AGMA 1103-H07 Tooth Proportions for Fine- Pitch Spur and Helical Gearing (Metric Edition)

8/15/2019 AGMA 1103-H07 Tooth Proportions for Fine- Pitch Spur and Helical Gearing (Metric Edition)

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A N S I / A G M A 1 1 0 3 - H 0 7

ANSI/AGMA 1103- H07(Metric Edition o

ANSI/AGMA 1003--H07)

AMERICAN NATIONAL STANDARD

Tooth Proportions for Fine-Pitch Spur and

Helical Gearing (Metric Edition)


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ii

Tooth Proportions for Fine--Pitch Spur and Helical Gearing (Metric Edition) ANSI/AGMA 1103--H07

Approval of an American National Standard requires verification by ANSI that the require-

ments for due process, consensus, and other criteria for approval have been met by the

standards developer.

Consensus is established when, in the judgment of the ANSI Board of Standards Review,substantial agreement has been reached by directly and materially affected interests.

Substantial agreement means much more than a simple majority, but not necessarily una-

nimity. Consensus requires that all views and objections be considered, and that a

concerted effort be made toward their resolution.

The use of American National Standards is completely voluntary; their existence does not

in any respect preclude anyone, whether he has approved the standards or not, from

manufacturing, marketing, purchasing, or using products, processes, or procedures not

conforming to the standards.

The American National Standards Institute does not develop standards and will in no

circumstances give an interpretation of any American National Standard. Moreover, no

person shall have the right or authority to issue an interpretation of an American NationalStandard in the name of theAmerican National Standards Institute. Requests forinterpre-

tation of this standard should be addressed to the American Gear Manufacturers

Association.

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 publication is the latest available from the

Association on the subject matter.

[Tables or other self--supporting sections may be referenced. Citations should read: See ANSI/AGMA 1103--H07, Tooth Proportions for Fine--Pitch Spur and Helical Gearing (Met- ric Edition), published by the American Gear Manufacturers Association,500 Montgomery

Street, Suite 350, Alexandria, Virginia 22314, http://www.agma.org.] Approved September 19, 2007

ABSTRACT

Tooth proportions forfine--pitch gearing are similarto those of coarse pitch gearing except in the matterof clear-ance. For20 degree profileangle fine--pitch gearing,this standard provides a systemof enlarged pinionswhichuse the involute formabove 5 degrees of roll. Data on 14--1/2 and 25 degree profileangle systems , as well as adiscussion of enlargement and tooth thickness are included in the annexes.

Published by

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

Copyright © 2007 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: 978--1--55589--903 --5

AmericanNationalStandard


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ANSI/AGMA 1103--H07AMERICAN NATIONAL STANDARD

iii© AGMA 2007 ---- All rights reserved

Contents

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

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

2 Normative references 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Terms and symbols 1. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 General features 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Basis for enlarged (long addendum) pinions 6. . . . . . . . . . . . . . . . . . . . . . . . . . . .

Bibliography 25. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Annexes

A Tooth proportions for 14--1/2 degree fine--pitch gearing 13. . . . . . . . . . . . . . . . . .

B Tooth proportions for 25 degree fine--pitch gearing 15. . . . . . . . . . . . . . . . . . . . .

C Helical pinion enlargement 16. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D Calculations to obtain standard clearance for enlarged pinions andstandard gears 18. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

E Comparative systems for selecting tooth thickness of pinions 20. . . . . . . . . . . .

Tables

1 Terms and symbols 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Diametral pitch, standard tooth proportions and formulas (inch system) 4. . . .

3 Standard diametral pitch tooth dimensions, inches 5. . . . . . . . . . . . . . . . . . . . . .

4 20° Profile angle -- enlarged spur pinions 9. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 20° Profile angle -- reduced spur gears 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Figures

1 Basic rack 3. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

2 Effect of profile shift (addendum modification) 6. . . . . . . . . . . . . . . . . . . . . . . . . . .3 Form diameter on undercut teeth 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4 Form diameter on fillet blend teeth 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5 Center distance and line of action 11. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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ANSI/AGMA 1103--H07 AMERICAN NATIONAL STANDARD

iv © AGMA 2007 ---- 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 Standard

1103--H07, Tooth Proportions for Fine--Pitch Spur and Helical Gearing (Metric Edition).]

As originally developed by the American Gear Manufacturers Association, this standard

was in two parts: the first part, Clearance for 20--Degree Pressure Angle Fine--Pitch Gears

(AGMA 470.01); and the second, 20--Degree Involute Fine--Pitch System for Spur Gears

(AGMA 207.02).

In May, 1949, the two standards were combined and completely re--edited. The next

revision of this standard was begun in 1955.

As a result of the increasing use of gears by sintering and injection molding process, and for

greater tooth strength, tooth forms for 25 degree pressure angle were included. Control

gearing containing large numbers of teeth was recognized by data on the 14--1/2 degree

pressure angle system in the information sheets.

AGMA 207.05, was approved by Sectional Committee B6 and by the sponsors, and

designated USA Standard B6.7--1967 as of September 18, 1967.

Due to difficulties encountered in fabricating gears with involute profiles to the base circle,

theFine--Pitch committeedevelopeda new setof tooth proportions forenlarged pinionsthat

would not require active tooth profiles below five degrees of roll. AGMA 207.06 was approved by the Fine--Pitch Gearing Committee in June, 1971 and

approved by the membership as of May, 1974.

ANSI/AGMA 1003--G93 was a revision of AGMA 207.06. The term “profile angle” was

introduced in place of the basic rack “pressure angle”. Metric data were added, including

ISO symbols. Tables for 20 degree profile angle were revised, and supported with simpler

equations and procedures. The lower range of tooth numbers was redone with less

enlargement, improved contactratio,and lessspecific sliding. Data for7 and8 tooth pinions

were omitted, as they require special design consideration beyond the scope of this

standard. A revised procedure was employed to verify undercut limits, superseding the

approximate and more conservative prior method. Formulas were suppliedfor all tabulated

data. The data on helical gearing was revised using a simple procedure to allow helical

configuration.

Information was added to clarify the distinction between form diameter as generated and

the limit diameter established by operational contact, which determines the contact ratio.

Clarification was made regarding categories of center distance which often was a source of

confusion in the prior standard. Cautionary notes were added to indicate that meshes

employing very small numbers of teeth,while geometricallycorrect,stillrequire analyses for

strength, durability, and clearances. The 5 degree form diameter enlargement method was

extended to include the 14--1/2 degree system, and revisions were made to the 25 degree

system.

ANSI/AGMA 1003--G93 was approved by the Fine--Pitch Gearing Committee in February,

1992 and approved by the AGMA Board of Directors as of May, 1992.

ANSI/AGMA 1103--H07 adds clause 4.9 on fillet root radius values due to cutting tool tipradius, and annex E, which compares several systems for selecting tooth thickness of

pinions.

The first draft of ANSI/AGMA 1103--H07 was made in September, 1999. It was approved by

the AGMA membershipin March,2006. Itwas approved as an American National Standard

on September 19, 2007..

Suggestions for improvement of this standard 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 2007 ---- All rights reserved

PERSONNEL of the AGMA Fine--Pitch Gearing Committee

Chairman: Daniel J. Seger Perry Technology Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . .

Vice Chairman: M. Khawar Anwar All American Mechanical Components and. . . . . . . . . . . . . . . . . . . . .

Gears, Inc.

ACTIVE MEMBERS

D.E. Bailey Rochester Gear, Inc.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

T.H. Dobosz MPC Products Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

M. Eichinger MPC Products Corporation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Y. Kotlyar Bodine Electric Company. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I. Laskin Consultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

H. Minasian Consultant. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .


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vi © AGMA 2007 ---- All rights reserved

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1© AGMA 2007 ---- All rights reserved


American National Standard --

Tooth Proportions for

Fine--Pitch Spur and He-

lical Gearing (Metric Edi-

tion)

1 Scope

This standard is applicable to external spur and heli-

cal gears with 1.25 through 0.2 module and a profile

angle of 20 degrees.

It only applies to standard gears with 24 teeth or

more; enlarged pinions with 9 through 23 teeth; and

reduced gears for meshing with enlarged pinions at

standard center distances.

Much of this same information is applicable to inter-

nal gears.

1.1 Tooth proportions

The tooth proportions shownherein may be used for

many gear designs of finer than 0.2 module; how-ever, such designs should be checked for suitability,

particularly in the areas of contact ratio, undercut-

ting, and clearance.

This standard is similar to ISO 53, Cylindrical gears

for general and heavy engineering -- Standard basic

rack tooth profile.

The main differencebetween the proportionsof fine--

pitch gears and those of coarse--pitch is in the clear-

ance. In fine--pitch gearing, wear on the points of the

cutting tools is proportionally greater than in coarse--

pitch tools. The fillet radius produced by such tooling

will therefore be proportionally greater. The in-

creased clearance in gearing of 1.25 module and

finer provides both for the relatively larger fillet and

also for foreign material that tends to accumulate at

the bottoms of the teeth.

