agma 929-a06 calculation of bevel gear top land and guidance on cutter edge radius

8/15/2019 AGMA 929-A06 Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius

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AGMA INFORMATION SHEET(This Information Sheet is NOT an AGMA Standard)

A G M A 9 2 9 - A 0 6

AGMA 929- A06

AMERICAN GEAR MANUFACTURERS ASSOCIATION

Calculation of Bevel Gear Top Land and

Guidance on Cutter Edge Radius


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ii

Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius AGMA 929--A06

CAUTION NOTICE: AGMA technical publications are subject to constant improvement,

revision or withdrawal as dictated by experience. Any person who refers to any AGMA

technical publication should be sure that the publicationis the latest available from the As-

sociation on the subject matter.

[Tables or other self--supporting sections may be referenced. Citations should read: See

AGMA 929--A06, Calculation of Bevel Gear Top Land and Guidance on Cutter Edge

Radius, published by the American Gear Manufacturers Association, 500 Montgomery

Street, Suite 350, Alexandria, Virginia 22314, http://www.agma.org.]

Approved August 22, 2006

ABSTRACT

This information sheet supplements ANSI/AGMA 2005--D03 with calculations for bevel gear top land and guid-

ance for selection of cutter edge radius for determination of tooth geometry. It integrates various publications

with modifications to include face hobbing. It adds top land calculations for non--generated manufacturing me-

thods. It is intended to provide assistance in completing the calculations requiring determination of top landsand cutter edge radii for gear capacity in accordance with ANSI/AGMA 2003--B97.

Published by

American Gear Manufacturers Association500 Montgomery Street, Suite 350, Alexandria, Virginia 22314

Copyright © 2006 by American Gear Manufacturers Association

All rights reserved.

No part of this publication may be reproduced in any form, in an electronicretrieval system or otherwise, without prior written permission of the publisher.

Printed in the United States of America

ISBN: 1--55589--873--4

AmericanGear

Manufacturers Association


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AGMA 929--A06AMERICAN GEAR MANUFACTURERS ASSOCIATION

iii© AGMA 2006 ---- All rights reserved

Contents

Page

Foreword iv. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

1 Scope 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Symbols, terminology and definitions 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Input data 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Calculations 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography 38. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Annexes

A Additional equations from ANSI/AGMA 2005 --D03 18. . . . . . . . . . . . . . . . . . . . . .

B Stock allowance and standard cutter specifications 23. . . . . . . . . . . . . . . . . . . . .

C Spiral bevel example problem 24. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D Hypoid example problem 31. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Tables

1 Symbols and terms 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Input variables 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Symbols and terms from ANSI/AGMA 2005--D03, table 9 7. . . . . . . . . . . . . . . . .4 Gear rotation factor, k E 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Suggested defaults for input data 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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AGMA 929--A06 AMERICAN GEAR MANUFACTURERS ASSOCIATION

iv © AGMA 2006 ---- All rights reserved

Foreword

[The foreword, footnotes and annexes, if any, in this document are provided for

informational purposes only and are not to be construed as a part of AGMA Information

Sheet 929--A06, Calculation of Bevel Gear Top Land andGuidance on CutterEdge Radius.]

The Bevel Gearing Committee recognized the need for additional equations to aid in the

design of bevel gears. The equations for geometry factors found in the annex of

ANSI/AGMA 2003--B97 require detailed information on the proposed cutting tool before aproper calculation can be performed. In addition, the minimum top land thickness is

required to aid in determining the maximum case depth allowed on carburized bevel gears.

The equations required for these values were not published in AGMA documentation, but

could be found, for some cases, in the publications listed in the bibliography of this

information sheet. AGMA 929--A06 expands on those equations to include gears

manufactured with the face hobbing cutting method.

In the case of non--generated gears, the equations in this document may yield different

values forpiniontop landthicknesses andgear tooth depth at thetoe and heel than obtained

on some well known commercial software. The pinion top land thickness is reduced by

curvature added to the pinion, a natural consequence of the non--generated gear member

having no profile curvature on the teeth. For the gear member, the non--generating processcuts a rootline tangent to the gear root cone,a rootline which does notwrap around the root

cone as in the generated case. This leaves the toe and heel ends of the tooth slots shallow

compared to the generated gear case, and the gear tooth space at the ends of the teeth

narrower. The non--generated gear is the imaginary generating gear for the pinion. So the

pinion teeth, which fit in the non--generated gear tooth slots, are thinner at the ends than

their generated gear counterparts.

The cutter edge radii calculated in this document are based on the geometrical conditions

present and include a manufacturing gauging flat. Individual blade manufacturers have

standard blade edge radii and manufacturing tolerances for their products which should be

considered when sourcing non--standard radii. It is recommended to work closely with the

blade supplier to ensure design specifications and sourced product specifications areconsistent.

The first draft of AGMA 929--A06 was made in February, 1999. It was approved by the

AGMA Technical Division Executive Committee in August, 2006.

Suggestions for improvement of this document will be welcome. They should be sent to the

American Gear Manufacturers Association, 500 Montgomery Street, Suite 350, Alexandria,

Virginia 22314.


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v© AGMA 2006 ---- All rights reserved

PERSONNEL of the AGMA Bevel Gear Committee

Chairman: Robert F. Wasilewski Arrow Gear Company. . . . . . . . . . . . . . . . . . . . . .

Vice Chairman: George Lian Amarillo Gear Company. . . . . . . . . . . . . . . . . . . . . . . . .

ACTIVE MEMBERS

T. Guertin Liebherr Gear Technology Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

J. Kolonko Rexnord Geared Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .T.J. Krenzer Gleason Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

P.A. McNamara Caterpillar, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

K. Miller Dana Spicer Off Highway Products. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

W. Tsung Dana Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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vi © AGMA 2006 ---- All rights reserved

(This page is intentionally blank)


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1© AGMA 2006 ---- All rights reserved


American Gear Manufacturers Association --

Calculation of BevelGear Top Land and

Guidance on Cutter

Edge Radius

1 Scope

Thisinformationsheet provides a setof equationsfor

the calculation of bevel gear top land and guidance

on cutter edge radius. It integrates the equations in

ANSI/AGMA 2005--D03, Design Manual for Bevel

Gears, and Gleason publication SD3124B,

Formulas for Cutter Specifications and Tooth Thick-

ness Measurements for Spiral Bevel and Hypoid

Gears, with modifications to include face hobbing,

and additions for the top land calculations for

non--generated manufacturing methods, to achieve

compatibility between publications.

It is intended to provide assistance in completing the

calculations requiring determination of top lands and

cutter edge radii in ANSI/AGMA 2003--B97, Ratingthe Pitting Resistance and Bending Strength of

Generated Straight Bevel, Zerol Bevel and Spiral

Bevel Gear Teeth.

Annexes are provided for additional related

information and calculation examples.

2 Symbols, terminology and definitions

2.1 Symbols and terminology

The equations in this information sheet are written in

terms generally used for hypoids. See table 1.

For other gears, thenomenclaturefrom ANSI/AGMA

2005--D03, table 9 are used (see table 3).

NOTE: Some of the symbols and terminology con-

tained in this document may differ from those used in

other documents and AGMA standards. Users of this

standard should assure themselves that they are using

the symbols, terminology and definitions in the manner

indicated herein.

Table 1 -- Symbols and terms

Symbol Term Units Where firstused

AiG, AiP Inner cone distance, gear or pinion inch Eq 7, Eq 1

AmG, AmP Mean cone distance, gear or pinion inch Eq 9, Eq 1

AoG, AoP Outer cone distance, gear or pinion inch Eq 7, Eq 3

AxG Cone distance for involute lengthwise curvature pointwhere normal circular pitch and slot width is a maximum

inch Eq 31

aG, aP Mean addendum, gear or pinion inch Eq 50, Eq 50

aiG, aiP Inner addendum, gear or pinion inch Eq 78, Eq 77

a′iG, a′iP Adjusted inner addendum, gear or pinion inch Eq 82, Eq 81

aoG,

aoP

Outer addendum, gear or pinion inch Eq 163, Eq 162

B Outer normal backlash allowance inch Eq 6

bG, bP Mean dedendum, gear or pinion inch Eq 19, Eq 22

biG, biP Inner dedendum, gear or pinion inch Eq 25, Eq 24

boG, boP Outer dedendum, gear or pinion inch Eq 20, Eq 22

bxG, bxP Dedendum at cone distance AxG, gear or pinion inch Eq 44, Eq 45

b′oG Theoretical outer gear dedendum inch Eq 19

c Clearance inch Eq 77

(continued)


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2 © AGMA 2006 ---- All rights reserved

Table 1 (continued)


D, d Pitch diameter, gear or pinion inch Eq 140, Eq 139

F G, F P Face width of gear or pinion inch Eq 25, Eq 2

F iP Hypoid pinion face width from calculation point to inside inch Eq 1

F oP Hypoid pinion face width from calculation point to outside inch Eq 3

F xG

Distance from mean cone to cone distance at involutecurvature

inch Eq 38

k E Gear rotation factor -- -- Eq 52

N , n Number of teeth, gear or pinion -- -- Eq 79, Eq 79

pm Mean circular pitch inch Eq 27

pn Mean normal circular pitch inch Eq 27

Q Intermediate factor inch Eq 35

q Generating angle at mean degrees Eq 9

qi Generating angle at inside degrees Eq 13

qo Generating angle at outside degrees Eq 11

qx Generating angle at involute curvature degrees Eq 39

RbNG1, RbNP2 Mean normal base radius, convex, gear or pinion inch Eq 143, Eq 142

RbNG2, RbNP1 Mean normal base radius, concave, gear or pinion inch Eq 144, Eq 141 RibVG, RibVP Inner base radius -- concave, gear or pinion inch Eq 90, Eq 87

