Dudley's Handbook of Practical Gear Design and Manufacture

Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Acknowledgments
Author
Contributors
Introduction
Uniqueness of This Book
Intended Audience
The Organization of This Book
1. Foundations of Advanced Gear Systems
1.1 The Law of Contact: The First Fundamental Law of Gearing
1.2 The Conjugate Action Law: The Second Fundamental Law of Gearing
1.2.1 Conjugate Action Law in Parallel-Axes Gearing
1.2.2 Conjugate Action Law in Intersected-Axes Gearing, and in Crossed-Axes Gearing
1.2.3 Examples of Violation of the Conjugate Action Law
1.3 The Law of Equal Base Pitches: The Third Fundamental Law of Gearing
Conclusion
References
Bibliography
2. Gear-Design Trends
2.1 Manufacturing Trends
2.2 Features of Gears of Different Kinds
2.3 Selection of the Right Kind of Gear
2.3.1 External Spur Gears
2.3.2 External Helical Gears
2.3.3 Internal Gears
2.3.4 Straight Bevel Gears
2.3.5 Zerol Bevel Gears
2.3.6 Spiral Bevel Gears
2.3.7 Hypoid Gears
2.3.8 Face Gears
2.3.9 Crossed-Helical Gears (Non-enveloping Worm Gears)
2.3.10 Single-Enveloping Worm Gears
2.3.11 Double-Enveloping Worm Gears
2.3.12 Spiroid Gears
Bibliography
3. Gear Types and Nomenclature
3.1 Types of Gears
3.1.1 Classifications
3.1.2 Parallel-Axes Gears
3.1.3 Nonparallel, Coplanar Gears (Intersecting-Axes)
3.1.4 Nonparallel, Non-coplanar Gears (Non-intersecting Axes)
3.1.5 Nonconjugate Gears
3.1.6 Special Gear Types
3.2 Nomenclature of Gears
3.2.1 Spur Gear Nomenclature and Basic Formulas
3.2.2 Helical Gear Nomenclature and Basic Formulas
3.2.3 Internal Gear Nomenclature and Formulas
3.2.4 Crossed Helical Gear Nomenclature and Formulas
3.2.5 Bevel Gear Nomenclature and Formulas
3.2.6 Worm Gear Nomenclature and Formulas
3.2.7 Face Gears
3.2.8 Spiroid Gear Nomenclature and Formulas
3.2.9 Helicon Gears
3.3 An Advanced Set of Terms and Definitions for Design Parameters in Gearing
References
Bibliography
4. Gear Tooth Design
4.1 Basic Requirements of Gear Teeth
4.1.1 Definition of Gear Tooth Elements
4.1.2 Basic Considerations for Gear Tooth Design
4.1.3 Long- and Short-Addendum Gear Design
4.1.4 Special Design Considerations
4.2 Standard Systems of Gear Tooth Proportions
4.2.1 Standard Systems for Spur Gears
4.2.2 System for Helical Gears
4.2.3 System for Internal Gears
4.2.4 Standard Systems for Bevel Gears
4.2.5 Standard Systems for Worm Gears
4.2.6 Standard System for Face Gears
4.2.7 System for Spiroid and Helicon Gears
4.3 General Equations Relating to Center-Distance
4.3.1 Center-Distance Equations
4.3.2 Standard Center-Distance
4.3.3 Standard Pitch Diameters
4.3.4 Operating Pitch Diameters
4.3.5 Operating Pressure Angle
4.3.6 Operating Center-Distance
4.3.7 Center-Distance for Gears Operating on Nonparallel Nonintersecting Shafts
4.3.8 Center-Distance for Worm Gearing
4.3.9 Reasons for Nonstandard Center-Distances
4.3.10 Nonstandard Center-Distances
4.4 Elements of Center-Distance
4.4.1 Effects of Tolerances on Center-Distance
