Advances in Gear Theory and Gear Cutting Tool Design

Advances in Gear Theory and Gear Cutting Tool Design
اسم المؤلف
Stephen P. Radzevich • Michael Storchak
التاريخ
11 يناير 2024
المشاهدات
294
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Advances in Gear Theory and Gear Cutting Tool Design
Stephen P. Radzevich • Michael Storchak
Editors
Contents
Part I Accomplishments in the Theory of Gearing
1 Fundamental Laws of Gearing 3
Stephen P. Radzevich
2 Gearing Theory Development: Geometry-Kinematic
Concepts . 39
Dmitry T. Babichev, Sergey Yu. Lebeded, and Michael Storchak
3 The Key Mistake in Generation of Conjugate Curves
and Surfaces 79
Stephen P. Radzevich
4 Meshing Limit Line of the Archimedes Worm Drive 127
Yaping Zhao and Tianfeng Wang
Part II Gear Manufacturing Methods
5 Gear Cutting with Disk-Shaped Milling Cutters . 151
Sergii Pasternak, Yurii M. Danylchenko, Michael Storchak,
and Oleksandr A. Okhrimenko
6 A Novel Design of Cutting Tool for Efficient Finishing
of G-Rotors . 181
Olexandr I. Skibinskyi and Andriy O. Hnatiuk
7 Interactive Control of the Teeth Gear Shaping in
the Cutting Tools Design . 205
Borys S. Vorontsov, Vitalii A. Pasichnyk, and
Yuliia V. Lashyna
8 Sinusoidal Gears and Alternative Method of
Tooth Generation 233
Ihor E. Hrytsay
xv9 Design of Technological Systems for Gear Finishing 255
Michael Storchak
Part III Gear Transmissions
10 Calculation of Gear Trains in Transmission Systems
of Vehicles 283
Vladimir B. Algin
11 Multispeed Planetary-Layshaft Transmissions
with Multipower Flow . 321
Konstantin B. Salamandra
12 Multiparameter Gears and Gear-Type Variators 361
Mykola E. Terniuk, Anatolii V. Kryvosheia,
Oleksandr V. Ustynenko, Oleksandr M. Krasnoshtan,
and Pavlo M. Tkach
13 Generalizing Structural Unified Model of the
Synthesis of Links of Flat-Toothed Gearing Systems 445
Yurii M. Danylchenko, Anatolii V. Kryvosheia,
Volodymyr Y. Melnyk, and Pavlo M. Tkach
14 Evolution, State of the Art, and Trends to Improve
Gear Tooth Strength 485
Eduard K. Posviatenko, Boris A. Lyashenko,
Nataliia I. Posviatenko, and Yaroslava O. Mozghova
Part IV In Memoriam of Professor Dmitry T. Babichev
15 Carefully, Scrupulously, Responsibly: In Memoriam
of Professor Dmitry T. Babichev . 509
V. E. Starzhinsky
Appendices . 519
Index . 621
xvi Contents
Index
A
Accepted calculation system, 452
Advanced generalized methods, 446
Antiquity Archimedes, 486
Approximate gear pairs, 32
Archimedes helicoid
equation of, 129
load-carrying capacity and surface
durability, 127
trajectory surface method, 128
unit normal vector of, 130
Archimedes worm
conical worm drive, 128
equation and unit normal vector, 131
formation principle for, 129, 130
meshing function of, 132, 133
meshing limit function, 134–137
worm gear tooth surface, 133
Archimedes worm gearing, 127
Architectonics, 285, 292, 293, 315
Asymmetric original contour, 217
Asymmetric tooth gears, 235
B
Base geometrical primitives, 511
BDT, 509–511, 515, 517
Bending stress, 238, 240
Bezier curve, 218
gear geometry, 215
generating surface, 209, 212
Biconvex-concave (BCC) teeth, 400
Break points, 476
C
CAD system, 194
Calculator module, 299, 300
CALS technologies, 448
Camus-Euler-Savary theorem (CES
theorem), 99
Cartesian coordinates, 558
Chain variators, 400
Charcoal, 494
Chemical and thermal processing (CTP), 500
Chip parameters, 241
Circular arc, 476
Closest distance of approach, 615–619
Coating, 498
Combined machining, 258, 269, 273
Complex geometric objects, 465
Complex mechanical gears and joints, 445
Complex original profiles, 469
Complex OShPs, 461
Complex-profile cylindrical gears, 446
Computer-aided design (CAD) systems, 377
Computer simulation, 253
Conjugate contours, 455
Conjugate gears, 454
Consequent coordinate system transformations
auxiliary orthogonal local coordinate
system, 607
Cartesian coordinate system, 608
closed loop, 605
homogenous matrix, 606
implementation, 605, 610
inverse coordinate system transformation,
606
linear transformation, 604
Consequent coordinate system transformations
(cont.)
