DUDLEY'S" HANDBOOK OF PRACTICAL GEAR DESIGN AND MANUFACTURE. Stephen P. Radzevich

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1 Second Edition DUDLEY'S" HANDBOOK OF PRACTICAL GEAR DESIGN AND MANUFACTURE Stephen P. Radzevich LßP) CRC Press VV J Taylors Francis Group Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an informa business

Preface Introduction Acknowledgments Author xv xix xxiii 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.

2 Preface Introduction Acknowledgments Author xv xix xxiii xxv 1 Gear Design Trends Small, Low-Cost Gears for Toys, Gadgets, and Mechanisms Appliance Gears Machine Tools Control Gears Vehicle Gears Transportation Gears Marine Gears Aerospace Gears Industrial Gearing Gears in the Oil and Gas Industry Mill Gears External Spur Gears External Helical Gears Internal Gears Straight Bevel Gears Zerol Bevel Gears Spiral Bevel Gears Hypoid Gears Face Gears Crossed-Helical Gears (Nonenveloping Worm Gears) Single-Enveloping Worm Gears Double-Enveloping Worm Gears Spiroid Gears 39 2 Gear Types and Nomenclature Types of Gears Classifications Parallel Axis Gears Spur Gears Helical Gears Internal Gears Nonparallel, Coplanar Gears (Intersecting Axes) Bevel Gears Face Gears (On-Center) Conical Involute Gearing Nonparallel, Noncoplanar Gears (Nonintersecting Axes) Crossed-Axis Helical Gears Cylindrical Worm Gearing 57 v

vi Contents 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.

3 vi Contents Single-Enveloping Worm Gearing Double-Enveloping Worm Gearing Hypoid Gears Spiroid and Helicon Gearing Face Gears (Off-Center) Special Gear Types Square or Rectangular Gears Triangular Gears Elliptical Gears Scroll Gears Multiple-Sector Gears Nomenclature of Gears Spur Gear Nomenclature and Basic Formulas Helical Gear Nomenclature and Basic Formulas Internal Gear Nomenclature and Formulas Crossed Helical Gear Nomenclature and Formulas Bevel Gear Nomenclature and Formulas Straight Spiral Zerol Worm Gear Nomenclature and Formulas Cylindrical Worm Gears Double-Enveloping Worm Gears Face Gears Spiroid Gear Nomenclature and Formulas Beveloid Gears 83 3 Gear Tooth Design Basic Requirements for Gear Tooth Design Definition of Gear Tooth Elements Basic Considerations for Gear Tooth Design Continuity of Action Conjugate Action Pitch Diameter Zones in Which Involute Gear Teeth Exist Pointed Teeth Undercut Long- and Short-Addendum Gear Design Addendum Modification for Gears Having a Few Teeth Speed-Increasing Drives Power Drives (Optimal Design) Low-Friction Gearing Special Design Considerations Interchangeability Tooth Thickness Tooth Profile Modifications Transverse of Profile Modification Allowances for Errors of Gear Manufacture Allowances for Deflection under Load 109

vii 3.1.4.7 Axial Modifications 110 3.1.4.8 Root Fillets Ill 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.

4 vii Axial Modifications Root Fillets Ill Effective Outside Diameter Width of Tip of Tooth Pointed Tooth Diameter Purpose of Backlash Backlash: Recommended Values Standard Systems of Gear Tooth Proportions Standard Systems for Spur Gears Limitations in Use of Standard Tables Standard Tooth Forms That Have Become Obsolete Brown and Sharp System AGMA 14.5 Composite System Fellows 20 Stub Tooth System AGMA 14.5 Full-Depth System Cycloidal Tooth Profiles Clockwork and Timer Tooth Profiles Specific Spur Gear Calculation Procedure Explanation and Discussion of Items in Table System for Helical Gears Selection of Tooth Form Selection of Helix Angle Face Width Specific Calculation Procedure for Helical Gears System for Internal Gears Special Calculations Specific Calculation Procedure for Internal Gears Standard Systems for Bevel Gears Discussion of 20 Straight Bevel Gear System Discussion of Spiral Bevel Gear System Discussion of the Zerol Bevel Gear System Special Tooth Forms Limitations in 20 Straight Bevel Gear System Limitations in Spiral Bevel Gear System Limitations in Zerol Bevel Gear System General Comments Standard Systems for Worm Gears General Practice Basic Tooth Forms for Worm Gearing Specific Calculations for Worm Gears Standard System for Face Gears Pinion Design Face Gear Design System for Spiroid and Helicon Gears Spiroid Gearing Helicon Gearing Detailed Calculations of Spiroid and Helicon Tooth Data General Equations Relating to Center Distance Center Distance Equations 156

viii Contents 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.