4.4.2 Machine Elements That Require Consideration in Critical Center-Distance Applications
4.4.3 Control of Backlash
4.4.4 Effects of Temperature on Center-Distance
4.4.5 Mounting Distance
Bibliography
5. Preliminary Design Considerations
5.1 Stress Formulas
5.1.1 Calculated Stresses
5.1.2 Gear-Design Limits
5.1.3 Gear-Strength Calculations
5.1.4 Gear Surface-Durability Calculations
5.1.5 Gear Scoring
5.1.6 Thermal Limits
5.2 Stress Formulas
5.2.1 Gear Specifications
5.2.2 Size of Spur and Helical Gears by Q-Factor Method
5.2.3 Indexes of Tooth Loading
5.2.4 Estimating Spur- and Helical-Gear Size by K-Factor
5.2.5 Estimating Bevel-Gear Size
5.2.6 Estimating Worm-Gear Size
5.2.7 Estimating Spiroid Gear Size
5.3 Data Needed for Gear Drawings
5.3.1 Gear Dimensional Data
5.3.2 Gear-Tooth Tolerances
5.3.3 Gear Material and Heat-Treatment Data
5.3.4 Enclosed-Gear-Unit Requirements
Bibliography
6. Design Formulas
6.1 Calculation of Gear-Tooth Data
6.1.1 Number of Pinion Teeth
6.1.2 Hunting Teeth
6.1.3 Spur-Gear-Tooth Proportions
6.1.4 Root Fillet Radii of Curvature
6.1.5 Long-Addendum Pinions
6.1.6 Tooth Thickness
6.1.7 Chordal Dimensions
6.1.8 Degrees Roll and Limit Diameter
6.1.9 Form Diameter and Contact Ratio
6.1.10 Spur-Gear Dimension Sheet
6.1.11 Internal-Gear Dimension Sheet
6.1.12 Helical-Gear Tooth Proportions
6.1.13 Helical-Gear Dimension Sheet
6.1.14 Bevel-Gear Tooth Proportions
6.1.15 Straight-Bevel-Gear Dimension Sheet
6.1.16 Spiral-Bevel-Gear Dimension Sheet
6.1.17 Zerol-Bevel-Gear Dimension Sheet
6.1.18 Hypoid-Gear Calculations
6.1.19 Face-Gear Calculations
6.1.20 Crossed-Helical-Gear Proportions
6.1.21 Single-Enveloping-Worm-Gear Proportions
6.1.22 Single-Enveloping Worm Gears
6.1.23 Double-Enveloping Worm Gears
6.2 Gear-Rating Practice
6.2.1 General Considerations in Rating Calculations
6.2.2 General Formulas for Tooth Bending Strength and Tooth Surface Durability
6.2.3 Geometry Factors for Strength
6.2.4 Overall Derating Factor for Strength
6.2.5 Geometry Factors for Durability
6.2.6 Overall Derating Factor for Surface Durability
6.2.7 Load Rating of Worm Gearing
6.2.8 Design Formulas for Scoring
6.2.9 Trade Standards for Rating Gears
6.2.10 Vehicle-Gear-Rating Practice
6.2.11 Marine-Gear-Rating Practice
6.2.12 Oil and Gas Industry Gear Rating
6.2.13 Aerospace-Gear-Rating Practice
References
7. Gear Reactions and Mountings
7.1 Mechanics of Gear Reactions
7.1.1 Summation of Forces and Moments
7.1.2 Application to Gearing
7.2 Basic Gear Reactions, Bearing Loads, and Mounting Types
7.2.1 The Main Source of Load
7.2.2 Gear Reactions to Bearing
7.2.3 Directions of Loads
7.2.4 Additional Considerations
7.2.5 Types of Mountings
7.2.6 Efficiencies
7.3 Basic Mounting Arrangements and Recommendations
7.3.1 Bearing and Shaft Alignment
7.3.2 Bearings
7.3.3 Mounting Gears to Shaft
7.3.4 Housing
7.3.5 Inspection Hole
7.3.6 Break-in
7.4 Bearing Load Calculations for Spur Gears
7.4.1 Spur Gears
7.4.2 Helical Gears
