CHAPTER 1 page 1..., ATURE, NOTATION AND

CONVENTIONS

TYPES OF GEAR1.1 Spur Gears1.2 Helical Gears1.3 Double-Helical Gears1.4 Crossed Helical Gears1.5 Conical Involute Gears1.6 Bevel Gears1.7 Spiral Bevel Gears1.8 Hypoid Gears1.9 Worm Gears

2.7 Relationship of Path of Contact to ToothProfile

2.8 Conjugate Profiles2.9 Progressive and Retrogressive Contact2.10 Corner or Edge Contact2.11 Concurrent Contact2.12 Interference and Undercutting2.13 Counterpart Racks2.14 I ntermati ng Series2.15 Straight-sided Rack: Involute Teeth2.16 Profile Shift (or Addendum Modification,

or Correction) of Involute Gears2.17 Involute Tooth Action at "Extended

Centres"

NOMENCLATURE1.10 Pitch: Pitch Circles1.11 Pitch Line1.12 Pitch Cylinders: Pitch Cones

I Tooth Profile Elements, Lengthwise Tooth Elements

Planes and AnglesTransverse, Normal and Axial PitchInvolute Base Dimensions

.," Reference, Basic, Nominal,Design and Standard Dimensions

,.19 Other Terminoloqy

CYLINDRICAL PITCH SURFACES2.18 Kinematic Pitch Surfaces of Spur Gears2.19 Tooth Spirals2.20 Crossed Pitch Cylinders2.21 The Normal Imaginary Rack2.22 Contact between Helical Tooth and Rack2.23 Involute Helicoid2.24 Zone of Contact2.25 The Common Normal: General Case2.26 Contact in the Normal Plane2.27 Contact of Crossed Helical Gears2.28 Conical Involute Gears

NOT A TIONGeneralPrinciples of the Present SystemDirections, LinearDirections, AngularShaft and Helix Angles

2 page 23

ES OF TOOTHT

CONICAL AND OTHER PITCHSURFACES

2.29 Pitch Surfaces of Straight Bevel Gears2.30 Common Pitch Plane and Tooth Spirals

of Spiral Bevel Gears2.31 The Common Normal of Bevel Gears2.32 The Imaginary Crown Wheel2.33 Cylindrical-gear Basis of Worm Gear

Action2.34 HvnArboloidal and HVDOid Gears

CHAPTER 3 page 35PRINCIPLES OF GEAR-TOOTHGENERATION

3.1 Process Categories3.2 Generation from a Rack: Spur Gears3.3 Helical Gear Planing3.4 Generation-grinding

.1 Angular Velocity Ratio

CONTACT IN A PLANEI Kinematic Pitch Circles

, Circular Pitch and Tooth Thickness.The Common Normal

Pressure AngleI Cycle of Contact: Path of Contact

Pitch Diameters and Standard CentreDistance

4.39 Crossed Helical Gears at Extended Centres

CONICAL INVOLUTE GEARS4.40 Principles4.41 Basic Dimensions of Conical Involute Gears

3.5 Worm Grinding3.6 Gear-shaper Processes3.7 Hobbing: Spur and Helical Gears3.8 Hobbing: Worm wheels3.9 Generation of Straight Bevel Gears3.10 Generation of Spiral Bevel and Hypoid

Gears3.11 Gear Shaving: Honing: Lapping3.12 Generating-cutter Forms3.13 Tooth Layout Procedure

BEVEL GEARS4.42 Pitch Cones: Pitch Angles4.43 Tooth-numbers: the Crown Wheel4.44 Virtual Gears4.45 Tooth-form: Straight Bevels4.46 Tooth-form: Spiral Bevels

WORM GEARS4.47 Worm Geometry

CHAPTER 4 page 46

ANAL YTICAL GEOMETRY

CHAPTER 5 page 76PRINCIPLES OF MEASUREMENT

5.1 General5.2 Principal Types of Error5.3 Pitch Errors5.4 Measurement of Pitch Errors5.5 Effect of Eccentricity on Apparent Pitch

