Precision CNC Machining for High-Performance Gears – Theory and Technology

Precision CNC Machining for High-Performance Gears – Theory and Technology
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SHILONG WANG, GUOLONG LI, CHI MA
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Precision CNC Machining for High-Performance Gears – Theory and Technology
SHILONG WANG
Chongqing University, Chongqing, China
GUOLONG LI
Chongqing University, Chongqing, China
CHI MA
Chongqing University, Chongqing, China
Contents
Preface vii
Acknowledgments ix

  1. Introduction 1
    1.1 Overview of high-performance gear 1
    1.2 High-performance gear CNC machining technology 4
    1.3 Status and development trend of CNC machining technology
    of high-performance gear 23
    1.4 Current situation and development trends of typical gear making machines 38
    1.5 Opportunities and challenges 40
    References 41
  2. Computational theory for precision machining
    of high-performance gear 49
    2.1 Modeling the modified tooth surface of high-performance gear 50
    2.2 Envelope principle of point-vector family 56
    2.3 First envelope calculation of point-vector family for a modified tooth profile 63
    2.4 Calculation of the second envelope modification of point-vector family 74
    References 86
  3. Method to reduce the principle errors in high-performance gear
    machining 87
    3.1 Method for reducing the tooth surface twist during forming machining
    for a modified gear 88
    3.2 Method for modified gear to reduce errors during generating machining 105
    3.3 Principle error of hob-relief grinding and its reduction method 118
    3.4 Method of error reduction for the gear shaper cutter grinding principle 128
    References 141
  4. Modeling methods and compensation techniques for multisource
    errors of the CNC gear machine tool 143
    4.1 Modeling and sensitivity analysis of the geometric error 144
    4.2 Tool error modeling of the CNC gear machine tool 161
    4.3 Modeling the force-induced geometric error in CNC gearing machines 176
    v4.4 Establishment of the thermal error model of the CNC gear machine tool 186
    4.5 Multisource errors compensation for the CNC gear machine tool 206
    References 239
  5. Design and optimization of the precision CNC gear machine tool 241
    5.1 Design of core functional components for precision CNC gear machine tool 242
    5.2 Thermal characteristics analysis and optimization of the precision CNC gear
    machine tool 258
    5.3 Design of high-speed dry cutting hob 290
    5.4 Gear manufacturing function software 294
    5.5 Application case 300
    References 303
  6. Optimization method of the grinding process parameters 305
    6.1 Process parameter optimization for tooth-surface precision 306
    6.2 Grinding parameter optimization for residual stress 315
    6.3 Process parameter optimization for energy consumption 326
    6.4 Process parameter optimization of gear-tooth machining considering
    precision and quality 337
    References 345
  7. High-speed dry-cutting process and automatic production line of gear 347
    7.1 High-speed dry cutting process of gear and key technology of automatic
    production line 349
    7.2 Automatic production line integration of high-speed dry cutting of gears 360
    7.3 Energy efficiency monitoring and process management system for
    high-speed dry cutting automatic production line for gears 363
    7.4 Demonstration of the high-speed dry cutting automation production
    line of gears 369
    References 371
    Index 373
    Index
    Note: Page numbers followed by f indicate figures and t indicate tables.