7.4.3 Gears in Trains
7.4.4 Idlers
7.4.5 Intermediate Gears
7.4.6 Planetary Gears
7.5 Bearing-Load Calculations for Helicals
7.5.1 Single-Helical Gears
7.5.2 Double-Helical Gears
7.5.3 Skewed or Crossed Helical Gears
7.6 Mounting Practice for Bevel and Hypoid Gears
7.6.1 Analysis of Forces
7.6.2 Rigid Mountings
7.6.3 Maximum Displacements
7.6.4 Rolling-Element Bearings
7.6.5 Straddle Mounting
7.6.6 Overhung Mounting
7.6.7 Gear Blank Design
7.6.8 Gear and Pinion Adjustments
7.6.9 Assembly Procedure
7.7 Calculation of Bevel and Hypoid Bearing Loads
7.7.1 Hand of Spiral
7.7.2 Spiral Angle
7.7.3 Tangential Load
7.7.4 Axial Thrust
7.7.5 Radial Load
7.7.6 Required Data for Bearing Load Calculations
7.8 Bearing Load Calculations for Worms
7.8.1 Calculation of Forces in Worm Gears
7.8.2 Mounting Tolerances
7.8.3 Worm Gear Blank Considerations
7.8.4 Run-in of Worm Gears
7.9 Bearing Load Calculations for Spiroid Gearing
7.10 Bearing Load Calculations for Other Gear Types
7.11 Design of the Body of the Gear
References
8. Compensation of Shaft Deflections through Gear Micro-„Geometry Modifications
8.1 Introduction
8.2 Determination of Errors of Alignment due to Shaft Deflections
8.2.1 Transmissions with Parallel Shafts
8.2.2 Transmissions with Intersecting Shafts
8.2.3 Transmissions with Crossing Shafts
8.3 Compensation of Errors of Alignment During Gear Generation
8.4 Numerical Examples
8.4.1 Spur Gearset
8.4.2 Spiral Bevel Gearset
8.4.3 Face Gearset
8.4.3.1 Alternative Methods of Compensating Shaft Deflections
8.4.3.1.1 Alternative Method 1: Application of Offset between the Axis of the Shaper and the Face Gear
8.4.3.1.2 Alternative Method 2: Application of a Shaper with 28 Teeth and No Compensations of Errors of Alignment
References
9. Special Design Problems in Gear Drives
9.1 Special Calculations of Involute Gear Geometry
9.1.1 Main Symbols and Definitions
9.1.2 Tooth Undercutting in External Gears
9.1.3 Tooth Tip Thickness and Tooth Pointing in External Gears
9.1.4 Interference of Profiles in External Gearing
9.1.5 Interference of Profiles in Internal Gearing
9.1.6 Measurements of Tooth Thickness
9.1.6.1 Direct Measurements of Tooth Thickness
9.1.6.2 Measurements of Base Tangent Length
9.1.6.3 Measurements Using Pins or Balls (Figure 9.16)
9.1.6.4 Measurements of Teeth with Profile Modifications
9.1.7 Profile Modification
9.1.7.1 Basics
9.1.7.2 Parameters of Linear Tip Relief
9.2 Examples of Calculation of Involute Gear Pairs Geometry
9.3 Analysis of Motion and Power Transmission in Complex Cylindrical Gear Drives
9.3.1 Definition of Gear Ratio
9.3.2 Basic Kinematic Diagrams and Gear Ratios of Planetary Gear Drives
9.2.3 MN Method of Kinematical Analysis
9.4 Efficiency of Cylindrical Involute Gear Drives and Complex Driving Systems
9.4.1 Efficiency of a Single Gear Pair
9.4.2 Efficiency of Planetary Gear Drives
9.4.2.1 Efficiency of Planetary Gear Drives 1CG (Figure 9.31)
9.4.2.2 Efficiency of Planetary Gear Drives 2CG Type A (Figure 9.33)