1.2 Number of teeth

Gear designs with low numbers of teeth should be

checked for suitability, particularly in the areas of

contactratio,undercutting,and clearance, as wellas

for strength and durability forload and life considera-

tions.

2 Normative references

The following standards contain provisions which,

through referencein this text, constitute provisionsof

this American National Standard. At the time of pub-

lication, the editions indicated were valid. All stan-

dards are subject to revision, and parties to

agreements based on this American National Stan-

dard are encouraged to investigate the possibility of

applyingthe most recenteditions of thestandardsin-

dicated below. AGMA 904--C96, Metric Usage

AGMA 917--B97, Design Manual for Fine--PitchGearing

ANSI/AGMA 1012--G05, Gear Nomenclature,Definitions of Terms with Symbols

ANSI/AGMA 1102--A03, Tolerance Specificationfor Gear Hobs

ANSI/AGMA 2002--B88, Tooth ThicknessSpecification and Measurement

ANSI B94.21, Shaper Cutters

3 Terms and symbols

3.1 Terms

The terms used, wherever applicable,conform to the

following standards:

ANSI/AGMA 1012--G05, Gear Nomenclature,Definitions of Terms with Symbols

AGMA 904--B89, Metric Usage

3.2 Symbols

Thesymbols used in this standard are shown intable

1.

NOTE: The symbols and definitions used in this stan-

dard may differ from other AGMA standards. The user

should not assume that familiar symbols can be used

without a careful study of these definitions.


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2 © AGMA 2007 ---- All rights reserved

Table 1 -- Terms and symbols

ISOSymbol

Description Units Wherefirst used

a Center distance mm Table 2

ad Calculated tight mesh center distance mm Eq 16

c Clearance mm Table 2

cp Clearance, gear tip to pinion root mm Table 4

d Pitch diameter mm Table 2d ae Outside diameter mm Table 2

d ae1 Outside diameter of pinion mm Eq 15

d ae2 Outside diameter of gear mm Eq 15

d f Root diameter mm Table 2

d 1 Standard pitch diameter of pinion mm Eq 15

d 2 Standard pitch diameter of gear mm Eq 15

ha Addendum mm Table 2

ha1 Addendum, pinion mm Table 4

ha2 Addendum, gear mm Table 5

hf Dedendum mm Table 2

ht Whole depth mm Table 2

hw Working depth mm Table 2

j Backlash mm 4.6

mn Module, normal mm Table 2

mt Module, transverse mm Table 2

p Circular pitch, normal mm Table 2

pt Circular pitch, transverse mm Table 2

rb1 Base radius of pinion mm Figure 5

rb2 Base radius of gear mm Figure 5

re1 Outside radius of pinion mm Figure 5

re2 Outside radius of gear mm Figure 5

rf max Fillet radius, maximum mm Table 2

se Tooth thickness at outside diameter mm 5.4sei1 Top land, pinion mm Table 4

sei2 Top land, gear mm Table 5

sn Tooth thickness, normal mm Table 2

st Tooth thickness, transverse mm Table 2

s1 Tooth thickness, pinion mm Eq 19

s2 Tooth thickness, gear mm Eq 19

z Number of teeth -- -- Table 2

z g Number of teeth, calculated -- -- Eq 20

z 1 Number of teeth, pinion -- -- Table 2

z 2 Number of teeth, gear -- -- Table 2

αd Transverse pressure angle at calculated tight mesh center distance degrees Eq 16αe Pressure angle at outside diameter degrees Eq 13

αn Profile angle, normal degrees Table 2

αt Basic rack transverse profile angle degrees Eq 20

α0 Profile angle degrees Table 2

βm Helix angle degrees Table 2

Δa Center distance enlargement with rack mm 5.9

Δha Addendum modification mm Eq 6

(continued)


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Table 1 (concluded)

ISOSymbol

Description Units Wherefirst used

Δs Tooth thickness modification mm Eq 4

Δ x Enlargement mm Eq 3

εβ Contact ratio -- -- Eq 15

εβx Calculated tight mesh contact ratio -- -- Eq 16

εx Contact ratio, enlarged -- -- Table 4

4 General features

4.1 Basic rack

The basic rack shown in figure 1 is used to illustrate

the tooth proportions covered by this standard. This

standard permits freedom of choice in making

changes in the gear tooth proportions to meet spe-

cial design conditions as long as the resulting gears

are fully conjugate to the basic rack. Such changes

may be indicated when a special contact ratio ormodification for tooth strength is desired.

4.1.1 Spur gears

The basic rack shown in figure 1 and the tooth pro-

portions shown in table 2 provide the basic design

data for spur gear teeth.

4.1.2 Helical gears

Helical teeth covered by this standard are conjugate

in the normal plane to the basic rack shown in figure

1 and table 2.

4.2 Pressure angle and profile angle

4.2.1 Pressure angle, α0

While profile angle is the slope of the cutting tool, a

pressure angle may be defined at any point on the

flank of a gear tooth. See ANSI/AGMA 1012--G05

for further discussion.

4.2.2 Profile angle

The standard profile angle is 20 degrees, and is rec-

ommended for most applications. In the annexes,

data may be found on 14--1/2 and 25 degree profile

angle systems. Profile angle of helical teeth is taken

in the normal plane.

In certain cases, notably some sintered or moldedgears, or in gearing where greatest strength and

wear resistance are desired, a 25 degree profile an-

gle may be required. Profile angles greater than 20

degrees tend to require the use of generating tools

having very narrow point widths. In addition, larger

profile angles require closer control on center dis-

tance tolerance for those gear trains in which back-

lash is critical.

In cases where considerations of angular position or

backlash are critical, and where both pinions and

gears contain relatively large numbers of teeth, a

14--1/2 degree profile angle may be desirable. Ingeneral, profile angles of less than 20 degrees re-

quire a greater amount of modification to avoid un-

dercut problems, and are limited to larger total

numbers of teeth in gear and pinion when operating

on a standard center distance.

Working

depth

Clearance

Wholedepth

Circularpitch

Addendum

Dedendum

Pitchline

Filletradius

Tooththickness

Profileangle

NOTE: Thevalueof thefillet radiusis determined by the

type and design of the cutting tool.Figure 1 -- Basic rack


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Table 2 -- Module, standard tooth proportions and formulas (metric system)

Tooth proportions

Item Spur Helical

Addendum, ha 1.000 mt 1.000 mn

Dedendum, hf 1.200 m t + 0.05 1.200 m n + 0.05Working depth, hw 2.000 m t 2.000 m n

Whole depth, ht 2.200 m t + 0.05 2.200 m n + 0.05Clearance, c (standard) 0.200 m t + 0.05 0.200 m n + 0.05Fillet radius, maximum, rf max(see 4.9)

c1 − sinα0

c1 − sinαn

Tooth thickness, st, sn at standardpitch diameter st =

π m t2

sn = π mn

2

Formulas

Circular pitch, pt, pn pt = π m t p = π m nPitch diameter, d (standard) z mt

z mncos βm

Outside diameter, d ae ( z + 2) m t z mncos βm+ 2mn

Root diameter, d f ( z − 2.4)mt − 0.100 ( z mn)

cos βm− (2.4 m n) − 0.100

Center distance, a (standard) z 1 + z 22

mt

z 1 + z 22 cos βm

mn

where

st is transverse tooth thickness at standard pitch p is normal circular pitch;diameter; βm is helix angle;

sn is normal tooth thickness at standard pitch z is number of teeth;diameter; z 1 is number of pinion teeth;

mn is normal module; z 2 is number of gear teeth;

mt is transverse module; α0 is profile angle; pt is transverse circular pitch; αn is normal profile angle.

4.3 Working depth, hw

The basic working depth is:

hw = 2.000 mn (1)

Teeth withthis depth are commonly referred to as full

depth teeth.

4.4 Addendum, ha

Standard addendum tooth proportions shown in

tables 2 and 3 are used for applications where the

number of teeth are equal to or exceed the minimum

numbers shown in annex C, table C.1.

Enlarged and reduced addendum proportions are

used to avoid objectionable undercut or for consid-

erations of tooth strength, contact ratio or center dis-

tance. Table 4 gives recommended tooth

proportions to avoid undercut problems in a mesh

with a pinion of a small number of teeth. Generally,

as the total number of teeth in gear and pinion gets

smaller, the contact ratio diminishes. Special atten-

tion must be given to avoid contact ratios below 1.2.

4.5 Clearance, c

Standard clearance for the module system is:

c = 0.200 m n + 0.05 (2)

Greater clearance than given in table 3 may be re-

quired if teeth are to be finished by a secondary op-

eration. While the required clearance may vary with

specific gear applications,a value of 0.350 mn should

provide the necessary amount in most cases. See

ANSI/AGMA 1102--A03, ANSI B94.21--1995, and

AGMA 917 --B97.


