Gear Technology Manual Modules

Index

Module 1 - DRIVE SYSTEMS

Author:	Mr Dieter Hofmann - Gear Design Unit University of Newcastle
Pages:	74
Tables:	8
Figures:	59
References:
Price:	(Modules 1-6 inclusive) Go to BGA Shop to Order

SYNOPSIS This module considers drive systems in relation to the characteristics of the driving and driven machinery. It examines the available options for torque and speed transformation, that is belts, chains, gears, and electric and hydraulic drives, and evaluates these for both constant and variable ratio drives.

Contents
Introduction
The Drive
Drive Functions

Torque and Speed Transformation
Synchronisation of Motion
Connection of Offset Shafts
Torque Control
Variable Speed
Torque Matching

Drive Matching
Determining the Drive Power
Determining the Drive Ratio and Torque
Constant Speed, Constant Torque Drives
Variable Speed, Constant Torque
Variable Speed, Variable Torque
Drive Options for Fixed Ratio Drives
Comparison of Mechanical Drives
Belt Drives
Flat Belts
V-Belt Drives
Toothed Belt Drives
Chain Drives
Friction Drives
Drive Options for Variable Ratio Drives
Multi-Speed Gear Drives
Automatic Gearboxes
Mechanical Continuously Variable Transmissions (CVT)
Hydrostatic Drives
Hydrodynamic Drives
Variable "Ratio" Electric Drives
Relative Costs of Alternative Drive Systems
Fixed Ratio Drives
Variable Ratio Drives
Constant Power
Constant Torque (Variable Speed)
Summary of Drive System Characteristics
Appendices
Characteristics of Prime Movers and Secondary Motors
Secondary Drives
Asynchronous AC motors
DC Motors
Heat Engines
Internal combustion (IC) Engines
Steam Turbines
Gas Turbines

Index
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SYNOPSISThis Module describes the functions of a gearbox as the link between driving and driven devices. It gives guidance on the specification and selection of the gearbox, and whether it should be a proprietary or custom-made design. Typical proprietary gearbox types are shown, with some price (1990) indications.

CONTENTS

Functions of gear drives
Transformation of torque and speed
Synchronisation of motions
Right angle drives
Special features
Features of gear systems
Notation
Transmission ratio i
Transmitted power P
Transmitted torque T
Mechanical arrangement
Referred inertias
Gear types
General
Spur gears
Helical gears
Bevel gears
Worm gears
Hypoid gears
Spiroid gears
Gearbox specification
General
Output speed and torque
Input speed and torque
Configuration
Shaft connections
Environmental conditions
Transmission error
Backlash
Vibration and noise
Other factors
Propriefary gears and gearboxes
The case for proprietary designs
Proprietary loose gears
Proprietary instrument gearboxes
Proprietary servo actuator gearboxes
Proprietary industrial gearboxes
General
Helical gear units
Bevel-helical units
Worm gear units
Epicydic gearboxes
Other types of gearbox
Custom-made gears and gearboxes
Installation of gearboxes

General
Alignment
Vibration and noise
Cooling
Access
Design policy
Safety factors
Design life and duty cycle

Acknowledgements and References
Appendix: Nomograms for backlash

Index
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Module 3 - BASIC GEAR GEOMETRY

Author:	Dr. Hellmuth Kohler of Sheffield University
Pages:	67
Tables:
Figures:	17
References:
Price:	(Modules 1-6 inclusive) Go to BGA Shop to Order

SYNOPSISThis module introduces the geometry of involute gears. Uniform motion transmission between two shafts defines cams of involute shape. Involute form tooth flanks allow simple gear definitions, and manufacture by the generation principle.

The dimensions of gears specified by chosen values of tooth number, size parameters, and tooth alignment (helix angle) are found, and the centre distance at which such gears mesh together in pairs is determined.

CONTENTS

Motion transmission
The Involute
Mathematical description of the involute - the 'inv a' function
Involute function calculations
The involute tooth form gear
Base pitch pb and base diameter d_b
Tooth thickness 's'
The infinitely large gear - the rack
The basic rack concept
Module
Diametral pitch
Rack flank angle

Rack generation of gear tooth forms
Simple spur gears
The spur gear reference circle Tip diameter
Root diameter
Addendum and dedendum