    A
    Adaptive neural fuzzy inference system (ANFIS)
    method, 13
    AISI 52100 steel, 16–17
    Automatic production line, 348–350f, 349
    chamfering process, 358–360, 359f
    characteristics, 349–350
    chip control technology, 349
    dry turning tool, new, 351t, 352f
    energy efficiency monitoring, 363–369
    heat accumulation, 349
    hobbing process and equipment, 351–358
    integration of high-speed dry cutting of gears
    linear layout truss-type, 361–363, 362f
    pin-type robot, 360–361, 361t, 361f
    parameters, 350, 351t
    process management system, 363–369
    spindle structure, 350, 351f
    Automobile gears, 348
    Auxiliary function module, 37
    Axial modification
    end-face profile, 55
    helix modifications, 54–56, 55f
    model, 352–354, 353f
    position, 54–55, 55f
    profile, 54, 56
    tooth repair shape, 54, 55f
    Axis compensation method
    EGB working principle, 209, 210f
    error compensation, 209–210
    grinding motion trajectory, 209–210, 210f
    motion axes, 207
    path planning measurement, 208
    point-vector quadratic envelope, 209
    thermal error compensation, 233–239
    three-dimensional (3D) model diagram, 206, 207f
    tooth surface
    creation coupling model, 208, 208f
    generation model, 208, 208f
    B
    Boundary constraints
    contact pair between hobbing machine table
    and platen, 253, 253f
    spindle transmission structure, 252, 252f
    table surface and body of hobbing machine, 253,
    253f
    worm gear, 252, 252f
    C
    Chamfering technology, 358–360, 359f
    Chinese gear industry, 1–2
    Chip-free machining method, 4
    CNC gear machine tool
    boundary constraints, 252–253, 252–253f
    error modeling, 161–176
    finite element
    mesh model, 251, 251f
    simulation, 253–257
    geometric error, 144–161
    high efficiency and precision multifunction, 303
    high-precision and high-speed rotary table,
    244–246, 246f
    high-speed precision hobbing spindle system,
    242–244
    large-scale hydrostatic rotary table, 247–251,
    247–248f
    multisource errors, 241
    structural optimization, 258
    CNC machining technology
    high-performance gear, 4–23
    status and development trend, 23–37
    Conical worm grinding wheel
    grinding motion model, 137–138
    grinding position and attitude, 135–137,
    136–137f
    parameters, 132–135, 133f, 138, 139t
    proposal, 130–132, 132f
    Coordinate systems, 123–124, 124f
    Coordinate transformation, 64, 71, 77–79
    Cubic boron nitride (CBN) modified honing
    process, 39–40
    Cutting force, geometric error, 176–177
    comparative analysis of M-value, 231–233, 232f
    compensation model, 228–230, 229t, 229f
    experimental principle of radial error, M value,
    230–231, 230–232f
    373Cutting force, geometric error (Continued)
    experimental scheme, 230
    gear M-value, 231, 232f
    Cutting heat, high-speed cutting, 14–18
    Cyclic grinding module, 37
    D
    Deflection
    diamond roller, 113–116, 114–115f
    rotor core, 263
    Diamond roller, 113–116, 114–115f
    DLL. See Dynamic link library (DLL)
    Double degree-of-freedom meshing analysis,
    178–182, 179–181f
    Drum modification, 91, 110
    Drum-shape modification, 82, 84f
    Dry cutting. See High-speed dry cutting process
    Dynamic link library (DLL), 299
    E
    Electric spindle tool post, 354–355, 355f
    Energy consumption model
    gear-machining machine, 326–335
    machine power, 326–327
    toothing process parameters, 335–337
    Energy efficiency monitoring, 363–369, 364f
    automatic NC programming, 368
    drawing process and production tasks, dynamic
    issue, 365
    dynamic monitoring system, 366–367
    equipment and production line, 366
    equipment running status monitoring and fault
    alarm management, 366
    optimization decision of process parameters, 368
    production schedule information collection, 365
