SIST ISO 6336-2:2002
(Main)Calculation of load capacity of spur and helical gears -- Part 2: Calculation of surface durability (pitting)
Calculation of load capacity of spur and helical gears -- Part 2: Calculation of surface durability (pitting)
Gives the fundamental formulae for use in the determination of the load capacity of cylindrical gears with involute internal or external teeth.
Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale -- Partie 2: Calcul de la résistance à la pression de contact (piqûres)
Izračun nosilnosti ravnozobih in poševnozobih zobnikov - 2. del: Izračun obratovalne vzdržljivosti zobnih bokov (jamičenje)
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INTERNATIONAL
IS0
STANDARD 63.36-2
First edition
1996-06-15
Calculation of load capacity of spur and
helical gears -
Part 2:
Calculation of surface durability (pitting)
Calcul de la capacit6 de charge des engrenages cylindriques ij dentures
droite et h6licoidale -
Partie 2: Calcul de la r&stance 9 la pression superficielle (piquage)
Reference number
IS0 6336~2:1996( E)
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IS0 6336-2: 1996(E)
Page
Scope
Normative references
Pitting damage and safety factors
Basic formulae
Zone factor, Z,, and single pair tooth contact factors, Z,
9
and Z,
15
6 Elasticity factor, Z,
16
7 Contact ratio factor, Z,
18
8 Helix angle factor, Zs
18
9 Strength for contact stress
19
10 Life factor, Z NT (for flanks)
21
11 Influences of the lubricant film, factors Z,, Z, and Z,
29
Work hardening factor, I,
12
30
13 Size factor, Zx
Annex
31
A Bibliography
0 IS0 1996
publication may be
All rights reserved. Unless otherwise specified, no part of this
mechanical, including
reproduced or utilized in any form or by any means, electronic or
photocopying and microfilm, without permission in writing from the publisher.
I Org anization for Standardi zation
lnternationa
eneve 20 l Switz erland
Case Postal e 56 . CH-121 IG
Printed in Switzerland
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@ IS0
IS0 6336-2: 1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
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 liason with ISO, also take part in the work. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the Technical Committeees are
circulated to the member bodies for voting. Publication as a International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard 6336-2 was prepared by Technical Committee
ISO/TCGO, Gears, Subcommittee SC2, Gear capacity calculation,
IS0 6336 consists of the following parts, under the general title
Calculation of load capacity of spur and helical gears:
- Part 1: Basic principles, introduction and general influence factors
- Part 2: Calculation of surface durability (pitting)
Calculation of tooth bending strength
- Part 3:
Strength and quality of materials
- Part 5:
Annex A is for information only.
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IS0 6336-2: 1996(E)
@ IS0
Introduction
Hertzian pressure, which serves as a basis for the calculation of contact
stress, is the basic principle used in this part of IS0 6336 for the
assessment of surface durability of cylindrical gears. It is a significant
indicator of the stress generated during tooth flank engagement.
However, it is not the sole cause of pitting, nor are the corresponding
subsurface shear stresses. There are other contributory influences; for
example, coefficient of friction, direction and magnitude of sliding and the
influence of lubricant on distribution of pressure. Development has not
yet advanced to the stage of directly including these in calculations of
load-bearing capacity; however, allowance is made for them to some
degree in the derating factors and choice of material property values.
In spite of shortcomings, Hertzian pressure is useful as a working
hypothesis, This is attributable to the fact that, for a given material,
limiting values of Hertzian pressure are preferably derived from fatigue
tests on gear specimens; thus additional relevant influences are included
in the values. Therefore, if the reference datum is located in the
application range, Hertzian pressure is acceptable as a design basis for
extrapolating from experimental data to values for gears of different
dimensions.
Several methods have been approved for the calculation of the
permissible contact stress and the determination of a number of factors
(see IS0 6336-l).
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IS0 6336-2: 1996(E)
INTERNATIONAL STANDARD @ IS0
Calculation of load capacity of spur and helical gears -
Part 2: Calculation of surface durability (pitting)
1 Scope
This part of IS0 6336 specifies the fundamental formulae for use in the determination of the surface
load capacity of cylindrical gears with involute internal or external teeth. It includes formulae for all
influences on surface durability for which quantitative assessments can be made. It applies
primarily to oil-lubricated transmissions, but may also be used to obtain approximate values for
(slow-running) grease-lubricated transmissions, as long as sufficient lubricant is present in the mesh
at all times.
The given formulae are valid for cylindrical gears with tooth profiles in accordance with the basic
rack standardized in IS0 53. They may be used for teeth where the actual transverse contact ratio
is less than can = 2,s. The results are in good agreement with other methods for the range as
indicated in the scope of IS0 6336-l.
The user of this part of IS0 6336 is cautioned that when the method specified is used for large helix
angles and large pressure angles, the calculated results should be confirmed by experience as by
method A.
These formulae cannot be directly applied for the assessment of types of gear tooth surface
damage such as plastic yielding, scratching, scuffing or any other than that described in clause 3.
The load capacity determined by way of the permissible contact stress is called the “surface load
capacity” or “surface durability ”.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute
provisions of this part of IS0 6336. At the time of publication, the editions indicated were valid. All
standards are subject to revision, and parties to agreements based on this part of IS0 6336 are
encouraged to investigate the possibility of applying the most recent editions of the standards
indicated below. Members of IEC and IS0 maintain registers of currently valid International
Standards.
IS0 53: 1974, Cylindrical gears for genera/ and heavy engineering - Basic rack.
IS0 6336-l : 1996, Calculation of load capacity of spur and helical cylindrical gears - Part I: Basic
principles, introduction and genera/ influence factors.
IS0 6336-5: 1996, Calculation of load capacity of cylindrical gears - Part-5: Strength and quality of
materials.
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IS0 6336-2: 1996(E) 63 IS0
3 Pitting damage and safety factors
If limits of the surface durability of the meshing flanks are exceeded, particles will break out of the
flanks, leaving pits.
The extent to which such pits can be tolerated (in size and number) varies within wide limits,
depending largely on the field of application. In some fields, extensive pitting can be accepted; in
other fields any appreciable pitting is to be avoided.
The following definitions, relevant to average working conditions help in distinguishing between
initial pitting and destructive pitting.
Linear or progressive increase of the total area of pits is unacceptable, however the effective tooth
bearing area may be enlarged by initial pitting, and the rate of generation of pits may subsequently
reduce (degressive pitting), or cease (arrested pitting). Such pitting is considered tolerable. In the
event of dispute, the following rule is determinant.
Pitting involving the formation of pits which increase linearly or progressively with time under
unchanged service conditions (linear or progressive pitting) is not acceptable. Damage assessment
shall include the entire active area of all the tooth flanks. The number and size of newly developed
pits in unhardened tooth flanks shall be taken into consideration. It is a frequent occurrence that
pits are formed on just one or only a few of the surface hardened gear tooth flanks. In such
circumstances, assessment shall be centred on the flanks actually pitted. Teeth suspected of being
especially at risk should be marked for critical examination if a quantitative evaluation is required.
In special cases, a first rough assessment can be based on considerations of the entire quantity of
wear debris. In critical cases, the condition of the flanks should be examined at least three times.
The first examination should, however, only take place after at least IO6 cycles of load. Further
examination should take place after a period of service depending on the results of the previous
examination.
If the deterioration by pitting is such that it puts human life in danger, or there is a risk of leading to
some grave consequences, then pitting is not tolerable. Due to stress concentration effects, a pit of
a diameter of 1 mm near the fillet of a through-hardened or case-hardened tooth of a gear may
become the origin of a crack which could lead to tooth breakage; for this reason, such a pit shall be
considered as intolerable (e.g. in aerospace transmissions).
Similar considerations are true for turbine gears. In general, during the long life (IO” to IO”
cycles) which is demanded of these gears, neither pitting nor unduly severe wear is tolerable. Such
damage could lead to unacceptable vibrations and excessive dynamic loads. Appropriately
generous safety factors should be included in the calculation, i.e. only a low probability of failure
can be tolerated.
In contrast, pitting over 100 % of the working flanks can be tolerated for some slow-speed industrial
gears with large teeth (e.g. module 25) made from low hardness steel where they will safely transmit
Individual pits may be up to 20 mm in diameter and 8 mm
the rated power for IO to 20 years.
deep. The apparently “destructive” pitting which occurs during the first two or three years of service
normally slows down. The tooth flanks become smoothed and work hardened to the extent of
increasing the surface Brinell hardness number by 50 % or more.
For such conditions, relatively low safety factors (in some cases less than one) can be chosen, with
A high factor of safety against tooth
a correspondingly higher probability of tooth surface damage.
breakage is necessary.
Comments on the choice of safety factor S, can be found in IS0 6336-1, subclause 4.1.3. It is
recommended that the manufacturer and customer agree on the values of the minimum safety
factor.
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IS0 6336-2: 1996(E)
4
Basic formulae
NOTE 1 - All symbols, terms and units are defined in IS0 6336-l.
The calculation of surface durability is based on the contact stress, c+, at the pitch point or at the
inner point of single pair tooth contact. The higher of the two values obtained is used to determine
capacity (determinant). oH and the permissible contact stress, dHPS shall be calculated separately
for wheel and pinion. OH shall be less than gHP* Three categories are recognized in the calculation
of OH as follows.
a) Spur gears
I) spur pinion: for a pinion, QH is usually calculated at the inner point of single pair tooth
contact. In special cases, OH at the pitch point is greater and thus determinant.
2) Spur wheel: in the case of external teeth, gH is usually calculated at the pitch point. In
special cases, particularly in the case of small transmission ratios (see 5.2), bH is greater at the
inner point of single pair tooth contact of the wheel and is thus determinant. For internal teeth,
OH is always calculated at the pitch point.
b) Helical gearing with overlap ratio Q L 1
o H is always calculated at the pitch point for pinion and wheel.
c) Helical gearing with overlap ratio eB < 1
In this case Q H is determined by linear interpolation between the two limit values, i.e. oH for spur
= 1 in which the determination of oH for each is to be based
gears and +, for helical gears with Ed
on the numbers of teeth on the actual gears.
