ISO 6336-2:2006
(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)
ISO 6336-2:2006 specifies the fundamental formulas for use in the determination of the surface load capacity of cylindrical gears with involute external or internal teeth. It includes formulas for all influences on surface durability for which quantitative assessments can be made. It applies primarily to oil-lubricated transmissions, but can 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.
Tragfähigkeitsberechnung von gerad- und schrägverzahnten Stirnrädern - Teil 2: Berechnung der Oberflächentragfähigkeit (Grübchenbildung)
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 (piqûre)
L'ISO 6336-2:2006 spécifie les formules de base à utiliser pour déterminer la capacité de charge à la pression de contact des engrenages cylindriques à denture extérieure ou intérieure 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. L'ISO 6336-2:2006 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.
Izračun nosilnosti ravnozobih in poševnozobih zobnikov - 2. del: Izračun obratovalne vzdržljivosti zobnih bokov (jamičenje)
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INTERNATIONAL ISO
STANDARD 6336-2
Second edition
2006-09-01
Corrected version
2007-04-01
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 (piqûre)
Reference number
ISO 6336-2:2006(E)
©
ISO 2006
---------------------- Page: 1 ----------------------
ISO 6336-2:2006(E)
PDF disclaimer
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shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In
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.
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Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation
parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In
the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below.
© ISO 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
---------------------- Page: 2 ----------------------
ISO 6336-2:2006(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms. 2
4 Pitting damage and safety factors . 2
5 Basic formulæ . 3
5.1 General. 3
5.2 Safety factor for surface durability (against pitting), S . 3
H
5.3 Contact stress, σ . 3
H
5.4 Permissible contact stress, σ . 5
HP
6 Zone factor, Z , and single pair tooth contact factors, Z and Z . 9
H B D
6.1 Zone factor, Z . 9
H
6.2 Single pair tooth contact factors, Z and Z , for ε u 2 . 10
B D α
6.3 Single pair tooth contact factors, Z and Z , for ε > 2. 11
B D α
7 Elasticity factor, Z . 11
E
8 Contact ratio factor, Z . 12
ε
8.1 Determination of contact ratio factor, Z . 13
ε
8.2 Calculation of transverse contact ratio, ε , and overlap ratio, ε . 14
α β
9 Helix angle factor, Z . 15
β
10 Strength for contact stress. 16
10.1 Allowable stress numbers (contact), σ , for Method B. 16
H lim
10.2 Allowable stress number values for Method B . 16
R
11 Life factor, Z (for flanks) . 16
NT
11.1 Life factor Z : Method A. 17
NT
11.2 Life factor Z : Method B . 17
NT
12 Influence of lubricant film, factors Z , Z and Z . 18
L v R
12.1 General. 18
12.2 Influence of lubricant film: Method A . 19
12.3 Influence of lubricant film, factors Z , Z and Z : Method B. 19
L v R
13 Work hardening factor, Z . 24
W
13.1 Work hardening factor, Z : Method A. 24
W
13.2 Work hardening factor, Z : Method B . 25
W
14 Size factor, Z . 29
X
Annex A (informative) Start of involute. 30
Bibliography . 33
© ISO 2006 – All rights reserved iii
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ISO 6336-2:2006(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 6336-2 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity
calculation.
This second edition cancels and replaces the first edition (ISO 6336-2:1996), Clause 13 of which has been
technically revised. It also incorporates the Technical Corrigenda ISO 6336-2:1996/Cor.1:1998 and
ISO 6336-2:1996/Cor.2:1999.
ISO 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)
⎯ Part 3: Calculation of tooth bending strength
⎯ Part 5: Strength and quality of materials
⎯ Part 6: Calculation of service life under variable load
This corrected version incorporates the following corrections:
⎯ the key to Figure 2 has been inverted, so that the descriptions of the axes now correspond correctly with
the figure;
⎯ in Figure 7, the description of the Y axis in the key has been given in English;
⎯ Equation (46) has been corrected;
⎯ the wording of 12.3.1.3.2 has been changed such that it now refers to roughness.
iv © ISO 2006 – All rights reserved
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ISO 6336-2:2006(E)
Introduction
Hertzian pressure, which serves as a basis for the calculation of contact stress, is the basic principle used in
this part of ISO 6336 for the assessment of the 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,
and 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 ISO 6336-1).
© ISO 2006 – All rights reserved v
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INTERNATIONAL STANDARD ISO 6336-2:2006(E)
Calculation of load capacity of spur and helical gears —
Part 2:
Calculation of surface durability (pitting)
IMPORTANT — The user of this part of ISO 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. In addition, it is important to note that best correlation has been obtained
for helical gears when high accuracy and optimum modifications are employed.
1 Scope
This part of ISO 6336 specifies the fundamental formulæ for use in the determination of the surface load
capacity of cylindrical gears with involute external or internal teeth. It includes formulæ for all influences on
surface durability for which quantitative assessments can be made. It applies primarily to oil-lubricated
transmissions, but can 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 formulæ are valid for cylindrical gears with tooth profiles in accordance with the basic rack
standardized in ISO 53. They may also be used for teeth conjugate to other basic racks where the actual
transverse contact ratio is less than ε = 2,5. The results are in good agreement with other methods for the
αn
range, as indicated in the scope of ISO 6336-1.
These formulæ 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 4.
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 referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336-1:2006, Calculation of load capacity of spur and helical gears — Part 1: Basic principles,
introduction and general influence factors
ISO 6336-5:2003, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of
material
© ISO 2006 – All rights reserved 1
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ISO 6336-2:2006(E)
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms, definitions, symbols and abbreviated terms given in ISO 1122-1
and ISO 6336-1 apply.
