ISO 9085:2002
(Main)Calculation of load capacity of spur and helical gears - Application for industrial gears
Calculation of load capacity of spur and helical gears - Application for industrial gears
The formulae specified in this International Standard are intended to establish a uniformly acceptable method for calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth. The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth finished by forging or sintering. It is not applicable to gears which have a poor contact pattern. This International Standard provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. Neither is it intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. CAUTION - The user is cautioned that the calculated results of this International Standard should be confirmed by experience.
Calcul de la capacité de charge des engrenages à denture droite et hélicoïdale — Application aux engrenages industriels
Les formules spécifiées dans la présente Norme internationale sont destinées à établir une méthode uniformément acceptable pour calculer la résistance à la formation de piqûres et la résistance à la flexion des engrenages industriels à dentures droite ou hélicoïdale. Les formules de capacité de charge de la présente Norme internationale ne sont pas applicables à d'autres types de détérioration de la denture des engrenages comme par exemple la déformation plastique, la formation de micropiqûres, le grippage, l'effondrement de la couche cémentée, l'adhésion et l'usure et elles ne sont pas applicables dans des conditions de vibrations qui risquent d'entraîner une rupture imprévisible du profil. Les formules de résistance à la flexion s'appliquent aux ruptures au niveau du profil de raccordement, mais elles ne s'appliquent pas aux ruptures sur le profil actif des dents, aux ruptures de la jante, ou aux ruptures du corps de roue au travers du voile et du moyeu. La présente Norme internationale ne s'applique pas aux dents finies par forgeage ou frittage. Elle ne s'applique pas aux engrenages qui ont une marque de portée médiocre. La présente Norme internationale fournit une méthode permettant de comparer différentes conceptions d'engrenages. Elle n'est pas destinée à assurer la performance des systèmes de transmission de puissance pour engrenage. Elle n'est pas non plus destinée à l'utilisation par des concepteurs de mécanique générale. Par contre, elle est destinée aux concepteurs d'engrenages expérimentés qui sont capables de sélectionner des valeurs raisonnables pour les facteurs figurant dans ces formules en se fondant sur leurs connaissances de conception similaires et leur compréhension des effets des sujets discutés. AVERTISSEMENT — L'utilisateur est mis en garde qu'il convient de confirmer par expérience les résultats calculés à partir de la présente Norme internationale.
Izračun nosilnosti ravnozobih in poševnozobih zobnikov - Uporaba za industrijska gonila
General Information
Overview
ISO 9085:2002 - Calculation of load capacity of spur and helical gears (application for industrial gears) specifies a uniform method to calculate pitting resistance and tooth bending strength for industrial spur and helical gears. It defines rating formulae and influence factors to enable comparison of gear designs, but it does not guarantee assembled drive-system performance. The standard is intended for experienced gear designers and requires confirmation of calculated results by field experience.
Key topics and requirements
- Scope and limitations: Applies to industrial gears with spur or helical teeth. Excludes failures such as plastic yielding, micropitting, scuffing, case crushing, welding, wear, rim or blank failures, vibratory conditions, forged/sintered tooth finishes and gears with a poor contact pattern.
- Primary calculations: Methods for evaluating surface durability (pitting) and tooth bending strength using established rating formulae.
- Influence factors covered in detail:
- Nominal and maximum tangential load, torque and power
- Application factor, internal dynamic factor and various face/ transverse load factors
- Helix-angle, contact-ratio and elasticity factors
- Life factors, work-hardening and lubrication-film influences
- Size, form and relative notch sensitivity factors for bending strength
- Safety and life assessment: Minimum safety factors for pitting and tooth breakage and guidance on selecting appropriate factor values.
- Normative and informative annexes: Includes normative guidance for less common gear designs and tooth stiffness parameters, plus informative guides on application factor values and crowning/end-relief.
- Intended user competency: Assumes user familiarity with ISO 6336 series and ISO 6336-5 for allowable stresses and material requirements.
Practical applications
- Use ISO 9085:2002 for:
- Comparing alternative gear geometries and materials during design iterations
- Evaluating gear load capacity, pitting risk, and tooth-root strength for industrial gearboxes
- Specifying design margins for heavy machinery, conveyors, reducers and similar industrial drives
- Not appropriate for predicting all in-service failures or for novice users without gear-design experience.
Who should use this standard
- Experienced gear designers and mechanical engineers
- Gear manufacturers and quality engineers
- Consultants performing gear rating and design validation
- Test labs verifying calculated capacities against empirical performance
Related standards (for context)
- ISO 6336 parts 1–3 (basic principles, pitting, bending)
- ISO 6336-5 (materials and allowable stresses)
- ISO 9084 (high speed gears) and ISO/TR 10495 (service life under variable loads)
Keywords: ISO 9085:2002, gear load capacity, spur gears, helical gears, pitting resistance, tooth bending strength, industrial gears, gear design, gear rating formulae.
Standards Content (Sample)
SLOVENSKI STANDARD
01-december-2002
,]UDþXQQRVLOQRVWLUDYQR]RELKLQSRãHYQR]RELK]REQLNRY8SRUDED]DLQGXVWULMVND
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Calculation of load capacity of spur and helical gears -- Application for industrial gears
Calcul de la capacité de charge des engrenages à denture droite et hélicoïdale --
Application aux engrenages industriels
Ta slovenski standard je istoveten z: ISO 9085:2002
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 9085
First edition
2002-02-01
Calculation of load capacity of spur and
helical gears — Application for industrial
gears
Calcul de la capacité de charge des engrenages à denture droite et
hélicoïdale — Application aux engrenages industriels
Reference number
©
ISO 2002
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ii © ISO 2002 – All rights reserved
Contents Page
Foreword.v
Introduction.vi
1 Scope .1
2 Normative references.1
3 Terms and definitions .2
4 Application .8
4.1 Design, specific applications .8
4.2 Safety factors .10
4.3 Input data.11
4.4 Face widths .11
4.5 Numerical equations .12
5 Influence factors .12
5.1 General.12
5.2 Nominal tangential load, F , nominal torque, T, nominal power, P .12
t
5.3 Non-uniform load, non-uniform torque, non-uniform power .12
5.4 Maximum tangential load, F , maximum torque, T , maximum power, P .13
t max max max
5.5 Application factor, K .13
A
5.6 Internal Dynamic Factor, K .13
v
5.7 Face load factor, K .17
H
β
5.8 Face load factor, K .23
F
β
5.9 Transverse load factors, K , K .24
Hα Fα
6 Calculation of surface durability (pitting) .26
6.1 Basic formulae .26
6.2 Single pair tooth contact factors, Z , Z .28
B D
6.3 Zone factor, Z .29
H
6.4 Elasticity factor, Z .30
E
6.5 Contact ratio factor, Z .30
ε
6.6 Helix angle factor, Z .31
β
6.7 Allowable stress numbers (contact), σ .31
H lim
6.8 Life factor, Z .32
NT
6.9 Influences on lubrication film formation, Z , Z and Z .32
L v R
6.10 Work hardening factor, Z .33
W
6.11 Size factor, Z .34
X
6.12 Minimum safety factor (pitting), S .34
H min
7 Calculation of tooth bending strength .34
7.1 Basic formulae .34
7.2 Form factor, Y , and stress correction factor, Y .36
F S
7.3 Helix angle factor, Y .40
β
7.4 Tooth-root reference strength, σ .40
FE
7.5 Life Factor, Y .41
NT
7.6 Relative notch sensitivity factor, Y .41
δ rel T
7.7 Relative surface factor, Y .43
R rel T
7.8 Size factor, Y .44
X
7.9 Minimum safety factor (tooth breakage), S .44
F min
Annex A (normative) Special features of less common gear designs .45
Annex B (normative) Tooth stiffness parameters c¢¢¢¢ and c .48
γ
Annex C (informative) Guide values for application factor, K .51
A
Annex D (informative) Guide values for crowning and end relief of teeth of cylindrical gears .54
Bibliography .57
iv © ISO 2002 – All rights reserved
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 3.
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 International Standard may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 9085 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2,
Gear capacity calculation.
Annexes A and B form a normative part of this International Standard. Annexes C and D are for information only.
Introduction
Procedures for the calculation of the load capacity of general spur and helical gears with respect to pitting and
bending strength appear in ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. This International Standard is
derived from ISO 6336-1, ISO 6336-2 and ISO 6336-3 by the use of specific methods and assumptions which are
considered to be applicable to industrial gears. Its application requires the use of allowable stresses and material
requirements which are to be found in ISO 6336-5.
vi © ISO 2002 – All rights reserved
INTERNATIONAL STANDARD ISO 9085:2002(E)
Calculation of load capacity of spur and helical gears —
Application for industrial gears
1 Scope
The formulae specified in this International Standard are intended to establish a uniformly acceptable method for
calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth.
The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such
as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory
conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable
to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the
gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth
finished by forging or sintering. It is not applicable to gears which have a poor contact pattern.
This International Standard provides a method by which different gear designs can be compared. It is not intended
to assure the performance of assembled drive gear systems. Neither is it intended for use by the general
engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting
reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the
effects of the items discussed.
CAUTION — The user is cautioned that the calculated results of this International Standard should be
confirmed by experience.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this International Standard. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this International Standard are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 54:1996, Cylindrical gears for general and heavy engineering — Modules
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
1)
deviations relevant to corresponding flanks of gear teeth
ISO 4287:1997, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Terms, definitions
and surface texture parameters
1) This was corrected and reprinted in 1997.
ISO 6336-1:1996, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors
ISO 6336-2:1996, Calculation of load capacity of spur and helical gears — Part 2: Calculation of surface durability
(pitting)
ISO 6336-3:1996, Calculation of load capacity of spur and helical gears — Part 3: Calculation of tooth bending
strength
ISO 6336-5:1996, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials
ISO 9084:2000, Calculation of load capacity of spur and helical gears — Application to high speed gears and gears
of similar requirements
ISO/TR 10495:1997, Cylindrical gears — Calculation of service life under variable loads — Conditions for
cylindrical gears accordance with ISO 6336
ISO/TR 13593:1999, Enclosed gear drives for industrial applications
3 Terms and definitions
For the purposes of this International Standard, the terms and definitions given in ISO 1122-1 apply. For the
symbols, see Table 1.