4.1 contact stress bH
As stated, the contact stress is to be calculated on the basis of Hertzian pressure (see introduction).
4.1 .l Contact stress for the pinion
The total tangential load in the case of gear trains with multiple transmission paths, planetary gear
systems, or split-path gear trains is not quite evenly distributed over the individual meshes
(depending on design, tangential speed and manufacturing accuracy). This is to be taken into
consideration by inserting a distribution factor KY to follow KA in equation (I), to adjust the average
tangential load per mesh as necessary.
. . .
(1)
a/j =
‘B OH0 {m ’ ‘HP
. . .
(2)
OH0 =zHzEz,z,
where
is the nominal contact stress at the pitch point; this is the stress induced in flawless
OH0
(error free) gearing by application of static nominal torque.
is the pinion single pair tooth contact factor (see 5.2). This converts contact stress at
the pitch point to the contact stress at the inner point of single pair tooth contact on the
pinion.
3
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IS0 6336-2: 1996(E) 0 IS0
is the application factor (see IS0 6336-l). It takes into account the load increment due
to externally influenced variations of input or output torque.
K is the dynamic factor (see IS0 6336-l). It takes into account load increments due to
V
internal dynamic effects.
is the face load factor for contact stress (see IS0 6336-l). It takes into account uneven
Kw
distribution of load over the facewidth, due to mesh misalignment caused by
inaccuracies in manufacture, elastic deformations, etc.
is the transverse load factor for contact stress (see IS0 6336-l). It takes into account
KH,
uneven load distribution in the transverse direction resulting, for example, from pitch
deviation.
NOTE 2 - See IS0 6336-1, subclause 4.1 .lO for the sequence in which factors KA, Kv, KHp, K,, are calculated.
is the permissible contact stress (see 4.2).
=HP
is the zone factor (see clause 5). It takes into account the flank curvatures at the pitch
point and transforms tangential load at the reference cylinder to tangential load at the
pitch cylinder.
is the elasticity factor (see clause 6). It takes into account specific properties of the
material, moduli of elasticity E 1, E, and Poisson ’s ratios vl, v2.
Z is the contact ratio factor (see clause 7). It takes into account the influence of the
6
effective length of the lines of contact.
is the helix angle factor (see clause 8). It takes into account influences of the helix
angle, such as the variation of the load along the lines of contact.
F is the nominal tangential load, the transverse load tangential to the reference cylinder.
t
The total tangential load per mesh shall be introduced for Ft in every case (even with
> 2). See IS0 6336-1, subclause 4.2, for the definition of Ft and comments on
p%ticular characteristics of double-helical gearing.
b is the facewidth (for a double helix gear b
= 2 bs). The value b of mating gears is the
smaller of the facewidths at the root circles of pinion and wheel ignoring any intentional
transverse chamfers or tooth-end rounding. Neither unhardened portions of surface-
hardened gear tooth flanks nor the transition zones shall be included.
d is the reference diameter of pinion.
1
u
is the gear ratio = z2/zl. For external gears u is positive, and for internal gears u is
negative.
4.1.2 Contact stress for the wheel
. . .
(3)
a# =
zD OH0 iKA Kv KH#3 KHa ’ ‘HP
where
is the single pair tooth contact factor of the wheel (see 5.2). This transforms contact
ZD
stress at the pitch point to contact stress at the inner point of single pair tooth contact
of the wheel.
See 4.1 .l for explanations of other symbols.
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IS0 6336-2: 1996(E)
0 IS0
4.2 Permissible contact stress, Q HP
The limit values of contact stresses (see clause 9) should preferably be derived from material tests
using meshing gears as test pieces (see introduction). The more closely test gears and test
conditions resemble the service gears and service conditions, the more relevant to the calculations
the derived values will be.
4.2.1 Determination of the permissible contact stress, Q HP9 principles, assumptions and
application
a) Method A
In method A the permissible contact stress o HP (or the pitting stress limit, OHG) for reference stress,
long and limited life and static stresses are calculated using equation (2) or (3) from the S-N curve
or damage curve derived from tests of actual gear pair duplicates under appropriate service
conditions.
The cost required for this method is in general only justifiable for the development of new products,
failure of which would have serious consequences (e.g. for manned space flight).
Similarly, the permissible stress values may be derived from consideration of dimensions, service
conditions and performance of carefully monitored reference gears. The more closely the
dimensions and service conditions of the actual gears resemble those of the reference gears, the
more effective will be the application of such values for purposes of design ratings or calculation
checks.
b) Method B
Damage curves, characterized by the allowable stress number values gH lim and the limited life
factors ZNT have been determined for a number of common gear materials and heat treatments from
results of gear loading tests with standard reference test gears.
These test gear values are converted to suit the dimensions and service conditions of the actual
gear pair using the (relative) influence factors for lubricant, Z,, pitch line velocity Zv, flank surface
roughness, Z,, work hardening, Z,, and size, Z,.
Method B is recommended for reasonably accurate calculation whenever pitting resistance values
are available from gear tests, from special tests or, if the material is similar, from IS0 6336-5 (see
introduction).
c) Methods C and D
In these methods which are derived from method B, the influence factors Z,, Z,, Z,, Z,,,, and Z, are
determined using simplified procedures.
d) Method B,
Material characteristic values are determined by rolling pairs of disks in loaded contact. The
magnitude and direction of the sliding speed in these tests should be adjusted to represent the in-
service slide and roll conditions of the tooth flanks in the areas at risk from pitting.
Method B, may be used when stress values derived from gear tests are not available. The method
is particularly suitable for the determination of the surface durability of various materials relative to
one another.
5
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0 IS0
IS0 6336-2: 1996(E)
4.2.2 Permissible contact stress, gHPS Method B
Z
. . .
OH lim NT q z, ZR z, zx = OHG
(4
OHP =
S
s
H min
H min
where
is the allowable stress number (contact) (see clause 9 and IS0 6336-5). It accounts for
OH lim
the influence of material, heat treatment and surface roughness of the standard
reference test gears.
is the life factor for contact stress (see clause 10). It accounts for higher load capacity
‘NT
for a limited number of load cycles.
is the pitting stress limit (= gHP sH min).
OHG
S H min is the minimum required safety factor for surface durability.
Factors Z,, Z, and Z, together cover the influence of the oil film on tooth contact stress.
is the lubricant factor (see clause 11). It accounts for the influence of the lubricant
viscosity.
is the roughness factor (see clause 11). It accounts for the influence of surface
ZR
roughness.
Z is the velocity factor (see clause 11). It accounts for the influence of pitch line velocity.
V
is the work hardening factor (see clause 12). It accounts for the effect of meshing with a
ZW
surface hardened or similarly hard mating gear.
is the size factor for contact stress (see clause 13). It accounts for the influence of the
ZX
tooth dimensions for the permissible contact stress.
a) Permissible contact stress (reference)
is derived from equation (4) with ZNT = 1 and
The permissible contact stress (reference), 0 HP refj
calculated following method B.
the influence factors gH lim)
ZL, Zv, Z,, ZW, ZR, Z)( and SH min
b) Permissible contact stress (static)
The permissible contact stress (static), 0 HP statf is determined in accordance with equation (4) with
all method B influence factors (for static stress).
4.2.3 Permissible contact stress for limited and long life, Method B
In method B, provision is made for determination of aHP b y g ra p hical or computed interpolation
between the value obtained for reference in accordance with 4.2.2 a) and the value obtained for
static stress in accordance with 4.2.2 b). Values appropriate to the relevant number 01 load cycles
A/, are indicated by the S-N curve. See clause 10.
4.2.3.1 Graphical values
Calculate o HP for reference stress and static stress in accordance with 4.2.2 and plot t t le S-N curve
See figure 1 for the principle. aHP for the relevant number of
corresponding to the life factor ZNT.
load cycles A/, may be read from this graph.
6
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@ IS0
IS0 6336-2: 1996(E)
n
CB
0
static limited life
long life
-
\
n
o=
u-l
ul
Q,
L
-e
u-l
-w
0
ccl
+J
c
0
0
a,
-
Q
.-
u-l
0
a-
E
L
I I IIIIII I I IIIIII I I Illlll I I IIIIII I I Illlll
I I Illlll
:
3 5
6
7
10 10 10 10
Number of load cycles, NL
I ml)
Figure 1 - Graphic determination of the permissible contact stress for a limited life,
in accordance with method B
4.2.3.2 Determination by calculation
calculate u HP ref for reference and 0 HP stat for static strength in accordance with 4.2.2 and, using
these results, determine 0 HP9 in accordance with method B for limited life and the number of load
cycles N, in the range as follows.
a) Structural and through-hardened steels, perlitic or bainitic spheroidal graphite cast iron, perlitic
malleable cast iron, case or surface hardened steel, if a certain number of pits is permissible:
For the limited life stress range, 6 x IO5 < N L 5 IO7 in accordance with figure 8:
. . .
(5)
Z
“HP = a HPref N
where
. . .
= 0,3705 log YE!!?
(6)
=P
a HPref
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IS0 6336-2:1996( E) 0 IS0
IO7 < N, I IO’ in accordance with figure 8:
For the limited life stress range,
109
. . .
(7)
Z
OHP = QHPref N = OHPref -
NL
. . .
= 0,2791 log TEE!!! (8)
=P
u HPref
b) Structural and through-hardened steel, perlitic or bainitic nodular cast iron, perlitic malleable cast
iron, case or surface hardened steel, when no pits are permissible:
5 5 x IO7 in accordance with figure 8:
For the limited life stress range, IO5 < N,
. . .