    remote diagnosis and management, 368–369
    task monitoring, 365
    tool changes, 367, 367f
    Enveloping process, 59–60, 60f
    Error compensation
    geometric, 224–228
    measurement and identification, transmission
    chain, 213–216, 213–214f, 214t
    thermal model (see Thermal errors)
    transmission chain errors, 210–213, 211f
    Error modeling
    grinding wheel error, 168–170, 168–169f
    hob error
    end-tooth profile, 161–164, 166, 166f
    error helicoid, 167–168, 167f
    gear hob, 161–164
    helicoid, 166, 166f
    parametric expression, 166
    tooth surface, 167
    worm grinding wheel (see Worm grinding wheel
    error)
    Error sensitivity analysis
    error model simplification, 148–149
    Morris method, 150–157, 153–156f, 156t
    Sobol method, 157–161, 160f
    F
    Finite element analysis (FEA) method, 177–178,
    177f, 273–274
    cloud chart for modal vibration
    column, large, 254, 254f
    column structure, 254, 257f
    hob box, large column and left body assembly,
    254, 256f
    left body, 254, 255f
    outer support structure, 254, 257f
    right body structure, 254, 258f
    sliding plate on hob box, 254, 254f
    table shell, 254, 257f
    table surface, 254, 256f
    tool holder of hob box and cover plate, 254,
    255f
    transmission mechanism, 254, 255f
    x-axis screw and screw chuck holder, 254, 256f
    hobbing machine, 253–254
    First envelope process
    comparative analysis, 72–73, 72t, 73–74f
    coordinate systems, 63–64, 64f
    of point vector, 66–69, 66–68f
    profile calculation of forming tools, 69–72,
    69–70f
    projection, 64–66, 65f
    Flywheel, 19
    Force-induced geometric error, 10–12
    cutting, 176–177, 176f
    finite element analysis (FEA) method, 177–178,
    177f
    mapping relationship
    double degree-of-freedom meshing analysis,
    178–182, 179–181f
    machining simulation, 182–186, 183t,
    184–185f
    374 IndexG
    Gear grinding processes, 32–34
    auxiliary function module, 37
    CNC machine, 303
    contact line, 89–90
    contact trace, 106
    cyclic grinding module, 37
    finite element model, large plane wheel, 287–290,
    287–290f
    five-axis linkage, 35, 35f
    gear making process, 22–23
    gear shaper cutter, 131–132, 132f, 138–141
    and hobbing, 22–23
    interface, 37
    machine tool status module, 37
    mapping relationship, 88, 89f
    numerical simulation, 140–141, 140–141f
    optimization, 21–23
    production process module, 37
    project management module, 36–37
    simulation process, 90–91, 90–91f
    temperature rise calculation, large plane wheel,
    283–287, 284f, 286f
    thermal characteristics, large plane wheel
    coordinate system, 281, 281f
    grinding wheel and tooth surface, 281–282,
    282f
    mirror heat source, 282–283, 282f
    schematic diagram, 280, 280f
    working principle, 279–280, 279f
    thermal deformation, 12
    three-dimensional model diagram, 35–36, 36f
    worm wheel, 5–6, 6f
    Gear hobbing machine, 4–5, 5f, 20, 28f, 243, 356,
    358f, 362
    and gear grinding processes, 22–23
    gear making machine tools, 18–19
    machining accuracy optimization
    algorithm flow, 309–310, 310f
    cumulative pitch errors, 309–310, 312f,
    313–315, 314f
    gear errors, 313, 314t
    helix errors, 309–310, 311f, 313–315,
    313f
    hobbing parameters, 309
    optimal process parameters, 313–315, 315t
    prediction, 309–310, 312t
    process parameters and gear errors, 309,
    311t
    single pitch errors, 309–310, 312f, 313–315,
    314f
    tooth profile errors, 309–310, 311f, 313–315,
    313f
    machining precision, 306
    power measurement, 333f
    process parameters, 21–23
    status and development
    CNC gear, intelligent, 24–25
    high-precision, high-stiffness, and
    high-reliability, 25
    high-speed and high-efficiency, 25–26
    large-scale CNC, 27–28
    wet and dry cutting, 26–27
    structure and function module, 28–32, 28f