local coordinate system, 604
local reference systems, 605
semi-orthogonal coordinate systems, 605
surface, 611
transition, 604
Contact geometry
actual value of angle, 555
converse indicatrix of conformity, 577, 578
degree of conformity, 563, 565
disk-type shaving cutter, 574
Dupin indicatrices, 556–559, 565–567, 572,
574–576
elements of gearing, 549
Euler equation, 568
Euler formula, 577
gear tooth flank, 573, 576, 577
higher-order analysis, 561
indicatrix of conformity, 567–569, 572,
573, 576, 578
kinematics, 549
line contact, 552
local reference system, 566
local relative orientation, 550, 552, 568
mating pinion tooth flank, 576, 577
matrix representation, 559, 560
operator of rotation, 555
point of contact, 565
quadratic equation, 554
quantitative evaluation, 562
quantitative measure, 550
radii of principal curvature, 568
relative orientation, 551
roots of equation, 573
smooth regular surfaces, 549, 550, 561
surface of relative curvature, 575
surfaces, 549
tangent directions, 553
tangent plane, 562
unit tangent vectors, 552
unit vectors, 553
violation of physical condition, 571
Continuity of action, 26
Continuous and discrete TiN coatings, 504
Contours of gear racks (CGR), 460
Convexity/concavity, 468
Coordinate system, 224
Coordinate system transformation
arbitrary axis, 587–589
Cartesian reference system, 589
conventional approach, 585, 586
conversion, 601, 602
dimension 4  4, 580, 581
Eulerian transformation, 586, 587
homogeneous coordinate vectors, 580
homogenous matrix, 603
inverse resultant, 590
linear, 590
linear transformation
coupled, 597–600
non-orthogonal reference system, 600
rolling, 592–597
screw motion, 591, 592
rotation, 583–585, 603
RPY-transformation, 602
translations, 581–583
unit vector, 603
Copying, 495
Cutting tool, 241
Cycloidal, 446
Cylindrical gearings, 446
Cylindrical gears
contours, 452
coupled toothed contours, 451
drawings, 454
external engagement, 453
non-contacting segments, 452
non-rollable profiles, 455
second design feature, 451
structural diagram, 454
theoretical and technological synthesis, 447,
451, 452, 456
theoretical shaping, 452, 454
D
Darboux frame, 541, 559
Deform 2DV11 cutting process rheological
modeling system, 246
Deform 3D system, 236, 244
Designing technological systems, 257, 277, 278
Diamond burnishing, 268
Diamond dresser gear, 277, 278
Diamond elastic gear hones, 261–263, 273,
276, 277
Differential-geometric method, 89, 90
Differentials, 322, 323, 326, 358
Digital computer models, 289
Digitalization, 283, 291
Digital stream, 291
Digital thread, 291
Digital twin (DT), 283–285, 290
Direction vector, 521
Disc-type gear milling cutter, 250
Disk gear contours, 471
622 IndexDisk-type milling cutters, 242
Domestic industry, 448
Domesticity, 517
Draftsman module, 299
Dressing tools, 277
DT of gear measuring center (DTGMC),
283, 284
Dual clutch layshaft transmissions
controls, 325
cost, 325
kinematic diagram, 325
power flow structure, 323
ratio, 325
structural diagram, 324
structure, 324
Dynamics, 286, 287, 291, 301–303
Dynamics models, 290
E
Eight-speed ID transmission, 338–340
Electrophysical methods, 277
Engagement zone, 56, 58, 63
Envelope curve, 95
Envelope surface, 79, 81, 89, 90, 106, 123, 124
Equivalent pulley-and-belt transmission, 12
conjugate action law, 92
features, 91
line of action, 93, 94
linear velocity, 91
principal features, kinematics, 95, 97, 98
rotation, 90
Equivalent stress, 238, 239
Euler-Savary equation, 21–26, 76
Euler-Savary theorem, 24
F
Finishing gear teeth, 495
First fundamental law of gearing, 102
Flat contours of gear wheels (FСGW), 460
Flat contours, matrix equation, 471
