ISO/TR 10300-30:2017

TECHNICAL ISO/TR
REPORT 10300-30
First edition
2017-12
Calculation of load capacity of bevel
gears —
Part 30:
ISO rating system for bevel and hypoid
gears — Sample calculations
Calcul de la capacité de charge des engrenages coniques —
Partie 30: Système d'évaluation ISO pour engrenages conique et
hypoïde - Type de calculs
Reference number
©
ISO 2017
© ISO 2017, Published in Switzerland
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ii © ISO 2017 – All rights reserved

Contents Page
Foreword iv
Introduction v
1 Scope 1
2 Normative references 1
3 Terms and definitions 2
4 Symbols and abbreviated terms 2
5 Application 10
5.1 General 10
5.2 Structure of calculation methods 10
Annex A (informative) Sample 1: Rating of a spiral bevel gear pair without hypoid
offset according to Method B1 and Method B2 12
Annex B (informative) Sample 2: Rating of a hypoid gear set according to Method B1
and Method B2 65
Anne
x C (informative)  Sample 3: Rating of a hypoid gear set according to Method B1
and Method B2 125
Annex D (informative)  Sample 4: Rating of a hypoid gear set according to Method B1
and Method B2 185
Annex E (informative) Graphical representation of the calculation results for
Sample 1 to Sample 4 243
Bibliography 246
© ISO 2017 – All rights reserved iii

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 (see 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 (see 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 voluntary nature of standards, the meaning of ISO specific terms and
expressions related to conformity assessment, as well as information about ISO's adherence to
the World Trade Organization (WTO) principles in the Technical Barriers to Trade (TBT), see the
following URL: www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 60, Gears, Subcommittee SC 2, Gear
capacity calculation.
A list of all parts in the ISO 10300 series can be found on the ISO website.
iv © ISO 2017– All rights reserved

Introduction
The ISO 10300 series consists of International Standards, Technical Specifications (TS) and
Technical Reports (TR) under the general title Calculation of load capacity of bevel gears
(see Table 1).
— International Standards contain calculation methods that are based on widely accepted
practices and have been validated.
— TS contain calculation methods that are still subject to further development.
— TR contain data that is informative, such as example calculations.
The procedures specified in ISO 10300‐1 to ISO 10300‐19 cover fatigue analyses for gear rating.
The procedures described in ISO 10300‐20 to ISO 10300‐29 are predominantly related to the
tribological behaviour of the lubricated flank surface contact. ISO 10300‐30 to ISO 10300‐39
include example calculations. The ISO 10300 series allows the addition of new parts under
appropriate numbers to reflect knowledge gained in the future.
Requesting standardized calculations according to ISO 10300 without referring to specific parts
requires the use of only those parts that are currently designated as International Standards (see
Table 1 for listing). When requesting further calculations, the relevant part or parts of ISO 10300
need to be specified. Use of a Technical Specification as acceptance criteria for a specific design
need to be agreed in advance between manufacturer and purchaser.
Table 1 — Overview of ISO 10300
International Technical Technical
Calculation of load capacity of bevel gears
Standard Specification Report
Part 1: Introduction and general influence factors X
Part 2: Calculation of surface durability (pitting) X
Part 3: Calculation of tooth root strength X
Part 4 to 19: to be assigned
Part 20: to be assigned for scuffing of bevel and hypoid
gears
Part 21 to 29: to be assigned
Part 30: ISO rating system for bevel and hypoid gears
X
— Sample calculations
At the time of publication of this document, some of the parts listed here were under development. Consult the ISO
website.
This document was prepared with sample calculations for different bevel gear designs. They are
intended for users of the ISO 10300 series to follow a whole calculation procedure formula by
formula. Practical experience has shown that this way, to get into a complex subject, is very
helpful.
On the other hand, this document is not intended for use by the average engineer. Rather, it is
aimed at the well‐versed engineer capable of selecting reasonable values for the parameters and
factors in these formulae based on knowledge of similar designs and on awareness of the effects
behind these formulae.
© ISO 2017 – All rights reserved v

vi © ISO 2017– All rights reserved

TECHNICAL REPORT ISO/TR 10300-30:2017(E)