9.4.2.3 Efficiency of Planetary Gear Drives 2CG Type B (Figure 9.34)
9.4.2.4 Efficiency of Planetary Gear Drives 2CG Type C (Figure 9.35)
9.4.2.5 Efficiency of Planetary Gear Drives 2CG Type D (Figure 9.36)
9.4.2.6 Efficiency of Planetary Gear Drives 3CG, (the Mesh Loss Only)
9.4.3 Efficiency of Planetary and Complex Gear Drives Built Up of Two or More Stages
9.5 Lubrication and Cooling of Gear Drives
9.5.1 Lubrication
9.5.2 Cooling
9.6 Design of Spur and Helical Gears
9.6.1 Pinions
9.6.2 Gears
9.6.2.1 Industrial Gears
9.6.2.2 Light-Weight Gears
9.6.2.3 Large-Diameter Gears
9.6.3 Arrangement of Gear Supports
References
10. Gear Materials
10.1 Steels for Gears
10.1.1 Mechanical Properties
10.1.2 Heat-Treating Techniques
10.1.3 Heat-Treating Data
10.1.4 Hardness Tests
10.2 Localized Hardening of Gear Teeth
10.2.1 Carburizing
10.2.2 Nitriding
10.2.2.1 Features of Nitriding Process
10.2.2.2 Nitride Case Depth
10.2.3 Induction Hardening Of Steel
10.2.3.1 Induction-Hardening by Scanning
10.2.3.2 Load-Carrying Capacity of Induction-Hardened Gear Teeth
10.2.4 Flame Hardening of Steel
10.2.5 Combined Heat Treatments
10.2.6 Metallurgical Quality of Steel Gears
10.2.6.1 Geometric Accuracy
10.2.6.2 Material Quality
10.2.6.3 Quality Items for Carburized Steel Gears
10.2.6.4 Quality Items for Nitrided Gears
10.2.6.5 Procedure to Get Grade 2 Quality
10.3 Cast Irons for Gears
10.3.1 Gray Cast Iron
10.3.2 Ductile iron
10.4 Nonferrous Gear Metals
10.4.1 Kinds of Bronze
10.4.2 Standard Gear Bronzes
10.5 Nonmetallic Gears
10.5.1 Thermosetting Laminates
10.5.2 Nylon Gears
References
11. Load Carrying Capacities, Strength Numbers, and Main Influence Parameters for Different Gear Materials and Heat Treatment Processes
11.1 Introduction
11.2 Fundamentals of Gear Stresses and the Determination of the Load Carrying Capacity
11.3 Overview of Typical Gear Failure Modes
11.4 Requirements on the Properties of Gear Steels
11.5 Steels for Quenching and Tempering
11.6 Steels for Surface Hardening
11.7 Steels for Nitriding
11.7.1 Tooth Root Bending Strength
11.7.2 Tooth Flank Load Carrying Capacity
11.7.3 Micropitting and Wear Performance
11.8 Steels for Case-Hardening and Carbonitriding
11.8.1 Influence of Gear Size
11.8.2 Influence of Case-Hardening Depth
11.8.3 Influence of Retained Austenite
11.8.4 Influence of Cryogenic Treatment
11.8.5 Influence of Residual Stress Condition
11.8.6 Influence on Tooth Root Load Carrying Capacity
11.8.7 Change in the Fracture Mode—Unpenned vs. Shot-Peened Condition
11.8.8 Stepwise S-N Curve
11.8.9 Increase of the Tooth Flank Load Carrying Capacity (Pitting)
11.9 Summary and Outlook
Acknowledgment
References
12. Gear Load Capacity Calculation: Based on ISO 6336
12.1 Introduction and History of ISO 6336
12.1.1 Introduction: Parts and Document Types
12.1.2 History
12.1.3 Overview and Structure of ISO 6336 Documents
12.2 Calculation of Surface Durability—ISO 6336-2:2019
12.2.1 Description of the Failure Mode Pitting
