ISO/TR 13989-2:2000
(Main)Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears — Part 2: Integral temperature method
Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears — Part 2: Integral temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques, coniques et hypoïdes — Partie 2: Méthode de la température intégrale
Izračun nosilnosti glede na toplotno razjedanje zobnih bokov valjastih, stožčastih in hipoidnih zobnikov - 2. del: Metoda povprečne temperature
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TECHNICAL ISO/TR
REPORT 13989-2
First edition
2000-03-15
Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears —
Part 2:
Integral temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques,
coniques et hypoïdes —
Partie 2: Méthode de la température intégrale
Reference number
ISO/TR 13989-2:2000(E)
©
ISO 2000
---------------------- Page: 1 ----------------------
ISO/TR 13989-2:2000(E)
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This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not
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© ISO 2000
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
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Tel. + 41 22 749 01 11
Fax + 41 22 734 10 79
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Printed in Switzerland
ii © ISO 2000 – All rights reserved
---------------------- Page: 2 ----------------------
ISO/TR 13989-2:2000(E)
Contents Page
Foreword.v
Introduction.vi
1 Scope .1
2 Normative references .1
3 Terms, definitions, symbols and units .1
3.1 Terms and definitions .1
3.2 Symbols and units.1
4 Field of application .6
4.1 Scuffing damage.6
4.2 Integral temperature criterion.7
5 Influence factors .7
5.1 Mean coefficient of friction� .7
mC
5.2 Run-in factor X .10
E
5.3 Thermal flash factor X .10
M
5.4 Pressure angle factor X .11
��
6 Calculation.12
6.1 Cylindrical gears.12
6.1.1 Scuffing safety factor S .12
intS
6.1.2 Permissible integral temperature� .12
intP
6.1.3 Integral temperature� .12
int
6.1.4 Flash temperature at pinion tooth tip� .13
flaE
6.1.5 Bulk temperature� .13
M
6.1.6 Mean coefficient of friction� .14
mC
6.1.7 Run-in factor X .14
E
6.1.8 Thermal flash factor X .14
M
6.1.9 Pressure angle factor X .14
��
6.1.10 Geometry factor at tip of pinion X .14
BE
6.1.11 Approach factor X .14
Q
6.1.12 Tip relief factor X .15
Ca
6.1.13 Contact ratio factor: X .16
ε
6.2 Bevel gears.19
6.2.1 Scuffing safety factor S .20
intS
6.2.2 Permissible integral temperature� .20
intP
6.2.3 Integral temperature� .20
int
6.2.4 Flash temperature at pinion tooth tip� .20
flaE
6.2.5 Bulk temperature� .20
M
6.2.6 Mean coefficient of friction� .20
mC
6.2.7 Run-in factor X .21
E
6.2.8 Thermal flash factor X .21
M
6.2.9 Pressure angle factor X .21
��
6.2.10 Geometry factor at tip of pinion X .21
BE
6.2.11 Approach factor X .21
Q
6.2.12 Tip relief factor X .21
Ca
6.2.13 Contact ratio factor X .22
ε
© ISO 2000 – All rights reserved iii
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ISO/TR 13989-2:2000(E)
6.3 Hypoid gears .22
6.3.1 Scuffing safety factor S .22
intS
6.3.2 Permissible integral temperature� .22
intP
6.3.3 Integral temperature� .22
int
6.3.4 Bulk temperature� .22
M
6.3.5 Mean coefficient of friction� .23
mC
6.3.6 Run-in factor X .23
E
6.3.7 Geometry factor X .23
G
6.3.8 Approach factor X .24
Q
6.3.9 Tip relief factor X .25
Ca
6.3.10 Contact ratio factor X .25
ε
6.3.11 Calculation of virtual crossed axes helical gears .25
6.4 Scuffing integral temperature.29
6.4.1 Scuffing integral temperature� .29
intS
6.4.2 Relative welding factor X .33
WrelT
Annex A (informative) Examples.34
Annex B (informative) Contact-time-dependent scuffing temperature.44
Bibliography .48
iv © ISO 2000 – All rights reserved
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ISO/TR 13989-2:2000(E)
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.
The main task of technical committees is to prepare International Standards, but in exceptional circumstances a
technical committee may propose the publication of a Technical Report of one of the following types:
� type 1, when the required support cannot be obtained for the publication of an International Standard, despite
repeated efforts;
� type 2, when the subject is still under technical development or where for any other reason there is the future
but not immediate possibility of an agreement on an International Standard;
� type 3, when a technical committee has collected data of a different kind from that which is normally published
as an International Standard ("state of the art", for example).
Technical Reports of types 1 and 2 are subject to review within three years of publication, to decide whether they
can be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be
reviewed until the data they provide are considered to be no longer valid or useful.
Technical Reports are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Attention is drawn to the possibility that some of the elements of this part of ISO/TR 13989 may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 13989-2, which is a Technical Report of type 2, was prepared by Technical Committee ISO/TC 60, Gears,
Subcommittee SC 2, Gear capacity calculation.
This document is being issued in the Technical Report (type 2) series of publications (according to
subclause G.3.2.2 of Part 1 of the ISO/IEC Directives, 1995) as a “prospective standard for provisional application”
in the field of scuffing load capacity of gears because there is an urgent need for guidance on how standards in this
field should be used to meet an identified need. In 1975, two methods to evaluate the risk of scuffing were
documented to be studied by ISO/TC 60. It was agreed that after a period of experience one method shall be selected.
Since the subject is still under technical development and there is a future possibility of an agreement on an
International Standard, the publication of a type 2 Technical Report was proposed.
This document is not to be regarded as an “International Standard”. It is proposed for provisional application so that
information and experience of its use in practice may be gathered. Comments on the content of this document
should be sent to the ISO Central Secretariat.
A review of this Technical Report (type 2) will be carried out not later than three years after its publication with the
options of: extension for another three years; conversion into an International Standard; or withdrawal.
ISO/TR 13989 consists of the following parts, under the general title Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears:
� Part 1: Flash temperature method
� Part 2: Integral temperature method
Annexes A and B of this part of ISO/TR 13989 are for information only.
© ISO 2000 – All rights reserved v
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ISO/TR 13989-2:2000(E)
Introduction
This part of ISO/TR 13989 describes the surface damage "warm scuffing" for cylindrical (spur and helical), bevel
and hypoid gears for generally used gear materials and different heat treatments. "Warm scuffing" is characterized
by typical scuffing and scoring marks, which can lead to increasing power loss, dynamic load, noise and wear. For
"cold scuffing", in general associated with low temperature and low speed, under approximately 4 m/s, and
through-hardened, heavily loaded gears, the equations are not suitable.
There is a particularly severe form of gear tooth surface damage in which seizure or welding together of areas of
tooth surfaces occurs, due to absence or breakdown of a lubricant film between the contacting tooth flanks of
mating gears, caused by high temperature and high pressure. This form of damage is termed "scuffing" and most
relevant when surface velocities are high. Scuffing may also occur for relatively low sliding velocities when tooth
surface pressures are high enough, either generally or, because of uneven surface geometry and loading, in
discrete areas.
Risk of scuffing damage varies with the properties of gear materials, the lubricant used, the surface roughness of
tooth flanks, the sliding velocities and the load. Excessive aeration or the presence of contaminants in the lubricant
such as metal particles in suspension, also increase the risk of scuffing damage. Consequences of the scuffing of
high speed gears include a tendency to high levels of dynamic loading due to increase of vibration, which usually
leads to further damage by scuffing, pitting or tooth breakage.
