ISO 21771:2007
(Main)Gears — Cylindrical involute gears and gear pairs — Concepts and geometry
Gears — Cylindrical involute gears and gear pairs — Concepts and geometry
ISO 21771:2007 specifies the geometric concepts and parameters for cylindrical gears with involute helicoid tooth flanks. Flank modifications are included. It also covers the concepts and parameters for cylindrical gear pairs with parallel axes and a constant gear ratio, which consist of cylindrical gears according to it. Gear and mating gear in these gear pairs have the same basic rack tooth profile.
Engrenages — Roues et engrenages cylindriques à développante — Concepts et géométrie
Zobniki - Evolventni valjasti zobnik in zobniške dvojice - Pojmi in geometrija
General Information
Relations
Standards Content (Sample)
SLOVENSKI STANDARD
01-julij-2008
1DGRPHãþD
SIST ISO/TR 4467:2002
Zobniki - Evolventni valjasti zobnik in zobniške dvojice - Pojmi in geometrija
Gears - Cylindrical involute gears and gear pairs - Concepts and geometry
Engrenages - Roues et engrenages cylindriques à développante - Concepts et
géométrie
Ta slovenski standard je istoveten z: ISO 21771:2007
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 21771
First edition
2007-09-01
Gears — Cylindrical involute gears and
gear pairs — Concepts and geometry
Engrenages — Roues et engrenages cylindriques à développante —
Concepts et géométrie
Reference number
©
ISO 2007
PDF disclaimer
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shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
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accepts no liability in this area.
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Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2007
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 either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2007 – All rights reserved
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Symbols, subscripts and units. 2
3.1 Symbols . 2
3.2 Subscripts . 8
3.3 Units . 9
4 Individual cylindrical gears. 10
4.1 Concepts for an individual gear . 10
4.2 Reference surfaces, datum lines and reference quantities. 12
4.3 Involute helicoids. 17
4.4 Angular pitch and pitches. 21
4.5 Diameters of gear teeth. 24
4.6 Gear tooth height. 24
4.7 Tooth thickness, space width. 25
5 Cylindrical gear pairs . 27
5.1 Concepts for a gear pair . 27
5.2 Mating quantities . 28
5.3 Calculation of the sum of the profile shift coefficients. 31
5.4 Tooth engagement. 32
5.5 Backlash . 40
5.6 Sliding conditions at the tooth flanks. 41
6 Tooth flank modifications . 44
6.1 Tooth flank modifications which restrict the usable flank . 44
6.2 Transverse profile modifications . 45
6.3 Flank line (helix) modifications . 48
6.4 Flank face modifications. 49
6.5 Descriptions of modifications by functions. 51
7 Geometrical limits. 52
7.1 Counterpart rack tooth profile. 53
7.2 Machining allowance. 54
7.3 Deviations in tooth thickness. 55
7.4 Generating profile shift, generating profile shift coefficient. 56
7.5 Generated root diameter . 57
7.6 Usable area of the tooth flank, tip and root form diameter . 57
7.7 Undercut . 59
7.8 Overcut . 59
7.9 Minimum tooth thickness at the tip circle of a gear. 59
Annex A (informative) Calculations related to tooth thickness. 60
Bibliography . 83
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. 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.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 21771 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 1, Nomenclature and
wormgearing.
This first edition of ISO 21771 cancels and replaces ISO/TR 4467:1982, of which it constitutes a technical
revision.
iv © ISO 2007 – All rights reserved
INTERNATIONAL STANDARD ISO 21771:2007(E)
Gears — Cylindrical involute gears and gear pairs — Concepts
and geometry
1 Scope
This International Standard specifies the geometric concepts and parameters for cylindrical gears with involute
helicoid tooth flanks. Flank modifications are included.
It also covers the concepts and parameters for cylindrical gear pairs with parallel axes and a constant gear
ratio, which consist of cylindrical gears according to it. Gear and mating gear in these gear pairs have the
same basic rack tooth profile.
The equations given are not restricted to the pressure angle,α = 20°.
P
The standard is structured as follows.
⎯ Listing of symbols and nomenclature for a unique description of gears and gear pairs (see Clause 3).
⎯ Equations and explanations of the relevant values for defining a cylindrical gear and its tooth system. The
equations for determination of the nominal values for zero-deviation gear description parameters are
stated for radial tooth dimensions (gear tooth heights), the distance between flanks of the same hand, the
distance between flanks of opposite hand, as well as the tooth flank characterizing parameters (see
Clause 4).
⎯ Equations and explanations of the relevant values for defining cylindrical gear pairs. The equations for the
essential parameters characterizing the engagement conditions of the unloaded gear pair are listed (see
Clause 5).
⎯ Equations and suggestions for desired flank modifications (see Clause 6).
⎯ Concepts and recommendations needed for a unique geometrical definition of the intended results from
manufacture (Clause 7).
⎯ Equations for determination of the nominal values or the limiting values for the most used inspection
methods for tooth thickness (see Annex A).