4 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 assessments, relevant to average working conditions, will 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 can be enlarged by initial pitting, and the rate of generation of pits could 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 that 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
6
examination should, however, only take place after at least 10 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 that it could lead 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 can 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).
10 11
Similar considerations are true for turbine gears. In general, during the long life (10 to 10 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 the rated power for
10 to 20 years. Individual pits may be up to 20 mm in diameter and 8 mm 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) may be chosen, with a
correspondingly higher probability of tooth surface damage. A high factor of safety against tooth breakage is
necessary.
Comments on the choice of safety factor S can be found in ISO 6336-1:2006, 4.1.7. It is recommended that
H
the manufacturer and customer agree on the values of the minimum safety factor.
2 © ISO 2006 – All rights reserved
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ISO 6336-2:2006(E)
5 Basic formulæ
5.1 General
The calculation of surface durability is based on the contact stress, σ , at the pitch point or at the inner point
H
of single pair tooth contact. The higher of the two values obtained is used to determine the load capacity
(determinant). σ and the permissible contact stress, σ , shall be calculated separately for wheel and pinion.
H HP
σ shall be less than σ . This comparison will be expressed in safety factors S and S which shall be
H HP H1 H2
higher than the agreed minimum safety factor S . Four categories are recognized in the calculation of σ ,
Hmin H
as follows.
a) Spur gears with contact ratio ε W 1:
α
⎯ for a pinion, σ is usually calculated at the inner point of single pair tooth contact. In special cases,
H
σ at the pitch point is greater and thus determinant;
H
⎯ for a spur wheel, in the case of external teeth, σ is usually calculated at the pitch point, however, in
H
special cases — particularly in the case of small transmission ratios (see 6.2), — σ is greater at the
H
inner point of single pair tooth contact of the wheel and is thus determinant; whereas, for internal
teeth, σ is always calculated at the pitch point.
H
b) Helical gears with contact ratio ε W 1 and overlap ratio ε W 1: σ is always calculated at the pitch point
α β H
for pinion and wheel.
c) Helical gears with contact ratio ε W 1 and overlap ratio ε < 1: σ is determined by linear interpolation
α β H
between the two limit values, i.e. σ for spur gears and σ for helical gears with ε = 1 in which the
H H β
determination of σ for each is to be based on the numbers of teeth on the actual gears.
H
d) Helical gears with ε u 1 and with ε > 1: not covered by ISO 6336 — a careful analysis of the contact
α γ
stress along the path of contact is necessary.
5.2 Safety factor for surface durability (against pitting), S
H
Calculate S separately for pinion and wheel:
H
σ
HG1
=> (1)
SS
H min
H1
σ
H1
σ
HG2
=> (2)
SS
H2 H min
σ
H2
Take σ in accordance with Equation (4) for the pinion and in accordance with Equation (5) for the wheel
H1,2
(see 5.1). Calculate σ for long life and static stress limits in accordance with Equation (6) and 5.4.2 a) and
HG
b). For limited life, calculate σ in accordance with Equation (6) and 5.4.3.
HG
NOTE This is the calculated safety factor with regard to contact stress (Hertzian pressure). The corresponding factor
relative to torque capacity is equal to the square of S .
H
For notes on minimum safety factor and probability of failure, see Clause 4 and ISO 6336-1:2006, 4.1.7.
5.3 Contact stress, σ
H
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 the mesh
© ISO 2006 – All rights reserved 3
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ISO 6336-2:2006(E)
load factor K to follow K in Equations (4) and (5), and to adjust the average tangential load per mesh as
γ A
necessary.
u+ 1
F
t
= (3)
σ ZZ Z Z
H0 HEεβ
db u
1
= (4)
σσZKKKK
H1BAH0 vHβHα
= (5)
σσZKKKK
H2DAH0 vHβHα
where
σ is the nominal contact stress at the pitch point, which is the stress induced in flawless (error-free)
H0
gearing by application of static nominal torque;
Z is the pinion single pair tooth contact factor of the pinion (see 6.2 and 6.3), which converts contact
B
stress at the pitch point to the contact stress at the inner point of single pair tooth contact on the
pinion;
Z is the single pair tooth contact factor of the wheel (see 6.2), which converts contact stress at the
D
pitch point to contact stress at the inner point of single pair tooth contact of the wheel;
K is the application factor (see ISO 6336-6), which takes into account the load increment due to
A
externally influenced variations of input or output torque;
K is the dynamic factor (see ISO 6336-1), which takes into account load increments due to internal
v
dynamic effects;
K is the face load factor for contact stress (see ISO 6336-1), which takes into account uneven
Hβ
distribution of load over the facewidth, due to mesh misalignment caused by inaccuracies in
manufacture, elastic deformations, etc.;
K is the transverse load factor for contact stress (see ISO 6336-1), which takes into account uneven
Hα
1)
load distribution in the transverse direction resulting, for example, from pitch deviation;
σ is the permissible contact stress (see 5.3);
HP
Z is the zone factor (see Clause 6), which takes into account the flank curvatures at the pitch point
H
and transforms tangential load at the reference cylinder to tangential load at the pitch cylinder;
Z is the elasticity factor (see Clause 7), which takes into account specific properties of the material,
E
moduli of elasticity E , E and Poisson's ratios ν , ν ;
1 2 1 2
Z is the contact ratio factor (see Clause 8), which takes into account the influence of the effective
ε
length of the lines of contact;
Z is the helix angle factor (see Clause 9), which takes into account influences of the helix angle, such
β
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 (see related
t
requirement, below);
b is the facewidth (for a double helix gear b = 2 b ) (see related requirement, below);
B
1) See ISO 6336-1:2006, 4.1.14, for the sequence in which factors K , K , K , K are calculated.
