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Index
Cover
Half Title
Title
Copyright
Contents
Preface to the Third Edition
Acknowledgments to the Third Edition
Preface to the First Edition
Acknowledgments to the First Edition
Author
Introduction
Chapter 1: Gear-Design Trends
1.1 Manufacturing Trends
1.1.1 Small, Low-Cost Gears for Toys, Gadgets, and Mechanisms
1.1.2 Appliance Gears
1.1.3 Machine Tools
1.1.4 Control Gears
1.1.5 Vehicle Gears
1.1.6 Transportation Gears
1.1.7 Marine Gears
1.1.8 Aerospace Gears
1.1.9 Industrial Gearing
1.1.10 Gears in the Oil and Gas Industry
1.1.11 Mill Gears
1.2 Selection of the Right Kind of Gear
1.2.1 External Spur Gears
1.2.2 External Helical Gears
1.2.3 Internal Gears
1.2.4 Straight Bevel Gears
1.2.5 Zerol Bevel Gears
1.2.6 Spiral Bevel Gears
1.2.7 Hypoid Gears
1.2.8 Face Gears
1.2.9 Crossed-Helical Gears (Nonenveloping Worm Gears)
1.2.10 Single-Enveloping Worm Gears
1.2.11 Double-Enveloping Worm Gears
1.2.12 Spiroid Gears
Chapter 2: Gear Types and Nomenclature
2.1 Types of Gears
2.1.1 Classifications
2.1.2 Parallel Axis Gears
2.1.2.1 Spur Gears
2.1.2.2 Helical Gears
2.1.2.3 Internal Gears
2.1.3 Nonparallel, Coplanar Gears (Intersecting Axes)
2.1.3.1 Bevel Gears
2.1.3.2 Face Gears (On-Center)
2.1.3.3 Conical Involute Gearing
2.1.4 Nonparallel, Noncoplanar Gears (Nonintersecting Axes)
2.1.4.1 Crossed Axis Helical Gears
2.1.4.2 Cylindrical Worm Gearing
2.1.4.3 Single-Enveloping Worm Gearing
2.1.4.4 Double-Enveloping Worm Gearing
2.1.4.5 Hypoid Gears
2.1.4.6 Spiroid and Helicon Gearing
2.1.4.7 Face Gears (Off-Center)
2.1.5 Special Gear Types
2.1.5.1 Square or Rectangular Gears
2.1.5.2 Triangular Gears
2.1.5.3 Elliptical Gears
2.1.5.4 Scroll Gears
2.1.5.5 Multiple-Sector Gears
2.2 Nomenclature of Gears
2.2.1 Spur Gear Nomenclature and Basic Formulas
2.2.2 Helical Gear Nomenclature and Basic Formulas
2.2.3 Internal Gear Nomenclature and Formulas
2.2.4 Crossed-Helical Gear Nomenclature and Formulas
2.2.5 Bevel Gear Nomenclature and Formulas
2.2.5.1 Straight
2.2.5.2 Spiral
2.2.5.3 Zerol
2.2.6 Worm Gear Nomenclature and Formulas
2.2.6.1 Cylindrical Worm Gears
2.2.6.2 Double-Enveloping Worm Gears
2.2.7 Face Gears
2.2.8 Spiroid Gear Nomenclature and Formulas
2.2.9 Beveloid Gears
2.2.10 An Advanced Set of Terms and Definitions for Design Parameters in Gearing
Chapter 3: Gear Tooth Design
3.1 Basic Requirements of Gear Teeth
3.1.1 Definition of Gear Tooth Elements
3.1.2 Basic Considerations for Gear Tooth Design
3.1.2.1 Continuity of Action
3.1.2.2 Conjugate Action
3.1.2.3 Pitch Diameter
3.1.2.4 Zones in Which Involute Gear Teeth Exist
3.1.2.5 Pointed Teeth
3.1.2.6 Undercut
3.1.3 Long- and Short-Addendum Gear Design
3.1.3.1 Addendum Modification for Gears Having Small Number of Teeth
3.1.3.2 Speed-Increasing Drives
3.1.3.3 Power Drives (Optimal Design)
3.1.3.4 Low-Friction Gearing
3.1.4 Special Design Considerations
3.1.4.1 Interchangeability
3.1.4.2 Tooth Thickness
3.1.4.3 Tooth Profile Modifications
3.1.4.4 Transverse of Profile Modification