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4.6 Tooth thickness, st, and backlash, j

The tooth thickness shown in the tables does not in-

clude an allowance for backlash when the gears are

meshed at standard center distances.

In general, the teeth of both members are reduced in

thickness to provide backlash. In cases of pinions

having small numbers of teeth,consideration maybe

given to applying more of the tooth thickness reduc-tion to thegear memberto provide therequired back-

lash. See ANSI/AGMA 2002--B88 for a more

detailed discussion of tooth thickness specification.

Allowance (thinning) for backlash must be

considered to allow for lubricant, temperature ef-

fects, and operational meshing conditions including

deflections, bearing runouts, and gear element vari-

ations. For a detailed discussion see [1]*

NOTE: The design tooth thickness is established from

engineering considerations. It is determined by gear

geometry, gear tooth strength, and backlash. Themethods for establishing design tooth thickness, for a

given application, are beyond the scope of this stan-

dard.

4.7 Whole depth, ht

The whole depth values shown in the tables will in-

crease in proportion to the amount of tooth thinning

in cutting the teeth, unless the outside diameter is

also modified.

The whole depth of enlarged and reduced adden-

dum gearing generated with pinion type shaper cut-

ters may be differentfrom that shown in thetables. In

order to control the whole depth of external gears,

the root diameter should be specified as a maximum

dimension only.

4.8 Generating tools

Standard generating tools (hobs or shaper cutters)

are used for either spur or helical gears. See AGMA

1102--A03 and ANSI B94.21--1995.

Table 2 gives the formulas for standard tooth propor-

tions without allowance for backlash. In order to

minimize the vast number of tools (cutters and mas-

ter gears) required for all possible modules, the fol-

lowing are recommended:

Modules:1.251.00.90.8

0.70.60.50.40.30.2

Table 3 shows the tooth dimensions for each modu-

le. Gear ratios at non--standard center distances

which are sometimes fixed by component design re-

quirements can usually be obtained using standard

pitch cutters and enlarging one or both of the mating

gears. See annex E.6.

Table 3 -- Standard module tooth dimensions, mm

1 2 3 4 5 6 7 8

Module Circular

pitchCircular

thicknessWorking

depthWholedepth

Clearance Addendum Dedendum

1.25 3.9270 1.9635 2.500 2.800 0.300 1.250 1.550

1.0 3.1416 1.5708 2.000 2.250 0.250 1.000 1.250

0.9 2.8274 1.4137 1.800 2.030 0.230 0.900 1.130

0.8 2.5133 1.2566 1.600 1.810 0.210 0.800 1.010

0.7 2.1991 1.0996 1.400 1.590 0.190 0.700 0.890

0.6 1.8850 0.9425 1.200 1.370 0.170 0.600 0.770

0.5 1.5708 0.7854 1.000 1.150 0.150 0.500 0.650

0.4 1.2566 0.6283 0.800 0.930 0.130 0.400 0.530

0.3 0.9425 0.4712 0.600 0.710 0.110 0.300 0.410

0.2 0.6283 0.3142 0.400 0.490 0.090 0.200 0.290

NOTE: All dimensions are given in millimeters.

* [ ] Numbers in brackets refer to the references in the bibliography.


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4.9 Tool tip radius

The basic rack for AGMA fine--pitch tooth propor-

tions has traditionally been shown with a zero fillet

radius. This implies a sharp corner on the tip of any

generating tool designed to conform to this basic

rack. In actual practice, the corner is made with a

small radius. Although the corresponding basic rack

fillet radiushas notbeen defined in previous versionsof this standard, the value commonly used by cutting

tool manufacturers in tooling such as hobs, typically

falls in the range of 0.1 to 0.3 × mn. See table 2 forfillet radius rfmax.

The introduction of manufacturing of fine--pitch

gears by moldingprocesses and the use of the basic

rack to graphically define gear tooth outlines in such

molds, has required reconsideration of this omis-

sion. The unquestioned use of thezero fillet radius in

the basic rack has led to the molding of fine--pitch

gears with excessively sharp fillets which unneces-

sarily diminish the gear strength and quality, see

ANSI/AGMA 1106--A97.

5 Basis for enlarged (long addendum) pin-

ions

5.1 Enlargement, Δ x

Pinions with small numbers of teeth are enlarged so

that a standard tooth thickness rack withan enlarged

addendum of (1.0 + 0.05) mt will start contact 5 de-grees above the base radius. The use of (0.05) extra

addendum provides an allowance for center dis-

tance variation and eccentricity of mating gear out-

side diameter. The 5 degrees avoids the use of the

involute in the area near the base circle.

A corresponding increase in tooth thickness is made

along with the addendum modification, see figure 2.

NOTE: Caution should be exercised in using enlarged

pinions in speed increasing drives to avoid excessivefriction, deflection, and possible lockup.

12 tooth1 module20° pressure angle1.5708 mm tooththickness at referencepitch diameter

12 tooth1 module20° pressure angle1.94703 mm tooth

thickness at referencepitch diameter

Figure 2 -- Effect of profile shift (addendum

modification)

5.2 Form diameter

Teeth designed in accordance with this standard will

have an involute profile between the 5 degree diam-

eter and that point where tip chamfer or edge roundbegins, see figures 3 and 4.

Base diameter

Root diameter

Involuteprofile

Filletzone

Form diameter

Limit diameter

Start of active

profile (SAP)

Top land Corner round

Figure 3 -- Form diameter on undercut teeth


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Base diameter

Form diameter

Involuteprofile

Filletzone Root diameter

Top land

Limit diameter

Tip chamfer

Diameter at 5°minimum roll angle

Figure 4 -- Form diameter on fillet blend teeth

This form diameter provides more than enoughlength of involute profile for meshing with any mating

gear, including a rack but does not always apply to

mating internal gears.

Any special tip relief or modification of involute profile

to suit design or operational requirements is beyond

the scope of this standard.

5.3 Limit diameter

The limit diameter is based on theactual contact with

a mating gear at the operating or working center dis-

tance. It may be shown on the drawing as an op-

tional specification thereby confining inspection to

functional requirements.

5.4 Top land, se

In order to avoid sharp tips and maintain a minimum

top land for strength and durability purposes, the en-

larged addendum (enlarged outside diameter) is re-

duced from the computed enlargement in the case of

pinions with very small numbers of teeth. In this

standard, the recommended minimum top land is

0.275 mt for spur gears and 0.275 mn for helicalgears. For power gearing, good design practice lim-

its the ratio of the top lands in a mesh.

5.5 Undercut

Conditions of undercut were computed by means of

the method in [2], and cross checked by the

equations of [3]. Undercut is avoided by addendum

modification.

The addendum modification, Δha, satisfies the re-quirement that any radial height undercut above the

base circle must not exceed the 5 degree roll angle

diameter, see figures 3 and 4.

5.6 Root diameter, d f

Since this system is based on the use of a standard

rack, the root diameter derives from the computed

(not truncated) outsidediameterof thepinionand the

outside diameter (reduced) of the gear. The root di-

ameter is specified as a maximum dimension and

generally is not toleranced. Highly stressed gearsmay require some limit, but would be used in con-

junction with a controlled root fillet radius as addi-

tional specification.

5.7 Mating gear (standard)

The mating gear to an enlarged pinion may be a

standard gear, in which case the center distance

must be enlarged for operation.

CAUTION: The center distance for tight mesh (zero

backlash)does notprovide thestandard clearance. It is

therefore necessary to increase the enlarged center

distance if thestandardclearanceis desired. When do-ing so, the mesh will incur some backlash increase at

the new working center distance. See annex D.

5.8 Mating gear (reduced -- short addendum)

The mating gear can be meshed at standard center

distance by reducing the mate in the same manner

and amount used to enlarge the pinion (except trun-

cation of top land).


14/32



5.9 Formula for enlargement of spur pinions

− cosα0 tan 5°) mt (3)

Δ x = 1.05 − 0.5 z 1 sin α0 sinα0

st = π2

+ Δs (4)

Δs = 2 Δ x tan α0 (5)Δha = Δ x (6)

1)

where

Δ x is enlargement = Δa, mm.

z 1 is number of pinion teeth;

α0 is transverse profile angle, degrees;

mt is transverse module, mm;

st is transverse tooth thickness, mm;

Δs is tooth thickness modification, mm;

Δha is addendum modification, mm;

Δa is center distance enlargement with rack,mm.

NOTE: Equation 3 is taken from reference [4] and con-

tains a mathematical error in the use of “tan 5°”. This

should have been “tan 4.98726°”, which is the equiva-

lent pressure angle for 5 degrees of roll angle. The use

of “tan 5°” provides a roll angle of 5.01273°.

Since the purpose is to avoid contact in this region, it

provides a slight extra allowance.

To avoid wholesale tabular corrections to long standing

data, the original equation has been retained.

