agma 1103-h07 tooth proportions for fine- pitch spur and helical gearing (metric edition)
TRANSCRIPT
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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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ANSI/AGMA 1103--H07AMERICAN NATIONAL STANDARD
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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ANSI/AGMA 1103--H07AMERICAN NATIONAL STANDARD
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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ANSI/AGMA 1103--H07 AMERICAN NATIONAL STANDARD
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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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ANSI/AGMA 1103--H07 AMERICAN NATIONAL STANDARD
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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).
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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 p t cosα0⎪⎪⎤
⎦− 2 a sinα0
2 p t cosα0
(15)
For non--standard center distance
εβx =⎪⎪
⎡
⎣
d 2ae1
− d 1 cosα02
2 p t cosα0⎪⎪⎤
⎦
+⎪⎪⎡
⎣
d 2ae2
− d 2 cosαo2
2 p t cosα0⎪⎪⎤
⎦− 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.
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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.
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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
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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
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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
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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
Tooththickness(enlarged)
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.
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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
Number ofteeth inpinion
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.
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Annex B
(informative)
Tooth proportions for 25 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 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
Tooththickness(enlarged)
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
Number ofteeth inpinion
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
[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).]
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
[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).]
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
[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).]
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-
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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.
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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