Flat gearing systems, 447, 459, 468, 471
Flat kinematic lines, 464, 467, 468
Flat original shaping profiles, 481
Flat shaping-producing technical system, 447
Floating point numbers, 521
Foreign scientists and programmers, 449
Form-generating technical system, 459, 481
Form-milling method, 495
Form-producing technical system, 449
Free rolling, 256, 261, 268
accuracy of machining gears, 266
method, 265
Free surfaces, 497
Friction force, 237, 246, 250, 253
Fundamental scientific studies, 449
G
Gauss’ characteristic equation, 542
Gaussian coordinates, 530, 531
Gear cutting, 152, 154, 155
Gear-cutting machine tools, 253
Gear finishing
design of technological systems, 256
design process, 256
Gear geometry, 212, 214, 216
Gear grinding, 258, 259, 497
and burnishing, 269
synthesized TS, 259
worm globe wheel, 277
zero method, 260
Gear load capacity, 504
Gear machining processes
advantages and disadvantages,
153, 154
disc-shaped milling tools, 155, 157, 158
with profile-dependent tools, 152
with profile-independent tools, 152
Gear manufacturing, 155
Gear Measuring Center (GMC), 283
Gear meshing theory, 509
Gear processing, 450
Gear ratio, 3
Gear teeth grinding, 497
Gear teeth honing, 496
Gear tooth flank hardening process
coatings, 504
CTP, 501
electron-beam unit, 501
IN, 501
IPTN, 502, 503
key issues, 500
local laser coating, 501
low-temperature carbonitriding, 500, 501
PVD, 503
shock-cyclic contact loading, 500
SPD, 502
standard technology, 500
surface hardening, 501
transition, 500
undulating wear, 500
Gear trains, 485–487
advancement, 488
architectonics, 292, 293, 315
DT (see Digital twin (DT))
GMC, 283
Index 623Gear trains (cont.)
reliability calculations, 284
strength calculation results, 284
Gear variators
structure and design
auxiliary and control functions, 392
control mechanisms, 392
freewheel mechanism, 392
impulse type, 395–400
kinematically accurate variator, 394
meshing wheels, 393
pulse-type variators, 395
transmissions and drives, 391
Gear wheels, 485
cutting tools, 495
mechanical engineering, 504
metals, 494
surface engineering, 499
Gearing
Camus-Euler-Savary theorem, 100
characteristic line, 81
common perpendiculars, 81
condition, 4
conjugacy, 79
conjugate action law, 11
conjugate tooth profiles, 15
contact point, 119
cycloidal gearing, 112, 114, 115, 117
design parameters, 6, 32
designing, 4
differential-geometric method, 83
driven shaft, 3
efficiency, 80
envelope surface of the second kind, 106
equation of conjugacy, 106
equivalent pulley-and-belt transmission, 13
features, 3
first fundamental law, 8, 10
first fundamental law of gearing, 105
fundamental law, 30, 31
gear tooth profile, 17
helical gearing, 117
helix angles, 4
instantaneous relative motions, 9
kinematic method, 83, 123
line of action, 83, 123
linear velocity, 7, 8, 17
mating pinion, 6, 7
method of common perpendiculars,
81, 83, 109
non-equivalency of deviations, 121, 122
parallel-axes gearing, 100–103
pitch circle, 82
pitch point, 118
power density, 81
requirements, 4
reversibly-enveloping surfaces,
107–108
rolling motion, 79
second fundamental law, 11, 106, 118
Shishkov equation of contact, 105, 123
spline-shaft, 110
surfaces feature, 9
tooth profile, 81, 111
transition, 110
transverse contact ratio, 5
Wildhaber-Novikov gearing, 120
Willis theorem, 100, 123
Gearing theory development
acceleration, 68
band and scale surfaces, 48
computer-aided design, 39
curvature variability, 47
geometric images, 39
kinematic methods
cutting edge, 66
kinematic methods
parameters field, 66
material layers, 66
shaping process, 68
kinematic profiling method, 70, 72–74
mathematical models, 46
maximum load capacity
