ISO 10300-1:2001
(Main)Calculation of load capacity of bevel gears - Part 1: Introduction and general influence factors
Calculation of load capacity of bevel gears - Part 1: Introduction and general influence factors
Calcul de la capacité de charge des engrenages coniques — Partie 1: Introduction et facteurs généraux d'influence
Izračun nosilnosti stožčastih zobnikov - 1. del: Uvod in koeficienti
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ISO 10300-1:2001 is a standard published by the International Organization for Standardization (ISO). Its full title is "Calculation of load capacity of bevel gears - Part 1: Introduction and general influence factors". This standard covers: Calculation of load capacity of bevel gears - Part 1: Introduction and general influence factors
Calculation of load capacity of bevel gears - Part 1: Introduction and general influence factors
ISO 10300-1:2001 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.
ISO 10300-1:2001 has the following relationships with other standards: It is inter standard links to ISO 10300-1:2014. Understanding these relationships helps ensure you are using the most current and applicable version of the standard.
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Standards Content (Sample)
INTERNATIONAL ISO
STANDARD 10300-1
First edition
2001-08-01
Calculation of load capacity of bevel
gears —
Part 1:
Introduction and general influence factors
Calcul de la capacité de charge des engrenages coniques —
Partie 1: Introduction et facteurs généraux d’influence
Reference number
©
ISO 2001
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ii © ISO 2001 – All rights reserved
Contents Page
Foreword.iv
Introduction.v
1 Scope .1
2 Normative references .1
3 Terms and definitions .2
4 Symbols and abbreviations.2
5 Application .10
6 External force and application factor, K .13
A
7 Dynamic factor, K .15
v
8 Face load factors, K , K .25
H� F�
9 Transverse load factors, K , K .27
H� F�
Annex A (normative) Calculation of bevel gear geometry.34
Annex B (informative) Values for application factor, K .45
A
Annex C (informative) Contact patterns.46
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 part of ISO 10300 may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 10300-1 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee
SC 2, Gear capacity calculation.
ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel gears:
� Part 1: Introduction and general influence factors
� Part 2: Calculation of surface durability (pitting)
� Part 3: Calculation of tooth root strength
Annex A forms an integral part of this part of ISO 10300. Annex B and annex C are for information only.
iv © ISO 2001 – All rights reserved
Introduction
Parts 1, 2 and 3 of ISO 10300, taken together with ISO 6336-5, are intended to establish general principles and
procedures for the calculation of the load capacity of bevel gears. Moreover, ISO 10300 has been designed to
facilitate the application of future knowledge and developments, as well as the exchange of information gained from
experience.
Several methods for the calculation of load capacity and various factors are specified by ISO 10300, whose
guidelines are complex, yet flexible. There could be differences of up to 20 % to 25 % between the results of
calculations carried out using method B with method B1 and method B2 with method C. The combined use of
methods B2 and C, considered the methods of greater simplification, provides a more conservative safety factor.
Detailed or simplified methods can be included, as appropriate, in application standards derived from ISO 10300 in
the fields of industrial and marine gears. However, it must be stressed that the methods’ use for specific
applications demands not only experience with combined calculation methods, but also a realistic and
knowledgeable appraisal of all relevant considerations, as well as appropriate safety factors.
The more detailed calculation methods of ISO 10300 are intended for the recalculation of the load capacity limits of
gears where all important data, such as existing gear sets and completed gear designs, is known. The approximate
methods of ISO 10300 are to be used for preliminary estimates of gear capacity where the final details of the gear
design are as yet unknown.
The procedures covered by ISO 10300 are based on both testing and theoretical studies. However, the results
obtained from its rating calculations may not be in good agreement with certain, previously accepted, gear-
calculation methods.
ISO 10300 provides methods by which different gear designs can be compared. It is not intended to ensure the
performance of assembled gear-drive systems. Neither is it intended for use by the average engineer. Rather, it is
aimed at the experienced gear designer capable of selecting reasonable values for the factors in these formulae,
based on knowledge of similar designs and on awareness of the effects of the items discussed.
INTERNATIONAL STANDARD ISO 10300-1:2001(E)
Calculation of load capacity of bevel gears —
Part 1:
Introduction and general influence factors
1 Scope
The formulae in ISO 10300 are intended to establish uniformly acceptable methods for calculating the pitting
resistance and bending-strength capacity of straight and helical (skew), zerol and spiral bevel gears except hypoid
gears. They are applicable equally to tapered depth and uniform depth teeth.
The formulae take into account the known major factors influencing gear-tooth pitting and fractures at the root fillet,
as well as allowing for the inclusion of new factors at a later date. The rating formulae are not applicable to other
types of gear-tooth deterioration such as plastic yielding, micropitting, case crushing, welding, and wear. The
bending-strength formulae are applicable to fractures at the tooth fillet, but not to those on the tooth-working profile
surfaces, nor to failure of the gear rim or of the gear blank through the web and hub. Pitting resistance and
bending-strength capacity rating systems for a particular category of bevel gear can be established by selecting
proper values for the factors used in the general formulae. ISO 10300 is not applicable to bevel gears which have
an inadequate contact pattern.
ISO 10300 is restricted to bevel gears whose virtual cylindrical gears have transverse contact ratios of ε <2. The
v�
given relations are valid for gears of which the sum of addendum modification factors of pinion and gear is zero, i.e.
the normal operating pressure angle of the gear pair is the same as the normal pressure angle of the basic rack.
NOTE Methods for the calculation of the load capacity of hypoid gears are indicated by the manufacturers of gear-cutting
machines.
CAUTION — The user is cautioned that when the methods are used for large spiral and pressure angles,
and for large face width b � 10 m , the calculated results of ISO 10300 should be confirmed by experience.
mn
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 10300. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 10300 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth.
ISO 6336-1, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors.
ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials.
ISO 10300-2, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability (pitting).
ISO 10300-3, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength.
ISO/TR 10495, Cylindrical gears — Calculation of service life under variable loads — Conditions for cylindrical
gears according to ISO 6336.
3 Terms and definitions
For the purposes of this part of ISO 10300, terms and definitions consistent with those given in ISO 53 and
ISO 1122-1 apply.
4 Symbols and abbreviations
The symbols used in this part of ISO 10300 (see Table 1) are based on those of ISO 701, while also including
symbols given in ISO 1328-1.
2 © ISO 2001 – All rights reserved
Table 1 — Symbols and abbreviations used in parts 1, 2 and 3 of ISO 10300
Symbol Description or term Unit
a centre distance of virtual cylindrical gear mm
v
a centre distance of virtual cylindrical gear in normal section mm
vn
face width mm
b
b calculated effective face width mm
ce
b effective face width mm
e
�b heel increment of face width mm
e
effective heel increment of face width mm
�b �
e
toe increment of face width mm
�b
i
effective toe increment of face width mm
�b�
i
c dimensionless parameter —
v
c mesh stiffness
N/(mm � µm)
�
c mesh stiffness for average conditions
N/(mm � µm)
�0
c� single stiffness (see ISO 6336-1) N/(mm � µm)
c � single stiffness for average conditions N/(mm � µm)
d outer pitch diameter mm
e
d mean pitch diameter mm
m
d
reference diameter of virtual cylindrical gear mm
v
d tip diameter of virtual cylindrical gear mm
va
d tip diameter of virtual cylindrical gear in normal section mm
van
d base diameter of virtual cylindrical gear mm
vb
d base diameter of virtual cylindrical gear in normal section mm
vbn
d
reference diameter of virtual cylindrical gear in normal section mm
vn
distance to a line of contact mm
f
*
f referreddistancetomiddlelineofcontact —
f profile form deviationµm
f�
f maximum distance to middle line of contact mm
max
f single pitch deviationµm
pt
f
effective pitch deviationµm
peff
f
load correction factor —
F
g assumed distance in locating weakest section mm
f0
g length of path of contact of virtual cylindrical gear mm
v�
g length of path of contact of virtual cylindrical gear in normal section mm
v�n
g
distance between the centre of the cutter edge radius and the centreline of mm
xb
the gear measured along the tool reference plane
g distance from centre of tooth tip edge radius to crown gear pitch surface mm
yb
measured in a direction perpendicular to pitch surface
Table 1 (continued)
Symbol Description Unit
g intermediate variable for calculating tooth strength factor mm
za
g intermediate variable for calculating tooth strength factor mm
zb
g intermediate variable for calculating tooth strength factor mm
J
intermediate variable for calculating tooth strength factor mm
g �
J
g projected length of instantaneous line of contact in lengthwise direction of mm
K
tooth
g length of action within the contact ellipse mm
η
g distance from centreline of crown gear (tool) space to tool centre tip edge mm
radius measured in mean normal section
g �� distance from mean section to centre of pressure measured in the mm
lengthwise direction along the tooth
h outer addendum mm
ae
h
mean addendum mm
am
h addendum of the basic rack profile mm
aP
h tool addendum mm
a0
h
outer dedendum mm
fe
h dedendum of the basic rack profile mm
fP
h mean dedendum mm
fm
h tool dedendum mm
f0
h bending moment arm for tooth root stress (load application at tooth tip) mm
Fa
h
load height from critical section mm
N
summation index —
k
constant of location —
k�
l length of contact line mm
b
l length of middle line of contact mm
bm
l � projected length of middle line of contact mm
bm
m
outer transverse module mm
et
m mean normal module mm
mn
m
mean transverse module mm
mt
m mass per mm facewidth reduced to the line of action of the dynamically kg/mm
red
equivalent cylindrical gears
*
m relative individual gear mass per unit facewidth referred to line of action kg/mm
–1
n rotational speed min
–1
n
resonance speed of pinion min
E1
peak load N/mm
p
protuberance of the tool mm
pr
p maximum peak load N/mm
max
*
referred peak load —
p
4 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
p transverse base pitch of virtual cylindrical gear mm
et
machining stock mm
q
exponent in the formula for lengthwise curvature factor —
q
q notch parameter —
s
q notch parameter of test gear —
sT
r cutter radius mm
c0
r
tooth fillet radius at the mean section mm
mf
r mean transverse radius to point of load application mm
my 0
distance from pitch circle to point of load application in mean normal mm
�r
y0
section
s transverse tooth thickness at the back cone mm
et
s mean normal topland mm
amn
s
mean normal circular thickness mm
mn
s amount of protuberance mm
pr
s mean transverse circular thickness mm
mt
s tooth root chord in calculation section mm
Fn
s one-half tooth thickness at critical section mm
N
u gear ratio of bevel gear —
u
gear ratio of virtual cylindrical gear —
v
v tangential speed at outer end (heel) of reference cone m/s
et
v maximum pitch line velocity at operating pitch diameter m/s
et max
v
tangential speed at reference cone at mid-facewidth m/s
mt
x profile shift coefficient —
hm
x
thickness modification coefficient —
sm
x pinion tooth strength factor mm
N
y running-in allowance for pitch error related to the smooth polished test µm
p
piece
y location of point of load application for maximum bending stress on path of mm
J
action
y location of point of load application on path of action mm
y
running-in allowance for pitch errorµm
�
z number of teeth —
z
number of teeth of virtual cylindrical gear —
v
z number of teeth of virtual cylindrical gear in normal section —
vn
auxiliary factor for dynamic factor —
A
* 2
A auxiliary value for load sharing factor
mm
m
* 2
A auxiliary value for load sharing factor
mm
r
Table 1 (continued)
Symbol Description Unit
A outer tooth thickness allowance mm
sne
* 2
A auxiliary value for load sharing factor
mm
t
auxiliary factor for dynamic factor —
B
quality grade —
C
C tip relief µm
a
C correction factor for tooth stiffness for non-average conditions —
b
C correction factor for tooth stiffness for non-average conditions —
F
C ,C ,C
factors for determining lubricant film factors —
ZL ZR ZV
modulus of elasticity, Young’s modulus N/mm
E
E, G, H auxiliary factors for tooth form factor —
auxiliary factor for mid-zone factor —
F
F nominal tangential force at reference cone at mid-facewidth N
mt
F decisive tangential force at reference cone at mid-facewidth N
mt H
Brinell hardness —
HB
constant; factor concerning tooth load —
K
K dynamic factor —
v
K application factor —
A
K
lengthwise curvature factor for bending stress —
F0
K transverse load factor for bending stress —
F�
K face load factor for bending stress —
F�
K transverse load factor for contact stress —
H�
K face load factor for contact stress —
H�
K
bearing factor —
H�-be
empirical constant used in stress correction formula —
L
L auxiliary factor for correction factor —
a
empirical constant used in stress correction formula —
M
reference speed for n —
N
E1
N number of load cycles —
L
empirical constant used in stress correction formula —
O
nominal power kW
P
–1
P outer diametral pitch inch
d
= CLA = AA arithmetic average roughnessµm
Ra
R outer cone distance mm
e
R mean cone distance mm
m
mean roughnessµm
Rz
Rz mean roughness of test gearµm
T
6 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
Rz mean roughness for gear pairs with ρ =10mm µm
10 red
S safety factor for bending stress (against breakage) —
F
S minimum safety factor for bending stress —
Fmin
S safety factor for contact stress (against pitting) —
H
S
minimum safety factor for contact stress —
Hmin
nominal torque Nm
T
tooth form factor —
Y
Y inertia factor —
i
Y stress concentration and stress correction factor —
f
Y bevel gear adjustment factor —
A
Y bending stress factor —
B
Y
compression stress factor —
C
Y tooth form factor for load application at tip —
