H a n d b o o k o f

Practical GearDesign and

Manufacture

DudleysS e c o n d E d i t i o n

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H a n d b o o k o f

Practical GearDesign and

Manufacture

DudleysS e c o n d E d i t i o n

Stephen P. Radzevich

CRC Press is an imprint of theTaylor & Francis Group, an informa business

Boca Raton London New York

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CRC PressTaylor & Francis Group6000 Broken Sound Parkway NW, Suite 300Boca Raton, FL 33487-2742

2012 by Taylor & Francis Group, LLCCRC Press is an imprint of Taylor & Francis Group, an Informa business

No claim to original U.S. Government works

Printed in the United States of America on acid-free paperVersion Date: 2011922

International Standard Book Number: 978-1-4398-6601-6 (Hardback)

This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the validity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material repro-duced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. If any copyright material has not been acknowledged please write and let us know so we may rectify in any future reprint.

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Library of Congress CataloginginPublication Data

Dudley, Darle W.[Handbook of practical gear design and manufacture.]

Dudleys handbook of practical gear design and manufacture. -- 2nd ed. / by Stephen P. Radzevich.p. cm.

Rev. ed. of: Handbook of practical gear design / Darle W. Dudley. 1994.Includes bibliographical references and index.ISBN 978-1-4398-6601-61. Gearing--Handbooks, manuals, etc. I. Radzevich, S. P. (Stepan Pavlovich) II. Dudley, Darle W.

Handbook of practical gear design. III. Title. IV. Title: Handbook of practical gear design and manufacture.

TJ184.D784 2012621.833--dc23 2011037473

Visit the Taylor & Francis Web site athttp://www.taylorandfrancis.comand the CRC Press Web site athttp://www.crcpress.com

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vContents

Preface..............................................................................................................................................xvIntroduction.................................................................................................................................. xixAcknowledgments..................................................................................................................... xxiiiAuthor........................................................................................................................................... xxv

1 GearDesignTrends................................................................................................................11.1. Small,.Low-Cost.Gears.for.Toys,.Gadgets,.and.Mechanisms..................................41.2. Appliance.Gears.............................................................................................................61.3. Machine.Tools.................................................................................................................71.4. Control.Gears..................................................................................................................81.5. Vehicle.Gears................................................................................................................ 101.6. Transportation.Gears................................................................................................... 121.7. Marine.Gears................................................................................................................ 131.8. Aerospace.Gears........................................................................................................... 151.9. Industrial.Gearing....................................................................................................... 161.10. Gears.in.the.Oil.and.Gas.Industry............................................................................ 181.11. Mill.Gears...................................................................................................................... 181.12. External.Spur.Gears..................................................................................................... 201.13. External.Helical.Gears.................................................................................................231.14. Internal.Gears............................................................................................................... 241.15. Straight.Bevel.Gears..................................................................................................... 261.16. Zerol.Bevel.Gears.........................................................................................................281.17. Spiral.Bevel.Gears........................................................................................................ 291.18. Hypoid.Gears................................................................................................................301.19. Face.Gears..................................................................................................................... 311.20. Crossed-Helical.Gears.(Nonenveloping.Worm.Gears)........................................... 321.21. Single-Enveloping.Worm.Gears.................................................................................341.22. Double-Enveloping.Worm.Gears............................................................................... 371.23. Spiroid.Gears................................................................................................................ 39

2 GearTypesandNomenclature........................................................................................... 412.1. Types.of.Gears.............................................................................................................. 41

2.1.1. Classifications.................................................................................................. 412.1.2. Parallel.Axis.Gears.........................................................................................44

2.1.2.1. Spur.Gears........................................................................................442.1.2.2. Helical.Gears....................................................................................452.1.2.3. Internal.Gears.................................................................................. 47

2.1.3. Nonparallel,.Coplanar.Gears.(Intersecting.Axes)......................................482.1.3.1. Bevel.Gears.......................................................................................482.1.3.2. Face.Gears.(On-Center)...................................................................532.1.3.3. Conical.Involute.Gearing...............................................................54

2.1.4. Nonparallel,.Noncoplanar.Gears.(Nonintersecting.Axes)....................... 552.1.4.1. Crossed-Axis.Helical.Gears...........................................................552.1.4.2. Cylindrical.Worm.Gearing............................................................ 57

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2.1.4.3. Single-Enveloping.Worm.Gearing................................................ 572.1.4.4. Double-Enveloping.Worm.Gearing.............................................. 592.1.4.5. Hypoid.Gears...................................................................................602.1.4.6. Spiroid.and.Helicon.Gearing......................................................... 612.1.4.7. Face.Gears.(Off-Center)..................................................................63

2.1.5. Special.Gear.Types..........................................................................................632.1.5.1. Square.or.Rectangular.Gears........................................................632.1.5.2. Triangular.Gears.............................................................................642.1.5.3. Elliptical.Gears................................................................................642.1.5.4. Scroll.Gears......................................................................................652.1.5.5. Multiple-Sector.Gears.....................................................................65

2.2. Nomenclature.of.Gears...............................................................................................662.2.1. Spur.Gear.Nomenclature.and.Basic.Formulas...........................................682.2.2. Helical.Gear.Nomenclature.and.Basic.Formulas.......................................682.2.3. Internal.Gear.Nomenclature.and.Formulas............................................... 702.2.4. Crossed.Helical.Gear.Nomenclature.and.Formulas.................................. 702.2.5. Bevel.Gear.Nomenclature.and.Formulas.................................................... 73

2.2.5.1. Straight.............................................................................................. 732.2.5.2. Spiral................................................................................................. 742.2.5.3. Zerol.................................................................................................. 74

2.2.6. Worm.Gear.Nomenclature.and.Formulas.................................................. 782.2.6.1. Cylindrical.Worm.Gears................................................................802.2.6.2. Double-Enveloping.Worm.Gears.................................................. 81

2.2.7. Face.Gears........................................................................................................ 812.2.8. Spiroid.Gear.Nomenclature.and.Formulas................................................. 812.2.9. Beveloid.Gears.................................................................................................83

3 GearToothDesign................................................................................................................853.1. Basic.Requirements.for.Gear.Tooth.Design.............................................................85

3.1.1. Definition.of.Gear.Tooth.Elements...............................................................853.1.2. Basic.Considerations.for.Gear.Tooth.Design..............................................88

3.1.2.1. Continuity.of.Action....................................................................... 893.1.2.2. Conjugate.Action............................................................................. 923.1.2.3. Pitch.Diameter................................................................................. 933.1.2.4. Zones.in.Which.Involute.Gear.Teeth.Exist.................................. 943.1.2.5. Pointed.Teeth................................................................................... 983.1.2.6. Undercut......................................................................................... 100