analysis of properties, 59
conjugate profiles, 59
curvature and contact stresses, 56, 63
curvature fields, 58
Euler-Savary equation, 56
Hertz equation, 56
kinetic characteristics, 57
kinetic quality parameters, 61
local geometric and kinematic
indices, 55
quality characteristics, 56
quality functions, 61
surfaces, 54
transmission ratio, 57
value of criterion, 54
multi-parameter, 44–46
penetration speed, 68
polylines, 47
quality characteristics, 49–51, 54
shaping alternative theory, 41–43
shaping processes, 48
software algorithms, 46
surface curvature study, 74–76
surface shaping processes, 39
unified geometric parameters, 47
624 IndexGears finishing
synthesized technological systems
(see Synthesized technological
systems)
Generalized geometric-kinematic diagram, 457,
474, 481
Generalized geometric-kinematic shaping
scheme, 471
Generalized kinematic diagram, 473
Generalized mathematical model, 455
Generalized OShP, 462
Generalized structural diagram
cylindrical gear wheel, 458
flat gearing, 459
OGC, 458
OShC, 458
straight and reverse links, 458
technological synthesis, 456
technological system, 459
theoretical shaping, 455
theoretical synthesis, 458
Generalized structural unified mathematical
model, 473
Generalized symmetrical original sharing
profile, 462
Generalized three-link mechanism
complexity, 322
degrees of freedom, 321
differentials, 322
German engineering practice, 322
modified designation, 322
torques, 322
Generalized unified mathematical
description, 462
Generalized unified matrix equation, 462
Generalized (universal) unified
mathematical models
classification feature, 450
flat gearing, 451
quality characteristics, 451
shape gearing, 450
structural diagram, 450
Generating enveloping process, 19
Generating surface, 206, 209–211
Generative machining processes, 246
Geometrical-kinematic conditions, 459
Geometrical-kinematic schemes, 457
Geometric-kinematic diagrams, 473
Geometric-kinematic shaping schemes, 473
Geometric-kinematic synthesis theory, 449
Grinding machining center, 202
Grinding wheels, 497
G-rotor hydraulic motors, 181
G-rotors
parameters, 182
properties and design of, 181
satellite machining technology, 192–194
spur wheels, 195, 197, 199, 200
working profiles in, 183, 185–187, 190, 191
H
Hardening deformations, 500
Heron of Alexandria’s “Toy Theatre”
automata, 486
High-precision mechanical spur gears, 445
Hobbing processes, 153, 239–241, 243, 244,
246, 247
Hydrogen-free nitriding, 498
Hydrogen-saturated parts, 501
I
IDDO transmission with single transition
shifts, 353–357
controls, 351
four dependent gear-shifting sequences, 350
functions, 352
kinematic diagram, 350
minimization of criterion, 350
restrictions, 349
switched-on transmission controls, 350
synthesized transmission, 350
three single transition shift
sequences, 351, 353
IFToMM Workshop, 511
Igor Tsitovich School (ITS), 289, 290
Individualization, 291
Industrial revolution, 491
Information model, gear transmission, 285
diagnostics, 312–313
dynamics, 301–306
evaluation, kinematic diagrams (KDs),
296–298
kinematic and quasi-static calculations,
298–301
lifetime expense and PHM, 313–314
reliability calculation, 308–310
special reliability calculation method,
310–312
synthesis of kinematic diagrams, 292–296
Information technologies, 448
Initial tool surfaces (ITS), 48
Insufficient lubrication, 503
Interconnected systems, 446
Internal combustion engines, 321
Index 625International Conference “KOD-2018”, 513
Involute gears
advantages, 233
breakage, 234
disadvantages, 233
in mechanical engineering, 233
model of strain, 234
overloads, 233
performance, measures, 235
Involute spur gears, 454