3.1.4.5 Allowances for Errors of Gear Manufacture
3.1.4.6 Allowances for Deflection under Load
3.1.4.7 Axial Modifications
3.1.4.8 Root Fillets
3.1.4.9 Effective Outside Diameter
3.1.4.10 Width of the Tip of the Tooth
3.1.4.11 Pointed Tooth Diameter
3.1.4.12 Purpose of Backlash
3.1.4.13 Backlash: Recommended Values
3.2 Standard Systems of Gear Tooth Proportions
3.2.1 Standard Systems for Spur Gears
3.2.1.1 Limitations in the Use of Standard Tables
3.2.1.2 Standard Tooth Forms That Have Become Obsolete
3.2.1.3 Brown and Sharp System
3.2.1.4 AGMA 14.5° Composite System
3.2.1.5 Fellows 20° Stub Tooth System
3.2.1.6 AGMA 14.5° Full-Depth System
3.2.1.7 Cycloidal Tooth Profiles
3.2.1.8 Clockwork and Timer Tooth Profiles
3.2.1.9 Specific Spur Gear Calculation Procedure
3.2.1.10 Explanation and Discussion of Items in Table 3.5
3.2.2 System for Helical Gears
3.2.2.1 Selection of Tooth Form
3.2.2.2 Selection of Helix Angle
3.2.2.3 Face Width
3.2.2.4 Specific Calculation Procedure for Helical Gears
3.2.3 System for Internal Gears
3.2.3.1 Special Calculations
3.2.3.2 Specific Calculation Procedure for Internal Gears
3.2.4 Standard Systems for Bevel Gears
3.2.4.1 Discussion of 20° Straight Bevel Gear System
3.2.4.2 Discussion of Spiral Bevel Gear System
3.2.4.3 Discussion of Zerol Bevel Gear System
3.2.4.4 Special Tooth Forms
3.2.4.5 Limitations in 20° Straight Bevel Gear System
3.2.4.6 Limitations in Spiral Bevel Gear System
3.2.4.7 Limitations in Zerol Bevel Gear System
3.2.4.8 General Comments
3.2.5 Standard Systems for Worm Gears
3.2.5.1 General Practice
3.2.5.2 Basic Tooth Forms for Worm Gearing
3.2.5.3 Specific Calculations for Worm Gears
3.2.6 Standard System for Face Gears
3.2.6.1 Pinion Design
3.2.6.2 Face Gear Design
3.2.7 System for Spiroid and Helicon Gears
3.2.7.1 Spiroid Gearing
3.2.7.2 Helicon Gearing
3.2.7.3 Detailed Calculations of Spiroid and Helicon Tooth Data
3.3 General Equations Relating to Center Distance
3.3.1 Center-Distance Equations
3.3.2 Standard Center Distance
3.3.3 Standard Pitch Diameters
3.3.4 Operating Pitch Diameters
3.3.5 Operating Pressure Angle
3.3.6 Operating Center Distance
3.3.7 Center Distance for Gears Operating on Nonparallel Nonintersecting Shafts
3.3.8 Center Distance for Worm Gearing
3.3.9 Reasons for Nonstandard Center Distances
3.3.10 Nonstandard Center Distances
3.4 Elements of Center Distance
3.4.1 Effects of Tolerances on Center Distance
3.4.2 Machine Elements That Require Consideration in Critical Center-Distance Applications
3.4.3 Control of Backlash
3.4.4 Effects of Temperature on Center Distance
3.4.5 Mounting Distance
Chapter 4: Preliminary Design Considerations
4.1 Stress Formulas
4.1.1 Calculated Stresses
4.1.2 Gear-Design Limits
4.1.3 Gear-Strength Calculations
4.1.3.1 Worst Load
4.1.3.2 Stress Concentration
4.1.3.3 Load Distribution
4.1.3.4 Dynamic Load
4.1.3.5 Finite Element
4.1.4 Gear Surface-Durability Calculations
4.1.4.1 Hertz Derivations
4.1.4.2 K Factor Derivations
4.1.4.3 Worst-Load Position
4.1.4.4 Endurance Limit