Fa
Y combined tooth form factor for generated gears —
FS
Y
bevel geometry factor (Method B2) —
J
Y bevel gear factor —
K
Y
load sharing factor (bending strength) —
LS
Y life factor of the standard test gear —
NT
Y combined geometry factor —
P
Y
surface factor of smooth specimen —
R
Y surface factor of test gear with roughness of Rz =10µm —
RT
T
Y
relative surface factor —
Rrel T
Y stress correction factor for load application at tooth tip —
Sa
Y stress correction factor for dimensions of standard test gear —
ST
Y
size factor for tooth root stress —
X
Y dynamic sensitivity factor of the gear to be determined —
�
Y dynamic sensitivity factor of the standard test gear —
�T
Y relative sensitivity factor —
� rel T
Y contact ratio factor (tooth root) —
�
Z
speed factor —
v
Z elasticity factor —
E
Z
zone factor —
H
Z bevel gear factor (flank) —
K
Z lubricant factor —
L
Z
load sharing factor —
LS
Table 1 (continued)
Symbol Description Unit
Z mid-zone factor —
M-B
Z life factor of the standard test gear —
NT
Z
roughness factor for contact stress —
R
Z size factor —
X
Z
work-hardening factor —
W
Z helix angle factor for contact stress —
�
� normal pressure angle at point of load application on the tooth centreline �
h
� normal pressure angle
�
n
� normal pressure angle of virtual cylindrical gear (=� ) �
vn n
transverse pressure angle of virtual cylindrical gear
� �
vt
working transverse pressure angle
� �
wt
load application angle at tip circle of virtual spur gear
� �
Fan
normal pressure angle at point of load application on the tooth surface
� �
L
� mean spiral angle �
m
� helix angle at base circle of virtual cylindrical gear �
vb
� auxiliary angle for tooth form and tooth correction factor �
a
� pitch angle �
� face angle
�
a
� root angle
�
f
transverse contact ratio of virtual cylindrical gear —
�
v�
� transverse contact ratio of virtual cylindrical gear in normal section —
v�n
overlap ratio of virtual cylindrical gear —
�
v�
� modified contact ratio —
v�
� load sharing ratio —
N
� addendum angle �
a
� dedendum angle �
f
� assumed angle in locating weakest section �
one half of angle subtended by normal circular tooth thickness at point of
� �
h
load application
� density kg/mm
� cutter edge radius mm
a0
� root fillet radius of basic rack for cylindrical gears mm
fP
� radius of relative curvature mm
red
� mm
fillet radius at point of contact of 30� tangent
Fn
gliding thickness mm
��
8 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
tensile strength N/mm
�
B
tooth root stress N/mm
�
F
nominal stress number (bending) N/mm
�
F lim
allowable stress number (bending) N/mm
�
FE
permissible tooth root stress N/mm
�
FP
local tooth root stress N/mm
�
F0
contact stress N/mm
�
H
� allowable stress number for contact stress N/mm
H lim
� permissible contact stress N/mm
HP
� nominal value of contact stress N/mm
H0
� stress at 0,2% permanent elongation N/mm
0,2
� angle between tangent of root fillet at weakest point and centreline of tooth �
auxiliary factor for tooth form and tooth correction factors —
�
Poisson’sratio —
�
� , � nominal kinematic viscosity of the oil at 40� C and 50� C respectively mm /s
40 50
� angular velocity rad/s
X �1
� relative stress drop in notch root
mm
X �1
relative stress drop in notch root of test gear
�
mm
T
shaft angle
� �
Other subscripts
tool
pinion
wheel
x
dynamically equivalent cylindrical gears
-A, -B, -B1, -
valueaccordingtomethod A, B, B1,B2orC
B2, -C
(1), (2)
trials of interpolation
*
value related to m (except m*)
mn
5 Application
5.1 Methods
5.1.1 General
ISO 10300 is intended mainly for the calculation of bevel gears for which the essential data is known from drawings
or measurement (recalculation). At the preliminary design stage, the available data is limited, and approximations
or empirical values may be used for some factors. Moreover, in certain application fields or for rough calculations
some factors may be assumed as unity or constant. However, a conservative safety factor (see 5.2) should be
chosen in such cases. Wherever there is disagreement, full-scale, full-load testing is preferred over any of the
methods A to C, while method A, if its accuracy and reliability are proven, is preferred over method B, which in turn
is preferred to method C.
5.1.2 Full-scale, full-load testing
The most valid method of predicting overall gear system performance is the full-scale, full-load testing of a specific
gear drive design in order to determine its capacity. This will not require verification by calculation using any of the
methods given. However, it is customary for bevel gears to be developed from a preliminary design according to
methods B or C, then refined by testing to achieve optimum tooth contact, smoothness of operation and
adjustability.
5.1.3 Method A
Where sufficient experience from the operation of other, similar designs is available, satisfactory guidance can be
obtained by the extrapolation of the associated test results or field data. The factors involved in this extrapolation
may be evaluated by the precise measurement and comprehensive mathematical analysis of the transmission
system under consideration, or from field experience. All gear and load data is required to be known for the use of
this method, which shall be clearly described and presented with all mathematical and test premises, boundary
conditions and any specific characteristics of the method that influence the result. The accuracy and the reliability
of the method must be demonstrated. Precision, for example, shall be demonstrated through comparison with
other, acknowledged gear measurements. The method should be approved by both the customer and the supplier.
5.1.4 Method B
Again, where sufficient experience from the operation of other, similar designs is available, satisfactory guidance
can be obtained by the extrapolation of the test results or field data associated with them. However, it is
recommended that the calculation methods be used for comparison of the designs. Additionally, approximate
methods are given for some factors, together with the assumptions relevant to their evaluation. The validity of these
assumptions for the given working conditions shall be checked.
5.1.5 Method C
Where suitable test results, or field experience from similar designs, are unavailable for use in the evaluation of
certain factors, further simplified calculation methods should be used. These are appropriate for particular fields of
application or on the basis of certain premises, for example, those relevant to an acceptance test.
5.2 Safety factors
The allowable probability of failure shall be carefully weighed when choosing a safety factor, in balancing reliability
against cost. If the performance of the gears can be accurately appraised by testing the unit itself under actual load
conditions, lower safety factors may be permitted. The safety factors shall be determined by dividing the specific
calculated strength by the specific operating stress.
In addition to this general requirement, and the special requirements relating to surface durability (pitting) and tooth
root strength given, respectively, in parts 2 and 3 of ISO 10300, safety factors shall be determined only after careful
consideration of the reliability of the material data and of the load values used for calculation. The allowable stress
10 © ISO 2001 – All rights reserved
numbers used for calculation are valid for a given probability of failure, or damage (the material values in
ISO 6336-5, for example, are valid for a 1 % probability of damage), the risk of damage being reduced as the safety
factors are increased, and vice versa. If loads, or the response of the system to vibration, are estimated rather than
measured, a larger factor of safety should be used.
The following variations shall also be taken into consideration in the determination of a safety factor:
� variations in gear geometry due to manufacturing tolerances;
� variations in alignment;
� variations in material due to process variations in chemistry, cleanliness and microstructure (material quality
and heat treatment);
� variations in lubrication and its maintenance over the service life of the gears.
The appropriateness of the safety factors will thus depend on the reliability of the assumptions, such as those
related to load, on which the calculations are based, as well as on the reliability required of the gears themselves,
in respect of the possible consequences of any damage that might occur in the case of failure.
Supplied gears or assembled gear drives should have a minimum safety factor for contact stress, S , value 1,0.
Hmin
The minimum bending-stress, S , value should be 1,3 for spiral bevel gears, and 1,5 for straight bevel gears or
Fmin
where� u 5�.
m
The minimum safety factors against pitting damage and tooth breakage should be agreed between supplier and
customer.
5.3 Rating factors
5.3.1 Testing
The most effective overall approach to gear-system performance management is through the full-scale, full-load
testing of a proposed new design. This approach, however, is limited by its high cost. Alternatively, where sufficient
experience of similar designs exists and results are available, a satisfactory solution can be obtained through
extrapolation from such data. On the other hand, where suitable test results or field data are unavailable, rating-
factor values should be chosen conservatively.
5.3.2 Manufacturing tolerances
Rating factors should be evaluated based on the minimum acceptable quality limits of the expected variation of
component parts in the manufacturing process. The accuracy grade should be determined using ISO 1328-1 with
single pitch deviation.
5.3.3 Implied accuracy
Where the empirical values for rating factors are given by curves, ISO 10300 provides curve-fitting equations to
facilitate computer programming.
NOTE The constants and coefficients used in curve fitting often have significant digits in excess of those implied by the
reliability of the empirical data.
5.4 Other factors to be considered
5.4.1 General
In addition to the factors considered that influence pitting resistance and bending strength, other, interrelated
system factors can have an important effect on overall transmission performance. Their possible effect on the
calculations should be considered.
5.4.2 Lubrication
The ratings determined by the formulae of ISO 10300 shall be valid only if the gear teeth are operated with a
lubricant of proper viscosity and additive package for the load, speed, and surface finish, and if there is a sufficient
quantity of lubricant on the gear teeth and bearings to lubricate and maintain an acceptable operating temperature.
5.4.3 Misalignment
Many gear systems depend on external supports such as machinery foundations to maintain alignment of the gear
mesh. If these supports are poorly designed, initially misaligned, or become misaligned during operation due to
elastic or thermal deflections or other influences, overall gear-system performance will be adversely affected.
5.4.4 Deflection
Deflection of gear-supporting housings, shafts, and bearings due to external overhung, transverse, and thrust loads
affects tooth contact across the mesh. Since deflection varies with load, it is difficult to obtain good tooth contact at
different loads. Generally, deflection due to external loads from driven and driving equipment reduces capacity, and
this, as well as deflection caused by internal forces, should be taken into account when determining the actual gear
tooth contact.
5.4.5 Materials and metallurgy
Most bevel gears are made from carburized case-hardened steel. Allowable stresses for this and other materials
should thus be based on tests on bevel gears wherever these are available. The allowable stress numbers, which
are based on different modes of steel-making and heat-treatment, shall be taken from ISO 6336-5. Hardness and
tensile strength as well as the quality grade shall also be criteria for choosing allowable stress numbers.
NOTE Higher-quality steel grades indicate higher allowable stress numbers, while lower-quality grades indicate lower
allowable stress numbers (see ISO 6336-5).
5.4.6 Residual stress
Any ferrous material having a case-core relationship is likely to have residual stress. If properly managed, such
stress will be compressive at the tooth surface, thereby enhancing the bending-fatigue strength of the gear tooth.
Shot-peening, case-carburizing and induction-hardening, if properly performed, are common methods of inducing
compressive pre-stress in the surface of the gear teeth. Improper grinding techniques after heat treatment may
reduce the residual compressive stresses or even introduce residual tensile stresses in the root fillets of the teeth,
thereby lowering the allowable stress numbers.
5.4.7 System dynamics
The method of analysis used includes a dynamic factor, K in formulae by derating the gears for increased loads
v,
caused by gear-tooth inaccuracies. Generally speaking, this provides simplified values for easy application.
The dynamic response of the system results in additional gear-tooth loads, due to the relative motions of the
connected masses of the driver and the driven equipment. The application factor, K , is intended to account for the
A
operating characteristics of the driving and driven equipment. It must be recognized, however, that if the operating
roughness of the drive, gearbox, or driven equipment causes excitation with a frequency that is near one of the
system’s major natural frequencies, resonant vibrations may cause severe overloads possibly several times higher
12 © ISO 2001 – All rights reserved
than the nominal load. Therefore, where critical service applications are concerned, performance of a vibration
analysis of the complete system is recommended. This analysis shall include the total system, including driver,
gearbox, driven equipment, couplings, mounting conditions and sources of excitation. Natural frequencies, mode
shapes, and the dynamic response amplitudes should be calculated.
5.4.8 Contact pattern
The teeth of most bevel gears are crowned in both their profile and lengthwise directions during the manufacturing
process in order to allow for deflection of the shafts and mountings. This results in a localized contact pattern
during roll testing under light loads. Under design load, unless otherwise specified, the tooth contact pattern is
spread over the tooth flank without concentrations of the pattern at the edges of either member. The application of
the rating formulae to bevel gears manufactured under conditions in which this process has not been carried out
and which do not have an adequate contact pattern may require modifications of the factors given in ISO 10300.
These gears are not covered.
NOTE The total load used for contact pattern analysis can include the effects of an application factor (see annex C for a
fuller explanation of tooth contact development).
5.4.9 Corrosion
Corrosion of the gear-tooth surface can have a significant detrimental effect on the bending strength and pitting
resistance of the teeth. However, the quantification of the effect of corrosion on gear teeth is beyond the range of
ISO 10300.