RibXG, RibXP Inner base radius -- convex, gear or pinion inch Eq 89, Eq 88

RiG, RiP Original inner pitch radius, gear or pinion inch Eq 76, Eq 75

RioG, RioP Inner outside radius, gear or pinion inch Eq 86, Eq 85

RNG, RNP Mean normal pitch radius, gear or pinion inch Eq 140, Eq 139

RoNG, RoNP Mean normal outside radius, gear or pinion inch Eq 146, Eq 145

R′bNG1, R′bNP2

Outer normal base radius, convex, gear or pinion inch Eq 160, Eq 159

R′bNG2, R′bNP1

Outer normal base radius, concave, gear or pinion inch Eq 161, Eq 158

R′iG, R′

iP New inner pitch radius, gear or pinion inch Eq 84, Eq 83

R′NG, R′NP Outer normal pitch radius, gear or pinion inch Eq 157, Eq 156

R′oNG, R′oNP Outer normal outside radius, gear or pinion inch Eq 163, Eq 162

R′′bNG1, R′′bNP2

Inner normal base radius, convex, gear or pinion inch Eq 179, Eq 178

R′′bNG2, R′′bNP1

Inner normal base radius, concave, gear or pinion inch Eq 180, Eq 177

R′′NG, R′′NP Inner mean normal pitch radius, gear or pinion inch Eq 176, Eq 175

R′′oNG, R′′oNP Inner normal outside radius, gear or pinion inch Eq 182, Eq 181

rc Cutter radius inch Eq 9

rTG, rTP Maximum blade edge radius, gear or pinion inch Eq 74, Eq 73

r1G, r1P Maximum blade edge radius for no running interference,

gear or pinion

inch Eq 74, Eq 73

r1VG, r1VP Maximum blade edge radius for no running interferenceconcave, gear or pinion

inch Eq 106, Eq 103

r1XG, r1XP Maximum blade edge radius for no running interferenceconvex, gear or pinion

inch Eq 105, Eq 104

r2G, r2P Maximum blade edge radius that can be manufactured,gear or pinion

inch Eq 74, Eq 73

r2RG, r2RP Roughing cutter edge radius, gear or pinion inch Eq 113, Eq 114

(continued)


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Table 1 (continued)


r3G, r3P Maximum blade edge radius to avoid mutilation, gear orpinion

inch Eq 74, Eq 73

r3VG, r3VP Maximum blade edge radius to avoid mutilation concave,gear or pinion

inch Eq 136, Eq 133

r3XG, r3XP Maximum blade edge radius to avoid mutilation convex,gear or pinion inch Eq 135, Eq 134

r′2RG, r′2RP Maximum roughing blade edge radius which can bemanufactured, gear or pinion

inch Eq 111, Eq 112

r′2VG, r′2VP Maximum finishing blade edge radius concave, defined bymaximum roughing blade edge radius and minimum stockallowance, gear or pinion

inch Eq 118, Eq 115

r′2XG, r′2XP Maximum finishing blade edge radius convex, defined bymaximum roughing blade edge radius and minimum stockallowance, gear or pinion

inch Eq 117, Eq 116

r′′2VG, r′′2VP Maximum finishing blade edge radius concave, gear orpinion

inch Eq 122, Eq 119

r′′2XG, r′′2XP Maximum finishing blade edge radius convex, gear or

pinion

inch Eq 121, Eq 120

S AG, S AP Stock allowance, gear or pinion inch Eq 65, Eq 66

S1 Crown gear to cutter center distance inch Eq 34

T mn, t mn Mean normal circular thickness at pitch line, gear orpinion

inch Eq 47, Eq 48

T n Gear mean normal circular thickness without backlash inch Eq 47

t iNG, t iNP Inner normal circular thickness at pitch line, gear or pinion inch Eq 189, Eq 188

t LiNG, t LiNP Inner normal top land, gear or pinion inch Eq 192, Eq 190

t LNG, t LNP Mean normal top land, gear or pinion inch Eq 154, Eq 152

t LoNG, t LoNP Outer normal top land, gear or pinion inch Eq 173, Eq 171

t mP Mean pinion transverse circular thickness inch Eq 49

t oNG, t oNP Outer normal circular thickness at pitch line, gear orpinion inch Eq 170, Eq 169

W Finishing point width gear (Unitool and single sided) inch Table 2

W BG, W BP Finishing blade point, gear or pinion inch Eq 69, Eq 70

W BRG, W BRP Roughing blade point, gear or pinion inch Eq 67, Eq 68

W ′e Effective gear point width inch Eq 52

W iG, W iP Inner slot width, gear or pinion inch Eq 59, Eq 60

W LG, W LP Minimum slot width, gear or pinion inch Eq 61, Eq 62

W MG, W MP Maximum slot width, gear or pinion inch Eq 63, Eq 64

W mG, W mP Mean slot width, gear or pinion inch Eq 50, Eq 51

W oG, W oP Outer slot width, gear or pinion inch Eq 55, Eq 56

W RG, W RP Roughing point width, gear or pinion inch Eq 65, Eq 66

W xG, W xP Slot width at AxG (maximum gear or pinion slot) inch Eq 57, Eq 58

xiVG, xiVP Limit tooth height for interference concave, gear or pinion inch Eq 102, Eq 97

xiXG, xiXP Limit tooth height for interference convex, gear or pinion inch Eq 101, Eq 99

y Amount of fillet mutilation permitted inch Eq 129

Γ, γ Pitch angle, gear or pinion degrees Eq 76, Eq 75

ΓR Gear root angle degrees Eq 17

ΔaG, ΔaP Change in inner addendum, gear or pinion inch Eq 80, Eq 79

(continued)


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Table 1 (continued)


ΔbiG Depth reduction on non-- generated gear at inside inch Eq 18

ΔboG Depth reduction on non--generated gear at outside inch Eq 17

ΔbxG Depth reduction on non--generated gear at involutecurvature

inch Eq 42

ΔcG, ΔcP Change in clearance, gear or pinion inch Eq 7, Eq 6

Δ f Width of blade flat inch Eq 111

Δqi Increment in generating angle at inside degrees Eq 16

Δqo Increment in generating angle at outside degrees Eq 15

Δqx Increment in generating angle at involute curvature degrees Eq 41

ΔW ′G, ΔW ′P Difference between minimum slot width and blade point,gear or pinion

inch Eq 128, Eq 127

Δφ2 Normal tilt of finishing cutter non-- generated degrees Eq 8

δG, δP Dedendum angle of gear or pinion degrees Eq 19, Eq 22

ηi Generating angle at inside degrees Eq 14

ηo Generating angle at outside degrees Eq 12

ηx Generating angle at involute curvature, for face hobbing degrees Eq 34

η1 Second auxiliary angle degrees Eq 10

ρiVG, ρiVP Inner profile radius of curvature concave, gear or pinion inch Eq 96, Eq 93

ρiXG, ρiXP Inner profile radius of curvature convex, gear or pinion inch Eq 95, Eq 94

ξ Angle between gear root plane and plane in which taper isspecified

degrees Eq 53

Σb Sum of pinion and gear mean dedendums inch Eq 28

Σbi Sum of pinion and gear inner dedendums inch Eq 30

Σbo Sum of pinion and gear outer dedendums inch Eq 29

Σbx Sum of pinion and gear dedendums at cone distance AxG inch Eq 46

Σφ Included pressure angle degrees Eq 5

φBXG Inside blade angle gear cutter (non--generating) degrees Eq 8φiV Inner pinion pressure angle -- concave degrees Eq 91

φiX Inner pinion pressure angle -- convex degrees Eq 92

φ1 Normal pressure angle, concave, pinion degrees Eq 5

φ2 Normal pressure angle, convex, pinion degrees Eq 5

φ1TG, φ2TP Pressure angle at tip of tooth, convex gear or pinion degrees Eq 150, Eq 149

φ2TG, φ1TP Pressure angle at tip of tooth, concave gear or pinion degrees Eq 151, Eq 148

φ′1TG, φ′2TP Pressure angle at tip of tooth, outer convex gear or pinion degrees Eq 167, Eq 166

φ′2TG, φ′1TP Pressure angle at tip of tooth, outer concave gear orpinion

degrees Eq 168, Eq 165

φ′′1TG, φ′′2TP Pressure angle at tip of tooth, inner convex gear or pinion degrees Eq 186, Eq 185

φ′′2TG, φ′′1TP Pressure angle at tip of tooth, inner concave gear orpinion degrees Eq 187, Eq 184

ψG, ψP Mean spiral angle, gear or pinion degrees Eq 9, Eq 139

ψiG, ψiP Inner spiral angle, gear or pinion degrees Eq 7, Eq 6

ψoG, ψoP Outer spiral angle, gear or pinion degrees Eq 7, Eq 6

ψxG Spiral angle at cone distance AxG degrees Eq 32

ΩVG, ΩVP Intermediate blade mutilation value concave, gear orpinion

inch2 Eq 132, Eq 129

ΩXG, ΩXP Intermediate blade mutilation value convex, gear or pinion inch2 Eq 131, Eq 130


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2.2 Definitions

This clause provides supplemental definitions for

bevel gear cutter and cutting method terminologies

referred to in this information sheet. The list of

definitions given here is not intended to be all

inclusive. For more detailed information regarding a

particular cutter design or cutting method, the user is

encouraged to consult the cutter manufacturer’sdata or machine tool manufacturer.