Calculation of load capacity of bevel gears —

Part 30: ISO rating system for bevel and hypoid
gears — Sample calculations
1 Scope
This document provides sample calculations for different bevel gear designs, how the load
capacity is numerically determined according to the methods and formulae of the
ISO 10300 series. The initial geometric gear data necessary for these calculations in accordance
with ISO 23509.
The term “bevel gear” is used to mean straight, helical (skew), spiral bevel, zerol and hypoid gear
designs. Where this document pertains to one or more, but not all, the specific forms are
identified.
The manufacturing process of forming the desired tooth form is not intended to imply any
specific process, but rather to be general in nature and applicable to all calculation methods of the
ISO 10300 series. The fact that there are bevel gear designs with tapered teeth and others where
the tooth depth remains constant along the face width (uniform depth) does not demand to apply
Method B2 for the first and Method B1 for the second tooth configuration.
The rating system of the ISO 10300 series is based on virtual cylindrical gears and restricted to
bevel gears whose virtual cylindrical gears have transverse contact ratios of ε < 2. Additionally,
vα
the given 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 the ISO 10300 series should be confirmed by experience.
mn
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content
constitutes requirements of this document. For dated references, only the edition cited applies.
For undated references, the latest edition of the referenced document (including any
amendments) applies.
ISO 10300‐1:2014, Calculation of load capacity of bevel gears — Part 1: Introduction and general
influence factors
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 2017 – All rights reserved 1

3 Terms and definitions
For the purposes of this document, the terms and definitions given in ISO 10300‐1 and
ISO 10300‐2 apply.
ISO and IEC maintain terminological databases for use in standardization at the following
addresses:
— ISO Online browsing platform: available at https://www.iso.org/obp
— IEC Electropedia: available at https://www.electropedia.org/
4 Symbols and abbreviated terms
For the purposes of this document, the symbols and units given in ISO 10300‐1:2014, Table 1 and
Table 2, as well as the abbreviated terms given in ISO 10300‐2:2014, Table 1, apply.
Table 2 — 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 related 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 mean addendum factor of wheel —
ham
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)
0’
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
2 © ISO 2017 – All rights reserved

Symbol Description or term Unit
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 mm
maxB
the contact pattern
f maximum distance to middle contact line at left side of mm
max0
the contact pattern
f single pitch deviation µm
pt
f effective pitch deviation µm
p eff
f Influence factor of limit pressure angle
αlim
g length of contact line (Method B2) mm
c
g length of path of contact of virtual cylindrical gear in transverse mm
vα
section
g related length of action in normal section —
vαn
g length of action from mean point to point of load application mm
J
(Method B2)
g relative length of action within the contact ellipse mm
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 mm
Fa
at tooth tip)
h load height from critical section (Method B2) mm
N
j outer normal backlash mm
en
′ —
contact shift factor
k
k clearance factor —
c
k depth factor —
d
k basic crown gear addendum factor (related to m ) —
hap mn
k basic crown gear dedendum factor (related to m ) —
hfp mn
k circular thickness factor —
t
l length of contact line (Method B1) mm
b
© ISO 2017 – All rights reserved 3

Symbol Description or term Unit
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 kg/mm
red
dynamically equivalent cylindrical gears
m* related individual gear mass per unit face width referred to kg/mm
the line of action
–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* related 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
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
4 © ISO 2017 – All rights reserved

Symbol Description or term Unit
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 (backlash included) —
sm
x thickness modification coefficient (theoretical) —
smn
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 µm
p
test piece
y location of point of load application for maximum bending stress mm
J
on path of action (Method B2)
y location of point of load application on path of action for mm
maximum root 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 , C constants for determining lubricant film factors —
ZL ZR ZV
E modulus of elasticity, Young’s modulus N/mm
E, G, H auxiliary variables for tooth form factor (Method B1) —
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 —
© ISO 2017 – All rights reserved 5

Symbol Description or term Unit
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 —
Hα
non‐hypoid gears
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 µm
ρ = 10 mm
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
6 © ISO 2017 – All rights reserved

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
Z elasticity factor —
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  nominal design pressure angle for drive side/coast side °
dD,C
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 °
Fan
(Method B1)
α normal pressure angle at point of load application (Method B2) °
L
β mean base spiral angle °
bm
β mean spiral angle °
m
© ISO 2017 – All rights reserved 7

