SIST ISO/TR 13989-1:2002
(Main)Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears -- Part 1: Flash temperature method
Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears -- Part 1: Flash temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques, coniques et hypoïdes -- Partie 1: Méthode de la température-éclair
Le concept fondamental selon Blok est applicable à tous les éléments de machine ayant des zones de contact mobiles. Les formules de température-éclair sont valables pour une zone de contact hertzien en forme de bande ou quasiment en forme de bande et pour des conditions de fonctionnement caractérisées par des nombres de Péclet suffisamment élevés.
Izračun nosilnosti glede na toplotno razjedanje zobnih bokov valjastih, stožčastih in hipoidnih zobnikov - 1. del: Metoda trenutne temperature
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TECHNICAL ISO/TR
REPORT 13989-1
First edition
2000-03-15
Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears —
Part 1:
Flash temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques,
coniques et hypoïdes —
Partie 1: Méthode de la température-éclair
Reference number
ISO/TR 13989-1:2000(E)
©
ISO 2000
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ISO/TR 13989-1:2000(E)
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ii © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Contents Page
Foreword.iv
Introduction.v
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 Scuffing and wear.6
4.1 Occurrence of scuffing and wear.6
4.2 Transition diagram.6
4.3 Friction at incipient scuffing.8
5 Basic formulae .8
5.1 Contact temperature.8
5.2 Flash temperature formula.9
5.3 Transverse unit load.10
5.4 Distribution of overall bulk temperatures .11
5.5 Rough approximation of a bulk temperature.12
6 Coefficient of friction.12
6.1 Mean coefficient of friction, method A.13
6.2 Mean coefficient of friction, method B .13
6.3 Mean coefficient of friction, method C .13
7 Parameter on the line of action .14
8 Approach factor .16
9 Load sharing factor .17
9.1 Buttressing factor.17
9.2 Spur gears with unmodified profiles .18
9.3 Spur gears with profile modification .19
9.4 Narrow helical gears with unmodified profiles.20
9.5 Narrow helical gears with profile modification.20
9.6 Wide helical gears with unmodified profiles.21
9.7 Wide helical gears with profile modification.21
9.8 Narrow bevel gears.22
9.9 Wide bevel gears.23
10 Scuffing temperature and safety.24
10.1 Scuffing temperature.24
10.2 Structural factor .24
10.3 Contact exposure time .25
10.4 Scuffing temperature in gear tests.26
10.5 Safety range .26
Annexe A (informative) Flash temperature formula presentation.28
Annexe B (informative) Optimal profile modification .35
Bibliography .37
© ISO 2000 – All rights reserved iii
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ISO/TR 13989-1:2000(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 13989-1, 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 13989 are for information only.
iv © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Introduction
Since 1990 the flash temperature method, presented in this part of ISO/TR 13989, was enriched with research for
short exposure times, consideration of transition diagrams, new approximations for the coefficient of friction, and
completely renewed load sharing factors. In 1991 Prof. Blok contributed an extension of the flash temperature
formula which made it directly applicable to hypoid gears.
The integral temperature, presented in ISO/TR 13989-2, averages the flash temperature and supplements empirical
influence factors to the hidden load sharing factor. The resulting value approximates the maximum contact
temperature, thus yielding about the same assessment of scuffing risk as the flash temperature method of this part
of ISO/TR 13989. The integral temperature method is less sensitive for those cases where there are local
temperature peaks, usually in gearsets that have low contact ratio or contact near the base circle or other sensitive
geometries.
The 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. In contrast to the relatively long time of development of fatigue
damage, one single momentary overload can initiate scuffing damage of such severity that affected gears may no
longer be used. According to Blok [12][13][14][15][16][17], high contact temperatures of lubricant and tooth surfaces
at the instantaneous contact position may effect a break-down of the lubricant film at the contact interface.
The interfacial contact temperature is conceived as the sum of two components:
� the interfacial bulk temperature of the moving interface, which, if varying, does so only comparatively slowly.
For evaluating this component, it may be suitably averaged from the two overall bulk temperatures of the two
rubbing teeth. The latter two bulk temperatures follow from the thermal network theory [18].
� the rapidly fluctuating flash temperature of the moving faces in contact. Special attention has to be paid to the
coefficient of friction. A common practice is the use of a coefficient of friction valid for regular working
conditions, although it may be stated that at incipient scuffing the coefficient of friction has significantly higher
values.
The complex relationship between mechanical, hydrodynamical, thermodynamical and chemical phenomena was
the objective of extensive research and experiments, which may induce various empirical influence factors. A direct
suppletion of empirical influence factors may enforce the related functional factors in the main formula to be fixated
to average values. However, correct treatment of functional factors (e.g. coefficient of friction, load sharing factor,
thermal contact coefficient) keeps the main formula intact, in confirmation with the experiments and practice.
Next to the maximum contact temperature, the progress of the contact temperature along the path of contact
provides necessary information to the gear design.
© ISO 2000 – All rights reserved v
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TECHNICAL REPORT ISO/TR 13989-1:2000(E)
Calculation of scuffing load capacity of cylindrical, bevel and
hypoid gears —
Part 1:
Flash temperature method
1 Scope
This part of ISO/TR 13989 specifies methods and formulae for evaluating the risk of scuffing, based on Blok's
contact temperature concept.
The fundamental concept according to Blok is applicable to all machine elements with moving contact zones. The
flash temperature formulae are valid for a band-shaped or approximately band-shaped Hertzian contact zone and
working conditions characterized by sufficiently high Péclet numbers.
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 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
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.
ISO 10825:1995, Gears — Wear and damage to gear teeth — Terminology.
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 and ISO 10825 apply.
3.2 Symbols and units
The symbols used in this part of ISO/TR 13989 are given in Table 1. The units of length metre, millimetre and
micrometre are chosen in accordance with common practice. To achieve a "coherent" system, the units for B , c ,
M �
X are adapted to the mixed application of metre and millimetre or millimetre and micrometre.
M
1) To be published.