2.2.1 Bevel gear cutter terminology

alternate blade. Any multiple blade face cutter

having successive blades that cut on opposite sides

of a tooth space.

blade flat. A flat land on the end of blades required

for blade manufacturing control.

blade point. The length across the end surface of a

blade or tool (measured along a radius of a circular

cutter), bounded by the extension of the cutting edgeand non--cutting edge of the blade.

blade, inside. A blade of a circular face cutter with a

cuttingedgethatproduces the convex side of a tooth

surface.

blade, outside. A blade of a circular face cutter with

a cutting edge that produces the concave tooth

surface.

coast side. Thesideofatoothflankthatisincontact

with the opposite flank of the mate when the gear set

is driven in the reverse direction.drive side. Theside of a tooth flank that is in contact

with the opposite flank of the mate when the gear set

is driven in the forward direction.

effective gear point width. Effective point width is

one half of the difference of the outside minus the

inside point diameters of a cutter. The effective point

width is not equal to the slot width produced on the

part whenindexing motion occursbetween drive and

coast side generation. For spread blade cutters, the

effective point width equals the actual cutter point

width. When indexing accounts for part of the slotwidth, the effective point width can be negative.

fillet mutilation. Fouling of tooth fillet by the

non--cutting side of the bladetip. This is caused by a

tool edge radius or a blade point which is too large.

point width. One half of the difference between the

inside and outside point diameters of an alternate

blade cutter.

2.2.2 Bevel gear cutting method terminology

completing. A machining process where the tooth

space is completed in one machining setup. Unlike

single side, single setting, or fixed setting methods

where the tooth space roughing and finishing are

carried out in separate machining setups.

cutter tilt. A change in the relative position between

workpiece and cutter, measured as an angle in thenormal, or axial, or both planes of the workpiece.

Formate. A term describing non--generated gear

members whose teeth have surfaces of revolution,

and straight profiles in their normal sections. Pinions

generated to run with such gears are called Formate

pinions.

non--generated method. A gear cutting process

where the tooth space is machined without generat-

ing motion (see Formate). The tooth surfaces are

formed by the sweep of a straight--sided cutting tool

and thus have straight profiles in any normal section.

single setting. A finishing method which is a

variation of the spread blade method. It is used on

wide face width gears to avoid having two cutter

blades cutting in the same slot at the same time.

single side. A cutting method which uses an

alternate blade cutter to separately cut the profiles

on each side of a tooth space, with independent

machine settings.

spread blade. A cutting method which uses a

circular face cutter with alternate inside and outsideblades to cut both sides ofa tooth space at the same

time.

Unitool. A method for producing pairs of spiral

bevel, zerol bevel or hypoid gears using the same

single face mill cutter for both members. The cutters

used with this method are designated as Unitool

cutters.

Versacut. A process which requires very fewcutters

to accommodate a wide variety of spiral bevel gears.

Thecutters used with this method are designated as

Versacut cutters.

3 Input data

The equations in this information sheet are intended

to be as general as possible. Many of the

calculations require knowledge of the specific cut-

ting method used in manufacture. Supplemental


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definitions to be used with the terms described in

ANSI/AGMA 2005--D03 for proper input data selec-

tion based on the manufacturing method used can

be found in 2.2.

Thetablesin thisclause describe thedata necessary

to complete the calculations of this information

sheet. In most cases the values can be obtained

from the calculations detailed in ANSI/AGMA2005--D03. Many of those calculations are dupli-

cated in annex A. Additional tables are provided

here to supplement those calculations.

3.1 Input variables

Table 2 contains all the input variables necessary for

the calculations used in this information sheet.

Table 2 -- Input variables

Symbol Term

AiG Inner gear cone distance

AmG Gear mean cone distance

AmP Pinion mean cone distance

AoG Gear outer cone distance

aG Gear mean addendum

aP Pinion mean addendum

aoG Outer gear addendum

aoP Outer pinion addendum

B Outer normal backlash allowance

bG Gear mean dedendum

bP Pinion mean dedendum

c Clearance

D Gear pitch diameter

d Pinion pitch diameter

F G Gear face width

F P Pinion face width

N Gear number of teeth

n Pinion number of teeth

pm Mean circular pitch

rc

Cutter radius

S AG Stock allowance, gear

S AP Stock allowance, pinion

T n Gear mean normal circularthickness without backlash

W Gear finishing point width (Unitooland single setting)

y Amount of fillet mutilation permitted

Symbol Term

Γ Gear pitch angle

ΓR Gear root angle

γ Pinion pitch angle

Δ f Width of blade flat

δG Dedendum angle of gear

δP Dedendum angle of pinion

φBXG Inside blade angle, gear cutter

(non--generating)φ1 Concave pinion normal pressure

angle

φ2 Convex pinion normal pressureangle (always negative)

ψG Gear mean spiral angle

ψP Pinion mean spiral angle

ψiG Inner gear spiral angle

ψiP Inner pinion spiral angle

ψoG Outer gear spiral angle

ψoP Outer pinion spiral angle

Additional input variables for face hobbing

Q Intermediate factor

S1 Crown gear to cutter centerdistance

ηi Generating angle at inside

ηo Generating angle at outside

η1 Second auxiliary angle

Additional input variables for hypoids

F iP Hypoid pinion face width fromcalculation point to inside

F oP Hypoid pinion face width fromcalculation point to outside

3.2 Variable substitutions

The calculations in this information sheet are written

in terms of hypoid gears. Many of the variables for

non--hypoid bevels are subscripted the same for

pinion and gear. Table3 provides a means forproper

substitution of these variables into the calculations

for hypoids.

3.3 Gear rotation factor

Table 4 provides for the proper selection of the inputvariable k E basedonthecuttingmethodtobeusedin

manufacture.

3.4 Additional input data

Table 5 contains some suggested default values for

variables not described in ANSI/AGMA 2005--D03.

Other values may be used if experience dictates.


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Table 3 -- Symbols and terms from ANSI/AGMA 2005--D03, table 9

Symbol

Equivalent symbolfrom ANSI/AGMA

2005 --D03 Term

AmG Am Gear mean cone distance

AmP Am Pinion mean cone distance

AoG Ao Gear outer cone distance

AoP Ao Pinion outer cone distance

F G F Gear face width

F P F Pinion face width

φ1 φ Pressure angle -- drive side

φ2 φ Pressure angle -- coast side, set φ2 to --φ1

ψG ψ Gear mean spiral angle

ψoG ψo Outer gear spiral angle

ψP ψ Pinion mean spiral angle

Table 4 -- Gear rotation factor, k E

Generating method Face hobbing Face milling k E

Spread blade X 0.0

Gleason and Klingelnberg X 1.0

Oerlikon not using a roughing blade X 1.0

Oerlikon using a roughing blade X 1.3

Straight bevels and planing generator 2 W mG pn

Unitool and single setting X 2W mG − W pn

Versacut and standard single side X 2W mG + bGtan φ1 − tan φ2 pn

Table 5 -- Suggested defaults for input data

Symbol Term Units Suggested default

φBXGInside blade angle of gear cutter (non--gener-ated gear only)

degrees Average pressure angle

For completing, use 0.000

S AP Stock allowance, pinion inch For rough and finish, use

actual or see annex BFor completing, use 0.000

S AG Stock allowance, gear inch For rough and finish, useactual or see annex B

y Amount of fillet mutilation permitted inch 0.002

Δ f Width of blade flat inch 0.008

Cutter radius (straight bevels) 10000rc

Cutter radius (all other bevels) nc

See ANSI/AGMA 2005--D03


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4 Calculations

4.1 General geometry

Inner pinion cone distance

Hypoids

iP = A

mP − F

iP

(1)

For all other bevels

iP = mP − 0.5 F P (2)

Outer pinion cone distance

Hypoids

oP = mP + F oP (3)

For all other bevels

oP = mP + 0.5 F P (4)

Included pressure angle

Σφ = φ1 − φ2 (5)

Change in clearance

Pinion

(6)ΔcP = B iP cos ψiP AoP cos ψoP

1sinφ1 − sinφ2

Gear

(7)ΔcG = iG cos ψiG

AoG cos ψoG

1sinφ1 − sinφ2

If ΔcP is greater than 0.75 c, or if ΔcG is greater than0.75 c, reduce B or increase the clearance c.

