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
...