2 © ISO 2002 – All rights reserved
Table 1 — Symbols and abbreviations used in this International Standard
Symbol Description or term Unit
a
a mm
centre distance
b facewidth mm
b
facewidth of an individual helix of a double helical gear mm
B
b
facewidth (pitting) mm
H
b
facewidth (tooth root) mm
F
b
reduced facewidth (facewidth minus end reliefs) mm
red
b
web thickness mm
s
b
length of end relief mm
I(II)
c
mean value of mesh stiffness per unit facewidth N/(mm׵m)
γ
N/(mm׵m)
c′ maximum tooth stiffness of one pair of teeth per unit facewidth (single stiffness)
d
tip diameter of pinion (or wheel) mm
a1,2
d
tip diameter of pinion (or wheel) of virtual spur gear mm
an1,2
d base diameter of pinion (or wheel) mm
b1,2
d
base diameter of pinion (or wheel) of virtual spur gear mm
bn1,2
d diameter of circle through outer point of single pair tooth contact of pinion, wheel of virtual mm
en1,2
spur gear
d root diameter of pinion, wheel mm
f1,2
d diameter at mid-tooth depth of pinion, wheel mm
m1,2
d reference diameter of pinion, wheel of virtual spur gear mm
n1,2
d
nominal shaft diameter for bending mm
sh
d internal diameter of hollow shaft mm
shi
d pitch diameter of pinion, wheel mm
w1,2
d diameter of a circle near the tooth-roots, containing the limits of the usable flanks of an mm
Nf2
internal gear or the larger external gear of a mating gear
d
reference diameter of pinion, wheel mm
1,2
f effective profile form deviation µm
f eff
f profile form deviation (the value for the total profile deviation F may be used alternatively for
µm
fα a
this, if tolerances complying with ISO 1328-1 are used)
f helix deviation due to manufacturing inaccuracies µm
ma
f transverse base pitch deviation (the values of f may be used for calculations in accordance µm
pb pt
with ISO 6336:1996, using tolerances complying with ISO 1328-1)
f effective transverse base pitch deviation µm
pb eff
f helix deviation due to elastic deflections µm
sh
f tooth alignment deviation (not including helix form deviation) µm
Hβ
g path length of contact mm
α
h tooth depth mm
Table 1 (continued)
Symbol Description or term Unit
h addendum mm
a
h
tool addendum mm
a0
h dedendum of tooth of an internal gear mm
f2
h dedendum of basic rack of cylindrical gears mm
fP
h
bending moment arm for load application at the outer point of single pair tooth contact mm
Fe
h dedendum of tooth of an internal gear, containing the limits of the usable flanks of an internal mm
Nf2
gear or the larger external gear of a mating gear
l bearing span mm
m normal module mm
n
m reduced gear pair mass per unit facewidth referenced to the line of action kg/mm
red
−1
n resonance speed
min
E
−1
n rotation speed of pinion, wheel
min
1,2
p normal base pitch mm
bn
p transverse base pitch mm
bt
pr protuberance of the tool mm
q finishing stock allowance mm
q
notch parameter s / 2ρ —
s
Fn F
q notch parameter of standard reference test gear —
sT
r base radius mm
b
s pinion offset from shaft centre line mm
s tooth-root chord at the critical section mm
Fn
s rim thickness mm
R
s residual fillet undercut mm
pr
a
u —
gear ratio | u | = | z /z | W 1
2 1
v m/s
circumferential speed (without subscript: at reference circle ª circumferential speed at
working pitch circle)
x profile shift coefficient of pinion, wheel —
1,2
y running-in allowance (pitch deviation) µm
f
y running-in allowance (profile deviation) µm
p
y running-in allowance for a gear pair µm
α
y running-in allowance (equivalent misalignment) µm
β
z
virtual number of teeth of a helical gear —
n
a
z number of teeth of pinion, wheel —
1,2
B
total facewidth of a double helical gear including the gap mm
B running-in parameter for determination of constant K —
f
B running-in parameter for determination of constant K
—
k
4 © ISO 2002 – All rights reserved
Table 1 (continued)
Symbol Description or term Unit
B running-in parameter for determination of constant K —
p
B constants for determination of F
—
1,2 βx
*
B constant for determination of the pinion offset —
C
tip relief µm
a
C tip relief resulting from running-in µm
ay
C constants for determination of constant K —
v1,2,3
C
basic rack factor —
B
C gear blank factor —
R
C crowning height µm
β
C constants for determination of q
—
1.9 s
E modulus of elasticity, Young's modulus N/mm
E auxiliary value for calculation of Y —
F
F N
mean transverse force at the reference cylinder (= F K K )
m
t A v
F (nominal) transverse tangential force at reference cylinder N
t
F maximum transverse tangential force at reference cylinder N
t max
F
determinant transverse force at the reference cylinder (= F K K K ) N
tH
t A v Hβ
F total helix deviation µm
β
F
initial equivalent misalignment (before running-in) µm
βx
G auxiliary value for calculation of Y —
F
H auxiliary value for calculation of Y —
F
*
J polar moment of inertia per unit face width Kg/mm
1,2
K constant for determination of K —
v
K dynamic factor —
v
K application factor —
A
K transverse load factor (root stress) —
Fα
K face load factor (root stress) —
Fβ
K transverse load factor (contact stress) —
Hα
K
face load factor (contact stress) —
Hβ
K mesh load factor (takes into account the uneven distribution of the load between meshes for —
g
multiple transmission paths)
K constant —
1,2
K′ constant for the pinion offset in relation to the torqued end —
L tooth root chord at the critical section, related to the bending moment arm relevant to load —
application at the outer point of single pair tooth contact
N resonance ratio —
N exponent —
F
Table 1 (continued)
Symbol Description or term Unit
N number of load cycles —
L
N
resonance ratio in the main resonance range —
S
M auxiliary values for the determination of Z —
1,2 B,D
P transmitted power kW
P maximum transmitted power kW
max
Ra arithmetic mean roughness value (as specified in ISO 4287:1997) µm
Rz mean peak-to-valley roughness (as specified in ISO 4287:1997) µm
Rz mean peak-to-valley roughness for the gear pair µm
S safety factor from tooth breakage —
F
S
minimum safety factor (tooth breakage) —
F min
S safety factor from pitting —
H
S minimum safety factor (pitting) —
H min
T pinion torque (nominal); wheel torque Nm
1,2
T maximum torque Nm
max
Y tooth form factor —
F
Y life factor for tooth-root stress —
N
Y life factor for tooth-root stress for reference test conditions —
NT
Y
surface factor —
R rel T
Y stress correction factor —
S
Y size factor (tooth root) —
X
Y
helix angle factor (tooth root) —
β
Y relative notch sensitivity factor —
δ rel T
Y contact ratio factor (tooth root) —
ε
Z
speed factor —
v
Z single pair tooth contact factors for the pinion, wheel —
B,D
Z elasticity factor
E 2
Nmm
Z
zone factor —
H
Z lubricant factor —
L
Z life factor for contact stress —
N
Z
life factor for contact stress for reference test conditions —
NT
Z roughness factor affecting surface durability —
R
Z work-hardening factor —
W
Z
size factor (pitting) —
X
Z helix angle factor (pitting) —
β
Z contact ratio factor (pitting) —
ε
6 © ISO 2002 – All rights reserved
Table 1 (continued)
Symbol Description or term Unit
α pressure angle at the outer point of single pair tooth contact of virtual spur gears °
en
normal pressure angle °
α
n
α transverse pressure angle °
t
α transverse pressure angle at the pitch cylinder °
wt
load direction angle, relevant to direction of application of load at the outer single pair tooth °
α
Fen
contact of virtual spur gears
α normal pressure angle of the basic rack for cylindrical gears °
Pn
helix angle at the reference cylinder °
β
β base helix angle °
b
°
g auxiliary angle for determination of α
e Fen
combined deflection of mating teeth assuming even load distribution over the facewidth µm
d
bth
ε transverse contact ratio —
α
transverse contact ratio of a virtual spur gear —
ε
αn
ε axial overlap ratio —
β
ε total contact ratio (ε = ε + ε ) —
g g α β
ν Poisson's contact ratio —
auxiliary value for calculation of Y —
θ
F
tip radius of the tool mm
ρ
a0
root fillet radius of the basic rack for cylindrical gears mm
ρ
fP
ρ radius of relative curvature mm
rel
ρ tooth-root fillet radius at the critical section mm
F
slip-layer thickness mm
ρ′
s tensile strength N/mm
B
tooth-root stress N/mm
s
F
s nominal stress number (bending) N/mm
F lim
s allowable stress number (bending) = σ Y N/mm
FE F lim ST
tooth-root stress limit N/mm
s
FG
s permissible tooth-root stress N/mm
FP
s nominal tooth-root stress N/mm
F0
calculated contact stress N/mm
s
H
s allowable stress number (contact) N/mm
H lim
s modified allowable stress number = σ S N/mm
HG HP H min
permissible contact stress N/mm
s
HP
s nominal contact stress N/mm
H0
Table 1 (continued)
Symbol Description or term Unit
s yield point N/mm
S
0,2 % proof stress N/mm
s
0,2
* −1
χ relative stress gradient in the root of a notch mm
* −1
relative stress gradient in a smooth polished test piece
χ mm
p
* −1
χ relative stress gradient in the root of the standard reference test gear mm
T
ω angular velocity of pinion, wheel rad/s
1,2
a
For external gear pairs, a, u, z and z are positive; for internal gear pairs, a, u and z are negative, and z positive.
1 2 2 1
4 Application
4.1 Design, specific applications
4.1.1 General
Gear designers must recognize that requirements for different applications vary considerably. Use of the
procedures of this International Standard for specific applications demands a careful appraisal of all applicable
considerations, in particular:
the allowable stress of the material and the number of load repetitions;
the consequences of any percentage of failure (failure rate);
the appropriate factor of safety.
Design considerations to prevent fractures emanating from stress raisers in the tooth flank, tip chipping and failures
of the gear blank through the web or hub should be analysed by general machine design methods.
Any variances according to the following shall be reported in the calculation statement.
a) If a more refined method of calculation is desired or if compliance with the restrictions given in 4.1 is for any
reason impractical, relevant factors may be evaluated according to the basic standard or another application
standard.
b) Factors derived from reliable experience or test data may be used instead of individual factors according to this
International Standard. Concerning this, the criteria for Method A in 4.1.8.1 of ISO 6336-1:1996 are applicable.
In other respects, rating calculations shall be strictly in accordance with this International Standard wherever
stresses, safety factors etc. are to be classified as being in accordance with this International Standard.
This International Standard recognizes the following types of industrial drive design.
Catalogue enclosed drives are designed to nominal load ratings for sale from catalogues or from stock. The
actual loads and operation conditions are not exactly known at the time of design.
NOTE The actual loads for each application are evaluated to select an appropriately sized unit from the catalogue. A
selection factor, based on experience with similar applications, is often used to reduce the catalogue rating to match the
application conditions (see ISO TR 13593).
Custom designed drives are aimed at a specific application where the operating conditions are known or
specified at the time of design.
8 © ISO 2002 – All rights reserved
This International Standard is applicable when the wheel blank, shaft/hub connections, shafts, bearings, housings,
threaded connections, foundations and couplings conform to the requirements regarding accuracy, load capacity
and stiffness which form the basis for the calculation of the load capacity of gears.
Although the method described in this International Standard is mainly intended for recalculation purposes, by
means of iteration it can also be used to determine the load capacities of gears. The iteration is accomplished by
selecting a load and calculating the corresponding safety factor against pitting, S , for the pinion. If S is greater
H1 H1
than S , the load is increased; if it is smaller than S , the load is reduced. This is done until the chosen load
H min H min
corresponds to S = S . The same method is used for the wheel (S = S ), and also for the safety factors
H1 H min H2 H min
against tooth breakage, S = S = S .
F1 F2 F min
4.1.2 Gear data
This International Standard is applicable within the following constraints.
a) Types of gear:
external and internal, involute spur, helical and double helical gears;
for double helical gears, it is assumed that the total tangential load is evenly distributed between the two
helices; if this is not the case (e.g. due to externally applied axial forces), this shall be taken into account;
the two helices are treated as two single helical gears in parallel.
b) Range of speeds:
2)
−1
n less than or equal to 3 600 min (synchronous speed of two-pole motor at 60 Hz current frequency) ;
subcritical range of speed (see K in 5.6);
v
at speeds of v < 1 m/s, gear load capacity is often limited by wear.
c) Gear accuracy:
accuracy grade 10 or better according to ISO 1328-1 (affects K , K and K ).
v Hα Hβ
d) Range of the transverse contact ratios of virtual spur gear pairs:
1,2 < ε < 1,9 (affects c′, c , K , K , K , K and K ).
α γ v Hβ Fα Hα Fβ
e) Range of helix angles:
β less than or equal to 30° (affects c′, c , K and K ).
γ v Hβ
4.1.3 Pinion and pinion shaft
This International Standard is applicable to pinions integral with shafts or bored pinions with s /d W 0,2 (this affects
R 1
c′, c , K , K ). It is assumed that the bored pinions will be mounted on solid shafts or on hollow shafts with
g v Hβ
d /d < 0,5 (this affects K ).
shi sh Hβ
4.1.4 Wheel blank, wheel rim
The given formulae are valid for spur and helical gears with a minimum rim thickness under the root of s W 3,5 m .
R n
The calculation of K assumes that wheel and wheel shaft are sufficiently stiff such that their deflections can be
Hβ
ignored.
2) For higher speeds, the requirements of ISO 6336 or ISO 9084 apply.
4.1.5 Materials
These include steels, nodular cast iron and grey cast iron (this affects Z , σ , σ , K , K , K , K and K ).
E H lim FE v Hβ Fβ Hα Fα
For materials and their abbreviations used in this International Standard, see Table 2.
Table 2 — Materials
Material Abbreviation
St
Steel (σ < 800 N/mm )
B
St (cast)
Cast steel, alloy or carbon, (σ W 800 N/mm )
B
V
Through-hardening steel, alloy or carbon, through hardened (σ W 800 N/mm )
B
Grey cast iron GG
Nodular cast iron (pearlitic, bainitic, ferritic structure) GGG (perl., bai., ferr.)
Black malleable cast iron (pearlitic structure) GTS (perl.)
Case-hardened steel, case hardened Eh
Steel and GGG, flame or induction hardened IF
Nitriding steel, nitrided NT (nitr.)
Through-hardening and case-hardening steel, nitrided NV (nitr.)
Through-hardening and case-hardening steel, nitrocarburized NV (nitrocar.)
4.1.6 Lubrication
The calculation procedures are valid for oil lubricated gears having sufficient lubricant of suitable viscosity at the
gear mesh and when the working temperature is also suitable (this affects lubricant film formation, i.e. the factors
Z , Z and Z ).
L v R
4.2 Safety factors
It is necessary to distinguish between the safety factor relative to pitting, S , and the safety factor relative to tooth
H
breakage, S .
F
For a given application, adequate gear load capacity is demonstrated by the computed values of S and S being
H F
equal to or greater than the values S and S , respectively.
H min F min
Choice of the value of a safety factor should be based on the degree of confidence in the reliability of the available
data and the consequences of possible failures.
Important factors to be considered are
a) that the validity of the material values in ISO 6336-5 is for 1 % probability of damage,
b) the specified quality and the effectiveness of quality control at all stages of manufacture,
c) the accuracy of specification of the service duty and external conditions, and
d) that tooth breakage is often considered to be a greater hazard than pitting.
Therefore, the chosen value for S should be greater than the value chosen for S .
F min H min
10 © ISO 2002 – All rights reserved
For calculation of the actual safety factor, see 6.1.5 (S , pitting) and 7.1.4 (S , tooth breakage). For minimum safety
H F
factors see 6.12 (pitting) and 7.9 (tooth breakage). However, it is recommended that the minimum values of the
safety factors should be agreed upon between the purchaser and the manufacturer.