For non--generated gears normal tilt of finishing

cutter

Δφ2 = φBXG − φ1 (8)

Generating angle at mean

Face milling

q = arctan rc cos ψG AmG − rc sin ψG

(9)Face hobbing

q = η1 + ψG (10)

Generating angle at outside

Face milling

qo = arctan rc cos ψoG AoG − rc sin ψoG (11)

Face hobbing

qo = ηo (12)

Generating angle at inside

Face milling

qi = arctan rc cos ψiG AiG − rc sin ψiG (13)Face hobbingqi = η i (14)

Increment in generating angle

Outside

Δqo = q − qo (15)

Inside

Δqi = q i − q (16)

Generated gears have slightly deeper teeth at the

toe and heel ends than non--generated gears

caused by the relative rolling action between cutter

and work piece. For non--generated gear depth

reduction:

Outside

ΔboG = AoG − AmG

2tanΔφ2

2 rc cos2 ψG

+ AoG sin

2Δqo

2tanΓR

(17)

Inside

ΔbiG = AmG − AiG

2tan Δφ2

2 rc cos2

ψG

+ AiG sin

2Δqi2tan Γ

R(18)

Theoretical outer gear dedendum

b′oG = bG + AoG − AmG tan δG (19)Outer gear dedendum

Non--generated gear

boG = b′oG − ΔboG (20)

Generated gear

boG = b′oG (21)

Outer pinion dedendumHypoid

boP = bP + F oP tan δP (22)

All other bevels

boP = bP + 0.5 F P tan δP (23)

Inner pinion dedendum

biP = boP − F P tan δP (24)


15/43



Inner gear dedendum

Non--generated gear

biG = b′oG − F G tan δG − ΔbiG (25)

Generated gear

biG = boG − F G tan δG (26)

Mean normal circular pitch

(27) pn = pm cos ψG

Sum of pinion and gear mean dedendums

Σb = bP + bG (28)

Sum of pinion and gear outer dedendums

Σbo = boP + boG (29)

Sum of pinion and gear inner dedendums

Σbi = b iP + biG (30)

Cone distance for involute lengthwise curvaturepoint where normal circular pitch and slot width is a

maximum for face milling

AxG = A2mG

− 2 AmG rc sin ψG + 2 r2c

(31)Spiral angle at cone distance AxG (face milling)

ψxG = arcsin rc AxG (32)For face hobbing iterate for cone distance and spiral

angle at involute lengthwise curvature point,

AxG,where normal circular pitch is a maximum.

Initial cone distance at involute lengthwise curvature

point

xG = AmG (33)

Generating angle at involute curvature for face

hobbing

ηx = arccos A2

xG + S2

1 − r2c

2 AxG S1(34)

Spiral angle at cone distance AxG for face hobbing

ψxG = arctan AxG − Q cosηx

Q sinηx(35)

Change AxG, until

(36) ηx − ψxG ≤ 0.0001For the second trial make

(37)xG = AxG + 0.0001 inch

For the third and subsequent trials iterate.

If AiG < AxG < AoG, calculate F xG, qx, Δqx, ΔbxG, bxPand Σbx; otherwise, set these items to zero.

Distance from mean cone to cone distance at

involute curvature

(38) F xG = AxG − AmG

Generating angle at involute curvatureFace milling

(39)qx = arctan rc cos ψxG AxG − rc sin ψxGFace hobbing

(40)qx = ηx

Increment in generating angle at involute curvature

(41)Δqx = q − qxDepth reduction on gear at involute curvature

Non--generated gear

(42)ΔbxG = F 2

xGtan Δφ2

2 rc cos2 ψG

+ AxG sin

2 Δqx

2 tan ΓR

Generated gear

(43)ΔbxG = 0

Gear dedendum at cone distance AxG

(44)bxG = bG + F xG tan δG − ΔbxGPinion dedendum at cone distance AxG

(45)bxP = bP + F xG tan δP

Sum of pinion and gear dedendums at conedistance AxG

(46)Σbx = bxP + bxG4.2 Slot width calculations and blade

specifications

4.2.1 Slot width calculations, mean

The following calculations for the mean normal

circular thickness for the gear and pinion are

modifications to the calculations in table 9 of

ANSI/AGMA 2005--D03. Backlash has been added

and the backlash is divided evenly between the twomembers. If the mean normal circular tooth thick-

nesses are otherwise available, bypass equations

47 and 48.

Mean normal gear circular thickness

(47)T mn = T n − AmG AoG

B cos ψG

2cosΣφ2 cos ψoG


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Mean normal pinion circular thickness

t mn = pn − T mn − AmG AoG

B cos ψG

cosΣφ2 cos ψoG

(48)

Mean pinion transverse circular thickness

t mP

= t mn

cos ψG(49)

Mean gear slot width

− aP − aG tan Σφ2 (50)W mG = pn − T mn −

Σb2tan φ1 − tan φ2

Mean pinion slot width

+ AmG cos ψG AoG cos ψoG

B

cos

Σφ

2

− W mG(51)

W mP = pn − Σb tan φ1 − tan φ2

Effective gear point width

W ′e = W mG −k E n

2(52)

4.2.2 Slot width calculation, outer

Angle between gear root plane and plane in which

taper is specified:

Single side and Versacut methods

ξ = δG (53)

All other cutting methods.

ξ = 0 (54)

Outer gear slot width

× t mP cos ψoG − AoG cos ψoG AmG cos ψG

+ AmG − AoGtan φ1 − tan φ2 tan ξ(55)

W oG = W ′e1 − AoG cos ψoG AmG cos ψG+ AoG AmG

× bGtan φ1 − tan φ2 + B

cosΣφ2

Outer pinion slot width

− W oG + B

cosΣφ

2

(56)

W oP = AoG cos ψoG AmG cos ψG

pn − Σbotan φ1 − tan φ2

If AiG


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Inner pinion slot width

− W iG + AiG cos ψiG AoG cos ψoG

B

cosΣφ2 (60)

W iP = AiG cos ψiG AmG cos ψG

pn − Σbi tan φ1 − tan φ2

4.2.4 Slot widths, minimum and maximum

Minimum gear slot width

W LG = minimum of W oG, W mG, or W iG(61)

Minimum pinion slot width

W LP = minimum of W oP, W mP, or W iP(62)

Maximum gear slot width

W MG = maximum of W oG, W xG, W iG, or W mG

(63)

Maximum pinion slot width

W MP = maximum of W oP, W xP, W iP, or W mP(64)

4.2.5 Point width and blade point calculations

Roughing cutter calculations for processes with

separate rough and finish operations and cutters:

Roughing point width

Gear

W RG = W LG − S AG (65)

Pinion

W RP = W LP − S AP (66)

Minimum roughing blade point

Gear

W BRG =W RG

2 + 0.001 (67)

Pinion

W BRP =W RP

2 + 0.001 (68)

Finishing blade point

Minimum for completing manufacturing methods

Gear

W BG =W LG

2 + 0.001 (69)

Pinion

W BP =W LP

2 + 0.001 (70)

Maximum for rough and finish methods

Gear

W BG =

W LG −

S AG

(71)

Pinion

W BP = W LP − S AP (72)

4.2.6 Standard blade point

Bevel gear blades are either sharpened on the rake

face or on the blade profile. For face sharpened

blades, the blade point and edge radius are formed

by the blade manufacturer. For each distinct blade

point, a separate cutter blade would be required. A

common practice is to consolidate similar sized

blade points into standard ones. A table of standard

blade points is included in annex B for reference.

When standard blade point is used, choose one that

satisfies the blade point equations given in 4.2.5.

Note that there may be more than one standard

blade point that would satisfy the blade point

equations. For profile sharpened blades, the

required blade point and edge radii are formed at

sharpening. Standardization of blade point is

generally not an issue.

The choice of blade point may affect maximum edgeradius that can be manufactured, see 4.3.2, and

maximum edge radius for avoiding mutilation, see

4.3.3. In general, a largerblade pointallows a larger

edge radius to be manufactured. However, the

larger blade point may reduce the maximum edge

radius for avoiding mutilation. It might be possible to

select a blade point, standard or otherwise, in an

attempt to balance the maximum edge radius that

can be manufactured and the maximum edge radius

for avoiding mutilation.

Cutters for the Unitool method use standard bladesexclusively. For each available cutter diameter, the

corresponding cutter blades have standard blade

point and edge radius. When a cutter diameter is

chosen, the blade point and tool edge radii are also

defined.

Consult the manufacturer for available cutter

information.


18/43



4.3 Cutter edge radius calculation

The cutter edge radius for a bevel gear should not

exceed the radius that would cause any of the

following conditions:

-- running interference, see 4.3.1;

-- unable to manufacture radius on blade, see

4.3.2;-- fillet mutilation, see 4.3.3.