4.1.4.5 Regimes of Lubrication
4.1.5 Gear Scoring
4.1.5.1 Hot and Cold Scoring
4.1.5.2 PVT Formula
4.1.5.3 Flash Temperature
4.1.5.4 Scoring Criterion
4.1.6 Thermal Limits
4.1.6.1 Thermal Limits at Regular Speed
4.1.6.2 Thermal Limits at High Speed
4.2 Stress Formulas
4.2.1 Gear Specifications
4.2.2 Size of Spur and Helical Gears by Q Factor Method
4.2.2.1 Face-Width Considerations
4.2.2.2 Weight from Volume
4.2.3 Indices of Tooth Loading
4.2.4 Estimating Spur- and Helical-Gear Sizes by K Factor
4.2.5 Estimating Bevel-Gear Size
4.2.6 Estimating Worm-Gear Size
4.2.7 Estimating Spiroid Gear Size
4.3 Data Needed for Gear Drawings
4.3.1 Gear Dimensional Data
4.3.2 Gear-Tooth Tolerances
4.3.3 Gear Material and Heat-Treatment Data
4.3.4 Enclosed Gear Unit Requirements
Chapter 5: Design Formulas
5.1 Calculation of Gear Tooth Data
5.1.1 Number of Pinion Teeth
5.1.2 Hunting Teeth
5.1.3 Spur Gear Tooth Proportions
5.1.4 Root Fillet Radii of Curvature
5.1.5 Long-Addendum Pinions
5.1.6 Tooth Thickness
5.1.6.1 Backlash
5.1.6.2 Tolerances and Tooth Thickness
5.1.7 Chordal Dimensions
5.1.8 Degrees Roll and Limit Diameter
5.1.9 Form Diameter and Contact Ratio
5.1.9.1 Form Diameter
5.1.9.2 Contact Ratio
5.1.10 Spur Gear Dimension Sheet
5.1.11 Internal Gear Dimension Sheet
5.1.12 Helical Gear Tooth Proportions
5.1.13 Helical Gear Dimension Sheet
5.1.14 Bevel Gear Tooth Proportions
5.1.15 Straight Bevel Gear Dimension Sheet
5.1.16 Spiral Bevel Gear Dimension Sheet
5.1.17 Zerol Bevel Gear Dimension Sheet
5.1.18 Hypoid Gear Calculations
5.1.19 Face Gear Calculations
5.1.20 Crossed-Helical Gear Proportions
5.1.21 Single-Enveloping Worm Gear Proportions
5.1.22 Single-Enveloping Worm Gears
5.1.23 Double-Enveloping Worm Gears
5.2 Gear-Rating Practice
5.2.1 General Considerations in Rating Calculations
5.2.1.1 Calculation Procedure
5.2.1.2 Grades of Material Quality
5.2.1.3 Reliability of Gears
5.2.2 General Formulas for Tooth Bending Strength and Tooth Surface Durability
5.2.2.1 Strength Formula
5.2.2.2 Durability Formula
5.2.2.3 Rating Curves of Stress versus Cycles
5.2.2.4 Rating Bevel Gears
5.2.3 Geometry Factors for Strength
5.2.3.1 Lack of Load Sharing
5.2.3.2 Helical Gears with Narrow Face Width
5.2.3.3 Geometry Factors for Strength for Some Standard Designs
5.2.4 Overall Derating Factor for Strength
5.2.4.1 Application Factor Ka
5.2.4.2 Load-Distribution Factor Km
5.2.4.3 Effect of Helix Error and Shaft Misalignment
5.2.4.4 Aspect Ratio Effects
5.2.4.5 Load-Distribution Factor Km for Bevel Gears
5.2.4.6 Size Factor Ks
5.2.4.7 Dynamic Load Factors Kv and Cv
5.2.5 Geometry Factors for Durability
5.2.6 Overall Derating Factor for Surface Durability
5.2.6.1 Size Factor Cs
5.2.6.2 Complementary Considerations
5.2.7 Load Rating of Worm Gearing
5.2.7.1 Crossed-Helical Gear Durability
5.2.7.2 Cylindrical Worm Gear Durability
5.2.7.3 Double-Enveloping Worm Gear Durability
5.2.7.4 Comparison of Double-Enveloping and Cylindrical Worm Gear Rating Procedures
5.2.8 Design Formulas for Scoring
