SIST ISO 10300-1:2015

INTERNATIONAL ISO
STANDARD 10300-1
Second edition
2014-04-01
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 2014
© ISO 2014
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ii © ISO 2014 – All rights reserved

Contents Page
Foreword .iv
Introduction .v
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 2
4 Symbols and units . 2
5 Application . 8
5.1 Calculation methods . 8
5.2 Safety factors . 9
5.3 Rating factors . 9
5.4 Further factors to be considered .10
5.5 Further influence factors in the basic formulae .11
6 External force and application factor, K .12
A
6.1 Nominal tangential force, torque, power.12
6.2 Variable load conditions .12
6.3 Application factor, K .
A 13
7 Dynamic factor, K .13
v
7.1 General .13
7.2 Design .14
7.3 Manufacturing .14
7.4 Transmission error .14
7.5 Dynamic response .15
7.6 Resonance .15
7.7 Calculation methods for K .
v 15
8 Face load factors, K , K .25
Hβ Fβ
8.1 General documents.25
8.2 Method A .25
8.3 Method B .25
8.4 Method C .26
9 Transverse load factors, K , K .27
Hα Fα
9.1 General comments .27
9.2 Method A .28
9.3 Method B .28
9.4 Method C .30
9.5 Running-in allowance, y .
α 31
Annex A (normative) Calculation of virtual cylindrical gears — Method B1 .35
Annex B (normative) Calculation of virtual cylindrical gears — Method B2 .47
Annex C (informative) Values for application factor, K .53
A
Annex D (informative) Contact patterns .54
Bibliography .58
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out
through ISO technical committees. Each member body interested in a subject for which a technical
committee has been established has the right to be represented on that committee. International
organizations, governmental and non-governmental, in liaison with ISO, also take part in the work.
ISO collaborates closely with the International Electrotechnical Commission (IEC) on all matters of
electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are
described in the ISO/IEC Directives, Part 1. In particular the different approval criteria needed for the
different types of ISO documents should be noted. This document was drafted in accordance with the
editorial rules of the ISO/IEC Directives, Part 2. www.iso.org/directives
Attention is drawn to the possibility that some of the elements of this document may be the subject of
patent rights. ISO shall not be held responsible for identifying any or all such patent rights. Details of any
patent rights identified during the development of the document will be in the Introduction and/or on
the ISO list of patent declarations received. www.iso.org/patents
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation on the meaning of ISO specific terms and expressions related to conformity
assessment, as well as information about ISO’s adherence to the WTO principles in the Technical Barriers
to Trade (TBT) see the following URL: Foreword - Supplementary information
The committee responsible for this document is ISO/TC 60, Gears, Subcommittee SC 2, Gear capacity
calculation.
This second edition cancels and replaces the first edition (ISO 10300-1:2001), which has been technically
revised.
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
iv © ISO 2014 – All rights reserved

Introduction
When ISO 10300:2001 (all parts, withdrawn) became due for (its first) revision, the opportunity was
taken to include hypoid gears, since previously the series only allowed for calculating the load capacity
of bevel gears without offset axes. The former structure is retained, i.e. three parts of the ISO 10300
series, together with ISO 6336-5, and it is intended to establish general principles and procedures for
rating of bevel gears. Moreover, ISO 10300 (all parts) is designed to facilitate the application of future
knowledge and developments, as well as the exchange of information gained from experience.
Several calculation methods, i.e. A, B and C, are specified, which stand for decreasing accuracy and
reliability from A to C because of simplifications implemented in formulae and factors. The approximate
methods in ISO 10300 (all parts) are used for preliminary estimates of gear capacity where the final
details of the gear design are not yet known. More detailed methods are intended for the recalculation
of the load capacity limits when all important gear data are given.
ISO 10300 (all parts) does not provide an upgraded calculation procedure as a method A, although it
would be available, such as finite element or boundary element methods combined with sophisticated
tooth contact analyses. The majority of Working Group 13 decided that neither is it sufficient for an
International Standard to simply refer to such a complex computer program, nor does it make sense to
explain it step by step in an International Standard.