4.3 Input data
The following data shall be available for the calculations:
a) gear data:
a, z , z , m , d , d , d , b, b , b , x , x , α , β, ε , ε (see ISO 53, ISO 54) (see 4.4 for definition of b, b and
1 2 n 1 a1 a2 H F 1 2 n α β H
b face widths);
F
b) cutter basic rack tooth profile:
h , ρ ;
a0 a0
c) design and manufacturing data:
C , C , f , S , S , Ra , Ra , Rz , Rz ;
a1 a2 pb H min F min
1 2 1 2
materials, material hardnesses and heat treatment details; gear accuracy grades, bearing span l, positions of
gears relative to bearings; dimensions of pinion shaft d and, when applicable, helix modification (crowning,
sh
end relief);
d) power data:
P or T or F , n , v , details of driving and driven machines.
t 1 1
Requisite geometrical data can be calculated according to national standards.
Information to be exchanged between manufacturer and purchaser should include data specifying material
preferences, lubrication, safety factor and externally applied forces due to vibrations and overloads (application
factor).
4.4 Face widths
The following face widths have to be distinguished.
b: the smaller of the facewidths of pinion and wheel measured at the pitch circles (for a double helical gear
b = 2 b ). Chamfers or rounding of tooth ends are to be ignored. Where the facewidths are offset, the length
H B
of the face in contact shall be used.
b : the facewidth at the pitch cylinder of the gear (for a double helical gear b = 2 b ). When the facewidth b
H H B H
is larger than that of its mating gear, b shall be based on the smaller facewidth, ignoring any intentional
H
transverse chamfers or tooth-end rounding. Neither unhardened portions of surface-hardened gear tooth flanks
nor the transition zones shall be included. Where the facewidths are offset, the length of the face in contact
shall be used.
b : the facewidth at the root cylinder of the gear (for a double helical gear b = 2 b ). When the facewidth b is
F F B F
larger than that of its mating gear, b shall be based on the smaller facewidth plus a length, not exceeding one
F
module of any extension at each end. However, if it is foreseen that because of crowning or because end relief
contact does not extend to the end of face, then the smaller facewidth shall be used for both pinion and wheel.
Where the facewidths are offset, the length of the face in contact shall be used.
4.5 Numerical equations
The units listed in clause 3 shall be used in all calculations. Information which will facilitate the use of this
International Standard is provided in annex C of ISO 6336-1:1996.
5 Influence factors
5.1 General
The influence factors K , K , K , K and K are all dependent on the tooth load. Initially this is the applied load
v Hα Hβ Fα Fβ
(nominal tangential load multiplied by the application factor).
The factors are also interdependent and shall therefore be calculated successively as follows:
a) K with the applied tangential load F K
v t A;
b) K or K with the recalculated load F K K ;
Hβ Fβ t A v
c) K or K with the applied tangential load F K .
Hα Fα t A
When a gear drives two or more mating gears, it is necessary to substitute K by K K . If possible, the mesh load
A A γ
factor, K , should be determined by measurement; alternatively, its value may be estimated from the literature.
γ
5.2 Nominal tangential load, F , nominal torque, T, nominal power, P
t
The nominal tangential load, F , is determined in the transverse plane at the reference cylinder. It is based on the
t
input torque to the driven machine. This is the torque corresponding to the heaviest regular working condition.
Alternatively, the nominal torque of the prime mover can be used as a basis if it corresponds to the torque
requirement of the driven machine, or some other suitable basis can be chosen.
2 000 T
19 098 ¥ 1000 PP1000
1,2
F = = = (1)
t
v
ddn
1,2 1,2 1,2
Fd
1000 9PP549
t1,2
T = = = (2)
1, 2
2000 ω n
1, 2 1, 2
TT ω n
Fv
1, 2 1,2 1, 2 1, 2
t
P = = = (3)
1000 1000 9 549
ddω n
1, 2 1, 2 1, 2 1, 2
v = = (4)
2 000 19 098
πnn
2000 v
1, 2 1, 2
ω== = (5)
1, 2
30 d 9 549
1, 2
5.3 Non-uniform load, non-uniform torque, non-uniform power
When the transmitted load is not uniform, consideration should be given not only to the peak load and its
anticipated number of cycles, but also to intermediate loads and their numbers of cycles. This type of load is
classed as a duty cycle and may be represented by a load spectrum. In such cases, the cumulative fatigue effect of
the duty cycle is considered in rating the gear set. A method of calculating the effect of the loads under this
condition is given in ISO TR 10495.
12 © ISO 2002 – All rights reserved
5.4 Maximum tangential load, F , maximum torque, T , maximum power, P
t max max max
This is the maximum tangential load F , (or corresponding torque, T , corresponding power, P ) in the
t max max max
variable duty range. Its magnitude can be limited by a suitably responsive safety clutch. F , T and P shall
t max max max
be known when safety from pitting damage and from sudden tooth breakage due to loading corresponding to the
static stress limit is determined (see 5.5).
5.5 Application factor, K
A
5.5.1 General
The factor K adjusts the nominal load F , in order to compensate for incremental gear loads from external sources.
A t
These additional forces are largely dependent on the characteristics of the driving and driven machines, as well as
the masses and stiffness of the system, including shafts and couplings used in service.
It is recommended that the purchaser and manufacturer/designer agree on the value of the application factor.
5.5.2 Method A — Factor K
A-A
K is determined in this method by means of careful measurements and a comprehensive analysis of the system,
A
or on the basis of reliable operational experience in the field of application concerned (see 5.3).
5.5.3 Method B — Factor K
A-B
If no reliable data, obtained as described in 5.5.2, is available, or even as early as the first design phase, it is
possible to use the guideline values for K as described in annex C.
A
5.6 Internal Dynamic Factor, K
v
5.6.1 General
The dynamic factor relates the total tooth load, including internal dynamic effects of a “multi-resonance” system, to
the transmitted tangential tooth load.
Method B of ISO 6336-1:1996 with modifications is used in this International Standard. When agreed between
manufacturer and purchaser, or when determining the catalogue presentation of the capacities of catalogue
enclosed drives, Method E of ISO 6336-1:1996 may be used to estimate the dynamic factor.
In this procedure it is assumed that the gear pair consists of an elementary single mass and spring system
comprising the equivalent masses of pinion and wheel, and the mesh stiffness of the contacting teeth. It is also
assumed that each gear pair functions as a single stage pair, i.e. the influence of other stages in a multiple-stage
gear system is ignored. This assumption is only tenable when the torsional stiffness (measured at the base radius
of the gears) of the shaft common to a wheel and a pinion is less than the mesh stiffness. See 5.6.3 and annex A
for the procedure dealing with very stiff shafts.
Forces caused by torsional vibrations of the shafts and coupled masses are not covered by K . These forces
v
should be included with other externally applied forces (e.g. with the application factor).
In multiple mesh gear trains, there are several natural frequencies. These can be higher or lower than the natural
frequency of a single gear pair which has only one mesh. When such gears run in the supercritical range, analysis
by Method A is recommended. See ISO 6336-1:1996, 6.3.1.
The specific load for the calculation of K is (F K )/b.
v t A
If (F K )/b > 100 N/mm, then F /b = (F K )/b,
t A m t A
if (F K )/b u 100 N/mm, then F /b = 100 N/mm.
t A m
When the specific loading (F K )/b < 50 N/mm, a particular risk of vibration exists (under some circumstances, with
t A
separation of working tooth flanks), above all for spur or helical gears of coarse accuracy grade running at higher
speed.
5.6.2 Calculation of the parameters required for evaluation of K
v
5.6.2.1 Calculation of the equivalent mass, m
red
a) Calculation of the equivalent mass m of a single-stage gear pair
red
**
JJ
= (6)
m
red
**22
+
JJrr
b2 b1
where
m is the equivalent mass of a gear pair, i.e. of the mass per unit facewidth of each gear, referred to its
red
base radius or to the line of action;
*
J are the polar moments of inertia per unit facewidth;
1,2
r are the base radii (= 0,5 d ).
b1,2 b1,2
b) Calculation of equivalent mass, m , of a multi-stage gear pair
red
See annex A.
c) Calculation of equivalent mass, m , of gears of less common designs
red
For information on the following cases, see A.1.2:
pinion shaft with diameter at mid-tooth depth, d , about equal to the shaft diameter;
m1
two rigidly connected, coaxial gears;
one large wheel driven by two pinions;
planetary gears;
idler gears.
5.6.2.2 Determination of the resonance running speed (main resonance) of a gear pair
a) Resonance running speed, n , of the pinion, in reciprocal minutes:
E1
30 ×10 c
γ
−1
n = min (7)
E1
π z
m
1red
with c from annex B.
γ
b) Resonance ratio, N
The ratio of pinion speed to resonance speed, the resonance ratio, N, is determined as follows.
14 © ISO 2002 – All rights reserved
nn πz m
11 1 red
N = = (8)
n 30 000
c
E1 γ
The resona
...
INTERNATIONAL ISO
STANDARD 9085
First edition
2002-02-01
Calculation of load capacity of spur and
helical gears — Application for industrial
gears
Calcul de la capacité de charge des engrenages à denture droite et
hélicoïdale — Application aux engrenages industriels
Reference number
©
ISO 2002
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ii © ISO 2002 – All rights reserved
Contents Page
Foreword.v
Introduction.vi
1 Scope .1
2 Normative references.1
3 Terms and definitions .2
4 Application .8
4.1 Design, specific applications .8
4.2 Safety factors .10
4.3 Input data.11
4.4 Face widths .11
4.5 Numerical equations .12
5 Influence factors .12
5.1 General.12
5.2 Nominal tangential load, F , nominal torque, T, nominal power, P .12
t
5.3 Non-uniform load, non-uniform torque, non-uniform power .12
5.4 Maximum tangential load, F , maximum torque, T , maximum power, P .13
t max max max
5.5 Application factor, K .13
A
5.6 Internal Dynamic Factor, K .13
v
5.7 Face load factor, K .17
H
β
5.8 Face load factor, K .23
F
β
5.9 Transverse load factors, K , K .24
Hα Fα
6 Calculation of surface durability (pitting) .26
6.1 Basic formulae .26
6.2 Single pair tooth contact factors, Z , Z .28
B D
6.3 Zone factor, Z .29
H
6.4 Elasticity factor, Z .30
E
6.5 Contact ratio factor, Z .30
ε
6.6 Helix angle factor, Z .31
β
6.7 Allowable stress numbers (contact), σ .31
H lim
6.8 Life factor, Z .32
NT
6.9 Influences on lubrication film formation, Z , Z and Z .32
L v R
6.10 Work hardening factor, Z .33
W
6.11 Size factor, Z .34
X
6.12 Minimum safety factor (pitting), S .34
H min
7 Calculation of tooth bending strength .34
7.1 Basic formulae .34
7.2 Form factor, Y , and stress correction factor, Y .36
F S
7.3 Helix angle factor, Y .40
β
7.4 Tooth-root reference strength, σ .40
FE
7.5 Life Factor, Y .41
NT
7.6 Relative notch sensitivity factor, Y .41
δ rel T
7.7 Relative surface factor, Y .43
R rel T
7.8 Size factor, Y .44
X
7.9 Minimum safety factor (tooth breakage), S .44
F min
Annex A (normative) Special features of less common gear designs .45
Annex B (normative) Tooth stiffness parameters c¢¢¢¢ and c .48
γ
Annex C (informative) Guide values for application factor, K .51
A
Annex D (informative) Guide values for crowning and end relief of teeth of cylindrical gears .54
Bibliography .57
iv © ISO 2002 – All rights reserved
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 3.
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 International Standard may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 9085 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2,
Gear capacity calculation.
Annexes A and B form a normative part of this International Standard. Annexes C and D are for information only.
Introduction
Procedures for the calculation of the load capacity of general spur and helical gears with respect to pitting and
bending strength appear in ISO 6336-1, ISO 6336-2, ISO 6336-3 and ISO 6336-5. This International Standard is
derived from ISO 6336-1, ISO 6336-2 and ISO 6336-3 by the use of specific methods and assumptions which are
considered to be applicable to industrial gears. Its application requires the use of allowable stresses and material
requirements which are to be found in ISO 6336-5.
vi © ISO 2002 – All rights reserved
INTERNATIONAL STANDARD ISO 9085:2002(E)
Calculation of load capacity of spur and helical gears —
Application for industrial gears
1 Scope
The formulae specified in this International Standard are intended to establish a uniformly acceptable method for
calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth.
The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such
as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory
conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable
to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the
gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth
finished by forging or sintering. It is not applicable to gears which have a poor contact pattern.
This International Standard provides a method by which different gear designs can be compared. It is not intended
to assure the performance of assembled drive gear systems. Neither is it intended for use by the general
engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting
reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the
effects of the items discussed.
CAUTION — The user is cautioned that the calculated results of this International Standard should be
confirmed by experience.