    numerical control (NC) code template, 29, 29t
    Siemens SINUMERIK 840Dsl, 30–31, 31f
    thermal error, 186–196
    compensation model, 195–196
    temperature variable, 192–196, 192–193f, 194t
    Gear machine. See also CNC gear machine tool
    large-scale gear machine tool, 301
    thermal error, 3
    tool transmission system, 2, 34
    Gear-machining machine, 347, 351–352, 360
    coordinate system, 330
    cutting edge trajectory, 330–332
    cutting power, 327, 329, 332
    cutting stage energy, 329, 329f
    energy consumption model, 326–335
    error modeling
    compensation technology, 7–8
    force-induced, 10–12
    machine tool geometric, 9–10
    thermal-induced, 12–14
    tool modeling, 7–8
    fitting curve of machine tool, 327, 328f
    gear hobbing machine power measurement, 333,
    333f
    gear workpiece, 331
    hobbing force, 332
    hobbing machine processing power, 327, 328f
    parameters, 333, 333t
    power measurements and prediction values,
    333–335, 334t
    precision, 306
    single tooth cutting simulation diagram, 331, 331f
    spindle speed, 327, 328t
    tooth-profile equation, 330
    Index 375Gear-making errors, 148–149
    Gear-making machine tool, 38–40
    compensation method, 9–10
    error modeling, 9–10
    rotary table, 19–21
    spindle system, 18–19
    thermal errors, 12–13
    Gear-making zero-programming system
    deformation error compensation, 234–235
    hobbing machine, 234–235, 237
    online temperature sensor arrangement, 235–236,
    236f
    principle, 234
    thermal error compensation, 236–237, 237f, 237t
    working gear and hob parameters, 236, 236t
    Y31200CNC6 hobbing machine, 236, 237f
    Gear manufacturing function software
    arbitrary modification module
    tooth direction, 297
    tooth profile, 296–297
    auxiliary function module, 296
    circulating grinding module, 296
    grinding wheel arbitrary modification module,
    297, 298f
    machine tool status module, 295
    production flow module, 295–296
    project management module, 294–297
    secondary development
    dynamic link library (DLL), 299
    installation, 300
    NC programming, 300
    visual interface design, 298–299
    tooth surface distortion control module, 297
    Gear profile, 100
    Gear shaper cutter
    conical worm grinding wheel, 130–135
    gear grinding, 128–129
    kinematic analysis, 135–138
    parameters, 138, 139t
    principle, 129–130, 129f, 131f
    simulation verification, 138–141
    Gear shaping machines, 38
    Gear-tooth machining, 3, 35–36, 40, 337–345,
    338f
    multiobjective parameter optimization algorithm
    competitive selection and cross variation,
    340–341
    elite strategy and population merging,
    342–343, 342f
    nondominated sorting and congestion
    calculation, 340
    population initialization, 339–340, 340–341t
    processing parameter
    characteristic quantities, 344
    correlation coefficient matrix calculation,
    343–344
    principal component score, 344–345, 345t
    standardized data processing in optimal
    frontier, 343
    Geometric error
    CNC gear machine tool motion chain, 144, 145f,
    146
    compensation
    CNC worm wheel gear grinding machine, 224
    cutting force, 228–233
    replacement value, 227
    spatial attitude error component, 225
    spatial error model, 224–225
    ternary linear equation system, 227
    value, 226–227
    elements, 146
    gear machine tool, 144, 145f, 146
    modeling, 9–10, 144–148, 145f
    motion axes, 144–146
    multisource, 144–146
    sensitivity analysis, 148–161
    spatial position error, 147–148
    transformation matrix, 147
    Geometric structure design, 241–242, 293, 294f
    chip grooves, 292
    coating, 292–293, 293f
    cutting edge length, 292
    heat treatment procedure, 293
    high-speed dry cutting hob, 293, 294f
    manufacturing procedure, 292
    multihead hob, 292
    shank mechanism, 291
    small diameter, 291, 291f