A v Hβ Hα
4 © ISO 2006 – All rights reserved
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ISO 6336-2:2006(E)
d is the reference diameter of pinion;
1
u is the gear ratio = z /z . For external gears u is positive, and for internal gears u is negative.
2 1
The total tangential load per mesh shall be introduced for F in every case (even with ε > 2). See
t αn
ISO 6336-1:2006, 4.2, for the definition of F and comments on particular characteristics of double-helical
t
gearing. 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.
5.4 Permissible contact stress, σ
HP
The limit values of contact stresses (see Clause 10) 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.
5.4.1 Determination of permissible contact stress σ — Principles, assumptions and application
HP
Several procedures for the determination of permissible contact stresses are acceptable. The method adopted
shall be validated by carrying out careful comparative studies of well-documented service histories of a
number of gears.
5.4.1.1 Method A
In Method A the permissible contact stress σ (or the pitting stress limit, σ ) for reference stress, long and
HP HG
limited life and static stresses is calculated using Equation (4) or (5) 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.
5.4.1.2 Method B
Damage curves, characterized by the allowable stress number values, σ , and the limited life factors, Z ,
H lim NT
have been determined for a number of common gear materials and heat treatments from the 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 Z , flank surface roughness Z , work
L v R
hardening Z and size Z .
W X
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 ISO 6336-5 (see Introduction).
5.4.1.3 Method B
R
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
R
particularly suitable for the determination of the surface durability of various materials relative to one another.
© ISO 2006 – All rights reserved 5
---------------------- Page: 10 ----------------------
ISO 6336-2:2006(E)
5.4.2 Permissible contact stress, σ : Method B
HP
The permissible contact stress is calculated from
σ Z σ
Hlim NT HG
σ = ZZ Z Z Z = (6)
HP Lv RW X
SS
H min Hmin
where
σ is the allowable stress number (contact) (see Clause 10 and ISO 6336-5), which accounts
H lim
for the influence of material, heat treatment and surface roughness of the standard reference
test gears;
Z is the life factor for test gears for contact stress (see Clause 11), which accounts for higher
NT
load capacity for a limited number of load cycles;
σ is the pitting stress limit (= σ S );
HG HP H min
S is the minimum required safety factor for surface durability.
H min
Z , Z , Z are factors that, together, cover the influence of the oil film on tooth contact stress;
L R v
Z is the lubricant factor (see Clause 12), which accounts for the influence of the lubricant
L
viscosity;
Z is the roughness factor (see Clause 12), which accounts for the influence of surface
R
roughness;
Z is the velocity factor (see Clause 12), which accounts for the influence of pitch line velocity;
v
Z is the work hardening factor (see Clause 13), which accounts for the effect of meshing with a
W
surface hardened or similarly hard mating gear.
Z is the size factor for contact stress (see Clause 14), which accounts for the influence of the
X
tooth dimensions for the permissible contact stress.
a) Permissible contact stress (reference), σ , is derived from Equation (6), with Z = 1 and the
HP ref NT
influence factors σ , Z , Z , Z , Z , Z , Z and S calculated using Method B.
H lim L v R W R X H min
b) Permissible contact stress (static), σ , is determined in accordance with Equation (6), with all
HP stat
influence factors (for static stress) following Method B.
5.4.3 Permissible contact stress for limited and long life: Method B
In Method B, provision is made for determination of σ by graphical or computed linear interpolation on a
HP
log-log scale between the value obtained for reference in accordance with 5.4.2 a) and the value obtained for
static stress in accordance with 5.4.2 b). Values appropriate to the relevant n
...
SLOVENSKI STANDARD
SIST ISO 6336-2:2008
01-julij-2008
1DGRPHãþD
SIST ISO 6336-2:2002
,]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)
Tragfähigkeitsberechnung von gerad- und schrägverzahnten Stirnrädern - Teil 2:
Berechnung der Oberflächentragfähigkeit (Grübchenbildung)
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 (piqûre)
Ta slovenski standard je istoveten z: ISO 6336-2:2006
ICS:
21.200 Gonila Gears
SIST ISO 6336-2:2008 en,fr
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
---------------------- Page: 1 ----------------------
INTERNATIONAL ISO
STANDARD 6336-2
Second edition
2006-09-01
Corrected version
2007-04-01
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 (piqûre)
Reference number
ISO 6336-2:2006(E)
©
ISO 2006
---------------------- Page: 2 ----------------------
ISO 6336-2:2006(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 2006
All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,
electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or
ISO's member body in the country of the requester.