3.1.3. Long-.and.Short-Addendum.Gear.Design................................................ 1013.1.3.1. Addendum.Modification.for.Gears.Having.a.Few.Teeth........ 1023.1.3.2. Speed-Increasing.Drives.............................................................. 1033.1.3.3. Power.Drives.(Optimal.Design).................................................. 1033.1.3.4. Low-Friction.Gearing................................................................... 105

3.1.4. Special.Design.Considerations................................................................... 1073.1.4.1. Interchangeability......................................................................... 1073.1.4.2. Tooth.Thickness............................................................................. 1073.1.4.3. Tooth.Profile.Modifications......................................................... 1093.1.4.4. Transverse.of.Profile.Modification.............................................. 1093.1.4.5. Allowances.for.Errors.of.Gear.Manufacture............................. 1093.1.4.6. Allowances.for.Deflection.under.Load...................................... 109

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3.1.4.7. Axial.Modifications....................................................................... 1103.1.4.8. Root.Fillets...................................................................................... 1113.1.4.9. Effective.Outside.Diameter.......................................................... 1133.1.4.10. Width.of.Tip.of.Tooth.................................................................... 1133.1.4.11. Pointed.Tooth.Diameter............................................................... 1143.1.4.12. Purpose.of.Backlash...................................................................... 1143.1.4.13. Backlash:.Recommended.Values................................................. 115

3.2. Standard.Systems.of.Gear.Tooth.Proportions....................................................... 1163.2.1. Standard.Systems.for.Spur.Gears............................................................... 116

3.2.1.1. Limitations.in.Use.of.Standard.Tables....................................... 1163.2.1.2. Standard.Tooth.Forms.That.Have.Become.Obsolete............... 1183.2.1.3. Brown.and.Sharp.System............................................................. 1193.2.1.4. AGMA.14.5.Composite.System.................................................. 1193.2.1.5. Fellows.20.Stub.Tooth.System.................................................... 1203.2.1.6. AGMA.14.5.Full-Depth.System.................................................. 1203.2.1.7. Cycloidal.Tooth.Profiles............................................................... 1213.2.1.8. Clockwork.and.Timer.Tooth.Profiles......................................... 1213.2.1.9. Specific.Spur.Gear.Calculation.Procedure................................ 1223.2.1.10. Explanation.and.Discussion.of.Items.in.Table3.5.................... 126

3.2.2. System.for.Helical.Gears.............................................................................. 1283.2.2.1. Selection.of.Tooth.Form................................................................ 1303.2.2.2. Selection.of.Helix.Angle............................................................... 1303.2.2.3. Face.Width...................................................................................... 1313.2.2.4. Specific.Calculation.Procedure.for.Helical.Gears.................... 132

3.2.3. System.for.Internal.Gears............................................................................ 1333.2.3.1. Special.Calculations...................................................................... 1353.2.3.2. Specific.Calculation.Procedure.for.Internal.Gears................... 136

3.2.4. Standard.Systems.for.Bevel.Gears.............................................................. 1363.2.4.1. Discussion.of.20.Straight.Bevel.Gear.System.......................... 1373.2.4.2. Discussion.of.Spiral.Bevel.Gear.System..................................... 1373.2.4.3. Discussion.of.the.Zerol.Bevel.Gear.System............................... 1383.2.4.4. Special.Tooth.Forms...................................................................... 1383.2.4.5. Limitations.in.20.Straight.Bevel.Gear.System......................... 1393.2.4.6. Limitations.in.Spiral.Bevel.Gear.System................................... 1413.2.4.7. Limitations.in.Zerol.Bevel.Gear.System.................................... 1413.2.4.8. General.Comments....................................................................... 141

3.2.5. Standard.Systems.for.Worm.Gears............................................................ 1433.2.5.1. General.Practice............................................................................. 1433.2.5.2. Basic.Tooth.Forms.for.Worm.Gearing........................................ 1443.2.5.3. Specific.Calculations.for.Worm.Gears....................................... 145

3.2.6. Standard.System.for.Face.Gears................................................................. 1463.2.6.1. Pinion.Design................................................................................ 1483.2.6.2. Face.Gear.Design........................................................................... 148

3.2.7. System.for.Spiroid.and.Helicon.Gears....................................................... 1493.2.7.1. Spiroid.Gearing............................................................................. 1513.2.7.2. Helicon.Gearing............................................................................ 1543.2.7.3. Detailed.Calculations.of.Spiroid.and.Helicon.Tooth.Data...... 155

3.3. General.Equations.Relating.to.Center.Distance.................................................... 1563.3.1. Center.Distance.Equations.......................................................................... 156

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3.3.2. Standard.Center.Distance............................................................................ 1593.3.3. Standard.Pitch.Diameters............................................................................ 1603.3.4. Operating.Pitch.Diameters.......................................................................... 1603.3.5. Operating.Pressure.Angle........................................................................... 1613.3.6. Operating.Center.Distance.......................................................................... 1623.3.7. Center.Distance.for.Gears.Operating.on.Nonparallel.

Nonintersecting.Shafts................................................................................ 1623.3.8. Center.Distance.for.Worm.Gearing........................................................... 1623.3.9. Reasons.for.Nonstandard.Center.Distances............................................. 1633.3.10. Nonstandard.Center.Distances................................................................... 163

3.4. Elements.of.Center.Distance..................................................................................... 1653.4.1. Effects.of.Tolerances.on.Center.Distance.................................................. 1653.4.2. Machine.Elements.that.Require.Consideration.in.Critical.Center.

Distance.Applications.................................................................................. 1683.4.3. Control.of.Backlash....................................................................................... 1713.4.4. Effects.of.Temperature.on.Center.Distance.............................................. 1723.4.5. Mounting.Distance....................................................................................... 174

4 PreliminaryDesignConsiderations................................................................................ 1774.1. Stress.Formulas:.Calculation.................................................................................... 177

4.1.1. Calculated.Stresses....................................................................................... 1774.1.2. Gear.Design.Limits....................................................................................... 1814.1.3. Gear.Strength.Calculations......................................................................... 181

4.1.3.1. Worst.Load..................................................................................... 1844.1.3.2. Stress.Concentration..................................................................... 1854.1.3.3. Load.Distribution.......................................................................... 1864.1.3.4. Dynamic.Load............................................................................... 1864.1.3.5. Finite.Element................................................................................ 187

4.1.4. Gear.Surface.Durability.Calculations........................................................ 1884.1.4.1. Hertz.Derivations.......................................................................... 1894.1.4.2. K-Factor.Derivations..................................................................... 1924.1.4.3. Worst-Load.Position...................................................................... 1934.1.4.4. Endurance.Limit............................................................................ 1934.1.4.5. Lubrication.Regimens................................................................... 194

