, 582
    Walschaert valve gear, 169
    Watt governor, 456
  • straight-line motion, 122, 126
    Weight, 18
    Wheel teeth, 315
  • trains, 366
    Whirling of shaft, several loads, 567
    , single concentrated load, 565
    Whitworth quick-return motion, 9
    Wilson epicyclic gear box, 402
    Work, 22
    -, rate of doing, 413
    Worm and wheel, 353
    , efficiency of, 356
    Wrapping machine mechanism, 83
    Yoke, Scotch, 12

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