Practical Gear Design and Manufacture Handbook

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Practical Gear Design and Manufacture Handbook

Practical Gear Design and Manufacture Handbook
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Practical Gear Design and Manufacture

Introduction

Gears are produced in enormous amounts—billions of gears are produced by industries every year. While the automotive industry ranks as the primary consumer of gears, numerous other industries also require huge amounts of gears: aerospace (helicopter transmission, etc ), construction machinery, and agricultural machinery, to name a few. If we place cost savings in the production of every gear in the range of just 10 cents, the total cost savings could reach hundreds of millions of dollars. This makes it clear that the processes of gear design and gear production require careful treatment

There is much room for gear engineers and gear practitioners to further improve cost saving processes The Gear Handbook can be helpful in solving many of the problems of both areas of gear design and gear production.

TOC

Preface xv
Introduction xix
Acknowledgments ..xxiii
Author xxv

1 Gear Design Trends .1
1.1. Small,.Low-Cost.Gears.for.Toys,.Gadgets,.and.Mechanisms .4
1.2. Appliance.Gears .6
1.3. Machine.Tools ..7
1.4. Control.Gears 8
1.5. Vehicle.Gears . 10
1.6. Transportation.Gears 12
1.7. Marine.Gears . 13
1.8. Aerospace.Gears .. 15
1.9. Industrial.Gearing . 16
1.10. Gears.in.the.Oil.and.Gas.Industry . 18
1.11. Mill.Gears . 18
1.12. External.Spur.Gears ..20
1.13. External.Helical.Gears .23
1.14. Internal.Gears 24
1.15. Straight.Bevel.Gears ..26
1.16. Zerol.Bevel.Gears 28
1.17. Spiral.Bevel.Gears ..29
1.18. Hypoid.Gears .30
1.19. Face.Gears 31
1.20. Crossed-Helical.Gears.(Nonenveloping.Worm.Gears) . 32
1.21. Single-Enveloping.Worm.Gears 34
1.22. Double-Enveloping.Worm.Gears . 37
1.23. Spiroid.Gears .39

2 Gear Types and Nomenclature . 41
2.1. Types.of.Gears .. 41
2.1.1. Classifications .. 41
2.1.2. Parallel.Axis.Gears ..44
2.1.2.1. Spur.Gears .44
2.1.2.2. Helical.Gears 45
2.1.2.3. Internal.Gears .47
2.1.3. Nonparallel,.Coplanar.Gears.(Intersecting.Axes) ..48
2.1.3.1. Bevel.Gears 48
2.1.3.2. Face.Gears.(On-Center) .53
2.1.3.3. Conical.Involute.Gearing 54
2.1.4. Nonparallel,.Noncoplanar.Gears.(Nonintersecting.Axes) ..55
2.1.4.1. Crossed-Axis.Helical.Gears ..55
2.1.4.2. Cylindrical.Worm.Gearing 57
2.1.4.3. Single-Enveloping.Worm.Gearing 57
2.1.4.4. Double-Enveloping.Worm.Gearing .59
2.1.4.5. Hypoid.Gears ..60
2.1.4.6. Spiroid.and.Helicon.Gearing 61
2.1.4.7. Face.Gears.(Off-Center) 63
2.1.5. Special.Gear.Types 63
2.1.5.1. Square.or.Rectangular.Gears ..63
2.1.5.2. Triangular.Gears ..64
2.1.5.3. Elliptical.Gears ..64
2.1.5.4. Scroll.Gears ..65
2.1.5.5. Multiple-Sector.Gears 65
2.2. Nomenclature.of.Gears ..66
2.2.1. Spur.Gear.Nomenclature.and.Basic.Formulas .68
2.2.2. Helical.Gear.Nomenclature.and.Basic.Formulas 68
2.2.3. Internal.Gear.Nomenclature.and.Formulas .. 70
2.2.4. Crossed.Helical.Gear.Nomenclature.and.Formulas . 70
2.2.5. Bevel.Gear.Nomenclature.and.Formulas .73
2.2.5.1. Straight .73
2.2.5.2. Spiral . 74
2.2.5.3. Zerol .. 74
2.2.6. Worm.Gear.Nomenclature.and.Formulas ..78
2.2.6.1. Cylindrical.Worm.Gears .80
2.2.6.2. Double-Enveloping.Worm.Gears .. 81
2.2.7. Face.Gears .. 81
2.2.8. Spiroid.Gear.Nomenclature.and.Formulas . 81
2.2.9. Beveloid.Gears .83

