Gears: Volume 2: Analysis of Load Carrying Capacity and Strength Design (Springer Series in Solid and Structural Mechanics, 11)

Aphorism
Preface
Contents
Symbols, Notations and Units
1 Load Carrying Capacity of Spur and Helical Gears: Influence Factors and Load Analysis
	1.1 Introduction
	1.2 Application Factor, KA
	1.3 Dynamic Factor, Kv
		1.3.1 Generality
		1.3.2 Method A for Determination of Kv - A
		1.3.3 Method B for Determination of Kv - B
		1.3.4 Method C for Determination of Kv - C
	1.4 Face Load Factors, KHβ and KFβ
		1.4.1 Generality
		1.4.2 Method A for Determination of KHβ - A and KFβ - A
		1.4.3 Method B for Determination of KHβ - B and KFβ - B
		1.4.4 Method C for Determination of KHβ - C and KFβ - C
	1.5 Transverse Load Factors, KHα and KFα
		1.5.1 Generality
		1.5.2 Method B for Determination of KHα - B and KFα - B
		1.5.3 Running-in Allowance for a Gear Pair
	1.6 Tooth Stiffness Parameters
	1.7 Load Distribution on Pairs of Teeth in Simultaneous Meshing
	1.8 Variable Load and Load Spectrum
	1.9 Determination of Application Factor, KA, from a Given Torque Spectrum
	References
2 Surface Durability (Pitting) of Spur and Helical Gears
	2.1 General Survey
	2.2 Pitting Damage and Safety Factor
	2.3 Theoretical Basis of Surface Durability Calculations
	2.4 Surface and Subsurface Stress States
	2.5 Other Considerations on the Pitting Generation
	2.6 Some Brief Reminder on the Elastohydrodynamic Lubrication Theory
	2.7 Conditions for EHD Lubrication, and Subsurface and Surface Fatigue Damage
	2.8 Calculation of Surface Durability: ISO Basic Formulae
	2.9 Influence Factors of the Hertzian Stress
		2.9.1 Zone Factor, ZH
		2.9.2 Single Pair Tooth Contact Factors, ZB andZD
		2.9.3 Elasticity Factor, ZE
		2.9.4 Contact Ratio Factor, Zε
		2.9.5 Helix Angle Factor, Zβ
	2.10 Influence Factors of the Permissible Contact Stress
		2.10.1 Allowable Stress Numbers for Contact and Bending
		2.10.2 Life Factor, ZNT
		2.10.3 Influence Factors of Lubricant Film, ZL , Zv andZR
		2.10.4 Work Hardening Factor, ZW
		2.10.5 Size Factor, ZX
		2.10.6 Minimum Safety Factor, SHmin
		2.10.7 Actual S-N Damage Curves, Obtained by Calculation
	2.11 Calculation Examples
	References
3 Tooth Bending Strength of Spur and Helical Gears
	3.1 Introduction and Brief History
	3.2 Fatigue Tooth Root Breakage and Safety Factor
	3.3 Lewis Analysis
	3.4 Stress State at the Tooth Root
	3.5 30° Tangent and Load Application at the Outer Point of Single Pair Gear Tooth Contact
