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Page 1

A Reference number
ISO 53:1998(E)

INTERNATIONAL
STANDARD

ISO
53

Second edition
1998-08-15

Cylindrical gears for general and heavy
engineering — Standard basic rack tooth
profile

Engrenages cylindriques de mécanique générale et de grosse
mécanique — Tracé de référence

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Page 2

ISO 53:1998(E)

© ISO 1998

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic
or mechanical, including photocopying and microfilm, without permission in writing from the publisher.

International Organization for Standardization
Case postale 56 • CH-1211 Genève 20 • Switzerland
Internet [email protected]

Printed in Switzerland

ii

Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.

Draft International Standards adopted by the technical committees are circulated to the member bodies for voting.
Publication as an International Standard requires approval by at least 75 % of the member bodies casting a vote.

International Standard ISO 53 was prepared by Technical Committee ISO/TC 60, Gears.

This second edition cancels and replaces the first edition (ISO 53:1974), which has been technically revised.

Annex A of this International Standard is for information only.

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 3

INTERNATIONAL STANDARD © ISO ISO 53:1998(E)

1

Cylindrical gears for general and heavy engineering —
Standard basic rack tooth profile

Scope

This International Standard specifies the characteristics of the standard basic rack tooth profile for cylindrical
involute gears (external or internal) for general and heavy engineering.

This International Standard applies to the standardized modules specified in ISO 54.

The defined profile does not take into account the possible cut-off of the height of internal teeth. This height is to be
calculated for each case.

The standard basic rack tooth profile defined in this International Standard constitutes a geometrical reference for
a system of involute gears in order to fix the sizes of their teeth. It does not constitute a definition of a cutter, but a
cutter may be defined from this standard basic rack tooth profile in order to realize a conforming profile.

2 Normative references

The following standards contain provisions which, through reference in this text, constitute provisions of this
International Standard. At the time of publication, the editions indicated were valid. All standards are subject to
revision, and parties to agreements based on this International Standard are encouraged to investigate the
possibility of applying the most recent editions of the standards indicated below. Members of IEC and ISO maintain
registers of currently valid International Standards.

ISO 54:1996, Cylindrical gears for general and for heavy engineering — Modules.

ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.

3 Terms and definitions

For the purposes of this International Standard, the terms and definitions given in ISO 1122-1 and the following
apply.

3.1
standard basic rack tooth profile
tooth profile normal section through the teeth of a basic rack which corresponds to an external gear with number of
teeth z = • and diameter d = •

Figure 1.

NOTE — The tooth of the standard basic rack tooth profile is bounded by the tip line at the top and by the parallel root line at
the bottom. The fillet between the straight part of the profile and the root line is a circular arc with a radius equal to r

fP
.

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 4

ISO 53:1998(E) © ISO

2

3.2
mating standard rack tooth profile
rack tooth profile symmetrical to the standard basic rack tooth profile about the datum line P-P and displaced by half
a pitch relative to it

Figure 1.

4 Symbols and units

See table 1.

Table 1 — Symbols and units

Symbol Description Unit

cP Bottom clearance between standard basic rack tooth and mating standard basic rack tooth mm

eP Spacewidth of standard basic rack mm

haP Addendum of standard basic rack tooth mm

hfP Dedendum of standard basic rack tooth mm

hFfP Straight portion of the standard basic rack tooth dedendum mm

hP Tooth depth of standard basic rack mm

hwP Common depth of standard basic rack and mating standard basic rack tooth mm

m Module mm

p Pitch mm

sP Tooth thickness of standard basic rack tooth mm

UFP Size of undercut mm

aFP Angle of undercut degrees

aP Pressure angle degrees

rfP Fillet radius of the basic rack mm

5 Standard basic rack tooth profile

5.1 The characteristics of the standard basic rack tooth profile are given in figure 1 and table 2. Additional basic
rack recommendations and applications are given in annex A.