3 Gear Tooth Design .85
3.1. Basic.Requirements.for.Gear.Tooth.Design .85
3.1.1. Definition.of.Gear.Tooth.Elements 85
3.1.2. Basic.Considerations.for.Gear.Tooth.Design .88
3.1.2.1. Continuity.of.Action ..89
3.1.2.2. Conjugate.Action ..92
3.1.2.3. Pitch.Diameter 93
3.1.2.4. Zones.in.Which.Involute.Gear.Teeth.Exist .94
3.1.2.5. Pointed.Teeth ..98
3.1.2.6. Undercut .. 100
3.1.3. Long-.and.Short-Addendum.Gear.Design 101
3.1.3.1. Addendum.Modification.for.Gears.Having.a.Few.Teeth .. 102
3.1.3.2. Speed-Increasing.Drives .. 103
3.1.3.3. Power.Drives.(Optimal.Design) .. 103
3.1.3.4. Low-Friction.Gearing . 105
3.1.4. Special.Design.Considerations . 107
3.1.4.1. Interchangeability . 107
3.1.4.2. Tooth.Thickness .. 107
3.1.4.3. Tooth.Profile.Modifications 109
3.1.4.4. Transverse.of.Profile.Modification . 109
3.1.4.5. Allowances.for.Errors.of.Gear.Manufacture .. 109
3.1.4.6. Allowances.for.Deflection.under.Load .. 109
3.1.4.7. Axial.Modifications .. 110
3.1.4.8. Root.Fillets .. 111
3.1.4.9. Effective.Outside.Diameter . 113
3.1.4.10. Width.of.Tip.of.Tooth .. 113
3.1.4.11. Pointed.Tooth.Diameter 114
3.1.4.12. Purpose.of.Backlash . 114
3.1.4.13. Backlash:.Recommended.Values . 115

3.2. Standard.Systems.of.Gear.Tooth.Proportions . 116
3.2.1. Standard.Systems.for.Spur.Gears 116
3.2.1.1. Limitations.in.Use.of.Standard.Tables 116
3.2.1.2. Standard.Tooth.Forms.That.Have.Become.Obsolete 118
3.2.1.3. Brown.and.Sharp.System . 119
3.2.1.4. AGMA.14.5°.Composite.System .. 119
3.2.1.5. Fellows.20°.Stub.Tooth.System . 120
3.2.1.6. AGMA.14.5°.Full-Depth.System .. 120
3.2.1.7. Cycloidal.Tooth.Profiles 121
3.2.1.8. Clockwork.and.Timer.Tooth.Profiles .. 121
3.2.1.9. Specific.Spur.Gear.Calculation.Procedure ..122
3.2.1.10. Explanation.and.Discussion.of.Items.in.Table 3.5 .. 126
3.2.2. System.for.Helical.Gears 128
3.2.2.1. Selection.of.Tooth.Form . 130
3.2.2.2. Selection.of.Helix.Angle 130
3.2.2.3. Face.Width .. 131
3.2.2.4. Specific.Calculation.Procedure.for.Helical.Gears .. 132
3.2.3. System.for.Internal.Gears . 133
3.2.3.1. Special.Calculations . 135
3.2.3.2. Specific.Calculation.Procedure.for.Internal.Gears . 136
3.2.4. Standard.Systems.for.Bevel.Gears .. 136
3.2.4.1. Discussion.of.20°.Straight.Bevel.Gear.System .. 137
3.2.4.2. Discussion.of.Spiral.Bevel.Gear.System . 137
3.2.4.3. Discussion.of.the.Zerol.Bevel.Gear.System . 138
3.2.4.4. Special.Tooth.Forms . 138
3.2.4.5. Limitations.in.20°.Straight.Bevel.Gear.System . 139
3.2.4.6. Limitations.in.Spiral.Bevel.Gear.System .. 141
3.2.4.7. Limitations.in.Zerol.Bevel.Gear.System 141
3.2.4.8. General.Comments .. 141
3.2.5. Standard.Systems.for.Worm.Gears 143
3.2.5.1. General.Practice .. 143
3.2.5.2. Basic.Tooth.Forms.for.Worm.Gearing . 144
3.2.5.3. Specific.Calculations.for.Worm.Gears 145
3.2.6. Standard.System.for.Face.Gears .. 146
3.2.6.1. Pinion.Design .. 148
3.2.6.2. Face.Gear.Design 148
3.2.7. System.for.Spiroid.and.Helicon.Gears . 149
3.2.7.1. Spiroid.Gearing .. 151
3.2.7.2. Helicon.Gearing . 154
3.2.7.3. Detailed.Calculations.of.Spiroid.and.Helicon.Tooth.Data 155
3.3. General.Equations.Relating.to.Center.Distance . 156
3.3.1. Center.Distance.Equations .. 156
3.3.2. Standard.Center.Distance . 159
3.3.3. Standard.Pitch.Diameters . 160
3.3.4. Operating.Pitch.Diameters .. 160
3.3.5. Operating.Pressure.Angle 161
3.3.6. Operating.Center.Distance .. 162
3.3.7. Center.Distance.for.Gears.Operating.on.Nonparallel. Nonintersecting.Shafts .. 162
3.3.8. Center.Distance.for.Worm.Gearing .. 162
3.3.9. Reasons.for.Nonstandard.Center.Distances 163
3.3.10. Nonstandard.Center.Distances . 163
3.4. Elements.of.Center.Distance . 165
3.4.1. Effects.of.Tolerances.on.Center.Distance .. 165
3.4.2. Machine.Elements.that.Require.Consideration.in.Critical.Center.
Distance.Applications . 168
3.4.3. Control.of.Backlash 171
3.4.4. Effects.of.Temperature.on.Center.Distance . 172
3.4.5. Mounting.Distance 174