5.2.8.1 Hot Scoring
5.2.8.2 Cold Scoring
5.2.8.3 Design Practice to Handle Scoring
5.2.9 Trade Standards for Rating Gears
5.2.10 Vehicle Gear Rating Practice
5.2.11 Marine Gear Rating Practice
5.2.12 Oil and Gas Industry Gear Rating
5.2.13 Aerospace Gear Rating Practice
Chapter 6: Gear Materials
6.1 Steels for Gears
6.1.1 Mechanical Properties
6.1.2 Heat Treatment Techniques
6.1.3 Heat Treatment Data
6.1.4 Hardness Tests
6.2 Localized Hardening of Gear Teeth
6.2.1 Carburizing
6.2.2 Nitriding
6.2.2.1 Features of Nitriding Process
6.2.2.2 Nitride Case Depth
6.2.3 Induction Hardening of Steel
6.2.3.1 Induction Hardening by Scanning
6.2.3.2 Load-Carrying Capacity of Induction-Hardened Gear Teeth
6.2.4 Flame Hardening of Steel
6.2.5 Combined Heat Treatments
6.2.6 Metallurgical Quality of Steel Gears
6.2.6.1 Quality Items for Carburized Steel Gears
6.2.6.2 Quality Items for Nitrided Gears
6.2.6.3 Procedure to Get Grade 2 Quality
6.3 Cast Irons for Gears
6.3.1 Gray Cast Iron
6.3.2 Ductile Iron
6.3.3 Sintered Iron
6.4 Nonferrous Gear Metals
6.4.1 Kinds of Bronze
6.4.2 Standard Gear Bronzes
6.5 Nonmetallic Gears
6.5.1 Thermosetting Laminates
6.5.2 Nylon Gears
Chapter 7: Direct Gear Design for Asymmetric Tooth Gears
7.1 Introduction
7.2 Geometry of Asymmetric Tooth Gears
7.3 Gear Mesh Characteristics
7.4 Asymmetric Tooth Gearing Limits
7.5 Tooth Geometry Optimization
7.5.1 Asymmetry Factor K Selection for Reversible Asymmetric Tooth Gears
7.5.2 Root Fillet Optimization
7.6 Analytical and Experimental Comparison of Symmetric and Asymmetric Tooth Gears
7.7 Implementation of Asymmetric Tooth Gears
Chapter 8: Finite-Element Analysis of Gears
8.1 Motivation
8.2 How It Works: Finite Element Basics
8.3 Solving the System of Equations
8.4 Substructuring
8.5 Deformation Model
8.6 Geometry
8.7 Contact Solver
8.8 Postprocessing
Chapter 9: Load Rating of Gears
9.1 Considerations
9.2 Main Nomenclature
9.3 Coplanar Gears (Involute Parallel Gears and Bevel Gears)
9.3.1 Power, Torque, and Tangential Load
9.3.1.1 Loading Levels
9.3.2 RH and RF, Resistance to Yielding
9.3.3 RH and RF, Life Curves
9.3.4 RH and RF, Conventional Fatigue Limits
9.3.5 RH—Synthetic Surface Loading Factor K
9.3.6 RF—Unit Load UL
9.3.7 Adaptation for Bevel Gears (Wt, K, UL)
9.3.8 Use of the Synthetic Factors K and UL
9.4 Coplanar Gears: Simplified Estimates and Design Criteria
9.4.1 Direct Assumption of the Synthetic Factors
9.4.2 Design Procedure
9.5 Coplanar Gears: Detailed Analysis, Conventional Fatigue Limits, and Service Factors
9.5.1 RH and RF, Overload Derating Factors
9.5.2 Power Sharing Factor Ksh
9.5.3 Application Factor Ka
9.5.4 Dynamic Factor Kv
9.5.4.1 Tangential Velocity
9.5.4.2 RHA and RFA
9.5.5 RHI and RFI, Ka
9.5.6 Dynamic Problems of Gears: Resonance and Vibration Conditions
9.5.7 Load Distribution Factor, Km
9.6 RH—Conventional Fatigue Limit of Factor K
9.6.1 RH—Preliminary Geometric Calculations
9.6.2 Adaption for Bevel Gears
9.6.3 RH—Unified Geometry Factor GH
9.6.3.1 RHA
9.6.3.2 RHI—Spur and Helical Gears