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this International Standard. For dated references, subsequent amendments to, or revisions of, any of these
publications do not apply. However, parties to agreements based on this International Standard are encouraged to
investigate the possibility of applying the most recent editions of the normative documents indicated below. For
undated references, the latest edition of the normative document referred to applies. Members of ISO and IEC
maintain registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile
ISO 54:1996, Cylindrical gears for general and heavy engineering — Modules
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
1)
deviations relevant to corresponding flanks of gear teeth
ISO 4287:1997, Geometrical Product Specifications (GPS) — Surface texture: Profile method — Terms, definitions
and surface texture parameters
1) This was corrected and reprinted in 1997.
ISO 6336-1:1996, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors
ISO 6336-2:1996, Calculation of load capacity of spur and helical gears — Part 2: Calculation of surface durability
(pitting)
ISO 6336-3:1996, Calculation of load capacity of spur and helical gears — Part 3: Calculation of tooth bending
strength
ISO 6336-5:1996, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials
ISO 9084:2000, Calculation of load capacity of spur and helical gears — Application to high speed gears and gears
of similar requirements
ISO/TR 10495:1997, Cylindrical gears — Calculation of service life under variable loads — Conditions for
cylindrical gears accordance with ISO 6336
ISO/TR 13593:1999, Enclosed gear drives for industrial applications
3 Terms and definitions
For the purposes of this International Standard, the terms and definitions given in ISO 1122-1 apply. For the
symbols, see Table 1.
2 © ISO 2002 – All rights reserved
Table 1 — Symbols and abbreviations used in this International Standard
Symbol Description or term Unit
a
a mm
centre distance
b facewidth mm
b
facewidth of an individual helix of a double helical gear mm
B
b
facewidth (pitting) mm
H
b
facewidth (tooth root) mm
F
b
reduced facewidth (facewidth minus end reliefs) mm
red
b
web thickness mm
s
b
length of end relief mm
I(II)
c
mean value of mesh stiffness per unit facewidth N/(mm׵m)
γ
N/(mm׵m)
c′ maximum tooth stiffness of one pair of teeth per unit facewidth (single stiffness)
d
tip diameter of pinion (or wheel) mm
a1,2
d
tip diameter of pinion (or wheel) of virtual spur gear mm
an1,2
d base diameter of pinion (or wheel) mm
b1,2
d
base diameter of pinion (or wheel) of virtual spur gear mm
bn1,2
d diameter of circle through outer point of single pair tooth contact of pinion, wheel of virtual mm
en1,2
spur gear
d root diameter of pinion, wheel mm
f1,2
d diameter at mid-tooth depth of pinion, wheel mm
m1,2
d reference diameter of pinion, wheel of virtual spur gear mm
n1,2
d
nominal shaft diameter for bending mm
sh
d internal diameter of hollow shaft mm
shi
d pitch diameter of pinion, wheel mm
w1,2
d diameter of a circle near the tooth-roots, containing the limits of the usable flanks of an mm
Nf2
internal gear or the larger external gear of a mating gear
d
reference diameter of pinion, wheel mm
1,2
f effective profile form deviation µm
f eff
f profile form deviation (the value for the total profile deviation F may be used alternatively for
µm
fα a
this, if tolerances complying with ISO 1328-1 are used)
f helix deviation due to manufacturing inaccuracies µm
ma
f transverse base pitch deviation (the values of f may be used for calculations in accordance µm
pb pt
with ISO 6336:1996, using tolerances complying with ISO 1328-1)
f effective transverse base pitch deviation µm
pb eff
f helix deviation due to elastic deflections µm
sh
f tooth alignment deviation (not including helix form deviation) µm
Hβ
g path length of contact mm
α
h tooth depth mm
Table 1 (continued)
Symbol Description or term Unit
h addendum mm
a
h
tool addendum mm
a0
h dedendum of tooth of an internal gear mm
f2
h dedendum of basic rack of cylindrical gears mm
fP
h
bending moment arm for load application at the outer point of single pair tooth contact mm
Fe
h dedendum of tooth of an internal gear, containing the limits of the usable flanks of an internal mm
Nf2
gear or the larger external gear of a mating gear
l bearing span mm
m normal module mm
n
m reduced gear pair mass per unit facewidth referenced to the line of action kg/mm
red
−1
n resonance speed
min
E
−1
n rotation speed of pinion, wheel
min
1,2
p normal base pitch mm
bn
p transverse base pitch mm
bt
pr protuberance of the tool mm
q finishing stock allowance mm
q
notch parameter s / 2ρ —
s
Fn F
q notch parameter of standard reference test gear —
sT
r base radius mm
b
s pinion offset from shaft centre line mm
s tooth-root chord at the critical section mm
Fn
s rim thickness mm
R
s residual fillet undercut mm
pr
a
u —
gear ratio | u | = | z /z | W 1
2 1
v m/s
circumferential speed (without subscript: at reference circle ª circumferential speed at
working pitch circle)
x profile shift coefficient of pinion, wheel —
1,2
y running-in allowance (pitch deviation) µm
f
y running-in allowance (profile deviation) µm
p
y running-in allowance for a gear pair µm
α
y running-in allowance (equivalent misalignment) µm
β
z
virtual number of teeth of a helical gear —
n
a
z number of teeth of pinion, wheel —
1,2
B
total facewidth of a double helical gear including the gap mm
B running-in parameter for determination of constant K —
f
B running-in parameter for determination of constant K
—
k
4 © ISO 2002 – All rights reserved
Table 1 (continued)
Symbol Description or term Unit
B running-in parameter for determination of constant K —
p
B constants for determination of F
—
1,2 βx
*
B constant for determination of the pinion offset —
C
tip relief µm
a
C tip relief resulting from running-in µm
ay
C constants for determination of constant K —
v1,2,3
C
basic rack factor —
B
C gear blank factor —
R
C crowning height µm
β
C constants for determination of q
—
1.9 s
E modulus of elasticity, Young's modulus N/mm
E auxiliary value for calculation of Y —
F
F N
mean transverse force at the reference cylinder (= F K K )
m
t A v
F (nominal) transverse tangential force at reference cylinder N
t
F maximum transverse tangential force at reference cylinder N
t max
F
determinant transverse force at the reference cylinder (= F K K K ) N
tH
t A v Hβ
F total helix deviation µm
β
F
initial equivalent misalignment (before running-in) µm
βx
G auxiliary value for calculation of Y —
F
H auxiliary value for calculation of Y —
F
*
J polar moment of inertia per unit face width Kg/mm
1,2
K constant for determination of K —
v
K dynamic factor —
v
K application factor —
A
K transverse load factor (root stress) —
Fα
K face load factor (root stress) —
Fβ
K transverse load factor (contact stress) —
Hα
K
face load factor (contact stress) —
Hβ
K mesh load factor (takes into account the uneven distribution of the load between meshes for —
g
multiple transmission paths)
K constant —
1,2
K′ constant for the pinion offset in relation to the torqued end —
L tooth root chord at the critical section, related to the bending moment arm relevant to load —
application at the outer point of single pair tooth contact
N resonance ratio —
N exponent —
F
Table 1 (continued)
Symbol Description or term Unit
N number of load cycles —
L
N
resonance ratio in the main resonance range —
S
M auxiliary values for the determination of Z —
1,2 B,D
P transmitted power kW
P maximum transmitted power kW
max
Ra arithmetic mean roughness value (as specified in ISO 4287:1997) µm
Rz mean peak-to-valley roughness (as specified in ISO 4287:1997) µm
Rz mean peak-to-valley roughness for the gear pair µm
S safety factor from tooth breakage —
F
S
minimum safety factor (tooth breakage) —
F min
S safety factor from pitting —
H
S minimum safety factor (pitting) —
H min
T pinion torque (nominal); wheel torque Nm
1,2
T maximum torque Nm
max
Y tooth form factor —
F
Y life factor for tooth-root stress —
N
Y life factor for tooth-root stress for reference test conditions —
NT
Y
surface factor —
R rel T
Y stress correction factor —
S
Y size factor (tooth root) —
X
Y
helix angle factor (tooth root) —
β
Y relative notch sensitivity factor —
δ rel T
Y contact ratio factor (tooth root) —
ε
Z
speed factor —
v
Z single pair tooth contact factors for the pinion, wheel —
B,D
Z elasticity factor
E 2
Nmm
Z
zone factor —
H
Z lubricant factor —
L
Z life factor for contact stress —
N
Z
life factor for contact stress for reference test conditions —
NT
Z roughness factor affecting surface durability —
R
Z work-hardening factor —
W
Z
size factor (pitting) —
X
Z helix angle factor (pitting) —
β
Z contact ratio factor (pitting) —
ε
6 © ISO 2002 – All rights reserved
Table 1 (continued)
Symbol Description or term Unit
α pressure angle at the outer point of single pair tooth contact of virtual spur gears °
en
normal pressure angle °
α
n
α transverse pressure angle °
t
α transverse pressure angle at the pitch cylinder °
wt
load direction angle, relevant to direction of application of load at the outer single pair tooth °
α
Fen
contact of virtual spur gears
α normal pressure angle of the basic rack for cylindrical gears °
Pn
helix angle at the reference cylinder °
β
β base helix angle °
b
°
g auxiliary angle for determination of α
e Fen
combined deflection of mating teeth assuming even load distribution over the facewidth µm
d
bth
ε transverse contact ratio —
α
transverse contact ratio of a virtual spur gear —
ε
αn
ε axial overlap ratio —
β
ε total contact ratio (ε = ε + ε ) —
g g α β
ν Poisson's contact ratio —
auxiliary value for calculation of Y —
θ
F
tip radius of the tool mm
ρ
a0
root fillet radius of the basic rack for cylindrical gears mm
ρ
fP
ρ radius of relative curvature mm
rel
ρ tooth-root fillet radius at the critical section mm
F
slip-layer thickness mm
ρ′
s tensile strength N/mm
B
tooth-root stress N/mm
s
F
s nominal stress number (bending) N/mm
F lim
s allowable stress number (bending) = σ Y N/mm
FE F lim ST
tooth-root stress limit N/mm
s
FG
s permissible tooth-root stress N/mm
FP
s nominal tooth-root stress N/mm
F0
calculated contact stress N/mm
s
H
s allowable stress number (contact) N/mm
H lim
s modified allowable stress number = σ S N/mm
HG HP H min
permissible contact stress N/mm
s
HP
s nominal contact stress N/mm
H0
Table 1 (continued)
Symbol Description or term Unit
s yield point N/mm
S
0,2 % proof stress N/mm
s
0,2
* −1
χ relative stress gradient in the root of a notch mm
* −1
relative stress gradient in a smooth polished test piece
χ mm
p
* −1
χ relative stress gradient in the root of the standard reference test gear mm
T
ω angular velocity of pinion, wheel rad/s
1,2
a
For external gear pairs, a, u, z and z are positive; for internal gear pairs, a, u and z are negative, and z positive.
1 2 2 1
4 Application
4.1 Design, specific applications
4.1.1 General
Gear designers must recognize that requirements for different applications vary considerably. Use of the
procedures of this International Standard for specific applications demands a careful appraisal of all applicable
considerations, in particular:
the allowable stress of the material and the number of load repetitions;
the consequences of any percentage of failure (failure rate);
the appropriate factor of safety.
Design considerations to prevent fractures emanating from stress raisers in the tooth flank, tip chipping and failures
of the gear blank through the web or hub should be analysed by general machine design methods.
Any variances according to the following shall be reported in the calculation statement.
a) If a more refined method of calculation is desired or if compliance with the restrictions given in 4.1 is for any
reason impractical, relevant factors may be evaluated according to the basic standard or another application
standard.
b) Factors derived from reliable experience or test data may be used instead of individual factors according to this
International Standard. Concerning this, the criteria for Method A in 4.1.8.1 of ISO 6336-1:1996 are applicable.
In other respects, rating calculations shall be strictly in accordance with this International Standard wherever
stresses, safety factors etc. are to be classified as being in accordance with this International Standard.
This International Standard recognizes the following types of industrial drive design.
Catalogue enclosed drives are designed to nominal load ratings for sale from catalogues or from stock. The
actual loads and operation conditions are not exactly known at the time of design.
NOTE The actual loads for each application are evaluated to select an appropriately sized unit from the catalogue. A
selection factor, based on experience with similar applications, is often used to reduce the catalogue rating to match the
application conditions (see ISO TR 13593).
Custom designed drives are aimed at a specific application where the operating conditions are known or
specified at the time of design.
8 © ISO 2002 – All rights reserved
This International Standard is applicable when the wheel blank, shaft/hub connections, shafts, bearings, housings,
threaded connections, foundations and couplings conform to the requirements regarding accuracy, load capacity
and stiffness which form the basis for the calculation of the load capacity of gears.
Although the method described in this International Standard is mainly intended for recalculation purposes, by
means of iteration it can also be used to determine the load capacities of gears. The iteration is accomplished by
selecting a load and calculating the corresponding safety factor against pitting, S , for the pinion. If S is greater
H1 H1
than S , the load is increased; if it is smaller than S , the load is reduced. This is done until the chosen load
H min H min
corresponds to S = S . The same method is used for the wheel (S = S ), and also for the safety factors
H1 H min H2 H min
against tooth breakage, S = S = S .