(9)
Z
OHP = CJ HPref N
where exp is as in equation (6)
c) Through-hardening or nitriding steel; gas nitrided, through-hardened, nitro-carburized; ferritic
nodular cast iron, grey cast iron:
s 2 x IO6 in accordance with figure 8:
For the limited life stress range, IO5 < N,
. . .
(IO)
Z
OHP = a HPref N
u HPstat
. . .
= 0,7686 log - (Ii)
exp
Q HPref
Corresponding calculations may be determined for the range of long life.
4.2.4 Permissible contact stress for reference and static strength, Methods C and D
The provisions of 4.2.2 and 4.2.3 are applicable to these methods with the influence factors Z,, Z,,
Z,, Z, and Z,, being determined in accordance with method C or D.
8
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@ IS0
IS0 6336-2: 1996(E)
4.3 Safety factor for surface durability (against pitting), sH
Calculate SH separately for pinion and wheel:
*HG
. . .
(12)
‘# = < ’ ‘H min
a) Method B
Calculate 0 Ho for long life and static stress limits in accordance with equation (4) and clauses 4.2.2
is in accordance with equation (4) and clause 4.2.3. Take Q H in
a) and b). For limited life QHG
accordance with equation (1) for the pinion and in accordance with equation (3) for the wheel (see
introduction to clause 4).
b) Methods C and D
be in accordance with equation (4) and clause 4.2.4, and aH as in 4.3 a).
Calculate 0 HG
safety factor with regard to contact stress (Hertzian pressure). The correspond ing
NOTE 3 - This is the calculated
factor relative to torque capacity is equal to the square of
SH*
For notes on minimum safety factor and probability of failure, see clause 3 and IS0 6336-1,
subclause 4.1.3.
5 Zone factor, ZH, and single pair tooth contact factors, ZB and ZD
These factors account for the influence of tooth flank curvature on contact stress.
5.1 Zone factor, zH
The zone factor, ZH, accounts for the influence on Hertzian pressure of tooth flank curvature at the
pitch point and transforms the tangential force at the reference cylinder to normal force at the pitch
cylinder.
5.1.1
Graphical values
ZH can be taken from figures 2 to 4 as a function of (xl + x2) / (zl + z2) and B for external and
internal gears having normal pressure angles Q n = 20°, 22,5O or 25 ”.
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IS0 6336-2: 1996(E)
\ \
\’
26
9
’ --“u,oos
I ‘\
25
9
t
I
\ \ \I \ \
\
24 \
B t--poos. A\
I
r\l
I==$ QOl --l-\\\-,yy\
23
9
\
.
MU,07 >, I\ !’ ?Y
22
9
21
9
Q)
II:
0
N
19
9
18
?
0 0 10 0 20 0 30 0
40 0
h elix angle at reference circle p ‘-b
Figure 2 - Zone factor, Z,, for a, = 20”
10
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IS0 6336-2: 1996fE)
30
9
29
?
28
s
I
‘n -
27
? “I
07
1
s
I
26
9 I
.
N
P
Om
25
9 I I I
t
I I I
24
9
I
t-t-o
r\l
23
9
I I
$
\I\\\\\
0 22
?
u
21
?
Q)
c
0
N
20
9
0906
19
9
07
8 3
9 08
18 do,-
? P
01
’ I
17
9
16
9
15
9
0 0 0
0
0
0 10
20 30
40
helix angle at reference circle p ,-w
Figure 3 - Zone factor, Z,, for an = 22,5O
11
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IS0 6336-2: 1996(E)
29
9
28
9
26
9
25
9
t
I
hl
23
9
21
9
Q)
c
0
N 20
9
17
9
16
?
0 0
10 0 20 0 30 0 40 0
h elix angle at reference circle p -W
Figure 4 - Zone factor, Z,, for an = 25”
12
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0 IS0 IS0 6336-2: 1996(E)
5.1.2 Determination by calculation
l . .
(13)
%=jJ
5.2 Single pair tooth contact factors, Z, and Z,, for c a I 2
The single pair tooth contact factors, Z, and Z,, are used to transform the contact stress at the
pitch point of spur gears to the contact stress at the inner point B of single pair tooth contact of the
pinion or at the inner point D of single pair tooth contact of the wheel if Z, > 1 or Z, > 1. See
figure 5 and the introduction to clause 4.
-
external gearing in ternal gearing
Figure 5 - Radii of curvature at the pitch point C and at the single pair tooth contact point B of
the pinion and D of the wheel for determination of the pinion single pair tooth contact factor Z,
in accordance with equation (14), and of the wheel single pair tooth contact factor Z, in
accordance with equation (15) (only for external spur gears)
In general, Z, should only be determined for gears when u < I,5 When u > 1,5, M, is usually less
than 1,O in which case Z, is made equal to 1,O in equation (15).
For internal gears, Z, shall be taken as equal to l,O.
13
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IS0 6336-2: 1996(E)
Determination by calculation:
-
M, =
. . .
(14)
tana wt
PC7 PC2
=
M2 =
I
q PO7 m2
. . .
(15)
jjF -ijF -(Ea-ljF
L L
See subclause 7.2.1 for calculations of the profile contact ratio E Q.
a) Spur gears: = I, if M, L 1; = l,ifM,d 1
ZB ZD
= M,,ifM, > 1; = M,, if M, > 1
ZB ZD
b) Helical gears with Q 2 1: ZB = ZD = 1
c) Helical gears with 6 B < 1: ZB and ZD are determined by linear interpolation between the values
for spur and helical gearing with cB 2 1:
- 1)andzBr 1
ZB=M~-C~ 1
(M
- 1) andZ+ 1
ZD=M,-ep 2
(M
If ZB or ZD are made equal to 1, the contact stresses calculated using equation (1) or (3) are the
values for the contact stress at the pitch cylinder.
d) Methods a), b) and c) apply to the calculation of contact stress when the pitch point lies in the
path of contact. If the pitch point C is determinant and lies outside the path of contact, then ZB
and/or ZD are determined for contact at the adjacent tip circle. For helical gearing when cP is less
than 1 ,O, ZB and ZD are determined by linear interpolation between the values (determined at the
pitch point or at the adjacent tip circle as appropriate) for spur gears and those helical gears with
Ep 2 1.
5.3 Single pair tooth contact factors, Z, and Z,, for c a > 2
In the case of meshing gear pairs of high precision with 2 < e a I 3, the entire tangential load in any
transverse plane is supported by two pairs, or three pairs, of teeth in continued succession. For
such gears, the calculation of contact stress is based on the outer point of two pair tooth contact.
The equations (14) and (15) in 5.2 are therefore suitable without modification, for the calculation of
shall be calculated using equation
M, and M, respectively. However, in such circumstances, aHO
(2) with substitution of the total tangential load for Ft. As a result of this, stress values are
overestimated, thus erring on the side of safety.
14
---------------------- Page: 18 ----------------------
@ IS0
IS0 6336-2: 1996(E)
6 Elasticity factor, Z,
The elasticity factor, Z,, takes into account the influences of the material properties E (modulus of
elasticity) and v (Poi
...
SLOVENSKI STANDARD
SIST ISO 6336-2:2002
01-julij-2002
,]UDþXQQRVLOQRVWLUDYQR]RELKLQSRãHYQR]RELK]REQLNRYGHO ,]UDþXQ
REUDWRYDOQHY]GUåOMLYRVWL]REQLKERNRY MDPLþHQMH
Calculation of load capacity of spur and helical gears -- Part 2: Calculation of surface
durability (pitting)
Calcul de la capacité de charge des engrenages cylindriques à dentures droite et
hélicoïdale -- Partie 2: Calcul de la résistance à la pression de contact (piqûres)
Ta slovenski standard je istoveten z: ISO 6336-2:1996
ICS:
21.200 Gonila Gears
SIST ISO 6336-2:2002 en
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
INTERNATIONAL
IS0
STANDARD 63.36-2
First edition
1996-06-15
Calculation of load capacity of spur and
helical gears -
Part 2:
Calculation of surface durability (pitting)
Calcul de la capacit6 de charge des engrenages cylindriques ij dentures
droite et h6licoidale -
Partie 2: Calcul de la r&stance 9 la pression superficielle (piquage)
Reference number
IS0 6336~2:1996( E)
---------------------- Page: 2 ----------------------
IS0 6336-2: 1996(E)
Page
Scope
Normative references
Pitting damage and safety factors
Basic formulae
Zone factor, Z,, and single pair tooth contact factors, Z,
9
and Z,
15
6 Elasticity factor, Z,
16
7 Contact ratio factor, Z,
18
8 Helix angle factor, Zs
18
9 Strength for contact stress
19
10 Life factor, Z NT (for flanks)
21
11 Influences of the lubricant film, factors Z,, Z, and Z,
29
Work hardening factor, I,
12
30
13 Size factor, Zx
Annex
31
A Bibliography
0 IS0 1996
publication may be
All rights reserved. Unless otherwise specified, no part of this
mechanical, including
reproduced or utilized in any form or by any means, electronic or
photocopying and microfilm, without permission in writing from the publisher.
I Org anization for Standardi zation
lnternationa
eneve 20 l Switz erland
Case Postal e 56 . CH-121 IG
Printed in Switzerland
---------------------- Page: 3 ----------------------
@ IS0
IS0 6336-2: 1996(E)
Foreword
IS0 (the International Organization for Standardization) is a worldwide
federation of national standards bodies (IS0 member bodies). The work of
preparing International Standards is normally carried out through IS0
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 liason with ISO, also take part in the work. IS0
collaborates closely with the International Electrotechnical Commission
(IEC) on all matters of electrotechnical standardization.
Draft International Standards adopted by the Technical Committeees are
circulated to the member bodies for voting. Publication as a International
Standard requires approval by at least 75 % of the member bodies casting
a vote.
