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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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AGMA 929--A06AMERICAN GEAR MANUFACTURERS ASSOCIATION
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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1© AGMA 2006 ---- All rights reserved
AGMA 929--A06AMERICAN GEAR MANUFACTURERS ASSOCIATION
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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Table 1 (continued)
Symbol Term Units Where firstused
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)
Symbol Term Units Where firstused
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)
Symbol Term Units Where firstused
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)
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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.
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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)
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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)
Maximum blade edge radius for no running
interference on gear tooth
Convex
r1XG = xiXG
1 − sinφ1(105)
Concave
r1VG = xiVG
1 + sinφ2(106)
Maximum blade edge radius for no running
interference on pinion tooth
if, r1VP < r1XP
r1P = r1VP (107)otherwise,
r1P = r1XP (108)
Maximum blade edge radius for no running
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
secφ1 − tan φ1(112)
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)
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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
secφ1 − tan φ1(119)
Convex
r″2XP =W BP − Δ f
secφ2 + tan φ2(120)
Maximum gear finishing blade edge radius
Convex
r″2XG =W BG − Δ f
secφ1 − tan φ1(121)
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)
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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)
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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)
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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
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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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Symbol Units VariablesEquationDescription
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
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Symbol Units VariablesEquationDescription
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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Symbol Units VariablesEquationDescription
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
defined by maximum roughing blade radius and
minimum stock allowance, convex
(eq 116) 0.04599 inch
r′2XG Maximum gear finishing blade edge radius
defined by maximum roughing blade radius and
minimum stock allowance, convex
(eq 117) 0.05425 inch
r′2VG Maximum gear finishing blade edge radius
defined by maximum roughing blade radius and
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
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Symbol Units VariablesEquationDescription
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
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Symbol Units VariablesEquationDescription
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
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8/15/2019 AGMA 929-A06 Calculation of Bevel Gear Top Land and Guidance on Cutter Edge Radius
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AGMA 929--A06 AMERICAN GEAR MANUFACTURERS ASSOCIATION
28 © AGMA 2006 ---- All rights reserved
Annex D
(informative)
Hypoid example problem
[This annex is provided for informational purposes only and should not be construe