High surface temperatures due to high surface pressures and sliding velocities can initiate the breakdown of
lubricant films. On the basis of this hypothesis two approaches to relate temperature to lubricant film breakdown
are presented:
� the flash temperature method (presented in ISO/TR 13989-1), based on contact temperatures which vary
along the path of contact;
� the integral temperature method (presented in this part of ISO/TR 13989), based on the weighted average of
the contact temperatures along the path of contact.
The integral temperature method is based on the assumption that scuffing is likely to occur when the mean value of
the contact temperature (integral temperature) is equal to or exceeds a corresponding critical value. The risk of
scuffing of an actual gear unit can be predicted by comparing the integral temperature with the critical value,
derived from a gear test for scuffing resistance of lubricants. The calculation method takes account of all significant
influence parameters, i.e. the lubricant (mineral oil with and without EP-additives, synthetic oils), the surface
roughness, the sliding velocities, the load, etc.
In order to ensure that all types of scuffing and comparable forms of surface damage due to the complex
relationships between hydrodynamical, thermodynamical and chemical phenomena are dealt with, further methods
of assessment may be necessary. The development of such methods is the objective of ongoing research.
vi © ISO 2000 – All rights reserved
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TECHNICAL REPORT ISO/TR 13989-2:2000(E)
Calculation of scuffing load capacity of cylindrical, bevel and
hypoid gears —
Part 2:
Integral temperature method
1 Scope
This part of ISO/TR 13989 specifies the integral temperature method for calculating the scuffing load capacity of
cylindrical, bevel and hypoid gears.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO/TR 13989. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this part of ISO/TR 13989 are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
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 6336-1:1996, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors.
1)
ISO 10300-1:— , Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors.
3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this part of ISO/TR 13989, the terms and definitions given in ISO 1122-1 apply.
3.2 Symbols and units
The symbols used in this part of ISO/TR 13989 are given in Table 1.
1) To be published.
© ISO 2000 – All rights reserved 1
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ISO/TR 13989-2:2000(E)
Table 1 — Symbols and units
Symbol Description Unit Reference
a centre distance mm —
a
virtual centre distance of virtual cylindrical gear mm ISO 10300-1
v
b face width, smaller value of pinion or wheel mm —
b
effective facewidth for scuffing mm Eq. (46)
eB
2
c specific heat capacity per unit volume N/(mm ·K) —
v
single stiffness N/(mm·µm) ISO 6336-1
c�
c mesh stiffness N/(mm·µm) ISO 6336-1
�
d referencecirclediameter mm —
d effective tip diameter mm —
Na
d tip diameter mm Eq. (69)
a
d base diameter mm Eq. (70)
b
d
diameter at mid-facewidth mm —
m
d reference circle of virtual crossed axes helical gear mm Eq. (68)
s
d reference diameter of virtual cylindrical gear mm ISO 10300-1
v
d tip diameter of virtual cylindrical gear mm ISO 10300-1
va
d base diameter of virtual cylindrical gear mm ISO 10300-1
vb
g recess path of contact of pinion, wheel mm Eqs. (90), (91)
an1,2
g approach path of contact of pinion, wheel mm Eqs. (90), (91)
fn1,2
g* sliding factor — Eq. (62)
h addendum at mid-facewidth of hypoid gear mm —
am
m module mm —
m normal module of hypoid gear at mid-facewidth mm —
mn
m normal module of virtual crossed axes helical gear mm Eq. (73)
sn
n number of meshing gears ——
p
p normal base pitch mm Eq. (74)
en
u gear ratio ——
u gear ratio of virtual cylindrical gear — ISO 10300-1
v
v reference line velocity m/s —
v tangential velocity of pinion, wheel of hypoid gear m/s Eqs. (77), (78)
t1,2
v
maximum sliding velocity at tip of pinion m/s Eq. (83)
g�1
v sliding velocity at pitch point m/s Eq. (82)
gs
v sliding velocity m/s Eqs. (84), (85)
g1,2
v sliding velocity m/s Eq. (87)
g�1
2 © ISO 2000 – All rights reserved
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ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
v sliding velocity m/s Eq. (88)
g�1
v tangential speed at reference cone at mid-facewidth of m/s —
mt
bevel gear
v sums of tangential speeds at pitch point m/s Eqs. (2), (47), (81)
ΣC
tangential speed m/s Eq. (79)
v
Σs
v tangential speed m/s Eq. (80)
Σh
w specific tooth load, scuffing N/mm Eq. (4)
Bt
z number of teeth ——
z number of teeth of virtual cylindrical gear — ISO 10300-1
v
1/2
B thermal contact coefficient N/(mm·s ·K) Eq. (12)
M
C ,C ,C weighting factors ——
1 2 2H
C nominal tip reliefµm —
a
C
effective tip reliefµm Eqs. (37), (38), (49)
eff
2
E module of elasticity (Young's modulus) N/mm —
F
nominal tangential load at reference cone at mid-facewidth N —
mt
F normal tooth load N Eq. (51)
n
F nominal tangential load at reference circle N —
t
K application factor — ISO 6336-1,
A
ISO 10300-1
K dynamic factor — ISO 6336-1,
v
ISO 10300-1
K = K transverse load factor (scuffing) — 6.2.4, ISO 6336-1,
B� H�
ISO 10300-1
K = K face load factor (scuffing) — ISO 6336-1
B� H�
ISO 10300-1, 6.2.4,
Eqs. (52), (53)
K helical load factor (scuffing) — Eq. (5), 6.2.4, 6.3.5
B�
K bearing factor — 6.3.3
B�be
K transverse load factor — ISO 6336-1,
H�
ISO 10300-1
K face load factor — ISO 6336-1,
H�
ISO 10300-1
K bearing factor — ISO 10300-1
H�be
L contact parameter — Eq. (55)
Ra
arithmetic mean roughnessµm Eq. (6)
S scuffing safety factor — Eq. (14)
intS
S minimum required scuffing safety factor ——
Smin
© ISO 2000 – All rights reserved 3
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ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
T torque of the pinion Nm —
1
T scuffing torque of test pinion Nm Eq. (96)
1T
X geometry factor at pinion tooth tip — Eq. (22)
BE
X
run-in factor — Eq. (8)
E
X tip relief factor — Eq. (32)
Ca
X geometry factor of hypoid gears — Eq. (54)
G
X lubricant factor — 5.1
L
X thermal flash factor — Eq. (9)
M
X approach factor — Eqs. (25), (26), (27)
Q
X roughness factor — Eq. (7)
R
X lubrication factor — 6.1.5.3
S
X welding factor of executed gear — Table 3
W
X welding factor of test gear — 6.4.2
WT
X relative welding factor — Eq. (102)
WrelT
X contact factor — Eq. (21)
mp
X pressure angle factor — Eqs. (13), (48)
��
X contact ratio factor — Eqs. (39) to (44)
ε
pressure angle °—
�
normal pressure angle at mid-facewidth of hypoid gear °—
�
mn
� normal pressure angle °—
n
normal pressure angle of crossed axes helical gear ° Eq. (64)
�
sn
� transverse pressure angle of crossed axes helical gear ° Eq. (66)
st
transverse pressure angle °—
�
t
� ´ transverse working pressure angle °—
t
transverse pressure angle of virtual cylindrical gear ° ISO 10300-1
�
vt
arbitrary angle ° Figure 2
�
y
helix angle °—
�
helix angle at base circle ° Eqs. (67), (71)
�
b
� helix angle at reference cone at mid-facewidth of hypoid °—
m
gear
� helix angle of virtual crossed axes helical gear ° Eq. (63)
s
auxiliary angle ° Eq. (86)
�
reference cone angle °—
�
4 © ISO 2000 – All rights reserved
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ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
recess contact ratio — Eqs. (28), (29)
�
a
� approach contact ratio — Eqs. (28), (29)
f
contact ratio in normal section of virtual crossed axes — Eqs. (92), (93)
�
n
helical gear
addendum contact ratio of the pinion — Eq. (30)
�
1