F1 F2 F min
4.1.2 Gear data
This International Standard is applicable within the following constraints.
a) Types of gear:
external and internal, involute spur, helical and double helical gears;
for double helical gears, it is assumed that the total tangential load is evenly distributed between the two
helices; if this is not the case (e.g. due to externally applied axial forces), this shall be taken into account;
the two helices are treated as two single helical gears in parallel.
b) Range of speeds:
2)
−1
n less than or equal to 3 600 min (synchronous speed of two-pole motor at 60 Hz current frequency) ;
subcritical range of speed (see K in 5.6);
v
at speeds of v < 1 m/s, gear load capacity is often limited by wear.
c) Gear accuracy:
accuracy grade 10 or better according to ISO 1328-1 (affects K , K and K ).
v Hα Hβ
d) Range of the transverse contact ratios of virtual spur gear pairs:
1,2 < ε < 1,9 (affects c′, c , K , K , K , K and K ).
α γ v Hβ Fα Hα Fβ
e) Range of helix angles:
β less than or equal to 30° (affects c′, c , K and K ).
γ v Hβ
4.1.3 Pinion and pinion shaft
This International Standard is applicable to pinions integral with shafts or bored pinions with s /d W 0,2 (this affects
R 1
c′, c , K , K ). It is assumed that the bored pinions will be mounted on solid shafts or on hollow shafts with
g v Hβ
d /d < 0,5 (this affects K ).
shi sh Hβ
4.1.4 Wheel blank, wheel rim
The given formulae are valid for spur and helical gears with a minimum rim thickness under the root of s W 3,5 m .
R n
The calculation of K assumes that wheel and wheel shaft are sufficiently stiff such that their deflections can be
Hβ
ignored.
2) For higher speeds, the requirements of ISO 6336 or ISO 9084 apply.
4.1.5 Materials
These include steels, nodular cast iron and grey cast iron (this affects Z , σ , σ , K , K , K , K and K ).
E H lim FE v Hβ Fβ Hα Fα
For materials and their abbreviations used in this International Standard, see Table 2.
Table 2 — Materials
Material Abbreviation
St
Steel (σ < 800 N/mm )
B
St (cast)
Cast steel, alloy or carbon, (σ W 800 N/mm )
B
V
Through-hardening steel, alloy or carbon, through hardened (σ W 800 N/mm )
B
Grey cast iron GG
Nodular cast iron (pearlitic, bainitic, ferritic structure) GGG (perl., bai., ferr.)
Black malleable cast iron (pearlitic structure) GTS (perl.)
Case-hardened steel, case hardened Eh
Steel and GGG, flame or induction hardened IF
Nitriding steel, nitrided NT (nitr.)
Through-hardening and case-hardening steel, nitrided NV (nitr.)
Through-hardening and case-hardening steel, nitrocarburized NV (nitrocar.)
4.1.6 Lubrication
The calculation procedures are valid for oil lubricated gears having sufficient lubricant of suitable viscosity at the
gear mesh and when the working temperature is also suitable (this affects lubricant film formation, i.e. the factors
Z , Z and Z ).
L v R
4.2 Safety factors
It is necessary to distinguish between the safety factor relative to pitting, S , and the safety factor relative to tooth
H
breakage, S .
F
For a given application, adequate gear load capacity is demonstrated by the computed values of S and S being
H F
equal to or greater than the values S and S , respectively.
H min F min
Choice of the value of a safety factor should be based on the degree of confidence in the reliability of the available
data and the consequences of possible failures.
Important factors to be considered are
a) that the validity of the material values in ISO 6336-5 is for 1 % probability of damage,
b) the specified quality and the effectiveness of quality control at all stages of manufacture,
c) the accuracy of specification of the service duty and external conditions, and
d) that tooth breakage is often considered to be a greater hazard than pitting.
Therefore, the chosen value for S should be greater than the value chosen for S .
F min H min
10 © ISO 2002 – All rights reserved
For calculation of the actual safety factor, see 6.1.5 (S , pitting) and 7.1.4 (S , tooth breakage). For minimum safety
H F
factors see 6.12 (pitting) and 7.9 (tooth breakage). However, it is recommended that the minimum values of the
safety factors should be agreed upon between the purchaser and the manufacturer.
4.3 Input data
The following data shall be available for the calculations:
a) gear data:
a, z , z , m , d , d , d , b, b , b , x , x , α , β, ε , ε (see ISO 53, ISO 54) (see 4.4 for definition of b, b and
1 2 n 1 a1 a2 H F 1 2 n α β H
b face widths);
F
b) cutter basic rack tooth profile:
h , ρ ;
a0 a0
c) design and manufacturing data:
C , C , f , S , S , Ra , Ra , Rz , Rz ;
a1 a2 pb H min F min
1 2 1 2
materials, material hardnesses and heat treatment details; gear accuracy grades, bearing span l, positions of
gears relative to bearings; dimensions of pinion shaft d and, when applicable, helix modification (crowning,
sh
end relief);
d) power data:
P or T or F , n , v , details of driving and driven machines.
t 1 1
Requisite geometrical data can be calculated according to national standards.
Information to be exchanged between manufacturer and purchaser should include data specifying material
preferences, lubrication, safety factor and externally applied forces due to vibrations and overloads (application
factor).
4.4 Face widths
The following face widths have to be distinguished.
b: the smaller of the facewidths of pinion and wheel measured at the pitch circles (for a double helical gear
b = 2 b ). Chamfers or rounding of tooth ends are to be ignored. Where the facewidths are offset, the length
H B
of the face in contact shall be used.
b : the facewidth at the pitch cylinder of the gear (for a double helical gear b = 2 b ). When the facewidth b
H H B H
is larger than that of its mating gear, b shall be based on the smaller facewidth, ignoring any intentional
H
transverse chamfers or tooth-end rounding. Neither unhardened portions of surface-hardened gear tooth flanks
nor the transition zones shall be included. Where the facewidths are offset, the length of the face in contact
shall be used.
b : the facewidth at the root cylinder of the gear (for a double helical gear b = 2 b ). When the facewidth b is
F F B F
larger than that of its mating gear, b shall be based on the smaller facewidth plus a length, not exceeding one
F
module of any extension at each end. However, if it is foreseen that because of crowning or because end relief
contact does not extend to the end of face, then the smaller facewidth shall be used for both pinion and wheel.
Where the facewidths are offset, the length of the face in contact shall be used.
4.5 Numerical equations
The units listed in clause 3 shall be used in all calculations. Information which will facilitate the use of this
International Standard is provided in annex C of ISO 6336-1:1996.
5 Influence factors
5.1 General
The influence factors K , K , K , K and K are all dependent on the tooth load. Initially this is the applied load
v Hα Hβ Fα Fβ
(nominal tangential load multiplied by the application factor).
The factors are also interdependent and shall therefore be calculated successively as follows:
a) K with the applied tangential load F K
v t A;
b) K or K with the recalculated load F K K ;
Hβ Fβ t A v
c) K or K with the applied tangential load F K .
Hα Fα t A
When a gear drives two or more mating gears, it is necessary to substitute K by K K . If possible, the mesh load
A A γ
factor, K , should be determined by measurement; alternatively, its value may be estimated from the literature.
γ
5.2 Nominal tangential load, F , nominal torque, T, nominal power, P
t
The nominal tangential load, F , is determined in the transverse plane at the reference cylinder. It is based on the
t
input torque to the driven machine. This is the torque corresponding to the heaviest regular working condition.
Alternatively, the nominal torque of the prime mover can be used as a basis if it corresponds to the torque
requirement of the driven machine, or some other suitable basis can be chosen.
2 000 T
19 098 ¥ 1000 PP1000
1,2
F = = = (1)
t
v
ddn
1,2 1,2 1,2
Fd
1000 9PP549
t1,2
T = = = (2)
1, 2
2000 ω n
1, 2 1, 2
TT ω n
Fv
1, 2 1,2 1, 2 1, 2
t
P = = = (3)
1000 1000 9 549
ddω n
1, 2 1, 2 1, 2 1, 2
v = = (4)
2 000 19 098
πnn
2000 v
1, 2 1, 2
ω== = (5)
1, 2
30 d 9 549
1, 2
5.3 Non-uniform load, non-uniform torque, non-uniform power
When the transmitted load is not uniform, consideration should be given not only to the peak load and its
anticipated number of cycles, but also to intermediate loads and their numbers of cycles. This type of load is
classed as a duty cycle and may be represented by a load spectrum. In such cases, the cumulative fatigue effect of
the duty cycle is considered in rating the gear set. A method of calculating the effect of the loads under this
condition is given in ISO TR 10495.
12 © ISO 2002 – All rights reserved
5.4 Maximum tangential load, F , maximum torque, T , maximum power, P
t max max max
This is the maximum tangential load F , (or corresponding torque, T , corresponding power, P ) in the
t max max max
variable duty range. Its magnitude can be limited by a suitably responsive safety clutch. F , T and P shall
t max max max
be known when safety from pitting damage and from sudden tooth breakage due to loading corresponding to the
static stress limit is determined (see 5.5).
5.5 Application factor, K
A
5.5.1 General
The factor K adjusts the nominal load F , in order to compensate for incremental gear loads from external sources.
A t
These additional forces are largely dependent on the characteristics of the driving and driven machines, as well as
the masses and stiffness of the system, including shafts and couplings used in service.
It is recommended that the purchaser and manufacturer/designer agree on the value of the application factor.
5.5.2 Method A — Factor K
A-A
K is determined in this method by means of careful measurements and a comprehensive analysis of the system,
A
or on the basis of reliable operational experience in the field of application concerned (see 5.3).
5.5.3 Method B — Factor K
A-B
If no reliable data, obtained as described in 5.5.2, is available, or even as early as the first design phase, it is
possible to use the guideline values for K as described in annex C.
A
5.6 Internal Dynamic Factor, K
v
5.6.1 General
The dynamic factor relates the total tooth load, including internal dynamic effects of a “multi-resonance” system, to
the transmitted tangential tooth load.
Method B of ISO 6336-1:1996 with modifications is used in this International Standard. When agreed between
manufacturer and purchaser, or when determining the catalogue presentation of the capacities of catalogue
enclosed drives, Method E of ISO 6336-1:1996 may be used to estimate the dynamic factor.
In this procedure it is assumed that the gear pair consists of an elementary single mass and spring system
comprising the equivalent masses of pinion and wheel, and the mesh stiffness of the contacting teeth. It is also
assumed that each gear pair functions as a single stage pair, i.e. the influence of other stages in a multiple-stage
gear system is ignored. This assumption is only tenable when the torsional stiffness (measured at the base radius
of the gears) of the shaft common to a wheel and a pinion is less than the mesh stiffness. See 5.6.3 and annex A
for the procedure dealing with very stiff shafts.
Forces caused by torsional vibrations of the shafts and coupled masses are not covered by K . These forces
v
should be included with other externally applied forces (e.g. with the application factor).
In multiple mesh gear trains, there are several natural frequencies. These can be higher or lower than the natural
frequency of a single gear pair which has only one mesh. When such gears run in the supercritical range, analysis
by Method A is recommended. See ISO 6336-1:1996, 6.3.1.
The specific load for the calculation of K is (F K )/b.
v t A
If (F K )/b > 100 N/mm, then F /b = (F K )/b,
t A m t A
if (F K )/b u 100 N/mm, then F /b = 100 N/mm.
t A m
When the specific loading (F K )/b < 50 N/mm, a particular risk of vibration exists (under some circumstances, with
t A
separation of working tooth flanks), above all for spur or helical gears of coarse accuracy grade running at higher
speed.
5.6.2 Calculation of the parameters required for evaluation of K
v
5.6.2.1 Calculation of the equivalent mass, m
red
a) Calculation of the equivalent mass m of a single-stage gear pair
red
**
JJ
= (6)
m
red
**22
+
JJrr
b2 b1
where
m is the equivalent mass of a gear pair, i.e. of the mass per unit facewidth of each gear, referred to its
red
base radius or to the line of action;
*
J are the polar moments of inertia per unit facewidth;
1,2
r are the base radii (= 0,5 d ).
b1,2 b1,2
b) Calculation of equivalent mass, m , of a multi-stage gear pair
red
See annex A.
c) Calculation of equivalent mass, m , of gears of less common designs
red
For information on the following cases, see A.1.2:
pinion shaft with diameter at mid-tooth depth, d , about equal to the shaft diameter;
m1
two rigidly connected, coaxial gears;
one large wheel driven by two pinions;
planetary gears;
idler gears.
5.6.2.2 Determination of the resonance running speed (main resonance) of a gear pair
a) Resonance running speed, n , of the pinion, in reciprocal minutes:
E1
30 ×10 c
γ
−1
n = min (7)
E1
π z
m
1red
with c from annex B.
γ
b) Resonance ratio, N
The ratio of pinion speed to resonance speed, the resonance ratio, N, is determined as follows.
14 © ISO 2002 – All rights reserved
nn πz m
11 1 red
N = = (8)
n 30 000
c
E1 γ
The resonance running speed may be above or below the running speed calculated from equation (8) because
of stiffnesses which have not been included (e.g. the stiffnesses of shafts, bearings or housings) and as a
result of damping. For reasons of safety, the resonance range is defined by the following.
