Theory of Gearing: Kinematics, Geometry, and Synthesis

Cover
Half Title
Title Page
Copyright Page
Table of Contents
Preface
Acknowledgments
Author
Introduction
Chapter 1 Non-Involute Gearing
1.1 Spur Non-Involute Gear Pairs
1.1.1 Pin Gearing
1.1.2 Lantern Gearing
1.1.3 Cycloid Gearing
1.1.4 Clock-Type Gearing
1.1.5 Special-Purpose Gearing
1.1.5.1 Roots Blower
1.1.5.2 Spur Rotors of Oil Pump
1.2 Peculiarities of Transmission of Rotary Motion by Means of Non-Involute Gears
1.2.1 On Violation of the Conjugate Action Law in Non-Involute Gearing
1.2.2 Interaction of Non-Involute Gear with Rack
1.3 Helical Non-Involute Gearing
1.3.1 Helical Rotors for Roots Blower
1.3.2 On Infeasibility of Dr. Wildhaber Helical Gearing (US Pat. No. 1,601,750)
PART I: Fundamentals
Chapter 2 Kinematics of Gear Pair
2.1 Transmission of Motion by Means of Gears
2.2 Gear Vector Diagram
2.2.1 Concept of Gear Vector Diagram
2.2.2 Kinds of Gear Vector Diagrams
2.2.2.1 Gear Vector Diagrams of Rotary-Negative Crossed-Axes Gear Pair
2.2.2.2 Gear Vector Diagrams of Rotary-Positive Crossed-Axes Gear Pair
2.2.2.3 Gear Vector Diagram of Rotary-Zero Crossed-Axes Gear Pair
2.2.2.4 Analytical Criterion of the Kind of Crossed-Axes Gear Pair
2.3 Classification of Possible Kinds of Gear Vector Diagrams
2.4 Complimentary Vectors of Gear Vector Diagrams
2.4.1 Centerline Vectors Associated with Gear Pair
2.4.2 Axial Vectors Associated with Gear Pair
2.4.3 Useful Kinematic and Geometric Formulas
Chapter 3 Principal Planes and Main Reference Systems Associated with Gear Pair
3.1 Principal Planes Associated with Gear Pair
3.1.1 Intersected-Axes Gearing
3.1.2 Parallel-Axes Gearing
3.2 Plane of Action in Gear Pair
3.2.1 Plane of Action in Intersected-Axes Gearing
3.2.2 Plane of Action in Parallel-Axes Gearing
3.3 Main Reference Systems Associated with Gear Pair
3.4 Transformation of the Main Coordinate Systems
3.4.1 Transition From the Gear Reference System to the Main Reference System
3.4.2 Transition From the Pinion Reference System to the Main Reference System
3.4.3 Transition From the Plane-of-Action Reference System to the Main Reference System
Chapter 4 Smooth Transmission of Uniform Rotary Motion: Three Fundamental Laws of Gearing
4.1 Transmission of Rotary Motion: The Present-Day Practice
4.2 The Law of Contact: The First Fundamental Law of Gearing
4.3 The Conjugate Action Law: The Second Fundamental Law of Gearing
4.3.1 Equivalent Pulley-and-Belt Transmission
4.3.2 Camus-Euler-Savary Theorem
4.3.3 Euler-Savary Equation
4.3.4 Peculiarities of Contact Geometry in Conjugate Gear Pairs
4.3.5 Brief Comments on Envelope Surfaces of the First and of the Second Kind
4.4 The Equal Base Pitches Law: The Third Fundamental Law of Gearing
4.5 On the Correlation of the Discussed Results with the Earlier Obtained Results
Chapter 5 Permissible Variation of the Design Parameters in Equivalent Pulley-and-Belt Transmission
PART II: Geometrically Accurate Gearing
SECTION II-A: Geometrically Accurate Gearing: Parallel-Axes Gearing
Chapter 6 Involute Gearing: Kinematics and Geometry
6.1 Principal Features of Parallel-Axes Gearing
6.1.1 Kinematics of Parallel-Axes Gearing
6.1.2 Gear Ratio in Parallel-Axes Gearing
6.1.3 Permissible Variation of Transverse Pressure Angle
6.2 Tooth Flank Generation
6.2.1 Desirable Line of Contact in a Gear Pair
6.2.2 Line of Action and Path of Contact in Parallel-Axes Gearing
6.2.3 Operating Base Pitch
6.2.4 Gear Tooth Flank of Favorable Geometry: General Approach
Chapter 7 Simplified Approach to Generation of Involute Gear Tooth Flank
7.1 Generation of Involute Tooth Profile
7.1.1 Involute Gear Tooth Profile
7.1.2 Gear Tooth Flank in the Lengthwise Direction of the Gear Tooth
7.1.2.1 Tooth Flank in Spur Involute Gear
7.1.2.2 Tooth Flank in Helical Involute Gear
7.1.2.3 Tooth Flank in Gear with Circular-Arc Teeth in the Lengthwise Direction