Maximum pinion blade edge radius

rTP = minimum of r1P, r2P, or r3P (73)

Maximum gear blade edge radius

rTG = minimum of r1G, r2G, or r3G (74)

4.3.1 Cutter edge radius for no running

interference

Virtual gear calculations

Original inner pinion pitch radius

(75) RiP = iP tanγ

cos2 ψiP

Original inner gear pitch radius

(76) RiG = iG tanΓ

cos2 ψiG

Pinion inner addendum

(77)aiP = b iG − c

Gear inner addendum

(78)aiG = b iP − c

Change in inner pinion addendum

(79)ΔaP = ΔcGn cosΓ

n cosΓ + N cos γ

Change in inner gear addendum

(80)ΔaG = ΔcP N cos γ

n cosΓ + N cos γ

Adjusted inner pinion addendum

(81)a′iP =

aiP +

ΔaP

Adjusted inner gear addendum

(82)a′iG = a iG + ΔaGNew inner pinion pitch radius

(83) R′iP = R iP − ΔaPNew inner gear pitch radius

(84) R′iG = R iG − ΔaG

Inner pinion outside radius

(85) RioP = R iP + aiPInner gear outside radius

(86) RioG = R iG + aiGInner pinion base radius

Concave

(87) RibVP = R iP cosφ1Convex

(88) RibXP = R iP cosφ2Inner gear base radius

Convex

(89) RibXG = R iG cosφ1Concave

(90) RibVG = R iG cosφ2Inner pinion pressure angle

Concave

(91)φiV = arccos RibVP R′iP Convex

(92)φiX = arccos RibXP R′iP Inner pinion profile radius of curvature

Concave

ÃiVP

= R′iP sinφiV − R2ioG

− R2ibXG

+ R′iG

sinφi

(93)

Convex

ÃiXP

= R′iP

sinφiX − R2

ioG − R2

ibVG + R′

iGsinφ

iX

(94)

Inner gear profile radius of curvature

Convex

ÃiXG

= R′iG

sinφiV − R2ioP

− R2ibVP

+ R′iP

sinφiV

(95)

Concave

ÃiVG

= R′iG

sinφiX − R2ioP

− R2ibXP

+ R′iP sinφiX(96)

Limit tooth height for interference, pinion, concave

Generated gear

xiVP

= RibVP

cosφ1 + ÃiVP sinφ1 − R iP + biP(97)


19/43



Non--generated gear

xiVP = c − ΔcP (98)

Limit tooth height for interference, pinion, convex

Generated gear

xiXP = R ibXP cosφ2 − ÃiXP sinφ2 − RiP + biP(99)

Non--generated gear

xiXP = c − ΔcP (100)

Limit tooth height for interference, gear

Convex

xiXG = R ibXG cosφ1 + ÃiXG sinφ1 − RiG + biG(101)

Concave

xiVG = R ibVG cosφ2 − ÃiVG sinφ2 − RiG + biG(102)

Maximum blade edge radius for no running

interference on pinion tooth

Concave

r1VP = xiVP

1 − sinφ1(103)

Convex

r1XP = xiXP

1 + sinφ2(104)


interference on gear tooth

Convex

r1XG = xiXG

1 − sinφ1(105)

Concave

r1VG = xiVG

1 + sinφ2(106)


interference on pinion tooth

if, r1VP < r1XP

r1P = r1VP (107)otherwise,

r1P = r1XP (108)


interference on gear tooth

if, r1VG < r1XG

r1G = r1VG (109)

otherwise,

r1G = r1XG (110)

4.3.2 Cutter edge radius which can be

manufactured

4.3.2.1 Roughing

Maximum gear roughing blade edge radius which

can be manufactured

r′2RG =W BRG − Δ

secφ1 − tan φ1(111)

Maximum pinion roughing blade edge radius which

can be manufactured

r′2RP =W BRP − Δ


Gear roughing cutter edge radius

r2RG = maximum of r′2RG or 0.010 inches(113)

Pinion roughing cutter edge radius

r2RP = maximum of r′2RP or 0.010 inches(114)

4.3.2.2 Finishing

The following four r′ finishing cutter calculations are

each defined by the roughing blade edge radius and

stock allowance for cutting processes that use

separate rough and finish operations and cutters:

Maximum pinion finishing blade edge radius defined

by maximum roughing blade radius and minimum

stock allowance

Concave

r′2VP = S AP

2 secφ1 − tan φ1 + r2RP (115)

Convex

r′2XP = S AP

2 secφ2 + tan φ2 + r2RP (116)

Maximum gear finishing blade edge radius defined

by maximum roughing blade radius and minimum

stock allowance

Convex

r′2XG = S AG

2 secφ1 − tan φ1 + r2RG (117)

Concave

r′2VG = S AG

2 secφ2 + tan φ2 + r2RG (118)


20/43



The following four r′′ calculations are as defined by

the finishing cutter:

The values of r′′ are never negative; if necessary

reduce Δ f :

Maximum pinion finishing blade edge radius

Concave

r″2VP =W BP − Δ f


Convex

r″2XP =W BP − Δ f

secφ2 + tan φ2(120)

Maximum gear finishing blade edge radius

Convex

r″2XG =W BG − Δ f


Concave

r″2VG =W BG − Δ f

secφ2 + tan φ2(122)

Maximum pinion blade edge radius which can be

manufactured

Rough and finish

r2P = minimum of r′2VP, r′2XP, r′′2VP, or r′′XP(123)

Completing

r2P = minimum of r′′2VP, or r′′2XP (124)

Maximum gear blade edge radius which can be

manufactured

Rough and finish

r2G = minimum of r′2VG, r′2XG, r′′2VG, or r′′XG

(125)

Completing

r2G = minimum of r′′2VG, or r′′2XG (126)

4.3.3 Cutter edge radius to avoid mutilation

Difference between pinion minimum slot width and

finishing blade point

ΔW ′P = W LP − W BP (127)

Difference between gear minimum slot width and

finishing blade point

ΔW ′G = W LG − W BG (128)

If any of the following Ω values are negative, reduce

W BP or W BG accordingly:

Pinion intermediate blade mutilation value

Concave

ΩVP = y2 + 2 y ΔW ′P secφ1 − tan φ1 (129)

Convex

ΩXP = y2 + 2 y ΔW ′P secφ2 + tan φ2 (130)

Gear intermediate blade mutilation value

Convex

ΩXG = y2 + 2 yΔW ′G secφ1 − tan φ1 (131)

Concave

ΩVG = y2 + 2 yΔW ′Gsecφ2 + tan φ2 (132)

Maximum pinion blade edge radius to avoid

mutilationConcave

r3VP = y + ΔW ′Psecφ2 + tan φ2 + ΩXP

secφ2 + tan φ22

(133)

Convex

r3XP = y + ΔW ′Psecφ1 − tanφ1 + ΩVP

secφ1 − tan φ12

(134)

Maximum gear blade edge radius to avoid mutilation

Convex

r3XG = y + ΔW ′Gsecφ2 + tan φ2 + ΩVG

secφ2 + tan φ22

(135)

Concave

r3VG = y + ΔW ′Gsecφ1 − tan φ1 + ΩXG

secφ1 − tanφ12

(136)Therefore, maximum pinion blade edge radius to

avoid mutilation

r3P = minimum of r3VP, or r3XP (137)

Therefore, maximum gear blade edge radius to

avoid mutilation

r3G = minimum of r3VG, or r3XG (138)


21/43



4.4 Top land formulas

4.4.1 Mean top lands

Mean normal pinion pitch radius

RNP = 0.5 d

cos γ cos2 ψP

AmP AoP (139)

Mean normal gear pitch radius

RNG = 0.5 D

cosΓ cos2 ψG

AmG AoG (140)

Mean normal pinion base radius

Concave

RbNP1 = RNP cosφ1 (141)

Convex

RbNP2 = RNP cosφ2 (142)

Mean normal gear base radius

Convex

RbNG1 = RNG cosφ1 (143)

Concave

RbNG2 = RNG cosφ2 (144)

Mean normal pinion outside radius

RoNP = RNP + aP (145)

Mean normal gear outside radius

Generated RoNG = RNG + aG (146)

Non--generated

RoNG = RNG − aP (147)

Pressure angle at tip of pinion tooth (mean)

Concave

φ1TP = arccos RbNP1 RoNP (148)Convex

φ2TP = arccos RbNP2 RoNP (149)Pressure angle at tip of gear tooth (mean)

Convex

φ1TG = arccos RbNG1 RoNG (150)

Concave

φ2TG = arccos RbNG2 RoNG (151)Mean normal pinion top land

Generated

− invφ2TP RoNP (152)

t LNP =

t mn

RNP +invφ

1 −invφ

1TP +inv

− φ

2

NOTE: “inv” is the mathematical function involute. It is

the tangent of the angle minus the angle in radians.