    Green manufacturing
    environmental impact, 347
    resource consumption, 347
    Green production, 348
    Grinding parameter
    and hobbing, 305
    mathematical relationship, 322–324
    residual stress, 315–326
    Grinding process
    gear, 315
    376 Indexhigh-performance gears, 305
    optimization process, 338f
    parameters, 337–338
    process parameter optimization, 306–315
    Grinding simulation, 138–140
    Grinding wheel
    arbitrary modification, 294, 297
    automatic modification, 303
    carborundum, 297
    CNC gear machine tool, 241–242
    and diamond roller, 295
    error, 168–170, 168–169f
    profile
    contour calculation, 125–126
    coordinate systems, 123–124, 124f
    relieving grinding wheel, 125–126
    SIEMENS numerical control programming
    language, 300
    tooth surface, 279–280, 282f
    H
    Heat accumulation, 349
    Heat dissipation
    forced convection
    by cooling system, 269
    heat transfer, 270–271
    and heat generation, 276–277
    natural convection, 270
    Heat source model
    ball screw pair, 267–268
    rolling bearing, 258–268, 260f
    rolling guide pair, 268
    servo/built-in motor, 261–267, 264f, 266t
    Helical tooth surfaces, 50, 50f, 64f
    High-performance gears, 2–4
    High-speed dry cutting process
    automatic production line, 349, 349–350f
    characteristics, 349–350
    chip control technology, 349
    heat accumulation, 349
    new dry turning tool, 351t, 352f
    parameters, 350, 351t
    spindle structure, 350, 351f
    line of gears, 369–370, 370t
    High-speed dry hobbing machine, 291f, 301–303,
    302f
    data acquisition flowchart, 196, 197f
    displacement data acquisition, 197–198, 198f
    environmental temperature, 198
    geometric structure design, 293, 294f
    chip grooves, 292
    coating, 292–293, 293f
    cutting edge length, 292
    heat treatment procedure, 293
    manufacturing procedure, 292
    multihead hob, 292
    shank mechanism, 291
    small diameter, 291
    recording device, 197–198, 198f
    sensors arrangement, 198, 199f
    temperature
    change curve, 198, 199f
    data acquisition, 197–198, 197f
    sensors, 198
    temperature-thermal error, 197–198
    thermal characteristics experiment, 196–199
    thermal error
    curve, 199, 200f
    modeling, 199–202, 200–201t, 201f
    principle, 196–199, 197f
    Hobbing error, 242–244, 242–243f, 245f
    end-tooth profile, 161–164, 166, 166f
    helicoid, 166–168, 166–167f
    parametric expression, 166
    tooth surface, 167
    Hobbing process, 87–88
    cutting edge, 330
    and equipment, 351–358
    gear (see Gear hobbing machine)
    and grinding machines, 305, 326–327
    high-speed dry cutting precision, 352–354, 353f
    machine processing, 328f
    optimization design
    high-speed dry cutting workbench, 355–358,
    357–358f
    modified hob, 354
    spindle, 354–355, 355–356f
    parameters, 306, 368
    precision prediction model, 306–309, 306–308f
    Hobbing tooth profile, 352–354, 353f
    Hobbing workbench
    damping mechanism, 356–358, 357f
    gear hobbing machine, 356
    high-speed dry cutting precision gear, 357,
    358f
    three-dimensional solid model, 356, 357f
    workbench design principle, 358
    Human-machine interface (HMI), 30
    Index 377I
    Improved particle swarm optimization (IPSO),
    308–310, 308f, 312t, 315
    K
    K-shape modification, 82, 84f
    L
    Large-scale precision CNC hobbing machine, 247,
    301, 302f
    Linear layout truss-type automatic production line,
    361–363, 362f
    M
    Machine tool geometric error modeling, 9–10
    Machining error
    contact trace calculation, 106
    tooth surface twist
    calculation model, 108–111, 108–109f
    in generating machining, 106–108, 107f
    Machining simulation, 182–186, 183t, 184–185f
    Material removal rate (MRR), 327
    Modified gear
    contact line, 89–90
    machining error analysis, 105–111
    modeling, 105–111