7.1.3 Tooth Flank Geometry in the Lengthwise Direction of Gear Tooth
7.1.4 Adopted Gear Terminology
7.2 Alternative Approach for Derivation of Equation of Involute Tooth Flank
7.2.1 Generation of Spur Gear Tooth Profile by Means of Straight Line
7.2.2 Generating Auxiliary Rack (Basic Rack) in Spur Gear
7.2.3 Alternative Approach for Derivation of Equation of Helical Involute Gear Tooth Flank
7.2.4 Generating Basic Rack of Helical Gear
7.2.5 Descriptive-Geometry-Based Approach for Determination of Straight Generating Line
7.2.5.1 Gear Base Helix Angle ψ[sub(b.g)]: General Approach
7.2.5.2 Base Diameter d[sub(b.g)] in Involute Gear
7.3 Comments to Peculiarities of Geometry of Involute Gear Tooth Flank
7.3.1 Characteristics of the Generating Basic Rack
7.3.2 Gears with Low Tooth Count
7.3.3 Length of Involute Tooth Profile
Chapter 8 Parallel-Axes Involute Gearing of Specific Design
8.1 Conical Involute Gearing
8.1.1 Kinematics of Conical Involute Gearing
8.1.2 Geometry of Tooth Flanks of Spur Conical Involute Gear
8.1.3 Geometry of Tooth Flanks of Conical Involute Gear with Helical Teeth
8.2 Internal Involute Gearing: Features of Kinematics and Geometry of Tooth Flanks
8.2.1 Features of Tooth Flank Geometry and Gear Design
8.2.2 Gear Coupling as a Reduced Case of Internal Parallel-Axes Gearing
8.2.3 On Commonality Between Internal Gearing and Strain Wave Gearing (Harmonic Drive)
8.3 Pinion Gear-to-Rack Mesh as Reduced Case of Parallel-Axes Involute Gear Pair
Chapter 9 Gear Tooth Profile Modification: Generating Rack Shift
9.1 Addendum Modification (Tooth Profile Shift)
9.2 Profile Shift Coefficient
9.3 Gear Tooth Flank Geometry Depending on Profile Shift Coefficient
9.4 Basic Equations for Gear Pair with Addendum Modification
9.4.1 Principle of Addendum Modification
9.4.2 External Spur and Helical Gear Pairs
9.5 Determination of Profile Shift Coefficients: Geometric Blocking Contours
Chapter 10 Interaction of Tooth Flanks in Parallel-Axes Involute Gearing
10.1 Interaction of Tooth Flanks in Spur Involute Gearing
10.2 Interaction of Tooth Flanks in Helical Involute Gearing
10.3 Transmission of Uniform Rotary Motion by Gear Teeth in Parallel-Axes Involute Gearing
10.4 Contact Ratio in Parallel-Axes Gearing
10.4.1 Length of Zone of Action in Parallel-Axes Gearing
10.4.1.1 Preliminary Remarks
10.4.1.2 Length of Zone of Action in External Gearing
10.4.1.3 Length of Zone of Action in Low-Tooth-Count Gearing
10.4.1.4 Length of Zone of Action in Internal Gearing
10.4.1.5 Length of Zone of Action in Pinion Gear-to-Rack Mesh
10.4.1.6 Face Advance (In Design of Helical and Other Non-Spur Gearing)
10.4.1.7 Highest and Lowest Points of Single-Tooth Contact
10.4.2 Contact Ratio: Generalized Approach
10.4.3 Impact of Tooth Flanks Elastic Deformation Into Contact Ratio in Gear Pair
10.5 External Involute Gear Pair
10.5.1 Main Design Parameters
10.5.2 Variation of Parameters of Tooth Flank Geometry
10.5.2.1 Normal Curvature at Point of Gear Tooth Flank
10.5.2.2 Variation of Gear Tooth Profile Angle and Helix Angle
10.5.3 Special Point of Meshing
10.6 Contact Motion Characteristics
10.6.1 Sliding Conditions
10.6.2 Specific Sliding
10.7 Elements of Dynamics in Geometrically Accurate Parallel-Axes Gearing
10.7.1 Forces Acting in Plane of Action
10.7.2 Forces Acting in Transverse Section of Geometrically Accurate Parallel-Axes Gear Pair
Chapter 11 Novikov/Conformal and High-Conformal Gearing
11.1 Introductory Remarks
11.1.1 A Brief Overview on Conformal Gearing: State-of-the-Art
11.1.1.1 An Assumed Origination of Conformal Gearing
11.1.1.2 The Power Density
11.1.1.3 Design Features of Conformal Gearing
11.1.2 Variety of Potential Designs of Conformal Gearing
11.2 Conformal Gearing (Novikov Gearing)
11.2.1 The Essence of Novikov Gearing
11.2.2 Kinematics of Parallel-Axes Gearing
11.2.3 Plane of Action
11.2.4 Operating Base Pitch