The 5 degree form diameter is based on the use of a

1.05 addendum rack, and is equivalent to the limit

diameter with this rack.

5.9.1 Equations for tables 4 and 52)

The following equations are used to determine the

values in tables 4 and 5:

× sinα0sinα0 − cosα0 tan5° (7)Δha = 1.05 − 0.5 z

d ae = z + 2 2 Δha (8) 1), 2)

ha = 1 Δha (9) 1), 2)

st = π2 Δs (10) 2)

d f = z − 2.4 2 Δ (11) 2), 3)

se = 0.275 min found by iteration of d ae

(12)

se = d aest z + inv α0 − inv αe (13)αe = cos−1 z cosα0d ae (14)

For standard center distance

εβ =⎪⎪

⎡

⎣

d 2ae1

− d 1 cosα02

2 p t cosα0⎪⎪⎤

⎦

+⎪⎪⎡

⎣

d 2ae2

− d 2 cosαo2


⎦− 2 a sinα0

2 p t cosα0

(15)

For non--standard center distance

εβx =⎪⎪

⎡

⎣

d 2ae1

− d 1 cosα02


⎦

+⎪⎪⎡

⎣

d 2ae2

− d 2 cosαo2


⎦− 2 ad sinαd

2 p t cosα0

(16)

where

d ae is outside diameter, mm;

z is number of teeth;

ha is addendum, mm;

d f is root diameter, mm;

se is tooth thickness at outside diameter,mm;

αe is pressure angle at outside diameter,mm;

εβ is contact ratio;

d ae1, d ae2 is outside diameter of pinion, gear,mm;

d 1, d 2 is standard pitch diameter of pinion,gear;

______________________ 1) Nominal equation, modified when pinion tooth is truncated for minimum top land.2) Sign determined by enlargement or reduction from standard.3) Actual root diameter is decreased by 0.10 mm.


15/32



pt is circular pitch, mm;

a is center distance (standard), mm;seeequation 17;

εβx is calculated tight mesh contact ratio;

ad is calculated tight mesh center dis-tance, mm;

αd is transverse pressure angle atcalculated tight mesh center distance

(enlarged), degrees.

5.10 Standard center distance (for standard

spur gears)

Standard gears, made to standard tooth proportions

without modification of addendum, dedendum, or

tooth thickness (other than for backlash), are run at

standard center distance. Data is shown without an

allowance for backlash.

a = z

1 + z

2

mt2 (17)

5.11 Standard center distance (for enlarged spur

pinions and reduced gears)

The data in this standard provide the proper dimen-

sional adjustment of each mating member to allow

them to run at the same (standard) center distance

as unmodified (standard) gears. Data is shown with-

out an allowance for backlash.

Table 4 provides data for enlarged pinions, and table

5 provides data for reduced gears.

The advantages of this system are: no change in

center distance is required; operating pressure an-

gle remains standard; and the contact ratio is slightly

greater than if the center distance were increased.

In most cases where gear trains include idler gears,

thestandardcenterdistancecannotbeusedwithen-

larged gears.

Table 4 -- 20° Profile angle -- enlarged spur pinions

Enlarged pinion dimensions (unit module)Enlarged center distance, pinion with

24 tooth gear

1 2 3 4 5 6 7 8 9

Numberof teeth

z 1

Outside di-ameter (en-

larged)d ae1

Addendum(enlarged)

ha1

Tooththickness(enlarged)

s1

Rootdiameter1)

(enlarged)d f

Topland sei1

Contactratioε x

Clearancegear tip to

pinion root2)

cp

Centerdistance

ad

9

10

11

12

13

14

15

16

17

18

19

20

21

2223

12.0144

13.0256

14.0304

15.0296

15.9448

16.8560

17.7671

18.6783

19.5894

20.5005

21.4117

22.3228

23.2340

24.145125.0562

1.5072

1.5128

1.5152

1.5148

1.4724

1.4280

1.3836

1.3391

1.2947

1.2503

1.2058

1.1614

1.1170

1.07261.0281

2.04405

2.01171

1.97937

1.94703

1.91469

1.88234

1.85000

1.81766

1.78532

1.75297

1.72063

1.68829

1.65595

1.623611.59126

7.9003

8.8114

9.7225

10.6337

11.5448

12.4560

13.3671

14.2783

15.1894

16.1005

17.0117

17.92258

18.8340

19.745120.6562

0.2750

0.2750

0.2750

0.2750

0.3401

0.3994

0.4513

0.4968

0.5370

0.5728

0.6046

0.6331

0.6585

0.68140.7020

1.209

1.261

1.310

1.358

1.383

1.407

1.429

1.450

1.471

1.492

1.511

1.531

1.550

1.5691.588

0.1308

0.1402

0.1489

0.1568

0.1640

0.1705

0.1764

0.1816

0.1861

0.1900

0.1932

0.1959

0.1978

0.19920.1999

17.08092

17.54587

18.01010

18.47360

18.93641

19.39851

19.85995

20.32072

20.78083

21.24027

21.69909

22.15726

22.61481

23.0717223.82799

NOTE 1: Multiply values in columns 2, 3, 4, 5, 6, 8 and 9 by module for millimeter units.

NOTE 2: Table values for contact ratio are for tight mesh conditions, with no allowance for tooth thinning. Contact ratio iscomputed for tight mesh and limit diameters. Columns 6, 7, 8 and 9 are for reference only and not tobe specified ondrawings.

NOTE 3: For 9 to 12 teeth the outside diameter is based on minimum top land requirement. See 5.4.

NOTE 4: Enlargement is not required for 24 teeth and higher.1) Actual root diameter is decreased by 0.10 mm.2) Actual clearance is increased by 0.05 mm.3) Refer to annex D for maintenance of standard 0.20 clearance.


16/32



Table 5 -- 20° Profile angle -- reduced spur gears

Reduced gear dimensions (unit pitch)Standard center distance,

a = 24.000

1 2 3 4 5 6 7 8

Number ofgear teeth

z 2

Outsidediameter

(reduced)d ae2

Addendum(reduced)

ha2

Tooththickness(reduced)

s2

Rootdiameter1)

(reduced)d f

Top land sei2

Contact ratio, z 1 mating with

z 2εβ

Number ofteeth inpinion

z 1

39

38

37

36

35

34

33

32

31

30

29

28

27

26

25

39.6997

38.7886

37.8775

36.9663

36.0552

35.1440

34.2329

33.3218

32.4106

31.4995

30.5883

29.6772

28.7660

27.8549

26.9438

0.3499

0.3943

0.4387

0.4832

0.5276

0.5720

0.6164

0.6609

0.7053

0.7497

0.7942

0.8386

0.8830

0.9275

0.9719

1.09754

1.12988

1.16222

1.19457

1.22691

1.25925

1.29159

1.32393

1.35628

1.38862

1.42096

1.45330

1.48565

1.51799

1.55033

35.2997

34.3886

33.4775

32.5663

31.6552

30.7440

29.8329

28.9218

28.0106

27.0995

26.1883

25.2772

24.3660

23.4549

22.5438

0.8414

0.8389

0.8357

0.8319

0.8273

0.8220

0.8158

0.8088

0.8008

0.7918

0.7817

0.7703

0.7577

0.7436

0.7279

1.250

1.313

1.372

1.427

1.457

1.484

1.507

1.528

1.546

1.562

1.574

1.585

1.593

1.598

1.601

9

10

11

12

13

14

15

16

17

18

19

20

21

22

23

NOTE 1: Multiply values in columns 2, 3, 4, 5 and 6 by module for millimeter units.

NOTE 2: Table values for contact ratio are for tight mesh conditions, with no allowance for tooth thinning. Contact ratiois computedfor tight mesh and limit diameters. Columns 6, 7 and 8 are for reference onlyand not tobe specified ondraw-ing.

1) Actual root diameter is decreased by 0.10 mm.

5.12 Enlarged center distance (for enlarged spur

pinion mating with a standard gear)

When an enlarged pinion and a standard gear are

meshed together, the center distance must be in-

creased. Data for the individual pinions is shown

without an allowance for backlash, see table 4. The

computation for the tight mesh center distance is de-

pendent upon the summation of the effects of the

tooth thickness of the pinion and the tooth thickness

of the gear. With an increase of center distance,

there is a slight increase in the operating pressure

angle.

ad = acosα0cosαd

(18)

inv αd = inv α0 +s1 + s2 − pt z 1 + z 2 m t

(19)

where

s1, s2 is tooth thickness of pinion, gear, mm;

pt is transverse circular pitch, mm;

z 2 is number of gear teeth.

The advantage of this system is that only the pinionsneed be changed from standard dimensions.

The disadvantages of this system are: center dis-

tance must be enlarged over standard; theoperating

pressure angle increases slightly with different com-

binations of pinions and gears; and the contact ratio

is slightly smaller than that obtained with the stan-

dard center distance system.