5.5 Influence and other factors in the basic formulae
Included in the basic formulae presented in ISO 10300 are factors reflecting gear geometry or established by
convention, which need to be calculated in accordance with their formulae.
Also included in the formulae in ISO 10300 are factors that reflect the effects of variations in processing or the
operating cycle of the unit. These are known as influence factors because they account for a number of influences.
Although treated as independent, they may nevertheless influence each other to an extent that is beyond
evaluation. They include the load factors, K , K , K , K , K and K , as well as those factors influencing
A v H� F� H� F�
allowable stresses.
Still other factors included reflect the mathematical relationship, stress vs. life.
The influence factors can be determined by various methods of calculation. These are qualified, as needed, by the
addition of subscripts A through C to the symbols. Unless otherwise specified (for example in an application
standard), the more accurate method is to be preferred for important transmissions. It is recommended that
supplementary subscripts be used whenever the method used for evaluation of a factor would not otherwise be
readily identifiable.
For some applications, it may be necessary to choose between factors determined using alternative methods (for
example, alternatives for the determination of the dynamic factor or the transverse load factor). When reporting the
calculation, the method used should be indicated by extending the subscript.
EXAMPLE K K
v-C, H�-B
6 External force and application factor, K
A
6.1 Nominal tangential force, torque, power
For the purposes of ISO 10300, pinion torque is used in the fundamental stress-calculation formulae. In order to
determine the bending moment on the tooth, or of the force on the tooth surface, the tangential force is calculated
within the stress formula, at the reference cone at mid-facewidth, as follows.
2000T
1,2
F= (1)
mt
d
m1,2
Fd
1000PP9549
mt m1,2
T= = = (2)
1,2
2000 � n
1,2 1,2
TT� n
F
v 1,2 1,2 1,2 1,2
mt mt
P= = = (3)
1000 1000 9549
d �
dn
mt1,2 1,2
m1,2 1,2
v= = (4)
mt
2000 19098
The nominal torque of the driven machine is decisive. This is the operating torque to be transmitted over a long
period of time and under the most severe, regular, working conditions.
EXAMPLE Maximum permanent rolling torque, torque from maximum hoisting weight.
The nominal torque of the driving machine may be used if it corresponds to the required torque of the driven
machine.
6.2 Variable load conditions
If the load is not uniform, a careful analysis of the gear loads should be made, in which the external and internal
dynamic factors are considered. It is recommended that all the different loads that occur during the anticipated life
of the gears, and the duration of each load, be determined. A method based on Miner’s Rule (see ISO/TR 10495)
shall be used for determining the equivalent life of the gears for the torque spectrum.
6.3 Application factor, K
A
In cases where no reliable experiences, or collective load spectra determined by practical measurement or
comprehensive system analysis, are available, calculate using the nominal tangential force F according to clause
mt
6.1 and an application factor, K . This application factor makes allowance for any externally applied dynamic loads
A
in excess of the nominal operating torque load, T .
6.3.1 Factors affecting external dynamic loads
In determining the application factor, account should be taken of the fact that many prime movers develop
momentary peak torques appreciably greater than those determined by the nominal ratings of either the prime
mover or of the driven equipment. There are many possible sources of dynamic overload which should be
considered, including:
� system vibration;
� critical speed;
� acceleration torques;
� overspeed;
� sudden variations in system operation;
� braking;
� negative torques, such as those produced by retarders on vehicles, which result in loading the reverse flanks
of the gear teeth.
14 © ISO 2001 – All rights reserved
Analysis for critical speeds within the operating range of the drive is essential. If critical speeds are present,
changes in the design of the overall drive system shall be made in order to either eliminate them or provide system
damping to minimize gear and shaft vibrations.
6.3.2 Establishment of application factors
Application factors are best established by a thorough analysis of service experience with a particular application.
For applications such as marine gears, which are subjected to cyclic peak torques (torsional vibrations) and are
designed for infinite life, the application factor can be defined as the ratio between cyclic peak torque and the
nominal rated torque. The nominal rated torque is defined by the rated power and speed.
If the gear is subjected to a limited number of loads in excess of the amount of cyclic peak torque, this influence
may be covered directly by means of cumulative fatigue or by means of an increased application factor
representing the influence of the load spectrum.
If service experience is unavailable, a thorough analytical investigation should be made. Annex B provides
approximate values if neither of these alternatives is possible.
7 Dynamic factor, K
v
7.1 General
The dynamic factor, K , makes allowance for the effects of gear tooth quality related to speed and load as well as
v
for the other parameters listed below (see 7.2 to 7.6). The dynamic factor relates the total tooth load, including
internal dynamic effects, to the transmitted tangential tooth load and is expressed as the sum of the internal
effected dynamic load and the transmitted tangential tooth load, divided by the transmitted tangential tooth load.
The parameters for the gear-tooth internal dynamic load fall into two categories: design and manufacturing.
7.2 Design
The design parameters include:
� pitchline speed;
� tooth load;
� inertia and stiffness of the rotating elements;
� tooth stiffness variation;
� lubricant properties;
� stiffness of bearings and case structure;
� critical speeds and internal vibration within the gear itself.
7.3 Manufacturing
The manufacturing parameters include:
� tooth spacing variations;
� runout of pitch surfaces with respect to the axis of rotation;
� tooth flank variations;
� compatibility of mating gear tooth elements;
� balance of parts;
� bearing fit and preload.
7.4 Transmission error
Even if the input torque and speed are constant, significant vibration of the gear masses and the resultant dynamic
tooth forces can exist. These forces result from the relative displacements between the mating gears as they
vibrate in response to an excitation known as transmission error. The ideal kinematics of a gear pair require a
constant ratio between the input and output. Transmission error is defined as the deviation from uniform relative
angular motion of the pair of meshing gears. It is influenced by all deviations from the ideal gear tooth form of the
actual gear design, the manufacturing procedure and the operational conditions. The operational conditions include
the following.
a) Pitch line speed. The frequencies of the excitation depend on the pitch line velocity and module.
b) Gear mesh stiffness variations as the gear teeth pass through the meshing cycle. This is a source of
excitation especially pronounced in straight- and zerol-bevel gears. Spiral-bevel gears with a modified contact
ratio > 2 have less stiffness variation.
c) Transmitted tooth load. Since deflections are load dependent, gear-tooth profile modifications can be
designed to give uniform velocity ratio only for one load magnitude. Loads different from the design load will
increase the transmission error.
d) Dynamic unbalance of the gears and shafts.
e) Application environment. Excessive wear and plastic deformation of the gear tooth profiles increase the
transmission error. Gears must have a properly designed lubrication system, enclosure, and seals to maintain
a safe operating temperature and contamination-free environment.
f) Shaft alignment. Gear-tooth alignment is influenced by load and thermal deformations of gears, shafts,
bearings and housings.
g) Tooth friction-induced excitation.
7.5 Dynamic response
The effects of dynamic tooth forces are influenced by the following:
� mass of the gears, shafts, and other major internal components;
� stiffness of the gear teeth, gear blanks, shafts, bearings and housings;
� damping, of which the principal
...
SLOVENSKI STANDARD
01-julij-2002
,]UDþXQQRVLOQRVWLVWRåþDVWLK]REQLNRYGHO 8YRGLQNRHILFLHQWL
Calculation of load capacity of bevel gears -- Part 1: Introduction and general influence
factors
Calcul de la capacité de charge des engrenages coniques -- Partie 1: Introduction et
facteurs généraux d'influence
Ta slovenski standard je istoveten z: ISO 10300-1:2001
ICS:
21.200 Gonila Gears
2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.
INTERNATIONAL ISO
STANDARD 10300-1
First edition
2001-08-01
Calculation of load capacity of bevel
gears —
Part 1:
Introduction and general influence factors
Calcul de la capacité de charge des engrenages coniques —
Partie 1: Introduction et facteurs généraux d’influence
Reference number
©
ISO 2001
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ii © ISO 2001 – All rights reserved
Contents Page
Foreword.iv
Introduction.v
1 Scope .1
2 Normative references .1
3 Terms and definitions .2
4 Symbols and abbreviations.2
5 Application .10
6 External force and application factor, K .13
A
7 Dynamic factor, K .15
v
8 Face load factors, K , K .25
H� F�
9 Transverse load factors, K , K .27
H� F�
Annex A (normative) Calculation of bevel gear geometry.34
Annex B (informative) Values for application factor, K .45
A
Annex C (informative) Contact patterns.46
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 part of ISO 10300 may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights.
International Standard ISO 10300-1 was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee
SC 2, Gear capacity calculation.
ISO 10300 consists of the following parts, under the general title Calculation of load capacity of bevel gears:
� Part 1: Introduction and general influence factors
� Part 2: Calculation of surface durability (pitting)
� Part 3: Calculation of tooth root strength
Annex A forms an integral part of this part of ISO 10300. Annex B and annex C are for information only.
iv © ISO 2001 – All rights reserved
Introduction
Parts 1, 2 and 3 of ISO 10300, taken together with ISO 6336-5, are intended to establish general principles and
procedures for the calculation of the load capacity of bevel gears. Moreover, ISO 10300 has been designed to
facilitate the application of future knowledge and developments, as well as the exchange of information gained from
experience.
Several methods for the calculation of load capacity and various factors are specified by ISO 10300, whose
guidelines are complex, yet flexible. There could be differences of up to 20 % to 25 % between the results of
calculations carried out using method B with method B1 and method B2 with method C. The combined use of
methods B2 and C, considered the methods of greater simplification, provides a more conservative safety factor.
Detailed or simplified methods can be included, as appropriate, in application standards derived from ISO 10300 in
the fields of industrial and marine gears. However, it must be stressed that the methods’ use for specific
applications demands not only experience with combined calculation methods, but also a realistic and
knowledgeable appraisal of all relevant considerations, as well as appropriate safety factors.
The more detailed calculation methods of ISO 10300 are intended for the recalculation of the load capacity limits of
gears where all important data, such as existing gear sets and completed gear designs, is known. The approximate
methods of ISO 10300 are to be used for preliminary estimates of gear capacity where the final details of the gear
design are as yet unknown.
The procedures covered by ISO 10300 are based on both testing and theoretical studies. However, the results
obtained from its rating calculations may not be in good agreement with certain, previously accepted, gear-
calculation methods.
ISO 10300 provides methods by which different gear designs can be compared. It is not intended to ensure the
performance of assembled gear-drive systems. Neither is it intended for use by the average engineer. Rather, it is
aimed at the experienced gear designer capable of selecting reasonable values for the factors in these formulae,
based on knowledge of similar designs and on awareness of the effects of the items discussed.
INTERNATIONAL STANDARD ISO 10300-1:2001(E)
Calculation of load capacity of bevel gears —
Part 1:
Introduction and general influence factors
1 Scope
The formulae in ISO 10300 are intended to establish uniformly acceptable methods for calculating the pitting
resistance and bending-strength capacity of straight and helical (skew), zerol and spiral bevel gears except hypoid
gears. They are applicable equally to tapered depth and uniform depth teeth.
The formulae take into account the known major factors influencing gear-tooth pitting and fractures at the root fillet,
as well as allowing for the inclusion of new factors at a later date. The rating formulae are not applicable to other
types of gear-tooth deterioration such as plastic yielding, micropitting, case crushing, welding, and wear. The
bending-strength formulae are applicable to fractures at the tooth fillet, but not to those on the tooth-working profile
surfaces, nor to failure of the gear rim or of the gear blank through the web and hub. Pitting resistance and
bending-strength capacity rating systems for a particular category of bevel gear can be established by selecting
proper values for the factors used in the general formulae. ISO 10300 is not applicable to bevel gears which have
an inadequate contact pattern.
ISO 10300 is restricted to bevel gears whose virtual cylindrical gears have transverse contact ratios of ε <2. The
v�
given relations are valid for gears of which the sum of addendum modification factors of pinion and gear is zero, i.e.
the normal operating pressure angle of the gear pair is the same as the normal pressure angle of the basic rack.
NOTE Methods for the calculation of the load capacity of hypoid gears are indicated by the manufacturers of gear-cutting
machines.
CAUTION — The user is cautioned that when the methods are used for large spiral and pressure angles,
and for large face width b � 10 m , the calculated results of ISO 10300 should be confirmed by experience.
mn
2 Normative references
The following normative documents contain provisions which, through reference in this text, constitute provisions of
this part of ISO 10300. For dated references, subsequent amendments to, or revisions of, any of these publications
do not apply. However, parties to agreements based on this part of ISO 10300 are encouraged to investigate the
possibility of applying the most recent editions of the normative documents indicated below. For undated
references, the latest edition of the normative document referred to applies. Members of ISO and IEC maintain
registers of currently valid International Standards.
ISO 53:1998, Cylindrical gears for general and heavy engineering — Standard basic rack tooth profile.
ISO 1122-1:1998, Vocabulary of gear terms — Part 1: Definitions related to geometry.
ISO 1328-1:1995, Cylindrical gears — ISO system of accuracy — Part 1: Definitions and allowable values of
deviations relevant to corresponding flanks of gear teeth.
ISO 6336-1, Calculation of load capacity of spur and helical gears — Part 1: Basic principles, introduction and
general influence factors.
ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials.
ISO 10300-2, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability (pitting).
ISO 10300-3, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength.
ISO/TR 10495, Cylindrical gears — Calculation of service life under variable loads — Conditions for cylindrical
gears according to ISO 6336.
3 Terms and definitions
For the purposes of this part of ISO 10300, terms and definitions consistent with those given in ISO 53 and
ISO 1122-1 apply.
4 Symbols and abbreviations
The symbols used in this part of ISO 10300 (see Table 1) are based on those of ISO 701, while also including
symbols given in ISO 1328-1.
2 © ISO 2001 – All rights reserved
Table 1 — Symbols and abbreviations used in parts 1, 2 and 3 of ISO 10300
Symbol Description or term Unit
a centre distance of virtual cylindrical gear mm
v
a centre distance of virtual cylindrical gear in normal section mm
vn
face width mm
b
b calculated effective face width mm
ce
b effective face width mm
e
�b heel increment of face width mm
e
effective heel increment of face width mm
�b �
e
toe increment of face width mm
�b
i
effective toe increment of face width mm
�b�
i
c dimensionless parameter —
v
c mesh stiffness
N/(mm � µm)
�
c mesh stiffness for average conditions
N/(mm � µm)
�0
c� single stiffness (see ISO 6336-1) N/(mm � µm)
c � single stiffness for average conditions N/(mm � µm)
d outer pitch diameter mm
e
d mean pitch diameter mm
m
d
reference diameter of virtual cylindrical gear mm
v
d tip diameter of virtual cylindrical gear mm
va
d tip diameter of virtual cylindrical gear in normal section mm
van
d base diameter of virtual cylindrical gear mm
vb
d base diameter of virtual cylindrical gear in normal section mm
vbn
d
reference diameter of virtual cylindrical gear in normal section mm
vn
distance to a line of contact mm
f
*
f referreddistancetomiddlelineofcontact —
f profile form deviationµm
f�
f maximum distance to middle line of contact mm
max
f single pitch deviationµm
pt
f
effective pitch deviationµm
peff
f
load correction factor —
F
g assumed distance in locating weakest section mm
f0
g length of path of contact of virtual cylindrical gear mm
v�
g length of path of contact of virtual cylindrical gear in normal section mm
v�n
g
distance between the centre of the cutter edge radius and the centreline of mm
xb
the gear measured along the tool reference plane
g distance from centre of tooth tip edge radius to crown gear pitch surface mm
yb
measured in a direction perpendicular to pitch surface
Table 1 (continued)
Symbol Description Unit
g intermediate variable for calculating tooth strength factor mm
za
g intermediate variable for calculating tooth strength factor mm
zb
g intermediate variable for calculating tooth strength factor mm
J
intermediate variable for calculating tooth strength factor mm
g �
J
g projected length of instantaneous line of contact in lengthwise direction of mm
K
tooth
g length of action within the contact ellipse mm
η
g distance from centreline of crown gear (tool) space to tool centre tip edge mm
radius measured in mean normal section
g �� distance from mean section to centre of pressure measured in the mm
lengthwise direction along the tooth
h outer addendum mm
ae
h
mean addendum mm
am
h addendum of the basic rack profile mm
aP
h tool addendum mm
a0
h
outer dedendum mm
fe
h dedendum of the basic rack profile mm
fP
h mean dedendum mm
fm
h tool dedendum mm
f0
h bending moment arm for tooth root stress (load application at tooth tip) mm
Fa
h
load height from critical section mm
N
summation index —
k
constant of location —
k�
l length of contact line mm
b
l length of middle line of contact mm
bm
l � projected length of middle line of contact mm
bm
m
outer transverse module mm
et
m mean normal module mm
mn
m
mean transverse module mm
mt
m mass per mm facewidth reduced to the line of action of the dynamically kg/mm
red
equivalent cylindrical gears
*
m relative individual gear mass per unit facewidth referred to line of action kg/mm
–1
n rotational speed min
–1
n
resonance speed of pinion min
E1
peak load N/mm
p
protuberance of the tool mm
pr
p maximum peak load N/mm
max
*
referred peak load —
p
4 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
p transverse base pitch of virtual cylindrical gear mm
et
machining stock mm
q
exponent in the formula for lengthwise curvature factor —
q
q notch parameter —
s
q notch parameter of test gear —
sT
r cutter radius mm
c0
r
tooth fillet radius at the mean section mm
mf
r mean transverse radius to point of load application mm
my 0
distance from pitch circle to point of load application in mean normal mm
�r
y0
section
s transverse tooth thickness at the back cone mm
et
s mean normal topland mm
amn
s
mean normal circular thickness mm
mn
s amount of protuberance mm
pr
s mean transverse circular thickness mm
mt
s tooth root chord in calculation section mm
Fn
s one-half tooth thickness at critical section mm
N
u gear ratio of bevel gear —
u
gear ratio of virtual cylindrical gear —
v
v tangential speed at outer end (heel) of reference cone m/s
et
v maximum pitch line velocity at operating pitch diameter m/s
et max
v
tangential speed at reference cone at mid-facewidth m/s
mt
x profile shift coefficient —
hm
x
thickness modification coefficient —
sm
x pinion tooth strength factor mm
N
y running-in allowance for pitch error related to the smooth polished test µm
p
piece
y location of point of load application for maximum bending stress on path of mm
J
action
y location of point of load application on path of action mm
y
running-in allowance for pitch errorµm
�
z number of teeth —
z
number of teeth of virtual cylindrical gear —
v
z number of teeth of virtual cylindrical gear in normal section —
vn
auxiliary factor for dynamic factor —
A
* 2
A auxiliary value for load sharing factor
mm
m
* 2
A auxiliary value for load sharing factor
mm
r
Table 1 (continued)
Symbol Description Unit
A outer tooth thickness allowance mm
sne
* 2
A auxiliary value for load sharing factor
mm
t
auxiliary factor for dynamic factor —
B
quality grade —
C
C tip relief µm
a
C correction factor for tooth stiffness for non-average conditions —
b
C correction factor for tooth stiffness for non-average conditions —
F
C ,C ,C
factors for determining lubricant film factors —
ZL ZR ZV
modulus of elasticity, Young’s modulus N/mm
E
E, G, H auxiliary factors for tooth form factor —
auxiliary factor for mid-zone factor —
F
F nominal tangential force at reference cone at mid-facewidth N
mt
F decisive tangential force at reference cone at mid-facewidth N
mt H
Brinell hardness —
HB
constant; factor concerning tooth load —
K
K dynamic factor —
v
K application factor —
A
K
lengthwise curvature factor for bending stress —
F0
K transverse load factor for bending stress —
F�
K face load factor for bending stress —
F�
K transverse load factor for contact stress —
H�
K face load factor for contact stress —
H�
K
bearing factor —
H�-be
empirical constant used in stress correction formula —
L
L auxiliary factor for correction factor —
a
empirical constant used in stress correction formula —
M
reference speed for n —
N
E1
N number of load cycles —
L
empirical constant used in stress correction formula —
O
nominal power kW
P
–1
P outer diametral pitch inch
d
= CLA = AA arithmetic average roughnessµm
Ra
R outer cone distance mm
e
R mean cone distance mm
m
mean roughnessµm
Rz
Rz mean roughness of test gearµm
T
6 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
Rz mean roughness for gear pairs with ρ =10mm µm
10 red
S safety factor for bending stress (against breakage) —
F
S minimum safety factor for bending stress —
Fmin
S safety factor for contact stress (against pitting) —
H
S
minimum safety factor for contact stress —
Hmin
nominal torque Nm
T
tooth form factor —
Y
Y inertia factor —
i
Y stress concentration and stress correction factor —
f
Y bevel gear adjustment factor —
A
Y bending stress factor —
B
Y
compression stress factor —
C
Y tooth form factor for load application at tip —
Fa
Y combined tooth form factor for generated gears —
FS
Y
bevel geometry factor (Method B2) —
J
Y bevel gear factor —
K
Y
load sharing factor (bending strength) —
LS
Y life factor of the standard test gear —
NT
Y combined geometry factor —
P
Y
surface factor of smooth specimen —
R
Y surface factor of test gear with roughness of Rz =10µm —
RT
T
Y
relative surface factor —
Rrel T
Y stress correction factor for load application at tooth tip —
Sa
Y stress correction factor for dimensions of standard test gear —
ST
Y
size factor for tooth root stress —
X
Y dynamic sensitivity factor of the gear to be determined —
�
Y dynamic sensitivity factor of the standard test gear —
�T
Y relative sensitivity factor —
� rel T
Y contact ratio factor (tooth root) —
�
Z
speed factor —
v
Z elasticity factor —
E
Z
zone factor —
H
Z bevel gear factor (flank) —
K
Z lubricant factor —
L
Z
load sharing factor —
LS
Table 1 (continued)
Symbol Description Unit
Z mid-zone factor —
M-B
Z life factor of the standard test gear —
NT
Z
roughness factor for contact stress —
R
Z size factor —
X
Z
work-hardening factor —
W
Z helix angle factor for contact stress —
�
� normal pressure angle at point of load application on the tooth centreline �
h
� normal pressure angle
�
n
� normal pressure angle of virtual cylindrical gear (=� ) �
vn n
transverse pressure angle of virtual cylindrical gear
� �
vt
working transverse pressure angle
� �
wt
load application angle at tip circle of virtual spur gear
� �
Fan
normal pressure angle at point of load application on the tooth surface
� �
L
� mean spiral angle �
m
� helix angle at base circle of virtual cylindrical gear �
vb
� auxiliary angle for tooth form and tooth correction factor �
a
� pitch angle �
� face angle
�
a
� root angle
�
f
transverse contact ratio of virtual cylindrical gear —
�
v�
� transverse contact ratio of virtual cylindrical gear in normal section —
v�n
overlap ratio of virtual cylindrical gear —
�
v�
� modified contact ratio —
v�
� load sharing ratio —
N
� addendum angle �
a
� dedendum angle �
f
� assumed angle in locating weakest section �
one half of angle subtended by normal circular tooth thickness at point of
� �
h
load application
� density kg/mm
� cutter edge radius mm
a0
� root fillet radius of basic rack for cylindrical gears mm
fP
� radius of relative curvature mm
red
� mm
fillet radius at point of contact of 30� tangent
Fn
gliding thickness mm
��
8 © ISO 2001 – All rights reserved
Table 1 (continued)
Symbol Description Unit
tensile strength N/mm
�
B
tooth root stress N/mm
�
F
nominal stress number (bending) N/mm
�
F lim
allowable stress number (bending) N/mm
�
FE
permissible tooth root stress N/mm
�
FP
local tooth root stress N/mm
�
F0
contact stress N/mm
�
H
� allowable stress number for contact stress N/mm
H lim
� permissible contact stress N/mm
HP
� nominal value of contact stress N/mm
H0
� stress at 0,2% permanent elongation N/mm
0,2
� angle between tangent of root fillet at weakest point and centreline of tooth �
auxiliary factor for tooth form and tooth correction factors —
�
Poisson’sratio —
�
� , � nominal kinematic viscosity of the oil at 40� C and 50� C respectively mm /s
40 50
� angular velocity rad/s
X �1
� relative stress drop in notch root
mm
X �1
relative stress drop in notch root of test gear
�
mm
T
shaft angle
� �
Other subscripts
tool
pinion
wheel
x
dynamically equivalent cylindrical gears
-A, -B, -B1, -
valueaccordingtomethod A, B, B1,B2orC
B2, -C
(1), (2)
trials of interpolation
*
value related to m (except m*)
mn
5 Application
5.1 Methods
5.1.1 General
ISO 10300 is intended mainly for the calculation of bevel gears for which the essential data is known from drawings
or measurement (recalculation). At the preliminary design stage, the available data is limited, and approximations
or empirical values may be used for some factors. Moreover, in certain application fields or for rough calculations
some factors may be assumed as unity or constant. However, a conservative safety factor (see 5.2) should be
chosen in such cases. Wherever there is disagreement, full-scale, full-load testing is preferred over any of the
methods A to C, while method A, if its accuracy and reliability are proven, is preferred over method B, which in turn
is preferred to method C.
5.1.2 Full-scale, full-load testing
The most valid method of predicting overall gear system performance is the full-scale, full-load testing of a specific
gear drive design in order to determine its capacity. This will not require verification by calculation using any of the
methods given. However, it is customary for bevel gears to be developed from a preliminary design according to
methods B or C, then refined by testing to achieve optimum tooth contact, smoothness of operation and
adjustability.
5.1.3 Method A
Where sufficient experience from the operation of other, similar designs is available, satisfactory guidance can be
obtained by the extrapolation of the associated test results or field data. The factors involved in this extrapolation
may be evaluated by the precise measurement and comprehensive mathematical analysis of the transmission
system under consideration, or from field experience. All gear and load data is required to be known for the use of
this method, which shall be clearly described and presented with all mathematical and test premises, boundary
conditions and any specific characteristics of the method that influence the result. The accuracy and the reliability
of the method must be demonstrated. Precision, for example, shall be demonstrated through comparison with
other, acknowledged gear measurements. The method should be approved by both the customer and the supplier.