11.2.5 Boundary Novikov Circle in Novikov/Conformal Gearing
11.2.6 Novikov/Conformal Gearing as a Reduced Kind of Involute Gearing
11.2.7 Constraints Onto the Design Parameters of Tooth Geometries in Novikov/Conformal Gearing
11.2.8 Fundamental Design Parameters in Novikov/Conformal Gearing
11.2.9 Tooth Flank Geometry in Novikov/Conformal Gearing
11.2.10 Configuration of Interacting Tooth Flanks at Point of Culmination
11.2.11 Design of Novikov/Conformal Gear Pair
11.2.12 Elements of Kinematics and Geometry of Novikov/Conformal Gearing
11.2.13 Line of Action and Path of Contact in Novikov/Conformal Gearing
11.2.14 Contact Ratio in Parallel-Axes Novikov/Conformal Gear Pair
11.2.15 Tooth Profile Sliding in Novikov/Conformal Gearing
11.2.16 Novikov/Conformal Gearing with Two Pseudo-Paths of Contact
11.2.17 Local and Global Contact Geometry of Interacting Tooth Flanks
11.2.18 The Power Density in Novikov/Conformal Gearing
11.3 High-Conformal Gearing
11.3.1 Contact Geometry in High-Conformal Gearing
11.3.2 High-Conformal Parallel-Axes Gearing
11.3.3 On the Accuracy Requirements for High-Conformal Parallel-Axes Gearing
11.4 On the Impossibility of Generating-Finishing of Gears for Novikov/Conformal Gearing and High-Conformal Gearing
11.4.1 Peculiarities of the Gear-Machining Mesh
11.4.2 Inevitable Violation of the Fundamental Laws of Gearing in the Gear-Machining Mesh
11.4.3 On the Inconsistency in Tooth Profile Curvatures
SECTION II-B: Geometrically Accurate Gearing: Intersected-Axes Gear Pairs
Chapter 12 Geometrically Accurate Intersected-Axes Gear Pairs
12.1 Earliest Designs of Intersected-Axes Gear Pairs
12.2 Kinematics of Intersected-Axes Gearing
12.3 Base Cones in Intersected-Axes Gearsets
12.3.1 Path of Contact, and Instantaneous Line of Action
12.3.2 Operating Base Pitch Calculation
12.4 Tooth Flanks in Gear for Geometrically Accurate Intersected-Axes Gearset
12.4.1 Applied Coordinate Systems and Linear Transformations
12.4.1.1 Main Reference Systems
12.4.1.2 Operators of Rolling
12.4.1.3 Operators of Linear Transformations Associated with the Gear Housing
12.4.2 Tooth Flank of a Gear in Intersected-Axes Gear Pair
12.4.3 Path of Contact Point
12.4.4 Intersected-Axes Gearing with Variable Pressure Angle
12.5 Analytical Representation of Conjugate Action Law in Intersected-Axes Gearing
12.6 Favorable Tooth Proportions in Intersected-Axes Gears
12.6.1 Angular Base Pitch
12.6.2 Transverse Pressure Angle
12.6.3 Angular Pitch
12.6.4 Angular Tooth Thickness, and Angular Space Width
12.6.5 Angular Backlash
12.6.6 Gear Tooth-Line and Gear Space-Line in Intersected-Axes Gears
12.6.7 Angular Addendum and Angular Dedendum
12.6.8 Specification of Design Parameters in Intersected-Axes Gearing
12.7 Tredgold Approximation
12.8 Principal Features of Geometrically Accurate Novikov/Conformal and High-Conformal Intersected-Axes Gearing
12.8.1 Path of Contact in Novikov Conformal/high-Conformal Intersected-Axes Gearing
12.8.2 Boundary Cone
12.8.3 Bearing Capacity of High-Conformal Gearing
12.9 Design Parameters in Novikov Conformal/High-Conformal Intersected-Axes Gearsets
Chapter 13 Interaction of Tooth Flanks in Geometrically Accurate Intersected-Axes Gearing
13.1 Kinematic and Geometric Elements of Interaction in Geometrically Accurate Intersected-Axes Gearset
13.1.1 Equivalent Pulley-and-Belt Transmission for Intersected-Axes Gearset
13.1.2 Path of Contact
13.1.3 Zone (Field) of Action in Intersected-Axes Gearing
13.2 Transmission of Uniform Rotary Motion in Intersected-Axes Gearing
13.3 Contact Ratio in Intersected-Axes Gearing
13.3.1 Transverse Contact Ratio
13.3.2 Face Contact Ratio
13.3.3 Total Contact Ratio
13.4 Contact Motion Characteristics in Intersected-Axes Gearing
13.4.1 Sliding in Geometrically Accurate Intersected-Axes Gearing
13.4.1.1 Descriptive Geometry-Based Solution to the Problem of Determination of Sliding in Geometrically Accurate Intersected-Axes Gearing