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units
Symbol Description Unit Reference
a centre distance mm Eq. (A.5)
a
b facewidth, smaller value for pinion or wheel mm Eq. (11)
b effective facewidth mm Eq. (12)
eff
b semi-width of Hertzian contact band mm Eq. (3)
H
½ ½ ½
B thermal contact coefficient N/(mm �m �s �K) Eq (A.13)
M
½ ½ ½
B thermal contact coefficient of pinion N/(mm �m �s �K) Eq. (3)
M1
½ ½ ½
B thermal contact coefficient of wheel N/(mm �m �s �K) Eq. (3)
M2
C tip relief of pinion �m Eq. (48)
a1
C tip relief of wheel �m Eq. (46)
a2
C optimal tip relief �m Eq. (46)
eff
C equivalent tip relief of pinion �mEq.(B.2)
eq1
C equivalent tip relief of wheel �mEq.(B.3)
eq2
C root relief of pinion �mEq.(B.3)
f1
C root relief of wheel �mEq.(B.2)
f2
c specific heat per unit mass of pinion J/(kg�K) Eq. (9)
M1
c specific heat per unit mass of wheel J/(kg�K) Eq. (10)
M2
c mesh stiffness N/(mm��m) Eq. (B.1)
�
d reference diameter of pinion mm Eq. (34)
1
d reference diameter of wheel mm Eq. (35)
2
d tip diameter of pinion mm Eq. (34)
a1
d tip diameter of wheel mm Eq. (35)
a2
2
E modulus of elasticity of pinion N/mm Eq. (A.10)
1
2
E modulus of elasticity of wheel N/mm Eq. (A.10)
2
2
E reduced modulus of elasticity N/mm Eq. (A.9)
r
F external axial force N Eq. (18)
ex
F normal load in wear test N Fig. 1
n
F nominal tangential force N Eq. (11)
t
H auxiliary dimension mm Eq. (B.3)
1
H auxiliary dimension mm Eq. (B.2)
2
h tip height in mean cone of pinion mm Eq. (43)
am1
h tip height in mean cone of wheel mm Eq. (44)
am2
2 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
K application factor — Eq. (11)
A
K transverse load factor (scuffing) — Eq. (11)
B�
K face load factor (scuffing) — Eq. (11)
B�
K transverse load factor (contact stress) — Eq. (15)
H�
K face load factor (contact stress) — Eq. (14)
H�
K multiple path factor — Eq. (11)
mp
K dynamic factor — Eq. (11)
v
m normal module mm Eq. (B.2)
n
n revolutions per minute of pinion r/min Eq. (5)
1
n number of mesh contacts — Eq. (16)
p
Pe Péclet number of pinion material — Eq. (9)
1
Pe Péclet number of wheel material — Eq. (10)
2
Q quality grade — Eq. (57)
Ra tooth flank surface roughness of pinion �m Eq. (28)
1
Ra tooth flank surface roughness of wheel �m Eq. (28)
2
R cone distance of mean cone mm Eq. (A.16)
m
r reference radius in mean cone of pinion mm Eq. (43)
m1
r reference radius in mean cone of wheel mm Eq. (44)
m2
S safety factor for scuffing — Eq. (100)
B
S load stage (in FZG test) — Eq. (99)
FZG
t contact exposure time of pinion �s Eq. (95)
1
t contact exposure time of wheel �s Eq. (96)
2
t contact exposure time at bend of curve �s Eq. (97)
c
t longest contact exposure time �s Eq. (95)
max
u gear ratio — Eq. (A.6)
u virtual ratio — Eq. (B.6)
v
v sliding velocity m/s Fig. 1
g
v tangential velocity of pinion m/s Eq. (3)
g1
v tangential velocity of wheel m/s Eq. (3)
g2
v sum of tangential velocities in pitch point m/s Eq. (25)
g�C
v pitch line velocity m/s Eq. (26)
t
w normal unit load N/mm Eq. (3)
Bn
w transverse unit load N/mm Eq. (5)
Bt
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
X buttressing factor — Eq. (54)
but
X buttressing value — Eq. (51)
butA
X buttressing value — Eq. (51)
butE
X geometry factor — Eq. (A.5)
G
X approach factor — Eq. (3)
J
X lubricant factor — Eq. (25)
L
–¾ –½ –½
X thermo-elastic factor K�N �s �m �mm Eq. (5)
M
X multiple mating pinion factor — Eq. (22)
mp
X roughness factor — Eq. (25)
R
X lubrication system factor — Eq. (22)
S
X structural factor — Eq. (94)
W
X angle factor — Eq. (A.6)
��
X load sharing factor — Eq. (3)
�
X gradient of the scuffing temperature — Eq. (97)
�
z number of teeth of pinion — Eq. (30)
1
z number of teeth of wheel — Eq. (30)
2
� transverse tip pressure angle of pinion ° Eq. (31)
a1
� transverse tip pressure angle of wheel ° Eq. (30)
a2
� transverse pressure angle ° Eq. (34)
t
� normal working pressure angle ° Eq. (A.2)
wn
� transverse working pressure angle ° Eq. (7)
wt
� pinion pressure angle at arbitrary point ° Eq. (29)
y1
� helix angle ° Eq. (18)
� base helix angle ° Eq. (49)
b
� base helix angle in midcone ° Eq. (50)
bm
� working helix angle ° Eq. (A.2)
w
� parameter on the line of action at point A — Eq. (24)
A
� parameter on the line of action at point AA — Eq. (68)
AA
� parameter on the line of action at point AB — Eq. (66)
AB
� parameter on the line of action at point AU — Eq. (49)
AU
� parameter on the line of action at point B — Eq. (31)
B
� parameter on the line of action at point BB — Eq. (70)
BB
� parameter on the line of action at point D — Eq. (32)
D
� parameter on the line of action at point DD — Eq. (72)
DD
� parameter on the line of action at point DE — Eq. (67)
DE
4 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
� parameter on the line of action at point E — Eq. (24)
E
� parameter on the line of action at point EE — Eq. (74)
EE
� parameter on the line of action at point EU — Eq. (49)
EU
� parameter on the line of action at point M — Eq. (86)
M
� parameter on the line of action at arbitrary point — Eq. (7)
y
� angle of direction of tangential velocity of pinion — Eq. (3)
1
� angle of direction of tangential velocity of wheel — Eq. (3)
2
� pitch cone angle of pinion ° Eq. (37)
1
� pitch cone angle of wheel ° Eq. (39)
2
� transverse contact ratio — Eq. (76)
�
� overlap ratio — Eq. (52)
�
� absolute (dynamic) viscosity at oil temperature mPa�s Eq. (27)
oil
� contact temperature °CEq.(1)
B
� maximum contact temperature °CEq.(2)
Bmax
� flash temperature K Eq. (1)
fl
� average flash temperature K Eq. (22)
flm
� maximum flash temperature K Eq. (2)
flmax
� maximum flash temperature at test K Eq. (94)
flmaxT
� bulk temperature °C Eq. (22)
M
� interfacial bulk temperature °CEq.(1)
Mi
� bulk temperature of pinion teeth °C Eq. (20)
M1
� bulk temperature of wheel teeth °C Eq. (20)
M2
� bulk temperature at test °C Eq. (94)
MT
� oil temperature before reaching the mesh °C Eq. (22)
oil
� scuffing temperature °C Eq. (94)
S
� scuffing temperature at long contact time °C Eq. (97)
Sc
� heat conductivity of pinion N/(s�K) Eq. (9)
M1
� heat conductivity of wheel N/(s�K) Eq. (10)
M2
� coefficient of friction in pin-and-ring test — Fig. 1
� mean coefficient of friction — Eq. (3)
m
� Poisson's ratio of pinion material — Eq. (A.10)
1
� Poisson's ratio of wheel material — Eq. (A.10)
2
© ISO 2000 – All rights reserved 5
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (concluded)
Symbol Description Unit Reference
� density of pinion material kg/m³ Eq. (9)
M1
� density of wheel material kg/m³ Eq. (10)
M2
� relative radius of curvature at pitch point mm Eq. (25)
relC
� radius of curvature at arbitrary point of pinion mm Eq. (5)
y1
� radius of curvature at arbitrary point of wheel mm Eq. (5)
y2
� relative radius of curvature at arbitrary point mm Eq. (5)
yrel
� shaft angle ° Eq. (A.15)
� quill shaft twist ° Eq. (17)
a
The term wheel is used for the mating gear of a pinion.
4 Scuffing and wear
4.1 Occurrence of scuffing and wear
When gear teeth are completely separated by a full fluid film of lubricant, there is no contact between the asperities
of the tooth surfaces, and usually there is no scuffing or wear. Here, the coefficient of friction is rather low. In
exceptional cases a damage similar to scuffing may be caused by a sudden thermal instability [19] in a thick oil film,
which phenomenon is not treated here.