Special attention must be paidto providing adequate

clearance with these meshes since the computed

tight mesh centerdistance does notprovide thestan-

dard clearance. An additional increase in the centerdistance may be required which results in a slight

backlash in the mesh, see annex D.

5.13 Center distance caution (enlarged pinion

meshing with enlarged pinion)

The design method shown in this standard is not in-

tended for use in meshing identical enlarged pinions

together, nor any combination of enlarged pinions


17/32



meshing together. While some combinations may

be successful, they are not recommended and have

been removed from this standard. Such gears re-

quire special design consideration,not only forclear-

ance and contact ratios, but for analysis for strength

and endurance and variousother considerationsbe-

yond the scope of this standard.

5.14 Contact ratio

The contact ratio is the number of angular pitches

through which a tooth surface rotates from the be-

ginning to the end of contact. It is obtained as the ra-

tio of the active length of action to the base pitch, see

figure 5 and equation 15. Contact ratio is related to

the center distance employed; i.e., standard, en-

larged, or working.

5.15 Enlargement criteria

Table C.1 in annex C lists the number of teeth belowwhich enlargement should be made to satisfy the 5°

angle minimum condition. The numbers of teeth are

calculated from equation 20 and rounded up to the

next integer value. The equation is based on condi-

tions in the transverse plane, including the 5° roll

angle and the basic rack transverse profile angle,αt.

z g = 2.10 cosβm

sinαt sinαt − cosαt tan5° (20)

where

z g is calculated number of teeth. Pinions with

numbers of teeth that exceed this value do

not require enlargement;

βm is helix angle, degrees;

αt is basic rack transverse profile angle,

degrees.

αt = tan−1

tan αncos βm

(21)

where

αn is normal profile angle, degrees;

βm is helix angle, degrees.

Pinions made withtoothnumbers largerthan z g allow

use of standard tooth proportion.

Basepitch

Activelength of action

α0

a

re2

re1

rb1

rb2

Key

re1, re2 is outside radius of pinion, gear, mm;

rb1, rb2 is base radius of pinion, gear, mm.

Figure 5 -- Center distance and line of action

5.16 Example (spur pinion center distance)

Findthe enlarged center distance, ad , ofa9toothen-

larged pinion running with a standard 24 tooth gear.This method finds the tight mesh center distance by

summation of the tooth thicknesses. See equation

18.

z 1 = 9

z 2 = 24

α0 = 20°

mt = 1

pt = π

s1 = 2.04405

s2 = p

2

The following equations (from 5.9 to 5.12) are used:

a = (9 + 24)

2 = 16.5

inv α0 = tan α0 − α0 = 0.0149044

+(2.04405 + 1.570796 − π)

(9 + 24) (1)

inv αd = 0.0149044

inv αd = 0.0292454


18/32



An accurate inverse involute is usually obtained by a

computer iteration process.

αd = 24.80595°

ad = 16.5000 cos 20°

cos 24.80595°

ad = 17.08092

Thetight mesh centerdistance from theabove equa-

tion is dimensionless. To find the center distance in

millimeters, multiply by the module, mt.

Example for 1 module:

ad = 17.08092 (1) = 17.08092 mm


19/32



Annex A

(informative)

Tooth proportions for 14--1/2 degree fine--pitch gearing

[This annex is provided for informational purposes only and should not be construed as a part of ANSI/AGMA1103--H07, Tooth Proportions for Fine--Pitch Spur and Helical Gearing (Metric Edition).]

Table A.1 -- 14--1/2° Profile angle — enlarged spur pinions

Enlarged pinion dimensions (unit pitch)Enlarged center distance, pinion

with 51 tooth gear

1 2 3 4 5 6 7 8 9

Numberof teeth

z 1

Outsidediameter

(enlarged)d ae1

Addendum(enlarged)

ha1


s1

Rootdiameter1)

(enlarged)d f

Top land sei1

Contactratioε x

Clearancegear tip to

pinion root2)

cp

Centerdistance

ad

11121314151617

181920212223242526272829303132

333435363738394041424344454647

484950

14.337515.383016.424117.461418.477819.436320.3948

21.353322.311823.270424.228925.187426.145927.104428.062929.021529.980030.938531.897032.855533.814034.7726

35.331136.689637.648138.606639,565140.523741.482242.440743.399244.357745.316346.274847.233348.191849.1503

50.108851.067452.0259

1.66881.69151.71201.73071.73891.71811.6974

1.67671.65591.63521.61441.59371.57301.55221.53151.51071.49001.46921.44851.42781.40701.3863

1.36551.34481.32411.30331.28261.26181.24111.22041.19961.17891.15811.13741.11661.09591.0752

1.05441.03371.0129

1.995881.985161.974431.963701.952971.942241.93152

1.920791.910061.899331.888601.877881.867151.856421.845691.834961.824231.813511.802781.792051.781321.77059

1.759871.749141.738411.727681.716951.706231.695501.684771.674041.663311.652591.641861.631131.620401.60967

1.598941.588221.57749

10.243611.202212.160813.119214.077815.036315.9948

16.953317.911818.870419.828920.787421.745922.704423.662924.621525.580026.538627.497028.455529.414030.3726

31.331132.289633.248134.206635.165136.123737.082238.040738.999239.957740.916341.874842.833343.791844.7503

45,708846.667447.6259

0.27500.27500.27500.27500.28840.34180.3898

0.43330.47290.50900.54230.57290.60130.62750.65200.67470.69600.71600.73470.75230.76890.7844

0.79910.81300.82620.83860.85040.86160.87220.88230.89190.90100.90960.91780.92560.93310.9402

0.94700.95340.9595

1.3761.4291.4791.5271.5701.5951.620

1.6441.6661.6881.7081.7281.7481.7661.7841.8011.8181.8351.8511.8661.8811.896

1.9111.9251.9391.9521.9661.9791.9922.0052.0182.0302.0422.0552.0672.0792.091

2.1032.1152.126

0.09110.09680.10240.10790.11310.11820.1231

0.12780.13240.13680.14100.14510.14900.15280.15640.15980.16310.16620.16920.17210.17480.1773

0.17970.18200.18420.18620.18800.18970.19130.19270.19410.19520.19630.19720.19800.19860.1992

0.19960.19980.2000

31.7128632.1979332.6827933.1674833.6519934.1363234.62049

35.1044835.5882936.0719536.5554337.0387837.5219538.0049638.4878138.9705139.4530639.9354740.4177240.8998341.3817841.86360

42.3452842.8268143.3082043.7894544.2705644.7515545.2323945.7130946.1936646.6740947.1544247.6345948.1146348.5945449.07432

49.5539750.0335250.51292

NOTE1: Multiply values in columns 2, 3, 4, 5, 6, 8 and 9 by module for millimeter units.

NOTE2: Table values for contact ratio are for tight mesh conditions, with no allowance for tooth thinning. Contact ratio is computed for actualmesh and limit diameters. Columns 6, 7, 8 and 9 are for reference only and not to be specified on drawings.

NOTE3: Enlarged pinions are designed to use the involute form above 5° of roll.

1) Actual root diameter is decreased by 0.10 mm.2) Actual clearance is increased by 0.05 mm.3) Enlargement is not required for 51 teeth and higher.4) For 11 to 14 teeth, the outside diameter is reduced to maintain 0.275 mn topland.


20/32



Table A.2 -- 14--1/2 degree profile angle -- reduced spur gears

Reduced gear dimensions (unit pitch)Standard center distance

a = 51.0000

1 2 3 4 5 6 7 8

Minimumnumber of

teeth ingear

z 2

Outsidediameter(reduced)

d ae2

Addendum(reduced)

ha2

Tooth thick-ness

(reduced) s

2

Rootdiameter1)

(reduced)d

f

Top land s

ei2

Contactratio z 1

mating with z 2εβ


z 1

91908988878685848382818079

78777675747372

91.356390.397889.439388.480887.522286.563785.605284.646783.688282.729681.771180.812679.8541

78.895677.937176.978576.020075.061574.103073.1445

0.17820.19890.21960.24040.26110.28190.30260.32330.34410.36480.38560.40630.4270

0.44780.46850.48930.51000.53080.55150.5722

1.145711.156441.167161.177891.188621.199351.210081.220811.231531.242261.252991.263721.27445

1.285171.295901.306631.317361.328091.338811.34954

86.956385.997885.039384.080883.122282.163781.205280.246779.288278.329677.371176.412675.4541

74.495673.537172.578571.620070.661569.703068.7445

1.05501.05491.05471.05441.05401.05351.05301.05241.05171.05091.05001.04901.0480

1.04681.04561.04411.04261.04101.03931.0376

1.3531.4171.4781.5371.5901.6251.6591.6901.7211.7501.7771.8031.828

1.8511.8741.8951.9151.9341.9521.970

11121314151617181920212223

24252627282930

71706968676665

64636261605958575655545352

72.186071.227470.268969.310468.351967.393466.4349

65.476364.517863.559362.600861.642360.683759.725258.766757.808256.849755.891254.932653.9741

0.59300.61370.63450.65520.67590.69670.7174

0.73820.75890.77960.80040.82110.84190.86260.88340.90410.92480.94560.96630.9871

1.360271.371001.381731.392451.403181.413911.42464

1.435371.446101.456821.467551.478281.489011.499741.510461.521191.531921.542651.553381.56410

67.786066.827465.868964.910463.951962.993462.0349

61.076360.117859.159358.200857.242356.283755.325254.366753.408252.449751.491250.532649.5741

1.03551.03341.03121.02891.02641.02371.0209

1.01801.01491.01161.00811.00451.00070.99660.99240.98790.98330.97840.97320.9678

1.9862.0012.0152.0292.0412.0532.064

2.0742.0832.0922.0992.1062.1132.1182.1232.1262.1302.1322.1342.135

31323334353637

38394041424344454647484950

NOTE 1: Multiply values in columns 2, 3, 4, 5 and 6 by module for millimeter units.