	3.6 Calculation of Tooth Bending Strength: ISO Basic Formulae
	3.7 Influence Factors for the Nominal Tooth Stress
		3.7.1 Stress Correction Factor, YS
		3.7.2 Helix Angle Factor, Yβ
		3.7.3 Rim Thickness Factor, YB
		3.7.4 Deep Tooth Factor, YDT
	3.8 Influence Factors of the Permissible Tooth Root Stress
		3.8.1 Allowable Stress Numbers for Contact and Bending
		3.8.2 Life Factor, YNT
		3.8.3 Relative Notch Sensitivity Factor, yδrelT
		3.8.4 Relative Surface Factor, YRrelT
		3.8.5 Size Factor, YX
		3.8.6 Minimum Safety Factor, SFmin
		3.8.7 Actual S-N Damage Curves, Obtained by Calculation
	3.9 Design Analysis to Determine the Module
	3.10 Mean Stress Influence Factor, YM
	3.11 Calculation Examples
	References
4 Load Carrying Capacity of Bevel Gears: Factors Influencing Load Conditions
	4.1 Introduction
	4.2 Calculation of Virtual Cylindrical Gears with Sub-method B1
	4.3 Calculation of Virtual Cylindrical Gears with Method B2
	4.4 Application Factor, KA
	4.5 Dynamic Factor, Kv
		4.5.1 Generality
		4.5.2 Method A for Determination of Kv - A
		4.5.3 Method B for Determination of Kv - B
		4.5.4 Method C for Determination of Kv - C
	4.6 Face Load Factors, KHβ and KFβ
		4.6.1 Generality
		4.6.2 Method C for Determination of the Face Load Factors, KHβ - C and KFβ - C
	4.7 Transverse Load Factors, KHα and KFα
		4.7.1 Generality
		4.7.2 Method B for Determination of the Transverse Load Factors, KHα - B and KFα - B
		4.7.3 Method C for Determination of the Transverse Load Factors, KHα- C and KFα- C
	References
5 Surface Durability (Pitting) of Bevel Gears
	5.1 General Aspects on Pitting Damage
	5.2 Calculation of Surface Durability: ISO Basic Formulae of Method B1
	5.3 Contact Stress Factors for Method B1
	5.4 Permissible Contact Stress Factors for Method B1
	5.5 Calculation of Surface Durability: ISO Basic Formulae of Method B2
	5.6 Contact Stress Factors for Method B2
	5.7 Common Factors for Method B1 and Method B2: Factors for Contact Stress and Permissible Contact Stress
		5.7.1 Elasticity Factor, ZE
		5.7.2 Lubricant Film Influence Factors, ZL, Zv, ZR
		5.7.3 Work Hardening Factor, ZW
		5.7.4 Life Factor, ZNT
	5.8 Calculation Examples
	References
6 Tooth Root Strength of Bevel Gears
	6.1 Introduction
	6.2 Calculation of Tooth Root Strength: ISO Basic Formulae of Method B1
	6.3 Tooth Root Stress Factors for Method B1
		6.3.1 Tooth Form Factor, YFa
		6.3.2 Stress Correction Factor, YSa
		6.3.3 Contact Ratio Factor, Yε
		6.3.4 Bevel Spiral Angle Factor, YBS
		6.3.5 Load Sharing Factor, YLS
	6.4 Permissible Tooth Root Stress Factors for Method B1
		6.4.1 Relative Surface Condition Factor, YRrelT - B1
		6.4.2 Relative Notch Sensitivity Factor, Yδ,relT - B1
	6.5 Calculation of Tooth Root Strength: ISO Basic Formulae of Method B2
	6.6 Tooth Root Stress Factors for Method B2
		6.6.1 Bending Strength Geometry Factor, YJ
		6.6.2 Additional Tooth Strength Parameters for Bevel and Hypoid Gears
		6.6.3 Root Stress Adjustment Factor, YA
	6.7 Permissible Tooth Root Stress Factors for Method B2
	6.8 Common Factors for Method B1 and Method B2: Factors for Permissible Tooth Root Stress
		6.8.1 Size Factor, YX
		6.8.2 Life Factor, YNT
	6.9 Calculation Examples
	References
7 Scuffing Load Carrying Capacity of Cylindrical, Bevel and Hypoid Gears: Flash Temperature Method
	7.1 Introduction
	7.2 Transition Diagram and Coefficient of Friction at Incipient Scuffing
	7.3 Contact Temperature
		7.3.1 General Relationship
		7.3.2 Interfacial Bulk Temperature and Overall Bulk Temperature
		7.3.3 Flash Temperature
	7.4 Coefficient of Friction
	7.5 Position of an Arbitrary Point on the Line of Action
		7.5.1 Cylindrical Gears
		7.5.2 Bevel Gears
	7.6 Optimum Profile Modification and Approach Factor
	7.7 Load Sharing Factor, XΓ
		7.7.1 General Premise
		7.7.2 Cylindrical Spur Gears
		7.7.3 Buttressing Factor, Xbut, Γ
		7.7.4 Cylindrical Helical Gears
		7.7.5 Wide and Narrow Bevel Gears
	7.8 Scuffing Temperature and Safety Factor
	7.9 Cold Scuffing Load Carrying Capacity