On the other hand, by means of such a computer program, a new calculation procedure for bevel and
hypoid gears on the level of method B was developed and checked. It is part of the ISO 10300 series as
submethod B1. Besides, if the hypoid offset, a, is zero, method B1 becomes identical to the set of proven
formulae of the former version of ISO 10300 (all parts):2001.
In view of the decision for ISO 10300 (all parts) to cover hypoid gears also, an annex, called: “Calculation
of virtual cylindrical gears — Method B2”, is included in this part of ISO 10300. Additionally, ISO 10300-2
is supplemented by a separate clause: “Gear flank rating formulae — Method B2”; regarding ISO 10300-3,
it was agreed that the former method B2, which uses the Lewis parabola to determine the critical section
in the root and not the 30° tangent at the tooth fillet as method B1 does, now be extended by the AGMA
methods for rating the strength of bevel gears and hypoid gears. It was necessary to present a new,
clearer structure of the three parts, which is illustrated in Figure 1 (of this part of ISO 10300). Note,
ISO 10300 (all parts) gives no preferences in terms of when to use method B1 and when method B2.
The procedures covered by ISO 10300 (all parts) are based on both testing and theoretical studies, but
it is possible that the results obtained from its rating calculations might not be in good agreement with
certain, previously accepted, gear calculation methods.
ISO 10300 (all parts) provides calculation procedures by which different gear designs can be compared.
It is neither meant to ensure the performance of assembled gear drive systems nor 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.
NOTE Contrary to cylindrical gears, where the contact is usually linear, bevel gears are generally manufactured
with profile and lengthwise crowning: i.e. the tooth flanks are curved on all sides and the contact develops an
elliptical pressure surface. This is taken into consideration when determining the load factors by the fact that the
rectangular zone of action (in the case of spur and helical gears) is replaced by an inscribed parallelogram for
method B1 and an inscribed ellipse for method B2 (see Annex A for method B1 and Annex B for method B2). The
conditions for bevel gears, different from cylindrical gears in their contact, are thus taken into consideration by
the longitudinal and transverse load distribution factors.
Key
a
One set of formulae for both, bevel and hypoid gears.
b
Separate sets of formulae for bevel and for hypoid gears.
Figure 1 — Structure of calculation methods in ISO 10300 (all parts)
vi © ISO 2014 – All rights reserved

INTERNATIONAL STANDARD ISO 10300-1:2014(E)
Calculation of load capacity of bevel gears —
Part 1:
Introduction and general influence factors
1 Scope
This part of ISO 10300 specifies the methods of calculation of the load capacity of bevel gears, the
formulae and symbols used for calculation, and the general factors influencing load conditions.
The formulae in ISO 10300 (all parts) are intended to establish uniformly acceptable methods for
calculating the pitting resistance and bending strength of straight, helical (skew), spiral bevel, Zerol and
hypoid gears. They are applicable equally to tapered depth and uniform depth teeth. Hereinafter, the
term “bevel gear” refers to all of these gear types; if not the case, the specific forms are identified.
The formulae take into account the known major factors influencing pitting on the tooth flank and
fractures in the tooth root. 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 active flank surfaces, to failures
of the gear rim or of the gear blank through the web and hub. Pitting resistance and bending strength
rating systems for a particular type of bevel gears can be established by selecting proper values for the
factors used in the general formulae. If necessary, the formulae allow for the inclusion of new factors at
a later date. Note, ISO 10300 (all parts) is not applicable to bevel gears which have an inadequate contact
pattern under load (see Annex D).
The rating system of ISO 10300 (all parts) is based on virtual cylindrical gears and restricted to bevel
gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. Additionally, the given
vα
relations are valid for bevel gears of which the sum of profile shift coefficients of pinion and wheel is
zero (see ISO 23509).
WARNING — The user is cautioned that when the formulae are used for large average mean spiral
angles (β +β )/2 > 45°, for effective pressure angles α > 30° and/or for large face widths
m1 m2 e
b > 13 m , the calculated results of ISO 10300 (all parts) should be confirmed by experience.
mn
2 Normative references
The following documents, in whole or in part, are normatively referenced in this document and are
indispensable to its application. For dated references, only the edition cited applies. For undated
references, the latest edition of the referenced document (including any amendments) applies.