Error5.6 The Significance of Pitch Errors5.7 Departures from Involute Profile5.8 Measurement of Involute Profiles5.9 Effect of Eccentricity on Profile Errors5.10 Error of Base Diameter, Pressure Angle or

Base Pitch5.11 Characteristic Involute Diagrams5.12 Lead Measurements5.13 Periodic Errors in Generation: Undulations5.14 Errors due to Faulty Setting of Cutters5.15 Measurement of Involute Helicoids along

the Generating Line5.16 Tooth-thickness Variations5.17 Composite Errors5.18 The Rolling Gear Test5.19 Master Worms5.20 Kinematic and Transmission Errors5.21 Visual Check of Tooth Bearing5'.22 Recording Tooth Surface Condition

CHAPTER 6 page 88SPUR GEARS

6.1 Pitch6.2 Tooth Proportions: Basic Racks6.3 Fine Pitch Gears6.4 Profile-shift: Pitch Diameter: Nominal

T ooth-form6.5 Limits of Profile-shift Coefficient6.6 Crest Width: Topping6.7 Radial Dimensions of Gears having

Nominal Tooth-form

CENTRE DISTANCE RATIO ANDTOOTH DA T A

6.8 Basic Data: }:;T and }:;I<: Ratio

SPUR GEARS4.1 Generation and Properties of I nvol utes4.2 Involute Geometry: Roll Angle: Polar Angle4.3 The Involute Function: Involute Polar

Coordinates4.4 Pitch Diameter: Base Diameter:

Generating Rack: Profile-shift: NominalTooth-form: Undercutting

4.5 Circular Thickness and Space-width4.6 Subtended Angles4.7 Base Pitch: Base Circular Thickness :

Thicknesses at other Radii: Crest Width4.8 Rectangular Coordinates4.9 Changes in Tooth-thickness4.10 T ooth-thickness Modification Coefficient4.11 Chordal Thickness4.12 Tangent Length: Roll Distance: Roll Angle4.13 Base Tangent (Span Gauging)4.14 Gauging IIOver Pins": Pitch-circle Pin:

Mean-depth Pin: Tip-circle Pin4.15 Magnification Factor4.16 Modes of Generation of an Involute

Helicoid4.17 Normal, Transverse and Axial Pitches4.18 Pressure Angles4.19 Nominal Tooth-form4.20 Base Dimensions of Involute Helicoid4.21 The Normal Helicoid4.22 Tangent Plane4.23 Normal Plane Section: Virtual Number of

Teeth4.24 Thickness Dimensions in Normal Plane4.25 Data for Axial Section4.26 Coordinates of Axial Section4.27 Base Tangent4.28 Gauging over Pins: Location of Pin:

Contact Angle: Magnification4.29 Pin-gauging with Odd Number of Teeth

SPUR AND HELICAL GEAR PAIRS4.30 ~ T and ~I<4.31 Standard Centre Distance C4.32 Extended Centre Distance Ce c-4.33 Extension Ratio Qe4.34 Extended and Close-mesh Pressure Angles4.35 Backlash at Nominal Thickness Zo4.36 Nominal Close-mesh Centre Distance

Cm nom4.37 Effect of Tooth-thickness Change on

Close-mesh Centre Distance4.38 Crossed Helical Gears: Helix Angles,

6.57 Design of Gear Blanks6.58 Data on Spur Gear Drawings

CHAPTER 7 page 128HELICAL GEARS

7.1 Pitch: Helix Angle: Conversion of Pitches7.2 Pitch Diameter: Transverse Pressure

Angle: Base Diameter: Base Helix Angle:Lead

7.3 Tooth Proportions7.4 Profile Shift: Nominal Tooth-form7.5 Radial Dimensions7.6 Virtual Numbers of Teeth: Normal Section7.7 Crest Width: Topping ,7.8 Facewidth: Axial Contact Ratio