Ion nitriding (IN), 501, 504
Ion-plasma thermo-cyclic nitriding (IPTN),
502, 503
K
Kinematic analysis, 511
Kinematic method, 34
analytical expressions, 85
geometry, 84, 85
linear velocity vector, 86, 88
matrix form, 84
motion, 84
Shishkov equation of contact, 84, 88, 90
traditional method, 90
unit normal vector, 86, 88
velocity, 84
Kinematic scheme, 489
Kinematic surfaces, 459
L
Layshaft transmissions, 323
two speeds, 324
Leibniz arithmometer, 488
Life-strength curves (LSCs), 307, 309
Lifetime expense, 291, 313–315
Lifetime forecasting, 313
Lifetime mechanics of machines (LMM),
289–291
Lincoln-type milling machines, 493
Linear diagrams, 455
Linear displacement, 169
Linear velocity vector, 17
Local laser coating, 501
Low-temperature carbonitriding, 501
LP-search method, 256, 257, 278
M
Machine parts properties, 497
Machining gear wheels, 495
Main lateral surface (MLS), 462
Mainardi-Codazzi relations of compatibility,
542
Mathcad environment, 465, 468
Mathematical model
form-shaping process, 159, 161, 162,
164–166, 168, 171, 174, 177
generalized form-shaping kinematics, 159
Mathematical models, 450, 456
Matrix equations, 467
Maudsley’s caliper, 493
Mechanical engineering, 448, 486
Meshing limit line
Archimedes worm, 134–136, 138
computing method of, 139, 140
gear drives, 128
in worm axial section, 145
Metal-cutting machines, 493
Microhardness distribution, 499
Microroughness, 249
Middle Ages, 486
Mobile machines, 286, 289, 291, 302
Modern mathematical methods, 445, 461
Modern planetary transmissions, 321
Modern universal milling machine, 493
Modified Simpson mechanism, 294, 295
Multiparameter gears
addendum modification coefficient, 411
application, 361
attributes, 375
auxiliary and control devices, 364
axial torques of resistance, 420
biconvex and biconvex shapes, 414
boundary values, 400
BСС-teeth, 402, 403
center of gravity, 417, 418
circular tooth, 422
classifications, 373
cogwheels, 423
complex geometry, 423
complex kinematic shaping schemes, 426
complex structural-parametric
optimization, 363
complex systems development, 361
components, 363
concretizing structures, 368
control dimensions, 408
control function, 367
coordinate axes, 403
cylindrical gear parameters, 401
cylindrical generating wheel, 438
cylindrical surface, 432
deforming and cutting tools, 439
electromechanical systems, 372
626 Indexelemental structure, 367
functionality, 373
gas turbine engines, 362
gear variators, 369
general functional three-stage approach, 363
generalized unified mathematical
model, 425
generating surface, 405
generatrix, 435
geometric 3D model, 433
geometric properties, 424
geometry, 405
implementation, 424
industrial market demand, 374
kinematic theoretical shaping, 430
machine and working gearing, 423
machine gearing, 407, 408
manufacture of wheels, 439
manufacturing method, 400
matrices, 434
matrix classification, 374
maximum angle, 413
maximum bending stresses, 415
mechanical engineering technology, 423
mechanisms, 361, 372
motion conversion scheme, 375
nonspecific product functions, 366
normal vector, 404
optimization, 424
parameters, 372, 434
partially specified elemental structure,
product, 367
physical effects, 372
point-type contact, 400
power gear variators, 362
power-to-weight ratio, 362
product functioning, 365
ratio control range, 375
secondary auxiliary function, 366
shaping process, 426
shaping surfaces, 428
solid model, 438
speed and power characteristics, 376
structure and design
auxiliary functions, 381
complex system theory, 377
cylinders, 387
element, 380
elementary mechanisms, 378
factors, 386
geometrical and kinematic features, 378
linear displacement, 389, 390