NOTE 2: Table values for contact ratio are for tight mesh conditions, with no allowance for tooth thinning. Contact ratio is computedfor actual mesh and limit diameters. Columns 6, 7 and 8 are for reference only and not to be specified on drawings.1) Actual root diameter is decreased by 0.10 mm.


21/32



Annex B

(informative)

Tooth proportions for 25 degree fine--pitch gearing


Table B.1 -- 25 degree profile angle -- enlarged spur pinions

Enlarged pinion dimensions (unit pitch)Enlarged center distance, pinion

with 15 tooth gear

1 2 3 4 5 6 7 8 9

Numberof teeth

z 1

Outsidediameter

(enlarged)d ae1

Addendum(enlarged)

ha1


s1

Rootdiameter1)

(enlarged)d f

Top land sei1

Contactratioεβ x

Clearancegear tip

to pinionroot2)

cp

Centerdistance

ad

8 10.6631 1.3316 2.00877 6.5392 0.2750 1.123 0.1654 11.93497

9 11.6203 1.3102 1.94111 7.3942 0.2750 1.174 0.1753 12.37237

10 12.5691 1.2846 1.87345 8.2490 0.2750 1.223 0.1836 12.80806

11 13.5040 1.2520 1.80579 9.1040 0.2807 1.269 0.1901 13.24207

12 14.3588 1.1794 1.73813 9.9588 0.3478 1.294 0.1950 13.67440

13 15.2138 1.1069 1.67047 10.8138 0.4034 1.319 0.1982 14.10509

14 16.0686 1.0343 1.60281 11.6686 0.4500 1.343 0.1999 14.53414

15 17.0000 1.0000 1.57080 12.6000 0.4743 1.358 0.2000 15.00000

NOTES

Multiply values in columns 2, 3, 4, 5, 6, 8 and 9 by module for millimeter units.

Table valuesfor contact ratio arefor tight mesh conditions, with no allowancefor tooth thinning. Contact ratio is computedfor actual mesh and limit diameters. Columns 6, 7, 8 and 9 are for reference only and not to be specified on drawings.

Enlarged pinions are designed to use the involute form above 5° of roll.1) Actual root diameter is decreased by 0.10 mm.2) Actual clearance is increased by 0.05 mm.3) Enlargement is not required for 16 teeth and higher.4) For 8 to 10 teeth, the outside diameter is reduced to maintain 0.275 mn top land.

Table B.2 -- 25 degree profile angle -- reduced spur gears

Reduced gear dimensions (unit pitch)Standard center distance

a = 15.0000

1 2 3 4 5 6 7 8

Number ofgear teeth

z 2

Outsidediameter

(reduced)d ae2

Addendum(reduced)

ha

Tooth thick-ness (re-

duced) s2

Rootdiameter1)

(reduced)d f

Top land sei2

Contactratio, z 1

mating with z 2εβ


z 1

22

21

20

19

18

17

16

15

23.0608

22.2059

21.3510

20.4961

19.6412

18.7862

17.9313

17.0000

0.5304

0.6029

0.6755

0.7480

0.8206

0.8931

0.9657

1.0000

1.13283

1.20049

1.26814

1.33580

1.40346

1.47112

1.53878

1.57080

18.6568

17.8059

16.9510

16.0961

15.2412

14.3862

13.5313

12.6000

0.6174

0.6058

0.5912

0.5734

0.5519

0.5261

0.4955

0.4743

1.181

1.236

1.284

1.325

1.341

1.351

1.357

1.358

8

9

10

11

12

13

14

15

NOTES

Multiply values in columns 2, 3, 4, 5 and 6 by module for millimeter units.

Table valuesfor contact ratio are fortightmesh conditions, with no allowance fortooththinning. Contact ratio is computedfor actual mesh and limit diameters. Columns 6, 7 and 8 are for reference only and not to be specified on drawings.1) Actual root diameter is decreased by 0.10 mm.


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Annex C

(informative)

Helical pinion enlargement


C.1 Helical gears

Helical gears may be enlarged and reduced in the

same manner as spur gears, but caution must be

observed in the translation for tooth thickness and

top land. Since enlargement is based upon the use

of standard tools, made to standard proportions in

the normal plane, conversions must be made for

transverse plane data and vice versa.

Since tabular data is not practical for the numerous

combinations of helical gears, it is necessary to

compute center distance, clearance, and contact

ratio for each combination. All data would be in

accordance with equations in table 2.

C.1.1 Example (standard helical pinion)

For a 23 degree helix angle and a 20 degree normal

pressure angle, the minimum number of teeth not

requiring enlargement is 19. See table C.1 andequation 20.

= 21.57398°

α0 = tan−1 tanαn

cos βm

α0 = tan−1 tan 20°

cos23°

= tan−1 0.39540

(C.1)

where

α0 is profile angle, transverse, degrees;

αn is profile angle, normal, degrees;

βm is helix angle, degrees;

Table C.1 -- Enlargement criteria

14.5° 20° 25°

Helix angle,

degrees

βm

Transverseprofile

angle, αpt

Numberof teeth

z g

Helix angle,

degrees

βm

Transverseprofile

angle, αpt

Numberof teeth

z g

Helix angle,

degrees

βm

Transverseprofile

angle, αpt

Numberof teeth

z g

0 14.5 50.62 0 20 23.63 0 25 14.47

5 14.553040 49.97 5 20.070308 23.36 5 25.083771 14.32

10 14.714048 48.07 10 20.283559 22.55 10 25.337611 13.85

15 14.988849 45.04 15 20.646896 21.25 15 25.769262 13.11

18 15.212411 42.77 18 20.941896 20.27 18 26.118938 12.54

20 15.387707 41.09 20 21.172832 19.54 20 26.392181 12.12

23 15.692808 38.37 23 21.573983 18.36 23 26.865777 11.44

25 15.926252 36.45 25 21.880232 17.52 25 27.226435 10.96

30 16.626985 31.42 30 22.795877 15.30 30 28.300052 9.66

35 17.521624 26.25 35 23.956803 12.99 35 29.650978 8.31

40 18.654748 21.22 40 25.413766 10.71 40 31.329769 6.9545 20.089512 16.54 45 27.236313 8.54 45 33.403198 5.65

NOTE:1) All numbers of teeth will be rounded to the next higher integer.2) Pinions with number of teeth that exceed this value do not require enlargement.


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For 1.25 normal module:

= 25.80106 (C.2)

d = z mncos βm

= 19(1.25)

cos 23°

(C.3)sn = π m n

2 = 1.96350

(C.4)s = sn

cos βm = 2.13306where

d is pitch diameter, mm;

z is number of teeth;

mn is module, normal, mm;

sn is tooth thickness, normal, mm;

s is tooth thickness, transverse, mm.

Computations are made in the transverse plane fora

summation of tooth thicknesses withthe mating gear

to obtain the tight mesh center distance, clearance,

and contact ratio.

C.1.2 Enlarged helical pinion

When dealing with a pinion having fewer teeth than

shown in table C.1, computation should be made for

the 5 degree requirement and also an investigation

of the undercut must be performed. Detailed

procedures for this are best left to a design manual,

and are considered beyond the scope of this

standard.


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Annex D

(informative)

Calculations to obtain standard clearance for enlarged pinions and standard gears


D.1 Introduction

When using enlarged pinions and standard gears,

special attention should be paid to providing ade-

quate clearance since the computed tight mesh dis-

tance does not provide the standard clearance. An

additional increase in the center distance may be re-

quired whichresults in a slightbacklash in the mesh.

This approach, however, reduces the contact ratio.

D.2 Clearance

Note that column 8 in table 4 indicates the clearance

for the tight mesh condition. Since the clearance is

less than 0.200 (for unit pitch), the working center

distance should be increased to obtain the desired

clearance, or the outside diameter of the reduced

gear can be reduced further without tooth thinning

adjustment.