BASIC DATA7.9 Standard Centre Distance C7.10 Extended Centre Distance Ce: Extension

Ratio Qe7.11 Distribution of ~k into kp and kw7.12 Choice of Basic Data, ~/{ = 0 (Standard

Centres)7.13 Choice of Basic Data, ~/{.* 0 (Extended

or Closed Centres)7.14 Round-number Helix Angles7.15 Simple Trains7.16 Compound Trains

Standard Centre Distance cExtended Centre Distance CeExtension Ratio Qe: Extended Pressure

Angle I/leExtended Pitch DiametersChoice of Tooth-numbersThe choice of ):::k: General):::k for Stipulated Centre Distance):::k for Alternative Tooth-sums):::k for Close-meshDistribution of kp and kw: GeneralChoice of kp and kw when ):::k = OChoice of kp and kw when ):::k * ONegative Values of ):::kSpeed-increasing GearsSimple TrainsInternal Gearing

CENTRE DIST ANCE AND BACKLASHConventions for Expressing Backlash andChanges of Tooth-thicknessNominal ThicknessBacklash at Nominal Thickness ZoNominal Backlash: Backlash Allowance:Tooth-thickness ToleranceBacklash Allowance in Simple TrainsBacklash Range: Minimum-backlash

RequirementNominal Close-mesh Centre DistanceCm nomValues for Nominal Backlash andTooth-thickness Tolerance BACKLASH AND BACKLASH

ALLOWANCES7.17 Conventions: Backlash7.18 Nominal Thickness7.19 Backlash at Nominal Thickness Zo7.20 Nominal Close-mesh Centre Distance

Cm nom7.21 Nominal Backlash Znom7.22 Backlash Allowance7.23 Backlash Allowances in Simple Helical

Trains7.24 Tooth-thickness Tolerances gtol

TOOTH- THICKNESS GAUGINGDIMENSIONS

7.25 Chordal Thickness7.26 Span:gauging7.27 Gauging Over Pins or Balls, External Teeth7.28 Gauging Internal Helical Teeth Between

Balls7.29 Roll-test Specifications for Helical Gears

REFINEMENTS OF SPECIFICATION7.30 General7.31 Profile and Helix Control.7.32 Start of Active Profiles: Roll Distances :

Roll Angles

CROSSED HELICAL GEARS7.33 Shaft and Helix Angle7.34 Centre Distance and Basic Data7.35 Preliminary Choice of Helix Angles:

Diameter Ratio Qd7.36 Choice of Tooth-numbers and Pitch7.37 Adjustment of Helix Angles

~

TOOTH- THICKNESS GAUGINGDIMENSIONSMagnification Factor M"Equivalent K"Chordal Thickness and Chordal HeightConstant ChordSpan-gauging: External TeethSpan-gauging: Internal TeethGauging 'lOver Pins", External GearsGauging "Between Pins", Internal GearsPin-gauging Involute SplinesThe Rolling-gear Test: Scope: DatumCentre DistanceRoll-test Specification, Product-gear PairRoll-test Specification, with Master Gear

REFINEMENTS OF SPECIFICA TIONTolerance and Tolerance Systems, GeneralTip-easingProfile ModificationStart of Active Profile: Form DiameterRoll Distances and Roll Angles :Completion of P~ofile DiagramsMinimum Tip Diameter of Master GearStart of Rack-generated Profile :Fillet-radius GeometryFillet Curves: Protuberance HobsTip Chamferin9-Rounding or End-chamferingCrowning

GENERALChoice of Facewidth

I

7.38 Virtual Numbers of Teeth: Profile-shift7.39 Examples7.40 Nominal Backlash and Tooth-thickness

Tolerance ,-

7.41 Backlash at Nominal Thickness andBacklash Allowance

7.42 Close-mesh Centre Distance7.43 Facewidth of Crossed Helical Gears7.44 Intermating Crossed Helical Gears7.45 DrawinQ Data. Helical Gears