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth
ISO 1328-2:1997, Cylindrical gears — ISO system of accuracy — Part 2: Definitions and allowable values of
deviations relevant to radial composite deviations and runout information
3 Symbols, subscripts and units
3.1 Symbols
Symbol Description Used in
a centre distance of a cylindrical gear pair 5.2.3
w
a centre distance in the generating gear unit 7.5
a centre distance for tooth flank engagement A.8
L
b facewidth 4.2.8
b usable facewidth 4.2.8
F
b contact line overlap (for measuring base tangent length) A.2.1
M
b active facewidth (the facewidth used) 5.4.7.2
w
c
tip clearance 5.2.7
c form over dimension 5.4.4
F
d
reference diameter 4.2.4
d tip diameter 4.5.3
a
d tip diameter of tool 7.5
a0
d tip diameter of overcut cylindrical gears A.9
aM
d base diameter 4.3.10
b
d base diameter of the pinion-type cutter 7.6
b0
d root diameter (nominal dimension) 4.5.4
f
d
root diameter produced 7.5
fE
d root diameter of the pinion-type cutter A.9
f0
d V-circle diameter 4.5.1
v
d working pitch diameter 5.2.5
w
d
Y-circle diameter 4.3.3
y
d tip form diameter 7.6
Fa
d tip form diameter of the pinion-type cutter 7.6
Fa0
d root form diameter 7.6
Ff
d diameter of circle through centre of ball A.5
K
d
diameter of a measuring circle A.2.1
M
d active tip diameter 5.4.1
Na
d start of active profile diameter (SAP diameter, active root diameter) 5.4.1
Nf
e space width on the reference cylinder 4.7.3
t
e
space width on the Y-cylinder 4.7.3
yt
2 © ISO 2007 – All rights reserved
Symbol Description Used in
e space width of the standard basic rack tooth profile 4.2.3
P
g length of addendum path of contact 5.4.5.2
a
g length of dedendum path of contact 5.4.5.2
f
g length of path of contact 5.4.5.2
α
g distance of a point Y from pitch point C 5.6.1
αy
g arc of contact 5.4.7.4
β
h tooth depth (between tip line and root line) 4.6.1
h addendum 4.6.2
a
h
addendum of the standard basic rack tooth profile Figure 4
aP
h addendum of the tool standard basic rack tooth profile 7.5
aP0
h dedendum 4.6.2
f
h dedendum of the standard basic rack tooth profile Figure 4
fP
h dedendum of the tool standard basic rack tooth profile A.9
fP0
h working depth of teeth in a gear pair 5.2.6
w
h depth of dedendum form of the standard basic rack tooth prof
...
INTERNATIONAL ISO
STANDARD 21771
First edition
2007-09-01
Gears — Cylindrical involute gears and
gear pairs — Concepts and geometry
Engrenages — Roues et engrenages cylindriques à développante —
Concepts et géométrie
Reference number
©
ISO 2007
PDF disclaimer
This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but
shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat
accepts no liability in this area.
Adobe is a trademark of Adobe Systems Incorporated.
Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2007
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 either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2007 – All rights reserved
Contents Page
Foreword. iv
1 Scope . 1
2 Normative references . 1
3 Symbols, subscripts and units. 2
3.1 Symbols . 2
3.2 Subscripts . 8
3.3 Units . 9
4 Individual cylindrical gears. 10
4.1 Concepts for an individual gear . 10
4.2 Reference surfaces, datum lines and reference quantities. 12
4.3 Involute helicoids. 17
4.4 Angular pitch and pitches. 21
4.5 Diameters of gear teeth. 24
4.6 Gear tooth height. 24
4.7 Tooth thickness, space width. 25
5 Cylindrical gear pairs . 27
5.1 Concepts for a gear pair . 27
5.2 Mating quantities . 28
5.3 Calculation of the sum of the profile shift coefficients. 31
5.4 Tooth engagement. 32
5.5 Backlash . 40
5.6 Sliding conditions at the tooth flanks. 41
6 Tooth flank modifications . 44
6.1 Tooth flank modifications which restrict the usable flank . 44
6.2 Transverse profile modifications . 45
6.3 Flank line (helix) modifications . 48
6.4 Flank face modifications. 49
6.5 Descriptions of modifications by functions. 51
7 Geometrical limits. 52
7.1 Counterpart rack tooth profile. 53
7.2 Machining allowance. 54
7.3 Deviations in tooth thickness. 55
7.4 Generating profile shift, generating profile shift coefficient. 56
7.5 Generated root diameter . 57
7.6 Usable area of the tooth flank, tip and root form diameter . 57
7.7 Undercut . 59
7.8 Overcut . 59
7.9 Minimum tooth thickness at the tip circle of a gear. 59
Annex A (informative) Calculations related to tooth thickness. 60
Bibliography . 83
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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. 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.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 21771 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 1, Nomenclature and
wormgearing.