D.3 Center distance (working)

The minimum center distance is determined by the

requirement for clearance, and is obtained by use of

the following equation. This approach also reduces

the contact ratio. (See table D.1)

aw =

d ae2 + d f12 + 0.20

(D.1)

where

aw is unit center distance, working;

d ae2 is unit outside diameter of gear;

d f1 is unit root diameter of pinion

Using the example from 5.16, where z 1 = 9, z 2 = 24,

and m = 1.0:

aw = 26 + 7.9003

2 + 0.20 = 17.15015

To obtain the actual number, multiply by the module

(17.15015 mn).

D.4 Backlash (minimum)

A minimum backlash accrues even without any con-

sideration for requirements by the necessity to pro-

vide clearance. The resulting minimum backlash is

determined by the following equation.

j = (π a w)

z 1 + z 2− π

2 (D.2)

j = (π 17.15015)

9 + 24 − π2

= 0.06189

Backlash for 1 module:

j = (0.06189)(1) = 0.062 mm

TableD.1 gives module values of minimum backlash

for meshes of enlarged pinions with a 24 tooth stan-

dard gear.

Table D.1 -- Working center distance,* enlarged

pinion with 24 tooth standard gear

(20 degree profile angle, unit pitch)

z 1 εβw aw min j

9 1.154 17.15015 0.06189

10 1.212 17.60570 0.05597

11 1.268 18.06125 0.05038

12 1.288 18.55785 0.04868

13 1.353 18.97240 0.0401114 1.381 19.42800 0.03538

15 1.408 19.88355 0.03090

16 1.434 20.33915 0.02664

17 1.459 20.79470 0.02258

18 1.482 21.25025 0.01872

19 1.505 21.70585 0.01504

20 1.527 22.16140 0.01152

21 1.548 22.61700 0.00817

22 1.568 23.07255 0.00495

23 1.588 23.52810 0.00188

24 1.602 24.00000 0.00000

*Based on standard clearance (0.200 mn) and data fromtables 4 and 5.

NOTE: Multiply third and fourth columns by module formillimeter units.


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D.5 Alternate (reduced gear)

In meshes with insufficient clearance, the outside di-

ameter of the gear can be further reduced without a

corresponding reduction in tooth thickness. This ap-

proach also reduces the contact ratio.

= 25.8615

(D.3)d ae2 = 2 ad − 0.200 − d f1= 2 (17.08092 − 0.200) − 7.9003

D.6 Contact ratio (working)

εβw

=

d 2ae1

− d 1

cosα2 + d 2ae2

− d 2

cosα22 p t cosα

(D.4)− 2 aw sinαw

2 p t cosα

where

εβw is contact ratio at working center distance;

αw is pressure angle, working, degrees.


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Annex E

(informative)

Comparative systems for selecting tooth thickness of pinions


E.1 Introduction

A variety of systems have been used for selecting

the tooth thickness and related tooth proportions for

pinions of relatively few teeth. One of these is de-

scribed in clause 4 and has been made part of this

standard. Other systems that are in use or have

been proposed are explained below and compared

to the standard version. All are subject to the same

requirements for an allowance (thinning) for back-

lash as described in 4.6. Any such reduction in tooth

thickness is generally accompanied, in external (or

internal) gears, by a reduction(or increase) in root di-

ameter as determined by the basic rack. Some spe-

cial manufacturing processes can produce the

thinning without a change in root diameter. This,

however, will result in reduced clearance at the root

when the thinned gears are tightly meshed. These

tooth thickness reductions may also be accompa-

nied by similar changes in outside (or inside) diame-

ter. When these changes are notmade, there will be

similar reductions in root clearance at the mating

gear.

E.2 Uniform tooth thickness

In this system, the tooth thickness is a uniform value

for all numbers of teeth, no matter how small. The

gears andcenterdistanceall follow thestandardpro-

portions defined by the equations listed in table 2.

This system is widely used for stock gears, where

any twogears (ofthe same pitch and pressure angle)

can be operated at the corresponding standard cen-

ter distance.

The simplicity of this system is offset by the disad-vantage of undercut present in all pinions with less

than some critical number of teeth, see E.3. In pin-

ions with very low numbers of teeth, the undercut is

very severe. For all undercut conditions, there is a

reduction in tooth bending strength and the introduc-

tion of other disadvantages in gear performance.

This practice is not recommended for original equip-

ment manufacturer (OEM) design.

E.3 Minimum enlargement to avoid undercut

In this system, the pinion tooth thicknesses are en-

larged but only by the minimum needed to avoid un-

dercut. The fillets blend into the involute tooth flanks

with the blend point located at the involute starting

point on the base circle. The amount of enlargement

is determined not only by the number of teeth but

also by the basic rack dedendum and fillet radius.

Since these fine--pitch basic rack features are not

simply related to module, because of the added 0.05

mm component, the amount of enlargement must be

determined separately for each module and for each

fillet radius. This is also true for the critical number of

teeth requiring enlargement.

For spur pinions, the critical number of teeth, z c, at

and below which enlargement is required to avoid

undercut, may be calculated as follows:

z c =2 hf0 − rf01 − sinα0

m sin2 α0 (E.1)rounded down to an integer

where

m is module, mm;

hf0 is basic rack dedendum, mm;

rf0 is basic rack fillet radius, mm;

α0 is profile angle, degrees.

With the basic rack information from table 3 and the

range of fillet radii proposed in 4.9, the critical num-

ber of teeth, as defined above, may be 17, 18 or 19

for some values of module and fillet radius. This

compares to the corresponding number of teeth, 23,

shown in table 4.

Use of this equation, and the related equations and

tables which follow, requires some understanding of the value of the fillet radius. Individual practice on

the part of gear cutting tool manufacturers will vary

and, even if supplied as advisory data, may not be

certified as closely controlled dimensions. For ap-

plications based on the use of tools for which exact

values are not known, adopting the smallest fillet ra-

dius in the proposed range will give the most conser-

vative results. Furthermore, there are also


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applications in which thetooth proportions willbe de-

fined graphically, as for plastic molding, powder met-

allurgy processing, or diecasting. In such cases, the

basic rack fillet radius can be selected to suit individ-

ual requirements and its value may then be used as

described here.

For spur pinions, the pinion enlargement, expressedas an increase in tooth thickness, Δs, may be calcu-

lated as follows:

− z 1tanα0 sin2α0 (m) (E.2)

Δs = 2tanα0hf0 − rf01 − sinα0

Values of this pinion tooth thicknessenlargement are

listed in tables E.1 to E.3. Values of addendum en-

largement,Δha, used to calculate outsidediameters,

can be found from:

Δha = Δs

2 tanα0 (E.3)

Table E.1 -- Minimum tooth thickness enlargement to avoid undercut for spur pinions based on fillet

radius r f0 = 0.1 x m

(dimensions in mm)

No. of Moduleteeth 1.25 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

9 0.4697 0.3830 0.3484 0.3137 0.2791 0.2444 0.2097 0.1751 0.1404 0.1057

10 0.4165 0.3405 0.3101 0.2797 0.2492 0.2188 0.1884 0.1580 0.1276 0.0972

11 0.3633 0.2979 0.2717 0.2456 0.2194 0.1933 0.1671 0.1410 0.1148 0.0887

12 0.3100 0.2553 0.2334 0.2115 0.1896 0.1677 0.1459 0.1240 0.1021 0.0802

13 0.2568 0.2127 0.1951 0.1775 0.1598 0.1422 0.1246 0.1069 0.0893 0.0717

14 0.2036 0.1702 0.1568 0.1434 0.1300 0.1167 0.1033 0.0899 0.0765 0.0632

15 0.1504 0.1276 0.1185 0.1093 0.1002 0.0911 0.0820 0.0729 0.0638 0.0546

16 0.0972 0.0850 0.0802 0.0753 0.0704 0.0656 0.0607 0.0558 0.0510 0.0461

17 0.0439 0.0424 0.0418 0.0412 0.0406 0.0400 0.0394 0.0388 0.0382 0.0376

18 --0.0093 --0.0001 0.0035 0.0072 0.0108 0.0145 0.0181 0.0218 0.0254 0.0291

19 --0.0625 --0.0427 --0.0348 --0.0269 --0.0190 --0.0111 --0.0032 0.0048 0.0127 0.0206

Table E.2 -- Minimum tooth thickness enlargement to avoid undercut for spur pinions based on fillet

radius r f0 = 0.3 x m

(dimensions in mm)