4 Preliminary Design Considerations .. 177
4.1. Stress.Formulas:.Calculation 177
4.1.1. Calculated.Stresses 177
4.1.2. Gear.Design.Limits 181
4.1.3. Gear.Strength.Calculations . 181
4.1.3.1. Worst.Load . 184
4.1.3.2. Stress.Concentration 185
4.1.3.3. Load.Distribution .. 186
4.1.3.4. Dynamic.Load . 186
4.1.3.5. Finite.Element .. 187
4.1.4. Gear.Surface.Durability.Calculations .. 188
4.1.4.1. Hertz.Derivations .. 189
4.1.4.2. K-Factor.Derivations 192
4.1.4.3. Worst-Load.Position . 193
4.1.4.4. Endurance.Limit . 193
4.1.4.5. Lubrication.Regimens . 194
4.1.5. Gear.Scoring .. 198
4.1.5.1. Hot.and.Cold.Scoring . 198
4.1.5.2. PVT.Formula . 199
4.1.5.3. Flash.Temperature 202
4.1.5.4. Scoring.Criterion 203
4.1.6. Thermal.Limits .205
4.1.6.1. Thermal.Limits.at.Regular.Speed ..205
4.1.6.2. Thermal.Limits.at.High.Speed .206
4.2. Stress.Formulas:.Special.Considerations .206
4.2.1. Gear.Specifications 207
4.2.2. Size.of.Spur.and.Helical.Gears.by.Q-Factor.Method 207
4.2.2.1. Face-Width.Considerations . 210
4.2.2.2. Weight.from.Volume 211
4.2.3. Indexes.of.Tooth.Loading . 213
4.2.4. Estimating.Spur.and.Helical.Gear.Size.by.K-Factor .. 214
4.2.5. Estimating.Bevel.Gear.Size . 215
4.2.6. Estimating.Worm.Gear.Size 220
4.2.7. Estimating.Spiroid.Gear.Size .223
4.3. Data.Needed.for.Gear.Drawings ..223
4.3.1. Gear.Dimensional.Data ..223
4.3.2. Gear.Tooth.Tolerances .226
4.3.3. Gear.Material.and.Heat.Treatment.Data 234
4.3.4. Enclosed.Gear.Unit.Requirements . 241