13.4.1.2 Analytical Solution to the Problem of Determination of Sliding in Geometrically Accurate Intersected-Axes Gearing
13.4.1.3 Specific Sliding in Geometrically Accurate Intersected-Axes Gearing
13.4.1.4 Features of Specific Sliding in Geometrically Accurate Intersected-Axes Gearing
13.5 Elements of Dynamics of Geometrically Accurate Intersected-Axes Gearing
13.5.1 Principal Assumption Adopted in Load Analysis of Geometrically Accurate Intersected-Axes Gearing
13.5.2 Forces of Interaction in Geometrically Accurate Intersected-Axes Gearing
13.5.2.1 Resultant Force Acting in Geometrically Accurate Intersected-Axes Gearing
13.5.2.2 Forces Acting on Gear and Pinion in Geometrically Accurate Intersected-Axes Gearing
13.5.2.3 Normal Force Acting on Gear in Geometrically Accurate Intersected-Axes Gearing
13.6 Testing of Geometrically Accurate Spiral Bevel Gears: Contact Pattern
13.6.1 Testing Conditions
13.6.2 Predicting Contact Geometry in Geometrically Accurate Spiral Bevel Gearing
SECTION II-C: Geometrically Accurate Gears: Crossed-Axes Gearing
Chapter 14 Geometrically Accurate Crossed-Axes Gear Pairs: R-Gearing
14.1 Kinematics of Crossed-Axes Gearing
14.2 Pressure Angle in Crossed-Axes Gearing
14.2.1 Crossed-Axes Gearing with Transverse Pressure Angle of a Constant Value
14.2.2 Crossed-Axes Gearing with Transverse Pressure Angle of a Variable Value
14.3 Base Cones in Crossed-Axes Gear Pair
14.4 Tooth Flank of a Gear in Geometrically Accurate Crossed-Axes Gear
14.4.1 Applied Coordinate Systems and Linear Transformations
14.4.1.1 Main Reference Systems
14.4.1.2 Operators of Rolling/Sliding
14.4.1.3 Operators Associated with Gear Housing
14.4.2 Gear Tooth Flank in Crossed-Axes Gearing
14.5 Fulfillment of Conjugate Action Law in R – Gearing
14.6 Desirable Tooth Proportions in Crossed-Axes Gear Pair
14.6.1 Operating Angular Base Pitch
14.6.2 Low-Tooth-Count Crossed-Axes Gears
14.6.3 Transverse Pressure Angle
14.6.4 Angular Pitch
14.6.5 Angular Tooth Thickness, and Angular Space Width, in the Round Basic Rack
14.6.6 Angular Addendum, and Angular Dedendum, in Round Basic Rack
14.6.7 Specification of the Design Parameters in Crossed-Axes Gearing
14.7 Backlash in Crossed-Axes Gearing
14.8 Possible Analogy of Tredgold Approximation for Crossed-Axes Gearing
14.9 Main Features of Geometrically Accurate Novikov/Conformal and High-Conformal Crossed-Axes Gearing
14.9.1 Path of Contact in Novikov/Conformal and High-Conformal Crossed-Axes Gearing
14.9.2 Boundary N-Cone in Novikov/Conformal, and High-Conformal Crossed-Axes Gearing
14.9.3 Bearing Capacity of Crossed-Axes Novikov/Conformal, and High-Conformal Gearing
14.10 Design Parameters of Novikov/Conformal, and High-Conformal Crossed-Axes Gearing
Chapter 15 Interaction of Gears in Geometrically Accurate Crossed-Axes Gearing
15.1 Interaction Between Tooth Flanks in Geometrically Accurate Crossed-Axes Gearing
15.1.1 Equivalent Pulley-and-Belt Transmission of Crossed-Axes Gear Pair
15.1.2 Path of Contact, and Instantaneous Line of Action
15.1.3 Zone of Action (Field of Action) in Crossed-Axes Gearing
15.2 Transmission of Uniform Rotary Motion by Means of Crossed-Axes Gearing
15.3 Contact Ratio in Crossed-Axes Gearing
15.4 Contact Motion Characteristics in Crossed-Axes Gearing
15.4.1 Sliding in Geometrically Accurate Crossed-Axes Gearing
15.4.2 Analytical Solution to the Problem of Determination of Sliding Velocity in Geometrically Accurate Crossed-Axes Gearing
15.4.3 Specific Sliding in Geometrically Accurate Crossed-Axes Gearing
15.4.4 Features of Specific Sliding in Geometrically Accurate Crossed-Axes Gearing
15.5 Elements of Dynamics of Geometrically Accurate Crossed-Axes Gearing
15.5.1 Principal Assumption Adopted in the Load Analysis of Geometrically Accurate Crossed-Axes Gearing
15.5.2 Forces of Interaction in Geometrically Accurate Crossed-Axes Gearing