Newton’s method, 391
pair of gears, 378
parameters, 377
pitch surface, 386
rotation transmission, 389
screw-nut system, 382
surface approximation, 391
toroidal dividing surface, 384
toroidal surface, 388
torque transmission, 390
transmission of rotation, 381
transmission-guiding mechanism, 387
transmissions, 377, 380
two-parameter gearing, 380
two-parameter transmission, 379
vehicle transmissions, 386
supersystem attributes, 364
sweeping and shaping movements, 437
symmetry operator, 433
technical design, 365
traditional and innovative multifunctional
variable, 363
transfer of torque, 372
transformations, 409
transformer technologies, 363
transition matrices, 405, 406
transmissions, 361, 366, 374
types of variators, 375
uniform rotational and translational
movements, 428
variable quantity, 409
X
nYnZn coordinate system, 403
Multiparameter mapping, 481
Multipower flow transmission operation
modes, 333
Multispeed transmissions, 325
N
Nartov caliper, 490
Newton-Raphson method, 620
Nominal, 451
Non-invariant characteristics, 467
Normal vector, 209
Novikov-Wildhaber profile, 452
Novokramatorsk Machine-Building Plant, 400
O
Operation conditions (OC), 307, 308, 315
Optimal, 455
Optimization problems, 255, 256
Original contours (OC), 460
Original generating contours (OGC), 458, 460
Index 627Original shaping contours (OShC), 458, 460
Original shaping profiles, 452, 454
Oscillating motion, 251
OShP coordinate system, 465
OShP elements, 459
OShP mathematical description, 465
P
Parallel-axes gearing, 14, 30
Parametric synthesis technique
differentials, 336
formulation solutions, features, 336
gear ratio values, 338
sequential stages, 336, 337
series of gear ratio, 335
speed ratio series, 337
Periodic reciprocating rectilinear motion, 252
Physical deposition from the gas phase
(PVD), 503
Plane gearing systems, 459
Plane kinematic lines, 467
Planetary gearset, 322
Planetary-layshaft transmissions
advantages, 326
basic structural diagrams, 326, 327
closed multipower flow structures, 358
controls, 326
controls switching, 358
design, 325
designations, 326
differentials, 328
gearsets, 326
kinematic diagrams
conditions and restrictions, 334, 335
parametric synthesis (see Parametric
synthesis technique)
sequential stages, 334
multipower flow, 326
operating modes, 326, 328
total speed estimation, 331–333
transmission speed, 326
Polygonal, 446
Position vector, 521
Power density, 122
Power train gears, requirements, 494
Power transmission, 486
Pressure angle, 207
Private geometrical-kinematic schemes, 476
Probabilistic calculations, 287–289
Profiling gears, 491
Prognostics and Heath Management (PHM),
292, 313
Pulse-type variators, 395
R
Radial-circular method (RCM), 241, 244, 253
and hobbing, 243, 247
method of gearing, 249
originality, 251
up-cut hobbing process, 248
versatility, 252
Reciprocating motion, 251
Reduced curvature, teeth surface, 229, 230
Regular mechanical system (RMS), 302,
303, 306
Reishauer machines, 497
Relative durations of operation conditions
(RDOC), 309
Relative sliding velocity, 220, 221
Relative velocity, 475
Reliability indexes, 284
Reliability theory, 289
Renaissance, 486
Responsibly, 510
Restriction formulation, 334
Reuleaux method, 83
REXS (Reusable Engineering EXchange
Standard), 284
Rigid cutter attachment, 489
Roll grinding, 497
Rolling, 455, 495
Rotating coordinate system, 131
Round Table meetings, 510
S
Scientific seminar, 511
Second fundamental law of gearing, 102
Second-order lever scheme, 489
Selective tracking, 258, 275–277
Self-propelled caliper, 489
Shaping gear contour, 475
Shaping kinematic diagram, 472
Shaping-producing system, 450