� addendum contact ratio of the wheel — Eq. (31)
2
contact ratio — Eq. (45)
�
�
transverse contact ratio of virtual cylindrical gear — ISO 10300-1
�
v�
tip contact ratio of virtual cylindrical pinion — ISO 10300-1
�
v1
tip contact ratio of virtual cylindrical wheel — ISO 10300-1
�
v2
Hertzian auxiliary coefficient — Figure 7, Eqs. (57), (59)
�
mean coefficient of friction — Eqs. (1), (1a)
�
mC
� dynamic viscosity at oil temperature —
mPa�s
oil
heat conductivity —
� N/(s�K)
M
Poisson's ratio ——
�
2
� kinematic viscosity of the oil at 40 �C mm /s; cSt —
40
radius of curvature at tip of the pinion, wheel mm Eqs. (23), (24)
�
E1,2
� relative radius of curvature at pitch point in normal section mm Eq. (76)
Cn
radius of curvature at pitch point in normal section mm Eq. (75)
�
n1,2
relative radius of curvature at pitch point mm Eq. (3)
�
redC
Hertzian auxiliary coefficient — Figure 7, Eqs. (58), (60)
�
Hertzian auxiliary angle ° Eqs. (56) to (60)
�
flash temperature at pinion tooth tip when load sharing is K Eq. (19)
�
flaE
neglected
mean flash temperature K Eq. (18)
�
flaint
� mean flash temperature of hypoid gear K Eq. (50)
flainth
integral temperature K Eq. (17)
�
int
permissible integral temperature K Eq. (16)
�
intP
scuffing integral temperature (allowable integral K Eq. (94)
�
intS
temperature)
� mean flash temperature of the test gear K Eqs. (96), (99), (101)
flaintT
oil sump or spray temperature °C —
�
oil
� bulk temperature °C Eq. (20)
M-C
© ISO 2000 – All rights reserved 5
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ISO/TR 13989-2:2000(E)
Table 1 (concluded)
Symbol Description Unit Reference
test bulk temperature Eqs. (95), (98), (100)
� �C
MT
axle angle of virtual crossed axes helical gear ° Eq. (72)
�
� axle angle of virtual crossed axes helical gear ° Eq. (65)
run-in grade — 5.2
�
E
parameter on the line of action — Eq. (10)
�
Subscripts:
1pinion
2 wheel
a tip diameter of the virtual gear
b base circle of the virtual gear
m mid-facewidth of bevel or hypoid gears
n normal section
s virtual crossed axes helical gear
t tangential direction
T test gear
4 Field of application
The calculation methods are based on results of the rig testing of gears run at pitch line velocities less than 80 m/s.
The equations can be used for gears which run at higher speeds, but with increasing uncertainty as speed
increases. The uncertainty concerns the estimation of bulk temperature, coefficient of friction, allowable
temperatures, etc. as speeds exceed the range with experimental background.
4.1 Scuffing damage
When once initiated, scuffing damage can lead to gross degradation of tooth flank surfaces, with increase of: power
loss, dynamic loading, noise and wear. It can also lead to tooth breakage if the severity of the operating conditions
is not reduced. In the event of scuffing due to an instantaneous overload, followed immediately by a reduction of
load, e.g. by load redistribution, the tooth flanks may self-heal by smoothing themselves to some extent. Even so,
the residual damage will continue to be a cause of increased power loss, dynamic loading and noise.
In most cases, the resistance of gears to scuffing can be improved by using a lubricant with enhanced E.P.
(extreme pressure) properties. It is important however, to be aware that some disadvantages attend the use of E.P.
oils — corrosion of copper, embrittlement of elastomers, lack of world-wide availability, etc. These disadvantages
are to be taken into consideration if optimum lubricant choice is to be made, which means: as few additives as
possible, but as many as necessary.
Due to continuous variation of different parameters, the complexity of the chemical properties and the thermo-
hydro-elastic processes in the instantaneous contact area, some scatter in the calculated assessments of
probability of scuffing risk is t
...
SLOVENSKI STANDARD
SIST ISO/TR 13989-2:2002
01-julij-2002
,]UDþXQQRVLOQRVWLJOHGHQDWRSORWQRUD]MHGDQMH]REQLKERNRYYDOMDVWLKVWRåþDVWLK
LQKLSRLGQLK]REQLNRYGHO 0HWRGDSRYSUHþQHWHPSHUDWXUH
Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears -- Part 2:
Integral temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques, coniques et
hypoïdes -- Partie 2: Méthode de la température intégrale
Ta slovenski standard je istoveten z: ISO/TR 13989-2:2000
ICS:
21.200 Gonila Gears
SIST ISO/TR 13989-2:2002 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO/TR 13989-2:2002
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SIST ISO/TR 13989-2:2002
TECHNICAL ISO/TR
REPORT 13989-2
First edition
2000-03-15
Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears —
Part 2:
Integral temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques,
coniques et hypoïdes —
Partie 2: Méthode de la température intégrale
Reference number
ISO/TR 13989-2:2000(E)
©
ISO 2000
---------------------- Page: 3 ----------------------
SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
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 2000
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 22 734 10 79
E-mail copyright@iso.ch
Web www.iso.ch
Printed in Switzerland
ii © ISO 2000 – All rights reserved
---------------------- Page: 4 ----------------------
SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Contents Page
Foreword.v
Introduction.vi
1 Scope .1
2 Normative references .1
3 Terms, definitions, symbols and units .1
3.1 Terms and definitions .1
3.2 Symbols and units.1
4 Field of application .6
4.1 Scuffing damage.6
4.2 Integral temperature criterion.7
5 Influence factors .7
5.1 Mean coefficient of friction� .7
mC
5.2 Run-in factor X .10
E
5.3 Thermal flash factor X .10
M
5.4 Pressure angle factor X .11
��
6 Calculation.12
6.1 Cylindrical gears.12
6.1.1 Scuffing safety factor S .12
intS
6.1.2 Permissible integral temperature� .12
intP
6.1.3 Integral temperature� .12
int
6.1.4 Flash temperature at pinion tooth tip� .13
flaE
6.1.5 Bulk temperature� .13
M
6.1.6 Mean coefficient of friction� .14
mC
6.1.7 Run-in factor X .14
E
6.1.8 Thermal flash factor X .14
M
6.1.9 Pressure angle factor X .14
��
6.1.10 Geometry factor at tip of pinion X .14
BE
6.1.11 Approach factor X .14
Q
6.1.12 Tip relief factor X .15
Ca
6.1.13 Contact ratio factor: X .16
ε
6.2 Bevel gears.19
6.2.1 Scuffing safety factor S .20
intS
6.2.2 Permissible integral temperature� .20
intP
6.2.3 Integral temperature� .20
int
6.2.4 Flash temperature at pinion tooth tip� .20
flaE
6.2.5 Bulk temperature� .20
M
6.2.6 Mean coefficient of friction� .20
mC
6.2.7 Run-in factor X .21
E
6.2.8 Thermal flash factor X .21
M
6.2.9 Pressure angle factor X .21
��
6.2.10 Geometry factor at tip of pinion X .21
BE
6.2.11 Approach factor X .21
Q
6.2.12 Tip relief factor X .21
Ca
6.2.13 Contact ratio factor X .22
ε
© ISO 2000 – All rights reserved iii
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
6.3 Hypoid gears .22
6.3.1 Scuffing safety factor S .22
intS
6.3.2 Permissible integral temperature� .22
intP
6.3.3 Integral temperature� .22
int
6.3.4 Bulk temperature� .22
M
6.3.5 Mean coefficient of friction� .23
mC
6.3.6 Run-in factor X .23
E
6.3.7 Geometry factor X .23
G
6.3.8 Approach factor X .24
Q
6.3.9 Tip relief factor X .25
Ca
6.3.10 Contact ratio factor X .25
ε
6.3.11 Calculation of virtual crossed axes helical gears .25
6.4 Scuffing integral temperature.29
6.4.1 Scuffing integral temperature� .29
intS
6.4.2 Relative welding factor X .33
WrelT
Annex A (informative) Examples.34
Annex B (informative) Contact-time-dependent scuffing temperature.44
Bibliography .48
iv © ISO 2000 – All rights reserved
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
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.