ISO 1122-1, Vocabulary of gear terms — Part 1: Definitions related to geometry
ISO 6336-5, Calculation of load capacity of spur and helical gears — Part 5: Strength and quality of materials
ISO 10300-2:2014, Calculation of load capacity of bevel gears — Part 2: Calculation of surface durability
(pitting)
ISO 10300-3:2014, Calculation of load capacity of bevel gears — Part 3: Calculation of tooth root strength
ISO 17485, Bevel gears — ISO system of accuracy
ISO 23509:2006, Bevel and hypoid gear geometry
3 Terms and definitions
For the purposes of this part of ISO 10300, terms and definitions given in ISO 1122-1 and ISO 23509
apply.
4 Symbols and units
For the purposes of this document, the symbols given in ISO 701, ISO 17485 and ISO 23509 apply.
Table 1 contains symbols and their units which are used at more than one places of ISO 10300 (all parts).
Other symbols, especially those of auxiliary variables, which are used in equations following closely
after their definitions, are not listed in Table 1. Table 2 contains general subscripts used in ISO 10300
(all parts).
Table 1 — Symbols and units used in ISO 10300 (all parts)
Symbol  Description or term Unit
a hypoid offset mm
a relative hypoid offset —
rel
a centre distance of virtual cylindrical gear pair mm
v
a centre distance of virtual cylindrical gear pair in normal section mm
vn
b face width mm
b relative base face width —
b
b calculated effective face width mm
ce
b effective face width (e.g. measured length of contact pattern) mm
eff
b face width of virtual cylindrical gears mm
v
b effective face width of virtual cylindrical gears mm
v,eff
c empirical parameter to determine the dynamic factor —
v
c mean value of mesh stiffness per unit face width N/(mm ⋅ µm)
γ
c mesh stiffness for average conditions N/(mm ⋅ µm)
γ0
c’ single stiffness 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 tolerance diameter according to ISO 17485 mm
T
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 root diameter of virtual cylindrical gear mm
vf
d reference diameter of virtual cylindrical gear in normal section mm
vn
e exponent for the distribution of the load peaks along the lines of contact —
f distance from the centre of the zone of action to a contact line mm
f maximum distance to middle contact line mm
max
f maximum distance to middle contact line at right side of contact pattern mm
maxB
f maximum distance to middle contact line at left side of contact pattern mm
max0
2 © ISO 2014 – All rights reserved

Table 1 (continued)
Symbol  Description or term Unit
f single pitch deviation µm
pt
f effective pitch deviation µm
p,eff
g length of contact line (method B2) mm
c
g length of path of contact of virtual cylindrical gear in transverse section mm
vα
g relative length of action in normal section —
vαn
g relative length of action to point of load application (method B2) —
J
g relative length of action within the contact ellipse —
η
h mean addendum mm
am
h tool addendum mm
a0
h mean dedendum mm
fm
h dedendum of the basic rack profile mm
fP
h mean whole depth used for bevel spiral angle factor mm
m
h relative mean virtual dedendum —
vfm
h bending moment arm for tooth root stress (load application at tooth tip) mm
Fa
h load height from critical section (method B2) mm
N
′
k contact shift factor —
l length of contact line (method B1) mm
b
l theoretical length of contact line mm
b0
l theoretical length of middle contact line mm
bm
m outer transverse module mm
et
m mean normal module mm
mn
m mean transverse module mm
mt
m mass per unit face width reduced to the line of action of dynamically equiva-
red
kg/mm
lent cylindrical gears
m* relative individual gear mass per unit face width referred to line of action kg/mm
–1
n rotational speed min
–1
n resonance speed of pinion min
E1
p peak load N/mm
p transverse base pitch (method B2) mm
et
p maximum peak load N/mm
max
p* relative peak load for calculating the load sharing factor (method B1) —
p relative mean normal pitch —
mn
p relative mean normal base pitch —
nb
p transverse base pitch of virtual cylindrical gear (method B1) mm
vet
q exponent in the formula for lengthwise curvature factor —
q notch parameter —
s
r cutter radius mm
c0
r tooth fillet radius at the root in mean section mm
mf
r mean pitch radius mm
mpt
r mean transverse radius to point of load application (method B2) mm
my 0
r relative mean virtual tip radius —
va
Table 1 (continued)
Symbol  Description or term Unit
r relative mean virtual pitch radius —
vn
s mean normal circular thickness mm