5 viii Contents Standard Center Distance Standard Pitch Diameters Operating Pitch Diameters Operating Pressure Angle Operating Center Distance Center Distance for Gears Operating on Nonparallel Nonintersecting Shafts Center Distance for Worm Gearing Reasons for Nonstandard Center Distances Nonstandard Center Distances Elements of Center Distance Effects of Tolerances on Center Distance Machine Elements that Require Consideration in Critical Center Distance Applications Control of Backlash Effects of Temperature on Center Distance Mounting Distance Preliminary Design Considerations Stress Formulas: Calculation Calculated Stresses Gear Design Limits Gear Strength Calculations Worst Load Stress Concentration Load Distribution Dynamic Load Finite Element Gear Surface Durability Calculations Hertz Derivations K-Factor Derivations Worst-Load Position Endurance Limit Lubrication Regimens Gear Scoring Hot and Cold Scoring PVT Formula Flash Temperature Scoring Criterion Thermal Limits Thermal Limits at Regular Speed Thermal Limits at High Speed Stress Formulas: Special Considerations Gear Specifications Size of Spur and Helical Gears by Q-Factor Method Face-Width Considerations Weight from Volume Indexes of Tooth Loading Estimating Spur and Helical Gear Size by K-Factor 214

ix 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.

6 ix Estimating Bevel Gear Size Estimating Worm Gear Size Estimating Spiroid Gear Size Data Needed for Gear Drawings Gear Dimensional Data Gear Tooth Tolerances Gear Material and Heat Treatment Data Enclosed Gear Unit Requirements Design Formulas Calculation of Gear Tooth Data Number of Pinion Teeth Hunting Teeth Spur Gear Tooth Proportions Root Fillet Radii of Curvature Long-Addendum Pinions Tooth Thickness Backlash Tolerances and Tooth Thickness Chordal Dimensions Degrees Roll and Limit Diameter Form Diameter and Contact Ratio Form Diameter Contact Ratio Spur Gear Dimension Sheet Internal Gear Dimension Sheet Helical Gear Tooth Proportions Helical Gear Dimension Sheet Bevel Gear Tooth Proportions Straight Bevel Gear Dimension Sheet Spiral Bevel Gear Dimension Sheet Zerol Bevel Gear Dimension Sheet Hypoid Gear Calculations Face Gear Calculations Crossed-Helical Gear Proportions Single-Enveloping Worm Gear Proportions Single-Enveloping Worm Gears Double-Enveloping Worm Gears Gear Rating Practice General Considerations in Rating Calculations Calculation Procedure Grades of Material Quality Reliability of Gears General Formulas for Tooth Bending Strength and Tooth Surface Durability Strength Formula Durability Formula Rating Curves of Stress versus Cycles Rating Bevel Gears 315

X Contents 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.

7 X Contents Geometry Factors for Strength Lack of Load Sharing Helical Gears with Narrow Face Width Geometry Factors for Strength for Some Standard Designs Overall De-Rating Factor for Strength Application Factor K a Load Distribution Factor K m Effect of Helix Error and Shaft Misalignment Aspect Ratio Effects Load Distribution Factor K m for Bevel Gears Size Factor K s Dynamic Load Factors K, and C v Geometry Factors for Durability Overall De-Rating Factor for Surface Durability Size Factor C s Complementary Considerations Load Rating of Worm Gearing Crossed-Helical Gear Durability Cylindrical Worm Gear Durability Double-Enveloping Worm Gear Durability Comparison of Double-Enveloping and Cylindrical Worm Gear Rating Procedures Design Formulas for Scoring Hot Scoring Cold Scoring Design Practice to Handle Scoring Trade Standards for Rating Gears Vehicle Gear Rating Practice Marine Gear Rating Practice Oil and Gas Industry Gear Rating Aerospace Gear Rating Practice ; Gear Materials Steels for Gears Mechanical Properties Heat-Treating Techniques Heat-Treating Data Hardness Tests Localized Hardening of Gear Teeth Carburizing Nitriding Features of Nitriding Process Nitride Case Depth Induction Hardening of Steel Induction Hardening by Scanning Load-Carrying Capacity of Induction-Hardened Gear Teeth Flame Hardening of Steel Combined Heat Treatments Metallurgical Quality of Steel Gears 402

xi 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.