The main task of technical committees is to prepare International Standards, but in exceptional circumstances a
technical committee may propose the publication of a Technical Report of one of the following types:
� type 1, when the required support cannot be obtained for the publication of an International Standard, despite
repeated efforts;
� type 2, when the subject is still under technical development or where for any other reason there is the future
but not immediate possibility of an agreement on an International Standard;
� type 3, when a technical committee has collected data of a different kind from that which is normally published
as an International Standard ("state of the art", for example).
Technical Reports of types 1 and 2 are subject to review within three years of publication, to decide whether they
can be transformed into International Standards. Technical Reports of type 3 do not necessarily have to be
reviewed until the data they provide are considered to be no longer valid or useful.
Technical Reports are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
Attention is drawn to the possibility that some of the elements of this part of ISO/TR 13989 may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 13989-2, which is a Technical Report of type 2, was prepared by Technical Committee ISO/TC 60, Gears,
Subcommittee SC 2, Gear capacity calculation.
This document is being issued in the Technical Report (type 2) series of publications (according to
subclause G.3.2.2 of Part 1 of the ISO/IEC Directives, 1995) as a “prospective standard for provisional application”
in the field of scuffing load capacity of gears because there is an urgent need for guidance on how standards in this
field should be used to meet an identified need. In 1975, two methods to evaluate the risk of scuffing were
documented to be studied by ISO/TC 60. It was agreed that after a period of experience one method shall be selected.
Since the subject is still under technical development and there is a future possibility of an agreement on an
International Standard, the publication of a type 2 Technical Report was proposed.
This document is not to be regarded as an “International Standard”. It is proposed for provisional application so that
information and experience of its use in practice may be gathered. Comments on the content of this document
should be sent to the ISO Central Secretariat.
A review of this Technical Report (type 2) will be carried out not later than three years after its publication with the
options of: extension for another three years; conversion into an International Standard; or withdrawal.
ISO/TR 13989 consists of the following parts, under the general title Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears:
� Part 1: Flash temperature method
� Part 2: Integral temperature method
Annexes A and B of this part of ISO/TR 13989 are for information only.
© ISO 2000 – All rights reserved v
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Introduction
This part of ISO/TR 13989 describes the surface damage "warm scuffing" for cylindrical (spur and helical), bevel
and hypoid gears for generally used gear materials and different heat treatments. "Warm scuffing" is characterized
by typical scuffing and scoring marks, which can lead to increasing power loss, dynamic load, noise and wear. For
"cold scuffing", in general associated with low temperature and low speed, under approximately 4 m/s, and
through-hardened, heavily loaded gears, the equations are not suitable.
There is a particularly severe form of gear tooth surface damage in which seizure or welding together of areas of
tooth surfaces occurs, due to absence or breakdown of a lubricant film between the contacting tooth flanks of
mating gears, caused by high temperature and high pressure. This form of damage is termed "scuffing" and most
relevant when surface velocities are high. Scuffing may also occur for relatively low sliding velocities when tooth
surface pressures are high enough, either generally or, because of uneven surface geometry and loading, in
discrete areas.
Risk of scuffing damage varies with the properties of gear materials, the lubricant used, the surface roughness of
tooth flanks, the sliding velocities and the load. Excessive aeration or the presence of contaminants in the lubricant
such as metal particles in suspension, also increase the risk of scuffing damage. Consequences of the scuffing of
high speed gears include a tendency to high levels of dynamic loading due to increase of vibration, which usually
leads to further damage by scuffing, pitting or tooth breakage.
High surface temperatures due to high surface pressures and sliding velocities can initiate the breakdown of
lubricant films. On the basis of this hypothesis two approaches to relate temperature to lubricant film breakdown
are presented:
� the flash temperature method (presented in ISO/TR 13989-1), based on contact temperatures which vary
along the path of contact;
� the integral temperature method (presented in this part of ISO/TR 13989), based on the weighted average of
the contact temperatures along the path of contact.
The integral temperature method is based on the assumption that scuffing is likely to occur when the mean value of
the contact temperature (integral temperature) is equal to or exceeds a corresponding critical value. The risk of
scuffing of an actual gear unit can be predicted by comparing the integral temperature with the critical value,
derived from a gear test for scuffing resistance of lubricants. The calculation method takes account of all significant
influence parameters, i.e. the lubricant (mineral oil with and without EP-additives, synthetic oils), the surface
roughness, the sliding velocities, the load, etc.
In order to ensure that all types of scuffing and comparable forms of surface damage due to the complex
relationships between hydrodynamical, thermodynamical and chemical phenomena are dealt with, further methods
of assessment may be necessary. The development of such methods is the objective of ongoing research.
vi © ISO 2000 – All rights reserved
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SIST ISO/TR 13989-2:2002
TECHNICAL REPORT ISO/TR 13989-2:2000(E)
Calculation of scuffing load capacity of cylindrical, bevel and
hypoid gears —
Part 2:
Integral temperature method
1 Scope
This part of ISO/TR 13989 specifies the integral temperature method for calculating the scuffing load capacity of
cylindrical, bevel and hypoid gears.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO/TR 13989. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this part of ISO/TR 13989 are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
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 6336-1:1996, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors.
1)
ISO 10300-1:— , Calculation of load capacity of bevel gears — Part 1: Introduction and general influence factors.
3 Terms, definitions, symbols and units
3.1 Terms and definitions
For the purposes of this part of ISO/TR 13989, the terms and definitions given in ISO 1122-1 apply.
3.2 Symbols and units
The symbols used in this part of ISO/TR 13989 are given in Table 1.
1) To be published.