    tooth surface
    errors, 111–118
    twist, 88–104
    Modified tooth surface, 50–56
    axial modification, 54–56, 55f
    first envelope calculation, 63–73, 64f
    spiral, 50–52
    tooth profile modification, 52–54, 53f
    Morris method
    analysis steps, 150–151
    cyclic sampling number, 152
    error identification, 156–157
    error reduction rate, 156–157, 157t
    geometric error tooth surface, 150
    input and output parameters, 150
    sensitivity analysis process, 152
    sensitivity index plot, 152–153, 153–156f
    tooth-surface error
    component, 153–156, 156t
    model, 150
    value interval, 151–152
    Multisource errors, 241
    axis compensation method, 206–210
    error compensation for transmission chain,
    210–223
    geometric error compensation, 224–233
    thermal error compensation, 233–239
    N
    NC control programming, 300
    Neural network (NN) algorithms,306–309,310f, 315
    P
    Particle swarm optimization (PSO), 307, 308f, 312t
    Pin-type robot, 360–361, 361t, 361f
    Point-vector family, 170
    approximation algorithm, 61–62, 61f
    composition, 56, 57f
    coordinate transformation, 64, 71, 77–79
    end surface profile, 62–63, 62f
    enveloping process, 59–60, 60f
    first envelope calculation, 63–73, 64f
    motion trajectory, 58–59, 59f
    rotational projection, 71–72, 72t, 72f
    second envelope modification, 74–85
    two-dimensional (2D) plane curves, 56–57, 57f
    three-dimensional (3D) space surfaces, 57–58, 58f
    Power honing, 39–40
    Principle error of hob-relief grinding
    chip-holding grooves, 118
    comparative verification grinding
    blade pitch circle, 128, 128t
    equal back angle cam, 126, 127f
    parameters, 126, 127t
    preshaving hob, 126, 127f
    gear-hob manufacturing process, 118
    grinding wheel profile, 123–126
    tooth tip curve, 119–123
    Process management system, 363–369, 364f
    automatic NC programming, 368
    drawing process and production tasks, dynamic
    issue, 365
    dynamic monitoring system, 366–367
    equipment and production line, 366
    equipment running status monitoring and fault
    alarm management, 366
    optimization decision of process parameters, 368
    production schedule information collection and
    task monitoring, 365
    remote diagnosis and management, 368–369
    tool change monitoring and management, 367,
    367f
    378 IndexProcess parameter optimization
    gear-machining machine, 326–335
    gear-tooth machining, 337–345
    hobbing precision prediction model, 306–309,
    306–308f
    machining accuracy
    algorithm flow, 309–310, 310f
    cumulative pitch errors, 309–310, 312f,
    313–315, 314f
    gear errors, 313, 314t
    helix errors, 309–310, 311f, 313–315, 313f
    hobbing parameters, 309
    optimal process parameters, 313–315, 315t
    prediction, 309–310, 312t
    process parameters and gear errors, 309,
    311t
    single pitch errors, 309–310, 312f, 313–315,
    314f
    tooth profile errors, 309–310, 311f, 313–315,
    313f
    Profile grinding, 6, 7f
    R
    Renishaw XL-80 laser, 151–152
    Residual stress, 316f
    alignment fixture, 315–318, 317–318f
    grinding parameters influence
    cutting depth, 318–320, 321t, 322f
    feed speed, 306–307, 320–321, 320t, 322f,
    324
    gear geometry specification, 318, 319t
    mathematical relationship, 322–324, 323t,
    323f
    measurement results, 320, 320t
    parameter levels, 319, 319t
    wheel speed, 320–321, 321t
    measurement method, 315–318, 317–318f
    self-balanced internal stress, 315
    surface stress influence, 324–326, 325f, 325t
    Roller deflection, 113–116, 114–115f
    Rotary table, 19–21
    accuracy, 247–248
    damping worm, 249–250, 250f
    high-precision, high-speed, 244–246, 246f
    hobbing machine, 247, 247–248f
    large-scale precision CNC hobbing machine,
    247
    large-size hydrostatic, 248–251, 249f
    transmission accuracy, 248