For thinner elastohydrodynamic films, incidental asperity contact takes place. As the mean film thickness
decreases, the number of contacts increases acccordingly. Abrasive wear, adhesive wear or scuffing becomes
possible. Abrasive wear may occur due to the rolling action of the gear teeth or the presence of abrasive particles in
the lubricant. Adhesive wear occurs by localized welding and subsequent detachment and transfer of particles from
one or both of the meshing teeth. Abrasive or adhesive wear may not be harmful if it is mild and if it subsides with
time, as in a normal run-in process.
In contrast to mild wear, scuffing is a severe form of adhesive wear that can result in progressive damage to the
gear teeth. In contrast to pitting and fatigue breakage which show a distinct incubation period, a short transient
overloading can result in scuffing failure.
Excessive aeration or the presence in the lubricant of contaminants such as metal particles in suspension, or water,
also increases the risk of scuffing damage. After scuffing, high speed gears tend to suffer high levels of dynamic
loading due to vibration which usually cause further damage by scuffing, pitting or tooth breakage.
)
2
In most cases, the resistance of gears to scuffing can be improved by using a lubricant with enhanced anti-scuff
additives. It is important, however, to be aware that some disadvantages attend the use of anti-scuff additives:
corrosion of copper, embrittlement of elastomers, lack of world-wide availability, etc.
The methods described are not suitable for "cold scuffing" which is in general associated with low speed, under
approx. 4 m/s, through-hardened heavily loaded gears of rather poor quality.
4.2 Transition diagram
The lubrication condition of sliding concentrated steel contacts, which operate in a liquid lubricant, can be described
[20][21][22][23] in terms of transition diagrams. A transition diagram according to Figure 1 is considered to be
applicable to contacts functioning at constant oil bath temperature.
2) The less correct designation Extreme Pressure, EP, is replaced by anti-scuff.
6 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
At combinations of normal force F and relative sliding velocity v which fall below the line A1-S, in region I, see
n g
Figure 1, the lubrication condition is characterized by a coefficient of friction of about 0,1 and a specific wear rate of
�2 3 �6 3
10 mm /(N�m) to 10 mm /(N�m) (i.e. volume wear per unit of normal force, per unit of sliding distance).
If, with v not above a value according to point S, the load is increased into region II, a transition into a second
g
condition of lubrication occurs. This mild wear lubrication condition is characterized by a coefficient of friction of
3 3
about 0,3 to 0,4 and a specific wear rate of 1 mm /(N�m) to5mm /(N�m).
Figure 1 — Transition diagram for contraform contacts with example of calculated contact temperatures
If load is increased still further, a transition into a third condition of lubrication, region III, occurs at intersection of the
line A2-S. This region is characterized by a coefficient of friction equal to 0,4 to 0,5. The wear rate, however, is
3 3
considerably higher, i.e. 100 mm /(N�m) to 1 000 mm /(N�m), than in regions I and II and the worn surfaces show
evidence of severe wear in the form of scuffing. If load increases at relative sliding velocities beyond point S, a
direct transition from region I to region III takes place.
There is strong evidence that the position of the line A1-S-A3 depends upon lubricant viscosity [24] as well as upon
Hertzian contact pressure [20][21]. At combinations of F and v that fall below this line, it is believed that the
n g
surfaces are kept apart by a thin lubricant film which is, however, penetrated by roughness asperities. In this
context, the term "partial elastohydrodynamic lubrication" has been used [21].
In region III liquid film effects are completely absent. This region is identical to the region of "incipient scuffing" [25].
There is evidence that the transition which occurs at intersecting the line A2-S is associated with reaching a critical
value of the contact temperature. This is the fundamental concept according to Blok.
The transition diagram shown is applicable to newly assembled, i.e. unoxidized steel contacts
...
SLOVENSKI STANDARD
SIST ISO/TR 13989-1:2002
01-julij-2002
,]UDþXQQRVLOQRVWLJOHGHQDWRSORWQRUD]MHGDQMH]REQLKERNRYYDOMDVWLKVWRåþDVWLK
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Calculation of scuffing load capacity of cylindrical, bevel and hypoid gears -- Part 1:
Flash temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques, coniques et
hypoïdes -- Partie 1: Méthode de la température-éclair
Ta slovenski standard je istoveten z: ISO/TR 13989-1:2000
ICS:
21.200 Gonila Gears
SIST ISO/TR 13989-1:2002 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
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SIST ISO/TR 13989-1:2002
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SIST ISO/TR 13989-1:2002
TECHNICAL ISO/TR
REPORT 13989-1
First edition
2000-03-15
Calculation of scuffing load capacity of
cylindrical, bevel and hypoid gears —
Part 1:
Flash temperature method
Calcul de la capacité de charge au grippage des engrenages cylindriques,
coniques et hypoïdes —
Partie 1: Méthode de la température-éclair
Reference number
ISO/TR 13989-1:2000(E)
©
ISO 2000
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SIST ISO/TR 13989-1:2002
ISO/TR 13989-1:2000(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.
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ii © ISO 2000 – All rights reserved
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SIST ISO/TR 13989-1:2002
ISO/TR 13989-1:2000(E)
Contents Page
Foreword.iv
Introduction.v
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 Scuffing and wear.6
4.1 Occurrence of scuffing and wear.6
4.2 Transition diagram.6
4.3 Friction at incipient scuffing.8
5 Basic formulae .8
5.1 Contact temperature.8
5.2 Flash temperature formula.9
5.3 Transverse unit load.10
5.4 Distribution of overall bulk temperatures .11
5.5 Rough approximation of a bulk temperature.12
6 Coefficient of friction.12
6.1 Mean coefficient of friction, method A.13
6.2 Mean coefficient of friction, method B .13
6.3 Mean coefficient of friction, method C .13
7 Parameter on the line of action .14
8 Approach factor .16
9 Load sharing factor .17
9.1 Buttressing factor.17
9.2 Spur gears with unmodified profiles .18
9.3 Spur gears with profile modification .19
9.4 Narrow helical gears with unmodified profiles.20
9.5 Narrow helical gears with profile modification.20
9.6 Wide helical gears with unmodified profiles.21
9.7 Wide helical gears with profile modification.21
9.8 Narrow bevel gears.22
9.9 Wide bevel gears.23
10 Scuffing temperature and safety.24
10.1 Scuffing temperature.24
10.2 Structural factor .24
10.3 Contact exposure time .25
10.4 Scuffing temperature in gear tests.26
10.5 Safety range .26
Annexe A (informative) Flash temperature formula presentation.28
Annexe B (informative) Optimal profile modification .35
Bibliography .37
© ISO 2000 – All rights reserved iii
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ISO/TR 13989-1:2000(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 13989-1, 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 13989 are for information only.
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SIST ISO/TR 13989-1:2002
ISO/TR 13989-1:2000(E)
Introduction
Since 1990 the flash temperature method, presented in this part of ISO/TR 13989, was enriched with research for
short exposure times, consideration of transition diagrams, new approximations for the coefficient of friction, and
completely renewed load sharing factors. In 1991 Prof. Blok contributed an extension of the flash temperature
formula which made it directly applicable to hypoid gears.