Chapter 16 Geometrically Accurate Worm-Gearing: Peculiarities of Kinematics and Geometry
16.1 Worm-Gearing: Accomplishments From the Ancient Times Till Now
16.1.1 Early Designs of Worm-Gearing
16.1.2 Worm-Gearing of Conventional Designs
16.1.3 Spiroid Gearing
16.1.4 Helicon Gearing
16.1.5 Internal Worm-Gearing
16.1.6 Worm-Gearing with Rolling Elements
16.2 Fundamentals of Worm-Gearing with Line Contact Between Worm Threads and Worm-Gear Tooth Flanks
16.2.1 Kinematics of Geometrically Accurate Worm-Gearing
16.2.2 Base Cones in Geometrically Accurate Worm-Gearing
16.2.3 Peculiarities of Sliding in Plane-of-Action Apex in Geometrically Accurate Worm-Gearing
16.3 Criterion to Distinguish Worm From Gear
16.4 Analysis of Design of Worm-Gear-Drive [Pat. No. 257,246, USSR, 1968]
PART III: Real Gears: Kinematics, Geometry, and Application
Chapter 17 Geometrically Accurate Real Gearing: S[sub(pr)] – Gear System
17.1 Preliminary Considerations
17.1.1 Root Causes for Real Gears Differ From Geometrically Accurate Gears
17.1.2 Applied Coordinate Systems
17.1.3 Displacements of Gear Axis of Rotation From its Desirable Configuration
17.1.4 Closest Distance of Approach Between Gear and Mating Pinion Axes of Rotation
17.2 Tooth Flank Geometry in Geometrically Accurate Real Gearing: S[sub(pr)] – Gear System
17.2.1 Tooth Flank Geometry in Geometrically Accurate Real Gearing
17.2.1.1 The Adopted Concept for Tooth Flank Generation of Gears for S[sub(pr)] – Gear System
17.2.1.2 Preferred Reference Systems
17.2.1.3 Derivation of Equation of Tooth Flank in S[sub(pr)] – Gearing
17.2.1.4 Angular Base Pitch in S[sub(pr)] – Gearing
17.2.1.5 Features of Interaction of Tooth Flanks in S[sub(pr)] – Gearing
17.2.2 Possible Improvement in Specification of Tooth Flank Geometry in S[sub(pr)] – Gearing
17.3 Redundant Parameter Elimination
17.3.1 Possible Correlation Between Displacements in S[sub(pr)] – Gearing
17.3.2 Account for the Normal Distribution of Manufacturing Errors Onto the Geometry of Tooth Flanks
17.4 Possibility of Implementation of the Concept of S[sub(pr)] – Gearing in Design of Gear Coupling
17.5 Possibility of Implementation of the Concept of S[sub(pr)] – Gearing in Point Contact Gear Systems
17.6 Correlation Among the Gear Systems of Different Kinds
PART IV: CΣu – Variable Gearing
Chapter 18 CΣu–var Gears: Kinematics, Geometry, and Novel Concept to Design Geometrically Accurate Gears
18.1 Preamble: Permissible Variation of Design Parameters in Equivalent Pulley-and-Belt Transmission
18.2 Fundamentals of Geometrically Accurate CΣu–var Gearing
18.3 Classification of Gear Vector Diagrams of CΣu–var Gear Pair
18.4 Tooth Flank Generation in Geometrically Accurate CΣu–var Gearing
18.5 A Key Mistake in Known Methods of Machining Gears for Geometrically Accurate CΣu–var Gearing
18.6 Examples of Application of CΣu–var Gearing
18.7 Possibility of Implementation of the Concept of S[sub(pr)] – Gearing in Design of Σ–var Gearing
PART V: On Synthesizing of Favorable Geometrically Accurate Gear Pairs
Chapter 19 Features of Contact Geometry
19.1 On the Meaning of the Term Synthesis of Favorable Gear Pair
19.2 Dupin Indicatrix
19.3 Indicatrix of Conformity at Point of Contact of a Gear and a Mating Pinion Tooth Flanks
19.4 Concept of Synthesizing of Favorable Geometrically Accurate Gear Pair
PART VI: Real Gears and Their Application
Chapter 20 Generic Gear Surfaces
20.1 Origination of Generic Gear Surface
20.2 Examples of Gear Pairs Composed of Gears with Generic Gear Surfaces Various Geometries
20.3 Evaluation of the Total Number of Possible Generic Gear Surfaces
20.3.1 Possible Profiles of Generic Gear Surface Constructed in Axial Section of Gear
20.3.2 Profile of Generic Gear Surface Constructed in Section by Plane at an Angle to Gear Axis
20.4 Possibility of Classification of Gear Pairs
20.5 Examples of Implementation of Classification of Gear Pairs