ISO copyright office
Case postale 56 • CH-1211 Geneva 20
Tel. + 41 22 749 01 11
Fax + 41 22 749 09 47
E-mail copyright@iso.org
Web www.iso.org
Published in Switzerland
ii © ISO 2006 – All rights reserved
---------------------- Page: 3 ----------------------
ISO 6336-2:2006(E)
Contents Page
Foreword. iv
Introduction . v
1 Scope . 1
2 Normative references . 1
3 Terms, definitions, symbols and abbreviated terms. 2
4 Pitting damage and safety factors . 2
5 Basic formulæ . 3
5.1 General. 3
5.2 Safety factor for surface durability (against pitting), S . 3
H
5.3 Contact stress, σ . 3
H
5.4 Permissible contact stress, σ . 5
HP
6 Zone factor, Z , and single pair tooth contact factors, Z and Z . 9
H B D
6.1 Zone factor, Z . 9
H
6.2 Single pair tooth contact factors, Z and Z , for ε u 2 . 10
B D α
6.3 Single pair tooth contact factors, Z and Z , for ε > 2. 11
B D α
7 Elasticity factor, Z . 11
E
8 Contact ratio factor, Z . 12
ε
8.1 Determination of contact ratio factor, Z . 13
ε
8.2 Calculation of transverse contact ratio, ε , and overlap ratio, ε . 14
α β
9 Helix angle factor, Z . 15
β
10 Strength for contact stress. 16
10.1 Allowable stress numbers (contact), σ , for Method B. 16
H lim
10.2 Allowable stress number values for Method B . 16
R
11 Life factor, Z (for flanks) . 16
NT
11.1 Life factor Z : Method A. 17
NT
11.2 Life factor Z : Method B . 17
NT
12 Influence of lubricant film, factors Z , Z and Z . 18
L v R
12.1 General. 18
12.2 Influence of lubricant film: Method A . 19
12.3 Influence of lubricant film, factors Z , Z and Z : Method B. 19
L v R
13 Work hardening factor, Z . 24
W
13.1 Work hardening factor, Z : Method A. 24
W
13.2 Work hardening factor, Z : Method B . 25
W
14 Size factor, Z . 29
X
Annex A (informative) Start of involute. 30
Bibliography . 33
© ISO 2006 – All rights reserved iii
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ISO 6336-2:2006(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.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.
The main task of technical committees is to prepare International Standards. Draft International Standards
adopted by the technical committees are circulated to the member bodies for voting. Publication as an
International Standard requires approval by at least 75 % of the member bodies casting a vote.
Attention is drawn to the possibility that some of the elements of this document may be the subject of patent
rights. ISO shall not be held responsible for identifying any or all such patent rights.
ISO 6336-2 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity
calculation.
This second edition cancels and replaces the first edition (ISO 6336-2:1996), Clause 13 of which has been
technically revised. It also incorporates the Technical Corrigenda ISO 6336-2:1996/Cor.1:1998 and
ISO 6336-2:1996/Cor.2:1999.
ISO 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)
⎯ Part 3: Calculation of tooth bending strength
⎯ Part 5: Strength and quality of materials
⎯ Part 6: Calculation of service life under variable load
This corrected version incorporates the following corrections:
⎯ the key to Figure 2 has been inverted, so that the descriptions of the axes now correspond correctly with
the figure;
⎯ in Figure 7, the description of the Y axis in the key has been given in English;
⎯ Equation (46) has been corrected;
⎯ the wording of 12.3.1.3.2 has been changed such that it now refers to roughness.
iv © ISO 2006 – All rights reserved
---------------------- Page: 5 ----------------------
ISO 6336-2:2006(E)
Introduction
Hertzian pressure, which serves as a basis for the calculation of contact stress, is the basic principle used in
this part of ISO 6336 for the assessment of the 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,
and 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 ISO 6336-1).
© ISO 2006 – All rights reserved v
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INTERNATIONAL STANDARD ISO 6336-2:2006(E)
Calculation of load capacity of spur and helical gears —
Part 2:
Calculation of surface durability (pitting)
IMPORTANT — The user of this part of ISO 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. In addition, it is important to note that best correlation has been obtained
for helical gears when high accuracy and optimum modifications are employed.
1 Scope
This part of ISO 6336 specifies the fundamental formulæ for use in the determination of the surface load
capacity of cylindrical gears with involute external or internal teeth. It includes formulæ for all influences on
surface durability for which quantitative assessments can be made. It applies primarily to oil-lubricated
transmissions, but can 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 formulæ are valid for cylindrical gears with tooth profiles in accordance with the basic rack
standardized in ISO 53. They may also be used for teeth conjugate to other basic racks where the actual
transverse contact ratio is less than ε = 2,5. The results are in good agreement with other methods for the
αn
range, as indicated in the scope of ISO 6336-1.
These formulæ 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 4.
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 referenced documents are indispensable for the application of this document. For dated
references, only the edition cited applies. For undated references, the latest edition of the referenced
document (including any amendments) applies.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336-1:2006, Calculation of load capacity of spur and helical gears — Part 1: Basic principles,
introduction and general influence factors
ISO 6336-5:2003, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of
material
© ISO 2006 – All rights reserved 1
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ISO 6336-2:2006(E)
3 Terms, definitions, symbols and abbreviated terms
For the purposes of this document, the terms, definitions, symbols and abbreviated terms given in ISO 1122-1
and ISO 6336-1 apply.
4 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 assessments, relevant to average working conditions, will 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 can be enlarged by initial pitting, and the rate of generation of pits could 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 that 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
6
examination should, however, only take place after at least 10 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 that it could lead 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 can 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).
10 11
Similar considerations are true for turbine gears. In general, during the long life (10 to 10 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 the rated power for
10 to 20 years. Individual pits may be up to 20 mm in diameter and 8 mm 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) may be chosen, with a
correspondingly higher probability of tooth surface damage. A high factor of safety against tooth breakage is
necessary.
Comments on the choice of safety factor S can be found in ISO 6336-1:2006, 4.1.7. It is recommended that
H
the manufacturer and customer agree on the values of the minimum safety factor.