5.1.4 Method B
Again, where sufficient experience from the operation of other, similar designs is available, satisfactory guidance
can be obtained by the extrapolation of the test results or field data associated with them. However, it is
recommended that the calculation methods be used for comparison of the designs. Additionally, approximate
methods are given for some factors, together with the assumptions relevant to their evaluation. The validity of these
assumptions for the given working conditions shall be checked.
5.1.5 Method C
Where suitable test results, or field experience from similar designs, are unavailable for use in the evaluation of
certain factors, further simplified calculation methods should be used. These are appropriate for particular fields of
application or on the basis of certain premises, for example, those relevant to an acceptance test.
5.2 Safety factors
The allowable probability of failure shall be carefully weighed when choosing a safety factor, in balancing reliability
against cost. If the performance of the gears can be accurately appraised by testing the unit itself under actual load
conditions, lower safety factors may be permitted. The safety factors shall be determined by dividing the specific
calculated strength by the specific operating stress.
In addition to this general requirement, and the special requirements relating to surface durability (pitting) and tooth
root strength given, respectively, in parts 2 and 3 of ISO 10300, safety factors shall be determined only after careful
consideration of the reliability of the material data and of the load values used for calculation. The allowable stress
10 © ISO 2001 – All rights reserved
numbers used for calculation are valid for a given probability of failure, or damage (the material values in
ISO 6336-5, for example, are valid for a 1 % probability of damage), the risk of damage being reduced as the safety
factors are increased, and vice versa. If loads, or the response of the system to vibration, are estimated rather than
measured, a larger factor of safety should be used.
The following variations shall also be taken into consideration in the determination of a safety factor:
� variations in gear geometry due to manufacturing tolerances;
� variations in alignment;
� variations in material due to process variations in chemistry, cleanliness and microstructure (material quality
and heat treatment);
� variations in lubrication and its maintenance over the service life of the gears.
The appropriateness of the safety factors will thus depend on the reliability of the assumptions, such as those
related to load, on which the calculations are based, as well as on the reliability required of the gears themselves,
in respect of the possible consequences of any damage that might occur in the case of failure.
Supplied gears or assembled gear drives should have a minimum safety factor for contact stress, S , value 1,0.
Hmin
The minimum bending-stress, S , value should be 1,3 for spiral bevel gears, and 1,5 for straight bevel gears or
Fmin
where� u 5�.
m
The minimum safety factors against pitting damage and tooth breakage should be agreed between supplier and
customer.
5.3 Rating factors
5.3.1 Testing
The most effective overall approach to gear-system performance management is through the full-scale, full-load
testing of a proposed new design. This approach, however, is limited by its high cost. Alternatively, where sufficient
experience of similar designs exists and results are available, a satisfactory solution can be obtained through
extrapolation from such data. On the other hand, where suitable test results or field data are unavailable, rating-
factor values should be chosen conservatively.
5.3.2 Manufacturing tolerances
Rating factors should be evaluated based on the minimum acceptable quality limits of the expected variation of
component parts in the manufacturing process. The accuracy grade should be determined using ISO 1328-1 with
single pitch deviation.
5.3.3 Implied accuracy
Where the empirical values for rating factors are given by curves, ISO 10300 provides curve-fitting equations to
facilitate computer programming.
NOTE The constants and coefficients used in curve fitting often have significant digits in excess of those implied by the
reliability of the empirical data.
5.4 Other factors to be considered
5.4.1 General
In addition to the factors considered that influence pitting resistance and bending strength, other, interrelated
system factors can have an important effect on overall transmission performance. Their possible effect on the
calculations should be considered.
5.4.2 Lubrication
The ratings determined by the formulae of ISO 10300 shall be valid only if the gear teeth are operated with a
lubricant of proper viscosity and additive package for the load, speed, and surface finish, and if there is a sufficient
quantity of lubricant on the gear teeth and bearings to lubricate and maintain an acceptable operating temperature.
5.4.3 Misalignment
Many gear systems depend on external supports such as machinery foundations to maintain alignment of the gear
mesh. If these supports are poorly designed, initially misaligned, or become misaligned during operation due to
elastic or thermal deflections or other influences, overall gear-system performance will be adversely affected.
5.4.4 Deflection
Deflection of gear-supporting housings, shafts, and bearings due to external overhung, transverse, and thrust loads
affects tooth contact across the mesh. Since deflection varies with load, it is difficult to obtain good tooth contact at
different loads. Generally, deflection due to external loads from driven and driving equipment reduces capacity, and
this, as well as deflection caused by internal forces, should be taken into account when determining the actual gear
tooth contact.
5.4.5 Materials and metallurgy
Most bevel gears are made from carburized case-hardened steel. Allowable stresses for this and other materials
should thus be based on tests on bevel gears wherever these are available. The allowable stress numbers, which
are based on different modes of steel-making and heat-treatment, shall be taken from ISO 6336-5. Hardness and
tensile strength as well as the quality grade shall also be criteria for choosing allowable stress numbers.
NOTE Higher-quality steel grades indicate higher allowable stress numbers, while lower-quality grades indicate lower
allowable stress numbers (see ISO 6336-5).
5.4.6 Residual stress
Any ferrous material having a case-core relationship is likely to have residual stress. If properly managed, such
stress will be compressive at the tooth surface, thereby enhancing the bending-fatigue strength of the gear tooth.
Shot-peening, case-carburizing and induction-hardening, if properly performed, are common methods of inducing
compressive pre-stress in the surface of the gear teeth. Improper grinding techniques after heat treatment may
reduce the residual compressive stresses or even introduce residual tensile stresses in the root fillets of the teeth,
thereby lowering the allowable stress numbers.
5.4.7 System dynamics
The method of analysis used includes a dynamic factor, K in formulae by derating the gears for increased loads
v,
caused by gear-tooth inaccuracies. Generally speaking, this provides simplified values for easy application.
The dynamic response of the system results in additional gear-tooth loads, due to the relative motions of the
connected masses of the driver and the driven equipment. The application factor, K , is intended to account for the
A
operating characteristics of the driving and driven equipment. It must be recognized, however, that if the operating
roughness of the drive, gearbox, or driven equipment causes excitation with a frequency that is near one of the
system’s major natural frequencies, resonant vibrations may cause severe overloads possibly several times higher
12 © ISO 2001 – All rights reserved
than the nominal load. Therefore, where critical service applications are concerned, performance of a vibration
analysis of the complete system is recommended. This analysis shall include the total system, including driver,
gearbox, driven equipment, couplings, mounting conditions and sources of excitation. Natural frequencies, mode
shapes, and the dynamic response amplitudes should be calculated.
5.4.8 Contact pattern
The teeth of most bevel gears are crowned in both their profile and lengthwise directions during the manufacturing
process in order to allow for deflection of the shafts and mountings. This results in a localized contact pattern
during roll testing under light loads. Under design load, unless otherwise specified, the tooth contact pattern is
spread over the tooth flank without concentrations of the pattern at the edges of either member. The application of
the rating formulae to bevel gears manufactured under conditions in which this process has not been carried out
and which do not have an adequate contact pattern may require modifications of the factors given in ISO 10300.
These gears are not covered.
NOTE The total load used for contact pattern analysis can include the effects of an application factor (see annex C for a
fuller explanation of tooth contact development).
5.4.9 Corrosion
Corrosion of the gear-tooth surface can have a significant detrimental effect on the bending strength and pitting
resistance of the teeth. However, the quantification of the effect of corrosion on gear teeth is beyond the range of
ISO 10300.
5.5 Influence and other factors in the basic formulae
Included in the basic formulae presented in ISO 10300 are factors reflecting gear geometry or established by
convention, which need to be calculated in accordance with their formulae.
Also included in the formulae in ISO 10300 are factors that reflect the effects of variations in processing or the
operating cycle of the unit. These are known as influence factors because they account for a number of influences.
Although treated as independent, they may nevertheless influence each other to an extent that is beyond
evaluation. They include the load factors, K , K , K , K , K and K , as well as those factors influencing
A v H� F� H� F�
allowable stresses.
Still other factors included reflect the mathematical relationship, stress vs. life.
The influence factors can be determined by various methods of calculation. These are qualified, as needed, by the
addition of subscripts A through C to the symbols. Unless otherwise specified (for example in an application
standard), the more accurate method is to be preferred for important transmissions. It is recommended that
supplementary subscripts be used whenever the method used for evaluation of a factor would not otherwise be
readily identifiable.
For some applications, it may be necessary to choose between factors determined using alternative methods (for
example, alternatives for the determination of the dynamic factor or the transverse load factor). When reporting the
calculation, the method used should be indicated by extending the subscript.
EXAMPLE K K
v-C, H�-B
6 External force and application factor, K
A
6.1 Nominal tangential force, torque, power
For the purposes of ISO 10300, pinion torque is used in the fundamental stress-calculation formulae. In order to
determine the bending moment on the tooth, or of the force on the tooth surface, the tangential force is calculated
within the stress formula, at the reference cone at mid-facewidth, as follows.
2000T
1,2
F= (1)
mt
d
m1,2
Fd
1000PP9549
mt m1,2
T= = = (2)
1,2
2000 � n
1,2 1,2
TT� n
F
v 1,2 1,2 1,2 1,2
mt mt
P= = = (3)
1000 1000 9549
d �
dn
mt1,2 1,2
m1,2 1,2
v= = (4)
mt
2000 19098
The nominal torque of the driven machine is decisive. This is the operating torque to be transmitted over a long
period of time and under the most severe, regular, working conditions.
EXAMPLE Maximum permanent rolling torque, torque from maximum hoisting weight.
The nominal torque of the driving machine may be used if it corresponds to the required torque of the driven
machine.
6.2 Variable load conditions
If the load is not uniform, a careful analysis of the gear loads should be made, in which the external and internal
dynamic factors are considered. It is recommended that all the different loads that occur during the anticipated life
of the gears, and the duration of each load, be determined. A method based on Miner’s Rule (see ISO/TR 10495)
shall be used for determining the equivalent life of the gears for the torque spectrum.
6.3 Application factor, K
A
In cases where no reliable experiences, or collective load spectra determined by practical measurement or
comprehensive system analysis, are available, calculate using the nominal tangential force F according to clause
mt
6.1 and an application factor, K . This application factor makes allowance for any externally applied dynamic loads
A
in excess of the nominal operating torque load, T .
6.3.1 Factors affecting external dynamic loads
In determining the application factor, account should be taken of the fact that many prime movers develop
momentary peak torques appreciably greater than those determined by the nominal ratings of either the prime
mover or of the driven equipment. There are many possible sources of dynamic overload which should be
considered, including:
� system vibration;
� critical speed;
� acceleration torques;
� overspeed;
� sudden variations in system operation;
� braking;
� negative torques, such as those produced by retarders on vehicles, which result in loading the reverse flanks
of the gear teeth.
14 © ISO 2001 – All rights reserved
Analysis for critical speeds within the operating range of the drive is essential. If critical speeds are present,
changes in the design of the overall drive system shall be made in order to either eliminate them or provide system
damping to minimize gear and shaft vibrations.
6.3.2 Establishment of application factors
Application factors are best established by a thorough analysis of service experience with a particular application.
For applications such as marine gears, which are subjected to cyclic peak torques (torsional vibrations) and are
designed for infinite life, the application factor can be defined as the ratio between cyclic peak torque and the
nominal rated torque. The nominal rated torque is defined by the rated power and speed.
If the gear is subjected to a limited number of loads in excess of the amount of cyclic peak torque, this influence
may be covered directly by means of cumulative fatigue or by means of an increased application factor
representing the influence of the load spectrum.
If service experience is unavailable, a thorough analytical investigation should be made. Annex B provides
approximate values if neither of these alternatives is possible.
7 Dynamic factor, K
v
7.1 General
The dynamic factor, K , makes allowance for the effects of gear tooth quality related to speed and load as well as
v
for the other parameters listed below (see 7.2 to 7.6). The dynamic factor relates the total tooth load, including
internal dynamic effects, to the transmitted tangential tooth load and is expressed as the sum of the internal
effected dynamic load and the transmitted tangential tooth load, divided by the transmitted tangential tooth load.
The parameters for the gear-tooth internal dynamic load fall into two categories: design and manufacturing.
7.2 Design
The design parameters include:
� pitchline speed;
� tooth load;
� inertia and stiffness of the rotating elements;
� tooth stiffness variation;
� lubricant properties;
� stiffness of bearings and case structure;
� critical speeds and internal vibration within the gear itself.
7.3 Manufacturing
The manufacturing parameters include:
� tooth spacing variations;
� runout of pitch surfaces with respect to the axis of rotation;
� tooth flank variations;
� compatibility of mating gear tooth elements;
� balance of parts;
� bearing fit and preload.
7.4 Transmission error
Even if the input torque and speed are constant, significant vibration of the gear masses and the resultant dynamic
tooth forces can exist. These forces result from the relative displacements between the mating gears as they
vibrate in response to an excitation known as transmission error. The ideal kinematics of a gear pair require a
constant ratio between the input and output. Transmission error is defined as the deviation from uniform relative
angular motion of the pair of meshing gears. It is influenced by all deviations from the ideal gear tooth form of the
actual gear design, the manufacturing procedure and the operational conditions. The operational conditions include
the following.
a) Pitch line speed. The frequencies of the excitation depend on the pitch line veloc
...