© ISO 2000 – All rights reserved 1
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Table 1 — Symbols and units
Symbol Description Unit Reference
a centre distance mm —
a
virtual centre distance of virtual cylindrical gear mm ISO 10300-1
v
b face width, smaller value of pinion or wheel mm —
b
effective facewidth for scuffing mm Eq. (46)
eB
2
c specific heat capacity per unit volume N/(mm ·K) —
v
single stiffness N/(mm·µm) ISO 6336-1
c�
c mesh stiffness N/(mm·µm) ISO 6336-1
�
d referencecirclediameter mm —
d effective tip diameter mm —
Na
d tip diameter mm Eq. (69)
a
d base diameter mm Eq. (70)
b
d
diameter at mid-facewidth mm —
m
d reference circle of virtual crossed axes helical gear mm Eq. (68)
s
d reference diameter of virtual cylindrical gear mm ISO 10300-1
v
d tip diameter of virtual cylindrical gear mm ISO 10300-1
va
d base diameter of virtual cylindrical gear mm ISO 10300-1
vb
g recess path of contact of pinion, wheel mm Eqs. (90), (91)
an1,2
g approach path of contact of pinion, wheel mm Eqs. (90), (91)
fn1,2
g* sliding factor — Eq. (62)
h addendum at mid-facewidth of hypoid gear mm —
am
m module mm —
m normal module of hypoid gear at mid-facewidth mm —
mn
m normal module of virtual crossed axes helical gear mm Eq. (73)
sn
n number of meshing gears ——
p
p normal base pitch mm Eq. (74)
en
u gear ratio ——
u gear ratio of virtual cylindrical gear — ISO 10300-1
v
v reference line velocity m/s —
v tangential velocity of pinion, wheel of hypoid gear m/s Eqs. (77), (78)
t1,2
v
maximum sliding velocity at tip of pinion m/s Eq. (83)
g�1
v sliding velocity at pitch point m/s Eq. (82)
gs
v sliding velocity m/s Eqs. (84), (85)
g1,2
v sliding velocity m/s Eq. (87)
g�1
2 © ISO 2000 – All rights reserved
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
v sliding velocity m/s Eq. (88)
g�1
v tangential speed at reference cone at mid-facewidth of m/s —
mt
bevel gear
v sums of tangential speeds at pitch point m/s Eqs. (2), (47), (81)
ΣC
tangential speed m/s Eq. (79)
v
Σs
v tangential speed m/s Eq. (80)
Σh
w specific tooth load, scuffing N/mm Eq. (4)
Bt
z number of teeth ——
z number of teeth of virtual cylindrical gear — ISO 10300-1
v
1/2
B thermal contact coefficient N/(mm·s ·K) Eq. (12)
M
C ,C ,C weighting factors ——
1 2 2H
C nominal tip reliefµm —
a
C
effective tip reliefµm Eqs. (37), (38), (49)
eff
2
E module of elasticity (Young's modulus) N/mm —
F
nominal tangential load at reference cone at mid-facewidth N —
mt
F normal tooth load N Eq. (51)
n
F nominal tangential load at reference circle N —
t
K application factor — ISO 6336-1,
A
ISO 10300-1
K dynamic factor — ISO 6336-1,
v
ISO 10300-1
K = K transverse load factor (scuffing) — 6.2.4, ISO 6336-1,
B� H�
ISO 10300-1
K = K face load factor (scuffing) — ISO 6336-1
B� H�
ISO 10300-1, 6.2.4,
Eqs. (52), (53)
K helical load factor (scuffing) — Eq. (5), 6.2.4, 6.3.5
B�
K bearing factor — 6.3.3
B�be
K transverse load factor — ISO 6336-1,
H�
ISO 10300-1
K face load factor — ISO 6336-1,
H�
ISO 10300-1
K bearing factor — ISO 10300-1
H�be
L contact parameter — Eq. (55)
Ra
arithmetic mean roughnessµm Eq. (6)
S scuffing safety factor — Eq. (14)
intS
S minimum required scuffing safety factor ——
Smin
© ISO 2000 – All rights reserved 3
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
T torque of the pinion Nm —
1
T scuffing torque of test pinion Nm Eq. (96)
1T
X geometry factor at pinion tooth tip — Eq. (22)
BE
X
run-in factor — Eq. (8)
E
X tip relief factor — Eq. (32)
Ca
X geometry factor of hypoid gears — Eq. (54)
G
X lubricant factor — 5.1
L
X thermal flash factor — Eq. (9)
M
X approach factor — Eqs. (25), (26), (27)
Q
X roughness factor — Eq. (7)
R
X lubrication factor — 6.1.5.3
S
X welding factor of executed gear — Table 3
W
X welding factor of test gear — 6.4.2
WT
X relative welding factor — Eq. (102)
WrelT
X contact factor — Eq. (21)
mp
X pressure angle factor — Eqs. (13), (48)
��
X contact ratio factor — Eqs. (39) to (44)
ε
pressure angle °—
�
normal pressure angle at mid-facewidth of hypoid gear °—
�
mn
� normal pressure angle °—
n
normal pressure angle of crossed axes helical gear ° Eq. (64)
�
sn
� transverse pressure angle of crossed axes helical gear ° Eq. (66)
st
transverse pressure angle °—
�
t
� ´ transverse working pressure angle °—
t
transverse pressure angle of virtual cylindrical gear ° ISO 10300-1
�
vt
arbitrary angle ° Figure 2
�
y
helix angle °—
�
helix angle at base circle ° Eqs. (67), (71)
�
b
� helix angle at reference cone at mid-facewidth of hypoid °—
m
gear
� helix angle of virtual crossed axes helical gear ° Eq. (63)
s
auxiliary angle ° Eq. (86)
�
reference cone angle °—
�
4 © ISO 2000 – All rights reserved
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Table 1 (continued)
Symbol Description Unit Reference
recess contact ratio — Eqs. (28), (29)
�
a
� approach contact ratio — Eqs. (28), (29)
f
contact ratio in normal section of virtual crossed axes — Eqs. (92), (93)
�
n
helical gear
addendum contact ratio of the pinion — Eq. (30)
�
1
� addendum contact ratio of the wheel — Eq. (31)
2
contact ratio — Eq. (45)
�
�
transverse contact ratio of virtual cylindrical gear — ISO 10300-1
�
v�
tip contact ratio of virtual cylindrical pinion — ISO 10300-1
�
v1
tip contact ratio of virtual cylindrical wheel — ISO 10300-1
�
v2
Hertzian auxiliary coefficient — Figure 7, Eqs. (57), (59)
�
mean coefficient of friction — Eqs. (1), (1a)
�
mC
� dynamic viscosity at oil temperature —
mPa�s
oil
heat conductivity —
� N/(s�K)
M
Poisson's ratio ——
�
2
� kinematic viscosity of the oil at 40 �C mm /s; cSt —
40
radius of curvature at tip of the pinion, wheel mm Eqs. (23), (24)
�
E1,2
� relative radius of curvature at pitch point in normal section mm Eq. (76)
Cn
radius of curvature at pitch point in normal section mm Eq. (75)
�
n1,2
relative radius of curvature at pitch point mm Eq. (3)
�
redC
Hertzian auxiliary coefficient — Figure 7, Eqs. (58), (60)
�
Hertzian auxiliary angle ° Eqs. (56) to (60)
�
flash temperature at pinion tooth tip when load sharing is K Eq. (19)
�
flaE
neglected
mean flash temperature K Eq. (18)
�
flaint
� mean flash temperature of hypoid gear K Eq. (50)
flainth
integral temperature K Eq. (17)
�
int
permissible integral temperature K Eq. (16)
�
intP
scuffing integral temperature (allowable integral K Eq. (94)
�
intS
temperature)
� mean flash temperature of the test gear K Eqs. (96), (99), (101)
flaintT
oil sump or spray temperature °C —
�
oil
� bulk temperature °C Eq. (20)
M-C
© ISO 2000 – All rights reserved 5
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SIST ISO/TR 13989-2:2002
ISO/TR 13989-2:2000(E)
Table 1 (concluded)
Symbol Description Unit Reference
test bulk temperature Eqs. (95), (98), (100)
� �C
MT
axle angle of virtual crossed axes helical gear ° Eq. (72)
�
� axle angle of virtual crossed axes helical gear ° Eq. (65)
run-in grade — 5.2
�
E
parameter on the line of action — Eq. (10)
�
Subscripts:
1pinion
2 wheel
a tip diameter of the virtual gear
b base circle of the virtual gear
m mid-facewidth of bevel or hypoid gears
n normal section
s virtual crossed axes helical gear
t tangential direction
T test gear
4 Field of application
The calculation methods are based on results of the rig testing of gears run at pitch line velocities less than 80 m/s.