International Standard 6336-2 was prepared by Technical Committee
ISO/TCGO, Gears, Subcommittee SC2, Gear capacity calculation,
IS0 6336 consists of the following parts, under the general title
Calculation of load capacity of spur and helical gears:
- Part 1: Basic principles, introduction and general influence factors
- Part 2: Calculation of surface durability (pitting)
Calculation of tooth bending strength
- Part 3:
Strength and quality of materials
- Part 5:
Annex A is for information only.
---------------------- Page: 4 ----------------------
IS0 6336-2: 1996(E)
@ IS0
Introduction
Hertzian pressure, which serves as a basis for the calculation of contact
stress, is the basic principle used in this part of IS0 6336 for the
assessment of surface durability of cylindrical gears. It is a significant
indicator of the stress generated during tooth flank engagement.
However, it is not the sole cause of pitting, nor are the corresponding
subsurface shear stresses. There are other contributory influences; for
example, coefficient of friction, direction and magnitude of sliding and the
influence of lubricant on distribution of pressure. Development has not
yet advanced to the stage of directly including these in calculations of
load-bearing capacity; however, allowance is made for them to some
degree in the derating factors and choice of material property values.
In spite of shortcomings, Hertzian pressure is useful as a working
hypothesis, This is attributable to the fact that, for a given material,
limiting values of Hertzian pressure are preferably derived from fatigue
tests on gear specimens; thus additional relevant influences are included
in the values. Therefore, if the reference datum is located in the
application range, Hertzian pressure is acceptable as a design basis for
extrapolating from experimental data to values for gears of different
dimensions.
Several methods have been approved for the calculation of the
permissible contact stress and the determination of a number of factors
(see IS0 6336-l).
---------------------- Page: 5 ----------------------
IS0 6336-2: 1996(E)
INTERNATIONAL STANDARD @ IS0
Calculation of load capacity of spur and helical gears -
Part 2: Calculation of surface durability (pitting)
1 Scope
This part of IS0 6336 specifies the fundamental formulae for use in the determination of the surface
load capacity of cylindrical gears with involute internal or external teeth. It includes formulae for all
influences on surface durability for which quantitative assessments can be made. It applies
primarily to oil-lubricated transmissions, but may also be used to obtain approximate values for
(slow-running) grease-lubricated transmissions, as long as sufficient lubricant is present in the mesh
at all times.
The given formulae are valid for cylindrical gears with tooth profiles in accordance with the basic
rack standardized in IS0 53. They may be used for teeth where the actual transverse contact ratio
is less than can = 2,s. The results are in good agreement with other methods for the range as
indicated in the scope of IS0 6336-l.
The user of this part of IS0 6336 is cautioned that when the method specified is used for large helix
angles and large pressure angles, the calculated results should be confirmed by experience as by
method A.
These formulae cannot be directly applied for the assessment of types of gear tooth surface
damage such as plastic yielding, scratching, scuffing or any other than that described in clause 3.
The load capacity determined by way of the permissible contact stress is called the “surface load
capacity” or “surface durability ”.
2 Normative references
The following standards contain provisions which, through reference in this text, constitute
provisions of this part of IS0 6336. At the time of publication, the editions indicated were valid. All
standards are subject to revision, and parties to agreements based on this part of IS0 6336 are
encouraged to investigate the possibility of applying the most recent editions of the standards
indicated below. Members of IEC and IS0 maintain registers of currently valid International
Standards.
IS0 53: 1974, Cylindrical gears for genera/ and heavy engineering - Basic rack.
IS0 6336-l : 1996, Calculation of load capacity of spur and helical cylindrical gears - Part I: Basic
principles, introduction and genera/ influence factors.
IS0 6336-5: 1996, Calculation of load capacity of cylindrical gears - Part-5: Strength and quality of
materials.
---------------------- Page: 6 ----------------------
IS0 6336-2: 1996(E) 63 IS0
3 Pitting damage and safety factors
If limits of the surface durability of the meshing flanks are exceeded, particles will break out of the
flanks, leaving pits.
The extent to which such pits can be tolerated (in size and number) varies within wide limits,
depending largely on the field of application. In some fields, extensive pitting can be accepted; in
other fields any appreciable pitting is to be avoided.
The following definitions, relevant to average working conditions help in distinguishing between
initial pitting and destructive pitting.
Linear or progressive increase of the total area of pits is unacceptable, however the effective tooth
bearing area may be enlarged by initial pitting, and the rate of generation of pits may subsequently
reduce (degressive pitting), or cease (arrested pitting). Such pitting is considered tolerable. In the
event of dispute, the following rule is determinant.
Pitting involving the formation of pits which increase linearly or progressively with time under
unchanged service conditions (linear or progressive pitting) is not acceptable. Damage assessment
shall include the entire active area of all the tooth flanks. The number and size of newly developed
pits in unhardened tooth flanks shall be taken into consideration. It is a frequent occurrence that
pits are formed on just one or only a few of the surface hardened gear tooth flanks. In such
circumstances, assessment shall be centred on the flanks actually pitted. Teeth suspected of being
especially at risk should be marked for critical examination if a quantitative evaluation is required.
In special cases, a first rough assessment can be based on considerations of the entire quantity of
wear debris. In critical cases, the condition of the flanks should be examined at least three times.
The first examination should, however, only take place after at least IO6 cycles of load. Further
examination should take place after a period of service depending on the results of the previous
examination.
If the deterioration by pitting is such that it puts human life in danger, or there is a risk of leading to
some grave consequences, then pitting is not tolerable. Due to stress concentration effects, a pit of
a diameter of 1 mm near the fillet of a through-hardened or case-hardened tooth of a gear may
become the origin of a crack which could lead to tooth breakage; for this reason, such a pit shall be
considered as intolerable (e.g. in aerospace transmissions).
Similar considerations are true for turbine gears. In general, during the long life (IO” to IO”
cycles) which is demanded of these gears, neither pitting nor unduly severe wear is tolerable. Such
damage could lead to unacceptable vibrations and excessive dynamic loads. Appropriately
generous safety factors should be included in the calculation, i.e. only a low probability of failure
can be tolerated.
In contrast, pitting over 100 % of the working flanks can be tolerated for some slow-speed industrial
gears with large teeth (e.g. module 25) made from low hardness steel where they will safely transmit
Individual pits may be up to 20 mm in diameter and 8 mm
the rated power for IO to 20 years.
deep. The apparently “destructive” pitting which occurs during the first two or three years of service
normally slows down. The tooth flanks become smoothed and work hardened to the extent of
increasing the surface Brinell hardness number by 50 % or more.
For such conditions, relatively low safety factors (in some cases less than one) can be chosen, with
A high factor of safety against tooth
a correspondingly higher probability of tooth surface damage.
breakage is necessary.
Comments on the choice of safety factor S, can be found in IS0 6336-1, subclause 4.1.3. It is
recommended that the manufacturer and customer agree on the values of the minimum safety
factor.
---------------------- Page: 7 ----------------------
@ IS0
IS0 6336-2: 1996(E)
4
Basic formulae
NOTE 1 - All symbols, terms and units are defined in IS0 6336-l.
The calculation of surface durability is based on the contact stress, c+, at the pitch point or at the
inner point of single pair tooth contact. The higher of the two values obtained is used to determine
capacity (determinant). oH and the permissible contact stress, dHPS shall be calculated separately
for wheel and pinion. OH shall be less than gHP* Three categories are recognized in the calculation
of OH as follows.
a) Spur gears
I) spur pinion: for a pinion, QH is usually calculated at the inner point of single pair tooth
contact. In special cases, OH at the pitch point is greater and thus determinant.
2) Spur wheel: in the case of external teeth, gH is usually calculated at the pitch point. In
special cases, particularly in the case of small transmission ratios (see 5.2), bH is greater at the
inner point of single pair tooth contact of the wheel and is thus determinant. For internal teeth,
OH is always calculated at the pitch point.
b) Helical gearing with overlap ratio Q L 1
o H is always calculated at the pitch point for pinion and wheel.
c) Helical gearing with overlap ratio eB < 1
In this case Q H is determined by linear interpolation between the two limit values, i.e. oH for spur
= 1 in which the determination of oH for each is to be based
gears and +, for helical gears with Ed
on the numbers of teeth on the actual gears.
4.1 contact stress bH
As stated, the contact stress is to be calculated on the basis of Hertzian pressure (see introduction).
4.1 .l Contact stress for the pinion
The total tangential load in the case of gear trains with multiple transmission paths, planetary gear
systems, or split-path gear trains is not quite evenly distributed over the individual meshes
(depending on design, tangential speed and manufacturing accuracy). This is to be taken into
consideration by inserting a distribution factor KY to follow KA in equation (I), to adjust the average
tangential load per mesh as necessary.
. . .
(1)
a/j =
‘B OH0 {m ’ ‘HP
. . .
(2)
OH0 =zHzEz,z,
where
is the nominal contact stress at the pitch point; this is the stress induced in flawless
OH0
(error free) gearing by application of static nominal torque.
is the pinion single pair tooth contact factor (see 5.2). This converts contact stress at
the pitch point to the contact stress at the inner point of single pair tooth contact on the
pinion.
3
---------------------- Page: 8 ----------------------
IS0 6336-2: 1996(E) 0 IS0
is the application factor (see IS0 6336-l). It takes into account the load increment due
to externally influenced variations of input or output torque.
K is the dynamic factor (see IS0 6336-l). It takes into account load increments due to
V
internal dynamic effects.
is the face load factor for contact stress (see IS0 6336-l). It takes into account uneven
Kw
distribution of load over the facewidth, due to mesh misalignment caused by
inaccuracies in manufacture, elastic deformations, etc.
is the transverse load factor for contact stress (see IS0 6336-l). It takes into account
KH,
uneven load distribution in the transverse direction resulting, for example, from pitch
deviation.
NOTE 2 - See IS0 6336-1, subclause 4.1 .lO for the sequence in which factors KA, Kv, KHp, K,, are calculated.
is the permissible contact stress (see 4.2).