Non--generated

(153)

− invφ2TP RoNP − T mn + aP tanφ1t LNP = t mn RNP + invφ1 − invφ1TP + inv− φ2

− tanφ2 − T mn RNG + invφ1 − invφ1TG

+ inv −φ2 − invφ2TG RoNG

Mean normal gear top land

Non--generated

t LNG = T mn − aGtan φ1 − tan φ2 (154)Generated

− inv φ2TG RoNG (155)

t LNG = T mn RNG + invφ1 − invφ1TG + inv−φ2

4.4.2 Outer top lands

Outer normal pinion pitch radius

R′NP = 0.5 d

cosγ cos2 ψoP(156)

Outer normal gear pitch radius

R′NG = 0.5

cosΓ cos2 ψoG(157)

Outer normal pinion base radius

Concave

R′bNP1 = R′NP cosφ1 (158)

Convex

R′bNP2 = R′NP cosφ2 (159)

Outer normal gear base radius

Convex

R′bNG1 = R′NG cosφ1 (160)


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Concave

R′bNG2 = R′NG cosφ2 (161)

Outer normal pinion outside radius

R′oNP = R′NP + aoP (162)

Outer normal gear outside radius

Generated

R′oNG = R′NG + aoG (163)

Non--generated

R′oNG = R′NG − aoP (164)

Pressure angle at tip of pinion tooth (outer)

Concave

φ′1TP = arccos R′bNP1 R′oNP

(165)

Convex

φ′2TP = arccos R′bNP2 R′oNP

(166)

Pressure angle at tip of gear tooth (outer)

Convex

φ′1TG = arccos R′bNG1 R′oNG

(167)

Concave

φ′2TG = arccos R′bNG2 R′oNG

(168)

Outer normal pinion circular thickness at pitch line

− B

cosΣφ2 (169)

t oNP = boG tan φ1 − tan φ2 + W oG

Outer normal gear circular thickness at pitch line

(170)

t oNG = boP tan φ1 − tan φ2 + W oP

− B

cos

Σφ

2

Outer normal pinion top landGenerated

− invφ′2TP

R′oNP (171)

t LoNP

= t oNP R′

NP+ invφ1 − invφ′1TP + inv−φ2

Non--generated

− t oNG

+ aoPtanφ1 − tanφ2

t LoNP

= t oNP R′

NP+ invφ1 − invφ′1TP + inv

−φ2

(172)

− invφ′2TP R′oNP

− t oNG R′

NG+ invφ1 − invφ′1TG + inv

−φ2

− invφ′2TG

R′oNG

Outer normal gear top land

Generated

− invφ′2TG R′oNG (173)

t LoNG

= t oNG R′

NG+ invφ1 − invφ′1TG + inv

−φ2

Non--generated

t LoNG = t oNG − aoGtan φ1 − tan φ2 (174)

4.4.3 Inner top lands

Inner mean normal pinion pitch radius

R″NP = 0.5 d

cos γ cos ψ2iP

iP

AoP (175)

Inner mean normal gear pitch radius

R″NG = 0.5 D

cosΓ cos2 ψiG

AiG AoG (176)

Inner normal pinion base radius

Concave

R″bNP1 = R″NP cosφ1 (177)

Convex

R″bNP2 = R″NP cosφ2 (178)

Inner normal gear base radiusConvex

R″bNG1 = R″NG cosφ1 (179)

Concave

R″bNG2 = R″NG cosφ2 (180)

Inner normal pinion outside radius

R″oNP = R″NP + aiP (181)


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Inner normal gear outside radius

Generated

R″oNG = R″NG+ aiG (182)

Non--generated

R″oNG = R″NG− aiP (183)

Pressure angle at tip of pinion tooth (inner)

Concave

φ″1TP = arccos R″bNP1 R″oNP (184)Convex

φ″2TP = arccos R″bNP2 R″oNP (185)Pressure angle at tip of gear tooth (inner)

Convex

φ″1TG = arccos R″bNG1 R″oNG (186)Concave

φ″2TG = arccos R″bNG2 R″oNG (187)Inner normal pinion thickness at pitch line

×cos ψiPcos ψoP

B

cosΣφ2 (188)

t iNP = b iGtan φ1 − tan φ2 + W iG − AiP AoP

Inner normal gear thickness at pitch line

×cos ψiGcos ψoG

B

cosΣφ2 (189)

t iNG = b iPtan φ1 − tan φ2 + W iP − AiG AoG

Inner normal pinion top land

Generated

− invφ″2TP R″oNP (190)

t LiNP

= t iNP R″NP

+ invφ1 − invφ″1TP+ inv−φ2

Non--generated

− t iNG

+ aiPtanφ1 − tanφ2

t LiNP

= t iNP R″NP

+ invφ1 − invφ″1TP+ inv−φ2

(191)

− invφ″

2TP R″

oNP

− t iNG R″NG

+ invφ1 − invφ″1TG+ inv−φ2

− invφ″2TG R″oNG

Inner normal gear top land

Generated

− invφ″2TG R″oNG (192)t LiNG =

t iNG

R″NG+ invφ1 − invφ″1TG+ inv−φ2

Non--generated

t LiNG = t iNG − aiG tan φ1 − tan φ2 (193)


24/43



Annex A

(informative)

Additional equations from ANSI/AGMA 2005--D03

[This annex is provided for informational purposes only and should not be construed as a part of AGMA 929--A06,

Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius.]

A.1 PurposeThis annex is to provide the user additional equa-

tions thatare in or derived from those in ANSI/AGMA

2005--D03. The additional symbols used in the

equations are defined in table A.1. Also see table 1.

Table A.1 -- Symbols

Symbol Term Units First used

E Hypoid offset in (mm) Eq. A.12

N S Number of blade groups -- -- Eq. A.3

N c Number of crown gear teeth -- -- Eq. A.3

RoG Outside gear pitch radius in (mm) Eq. A.17

Z Gear pitch apex beyond crossing point in (mm) Eq. A.12

γi Pinion inside pitch angle deg (rad) Eq. A.14γoo Outer pinion pitch angle deg (rad) Eq. A.20

γR Pinion root angle deg (rad) Eq. A.23

ΔΣ Shaft angle departure from 90° deg (rad) Eq. A.12

εi Pinion offset angle in axial plane at inside deg (rad) Eq. A.13

εi’ Pinion offset angle in pitch plane at inner end deg (rad) Eq. A.15

εo Pinion offset angle in face plane deg (rad) Eq. A.19

εo’ Pinion offset angle in pitch plane at outer end deg (rad) Eq. A.21

η1 Second auxiliary angle deg (rad) Eq. A.8

ζi Intermediate angle deg (rad) Eq. A.12

ζo Intermediate angle deg (rad) Eq. A.18

A.2 Common equations

inner gear cone distance

AiG = AmG − 0.5 F G (A.1)

inner gear spiral angle (face milling)

ψiG = arcsin2 AmG rc sin ψG − A2mG + A2iG2 AiG rc (A.2)

intermediate variable (face hobbing)

Q = S1

1 + N S N c

(A.3)

generating angle at inside (face hobbing)

ηi = arccos A2iG + S21 − r2c2 AiG S1 (A.4)

inner gear spiral angle (face hobbing)

ψiG = arctan AiG − Q cos ηiQ sinηi (A.5)generating angle at outside (face hobbing)

ηo = arccos A2oG + S21 − r2c2 AoG S1 (A.6)outer gear spiral angle (face hobbing)

ψoG = arctan AoG − Q cos ηoQ sinηo (A.7)second auxiliary angle (face hobbing)

cosη1 = mG cos ψG

S1 N c N c + N S (A.8)


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A.3 Spiral bevels

inner pinion spiral angle equals inner gear spiral

angle

ψiP = ψ iG (A.9)

outer pinion spiral angle equals outer gear spiral

angle

ψoP =

ψoG (A.10)

A.4 Hypoids

inside gear pitch radius

RiG = A iG sinΓ (A.11)

intermediate angle

ζi = arctan E tanΔΣ cosΓ AiG − Z cosΓ (A.12)pinion inner offset angle in axial plane

εi + ζ i = arcsin E cos ζ

i

sinΓ

AiG − Z cosΓ (A.13)pinion inside pitch angle

γi = arcsinsinΔΣ sinΓ + cosΔΣcosΓ cos εi(A.14)

pinion offset angle in pitch plane at inner end

ε′i = arcsin sin εicos γi (A.15)

inner pinion spiral angle

ψiP = ψ iG + ε′i (A.16)

outside gear pitch radius

RoG = AoG sinΓ (A.17)

intermediate angle

ζo = arctan E tanΔΣ cosΓ AoG − Z cosΓ (A.18)pinion outer offset angle in axial plane

εo + ζo = arcsin E cos ζo sinΓ AoG − Z cosΓ (A.19)outer pinion pitch angle

γoo = arcsinsinΔΣ sinΓ + cos ΔΣ cosΓ cos εo

(A.20)

pinion offset angle in pitch plane at outer end

ε′o = arcsin sin εocos γoo (A.21)outer pinion spiral angle

ψoP = ψoG + ε′o (A.22)

pinion dedendum angle

δP = γ − γR (A.23)


26/43



Annex B

(informative)

Stock allowance and standard cutter specifications

[This annex is provided for informational purposes only and should not be construed as a part of AGMA 929--A06,

Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius.]

B.1 Purpose

This annex provides information on typical stockallowance and standard cutter specifications.

B.2 Stock allowance

For rough and finish cutting methods, if the informa-

tion on the stock allowance is not available, the

following default stock allowance can be used for

calculating point width and blade point (see 4.2.5).

Table B.1 -- Default stock allowances (inch)

Diametral pitch Pinion Gear

P d < 3.0 0.025 0.030

3.0 ≤ P d < 7.0 0.025 0.020

7.0 ≤ P d < 10.0 0.010 0.010

10.0 ≤ P d 0.000 0.000

B.3 Standard blade point table

The following table of standard blade points is used

for some of the face milling cutting methods dis-

cussed in AGMA 929--A06. The table should not be

construed to be all inclusive.

Consult the manufacturer for accurate cutter

information.

Table B.2 -- Standard blade specifications, face

milled (inch)

Point width range Blade point

0.015 -- 0.015 0.010

0.020 -- 0.020 0.012

0.025 -- 0.025 0.015

0.030 -- 0.035 0.020

0.040 -- 0.045 0.025

0.050 -- 0.055 0.030

0.060 -- 0.070 0.040

0.080 -- 0.090 0.050

0.100 -- 0.120 0.065

0.130 -- 0.130 0.080

0.160 -- 0.160 0.100

0.170 -- 0.170 0.110

0.190 -- 0.190 0.125

0.210 -- 0.210 0.150


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Annex C

(informative)

Spiral bevel example problem

[This annex is provided for informational purposes only and should not be construed as a part of AGMA 929--A06,Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius.]