20.6 Auxiliary Generating Racks of Possible Geometries
Chapter 21 Approximate Real Gearing
21.1 Approximate Real Parallel-Axes Gearing
21.2 Approximate Real Intersected-Axes Gearing
21.2.1 Root Causes for Inaccuracies in Real Intersected-Axes Gears
21.2.2 Approximate Real Intersected-Axes Gears
21.2.2.1 Straight Tooth Bevel Gears
21.2.2.2 Spiral Bevel Gears
21.2.2.3 Face Gears
21.2.3 Generation of Tooth Flanks of Gears for Intersected-Axes Gearing
21.2.3.1 Generation of Tooth Flanks of Straight Bevel Gears
21.2.3.2 Generation of Tooth Flanks of Spiral Bevel Gears
21.2.3.3 Tooth Flanks of Bevel Gears Cut Using Continuous-Indexing Method of Gear Machining
21.2.4 Examples of Approximate Real Intersected-Axes Gear Pairs
21.3 Approximate Real Crossed-Axes Gearing
21.4 Worm Gearing
21.5 Tooth Flank Modification
21.5.1 Brief Historical Overview on Gear Tooth Flank Modification
21.5.2 Requirements to Design Parameters of Modified Portions of Tooth Flanks
21.5.3 Kinds of Tooth Flank Modifications
21.5.3.1 Tooth Flank Modifications Which Restrict the Usable Flank
21.5.3.2 Transverse Profile Modifications
21.5.3.3 Flank Line (Helix) Modifications
21.5.3.4 Flank Face Modifications
21.5.4 Description of Modifications by Functions
21.5.5 On the Most Favorable Modification of Gear Tooth Flanks
Chapter 22 Local Geometry of Interacting Gear Tooth Flanks
22.1 Local Geometry of Interacting Tooth Flanks in Parallel-Axes Gearing
22.1.1 Kinematics of Interaction of Gear Tooth Flanks
22.1.2 Local Geometry of Interacting Tooth Flanks
22.2 Local Geometry of Interacting Tooth Flanks in Intersected-Axes Gearing
22.2.1 Kinematics of Interaction of Tooth Flanks
22.2.2 Local Geometry of Interacting Tooth Flanks
22.3 Local Geometry of Interacting Tooth Flanks in Crossed-Axes Gearing
22.3.1 Kinematics of Interaction of Tooth Flanks
22.3.2 Local Geometry of Interacting Tooth Flanks
22.4 Local Geometry of Interacting Tooth Flanks in Novikov/Conformal and in High-Conformal Gearing
22.4.1 Kinematics of Interacting Tooth Flanks
22.4.2 Geometry of Interacting Tooth Flanks
Chapter 23 Strength of Gear Teeth
23.1 Contact Strength of Gear Tooth in Low-Tooth-Count Gearing
23.1.1 Adopted Principal Assumptions
23.1.1.1 Comments on Analytical Description of Local Geometry of Contacting Surfaces Loaded by Normal Force: Hertz Proportional Assumption
23.1.1.2 Assumption of Even Torque Share
23.1.2 Principal Features of Low-Tooth-Count Gears
23.1.3 Analytical Model for Calculation Contact Stress
23.1.4 Formula for Calculation Hertz Contact Stress
23.1.5 Specific Pressure Factor
23.1.6 Combined Compressive-Shear Stress in Low-Tooth-Count Gearing
23.2 Bending Strength of Gear Teeth
23.2.1 Comments on Lewis' Formula
23.2.1.1 Cantilever Beam of Equal Strength
23.2.1.2 Lewis' Formula for the Calculation of Bending Strength of Gear Teeth
23.3 Effective Length of Line of Contact
23.3.1 Length of Single Line of Contact in Parallel-Axes Gearing
23.3.2 Effective Length of Lines of Contact in Parallel-Axes Gearing
23.3.2.1 Effective Length of Lines of Contact in Spur Parallel-Axes Gearing
23.3.2.2 Effective Length of Lines of Contact in Helical Parallel-Axes Gearing
23.4 Loading of Gear Teeth
23.5 Method for Simulation of Interaction of Gear and Mating Pinion Tooth Flanks
Chapter 24 SPTS – Split Power Transmission Systems
24.1 Root Cause for Unequal Torque Sharing in a Split Torque Transmission
24.2 Mobility of Split Power Transmission Systems
24.3 Power Density of Gear Transmission Systems
24.4 Epicyclic Gear Drives
24.5 Structural Formula for Planetary Gear Drives
24.6 Correspondence Among Angular Velocities of All the Members in Planetary Gear Drive
24.7 Formulating the Problem of Equal Load Sharing in Planetary Gear Drives: State-of-the-Art
24.7.1 Ordinary Planetary Gear Drives
24.7.2 Planetary Gear Drives with Flexible Pins