12.2.2 Basic Calculation Principles
12.2.2.1 Strength Analysis and Safety Factor
12.2.2.2 Contact Stress σH
12.2.2.3 Pitting Stress Limit σHG
12.2.3 New Aspects and Updates of the Standard
12.2.3.1 Contact Factor ZB,D - Factor fZCa
12.2.3.2 Work Hardening Factor ZW
12.2.4 Calculation Example
12.2.5 Summary
12.2.6 Outlook
12.3 Calculation of Tooth Bending Strength - ISO 6336-3:2019
12.3.1 Description of the Failure Mode Tooth Root Breakage
12.3.2 Basic Calculation Principles
12.3.2.1 Strength Analysis and Safety Factor
12.3.2.2 Tooth Root Stress σF
12.3.2.3 Bending Stress Limit σFG
12.3.3 New Aspects and Updates of the Standard
12.3.3.1 Form Factor YF—Load Distribution Influence Factor fε
12.3.3.2 Form Factor YF - Tooth Root Geometry of Internal Gears
12.3.3.3 Helix Angle Factor Yβ
12.3.3.4 Relative Notch Sensitivity Factor YδrelT
12.3.4 Calculation Example
12.3.5 Summary
12.3.6 Outlook
12.4 Calculation of Micropitting Load Capacity— ISO/TS 6336-22:2018
12.4.1 Description of the Failure Mode Micropitting
12.4.2 Basic Calculation Principles
12.4.2.1 Specific Lubricant Film Thickness λGF,Y
12.4.2.2 Permissible Specific Lubricant Film Thickness (According to the FZG Micropitting Test According to FVA 54/7)
12.4.2.3 Limits of the Calculation Method
12.4.3 Micropitting Test Procedures
12.4.3.1 FZG Micropitting Test According to FVA-Information Sheet 54/7
12.4.3.2 DIN 3990-16:2020
12.4.4 Calculation Example
12.4.5 Summary
12.4.6 Outlook
12.5 Calculation of Tooth Flank Fracture Load Capacity—ISO/TS 6336-4:2019
12.5.1 Description of the Failure Mode Tooth Flank Fracture
12.5.2 Basic Calculation Principles
12.5.3 Influences on Tooth Flank Fracture
12.5.4 Calculation Example
12.5.5 Summary
12.5.6 Outlook
References
13. Potential and Challenges of High-Performance Plastic Gears
13.1 Introduction
13.2 State of the Art and Application of Plastic Gears
13.2.1 Materials and Properties
13.2.2 Manufacturing
13.2.3 Design
13.2.4 Fields of Application
13.3 Design and Calculation Methods for Plastic Gear Applications
13.3.1 Tooth Temperature
13.3.2 Tooth Load Carrying Capacity acc. to VDI 2736
13.3.2.1 Tooth Root Load Carrying Capacity
13.3.2.2 Tooth Flank Load Carrying Capacity
13.3.2.3 Frictional Wear Load Carrying Capacity
13.4 Recent Research Results
13.4.1 Thermal Behavior
13.4.2 Low Loss Plastic Gears
13.4.3 Tooth Root Load Carrying Capacity
13.4.4 Flank Load Carrying Capacity
13.4.5 Tribology
13.5 Challenges for the Future Application of Plastic Gears
13.6 Conclusion
Nomenclature
References
14. The Kinds and Causes of Gear Failures
14.1 Analysis of Gear-System Problems
14.1.1 Determining the Problem
14.1.2 Possible Causes of Gear-System Failures
14.1.3 Incompatibility in Gear Systems
14.1.4 Investigation of Gear Systems
14.2 Analysis of Tooth Failures and Gear-Bearing Failures
14.2.1 Nomenclature of Gear Failure
14.2.2 Tooth Breakage
14.2.3 Pitting of Gear Teeth
14.2.4 Scoring Failures
14.2.5 Wear Failures
14.2.6 Gearbox Bearings