Shaving cutter, 495
Shishkov equation, 9, 34, 102
Simulation-based model, 283
Single standard original contour, 454
Sinusoidal, 446
Sinusoidal asymmetric tooth gears, 252
Sinusoidal bevel gear, 252
Sinusoidal gears
advantages, 235
contact tension area, 240
design, 235
frictional forces, 237
mating gears, 235
RCM, 239–241
628 Indexresearch methods, 236
stress reduction, 238
SKOSIR software module, 301
Software interface, 218
SolidWorks software, 236, 237, 244
Spatial form-generating technical system, 481
Specific sliding coefficients, 227
Specific tractive forces (STF), 287
Stationary clock regulator, 488
Steel grades, 495
Straight and reverse shaping, 476
Stress relaxation, 504
Structural diagrams, 325
Subsystem’s limitations, 454
Surface engineering, 498
Surface hardening, 501
Surface layer modification, 499
Surface plastic deformation (SPD), 268, 502
Surfaces
Bonnet theorem, 540
Cartesian reference system, 529, 543
curvatures, 541
derived vectors, 544, 545
Euler formula, 547
first fundamental form, 534–536
formulae transformations, 546
Gauss characteristic equation, 540
gear-cutting tool design, 529
gear tooth flank, 530, 531, 540, 541,
544–546
geometry, 547
local frame, 533
Mainardi-Codazzi relations, 540
natural kind, 543
second fundamental form, 536–539
tangent plane, unit normal vector, 531–533
tangent vectors, 544, 545
Symmetrical initial contour, 217
Synthesized kinematic diagram, 338
Synthesized technological systems
combined machining methods, 268–273
multi-tool setup systems, 273–274
selective tracking systems, 275–277
shaping systems for gear tools, 277
systems with free rolling, 261–268
systems with rigid kinematic connection,
258–261
System elements, 459
System theory, 289
T
Task and theoretical shaping (design), 446
Technical systems, 449
Technically complicated item (TCI), 289,
313, 314
Technological systems (TS)
design, 255, 256
finishing gear wheels, 256
optimization problems, 255
parametric optimization algorithm, 257
principles, 256
structural selection and gears finishing, 257
technological systems and gears
finishing, 258
Teeth grinding, 497
Teeth surfaces, of cut gears, 216, 217
Teeth working surfaces, 228
Theoretical geometric-kinematic synthesis, 449
Theoretical shaping, 450
Theory and practice of gearing, 509
Theory of meshing and surface forming, 510
Theory of transport and traction machines, 286
Three-dimensional half-space, 498
Three-link planetary gearset, 321
Toothed tool shaping systems, 277
Traditional vacuum nitriding, 502
Transformation matrices, 464
Transmission dynamics, 301
Transmissions synthesis with three power flows
11-speed transmission, 344, 346, 348
14-speed transmission, 342, 343
Transmissions synthesis with three power flows
and single transition shifts
IDD transmission (see IDD transmission
with single transition shift)
IDDO transmission with single transition
shifts, 353–357
neighbor speeds, 349
pair of controls, 349
parametric synthesis technique, 349
Transmissions synthesis with two power flows
eight-speed transmission, 338–340
12-speed transmission, 340
Triple scalar product, 20
Truncated epicycloids, 191
Two-speed layshaft transmission, 323
U
Undeformed chips, 236, 243–245
V
V-belt variators, 399
Vectors
components, 523
fundamental properties, 522
Index 629Vectors (cont.)
lagrange equation, 526
matrices, 527
product, 525
scalar product, 524
surface generation, 521
triple scalar product, 525, 526
types, 521
Visual Statics package, 301
W
Water wheels, 486
Western European, 488
Working diamond elements, 262
Worm gear grinding, 259
Worm wheel grinding technology, 195

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