9.6.4 RH—Comments and Comparisons on the Unified Geometry Factor GH
9.6.5 RH—Elastic Coefficient CP and Conventional Fatigue Limit sc lim of the Hertzian Pressure
9.6.6 RH—Adaptation Factor AH
9.6.6.1 RHA
9.6.6.2 RHI
9.6.6.3 RHI Lubrication Factor
9.6.6.4 RHI Velocity Factor
9.6.6.5 RHI Roughness Factor
9.6.7 RH—Hertzian Pressure
9.6.8 RH—Service Factor CSF (Only for One Loading Level)
9.6.9 Power Capacity Tables
9.7 RF—Conventional Fatigue Limit of Factor UL
9.7.1 RF—Geometry Factor Jn
9.7.2 RF—Adaptation Factor AF
9.7.3 RF—Size Factor Ks
9.7.4 RF—Conventional Fatigue Limit of the Fillet Stress st lim
9.7.5 RF—Tooth Root Stress at Fillet st
9.7.6 RF—Service Factor KSF (Only for One Loading Level)
9.8 Coplanar Gears: Detailed Life Curves and Yielding
9.8.1 Definition of the Life Curves and Gear Life Ratings for One Loading Level
9.8.2 Yielding
9.8.2.1 RH
9.8.2.2 RHI
9.8.2.3 RF
9.8.2.4 RFA
9.8.2.5 RFI
9.8.3 Tooth Damage and Cumulative Gear Life
9.8.4 Reliability
9.9 Coplanar Gears: Prevention of Tooth Wear and Scoring
9.9.1 Progressive Tooth Wear
9.9.2 Scoring and Scuffing
9.10 Crossed-Helical Gears
9.11 Hypoid Gears
9.12 Worm Gearing
9.12.1 Cylindrical Worm Gearing
9.13 State of the Standards for Load Rating of Gears
Chapter 10: Gear Manufacturing Methods
10.1 Gear Tooth Cutting
10.1.1 Gear Hobbing
10.1.2 Shaping Pinion Cutter
10.1.3 Shaping Rack Cutter
10.1.4 Cutting Bevel Gears
10.1.5 Gear Milling
10.1.6 Broaching Gears
10.1.7 Punching Gears
10.1.8 G-TRAC Generating
10.2 Gear Grinding
10.2.1 Form Grinding
10.2.1.1 Ceramic Form Grinding
10.2.1.2 Borazon Form Grinding
10.2.2 Generating Grinding—Disk Wheel
10.2.3 Generating Grinding—Bevel Gears
10.2.4 Generating Grinding—Threaded Wheel
10.2.5 Thread Grinding
10.3 Gear Shaving, Rolling, and Honing
10.3.1 Rotary Shaving
10.3.2 Rack Shaving
10.3.3 Gear Rolling
10.3.4 Gear Honing
10.4 Gear Measurement
10.4.1 Gear Accuracy Limits
10.4.2 Machines to Measure Gears
10.5 Gear Casting and Forming
10.5.1 Cast and Molded Gears
10.5.2 Sintered Gears
10.5.3 Cold-Drawn Gears and Rolled Worm Threads
Chapter 11: Design of Tools to Make Gear Teeth
11.1 Shaper-Cutters
11.2 Gear Hobs
11.3 Spur Gear Milling Cutters
11.4 Worm Milling Cutters and Grinding Wheels
11.5 Gear Shaving Cutters
11.6 Punching Tools
11.7 Sintering Tools
Chapter 12: The Kinds and Causes of Gear Failures
12.1 Analysis of Gear System Problems
12.1.1 Determining the Problem
12.1.2 Possible Causes of Gear System Failures
12.1.3 Incompatibility in Gear Systems
12.1.4 Investigation of Gear Systems
12.2 Analysis of Tooth Failures and Gear Bearing Failures
12.2.1 Nomenclature of Gear Failure
12.2.2 Tooth Breakage
12.2.3 Pitting of Gear Teeth
12.2.4 Scoring Failures
12.2.5 Wear Failures
12.2.6 Gearbox Bearings
12.2.7 Rolling-Element Bearings
12.2.8 Sliding-Element Bearings
12.3 Some Causes of Gear Failure Other than Excess Transmission Load
12.3.1 Overload Gear Failures
12.3.2 Gear Casing Problems
12.3.3 Lubrication Failures
12.3.4 Thermal Problems in Fast-Running Gears