14.2.7 Rolling-Element Bearings
14.2.8 Sliding-Element Bearings
14.3 Some Causes of Gear Failure other than Excess Transmission Load
14.3.1 Overload Gear Failures
14.3.2 Gear-Casing Problems
14.3.3 Lubrication Failures
14.3.4 Thermal Problems in Fast-Running Gears
15. Load Rating of Gears
15.1 Main Nomenclature
15.2 Coplanar Gears (Involute Parallel Gears and Bevel Gears)
15.3 Coplanar Gears: Simplified Estimates and Design Criteria
15.4 Coplanar Gears: Detailed Analysis, Conventional Fatigue Limits, and Service Factors
15.5 RH—Conventional Fatigue Limit of Factor K
15.5.1 RH—Preliminary Geometric Calculations
15.5.2 Adaption for Bevel Gears
15.5.3 RH—Unified Geometry Factor GH
15.5.4 RH—Comments and Comparisons on the Unified Geometry Factor GH
15.5.5 RH—Elastic Coefficient Dp and Conventional Fatigue Limit sclim of the Hertzian Pressure
15.5.6 RH—Adaptation Factor, AH
15.5.7 RH—Hertzian Pressure
15.5.8 RH—Service Factor, CSF (Only for One Loading Level)
15.5.9 Power Capacity Tables
15.6 RF—Conventional Fatigue Limit of Factor UL
15.6.1 RF—Geometry Factor, Jn
15.6.2 RF—Adaptation Factor, AF
15.6.3 RF—Size Factor, Ks
15.6.4 RF—Conventional Fatigue Limit of the Fillet Stress, stlim
15.6.5 RF—Tooth Root Stress at Fillet, st
15.6.6 RF—Service factor, KSF (Only for One Loading Level)
15.7 Coplanar Gears: Detailed Life Curves and Yielding
15.7.1 Definition of the Life Curves and Gear Life Ratings for One Loading Level
15.7.2 Yielding
15.7.3 Tooth Damage and Cumulative Gear Life
15.7.4 Reliability
15.8 Coplanar Gears: Prevention of Tooth Wear and Scoring
15.8.1 Progressive Tooth Wear
15.8.2 Scoring and Scuffing
15.9 Crossed Helical Gears
15.10 Hypoid Gears
15.11 Worm Gearing
16. Gear-Manufacturing Methods
16.1 Gear-Tooth Cutting
16.1.1 Gear Hobbing
16.1.2 Shaping—Pinion Cutter
16.1.3 Shaping—Rack Cutter
16.1.4 Cutting Bevel Gears
16.1.5 Gear Milling
16.1.6 Broaching Gears
16.1.7 Punching Gears
16.1.8 G-TRAC Generating
16.2 Gear Grinding
16.2.1 Form Grinding
16.2.2 Generating Grinding—Disk Wheel
16.2.3 Generating grinding—bevel gears
16.2.4 Generating Grinding—Threaded Wheel
16.2.5 Thread Grinding
16.3 Gear Shaving, Rolling, and Honing
16.3.1 Rotary Shaving
16.3.2 Rack Shaving
16.3.3 Gear Rolling
16.3.4 Gear Honing
16.4 Gear Measurement
16.4.1 Gear Accuracy Limits
16.4.2 Machines to Measure Gears
16.5 Gear Casting and Forming
16.5.1 Cast and Molded Gears
16.5.2 Sintered Gears
16.5.3 Cold-Drawn Gears and Rolled Worm Threads
Reference
17. Design of Tools to Make Gear Teeth
17.1 Shaper Cutters
17.2 Gear Hobs
17.3 Spur-Gear Milling Cutters
17.4 Worm Milling Cutters and Grinding Wheels
17.5 Gear-Shaving Cutters
17.6 Punching Tools
17.7 Sintering Tools
References
18. Dynamic Model of Technological System for Gear Finishing
18.1 Introduction
18.2 Development of a Generalized Dynamic Model
18.3 Determining the Model Parameters
18.4 Objective Functions of the Dynamic Model
18.5 Synthesis of Tools and Parameters of the Technological System
