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 |  موضوع: كتاب The Theory of Machines الإثنين 08 يناير 2024, 12:25 am | |
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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
و المحتوى كما يلي :
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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