General spur gears
Rack displacement factor 'x' (addendum modification coefficient)
General spur gear dimensions for non-zero 'x'
Tip diameter
Root diameter
Permissible parameters of a gear
Graphical recommendations for x
Helical gears
The transverse pitch and the helical gear reference circle
Tip diameter
Root diameter
Permissible parameters of a helical gear (limits on x and x)
Lead and helix angles
Reference helix angle
Variation of helix angle with radius
Axial pitch
Base helix angle
Tooth thickness
Arc thickness on the reference circle
The relationships between st_ref s_tb and s_ty
Transverse and normal tooth thicknesses
Helical gears - the equivalent virtual spur gear
Involute spur and helical gear PAIRS
Working pressure angle _tw
Pitch circles (meshing or working circles)
Centre distance

Unmodified spur gears (x = 0)
Gears in general
Using the equations
A simple method for = 20°

Practical values of the addendum modification coefficient sum x = (x₁+ x₂)
Allocation of x between the gear pair
Conditions for good continuity of tooth action
Contact ratio
Active profile
Single pair and double pair contact
Formula collection

Index
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Module 4 - DESIGN AND STRESS ANALYSIS OF SPUR AND HELICAL GEARS

Author:	Mr Dieter Hofmann - Gear Design Unit University of Newcastle
Pages:	120
Tables:	28
Figures:	44
References:
Price:	(Modules 1-6 inclusive) Go to BGA Shop to Order

SYNOPSIS This module introduces the design of involute spur and helical gears. In Part I it deals with the specification of gears, gear load histograms, gear reliability, metallic and non-metallic gear materials and their fatigue properties.

The sizing of gears for a specific duty using an approximate synthesis method is outlined. In Part II (Section 4.8 onward) the stress analysis to current Gear Standards is introduced, and the stress analysis of a known pair of gears using a method based on BS 436(1986) and ISO/DIN 3990(1987) demonstrated. The derivation of basic stressing formulae is appended, as are some relevant extracts from standards.

CONTENTS

Introduction

Part 1

Specification, Design Life, Reliability
Design Load
Design Load based on Application Factor K_A
Design Load based on Load Histograms
Calculation of Equivalent Load
Example 4.1
Example 4.2
Gear Reliability
Relationship between stress, strength, reliability
Safety Factors for Stress, S_F and S_H
Selection of Gear Materials and Permissible Stress Levels
Steel Gears
Steel Gears - Heat Treatment
Steel Gears - Fatigue strength
Steel Gears - Material costs
Steel Gears - Permissible stress
Non-metallic Gears
Non-metallic gears - Physical Properties
Non-metallic gears - Permissible Stress
Basic Design Decisions
Spur or Helical Gears
Ratio Split
Facewidth Ratio
Gear Accuracy
Sizing a Metallic Gear Pair - First Estimate
Specification
Permissible Stress
Permissible Surface Stress
Permissible Bending Stress
Facewidth
Approximate Gear Sizing for Contact Stress
Centre Distance not prescribed
Centre Distance fixed
Check of minimum number of teeth on pinion
Minimum module
Approximate Gear Sizing for Bending Strength
Check of Face-Load Factor K_Hß
Sizing a Non-Metallic Gear Pair - First Estimates
Example, Approximate Sizing
Specification
Permissible Stress
Facewidth
Sizing the Gear for Contact Strength
Check of Minimum Module for Strength
Selecting a Helix Angle
Check of Minimum Number of Teeth
Check of Required Accuracy
Preliminary Gear Specification

Part 2

Gear Stress Analysis
Nominal Contact (Hertzian) Stress, H_o
Zone Factor, Z_H
Elasticity Factor, Z_E
Contact Ratio Factor, Z_E
Helix Angle Factor, Z_ß
Nominal Bending Stress, _Fo
Form and Stress Factor, Y_FS
Contact ratio Factor, Y_E
Helix Angle Factor, Y_ß
Real Contact and Bending Stress, _H
Dynamic Factor, K_V
Face Load Distribution Factor, K_Hß, K_Fß
Face Load Distribution Factor for Contact Stress, K_Hß
Face Load Distribution Factor for Bending Stress, F_Fß

Transverse Load Distribution Factor, K_H, K_F
Example, Stress Analysis
Nominal Contact Stress, _Ho
Nominal Bending Stress, _Fo
Real Contact and Bending Stress, _F, _H
Dynamic Factor, K_V
Face Load Distribution Factor, K_Hß, K_Fß
Transverse Load Distribution Factor, K_H, K_F
Safety Factors for Contact Stress
Safety Factors for Bending Stress
Design Refinement
Revised Size for Contact Strength
Revised Size for Bending Strength
Gear Stress Analysis to Gearing Standards [BS 436 Pt.31986, DIN 3990 Pt.l-51987, ISO 6336 (Draft)]
Comparison of Gear Fatigue Strength
Comparison of Factors of Safety
Formulae
Literature
Appendices
Derivation of Gear Stress Formula
Root Bending Stress
Contact Stress
Gears as 3 Dimensional Loaded Structures and Lead Correction
Mesh Stiffness and Deflection
Quantifying the Effect of Misalignment
Lead Correction and Crowning
Lead Correction
Crowning
Extracts from BS 436 Pt.2 (1970)
Results of Gear Stress Analysis to BS 436 Pt.3 (1986) and ISO/DIN 3990 (1987)