The integral temperature, presented in ISO/TR 13989-2, averages the flash temperature and supplements empirical
influence factors to the hidden load sharing factor. The resulting value approximates the maximum contact
temperature, thus yielding about the same assessment of scuffing risk as the flash temperature method of this part
of ISO/TR 13989. The integral temperature method is less sensitive for those cases where there are local
temperature peaks, usually in gearsets that have low contact ratio or contact near the base circle or other sensitive
geometries.
The 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. In contrast to the relatively long time of development of fatigue
damage, one single momentary overload can initiate scuffing damage of such severity that affected gears may no
longer be used. According to Blok [12][13][14][15][16][17], high contact temperatures of lubricant and tooth surfaces
at the instantaneous contact position may effect a break-down of the lubricant film at the contact interface.
The interfacial contact temperature is conceived as the sum of two components:
� the interfacial bulk temperature of the moving interface, which, if varying, does so only comparatively slowly.
For evaluating this component, it may be suitably averaged from the two overall bulk temperatures of the two
rubbing teeth. The latter two bulk temperatures follow from the thermal network theory [18].
� the rapidly fluctuating flash temperature of the moving faces in contact. Special attention has to be paid to the
coefficient of friction. A common practice is the use of a coefficient of friction valid for regular working
conditions, although it may be stated that at incipient scuffing the coefficient of friction has significantly higher
values.
The complex relationship between mechanical, hydrodynamical, thermodynamical and chemical phenomena was
the objective of extensive research and experiments, which may induce various empirical influence factors. A direct
suppletion of empirical influence factors may enforce the related functional factors in the main formula to be fixated
to average values. However, correct treatment of functional factors (e.g. coefficient of friction, load sharing factor,
thermal contact coefficient) keeps the main formula intact, in confirmation with the experiments and practice.
Next to the maximum contact temperature, the progress of the contact temperature along the path of contact
provides necessary information to the gear design.
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SIST ISO/TR 13989-1:2002
TECHNICAL REPORT ISO/TR 13989-1:2000(E)
Calculation of scuffing load capacity of cylindrical, bevel and
hypoid gears —
Part 1:
Flash temperature method
1 Scope
This part of ISO/TR 13989 specifies methods and formulae for evaluating the risk of scuffing, based on Blok's
contact temperature concept.
The fundamental concept according to Blok is applicable to all machine elements with moving contact zones. The
flash temperature formulae are valid for a band-shaped or approximately band-shaped Hertzian contact zone and
working conditions characterized by sufficiently high Péclet numbers.
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 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
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.
ISO 10825:1995, Gears — Wear and damage to gear teeth — Terminology.
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 and ISO 10825 apply.
3.2 Symbols and units
The symbols used in this part of ISO/TR 13989 are given in Table 1. The units of length metre, millimetre and
micrometre are chosen in accordance with common practice. To achieve a "coherent" system, the units for B , c ,
M �
X are adapted to the mixed application of metre and millimetre or millimetre and micrometre.
M
1) To be published.
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units
Symbol Description Unit Reference
a centre distance mm Eq. (A.5)
a
b facewidth, smaller value for pinion or wheel mm Eq. (11)
b effective facewidth mm Eq. (12)
eff
b semi-width of Hertzian contact band mm Eq. (3)
H
½ ½ ½
B thermal contact coefficient N/(mm �m �s �K) Eq (A.13)
M
½ ½ ½
B thermal contact coefficient of pinion N/(mm �m �s �K) Eq. (3)
M1
½ ½ ½
B thermal contact coefficient of wheel N/(mm �m �s �K) Eq. (3)
M2
C tip relief of pinion �m Eq. (48)
a1
C tip relief of wheel �m Eq. (46)
a2
C optimal tip relief �m Eq. (46)
eff
C equivalent tip relief of pinion �mEq.(B.2)
eq1
C equivalent tip relief of wheel �mEq.(B.3)
eq2
C root relief of pinion �mEq.(B.3)
f1
C root relief of wheel �mEq.(B.2)
f2
c specific heat per unit mass of pinion J/(kg�K) Eq. (9)
M1
c specific heat per unit mass of wheel J/(kg�K) Eq. (10)
M2
c mesh stiffness N/(mm��m) Eq. (B.1)
�
d reference diameter of pinion mm Eq. (34)
1
d reference diameter of wheel mm Eq. (35)
2
d tip diameter of pinion mm Eq. (34)
a1
d tip diameter of wheel mm Eq. (35)
a2
2
E modulus of elasticity of pinion N/mm Eq. (A.10)
1
2
E modulus of elasticity of wheel N/mm Eq. (A.10)
2
2
E reduced modulus of elasticity N/mm Eq. (A.9)
r
F external axial force N Eq. (18)
ex
F normal load in wear test N Fig. 1
n
F nominal tangential force N Eq. (11)
t
H auxiliary dimension mm Eq. (B.3)
1
H auxiliary dimension mm Eq. (B.2)
2
h tip height in mean cone of pinion mm Eq. (43)
am1
h tip height in mean cone of wheel mm Eq. (44)
am2
2 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
K application factor — Eq. (11)
A
K transverse load factor (scuffing) — Eq. (11)
B�
K face load factor (scuffing) — Eq. (11)
B�
K transverse load factor (contact stress) — Eq. (15)
H�
K face load factor (contact stress) — Eq. (14)
H�
K multiple path factor — Eq. (11)
mp
K dynamic factor — Eq. (11)
v
m normal module mm Eq. (B.2)
n
n revolutions per minute of pinion r/min Eq. (5)
1
n number of mesh contacts — Eq. (16)
p
Pe Péclet number of pinion material — Eq. (9)
1
Pe Péclet number of wheel material — Eq. (10)
2
Q quality grade — Eq. (57)
Ra tooth flank surface roughness of pinion �m Eq. (28)
1
Ra tooth flank surface roughness of wheel �m Eq. (28)
2
R cone distance of mean cone mm Eq. (A.16)
m
r reference radius in mean cone of pinion mm Eq. (43)
m1
r reference radius in mean cone of wheel mm Eq. (44)
m2
S safety factor for scuffing — Eq. (100)
B
S load stage (in FZG test) — Eq. (99)
FZG
t contact exposure time of pinion �s Eq. (95)
1
t contact exposure time of wheel �s Eq. (96)
2
t contact exposure time at bend of curve �s Eq. (97)
c
t longest contact exposure time �s Eq. (95)
max
u gear ratio — Eq. (A.6)
u virtual ratio — Eq. (B.6)
v
v sliding velocity m/s Fig. 1
g
v tangential velocity of pinion m/s Eq. (3)
g1
v tangential velocity of wheel m/s Eq. (3)
g2
v sum of tangential velocities in pitch point m/s Eq. (25)
g�C
v pitch line velocity m/s Eq. (26)
t
w normal unit load N/mm Eq. (3)
Bn
w transverse unit load N/mm Eq. (5)
Bt
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
X buttressing factor — Eq. (54)
but
X buttressing value — Eq. (51)
butA
X buttressing value — Eq. (51)
butE
X geometry factor — Eq. (A.5)
G
X approach factor — Eq. (3)