4.1.5. Gear.Scoring.................................................................................................. 1984.1.5.1. Hot.and.Cold.Scoring................................................................... 1984.1.5.2. PVT.Formula.................................................................................. 1994.1.5.3. Flash.Temperature........................................................................ 2024.1.5.4. Scoring.Criterion........................................................................... 203

4.1.6. Thermal.Limits.............................................................................................. 2054.1.6.1. Thermal.Limits.at.Regular.Speed............................................... 2054.1.6.2. Thermal.Limits.at.High.Speed.................................................... 206

4.2. Stress.Formulas:.Special.Considerations................................................................ 2064.2.1. Gear.Specifications....................................................................................... 2074.2.2. Size.of.Spur.and.Helical.Gears.by.Q-Factor.Method.............................. 207

4.2.2.1. Face-Width.Considerations.......................................................... 2104.2.2.2. Weight.from.Volume..................................................................... 211

4.2.3. Indexes.of.Tooth.Loading............................................................................ 2134.2.4. Estimating.Spur.and.Helical.Gear.Size.by.K-Factor................................ 214

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4.2.5. Estimating.Bevel.Gear.Size......................................................................... 2154.2.6. Estimating.Worm.Gear.Size........................................................................ 2204.2.7. Estimating.Spiroid.Gear.Size......................................................................223

4.3. Data.Needed.for.Gear.Drawings.............................................................................2234.3.1. Gear.Dimensional.Data................................................................................2234.3.2. Gear.Tooth.Tolerances.................................................................................. 2264.3.3. Gear.Material.and.Heat.Treatment.Data...................................................2344.3.4. Enclosed.Gear.Unit.Requirements............................................................. 241

5 DesignFormulas.................................................................................................................. 2435.1. Calculation.of.Gear.Tooth.Data............................................................................... 243

5.1.1. Number.of.Pinion.Teeth.............................................................................. 2435.1.2. Hunting.Teeth............................................................................................... 2485.1.3. Spur.Gear.Tooth.Proportions...................................................................... 2495.1.4. Root.Fillet.Radii.of.Curvature..................................................................... 2515.1.5. Long-Addendum.Pinions............................................................................2535.1.6. Tooth.Thickness............................................................................................ 257

5.1.6.1. Backlash.......................................................................................... 2575.1.6.2. Tolerances.and.Tooth.Thickness................................................. 258

5.1.7. Chordal.Dimensions.................................................................................... 2585.1.8. Degrees.Roll.and.Limit.Diameter.............................................................. 2605.1.9. Form.Diameter.and.Contact.Ratio.............................................................264

5.1.9.1. Form.Diameter...............................................................................2645.1.9.2. Contact.Ratio.................................................................................. 265

5.1.10. Spur.Gear.Dimension.Sheet........................................................................ 2665.1.11. Internal.Gear.Dimension.Sheet.................................................................. 2685.1.12. Helical.Gear.Tooth.Proportions.................................................................. 2725.1.13. Helical.Gear.Dimension.Sheet.................................................................... 2775.1.14. Bevel.Gear.Tooth.Proportions..................................................................... 2795.1.15. Straight.Bevel.Gear.Dimension.Sheet........................................................2835.1.16. Spiral.Bevel.Gear.Dimension.Sheet...........................................................2855.1.17. Zerol.Bevel.Gear.Dimension.Sheet............................................................2885.1.18. Hypoid.Gear.Calculations........................................................................... 2895.1.19. Face.Gear.Calculations................................................................................. 2905.1.20. Crossed-Helical.Gear.Proportions............................................................. 2935.1.21. Single-Enveloping.Worm.Gear.Proportions............................................. 2965.1.22. Single-Enveloping.Worm.Gears................................................................. 2975.1.23. Double-Enveloping.Worm.Gears................................................................ 299

5.2. Gear.Rating.Practice..................................................................................................3035.2.1. General.Considerations.in.Rating.Calculations.......................................303

5.2.1.1. Calculation.Procedure..................................................................3055.2.1.2. Grades.of.Material.Quality..........................................................3065.2.1.3. Reliability.of.Gears........................................................................ 307

5.2.2. General.Formulas.for.Tooth.Bending.Strength.and.Tooth.Surface.Durability....................................................................................................... 3075.2.2.1. Strength.Formula..........................................................................3085.2.2.2. Durability.Formula.......................................................................3085.2.2.3. Rating.Curves.of.Stress.versus.Cycles....................................... 3135.2.2.4. Rating.Bevel.Gears........................................................................ 315

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5.2.3. Geometry.Factors.for.Strength................................................................... 3165.2.3.1. Lack.of.Load.Sharing.................................................................... 3175.2.3.2. Helical.Gears.with.Narrow.Face.Width..................................... 3175.2.3.3. Geometry.Factors.for.Strength.for.Some.Standard.Designs..... 318

5.2.4. Overall.De-Rating.Factor.for.Strength....................................................... 3195.2.4.1. Application.Factor.Ka.................................................................... 3225.2.4.2. Load.Distribution.Factor.Km........................................................ 3225.2.4.3. Effect.of.Helix.Error.and.Shaft.Misalignment.......................... 3245.2.4.4. Aspect.Ratio.Effects...................................................................... 3275.2.4.5. Load.Distribution.Factor.Km.for.Bevel.Gears............................ 3285.2.4.6. Size.Factor.Ks..................................................................................3305.2.4.7. Dynamic.Load.Factors.Kv.and.Cv................................................330

5.2.5. Geometry.Factors.for.Durability................................................................3335.2.6. Overall.De-Rating.Factor.for.Surface.Durability.....................................335

5.2.6.1. Size.Factor.Cs..................................................................................3365.2.6.2. Complementary.Considerations.................................................338

5.2.7. Load.Rating.of.Worm.Gearing................................................................... 3395.2.7.1. Crossed-Helical.Gear.Durability................................................ 3395.2.7.2. Cylindrical.Worm.Gear.Durability............................................ 3415.2.7.3. Double-Enveloping.Worm.Gear.Durability..............................3465.2.7.4. Comparison.of.Double-Enveloping.and.Cylindrical.