mn
s amount of protuberance at the tool mm
pr
s tooth root chord in calculation section mm
Fn
s one-half tooth thickness at critical section (method B2) mm
N
u gear ratio of bevel gear —
u gear ratio of virtual cylindrical gear —
v
v tangential speed at outer end (heel) of the reference cone m/s
et
v maximum pitch line velocity at operating pitch diameter m/s
et,max
v sliding velocity in the mean point P m/s
g
v sliding velocity parallel to the contact line m/s
g,par
v sliding velocity vertical to the contact line m/s
g,vert
v tangential speed at mid-face width of the reference cone m/s
mt
v sum of velocities in the mean point P m/s
Σ
v sum of velocities in profile direction m/s
Σh
v sum of velocities in lengthwise direction m/s
Σl
v sum of velocities vertical to the contact line m/s
Σ,vert
w angle of contact line relative to the root cone °
x profile shift coefficient —
hm
x thickness modification coefficient —
sm
x tooth strength factor (method B2) mm
N
x distance from mean section to point of load application mm
oo
y running-in allowance for pitch deviation related to the polished test piece µm
p
y location of point of load application for maximum bending stress on path of
J
mm
action (method B2)
y location of point of load application on path of action for maximum root
mm
stress
y running-in allowance for pitch error µm
α
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
z number of blade groups of the cutter —
A auxiliary factor for calculating the dynamic factor K —
v-C
A* related area for calculating the load sharing factor Z mm
LS
A outer tooth thickness allowance mm
sne
B accuracy grade according to ISO 17485 —
C correction factor of tooth stiffness for non average conditions —
F
C correction factor for the length of contact lines —
lb
C , C , constants for determining lubricant film factors
ZL ZR
—
C
ZV
E modulus of elasticity, Young’s modulus N/mm
E, G, H auxiliary variables for tooth form factor (method B1) —
4 © ISO 2014 – All rights reserved

Table 1 (continued)
Symbol  Description or term Unit
F auxiliary variable for mid-zone factor —
F nominal tangential force at mid-face width of the reference cone N
mt
F determinant tangential force at mid-face width of the reference cone N
mtH
F nominal normal force N
n
F nominal tangential force of virtual cylindrical gears N
vmt
HB Brinell hardness —
K constant; factor for calculating the dynamic factor K —
v─B
K dynamic factor —
v
K * preliminary dynamic factor for non-hypoid gears —
v
K application factor —
A
K lengthwise curvature factor for bending stress —
F0
K transverse load factor for bending stress —
Fα
K face load factor for bending stress —
Fβ
K transverse load factor for contact stress —
Hα
K * preliminary transverse load factor for contact stress for non-hypoid gears —
Hα
K face load factor for contact stress —
Hβ
K mounting factor —
Hβ-be
N reference speed related to resonance speed n —
E1
N number of load cycles —
L
P nominal power kW
Ra = CLA = AA arithmetic average roughness µm
R outer cone distance mm
e
R mean cone distance mm
m
R relative mean back cone distance —
mpt
Rz mean roughness µm
Rz mean roughness for gear pairs with relative curvature radius ρ = 10 mm µm
10 rel
S safety factor for bending stress (against breakage) —
F
S minimum safety factor for bending stress —
F,min
S safety factor for contact stress (against pitting) —
H
S minimum safety factor for contact stress —
H,min
T nominal torque of pinion and wheel Nm
1,2
W wheel mean slot width mm
m2
Y tooth form factor of pinion and wheel (method B2) —
1,2
Y stress concentration and stress correction factor (method B2) —
f
Y inertia factor (bending) —
i
Y root stress adjustment factor (method B2) —
A
Y bevel spiral angle factor —
BS
Y tooth form factor for load application at the tooth tip (method B1) —
Fa
Y combined tooth form factor for generated gears —
FS
Y bending strength geometry factor (method B2) —
J
Y load sharing factor (bending) —
LS
Table 1 (continued)
Symbol  Description or term Unit
Y life factor (bending) —
NT
Y relative surface condition factor —
R,Rel T
Y stress correction factor for load application at the tooth tip —
Sa
Y stress correction factor for dimensions of the standard test gear —
ST
Y size factor for tooth root stress —
X
Y relative notch sensitivity factor —
δ,rel T
Y contact ratio factor for bending (method B1) —
ε
Z inertia factor (pitting) —
i
Z speed factor —
v
Z contact stress adjustment factor (method B2) —
A
2 1/2
Z elasticity factor (N/mm )
E