	7.10 Some In-depth Information on the Warm Scuffing
	7.11 Empirical Formulae
	References
8 Scuffing Load Carrying Capacity of Cylindrical, Bevel and Hypoid Gears: Integral Temperature Method
	8.1 Introduction
	8.2 Mean Coefficient of Friction
	8.3 Other Common Influence Factors
	8.4 Scuffing Safety Factor and Permissible Integral Temperature
	8.5 Integral Temperature of Cylindrical Gears
	8.6 Integral Temperature of Bevel Gears
	8.7 Integral Temperature of Hypoid Gears
	8.8 Virtual Crossed Axes Helical Gears
	8.9 Scuffing Integral Temperature
	8.10 Calculation Examples
	8.11 Flash Temperature or Integral Temperature?
	References
9 Wear Load Capacity Rating of Gears
	9.1 Introduction
	9.2 Generation Mechanism of Abrasive Wear and Influences
	9.3 Classical Wear Theories
	9.4 Assessment of Tooth Wear Linear Progression
	9.5 Additional Considerations on the Gear Wear
	References
10 Micropitting Load Capacity of Spur and Helical Gears
	10.1 Generality
	10.2 Issues to Be Solved for a Reliable Calculation of Micropitting Load Carrying Capacity of Cylindrical Spur and Helical Gears
	10.3 Ideal Characteristics of a General Micropitting Model for Gears
	10.4 A Tribological-Dynamic Model for Cylindrical Spur Gears
		10.4.1 Rigid-Body Dynamic Sub-Model
		10.4.2 EHL-Tribological Sub-model
		10.4.3 Tribological-Dynamic Model
	10.5 Other Interesting Contributions for a General Micropitting Model of Spur Gears
		10.5.1 Three-Dimensional Contact Sub-model
		10.5.2 Multi-axial Fatigue Sub-model
	10.6 Calculation of Micropitting Load Carrying Capacity of Cylindrical Spur and Helical Gears: ISO Basic Formulae
	10.7 Permissible Specific Lubricant Film Thickness, λGFP
	10.8 Local Specific Lubricant Film Thickness, λGF, Y
		10.8.1 Normal Radius of Relative Curvature, ρn,Y, at Point Y
		10.8.2 Material Parameter, GM
		10.8.3 Local Velocity Parameter, UY
		10.8.4 Local Load Parameter, WY
		10.8.5 Local Sliding Parameter, SGF,Y
		10.8.6 Load Sharing Factor, XY
		10.8.7 Local Buttressing Factor, Xbut,Y
		10.8.8 Cylindrical Helical Gears
		10.8.9 Local Contact Temperature, B,Y
	10.9 Calculation Examples
	10.10 Topography and Texture of Surfaces
		10.10.1 Basic Concepts
		10.10.2 Main Surfaces
		10.10.3 Surface Texture Parameters
		10.10.4 Function Related Parameters
		10.10.5 Volume Parameters
		10.10.6 Roughness
	References
11 Tooth Flank Breakage Load Carrying Capacity of Spur and Helical Gears
	11.1 Introduction
	11.2 TFF and TIFF Failure Mechanisms
	11.3 Fundamentals on the TIFF and TFF Calculation Methods
	11.4 An Interesting Method of TIFF and TFF Risk Evaluation
		11.4.1 General Concepts and Main Assumptions
		11.4.2 Hardness Profile and Material Properties
		11.4.3 Residual Stresses
		11.4.4 Fatigue Crack Initiation Criterion
	11.5 A Refined TFF-Risk Assessment Model
	11.6 A Practical-Oriented Calculation Approach for TFF-Risk Assessment
	11.7 Some Insights on the Multiaxial Stress State that Originates Crack Initiation for TIFF and TFF
		11.7.1 General Concepts
		11.7.2 Weakest Link Theory and Classical Multiaxial Criteria
		11.7.3 A General Fatigue Criterion for Multiaxial Stress
		11.7.4 Modification of the Shear Stress Intensity Hypothesis
	11.8 Calculation of Tooth Flank Fracture Load Carrying Capacity of Cylindrical Spur and Helical Gears: ISO Basic Formulae
		11.8.1 General
		11.8.2 ISO Formulae for TFF Assessment
	11.9 Local Material Strength
		11.9.1 Hardness Depth Profile
	References
Appendix  Load Carrying Capacity of Worm Gears
A.1 General Information
A.2 Security Against the Main Types of Damage
A.2.1 Safety Against Wear
A.2.2 Safety Against Surface Durability (Pitting)
A.2.3 Security Against Shear Tooth Breakage
A.2.4 Security Against Worm Shaft Deflection
A.2.5 Security Against Working Temperature
A.2.5.1 Security Against Working Temperature for Splash Lubrication
A.2.5.2 Security Against Working Temperature for Oil Spray Lubrication
A.3 Security Against Other Types of Damage
References
Index of Standards
Author Index
Subject Index