The equations can be used for gears which run at higher speeds, but with increasing uncertainty as speed
increases. The uncertainty concerns the estimation of bulk temperature, coefficient of friction, allowable
temperatures, etc. as speeds exceed the range with experimental background.
4.1 Scuffing damage
When once initiated, scuffing damage can lead to gross degradation of tooth flank surfaces, with increase of: power
loss, dynamic loading, noise
...
RAPPORT ISO/TR
TECHNIQUE 13989-2
Première édition
2000-03-15
Calcul de la capacité de charge au grippage
des engrenages cylindriques, coniques et
hypoïdes —
Partie 2:
Méthode de la température intégrale
Calculation of scuffing load capacity of cylindrical, bevel and hypoid
gears —
Part 2: Integral temperature method
Numéro de référence
ISO/TR 13989-2:2000(F)
©
ISO 2000
---------------------- Page: 1 ----------------------
ISO/TR 13989-2:2000(F)
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ii © ISO 2000 – Tous droits réservés
---------------------- Page: 2 ----------------------
ISO/TR 13989-2:2000(F)
Sommaire Page
Avant-propos.v
Introduction.vii
1 Domaine d’application.1
2Références normatives .1
3 Termes, définitions, symboles et unités .1
3.1 Termes et définitions.1
3.2 Symboles et unités .2
4 Domaine d'application.6
4.1 Détérioration par grippage.6
4.2 Critère de la température intégrale .7
5 Facteurs d'influence .7
5.1 Coefficient de frottement moyen� .7
mC
5.2 Facteur de rodage X .10
E
5.3 Facteur thermique éclair X .10
M
5.4 Facteur d'angle de pression X .11
��
6 Calcul .12
6.1 Engrenages cylindriques .12
6.1.1 Coefficient de sécurité au grippage S .12
intS
6.1.2 Température intégrale admissible� .12
intP
6.1.3 Température intégrale� .13
int
6.1.4 Température-éclair en tête de dent du pignon� .13
flaE
6.1.5 Température de masse� .13
M
6.1.6 Coefficient moyen de frottement� .14
mC
6.1.7 Facteur de rodage X .14
E
6.1.8 Facteur thermique éclair X .14
M
6.1.9 Facteur d'angle de pression X .14
��
6.1.10 Facteur géométrique en tête du pignon X .14
BE
6.1.11 Facteur d'approche X .14
Q
6.1.12 Facteur de dépouille de tête X .15
Ca
6.1.13 Facteur de rapport de conduite X .17
�
6.2 Engrenages coniques.20
6.2.1 Coefficient de sécurité au grippage S .20
intS
6.2.2 Température intégrale admissible� .20
intP
6.2.3 Température intégrale� .20
int
6.2.4 Température-éclair en tête de dent du pignon� .20
flaE
6.2.5 Température de masse� .20
M
6.2.6 Coefficient de frottement moyen� .21
mC
6.2.7 Facteur de rodage X .21
E
6.2.8 Facteur thermique éclair X .21
M
6.2.9 Facteur d'angle de pression X .21
��
6.2.10 Facteur géométrique en tête du pignon X .21
BE
6.2.11 Facteur d'approche X .21
Q
6.2.12 Facteur de dépouille de tête X .22
Ca
© ISO 2000 – Tous droits réservés iii
---------------------- Page: 3 ----------------------
ISO/TR 13989-2:2000(F)
6.2.13 Facteur de rapport de conduite X .22
�
6.3 Engrenages hypoïdes.22
6.3.1 Coefficient de sécurité au grippage S .22
intS
6.3.2 Température intégrale admissible� .22
intP
6.3.3 Température intégrale� .23
int
6.3.4 Température de masse� .23
M
6.3.5 Coefficient de frottement moyen� .23
mC
6.3.6 Facteur de rodage X .23
E
6.3.7 Facteur géométrique X .23
G
6.3.8 Facteur d'approche X .25
Q
6.3.9 Facteur de dépouille de tête X .25
Ca
6.3.10 Facteur de rapport de conduite X .25
�
6.3.11 Calcul des engrenages gauches hélicoïdaux équivalents .25
6.4 Température intégrale de grippage.29
6.4.1 Température intégrale de grippage� .29
intS
6.4.2 Facteur relatif de soudure X .33
WrelT
Annexe A (informative) Exemples.34
Annexe B (informative) Température de grippage en fonction de la durée de contact.44
Bibliographie .48
iv © ISO 2000 – Tous droits réservés
---------------------- Page: 4 ----------------------
ISO/TR 13989-2:2000(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
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jugées valables ou utiles.
Les rapports techniques sont rédigés conformément aux règles données dans les Directives ISO/CEI, Partie 3.
L’attention est appelée sur le fait que certains des éléments delaprésente partie de l’ISO TR 13989 peuvent faire
l’objet de droits de propriété intellectuelle ou de droits analogues. L’ISO ne saurait être tenue pour responsable de
ne pas avoir identifié de tels droits de propriété et averti de leur existence.
L’Amendement au Rapport technique ISO/TR 13989-2: a étéélaboré par le comité technique ISO/TC 60,
Engrenages, sous-comité SC 2, Calcul de la capacité des engrenages.
Le présent document est publié dans la série des Rapports techniques de type 2 (conformément au paragraphe
G.3.2.2. de la partie 1 des Directives ISO/CEI, 1995) comme «norme prospective d’application provisoire» dans le
domaine de [à décrire] en raison de l’urgence d’avoir une indication quant à la manière dont il convient d’utiliser les
normes dans ce domaine pour répondre à un besoin déterminé.
Ce document ne doit pas être considéré comme une «Norme internationale». Il est proposé pour une mise en
œuvre provisoire, dans le but de recueillir des informations et d’acquérir de l’expérience quant à son application
dans la pratique. Il est de règle d’envoyer les observations éventuelles relatives au contenu de ce document au
Secrétariat central de l’ISO.
Il sera procédéà un nouvel examen de ce Rapport technique de type 2 trois ans au plus tard après sa publication,
avec la faculté d’en prolonger la validité pendant trois autres années, de le transformer en Norme internationale ou
de l’annuler.