2 © ISO 2006 – All rights reserved
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ISO 6336-2:2006(E)
5 Basic formulæ
5.1 General
The calculation of surface durability is based on the contact stress, σ , at the pitch point or at the inner point
H
of single pair tooth contact. The higher of the two values obtained is used to determine the load capacity
(determinant). σ and the permissible contact stress, σ , shall be calculated separately for wheel and pinion.
H HP
σ shall be less than σ . This comparison will be expressed in safety factors S and S which shall be
H HP H1 H2
higher than the agreed minimum safety factor S . Four categories are recognized in the calculation of σ ,
Hmin H
as follows.
a) Spur gears with contact ratio ε W 1:
α
⎯ for a pinion, σ is usually calculated at the inner point of single pair tooth contact. In special cases,
H
σ at the pitch point is greater and thus determinant;
H
⎯ for a spur wheel, in the case of external teeth, σ is usually calculated at the pitch point, however, in
H
special cases — particularly in the case of small transmission ratios (see 6.2), — σ is greater at the
H
inner point of single pair tooth contact of the wheel and is thus determinant; whereas, for internal
teeth, σ is always calculated at the pitch point.
H
b) Helical gears with contact ratio ε W 1 and overlap ratio ε W 1: σ is always calculated at the pitch point
α β H
for pinion and wheel.
c) Helical gears with contact ratio ε W 1 and overlap ratio ε < 1: σ is determined by linear interpolation
α β H
between the two limit values, i.e. σ for spur gears and σ for helical gears with ε = 1 in which the
H H β
determination of σ for each is to be based on the numbers of teeth on the actual gears.
H
d) Helical gears with ε u 1 and with ε > 1: not covered by ISO 6336 — a careful analysis of the contact
α γ
stress along the path of contact is necessary.
5.2 Safety factor for surface durability (against pitting), S
H
Calculate S separately for pinion and wheel:
H
σ
HG1
=> (1)
SS
H min
H1
σ
H1
σ
HG2
=> (2)
SS
H2 H min
σ
H2
Take σ in accordance with Equation (4) for the pinion and in accordance with Equation (5) for the wheel
H1,2
(see 5.1). Calculate σ for long life and static stress limits in accordance with Equation (6) and 5.4.2 a) and
HG
b). For limited life, calculate σ in accordance with Equation (6) and 5.4.3.
HG
NOTE This is the calculated safety factor with regard to contact stress (Hertzian pressure). The corresponding factor
relative to torque capacity is equal to the square of S .
H
For notes on minimum safety factor and probability of failure, see Clause 4 and ISO 6336-1:2006, 4.1.7.
5.3 Contact stress, σ
H
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 the mesh
© ISO 2006 – All rights reserved 3
---------------------- Page: 9 ----------------------
ISO 6336-2:2006(E)
load factor K to follow K in Equations (4) and (5), and to adjust the average tangential load per mesh as
γ A
necessary.
u+ 1
F
t
= (3)
σ ZZ Z Z
H0 HEεβ
db u
1
= (4)
σσZKKKK
H1BAH0 vHβHα
= (5)
σσZKKKK
H2DAH0 vHβHα
where
σ is the nominal contact stress at the pitch point, which is the stress induced in flawless (error-free)
H0
gearing by application of static nominal torque;
Z is the pinion single pair tooth contact factor of the pinion (see 6.2 and 6.3), which converts contact
B
stress at the pitch point to the contact stress at the inner point of single pair tooth contact on the
pinion;
Z is the single pair tooth contact factor of the wheel (see 6.2), which converts contact stress at the
D
pitch point to contact stress at the inner point of single pair tooth contact of the wheel;
K is the application factor (see ISO 6336-6), which takes into account the load increment due to
A
externally influenced variations of input or output torque;
K is the dynamic factor (see ISO 6336-1), which takes into account load increments due to internal
v
dynamic effects;
K is the face load factor for contact stress (see ISO 6336-1), which takes into account uneven
Hβ
distribution of load over the facewidth, due to mesh misalignment caused by inaccuracies in
manufacture, elastic deformations, etc.;
K is the transverse load factor for contact stress (see ISO 6336-1), which takes into account uneven
Hα
1)
load distribution in the transverse direction resulting, for example, from pitch deviation;
σ is the permissible contact stress (see 5.3);
HP
Z is the zone factor (see Clause 6), which takes into account the flank curvatures at the pitch point
H
and transforms tangential load at the reference cylinder to tangential load at the pitch cylinder;
Z is the elasticity factor (see Clause 7), which takes into account specific properties of the material,
E
moduli of elasticity E , E and Poisson's ratios ν , ν ;
1 2 1 2
Z is the contact ratio factor (see Clause 8), which takes into account the influence of the effective
ε
length of the lines of contact;
Z is the helix angle factor (see Clause 9), which takes into account influences of the helix angle, such
β
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 (see related
t
requirement, below);
b is the facewidth (for a double helix gear b = 2 b ) (see related requirement, below);
B
1) See ISO 6336-1:2006, 4.1.14, for the sequence in which factors K , K , K , K are calculated.
A v Hβ Hα
4 © ISO 2006 – All rights reserved
---------------------- Page: 10 ----------------------
ISO 6336-2:2006(E)
d is the reference diameter of pinion;
1
u is the gear ratio = z /z . For external gears u is positive, and for internal gears u is negative.
2 1
The total tangential load per mesh shall be introduced for F in every case (even with ε > 2). See
t αn
ISO 6336-1:2006, 4.2, for the definition of F and comments on particular characteristics of double-helical
t
gearing. 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.
5.4 Permissible contact stress, σ
HP
The limit values of contact stresses (see Clause 10) 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.