Z face width factor —
FW
Z hypoid factor —
Hyp
Z pitting resistance geometry factor (method B2) —
I
Z bevel gear factor (method B1) —
K
Z lubricant factor —
L
Z load sharing factor (method B1) —
LS
Z mid-zone factor —
M-B
Z life factor (pitting) —
NT
Z roughness factor for contact stress —
R
Z bevel slip factor —
S
Z work hardening factor —
W
Z size factor —
X
α adjusted pressure angle (method B2) °
a
α normal pressure angle at tooth tip °
an
α effective pressure angle in transverse section °
et
α effective pressure angle for drive side/coast side °
eD,C
α limit pressure angle in wheel root coordinates (method B2) °
f
α limit pressure angle °
lim
α generated pressure angle for drive side/coast side °
nD,C
α transverse pressure angle of virtual cylindrical gears °
vet
α load application angle at tooth tip of virtual cylindrical gear (method B1) °
Fan
α normal pressure angle at point of load application (method B2) °
L
β mean base spiral angle °
bm
β mean spiral angle °
m
β helix angle of virtual gear (method B1), virtual spiral angle (method B2) °
v
β helix angle at base circle of virtual cylindrical gear °
vb
β inclination angle of contact line °
B
γ auxiliary angle for length of contact line calculation (method B1) °
′
γ projected auxiliary angle for length of contact line °
γ auxiliary angle for tooth form and tooth correction factor °
a
6 © ISO 2014 – All rights reserved

Table 1 (continued)
Symbol  Description or term Unit
δ pitch angle of bevel gear °
δ face angle °
a
δ root angle °
f
ε transverse contact ratio of virtual cylindrical gears —
vα
ε transverse contact ratio of virtual cylindrical gears in normal section —
vαn
ε face contact ratio of virtual cylindrical gears —
vβ
ε virtual contact ratio (method B1), modified contact ratio (method B2) —
vγ
ε load sharing ratio for bending (method B2) —
N
ε load sharing ratio for pitting (method B2) —
NI
ζ pinion offset angle in axial plane °
m
ζ pinion offset angle in pitch plane °
mp
ζ pinion offset angle in root plane °
R
ϑ auxiliary quantity for tooth form and tooth correction factors radiant
ϑ auxiliary angle for virtual face width (method B1) °
mp
θ angular pitch of virtual cylindrical wheel radiant
v2
ξ assumed angle in locating weakest section radiant
ξ one half of angle subtended by normal circular tooth thickness at point of
h
radiant
load application
ρ density of gear material kg/mm
ρ cutter edge radius mm
a0
ρ fillet radius at point of contact of 30° tangent mm
F
ρ fillet radius at point of contact of 30° tangent in normal section mm
Fn
ρ root fillet radius of basic rack for cylindrical gears mm
fP
ρ radius of relative curvature vertical to contact line at virtual cylindrical
rel
mm
gears
ρ relative radius of profile curvature between pinion and wheel (method B2) —
t
ρ relative edge radius of tool —
va0
′
ρ slip layer thickness mm
σ tooth root stress N/mm
F
σ nominal stress number (bending) N/mm
F,lim
σ allowable stress number (bending) N/mm
FE
σ permissible tooth root stress N/mm
FP
σ contact stress N/mm
H
σ allowable stress number for contact stress N/mm
H,lim
σ permissible contact stress N/mm
HP
τ angle between tangent of root fillet at weakest point and centreline of tooth °
ν Poisson’s ratio —
ν lead angle of face hobbing cutter °
ν , ν nominal kinematic viscosity of the oil at 40 °C and 50 °C respectively mm /s
40 50
φ auxiliary angle to determine the position of the pitch point °
ω angular velocity rad/s
Table 1 (continued)
Symbol  Description or term Unit
ω angle between the sum of velocities vector and the trace of pitch cone °
Σ
X −1
χ relative stress drop in notch root mm
X −1
χ relative stress drop in notch root of standardized test gear mm
T
Σ shaft angle °
Table 2 — General subscripts in ISO 10300 (all parts)
Subscripts Description
0 tool
1 pinion
2 wheel
A, B, B1, B2, C value according to method A, B, B1, B2 or C
D Drive flank
C Coast flank
T relative to standardized test gear dimensions
(1), (2) trials of interpolation
5 Application
5.1 Calculation methods
5.1.1 General
ISO 10300 (all parts) provides the procedures to predict load capacity of bevel gears. The most valid
method is full-scale and full-load testing of a specific gear set design. However, at the design stage or in
certain fields of application, some calculation methods are needed to predict load capacity. Therefore,
methods A, B and C are used in this part of ISO 10300, while method A, if its accuracy and reliability are
proven, is preferred over method B, which in turn is preferred over method C.