< N u 1,15 (9)
N
S
At loads such that (F K )/b is less than 100 N/mm, the lower limit of resonance ratio N is determined as
t A S
follows:
if (F K )/b < 100 N/mm, then
t A
FK
tA
N = 0,5 + 0,35 (10)
S
b ¥100
if (F K )/b W 100 N/mm, then
t A
N = 0,85 (11)
5.6.2.3 Gear accuracy and running-in parameters B , B , B
p f k
B , B and B are non-dimensional parameters used to take into account the effect of tooth deviations and profile
p f k
3)
modifications on the dynamic load.
c¢ f
pb eff
B = (12)
p
/ FK b
()
tA
c¢ f
f eff
B = (13)
f
/ ()FK b
tA
cC¢
a
B = 1 – (14)
k
/ (FKb
)
tA
with
c′ from annex B;
C design amount for profile modification (tip relief at the beginning and end of tooth engagement). A value
a
C from running-in shall be substituted for C in equation (14) in the case of gears with
...
NORME ISO
INTERNATIONALE 9085
First édition
2002-02-01
Calcul de la capacité de charge des
engrenages à denture droite et
hélicoïdale — Application aux engrenages
industriels
Calculation of load capacity of spur and helical gears — Application for
industrial gears
Numéro de référence
©
ISO 2002
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Imprimé en Suisse
ii © ISO 2002 – Tous droits réservés
Sommaire Page
Avant-propos .v
Introduction.vi
1 Domaine d'application .1
2 Références normatives .1
3 Termes, définitions et symboles.2
4 Application .8
4.1 Conception, applications spécifiques.8
4.2 Coefficients de sécurité .11
4.3 Données d’entrée.11
4.4 Largeurs de denture.12
4.5 Équations numériques.12
5 Facteurs d’influence.12
5.1 Généralités .12
5.2 Charge tangentielle nominale, F , couple nominal, T, puissance nominale P.12
t
5.3 Charge non uniforme, couple non uniforme, puissance non uniforme.13
5.4 Charge tangentielle maximale, F , couple maximal T , puissance maximale, P .13
t max max max
5.5 Facteur d’application, K .13
A
5.6 Facteur dynamique interne, K .14
v
5.7 Facteur de distribution longitudinale de la charge, K .18
Hβ
5.8 Facteur de distribution longitudinale de la charge, K .24
Fβ
5.9 Facteurs de distribution de la charge, K , K .25
hα fα
6 Calcul de la résistance à la pression de contact (piqûres) .27
6.1 Formules de base .27
6.2 Facteurs de contact unique, Z , Z .29
B D
6.3 Facteur géométrique, Z .30
H
6.4 Facteur d'élasticité, Z .31
E
6.5 Facteur de rapport de conduite, Z .31
ε
6.6 Facteur d'angle d'hélice, Z .32
β
6.7 Valeurs de contrainte de référence (pression), σ .32
H lim
6.8 Facteur de durée de vie, Z .33
NT
6.9 Influences sur la formation du film lubrifiant, Z , Z et Z .33
L v R
6.10 Facteur de rapport de dureté, Z .34
W
6.11 Facteur de dimension, Z .34
X
6.12 Coefficient de sécurité minimal (formation de piqûres) S .35
H min
7 Calcul de la résistance à la flexion des dents .35
7.1 Formules de base .35
7.2 Facteur de forme, Y , et facteur de concentration de contrainte Y .37
F S
7.3 Facteur d'angle d'hélice, Y .41
β
7.4 Résistance de référence en pied de dent, σ .42
FE
7.5 Facteur de durée de vie, Y .42
NT
7.6 Facteur de sensibilité relative à l’entaille, Y .42
δ rel T
7.7 Facteur relatif d’état de surface, Y .44
R rel T
7.8 Facteur de dimension, Y .45
X
7.9 Coefficient de sécurité minimum (rupture de dent), S .45
F min
Annexe A (normative) Propriétés spéciales des architectures d’engrenages moins courantes .46
Annexe B (normative) Paramètres de rigidité de denture c¢ et c .49
γ
Annexe C (informative) Valeurs indicatives pour le facteur d’application, K .52
A
Annexe D (informative) Valeurs indicatives pour le bombé et les dépouilles d’extrémité des dents
d'engrenages cylindriques .55
Bibliographie .58
iv © ISO 2002 – Tous droits réservés
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 3.
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 de la présente Norme internationale 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.
La Norme internationale ISO 9085 a été élaborée par le comité technique ISO/TC 60, Engrenages, sous-comité
SC 2, Calcul de la capacité des engrenages.
Les annexes A et B constituent des éléments normatifs de la présente Norme internationale. Les annexes C et D
sont données uniquement à titre d'information.
Introduction
Les méthodes de calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale
d’usage général, en termes de formation des piqûres et de résistance à la flexion, sont données dans l’ISO 6336-1,
l’ISO 6336-2, l’ISO 6336-3 et l’ISO 6336-5. La présente Norme internationale est dérivée de l’ISO 6336-1, de
l’ISO 6336-2 et de l’ISO 6336-3 de par l’utilisation des méthodes et des hypothèses spécifiques qui sont
considérées comme applicables aux engrenages marins. Son application requiert l’utilisation des contraintes
admissibles et des exigences sur les matériaux qui se trouvent dans l’ISO 6336-5.
vi © ISO 2002 – Tous droits réservés
NORME INTERNATIONALE ISO 9085:2002(F)
Calcul de la capacité de charge des engrenages à denture droite et
hélicoïdale — Application aux engrenages industriels
1 Domaine d'application
Les formules spécifiées dans la présente Norme internationale sont destinées à établir une méthode uniformément
acceptable pour calculer la résistance à la formation de piqûres et la résistance à la flexion des engrenages
industriels à dentures droite ou hélicoïdale.
Les formules de capacité de charge de la présente Norme internationale ne sont pas applicables à d’autres types
de détérioration de la denture des engrenages comme par exemple la déformation plastique, la formation de micro-
piqûres, le grippage, l’effondrement de la couche cémentée, l'adhésion et l’usure et elles ne sont pas applicables
dans des conditions de vibrations qui risquent d’entraîner une rupture imprévisible du profil. Les formules de
résistance à la flexion s’appliquent aux ruptures au niveau du profil de raccordement, mais elles ne s’appliquent
pas aux ruptures sur le profil actif des dents, aux ruptures de la jante, ou aux ruptures du corps de roue au travers
du voile et du moyeu. La présente Norme internationale ne s’applique pas aux dents finies par forgeage ou frittage.
Elle ne s’applique pas aux engrenages qui ont une marque de portée médiocre.
La présente Norme internationale fournit une méthode permettant de comparer différentes conceptions
d’engrenages. Elle n’est pas destinée à assurer la performance des systèmes de transmission de puissance pour
engrenage. Elle n’est pas non plus destinée à l’utilisation par des concepteurs de mécanique générale. Par contre,
elle est destinée aux concepteurs d’engrenages expérimentés qui sont capables de sélectionner des valeurs
raisonnables pour les facteurs figurant dans ces formules en se fondant sur leurs connaissances de conception
similaires et leur compréhension des effets des sujets discutés.
AVERTISSEMENT — L'utilisateur est mis en garde qu'il convient de confirmer par expérience les résultats
calculés à partir de la présente Norme internationale.
2 Références normatives
Les documents normatifs suivants contiennent des dispositions qui, par suite de la référence qui y est faite,
constituent des dispositions valables pour la présente Norme internationale. Pour les références datées, les
amendements ultérieurs ou les révisions de ces publications ne s’appliquent pas. Toutefois, les parties prenantes
aux accords fondés sur la présente Norme internationale sont invitées à rechercher la possibilité d'appliquer les
éditions les plus récentes des documents normatifs indiqués ci-après. Pour les références non datées, la dernière
édition du document normatif en référence s’applique. Les membres de l'ISO et de la CEI possèdent le registre des
Normes internationales en vigueur.
ISO 53:1998, Engrenages cylindriques de mécanique générale et de grosse mécanique — Tracé de référence
ISO 54:1996, Engrenages cylindriques de mécanique générale et de grosse mécanique — Modules
ISO 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques
ISO 1328-1:1995, Engrenages cylindriques — Système ISO de précision — Partie 1: Définitions et valeurs
1)
admissibles des écarts pour les flancs homologues de la denture
1) Corrigée et réimprimée en 1997.
ISO 4287:1997, Spécification géométrique des produits (GPS) — État de surface: Méthode du profil — Termes,
définitions et paramètres d’état de surface
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 6336-2:1996, 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)
ISO 6336-3:1996, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 3: Calcul de la résistance à la flexion en pied de dent
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 9084:2000, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Application aux engrenages grande vitesse et aux engrenages d'exigences similaires
ISO/TR 10495:1997, Engrenages cylindriques — Calcul de la durée de vie en service sous charge variable —
Conditions pour les engrenages cylindriques conformément à l'ISO 6336
ISO/TR 13593:1999, Transmissions de puissance par engrenages sous carter pour usage industriel
3 Termes, définitions et symboles
Pour les besoins de la présente Norme internationale, les termes et définitions donnés dans l’ISO 1122-1
s’appliquent. Pour les symboles, voir le Tableau 1.
2 © ISO 2002 – Tous droits réservés
Tableau 1 — Symboles et abréviations utilisées dans la présente Norme internationale
Symbole Désignation ou terme Unité
a
a mm
Entraxe
b Largeur de denture mm
b
Largeur d’une hélice individuelle d’une roue à denture hélicoïdale double mm
B
b Largeur de denture (formation de piqûres) mm
H
b
Largeur de denture (pied de dent) mm
F
b Largeur de denture réduite (largeur de denture moins dépouille d’extrémité) mm
red
b Épaisseur du voile mm
s
b
Longueur de dépouille d’extrémité mm
l(ll)
c Valeur moyenne de la rigidité d’engrènement par unité de largeur de denture
N/(mm׵m)
γ
c¢ Rigidité maximale d’une paire de dents par unité de largeur de denture (rigidité simple) N/(mm◊µm)
d Diamètre de tête de pignon, de la roue mm
a1,2
d Diamètre de tête du pignon, de la roue d’un engrenage à denture droite équivalent mm
an1,2
d Diamètre de base de pignon, de la roue mm
b1,2
d Diamètre de base du pignon, de la roue d’un engrenage à denture droite équivalent mm
bn1,2
d Diamètre du cercle passant par le point le plus haut de contact unique du pignon, de la roue mm
en1,2
d’un engrenage à denture droite équivalent
d Diamètre de pied de pignon, de la roue mm
f1,2
d Diamètre à mi-hauteur de denture du pignon, de la roue mm
m1,2
d Diamètre du cercle de référence du pignon, de la roue d’un engrenage à denture droite mm
n1,2
équivalent
d Diamètre nominal des arbres pour la flexion mm
sh
d Diamètre intérieur d’arbre creux mm
shi
d Diamètre primitif de fonctionnement du pignon, de la roue mm
w1,2
d
Diamètre de cercle près du pied de dent, contenant les limites des flancs utilisables d’une mm
N1,2
roue à denture intérieure ou la plus grande à denture extérieure d’un couple conjugué.