Symbol Description or term Unit
β helix angle of virtual gear (Method B1), °
v
virtual spiral angle (Method B2)
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
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 —
θ auxiliary angle for virtual face width (Method B1) °
mp
θ  addendum angle of wheel °
a2
θ  dedendum angle of wheel °
f2
θ  angular pitch of virtual cylindrical wheel radiant
v2
ξ assumed angle in locating weakest section °
ξ one half of angle subtended by normal circular tooth thickness °
h
at point of 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 mm
rel
virtual cylindrical gears
ρ radius of relative profile curvature (Method B2) mm
t
ρ  relative edge radius of tool —
va0
ρ′ slip layer thickness mm
8 © ISO 2017 – All rights reserved

Symbol Description or term Unit
σ tooth root stress N/mm
F
σ  nominal tooth root stress N/mm
F0
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
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 mm
relative stress drop in notch root of standardized test gear
T
Σ shaft angle °
Table 3 — Generally used 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
© ISO 2017 – All rights reserved 9

5 Application
5.1 General
This document provides four sample calculations:
— Sample 1 is a rating of a spiral bevel gear pair without hypoid offset according to Method B1
and Method B2 (see Annex A);
— Sample 2 is a rating of a hypoid gear set according to Method B1 and Method B2 (see
Annex B);
— Sample 3 is a rating of a hypoid gear set according to Method B1 and Method B2 (see
Annex C);
— Sample 4 is a rating of a hypoid gear set according to Method B1 and Method B2 (see
Annex D).
5.2 Structure of calculation methods
Figure 1 shows three boxes that represent the individual three parts of ISO 10300. However,
these boxes are subdivided into a left side where influence factors are determined on the basis of
mainly operational data according to Methods A, B or C (see ISO 10300‐1:2014, 5.1) and a right
side where separate calculation procedures are provided according to Method B1 and Method B2
which are assumed to have the same level B but different approaches. These two methods refer to
the determination of virtual cylindrical gears in ISO 10300‐1, the gear flank rating formulae in
ISO 10300‐2 and the gear tooth rating formulae in ISO 10300‐3.
10 © ISO 2017 – All rights reserved

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)
© ISO 2017 – All rights reserved 11

Annex A
(informative)
Sample 1: Rating of a spiral bevel gear pair without hypoid offset
according to Method B1 and Method B2
A.1 Initial data
Sample 1 is for a spiral bevel gear pair without hypoid offset which uses Method 0 according to
ISO 23509.
Table A.1 — Initial data for pitch cone parameters
Symbol Description Method 0 Method 1 Method 2 Method 3
Σ  shaft angle 90° X X X
a  hypoid offset 0 mm X X X
z number of teeth 14/39 X X X
1,2
d mean pitch diameter of wheel — — X —
m2
d outer pitch diameter of wheel 176,893 mm X — X
e2
b wheel face width 25,4 mm X X X
β mean spiral angle of pinion 35° X — —
m1
β mean spiral angle of wheel 35° — X X
m2
r cutter radius 114,3 mm X X X
c0
number of blade groups
z — — X X
(only face hobbing)
12 © ISO 2017 – All rights reserved

Table A.2 — Input data for tooth profile parameters
Data type I Data type II
Symbol Description Symbol Description
α 20°
dD
α 20°
dC
f 0
αlim
x — c 0,247 37
hm1 ham
k — k 2,000
hap d
k — k 0,125
hfp c
k 0,091 5
t
x —
smn
W —
m2
j 0,127 mm
en
θ 2,134 2°
a2
θ 6,493 4°
f2
ρ  0,8 mm/0,8 mm
a01D,C
ρ  1,2 mm/1,2 mm
a02D,C
s 0 mm/0 mm
pr1D,C
s 0 mm/0 mm
pr2D,C
© ISO 2017 – All rights reserved 13