J
X lubricant factor — Eq. (25)
L
–¾ –½ –½
X thermo-elastic factor K�N �s �m �mm Eq. (5)
M
X multiple mating pinion factor — Eq. (22)
mp
X roughness factor — Eq. (25)
R
X lubrication system factor — Eq. (22)
S
X structural factor — Eq. (94)
W
X angle factor — Eq. (A.6)
��
X load sharing factor — Eq. (3)
�
X gradient of the scuffing temperature — Eq. (97)
�
z number of teeth of pinion — Eq. (30)
1
z number of teeth of wheel — Eq. (30)
2
� transverse tip pressure angle of pinion ° Eq. (31)
a1
� transverse tip pressure angle of wheel ° Eq. (30)
a2
� transverse pressure angle ° Eq. (34)
t
� normal working pressure angle ° Eq. (A.2)
wn
� transverse working pressure angle ° Eq. (7)
wt
� pinion pressure angle at arbitrary point ° Eq. (29)
y1
� helix angle ° Eq. (18)
� base helix angle ° Eq. (49)
b
� base helix angle in midcone ° Eq. (50)
bm
� working helix angle ° Eq. (A.2)
w
� parameter on the line of action at point A — Eq. (24)
A
� parameter on the line of action at point AA — Eq. (68)
AA
� parameter on the line of action at point AB — Eq. (66)
AB
� parameter on the line of action at point AU — Eq. (49)
AU
� parameter on the line of action at point B — Eq. (31)
B
� parameter on the line of action at point BB — Eq. (70)
BB
� parameter on the line of action at point D — Eq. (32)
D
� parameter on the line of action at point DD — Eq. (72)
DD
� parameter on the line of action at point DE — Eq. (67)
DE
4 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (continued)
Symbol Description Unit Reference
� parameter on the line of action at point E — Eq. (24)
E
� parameter on the line of action at point EE — Eq. (74)
EE
� parameter on the line of action at point EU — Eq. (49)
EU
� parameter on the line of action at point M — Eq. (86)
M
� parameter on the line of action at arbitrary point — Eq. (7)
y
� angle of direction of tangential velocity of pinion — Eq. (3)
1
� angle of direction of tangential velocity of wheel — Eq. (3)
2
� pitch cone angle of pinion ° Eq. (37)
1
� pitch cone angle of wheel ° Eq. (39)
2
� transverse contact ratio — Eq. (76)
�
� overlap ratio — Eq. (52)
�
� absolute (dynamic) viscosity at oil temperature mPa�s Eq. (27)
oil
� contact temperature °CEq.(1)
B
� maximum contact temperature °CEq.(2)
Bmax
� flash temperature K Eq. (1)
fl
� average flash temperature K Eq. (22)
flm
� maximum flash temperature K Eq. (2)
flmax
� maximum flash temperature at test K Eq. (94)
flmaxT
� bulk temperature °C Eq. (22)
M
� interfacial bulk temperature °CEq.(1)
Mi
� bulk temperature of pinion teeth °C Eq. (20)
M1
� bulk temperature of wheel teeth °C Eq. (20)
M2
� bulk temperature at test °C Eq. (94)
MT
� oil temperature before reaching the mesh °C Eq. (22)
oil
� scuffing temperature °C Eq. (94)
S
� scuffing temperature at long contact time °C Eq. (97)
Sc
� heat conductivity of pinion N/(s�K) Eq. (9)
M1
� heat conductivity of wheel N/(s�K) Eq. (10)
M2
� coefficient of friction in pin-and-ring test — Fig. 1
� mean coefficient of friction — Eq. (3)
m
� Poisson's ratio of pinion material — Eq. (A.10)
1
� Poisson's ratio of wheel material — Eq. (A.10)
2
© ISO 2000 – All rights reserved 5
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SIST ISO/TR 13989-1:2002
ISO/TR 13989-1:2000(E)
Table 1 — Symbols and units (concluded)
Symbol Description Unit Reference
� density of pinion material kg/m³ Eq. (9)
M1
� density of wheel material kg/m³ Eq. (10)
M2
� relative radius of curvature at pitch point mm Eq. (25)
relC
� radius of curvature at arbitrary point of pinion mm Eq. (5)
y1
� radius of curvature at arbitrary point of wheel mm Eq. (5)
y2
� relative radius of curvature at arbitrary point mm Eq. (5)
yrel
� shaft angle ° Eq. (A.15)
� quill shaft twist ° Eq. (17)
a
The term wheel is used for the mating gear of a pinion.
4 Scuffing and wear
4.1 Occurrence of scuffing and wear
When gear teeth are completely separated by a full fluid film of lubricant, there is no contact between the asperities
of the tooth surfaces, and usually there is no scuffing or wear. Here, the coefficient of friction is rather low. In
exceptional cases a damage similar to scuffing may be caused by a sudden thermal instability [19] in a thick oil film,
which phenomenon is not treated here.
For thinner elastohydrodynamic films, incidental asperity contact takes place. As the mean film thickness
decreases, the number of contacts increases acccordingly. Abrasive wear, adhesive wear or scuffing becomes
possible. Abrasive wear may occur due to the rolling action of the gear teeth or the presence of abrasive particles in
the lubricant. Adhesive wear occurs by localized welding and subsequent detachment and transfer of particles from
one or both of the meshing teeth. Abrasive or adhesive wear may not be harmful if it is mild and if it subsides with
time, as in a normal run-in process.
In contrast to mild wear, scuffing is a severe form of adhesive wear that can result in progressive damage to the
gear teeth. In contrast to pitting and fatigue breakage which show a distinct incubation period, a short transient
overloading can result in scuffing failure.
Excessive aeration or the presence in the lubricant of contaminants such as metal particles in suspension, or water,
also increases the risk of scuffing damage. After scuffing, high speed gears tend to suffer high levels of dynamic
loading due to vibration which usually cause further damage by scuffing, pitting or tooth breakage.
)
2
In most cases, the resistance of gears to scuffing can be improved by using a lubricant with enhanced anti-scuff
additives. It is important, however, to be aware that some disadvantages attend the use of anti-scuff additives:
corrosion of copper, embrittlement of elastomers, lack of world-wide availability, etc.
The methods described are not suitable for "cold scuffing" which is in general associated with low speed, under
approx. 4 m/s, through-hardened heavily loaded gears of rather poor quality.
4.2 Transition diagram
The lubrication condition of sliding concentrated steel contacts, which operate in a liquid lubricant, can be described
[20][21][22][23] in terms of transition diagrams. A transition diagram according to Figure 1 is considered to be
applicable to contacts functioning at constant oil bath temperature.
2) The less correct designation Extreme Pressure, EP, is replaced by anti-scuff.
6 © ISO 2000 – All rights reserved
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ISO/TR 13989-1:2000(E)
At combinations of normal force F and relative sliding velocity v which fall below the line A1-S, in region I, see
n g
Figure 1, the lubrication condition is characterized by a coefficient of friction of about 0,1 and a specific wear rate of
�2 3 �6 3
10 mm /(N�m) to 10 mm /(N�m) (i.e. volume wear per unit of normal force, per unit of sliding distance).
If, with v not above a value according to point S, the load is increased into region II, a transition into a second
g
condition of lubrication occurs. This mild wear lubrication condition is characterized by a coefficient of friction of
3 3
about 0,3 to 0,4 and a specific wear rate of 1 mm /(N�m) to5mm /(N�m).