Chapter 13: Special Design Problems
13.1 Center Distance Problems
13.2 Profile Modification Problems
13.3 Load Rating Problem
Chapter 14: Gear Reactions and Mountings
14.1 Mechanics of Gear Reactions
14.1.1 Summation of Forces and Moments
14.1.2 Application to Gearing
14.2 Basic Gear Reactions, Bearing Loads, and Mounting Types
14.2.1 The Main Source of Load
14.2.2 Gear Reactions to Bearing
14.2.3 Directions of Loads
14.2.4 Additional Considerations
14.2.5 Types of Mountings
14.2.6 Efficiencies
14.3 Basic Mounting Arrangements and Recommendations
14.3.1 Bearing and Shaft Alignment
14.3.2 Bearings
14.3.3 Mounting Gears to Shaft
14.3.4 Housing
14.3.5 Inspection Hole
14.3.6 Break-In
14.4 Bearing Load Calculations for Spur Gears
14.4.1 Spur Gears
14.4.2 Helical Gears
14.4.3 Gears in Trains
14.4.4 Idlers
14.4.5 Intermediate Gears
14.4.6 Planetary Gears
14.4.6.1 One Planet
14.4.6.2 Several Planets
14.5 Bearing Load Calculations for Helicals
14.5.1 Single-Helical Gears
14.5.2 Double-Helical Gears
14.5.3 Skewed or Crossed-Helical Dears
14.6 Mounting Practice for Bevel and Hypoid Gears
14.6.1 Analysis of Forces
14.6.2 Rigid Mountings
14.6.3 Maximum Displacements
14.6.4 Rolling-Element Bearings
14.6.5 Straddle Mounting
14.6.6 Overhung Mounting
14.6.7 Gear Blank Design
14.6.8 Gear and Pinion Adjustments
14.6.9 Assembly Procedure
14.7 Calculation of Bevel and Hypoid Bearing Loads
14.7.1 Hand of Spiral
14.7.2 Spiral Angle
14.7.3 Tangential Load
14.7.4 Axial Thrust
14.7.5 Radial Load
14.7.6 Required Data for Bearing Load Calculations
14.8 Bearing Load Calculations for Worms
14.8.1 Calculation of Forces in Worm Gears
14.8.2 Mounting Tolerances
14.8.3 Worm Gear Blank Considerations
14.8.4 Run-In of Worm Gears
14.9 Bearing Load Calculations for Spiroid Gearing
14.10 Bearing Load Calculations for Other Gear Types
14.11 Design of the Body of the Gear
Chapter 15: Gear Vibration
15.1 Fundamentals of Vibration
15.2 Measurement of Vibration
15.2.1 Examples of Sensing Devices
15.2.2 Practical Problems in Vibration Measurement
15.3 Some Examples of Vibration in Geared Units
15.4 Approximate Vibration Limits
15.4.1 Velocity Limits
15.4.2 Acceleration Limits
15.4.3 Proximity Probes
15.4.4 Displacement Limits
15.4.5 General Vibration Tendencies
15.4.6 Trade Standard
15.5 Control of Vibration in Manufacturing Gears and in the Field
15.5.1 Testing of Gear Units at the Gear Factory
15.5.2 Tests of the Assembled Power Package
15.5.3 Vibration Tests in the Field
15.6 Vibration Analysis Technique
Literature
Appendix A: The Evolution of the Gear Art
Appendix B: Complementary Material
Appendix C: Numerical Data Tables
Appendix D: On the Concept of Novikov Gearing and on the Inadequacy of the Terms Wildhaber–Novikov Gearing and W-N Gearing
Appendix E: An Improved Load-Equalizing Means for Planetary Pinions
Appendix F: Geometrically Accurate (Ideal or Perfect) Crossed-Axis Gearing with Line Contact between the Tooth Flanks of the Gear and the Pinion
Index
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