d Diamètre de référence du pignon, de la roue mm
1,2
f Écart de forme effectif du profil µm
feff
f
Écart de forme du profil (la valeur de l’écart total F peut être utilisée en remplacement si les µm
fα
a
tolérances utilisées sont conformes à l’ISO 1328-1:1995)
f Écart d’hélice dû aux imprécisions de fabrication µm
ma
f Écart du pas de base apparent (les valeurs de f peuvent être utilisées pour les calculs µm
pb pt
selon l’ISO 6336, avec des tolérances conformes à ISO 1328-1:1995)
f Écart du pas de base apparent effectif µm
pb eff
f Écart d’hélice dû aux déformations élastiques µm
sh
f Écart d’alignement de la denture (non compris l’écart de forme de l’hélice) µm
Hβ
g
Longueur de conduite mm
α
h Hauteur de denture mm
Tableau 1 (suite)
Symbole Désignation ou terme Unité
h Saillie mm
a
h
Saillie d'outil mm
a0
h Creux de dent d’une roue à denture intérieure mm
f2
h Creux du tracé de référence des roues cylindriques mm
fP
h
Bras de levier pour application de la charge au point le plus haut de contact unique mm
Fe
h Creux de dent d’une roue à denture intérieure, contenant les limites des flancs utilisables mm
Nf2
d’une roue à denture intérieure ou de la roue à denture extérieure la plus grande d’une
engrenage conjugué
l Écartement entre paliers mm
m
Module normal mm
n
m Masse réduite de l’engrenage par unité de largeur de denture par rapport à la ligne d’action kg/mm
red
−1
n Vitesse de résonance min
E
−1
n
Vitesse de rotation du pignon, de la roue min
1,2
p Pas de base normal mm
bn
p Pas de base apparent mm
bt
pr
Protubérance de l’outil mm
q Surépaisseur de finition mm
q Paramètre d’entaille s /2ρ —
s Fn F
q Paramètre d’entaille de la roue d’essai de référence —
sT
r Rayon de base mm
b
s
Décalage du pignon par rapport au plan médian du réducteur mm
s
Corde du pied de dent au niveau de la section critique mm
Fn
s Épaisseur de jante mm
R
s Dégagement de pied de dent résiduel mm
pr
a
u
—
Rapport d’engrenage u = z /z W 1
2 1
m/s
ν Vitesse tangentielle (sans indice: valeur de référence ≈ Vitesse primitive au cercle primitif de
fonctionnement)
x Coefficient de déport du pignon, de la roue —
1,2
y Tolérance de rodage (écart de pas) µm
f
y Tolérance de rodage (écart de profil) µm
p
y Tolérance de rodage pour un engrenage µm
α
y Tolérance de rodage (désalignement équivalent) µm
β
z Nombre de dents de la roue à denture droite équivalente d’une roue à denture hélicoïdale —
n
z Nombre de dents du pignon, de la roue (voir note de bas de page 1) —
1,2
B Largeur de denture totale d’une roue à denture chevron, y compris la gorge centrale mm
B Paramètre de rodage pour la détermination de la constante K —
f
4 © ISO 2002 – Tous droits réservés
Tableau 1 (suite)
Symbole Désignation ou terme Unité
B Paramètre de rodage pour la détermination de la constante K —
k
B Paramètre de rodage pour la détermination de la constante K
—
p
B Constantes pour la détermination de F —
1,2 βx
B* Constante pour la détermination du décalage du pignon —
C Dépouille de tête µm
a
C Dépouille de tête provenant du rodage µm
ay
C Constantes pour la détermination de la constante K
—
v1,2,3
C Facteur du tracé de référence —
B
C Facteur de corps de roue —
R
C Hauteur du bombé µm
β
C Constantes pour la détermination de q —
1.9 s
E Module d’élasticité, Module de Young N/mm
E Valeur auxiliaire pour le calcul de Y —
F
F Force apparente moyenne sur le cylindre de référence (= F K K ) N
m t A v
F Force tangentielle apparente (nominale) sur le cylindre de référence N
t
F
Force tangentielle apparente maximale sur le cylindre de référence N
t max
F N
Force apparente dimensionnante sur le cylindre de référence (= F K K K )
tH
t A v Hβ
F
Écart total d’hélice µm
β
F Désalignement équivalent initial (avant rodage) µm
βx
G Valeur auxiliaire pour le calcul de Y —
F
H Valeur auxiliaire pour le calcul de Y
—
F
J* Moment d’inertie polaire par unité de largeur de denture
kg⋅mm
1,2
K Constante pour la détermination de K —
v
K
Facteur dynamique —
v
K Facteur d’application —
A
K Facteur de distribution transversale de la charge (contrainte au pied de dent) —
Fα
K Facteur de distribution longitudinale de la charge (contrainte au pied de dent) —
Fβ
K Facteur de distribution transversale de la charge (pression de contact) —
Hα
K Facteur de distribution longitudinale de la charge (pression de contact) —
Hβ
K Facteur de répartition de charge (prend en compte la répartition inégale de la charge entre —
γ
les engrènements pour des engrenages à engrènements multiples)
K Constante —
1,2
K′ Constante pour le décalage du pignon par rapport à l’extrémité d’arbre où est appliqué le —
couple
L Corde du pied de dent à la section critique, par rapport au bras de levier pour application de —
la charge au point le plus haut de contact unique
Tableau 1 (suite)
Symbole Désignation ou terme Unité
N Facteur de résonance —
N Exposant —
F
N Nombre de cycles de mise en charge —
L
N Facteur de résonance dans le domaine de résonance principale —
S
M Valeurs auxiliaires pour la détermination de Z —
1,2 B,D
P Puissance transmise kW
P Puissance transmise maximale —
max
Ra
Valeur de rugosité moyenne arithmétique (telle que spécifiée dans l’ISO 4287:1997) µm
Rz Rugosité crête à crête moyenne (telle que spécifiée dans l’ISO 4287:1997) µm
Rz Rugosité crête à crête moyenne pour une paire de roue µm
S Coefficient de sécurité contre la rupture de dent —
F
S Coefficient de sécurité minimum (rupture de dent) —
F min
S Coefficient de sécurité contre formation de piqûres —
H
S Coefficient de sécurité minimum (formation de piqûres) —
H min
T Couple sur le pignon (nominal); couple sur la roue Nm
1,2
T Couple maximal Nm
max
Y
Facteur de forme de dent —
F
Y Facteur de durée de vie pour la contrainte au pied de dent —
N
Y Facteur de durée de vie pour la contrainte au pied de dent dans les conditions d’essai de —
NT
référence
Y
Facteur relatif d'état de surface —
R rel T
Y Facteur de concentration de contrainte —
S
Y Facteur de dimension (pied de dent) —
X
Y
Facteur d’angle d’hélice (pied de dent) —
β
Y Facteur de sensibilité relative à l’entaille
δ rel T
Y Facteur de rapport de conduite (pied de dent) —
ε
Z
Facteur de vitesse —
v
Z Facteurs de contact unique pour le pignon, pour la roue —
B,D
Z Facteur d’élasticité
E N/mm²
Z
Facteur de géométrique —
H
Z Facteur du lubrifiant —
L
Z Facteur de durée de vie pour la pression de contact —
N
Z
Facteur de durée de vie pour la pression de contact dans les conditions de l’essai de —
NT
référence
Z Facteur de rugosité vis-à-vis de la tenue à la pression de contact —
R
Z Facteur de rapport de dureté —
W
6 © ISO 2002 – Tous droits réservés
Tableau 1 (suite)
Symbole Désignation ou terme Unité
Z Facteur de dimension (formation de piqûres) —
X
Z
Facteur d’angle d’hélice (formation de piqûres) —
β
Z Facteur de rapport de conduite (formation de piqûres) —
e
α Angle de pression au point le plus haut de contact unique de roues à denture droite °
en
équivalentes
Angle de pression normal °
α
n
α Angle de pression apparent °
t
α Angle de pression apparent au cylindre primitif de fonctionnement °
wt
α Angle de direction de la charge, relatif à la direction de l’application de la charge au point le °
Fen
plus haut de contact unique de roues à denture droite équivalente.
α Angle de pression normal du tracé de référence pour les engrenages cylindriques °
Pn
Angle d’hélice (sans indice — au cylindre de référence) °
β
β Angle d’hélice de base °
b
°
γ Angle auxiliaire pour la détermination de α
e Fen
δ Déflection combinée des dents conjuguées en supposant une distribution uniforme de µm
bth
charge sur la largeur de denture
Rapport de conduite apparente —
ε
α
ε Rapport de conduite apparent d’un engrenage à denture droite équivalent —
αn
ε Rapport de recouvrement hélicoïdal —
β
—
ε Rapport de conduite total (ε = ε + ε )
γ γ α β
ν Coefficient de Poisson —
Valeur auxiliaire pour le calcul de Y —
θ
F
ρ Rayon de tête de l’outil mm
a0
Rayon du profil de raccordement du pied du tracé de référence pour les roues cylindriques mm
ρ
fP
ρ Rayon de courbure relative mm
rel
ρ Rayon du profil de raccordement du pied de dent à la section critique mm
F
Couche de glissement mm
ρ¢
σ Résistance à la traction N/mm
B
σ Contrainte au pied de dent N/mm
F
σ Valeur de la contrainte de référence (flexion) N/mm
F lim
N/mm
σ Valeur de la contrainte admissible de référence (flexion) = σ Y
FE F lim ST
σ Contrainte au pied de dent limite N/mm
FG
σ Contrainte au pied de dent admissible N/mm
FP
Contrainte au pied de dent de base N/mm
σ
F0
Pression de contact effective N/mm
σ
H
Tableau 1 (suite)
Symbole Désignation ou terme Unité
σ Pression de contact de référence N/mm
H lim
N/mm
σ Pression de contact admissible modifiée = s S
HG HP H min
σ Pression de contact admissible N/mm
HP
σ Pression de contact de base N/mm
H0
Limite élastique N/mm
σ
S
Limite élastique conventionnelle à 0,2 % d’allongement N/mm
σ
0,2
−1
χ* Gradient de contrainte relatif en fond d’entaille mm
−1
χ* Gradient de contrainte relatif dans une pièce d’essai polie mm
p
−1
χ* Gradient de contrainte relatif dans le pied d’une roue d’essai de référence mm
T
w Vitesse angulaire de pignon, de roue rad/s
1,2
a
Pour les engrenages à denture extérieure, a, u, z et z sont positifs; pour les engrenages à denture intérieure, a, u et z sont négatifs, et
1 2 2
z positif.
4 Application
4.1 Conception, applications spécifiques
4.1.1 Généralités
Les concepteurs d’engrenages doivent savoir que les exigences pour des applications différentes varient de façon
considérable. L’utilisation des méthodes de la présente Norme internationale pour les applications spécifiques
exige une évaluation attentive de toutes les considérations applicables, en particulier:
de la contrainte admissible par le matériau et le nombre de cycles de mise en charge;
des conséquences du pourcentage éventuel de défaillances (taux de défaillance);
du coefficient de sécurité approprié.
Il convient d’analyser, par des méthodes générales de conception mécanique, les considérations de conception
afin d’éviter les ruptures provenant des points de concentration de contrainte dans le flanc des dents, l’écornage
des sommets et les fissures du corps de roue à travers le voile et le moyeu,
Tous les variantes selon les points suivants doivent être consignées dans le rapport de calcul:
a) Si une méthode de calcul plus affinée est souhaitée ou si la conformité avec les restrictions de 4.1 est
impossible pour une raison quelconque, les facteurs pertinents peuvent être évalués selon la norme de
référence ou toute autre norme d'application.
b) Des facteurs déduits à partir d'une expérience fiable ou des données d'essai peuvent être utilisés à la place
des facteurs individuels selon la présente Norme internationale. À cet égard, les critères pour la méthode A de
4.1.8.1 de l'ISO 6336-1:1996 sont applicables.
À d'autres égards, les calculs de la capacité de charge doivent être strictement conformes à la présente Norme
internationale pour que les contraintes, les coefficients de sécurité, etc., puissent être classés selon la présente
Norme internationale.
8 © ISO 2002 – Tous droits réservés
La présente Norme internationale reconnaît deux types de conceptions de systèmes de transmission industriels.
transmissions sous carter catalogue, calculées pour des valeurs de charge nominale pour la vente par
catalogue ou sur stock. Les charges réelles et les conditions de fonctionnement ne sont pas exactement
connues au moment de la conception.
NOTE Les charges réelles pour chaque application sont évaluées pour sélectionner un appareil correctement
dimensionné dans le catalogue. Un facteur de sélection, basé sur l’expérience d’applications similaires, est souvent utilisé
pour réduire la valeur de la capacité de charge catalogue afin qu’elle corresponde aux conditions d’applications (voir
l'ISO/TR 13593).
transmissions spéciales destinées à une application spécifique pour laquelle les conditions de
fonctionnement sont connues ou spécifiées au moment de la conception.
La présente Norme internationale s'applique quand le corps de roue, les liaisons arbre/moyeu, les arbres, les
paliers, les logements, les liaisons filetées, les fondations et les accouplements sont conformes aux prescriptions
concernant la précision, la capacité de charge et la rigidité qui forment la base de calcul de la capacité de charge
des engrenages.
Bien que la méthode décrite dans la présente Norme internationale soit surtout destinée à des fins de recalcul, par
itération, elle peut aussi être utilisée afin de déterminer la capacité de charge des engrenages. L’itération se fait en
sélectionnant une charge et en calculant le coefficient de sécurité correspondant contre la formation de piqûres,
S , pour le pignon. Si S est supérieur à S , la charge est augmentée; s’il est inférieur à S , la charge est
H1 H1 H min H min
réduite. Ainsi de suite jusqu’à ce que la charge choisie corresponde à S = S . La même méthode est utilisée
H1 H min
pour la roue (S = S ) ainsi que pour les coefficients de sécurité contre la rupture des dents S = S = S .
H2 H min F1 F2 F min
4.1.2 Données sur l’engrenage
La présente Norme internationale s’applique dans la limite des contraintes suivantes:
a) Types d’engrenage:
roue à denture droite à profil développante de cercle, roue à denture hélicoïdale et roue à denture
chevron à denture extérieure et à denture intérieure;
pour les roues à denture chevron, il est supposé que la charge tangentielle totale est répartie
équitablement entre les deux hélices. Si ce n’est pas le cas, par exemple en raison des forces axiales
appliquées de l’extérieur, il faut en tenir compte. Les deux hélices sont traitées comme deux roues à
denture hélicoïdale simples en parallèle.
b) Domaine des vitesses:
−1
n égal ou inférieur à 3 600 min (vitesse synchrone d’un moteur bipolaire à une fréquence de courant de
2)
60 Hz) ;
domaine de vitesses subcritiques (voir K , en 5.6);
v
à des vitesses v < 1 m/s, la capacité de charge des engrenages est souvent limitée par l’usure.
c) Précision des engrenages:
classe de précision 10 ou supérieure selon l’ISO 1328-1 (affecte K , K et K ).
v Hα Hβ
2) Pour des vitesses supérieures, les exigences de l’ISO 6336 ou de l’ISO 9084 s’appliquent.
d) Domaine des rapports de conduite apparents d’engrenages à denture droite équivalents
1,2 < ε < 1,9 (affecte c′, c , K , K , K , K , et K ).