Worm.Gear.Rating.Procedures...................................................3495.2.8. Design.Formulas.for.Scoring......................................................................350

5.2.8.1. Hot.Scoring....................................................................................3505.2.8.2. Cold.Scoring................................................................................... 3555.2.8.3. Design.Practice.to.Handle.Scoring.............................................360

5.2.9. Trade.Standards.for.Rating.Gears.............................................................. 3615.2.10. Vehicle.Gear.Rating.Practice.......................................................................3635.2.11. Marine.Gear.Rating.Practice.......................................................................3655.2.12. Oil.and.Gas.Industry.Gear.Rating............................................................. 3675.2.13. Aerospace.Gear.Rating.Practice.................................................................368

6 GearMaterials...................................................................................................................... 3716.1. Steels.for.Gears........................................................................................................... 371

6.1.1. Mechanical.Properties................................................................................. 3716.1.2. Heat-Treating.Techniques............................................................................ 3756.1.3. Heat-Treating.Data........................................................................................ 3796.1.4. Hardness.Tests.............................................................................................. 381

6.2. Localized.Hardening.of.Gear.Teeth........................................................................3836.2.1. Carburizing...................................................................................................3836.2.2. Nitriding......................................................................................................... 389

6.2.2.1. Features.of.Nitriding.Process...................................................... 3896.2.2.2. Nitride.Case.Depth....................................................................... 392

6.2.3. Induction.Hardening.of.Steel...................................................................... 3936.2.3.1. Induction.Hardening.by.Scanning............................................. 3956.2.3.2. Load-Carrying.Capacity.of.Induction-Hardened.Gear.Teeth......398

6.2.4. Flame.Hardening.of.Steel............................................................................4006.2.5. Combined.Heat.Treatments........................................................................ 4016.2.6. Metallurgical.Quality.of.Steel.Gears.......................................................... 402

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6.2.6.1. Quality.Items.for.Carburized.Steel.Gears................................. 4026.2.6.2. Quality.Items.for.Nitrided.Gears................................................4046.2.6.3. Procedure.to.Get.Grade2.Quality..............................................405

6.3. Cast.Irons.for.Gears...................................................................................................4066.3.1. Gray.Cast.Iron............................................................................................... 4076.3.2. Ductile.Iron....................................................................................................4086.3.3. Sintered.Iron.................................................................................................. 410

6.4. Nonferrous.Gear.Metals........................................................................................... 4116.4.1. Kinds.of.Bronze............................................................................................. 4116.4.2. Standard.Gear.Bronzes................................................................................ 413

6.5. Nonmetallic.Gears..................................................................................................... 4146.5.1. Thermosetting.Laminates........................................................................... 4146.5.2. Nylon.Gears................................................................................................... 416

7 Gear-ManufacturingMethods......................................................................................... 4197.1. Gear.Tooth.Cutting.................................................................................................... 419

7.1.1. Gear.Hobbing................................................................................................ 4197.1.2. ShapingPinion.Cutter...............................................................................4267.1.3. ShapingRack.Cutter.................................................................................. 4317.1.4. Cutting.Bevel.Gears......................................................................................4357.1.5. Gear.Milling..................................................................................................4387.1.6. Broaching.Gears............................................................................................4427.1.7. Punching.Gears.............................................................................................4447.1.8. G-TRAC.Generating.....................................................................................446

7.2 Gear.Grinding............................................................................................................4487.2.1. Form.Grinding..............................................................................................448

7.2.1.1. Ceramic.Form.Grinding...............................................................4497.2.1.2. Borazon.Form.Grinding............................................................... 452

7.2.2. Generating.GrindingDisk.Wheel...........................................................4537.2.3. Generating.GrindingBevel.Gears........................................................... 4567.2.4. Generating.GrindingThreaded.Wheel................................................... 4597.2.5. Thread.Grinding........................................................................................... 462

7.3. Gear.Shaving,.Rolling,.and.Honing........................................................................4657.3.1. Rotary.Shaving..............................................................................................4657.3.2. Rack.Shaving................................................................................................. 4707.3.3. Gear.Rolling................................................................................................... 4707.3.4. Gear.Honing.................................................................................................. 473

7.4. Gear.Measurement.................................................................................................... 4757.4.1. Gear.Accuracy.Limits................................................................................... 4767.4.2. Machines.to.Measure.Gears........................................................................ 481

7.5. Gear.Casting.and.Forming....................................................................................... 4877.5.1. Cast.and.Molded.Gears................................................................................ 4877.5.2. Sintered.Gears...............................................................................................4887.5.3. Cold-Drawn.Gears.and.Rolled.Worm.Threads........................................ 489

8 DesignofToolstoMakeGearTeeth............................................................................... 4918.1. Shaper.Cutters............................................................................................................ 4918.2. Gear.Hobs.................................................................................................................... 5028.3. Spur.GearMilling.Cutters....................................................................................... 515

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8.4. Worm-Milling.Cutters.and.Grinding.Wheels....................................................... 5178.5. Gear-Shaving.Cutters................................................................................................ 5228.6. Punching.Tools........................................................................................................... 5258.7. Sintering.Tools............................................................................................................ 526

9 KindsandCausesofGearFailures................................................................................. 5299.1. Analysis.of.Gear-System.Problems......................................................................... 529

9.1.1. Determining.the.Problem............................................................................ 5299.1.2. Possible.Causes.of.Gear-System.Failures.................................................. 5319.1.3. Incompatibility.in.Gear.Systems................................................................5339.1.4. Investigation.of.Gear.Systems.....................................................................534

9.2. Analysis.of.Tooth.Failures.and.Gear-Bearing.Failures........................................ 5359.2.1. Nomenclature.of.Gear.Failure.................................................................... 5369.2.2. Tooth.Breakage.............................................................................................. 5369.2.3. Pitting.of.Gear.Teeth....................................................................................5409.2.4. Scoring.Failures.............................................................................................5429.2.5. Wear.Failures.................................................................................................5449.2.6. Gearbox.Bearings..........................................................................................5479.2.7. Rolling-Element.Bearings............................................................................5489.2.8. Sliding-Element.Bearings............................................................................550

9.3. Some.Causes.of.Gear.Failure.Other.than.Excess.Transmission.Load................ 5529.3.1. Overload.Gear.Failures................................................................................ 5539.3.2. Gear-Casing.Problems.................................................................................5549.3.3. Lubrication.Failures...................................................................................... 5559.3.4. Thermal.Problems.in.Fast-Running.Gears............................................... 561

10 SpecialDesignProblems...................................................................................................56510.1. Center.Distance.Problems.........................................................................................56510.2. Profile.Modification.Problems.................................................................................. 57610.3. Load.Rating.Problem.................................................................................................585

11 GearReactionsandMountings........................................................................................ 59111.1. Mechanics.of.Gear.Reactions................................................................................... 591

11.1.1. Summation.of.Forces.and.Moments.......................................................... 59111.1.2. Application.to.Gearing................................................................................. 594

11.2. Basic.Gear.Reactions,.Bearing.Loads,.and.Mounting.Types............................... 59511.2.1. Main.Source.of.Load.................................................................................... 59511.2.2. Gear.Reactions.to.Bearing........................................................................... 59611.2.3. Directions.of.Loads....................................................................................... 59711.2.4. Additional.Considerations.......................................................................... 59711.2.5. Types.of.Mountings...................................................................................... 59811.2.6. Efficiencies.....................................................................................................600