ISO 10300 (all parts) allows the use of mixed factor rating methods within method B1 or method B2. For
example: method B for dynamic factor K can be used with method C face load factor K .
v-B Hβ-C
5.1.2 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
are 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 shall 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.
5.1.3 Method B
Method B provides the calculation formulae to predict load capacity of bevel gears for which the essential
data are known. However, sufficient experience from the operation of other, similar designs is needed
in the evaluation of certain factors even in this method. The validity of these evaluations for the given
operating conditions shall be checked.
8 © ISO 2014 – All rights reserved

5.1.4 Method C
Where suitable test results or field experience from similar designs, are unavailable for use in the
evaluation of certain factors, a further simplified calculation method, method C, should be used.
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 calculated permissible stress by the specific evaluated operating stress.
In addition to this general requirement, and the special requirements relating to surface durability
(pitting) and tooth root strength (see ISO 10300-2 and ISO 10300-3, respectively), 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 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 of gear members;
— 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
H,min
of 1,0. The minimum bending stress value S should be 1,3 for spiral bevel including hypoid gears,
F,min
and 1,5 for straight bevel gears or those with β ≤ 5°.
m
The minimum safety factors against pitting damage and tooth breakage should be agreed between the
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. 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 not available, 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, B, shall preferably be
determined as specified in ISO 17485, e.g. single pitch deviation for calculating the dynamic factor K .
v-B
5.3.3 Implied accuracy
Where the empirical values for rating factors are given by curves, this part of 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 Further 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 10300-2 and ISO 10300-3 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 case-hardened steel. Allowable stress numbers for this and other
materials shall be taken preferably from ISO 6336-5 because these are determined by a multitude of
tests on spur gears for which the material strains can be calculated very precisely. Additionally, different
modes of steel making and heat treatment are considered in ISO 6336-5. Hardness and tensile strength
as well as the quality grade shall also be criteria for choosing permissible 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 might reduce the residual compressive stresses or even introduce
residual tensile stresses in the root fillets of the teeth, thereby lowering the allowable stress numbers.
10 © ISO 2014 – All rights reserved

5.4.7 System dynamics
The method of analysis used in this part of ISO 10300 includes a dynamic factor, K , which derates the
v
gears for increased loads 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
A
account for the operating characteristics of the driving and driven equipment. It should 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 can cause
severe overloads possibly several times higher 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 comprise 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 crowning
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 gear 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 this part of ISO 10300. Such gears are not covered by ISO 10300 (all
parts).
NOTE The total load used for contact pattern analysis can include the effects of an application factor (see
Annex D 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 (all parts).
5.5 Further influence factors in the basic formulae
The basic formulae presented in ISO 10300-2 and ISO 10300-3 include factors reflecting gear geometry
or being established by convention, which need to be calculated in accordance with their formulae.
In the formulae in ISO 10300 (all parts), there are also factors that reflect the effects of variations in
processing or the operating cycle
...