Figure 1 — Transition diagram for contraform contacts with example of calculated contact temperatures
If load is increased still further, a transition into a third condition of lubrication, region III, occurs at intersection of the
line A2-S. This region is ch
...
RAPPORT ISO/TR
TECHNIQUE 13989-1
Première édition
2000-03-15
Calcul de la capacité de charge au grippage
des engrenages cylindriques, coniques et
hypoïdes —
Partie 1:
Méthode de la température-éclair
Calculation of scuffing load capacity of cylindrical, bevel and hypoid
gears —
Part 1: Flash temperature method
Numéro de référence
ISO/TR 13989-1:2000(F)
©
ISO 2000
---------------------- Page: 1 ----------------------
ISO/TR 13989-1:2000(F)
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ii © ISO 2000 – Tous droits réservés
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ISO/TR 13989-1:2000(F)
Sommaire Page
Avant-propos.iv
Introduction.vi
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 Grippage et usure .6
4.1 Apparition du grippage et de l'usure .6
4.2 Diagramme de transition.7
4.3 Frottement à l'amorçage du grippage.8
5 Formules de base .9
5.1 Température de contact .9
5.2 Formule de la température-éclair .9
5.3 Charge unitaire apparente .11
5.4 Répartition des températures de masse globales.12
5.5 Approximation grossière de la température de masse.13
6 Coefficient de frottement .13
6.1 Coefficient de frottement moyen, méthode A.14
6.2 Coefficient de frottement moyen, méthode B.14
6.3 Coefficient de frottement moyen, méthode C.14
7 Paramètre sur la ligne d'action.15
8 Facteur d'approche.17
9 Facteur de répartition de charge.18
9.1 Facteur de contrefort.18
9.2 Engrenages à denture droite à profils non corrigés .19
9.3 Engrenages à denture droite à profils corrigés.20
9.4 Engrenages à denture hélicoïdale étroits à profils non corrigés.21
9.5 Engrenages à denture hélicoïdale étroits à profils corrigés .21
9.6 Engrenages à denture hélicoïdale larges à profils non corrigés.22
9.7 Engrenages à denture hélicoïdale larges à profils corrigés.22
9.8 Engrenages coniques étroits.23
9.9 Engrenages coniques larges.24
10 Température de grippage et sécurité.25
10.1 Température de grippage.25
10.2 Facteur de structure .25
10.3 Durée de contact.26
10.4 Température de grippage dans les essais d'engrenage.27
10.5 Domaine de sécurité.27
Annexe A (informative) Présentation de la formule de la température-éclair.29
Annexe B (informative) Correction de profil optimale .36
Bibliographie .38
© ISO 2000 – Tous droits réservés iii
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ISO/TR 13989-1:2000(F)
Avant-propos
L'ISO (Organisation internationale de normalisation) est une fédération mondiale d'organismes nationaux de
normalisation (comités membres de l'ISO). L'élaboration des Normes internationales est en général confiée aux
comités techniques de l'ISO. Chaque comité membre intéressé par une étudealedroit de fairepartieducomité
technique créé à cet effet. Les organisations internationales, gouvernementales et non gouvernementales, en
liaison avec l'ISO participent également aux travaux. L'ISO collabore étroitement avec la Commission
électrotechnique internationale (CEI) en ce qui concerne la normalisation électrotechnique.
La tâche principale des comités techniques est d'élaborer les Normes internationales. Exceptionnellement, un
comité technique peut proposer la publication d'un rapport technique de l'un des types suivants:
� type 1, lorsque, en dépit de maints efforts, l'accord requis ne peut être réalisé en faveur de la publication d'une
Norme internationale;
� type 2, lorsque le sujet en question est encore en cours de développement technique ou lorsque, pour toute
autre raison, la possibilité d'un accord pour la publication d'une Norme internationale peut être envisagée pour
l'avenir mais pas dans l'immédiat;
� type 3, lorsqu'un comité technique a réuni des données de nature différente de celles qui sont normalement
publiées comme Normes internationales (ceci pouvant comprendre des informations sur l'état de la technique,
par exemple).
Les rapports techniques des types 1 et 2 font l'objet d'un nouvel examen trois ans au plus tard après leur
publicationafindedécider éventuellement de leur transformation en Normes internationales. Les rapports
techniques de type 3 ne doivent pas nécessairement être révisés avant que les données fournies ne soient plus
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'ISO/TR 13989-1, rapport technique du type 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 la capacité de charge au grippage des engrenages 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. En 1975, deux méthodes de calcul pour évaluer le risque de grippage ont été documentées pour être
étudiées par le comité technique ISO/TC 60. Il a été admis qu'après une période d'expérimentation, une seule
méthode doit être adoptée. Étant donné que le sujet est encore en développement technique et qu'il y a une
possibilité future d'un accord en tant que Norme internationale, la publication en tant que Rapport technique de
type2a été proposée.
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.
iv © ISO 2000 – Tous droits réservés
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ISO/TR 13989-1:2000(F)
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.
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.
© ISO 2000 – Tous droits réservés v
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ISO/TR 13989-1:2000(F)
Introduction
Depuis 1990, la méthode de la température-éclair, présentée dans la présente partie de l’ISO/TR 13989, a été
enrichie par des recherches sur les temps de contact de courte durée, sur la prise en compte des diagrammes de
transition, sur de nouvelles approximations sur le coefficient de frottement et sur un renouvellement complet des
facteurs de répartition de charge. En 1991, le Professeur Blok a apporté une extension de la formulation de la
température-éclair, la rendant directement applicable aux engrenages hypoïdes.
La méthode de la température intégrale, présentée dans l’ISO/TR 13989-2, moyenne la température-éclair et ajoute
des facteurs d'influence empiriques au facteur de répartition de charge. Les valeurs résultantes arrondissent la
température maximale de contact, donnant alors à peu de chose prèsla même évaluation du risque de grippage
que la méthode de la température-éclair delaprésente partie de l’ISO/TR 13989. La méthode de la température
intégrale est moins sensible dans les cas présentant des pics de température localisés, habituellement dans les
ensembles d'engrenages qui ont des faibles rapports de conduite ou qui présentent des contacts au voisinage du
cercle de base ou des géométries sensibles.
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. Par opposition au
développement relativement long de la détérioration par fatigue, une surcharge instantanée unique peut initier la
détérioration par grippage avec une telle sévérité que l'engrenage ne pourra être utilisé plus longtemps. D'après
Blok [12][13][14][15][16][17], des températures de contact élevées du lubrifiant et des surfaces de denture au point
de contact instantané peuvent entraîner une rupture du film de lubrifiant à l'interface du contact.
La température de contact à l'interface résulte de la somme de deux composantes:
� la température de masse de l'interface en mouvement, qui, si elle varie, le fait comparativement lentement.
Pour évaluer cette composante, elle peut être moyennée à partir des deux températures de masse des deux
dentures frottantes. Ces deux dernières températures de masse se déduisent de la théorie des réseaux
thermiques [18];
� la fluctuation rapide de la température-éclair des surfaces en contact en mouvement. Une attention toute
particulière doit être apportée au coefficient de frottement. La pratique habituelle est d'utiliser un coefficient de
frottement valide pour des conditions de fonctionnement normales, bien qu'il soit établi qu'au commencement
du grippage le coefficient de frottement atteint des valeurs plus élevées.