Table A.3 and Table A.4 show geometric and operational data and text for explanation.
Table A.3 — Geometric data from calculation according to ISO 23509
Symbol Description Values Symbol Description Value
mean pitch diameter 54,918 mm/ offset angle
d ζ 0°
m1,2 mp
of pinion/wheel 152,987 mm on pitch plane
mean addendum 4,836 mm/ pinion offset angle
h ζ 0°
am1,2 R
of pinion/wheel 1,591 mm on root plane
mean dedendum 2,394 mm/ outer cone distance
h R 93,973 mm
fm1,2 e1,2
of pinion/wheel 5,639 mm on pinion and wheel
effective pressure angle mean cone distance
α 20°/20° R 81,273 mm
eD,C m1,2
for drive side/coast side on pinion and wheel
generated pressure angle pitch angle 19,747°/
α 20°/20° δ
nD,C 1,2
for drive side/coast side on pinion/wheel 70,253°
face angle 26,240°/
α limit pressure angle 0° δ
lim a1,2
on pinion/wheel 72,387°
root angle 17,613°/
m mean normal module 3,213 mm δ
mn f1,2
on pinion/wheel 63,760°
thickness modification
basic crown gear 0,037/
k 1,25 x coefficient on
hfp sm1,2
dedendum factor −0,055
pinion/wheel
pinion offset angle
ζ 0,000° m outer transverse module 4,536 mm
m et2
on axial plane
mean normal circular
6,465 mm/
s  tooth thickness
mn1,2
3,511 mm
of pinion/wheel
14 © ISO 2017 – All rights reserved

Table A.4 — Operation parameters and additional considerations
Symbol Description Value
Additional data
wheel profile generated
roughing/finishing method face milling
b effective face width on wheel 0,85 · b
2eff 2
profile crowning low
verification of contact pattern checked under light test load for each gear
mounting conditions of pinion and wheel one member cantilever‐mounted
Operation parameters
T pinion torque 300 Nm
−1
n pinion rotational speed 1 200 min
K application factor 1,1
A
active flank drive
Material data for pinion and wheel (case hardened steel)
σ allowable stress number (contact) 1 500 N/mm
H lim
σ nominal stress number (bending) 480 N/mm
F lim
surface hardness same for pinion and wheel
Quality parameters
R flank roughness on pinion/wheel 8 μm/8 μm
z
R tooth root roughness on pinion/wheel 16 μm/16 μm
z
f single pitch deviation on pinion/wheel 12 μm/26 μm
pt
Lubrication parameters
oil type ISO‐VG‐150
oil temperature 90 °C
© ISO 2017 – All rights reserved 15

A.2 Calculation of Sample 1 according to Method B1
Table A.5 — Virtual cylindrical gears
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Virtual cylindrical gears in transverse section
d
m1
Reference diameter
(A.1) 58,349 mm E: A.1
d 
on pinion
v1
cos
Reference diameter
du d (A.2) 452,802 mm E: A.4
on wheel v2 v1

m1 m2
Helix angle (A.3) 35° E: A.8
 
v
Transverse pressure
 arctan tancos
 
vet e v
angle of virtual (A.4) 23,957° E: A.10
cylindrical gears
since  =  for drive side
e eD
mm cos
Transverse module (A.5) 3,922 mm E: A.11
vt mn v
Number of teeth on
zd m
(A.6) 14,876 E: A.12
v1 v1 vt
pinion
Number of teeth on
zd m
(A.7) 115,441 E: A.12
v2 v2 vt
wheel
uz z
Gear ratio (A.8) 7,760 E: A.13
vv2v1
16 © ISO 2017 – All rights reserved

Table A.5 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Auxiliary angle for
arctan sin tan
(A.9) 0° E: A.21
 
mp 2 m
virtual face width
Projected auxiliary
' 2
angle for length of (A.10) 0° E: A.20
mp mp
contact line
Centre distance
add 2
of virtual cylindrical (A.11) 255,576 mm E: A.5

vv1 v2
gear pair
Helix angle of virtual
 arcsin sincos
 
vb v e
cylindrical gear at base (A.12) 32,615° E: A.16
circle
since  =  for drive side
e eD
Tip diameter on pinion dd2 h (A.13) 68,021 mm E: A.6
va1 v1 am1
dd2 h
Tip diameter on wheel (A.14) 455,984 mm E: A.6
va2 v2 am2
dd2 h
Root diameter on pinion (A.15) 53,561 mm E: A.7
vf1 v1 fm1
Root diameter on wheel dd2 h (A.16) 441,524 mm E: A.7
vf2 v2 fm2
Base diameter on pinion dd cos (A.17) 53,323 mm E: A.9
vb1 v1 vet
dd cos
Base diameter on wheel (A.18) 413,794 mm E: A.9
vb2 v2 vet
pmp cos cos
Transverse base pitch (A.19) 11,261 mm E: A.17
vet mn vet v
© ISO 2017 – All rights reserved 17