CHAPTER 8 page 142BEVEL GEARS

9.7 Base Dimensions of the Thread Surface9.8 Worm Thread Proportions9.9 Depth Modification9.10 Preferred Values of m and q9.11 Choice of i, T, q and m9.12 Shafts at Right Angles9.13 Facewidth of Worm: End-finish: Balance9.14 Profile-shift Coefficient9.15 Axial Section of Worm Threads9.16 Ball-gauging Worm Threads9.17 Span-gauging Dimensions9.18 Constant-chord Thickness of Worm

Threads9.19 Extended or Closed Centre Distance9.20 Radial Dimensions of Worm wheels9.21 Facewidths of Worm wheel : Rim Sections9.22 Backlash9.23 Tooth Contact Marking: Entry Gap9.24 Drawing Data. Worm Gears

TOOTH-NUMBERS AND PITCH8.1 Tooth-numbers8.2 Pitch8.3 Pitch Angles8.4 Cone Distance and Facewidths8.5 The Generating Crown Wheel8.6 VirtLJiil Tooth-numbers CHAPTER 10 page 166

FIXED-AXIS GEAR TRAINSSTRAIGHT BEVEL GEARS

8.7 General8.8 Tooth Proportions and Pressure Angle8.9 Profile-shift8.10 Choice of Profile-shift Coefficient8.11 Principal Dimensions, Straight Bevel Gears8.12 Mounting Distance8.13 Nominal Circular Thickness:

Tooth-thickness Modification: CrestWidth

8.14 Tooth Angle8.15 Backlash8.16 Tooth-thickness Tolerance8.17 Chordal Thickness on Pitch Circle8.18 Constant Chord8.19 Tooth Bearing: Crowning8.20 Refinements of Tooth Profile

10.1 Types of Gear Train10.2 Tooth-number Calculations, General10.3 Conjugate Fractions10.4 The Brocot Table10.5 Derived Conjugate Fractions10.6 Derivation of Intermediate Fractions10.7 Example10.8 The Factor Table10.9 To Find a Fraction Conjugate to a

Given Fraction10.10 The Angular Vernier10.11 Link-mounted Gear Trains10.12 Closed Trains10.13 Assembly of Multiple-contact Trains10.14 Multi-ratio Trains10.15 Tooth Contact Frequency10.16 Skeleton Diagrams10.17 RefArAncA~

CHAPTER 11 page 180PLANETARY TRAINS

11.1 Nomenclature11.2 Algebraic Signs11.3 Notation

SPIRAL BEVEL GEARS8.21 General8.22 Spiral Angle: Hand of Spirals8.23 Face Contact Ratio8.24 Influence of Form of Tooth Spiral8.25 Tooth Proportions: Gleason-type Spiral

Bevel Gears8.26 Oblique Spiral Bevel Gears8.27 Klingelnberg "Palloid" Spiral Bevel Gears8.28 Tooth-thickness Dimensions8.29 Hypoid Gears8.30 Drawing Data, Bevel Gears

CHAPTER 9 page 153WORM GEARS

-9.1 General9.2 Worm Thread Forms9.3 The Use of the Module9.4 The Designation "tITlqlm" : The

Corresponding Spur Gears9.5 Lead Angle: Lead: Normal Module9.6 Worm Thread Form: Basic and

Generating Racks

SIMPLE PLANET ARY TRAINS11.4 Typical Arrangements11.5 Speed-ratios by the Tabular Method11.6 The Method of Fixed-carrier Ratios11.7 The Sun/Planet/Annulus Train11.8 High-ratio Trains: Conjugate Sun/Planet

Ratios11.9 Direction of Power-flow: Fixed-carrier

Efficiency11.10 Torque Distribution11.11 Epicyclic Efficiency11.12 I nternally-transmitted Power11.13 The Simple Differential

COMPOUND AND COUPLEDPLANET ARY TRAINSCompound Planetary TrainsExamples of Compound Planetary TrainsCoupled Planetary TrainsThe Compound DifferentialCoupled DifferentialsDifferential Infinitely-variable Gears