© ISO 2000 – Tous droits réservés v
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ISO/TR 13989-2:2000(F)
L'ISO TR 13989 comprend les parties suivantes, présentées sous le titre général Calcul de la capacité de charge
au grippage des engrenages cylindriques, coniques et hypoïdes:
� Partie 1: Méthode de la température-éclair
� Partie 2: Méthode de la température intégrale
Les annexes A et B de la présente partie de l’ISO/TR 13989 sont données uniquement à titre d’information.
vi © ISO 2000 – Tous droits réservés
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ISO/TR 13989-2:2000(F)
Introduction
La présente partie de l’ISO/TR 13989 décrit la détérioration de surface d'engrenages cylindriques «grippage à
chaud» (à denture droite et hélicoïdale), coniques et hypoïdes, pour les matériaux d'engrenages généralement
utilisés combinésavecdifférents traitements thermiques. Le «grippage à chaud» est caractérisé par des marques
de grippage et de griffures typiques qui peuvent donner lieu à une augmentation de la perte de puissance, de la
charge dynamique, du bruit et de l'usure. Pour le «grippage à froid»,engénéral associéà des engrenages à basse
température et faible vitesse, tournant à des vitesses inférieures à 4 m/s environ, trempés à cœur et soumis à des
charges élevées, les équations ne conviennent pas
Il s'agit là d'une forme particulièrement sévère de détérioration de la surface de la denture d'un engrenage, au cours
de laquelle un arrachement ou une soudure par fusion des surfaces en contact apparaît, due à l'absence ou à la
rupture du film de lubrifiant entre les flancs de dents en contact d'engrenages conjugués, due à des températures et
des pressions élevées.Cette formededétérioration est appelée «grippage»; elle est d'autant plus importante que
les vitesses de surface sont élevées. Le grippage peut également apparaître à de faibles vitesses de glissement
lorsque les pressions à la surface des dentures sont suffisamment élevées, soit de manière uniforme, soit dans des
zones discrètes du fait d'une géométrie et d'une distribution de charge sur les flancs inégales.
Le risque de détérioration par grippage varie selon les propriétés des matériaux des dentures, le lubrifiant utilisé,la
rugosité de surface des flancs de denture, les vitesses de glissement et la charge. Une aération excessive ou la
présence de contaminants dans le lubrifiant, tels que des particules métalliques en suspension, augmente
également le risque de détérioration par grippage. En conséquence du grippage, les engrenages à grande vitesse
peuvent subir des niveaux de charge dynamique élevés du fait de l'augmentation des vibrations qui conduisent
généralement à une détérioration accrue par grippage, formation de piqûres ou rupture de dent.
Les températures superficielles élevées, induites par des pressions de contact et des vitesses de glissement
élevées peuvent conduire à la rupture des films de lubrifiant. Sur la base de cette hypothèse, deux approches
permettant de corréler la température et la rupture du film de lubrifiant sont présentées:
� la méthode de la température-éclair (présentée dans l’ISO/TR 13989-1), basée sur les températures de contact
qui varient sur la longueur de conduite;
� la méthode de la température intégrale (présentée dans la présente partie de l’ISO/TR 13989), baséesur la
moyenne pondérée des températures de contact sur la longueur de conduite.
La méthode de la température intégrale est basée sur l'hypothèse que le grippage apparaît probablement lorsque la
valeur moyenne de la température de contact (température intégrale) est supérieure ou égale à une valeur critique
correspondante. Le risque de grippage d'une transmission par engrenages réelle peut être prédit en comparant la
température intégrale à la valeur critique, issue d'essais sur engrenages de la résistance des lubrifiants au
grippage. La méthode de calcul tient compte de tous les paramètres d'influence significatifs, c'est-à-dire le lubrifiant
(huile minérale sans ou avec additifs EP, huile synthétique), la rugosité de surface, les vitesses de glissement, la
charge, etc.
Il est admis que d'autres méthodes peuvent être nécessaires afin de s'assurer que tous les types de grippage et
formes comparables de détérioration de surface dus aux interactions complexes entre phénomènes
hydrodynamiques, thermodynamiques et chimiques, sont traités. Le développement de ces méthodes fait
actuellement l'objet de recherches poussées.
© ISO 2000 – Tous droits réservés vii
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RAPPORT TECHNIQUE ISO/TR 13989-2:2000(F)
Calcul de la capacité de charge au grippage des engrenages
cylindriques, coniques et hypoïdes —
Partie 2:
Méthode de la température intégrale
1 Domaine d’application
La présente partie de l’ISO/TR 13989 spécifielaméthode de la température intégrale pour calculer la capacité de
charge au grippage des engrenages cylindriques, coniques et hypoïdes.
2Références normatives
Les documents normatifs suivants contiennent des dispositions qui, par suite de la référence qui y est faite,
constituent des dispositions valables pour la présente partie de l’ISO/TR 13989. Pour les références datées, les
amendements ultérieurs ou les révisions de ces publications ne s’appliquent pas. Toutefois, les parties prenantes
aux accords fondés sur la présente partie de l'ISO/TR 13989 sont invitées à rechercher la possibilité d'appliquer les
éditions les plus récentes des documents normatifs indiqués ci-après. Pour les références non datées, la dernière
édition du document normatif en référence s’applique. Les membres de l'ISO et de la CEI possèdent le registre des
Normes internationales en vigueur.
ISO 53:1998, Engrenages cylindriques de mécanique générale et de grosse mécanique — Tracé de référence.
ISO 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques.
ISO 1328-1:1995, Engrenages cylindriques — Système ISO de précision — Partie 1: Définitions et valeurs
admissibles des écarts pour les flancs homologues de la denture.
ISO 6336-1:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 1: Principes de base, introduction et facteurs généraux d'influence.
1)
ISO 10300-1:— , Calcul de la capacité de charge des engrenages coniques — Partie 1: Introduction et facteurs
généraux d’influence.
3 Termes, définitions, symboles et unités
3.1 Termes et définitions
Pour les besoins de la présente partie de l'ISO/TR 13989, les termes et définitions donnés dans l’ISO 1122-1
s'appliquent.
1) À publier.
© ISO 2000 – Tous droits réservés 1
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ISO/TR 13989-2:2000(F)
3.2 Symboles et unités
Les symboles utilisés dans la présente partie de l’ISO/TR 13989 sont donnés dans le Tableau 1.