Table A.5 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Length of path of contact
of virtual cylindrical
22 2 2

gd dd sinddd sin (A.20) 13,121 mm E: A.18
v  va1 vb1 v1 vet  va2 vb2 v2 vet
gear in transverse 

section
 gp
Transverse contact ratio (A.21) 1,165 E: A.23
vvvet

bgcos2  cos tan 2
   
2 eff mp v vet mp

Effective face width

b  (A.22) 21,590 mm E: A.19
v eff
with b = 0,85·b
2 eff 2
1tan'tan 2

mp
b
v eff
Face width bb (A.23) 25,400 mm E: A.22
v2
b
2 eff
Virtual cylindrical gears in normal section
Number of pinion teeth
z
v1
z 
of virtual cylindrical (A.24) 25,596 E: A.38
vn1
cos  cos
gears
vb v
Number of wheel teeth
zuz
of virtual cylindrical (A.25) 198,632 E: A.39
vn2 v vn1
gears
Reference diameter
dz m
(A.26) 82,241 mm E: A.40
vn1 vn1 mn
on pinion
Reference diameter
dz m (A.27) 638,203 mm E: A.40
vn2 vn2 mn
on wheel
18 © ISO 2017 – All rights reserved

Table A.5 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
dd2h
Tip diameter on pinion (A.28) 91,913 mm E: A.41
van1 vn1 am1
Tip diameter on wheel dd2h (A.29) 641,385 mm E: A.41
van2 vn2 am2
dd cos
Base diameter on pinion (A.30) 77,281 mm E: A.42
vbn1 vn1 e
dd cos
Base diameter on wheel (A.31) 599,715 mm E: A.42
vbn2 vn2 e
b sin
v eff v
Face contact ratio   (A.32) 1,227 E: A.24
vβ
p m
mn

Virtual contact ratio (A.33) 2,392 E: A.25
vv  vβ
Inclination angle
 arctan tansin
(A.34) 13,468° E: A.36
 
Bve
of contact line
-1


Radius of relative
costan -tan tan tan


nD nD lim mp B
curvature in normal (A.35) 13,173 mm E: A.37a
 =

t

coscos
section at the mean point 11
m1 m2



cosRRtan tan
mpm2 2 m1 1

Radius of relative
curvature vertical  cos (A.36) 12,459 mm E: A.35
rel t B
to the contact line
© ISO 2017 – All rights reserved 19

Table A.6 — General influence factors
References to
ISO ISO ISO
Description Formula Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
2000 T
Nominal tangential
F 
(A.37) 10 925,4 N E: 1
mt1
force of bevel gears
d
m1
Nominal tangential
cos
v
force of virtual FF (A.38) 10 925,4 N E: 2
vmt mt1
cos
cylindrical gears
m1
Nominal tangential
dn
m 1 1
v 
speed at mean point (A.39) 3,451 m/s E: 5
mt 1
of the pinion
Nominal tangential
dn
m 2 2
v 
speed at mean point (A.40) 3,451 m/s E: 5
mt 2
of the wheel
Correction factor for
non‐average conditions
C
(A.41) 1,000 E: 12a
F
for F K / b 
vmt A veff
100 N/mm
Mean value of mesh
cc C
stiffness per unit face (A.42) E: 11
 F
N/(mm · m)
width
Single stiffness (A.43) E: 17
cc'' C
0F
N/(mm · m)
Max. single pitch
f
deviation as given (A.44) 26 m
pt
in Table A.4.
20 © ISO 2017 – All rights reserved