5 Design Formulas 243
5.1. Calculation.of.Gear.Tooth.Data . 243
5.1.1. Number.of.Pinion.Teeth 243
5.1.2. Hunting.Teeth .. 248
5.1.3. Spur.Gear.Tooth.Proportions . 249
5.1.4. Root.Fillet.Radii.of.Curvature 251
5.1.5. Long-Addendum.Pinions .253
5.1.6. Tooth.Thickness .. 257
5.1.6.1. Backlash 257
5.1.6.2. Tolerances.and.Tooth.Thickness .258
5.1.7. Chordal.Dimensions 258
5.1.8. Degrees.Roll.and.Limit.Diameter ..260
5.1.9. Form.Diameter.and.Contact.Ratio .264
5.1.9.1. Form.Diameter .264
5.1.9.2. Contact.Ratio .265
5.1.10. Spur.Gear.Dimension.Sheet 266
5.1.11. Internal.Gear.Dimension.Sheet 268
5.1.12. Helical.Gear.Tooth.Proportions 272
5.1.13. Helical.Gear.Dimension.Sheet ..277
5.1.14. Bevel.Gear.Tooth.Proportions 279
5.1.15. Straight.Bevel.Gear.Dimension.Sheet ..283
5.1.16. Spiral.Bevel.Gear.Dimension.Sheet ..285
5.1.17. Zerol.Bevel.Gear.Dimension.Sheet 288
5.1.18. Hypoid.Gear.Calculations 289
5.1.19. Face.Gear.Calculations 290
5.1.20. Crossed-Helical.Gear.Proportions . 293
5.1.21. Single-Enveloping.Worm.Gear.Proportions 296
5.1.22. Single-Enveloping.Worm.Gears .. 297
5.1.23. Double-Enveloping.Worm.Gears .299
5.2. Gear.Rating.Practice ..303
5.2.1. General.Considerations.in.Rating.Calculations 303
5.2.1.1. Calculation.Procedure 305
5.2.1.2. Grades.of.Material.Quality .306
5.2.1.3. Reliability.of.Gears 307
5.2.2. General.Formulas.for.Tooth.Bending.Strength.and.Tooth.Surface Durability .307
5.2.2.1. Strength.Formula ..308
5.2.2.2. Durability.Formula ..308
5.2.2.3. Rating.Curves.of.Stress.versus.Cycles 313
5.2.2.4. Rating.Bevel.Gears 315
5.2.3. Geometry.Factors.for.Strength . 316
5.2.3.1. Lack.of.Load.Sharing .. 317
5.2.3.2. Helical.Gears.with.Narrow.Face.Width . 317
5.2.3.3. Geometry.Factors.for.Strength.for.Some.Standard.Designs .. 318
5.2.4. Overall.De-Rating.Factor.for.Strength . 319
5.2.4.1. Application.Factor.Ka ..322
5.2.4.2. Load.Distribution.Factor.Km ..322
5.2.4.3. Effect.of.Helix.Error.and.Shaft.Misalignment .. 324
5.2.4.4. Aspect.Ratio.Effects . 327
5.2.4.5. Load.Distribution.Factor.Km.for.Bevel.Gears . 328
5.2.4.6. Size.Factor.Ks .330
5.2.4.7. Dynamic.Load.Factors.Kv.and.Cv 330
5.2.5. Geometry.Factors.for.Durability .333
5.2.6. Overall.De-Rating.Factor.for.Surface.Durability .335
5.2.6.1. Size.Factor.Cs .336
5.2.6.2. Complementary.Considerations .338
5.2.7. Load.Rating.of.Worm.Gearing .339
5.2.7.1. Crossed-Helical.Gear.Durability 339
5.2.7.2. Cylindrical.Worm.Gear.Durability ..341
5.2.7.3. Double-Enveloping.Worm.Gear.Durability 346
5.2.7.4. Comparison.of.Double-Enveloping.and.Cylindrical Worm.Gear.Rating.Procedures 349
5.2.8. Design.Formulas.for.Scoring .350
5.2.8.1. Hot.Scoring 350
5.2.8.2. Cold.Scoring ..355
5.2.8.3. Design.Practice.to.Handle.Scoring 360
5.2.9. Trade.Standards.for.Rating.Gears .. 361
5.2.10. Vehicle.Gear.Rating.Practice ..363
5.2.11. Marine.Gear.Rating.Practice ..365
5.2.12. Oil.and.Gas.Industry.Gear.Rating . 367
5.2.13. Aerospace.Gear.Rating.Practice ..368