11.3. Basic.Mounting.Arrangements.and.Recommendations......................................60011.3.1. Bearing.and.Shaft.Alignment..................................................................... 60111.3.2. Bearings.......................................................................................................... 60111.3.3. Mounting.Gears.to.the.Shaft....................................................................... 60211.3.4. Housing..........................................................................................................60311.3.5. Inspection.Hole.............................................................................................60311.3.6. Break-In..........................................................................................................603

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xiiiContents

11.4. Bearing.Load.Calculations.for.Spur.Gears............................................................60411.4.1. Spur.Gears.....................................................................................................60411.4.2. Helical.Gears.................................................................................................60611.4.3. Gears.in.Trains..............................................................................................60611.4.4. Idlers...............................................................................................................60611.4.5. Intermediate.Gears....................................................................................... 60711.4.6. Planetary.Gears.............................................................................................609

11.4.6.1. One.Planet......................................................................................60911.4.6.2. Several.Planets...............................................................................609

11.5. Bearing-Load.Calculations.for.Helicals.................................................................. 61011.5.1. Single.Helical.Gears..................................................................................... 61011.5.2. Double.Helical.Gears.................................................................................... 61211.5.3. Skewed-.or.Crossed-Helical.Gears............................................................. 613

11.6. Mounting.Practice.for.Bevel.and.Hypoid.Gears................................................... 61511.6.1. Analysis.of.Forces......................................................................................... 61511.6.2. Rigid.Mountings........................................................................................... 61611.6.3. Maximum.Displacements............................................................................ 61611.6.4. Rolling-Element.Bearings............................................................................ 61911.6.5. Straddle.Mounting........................................................................................ 61911.6.6. Overhung.Mounting.................................................................................... 61911.6.7. Gear.Blank.Design........................................................................................ 62211.6.8. Gear.and.Pinion.Adjustments..................................................................... 62511.6.9. Assembly.Procedure..................................................................................... 626

11.7. Calculation.of.Bevel.and.Hypoid.Bearing.Loads.................................................. 62711.7.1. Hand.of.Spiral............................................................................................... 62711.7.2. Spiral.Angle................................................................................................... 62711.7.3. Tangential.Load............................................................................................ 62811.7.4. Axial.Thrust................................................................................................... 62911.7.5. Radial.Load.................................................................................................... 62911.7.6. Required.Data.for.Bearing.Load.Calculations......................................... 637

11.8. Bearing.Load.Calculations.for.Worms................................................................... 63911.8.1. Calculation.of.Forces.in.Worm.Gears........................................................64011.8.2. Mounting.Tolerances....................................................................................64211.8.3. Worm.Gear.Blank.Considerations..............................................................64211.8.4. Run-In.of.Worm.Gears.................................................................................642

11.9. Bearing.Load.Calculations.for.Spiroid.Gearing....................................................64411.10. Bearing.Load.Calculations.for.Other.Gear.Types.................................................64811.11. Design.of.the.Body.of.the.Gear................................................................................648

12 GearVibration...................................................................................................................... 65112.1. Fundamentals.of.Vibration....................................................................................... 65112.2. Measurement.of.Vibration........................................................................................654

12.2.1. Examples.of.Sensing.Devices......................................................................65512.2.2. Practical.Problems.in.Vibration.Measurement......................................... 657

12.3. Some.Examples.of.Vibration.in.Geared.Units....................................................... 65712.4. Approximate.Vibration.Limits.................................................................................660

12.4.1. Velocity.Limits.............................................................................................. 66112.4.2. Acceleration.Limits....................................................................................... 66212.4.3. Proximity.Probes.......................................................................................... 662

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xiv Contents

12.4.4. Displacement.Limits..................................................................................... 66212.4.5. General.Vibration.Tendencies.....................................................................66312.4.6. Trade.Standard..............................................................................................663

12.5. Control.of.Vibration.in.Manufacturing.Gears.and.in.the.Field..........................66512.5.1. Testing.of.Gear.Units.at.the.Gear.Factory.................................................66612.5.2. Tests.of.Assembled.Power.Package............................................................66612.5.3. Vibration.Tests.in.the.Field.......................................................................... 667

12.6. Vibration.Analysis.Technique..................................................................................668

AppendixA:EvolutionofGearArt........................................................................................ 671

AppendixB:ComplementaryMaterial.................................................................................. 717

AppendixC:NumericalDataTables......................................................................................771

AppendixD:OntheConceptofNovikovGearingandtheInadequacyoftheTermsWildhaberNovikovGearingandWNGearing..................803

References....................................................................................................................................835

Index.............................................................................................................................................847

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xv

Preface

This. publication. is. dedicated. to. engineers. who. work. in. the. field. of. gears. and. gear.production.

Gearing.is.a.specific.area.of.mechanical.engineering..Gearing.encompasses.gear.design,.production,. inspection,.and. implementation,.as.well.as.some.other.supplementary.sub-jects..This.book.is.primarily.focused.on.gear.design.and.gear.production.

This.book.is.a.revised,.updated,.and.enlarged.version.of.the.earlier.published.book.by.Darle.W..Dudley.entitled.Handbook of Practical Gear Design..The.book.was.first.published.by.McGraw-Hill.Book.Company.in.1984,.and.by.CRC.Press.ten.years.later.in.1994..Both.editions.originated.from.an.earlier.book.by.the.same.author.entitled.Practical Gear Design,.which.was.published.by.McGraw-Hill.Book.Company.in.1954..The.last.edition.(1984/1994).of.the.Gear Handbook.is.highly.recognized.by.the.gear.community.worldwide.

As.time.passes.new.knowledge.is.accumulated.by.the.gear.industry,.and.along.with.that.some.of.the.experiences.summarized.in.the.Gear Handbook.have.become.obsolete..Obsolete.data.should.be.removed.from.the.book,.while.novel.data.in.the.field.should.be.added.

Keeping.in.mind.the.importance.of.the.Gear Handbook.for.practical.gear.engineers.and.practitioners,.I.appreciated.and.supported.the.attempt.undertaken.by.CRC.Press.to.revise,.update,.and.enlarge.the.1994.edition.of.the.Handbook.

Among.the.critical.problems.that.arose.when.working.on.the.new.edition.of.the.Gear Handbook.were.as.follows:

. The.new.edition.of.the.Gear Handbook.should.fulfill.the.current.demands.of.the.gear.industry..This.requires.a.significant.revision.of.the.original.text.

. At.that.same.time.much.effort.was.undertaken.to.preserve.the.original.text.of.the.Handbook.to.retain.the.tone.of.Dudleys.text.

This. contradiction. between. the. desire. to. comprehensively. update. the. book. and. the.desire.to.limit.the.revisions.culminated.in.the.compromise.to.entitle.the.book.as.Dudleys Handbook of Practical Gear Design and Manufacture.