5.4.1 Determination of permissible contact stress σ — Principles, assumptions and application
HP
Several procedures for the determination of permissible contact stresses are acceptable. The method adopted
shall be validated by carrying out careful comparative studies of well-documented service histories of a
number of gears.
5.4.1.1 Method A
In Method A the permissible contact stress σ (or the pitting stress limit, σ ) for reference stress, long and
HP HG
limited life and static stresses is calculated using Equation (4) or (5) 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.
5.4.1.2 Method B
Damage curves, characterized by the allowable stress number values, σ , and the limited life factors, Z ,
H lim NT
have been determined for a number of common gear materials and heat treatments from the 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 Z , flank surface roughness Z , work
L v R
hardening Z and size Z .
W X
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 ISO 6336-5 (see Introduction).
5.4.1.3 Method B
R
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
R
particularly suitable for the determination of the surface durability of various materials relative to one another.
© ISO 2006 – All rights reserved 5
---------------------- Page: 11 ----------------------
ISO 6336-2:2006(E)
5.4.2 Permissible contact stress, σ : Method B
HP
The permissible contact stress is calculated from
σ Z σ
Hlim NT HG
σ = ZZ Z Z Z = (6)
HP Lv RW X
SS
H min Hmin
where
σ is the allowable stress number (contact) (see Clause 10 and ISO 6336-5), which accounts
H lim
for the influence of material, heat treatment and surface roughness of the standard reference
test gears;
Z is the life factor for test gears for contact stress (see Clause 11), which accounts for higher
NT
load capacity for a limited number of load cycles;
σ is the pitting stress limit (= σ S );
HG HP H min
S is the minimum required safety factor for surface durability.
H min
Z , Z , Z are factors that, together, cover the influence of the oil film on tooth contact stress;
L R v
Z is the lubricant factor (see Clause 12), which accounts for the influence of the lubricant
L
viscosity;
Z is the roughness factor (see Clause 12), which accounts for the influence of surface
R
roughness;
Z is the velocity factor (see Clause 12), which accounts for the influence of pitch line velocity;
v
Z is the work hardening factor (see Clause 13), which accounts for the effect of meshing with a
W
surface hardened or similarly h
...
NORME ISO
INTERNATIONALE 6336-2
Deuxième édition
2006-09-01
Version corrigée
2007-04-01
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 (piqûre)
Calculation of load capacity of spur and helical gears —
Part 2: Calculation of surface durability (pitting)
Numéro de référence
ISO 6336-2:2006(F)
©
ISO 2006
---------------------- Page: 1 ----------------------
ISO 6336-2:2006(F)
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ii © ISO 2006 – Tous droits réservés
---------------------- Page: 2 ----------------------
ISO 6336-2:2006(F)
Sommaire Page
Avant-propos. iv
Introduction . v
1 Domaine d'application. 1
2 Références normatives . 1
3 Termes, définitions, symboles et termes abrégés . 2
4 Détérioration par piqûres et coefficients de sécurité . 2
5 Formules de base . 3
5.1 Généralités . 3
5.2 Coefficient de sécurité pour la résistance à la pression superficielle (contre la formation
de piqûres), S . 3
H
5.3 Pression de contact, σ . 4
H
5.4 Pression de contact admissible, σ . 5
HP
6 Facteur géométrique, Z , et facteurs de contact unique, Z et Z . 9
H B D
6.1 Facteur géométrique, Z . 9
H
6.2 Facteurs de contact unique, Z et Z , pour ε u 2. 10
B D α
6.3 Facteurs de contact unique, Z et Z , pour ε > 2 . 12
B D α
7 Facteur d'élasticité, Z . 12
E
8 Facteur de rapport de conduite, Z . 13
ε
8.1 Détermination du facteur de rapport de conduite, Z . 13
ε
8.2 Calcul du rapport de conduite apparent ε et du rapport de recouvrement ε . 15
α β
9 Facteur d'angle d'hélice, Z . 16
β
10 Résistance pour la pression de contact. 17
10.1 Contraintes nominales de référence (pression de contact), σ , pour la Méthode B . 17
H lim
10.2 Valeurs de contrainte nominale de référence pour la méthode B . 17
R
11 Facteur de durée de vie, Z (pour les flancs). 17
NT
11.1 Facteur de durée de vie, Z : Méthode A . 18
NT
11.2 Facteur de durée de vie, Z : Méthode B . 18
NT
12 Influences du film lubrifiant, facteurs Z , Z et Z . 19
L v R
12.1 Généralités . 19
12.2 Influence du film lubrifiant: Méthode A . 20
12.3 Influence du film lubrifiant, facteurs Z , Z et Z : Méthode B. 20
L v R
13 Facteur d'écrouissage, Z . 25
W
13.1 Facteur d'écrouissage, Z : Méthode A . 25
W
13.2 Facteur d'écrouissage, Z : Méthode B . 26
W
14 Facteur de dimension, Z . 29
X
Annexe A (informative) Début de développante. 30
Bibliographie . 33
© ISO 2006 – Tous droits réservés iii
---------------------- Page: 3 ----------------------
ISO 6336-2:2006(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 Normes internationales sont rédigées conformément aux règles données dans les Directives ISO/CEI,
Partie 2.
La tâche principale des comités techniques est d'élaborer les Normes internationales. 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.
L'attention est appelée sur le fait que certains des éléments du présent document 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 6336-2 a été élaborée par le comité technique ISO/TC 60, Engrenages, sous-comité SC 2, Calcul de la
capacité des engrenages.