    worm gear, 247, 248f
    worm transmission, 249–250, 250f
    Rotational projection, 71–72, 72t, 72f
    S
    Second envelope process
    comparative analysis, 80–85
    coordinate transformation, 77–79
    of point-vector family, 74–77, 75–78f, 83–85, 85f
    spiral projection, 79–80
    Shaving process, 38–39
    SIEMENS840Dsl CNC system, 294
    Siemens SINUMERIK 840Dsl
    COM (commercial) technology, 32
    full PC integrated control system, 31
    human-machine interface (HMI), 30–31
    numerical control system, 30
    OPC standard, 32
    software system, 30, 31f
    Simulation envelope surface
    contact line shape on tooth surface error, 95–97,
    95–96f
    distribution, 91–92, 94f
    errors, 91–92, 93t
    spatial contact lines, 91
    tooth profile error, 103, 104–105f
    tooth surface error
    additional rotation of c-axis, 99–100, 99f
    additional rotation on x-axis, 97–98, 97f
    Sobol method
    first-order sensitivity index, 159
    flowchart calculation, 160, 160f
    geometric error probability distribution, 161
    global sensitivity analysis method, 157–159
    higher-order function terms, 158
    identification process, 158
    Monte Carlo integral method, 159
    sampling sequence probability statistics, 161, 162t
    sensitivity analysis method, 160–161, 163–165f
    tooth-surface error component, 161, 165t
    SPARTApro software, 11–12
    Spindle system, 18–19, 242–244, 242–243f, 245f
    Spiral tooth surface
    coordinate system, 63
    gear end plane profile, 57–58
    modeling, 50–52, 50f
    point-vector family, 66
    tool coordinate system, 64
    Standard involute profile, 82, 83f
    Index 379T
    Temperature field control technology, 14–18, 15f
    Thermal characteristics
    in gear grinding, 278–290
    heat dissipation, 269–271
    heat source analysis, 258–268
    for tool holder
    analysis method, 271
    finite element analysis (FEA), 273–274, 273f
    high-speed dry cutting, 271, 271f
    thermal-structure coupling analysis, 272, 272f
    three-dimensional geometric model, 272,
    273f
    Thermal deformation, 12, 187–192, 187–188f, 190f,
    233–234, 233f, 235f
    displacement and temperature test data, 191–192,
    191f, 191t
    experimental test platform, 187–190, 188f, 190f
    model, 186–187, 187f
    Thermal errors, 12–13
    CNC gear machine tool
    compensation, 234–239
    thermal deformation, 233–234, 233f
    compensation
    model, 195–196
    technology, 234–237
    continuous generating grinding machine
    automobile transmission gears, 202
    double meshing gear tester, 202, 203f
    experiment site, 202, 203f
    gear M-value, 202, 204f
    installation position, 202, 202f
    prediction model, 205
    probabilistic neural network structure,
    205–206, 205–206f
    radial thermal error modeling steps, 205,
    205f
    temperature curve, 202, 204–205, 204f
    high-speed dry hobbing machine, 196–202
    spiral compensation structure, 237–239, 238f
    temperature variable, 192–196, 192–193f, 194t
    vertical gear hobbing machine, 186–196
    Thermal-induced error
    compensation methods, 14
    error modeling, 13–14
    temperature measurement points, 13
    Three-dimensional (3D) modeling software, 11–12,
    138–140
    Ti6Al4Vdrymilling, 18
    Tool error model
    grinding wheel error, 168–170, 168–169f
    hob, 161–168, 166–167f
    worm grinding wheel (see Worm grinding
    wheel error)
    Tool holder
    analysis method, 271
    finite element analysis (FEA), 273–274, 273f
    high-speed dry cutting, 271, 271f
    numerical simulation analysis
    steady temperature field, 274–275, 274f
    steady thermal deformation, 275–276, 276f
    transient temperature field, 276–277, 277f
    transient thermal deformation, 277–278, 278f
    thermal-structure coupling analysis, 272, 272f
    three-dimensional geometric model, 272, 273f
    Tool spindle system, 241–244, 242–243f, 245f
    Tooth flank surface, 120–121, 121f