Tableau 1 — Symboles et unités
Symbole Description Unité Référence
a entraxe mm —
entraxe équivalent de l'engrenage cylindrique à denture
a
mm ISO 10300-1
v
droite équivalent
b largeur de denture, plus petite valeur du pignon ou de la roue mm —
b largeur de denture effective pour le grippage mm Éq. (46)
eB
2
c
capacité thermique spécifique par unité de volume N/(mm ·K) —
v
c� raideur simple N/(mm·µm) ISO 6336-1
c
raideur d'engrènement N/(mm·µm) ISO 6336-1
�
d diamètrederéférence mm —
d
diamètre actif de tête mm —
Na
d
diamètredetête mm Éq. (69)
a
d
diamètredebase mm Éq. (70)
b
d diamètre à mi-largeur de la denture mm —
m
cercle de référence d'une roue équivalente d'un
d
mm Éq. (68)
s
engrenage gauche hélicoïdal
diamètrederéférence de la roue cylindrique à denture
d
mm ISO 10300-1
v
droite équivalente
diamètredetête de la roue cylindrique à denture droite
d
mm ISO 10300-1
va
équivalente
diamètre de base de la roue cylindrique à denture droite
d
mm ISO 10300-1
vb
équivalente
g longueur de retraite du pignon, de la roue mm Éqs. (90), (91)
an1,2
g
longueur d'approche du pignon, de la roue mm Éqs. (90), (91)
fn1,2
g*
facteur de glissement —Éq. (62)
h
saillie à mi-largeur de la denture d'engrenage hypoïde mm —
am
m module mm —
module réel à mi-largeur de la denture d'engrenage
m
mm —
mn
hypoïde
m
module réel d'engrenage gauche hélicoïdal équivalent mm Éq. (73)
sn
n
nombre de roues dentées en prise ——
p
p
pas de base réel mm Éq. (74)
en
u rapport d'engrenage ——
u
rapport d'engrenage de l'engrenage cylindrique équivalent — ISO 10300-1
v
2 © ISO 2000 – Tous droits réservés
---------------------- Page: 9 ----------------------
ISO/TR 13989-2:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
v vitesse de la ligne de référence m/s —
vitesse tangentielle du pignon, de la roue d'un engrenage
v
m/s Éqs. (77), (78)
t1,2
hypoïde
v
vitesse de glissement maximale à la tête de pignon m/s Éq. (83)
g�1
v
vitesse de glissement au point primitif m/s Éq. (82)
gs
v
vitesse de glissement m/s Éqs. (84), (85)
g1,2
v
vitesse de glissement m/s Éq. (87)
g�1
v
vitesse de glissement m/s Éq. (88)
g�1
vitesse tangentielle au cône de référence à mi-largeur de
v m/s —
mt
la denture d'engrenage conique
v
somme des vitesses tangentielles au point primitif m/s Éqs. (2), (47), (81)
�C
v
vitesse tangentielle m/s Éq. (79)
�s
v
vitesse tangentielle m/s Éq. (80)
�h
w
charge spécifique sur les dents, grippage N/mm Éq. (4)
Bt
z nombre de dents ——
z nombre de dents de l'engrenage cylindrique équivalent — ISO 10300-1
v
1/2
B
coefficient de contact thermique N/(mm·s ·K) Éq. (12)
M
C ,C ,C
facteurs de pondération ——
1 2 2H
C
dépouille de tête nominaleµm —
a
C
dépouille de tête effectiveµm Éqs. (37), (38), (49)
eff
2
E module d'élasticité (module de Young) N/mm —
charge tangentielle nominale au cône de référence à mi-
F N —
mt
largeur de la denture
F
charge réelle sur les dents N Éq. (51)
n
F
charge tangentielle nominale au cercle de référence N —
t
K
facteur d'application — ISO 6336-1, ISO 10300-1
A
K
facteur dynamique — ISO 6336-1, ISO 10300-1
v
= K facteur de distribution transversale de la charge
6.2.4, ISO 6336-1,
H�
K
—
B�
ISO 10300-1
(grippage)
= K facteur de distribution longitudinale de la charge ISO 6336-1 ISO 10300-1,
H�
K
—
B�
6.2.4, Éqs. (52), (53)
(grippage)
K
facteur de charge hélicoïdale (grippage) —Éq. (5), 6.2.4, 6.3.5
B�
K
facteur de portée — 6.3.3
B�be
K
facteur de distribution transversale de la charge — ISO 6336-1, ISO 10300-1
H�
K
facteur de distribution longitudinale de la charge — ISO 6336-1, ISO 10300-1
H�
© ISO 2000 – Tous droits réservés 3
---------------------- Page: 10 ----------------------
ISO/TR 13989-2:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
K
facteur de portée — ISO 10300-1
H�be
L paramètre de contact —Éq. (55)
Ra rugosité moyenne arithmétiqueµm Éq. (6)
S
coefficient de sécurité au grippage —Éq. (14)
intS
S
coefficient de sécurité au grippage minimal exigé— —
Smin
T
couple sur le pignon Nm —
1
T
couple de grippage sur le pignon d'essai Nm Éq. (96)
1T
X
facteur géométrique en tête de dent du pignon —Éq. (22)
BE
X
facteur de rodage —Éq. (8)
E
X
facteur de dépouille de tête —Éq. (32)
Ca
X
facteur géométrique des engrenages hypoïdes —Éq. (54)
G
X
facteur lubrifiant — 5.1
L
X
facteur thermique éclair —Éq. (9)
M
X
facteur d'approche —Éqs. (25), (26), (27)
Q
X
facteur de rugosité—Éq. (7)
R
X facteur de lubrification — 6.1.5.3
S
X facteur de soudure de l'engrenage fabriqué— Tableau 3
W
X
facteur de soudure de l'engrenage d'essai — 6.4.2
WT
X
facteur relatif de soudure —Éq. (102)
WrelT
X
facteur de contact —Éq. (21)
mp
X
facteur d'angle de pression —Éqs. (13), (48)
��
X
facteur de rapport de conduite —Éqs. (39) à (44)
�
angle de pression °—
�
angle de pression réel à mi-largeur de denture pour
�
°—
mn
l'engrenage hypoïde
�
angle de pression réel °—
n
� angle de pression réel de l'engrenage gauche hélicoïdal °Éq. (64)
sn
angle de pression apparent de l'engrenage gauche
� °Éq. (66)
st
hélicoïdal
�
angle de pression apparent °—
t
� � angle de pression apparent de fonctionnement °—
t
angle de pression apparent pour l'engrenage cylindrique
� ° ISO 10300-1
vt
équivalent
� angle d'incidence arbitraire ° Figure 2
y
4 © ISO 2000 – Tous droits réservés
---------------------- Page: 11 ----------------------
ISO/TR 13989-2:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
� angle d'hélice °—
�
angle d'hélice de base °Éqs. (67), (71)
b
angle d'héliceaucône de référence à mi-largeur de la
�
°—
m
denture pour l'engrenage hypoïde
angle d'hélice pour l'engrenage gauche hélicoïdal
�
°Éq. (63)
S
équivalent
� angle auxiliaire °Éq. (86)
� angle du cône de référence °—
� rapport de retrait —Éqs. (28), (29)
a
�
rapport d'approche —Éqs. (28), (29)
f
rapport de conduite du profil réel pour l'engrenage gauche
� —Éqs. (92), (93)
n
hélicoïdal équivalent
� rapport de conduite de saillie du pignon —Éq. (30)
1
�
rapport de conduite de saillie de la roue —Éq. (31)
2
� rapport de conduite —Éq. (45)
�
rapport de conduite apparent pour l'engrenage cylindrique
� — ISO 10300-1
v�
équivalent
rapport de conduite de tête pour le pignon cylindrique
� — ISO 10300-1
v1
équivalent
rapport de conduite de tête pour la roue cylindrique
�
— ISO 10300-1
v2
équivalente
� coefficient auxiliaire hertzien — Figure 7, Éqs. (57), (59)
�
coefficient de frottement moyen —Éqs. (1), (1a)
mC
�
viscosité dynamique à la température de l'huile mPa�s —
oil
� conductivité thermique N/(s�K) —
M
� coefficient de Poisson ——
2
� viscosité cinématique de l'huile à 40 °Cmm /s; cSt —
40
� rayondecourbureentête du pignon, de la roue mm Éqs. (23), (24)
E1,2
rayon de courbure équivalent au point primitif dans le plan
� mm Éq. (76)
Cn
normal
�
rayon de courbure au point primitif dans le plan normal mm Éq. (75)
n1,2
� rayon de courbure équivalent au point primitif mm Éq. (3)
redC
� coefficient auxiliaire hertzien — Figure 7, Éqs. (58), (60)
� angle auxiliaire hertzien °Éqs. (56) à (60)
température-éclair à la tête de dent de pignon lorsque la
� répartition de charge entre dents n'est pas prise en K Éq. (19)
flaE
compte
© ISO 2000 – Tous droits réservés 5
---------------------- Page: 12 ----------------------
ISO/TR 13989-2:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
�
température-éclair moyenne K Éq. (18)
flaint
� température-éclair moyenne pour l'engrenage hypoïde K Éq. (50)
flainth
�
température intégrale K Éq. (17)
int
� température intégrale admissible K Éq. (16)
intP
température intégrale de grippage (température intégrale
�
K Éq. (94)
intS
acceptable)
�
température-éclair moyenne de l'en
...
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