Two.options.were.considered.The. first. is. to. make. significant. changes. to. the. original. text. of. Dudleys. book.. By. fol-

lowing.this.path,.the.charm.and.philosophy.of.Dudleys.book.would.be.lost.(or.it.will.be.largely.ruined)..In.this.case.Dudleys.book.will.no.longer.be.Dudleys.book..It.will.be.a.different.book.on.gearing.having.no.need.for.the.word.Dudleys.in.the.title.

The.second.option.is.to.keep.the.original.text.of.Dudleys.book.as.intact.as.possible..In.this.case.Dudleys.philosophy.and.his.vision/understanding.of.gearing.can.be.preserved.

Both.options.have.their.own.merit,.and.it.was.hard.to.make.a.decision.which.way.to.fol-low..Ultimately,.the.decision.to.make.reasonable.but.limited.changes.to.the.original.text.(where.appropriate).was.made..With.that.said,.some.repetitions.are.inevitable,.and.the.best.effort.was.made.to.minimize.these.repetitions.

Before.beginning.the.revision.of.the.Gear Handbook,.all.earlier.editions.of.Dudleys.book.[starting.from.the.1954.McGraw-Hill.edition,.and.ending.with.the.latest.1994.CRC.Press.edition. (including. the. 1962. and. 1984. McGraw-Hill. editions)]. were. carefully. studied.. To.update.the.book,.obsolete.material.was.removed.from.the.text.body.where.appropriate,.

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xvi Preface

and.several.new.chapters.and.new.appendices.were.added..The.author.appreciates.CRC.Press. for. the. idea. to. publish. a. new. revised. and. updated. edition. of. the. Gear Handbook..Personal. thanks. go. to. Mr.. Jonathan. W.. Plant,. executive. editor,. Mechanical,. Aerospace,.Nuclear.and.Energy.Engineering,.who.has.approached.the.author.with.the.proposal. to.revise.the.Gear Handbook,.and.to.prepare.this.new.edition.for.publication.by.CRC.Press.

StephenP.RadzevichSterling Heights, Michigan

PRE FAC E( TOT hE198 4 / 19 94EDI T ION )

This.is.a.revision.of.the.book.Practical Gear Design,.published.by.the.McGraw-Hill.Book.Company.in.1954..This.book.is.now.called.a.handbook.because.of.its.broader.coverage.of.subjects.pertaining.to.gear.design.and.the.recognition.that.the.content.of.the.original.book.made.it.a.lasting.reference.that.saw.constant.use.in.day-to-day.gear.work.

Although.this.revision.is.broader.in.scope.and.has.more.pages,.the.plan.of.the.book.and.the.way.many.aspects.of.the.gear.art.are.treated.has.been.kept.just.the.same..Those.famil-iar.with.Practical Gear Design.will.find.themselves.right.at.home.as.they.read.the.Handbook of Practical Gear Design..The.main.difference.is.that.new.things.learned.in.the.1960s.and.1970s.about.how.to.better.design,.build,.and.use.gears.are.included.in.this.book..Gear.tech-nology.has.made.rapid.progress,.just.as.space.technology.and.computer.technology.have.made.rapid.progress.in.the.same.time.period.

This.book.has.been.written.with.the.general.engineer.or.technician.in.mind..It. is.my.hope.that.alert.shop.planning.engineers,.tool.engineers,.engineering.students,.cost.ana-lysts,. shop. supervisors,. and. progressive. machine-tool. operators. will. find. this. book. of.value.and.assistance.when.confronted.with.problems.involving.gear.design.or.manufac-ture.or.involving.failure.in.service.

The.scope.of.the.work.includes.the.geometry.of.gear.design,.manufacturing.methods,.and.causes.of.gear.installation.failures..A.gear.design.is.not.good.design.unless.it.is.practi-cal.and.economical.to.manufacture.and.unless.it.is.well.enough.thought.out.to.meet.all.the.hazards.of.service.in.the.field..It.has.been.my.aim.to.show.how.a.practical.gear.design.must.be.based.on.the.limitations.and.availability.of.machine.tools.and.tooling.setup.

As.in.most.phases.of.engineering,.there.are.often.divergent.methods.advocated.to.gain.a.given.result..The.gearing.art.is.no.exception..For.instance,.in.Chapter.7,.equations.are.given.to.calculate. the. length.of. time.required.to.make.gear. teeth.by.various.processes..Several.experts.in.the.gear.field.reviewed.the.data.and.equations.in.this.chapter..Their.comments.indicated.that.the.data.would.be.very.helpful.to.most.designers,.but.they.also.pointed.out.that.some.gear.designs.would.be.difficult.to.manufacture.and.a.shop.mightthrough.no.fault.of.its.ownbe.unable.to.meet.production.rates.estimated.by.the.material.in.this.chapter.

In.spite.of.all. that.has.been. learned.about.how.to.design.gears,.how.to.rate. them.for.load-carrying.capacity,.and.how.to.use.them.properly.in.service,.there.is.still.an.urgent.need.to.do.more.bench.testing,.to.make.better.analyses.of.gear-tooth.stresses,.and.to.learn.more.about.effects.of.lubricants,.variations.in.gear.material.quality,.and.peculiarities.of.the.environment.(corrosion,.dirt.in.the.oil,.temperature.transients,.load.transients,.etc.).in.which.the.gears.operate.

This.book.refers.to.many.standards.for.gears.that.are.in.current.use..It.can.be.expected.that.present.standards.will.be.revised.and.enlarged.as.gear.technology.progresses..This.book,.in.several.places,.advises.the.reader.to.expect.more.and.better.standards.for.gear.work. as. the. years. go. by.. The. book. gives. practical. advice. about. what. to. do,. but. it. also.

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xviiPreface

cautions.the.reader.to.always.consider.the.latest.rules.and.data.in.a.constantly.changing.array.of.gear.trade.standards.

AC K NOW lEDGM EN TS

The.writing.of.a.technical.book.covering.a.whole.field.of.work.is.a.very.sizable.project..The.author.is.faced.not.only.with.organizing.and.writing.the.text.material.and.equations.but.also.with.computing.data,.preparing.tables.and.figures,.and.locating.good.reference.data.for.a.multiplicity.of.items.

I.wish.to.wholeheartedly.thank.all.of.the.people.who.have.helped.prepare.this.work.The. initial. typing. and. equation. work. was. done. by. Mrs.. M.. Irene. Galarneau. (a. long-

time.secretary.of.mine),.Mrs..Violet.Daughters,.and.Mrs..Dorothy.Dudley.(my.wife)..The.final. typing,. proofreading,. and. preparation. of. illustrations. was. done. by. Mrs.. Carolyn.Strickland.(a.technical.assistant).