References
19. Powder Metal Gears
19.1 Introduction
19.2 PM Materials for Gears
19.2.1 As Sintered (S)
19.2.2 Sinter Hardened (SH)
19.2.3 Quench and Temper (QT)
19.2.4 Induction Hardening (IH)
19.2.5 Case Carburizing and Tempering (CQT)
19.3 Manufacturing
19.3.1 Compaction
19.3.2 Sintering
19.3.3 Post Processing
19.3.3.1 Roll Densification
19.3.3.2 Hard Finishing
19.3.3.3 Peening and Shot Blasting
19.3.3.4 Hardening
19.3.3.5 Wire EDM
19.3.3.6 Welding
19.4 Tolerances
19.5 Productivity
19.6 Powder Metal Gear Macro Design
19.7 Powder Metal Micro Design
19.7.1 Root Optimization
19.8 Stress Calculations of PM Gears
19.9 PM Specific Standards
19.9.1 MPIF 35
19.9.2 AGMA 6008
19.9.3 AGMA 944
19.9.4 AGMA 942
19.9.5 AGMA 930
References
20. 3D Printed Gears
20.1 Introduction
20.2 Plastic Gears
20.2.1 Fused Filament Deposition (FFD)
20.2.2 Stereo Lithography (SL)
20.2.3 Selective Laser Sintering (SLS)
20.3 Steel Gears
20.3.1 Fused Filament Deposition (FFD)
20.3.2 Laser and Electron Beam Methods (LPBF, EB-PBF)
20.3.3 Binder Jet (BJ)
20.4 Steels for Powder Bed Printing
20.5 Post Processing of AM Steel Gears
20.6 Final Remarks
References
21. Gear Noise and Vibration (NVH)
21.1 Fundamentals of Gear Noise
21.1.1 Transfer Path of Vibration
21.1.2 Gear Noise Excitation
21.1.3 Eigenfrequency and Resonance
21.2 Calculation Methods to Evaluate Gear Noise Excitation
21.2.1 Differential Equation for Vibration Phenomena
21.2.2 Transmission Error by Quasi-static Approach
21.2.3 Tooth Force Excitation by Quasi-static Approach
21.2.4 Dynamic approach
21.2.5 Evaluation by Characteristic Values
21.3 Measurement of Vibration
21.3.1 Sensors and Measurement Results
Angle Measurement
21.3.2 Positioning of Sensors and Operating Range
21.3.3 Sources of Possible Errors
Nyquist-Shannon Sampling Theorem
Aliasing
Electromagnetic Compatibility
Further Environment Influences
21.4 Condition Monitoring
Evaluation of Vibration Measurement Data
References
22. Planetary Gear Trains
22.1 Introduction
22.2 Types of Simple Planetary Gear Trains
22.3 Specific Conditions of Planetary Gear Trains
Mounting (Assembly) Condition
Coaxiality Condition
Adjacent Condition
22.4 Meshing Geometry of Planetary Gear Trains
22.5 Torque Method for Kinematic and Power Analysis of Planetary Gear Trains
22.6 Type of Powers, Losses, and Basic Efficiency of Planetary Gear Trains
22.7 Efficiency of Planetary Gear Trains
22.8 Load Capacity of Gears of Planetary Gear Train
22.9 Load Distribution Between the Planets, Its Unevenness, and Equalization
Negative Influencing Factors (Figure 22.19)
Positive Influencing Factors
Non-influencing (Neutral) Factors
Other Influencing Factors
22.10 Types of Compound Planetary Gear Trains
22.11 Two-Carrier Compound Planetary Gear Trains
22.12 Three-Carrier Compound Planetary Gear Trains
22.13 Four-Carrier Compound Planetary Gear Trains
22.14 Wolfrom Planetary Gear Train
22.15 Ravigneaux Planetary Gear Train
22.16 Warning—Planetary Gear Trains
References
Index