=HP
is the zone factor (see clause 5). It takes into account the flank curvatures at the pitch
point and transforms tangential load at the reference cylinder to tangential load at the
pitch cylinder.
is the elasticity factor (see clause 6). It takes into account specific properties of the
material, moduli of elasticity E 1, E, and Poisson ’s ratios vl, v2.
Z is the contact ratio factor (see clause 7). It takes into account the influence of the
6
effective length of the lines of contact.
is the helix angle factor (see clause 8). It takes into account influences of the helix
angle, such as the variation of the load along the lines of contact.
F is the nominal tangential load, the transverse load tangential to the reference cylinder.
t
The total tangential load per mesh shall be introduced for Ft in every case (even with
> 2). See IS0 6336-1, subclause 4.2, for the definition of Ft and comments on
p%ticular characteristics of double-helical gearing.
b is the facewidth (for a double helix gear b
= 2 bs). The value b of mating gears is the
smaller of the facewidths at the root circles of pinion and wheel ignoring any intentional
transverse chamfers or tooth-end rounding. Neither unhardened portions of surface-
hardened gear tooth flanks nor the transition zones shall be included.
d is the reference diameter of pinion.
1
u
is the gear ratio = z2/zl. For external gears u is positive, and for internal gears u is
negative.
4.1.2 Contact stress for the wheel
. . .
(3)
a# =
zD OH0 iKA Kv KH#3 KHa ’ ‘HP
where
is the single pair tooth contact factor of the wheel (see 5.2). This transforms contact
ZD
stress at the pitch point to contact stress at the inner point of single pair tooth contact
of the wheel.
See 4.1 .l for explanations of other symbols.
---------------------- Page: 9 ----------------------
IS0 6336-2: 1996(E)
0 IS0
4.2 Permissible contact stress, Q HP
The limit values of contact stresses (see clause 9) should preferably be derived from material tests
using meshing gears as test pieces (see introduction). The more closely test gears and test
conditions resemble the service gears and service conditions, the more relevant to the calculations
the derived values will be.
4.2.1 Determination of the permissible contact stress, Q HP9 principles, assumptions and
application
a) Method A
In method A the permissible contact stress o HP (or the pitting stress limit, OHG) for reference stress,
long and limited life and static stresses are calculated using equation (2) or (3) from the S-N curve
or damage curve derived from tests of actual gear pair duplicates under appropriate service
conditions.
The cost required for this method is in general only justifiable for the development of new products,
failure of which would have serious consequences (e.g. for manned space flight).
Similarly, the permissible stress values may be derived from consideration of dimensions, service
conditions and performance of carefully monitored reference gears. The more closely the
dimensions and service conditions of the actual gears resemble those of the reference gears, the
more effective will be the application of such values for purposes of design ratings or calculation
checks.
b) Method B
Damage curves, characterized by the allowable stress number values gH lim and the limited life
factors ZNT have been determined for a number of common gear materials and heat treatments from
results of gear loading tests with standard reference test gears.
These test gear values are converted to suit the dimensions and service conditions of the actual
gear pair using the (relative) influence factors for lubricant, Z,, pitch line velocity Zv, flank surface
roughness, Z,, work hardening, Z,, and size, Z,.
Method B is recommended for reasonably accurate calculation whenever pitting resistance values
are available from gear tests, from special tests or, if the material is similar, from IS0 6336-5 (see
introduction).
c) Methods C and D
In these methods which are derived from method B, the influence factors Z,, Z,, Z,, Z,,,, and Z, are
determined using simplified procedures.
d) Method B,
Material characteristic values are determined by rolling pairs of disks in loaded contact. The
magnitude and direction of the sliding speed in these tests should be adjusted to represent the in-
service slide and roll conditions of the tooth flanks in the areas at risk from pitting.
Method B, may be used when stress values derived from gear tests are not available. The method
is particularly suitable for the determination of the surface durability of various materials relative to
one another.
5
---------------------- Page: 10 ----------------------
0 IS0
IS0 6336-2: 1996(E)
4.2.2 Permissible contact stress, gHPS Method B
Z
. . .
OH lim NT q z, ZR z, zx = OHG
(4
OHP =
S
s
H min
H min
where
is the allowable stress number (contact) (see clause 9 and IS0 6336-5). It accounts for
OH lim
the influence of material, heat treatment and surface roughness of the standard
reference test gears.
is the life factor for contact stress (see clause 10). It accounts for higher load capacity
‘NT
for a limited number of load cycles.
is the pitting stress limit (= gHP sH min).
OHG
S H min is the minimum required safety factor for surface durability.
Factors Z,, Z, and Z, together cover the influence of the oil film on tooth contact stress.
is the lubricant factor (see clause 11). It accounts for the influence of the lubricant
viscosity.
is the roughness factor (see clause 11). It accounts for the influence of surface
ZR
roughness.
Z is the velocity factor (see clause 11). It accounts for the influence of pitch line velocity.
V
is the work hardening factor (see clause 12). It accounts for the effect of meshing with a
ZW
surface hardened or similarly hard mating gear.
is the size factor for contact stress (see clause 13). It accounts for the influence of the
ZX
tooth dimensions for the permissible contact stress.
a) Permissible contact stress (reference)
is derived from equation (4) with ZNT = 1 and
The permissible contact stress (reference), 0 HP refj
calculated following method B.
the influence factors gH lim)
ZL, Zv, Z,, ZW, ZR, Z)( and SH min
b) Permissible contact stress (static)
The permissible contact stress (static), 0 HP statf is determined in accordance with equation (4) with
all method B influence factors (for static stress).
4.2.3 Permissible contact stress for limited and long life, Method B
In method B, provision is made for determination of aHP b y g ra p hical or computed interpolation
between the value obtained for reference in accordance with 4.2.2 a) and the value obtained for
static stress in accordance with 4.2.2 b). Values appropriate to the relevant number 01 load cycles
A/, are indicated by the S-N curve. See clause 10.
4.2.3.1 Graphical values
Calculate o HP for reference stress and static stress in accordance with 4.2.2 and plot t t le S-N curve
See figure 1 for the principle. aHP for the relevant number of
corresponding to the life factor ZNT.
load cycles A/, may be read from this graph.
6
---------------------- Page: 11 ----------------------
@ IS0
IS0 6336-2: 1996(E)
n
CB
0
static limited life
long life
-
\
n
o=
u-l
ul
Q,
L
-e
u-l
-w
0
ccl
+J
c
0
0
a,
-
Q
.-
u-l
0
a-
E
L
I I IIIIII I I IIIIII I I Illlll I I IIIIII I I Illlll
I I Illlll
:
3 5
6
7
10 10 10 10
Number of load cycles, NL
I ml)
Figure 1 - Graphic determination of the permissible contact stress for a limited life,
in accordance with method B
4.2.3.2 Determination by calculation
calculate u HP ref for reference and 0 HP stat for static strength in accordance with 4.2.2 and, using
these results, determine 0 HP9 in accordance with method B for limited life and the number of load
cycles N, in the range as follows.
a) Structural and through-hardened steels, perlitic or bainitic spheroidal graphite cast iron, perlitic
malleable cast iron, case or surface hardened steel, if a certain number of pits is permissible:
For the limited life stress range, 6 x IO5 < N L 5 IO7 in accordance with figure 8:
. . .
(5)
Z
“HP = a HPref N
where
. . .
= 0,3705 log YE!!?
(6)
=P
a HPref
---------------------- Page: 12 ----------------------
IS0 6336-2:1996( E) 0 IS0
IO7 < N, I IO’ in accordance with figure 8:
For the limited life stress range,
109
. . .
(7)
Z
OHP = QHPref N = OHPref -
NL
. . .
= 0,2791 log TEE!!! (8)
=P
u HPref
b) Structural and through-hardened steel, perlitic or bainitic nodular cast iron, perlitic malleable cast
iron, case or surface hardened steel, when no pits are permissible:
5 5 x IO7 in accordance with figure 8:
For the limited life stress range, IO5 < N,
. . .
(9)
Z
OHP = CJ HPref N
where exp is as in equation (6)
c) Through-hardening or nitriding steel; gas nitrided, through-hardened, nitro-carburized; ferritic
nodular cast iron, grey cast iron:
s 2 x IO6 in accordance with figure 8:
For the limited life stress range, IO5 < N,
. . .
(IO)
Z
OHP = a HPref N
u HPstat
. . .
= 0,7686 log - (Ii)
exp
Q HPref
Corresponding calculations may be determined for the range of long life.
4.2.4 Permissible contact stress for reference and static strength, Methods C and D
The provisions of 4.2.2 and 4.2.3 are applicable to these methods with the influence factors Z,, Z,,
Z,, Z, and Z,, being determined in accordance with method C or D.
8
---------------------- Page: 13 ----------------------
/
@ IS0
IS0 6336-2: 1996(E)
4.3 Safety factor for surface durability (against pitting), sH
Calculate SH separately for pinion and wheel:
*HG
. . .
(12)
‘# = < ’ ‘H min
a) Method B
Calculate 0 Ho for long life and static stress limits in accordance with equation (4) and clauses 4.2.2
is in accordance with equation (4) and clause 4.2.3. Take Q H in
a) and b). For limited life QHG
accordance with equation (1) for the pinion and in accordance with equation (3) for the wheel (see
introduction to clause 4).
b) Methods C and D
be in accordance with equation (4) and clause 4.2.4, and aH as in 4.3 a).
Calculate 0 HG
safety factor with regard to contact stress (Hertzian pressure). The correspond ing
NOTE 3 - This is the calculated
factor relative to torque capacity is equal to the square of
SH*
For notes on minimum safety factor and probability of failure, see clause 3 and IS0 6336-1,
subclause 4.1.3.
5 Zone factor, ZH, and single pair tooth contact factors, ZB and ZD
These factors account for the influence of tooth flank curvature on contact stress.
5.1 Zone factor, zH
The zone factor, ZH, accounts for the influence on Hertzian pressure of tooth flank curvature at the
pitch point and transforms the tangential force at the reference cylinder to normal force at the pitch
cylinder.