DETAIL DESIGNChoice of Tooth-numbers for AssemblyProfile-shift of Sun/Planet/Annulus TrainsPlanet SpeedFrequency of Load-application"Float"

0 ._0. 12 page 200

TACT GEOMETRY

Modes of Relative Surface MotionContact-motion CharacteristicsContact-velocity RelationshipsSimulation of Tooth-contact Conditions

13.2 Tangential Load, Bevel Gears13.3 Tangential Load, Worm Gears13.4 Load per Inch of Facewidth, Spur and

Helical Gears13.5 Equivalent Load per Inch of Facewidth,

Bevel Gears13.6 Resultant and Radial Tooth-loads, Spur

Gears13.7 Resultant, Radial and Axial Tooth Loads,

Helical and Worm Gears13.8 Resultant, Radial and Axial Loads,

Straight Bevel Gears13.9 Resultant, Radial and Axial Tooth Loads,

Spiral Bevel Gears13.10 Contact-line Loading, Spur Gears13.11 Contact-line Loading, Helical Gears13.12 Contact-line Loading, Bevel Gears13.13 Tooth Deflection13.14 Combined Deflection, Single-pair Contact13.15 Double-pair Contact13.16 Profile Modification: Static Transmission

Error13.17 Stress-increase due to Simple

Malalignment13.18 Bending and Torsional Deflection of

Pinions13.19 Dynamic Loading13.20 References

CHAPTER 14 page 227BEARING LOADS

14.1 General14.2 Plane of Reference14.3 Spur Gears, Straddle Mounted14.4 Spur Gears, Overhung14.5 Single-helical Gears, Straddle Mounted14.6 Single-helical Gears, Overhung14.7 Bevel Gears14.8 Worm Gears and Crossed Helical Gears14.9 Shafts Carrying Two or More Gears14.10 Intermediate Shafts14.11 Torque Reaction

CHAPTER 15 page 234GEARS IN SERVICE

15.1 General15.2 Practical Causes of Gear Failure15.3 Classification of Gear-tooth Failures

SPUR GEARSContact Ratio at Standard Centres :Addendum Contact RatioContact Ratio at Extended Centres :Contact-ratio Decrement: ExtensionContact-ratio FactorAddendum Contact-ratios of EngagementAddenda of Engagement at ExtendedCentres: Addendum RatioInternal Gears: Contact Conditions: TipInterference: TrimmingRadii of Curvature, General CaseRadii of Curvature, Involute ProfilesContact Velocities, General CaseContact Velocities, Involute Gears

Equivalent Cylinders

HELICAL GEARSZone of Contact: Inclination of Contact LineTransverse, Normal and Axial ContactRatiosCalculation of Contact RatioPressure Angles of Engagement atExtended CentresTrue Length of Contact LineFractional Axial Contact RatiosRadii of Curvature of Helical TeethContact Velocities of Helical GearsContact Velocities of Crossed Helical GearsBevel Gears: The Virtual Spur or HelicalGears .Zone of Contact, Involute Helicoid Worm,~ = 90 degreesContact Velocities of Worm GearsCurvature

, -" 13 page 216

TOOTH LOADS

Tangential Load, Spur and Helical Gears

GROUP I: FRACTURES15.4 Typical Bending-fatigue Fracture15.5 Fatigue Failure Accelerated by

Lengthwise Maldistribution15.6 Fatigue Failure and Fillet Radius15.7 Fatigue Failure Induced by Careless

Dressing or Tooth-rounding15.8 Grinding Cracks15.9 Fractures Originating at Damaged Area

of Surface15.10 Tip Crumbling15.11 Rim Fractures15.12 Worm wheel Tooth Fractures

GROUP II: SURFACE FAILURES DUETO INTERNAL STRESS

15.13 Pitting15.14 Pitch-Iine Fissure of Case-hardened Gears15.15 Flaking and Case-crushing15.16 Fine Flaking15.17 Smooth Abrasion15.18 Plastic Flow: Rippling