This first edition of ISO 21771 cancels and replaces ISO/TR 4467:1982, of which it constitutes a technical
revision.
iv © ISO 2007 – All rights reserved
INTERNATIONAL STANDARD ISO 21771:2007(E)
Gears — Cylindrical involute gears and gear pairs — Concepts
and geometry
1 Scope
This International Standard specifies the geometric concepts and parameters for cylindrical gears with involute
helicoid tooth flanks. Flank modifications are included.
It also covers the concepts and parameters for cylindrical gear pairs with parallel axes and a constant gear
ratio, which consist of cylindrical gears according to it. Gear and mating gear in these gear pairs have the
same basic rack tooth profile.
The equations given are not restricted to the pressure angle,α = 20°.
P
The standard is structured as follows.
⎯ Listing of symbols and nomenclature for a unique description of gears and gear pairs (see Clause 3).
⎯ Equations and explanations of the relevant values for defining a cylindrical gear and its tooth system. The
equations for determination of the nominal values for zero-deviation gear description parameters are
stated for radial tooth dimensions (gear tooth heights), the distance between flanks of the same hand, the
distance between flanks of opposite hand, as well as the tooth flank characterizing parameters (see
Clause 4).
⎯ Equations and explanations of the relevant values for defining cylindrical gear pairs. The equations for the
essential parameters characterizing the engagement conditions of the unloaded gear pair are listed (see
Clause 5).
⎯ Equations and suggestions for desired flank modifications (see Clause 6).
⎯ Concepts and recommendations needed for a unique geometrical definition of the intended results from
manufacture (Clause 7).
⎯ Equations for determination of the nominal values or the limiting values for the most used inspection
methods for tooth thickness (see Annex A).
2 Normative references
The following referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth
ISO 1328-2:1997, Cylindrical gears — ISO system of accuracy — Part 2: Definitions and allowable values of
deviations relevant to radial composite deviations and runout information
3 Symbols, subscripts and units
3.1 Symbols
Symbol Description Used in
a centre distance of a cylindrical gear pair 5.2.3
w
a centre distance in the generating gear unit 7.5
a centre distance for tooth flank engagement A.8
L
b facewidth 4.2.8
b usable facewidth 4.2.8
F
b contact line overlap (for measuring base tangent length) A.2.1
M
b active facewidth (the facewidth used) 5.4.7.2
w
c
tip clearance 5.2.7
c form over dimension 5.4.4
F
d
reference diameter 4.2.4
d tip diameter 4.5.3
a
d tip diameter of tool 7.5
a0
d tip diameter of overcut cylindrical gears A.9
aM
d base diameter 4.3.10
b
d base diameter of the pinion-type cutter 7.6
b0
d root diameter (nominal dimension) 4.5.4
f
d
root diameter produced 7.5
fE
d root diameter of the pinion-type cutter A.9
f0
d V-circle diameter 4.5.1
v
d working pitch diameter 5.2.5
w
d
Y-circle diameter 4.3.3
y
d tip form diameter 7.6
Fa
d tip form diameter of the pinion-type cutter 7.6
Fa0
d root form diameter 7.6
Ff
d diameter of circle through centre of ball A.5
K
d
diameter of a measuring circle A.2.1
M
d active tip diameter 5.4.1
Na
d start of active profile diameter (SAP diameter, active root diameter) 5.4.1
Nf
e space width on the reference cylinder 4.7.3
t
e
space width on the Y-cylinder 4.7.3
yt
2 © ISO 2007 – All rights reserved
Symbol Description Used in
e space width of the standard basic rack tooth profile 4.2.3
P
g length of addendum path of contact 5.4.5.2
a
g length of dedendum path of contact 5.4.5.2
f
g length of path of contact 5.4.5.2
α
g distance of a point Y from pitch point C 5.6.1
αy
g arc of contact 5.4.7.4
β
h tooth depth (between tip line and root line) 4.6.1
h addendum 4.6.2
a
h
addendum of the standard basic rack tooth profile Figure 4
aP
h addendum of the tool standard basic rack tooth profile 7.5
aP0
h dedendum 4.6.2
f
h dedendum of the standard basic rack tooth profile Figure 4
fP
h dedendum of the tool standard basic rack tooth profile A.9
fP0
h working depth of teeth in a gear pair 5.2.6
w
h depth of dedendum form of the standard basic rack tooth profile Figure 4
FfP
h radius of the tip corner chamfering or tip corner rounding 6.1.2
K
h tooth depth of standard basic rack tooth profile Figure 4
P
inv involute function 4.3.9
j contact backlash 5.5
bn
j
radial backlash 5.5
r
j circumferential backlash at the reference circle 5.5.2
t
j circumferential backlash at the pitch circle 5.5
wt
k number of teeth, spaces or pitches in a span (e.g. number of teeth A.2.1
spanned)
k
addendum modification coefficient 4.5.2
l path of engagement 5.4.8
max
∑l sum of path of contact 5.4.8
m normal module 4.2.7
n
m transverse module 4.2.7
t
m axial
...
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