5.1.1
Graphical values
ZH can be taken from figures 2 to 4 as a function of (xl + x2) / (zl + z2) and B for external and
internal gears having normal pressure angles Q n = 20°, 22,5O or 25 ”.
---------------------- Page: 14 ----------------------
IS0 6336-2: 1996(E)
\ \
\’
26
9
’ --“u,oos
I ‘\
25
9
t
I
\ \ \I \ \
\
24 \
B t--poos. A\
I
r\l
I==$ QOl --l-\\\-,yy\
23
9
\
.
MU,07 >, I\ !’ ?Y
22
9
21
9
Q)
II:
0
N
19
9
18
?
0 0 10 0 20 0 30 0
40 0
h elix angle at reference circle p ‘-b
Figure 2 - Zone factor, Z,, for a, = 20”
10
---------------------- Page: 15 ----------------------
IS0 6336-2: 1996fE)
30
9
29
?
28
s
I
‘n -
27
? “I
07
1
s
I
26
9 I
.
N
P
Om
25
9 I I I
t
I I I
24
9
I
t-t-o
r\l
23
9
I I
$
\I\\\\\
0 22
?
u
21
?
Q)
c
0
N
20
9
0906
19
9
07
8 3
9 08
18 do,-
? P
01
’ I
17
9
16
9
15
9
0 0 0
0
0
0 10
20 30
40
helix angle at reference circle p ,-w
Figure 3 - Zone factor, Z,, for an = 22,5O
11
---------------------- Page: 16 ----------------------
IS0 6336-2: 1996(E)
29
9
28
9
26
9
25
9
t
I
hl
23
9
21
9
Q)
c
0
N 20
9
17
9
16
?
0 0
10 0 20 0 30 0 40 0
h elix angle at reference circle p -W
Figure 4 - Zone factor, Z,, for an = 25”
12
---------------------- Page: 17 ----------------------
0 IS0 IS0 6336-2: 1996(E)
5.1.2 Determination by calculation
l . .
(13)
%=jJ
5.2 Single pair tooth contact factors, Z, and Z,, for c a I 2
The single pair tooth contact factors, Z, and Z,, are used to transform the contact stress at the
pitch point of spur gears to the contact stress at the inner point B of single pair tooth contact of the
pinion or at the inner point D of single pair tooth contact of the wheel if Z, > 1 or Z, > 1. See
figure 5 and the introduction to clause 4.
-
external gearing in ternal gearing
Figure 5 - Radii of curvature at the pitch point C and at the single pair tooth contact point B of
the pinion and D of the wheel for determination of the pinion single pair tooth contact factor Z,
in accordance with equation (14), and of the wheel single pair tooth contact factor Z, in
accordance with equation (15) (only for external spur gears)
In general, Z, should only be determined for gears when u < I,5 When u > 1,5, M, is usually less
than 1,O in which case Z, is made equal to 1,O in equation (15).
For internal gears, Z, shall be taken as equal to l,O.
13
---------------------- Page: 18 ----------------------
IS0 6336-2: 1996(E)
Determination by calculation:
-
M, =
. . .
(14)
tana wt
PC7 PC2
=
M2 =
I
q PO7 m2
. . .
(15)
jjF -ijF -(Ea-ljF
L L
See subclause 7.2.1 for calculations of the profile contact ratio E Q.
a) Spur gears: = I, if M, L 1; = l,ifM,d 1
ZB ZD
= M,,ifM, > 1; = M,, if M, > 1
ZB ZD
b) Helical gears with Q 2 1: ZB = ZD = 1
c) Helical gears with 6 B < 1: ZB and ZD are determined by linear interpolation between the values
for spur and helical gearing with cB 2 1:
- 1)andzBr 1
ZB=M~-C~ 1
(M
- 1) andZ+ 1
ZD=M,-ep 2
(M
If ZB or ZD are made equal to 1, the contact stresses calculated using equation (1) or (3) are the
values for the contact stress at the pitch cylinder.
d) Methods a), b) and c) apply to the calculation of contact stress when the pitch point lies in the
path of contact. If the pitch point C is determinant and lies outside the path of contact, then ZB
and/or ZD are determined for contact at the adjacent tip circle. For helical gearing when cP is less
than 1 ,O, ZB and ZD are determined by linear interpolation between the values (determined at the
pitch point or at the adjacent tip circle as appropriate) for spur gears and those helical gears with
Ep 2 1.
5.3 Single pair tooth contact factors, Z, and Z,, for c a > 2
In the case of meshing gear pairs of high precision with 2 < e a I 3, the entire tangential load in any
transverse plane is supported b
...
NORME ISO
INTERNATIONALE 6336-2
Première édition
1996-06-15
Calcul de la capacité de charge des
engrenages cylindriques à dentures droite
et hélicoïdale —
Partie 2:
Calcul de la résistance à la pression de
contact (piqûres)
Calculation of load capacity of spur and helical gears —
Part 2: Calculation of surface durability (pitting)
Numéro de référence
ISO 6336-2:1996(F)
©
ISO 1996
---------------------- Page: 1 ----------------------
ISO 6336-2:1996(F)
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Version française parue en 2002
Imprimé en Suisse
ii © ISO 1996 – Tous droits réservés
---------------------- Page: 2 ----------------------
ISO 6336-2:1996(F)
Sommaire Page
Avant-propos . iv
Introduction. v
1 Domaine d'application . 1
2 Références normatives. 1
3 Endommagement par piqûres et coefficients de sécurité. 2
4 Formules de base. 3
5 Facteur géométrique, Z , et facteurs de contact unique, Z et Z . 9
H B D
6 Facteur d'élasticité, Z .14
E
7 Facteur de rapport de conduite, Z . 16
ε
8 Facteur d'angle d'hélice, Z . 17
β
9 Résistance pour la pression de contact . 18
10 Facteur de durée de vie, Z (pour les flancs) . 19
NT
11 Influences du film lubrifiant, facteurs Z , Z et Z . 21
L v R
12 Facteur de rapport de dureté, Z . 28
W
13 Facteur dimension, Z . 30
x
Bibliographie. 31
© ISO 1996 – Tous droits réservés iii
---------------------- Page: 3 ----------------------
ISO 6336-2:1996(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 étude a le droit de faire partie du comité
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.
Les projets de Normes internationales adoptés par les comités techniques sont soumis aux comités membres pour
vote. Leur publication comme Normes internationales requiert l'approbation de 75 % au moins des comités
membres votants.
La Norme internationale ISO 6336-2 a été élaborée par le comité technique ISO/TC 60, Engrenages, sous-comité
SC 2, Calcul de la capacité des engrenages.
L'ISO 6336 comprend les parties suivantes, présentées sous le titre général 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
— Partie 2: Calcul de la résistance à la pression de contact (piqûres)
— Partie 3: Calcul de la résistance à la flexion en pied de dent
— Partie 5: Résistance et qualité des matériaux
La présente version française inclut les rectificatifs techniques ISO 6336-2:2001/Cor.1:1998 et Cor.2:1999 à la
version anglaise.
iv © ISO 1996 – Tous droits réservés
---------------------- Page: 4 ----------------------
ISO 6336-2:1996(F)
Introduction
La pression de Hertz, utilisée comme modèle de calcul de la pression de contact, est le principe de base utilisé
dans la présente partie de l'ISO 6336 pour l'évaluation de la résistance à la pression superficielle des engrenages
cylindriques. Elle est un indicateur significatif de la pression générée au cours du contact des flancs. Toutefois, elle
n'est pas la cause unique de la formation de piqûres, de même que ne le sont pas les contraintes de cisaillement
en sous-couche correspondantes. Il existe d'autres influences qui y contribuent, par exemple, le coefficient de
frottement, la direction et l'amplitude du glissement et l'influence du lubrifiant sur la répartition de la pression. Le
développement n'est pas encore suffisamment avancé pour les inclure directement dans les calculs de la capacité
de charge, mais il en est tenu compte, dans une certaine mesure, dans les facteurs de déclassement et dans le
choix des valeurs des propriétés des matériaux.
En dépit d'insuffisances, la pression de Hertz est très utile comme hypothèse de travail. Ceci peut être attribué au
fait que, pour un matériau donné, les valeurs limites de la pression de Hertz sont de préférence déterminées à
partir d'essais de fatigue réalisés sur des éprouvettes d'engrenages. Ainsi, des influences supplémentaires
correspondantes sont incluses dans les valeurs. Par conséquent, si la donnée de référence se situe dans le
domaine d'application, la pression de Hertz peut être acceptée comme base de calcul pour extrapoler des valeurs
pour des engrenages de différentes dimensions à partir des données d'expérience.
Plusieurs méthodes sont admises pour le calcul de la pression de contact admissible et la détermination d'un grand
nombre de facteurs (voir l'ISO 6336-1).
© ISO 1996 – Tous droits réservés v
---------------------- Page: 5 ----------------------
NORME INTERNATIONALE ISO 6336-2:1996(F)
Calcul de la capacité de charge des engrenages cylindriques à
dentures droite et hélicoïdale —
Partie 2:
Calcul de la résistance à la pression de contact (piqûres)
1 Domaine d'application
La présente partie de l'ISO 6336 spécifie les formules de base à utiliser pour déterminer la capacité de charge à la
pression de contact des engrenages cylindriques à denture intérieure ou extérieure à profil en développante de
cercle. Elle inclut les formules relatives à tous les facteurs d'influence sur la résistance à la pression de contact
pour lesquels une évaluation quantitative est possible. Elle s'applique essentiellement aux transmissions lubrifiées
à l'huile, mais peut également être utilisée pour obtenir des valeurs approximatives dans le cas des transmissions
lubrifiées à la graisse (à faible vitesse), tant qu'il y a, à tout moment, une quantité suffisante de lubrifiant au niveau
de l'engrènement.