GROUP III: SURFACE DAMAGEFOLLOWING OIL-FILM BREAKDOWN

15.19 General15.20 Scuffing: Scoring: Tearing15.21 Ridging and Grooving15.22 Low-speed Wear

17.11 Zone Factor17.12 Criteria of Contact-loading, Worm Gears17.13 Contact Stresses, Crossed Helical Gears17.14 Sub-surface Stresses: Case-depth17.15 General17.16 Pressure/Temperature/Viscosity

Characteristics17.17 Oil-film Entrainment and Pressure

Distribution17.18 Film Thickness17.19 Phenomena within the Oil-film17.20 The Coefficient of Friction17.21 Temperature Flash17.22 Scuffing Criteria17.23 Influences of Contact Phenomena on

Contact-stress Criteria17.24 References

CHAPTER 18 page 276GEAR MATERIALS

GEAR NOISE15.23 Types of Gear Noise15.24 Origins of Gear Noise15.25 Noise Diagnosis15.26 The Attack on GAar Noi~A

CHAPTER 16 page 248BENDING STRESS

18.1 General18.2 The Significance of the Conventional

Properties18.3 Cast Iron18.4 Carbon Steels18.5 Alloy Steels18.6 Case-hardened Steels18.7 Nitrided Steels18.8 Flame-hardening18.9 Induction Hardening18.10 Non-ferrous Metals18.11 Non-metallic Materials18.12 Surface Treatments for Steel Gears18.13 Residual Stresses18.14 Surface Effects

16.1 General16.2 Nominal Stress16.3 The Choice of Critical Section16.4 The Choice of Load-point16.5 Stress-concentration .16.6 Design Strength Factor: Tip Strength

Factor16.7 Calculation of Tip Strength Factor:

Radius of Curvature at the Stress-point16.8 Graphical Determination of Tip Strength

Factor16.9 Calculation of Strength Factor for Other

Load-poi nts16.10 Design Strength Factors, Spur Gears16.11 Strength Factor, Straig ht Bevel Gears16.12 Strength Factor, Helical Gears16.13 Effect of Axial Contact Ratio16.14 Strength Factor, Spiral Bevel Gears16.15 Effects of Thickness Modification16.16 Tooth Overhang16.17 Bending Stresses and Deflection,

Wormshafts16.18 Stresses in Worm wheel Teeth

CHAPTER 17 page 259CONTACT STRESS CRITERIA

FATIGUE CHARACTERISTICS18.15 Fatigue Strength in Bending18.16 The S-N Curve18.17 Confidence-limits18.18 Characteristics of S-N Curves18.19 Analytical Treatment of the S-N Curve18.20 Variable Loading: Cumulative Fatigue

Damage1.8.21 The Sb-N Curve at Low Values of N18.22 Resistance to Reversed Loading18.23 Effects of Stress-concentration ;

Stress-concentration Factor18.24 The "Size-effect"18.25 Variations in Bending-fatigue Properties18.26 Fatigue under Contact Stress: Pitting18.27 References

CHAPTER 19 page 290CALCULATED STRESSES ANDDESIGNED LIFE

19.1 General19.2 Loading, Spur and Helical Gears19.3 Calculated Bending Stress, Spur Gears19.4 Calculated Contact Stress, Spur Gears19.5 Calculated BendinQ Stress, Helical Gears

17.1 General17.2 Hertzi~n Compressive Stress17.3 The Criterion "Sc"17.4 The Criterion "K"17.5 Calculation of Sc, Spur Gears17.6 Calculation of K and Sc, Helical Gears17.7 Calculation of K and Sc, Straight Bevel

Gears17.8 Calculation of K and Sc, Spiral Bevel

Gears17.9 Effect of Axial Contact Ratio17.10 Effect of Lengthwise Maldistribution

iCalculated Contact Stress, Helical GearsLoading, Bevel GearsCalculated Bending Stress, StraightBevel GearsCalculated Contact Stress, StraightBevel Gears