No. of Moduleteeth 1.25 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

9 0.5895 0.4788 0.4346 0.3904 0.3461 0.3019 0.2576 0.2134 0.1691 0.1249

10 0.5362 0.4363 0.3963 0.3563 0.3163 0.2763 0.2363 0.1963 0.1564 0.1164

11 0.4830 0.3937 0.3580 0.3222 0.2865 0.2508 0.2150 0.1793 0.1436 0.1079

12 0.4298 0.3511 0.3196 0.2882 0.2567 0.2252 0.1938 0.1623 0.1308 0.0993

13 0.3766 0.3085 0.2813 0.2541 0.2269 0.1997 0.1725 0.1453 0.1180 0.0908

14 0.3233 0.2660 0.2430 0.2200 0.1971 0.1741 0.1512 0.1282 0.1053 0.0823

15 0.2701 0.2234 0.2047 0.1860 0.1673 0.1486 0.1299 0.1112 0.0925 0.0738

16 0.2169 0.1808 0.1664 0.1519 0.1375 0.1230 0.1086 0.0942 0.0797 0.0653

17 0.1637 0.1382 0.1280 0.1179 0.1077 0.0975 0.0873 0.0771 0.0669 0.0568

18 0.1105 0.0957 0.0897 0.0838 0.0779 0.0720 0.0660 0.0601 0.0542 0.0482

19 0.0572 0.0531 0.0514 0.0497 0.0481 0.0464 0.0447 0.0431 0.0414 0.0397


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E.4 Minimum enlargement to avoid contact on

involute in first 5 of roll angle

This system is based on almost the same principles

as described in 5.1. The pinion tooth thickness en-

largement is selected so that the mating gear, with

any predetermined tooth thickness and outside di-

ameter, when tightly meshed with the pinion, will not

contact the involute flank of the pinion in its first 5° of roll angle. This description allows for a mating gear

of any design, while the mating gear specified in 5.1

is limited to a rack of standard proportions,exceptfor

a 5 percent increase in addendum. Theuse of a rack

represents the most demanding condition when it

comes to introducing enlargement and the in-

creased addendum carriesthe process even further.

It requires greater pinion enlargement than would

otherwise be needed to meet the contact require-

ment with most mating gears. This also applies to a

mating gear whose otherwise standard proportions

have a similarly increased addendum.

The practice of limiting the mating gear to a rack has

the single advantage that the corresponding values

of pinion enlargement can be presented in tabulated

form, thereby avoiding a calculation which was once

seen as cumbersome. Modern methods of calcula-

tion have largelyremoved this advantage, permitting

the use of the more general mating gear condition.

This new calculation is as follows:

αw = arctan⎨⎧⎩ α0

u + 1⎪⎡⎣1 +1 + d 2ae2 − d 2b2d b1 θ2

0.5

⎪⎤⎦⎬⎫⎭

(E.4)

where

αw is operating pressure angle, degrees;

α0 is arctan εLP (radians);

εLP is limiting roll angle on the pinion (5° or

0.087267 in this system);

u is gear ratio = z 2 z 1

;

d ae2 is outside diameter of the mating gear, mm;

d b2 is base circle diameter of the mating gear,

mm;

d b1 is base circle diameter of the pinion, mm.

Pinion tooth thickness enlargement, Δs1.

− s2 − π m2 (E.5)Δs1 = z 1 + z 2(inv αw) − inv α0 (m)

where

Δs1 pinion tooth thickness enlargement;

z 1 is number of pinion teeth;

z 2 is number of mating gear teeth;

s2 is tooth thickness of mating gear.

E.5 Comparison of tooth enlargement systems

Enlarging the pinion tooth thickness not only accom-

plishes the particular objectives, but also introduces

the following effects:

-- tends to increase the pinion tooth bending

strength;

-- decreases the top land (for pinions with very few

teeth, this may limit the outside diameter, see5.4);

-- increases the center distance (unless corre-

sponding reductions in tooth thickness are made

to the mating gear, see 5.11);

-- reduces the contact ratio.

The first of these effects may be considered favor-

able, and the second and third of secondary signifi-

cance. However, the reduction in contact ratio is

often a negative, especially when manufacturing

variations are applied. The contributing variations

will be in the form of runout of each gear, reduction inoutside diameter of each gear, and increases in cen-

ter distance from a tight mesh condition. The finer

the pitch, the greater the difficulty in designing with

such variations and also trying to ensure a minimum

contact ratio of 1.2, as recommended in 4.4.

This contactratio issue suggests that pinion enlarge-

ment be kept to the minimum required to accomplish

its primary objectives. The use of the system de-

scribed in E.4 in place of the system defined in 4.1

helps in this respect, especially when the mating

gear does not have high numbers of teeth. The sys-tem ofE.3 should also be considered when loadsare

moderate and involute accuracy will be adequate. In

cases of manufacturing variations interfering with

adequate contact ratio, and where the other gear op-

erating conditions permit, pinions with some under-

cut may be part of the optimum design.

Table E.3 illustrates the relative effect of the four pin-

ion enlargement design methods. In these exam-


29/32



ples, using unit module, the pinion has 12 teeth and

thegear has 24 teeth. The pinion is changed accord-

ing to each method with the gear kept at its standard

tooth thickness and outside diameter. Contact ratio

values are supplied for two sets of center distance.

The first, labelled the “tight” center distance, is the

tightly meshed center distance for the standard gear

and each pinion with its own tooth thickness. Thesecond, labelled the “loose” center distance, is

based on adding 0.40 to each tight center distance.

This addition represents some moderate cumulative

allowance for the kinds of manufacturing variations

noted above.

E.6 Tooth thicknesses for preset centerdistance

The general design procedure followed in the stan-

dard establishes tooth thicknesses of the two matinggears and assigns a corresponding center distance.

However, there may be a design problem in which a

preset center distance is specified and the tooth

thicknesses are to be selected to suit this preset val-

ue. This selection may be made in the two steps de-

scribed as follows:

E.6.1 Combined tooth thickness

The first step determines the combined tooth thick-

ness of the two gears based on the specified center

distance and the corresponding backlash.

E.6.1.1 Spur gears

For spur gears, starting with thecalculation of theop-

erating pressure angle:

αw = arccos z 1 + z 2 cosα0 (m)2 aw (E.6)where

αw is operating pressure angle, degrees;

aw is the specified (or actual) center distance,

mm.

The combined tooth thickness:

m z 1 + z 2inv αw − inv α0 + π − j(E.7)

s1 + s2 =

where

s1 is tooth thickness of the pinion, mm;

s2 is tooth thickness of the gear, mm;

j is backlash, mm.

E.6.1.2 Helical gears

For helical gears, starting with the calculation for the

transverse profile angle:

αt = arctan tan αncos β (E.8)where

αt is transverse profile angle, degrees;

αn is normal profile angle, degrees;

β is helix angle, degrees.

Table E.3 -- Pinion enlargement design examples ( m = 1)

Pinion descriptionmethod Pinion ( z 1 = 12) Gear ( z2 = 24) Tight Loose

Ref.clause

Table/ equation

Tooththickness

Outsidediameter

Tooththickness

Outsidediameter

Centerdistance

Contactratio

Centerdistance

Contactratio

4 4 1.9470 15.0296 1.5708 26.0000 18.4736 1.358 18.8736 1.038

E.2 2 1.5708 14.0000 1.5708 26.0000 18.0000 1.4051) 18.4000 1.143

E.3 E.2(m = 1.27)

1.8668 14.8133 1.5708 26.0000 18.3786 1.383 18.7786 1.055

E.4 Eq E.5 1.8000 14.6298 1.5708 26.0000 18.2973 1.406 18.6973 1.071

NOTE:1) Thepinion is undercut in this designand, at the“tight” center distance, a portion of thetip of themating gear “engages”in the undercut area and does not contribute to contact ratio. At the “loose” center distance, there is no “engagement”in the undercut area and the full mating tooth contributes to contact ratio.


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The transverse operating pressure angle:

αwt = arccos z 1 + z 2 cosαt (mn)2 a w (cos β) (E.9)where

αwt is transverse operating pressure angle,

degrees;

mn is normal module, mm.

The combined normal tooth thickness:

sn1 + sn2 =

(E.10)

mn z 1 + z 2inv αwt − inv α t + π − jn

where

sn1 is normal tooth thickness of the pinion, mm;

sn2 is normal tooth thickness of the gear, mm;

jn is normal backlash, mm.

E.6.2 Individual tooth thickness

The combined tooth thickness may then be split into

individual values to bestsuit other design objectives.

Some suggested guidelines are:

-- if the two gears have approximately the samenumber of teeth (and areof equal--strength mate-

rials), use equal tooth thicknesses;

-- if the pinion has a low number of teeth, make its

tooth thickness conform to one of the

recommendations;

-- if these guidelines result in tooth thicknesses that

are undercut or otherwise unsatisfactory, con-

sider changing the numbers of teeth.


31/32



Bibliography

The following documents are either referenced in the text of ANSI/AGMA 1103--H07, Tooth Proportions for

Fine--Pitch Spur and Helical Gearing (Metric Edition), or indicated for additional information.

References

1. Smith, L. J., Assured Backlash Control -- The

AGMA 1103-H07 Tooth Proportions for Fine- Pitch Spur and Helical Gearing (Metric Edition)

Documents

Transcript of AGMA 1103-H07 Tooth Proportions for Fine- Pitch Spur and Helical Gearing (Metric Edition)