Many.of.the.illustrations.in.the.book.have.been.furnished.by.companies.that.have.also.helped.me.get.items.of.technical.data..(Note.the.company.names.given.in.the.figure.leg-ends.).The.assistance.of.all.of.these.companies.is.greatly.appreciated.

The.American.Gear.Manufacturers.Association.(AGMA).has.been.most.helpful.to.me..The.officers.and.staff.are.dedicated.to.the.advancement.of.gear.technology.and.have.long.provided. forums. for. the.decision.and.evaluation.of.gear.experience..The.great.body.of.standards.that.have.been.issued.by.AGMA.is.of.immense.reference.value..The.reader.will.note.that.this.book.has.made.much.use.of.AGMA.standards.

I. wish. to. particularly. acknowledge. the. assistance. of. a. few. individuals. with. unusual.knowledge.and.experience.in.the.gear.trade.

Dr.. Hans. Winter. of. the. Technical. University. of. Munich. in. Germany. (Technische.Universitt.Mnchen).has.reviewed.parts.of.this.book.and.has.helped.me.obtain.data.and.a.better.understanding.of.the.many.aspects.of.gear.research.and.gear.rating.

Dr..Giovanni.Castellani,.a.gear.consultant.in.Modena,.Italy,.has.helped.me.in.comparing.European.and.American.gear.rating.practices.and.gear-tooth.accuracy.limits.

Mr..Eugene.Shipley.of.Mechanical.Technology.Inc.. in.Latham,.New.York,.has.helped.meon.the.basis.of.his.worldwide.experience.with.gears.in.servicein.many.discussions.about.gear.wear.and.gear.failures.

Dr..Daniel.Diesburg.of.the.Climax.Molybdenum.Company.in.Ann.Arbor,.Michigan,.was.most.helpful.in.reviewing.data.on.gear.metals.and.gear.heat-treating.procedures.

Mr..Dennis.Townsend.of.the.NASA.Lewis.Research.Center.in.Cleveland,.Ohio,.has.done.unusual.research.work.and.also.has.brought.together.many.key.people.in.the.gear.trade.under.the.auspices.of.ASME.international.meetings..The.international.ASME.gear.meet-ing.in.Chicago,.Illinois,.in.1977.was.of.much.value.to.me.

Dr..Aizoh.Kubo.of.Kyoto.University.in.Kyoto,.Japan,.has.directly.contributed.to.this.book.in.the.section.on.dynamic.loading..Indirectly,.he.has.helped.me.greatly.in.getting.to.know.the.leading.people.in.gear.research.in.Japan.

While.I.acknowledge.with.much.thanks.the.assistance.of.these.and.many.other.experts.during. this. work,. I. must. accept. the. responsibility. for. having. made. the. final. decisions.onthe.technical.content.of.this.book..I.have.tried.to.present.a.fair.consensus.of.opinion.and.the.best.gear.design.guidance.from.all.the.somewhat.divergent.theories.and.practices.in.the.gear.field.

DarleW.DudleySan Diego, California

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xix

Introduction

This. book. (hereafter. the. Gear Handbook). deals. with. gears. and. gearing. in. both. aspects,.namely.gear.design.and.gear.production.

Gears.are.produced. in.enormous.amountsbillions.of.gears.are.produced.by. indus-tries.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.

UniquenessofThisBook

Many.books.on.gears.and.gearing,.in.both.the.design.and.manufacture.areas,.have.been.published.thus.far..This.second.edition.of.the.Gear.Handbook.is.a.unique.one.many.reasons.

First,. the.Gear.Handbook. is.based.on.practical.experience.of.designing.and.producing.gears..The.collection.of.data.in.the.Gear.Handbook.is.invaluable.to.practitioners.in.areas.of.both.gear.design.and.gear.production.

Second,.this.second.edition.of.the.Gear.Handbook. is.significantly.enlarged.in.compari-son. to. the. earlier. 1994. edition.. New. chapters. and. a. few. more. appendices. were. added..This.makes.the.Gear.Handbook.a.comprehensive.source.of.information.for.those.who.are.involved.in.the.design.and.production.of.gears.

Third,.the.uniqueness.of.the.Gear.Handbook.is.proven.by.several.earlier.editions,.starting.from.the.1954.edition..For.decades.the.earlier.editions.of.the.book.have.been.successfully.used.by.gear.experts.worldwide.. It. is.anticipated.that. this.newly.revised,.updated,.and.enlarged.edition.of.the.Gear.Handbook.will.be.acknowledged.by.the.reader.

IntendedAudience

Many. readers. will. benefit. from. the. Gear. Handbook,. specifically. mechanical. and. manu-facturing.engineers.involved.in.continuous.design.and.manufacturing.process.improve-ment,.and.those.who.are.active.or.intend.to.become.active.in.the.field..Among.them.are.senior.undergraduate.and.graduate.university.students.of.mechanical.and.manufacturing.engineering.

The.Gear.Handbook.is.intended.to.be.used.as.a.reference.book,.as.well.as.an.invaluable.source.of.practical.data.for.gear.design.engineers.and.gear.manufacturers.

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xx Introduction

OrganizationofThisBook

The.Handbook.is.organized.into.twelve.chapters.followed.by.four.appendices.Gear.design.trends.are.considered.in.Chapter.1..Both.manufacturing.trends,.as.well.as.

selection.of.the.right.kind.of.gear.are.disclosed.The. subsection. Manufacturing. Trends. encompasses. small,. low-cost. gears. for. toys,.

gadgets,.and.mechanisms,.and.then.the.application.gearscontrol.gears,.vehicle.gears,.marine.gears,.aerospace.gears,.and.othersare.discussed.

The.kinds.of.external.spur.and.helical.gears,.straight.bevel.gears,.spiral.bevel.gears,.hyp-oid,.and.face.gears.are.covered.in.the.subsection.Selection.of.Right.Kind.of.Gear.

Gear.types.and.nomenclature.are.discussed.in.Chapter.2..The.discussion.begins.with.classification. of. gears,. which. includes. parallel. axis. gearing,. nonparallel. coplanar. gears.operating.on.intersecting.axes,.nonparallel.noncoplanar.gears.operating.on.nonintersect-ing.axes,.and.special.gear.types..The.discussion.is.followed.by.nomenclature.of.all.practi-cal.kinds.of.gears,.which.includes,.but.is.not.limited.to,.nomenclature.of.spur.and.helical.gears,.both.external.and.internal;.crossed.helical.gear.nomenclature.and.formulas;.bevel.gear.nomenclature.and.formulas;.worm.gear.nomenclature.and.formulas;.and.nomencla-ture.of.face.gears,.beveloid.gears,.and.other.gear.types.

Gear.tooth.design.is.discussed.in.Chapter.3..This.includes.basic.requirements.of.gear.teeth,. standard. systems. of. gear. tooth. proportions,. general. equations. relating. to. center.distance,.along.with.elements.of.center.distance.