.." Calculated Bending S;tress, Spiral BevelGears

.11 Calculated Contact Stress, Spiral BevelGearsLoading, Worm GearsCalculated Bending Stress, Worm wheelCalculated Contact Stress, Worm wheelCalculated Bending Stress, Wormshafts

I Loading and Contact Stress, CrossedHelical Gears

I Calculated Stresses in Hypoid Gears

20.18 Loading Criteria20.19 Allowable Stresses: Spur, Helical and

Bevel Gears20.20 Allowable Stresses: Worm Gears20.21 Life Rating20.22 Vehicle Transmissions: Mileage Rating20.23 Basic Stress: Endurance Stress :

Application Factor: Stresses in MetricUnits

20.24 Bending Stress-concentration Factor20.25 Lubrication Factor20.26 Some Application Factors from Practice

STRESS-COMPARISON20.27 Stress-comparison, General: Unfactored

Stress20.28 Speed-factored Stresses20.29 Life-factored Stresses20.30 Stress-comparison by Application Factor20.31 The Analysis of Application Factors20.32 The Analysis of Test Data20.33 Comparison with Practice in the Rating

of Rolling Bearings

CHAPTER 21 page 334LUBRICATION AND COOLING

21.1 Requirements of a Lubricating System

THE APPLICATION AND FLOWCONTROL OF LUBRICANT

21.2 Splash Lubrication21.3 Spray Lubrication21.4 Oi I Control

THE CHOICE OF LUBRICANT21.5 General21.6 The Economics of Lubrication21.7 The Choice of Lubricant21.8 Quantity of Lubricant

COOLING21.9 Rate of Heat Generation21.10 Heat Dissipation by Natural Convection21.11 Air-draught Cooling21.12 Liquid Cooling21.13 Temperature- Time Curves: Time Constant21.14 Prediction of Equilibrium Temperature21.15 Intermittent Running21.16 Estimation of Efficiency from

Temperature Rise21.17 Significance of Temperature Rise

LIFE CALCULA TIONSDesigned Life: Duty Cycle: Equivalent LifeReversing Load-directionMultiple ContactEquivalent Running Time and EquivalentLifeBlock Load DiagramDuty-cycle DiagramConstant Torque, Uniformly-varying SpeedConstant Speed, Uniformly-varying TorqueVarying Torque and SpeedGeneral Case of Varying Torque andSpeed

20 page 309STRESSES AND RATING

~

The Expression of Load-capacityBasic Stresses and Modifying Factors,GeneralLogarithmic Life Factors

RATING FORMULAEBasic Stresses in British StandardSpecificationsSpeed Factors for "Strength" in B.S.Specificatil.JnsEquivalent Basic Bending Stresses ofB.S.436: 1940Speed Factors for "Wear" in B.S.SpecificationsEquivalent Contact-stress Rating in B.S.SpecificationsRules of Lloyd's Register of Shipping

, N.C.B. Specification No. 383/1963-WindingEngine Reducti011 Gears

1 Horsepower Rating Formulae.The Four Ratings: Limiting Rating :

Design MarginFactor of Safety: Margin of SafetyThe Size Criterion C2. fBevel Gear Rating Formulae

, Worm Gear Rating: B.S. 721: 1963

DOMESTIC RA TINGS: The Domestic Stress Problem

,

CHAPTER 22 page 345EFFICIENCY AND TESTING

22.1 Instantaneous Efficiency, Spur Gears22.2- Efficiency over the Cycle of Engagement22.3 Tooth-loss Factor, Spur Gears22.4 Tooth-loss Factor, Internal Spur Gears22.5 Tooth-loss Factor, Helical Gears22.6 Tooth-loss Factors, Bevel Gears22.7 The Coefficient of Friction