6 Gear Materials . 371
6.1. Steels.for.Gears .. 371
6.1.1. Mechanical.Properties 371
6.1.2. Heat-Treating.Techniques . 375
6.1.3. Heat-Treating.Data . 379
6.1.4. Hardness.Tests . 381
6.2. Localized.Hardening.of.Gear.Teeth 383
6.2.1. Carburizing 383
6.2.2. Nitriding 389
6.2.2.1. Features.of.Nitriding.Process 389
6.2.2.2. Nitride.Case.Depth .. 392
6.2.3. Induction.Hardening.of.Steel . 393
6.2.3.1. Induction.Hardening.by.Scanning 395
6.2.3.2. Load-Carrying.Capacity.of.Induction-Hardened.Gear.Teeth 398
6.2.4. Flame.Hardening.of.Steel .400
6.2.5. Combined.Heat.Treatments 401
6.2.6. Metallurgical.Quality.of.Steel.Gears .402
6.2.6.1. Quality.Items.for.Carburized.Steel.Gears 402
6.2.6.2. Quality.Items.for.Nitrided.Gears 404
6.2.6.3. Procedure.to.Get.Grade 2.Quality .405
6.3. Cast.Irons.for.Gears 406
6.3.1. Gray.Cast.Iron ..407
6.3.2. Ductile.Iron .408
6.3.3. Sintered.Iron .. 410
6.4. Nonferrous.Gear.Metals . 411
6.4.1. Kinds.of.Bronze 411
6.4.2. Standard.Gear.Bronzes .. 413
6.5. Nonmetallic.Gears .. 414
6.5.1. Thermosetting.Laminates 414
6.5.2. Nylon.Gears 416

7 Gear-Manufacturing Methods .. 419
7.1. Gear.Tooth.Cutting . 419
7.1.1. Gear.Hobbing 419
7.1.2. Shaping—Pinion.Cutter .426
7.1.3. Shaping—Rack.Cutter . 431
7.1.4. Cutting.Bevel.Gears ..435
7.1.5. Gear.Milling ..438
7.1.6. Broaching.Gears ..442
7.1.7. Punching.Gears 444
7.1.8. G-TRAC.Generating .446
7.2 Gear.Grinding 448
7.2.1. Form.Grinding .448
7.2.1.1. Ceramic.Form.Grinding 449
7.2.1.2. Borazon.Form.Grinding 452
7.2.2. Generating.Grinding—Disk.Wheel ..453
7.2.3. Generating.Grinding—Bevel.Gears ..456
7.2.4. Generating.Grinding—Threaded.Wheel 459
7.2.5. Thread.Grinding . 462
7.3. Gear.Shaving,.Rolling,.and.Honing 465
7.3.1. Rotary.Shaving .465
7.3.2. Rack.Shaving . 470
7.3.3. Gear.Rolling 470
7.3.4. Gear.Honing .. 473
7.4. Gear.Measurement . 475
7.4.1. Gear.Accuracy.Limits .. 476
7.4.2. Machines.to.Measure.Gears 481
7.5. Gear.Casting.and.Forming 487
7.5.1. Cast.and.Molded.Gears ..487
7.5.2. Sintered.Gears ..488
7.5.3. Cold-Drawn.Gears.and.Rolled.Worm.Threads .489

8 Design of Tools to Make Gear Teeth . 491
8.1. Shaper.Cutters 491
8.2. Gear.Hobs ..502
8.3. Spur.Gear–Milling.Cutters 515
8.4. Worm-Milling.Cutters.and.Grinding.Wheels . 517
8.5. Gear-Shaving.Cutters 522
8.6. Punching.Tools .. 525
8.7. Sintering.Tools 526

9 Kinds and Causes of Gear Failures 529
9.1. Analysis.of.Gear-System.Problems . 529
9.1.1. Determining.the.Problem . 529
9.1.2. Possible.Causes.of.Gear-System.Failures .. 531
9.1.3. Incompatibility.in.Gear.Systems .533
9.1.4. Investigation.of.Gear.Systems 534
9.2. Analysis.of.Tooth.Failures.and.Gear-Bearing.Failures .535
9.2.1. Nomenclature.of.Gear.Failure ..536
9.2.2. Tooth.Breakage .536
9.2.3. Pitting.of.Gear.Teeth 540
9.2.4. Scoring.Failures 542
9.2.5. Wear.Failures .544
9.2.6. Gearbox.Bearings 547
9.2.7. Rolling-Element.Bearings .548
9.2.8. Sliding-Element.Bearings .550
9.3. Some.Causes.of.Gear.Failure.Other.than.Excess.Transmission.Load . 552
9.3.1. Overload.Gear.Failures ..553
9.3.2. Gear-Casing.Problems 554
9.3.3. Lubrication.Failures ..555
9.3.4. Thermal.Problems.in.Fast-Running.Gears .. 561

10 Special Design Problems 565
10.1. Center.Distance.Problems ..565
10.2. Profile.Modification.Problems . 576
10.3. Load.Rating.Problem .585