Les relations complexes entre les phénomènes mécaniques, hydrodynamiques, thermodynamiques et chimiques
furent l'objet d'importantes recherches et expérimentations, qui peuvent induire différents facteurs d'influence
empiriques. Une suppléance directe des facteurs d'influence empiriques peut renforcer les paramètres fonctionnels
associés dans la formule de base et les fixer à des valeurs moyennes. Cependant, un traitement correct des
paramètres fonctionnels (c'est-à-dire coefficient de frottement, facteur de répartition de charge, coefficient
thermique de contact) garde la formule principale intacte, ce qui est confirmé avec l'expérimentation et la pratique.
À côté de la température maximale de contact, l'évolution de la température de contact le long de la ligne d'action
fournit l'information nécessaire pour la conception de l'engrenage.
vi © ISO 2000 – Tous droits réservés
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RAPPORT TECHNIQUE ISO/TR 13989-1:2000(F)
Calcul de la capacité de charge au grippage des engrenages
cylindriques, coniques et hypoïdes —
Partie 1:
Méthode de la température-éclair
1 Domaine d’application
La présente partie de l’ISO/TR 13989 spécifie les méthodes et les formules pour l'évaluation des risques de
grippage, en se basant sur le concept de la température de contact de Blok.
Le concept fondamental selon Blok est applicable à tous les éléments de machine ayant des zones de contact
mobiles. Les formules de température-éclair sont valables pour une zone de contact hertzien en forme de bande ou
quasiment en forme de bande et pour des conditions de fonctionnement caractérisées par des nombres de Péclet
suffisamment élevés.
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 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques.
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.
ISO 10825:1995, Engrenages — Usure et défauts des dentures — Terminologie.
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 et
l’ISO 10825 s'appliquent.
1) À publier.
© ISO 2000 – Tous droits réservés 1
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ISO/TR 13989-1:2000(F)
3.2 Symboles et unités
Les symboles utilisés dans la présente partie de l'ISO/TR 13989 sont donnés dans le Tableau 1. Les unitésde
longueur mètre, millimètre et micromètre sont choisies conformément à l'usage en la matière. Pour obtenir un
système cohérent, les unités pour B , c�, X sont adaptées à l'application combinéedemètre et millimètreoude
M M
millimètre et micromètre.
Tableau 1 — Symboles et unités
Symbole Description Unité Référence
a entraxe mm Éq. (A.5)
largeur de denture, plus petite valeur du pignon ou de la
b mm Éq. (11)
a
roue
b
largeur de denture effective mm Éq. (12)
eff
b
demi-largeur de la bande de contact hertzien mm Éq. (3)
H
½ ½ ½
B
coefficient de contact thermique Éq. (A.13)
M
N/(mm �m �s �K)
½ ½ ½
B
coefficient de contact thermique du pignon Éq. (3)
M1
N/(mm �m �s �K)
½ ½ ½
B
coefficient de contact thermique de la roue Éq. (3)
M2
N/(mm �m �s �K)
C
dépouille de tête du pignon �m Éq. (48)
a1
C dépouille de tête de la roue Éq. (46)
�m
a2
C dépouille de tête optimale Éq. (46)
�m
eff
C
dépouille de tête équivalente du pignon Éq. (B.2)
�m
eq1
C
dépouille de tête équivalente de la roue �m Éq. (B.3)
eq2
C
dépouille de pied du pignon �m Éq. (B.3)
f1
C
dépouille de pied de la roue �m Éq. (B.2)
f2
c
chaleur spécifique par unité de masse du pignon J/(kg�K) Éq. (9)
M1
c
chaleur spécifique par unité de masse de la roue J/(kg�K) Éq. (10)
M2
raideur d'engrènement (Éq. B.1)
c� N/(mm��m)
d
diamètrederéférence du pignon mm Éq. (34)
1
d
diamètrederéférencedelaroue mm Éq. (35)
2
d
diamètredetête du pignon mm Éq. (34)
a1
d
diamètredetête de la roue mm Éq. (35)
a2
2
E
module d'élasticité du pignon N/mm Éq. (A.10)
1
2
E
module d'élasticité de la roue N/mm Éq. (A.10)
2
2
E module d'élasticité réduit N/mm Éq. (A.9)
r
F force axiale externe N Éq. (18)
ex
F
charge réelle de l'essai d'usure N Figure. 1
n
F
force tangentielle nominale N Éq. (11)
t
2 © ISO 2000 – Tous droits réservés
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ISO/TR 13989-1:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
H
dimension auxiliaire mm Éq. (B.3)
1
H
dimension auxiliaire mm Éq. (B.2)
2
h saillie de denture au cône moyen du pignon mm Éq. (43)
am1
h saillie de denture au cônemoyendelaroue mm Éq. (44)
am2
K
facteur d'application —Éq. (11)
A
K
facteur de distribution transversale de la charge (grippage) —Éq. (11)
B�
K
facteur de distribution longitudinale de la charge (grippage) —Éq. (11)
B�
facteur de distribution transversale de la charge
K
—Éq. (15)
H�
(pression de contact)
facteur de distribution longitudinale de la charge
K
—Éq. (14)
H�
(pression de contact)
K
facteur d'engrènement multiple —Éq. (11)
mp
K
facteur dynamique —Éq. (11)
v
m
module normal mm Éq. (B.2)
n
n
vitesse de rotation par minute du pignon r/min Éq. (5)
1
n nombre de contacts d'engrènement —Éq. (16)
p
Pe nombre de Péclet du matériau du pignon —Éq. (9)
1
Pe
nombre de Péclet du matériau de la roue —Éq. (10)
2
Q
classe de précision —Éq. (57)
Ra
rugosité de surface du flanc de dent du pignon �m Éq. (28)
1
Ra
rugosité de surface du flanc de dent de la roue �m Éq. (28)
2
R
génératriceducône complémentaire moyen mm Éq. (A.16)
m
r rayonderéférenceducône moyen du pignon mm Éq. (43)
m1
r rayonderéférenceducônemoyendelaroue mm Éq. (44)
m2
S
coefficient de sécurité relatif au grippage —Éq. (100)
B
S
niveau de charge (en essai FZG) —Éq. (99)
FZG
t
durée de contact sur le pignon �s Éq. (95)
1
t
durée de contact sur la roue �s Éq. (96)
2
t
durée de contact au coude de la courbe �s Éq. (97)
c
t
durée de contact la plus longue �s Éq. (95)
max
u rapport d'engrenage —Éq. (A.6)
u
rapport équivalent —Éq. (B.6)
v
v
vitesse de glissement m/s Figure 1
g
v
vitesse tangentielle du pignon m/s Éq. (3)
g1
© ISO 2000 – Tous droits réservés 3
---------------------- Page: 9 ----------------------
ISO/TR 13989-1:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
v
vitesse tangentielle de la roue m/s Éq. (3)
g2
v
somme des vitesses tangentielles au point primitif m/s Éq. (25)
g�C
v
vitesse tangentielle au primitif de fonctionnement m/s Éq. (26)
t
w
charge unitaire normale N/mm Éq. (3)
Bn
w
charge unitaire apparente N/mm Éq. (5)
Bt
X
facteur de contrefort —Éq. (54)
but
X
valeur de contrefort —Éq. (51)
butA
X valeur de contrefort —Éq. (51)
butE
X facteur géométrique —Éq. (A.5)
G
X facteur d'approche —Éq. (3)
J
X facteur lubrifiant —Éq. (25)