APPENDIX 7 page 429CALCULATION SEQUENCES

22.8 Data for Calculating fL, Spur Gears22.9 Data for Calculating fL, Helical Gears22.10 Analysis of Efficiency Tests22.11 Condensed Formula for Tooth Loss22.12 Worm Gear Efficiency, Shaft Angle

90 degrees22.13 Efficiency when}:; ""' 90 degrees22.14 Coefficient of Friction, Worm Gears22.15 Efficiency of Crossed Helical Gears22.16 Irreversible Worm Gears

TESTING22.17 Significance of Efficiency and Efficiency-

loss22.18 Sources of Power Loss22.19 Relationships between Losses and

Efficiency22.20 Thermal Measurement of Efficiency22.21 Mechanical Measurement of Efficiency22.22 Closed-circuit Test Arrangements22.23 Calculation of Efficiency in Closed-circuit

Tests22.24 References

1 Profile-shift, tooth-thickness and back~sh,spur and helical gears

2 Crest-width and topping, spur and helicalpinions .

3 Radial dimensions, spur gear pair4 Radial dimensions, leads, helical gear pair5 Chordal dimensions, spur and helical gears6 Span-gauge dimensions, spur gears7 Pin-gauging dimensions, spur gears8 Span-gauge dimensions, helical gears9 Pin or ball gauging, helical gears

10 Contact ratio: spur, helical and crossedhelical and bevel gears

11 Roll angles and distances, spur and helical

gears12 Tooth and blank dimensions, straight bevel

gears12A Preliminary data, straight bevel gears, ~

not 90 degrees13 Tooth and blank dimensions, wormgearsAPPENDIX 1 page 358

ACCURACY OF CALCULATION

, .APPENDIX 2 page 359INTERPOLATION

APPEN DIX 8CHARTS

page 458

APPENDIX 3 page 361DESIGN CALCULATIONS INMETRIC UNITS

APPENDIX 4 page 366TRIGONOMETRICAL RELATIONSHIPS

APPENDIX 5 page 366ANGULAR MEASUREMENT

APPENDIX 6 page 367GEAR DESIGN TABLES

1 Tooth proportions2 Trigonometrical functions3 Involute functions (short table)4 Involute polar coordinates5 Functions of helix angle a6 Functions of number of teeth T7 Functions of profile-shift coefficient k8 Functions of extension ratio Qe8A Extension contact-ratio factor KD.8B Contact-stress conversion factor CK9 Addendum contact-ratio factor Kc

10 Span-gauging factor Kn11 Factor table12 Bevel gear and Brocot table13 Tooth-numbers in sun/planet/annulus

trains14 Interpolation coefficients B15 Helical contact-stress conversion factor CKH

1 Crest width, full-depth teeth, 1/1 = 20 deg.2 Chordal decrement and height increment3 Tip-circle pin diameter, full-depth teeth,

1/1 =.20 deg.4 Distribution of profile-shift5A Tip strength factors, 8.S. Class A2/858 Tip strength factors, full-depth teeth,

1/1 = 20 deg, shaved5C Tip strength factors, bevel gear teeth,

1/1 = 20 deg.5D Tip strength factors, stub teeth, 0.8 depth,

1/1 = 20 deg.6 Strength factors, 8.S. Class A2/8, ~k = 06A Strength factors, 8.S. Class A2/8, ~k = 0.57 A Contact ratios, full-depth teeth, 1/1 = 20 deg,

~k=O78 Contact ratios, full-depth teeth, 1/1 = 20 deg,

~k = 0.58 Logarithmic life factors9A Ratio QR/y = fillet radius/beam depth,

8.S. Class A2/898 QR/y, full-depth teeth, 1/1 = 20 deg, shavedgc QR/y, bevel gear teeth, 1/1 = 20 deg9D QR/y, stub teeth, 0.8 depth, 1/1 = 20 deg

10 Values of Cs for variable torql!e11 Values of Ca and Cr for variable torque

and speed12 Coefficients of friction13 Worm gear efficiency