Index
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Module 5 - GEARBOX DESIGN

Author:	Dr. Hellmuth Kohler of Sheffield University
Pages:	50
Tables:	6
Figures:	17
References:	35
Price:	(Modules 1-6 inclusive) Go to BGA Shop to Order

SYNOPSIS This module introduces the overall design of the gearbox to house the specified gears.

The loads which the gears transmit to the gearcase are found, the strength and deflection of shafts and gearcase considered, and the various elements which are necessary to complete the design of the complete transmission are reviewed.

CONTENTS

The complete gearbox
The gearcase - overview of functional aspects
Detailed consideration of the various elements
Power and torques
Tooth forces in a gear pair
Forces on bearings
Illustrative example
Other forces influencing gearbox design
Connections to the gearbox
Inertia and gyroscopic forces
Bearing forces due to system transients
Shaft design
Mounting of gears on shafts
Features of gear mounting methods
Shaft strength and stiffness
Stress concentration factors
Detailed design of wheel and pinion
Shaft location - bearings and housings
Rolling contact bearings
Rolling bearing lubrication
Plain (hydrodynamic) bearings
Bearing housings
Interfaces to connected system components
Coupling to the attached machinery
Shaft seals
Casing design
Types of gearcase
Materials
Strength and stiffness
Simple model of gearcase - design to achieve adequate stiffness
Oil containment, gaskets
Provision for mounting,1ining up, lifting and assembly
Oil supply systems for gears and bearings
Choice of gear lubricant
Type of lubrication system
Splash or dip system
Spray lubrication and oil circulation systems
Oil filtration
Oil sprayers
Excess oil - a noise hazard
Cooling systems - overall and oil cooling
Cooling by natural convection and radiation
Assisted cooling
Thermal distortions
Maintenance provision
Condition monitoring
Laying on of hands
Temperature monitoring
Oil condition monitoring
Vibration monitoring
References

Index
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Module 6 - MANUFACTURE AND METROLOGY OF SPUR AND HELICAL GEARS

Author:	Prof. Bob Munro at Huddersfield University
Pages:	44
Tables:
Figures:	39
References:
Price:	(Modules 1-6 inclusive) Go to BGA Shop to Order

SYNOPSIS This module gives guidance on the information that the gear designer should know, so as to specify what has to be made. It briefly describes some of the more common manufacturing processes for spur and helical gears, but is not intended to be a detailed description of gear manufacture.

This Module makes use of a number of gear formulae, all of which are explained, and in many cases derived, in Module 3.

CONTENTS

Reference axis
Basic manufacturing information needed
General
Tooth module m
Reference diameter dref and helix angle ß
Base circle diameter d_b
Depth of insertion of cutter and tooth thickness
Tolerance considerations
General
Rating
Kinematic accuracy
Backlash
Cost
Specification of tolerances
Classification
Elemental tolerances
Involute profile tolerances
Alignment (helix/lead) tolerances
Pitch tolerances
Radial runout tolerances
Composite tolerances
Dual flank composite tolerances
Single flank composite tolerances
Tooth thickness and backlash
Gear quality grades
Supplementary information
Classification of manufacturing processes
Classification by principle used
Generation
Form machining
Form moulding
Classification by tool type
Classification by machine construction
Survey of manufacturing processes
The hobbing process
The shaping and planing processes
Grinding processes for finishing
The tooth fillet Flat disc grinding principle (Maag)
Involute helicoid principle (Reishauer)
Single conical wheel principle (Hofler, Niles)
Form grinding (Liebherr, Pfauter-Kapp, Maag)
Producing hardened gears
General
Using the shaving process
Grinding
Hard (skive) hobbing
Choice of process
General
Availability
Expertise
Quantity and variety
Accuracy
Cost and machining times
Small involute and heliX modifications (reliefs)
Workholding
General
Eccentric running
Cutting distortion
Acknowledgements and references
Appendix 6.I Drawing information
Appendix 6.2 Start of active profile and length of roll
Appendix 6.3 Tooth thickness calculations
Appendix 6.4 Glossary of gear manufacturing processes

Index
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