24.8 Alternative Approach for Equal Torque Sharing in Split Power Transmission
24.8.1 Planetary Gear Drive with Elastomeric Load-Sharing Device
24.8.2 Elastic Load-Sharing Device
24.8.2.1 Elastic Properties of Elastic Load-Sharing Device
24.8.2.2 Examples of Implementation of Elastic Load-Sharing Device
24.9 Main Features of Split Power Transmission Systems with Preloaded Elastic Load-Sharing Devices
Chapter 25 Vector Approach in Kinematic and Dynamic Analysis of Complex Gear Transmission Systems
25.1 Possible Kinds of Graphical Representation of Rotating Gear
25.2 Vector Diagrams of Complex Gear Transmission Systems
25.3 Features of Vector Diagrams of Complex Gear Transmission Systems with Intersected-Axes and Crossed-Axes Gear Pairs
25.3.1 Elementary Gear Vector Diagram of Intersected-Axes Gear Pair
25.3.2 Elementary Gear Vector Diagram of Crossed-Axes Gear Pair
Chapter 26 Gear Ratio of Multistage Gear Transmission System
26.1 Principal Kinematic Relationships in Multistage Gear Transmission System
26.1.1 Range Ratio of Speed Variation of Gear Transmission System
26.1.2 Characteristics of Transmission Group
26.2 Analytical Method for Determining Transmission Ratios
26.3 Rotational Speed Chart
26.4 Broken Geometric Series
26.5 Minimum Number of Gear Pairs
26.6 Determining Tooth Number of Gears of Group Transmissions
Chapter 27 Gear Accuracy
27.1 Inspection of Gears for Parallel-Axes Gear Pairs
27.1.1 Concept of Inspection of Involute Gear Tooth Profile
27.1.2 Span Measurement
27.1.3 Constant Chord Tooth Thickness
27.1.4 Tooth Thickness Measurement in Internal Gear
27.2 Inspection of Gears for Intersected-Axes Gear Pairs
27.2.1 Concept of Inspection of Bevel Gear Tooth Profile
27.2.2 Concept of Inspection of Bevel Gear in Lengthwise Direction of Gear Teeth
27.3 Inspection of Gears for Crossed-Axes Gear Pairs
27.3.1 Concept of Inspection of Gear Tooth Profile
27.3.2 Concept of Inspection of Gear in Lengthwise Direction of Gear Teeth
27.4 Mounting Distance: Accuracy of Axial Location of Gears in the Gear Housing
27.4.1 On the Correlation Between the Tooth Flank Geometry and the Mounting Distance
27.4.2 Mounting Distance in Intersected-Axes Gearing
27.4.2.1 Relative Disposition of Base Cones in Intersected-Axes Gearing
27.4.2.2 Edge Contact in Misaligned Intersected-Axes Gearing
27.4.2.3 Disposition of Base Cone of a Gear in Relation to the Plane of Action in Intersected-Axes Gearing
27.4.2.4 Mounting of Gears in Intersected-Axes Gear Housing
27.4.2.5 Tolerance for the Accuracy of the Mounting Distance in Intersected-Axes Gearing
27.4.3 Mounting Distance in Crossed-Axes Gearing
27.4.3.1 Relative Disposition of Base Cones in Crossed-Axes Gearing
27.4.3.2 Disposition of Base Cone of a Gear in Relation to the Plane of Action in Crossed-Axes Gearing
27.4.3.3 Mounting of Gears in Crossed-Axes Gear Housing
27.4.3.4 Tolerance for the Accuracy of the Mounting Distance in Crossed-Axes Gearing
27.5 Contact Pattern
27.6 Permissible Alteration to Bevel Gear Tooth Flank Geometry
Chapter 28 Gear Noise and Vibration
28.1 Root Causes for Vibration Generation and Noise Excitation
28.1.1 Root Cause for Vibration Generation and Noise Excitation in Geometrically Accurate Gearing
28.1.2 Root Cause for Vibration Generation and Noise Excitation in Approximate Gear Pairs
28.1.2.1 Violation of the Law of Contact
28.1.2.2 Violation of the Conjugate Action Law
28.1.2.3 Violation of the Equality of Base Pitches
28.2 Transmission Error
28.2.1 On the Nature of Transmission Error
28.2.2 Determination of Transmission Error
28.2.3 Base Pitch Variation of Rotation Vector
28.3 Variation of Axial and Radial Forces
28.4 Alternative Causes of Noise Excitation in Gear Pair
28.4.1 Influence of Contact Ratio
28.4.2 Influence of Location of the Point at Which the Resultant Load Is Applied
28.5 On a Possibility of Prediction of Gear Noise Excitation