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Running‐in allowance
y 0,075 f
for case hardened and (A.45) 1,950 m E: 43
 pt
nitrided gears
Effective pitch deviation
f = f  y
(A.46) 24,050 µm E: 16
p eff pt p
with y = y
p 
d
* m1
Relative pinion mass
m   p
8  
per unit face width
cos  /2

nD nC
  (A.47) 0,011 kg/mm E: 13
reduced to the line of
action
where ρ is the density of the gear material
−6 3
(for steel ρ = 7,8610 kg/mm)
d
* m2
Relative wheel mass m   p
 
per unit face width
cos  /2

nD nC
  (A.48) 0,082 kg/mm E: 13
reduced to the line of
action
where ρ is the density of the gear material
−6 3
(for steel ρ = 7,8610 kg/mm)
Mass reduced to the line
**
mm
of action of the
m 
(A.49) 0,009 kg/mm E: 10
red
dynamically equivalent **
mm
cylindrical gear pair
c
Resonance speed of 30  10 
−1
(A.50) 31 565 min E: 9
n 
E1
pinion
p zm
1red
© ISO 2017 – All rights reserved 21

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
n
Dimensionless reference 1
N
(A.51) 0,038 E: 8
speed
n
E1
c = c + c (A.52) 0,592 T: 3
v1,2 v1 v2
For virtual contact ratio, c (A.53) 0,115 T: 3
v3
 = 2,392 > 2 as given
v
c (A.54) 0,473 T: 3
v4
in ISO 10300−1:2014,
Table 1 (A.55) 0,654 T: 3
cv5,6
c (A.56) 0,993 T: 3
v7
Constant for the dynamic
bf c '
vp eff
factor with K = 1,1
Kcc (A.57) 0,537 E: 15
A
v1,2 v3
FK
as given in Table A.4. vmt A
Dynamic factor K − B = N∙K + 1 (A.58) 1,020 E: 14
v 1
Determination of the length of contact lines
f = +p cos (A.59) 9,485 mm T: A.2
t vet vb
For virtual contact ratio,
f (A.60) 0,000 mm T: A.2
m
 = 1,227, ε ≥ 1
v v
f = −p cos (A.61) −9,485 mm T: A.2
r vet vb
22 © ISO 2017 – All rights reserved

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure

fg b tantan cos (A.62) 11,345 mm E: A.31

vv eff vb
maxB vb

Maximum distances 1

(A.63) −0,292 mm E: A.32
f  gbtantan cos

vv eff vb
from middle contact line max0 vb

f = f
max maxB
(A.64) 11,345 mm
since f > f
maxB max0
Theoretical length
(A.65) 24,345 mm E: A.27
lxxyy
 
of contact line
b0 1 2 1 2
© ISO 2017 – All rights reserved 23

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure

b
v eff
ffcostansin gb tan

vb vb vb vα v eff

(A.66) 21,048 mm E: A.28

x 
tantan
vb

b
v eff
ffcostansin gb tan

vb vb vb v v eff

Theoretical length

x 
of middle contact line
(A.67) 0,542 mm E: A.29
tantan
calculated with f = f
vb
m
for contact stress as
NOTE ISO 10300−1:2014, Formula (A.29) is a misprint.
specified in
The operator in the second parenthesis should be “−”.
ISO 10300−2:2014, 6.1

b
v eff
yx tanfcos tanfsin 
(A.68) −6,561 mm E: A.30
1 1 vb vb vb vb



b
v eff
yx tanfcos tanfsin  (A.69) 6,561 mm E: A.30
2 2 vb vb vb vb





b
f

veff

Correction factor C11  (A.70) 0,078 E: A.34
lb



fb
max v



ll1C
Length of contact line (A.71) 22,445 mm E: A.26

bb0 lb
24 © ISO 2017 – All rights reserved

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Length of middle
ll (A.72) 22,445 mm
bm b
contact line
Load sharing factor (pitting)
Exponent for calculation
of parabolic distribution e (A.73) 3 T: 3
of peak loads
e