Cette deuxième édition annule et remplace la première édition (ISO 6336-2:1996), dont l'Article 13 a fait l'objet
d'une révision technique. Elle incorpore également les Rectificatifs techniques ISO 6336-2:1996/Cor.1:1998 et
ISO 6336-2:1996/Cor.2:1999.
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 facteur généraux d'influence
⎯ Partie 2: Calcul de la résistance à la pression de contact (piqûre)
⎯ Partie 3: Calcul de la résistance à la flexion en pied de dent
⎯ Partie 5: Résistance et qualité des matériaux
⎯ Partie 6: Calcul de la durée de vie en service sous charge variable
Cette version corrigée a été modifiée sur les points suivants:
⎯ l’Équation (46) a été corrigée;
⎯ le paragraphe 12.3.1.3.2 a été réécrit de sorte à faire référence à la rugosité de surface.
iv © ISO 2006 – Tous droits réservés
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ISO 6336-2:2006(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 qu'ils soient
directement inclus dans les calculs de la capacité de charge, toutefois ces derniers sont pris en compte dans
une certaine mesure dans les facteurs 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
issues des essais de fatigue sur les 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 2006 – Tous droits réservés v
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NORME INTERNATIONALE ISO 6336-2:2006(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 (piqûre)
IMPORTANT — L'utilisateur de la présente partie de l'ISO 6336 est mis en garde que, lorsqu'il utilise la
méthode spécifiée pour des grands angles d'hélice et des grands angles de pression importants, il
convient que les résultats calculés soient confirmés par l'expérience ainsi que par la Méthode A. De
plus, il est important de noter que la meilleure corrélation est obtenue pour les engrenages
hélicoïdaux quand une grande exactitude et des modifications optimales sont utilisées.
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 extérieure ou intérieure 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. La présente partie de l'ISO 6336
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 combinées à d'autres
crémaillères de référence dont le rapport de conduite apparent virtuel est inférieur à ε = 2,5. Les résultats
αn
sont en concordance avec ceux obtenus par d'autres méthodes pour la plage indiquée dans le domaine
d'application de l'ISO 6336-1.
Ces formules ne peuvent être directement appliquées pour l'évaluation des types de détérioration de surface
de dentures d'engrenage tels que la déformation plastique, les griffures, le grippage ou toute autre que celle
décrite à l'Article 4.
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 superficielle».
2 Références normatives
Les documents de référence suivants sont indispensables pour l'application du présent document. Pour les
références datées, seule l'édition citée s'applique. Pour les références non datées, la dernière édition du
document de référence s'applique (y compris les éventuels amendements).
ISO 53:1998, Engrenages cylindriques de mécanique générale et de grosse mécanique — Crémaillère de
référence
ISO 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques
ISO 6336-1:2006, 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 6336-5:2003, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et
hélicoïdale — Partie 5: Résistance et qualité des matériaux
© ISO 2006 – Tous droits réservés 1
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ISO 6336-2:2006(F)
3 Termes, définitions, symboles et termes abrégés
Pour les besoins du présent document, les termes, les définitions, les symboles et les termes abrégés donnés
dans l'ISO 1122-1 et dans l’ISO 6336-1 s'appliquent.
4 Détérioration 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
piqûres nombreuses peuvent être admises; dans d'autres domaines, toute formation de piqûres conséquente
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.
La formation de piqûres augmentant de manière linéaire ou progressive avec le temps dans des conditions de
service non modifiées (piqûres linéaires ou évolutives) n'est pas acceptable. 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 l'état des flancs au moins trois
6
fois. Il est toutefois 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
10 11
durée de vie (10 à 10 cycles) que l'on exige de ces engrenages, aucune piqûre ni aucune usure
anormalement importante 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 ans
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.
2 © ISO 2006 – Tous droits réservés
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ISO 6336-2:2006(F)
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 dans l'ISO 6336-1:2006, 4.1.7. Il est
H
recommandé que le fabricant et le client conviennent des valeurs du coefficient de sécurité minimal.
5 Formules de base
5.1 Généralités
Le calcul de la résistance à la pression de contact est basé sur la pression de contact, σ , au point primitif ou
H
au point le plus bas de contact unique. La plus grande des deux valeurs obtenues est utilisée pour déterminer
la capacité de charge (déterminant). σ et la pression de contact admissible, σ , doivent être calculées
H HP
séparément pour le pignon et la roue. σ doit être inférieur à σ . Cette comparaison est exprimée en
H HP
coefficients de sécurité S et S qui doivent être supérieurs au coefficient de sécurité minimal convenu,
H1 H2
s . Les quatre catégories suivantes sont reconnues dans le calcul de σ :
H min H
a) Engrenages cylindriques à denture droite avec rapport de conduite ε W 1:
α
⎯ pour un pignon, σ est habituellement calculée au point le plus bas de contact unique; dans les cas
H
particuliers, σ est supérieure au point primitif et donc dimensionnante;
H
⎯ pour une roue, dans le cas d'une denture extérieure, σ est habituellement calculée au point primitif,
H
néanmoins, dans les cas particuliers — plus particulièrement pour des rapports de transmission peu
importants (voir 6.2) — σ est supérieure au point le plus bas de contact unique de la roue et est
H
donc dimensionnante. Pour une denture intérieure, σ est toujours calculée au point primitif.
H
b) Engrenage à denture hélicoïdale avec rapport de conduite ε W 1 et rapport de recouvrement ε W 1: σ
α β H
est toujours calculée au point primitif pour le pignon et la roue.
c) Engrenage à denture hélicoïdale avec rapport de conduite ε W 1 et rapport de recouvrement ε < 1: σ
α β H
est déterminée par interpolation linéaire entre les deux valeurs limites, c'est-à-dire σ pour les
H
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 réels.