L
–¾ –½ –½
X
facteur thermoélastique Éq. (5)
M
K�N �s �m �mm
X
facteur de pignons conjugués multiples —Éq. (22)
mp
X facteur de rugosité—Éq. (25)
R
X facteur système de lubrification —Éq. (22)
S
X facteur de structure —Éq. (94)
W
X facteur d'angle —Éq. (A.6)
��
X
facteur de répartition de charge —Éq. (3)
�
X
gradient de la température de grippage —Éq. (97)
�
z nombre de dents du pignon —Éq. (30)
1
z nombre de dents de la roue —Éq. (30)
2
�
angle de pression de tête apparent du pignon °Éq. (31)
a1
� angle de pression de tête apparent de la roue °Éq. (30)
a2
angle de pression apparent °Éq. (34)
�
t
� angle de pression de fonctionnement normal °Éq. (A.2)
wn
�
angle de pression de fonctionnement apparent °Éq. (7)
wt
�
angle d'incidence du pignon en un point quelconque °Éq. (29)
y1
� angle d'hélice °Éq. (18)
�
angle d'hélice de base °Éq. (49)
b
�
angle d'hélicedebaseaudemi-cône °Éq. (50)
bm
� angle d'hélice de fonctionnement °Éq. (A.2)
w
�
paramètre sur la ligne d'action au point A —Éq. (24)
A
� paramètre sur la ligne d'action au point AA —Éq. (68)
AA
4 © ISO 2000 – Tous droits réservés
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ISO/TR 13989-1:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
�
paramètre sur la ligne d'action au point AB —Éq. (66)
AB
� paramètre sur la ligne d'action au point AU —Éq. (49)
AU
�
paramètre sur la ligne d'action au point B —Éq. (31)
B
� paramètre sur la ligne d'action au point BB —Éq. (70)
BB
� paramètre sur la ligne d'action au point D —Éq. (32)
D
�
paramètre sur la ligne d'action au point DD —Éq. (72)
DD
� paramètre sur la ligne d'action au point DE —Éq. (67)
DE
� paramètre sur la ligne d'action au point E —Éq. (24)
E
�
paramètre sur la ligne d'action au point EE —Éq. (74)
EE
�
paramètre sur la ligne d'action au point EU —Éq. (49)
EU
� paramètre sur la ligne d'action au point M —Éq. (86)
M
�
paramètre sur la ligne d'action en un point arbitraire —Éq. (7)
y
�
angle de direction de la vitesse tangentielle du pignon —Éq. (3)
1
� angle de direction de la vitesse tangentielle de la roue —Éq. (3)
2
�
angle du cône primitif de fonctionnement du pignon °Éq. (37)
1
�
angle du cône primitif de fonctionnement de la roue °Éq. (39)
2
�
rapport de conduite apparent —Éq. (76)
�
�
rapport de recouvrement —Éq. (52)
�
�
viscosité absolue (dynamique) à la température de l'huile mPa�s Éq. (27)
oil
�
température de contact °C Éq. (1)
B
� température de contact maximale °C Éq. (2)
Bmax
�
température-éclair K Éq. (1)
fl
�
température-éclair moyenne K Éq. (22)
flm
� température-éclair maximale K Éq. (2)
flmax
�
température-éclair maximale en cours d'essai K Éq. (94)
flmaxT
�
température de masse °C Éq. (22)
M
� température de masse interfaciale °C Éq. (1)
Mi
�
température de masse des dents du pignon °C Éq. (20)
M1
�
température de masse des dents de la roue °C Éq. (20)
M2
�
température de masse en cours d'essai °C Éq. (94)
MT
� température d'huile avant d'atteindre l'engrènement °C Éq. (22)
oil
© ISO 2000 – Tous droits réservés 5
---------------------- Page: 11 ----------------------
ISO/TR 13989-1:2000(F)
Tableau 1 — Symboles et unités (suite)
Symbole Description Unité Référence
�
température de grippage °C Éq. (94)
S
� température de grippage pour une durée de contact longue °C Éq. (97)
Sc
�
conductivité thermique du pignon N/(s�K) Éq. (9)
M1
�
conductivité thermique de la roue N/(s�K) Éq. (10)
M2
� coefficient de frottement dans l'essai pion-disque — Figure 1
�
coefficient de frottement moyen —Éq. (3)
m
�
coefficient de Poisson du matériau du pignon —Éq. (A.10)
1
� coefficient de Poisson du matériau de la roue —Éq. (A.10)
2
3
�
densité du matériau du pignon kg/m Éq. (9)
M1
3
� densité du matériau de la roue kg/m Éq. (10)
M2
� rayon de courbure relatif au point primitif mm Éq. (25)
relC
�
rayon de courbure en un point quelconque du pignon mm Éq. (5)
y1
� rayon de courbure en un point quelconque de la roue mm Éq. (5)
y2
� rayon de courbure relatif en un point quelconque mm Éq. (5)
yrel
� angle des axes °Éq. (A.15)
� torsion d'arbre torsible °Éq. (17)
a
Le terme roue est utilisé pour le mobile conjugué d'un pignon.
4 Grippage et usure
4.1 Apparition du grippage et de l'usure
Lorsque les dents d'engrenage sont entièrement séparées par un film fluide complet de lubrifiant, il n'y a pas de
contact entre les aspérités de surface des dents et, habituellement, il n'y a pas de grippage ou d'usure. Dans ce
cas, le coefficient de frottement est plutôt faible. Dans des cas exceptionnels, une détérioration semblable au
grippage peut être provoquée par une instabilité thermique soudaine [19] dans un film d'huile épais, mais ce
phénomène n'est pas traité dans la présente partie de l’ISO/TR 13989.
Pour des films élastohydrodynamiques plus minces, il y a contact fortuit des aspérités. Au fur et à mesure que
l'épaisseur moyenne du film décroît, le nombre de contacts augmente. L'usure par abrasion, l'usure par micro-
soudage ou le grippage deviennent alors possibles. L'usure par abrasion peut apparaîtredufaitdel'actionde
roulement des dents d'engrenage ou du fait de la présence de particules abrasives dans le lubrifiant. L'usure par
adhésion est due à une soudure par fusion locale suivie d'un arrachement et d'un transfert des particules de l'une
ou des deux dents en prise. L'usure abrasive ou par adhésion peut ne pas être nuisible si elle est modérée et si elle
s'atténue avec le temps, comme lors d'un processus normal de rodage.
Contrairement à l'usure modérée, le grippage est une forme grave d'usure par adhésion qui peut entraîner une
détérioration progressive des dents des roues. Contrairement à la formation de piqûres et à la rupture de fatigue qui
présentent une période d'incubation, une surcharge provisoire de courte durée peut entraîner une défaillance par
grippage.
Une aération excessive ou la présence de contaminants dans le lubrifiant, tels que des particules métalliques en
suspension ou de l'eau, augmente également le risque de détérioration par grippage. Après grippage, les
engrenages à grande vitesse sont soumis à des charges dynamiques élevées produites par des vibrations qui
conduisent généralement à une détérioration ultérieure par grippage, pitting ou rupture de dent.
6 © ISO 2000 – Tous droits réservés
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ISO/TR 13989-1:2000(F)
Dans la plupart des cas, la résistance des engrenages au grippage peut être améliorée en util
...
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