Preliminary.design.considerations.are.summarized.in.Chapter.4..Here,.stress.formula.is.discussed.in.detail..This.consideration.is.followed.by.data.needed.for.gear.drawings.

Design.formulas.are.discussed.in.Chapter.5..Calculation.of.gear.tooth.data.and.gear.rat-ing.practice.are.covered.in.this.chapter.

Chapter.6.is.devoted.to.consideration.of.gear.materials..Steel.for.gears,.localized.harden-ing.of.gear.teeth,.cast.irons.for.gears,.as.well.as.nonferrous.gear.metals.and.nonmetallic.gears.are.considered.in.this.section.of.the.book.

In. parallel. to. gear. design,. gear. manufacturing. methods. are. considered. in. the. book..Chapter. 7. is. devoted. to. a. detailed. consideration. of. various. methods. for. producing. the.gears..This.includes.gear.tooth.cutting.by.hobbing,.shaping,.milling,.broaching,.and.oth-ers.. Gear-grinding. methods,. such. as. form. grinding,. generating. grinding,. and. thread.grinding.are.discussed..This.subsection.of.the.chapter.is.followed.by.a.discussion.on.gear.shaving,.rolling,.and.honing.methods..The.consideration.of.the.gear.manufacturing.meth-ods.ends.with.a.discussion.of.gear.casting.and.forming.methods.

Design.of.tools.used.to.make.gear.teeth.is.discussed.in.Chapter.8..Design.of.shaper.cut-ters,.gear.hobs,.spur-gear.milling.cutter,.gear-shaving.cutter,.punch.tools,.and.sintering.tools.are.considered.in.this.section.of.the.book.

Chapter.9. is.devoted. to.consideration.of. the.kinds.and.causes.of.gear. failures..This.includes. an. analysis. of. gear. system. problems,. an. analysis. of. tooth. failures. and. gear-bearing.failures,.along.with.the.consideration.of.some.causes.of.gear.failure.other.than.excess.transmission.load.

Special.design.problems.are.discussed.in.Chapter.10..Center.distance.problems,.profile.modification.problems,.as.well.as.load.rating.problems.are.considered.in.detail.in.this.sec-tion.of.the.book.

Gear.reactions.and.mountings.are.outlined.in.Chapter.11..The.discussion.begins.with.an.analysis.of.mechanics.of.gear.reactions,.which.is.then.followed.by.consideration.of.basic.reactions,. bearing. loads,. and. mounting. types.. Then. basic. mounting. arrangements. are.

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xxiIntroduction

considered.and.corresponding.recommendations.are.given..This.subsection.of.the.book.is.followed.by.an.analysis.of.bearing.load.calculations.for.spur.and.for.helical.gears..Then.mounting.practice.for.bevel.and.hypoid.gears.along.with.calculation.of.bevel.and.hypoid.bearing.loads.is.considered..This.section.of.the.book.ends.with.an.analysis.of.bearing.load.calculations.for.worms,.Spiroid,.and.other.gear.types,.as.well.as.of.the.design.of.the.gear.body.

Finally,.gear.vibration.is.discussed.in.Chapter.12..This.section.of.the.book.begins.with.the.fundamentals.of.vibration..Then.measurement.of.vibration. is.considered..Examples.of.vibration.in.geared.units.are.provided..Approximate.vibration.limits.are.outlined,.and.control.of.vibration.in.manufacturing.gears.and.in.the.field.are.discussed.

Four.appendices.are.attached.at.the.very.end.of.the.book.

Appendix.A:.Evolution.of.Gear.ArtAppendix.B:.Complementary.MaterialAppendix.C:.Numerical.Data.TablesAppendix.D:.On.the.Concept.of.Novikov.Gearing.and.the.Inadequacy.of.the.Terms.

WildhaberNovikov.Gearing.and.WN.Gearing.

StephenP.Radzevich

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xxiii

Acknowledgments

The.author.would.like.to.share.the.credit.for.any.success.of.the.Gear Handbook.to.the.many.discussions.on. the.subject.with.numerous. representatives.of. the.gear.community,.both.domestic.and.international.

The.contribution.of.many.friends.and.colleagues.in.overwhelming.numbers.cannot.be.acknowledged.individually,.and.as.much.as.our.benefactors.have.contributed,.their.kind-ness.and.help.must.go.unrecorded.

Special. thanks. go. to. Mr.. Jonathan. W.. Plant,. senior. editor,. Mechanical,. Aerospace,.Nuclear.&.Energy.Engineering,.for.his.idea.to.revise.the.1994.edition.of.the.Gear Handbook,.and.in.this.way.to.make.the.revised,.updated,.and.enlarged.edition.available.to.the.gear.community.worldwide.

Many.thanks.also. to.Ms.. Jill. J.. Jurgensen,.senior.project.coordinator,.Editorial.Project.Development,. for. the.comprehensive.support.during.the.publication.process,.as.well.as.to.those.at.CRC.Press.who.took.over.the.final.stages.and.who.will.have.to.cope.with.the.marketing.and.sales.of.the.fruit.of.my.efforts.

My.special.thanks.to.my.wife,.Natasha,.for.her.tolerance,.support,.encouragement,.end-less.patience,.and.love.

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xxv

Author

Dr. Stephen P.Radzevich. is. a.professor.of.mechanical. engineering. and.a.professor.of.manufacturing. engineering.. He. received. the. M.Sc.. (1976),. Ph.D.. (1982),. and. Dr.(Eng)Sc..(1991)all.in.mechanical.engineering..Dr..Radzevich.has.extensive.industrial.experience.in.gear.design.and.manufacture..He.has.developed.numerous.software.packages.dealing.with.CAD.and.CAM.of.precise.gear.finishing.for.a.variety.of.industrial.sponsors..His.main.research.interest.is.kinematic.geometry.of.surface.generation,.with.a.focus.on:.(a)precision.gear.design;.(b).high.power.density.gear.trains;.(c).torque.share.in.multiflow.gear.trains;.(d).design.of.special.purpose.gear.cutting/finishing.tools;.and.(e).design.and.machining.(fin-ishing).of.precision.gears.for.low-noise/noiseless.transmissions.of.cars,.light.trucks,.and.other.vehicles..Dr..Radzevich.has.spent.over.35.years.developing.software,.hardware,.and.other.processes.for.gear.design.and.optimization..Besides.his.work.in.industry,.he.trains.engineering.students.at.universities.and.gear.engineers. in.companies..He.has.authored.and.coauthored.more. than.30.monographs,.handbooks,.and. textbooks,.as.well.as.more.than.250.scientific.papers,.and.holds.over.220.patents.on.inventions.in.the.field.

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ContentsPrefaceIntroductionAcknowledgmentsAuthor