NORME ISO
INTERNATIONALE 10300-1
Première édition
2001-08-01
Calcul de la capacité de charge des
engrenages coniques —
Partie 1:
Introduction et facteurs généraux
d'influence
Calculation of load capacity of bevel gears —
Part 1: Introduction and general influence factors
Numéro de référence
©
ISO 2001
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ii © ISO 2001 – Tous droits réservés
Sommaire Page
Avant-propos.iv
Introduction.v
1 Domaine d'application.1
2Références normatives .1
3Termesetdéfinitions.2
4 Symboles et abréviations .2
5 Application .10
6 Force extérieure et facteur d'application, K .14
A
7 Facteur dynamique, K .15
v
8 Facteurs de distribution longitudinale de la charge, K , K .25
H� F�
9 Facteurs de distribution transversale de la charge, K , K .28
H� F�
Annexe A (normative) Calcul de la géométrie des engrenages coniques .34
Annexe B (informative) Valeurs pour le facteur d'application, K .45
A
Annexe C (informative) Marques de portée .46
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 confiéeaux
comités techniques de l'ISO. Chaque comité membre intéressé par une étude aledroit de fairepartie ducomité
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 delaprésente partie de l’ISO 10300 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 10300-1 a étéélaborée par le comité technique ISO/TC 60, Engrenages, sous-comité
SC 2, Calcul de la capacité des engrenages.
L'ISO 10300 comprend les parties suivantes, présentées sous le titre général Calcul de la capacité de charge des
engrenages coniques:
� Partie 1: Introduction et facteurs généraux d'influence
� Partie 2: Calcul de la résistance à la pression superficielle (formation des piqûres)
� Partie 3: Calcul de la résistance du pied de dent
L'annexe A constitue un élément normatif de la présente partie de l'ISO 10300. Les annexes B et C sont données
uniquement à titre d'information.
iv © ISO 2001 – Tous droits réservés
Introduction
La présente partie de l'ISO 10300, l'ISO 10300-2 et l'ISO 10300-3, ainsi que l'ISO 6336-5, établissent les principes
généraux et les procédures pour le calcul de la capacité de charge des engrenages coniques. Ainsi, l'ISO 10300 a
été conçue pour faciliter l'application des connaissances et du développement futurs, ainsi que les échanges
d'informations acquises par expérience.
Plusieurs méthodes de calcul de la capacité de charge et de différents facteurs sont spécifiées dans l'ISO 10300,
dont les lignes directrices sont complexes, mais malgré tout flexibles. Il peut y avoir des différences jusqu’à 20 % à
25 % entre les résultats des calculs réalisés à l'aide de la méthode B avec la méthode B1 et la méthode B2 avec la
méthode C. L’utilisation combinéedes méthodes B2 et C, considérées comme des méthodes de grande
simplification, fournit un coefficient de sécurité plus conservateur. Des méthodes détaillées ou simplifiées peuvent
être introduites, comme approprié, dans des normes d'application dérivées de la présente partie de l'ISO 10300,
couvrant les engrenages industriels et les engrenages marins. Néanmoins, il faudra se rappeler que l’utilisation de
ces méthodes pour des applications spécifiques n’exige pas seulement de l’expérience dans la combinaison des
méthodes de calcul, mais également une évaluation réaliste et bien informée de toutes les considérations
applicables, ainsi que des coefficients de sécurité appropriés.
Les méthodes détaillées de calcul contenues dans l'ISO 10300 sont destinées au calcul de vérification des limites
de capacité de charge des engrenages, lorsque toutes les données importantes sont connues, comme les
engrenages existants et les conceptions achevées d'engrenages. Les méthodes approximatives de l'ISO 10300
peuvent être utilisées pour des estimations préliminaires de la capacité de charge de l'engrenage, lorsque les
derniers détails de sa conception ne sont pas connus.
L'ISO 10300 comporte des procédures basées sur des études théoriques et des essais. Toutefois, les résultats
obtenus de ces calculs de la capacité de charge peuvent ne pas être en bon accord avec certaines méthodes de
calcul acceptées antérieurement.
L'ISO 10300 fournit une méthode au moyen de laquelle différentes conceptions d'engrenages peuvent être
comparées. Elle n'est pas destinée à assurer la performance des transmissions de puissance d’engrenages
assemblées. Elle n'est pas destinée àêtre utilisée par un public d’ingénieurs généralistes. Au contraire, elle est
destinée àêtre utilisée par des concepteurs d'engrenages expérimentés qui sont capables de sélectionner des
valeurs raisonnables pour les facteurs de ces formules, sur la base de leur connaissance de conceptions similaires
et de leur conscience des effets des points évoqués.
NORME INTERNATIONALE ISO 10300-1:2001(F)
Calcul de la capacité de charge des engrenages coniques —
Partie 1:
Introduction et facteurs généraux d'influence
1 Domaine d'application
Les formules de l’ISO 10300 sont destinées àétablir une méthode, uniformément acceptable, de calcul de la
résistance à la formation des piqûres et de la capacité de résistance à la flexion des engrenages coniques droits,
coniques hélicoïdaux, coniques «zerol» et spiro-coniques, à l'exception des engrenages hypoïdes. Elles sont
applicables également aux dents à hauteur variable et aux dents à hauteur constante.
Les formules de l’ISO 10300 prennent en compte les principaux facteurs actuellement connus influençant la
formation des piqûres sur des dentures et les ruptures dans le profil de raccordement en pied de dent, ce qui
permet l'ajout de nouveaux facteurs à une date ultérieure. Les formules de calcul contenues dans l’ISO 10300 ne
s'appliquent pas aux autres types de détérioration des dentures, comme la déformation plastique, les micropiqûres,
l'effondrement de la couche cémentée, les soudures et l'usure. Les formules de résistance à la flexion s'appliquent
aux ruptures du profil de raccordement en pied de dent, mais non aux ruptures du profil actif de la dent, à la
rupture de la jante ou aux ruptures du corps de roue à travers le voile et le moyeu. Les systèmes de détermination
de la résistance à la formation de piqûres etdelarésistance à la flexion, pour une catégorie particulière
d'engrenages coniques, peuvent être établis en choisissant des valeurs correctes pour les facteurs utilisésdans
cesformulesgénérales. L’ISO 10300 ne s'applique pas aux engrenages coniques ayant une portée de contact non
appropriée.
L’ISO 10300 est limitée aux engrenages coniques, dont les engrenages cylindriques équivalents ont des rapports
de conduite apparents de � < 2. Les relations qui sont données sont valables pour des engrenages dont la
v�
somme des coefficients de déport du pignon et de la roue est nulle, à savoir l'angle de pression de fonctionnement
normal de l'engrenage est le même que l'angle de pression normale du tracé de référence.
NOTE Les méthodes pour calculer la capacité de charge des engrenages hypoïdes sont indiquées par les fabricants de
machines de taillage d'engrenages.
AVERTISSEMENT — L'utilisateur est mis en garde sur le fait qu’il convient que, lorsque ces méthodes sont
utilisées pour des angles de spirale et de pression importants, et pour de grandes largeurs de denture
b � m ,lesrésultats des calculs effectués conformément à l’ISO 10300 soient confirmés par l'expérience.
mn
2Références normatives
Les documents normatifs suivants contiennent des dispositions qui, par suite de la référence qui y est faite,
constituent des dispositions valables pour la présente partie de l’ISO 10300. Pour les références datées, les
amendements ultérieurs ou les révisions de ces publications ne s'appliquent pas. Toutefois, les parties prenantes
aux accords fondés sur la présente partie de l’ISO 10300 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 delaCEI possèdent le registre des
Normes internationales en vigueur.
ISO 53:1998, Engrenages cylindriques de mécanique générale et de grosse mécanique — Tracé de référence.
ISO 1122-1:1998, Vocabulaire des engrenages — Partie 1: Définitions géométriques.
ISO 1328-1:1995, Engrenages cylindriques — Système ISO de précision — Partie 1: Définitions et valeurs
admissibles des écarts pour les flancs homologues de la denture.
ISO 6336-1, Calcul de la capacité de charge des engrenages cylindriques à dentures droite et hélicoïdale —
Partie 1: Principes de base, introduction et facteurs généraux d'influence.
ISO 6336-5, Calcul de la capacité de charge des engrenages cylindriques à denture droite et hélicoïdale —
Partie 5: Résistance et qualité des matériaux.
ISO 10300-2, Calcul de la capacité de charge des engrenages coniques — Partie 2: Calcul de la résistance à la
pression superficielle (formation des piqûres).
ISO 10300-3, Calcul de la capacité de charge des engrenages coniques — Partie 3: Calcul de la résistance du
pied de dent.
ISO/TR 10495, Engrenages cylindriques — Calcul de la durée de vie en service sous charge variable —
Conditions pour les engrenages cylindriques conformément à l'ISO 6336.
3 Termes et définitions
Pour les besoins de la présente partie de l’ISO 10300, les termes et définitions donnés dans l’ISO 53 et
l’ISO 1122-1 s’appliquent.
4 Symboles et abréviations
Les symboles utilisésdanslaprésente partie de l’ISO 10300 (voir Tableau 1) sont ceux de l'ISO 701, tout en
incluant également les symboles donnés dans l’ISO 1328-1.
2 © ISO 2001 – Tous droits réservés
Tableau 1 — Symboles et abréviations utilisésdansla présente partie de l'ISO 10300, l'ISO 10300-2
et l'ISO 10300-3
Symbole Description Unité
a
entraxe de l'engrenage cylindrique équivalent mm
v
a entraxe de l'engrenage cylindrique équivalent dans une section normale mm
vn
b largeur de denture mm
b largeur de denture effective calculéemm
ce
b
largeur de denture effective mm
e
∆b incrément de la largeur de denture au talon mm
e
∆b � incrément effectif de la largeur de denture au talon mm
e
∆b incrément de la largeur de denture à la pointe mm
i
incrément effectif de la largeur de denture à la pointe mm
∆b�
i
c paramètre sans dimension —
v
c rigidité de l'engrènement .
� N/(mm µm)
c rigidité de l'engrènement dans des conditions moyennes .
�0 N/(mm µm)
rigidité simple (voir l'ISO 6336-1) .
c�
N/(mm µm)
rigidité simple dans des conditions moyennes .