Symbol Description Equation Variables Units

Type of gears Spiral

Face hobbing or face milling Face milled

Generated or non--generated Generated

Completing or rough and finish, pinion Completing

Completing or rough and finish, gear Completing

Table 2

AiG Inner gear cone distance 2.69971 inch

AmG Gear mean cone distance 3.19971 inch

AmP Pinion mean cone distance 3.19971 inch

AoG Gear outer cone distance 3.69971 inch

aG Gear mean addendum 0.06259 inch

aP Pinion mean addendum 0.19043 inchaoG Outer gear addendum 0.08122 inch

aoP Outer pinion addendum 0.24734 inch

B Outer normal backlash allowance 0.00500 inch

bG Gear mean dedendum 0.22206 inch

bP Pinion mean dedendum 0.09422 inch

c Clearance 0.03163 inch

D Gear pitch diameter 6.96429 inch

d Pinion pitch diameter 2.50000 inch

F G Gear face width 1.00000 inch

F P Pinion face width 1.00000 inch

N Gear number of teeth 39.00000 -- --n Pinion number of teeth 14.00000 -- --

pm Mean circular pitch 0.48518 inch

rc Cutter radius table 5 inch

S AP Pinion stock allowance table 5 inch

S AG Gear stock allowance table 5 inch

T n Gear mean normal zero backlash circular thickness at pitch line 0.14817 inch

W Gear finishing point width table 5 inch

y Amount of fillet mutilation permitted table 5 inch

Γ Gear pitch angle 70.25316 degrees

ΓR Gear root angle 63.75967 degrees

Δ f Width of blade flat table 5 inch

γ Pinion pitch angle 19.74684 degrees

δG Dedendum angle of gear 6.49349 degrees

δP Dedendum angle of pinion 2.13424 degrees

φ1 Concave pinion normal pressure angle 20.00000 degrees

φ2 Convex pinion normal pressure angle --20.00000 degrees

ψG Gear mean spiral angle 35.00000 degrees

ψP Pinion mean spiral angle 35.00000 degrees

ψiG Inner gear spiral angle 33.94561 degrees


28/43



Symbol Units VariablesEquationDescription

ψiP Inner pinion spiral angle 33.94561 degrees

ψoG Outer gear spiral angle 36.84576 degrees

ψoP Outer pinion spiral angle 36.84576 degrees

Additional input variables for face hobbing (Table 2)

Q Intermediate factor Not applicable

S1 Crown gear to cutter center dist Not applicable inch

η1 Second auxiliary angle Not applicable degreesηo Generating angle at outside Not applicable degrees

ηi Generating angle at inside Not applicable degrees

Additional input for hypoids

F oP Hypoid pinion face width from calculation point to outside Not applicable degrees

F iP Hypoid pinion face width from calculation point to inside Not applicable degrees

Table 4

Method Cutting method Spread blade

k E Gear rotation factor 0.00000

Table 5

φBXG Inside blade angle gear cutter (non--generated) Not applicable degrees

S AP Pinion stock allowance 0.00000 inch S AG Gear stock allowance 0.00000 inch

y Amount of fillet mutilation permitted 0.00200 inch

Δ f Width of blade flat 0.00800 inch

rc Cutter radius 4.50000 inch

4 Calculations

4.1 General geometry

AiP Inner pinion cone distance (eq 1 or 2) 2.69971 inch

AoP Outer pinion cone distance (eq 3 or 4) 3.69971 inch

Σφ Included pressure angle (eq 5) 40.00000 degrees

ΔcP Change in pinion clearance (eq 6) 0.00553 inch

ΔcG

Change in gear clearance (eq 7) 0.00553 inch

Δφ2 Normal tilt of f inishing cutter (non--generated) (eq 8) Not applicable degrees

q Generating angle at mean (eq 9 or 10) 80.47339 degrees

qo Generating angle at outside (eq 11 or 12) 74.46243 degrees

qi Generating angle at inside (eq 13 or 14) 87.13405 degrees

Δqo Increment in generating angle at outside (eq 15) 6.01095 degrees

Δqi Increment in generating angle at inside (eq 16) 6.66066 degrees

ΔboG Depth reduction on non--generated gear at

outside

(eq 17) Not applicable inch

ΔbiG Depth reduction on non--generated gear at

inside

(eq 18) Not applicable inch

b′oG Theoretical outer gear dedendum (eq 19) 0.27897 inch

boG Outer gear dedendum (eq 20 or 21) 0.27897 inch

boP Outer pinion dedendum (eq 22 or 23) 0.11285 inch

biP Inner pinion dedendum (eq 24) 0.07559 inch

biG Inner gear dedendum (eq 25 or 26) 0.16515 inch

pn Mean normal circular pitch (eq 27) 0.39744 inch

Σb Sum of pinion and gear mean dedendums (eq 28) 0.31628 inch

Σbo Sum of pinion and gear outer dedendums (eq 29) 0.39182 inch

Σbi Sum of pinion and gear inner dedendums (eq 30) 0.24074 inch


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AxG Cone distance for involute lengthwise curvature

point where normal circular pitch and slot width

is a maximum

(eq 31) 5.84984 inch

ψxG Spiral angle at cone distance AxG (eq 32 or 35) 50.28674 degrees

ηx Generating angle at involute curvature (eq 34) Not applicable degrees

F xG Distance from mean cone to cone distance at

involute curvature

(eq 38) 0.00000 inch

qx Generating angle at involute curvature (eq 39 or 40) 0.00000 degrees

Δqx Increment in generating angle at involute

curvature

(eq 41) 0.00000 degrees

ΔbxG Depth reduction on non--generated gear at

involute curvature

(eq 42 or 43) 0.00000 inch

bxG Gear dedendum at cone distance AxG (eq 44) 0.00000 inch

bxP Pinion dedendum at cone distance AxG (eq 45) 0.00000 inch

Σbx Sum of pinion and gear dedendums at cone

distance AxG

(eq 46) 0.00000 inch

4.2 Slot width calculations and blade specifications

4.2.1 Slot width calculations, meanT mn Mean normal gear circular thickness (eq 47) 0.14581 inch

t mn Mean normal pinion circular thickness (eq 48) 0.24691 inch

t mP Mean pinion transverse circular thickness (eq 49) 0.30142 inch

W mG Mean gear slot width (eq 50) 0.08997 inch

W mP Mean pinion slot width (eq 51) 0.08194 inch

W ′e Effective gear point width (eq 52) 0.08997 inch

4.2.2 Slot width calculation, outer

ζ Angle between gear root plane and plane in

which taper is specified

(eq 53 or 54) 0.00000 degrees

W oG Outer gear slot width (eq 55) 0.08997 inch

W oP

Outer pinion slot width (eq 56) 0.07906 inch

W xG Slot width at AxG, gear (maximum gear slot

width)

(eq 57) 0.00000 inch

W xP Slot width at AxG, pinion (maximum pinion slot

width)

(eq 58) 0.00000 inch

4.2.3 Sloth width calculation, inner

W iG Inner gear slot width (eq 59) 0.08997 inch

W iP Inner pinion slot width (eq 60) 0.07840 inch

4.2.4 Sloth widths, minimum and maximum

W LG Minimum gear slot width (eq 61) 0.08997 inch

W LP Minimum pinion slot width (eq 62) 0.07840 inch

W MG Maximum gear slot width (eq 63) 0.08997 inch

W MP Maximum pinion slot width (eq 64) 0.08194 inch

4.2.5 Point width and blade point calculations

W RG Gear roughing point width (eq 65) 0.08997 inch

W RP Pinion roughing point width (eq 66) 0.07840 inch

W BRG Minimum gear roughing blade point (eq 67) 0.04599 inch

W BRP Minimum pinion roughing blade point (eq 68) 0.04020 inch

W BG Gear finishing blade point (eq 69 or 71) 0.04599 inch

W BP Pinion finishing blade point (eq 70 or 72) 0.04020 inch


30/43




4.3 Cutter edge radius calculations

rTP Maximum pinion blade edge radius (eq 73) 0.04063 inch

rTG Maximum gear blade edge radius (eq 74) 0.05425 inch

4.3.1 Cutter edge radius for no running interference

RiP Original inner pinion pitch radius (eq 75) 1.40824 inch

RiG Original inner gear pitch radius (eq 76) 10.92822 inch

aiP Pinion inner addendum (eq 77) 0.13352 inchaiG Gear inner addendum (eq 78) 0.04396 inch