H
d) Engrenage à denture hélicoïdale avec ε u 1 et ε > 1: n'est pas couvert par l’ISO 6336 — il est
α γ
nécessaire de procéder à une analyse attentive de la pression de contact le long de la ligne de conduite.
5.2 Coefficient de sécurité pour la résistance à la pression superficielle (contre la formation
de piqûres), S
H
Calculer S séparément pour le pignon et la roue:
H
σ
HG1
=> (1)
SS
H min
H1
σ
H1
σ
HG2
=> (2)
SS
H2 H min
σ
H2
Prendre σ conformément à l'Équation (4) pour le pignon et conformément à l'Équation (5) pour la roue
H1,2
(voir 5.1). Calculer σ pour les limites de grande durée de vie et de contrainte statique conformément à
HG
l'Équation (6) et à 5.4.2 a) et b). Pour la durée de vie limitée, σ est conforme à l'Équation (6) et à 5.4.3.
HG
NOTE Ceci est le coefficient de sécurité calculé par rapport à la pression de contact (pression de Hertz). Le facteur
correspondant relatif à la capacité de charge en couple est égal au carré de la valeur de S .
H
© ISO 2006 – Tous droits réservés 3
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ISO 6336-2:2006(F)
Pour les notes relatives au coefficient de sécurité minimal et à la probabilité de rupture, voir l'Article 4 et
l'ISO 6336-1:2006, 4.1.7.
5.3 Pression de contact, σ
H
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 les Équations (4) et (5) un
facteur de distribution K suite à K , afin d'adapter la force tangentielle moyenne par contact si nécessaire.
γ A
u+ 1
F
t
= (3)
σ ZZ Z Z
H0 HEεβ
db u
1
= (4)
σσZKKKK
BAvHβHα
H1 H0
= (5)
σσZKKKK
H2DAH0 vHβHα
où
σ est la pression de contact de base au point primitif, qui 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 6.2 et 6.3), qui convertit la pression de contact au
B
point primitif en pression de contact au point le plus bas de contact unique sur le pignon;
Z est le facteur de contact unique de la roue (voir 6.2), qui convertit la pression de contact au point
D
primitif en pression de contact au point le plus bas de contact unique de la roue;
K est le facteur d'application (voir l'ISO 6336-6), qui prend en compte l'accroissement des forces dû à
A
des variations d'influence extérieure du couple d'entrée ou de sortie;
K est le facteur dynamique (voir l'ISO 6336-1), qui prend en compte les accroissements de forces
v
dus aux effets dynamiques internes;
K est le facteur de distribution longitudinale de la charge pour la pression de contact (voir
Hβ
l'ISO 6336-1), qui 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
Hα
l'ISO 6336-1), qui prend en compte la distribution non uniforme de la charge dans le sens
1)
transversal suite, par exemple, à un écart de pas ;
σ est la pression de contact admissible (voir 5.4);
HP
Z est le facteur géométrique (voir l'Article 6). Il prend en compte les courbures de flanc au point
H
primitif et 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 l'Article 7). Il prend en compte les propriétés spécifiques du matériau,
E
les modules d'élasticité E , E et les coefficients de Poisson ν , ν ;
1 2 1 2
1) Voir l'ISO 6336-1:2006, 4.1.14, pour l'ordre de calcul des facteurs K , K , K , K .
A v Hβ Hα
4 © ISO 2006 – Tous droits réservés
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ISO 6336-2:2006(F)
Z est le facteur de rapport de conduite (voir l'Article 8). Il prend en compte l'influence de la longueur
ε
effective des lignes de contact;
Z est le facteur d'angle d'hélice (voir l'Article 9). Il prend en compte les influences de l'angle d'hélice,
β
telles que la variation de la force le long des lignes de contact;
F est la force tangentielle nominale, la force transversale tangentielle au cylindre de référence (voir
t
les exigences pertinentes ci-après);
b est la largeur de denture (pour un engrenage à denture en chevron b = 2 b ) (voir les exigences
B
pertinentes ci-après);
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
2 1
les engrenages à denture intérieure, u est négatif.
La force tangentielle totale par engrènement doit être introduite pour F dans tous les cas (même avec ε > 2).
t αn
Voir l'ISO 6336-1:2006, 4.2, pour la définition de F et les commentaires relatifs aux caractéristiques
t
particulières d'un engrenage à denture en chevron. La valeur b des 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'engrenage durcis superficiellement ni les zones de transition ne
doivent être incluses
5.4 Pression de contact admissible, σ
HP
Il convient que les valeurs limites des pressions de contact (voir l'Article 10) 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.
5.4.1 Détermination de la pression de contact admissible, σ — Principes, hypothèses et
HP
application
Plusieurs méthodes sont admises pour le calcul de la pression de contact admissible. La méthode adoptée
doit être validée en réalisant des études comparatives attentives des historiques de service bien documentés
d'un grand nombre d'engrenages.
5.4.1.1 Méthode A
Dans la méthode A, la pression de contact admissible σ (ou la limite de pression de piqûre, σ ) pour la
HP HG
contrainte de référence, les longues durées de vie, les durées de vie limitées et les contraintes statiques est
calculée à l'aide de l'Équation (4) ou (5) à partir de la courbe S-N ou courbe de détérioration 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 admissible peuvent être issues de la prise en considération des
dimensions, des conditions de service et de 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
...
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