11 Gear Reactions and Mountings . 591
11.1. Mechanics.of.Gear.Reactions .. 591
11.1.1. Summation.of.Forces.and.Moments . 591
11.1.2. Application.to.Gearing 594
11.2. Basic.Gear.Reactions,.Bearing.Loads,.and.Mounting.Types . 595
11.2.1. Main.Source.of.Load 595
11.2.2. Gear.Reactions.to.Bearing 596
11.2.3. Directions.of.Loads 597
11.2.4. Additional.Considerations .. 597
11.2.5. Types.of.Mountings .. 598
11.2.6. Efficiencies ..600
11.3. Basic.Mounting.Arrangements.and.Recommendations ..600
11.3.1. Bearing.and.Shaft.Alignment 601
11.3.2. Bearings . 601
11.3.3. Mounting.Gears.to.the.Shaft ..602
11.3.4. Housing .603
11.3.5. Inspection.Hole 603
11.3.6. Break-In .603
11.4. Bearing.Load.Calculations.for.Spur.Gears 604
11.4.1. Spur.Gears ..604
11.4.2. Helical.Gears .606
11.4.3. Gears.in.Trains .606
11.4.4. Idlers 606
11.4.5. Intermediate.Gears 607
11.4.6. Planetary.Gears 609
11.4.6.1. One.Planet ..609
11.4.6.2. Several.Planets .609
11.5. Bearing-Load.Calculations.for.Helicals 610
11.5.1. Single.Helical.Gears . 610
11.5.2. Double.Helical.Gears 612
11.5.3. Skewed-.or.Crossed-Helical.Gears . 613
11.6. Mounting.Practice.for.Bevel.and.Hypoid.Gears 615
11.6.1. Analysis.of.Forces .. 615
11.6.2. Rigid.Mountings . 616
11.6.3. Maximum.Displacements . 616
11.6.4. Rolling-Element.Bearings . 619
11.6.5. Straddle.Mounting . 619
11.6.6. Overhung.Mounting 619
11.6.7. Gear.Blank.Design . 622
11.6.8. Gear.and.Pinion.Adjustments 625
11.6.9. Assembly.Procedure . 626
11.7. Calculation.of.Bevel.and.Hypoid.Bearing.Loads .. 627
11.7.1. Hand.of.Spiral .. 627
11.7.2. Spiral.Angle 627
11.7.3. Tangential.Load .. 628
11.7.4. Axial.Thrust 629
11.7.5. Radial.Load . 629
11.7.6. Required.Data.for.Bearing.Load.Calculations .. 637
11.8. Bearing.Load.Calculations.for.Worms .639
11.8.1. Calculation.of.Forces.in.Worm.Gears ..640
11.8.2. Mounting.Tolerances 642
11.8.3. Worm.Gear.Blank.Considerations ..642
11.8.4. Run-In.of.Worm.Gears 642
11.9. Bearing.Load.Calculations.for.Spiroid.Gearing .644
11.10. Bearing.Load.Calculations.for.Other.Gear.Types .648
11.11. Design.of.the.Body.of.the.Gear ..648

12 Gear Vibration . 651
12.1. Fundamentals.of.Vibration 651
12.2. Measurement.of.Vibration .654
12.2.1. Examples.of.Sensing.Devices .655
12.2.2. Practical.Problems.in.Vibration.Measurement ..657
12.3. Some.Examples.of.Vibration.in.Geared.Units .657
12.4. Approximate.Vibration.Limits 660
12.4.1. Velocity.Limits . 661
12.4.2. Acceleration.Limits 662
12.4.3. Proximity.Probes 662

12.4.4. Displacement.Limits . 662
12.4.5. General.Vibration.Tendencies 663
12.4.6. Trade.Standard .663
12.5. Control.of.Vibration.in.Manufacturing.Gears.and.in.the.Field ..665
12.5.1. Testing.of.Gear.Units.at.the.Gear.Factory .666
12.5.2. Tests.of.Assembled.Power.Package 666
12.5.3. Vibration.Tests.in.the.Field .. 667
12.6. Vibration.Analysis.Technique .668

Appendix A: Evolution of Gear Art . 671
Appendix B: Complementary Material . 717
Appendix C: Numerical Data Tables ..771
Appendix D: On the Concept of Novikov Gearing and the Inadequacy of the Terms “Wildhaber–Novikov Gearing” and “W–N Gearing” 803
References ..835