Les formules données conviennent pour les engrenages cylindriques à profils de dents conformes au tracé de
référence normalisée dans l'ISO 53. Elles peuvent être utilisées pour les dentures dont le rapport de conduite
apparent virtuel est inférieur à ε = 2,5. Les résultats sont en bon accord avec les autres méthodes pour la plage
αn
indiquée dans le domaine d'application de l'ISO 6336-1.
L'utilisateur de la présente partie de l'ISO 6336 est mis en garde que, lorsqu'il utilise la méthode spécifiée pour des
angles d'hélice et des angles de pression importants, il lui faut confirmer par l'expérience ainsi que par la
méthode A les résultats calculés.
Ces formules ne peuvent être directement appliquées pour l'évaluation des types d'endommagement de surface de
dentures d'engrenage tels que la déformation plastique, les griffures, le grippage ou toute autre que celle décrite à
l'article 3.
La capacité de charge déterminée au moyen de la pression de contact admissible est appelée «capacité de charge
à la pression de contact» ou «résistance à la pression de contact».
2 Références normatives
Les normes suivantes contiennent des dispositions qui, par suite de la référence qui y est faite, constituent des
dispositions valables pour la présente partie de l'ISO 6336. Au moment de la publication, les éditions indiquées
étaient en vigueur. Toute norme est sujette à révision et les parties prenantes des accords fondés sur la présente
partie de l'ISO 6336 sont invitées à rechercher la possibilité d'appliquer les éditions les plus récentes des normes
indiquées ci-après. Les membres de l'ISO et de la CEI possèdent le registre des Normes internationales en vigueur
à un moment donné.
ISO 53:1974, Engrenages cylindriques de mécanique générale et de grosse mécanique — Crémaillère de
référence
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
ISO 6336-5:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 5: Résistance et qualité des matériaux
© ISO 1996 – Tous droits réservés 1
---------------------- Page: 6 ----------------------
ISO 6336-2:1996(F)
3 Endommagement par piqûres et coefficients de sécurité
Lorsque les limites de la résistance à la pression de contact des flancs en contact sont dépassées, des particules
se détachent des flancs, formant ainsi des piqûres.
Le domaine dans lequel ces piqûres peuvent être tolérées (en ce qui concerne leur taille et leur nombre) varie dans
une large mesure, essentiellement en fonction du domaine d'application. Dans certains domaines, des nombreuses
piqûres peuvent être admises; dans d'autres domaines, toute formation de piqûres conséquentes doit être évitée.
Les définitions suivantes, correspondant à des conditions moyennes de fonctionnement, permettent de différencier
les piqûres naissantes des piqûres destructives.
Une augmentation linéaire ou progressive de la surface totale des piqûres n'est pas acceptable; toutefois la zone
de portée effective de la denture peut être élargie par la formation de piqûres naissantes, et le taux de génération
des piqûres peut ainsi être réduit (piqûres dégressives) ou stoppé (piqûres stabilisées). Ce type de piqûres est
considéré comme acceptable. En cas de conflit, la règle suivante est déterminante.
Les piqûres qui augmentent de manière linéaire ou progressive avec le temps dans des conditions de service non
modifiées (piqûres évolutives) ne sont pas acceptables. L'évaluation de la détérioration doit inclure la surface
active totale de tous les flancs. Le nombre et la taille des piqûres récentes apparues sur les flancs non durcis
doivent être pris en considération. Il est fréquent que les piqûres n'apparaissent que sur un seul ou quelques flancs
de denture d'engrenages durcis superficiellement. Dans ces cas, l'évaluation doit être centrée sur les flancs
présentant effectivement des piqûres. Il convient que les dents, dont on pense qu'elles sont particulièrement
exposées à un risque, soient repérées pour être soumises à un examen critique lorsqu'une évaluation quantitative
est exigée.
Dans les cas particuliers, une première évaluation globale peut être basée sur la prise en compte de l'ensemble
des débris d'usure. Dans les cas critiques, il convient d'examiner au moins trois fois l'état des flancs. Il est toutefois
6
recommandé de procéder au premier examen après au moins 10 cycles de mise en charge. Il y a lieu de procéder
à un autre examen après une durée de service en fonction des résultats de l'examen précédent.
Lorsque la dégradation par formation de piqûres est telle qu'elle met en danger la vie humaine, ou lorsqu'il existe
un risque de graves conséquences, les piqûres ne peuvent pas alors être tolérées. En raison des effets de
concentration de contrainte, une piqûre de 1 mm de diamètre à proximité du profil de raccordement d'une dent
d'engrenage traitée dans la masse ou durcie superficiellement, peut constituer l'origine d'une fissure susceptible
d'entraîner la rupture de la denture; pour cette raison, cette piqûre doit être considérée comme intolérable (par
exemple dans les transmissions aéronautiques).
Des considérations similaires s'appliquent aux engrenages de turbine. En général, au cours de la longue durée de
10 11
vie (10 à 10 cycles) que l'on exige de ces engrenages, aucune piqûre ni aucune usure anormalement
importantes ne peuvent être tolérées. Ce type de détérioration peut entraîner des vibrations inacceptables et des
charges dynamiques excessives. Il convient d'inclure dans le calcul des coefficients de sécurité appropriés,
c'est-à-dire que seule une faible probabilité de détérioration peut être tolérée.
Par opposition, des piqûres sur une surface équivalente à 100 % des flancs actifs peuvent être tolérées pour
certains engrenages de type industriel à vitesse lente et à dentures de grande dimension (par exemple module 25)
en acier à faible dureté, qui transmettront la puissance nominale en toute sécurité pendant 10 à 20 ans. Les
piqûres individuelles peuvent avoir un diamètre équivalent à 20 mm et une profondeur équivalent à 8 mm. Les
piqûres d'apparence «destructive» qui se produisent au cours des deux ou trois premières années de service
diminuent habituellement. Les flancs deviennent lisses et écrouis au point que la dureté Brinell de surface
augmente de 50 % ou plus.
Pour ce type de conditions, des coefficients de sécurité relativement faibles (dans certains cas inférieurs à un)
peuvent être choisis, avec une probabilité correspondante de détérioration de la surface de denture plus élevée.
L'utilisation d'un coefficient de sécurité élevé contre la rupture en pied de dent est nécessaire.
Les commentaires relatifs au choix du coefficient de sécurité S figurent en 4.1.3 de l'ISO 6336-1. Il est
H
recommandé que le fabricant et le client conviennent des valeurs du coefficient de sécurité minimal.
2 © ISO 1996 – Tous droits réservés
---------------------- Page: 7 ----------------------
ISO 6336-2:1996(F)
4 Formules de base
NOTE 1 Tous les symboles, termes et unités sont définis dans l'ISO 6336-1.
Le calcul de la résistance à la pression de contact est basé sur la pression de contact, σ , au point primitif ou au
H
point le plus bas de contact unique. La plus grande des deux valeurs obtenues est utilisée pour déterminer la
capacité (dimensionnante). σ et la pression de contact admissible, σ , doivent être calculées séparément pour le
H HP
pignon et la roue. σ doit être inférieure à σ . Les trois catégories suivantes sont reconnues dans le calcul de σ .
H HP H
a) Engrenages cylindriques à denture droite:
1) Pignon à denture droite: pour un pignon, σ est habituellement calculée au point le plus bas de contact
H
unique. Dans les cas particuliers, σ est supérieure au point primitif et donc dimensionnante.
H
2) Roue à denture droite: dans le cas d'une denture extérieure, σ est habituellement calculée au point
H
primitif. Dans les cas particuliers, plus particulièrement pour des rapports de transmission peu importants
(voir 5.2), σ est supérieure au point le plus bas de contact unique de la roue et est donc dimensionnante.
H
Pour une denture intérieure, σ est toujours calculée au point primitif.
H
b) Engrenage à denture hélicoïdale avec rapport de recouvrement ε W 1
β
σ est toujours calculée au point primitif pour le pignon et la roue.
H
c) Engrenage à denture hélicoïdale avec rapport de recouvrement ε < 1
β
Dans ce cas, σ est déterminée par interpolation linéaire entre les deux valeurs limites, c'est-à-dire σ pour
H H
les engrenages à denture droite et σ pour les engrenages à denture hélicoïdale avec ε = 1 dans laquelle la
H β
détermination de chaque valeur de σ doit être basée sur les nombres de dents des roues dentées réelles.
H
4.1 Pression de contact, σ
H
Comme indiqué, la pression de contact doit être calculée sur la base de la pression de Hertz (voir Introduction).
4.1.1 Pression de contact pour le pignon
La force tangentielle totale, dans le cas de trains d'engrenages à contacts multiples, de systèmes d'engrenages
planétaires ou de trains d'engrenages à division de puissance, n'est pas répartie de manière uniforme sur les
engrènements individuels (en fonction de la conception, de la vitesse tangentielle et de la précision de fabrication).
Ceci doit être pris en considération en intégrant, dans l'équation (1), un facteur de distribution K suite à K , afin
γ A
d'adapter la force tangentielle moyenne par contact, si nécessaire.
σ=ZKσ KKK uσ (1)
H B H0 A v HβαH HP
F u+ 1
t
σ=ZZ Z Z (2)
H0 H E εβ
db u
1
où
σ est la pression de contact de base au point primitif; c'est la pression induite dans un engrenage
H0
géométriquement parfait (exempt d'écart) par application d'un couple nominal statique;
Z est le facteur de contact unique du pignon (voir 5.2). Il convertit la pression de contact au point primitif
B
en pression de contact au point le plus bas de contact unique sur le pignon;
K est le facteur d'application (voir l'ISO 6336-1). Il prend en compte l'accroissement des forces dû à des
A
variations d'influence extérieure du couple d'entrée ou de sortie;
© ISO 1996 – Tous droits réservés 3
---------------------- Page: 8 ----------------------
ISO 6336-2:1996(F)
K est le facteur dynamique (voir l'ISO 6336-1). Il prend en compte les accroissements de forces dus aux
v
effets dynamiques internes;
K est le facteur de distribution longitudinale de la charge pour la pression de contact (voir l'ISO 6336-1).