c �
N/(mm µm)
d
diamètre de référence extérieur mm
e
d diamètre primitif moyen
mm
m
d diamètre de référence de l'engrenage cylindrique équivalent mm
v
d
diamètre de tête de l'engrenage cylindrique équivalent mm
va
d diamètre de tête de l'engrenage cylindrique équivalent dans une section normale
mm
van
d diamètre de base de l'engrenage cylindrique équivalent mm
vb
d diamètre de base de l'engrenage cylindrique équivalent dans une section normale
mm
vbn
d diamètre de référence de l'engrenage cylindrique équivalent dans une section normale
mm
vn
f
distance à une ligne de contact mm
*
f distance référencée à la ligne de contact du milieu —
f écart de forme du profil
µm
f�
f distance maximale à la ligne de contact du milieu
mm
max
f écart individuel du pas
µm
pt
f
écart effectif du pas µm
peff
f facteur de correction de la charge
—
F
g valeur supposée de la distance de positionnement de la section la plus faible
mm
f0
g
longueur de conduite de l'engrenage cylindrique équivalent mm
v�
g longueur de conduite de l'engrenage cylindrique équivalent dans une section normale
mm
v�n
distance entre le centre du rayon d'arrondi de sommet de dent d'outil et la ligne des
g
mm
xb
centres de la roue, mesuré le long du plan de référencedel'outil
Tableau 1 (suite)
Symbole Description Unité
distance depuis le centre du rayon de sommet de dent d'outil jusqu'à la surface primitive
g
mm
yb
bombée de la roue, mesurée dans une direction perpendiculaire à la surface primitive
g variable intermédiaire pour calculer le facteur de résistance en pied de dent mm
za
g variable intermédiaire pour calculer le facteur de résistance en pied de dent mm
zb
g variable intermédiaire pour calculer le facteur de résistance en pied de dent mm
J
g � variable intermédiaire pour calculer le facteur de résistance en pied de dent mm
J
g longueur projetée des lignes de contact instantanées suivant la largeur de la dent mm
K
g
longueur de conduite dans l'ellipse de contact mm
η
distance entre la ligne de symétrie des centres de l'espace entre les dents de l'outil et le
g mm
centre d'arrondi du sommet de dent d'outil mesuré dans le plan moyen réel
distance depuis la section moyenne au centre de pousséemesurée suivant la largeur de mm
g ��
la dent
h saillie à l'extrémité extérieure mm
ae
h saillie moyenne mm
am
h saillie du tracé de référence mm
aP
h
saillie d'outil mm
a0
h creux à l'extrémité extérieure de la dent
mm
fe
h creux de dent du tracé de référence
mm
fP
h
creux de dent moyen mm
fm
h creux d'outil
mm
f0
hauteur du bras de levier pour la contrainte de flexion en pied de dent (application de la
h
mm
Fa
charge au sommet de dent)
h
hauteur de la charge à partir de la section critique mm
N
k indice de sommation —
k� constante de localisation —
l longueur de la ligne de contact
mm
b
l longueur de la ligne de contact du milieu mm
bm
l� longueur projetée de la ligne de contact du milieu
mm
bm
m module apparent extérieur mm
et
m
module normal moyen mm
mn
m module apparent moyen mm
mt
masse réduite par millimètre de largeur de denture rapportée à la ligne d'action de kg/mm
m
red
l'engrenage cylindrique dynamiquement équivalent
*
m moment d'inertie d'une roue par unité de largeur divisé par le rayon de base au carré kg/mm
�1
n vitessederotation
min
�1
n vitessederésonance du pignon
E1 min
p crête de charge N/mm
pr protubérancedel'outil mm
4 © ISO 2001 – Tous droits réservés
Tableau 1 (suite)
Symbole Description Unité
p crête de charge maximale N/mm
max
*
p crête de charge référencée —
p pas de base apparent de l’engrenage cylindrique équivalent mm
et
q
surépaisseur de taillage mm
q exposant dans la formule pour le facteur de courbure longitudinale —
q paramètre d'entaille —
s
q
paramètre d'entaille de l'engrenage d'essai —
sT
r rayondefraise mm
c0
r rayon d'arrondi de profil de raccordement dans la section moyenne mm
mf
r
rayon équivalent moyen du point d'application de la charge mm
my 0
distance de la tête du cercle au point d'application de la charge dans une section normale mm
�r
y0
s
épaisseur transversale de dent sur le cône arrière mm
et
s sommet de dent normal moyen mm
amn
s épaisseur circulaire normale moyenne mm
mn
s
protubérance mm
pr
s épaisseur circulaire transversale moyenne mm
mt
s corde en pied de dent dans la section critique mm
Fn
s demi-épaisseur de la dent à la section critique mm
N
u rapport d'engrenage de l'engrenage conique —
u rapport d'engrenage de l'engrenage cylindrique équivalent —
v
� vitesse tangentielle à l'extrémité extérieure (talon) au cône de référence
m/s
et
vitesse de la ligne primitive maximale au diamètre primitif de fonctionnement
� m/s
et max
� vitesse tangentielle au cône de référence à mi-largeur de denture
m/s
mt
x coefficient de déport
—
hm
x
coefficient pour la modification de l'épaisseur —
sm
x facteur de résistance de la dent du pignon
mm
N
y
tolérance de rodage pour l'écart de pas relativement à la pièce d'essai polie µm
p
position du point d'application de la charge sur la ligne d'action pour la contrainte de
y
mm
J
flexion maximum
y position du point d'application de la charge sur la ligne d'action
mm
y tolérance de rodage vis-à-vis de l’écart de pas
µm
�
z nombre de dents —
z nombre de dents de l'engrenage cylindrique équivalent
—
v
z nombre de dents de l'engrenage cylindrique équivalent dans une section normale
—
vn
A
facteur auxiliaire pour le facteur dynamique —
* 2
A valeur auxiliaire pour le facteur de répartition de la charge
mm
m
Tableau 1 (suite)
Symbole Description Unité
* 2
A valeur auxiliaire pour le facteur de répartition de la charge
mm
r
A tolérance d’épaisseur de la denture sur le cône extérieur mm
sne
* 2
A valeur auxiliaire pour le facteur de répartition de la charge
mm
t
B facteur auxiliaire pour le facteur dynamique —
C
classe de précision —
C dépouille de tête µm
a
C facteur de correction de la rigidité de denture pour des conditions non moyennes —
b
C facteur de correction de la rigidité de denture pour des conditions non moyennes —
F
C ,C ,C
facteurs pour déterminer les facteurs de film lubrifiant —
ZL ZR ZV
modules d'élasticité
E N/mm
E, G, H
facteur auxiliaire pour le facteur de forme de la dent —
F facteur auxiliaire pour le facteur géométrique moyen —
F force tangentielle nominale sur le cône de référence à mi-largeur de denture
N
mt
F
force tangentielle de calcul sur le cône de référence à mi-largeur de denture N
mt H
HB dureté Brinell —
K
constante, facteur concernant la charge de la dent —
K facteur dynamique —
v
K facteur d'application
—
A
K facteur de courbure longitudinale pour la contrainte de flexion
—
F0
K facteur de distribution transversale de la charge pour la contrainte de flexion
—
F�
K facteur de distribution longitudinale de la charge pour la contrainte de flexion
—
F�
K facteur de distribution transversale de la charge pour la pression de contact —
H�
K facteur de distribution longitudinale de la charge pour la pression de contact —
H�
K
facteur de montage —
H�-be
L constante empirique utilisée dans la formule de concentration de contrainte —
L facteur auxiliaire pour le facteur de concentration de contrainte —
a
M
constante empirique utilisée dans la formule de concentration de contrainte —
N facteur de résonance relatif à n —
E1
N
nombre decyclesdemise encharge —
L
O constante empirique utilisée dans la formule de correction de contrainte —
P
puissance nominale kW
�1
P
diamétral pitch extérieur
d inch
Ra rugosité moyenne arithmétiqueµm
R
génératrice extérieureducône de référence mm
e
R génératrice moyenne du cône de référence mm
m
Rz rugosité moyenne µm
6 © ISO 2001 – Tous droits réservés
Tableau 1 (suite)
Symbole Description Unité
Rz rugosité moyenne d'engrenage d'essaiµm
T
Rz rugosité moyenne pour une paire de roue ayant � =10mm µm
10 red
S coefficient de sécurité pour la contrainte de flexion (contre la rupture) —
F
S coefficient de sécurité minimum pour la contrainte de flexion —
Fmin
S
coefficient de sécurité pour la pression de contact (contre la formation de piqûres) —
H
S coefficient de sécurité minimum pour la pression de contact —
Hmin
T couple nominal Nm
Y facteur de forme de la dent —
Y facteur d'inertie —
i
Y facteur de concentration de contrainte et de correction de contrainte —
f
Y
facteur d'ajustement de l'engrenage conique —
A
Y facteur de contrainte de flexion —
B
Y facteur de contrainte de compression —
C
Y
facteur de forme pour une charge appliquée ausommet dedent —
Fa
Y facteur de forme combiné pour des roues obtenues par génération —
FS
Y
facteur géométrique conique (méthode B2) —
J
Y facteur d'engrenage conique —
K
Y facteur de répartition de charge (contrainte de flexion) —
LS
Y
facteur de durée de vie d'un engrenage d'essai de référence —
NT
Y facteur géométrique combiné—
P
Y facteur d'état de surface de l'éprouvette lisse —
R
facteur d'état de surface de l'engrenage d'essai, avec une rugosité Rz =10µm
Y —
RT T
Y facteur de rugosité relative —
RrelT
facteur de concentration de contrainte pour l'application de la charge au sommet de la —
Y
Sa
dent
facteur de concentration de contrainte déterminé pour les dimensions de la roue d’essai —
Y
ST
de référence
Y facteur de dimension pour la contrainte en pied de dent —
X
Y facteur de sensibilité dynamique de l'engrenage à déterminer —
�
Y facteur de sensibilité dynamique de l'engrenage d'essai de référence —
�T
Y facteur de sensibilité relative —
� rel T
Y
facteur de rapport de conduite (pied de dent) —
�
Z facteur de vitesse —
�
Z facteur d'élasticité —
E
Z
facteur géométrique —
H
Z facteur de l'engrenage conique (flanc) —
K
Tableau 1 (suite)
Symbole Description Unité
Z facteur de lubrifiant —
L
Z
facteur de répartition de charge —
LS
Z facteur géométrique moyen —
M-B
Z facteur de durée de vie d'un engrenage d'essai de référence —
NT
Z
facteur de rugosité pour la pression de contact —
R
Z facteur de dimension —
X
Z facteur de rapport de dureté—
W
Z
facteur d'angle d'hélice pour pression de contact —
�
angle de pression normal au point d'application de la charge sur le centre de la ligne de la �
��
h
dent
� angle de pression normal �
n
� angle de pression normal d'un engrenage cylindrique équivalent (=� ) �
vn n
angle de pression apparent de l’engrenage cylindrique équivalent
� �
vt
angle de pression apparent de fonctionnement
�
�
wt
angle d'application de la charge au cercle de tête de l'engrenage cylindrique à denture
�
�
Fan
droite équivalente
� angle de pression normal au point d'application de la charge àlasurfacedeladent
�
L
� angle de spirale sur le cône de référence à mi-largeur de denture �
m
angle d'hélice aucercledebase del’engrenage cylindrique équivalent
� �
vb
angle auxiliaire pour le facteur de forme et de concentration de contrainte
� �
a
� angle primitif �
angle de cône de tête
� �
a
� angle de cône de pied �
f
� rapport de conduite apparent de l’engrenage cylindrique équivalent —
v�
rapport de conduite apparent de l’engrenage cylindrique équivalent dans la section —
�
v�n
normale
� rapport de recouvrement de l’engrenage cylindrique équivalent —
v�
rapport de conduite total de l’engrenage cylindrique équivalent —
�
v�
rapport de répartition de charge —
�
N
� angle de saillie �
a
� angle de creux
�
f
angle supposé de positionnement de la section la plus faible
� �
demi-angle inscrit de l'arc correspondant à l'épaisseur curviligne normale au point
�
�
h
d'application de la charge
� densité
kg/mm
� rayondetête d'outil mm
a0
8 © ISO 2001 – Tous droits réservés
Tableau 1 (suite)
Symbole Description Unité
rayond'arrondienpieddedent du tracé de référence de la roue cylindrique mm
�
fP
rayon de courbure relative mm
�
red
� rayon d'arrondi au point de contact de la tangente à 30° mm
Fn
épaisseur de glissement mm
��
résistance mécanique
� N/mm
B
� contrainte effective en pied de dent
N/mm
F
contrainte nominale de référence (flexion)
� N/mm
F lim
contrainte de référence (flexion)
� N/mm
FE
� contrainte admissible en pied de dent
N/mm
FP
contrainte de base en pied de dent
� N/mm
F0
pression de contact
� N/mm
H
� contrainte nominale de référence pour la pression de contact
N/mm
H lim
pression de contact admissible
� N/mm
HP
valeur de base de la pression de contact
� N/mm
H0
� limite élastique à 0,2 % de l'allongement permanent
N/mm
0,2
angle entre la tangente au profil de raccordement en pied de dent et l'axe de symétrie de
�
�
la dent
� facteur auxiliaire des facteurs de forme et de concentration de contrainte —
coefficient de Poisson —
�
� , � viscosité cinématique de l'huile à 40 °Cet50 °C, respectivement
mm /s
40 50
vitesse angulaire
� rad/s
X �1
� réduction relative de la contrainte pour un pied de dent entaillé
mm
X �1
réduction relative de la contrainte pour un pied de dent entaillé de la roue d'essai
�
mm
T
� angle des axes �
Autres indices
0 outil
1 pignon
2 roue
x engrenages cylindriques dynamiquement équivalents
-A, -B, -B1, valeurs selon la méthode A, B, B1, B2 ou C
-B2, -C
(1), (2) essais d'interpolation
* valeur relative à m (sauf m*)
mn
5 Application
5.1 Méthodes
5.1.1 Généralités
L'ISO 10300 est principalement destinéeau calculdevérification des engrenages coniques pour lesquels les
données essentielles sont connues à partir de plans ou de mesures (recalcul). À l'étape de la conception
préliminaire, les données disponibles sont limitées et des approximations ou des valeurs empiriques peuvent être
utilisées pour certains facteurs. Ainsi, pour certains domaines d'application ou pour des calculs grossiers, il est
acceptable de supposer certains facteurs égaux à l'unité ou à des constantes. Néanmoins, il convient qu'un
coefficient de sécurité conservateur (voir 5.2) soit choisi dans un tel cas. En cas de controverse, un essai en vraie
grandeur et à pleine charge est préféréà toute méthode A à C, tandis que la méthode A, si sa précision et sa
fiabilité sont prouvées, est préférée à la méthode B, qui est elle-même est préférée à la méthode C.
5.1.2 Essai en vraie grandeur et à pleine charge
La méthode la plus valable pour prévoir la performance globale d'un système est l'essai en vraie grandeur et à
pleine charge d'une transmission de puissance par engrenages de conception spécifique, afin de déterminer sa
capacité. Cela n'exige pas de vérification par calculs utilisant n'importe laquelle des méthodes. Néanmoins, les
conceptions des engrenages coniques sont généralement élaborées à partir d'une conception préliminaire
conforme aux méthodes B ou C, et ensuite affinées par des essais, afin d'obtenir un contact de dent optimal, une
douceur de fonctionnement et une capacité d'ajustement.