8 xi Quality Items for Carburized Steel Gears Quality Items for Nitrided Gears Procedure to Get Grade 2 Quality Cast Irons for Gears Gray Cast Iron Ductile Iron Sintered Iron Nonferrous Gear Metals Kinds of Bronze Standard Gear Bronzes Nonmetallic Gears Thermosetting Laminates Nylon Gears Gear-Manufacturing Methods Gear Tooth Cutting GearHobbing Shaping Pinion Cutter Shaping Rack Cutter Cutting Bevel Gears Gear Milling Broaching Gears Punching Gears G-TRAC Generating Gear Grinding Form Grinding Ceramic Form Grinding Borazon Form Grinding Generating Grinding Disk Wheel Generating Grinding Bevel Gears Generating Grinding Threaded Wheel Thread Grinding Gear Shaving, Rolling, and Honing Rotary Shaving Rack Shaving Gear Rolling Gear Honing Gear Measurement Gear Accuracy Limits Machines to Measure Gears Gear Casting and Forming Cast and Molded Gears Sintered Gears Cold-Drawn Gears and Rolled Worm Threads Design of Tools to Make Gear Teeth Shaper Cutters Gear Hobs 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 Kinds and Causes of Gear Failures 529 9.

9 8.4 Worm-Milling Cutters and Grinding Wheels Gear-Shaving Cutters Punching Tools Sintering Tools 526 Kinds and Causes of Gear Failures Analysis of Gear-System Problems Determining the Problem Possible Causes of Gear-System Failures Incompatibility in Gear Systems Investigation of Gear Systems Analysis of Tooth Failures and Gear-Bearing Failures Nomenclature of Gear Failure Tooth Breakage Pitting of Gear Teeth Scoring Failures Wear Failures Gearbox Bearings Rolling-Element Bearings Sliding-Element Bearings Some Causes of Gear Failure Other than Excess Transmission Load Overload Gear Failures Gear-Casing Problems Lubrication Failures Thermal Problems in Fast-Running Gears 561 Special Design Problems Center Distance Problems Profile Modification Problems Load Rating Problem 585 Gear Reactions and Mountings Mechanics of Gear Reactions Summation of Forces and Moments Application to Gearing Basic Gear Reactions, Bearing Loads, and Mounting Types Main Source of Load Gear Reactions to Bearing Directions of Loads Additional Considerations Types of Mountings Efficiencies Basic Mounting Arrangements and Recommendations Bearing and Shaft Alignment Bearings Mounting Gears to the Shaft Housing Inspection Hole Break-In 603

xiii 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.

10 xiii 11.4 Bearing Load Calculations for Spur Gears Spur Gears Helical Gears Gears in Trains Idlers Intermediate Gears Planetary Gears One Planet Several Planets Bearing-Load Calculations for Helicals Single Helical Gears Double Helical Gears Skewed- or Crossed-Helical Gears Mounting Practice for Bevel and Hypoid Gears Analysis of Forces Rigid Mountings Maximum Displacements Rolling-Element Bearings Straddle Mounting Overhung Mounting Gear Blank Design Gear and Pinion Adjustments Assembly Procedure Calculation of Bevel and Hypoid Bearing Loads Hand of Spiral Spiral Angle Tangential Load Axial Thrust Radial Load Required Data for Bearing Load Calculations Bearing Load Calculations for Worms Calculation of Forces in Worm Gears Mounting Tolerances Worm Gear Blank Considerations Run-in of Worm Gears Bearing Load Calculations for Spiroid Gearing Bearing Load Calculations for Other Gear Types Design of the Body of the Gear Gear Vibration Fundamentals of Vibration Measurement of Vibration Examples of Sensing Devices Practical Problems in Vibration Measurement Some Examples of Vibration in Geared Units Approximate Vibration Limits Velocity Limits Acceleration Limits Proximity Probes 662

xiv Contents 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.

11 xiv Contents Displacement Limits General Vibration Tendencies Trade Standard Control of Vibration in Manufacturing Gears and in the Field Testing of Gear Units at the Gear Factory Tests of Assembled Power Package Vibration Tests in the Field 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 Index 847

GEARING. Theory of. Stephen. Kinetics, Geometry, and Synthesis. P. Radzevich. /Ov CRC Press yc*** J Taylor& Francis Croup Boca Raton

GEARING. Theory of. Stephen. Kinetics, Geometry, and Synthesis. P. Radzevich. /Ov CRC Press yc*** J Taylor& Francis Croup Boca Raton Theory of GEARING Kinetics, Geometry, and Synthesis Stephen P. Radzevich /Ov CRC Press yc*** J Taylor& Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Group, an