    Toothing process parameter optimization,
    336–337
    energy consumption model, 335–336
    genetic algorithm, 336, 337f
    Tooth profile errors, 103, 104–105f, 111, 313–315,
    313f
    Tooth profile modification
    coordinate system, 53
    curves, 53, 53f, 80–81, 81f
    point vectors, 81–82
    tooth root trimming, 52
    Tooth surface integrity, 337–338
    Tooth surface precision
    cutting forces, 308–309
    gear hobbing, 306
    improved particle swarm optimization (IPSO),
    308, 308f
    mapping, 306–307, 307f
    neural network (NN) algorithms, 307
    particle swarm optimization (PSO), 307, 308f
    process parameters, 306–307
    Tooth surface quality
    gear-tooth machining, 337–345
    optimization process, 337, 338f
    process parameters, 337
    Tooth surfaces, 88f. See also Modified tooth surface
    axial modification, 54–56, 55f
    coordinate system, 64
    creation coupling model, 208, 208f
    380 Indexdistortion control module, 297
    errors reduction
    additional rotation of the X-axis, 100–102,
    102–103f
    contact lines shapes, 92t, 100, 101f
    during generating machining, 111–118,
    112f
    gear, 80
    generation model, 208, 208f
    grinding gear
    contact line, 89–90
    mapping relationship, 88, 89f
    simulation process, 90–91, 90–91f
    measurement, 207, 208f
    optimization
    wheel installation angle, 103, 104f
    wheel profile, 103–104, 105f
    point vector (see Point-vector family)
    quality
    gear-tooth machining, 337–345
    optimization process, 337, 338f
    process parameters, 337
    simulation envelope surface, 93–100, 94f
    spiral, 50–52
    twist analysis, 91–93, 92t, 92f
    calculation model, 108–111
    errors reduction, 100–102
    machining, 106–108
    modified gear, 88–104
    simulation envelope surface, 93–100
    tool envelope plane, 88–91
    Tooth tip curve
    equal back angle hob, 121–123, 122f
    hobs geometry, 119–120, 120f
    tooth flank surface, 120–121, 121f
    Torque motor, 20–21
    Transmission chain errors, 210–213, 211f
    experiments, 219–223, 220t, 220f
    compensation of eI, 220–222, 221–222f
    compensation of el, 222–223, 223f
    measurement and identification, 213–216,
    213–214f, 214t
    principle, compensation, 216–219, 217–218f
    Trial-and-error method, 3, 22
    Truss-type automatic production line, 361–363,
    362f
    Two-dimensional (2D) simulations, 11–12
    V
    Vertical gear hobbing machine
    thermal deformation, 186–192, 187–188f, 190f
    thermal error modeling
    compensation model, 195–196
    temperature variable, 192–196, 192–193f, 194t
    Vibration error, 143–144
    Visual interface design, 298–299
    W
    Workbench, hobbing
    damping mechanism, 356–358, 357f
    gear hobbing machine, 356
    high-speed dry cutting precision gear, 357, 358f
    three-dimensional solid model, 356, 357f
    workbench design principle, 358
    Worm gear shaft lead, 116–118, 117f
    Worm grinding wheel error, 5–6, 6f
    error separation, 174
    forming dressing, 174–175, 174f
    functional model, 174
    gear end face profile, 172, 172f
    grinding process, 173–174
    mapping relationship, 170, 171f
    point trimming, 174–175, 175f
    point-vector family, 170
    reverse compensation profile, 173, 173f
    reverse profile compensation, 174–175, 175f
    spiral surface, 172
    tooth-profile error, 172–173
    tooth surface of gear, 170, 171f, 172
    two-dimensional (2D) point-vector family, 170
    Worm-wheel generating grinding gears, 106
    Y
    Y31200CNC6 hobbing machine, 236, 237f
    Yttrium aluminum garnet (YAG) tool, 17–18
    Z
    Zero-programming system
    deformation error compensation, 234–235
    hobbing machine, 234–235, 237
    online temperature sensor arrangement, 235–236,
    236f
    principle, 234
    thermal error compensation, 236–237, 237f, 237t
    working gear and hob parameters, 236, 236t

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