5.2 The standard basic rack tooth profile with module m has a pitch p = π m.

5.3 The flanks of the standard basic rack tooth profile are straight for the section haP plus hFfP.

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 5

© ISO ISO 53:1998(E)

3

Key

1 Standard basic rack profile

2 Datum line

3 Tip line

4 Root line

5 Mating standard basic rack tooth profile

Figure 1 — Standard basic rack tooth profile and mating standard basic rack tooth profile

Table 2 — Standard basic rack proportions

Item Standard basic rack value

aP 20°

haP 1 m

cP 0,25 m

hfP 1,25 m

r fP 0,38 m

5.4 On the line P-P the tooth thickness is equal to the space-width, i.e. half the pitch.

s e
p m

P P 2 2
= = =

p
(1)

where

sP is the tooth thickness of standard basic rack tooth;

eP is the spacewidth of standard basic rack;

p is the pitch;

m is the module.

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 6

ISO 53:1998(E) © ISO

4

5.5 The flanks of the standard basic rack tooth profile are inclined at the pressure angle, aP, to a line normal to the
datum line P-P.

5.6 The tip line and the root line are respectively parallel to the datum line P-P at distances of haP and hfP.

5.7 The active tooth depth, hwp, of the standard basic rack tooth profile and the mating standard basic rack tooth
profile is equal to 2haP.

5.8 The dimensions of the standard basic rack tooth profile use line P-P as the base datum.

5.9 The fillet radius of the standard basic rack, rfP, is determined by the standard clearance, cP.

For a basic rack, where αP = 20, cP < 0,295 m and hFfP = 1 m:

r
afPm ax 1

=


cP

Psin
(2)

where

rfP max is the maximum fillet radius of the basic rack;

cP is the bottom clearance between standard basic rack tooth and mating standard basic rack tooth;

aP is the pressure angle.

For a basic rack, where αP = 20° and 0,295 m < cP < 0,396 m:

( )[ ]
r

a

afPmax tan[(90 ) / 2]
=





pm h/ tan4 fP P

P
o

(3)

where hfP is the dedendum of the basic rack tooth.

The centre of rfP max is on the centre of the rack space.

NOTE — The actual root fillet, which is outside the active profile, can vary depending on influences such as the method of
manufacturing, profile shift and number of teeth.

5.10 The dimensions of the standard basic rack tooth profile cP, haP, hfP and hwP may also be quoted as a multiple of
the module m, i.e. relating to m = 1. In this case, they are identified by an asterisk, for example

hfP = hfP*◊ m

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 7

© ISO ISO 53:1998(E)

5

Annex A
(informative)

Basic rack recommendations for various applications

A.1 Application of basic rack forms

Alternative basic rack tooth profiles may be used based on application requirements

— Standard basic rack tooth profile type A is recommended for gears transmitting high torques.

— Basic rack tooth profile types B and C are recommended for normal service. Type C may be applied for
manufacturing with some standard hobs.

— Basic rack tooth profile type D is equivalent to a full radius form for the fillet. The enlarged dedendum,
hfP = 1,4 m, with the associated fillet radii, rfP = 0,39 m, permits the finishing tool to work without interference,
while maintaining the maximum fillet radius. This profile is recommended for high-precision gears transmitting
high torques and consequently with tooth flanks finished by grinding or shaving. Care should be taken to avoid
creating notches in the fillet during finishing, which would create stress concentrations.

Characteristics of the basic rack tooth profile types are given in table A.1.

Table A.1 — Basic rack tooth profiles

Types of basic rack tooth profile

A B C D

aP 20° 20° 20° 20°

haP 1 m 1 m 1 m 1 m

cP 0,25 m 0,25 m 0,25 m 0,4 m

hfP 1,25 m 1,25 m 1,25 m 1,4 m

rfP 0,38 m 0,3 m 0,25 m 0,39 m

A.2 Basic rack tooth profiles with undercut

A basic rack tooth profile with a chosen undercut, UFP, and angle of undercut, aFP, is used for gears cut by a
protuberance tool and finished by grinding or shaving, see figure A.1. The specific values of UFP and aFP depend on
influences such as the method of manufacturing, which are not specified in this International Standard.

Symbol

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 8

ISO 53:1998(E) © ISO

6

Figure A.1 — Basic rack tooth profile with a chosen undercut

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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Page 9

Copyright International Organization for Standardization
Provided by IHS under license with ISO

Not for ResaleNo reproduction or networking permitted without license from IHS

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