ΔaP Change in inner pinion addendum (eq 79) 0.00063 inch

ΔaG Change in inner gear addendum (eq 80) 0.00490 inch

a′iP Adjusted inner pinion addendum (eq 81) 0.13415 inch

a′iG Adjusted inner gear addendum (eq 82) 0.04885 inch

R′iP New inner pinion pitch radius (eq 83) 1.40761 inch

R′iG New inner gear pitch radius (eq 84) 10.92333 inch

RioP Inner pinion outside radius (eq 85) 1.54176 inch

RioG Inner gear outside radius (eq 86) 10.97218 inch

RibVP Inner pinion base radius, concave (eq 87) 1.32331 inch

RibXP

Inner pinion base radius, convex (eq 88) 1.32331 inch

RibXG Inner gear base radius, convex (eq 89) 10.26917 inch

RibVG Inner gear base radius, concave (eq 90) 10.26917 inch

φiV Inner pinion pressure angle, concave (eq 91) 19.92929 degrees

φiX Inner pinion pressure angle, convex (eq 92) 19.92929 degrees

ρiVP Inner pinion profile radius of curvature, concave (eq 93) 0.33882 inch

ρiXP Inner pinion profile radius of curvature, convex (eq 94) 0.33882 inch

ρiXG Inner gear profile radius of curvature, convex (eq 95) 3.41201 inch

ρiVG Inner gear profile radius of curvature, concave (eq 96) 3.41201 inch

xiVP Limit tooth height for interference pinion,

concave

(eq 97 or 98) 0.02674 inch

xiXP Limit tooth height for interference pinion, convex (eq 99 or 100) 0.02674 inch

xiXG Limit tooth height for interference gear, convex (eq 101) 0.05377 inch

xiVG Limit tooth height for interference gear, concave (eq 102) 0.05377 inch

r1VP Maximum blade edge radius for no running

interference pinion, concave

(eq 103) 0.04063 inch

r1XP Maximum blade edge radius for no running

interference pinion, convex

(eq 104) 0.04063 inch

r1XG Maximum blade edge radius for no running

interference gear, convex

(eq 105) 0.08171 inch

r1VG Maximum blade edge radius for no running

interference gear, concave

(eq 106) 0.08171 inch

r1P Maximum blade edge radius for no running

interference on pinion

(eq 107 or 108) 0.04063 inch

r1G Maximum blade edge radius for no running

interference on gear

(eq 109 or 110) 0.08171 inch


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4.3.2 Cutter edge radius which can be manufactured

4.3.2.1 Roughing

r′2RG Maximum gear roughing blade edge radius

which can be manufactured

(eq 111) 0.05425 inch

r′2RP Maximum pinion roughing blade edge radius

which can be manufactured

(eq 112) 0.04599 inch

r2RG Gear roughing cutter edge radius (eq 113) 0.05425 inchr2RP Pinion roughing cutter edge radius (eq 114) 0.04599 inch

4.3.2.2 Finishing

r′2VP Maximum pinion finishing blade edge radius

defined by maximum roughing blade radius and

minimum stock allowance, concave

(eq 115) 0.04599 inch

r′2XP Maximum pinion finishing blade edge radius


minimum stock allowance, convex

(eq 116) 0.04599 inch

r′2XG Maximum gear finishing blade edge radius


minimum stock allowance, convex

(eq 117) 0.05425 inch

r′2VG Maximum gear finishing blade edge radius


minimum stock allowance, concave

(eq 118) 0.05425 inch

r′′2VP Maximum pinion finish blade edge radius

concave

(eq 119) 0.04599 inch

r′′2XP Maximum pinion finish blade edge radius

convex

(eq 120) 0.04599 inch

r′′2XG Maximum gear finish blade edge radius, convex (eq 121) 0.05425 inch

r′′2VG Maximum gear finish blade edge radius,

concave

(eq 122) 0.05425 inch

r2P Maximum pinion blade edge radius that can bemanufactured

(eq 123 or 124) 0.04599 inch

r2G Maximum gear blade edge radius that can be

manufactured

(eq 125 or 126) 0.05425 inch

4.3.3 Cutter edge radius to avoid mutilation

ΔW ′P Difference between pinion minimum slot width

and finishing blade point

(eq 127) 0.03820 inch

ΔW ′G Difference between gear minimum slot width

and finishing blade point

(eq 128) 0.04399 inch

ΩVP Pinion intermediate blade mutilation value,

concave

(eq 129) 0.00011 inch2

ΩXP Pinion intermediate blade mutilation value,

convex

(eq 130) 0.00011 inch2

ΩXG Gear intermediate blade mutilation value,

convex

(eq 131) 0.00013 inch2

ΩVG Gear intermediate blade mutilation value,

concave

(eq 132) 0.00013 inch2

r3VP Maximum pinion blade edge radius to avoid

mutilation, concave

(eq 133) 0.08013 inch


32/43




r3XP Maximum pinion blade edge radius to avoid

mutilation, convex

(eq 134) 0.08013 inch

r3XG Maximum gear blade edge radius to avoid

mutilation, convex

(eq 135) 0.08990 inch

r3VG Maximum gear blade edge radius to avoid

mutilation, concave

(eq 136) 0.08990 inch

r3P Maximum pinion blade edge radius to avoidmutilation

(eq 137) 0.08013 inch

r3G Maximum gear blade edge radius to avoid

mutilation

(eq 138) 0.08990 inch

4.4 Top land formulas

4.4.1 Mean top lands

RNP Mean normal pinion pitch radius (eq 139) 1.71177 inch

RNG Mean normal gear pitch radius (eq 140) 13.28366 inch

RbNP1 Mean normal pinion base radius, concave (eq 141) 1.60853 inch

RbNP2 Mean normal pinion base radius, convex (eq 142) 1.60853 inch

RbNG1 Mean normal gear base radius, convex (eq 143) 12.48256 inch

RbNG2 Mean normal gear base radius, concave (eq 144) 12.48256 inch

RoNP Mean normal pinion outside radius (eq 145) 1.90220 inch

RoNG Mean normal gear outside radius (eq 146 or 147) 13.34625 inch

φ1TP Pressure angle at tip of pinion tooth, concave (eq 148) 32.26164 degrees

φ2TP Pressure angle at tip of pinion tooth, convex (eq 149) 32.26164 degrees

φ1TG Pressure angle at tip of gear tooth, concave (eq 150) 20.72564 degrees

φ2TG Pressure angle at tip of gear tooth, convex (eq 151) 20.72564 degrees

t LNP Mean normal pinion top land (eq 152 or 153) 0.07175 inch

t LNG Mean normal gear top land (eq 154 or 155) 0.09992 inch

4.4.2 Outer top lands

R′NP Outer normal pinion pitch radius (eq 156) 2.07384 inch

R′NG Outer normal gear pitch radius (eq 157) 16.09347 inch

R′bNP1 O uter normal pinion base radius, concave (eq 158) 1.94878 inch R′bNP2 Outer normal pinion base radius, convex (eq 159) 1.94878 inch

R′bNG1 Outer normal gear base radius, convex (eq 160) 15.12291 inch

R′bNG2 Outer normal gear base radius, concave (eq 161) 15.12291 inch

R′oNP Outer normal pinion outside radius (eq 162) 2.32118 inch

R′oNG Outer normal gear outside radius (eq 163 or 164) 16.17469 inch

φ′1TP Pressure angle at tip of pinion tooth outer,

concave

(eq 165) 32.90619 degrees

φ′2TP Pressure angle at tip of pinion tooth outer,

convex

(eq 166) 32.90619 degrees

φ′1TG Pressure angle at tip of gear tooth outer, convex (eq 167) 20.77605 degrees

φ′2TG Pressure angle at tip of gear tooth outer,concave

(eq 168) 20.77605 degrees

t oNP Pinion outer normal circular thickness at pitch

line

(eq 169) 0.28773 inch

t oNG Gear outer normal circular thickness at pitch l ine (eq 170) 0.15589 inch


33/43




t LoNP Outer normal pinion top land (eq 171 or 172) 0.05345 inch

t LoNG Outer normal gear top land (eq 173 or 174) 0.09614 inch

4.4.3 Inner top lands

R′′NP Inner mean normal pinion pitch radius (eq 175) 1.40824 inch

R′′NG Inner mean normal gear pitch radius (eq 176) 10.92822 inch

R′′bNP1 Inner normal pinion base radius, concave (eq 177) 1.32331 inch

R′′bNP2 Inner normal pinion base radius, convex (eq 178) 1.32331 inch R′′bNG1 Inner normal gear base radius, convex (eq 179) 10.26916 inch

R′′bNG2 Inner normal gear base radius, concave (eq 180) 10.26916 inch

R′′oNP Inner normal pinion outside radius (eq 181) 1.54176 inch

R′′oNG Inner normal gear outside radius (eq 182 or 183) 10.97217 inch

φ′′1TP Pressure angle at tip of pinion tooth inner,

concave

(eq 184) 30.87230 degrees

φ′′2TP Pressure angle at tip of pinion tooth inner,

convex

(eq 185) 30.87230 degrees

φ′′1TG Pressure angle at tip of gear tooth inner, convex (eq 186) 20.62140 degrees

φ′′2TG Pressure angle at tip of gear tooth inner,

concave

(eq 187) 20.62140 degrees

t iNP Inner normal pinion thickness at pitch line (eq 188) 0.20617 inch

t iNG Inner normal gear thickness at pitch line (eq 189) 0.12940 inch

t LiNP Inner normal pinion top land (eq 190 or 191) 0.08972 inch

t LiNG Inner normal gear top land (eq 192 or 193) 0.09731 inch


34/43



Annex D

(informative)

Hypoid example problem

[This annex is provided for informational purposes only and should not be construe

agma 929-a06 calculation of bevel gear top land and guidance on cutter edge radius

Documents