Chapter 29 Design Peculiarities of Geometrically Accurate and Almost Geometrically Accurate Gears
29.1 Design Peculiarities of Gears for R – Gearing
29.1.1 Essence of Kinematics in Crossed-Axes Gearing
29.1.2 Base Cones
29.1.3 Tooth Flanks in Geometrically Accurate Crossed-Axes Gears
29.2 Permissible Simplification: Design Peculiarities of Gears for R[sub(sp)] – Gearing
Chapter 30 A Brief Overview on Evolution of the Scientific Theory of Gearing
30.1 Preliminary Remarks
30.2 Three Main Periods in the Evolution of the Gear Art and Gear Science
30.2.1 Pre-Eulerian Period of Evolution of the Gear Art
30.2.2 The Time When the Fundamental Contribution by Leonhard Euler has Been Done – the Origin of the Scientific Theory of Gearing
30.2.2.1 Involute Tooth Profile for Parallel-Axes Gearing
30.2.2.2 The Euler-Savary Formula
30.2.2.3 Leonhard Euler and the Euler-Savary Formula
30.2.2.4 Equivalent Pulley-and-Belt Transmission
30.2.3 Post-Eulerian Period of Evolution of the Theory of Gearing
30.2.3.1 Robert Willis and the Fundamental Theorem of Parallel-Axes Gearing
30.2.3.2 A Mistake (1842) Committed by Theodore Olivier
30.2.3.3 Miscellaneous Improvements to the Gear Art
30.2.3.4 The Research Carried Out by Chaim Gochman
30.2.3.5 Equality of Base Pitches in Geometrically Accurate Parallel-Axes Gearing
30.2.3.6 Geometrically Accurate Worm Gearing
30.2.3.7 Shishkov Equation of Contact, n[sub(g)] · V[sub(Σ)] = 0
30.2.3.8 Diagram of Screw (by Professor A. F. Nikolayev) and its Application in Gearing
30.2.3.9 Principal Planes, and Reference Systems Associated with Gear Pair
30.2.3.10 Contact Geometry: Indicatrix of Conformity at Point of Contact of Tooth Flanks
30.2.3.11 Condition of Conjugacy of Interacting Tooth Flanks (General Case: for Gears of all Kinds)
30.2.3.12 Angular Base Pitches: Operating Angular Base Pitch in Gear Pair
30.2.3.13 Crossed-Axes Gearing with Line Contact Between the Tooth Flanks (R-Gearing)
30.2.3.14 Scientific Classification of Gearing
30.2.3.15 Geometrically Accurate Real Gearing
30.2.3.16 Generalized Equation of Conjugacy of Interacting Tooth Flanks: for Gearing of All Kinds
30.3 Other Contributions to the Field of Geometrically Accurate Gearing
30.3.1 Tooth Flank Geometry in Geometrically Accurate Intersected-Axes Gearing
30.3.2 Contribution by Prof. N. I. Kolchin
30.3.3 Contribution by Prof. V. L. Novikov
30.3.4 Contribution by Prof. V. A. Gavrilenko
30.3.5 Contribution by Prof. E. B. Vulgakov
30.3.6 Contribution by the Other Gear Theoreticians
30.3.7 Contribution by Walton Musser
30.4 Developments in the Field of Geometrically Inaccurate Gearing
30.4.1 Samuel Cone Double-Enveloping Worm Gearing
30.4.2 Approximate (Geometrically Inaccurate) Bevel Gearing
30.4.3 Approximate (Geometrically Inaccurate) Crossed-Axes Gearing
30.4.4 Approximate (Geometrically Inaccurate) Crossed-Axes Gearing: Face Gearing
30.5 Theory of Gearing at the Beginning of the Twenty-First Century: State-of-the-Art
30.6 Favorable Approximate Gearing
30.7 Accomplishments in the Field of Non-Circular Gearing
30.8 Tentative Chronology of Evolution of the Theory of Gearing
30.9 On the Other Efforts that Pertain to Evolution of Scientific Theory of Gearing
Chapter 31 On the Lack of Understanding of the Scientific Theory of Gearing by the Majority of Gear Scientists and Engineers
Appendix A: Elements of Vector Calculus
Appendix B: Elements of Differential Geometry of Surfaces
Appendix C: Change of Surface Parameters
Appendix D: Applied Coordinate Systems and Linear Transformations
Appendix E: Contact Geometry of a Gear and a Mating Pinion Tooth Flanks
Appendix F: The Closest Distance of Approach of Tooth Flanks of a Gear, and a Mating Pinion
Appendix G: Engineering Formulae for Specification of Gear Tooth Flank
Appendix H: On the Inadequacy of the Terms Wildhaber-Novikov Gearing, and W-N Gearing
Conclusion
Notation
Glossary
References
Bibliography
Index