5.1.3 Méthode A
Lorsqu'on dispose d'une expérience suffisante du fonctionnement de conceptions similaires, des indications
satisfaisantes peuvent être obtenues par extrapolation des résultats d'essais obtenus ou des données de
fonctionnement. Les facteurs sont évalués au moyen d'une mesure précise et d'une analyse mathématique
complète du système de transmission considéré,ou à partir de données expérimentales. Toutes les données
concernant l'engrenage et les charges doivent être connues à cette fin. Dans ce cas, la méthode choisie doit être
clairement décrite; toutes les hypothèses mathématiques et d'essai, les conditions limites ainsi que les
caractéristiques spécifiques de la méthode, qui influencent le résultat des calculs, doivent être présentées. La
précision et la fiabilité de la méthode doivent être démontrées, par exemple en déterminant la précision, par
comparaison avec des mesures connues sur d'autres engrenages. Il convient que la méthode de calcul soit
approuvée par l'acheteur et le vendeur.
5.1.4 Méthode B
Lorsqu'une expérience suffisante du fonctionnement de conceptions similaires est disponible, des indications
satisfaisantes peuvent être obtenues par extrapolation des résultats d'essais précédents ou de données de terrain.
Toutefois, il est recommandé que les méthodes de calcul soient utilisées pour comparer les conceptions. En outre,
des méthodes approchées sont données pour certains facteurs, avec des hypothèses adaptées à leur évaluation.
La validité de ces hypothèses pour les conditions de fonctionnement données doit être vérifiée.
5.1.5 Méthode C
Lorsque des résultats d'essais appropriés ou une expérience en service, à partir de conceptions similaires, ne sont
pas disponibles pour l'évaluation de certains facteurs, il convient d'utiliser d'autres méthodes simplifiées. Celles-ci
sont applicables à un certain domaine d'application ou avec certaines hypothèses, par exemple celles
correspondant à un essai de réception.
5.2 Facteurs de sécurité
La probabilité admissible de défaillance et le coefficient de sécurité doivent être soigneusement choisis afin de
satisfaire à la fiabilité exigée à un coût justifiable. Si la performance des engrenages peut être précisément évaluée
par le biais d’un essai de l'appareil réel dans des conditions de charge réelles, des coefficients de sécurité
10 © ISO 2001 – Tous droits réservés
inférieurs peuvent être admis. Les coefficients de sécurité doivent être déterminésendivisant la résistance
spécifique calculée par la contrainte de fonctionnement spécifique.
Outre les exigences générales, et les exigences particulières concernant la résistance à la pression superficielle
(piqûres) et la résistance du pied de dent données, respectivement, dans l'ISO 10300-2 et l'ISO 10300-3, des
facteurs de sécurité doivent être déterminés seulement après avoir tenu compte de la fiabilité des données
relatives aux matériaux et de la fiabilité des valeurs de charge utilisées pour le calcul. Les contraintes admissibles
de référence utilisées dans le calcul sont valables pour une probabilité donnéede défaillance, ou détérioration (les
valeurs des matériaux de l'ISO 6336-5, par exemple, sont valables pour une probabilité de 1 % de détérioration), le
risque de détérioration diminuant avec l'augmentation des coefficients de sécurité et inversement. Si les charges,
ou la réponse du système aux vibrations, sont estimées plutôt que mesurées, il convient d'utiliser un coefficient de
sécurité plus important.
Les différences suivantes doivent êtreprisesenconsidération dans la détermination du facteur de sécurité:
� différences dans la géométrie de l'engrenage dues aux tolérances de fabrication;
� différences dans l'alignement;
� différences dans le matériau dues aux différences de process en chimie, à la pureté et à la microstructure
(qualité du matériau et traitement thermique);
� différences dans la lubrification et l'entretien pendant la vie en service des engrenages.
L'applicabilité des facteurs de sécurité dépendra donc de la fiabilité des hypothèses, telles que celles relatives à la
charge, sur lesquelles les calculs sont basés, de même que de la fiabilité requise pour les engrenages eux-mêmes,
eu égard aux conséquences possibles de toute détérioration qui pourraient se produire dans le cas de défaillances.
Il convient que les engrenages ou les transmissions de puissance par engrenages assemblées aient une valeur du
coefficient de sécurité minimum pour la pression de contact, S , qui soit 1,0. Il est recommandé que la valeur du
Hmin
coefficient de sécurité minimum pour la contrainte de flexion, S , soit 1,3 pour les engrenages spiro-conique, et
Fmin
1,5 pour les engrenages coniques à denture droite lorsque� u 5�
m
Les coefficients de sécurité minimaux contre la détérioration due à la formation de piqûres et à la rupture de dent
doivent faire l'objet d'un accord entre le client et le fournisseur.
5.3 Facteurs de calcul
5.3.1 Essais
La plus effective approche globale de la gestion de la performance d'un système d'engrenages se fait par un essai
en vraie grandeur et à pleine charge d'une nouvelle conception proposée. Cependant, cette approche est limitée
du fait de son coût élevé. Alternativement, lorsqu'une expérience suffisante existe pour des conceptions similaires
et que les résultats sont valables, une solution satisfaisante peut être obtenue par extrapolation de telles données.
Par contre, lorsque des résultats d'essai ou des données de service correctes ne sont pas disponibles, il convient
de choisir avec prudence des valeurs pour les facteurs d'évaluation.
5.3.2 Tolérances de fabrication
Il convient d'évaluer les facteurs de calcul sur la base de limites de qualité minimales acceptables de la variation
souhaitée des composants dans le processus de fabrication. Il convient de déterminer la classe de précision en
utilisant l'écart individuel de pas de l'ISO 1328-1.
5.3.3 Précision implicite
Lorsque des valeurs empiriques pour certains facteurs sont données par des courbes, l'ISO 10300 fournit des
équations de lissage des courbes afin de faciliter la programmation informatique.
NOTE Les constantes et les coefficients utilisés dans les équations de lissage de courbes ont souvent des chiffres
significatifs qui dépassent ceux issus de la fiabilité des données empiriques.
5.4 Autres facteurs à considérer
5.4.1 Généralités
Outre les facteurs pris en considération, qui influencent la résistance à la formation de piqûres et la résistance à la
flexion, d'autres facteurs interdépendants peuvent avoir un effet important sur la performance de transmission
globale. Il convient que leur possible influence sur les calculs soit prise en compte.
5.4.2 Lubrification
Les capacitésdéterminées à partir des formules de l'ISO 10300 ne doivent être valables que si les dentures
fonctionnent avec un lubrifiant ayant une viscosité et un volume d'additifs corrects pour la charge, la vitesse et l'état
de surface, et s'il y a une quantité suffisante de lubrifiant dans la denture et les paliers pour lubrifier et conserver
une température de fonctionnement acceptable.
5.4.3 Écarts d'alignement
De nombreux systèmes d'engrenages dépendent des supports externes, comme les fondations, pour conserver
l'alignement de l'engrènement. Si ces supports sont mal conçus, mal alignés à l'origine ou se désalignent en
serviceenraison de déformations élastiques ou thermiques ou sous d'autres influences, la performance globale du
système d'engrenages en sera affectéedefaçon défavorable.
5.4.4 Déformation
La déformation du carter supportant les engrenages, les arbres et les paliers, due à des charges externes en porte-
à-faux, transversales et axiales, affecte le contact d'engrènement. Étant donné queladéformation varie selon la
charge, il est difficile d'obtenir un bon contact pour des charges différentes. Généralement, la déformation due aux
charges externes provenant des équipements menés et menants réduit la capacité de charge, et il convient que
cela, ainsi que les déformations provoquées par des forces internes soient pris en considération lors de la
détermination du contact réel de la denture.
5.4.5 Matériaux et métallurgie
La plupart des engrenages coniques sont fabriquésen acier cémenté-trempé. Il convient que les contraintes
admissibles pour ce matériau et pour d'autres matériaux soient déterminées, de préférence, à partir d'essais
effectués sur des engrenages coniques, s'ils existent. Les contraintes admissibles de référence doivent être prises
de l'ISO 6336-5. Elles se basent sur différents modes d’élaboration de l'acier et sur les méthodes de traitement
thermique. La dureté et la résistance à la rupture, ainsi que la classe de qualité, constituent les critères pour les
contraintes admissibles de référence.
NOTE Des classes de qualité supérieures de l'acier indiquent l'utilisation de contraintes admissibles de référence
supérieures, tandis que des classes de qualité inférieures de l'acier indiquent l'utilisation de contraintes admissibles de
référence inférieures (voir l'ISO 6336- 5).
5.4.6 Contrainte résiduelle
Tout matériau ferreux ayant une relation couche durcie-cœur est susceptible d’avoir des contraintes résiduelles. Si
elles sont gérées correctement, ces contraintes sont compressives à la surface de la dent, et augmentent ainsi la
résistance à la fatigue de flexion de la denture. Le grenaillage, la cémentation et la trempe par induction, s'ils sont
effectués correctement, sont des méthodes courantes permettant d'induire une précontrainte de compression à la
surface de la denture. Des techniques de rectification non appropriées après le traitement thermique peuvent
réduire les contraintes résiduelles de compression, ou même introduire des contraintes résiduelles de traction dans
le profil de raccordement de pied de dent, réduisant ainsi les contraintes admissibles de référence.
12 © ISO 2001 – Tous droits réservés
5.4.7 Dynamique des systèmes
La méthode d'analyse utilisée inclut un facteur dynamique, K , dans les formules en réduisant la puissance des
v
engrenages pour des augmentations de charge provoquées par des écarts de précision dans les dentures. En
général, des valeurs simplifiées sont données pour une application facile.
La réponse dynamique du système aboutit à des charges supplémentaires sur les dentures dues aux mouvements
relatifs des masses connectées des équipements menants et menés. Le facteur d'application, K , est destinéà
A
rendre compte des caractéristiques de fonctionnement des équipements menants et menés. Il doit être reconnu,
uniquement, si la rudesse de fonctionnement de la machine menante, du train d'engrenages ou de l'équipement
mené provoque une excitation, avec une fréquence qui est proche d'une des fréquences propres du système, des
vibrations de résonance peuvent entraîner des surcharges sévères qui peuvent être plusieurs fois plus élevées que
la charge nominale. Pour des applications de service critiques, il est recommandé d’effectuer une analyse vibrative
sur le système complet. Cette analyse doit comporter le système complet de la machine menante, du train
d'engrenages, de la machine menée, des accouplements, des conditions de montage et des sources d'excitation. Il
convient de calculer les fréquences propres, la forme des modes et les amplitudes de réponse dynamique.
5.4.8 Marque de portée
Les dents de la plupart des engrenages coniques sont bombées, à la fois dans le sens du profil et dans celui de la
longueur, pendant l'opération de fabrication, afin de les adapter à la déformation des arbres et aux assemblages.
Cela aboutit à une marque de portée localisée pendant l'essai d’engrènement avec des charges légères. Sous la
charge de conception, il convient, sauf indication contraire, d'étendre la marque de portée sur tout le flanc de dent,
sans concentrations de la marque sur les bords de l'un ou de l'autre membre. L'application des formules de calcul
de la capacité aux engrenages coniques pour lesquels cette condition n'est pas satisfaite peut exiger la
modification des facteurs donnés dans l'ISO 10300. Ces engrenages ne sont pas couverts.
NOTE La charge totale utilisée pour l'analyse de la marque de portée peut inclure l’influence d'un facteur d'application (voir
annexe C pour une explication plus complète du développement de la marque de la dent).
5.4.9 Corrosion
La corrosion de la surface des dents peut avoir un effet nuisible important sur la résistance des dents à la flexion et
la résistance à la formation de piqûres. Pourtant, la quantification de l'effet de la corrosion sur les dents ne fait pas
l'objet de l'ISO 10300.
5.5 Influence et autre facteurs dans les formules de base
Dans les formules de base de l'ISO 10300 sont inclus les facteurs qui reflètent la géométrie de l'engrenage ou qui
ont étéétabli par convention, et qui ont besoin d'être calculés conformément à leur formule.
Également inclus dans les formules de base de l'ISO 10300, les facteurs qui reflètent les effets des variations dans
le process de réalisation ou les effets des variations dans le cycle de fonctionnement de l'appareil (facteurs
d'«influence»). Ces facteurs rendent compte de nombreuses influences et sont traités comme des facteurs
indépendants. Cependant, ils peuvent s'influencer les uns les autres dans une mesure qui ne peut être évaluée. Ils
comprennent les facteurs de charge, K , K , K et K K et K , ainsi que les facteurs influençant les
A v H� F� H� F�
contraintes admissibles.
D'autres facteurs encore, qui reflètent le rapport mathématique entre la contrainte et la duréede vie.
Les facteurs d'influences peuvent être déterminés à l'aide de différentes méthodes. Celles-ci sont qualifiées,
comme exigé, en ajoutant les indices A à C aux symboles. Sauf spécifications contraires (par exemple dans une
norme d'application), la méthodelaplus précise doit être choisie de préférence pour des transmissions
importantes. Il est recommandé d'utiliser des indices supplémentaires quand la méthode utilisée pour l'évaluation
d'un facteur n'est pas facilement identifiable.
Pour certaines applications, il peut être nécessaire de choisir entre des facteurs déterminés en utilisant les
méthodes alternatives (par exemple celles pour la détermination du facteur dynamique ou du fa
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