Hβ
Il prend en compte la distribution non uniforme de la charge sur la largeur de denture due à un
désalignement de l'engrènement provoqué par les imprécisions de fabrication, les déformations
élastiques, etc.;
K est le facteur de distribution transversale de la charge pour la pression de contact (voir l'ISO 6336-1).
Hα
Il prend en compte la distribution non uniforme de la charge dans le sens transversal suite, par
exemple, à un écart de pas;
NOTE 2 Voir l'ISO 6336-1, paragraphe 4.1.10, pour l'ordre de calcul des facteurs K , K , K , K .
A v Hβ Hα
σ est la pression de contact admissible (voir 4.2);
HP
Z est le facteur géométrique (voir article 5). Il prend en compte les courbures de flanc au point primitif et
H
transforme la force tangentielle sur le cylindre de référence en force tangentielle sur le cylindre primitif
de fonctionnement;
Z est le facteur d'élasticité (voir article 6). Il prend en compte les propriétés spécifiques du matériau, les
E
modules d'élasticité E , E et les coefficients de Poisson ν , ν ;
1 2 1 2
Z est le facteur de rapport de conduite (voir article 7). Il prend en compte l'influence de la longueur
ε
effective des lignes de contact;
Z est le facteur d'hélice (voir article 8). Il prend en compte les influences de l'angle d'hélice, telles que la
β
variation de la force le long des lignes de contact;
F est la force tangentielle nominale, tangente au cylindre de référence. La force tangentielle totale par
t
engrènement doit être introduite pour F dans tous les cas (même avec ε > 2). Voir ISO 6336-1,
t αn
paragraphe 4.2, pour la définition de F et les commentaires relatifs aux caractéristiques particulières
t
d'un engrenage à denture en chevron;
b est la largeur de denture (pour un engrenage à denture en chevron b = 2 b ). La valeur b des
B
engrenages conjugués est la plus petite valeur des largeurs de denture au niveau des cercles de pied
du pignon et de la roue, en ne tenant pas compte de tous chanfreins apparents intentionnels ou de
toute dépouille de l'extrémité de la denture. Ni les parties non trempées des flancs de denture
d'engrenages durcis superficiellement, ni les zones de transition ne doivent être incluses;
d est le diamètre de référence du pignon;
1
u est le rapport d'engrenage = z /z . Pour les engrenages à denture extérieure, u est positif, et pour les
2 1
engrenages à denture intérieure, u est négatif.
4.1.2 Pression de contact pour la roue
σ=ZKσ KKK uσ (3)
H D H0 A v HβαH HP
où
Z est le facteur de contact unique de la roue (voir 5.2). Ce facteur transforme la pression de contact au
D
point primitif en pression de contact au point le plus bas de contact unique de la roue.
Voir 4.1.1 pour les explications des autres symboles.
4 © ISO 1996 – Tous droits réservés
---------------------- Page: 9 ----------------------
ISO 6336-2:1996(F)
4.2 Pression de contact admissible, σ
HP
Il convient que les valeurs limites des pressions de contact (voir article 9) soient de préférence déduites de
données d'essais qui utilisent les roues dentées comme éprouvettes d'essai (voir l'Introduction). Plus les
engrenages et les conditions d'essai ressemblent étroitement aux engrenages et aux conditions de service, plus
les valeurs obtenues correspondront aux calculs.
4.2.1 Détermination de la pression de contact admissible, σ , principes, hypothèses et application
HP
a) Méthode A
Dans la méthode A, la pression de contact admissible, σ , (ou la contrainte nominale de référence modifiée,
HP
σ ) pour la contrainte de référence, les longues durées de vie, les durées de vie limitées et les contraintes
HG
statiques sont calculées à l'aide de l'équation (2) ou (3) à partir de la courbe S-N ou courbe
d'endommagement déterminée à partir d'essais réalisés avec des répliques de roues réelles dans des
conditions de service appropriées.
Le coût de cette méthode se justifie généralement uniquement pour le développement de nouveaux produits,
dont la détérioration aurait de graves conséquences (par exemple pour les vols spatiaux habités).
De façon similaire, les valeurs de pression admissibles peuvent être obtenues en prenant en considération les
dimensions, les conditions de service et la performance des engrenages de référence contrôlés avec le plus
grand soin. Plus les dimensions et les conditions de service des engrenages réels ressemblent étroitement à
celles des engrenages de référence, plus l'application de ces valeurs sera efficace pour des puissances
calculées ou des vérifications de calculs.
b) Méthode B
Les courbes d'endommagement, caractérisées par les valeurs de contrainte nominale de référence, σ , et
H lim
les facteurs de durée de vie Z , sont déterminées pour un certain nombre de matériaux d'engrenages
NT
courants et de traitements thermiques à partir des résultats des essais en charge d'engrenages avec les
engrenages de référence normalisés.
Ces valeurs d'essais sur engrenages sont converties pour s'adapter aux dimensions et aux conditions de
service de l'engrenage réel, en utilisant les facteurs d'influence (relative) de lubrifiant, Z , de vitesse
L
tangentielle, Z , de rugosité des flancs, Z , de rapport de dureté, Z , et de dimension, Z .
v R W x
La méthode B est recommandée pour un calcul raisonnablement précis lorsque les valeurs de résistance à la
formation de piqûres sont obtenues à partir des essais d'engrenages, d'essais particuliers ou, si le matériau
est similaire, à partir de l'ISO 6336-5 (voir Introduction).
c) Méthodes C et D
Avec ces méthodes, qui sont déduites de la méthode B, les facteurs d'influence Z , Z , Z , Z et Z sont
L v R W x
déterminés en utilisant des méthodes simplifiées.
d) Méthode B
R
Les valeurs caractéristiques des matériaux sont déterminées en procédant à un essai de roulement de paires
de disques en contact sous charge. Il convient d'adapter l'amplitude et la direction de la vitesse de glissement
dans ces essais pour représenter les conditions de glissement et de roulement en service des flancs dans les
zones exposées à un risque de formation de piqûres.
La méthode B peut être utilisée lorsque l'on ne dispose pas de valeurs de contrainte déterminées par des
R
essais d'engrenages. La méthode convient tout particulièrement à la détermination de la résistance à la
pression de contact de différents matériaux les uns par rapport aux autres.
© ISO 1996 – Tous droits réservés 5
---------------------- Page: 10 ----------------------
ISO 6336-2:1996(F)
4.2.2 Pression de contact admissible, σ , méthode B
HP
σ Z
σ
Hlim NT
HG
σ= ZZ Z Z Z= (4)
HP L v R W x
SS
Hmin Hmin
où
σ est la contrainte nominale de référence (pression de contact) (voir article 9 et l'ISO 6336-5). Elle
H lim
prend en compte l'influence du matériau, le traitement thermique et la rugosité de surface des
engrenages de référence normalisés;
Z est le facteur de durée de vie pour la pression de contact (voir article 10). Il prend en compte une
NT
capacité de charge plus élevée pour un nombre limité de cycles de mise en charge;
σ est la contrainte nominale de référence modifiée (= σ S );
HG HP H min
S est le coefficient de sécurité minimal exigé pour la résistance à la pression de contact.
H min
Les facteurs Z , Z et Z tiennent compte de l'influence du film lubrifiant sur la pression de contact.
L R v
Z est le facteur lubrifiant (voir article 11). Il prend en compte l'influence de la viscosité du lubrifiant;
L
Z est le facteur de rugosité (voir article 11). Il prend en compte l'influence de la rugosité de surface;
R
Z est le facteur de vitesse (voir article 11). Il prend en compte l'influence de la vitesse tangentielle;
v
Z est le facteur de rapport de dureté (voir article 12). Il prend en compte l'effet d'engrènement avec une
W
roue conjuguée durcie superficiellement ou durcie de façon similaire;
Z est le facteur de dimension à la pression de contact (voir article 13). Il prend en compte l'influence
x
des dimensions de la denture pour la pression de contact admissible.
a) Pression de contact admissible (de référence)
La pression de contact admissible (de référence), σ , est déterminée par l'équation (4), avec Z = 1 et les
HP ref NT
facteurs d'influence σ , Z , Z , Z , Z , Z et S sont calculés selon la méthode B.
H lim L v R W x H min
b) Pression de contact admissible (statique)
La pression de contact admissible (statique), σ , est déterminée conformément à l'équation (4) avec tous
HP stat
les facteurs d'influence de la méthode B (pour la pression statique).
4.2.3 Pression de contact admissible pour une durée de vie limitée et infinie, méthode B
La méthode B prévoit la détermination de σ , par interpolation graphique ou mathématique entre la valeur
HP
obtenue pour la pression de référence conformément à 4.2.2 a) et la valeur obtenue pour la pression statique
conformément à 4.2.2 b). Les valeurs appropriées au nombre correspondant de cycles de mise en charge N sont
L
indiquées par la courbe S-N. Voir article 10.
4.2.3.1 Valeurs graphiques
Calculer σ pour la pression de référence et la pression statique conformément à 4.2.2 et tracer la courbe S-N
HP
correspondant au facteur de durée de vie Z . Voir la Figure 1 pour le principe de ce calcul. σ pour le nombre
NT HP
correspondant de cycles de mise en charge N peut être lue sur le graphique.
L
6 © ISO 1996 – Tous droits réservés
---------------------- Page: 11 ----------------------
ISO 6336-2:1996(F)
Figure 1 — Détermination graphique de la pression de contact admissible pour une durée de vie limitée,
conformément à la méthode B
4.2.3.2 Détermination par calcul
Calculer σ pour la résistance de référence et σ pour la résistance statique conformément à 4.2.2 et, à
HP ref HP stat
l'aide de ces résultats, déterminer σ , conformé
...
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