f E: 7

Related peak load (A.74)
p *1
F: 2

f
max

e

f
Related peak load at
t

(A.75) 0,416
p *1
t
tip contact line

f
max

e

f
Related peak load
m

(A.76) 1,000
p *1
at middle contact line m

f
max

e

f
Related peak load at
r

(A.77) 0,416
p *1
root contact line r

f
max

E: 8
Related area Ap** l p (A.78)
b
4 F: 2
© ISO 2017 – All rights reserved 25

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Related area at tip
A** pl p (A.79) 1,279 mm
tt bt
contact line
Related area at middle 1
(A.80) 17,628 mm
Ap** l p
mm bm
contact line
Related area at root
A** pl p (A.81) 1,279 mm
rr br
contact line
A *
m
Load sharing factor Z  (A.82) 0,934 E: 10
LS
AA**A*
tm r
Face load factors (Calculation according to Method C)
KK1,5
Load distribution factor (A.83) 1,650 E: 27
Hβ--C Hβbe
with K (A.84) 1,100 T:4
H ‐be
b
KK K
Load distribution factor (A.85) 1,650 E: 28
Fβ--C HβC F0
with K (A.86) 1,000 E: 29b
F0
Transverse load factors (Calculation according to Method B)
Determinant tangential
F = F K K K
force at mid face width mtH vm A v Hb (A.87) 20 226,2 N E: 37
t
on the pitch cone
26 © ISO 2017 – All rights reserved

Table A.6 — continued
References to
ISO ISO ISO
Description Formula  Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Transverse load factors
2 1 cf y
   
for bevel gear with
vγ γ pt 
**
(A.88) 1,161 E: 38
KK0,90,4 
virtual contact ratio
HF
 Fb
vγ mtH v
 = 2,392 > 2
v
2 a
Relative hypoid offset (A.89) 0,000 E: 35
a 
rel
d
m2
*
K 1
*
H
Transverse load factors (A.90) 1,161 E: 34
KKK a
HF H rel
0,1
© ISO 2017 – All rights reserved 27

Table A.7 — Calculation of surface durability (pitting)
References to
ISO ISO ISO
Description Formula Result
10300―1 10300―2 10300―3
E: Formula  T: Table   F: Figure
Z-factors
Factors for calculation F = 
(A.91) 1,165 T: 2
1 vα
of mid‐zone factor for
F = 
(A.92) 1,165 T: 2
 = 1,227 ≥ 1 2 vα
v
tan
vet
Z 
MB-
 
  
Mid‐zone factor dd (A.93) 0,916 E: 6
pp 
va1 va2
11FF 
 
  
dz d z
vb1 v1 vb2 v2
 
Z 
E
22 189,800

11
Elasticity factor (A.94) E: 51
1 2

(N/mm2)1/2
p 

EE

Bevel gear factor ZK (A.95) 0,850 E: 11
28 © ISO 2017 – All rights reserved

Table A.7 — continued
References to
ISO ISO ISO
Description Formula Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
 850
H lim
C0,08 0,83
ZL
(A.96) 0,910 E: 54
using  = 1 200 N/mm, which is the upper allowed limit in the
Hlim
above formula.
Lubricant factor
4 1,0 C
 
ZL
ZC
LZL
(A.97) 0,992 E: 53

1,2


40
 850
H lim
C0,08 0,85
ZV
(A.98) 0,930 E: 56
using  = 1 200 N/mm, which is the upper allowed limit in the
Hlim
above formula.
Speed factor
2 1,0 C
 
ZV
ZC
vZV
(A.99) 0,974 E: 55
0,8
v
mt2
© ISO 2017 – All rights reserved 29

Table A.7 — continued
References to
ISO ISO ISO
Description Formula Result
10300-1 10300-2 10300-3
E: Formula  T: Table   F: Figure
Rz  Rz
Rz (A.100) 7,435 µm E: 57
2 
Roughness factor with
1000
H lim
the radius of relative
C0,12
ZR
curvature 5000
(A.101) 0,080 E: 59
ρ = ρ = 12,459 mm
rel
for Method B1
using  = 1 200 N/mm, which is the upper allowed limit in the
Hlim
(see ISO 10300−1:2014,
above formula.
Annex A)
C
ZR

(A.102) 0,930 E: 58
Z 
R

Rz
10
Product of the lubricant
Z Z Z (A.103) 0,899
L v R
influence factors
Size factor Z for Method B1 (see ISO 10300−1:2014, 6.5.1) (A.104) 1,000
X
ZHyp
Hypoid factor (A.105) 1,000 E: 12
Set ZHyp = 1,0 for non-offset.
Life factor for pinion ZNT,1 (A.106) 1,000 T: 4
Life factor for wheel ZNT,2 (A.107)
...