α γ v Hβ Fβ Hα Fα
e) Domaine des angles d’hélice
β inférieur ou égal à 30 ° (affecte c¢, c , K et K ).
γ v Hβ
4.1.3 Pignon et pignon arbré
La présente Norme internationale s’applique aux pignons pleins arbrés ou aux pignons creux avec s /d W 0,2
R 1
(affecte c¢, c , K , K ). Il est supposé que les pignons alésés seront montés sur des arbres pleins ou sur des
γ v Hβ
arbres creux avec d /d < 0,5 (cela affecte K )
shi sh Hβ
4.1.4 Corps de roue, jante de roue
Les formules données sont valables pour les engrenages à dentures droite et hélicoïdale avec une épaisseur de
jante minimale sous le pied de S W 3,5m . Le calcul de K suppose que la roue et l’arbre de roue sont
R n Hβ
suffisamment rigides pour que leurs flèches puissent être ignorées.
4.1.5 Matériaux
Ils comprennent les aciers, la fonte à graphite sphéroïdale et la fonte grise (cela affecte Z , σ , σ , K , K ,
E H lim FE v Hβ
K , K et K ). Pour les matériaux et leurs abréviations utilisées dans la présente Norme internationale, voir le
Fβ Hα Fα
Tableau 2.
Tableau 2 — Matériaux
Matériau Abréviation
Acier (s < 800 N/mm ) St
B
Acier au carbone ou acier allié moulé (σ W 800 N/mm ) St (moulé)
B
Acier au carbone ou acier allié trempé à cœur (σ < 800 N/mm ) V
B
Fonte grise GG
Fonte à graphite sphéroïdal (structure perlitique, bainitique, ferritique) GGG (perl., bai., ferr.)
Fonte noire malléable (structure perlitique) GTS (perl.)
Acier cémenté Eh
Acier et fonte à graphite sphéroïdal, durci superficiellement à la flamme IF
Acier de nitruration, nitruré NT (nitr.)
Acier traité à cœur et cémenté, nitruré NV (nitr.)
Acier traité à cœur et cémenté, nitrocarburé NV (nitrocar.)
4.1.6 Lubrification
Les méthodes de calcul sont valables pour les engrenages lubrifiés à l’huile qui ont une quantité suffisante de
lubrifiant d’une viscosité adaptée à l’engrènement et quand la température de service est également adaptée (cela
affecte la formation du film de lubrifiant, c’est-à-dire les facteurs Z , Z et Z ).
L V R
10 © ISO 2002 – Tous droits réservés
4.2 Coefficients de sécurité
Il est nécessaire de distinguer entre le coefficient de sécurité concernant la formation de piqûres, S , et le
H
coefficient de sécurité concernant la rupture de dent, S .
F
Pour une application donnée, une capacité de charge adéquate pour les engrenages est démontrée lorsque les
valeurs calculées de S et S sont égales ou supérieures aux valeurs S et S respectivement.
H F H min F min
Il y a lieu de baser le choix de la valeur d’un coefficient de sécurité sur le niveau de confiance dans la fiabilité des
données disponibles et sur les conséquences des défaillances éventuelles.
Les facteurs à prendre en compte sont les suivants:
a) que la validité des valeurs données dans l’ISO 6336-5 est pour une probabilité de détérioration de 1 %;
b) la qualité spécifiée et l’efficacité de la maîtrise du contrôle qualité à tous les stades de la fabrication,
c) la précision des spécifications du service et des conditions externes, et
d) la rupture des dents qui est souvent considérée comme un risque plus grand que la formation de piqûres.
Par conséquent, il est recommandé de choisir une valeur de S qui soit supérieure à celle de S .
Fmin Hmin
Pour le calcul du coefficient de sécurité réel, voir 6.1.5 (S , formation de piqûres) et 7.1.4 (S , rupture de dents).
H F
Pour les coefficients de sécurité minimaux, voir 6.12 (piqûres) et 7.9 (rupture de dents). Cependant, il est
recommandé que l’acheteur et le fabricant se mettent d’accord sur les valeurs minimales des coefficients de
sécurité.
4.3 Données d’entrée
Les données suivantes doivent être disponibles pour les calculs:
a) données sur les roues dentées:
a, z , z , m , d , d , d b b , b , x , x , α , β, ε , ε (voir ISO 53, ISO 54) (voir 4.4 pour la définition des
1 2 n 1 a1 a2, , H F 1 2 n α β
largeurs de denture b, b et b );
H F
b) profil de denture du tracé de référence de l’outil:
h , r (voir ISO 53);
a0 a0
c) données de conception et de fabrication:
C , C , f , S , S , Ra , Ra , Rz , Rz ;
a1 a2 pb H min F min
1 2 1 2
les détails sur les matériaux, les duretés et le traitement thermique des matériaux, la classe de précision des
engrenages, l’écartement entre paliers l, les positions des roues dentées par rapport aux paliers; les
dimensions de l’arbre du pignon, d , et, le cas échéant, les modifications de l’hélice (bombé, dépouille
sh
d’extrémité);
d) données de puissance:
P ou T ou F , n , n , détails des machines menantes ou menées.
t 1 1
Les données géométriques nécessaires peuvent être calculées selon les normes nationales.
Il convient que les informations que doivent s’échanger le fabricant et l’acheteur incluent les données spécifiant les
préférences en matière de matériaux, la lubrification, le coefficient de sécurité et les forces extérieures appliquées
dues aux vibrations et aux surcharges (facteur d’application).
4.4 Largeurs de denture
Les largeurs de denture suivantes doivent être distinguées:
b: la plus petite des largeurs de denture du pignon et de la roue mesurées sur les cercles primitifs de
fonctionnement (pour une roue à chevrons, b = 2b ). Les chanfreins ou les arrondis des extrémités des dents
H B
sont à ignorer. Quand les largeurs de denture sont décalées, la longueur de denture en contact doit être
utilisée.
b : la largeur de denture au cercle primitif de la roue (pour une roue à chevrons, b = 2b ). Quand la largeur
H H B
de denture b est plus grande que celle de sa roue conjuguée, b doit être basé sur la plus petite largeur de
H H
denture sans tenir compte des chanfreins ou de l’arrondi d’extrémité de dent intentionnels. Ni les portions non
durcies des flancs des roues durcies superficiellement ni les zones de transition ne doivent être introduites.
Quand les largeurs de denture sont décalées, la largeur de denture en contact doit être utilisée.
b : la largeur de denture au cylindre de pied de la roue (pour une roue à chevrons, b = 2b ). Quand la largeur
F F B
de denture b est plus grande que celle de sa roue conjuguée, b doit être basé sur la petite largeur de
F F
denture plus une longueur, ne dépassant pas un module d’une extension quelconque à une extrémité de dent.
Cependant, s’il est prévu qu’en raison du bombé ou de la dépouille d’extrémité, la conduite ne s’étend pas
jusqu’à l’extrémité de la denture, il faut alors utiliser la plus petite largeur de denture pour le pignon et la roue.
Quand les largeurs de denture sont décalées, la largeur de denture en contact doit être utilisée.
4.5 Équations numériques
Les unités énumérées à l’article 3 doivent être utilisées dans tous les calculs. Des informations pour faciliter
l’utilisation de la présente Norme internationale sont données dans l’annexe C de l’ISO 6336-1:1996.
5 Facteurs d’influence
5.1 Généralités
Les facteurs d’influence, K , K , K , K et K , dépendent tous de la charge correspondante sur la dent. Il s’agit
v Hα Hβ Fα Fβ
initialement de la charge appliquée (charge tangentielle nominale multipliée par le facteur d’application). Les
facteurs sont également interdépendants et doivent, par conséquent, être calculés successivement de la manière
suivante:
a) K avec la charge tangentielle appliquée F K ;
v t A
b) K ou K avec la charge recalculée F K K ;
Hb Fb t A v
c) K ou K avec la charge tangentielle appliquée F K .
Ha Fa t A
Quand une roue dentée mène deux roues conjuguées ou plus, il est nécessaire de remplacer K par K K . Si c’est
A A γ
possible, il est préférable que le facteur de répartition de la charge, K soit déterminé par mesure; alternativement,
γ
sa valeur peut être déterminée à partir des informations disponibles.
5.2 Charge tangentielle nominale, F , couple nominal, T, puissance nominale P
t
La charge tangentielle nominale, F , est déterminée dans le plan apparent au niveau du cylindre de référence. Elle
t
est fondée sur le couple en entrée vers la machine menée. Ce couple correspond à la condition de fonctionnement
12 © ISO 2002 – Tous droits réservés
régulier la plus sévère. Une autre solution consiste à utiliser comme base le couple nominal de la machine motrice
s’il correspond au couple requis de la machine menée ou toute autre base appropriée.
2 000 T
19 098 ¥ 1000 PP1000
1,2
F = = = . (1)
t
v
ddn
1,2 1,2 1,2
Fd
1000 9PP549
t1,2
T = = = (2)
1, 2
2000 ω n
1, 2 1, 2
TT ω n
Fv
1, 2 1,2 1, 2 1, 2
t
P = = = (3)
1000 1000 9 549
ddω n
1, 2 1, 2 1, 2 1, 2
v = = (4)
2 000 19 098
πnn
2000 v
1, 2 1, 2
ω== = (5)
1, 2
30 d 9 549
1, 2
5.3 Charge non uniforme, couple non uniforme, puissance non uniforme
Lorsque la charge transmise n’est pas uniforme, il convient de tenir compte non seulement du pic de charge et du
nombre de cycles estimé, mais aussi des charges intermédiaires et de leurs nombres de cycles. Ce type de charge
est classé comme un cycle de service et il peut être représenté par un spectre de charge. Dans de tels cas, l’effet
de fatigue cumulé du cycle de service est pris en compte dans le calcul de la capacité de charge de l'engrenage.
Une méthode de calcul de l’effet des charges dans de telles conditions est donnée dans l’ISO/TR 10495.
5.4 Charge tangentielle maximale, F , couple maximal T , puissance maximale, P
t max max max
Il s’agit de la charge tangentielle maximale, F , (ou bien le couple maximal correspondant, T , ou la
t max max
puissance maximale correspondante, P ) dans la plage de service variable. Son amplitude peut être limitée par
max
un accouplement de sécurité de sensibilité appropriée. F , T et P doivent être connus quand la sécurité
t max max max
contre les détériorations par piqûres et par rupture brutale de dents sous l’effet de la charge correspondant à la
limite de contrainte statique est déterminée (voir 5.5).
5.5 Facteur d’application, K
A
5.5.1 Généralités
Le facteur K corrige la charge nominale F , afin de compenser les surcharges d’engrènement dues aux sources
A t
extérieures. Ces forces supplémentaires dépende
...
Frequently Asked Questions
ISO 9085:2002 is a standard published by the International Organization for Standardization (ISO). Its full title is "Calculation of load capacity of spur and helical gears - Application for industrial gears". This standard covers: The formulae specified in this International Standard are intended to establish a uniformly acceptable method for calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth. The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth finished by forging or sintering. It is not applicable to gears which have a poor contact pattern. This International Standard provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. Neither is it intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. CAUTION - The user is cautioned that the calculated results of this International Standard should be confirmed by experience.
The formulae specified in this International Standard are intended to establish a uniformly acceptable method for calculating the pitting resistance and bending strength capacity of industrial gears with spur or helical teeth. The rating formulae in this International Standard are not applicable to other types of gear tooth deterioration such as plastic yielding, micropitting, scuffing, case crushing, welding and wear, and are not applicable under vibratory conditions where there may be an unpredictable profile breakdown. The bending strength formulae are applicable to fractures at the tooth fillet, but are not applicable to fractures on the tooth working profile surfaces, failure of the gear rim, or failures of the gear blank through web and hub. This International Standard does not apply to teeth finished by forging or sintering. It is not applicable to gears which have a poor contact pattern. This International Standard provides a method by which different gear designs can be compared. It is not intended to assure the performance of assembled drive gear systems. Neither is it intended for use by the general engineering public. Instead, it is intended for use by the experienced gear designer who is capable of selecting reasonable values for the factors in these formulae based on knowledge of similar designs and awareness of the effects of the items discussed. CAUTION - The user is cautioned that the calculated results of this International Standard should be confirmed by experience.
ISO 9085:2002 is classified under the following ICS (International Classification for Standards) categories: 21.200 - Gears. The ICS classification helps identify the subject area and facilitates finding related standards.
You can purchase ISO 9085:2002 directly from iTeh Standards. The document is available in PDF format and is delivered instantly after payment. Add the standard to your cart and complete the secure checkout process. iTeh Standards is an authorized distributor of ISO standards.
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